Текст
H3HKH H TeXHHKH
P.ll. T
M
HrC
CnpaBO"lHL4K
L4H>KeHepa -
MeXaHL4Ka
nepeBOA c aHrnMMCKOrO
nOA PeAaK4MeM LI1.IO. WKaAMHOM
TEXHOCCI>EPA
MOCKBa
2008
THMHHrc P.JI.
CnpaBOqHHK HIDKeHepa-MeXaHHKa
MOCKBa:
TexHoc epa, 2008. - 632 c. ISBN 978-5-94836-183-3
CnpaBOQHHK no,nrOTOBJIeH B nOMOm;b HH)I{eHepaM-MexaHHKaM, 3aH TbIM
npoeKTHpOBaHHeM H H3rOTOBJIeHHeM TeXHHtJeCKHX H3,neJIHH H o6opy,noBaHH .
M3,naHHe yqHTbIBaeT H3MeHeHH B TeXHOJIOrH X H CTaH,napTax HHxeHepHoro
npoeKTHpOBaHH H co,nepXHT BCIO caMYIO Heo6xo,nHMYIO HH<popMaUHIO no
pa3pa6oTKe npoeKTOB, TeopHH, MaTepHarraM H HX CBOHCTBaM.
KHHra npe,nHa3HaqeHa ,nJI HH)I{eHepOB-MexaHHKOB, cTy,neHTOB, a TaIOKe
Bcex, KOMY Tpe6yeTc qaCTO 06palI(aTbC K TeXHHqeCKOH HH<popMaUHH.
Newnes Mechanical
Engineer's Pocket Book
Third edition
Roger L. Timings
. Awl.1tIIO*. BmfON. HtatMfIc;.1.QNDOH . NfwY()IIIl.
()XJON) . PAM . SNlOIrGO . SAIl fttAHclSCO . s..cwo.
. SVOMY . TOitYO
ELSEVIBR Newnes is MI impflnt of EbMIr .......
@ 2006, Elsevier Ltd.
@ 2008, 3AO «PMIJ; «TexHoc<pepa», nepeBO,n Ha PYCCKHH 3bIK,
OpHrHHaJI - MaKeT, o<popMJIeHHe
ISBN 978-5-94836-183-3
ISBN 978-0-75066-508-7 (anrJl.)
COAEP>KAHME
BBe.neHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
TIpe.nHCJIOBHe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
BJIaro.napHOCTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
fJlaBa t. HlDKeHepHaJl MaTeMaTHKa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.1. fpeqeCKHH aJIcpaBHT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.2. MaTeMaTHqeCKHe CHMBOJIbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.3. E.nHHHnbI H3MepeHIDI: CM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3.1. OCHoBHbIe H .nonOJIHHTeJIbHbIe BeJIHqHHbI. . . . . . . . . . . . . . . . . . . . . . . 23
1.3.2. TIpoH3Bo.nHbIe BeJIHqHHbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3.3. E.nHHHnbI H3MepeHIDI, He BXO,nHW;He B CHCTeMY CM. . . . . . . . . . . . . . . . 24
1.3.4. TIpHMeqaHIDI OTHOCHTeJIbHO 3anHCH pa3MepHOCTeH . . . . . . . . . . . . . . . . 25
1.3.5. ,LJ;OJIbHbIe H :KpaTHbIe e.nHHHnbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.4. K03cpcpHnHeHTbI npeo6pa30BaHIDI ,WUI e.nHHHn H3MepeHIDI <I><I>C H CM . . . . . 26
1.5. TIpe.nnOqTHTeJIbHbIe qHCJIa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.6. Onpe.neJIeHHe pa3MepOB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.6.1. TI.1IocKHe CPHrypbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.6.2. 06DeMHbIe cpHrypbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.7. CTeneHH, KOpHH H o6paTHbIe BeJIIftIHHbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.8. TIporpeccHH................................................ 34
1.8.1. ApHcpMeTHqeCKaH nporpeCCIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.8.2. feoMe1]>H'IeCKaH nporpeCCIDI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.8.3. fapMOHHqeCKaH nporpeCCIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.9. TpHroHoM e1]>HqeCKHe CPOPMYJIbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.9.1. OCHoBHbIe onpe.neJIeHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.9.2. T ox,n eCTBa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.9.3. COCTaBHbIe cpOPMYJIbI H cpOPMYJIbI .nBoHHoro yrJIa . . . . . . . . . . . . . . . . . 36
1.9.4. <l>OPMYJIbI «npOH3Be.neHHe-CYMMa» . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.9.5. <l>OPMYJIbI 1]>eyrOJIbHHKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.10. Kpyr H OKpyxHOCTb: HeKOTopbIe onpe.neJIeHIDI H CBOHCTBa. . . . . . . . . . . . . . . 36
1.10.1. Kpyr: TIJIOW;a,nb H ,WIHHa O:KpyxHOCTH. . . . . . . . . . . . . . . . . . . . . . . . .37
1.11. Kaa,npaTHbIe ypaBHeHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.12. HaTYPaJIbHbIe JIOrapHcpMbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.13. CTaTHcTHKa: BBe.neHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.13.1. OCHoBHbIe nOIDITIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.13.2. BepO.SlTHOCTb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1.13.3. BHHOMHaJIbHOe pacnpe.neJIeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1.13.4. Pacnpe.neJIeHHe nyaccoHa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.13.5. HOpMaJIbHOe pacnpe.neJIeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.14. ,LJ;HcpcpepeHnHaJIbHOe HCqHCJIeHHe (npoH3Bo.nHbIe) . . . . . . . . . . . . . . . . . . . . . 42
1.15. I1HTerpaJIbHoe HCqHCJIeHHe (Heonpe.neJIeHHbIe HHTerpaJIbI). . . . . . . . . . . . . . . 43
1.15.1. MHTerpHpoBaHHe no qaCT.SIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.15.2. Onpe.neJIeHHbIe HHTerpaJIbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
CoiJep:JICaHUe
1.16. BHHOM HbIOToHa (6HHOMHaJIbHaH TeopeMa) . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.17. Pa3JIOXeHHe B PM MaKJIOpeHa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.18. Pa3JIOXeHHe B PM TeKrropa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
fJlaBa 2. HlDKeHepaaJl CTaTHKa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.1. HIDKeHepHaH CTaTHKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.2. Macca, CHJIa H Bec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.2.1. Macca. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.2.2. CHJIa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.2.3. BeKTOpbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.2.4. Bec. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.2.5. Macca Ha e,lJ;HHH 06'beMa (nrroTHocTb) . . . . . . . . . . . . . . . . . . . . . . . 47
2.2.6. Bec B e,lJ;HHHnax OObeMa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.7. OTHOCHTeJIbHaH nrrOTHOCTb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.8. ,LJ;aBJIeHHe (:>KH,l.(KOCTH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3. BeKTOpHbIe ,lJ;HarpaMMbI CHJI: rpacpH'IeCKOe pemeHHe . . . . . . . . . . . . . . . . . . . 50
2.3.1. PaBHO,lJ;e:HCTByIOInHe CHJIbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50
2.3.2. TIapaJIJIeJIorpaMM CHJI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.3.3. YpaBHoBemHBaIOInaH CHJIa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.3.4. Pa3JIOXeHHe CHJI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.3.5. PaBHoBecHe 1]>ex CHJI (1]>eyrOJIbHHK CHJI) . . . . . . . . . . . . . . . . . . . . . . . 53
2.3.6. MHoroyrOJIbHHK CHJI: nOC1]>oeHHe ,lJ;HarpaMMbI MaKCBeJIJIa-KpeMoHbI . . 54
2.3.7. HenepeCeKaIOInHeCg KonrraHapHbIe CHJIbI (BepeBOqHbI:H
MHoroyrOJIbHHK). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.4. MOMeHTbI CHJI, neH1]> TIDKeCTH H neH1]>bI TIDKeCTH nrroInane:H . . . . . . . . . . . . 56
2.4.1. MOMeHTbI CHJI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.4.2. TIpHHnHn MOMeHTOB (HcnOJIb3yeMaH TepMHHOJIOrIDI). . . . . . . . . . . . . . . 57
2.4.3. TIpHHnHn MOMeHTOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.4.4. PaBHoBecHe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.5. Pa3HOBHJJ;HOCTH pbftlarOB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.5.1. PbfllarH nepBoro pO,lJ;a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.5.2. PbfllarH BToporo pO,lJ;a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.5.3. PbfllarH 1]>eTbero pO,lJ;a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.6. QeH1]> TIDKeCTH, reOMe1]>HqeCKH:H neH1]> cpHrypbI H paBHOBeCHe . . . . . . . . . . . 63
2.6.1. QeH1]> TIDKeCTH (TBep,lJ;Oe TeJIo) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.6.2. QeH1]> TIDKeCTH HeO,lJ;HOpO,lJ;HbIX H COCTaBHbIX TBep,lJ;bIX TeJI. . . . . . . . . . . 64
2.6.3. QeH1]> TIDKeCTH (TOHKaH nrracTHHa) . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.6.4. feOMe1]>HqeCKHe neH1]>bI CPHryp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.6.5. PaBHoBecHe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.7. TpeHHe................................................... 68
2.7.1. CMa3Ka. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.7.2. 3aKoHbI 1]>eHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.7.3. K03CPCPHnHeHT 1]>eHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2. 7 .4. Y rOJI 1]>e HIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.7.5. TpeHHe Ha HaKJIOHHO:H nrrOCKOCTH. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.7.6. YroJI 1]>eHIDI nOKOg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.8. HanpIDKeHHe H ,lJ;ecpopManIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.8.1. HOpMaJIbHOe HanpIDKeHHe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.8.2. HanpIDKeHHe C,lJ;BHra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.8.3. OTHOCHTeJIbHaH JIHHe:HHaH ,lJ;ecpopManIDI. . . . . . . . . . . . . . . . . . . . . . . . 73
2.8.4. ,LJ;ecpopManIDI C,lJ;BHra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.8.5. M O,zryJIb ynpyrOCTH (3aKoH fYKa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.8.6. MO,zryJIb C,lJ;BHra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.8.7. HanpIDKeHHe KpyqeHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75
COOep:JICllHUe
2.8.8. KOJIbIJ;eBOe HanpIDKeHHe B TOHKHX IJ;HJIHHJ(pH'IeCKHX 060JIOQKax. . . . . . . 76
2.8.9. TIpO,lJ;OJIbHOe HanpIDKeHHe B TOHKHX IJ;HJIHHJ(pH'IeCKHX 060JIOQKax . . . . . 77
2.9. BaJIKH.................................................... 77
2.9.1. YCHJIHe C,lJ;BHra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77
2.9.2. H3rH6aIOInHH MOMeHT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.9.3. )J;HarpaMMbI YCHJIIDI C,lJ;BHra H H3rH6aIOInerO MOMeHTa . . . . . . . . . . . . . . 79
2.9.4. BaJIKH (KOHCOJIb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.10. HanpIDKeHHe, ,lJ;ecpopMaIJ;IDI H H3m6 6aJIOK. . . . . . . . . . . . . . . . . . . . . . . . . . 86
2.10.1. H3rH6aIOInee HanpIDKeHHe H HeH1]>aJIbHaH JIHHIDI . . . . . . . . . . . . . . . . 86
2.11. <l>epMbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
2.11.1. MeTO,lJ; CeqeHHH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
2.12. fHJJ;pOCTaTH'IeCKOe ,lJ;aBJIeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.12.1. )J;aBJIeHHe Ha nOBepXHOCTb, HaxO,nHIUYIOCg B XH,l.(KOCTH . . . . . . . . . . . . 94
2.12.2. 3aKoH TIaCKaIDI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
fJlaBa 3. HlDKeHepHu ,lOIHaMHKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.1. HIDKeHepHaH ,lJ;HHaMHKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.2. Pa60Ta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.3. 3HepfHH.................................................. 98
3.3.1. CoxpaHeHHe 3HeprHH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.4. MOInHOCTb................................................. 99
3.5. K03cpcpHIJ;HeHT nOJIe3HOrO ,lJ;eHCTBIDI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.6. CKOpOCTb H YCKopeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.6.1. MO,zryJIb CKOpOCTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.6.2. CKOpOCTb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.6.3. Y CKopeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.6.4. YpaBHeHIDI, OTHOCgInHeCg K CKOpOCTH H YCKopeHHIO . . . . . . . . . . . . . 101
3.6.5. HMnYJIbc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1
3.6.6. 3aKOHbI MexaHHKH HbIOTOHa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.6.7. fpaBHTaIJ;IDI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
3.6.8. CoxpaHeHHe HMnyJIbCa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.6.9. B03,lJ;eHCTBHe C1]>YH XH,l.(KOCTH Ha HenO,lJ;BIDKHOe TeJIO . . . . . . . . . . . . . 103
3 .6.10. HH ep IJ;IDI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.6.11. ConpOTHBJIeHHe ,lJ;BIDKeHHIO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.7. BpaInaTeJIbHOe ,lJ;BIDKeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.7.1. Pa,nHaHbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3. 7 . 2. Y rOJI no BO pOTa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.7.3. YrJIOBaH CKOpOCTb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.7.4. CooTHomeHHe Mex,ny yrJIOBOH H JIHHeHHOH CKOPOCTgMH. . . . . . . . . . . 108
3.7.5. YrJIOBOe YCKopeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.7.6. MOMeHT BpaIneHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.7.7. Pa60Ta MOMeHTa BpaIneHIDI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.7.8. [(eH1]>oc1]>eMHTeJIbHOe YCKopeHHe H IJ;eH1]>OC1]>eMHTeJIbHaH CHJIa. . . . . 110
3.7.9. [(eH1]>o6e:>KHaH CHJIa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112
3.8. YpaBHoBemHBaHHe BpaInaIOInHXCg Macc . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.8.1. YpaBHoBemHBaHHe KOMTIJIaHapHbIX Macc (cTaTHqeCKOe paBHoBecHe). . . 112
3.8.2. YpaBHoBemHBaHHe KOMTIJIaHapHbIX Macc (,lJ;HHaMH'IeCKOe paBHoBecHe) 114
3.9. OTHOCHTeJIbHbIe CKOpOCTH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.9.1. OTHOCHTeJIbHbIe CKOpOCTH (HeCOe,lJ;HHeHHbIe TeJIa). . . . . . . . . . . . . . . . 115
3.9.2. OTHOCHTeJIbHbIe CKOpOCTH (cOe,lJ;HHeHHbIe TeJIa) . . . . . . . . . . . . . . . . . 117
3.10. KHHeMaTHKa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.10.1. BaJIJIHCTHKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.11. KHHeTHKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3.11.1. BceMHpHoe TgrOTeHHe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
CoiJep:JICaHUe
3.11.2. JIHHe:HHOe nepeMeIneHHe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3.11.3. TIepeMeIneHHe no KpHBOJIHHe:HHO:H 1]>aeKTopHH. . . . . . . . . . . . . . . . . 121
3.11.4. KOHHqeCKH:H MaJITHHK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
3.11.5. BpaIneHHe TeJIa BOKpyr HenO,lJ;BIDKHO:H OCH . . . . . . . . . . . . . . . . . . . . 122
3. 11.6. Pa,nHYC KpHBH3HbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.11.7. [(eH1]> CTOJIKHOBeHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.11.8. MOMeHT HMnYJIbCa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.12. TIpocToe rapMOHHqeCKOe ,lJ;BIDKeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.12.1. MaTeMaTHqeCKH:H MagTHHK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
3.12.2. Co6cTBeHHbIe KOJIe6aHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
3.13. fH,lJ;pO,lJ;HHaMHKa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
3.13.1. CKOPOCTb TeqeHHg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129
3.13.2. HenpepbIBHoCTb TeqeHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.13.3. 3HepIWI ,lJ;B e:HCg Te e:H Cpe,lJ;bI (ypaBHeHHe BepHYJIJIH) . . . . . . 130
3.13.4. TeqeHHe qepe3 OTBepCTHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
3.13.5. Bg3KOCTb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
3.13.6. <l>oPMYJIa TIya3eitrnI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
3.13.7. 3aKoH CToKca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
fJlaBa 4. KpenelKllbie ,neTaJlH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.1. BHHToBbIe Kpene)I{HbIe H3,lJ;eJIIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.1.1. Pa3MepbI H COOTHomeHIDI Ha qepTexax . . . . . . . . . . . . . . . . . . . . . . . 133
4.1.2. Pa3JIHqHbIe rOJIOBKH BHHTOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.1.3. Pa3JIHQHbIe KOHnbI BHHTOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.1.4. BHHTbI C meCTHrpaHHbIM yrJIy6JIeHHeM B rOJIOBKe . . . . . . . . . . . . . . . . 135
4.1.5. TIpaKTHQeCKOe npHMeHeHHe BHHTOBbIX Kpene)I{HbIX H3,lJ;eJIH:H . . . . . . . . 135
4.1.6. TpaneneH,L(aJIbHaJI pe3b6a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.1.7. TIpgMOyrOJIbHWI pe3b6a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.1.8. YnopHaJI pe3b6a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.1.9. OC1]>OyrOJIbHaJI pe3b6a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.1.10. OCHOBHaJI ,lJ;IO:HMOBWI pe3b6a (55°): nHJIHHJ(pHQeCKaJI pe3b6a. . . . . . . . 137
4.1.11. <l>OPMbI ISO Me1]>HQeCKO:H H ISO 60° YHHcpHnHpoBaHHO:H pe3b6bI . . . . 137
4.1.12. BBe,lJ;eHHe B BHHTOBbIe Kpene)I{HbIe H3,lJ;eJIHH . . . . . . . . . . . . . . . . . . . 137
4.1.13. BS EN ISO 4014: 2001. DOJITbI C mecTHrpaHHO:H rOJIOBKO:H -
KJIaCCbI H3,lJ;eJIIDI A H B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
4.1.14. BS BS EN ISO 4016: 2001. BOJITbI C mecTHrpaHHO:H rOJIOBKO:H -
KJIacc H3,lJ;eJIIDI C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
4.1.15. BS EN ISO 4017: 2001. BHHTbI C mecTHrpaHHO:H rOJIOBKO:H -
KJIaCCbI H3,lJ;eJIIDI A H B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.1.16. BS EN ISO 4018: 2001. BHHTbI c mecTHrpaHHO:H rOJIOBKO:H -
KJIaCC H3,lJ;eJIHH C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4.1.17. BS EN ISO 4032: 2001. illecTHrpaHHbIe ra:HKH HCnOJIHeHIDI 1 -
KJIaCCbI H3,lJ;eJIIDI A H B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
4.1.18. BS. EN ISO 4033: 2001. illecTHrpaHHbIe ra:HKH HCnOJIHeHIDI 2 -
KJIaCCbI H3,lJ;eJIIDI A H B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
4.1.19. BS EN ISO 4034: 2001. illecTHrpaHHbIe ra:HKH HCnOJIHeHIDI 1 -
KJIacc H3,lJ;eJIIDI C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
4.1.20. BS EN ISO 4035: 2001. illecTHrpaHHbIe HH3KHe ra:HKH
(c cpJIaHneM) - KJIaCCbI H3,lJ;eJIHH A H B . . . . . . . . . . . . . . . . . . . . . . 167
4.1.21. BS EN ISO 4036: 2001. illecTHrpaHHbIe HH3KHe ra:HKH
(6e3 cpJIaHQa) - KJIacc H3,lJ;eJIHg B . . . . . . . . . . . . . . . . . . . . . . . . . . 168
4.1.22. BS EN ISO 8765: 2001. BOJITbI C mecTHrpaHHO:H rOJIOBKO:H
C Me1]>HQeCKOH MeJIKO:H pe3b6o:H - KJIaCCbI H3,lJ;eJIIDI A H B . . . . . . . . 169
CoiJepxaHue
4.1.23. BS EN ISO 8676: 2001. BHHTbI C mecTHrpaHHO:H rOJIOBKO:H
C MeT})H'IeCKO:H MeJIKO:H pe3b6o:H - KJIaCCbI H3,l1;eJIIDI A H B. . . . . . . . . . . . 123
4.1.24. BS EN ISO 8673: 2001. illecTHrpaHHbIe ra:HKH HCnOJIHeHIDI 1
C Me1]>H'IeCKO:H MeJIKO:H pe3b6o:H - KJIaCCbI H3,l1;eJIIDI A H B. . . . . . . . . . . . 181
4.1.25. BS EN ISO 8674: 2001. illeCTHyrOJIbHbIe ra:HKH HCnOJIHeHIDI 2
C Me1]>H'IeCKO:H MeJIKO:H pe3b6o:H - KJIaCCbI H3,l1;eJIIDI A H B. . . . . . . . . . . . 183
4.1.26. BS EN ISO 8675: 2001. illecTHrpaHHbIe HH3KHe ra:HKH
C Me1]>H'IeCKO:H MeJIKO:H pe3b6o:H - KJIaCCbI H3,l1;eJIIDI A H B. . . . . . . . . . . . 184
4.1.27. BS 7764: 1994. illecTHrpaHHbIe npope3HbIe H KOpOHqaTbIe ra:HKH. . . . . . . . 186
4.1.28. BS EN ISO 898-1: 1999. TIpOqHOCTHbIe CBO:HCTBa Kpene:>KHbIX H3,l1;eJIH:H:
60JITbI, BHHTbI H mnHJIbKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
4.1.29. BS EN ISO 898-1: 1999. MapKHpoBKa. . . . . . . . . . . . . . . . . . . . . . . . . . .197
4.1.30. BS EN 20898-2: 1994. MeXaHHqeCKHe CBO:HCTBa Kpene:>KHbIX H3,l1;eJIH:H:
ra:HKH C YCTaHOBJIeHHbIMH 3HaqeHIDIMH np06HO:H HarpY3KH -
KPynHaR pe3b6a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
4.1.31. BS EN ISO 898-6: 1996. MeXaHHqeCKHe CBO:HCTBa KPene:>KHbIX H3,l1;eJIH:H:
ra:HKH C YCTaHOBJIeHHbIMH 3HaqeHIDIMH np06HO:H HarpY3KH -
MeJIKaH pe3b6a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
4.1.32. BS EN 20898-7: 1995. MeXaHH'IeCKHe CBO:HCTBa Kpene:>KHbIX H3,l1;eJIH:H:
HcnbITaHHe Ha KpyrgW;HH MOMeHT H MHHHMaJIbHbIe KpyrgW;He MOMeHTbI
AIDI 60JITOB H BHHTOB C HOMHHaJIbHbIMH ,lI;HaMe1]>aMH 1-10 MM . . . . . . . . .208
4.1.33. BS EN ISO 4762: 2004. Me1]>HqeCKH:H BHHT C nHJIHHJ(pHqeCKO:H rOJIOBKO:H
H meCTHrpaHbIM yr.rry6JIeHHeM no,ll; KJIIOq . . . . . . . . . . . . . . . . . . . . . . . . . 208
4.1.34. BS EN ISO 10642: 2004. BHHTbI C nOTa:HHO:H rOJIOBKO:H H meCTHrpaHbIM
yr.rry6JIeHHeM no,ll; KJIIOq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
4.1.35. BS4827 ISO Me1]>H'IeCKHe BHHTOBbIe pe3b6bI, MHHHaTIOpHaR CepHg . . . . . . 217
4.1.36. BS3643-1j2 ISO MeTpH'IeCKHe BHHTOBbIe pe3b6bI: cepIDI C nOCTOgHHbIM
marOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
4.1.37. BS EN ISO 228-1: 2003. Tpy6HbIe pe3b6bI He 06eCneqHBaIOW;He
repMeTH'IHOCTb COe,ll;HHeHHH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
4.1.38. ISO. Tpy6HaR KOHlf1IeCKaR pe3b6a: OCHOBHbIe pa3MepbI . . . . . . . . . . . . . . . 226
4.1.39. BpHTaHCKaR ,lI;IO:HMOBaR pe3b6a (BSW), 60JITbI H ra:HKH . . . . . . . . . . . . . . . 228
4.1.40. BpHTaHCKaR MeJIKaR ,lI;IO:HMOBaR pe3b6a (BSF), 60JITbI H ra:HKH. . . . . . . . . . 229
4.1.41. ISO YHHcpHnHpOBaHHaR TOqHOCTb BHyTpeHHe:H pe3b6bI: PM C KpynHO:H
pe3b6o:H (UN C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
4.1.42. ISO YHHcpHnHpOBaHHaR TOqHOCTb HapyxHO:H pe3b6bI: PM C KPynHO:H
pe3b6o:H (UN C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
4.1.43. ISO YHHcpHnHpOBaHHaR TOqHOCTb BHyTpeHHe:H pe3b6bI: PM C MeJIKO:H
pe3b6o:H (UNF). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
4.1.44. ISO YHHcpHnHpOBaHHaR TOqHOCTb HapyxHO:H pe3b6bI: PM C MeJIKO:H
pe3b6o:H (UN F). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
4.1.45. BA: npocpHJIb 6pHTaHCKO:H CTaHJ(apTHO:H pe3b6bI . . . . . . . . . . . . . . . . . . . . 234
4.1.46. BA: 6pHTaHcKHe CTaHJ(apTHbIe BHyrpeHHHe H HapyxHbIe BHHTOBbIe pe3b6bI 234
4.1.47. Pa3MepbI CBepJI AIDI oTBepCTH:H no,ll; BA pe3b6y H AIDI CKB03HbIX oTBepCTH:H
C 3a30pOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
4.1.48. Pa3MepbI CBepJI AIDI oTBepCTH:H no,ll; ISO Me1]>JItIeCKYIO pe3b6y H
AIDI CKB03HbIX oTBepCTH:H C 3a30pOM: pe3b6a C KpynHbIM marOM. . . . . . . . . 235
4.1.49. Pa3MepbI CBepJI AIDI oTBepCTH:H no,ll; ISO MeTpHqecKYIO pe3b6y H
AIDI CKB03HbIX oTBepCTH:H C 3a30poM: PM C KpynHO:H pe3b6o:H . . . . . . . . . . 236
4.1.50. Pa3MepbI CBepJI AIDI oTBepCTH:H no,ll; ISO YHHcpHnHpOBaHHyK> pe3b6y H
AIDI CKB03HbIX oTBepCTH:H C 3a30pOM: pe3b6a C MeJIKHM marOM. . . . . . . . . . 236
4.1.51. Pa3MepbI CBepJI AIDI oTBepCTH:H no,ll; ISO YHHcpHnHpOBaHHyIO pe3b6y H
AIDI CKB03HbIX oTBepCTH:H C 3a30pOM: pe3b6a C MeJIKHM marOM. . . . . . . . . . 237
CoiJep:JICaHUe
4.1.52. Pa3MepbI CBepJI AIDI oTBepcTHH no,ll; ISO MeTPHqeCKYIO pe3b6y H AIDI
CKB03HbIX oTBepcTHH C 3a30pOM: MHHHaTIOpHaH cepIDI . . . . . . . . . . . . 238
4.1.53. Pa3MepbI CBepJI AIDI oTBepcTHH no,ll; BSW pe3b6y H AIDI CKB03HbIX
oTBepcTHH C 3a30pOM pe3b6bI, Hape3HbIe H npOqHw;aIOW;He MeT'lHKH . . 238
4.1.54. Pa3MepbI CBepJI AIDI oTBepcTHH no,ll; BSF pe3b6y H AIDI CKB03HbIX
oTBepcTHH C 3a30pOM pe3b6bI, Hape3HbIe H npOqHw;aIOW;He MeT'lHKH . . 238
4.1.55. llJIocKHe maH6bI, qHCTbIe: MeT})H'IeCKHH PM . . . . . . . . . . . . . . . . . . . 239
4.1.56. llJIocKHe maH6bI, qepHbIe: MeTPHqeCKHH PM . . . . . . . . . . . . . . . . . . . 240
4.1.57. YCTPOHCTBa AIDI CTonopeHIDI, OCHOBaHHbIe Ha TPeHHH . . . . . . . . . . . . 241
4.1.58. YCTPoHcTBa AIDI CTonopeHIDI, OCHOBaHHbIe Ha MeXaHHqeCKOH
4>HKCaIJ;HH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
4.1.59. TIpyxHHHaH maH6a C KBa,npaTHbIM nOnepeqHbIM CeqeHHeM:
MeTPHqeCKHH PM, THn A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
4.1.60. TIPyxHHHaH maH6a C npgMoyrOJIbHbIMH KOHIJ;aMH: MeTPHqeCKaH
cepIDI, THnbI B H BP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
4.1. 1. TIpyxHHHaH ,lI;ByxBHTKOBaH maH6a C npgMoyrOJIbHbIM nOnepeqHbIM
CeqeHHeM: MeTPHqeCKHH PM, HCnOJIHeHHe D. . . . . . . . . . . . . . . . . . . 245
4.1.62. TIpyxHHHbIe maH6bI C 3y6bgMH, MeTPHqeCKHe . . . . . . . . . . . . . . . . . . 247
4.1.63. CTOnOpHaH maH6bI C 3y6bgMH, MeTPHqeCKHe . . . . . . . . . . . . . . . . . . . 248
4.1.64. ISO MeTPHqeCKaH npyxHHHaH BOJIHHCTaH maH6a: o6w;ee
MaIDHHocTPoeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
4.1.65. TIP04>HJIb na30B no,ll; T -06pa3HYIO rOJIOBKY 60JITa . . . . . . . . . . . . . . . . 251
4.1.66. Pa3MepbI 60JITOB H raeK K T -o6pa3HbIM na3aM . . . . . . . . . . . . . . . . . . 252
4.1.67. Pa3MepbI mnOHOK AIDI T -o6pa3HbIX na30B . . . . . . . . . . . . . . . . . . . . . 253
4.2. 3aKJIenOqHbIe COe,ll;HHeHIDI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
4.2.1. THnH'IHbIe rOJIOBKH H CTep)l(}lH 3aKJIenOK . . . . . . . . . . . . . . . . . . . . . . 255
4.2.2. THnHqHbIe 3aKJIenOqHbIe COe,ll;HHeHIDI BHaXJIeCTKY . . . . . . . . . . . . . . . . 256
4.2.3. THnHqHbIe CTbIKOBbIe 3aKJIenOqHbIe COe,ll;HHeHIDI . . . . . . . . . . . . . . . . . 257
4.2.4. CooTHomeHIDI Me)l{):(y ,lI;HaMeTPOM OTBepCTIDI H ,WIHHOH 3aKJIenKH . . . . . 258
4.2.5. 3aKJIenKH C nOJIYKPyrJIOH 3aKJIa,nHoH rOJIOBKOH, H3rOTOBJIeHHbIe
XOJIO,lUlOH mTaMnOBKOH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
4.2.6. 3aKJIenKH C nOJIyKpyrJIOH 3aKJIa,nHoH rOJIOBKOH, H3rOTOBJIeHHbIe
rOpgqeH mTaMnOBKOH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
4.2.7. TIpe,ll;nOJIaraeMbIH ,lI;Hana30H HOMHHaJIbHbIX ,WIHH, CBg3aHHbIX
C ,lI;HaMeT})OM CTep)l(}leH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
4.2.8. POP@ 3aKJIenKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
4.2.9. 0630p BH,L(OB POP@ 3aKJIenOK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
4.2.10. TIpaKTHQeCKHe peKOMeHJ(aIJ;HH no HCnOJIb30BaHHIO :KpenrreHHH . . . . . . 263
4.2.11. BbI60p POP@ (HJIH BbITIDKHbIX) 3aKJIenOK. . . . . . . . . . . . . . . . . . . . . . 264
4.2.12. PeKOMeHJ(aIJ;HH no npOeKTHpOBaHHIO . . . . . . . . . . . . . . . . . . . . . . . . . 265
4.2.13. POP@ «F» cepIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
4.2.14. CTaHJ(apTHbIe 3aKJIenKH (c OTKpbITbIM TOPIJ;OM) H3 cnrraBa aJIIOMHHHH-
MarHHH 3,5 %. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
4.2.15. CTaHJ(apTHbIe 3aKJIenKH (c OT:KpbITbIM TOpIJ;OM) H3 yrJIepO,ll;HCTOH CTaJIH 274
4.2.16. 3aKpbITbIe 3aKJIenKH H3 cnrraBa aJIIOMHHHH-MarHHH 5%. . . . . . . . . . . . 276
4.2.17. 3aKJIenOQHbIe raHKH (<<raeqHbIe 3aKJIenKH») . . . . . . . . . . . . . . . . . . . . 277
4.2.18. POP@ pe3b6oBbIe 3aKJIenKH: npHMeHeHHe . . . . . . . . . . . . . . . . . . . . . 277
4.2.19. POP@ pe3b6oBbIe 3aKJIenKH: YCTaHOBKa. . . . . . . . . . . . . . . . . . . . . . .278
4.2.20. POP@ faHKa: CTaJIb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
4.3. <l>aJIbIJ;eBbIe COe,ll;HHeHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
4.3.1. <l>aJIbIJ;eBbIe COe,ll;HHeHIDI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .281
4.3.2. TIPHnyCKH Ha 4>aJIbIJ;eBbIe COe,ll;HHeHIDI . . . . . . . . . . . . . . . . . . . . . . . . 282
4.4. Pa3JIHqHbIe Kpene)l(}lbIe H3,l1;eJIIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
4.4.1. KOHHqeCKHe mTH4>TbI, He3aKaJIeHHbIe . . . . . . . . . . . . . . . . . . . . . . . . . 283
COOep:JICaHue
4.4.2. TIpyxHHHbIe HapyxHbIe KOJIbna: Me1]>HqeCKaH cepIDI . . . . . . . . . . . . . 285
4.4.3. CTonopHbIe KOJIbna, BHYTPeHHHe: Me1]>HqeCKaH cepIDI . . . . . . . . . . . . 288
4.5. CKJIeHBaHHe MeTaJIJIOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
4.5.1. AHa3po6HbIe KJIeH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
4.5.2. KneH Y<I>-oTBep)l{)];eHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
4.5.3. [(HaHOaKpHJIaTHbIe KJIeH - aHHOHHaH nOJIHMepH3anIDI. . . . . . . . . . . . 293
4.5.4. Mo,n;HcpHnHpoBaHHbIe aKpHJIOBbIe KJIeH - OTBep)l{)];eHHe
C HCnOJIb30BaHHeM aKTHBaTOpOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
4.5.5. KneH, OTBep)l{)];eHHe KOTOpbIX npOHcxo,n;HT no,n; B03,n;eHcTBHeM
BJIaxHOCTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
4.5.6. 3nOKCH,L(HbIe KJIeH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
4.5.7. BoccTaHOBHTeJIbHbIH nponecc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
4.5.8. KneeBoe coe,n;HHeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
fJlaBa 5. MeXalfll1leCKHe nepe,ZJ;a1JH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
5.1. MeXaHH'IeCKHe nepe,n;aqH: 3y6qaTbIe nepe,n;aqH. . . . . . . . . . . . . . . . . . . . . . . . 299
5.1.1. HeKoTopbIe THnH'IHbIe 3y6qaTbIe nepe,n;aqH. . . . . . . . . . . . . . . . . . . . . 299
5.1.2. TIpocTbIe npgMo3y6ble nHJIHHJ(pHqeCKHe nepe,n;aqH . . . . . . . . . . . . . . . 301
5.1.3. CTyIIeHqaTaH npgMo3y6aH 3y6qaTag nepe,n;aqa. . . . . . . . . . . . . . . . . . . 302
5.1.4. 3BOJIbBeHTa KpHBOH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
5.1.5. OCHOBbI reOMe1]>HH 3y6qaTOrO KOJIeCa . . . . . . . . . . . . . . . . . . . . . . . . 304
5.1.6. illar 3anenrreHIDI 3y6beB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
5.1.7. BbIcoTa 3y6beB KOJIeCa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
5.1.8. 3JIeMeHTbI CTaHJ(apTHOro 3y6qaTOrO KOJIeCa (,n;IOHMbI) . . . . . . . . . . . . . 309
5.1.9. 3JIeMeHTbI MeJIKOMO,LJ;yJIbHOrO 3y6qaTOrO KOJIeCa (,n;IOHMbI) . . . . . . . . . . 309
5.1.10. 3JIeMeHTbI CTaHJ(apTHOro 3y6qaTOrO KOJIeCa C YKopOqeHHbIMH 3y6bgMH
(,n;IO HMbI). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
5.1.11. 3JIeMeHTbI CTaHJ(apTHOro 3y6qaTOrO KOJIeCa (Me1]>H'IeCKaH cHcTeMa). . . 311
5.1.12. ByJ(BeHHbIe 0603HaqeHIDI ,lJ;.IDI pa3MepHocTeH 3y6qaTOrO KOJIeCa H
BbJ1IHCJIeHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
5.1.13. OCHoBHbIe cpOPMYJIbI ,lJ;.IDI npgMo3y6oro nHJIHHJ(pH'IeCKOrO 3y6qaTOrO
KOJIeCa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
5.1.14. OCHoBHbIe ypaBHeHIDI Koco3y6oro nHJIHHJ(pH'IeCKOrO 3y6QaTOrO KOJIeCa 314
5.1.15. BcnoMOraTeJIbHbIe ypaBHeHIDI A1llI 3y6QaTOrO KOJIeca. . . . . . . . . . . . . . 315
5.1.16. TepMHHOJIOrIDI npgMo3y6oH KOHHQeCKOH 3y6QaTOH nepe,n;aqH . . . . . . .316
5.1.17. TepMHHOJIOrIDI QepBgtIHOrO 3anenrreHIDI (QepBgK H QepBHQHOe KOJIeco) 316
5.2. MeXaHHQeCKHe nepe,n;aQH: peMeHHbIe nepe,n;aQH. . . . . . . . . . . . . . . . . . . . . . . 317
5.2.1. npOCTbIe nrrOCKopeMeHHbIe nepe,n;aQH . . . . . . . . . . . . . . . . . . . . . . . .317
5.2.2. CTyIIeHQaTbIe nrrOCKopeMeHHbIe nepe,n;aQH . . . . . . . . . . . . . . . . . . . . . 318
5.2.3. THnH'IHbIe HaTIDKHbIe YC1]>OHCTBa . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
5.2.4. THnHQHble npHMeHeHIDI KJIHHOBbIX H CHHXpOHHbIX peMeHHbIX nepe,n;aQ 320
5.2.5. ULTRAFLEX@ KJIHHOBbIe peMHH C o6epTKoH 60KOBbIX rpaHeH H
Y3KHM CeQeHHeM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
5.2.6. FO@-Z MOW;HbIe 3y6QaTble KJIHHOBbIe peMHH 6e3 o6epTKH 60KOBbIX
rpaHeH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
5.2.7. MULTIFLEX@ KJIHHOBbIe peMHH C o6epTKoH 60KOBbIX rpaHeH
H KJIaCCHQeCKHM CeQeHHeM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
5.2.8. MULTIBELT MHoropyqbeBbIe KJIHHOBbIe peMHH . . . . . . . . . . . . . . . . 326
5.2.9. illKHBbI KJIHHOBbIX peMHeH, COOTBeTCTByIOW;He CTaHJ(apTaM BS 3790
H DIN 2211 ,lJ;.IDI peMHeH FO@-Z H ULTRAFLEX@. Rz xx
0603HaQaeT mepOXOBaTOCTb nOBepXHOCTH .... . . . . . . . . . . . . . . . . . 327
5.2.10. illKHBbI KJIHHOBbIX peMHeH, COOTBeTCTByIOW;He CTaHJ(apTY DIN 2217
qacTb 1 A1llI peMHeH FO@-Z H MULTIFLEX@ . . . . . . . . . . . . . . . . . 328
5.2.11. illKHBbI C r.rry6oKHMH KaHaBKaMH . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
(:;, COOep:JICaHUe
5.2.12. CHHXpoHHbIe peMeHHbIe nepe,n;aqH: BBe,n;eHHe. . . . . . . . . . . . . . . . . . . 330
5.2.13. CHHXpoHHbIe peMeHHbIe nepe,n;aqH: THnbI H pa3MepbI peMHeH . . . . . . . 334
5.2.14. CHHXpoHHbIe peMeHHbIe nepe,n;aqH: mKHBbI . . . . . . . . . . . . . . . . . . . . 339
5.2.15. SYNCHROBELT@ HTD KOHCTPYKD:IDI . . . . . . . . . . . . . . . . . . . . . . . 342
5.2.16. SYNCHROBELT@ HTD CHHXpOHHbIe (3y6qaTbIe) peMHH: npocpHJIH
pacnpe,n;eJIeHIDI 3y6beB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
5.2.17. CHHXpoHHbIe (3y6qaTbIe) peMHH: H3MepeHHe ,WIHHbI. . . . . . . . . . . . . .346
5.2.18. SYNCHROBELT@ HTD 3y6qaTbIe mKHBbI: npe,n;nOqTHTeJIbHbIe
pa3MepbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
5.3. MeXaHHqeCKHe nepe,n;aqH: n;enHbIe nepe,n;aqH. . . . . . . . . . . . . . . . . . . . . . . . . 350
5.3.1. Pa60qHe xapaKTepHCTHKH n;eneH . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
5.3.2. K03cpcpHn;HeHT H3Hoca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
5.3.3. THnbI I.J;eneH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
5.3.4. Me)l{):(YHapo,n;HbIe CTaH,n;apTbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
5.3.5. HopMaTHBHbIe CCbillKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
5.3.6. TIpeH ecTBa n;enHbIX nepe,n;aq. . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
5.3.7. TIpeH ecTBa I.J;enHbIX npHBo,n;OB. . . . . . . . . . . . . . . . . . . . . . . . . . .358
5.3.8. COBMecTHMocTb 3Be3,n;OqKH H n;enH . . . . . . . . . . . . . . . . . . . . . . . . . . 360
5.3.9. PacnOJIOXeHHe npHBo,n;a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
5.3.10. MeTo,n; BbI60pa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
5.3.11. On;eHKa xapaKTepHCTHK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
5.3.12. OI.J;eHKa xapaKTepHCTHK I.J;eneH, H3rOTOBJIeHHbIX no
EBponeHCKOM)' CTaH,n;apTY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
5.3.13. On;eHKa xapaKTepHCTHK n;eneH, H3rOTOBJIeHHbIX no CTaH,L:(apTY ANSI . . 373
5.3.14. TIpoBHcaHHe I.J;enH..................................... .374
5.3.15. CMa3bIBaHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
5.3.16. MeTo,n;bI CMa3bIBaHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
5.3.17. nO,n;'beMHbIe YCTPoHCTBa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
5.3.18. ANSI X-,n;Hana30H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
5.3.19. <l>aKTopbI, BJIIDIIOIUHe Ha CpOK CJl)')K6bI I.J;enH . . . . . . . . . . . . . . . . . . . 379
5.3.20. YATIHHeHHe n;enH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
5.3.21. COrJlaCOBaHHe (BbIpaBHHBaHHe) n;eneH. . . . . . . . . . . . . . . . . . . . . . . . 382
5.3.22. 113MepeHHe H3Hoca I.J;enH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
5.3.23. PeMoHT H 3aMeHa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
5.3.24. PeryJIHpOBKa I.J;enH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
5.3.25. KOHCTPYKTOpCKHe H,L(eH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
5.3.26. Ta6JIHI.J;a K03cpcpHI.J;HeHTOB ,n;HaMeTPa HaqaJIbHOH OKpyxHOCTH . . . . . . . 388
5.3.27. npHBO,n;bI mar 3a marOM: npHMep nepBbIH . . . . . . . . . . . . . . . . . . . . . 389
5.3.28. npHBO,n;bI mar 3a marOM: npHMep BTOpOH . . . . . . . . . . . . . . . . . . . . . 391
5.3.29. npHBO,n;bI mar 3a marOM: npHMep TPeTHH. . . . . . . . . . . . . . . . . . . . . . 394
5.3.30. npe,n;ocTepexeHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
5.4. MeXaHHqeCKaH nepe,n;aqa: BaJIbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
5.4.1. Kaa,npaTHbIe H npHMoyrOJIbHble npH3MaTHqeCKHe IIInOHKH,
MeTPHqeCKaH cepIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
5.4.2. Pa3MepbI H ,n;onYCKH ,WIH KBa,npaTHbIX H npSlMoyrOJIbHbIX
npH3MaTHqeCKHX mnOHOK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
5.4.3. Kaa,npaTHbIe H npSlMoyrOJIbHbIe KJIHHOBbIe mnOHKH, MeTPHqeCKag
CepHg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
5.4.4. Pa3MepbI H ,n;onYCKH ,lI;illI KBa,npaTHbIX H npHMoyrOJIbHbIX KJIHHOBbIX
mnOHOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
5.4.5. CerMeHTHbIe mnOHKH H na3bI ,lI;illI mnOHOK, MeTPHqeCKaH cepIDI . . . . . 406
5.4.6. Pa3MepbI H ,l(OnyCKH ATIH cerMeHTHbIX mnOHOK. . . . . . . . . . . . . . . . . . 408
5.4.7. THnbI KOHI.J;OB BaJIOB: OCHOBHbIe COOTHomeHIDI. . . . . . . . . . . . . . . . . . 409
CoiJep:JICaHUe
5.4.8. Pa3MepbI H ,n;OrryCKH IJ;HJIHH,lJ;pHqeCKHX KOHIJ;OB BaJIOB, ,LUIHHHOe
H KopOTKoe HCnOJIHeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
5.4.9. Pa3MepbI KOHHqeCKHX KOHIJ;OB BaJIOB C npH3MaTHqeCKHMH mnOHKaMH,
,LUIHHHOe HCnOJIHeHHe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
5.4.10. Pa3MepbI KOHHqeCKHX KOHIJ;OB BaJIOB C ,n;HaMe1'paMH CBbIme 220 MM
C na3aMH AIDI mnOHOK, napaJIJIeJIbHbIMH nOBepXHOCTH BaJIa, ,LUIHHHOe
HCnOJIHeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
5.4.11. Pa3MepbI KOHH1IeCKHX KOHIJ;OB BaJIOB C npH3MaTHqeCKHMH mnOHKaMH,
KopOTKoe HCnOJIHeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
5.4.12. ,lJ;orrycKaeMbIe BpaInalOInHe MOMeHTbI. . . . . . . . . . . . . . . . . . . . . . . . . 417
5.4.13. llpHM060qHbIe lIIJIHIJ;bI AIDI IJ;HJIHH,lJ;pH1IeCKHX BaJIOB, Me1'pHqeCKHe
e,n;HHHIJ;bI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
5.5. KOHYCbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
5.5.1. CaMo3IDKHMHbIe Mop3e H Me1'pHqeCKHe 5% KOHYCbI . . . . . . . . . . . . . .421
5.5.2. KOH)'CHbIe KOHIJ;bI mnHH,lJ;eJIeH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
5.5.3. KOH)'CbI AIDI XBOCTOBHKOB HHCTPYMeHTOB. . . . . . . . . . . . . . . . . . . . . . 435
5.5.4. <l>JIaHIJ;bI HHCTPYMeHTaJIbHOH onpaBKH . . . . . . . . . . . . . . . . . . . . . . . . 437
5.5.5. KOHYC BpH,l()KlIOpT R8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
5.6. CHcTeMbI 06'beMHOH nepe,n;aqH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
5.6.1. THnHqHaH nHeBMaTHqeCKaH CHCTeMa . . . . . . . . . . . . . . . . . . . . . . . . . 439
5.6.2. THnH1IHaH fH,ll;paBJIHqeCKaH CHCTeMa . . . . . . . . . . . . . . . . . . . . . . . . . 441
5.6.3. BH,lI;bI B03,[(yuIHbIX KOMnpeccopOB . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
5.6.4. fH,ll;paBJIHqeCKHe HaCOCbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
5.6.5. I1CnOJIHHTeJIbHbIe MexaHH3MbI (JIHHeHHbIe) . . . . . . . . . . . . . . . . . . . . 450
5.6.6. I1CnOJIHHTeJIbHbIe MexaHH3MbI (BpaInaTeJIbHbIe) . . . . . . . . . . . . . . . . . 452
5.6.7. I1CnOJIHHTeJIbHbIe MexaHH3MbI CMemaHHOfO THna . . . . . . . . . . . . . . . .454
5.6.8. 0603HaqeHIDI AIDI fH,ll;paBJIH1IeCKHX CHCTeM . . . . . . . . . . . . . . . . . . . . 454
5.6.9. ,lJ;aHHbIe AIDI paCqeTOB 06'beMHOH fH,ll;pOnepe,n;aqH (OCHoBHbIe
<POPMYJIbI). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
5.6.10. llpoeKTHbIe ,L(aHHbIe 06'beMHOH fH,ll;pOnepe,n;aqH (rH,ll;paBJIHqeCKHe
IJ;HJIHH,n;p bI ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
5.6.11. ,lJ;aHHbIe ,L(JUI paCqeTOB 06'beMHOH fH,ll;pOnepe,n;aqH (rH,ll;paBJIHqeCKHe
Tpy6bI H lIIJIaHfH) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459
5.6.12. ,lJ;aHHbIe ,WUI paCqeTOB 06'beMHOH fH,ll;pOnepe,n;aqH (pa60qHe XH,l(KOCTH,
fepMeTHKH H KOH1'pOJIb 3arpH3HeHHocTH). . . . . . . . . . . . . . . . . . . . . . 460
5.6.13. ,lJ;aHHbIe AIDI paCqeTOB 06'beMHOH rH,ll;ponepe,n;aqH (fH,ll;paBJIHqeCKHe
aKKYMYJIHTOpbI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463
5.6.14. ,lJ;aHHbIe ,LUIH paCqeTOB 06'beMHOH fH,ll;pOnepe,n;aqH (fH,ll;paBJIH1IeCKOe
OXJIIDK,LJ;eHHe H HarpeB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464
5.6.15. ,lJ;aHHbIe AIDI paCqeTOB 06'beMHOH fH,ll;pOnepe,n;aqH (KJIanaHbI) . . . . . . . . 465
5.6.16. ,lJ;aHHbIe ,L(JUI paCqeTOB 06'beMHOH rH,ll;ponepe,n;aqH (nHeBMaTH1IeCKHe
IJ;HJIHH,lJ;pbI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
5.6.17. llpoeKTHbIe ,n;aHHbIe 06'beMHOH fH,ll;pOnepe,n;aqH (yruIOTHeHHe,
<pHJIb1'paIJ;IDl H cMa3Ka). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
5.6.18. ,lJ;aHHbIe AIDI paCqeTOB 06'beMHOH fH,ll;pOnepe,n;aqH (B03,n;ymHbIe
KOMnpeccopbI). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
5.6.19. ,lJ;aHHbIe AIDI paCqeTOB 06'beMHOH fH,ll;pOnepe,n;aqH (Ta6JIHIJ;bI
H K03<P<PHIJ;HeHTbI nepeCqeTa B nHeBMaTHKe) . . . . . . . . . . . . . . . . . . . 472
5.6.20. HopMaTHBHbIe CCbIDKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
fJIaBa 6. MamHHocTpOHTeJIbHbIe MaTepHaJIbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
6.1. MeXaHHqeCKHe CBOHCTBa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
6.1.1. llpOqHOCTb Ha paCTIDKeHHe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
6.1.2. llpOqHOCTb Ha C)KaTHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
COOep:JICaHUe
6.1. 3 . II po qH OCTb Ha c,n;BHr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
6.1.4. llpOqHOCTb npH y,n;ape: y,n;apHaH BH3KOCTb . . . . . . . . . . . . . . . . . . . . . 478
6.1.5. Y npyrocTb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
6.1.6. llrracTHqHOCTb......................................... 479
6.1.7. BH3KOCTb............................................. 479
6.1.8. KOBKOCTb............................................ 480
6.1.9. TBep,lJ;OCTb........................................... .480
6.1.10. McnbITaHHe Ha paCTIDKeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
6.1.11. MHTepnpeTanIDI HcnbITaHIDI Ha paCTIDKeHHe: MaTepHaJIa
C BbIpIDKeHHbIM npe,lJ;eJIOM Tex:yqeCTH. . . . . . . . . . . . . . . . . . . . . . . . . 481
6.1.12. MHTepnpeTanHH HcnbITaHIDI Ha paCTIDKeHHe: YCJIOBHbIH npe,lJ;eJI
Tex:yqeCTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
6.1.13. MHTepnpeTanIDI HcnbITaHIDI Ha paCTIDKeHHe: CeKYIIJ;HH MO.nyJIb . . . . . . 483
6.1.14. McnbITaHHe Ha y,n;apHYIO BH3KOCTb: no M30.ny. . . . . . . . . . . . . . . . . . . 484
6.1.15. McnbITaHHe Ha y,n;apHYIO BH3KOCTb: no IIlapnH. . . . . . . . . . . . . . . . . .484
6.1.16. MHTepnpeTanIDI pe3YJIbTaTOB HcnbITaHIDI Ha y,lJ;apHYIO BH3KOCTb. . . . . . 485
6.1.17. Onpe,n;eJIeHHe TBep,n;OCTH no BpHHeJIIO . . . . . . . . . . . . . . . . . . . . . . . . 485
6.1.18. Onpe,lJ;eJIeHHe TBep,n;OCTH no BHKKepcy. . . . . . . . . . . . . . . . . . . . . . . . 486
6.1.19. Onpe,n;eJIeHHe TBep,n;OCTH no POKBeJIJIy . . . . . . . . . . . . . . . . . . . . . . . . 486
6.1.20. Onpe,lJ;eJIeHHe TBep,n;OCTH no POKBeJIJIy (npH )'MeHbmeHHbIX
no cpaBHeHHIO C 06bNHbIMH HarpY3KaMH) . . . . . . . . . . . . . . . . . . . . . 487
6.1.21. CpaBHHTeJIbHaH mKaJIa TBep,n;OCTH . . . . . . . . . . . . . . . . . . . . . . . . . . .488
6.2. qepHbIe MeTaJIJIbI H cn.rraBbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
6.2.1. qepHbIe MeTaJIJIbI: HeJIerHpOBaHHaH yrJIepO,lJ;HCTaH CTaJIb . . . . . . . . . . . 489
6.2.2. BJIIDIHHe co,n;ep)KaHIDI yrJIepo,n;a Ha C1'pyKTypy, CBOHCTBa
H npHMeHeHHe HeJIerHpOBaHHbIX yrJIepo,n;HCTbIX CTaJIeH. . . . . . . . . . . . 490
6.2.3. qepHbIe MeTaJIJIbI: JIerHPYIOInHe 3JIeMeHTbI. . . . . . . . . . . . . . . . . . . . . 491
6.2.4. BpHTaHcKHe CTaH,ll;apTbI, OTHOCHInHeCH K qepHbIM MeTaJIJIaM . . . . . . . . 492
6.2.5. HeKoTopbIe THnHqHbIe CTaJIH H HX npHMeHeHHe . . . . . . . . . . . . . . . . . 495
6.2.6. HeKoTopbIe THnHqHbIe HHC1'p)'MeHTaJIbHbIe CTaJIH . . . . . . . . . . . . . . . . 502
6.2.7. qyryH (cepbIH) C n.rraCTHHqaTbIM rpa<J;>HToM . . . . . . . . . . . . . . . . . . . . 504
6.2.8. BS EN 1561: 1997 CepbIe qyryHbI . . . . . . . . . . . . . . . . . . . . . . . . . . . 505
6.2.9. KOBKHe qyryHbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
6.2.10. qyryH C mapOBH,lJ;HbIM rpa<J;>HToM. . . . . . . . . . . . . . . . . . . . . . . . . . . .510
6.2.11. JIerHpoBaHHbIe qyryHbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512
6.2.12. CocTaB, CBOHCTBa H npHMeHeHHe HeKOTopbIX THnWlHbIX qyryHOB. . . . . 514
6.3. I(BeTHbIe MeTaJIJIbI H cn.rraBbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
6.3.1. I(BeTHbIe MeTaJIJIbI H cn.rraBbI. BBe,lJ;eHHe. . . . . . . . . . . . . . . . . . . . . . .515
6.3.2. Cn.rraBbI C BbICOKHM co,n;ep)KaHHeM Me,n;H . . . . . . . . . . . . . . . . . . . . . . 515
6.3.3. KOBaHaH Me,lJ;b H Me,lJ;HbIe cn.rraBbI: KO,n; COCTOHHIDI. . . . . . . . . . . . . . . . 516
6.3.4. BpHTaHcKHe CTaH,lJ;apTbI, OTHOCHInHeCH K Me,lJ;H H Me,lJ;HbIM cn.rraBaM . . . 517
6.3.5. llpyTKH H npo<J;>HJIH H3 Me,n;H H Me,n;HbIX cn.rraBOB . . . . . . . . . . . . . . . . 518
6.3.6. ,lJ;e<J;>opMHpyeMaH Me,lJ;b H Me,n;HbIe cn.rraBbI. . . . . . . . . . . . . . . . . . . . . . 522
6.3.7. ,lJ;e<J;>opMHpyeMaH Me,n;b H Me,lJ;HbIe cn.rraBbI. . . . . . . . . . . . . . . . . . . . . . 526
6.3.8. nHCTOBaH, nOJIOCOBaH Me,n;b H Me,lJ;HaH <J;>OJIbra. . . . . . . . . . . . . . . . . . . 528
6.3.9. naT)'HHbIe JIHCTbI, nOJIOCbI H <J;>OJIbra: ,n;ByxKOMnOHeHTHbIe (6HHapHbIe)
cn.rraBbI Me,n;H H nHHKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . · · . . . 529
6.3.10. naT)'HHbIe JIHCTbI, nOJIOCbI H <J;>OJIbra: CnenHaJIbHbIe cn.rraBbI
H JIerHpOBaHHaH JIaT)'Hb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . · . . . . 531
6.3.11. nHCTbI, nOJIOCbI H <J;>OJIbra H3 <J;>OC<J;>OpHCTOH 6pOH3bI . . . . . . . . . . . . . . 532
6.3.12. Cn.rraBbI aJIlOMHHHeBoH 6pOH3bI. BBe,n;eHHe. . . . . . . . . . . . . . . . . . . . . 534
6.3.13. nHCTbI, nOJIOCbI H <J;>OJIbra H3 aJIlOMHHHeBOH 6POH3bI. . . . . . . . . . . . . . 534
6.3.14. Me,n;Ho-HHKeJIeBbIe (KYJIPO-HHKeJIeBbIe) JIHCTbI, nOJIOCbI H <J;>OJIbra . . . . 535
6.3.15. HHKeJIb-Cepe6pHHbIe JIHCTbI, nOJIOCbI H <J;>OJIbra. . . . . . . . . . . . . . . . . . 536
CoiJep:JICaHUe
6.3.16. CMemaHHbIe ,L(e<J;>opMHpyeMbIe Me,L(HbIe CnrraBbI. . . . . . . . . . . . . . . . . .537
6.3.17. Me,L(HbIe cnrraBbI AIDI JIHTbH: rpynna A. . . . . . . . . . . . . . . . . . . . . . . .540
6.3.18. Me,L(HbIe cnrraBbI AIDI JIHTbH: rpynna B. . . . . . . . . . . . . . . . . . . . . . . . 542
6.3.19. Me,L(HbIe CnJIaBbI AIDI JIHTbH: rpynna C. . . . . . . . . . . . . . . . . . . . . . . . 544
6.3.20. Me,L(HbIe cnrraBbI AIDI JIHTbH: THnHqHbIe CBOHCTBa H 3HaqeHIDI
xeCTKOCTH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546
6.3.21. .AJIIOMHHHH H aJIlOMHHHeBbIe cnrraBbI. . . . . . . . . . . . . . . . . . . . . . . . . 548
6.3.22. BpHTaHCKMe CTaH,napTbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549
6.3.23. llrrHTbI, JIHCTbI H nOJIOCbI H3 qHCTOrO aJIlOMHHIDI . . . . . . . . . . . . . . . . 549
6.3.24. TIJIHTbI, JIHCTbI H nOJIOCbI H3 aJIlOMHHHeBoro cnrraBa:
6e3 TepMHqeCKOH o6pa6oTKM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
6.3.25. llrrHTbI, JIHCTbI H nOJIOCbI H3 aJIlOMHHHeBoro cnrraBa:
TepMHqeCKaH o6pa6oTKa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552
6.3.26. TIpyrKM, mTaMnOBaHHbIe 1py6bI H npo<J;>MJIH H3 aJIlOMHHIDI
H aJIlOMHHHeBoro cnrraBa AIDI o6w;ero MamHHOC1pOeHIDI:
6e3 TepMHqeCKOH o6pa6oTKM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
6.3.27. TIpyrKM, mTaMnOBaHHbIe 1py6bI H npo<J;>MJIH H3 aJIlOMHHHeBoro
cnrraBa ,L(. UI o6w;ero MamHHOC1poeHIDI: TepMlNeCKaH o6pa6oTKa . . . . . 555
6.3.28. nHTbIe aJIlOMHHHeBbIe cnrraBbI, rpynna A: o6w;ee Ha3HaqeHHe . . . . . . . 557
6.3.29. nHTbIe aJIlOMHHHeBbIe cnrraBbI, rpynna B: CneI(HaJIbHOe Ha3HaqeHHe . . 558
6.3.30. nHTbIe aJIlOMHHHeBbIe cnrraBbI, rpynna C: CneIJ;HaJIbHOe Ha3HaqeHHe
H orpaHHqeHHaH npHMeHHMOCTb . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
6.3.31. nHTbIe aJIlOMHHHeBbIe cnrraBbI: MeXaHHqeCKMe CBOHCTBa . . . . . . . . . . . 560
6.3.32. BS EN 29453: 1993 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561
6.3.33. THnHqHbIe npHMeHeHIDI MHrKOrO npHnOH . . . . . . . . . . . . . . . . . . . . . 563
6.3.34. TIaHKa cepe6pHHbIM npHnoeM (naHKa TBep,L(bIM npHnoeM) . . . . . . . . . . 563
6.3.35. fpynna AG: naHKa cepe6pHHbIM TBep,L(bIM npHnoeM . . . . . . . . . . . . . . 564
6.4. Pa3MepbI MeTaJIJIHqeCKMX H3,L(eJIHH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
6.4.1. Pa3MepbI MeTaJIJIHqeCKMX H3,L(eJIHH: BBe,L(eHHe B BS 6722: 1986 . . . . . . . 565
6.4.2. PeKOMeH.nYeMbIe ,L(HaMe1pbI npOBOJIOKM, Me1plNeCKMe. . . . . . . . . . . . . 566
6.4.3. P KOMeH.nYeMbIe pa3MepbI npyrKoB H nrrocKMX H3,L(eJIHH . . . . . . . . . . . 567
6.4.4. PeKOMeH.nYeMbIe mHpHHa H ,L(JIHHa nrrOCKMX H3,L(eJIHH . . . . . . . . . . . . . 567
6.4.5. Macca Me1plNeCKMX npyrKoB KpyrJIOrO H KBan;paTHoro CeqeHIDI . . . . . 568
6.4.6. Pa3MepbI npyrKoB meCTMyrOJIbHOrO CeqeHIDI AIDI BHHTOBbIX KpenexeH,
Me1pHqeCKMe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
6.4.7. Pa3MepbI KaJIH6pOB H MX 3KBHBaJIeHTbI . . . . . . . . . . . . . . . . . . . . . . . 570
6.5. TIOJIHMepHbIe MaTepHaJIbI (nrracTMaccbI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571
6.5.1. llOJIHMepHbIe MaTepHaJIbI (nrracTMaccbI). BBe,L(eHHe. . . . . . . . . . . . . . .571
6.5.2. HeKoTopbIe BIDKHbIe TepMOpeaKTHBHbIe nOJIHMepbI . . . . . . . . . . . . . . . 573
6.5.3. HeKoTopbIe BIDKHbIe TepMOnrraCTINHbIe nOJIHMepbI . . . . . . . . . . . . . . . 574
--
----
fJIaBa 7. Ha3Ha1JeHHe JIHHeHHbIX H reOMeTpH1JeCKHX JJ;OnyCKOB. . . . . . . . . . . . . . . . . 575
7.1. Ha3HaqeHHe JIHHeHHbIX ,L(OnYCKOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575
7 .1.1. onycKM H nOCan;KM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575
7.1.2. THnbI nOCan;OK. . .A--O-- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577
7.1.3. T OqHOCTb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577
7.2. CTaH,napTHaH CHCTeMa ,nOnyCKOB H nOCan;OK. BBe,L(eHHe . . . . . . . . . . . . . . . . . 578
7.2.1. llpHMeHeHHe Ta6JIHIJ; ,L(OnYCKOB H nOCan;OK. .. . . . . . . . . . . . . . . . . . . . 579
7.2.2. BbI60p TOqHOCTH ,L(onycKa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580
7.3. Ha3HaqeHHe ,L(OnYCKOB <J;>OpMbI H pacnOJIOXeHIDI nOBepXHocTeH . . . . . . . . . . . 583
7.3.1. Ha3HaqeHHe ,L(OnyCKOB <J;>OpMbI (OCHoBHbIe nOIDITHH). . . . . . . . . . . . . . 584
7.3.2. PaMKa ,L(OnYCKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
7 .3.3. OnyCK <J;>OpMbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
7.3.4. TIoJIe ,L(OnYCKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
CoiJep:JICaHUe
7.3.5. 3aBHcHMbIH ,Z:(OrryCK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587
7.3.6. 06JIaCTH npHMeHeHIDI ,Z:(OrryCKOB <pOpMbI H pacnOJIOXeHIDI
nOBepXHocTeH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588
7.4. ,lI;eHcTBHTeJIbHbIH pa3Mep. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590
7.5. 3KOHOMHqeCKHH 3<p<peKT ,Z:(onYCKa <pOpMbI . . . . . . . . . . . . . . . . . . . . . . . . . . 591
fJIaBa 8. ABToMaTH3HpoBaHHoe KOHCTPYHPOBaHHe. . . . . . . . . . . . . . . . . . . . . . . . . . 593
8.1. qllYTHna CNC............................................ .593
8.1.1. THnHqHbIe 06JIaCTH npHMeHeHIDI qHCJIOBOrO nporpaMMHoro
ynpaBJIeHIDI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593
8.1.2. llpeHMYJl(eCTBa H orpaHHQeHIDI qllY . . . . . . . . . . . . . . . . . . . . . . . . 593
8.1.3. YnpaBlliIeMbIe Koop,Z:(HHaTbI CTaHKOB . . . . . . . . . . . . . . . . . . . . . . . . . 595
8.1.4. CHCTeMbI ynpaBJIeHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596
8.1.5. <l>opMaT H TepMHHOJIOrIDI nporpaMMbI . . . . . . . . . . . . . . . . . . . . . . . . 597
8.1.6. <l>opMaT C an;peCOM B KaJK,LJ;OM CJIOBe . . . . . . . . . . . . . . . . . . . . . . . . . 598
8.1.7. KO,Z:(HpoBaHHaH HH<popManIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598
8.1.8. Bxo,Z:(HbIe ,Z:(aHHbIe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
8.1.9. KoppeKUIDI Ha ,Z:(JIHHY HHCTPYMeHTa: <ppe3epoBaHHe . . . . . . . . . . . . . . 602
8.1.10. KOMneHcanIDI Ha ,Z:(HaMe1p <ppe3bI: <ppe3epoBaHHe. . . . . . . . . . . . . . . .603
8.1.11. MeTo,Z:(bI nporpaMMHpOBaHIDI: <ppe3epoBaHHe H CBepJIeHHe. . . . . . . . . . 605
8.1.12. llpHMep nporpaMMbI: <ppe3epoBaHHe . . . . . . . . . . . . . . . . . . . . . . . . .606
8.1.13. KoppeKUIDI Ha HHC1pYMeHT: o6pa6oTKa Ha TOKapHOM CTaHKe. . . . . . . .608
8.1.14. KoppeKUIDI Ha pan;HYC BepmHHbI pe3na: TOKapHbIH CTaHOK . . . . . . . . . 609
8.1.15. MeTo,Z:(bI nporpaMMHpOBaHIDI: o6pa6oTKa Ha TOKapHOM CTaHKe. . . . . . . 610
8.1.16. llpHMep nporpaMMbI: o6pa6oTKa Ha TOKapHOM CTaHKe . . . . . . . . . . . . 612
8.1.17. CJIOBapb TepMHHOB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614
8.2. ABToMaTH3HpoBaHHoe npOeKTHpOBaHHe (CAD) . . . . . . . . . . . . . . . . . . . . . . . 617
8.2.1. BBe,Z:(eHHe B aBTOMaTH3HpOBaHHoe npoeKTHpOBaHHe . . . . . . . . . . . . . . . 617
8.2.2. AnnapaTHoe 06eCneQeHHe CHCTeMbI CAD . . . . . . . . . . . . . . . . . . . . . . 619
8.2.3. llporpaMMHoe o6eCneQeHHe CHCTeMbI CAD. . . . . . . . . . . . . . . . . . . . . 622
8.2.4. ABToMaTH3HpoBaHHoe npoeKTHpOBaHHe H npOH3BO,Z:(CTBO. . . . . . . . . . . . 623
8.2.5. llpeHM ecTBa H orpaHHQeHHH CAD . . . . . . . . . . . . . . . . . . . . . . . . . 624
8.3. llpOMbIIIIJIeHHbIe P060TbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624
8.3.1. BBe,Z:(eHHe B po6oTOTeXHHKY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .624
8.3.2. YnpaBJIeHHe P060TOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625
8.3.3. feoMeTpIDI PYKH po6oTa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
BBE.QEHME
IIpOIIIJIO yxe 14 JIeT C Tex lIOp, KaK lIepBoe H3,l(aHHe ClIpaBOqHHKa HIDKeHepa-Me-
xaHHKa 6 bill 0 BbIrryI.l(eHO B ero CylI(eCTByrolI(eM <popMaTe. XOT.H B TeKCT BToporo H3-
,l(aHIDI, orry6JIHKOBaHHoro lIpH6JIH3HTeJIbHO 7 JIeT Ha3M, 6billO BKJIlOqeHO MHoxe-
CTBO 06HOBJIeHHH 6pHTaHcKHX CTaH)];apTOB, CTPYKTYPa KHHrH He H3MeHHJIaCb.
B TeqeHHe 14 JIeT, C MOMeHTa BbIxo,n;a lIepBoro H3,n;aHIDI CnpaBOqHHKa HIDKeHe-
pa-MexaHHKa, 6pHTaHcKoe MaIIIHHOCTPoeHHe lIpeTeplIeJIO PM cylI(ecTBeHHbIX H3-
MeHeHHH C nepeMeII eHHeM aKUeHTa C lIpOH3Bo,n;cTBa Ha npOeKTHpOBaHHe H pa3BH-
THe. B TO xe caMoe BpeM.H lIpOH3BO,n;CTBO B 3HaqHTeJIbHOH CTeneHH lIepeMeCTHJIOCb
B BOCTOqHylO EBpony, A3HIO H Ha ,lJ;aJIbHHH BOCTOK C ueJIblO YMeHbIIIeHIDI 3KCnrry-
aTaUHOHHbIX pacxo,n;OB B YCJIOBIDIX Bce 60JIbIIIeH KOHKYPeHUHH Ha rJI06aJIbHOM
pbIHKe.
IIo3ToMY lIepe,l( BbIrryCKOM 3Toro TpeTbero H3,l(aHIDI ClIpaBOQHHKa H3,n;aTeJIH H
aBTOp npe,l(npHIDIJIH IIIHpOKoe H3yqeHHe pbIHKa. fJIaBHbIe pe3YJIbTaTbI 3Toro HCCJIe-
,l(OBaHHR nOKa3aJIH, qTO:
. nOTpe6HOCTb B ClIpaBOqHHKe no meXHOJl02UU npou38oiJcm8a CMeHHJIaCb no-
TPe6HOCTblO B CnpaBOqHHKe no UH'JICeHepHOMY npoeKmup08aHUlO;
. 60JIbIIIe HH<popMaUHH TPe6yeTcH no TaKHM 06JIaCTHM, KaK pOJIHKOBbIe uelI-
HbIe lIpHBO,n;bI, lIHeBMaTHqeCKHe H rH,ll;paBJIHqeCKHe CHCTeMbI B pa3,n;eJIe, lIO-
CBHlI(eHHOM MeXaHHqeCKHM nepe,n;aqaM;
. 60JIbIIIe HH<popMaUHH TPe6yeTcH lIO BonpocaM UH'JICeHepHOU cmamUKU, iJuHa-
MUKU H MameMamUKU;
. pa3,n;eJIbI, HHTepec K KOTOpbIM CHH3HJICH, KacalOTCR pe Hx HHCTPYMeHTOB.
B HaCTOHI..I.J;ee BpeM.H ,l(aHHbIe 0 pe Hx HHCTPYMeHTax npe,n;CTaBJI.HIOTCH Me-
Hee Ba)l{HbIMH, nOCKOJIbKY aKUeHT CMeCTHJICH OT npOH3Bo,n;CTBa K npoeKTHpo-
BaHHIO. KpOMe Toro, ,n;aHHbIe 0 pe Hx HHCTPYMeHTax Tenepb IIIHpOKO
npe,n;CTaBJIeHbI Ha HHTepHeT-CTPaHHuax lIpOH3Bo,n;HTeJIeH pe HX HHCTPy-
MeHTOB. IIepeqeHb lIOJIe3HbIX Be6-caHTOB BKJIlOqeH B IIpHJIoxeHHe 4.
PoiJ'JICep JI. TUMUH2C (2005)
npE.QMCnOBME
KaK CKa3aHO BO BBe,n;eHHH, 3TO HOBOe H3,n;aHHe ClIpaBOqHHKa HIDKeHepa-MeXaHHKa
0TPIDKaeT H3MeIDIlOmyIOCH lIpHpO,n;y MaIIIHHOCTPOeHIDI H CB.H3aHHbIe C HeH TeXHO-
JIOrHH B BeJIHK06pHTaHHH. MHOrHe H3 6pHTaHCKHX CTaH,ll;apTOB (BS), UHTHpyeMbIe
B lIpe,n;bLl(ylI(HX H3,n;aHIDIX, 6billH HClIpaBJIeHbI HJIH y,n;aJIeHbI H 3aMeHeHbI Ha CTaH-
,n;apTbI BS EN H BS EN ISO. KaTaJIOr 6pHTaHcKHX CTaH,ll;apTOB 60JIbIIIe He ,n;OCT}'-
neH B 6)'Ma)l{HOM BapHaHTe, O,L(HaKO H3,n;aH Ha KOMnaKT-,n;HCKe.
CxeMLI YCJIOBHLIX 0603HaqeHHH CTaH,ZJ;apTOB
CTaH,ll;apTbI B KaTaJIOre 3aKo,n;HpOBaHbI, KaK lIOKa3aHO Ha CJIe,n;yrolI(eM npHMepe.
Pa3JIHqHbIe 3JIeMeHTbI lIOMeqeHbI 6YKBaMH A-J. KrrlOq 06'b.HCIDIeT K3.)I()J;bIH 3JIe-
MeHT. He Bce 3JIeMeHTbI BCTpeqaIOTC.H B K3.)I()J;OM CTaH,ll;apTe.
ABC
I I I
BS 1361: 1971 (1986)
D
I
"* IEC 269-1
npe,n;oxpaHHTeJIH nJIaBKHe ,ZJ;JIB D;eneii nepeMeHHoro TOKa B 6LITOBLIX nOMem;eHHJIX.
Tpe6oBaHIDI, KJIaCCbI H HClIbITaHIDI ,LUI.H IIJIaBKHX BCTaBOK, OCHOBaHHH npe,n;o-
xpaHHTeJI.H H ,n;epxaTeJIeH IIJIaBKHX BCTaBOK. Pa3MepbI H BpeM.HTOKOBbIe 30HbI ,LUI.H
IIJIaBKHX BCTaBOK. THII I-KJIacc 240B H 5-45A,LUI.H 3aMeHbI lIoTPe6HTeJI.HMH B 6bITO-
BbIX YCJIOBIDIX; THn II - KJIacc 415 B H 60, 80 HJIH 100A,LUI.H HClIOJIb30BaHHR npe,n;-
CTaBHTeJI.HMH lIOCTaBII(HKOB 3JIeKTp03HeprHH BO BXO,L(HbIX 6JIOKaX )I{HJIbIX HJIH aHa-
JIOrHQHbIX lIOMelI(eHHH.
G
I
AMD 4171, HHBapb 1983 (Gr 0) R 00000821
AMD 4795, HHBapb 1985 (Gr 2) R 00000833 - E
AMD 6692, HHBapb 1991 (FOC) 00000845
J - A5, 44 CTpaHHUbI
00000818
I
I
Gr7
I
H
PEL/32
I
F
llpeOUCIl08ue
A - l1.neHTH<pHKaTOp H3,n;eJIIDI.
B - ,lJ;aTa lIepBOH rry6JIHKaUHH.
C - ITO,n;TBep)l{)];eH B 1986 r., YKa3bIBaeT Ha rrpo,n;OJDKeHHe ,n;eHcTBIDI CTaH,ll;apTa
6e3 lIOJIHOH nepepa60TKH.
D - = - l1.neHTWlHbIH CTaH,ll;apr: rry6JIHKaUIDI BSI H,lI;eHTWlHa BO Bcex lIo,n;p06-
HOCTRX COOTBeTCTByrolI(eM)' eBporreHCKOM)' H/HJIH MeX,ZJyHapo,n;HOM)' CTaH,ll;apTY.
HJIH = - (TeXHWlecKH) 3KBHBaJIeHTHbIH CTaH,ll;apT: rry6JIHKaUIDI BSI BO Bcex
TeXHWlecKHX OTHOIIIeHIDIX aHaJIOrWlHa COOTBeTCTByromeMY eBpolIeHcKOM)' H/HJIH
MeX,ZJyHapo,n;HOM)' CTaH,ll;apTY, XOT.H <POPMYJIHpOBKa H lIpe,n;CTaBJIeHHe MOryT OTJIH-
qaTbCH B 3HaqHTeJIbHOH CTerreHH.
HJIH '* - OTHOC.HII(HHCH K TOM)' xe BOlIPOCY, HO He 3KBHBaJIeHTHbIH CTaH,ll;apT:
rry6JIHKaUIDI BSI, KOTOpasI OlIHCbIBaeT lIpe,n;MeTbI, aHaJIOrHqHbIe onHcaHHbIM B eB-
pOlIeHCKOM H/HJIH MeX,ZJyHapo,n;HOM CTaH,ll;apTe. Co,n;epxaHHe, o,n;HaKO, HCKJIlOqaeT
nOJIHyIO H,lI;eHTWlHOCTb HJIH TeXHHqecKYIO 3KBHBaJIeHTHOCTb.
E - YHHKaJIbHbIH KO,n; H3,L(eJIIDI ,LUI.H lIonpaBOK.
F - TeXHWlecKHH KOMHTeT BSI HeceT OTBeTCTBeHHOCTb 3a 3TY rry6JIHKaUHIO.
G - ITolIpaBKH BKJIlOqeHbI B lIepeH3,n;aHHbIH TeKCT. OTcyrcTBHe R 03HaqaeT,
qTO lIOlIpaBKH He .HBJI.HIOTC.H qaCTblO TeKCTa.
H - :QeHa rpynnbI: 06paTHTeCb K KJIanaHY Ha BHyrpeHHeH CTopOHe 3MHeM 06-
JIO)l{lGf KaTaJIOra.
I - YHHKaJIbHbIH KO,n; H3,n;eJIIDI.
J - BOJIbIIIHHCTBO HOBbIX H lIepepa60TaHHbIX CTaH,ll;apTOB ny6JIHKYIOTC.H B <pop-
MaTe A4. Pa3MepbI, OTJIWlHbIe OT A4, BKJIlOqeHbI B ClIHCOK.
nonpaBKH
Bce OT,n;eJIbHbIe lIorrpaBKH K MOMeHTY BbInYCKa BKJIlOqeHbI BMeCTe C JII06bIMH
OCHOBHbIMH rry6JIHKaUIDIMH. :QeHbI YKa3aHbI B lIpHJIOXeHHH. ECJIH lIOlIpaBKa
BKJIlOqeHa B Oqepe,n;Hoe H3,n;aHHe, TeKCT co,n;ep)I{HT YKa3aHHe, npHBJIeKalOlI(ee K HeM
BHHMaHHe, H lIOMeTKH Ha noIDIX B cooTBeTcTByrolI(HX MecTax Ha HCnpaBJIeHHbIX
cTPaHHUax.
0630P
IIoJIHTHKa BSI ,LUI.H K3.)I()];orO CTaH,ll;apTa 3aKJIIOQaeTC.H B lIepecMoTPe ero OTBeT-
CTBeHHbIM TeXHHqeCKHM KOMHTeTOM, He 60JIee qeM qepe3 5 JIeT nOCJIe rry6JIHKa-
UHH, qT06bI yCTaHoBHTb, .HBJI.HeTC.H JIH OH Bce elI(e ,n;eHCTByroII(HM, H, eCJIH HeT,
OlIpe,n;eJIHTb H npe,n;lIpHIDITb lIO,n; KOHTpOJIeM COOTBeTCTByrolI(He MepbI. 06CTO.HTeJIb-
CTBa MOryT npHBeCTH K 60JIee paHHeMY lIepeCMOTPY.
IIpH paCCMOTPeHHH CTaH,ll;apTa KOMHTeT MoxeT BbI6paTb O,n;HH H3 QeTbIpex Ba-
pHaHTOB:
. Om038aHue: YKa3bIBaeT, QTO CTaH,ll;apT 60JIee He HBJI.HeTCR ,n;eHCTByroII(HM.
. 06ofl8JleHUe 06 ycmape8aHUU: YKa3bIBaeT B lIonpaBKe, qTO CTaH,ll;apT He peKO-
MeH,D;yeTC.H ,LUI.H HClIOJIb30BaHIDI B HOBOM o6opy,n;OBaHHH, HO ,n;OJDKeH 6MTb
coxpaHeH lIPH 06CJI}T)KHBaHHH cyru;eCTByrolI(ero o6opy,n;OBaHIDI C MHTeJIbHbIM
O)l{H,ll;aeMbIM CpOKOM CJIy:>K6bI.
llpeducno8ue
. llepeCMOmp: BOBJIeqeHHe npOue,n;ypbI HOBbIX npOeKTOB.
. lloiJm8ep'JICiJeHUe: YKa3bIBaeT, qTO CTaH,lJ;apT lIpO,n;OJl)l{aeT ,n;eHCTBOBaTb 6e3
nOJIHOrO lIepeCMOTPa. IIocJIe lIO,n;TBep)l{)];eHIDI lIy6JIHKaUHH Ha KOnHH CTa-
BHTCH HOBaR lIeqaTb C MeCRueM H rO,n;OM lIO,L(TBep)l{)];eHIDI.
IIpH pa3pa60TKe HOBbIX lIpOeKTOB H3,n;eJIHH H 060py,n;OBaHIDI BCer,n;a ,n;OJDKHbI
HClIOJIb30BaTbC.H nOCJIe,n;HHe BbIrryCKH CTaH,lJ;apTOB. O,n;HaKO MHOrHe H3,n;eJIIDI BCe
eI..I.J;e H3rOTaBJIHBalOTCH lIO YCTapeBalOlI(HM H YCTapeBIIIHM CTaH,lJ;apTaM, qT06bI y,n;OB-
JIeTBOpHTb BCe elI(e YCTOHqHBbIH ClIpOC. 3TO ,n;eJIaeTC.H He TOJIbKO B ueJI.HX TeXHWle-
CKoro 06CJI}')KHBaHIDI, HO TaIOKe H M.H TeKYIJ,J;ero lIpOH3Bo,n;CTBa TaM, r,n;e PbIHOq-
HbIe CHJIbI elI(e He nOTPe60BaJIH 06HOBJIeHIDI pa3pa60TKH. 3TO oc06eHHO KaCaeTC.H
BHHTOBbIX KpelIe)I{HbIX H3,n;eJIHH. IIo 3TOH lIpHqHHe 6billH coxpaHeHbI Ta6JIHUbI
BHHTOBbIX pe3b6 H3 lIpe,n;bI,lJ;yru;HX H3,n;aHHH HapMY C HOBbIMH TPe60BaHIDIMH
BE EN ISO.
HOBbIe CTaH,lJ;apTbI, KaK lIpaBHJIO, HBJI.HIOTC.H 60JIee ,n;eTaJIbHbIMH H OlIHCaTeJIb-
HbIMH, qeM HX lIpe,n;IIIeCTBeHHHKH, n03TOM)' B 3TOT ClIpaBOqHHK MOryT 6bITb BKJIIO-
qeHbI TOJIbKO HaH60JIee cyru;eCTBeHHbIe HH<popMaUHOHHbIe Ta6JIHUbI. IIpH He06xo-
,n;HMOCTH 3a ,n;aJIbHeHIIIeH HH<popMaUHeH Bcer,n;a CJIe,n;yeT 06palI(aTbCR K nOJIHbIM
CTaH,lJ;apTaM, H ClIHCOK 6H6JIHOTeK, no,n,n;ep)I{HBaIOII(HX lIOJIHbIe Ha60pbI COBpeMeH-
HbIe CTaH,L(apTOB, BKJIlOqeH B lIpHJIOXeHHe B KOHue 3TOH KHHrH. CTaH,lJ;apTbI, YKa-
3aHHbIe B ClIpaBOqHHKe, 6billH nOCJIe,n;HHMH Ha MOMeHT lIy6JIHKaUHH, HO, BBH,lJ;Y
nOJIHTHKH peryJIHpHbIX lIepeCMOTpOB BSI, HeKOTopbIe H3 HHX MOryT CTaTb npe,n;Me-
TOM nepeCMOTpa B TeqeHHe BpeMeHH cyru;eCTBOBaHIDI 3TOH KHHrH. IIo 3TOM npHqH-
He CTaTYC YKa3aHHbIX CTaH,lJ;apTOB Bcer,n;a CJIe,n;yeT npOBep.HTb. B03MO)I{HbI KOHCYJIb-
TaUHH TeJIe<poHY ceTH no,n,n;ep)l{lGf BSI.
3TOT CnpaBOqHHK 6bill no,n;rOTOBJIeH B nOMOlI(b HIDKeHepaM-MexaHHKaM, 3aH.H-
TbIM B npoeKTHpOBaHHH, pa3pa60TKe H npOH3Bo,n;CTBe TeXHHQeCKHX H3,n;eJIHH H 060-
PY,L(OBaHH.H. OH TaIOKe lIOJIe3eH B KaqeCTBe HCTOqHHKa HH<popMaUHH BceM TeM HH-
xeHepaM, KOM)' 6bICTPO H exe,n;HeBHO TPe6yroTC.H HopMaTHBHO-TeXHHqeCKHe ,n;aH-
HbIe. ,lJ;JIR y,n;06cTBa CCbillOK 3Ta KHHra pa3,n;eJIeHa Ha 8 OCHOBHbIX pa3,L(eJIOB:
1. HIDKeHepHaR MaTeMaTHKa
2. HIDKeHepHaR CTaTHKa
3. HIDKeHepHaJI ,L(HHaMHKa
4. KpelIe)I{HbIe ,n;eTaJIH
5. MeXaHHqeCKHe lIepe,n;aqH
6. MalIIHHocTpOHTeJIbHbIe MaTepHaJIbI
7. Ha3HaqeHHe JIHHeHHbIX H reOMeTPHqeCKHX ,n;OrryCKOB
8. ABToMaTH3HpoBaHHoe KOHCTpYHPOBaHHe
B paMKax 3THX OCHOBHbI 3,n;eJIOB MaTepHaJI c06paH B JIOrlftleCKOM lIOCJIe,n;o-
BaTeJIbHOCTH M.H y,n;06cTBa 0<:. " " eHHM H COOTBeTCTBeHHO lIpOHYMepOBaH. 3TO lIO-
3BOJIReT qHTaTeJIIO HanpaBJIRTbC.H Henocpe,n;CTBeHHO K TPe6yeMOM)' IIYHIcry npH no-
MOI..I.J;H HCqepnbIBalOlI(e nOJIHOrO co,n;epxaHIDI H no,n;p06Horo aJI<paBHTHoro YKa3a-
TeJIR.
3TOT CnpaBOqHHK He yqe6HHK, a C60PHHK lIOJIe3HOH HH<popMaUHH. II03TOM)' B
pa3,n;eJIbI, CBR3aHHbIe C MaTeMaTHKOH, CTaTHKOM H ,L(HHaMHKOH, pa60qHe npHMepbI
BKJIlOqeHbI TOJIbKO TaM, r,n;e HHaqe MOrJIH 6bI B03HHKJIyTb He,n;opa3)'MeHIDI. ABTOp
IIpeouCJl()(Jue
lIpH3HaTeJIeH BpHTaHCKOM)' HHCTH1)'TY CTaH,ll;apTOB H BCeM HH,nyCTPHaJIbHbIM H
KOMMepqeCKHM KOMlIaHIDIM B BeJIHK06pHTaHHH H 3a py6exoM, KOTOpbIe lIOMOrJIH
06eCneqHTb COBpeMeHHbIe ,n;aHHbIe lIO TaKOM)' 60JIbIIIOM)' KOJIHqeCTBY 06JIaCTeH
TeXHHKH. K COXaJIeHHIO, OrpaHWleHHOe lIpOCTPaHCTBO 3TOH KHHrH n03BOJIHJIO
BKJIlOqHTb TOJIbKO KpaTKHe 0630pbI H3 BCerO pa3H006pa3IDI npe,n;OCTaBJIeHHOrO Ma-
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PoiJ'JICep JI. TUMUH2C (2005)
SnArO.QAPHOCTM
MbI XOTeJIH 6bI lI06JIaro,n;apHTb BCe KOMlIaHHH, JII06e3HO lIpe,n;OCTaBHBIIIHe aBTOp-
CKHe MaTepHaJIbI, HClIOJIb3yeMbIe B ,n;aHHOM H3,n;aHHH:
British Fluid Power Association (BFPA) (Pa3,n;eJIbI 5.6.9-5.6.18, 5.6.20).
ContiTech United Kingdom Ltd. (Pa3,n;eJIbI 5.2.4-5.2.18).
David Brown Engineering Ltd. (Pa3,n;eJI 5.1.1).
Henkel Loctite Adhesives Ltd. (Pa3,neJIbI 4.5.1-4.5.9).
IMI Norgren Ltd. (Pa3,n;eJI 5.6.19).
National Broach & Machine Co. (Pa3,n;eJIbI 5.1.4-5.1.17).
Renold pIc. (Pa3,n;eJIbI 5.3-5.4,5.3.10-5.3.13,5.3.16,5.3.18-5.3.19,5.3.21-
5.3.22, 5.3.27-5.3.30).
Emhart Teknologies (Tucker Fasteners Ltd.) (Pa3,n;eJIbI 4.2.8-4.2.18).
ButteIWorth Heinemann 3a pa3peIIIeHHe BOClIpOH3BeCTH ,n;aHHbIe H3 KHHrH Hig-
gins, R.A., «CBoHcTBa MaTepHaJIOB» B pa3,neJIax 6.2.2 H 6.2.3.
ButteIWorth Heinemann 3a pa3peIIIeHHe BOClIpOH3BeCTH ,n;aHHbIe H3 KHHrH Parr,
Andrew, «fH,ll;paBJIHKa H lIHeBMaTHKa» B pa3,n;eJIaX 5.6.1-5.6.4.
Newnes 3a pa3peIIIeHHe BOClIpOH3BeCTH ,n;aHHbIe H3 KHHfH Stacey, Chris,
«IIpaKTWlecKasI lIHeBMaTHKa» B pa3,n;eJIe 5.6.3.
Pearson Education Ltd. 3a pa3peIIIeHHe BocnpOH3BeCTH ,n;aHHbIe H3 KHHfH Ti-
mings, R. L., «MaTepHaJIoBe,n;eHHe», TOMa 1 H 2, B pa3,n;eJIax 6.1.1-6.1.21 H 7.1-7.5.
BbI,ll;ep)l{lGf H3 6pHTaHcKHx CTaH,ll;apTOB, BOClIpOH3Be,n;eHHbIe C pa3peIIIeHIDI BSI.
IIOJIHbIe KonHH 3THX ,n;OKYMeHTOB MOryr 6bITb nOJIyqeHbI lIO lIOQTe OT BSI Sales,
Linford Wood, Milton Keynes, Bucks., MK14 6LE.
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YfJIOBaH CKOpOCTb
1 060pOT/MHH 1=0,10472 panic 11 pa.n!c 1=9,5493 060pOT/MHH.
IlrroIUanb
1 ,ruoHM =6,4516 CM 1 CM =0,15500 ,ruoHM
I<pYT =0,092903 M 1 M =10,764 <PYT
1 Hp,n =0,83613M 1M =1,1960 Hp,n
1 aKp =0,40469 fa 1 fa =2,4711 aIq)
II.JJomOCTh
1 <PYHT/<PYT 1=16,018 Kr/M 11 Kr/M 1=0,062428 <PYHT/<PYT
3uepl1lJl
1 <PYT nayH,ZJ;aJIb =0,042140,lQK 1 ,lQK =23,730 <PYT nayH,ZJ;aJIb
1 <PYT <PYHT-CHJIa =1,355 82 ,lQK 1 ,lQK =0,73756 <PYT <PYHT-CHJIa
1 KBT 'lac =3,6000 M,[(x 1 M,[(x =0,27778 KBT 'lac
1 TepM =0,10551 f,lQK 1 f,lQK =9,4781 TepM
CHJla
1 nayH,ZJ;aJIb =0,13826 H IH =7,2330 nayH,ZJ;aJIb
1 <PYHT-CHJIa =4,4482 H 1H =0,22481 <PYHT-cHJIa
,nmma
1 ,nIOHM =2,5400 CM 1 CM =0,39370,lUOHM
I<pYT = 0,30480 M 1 M =3,2808 <PYT
1 Hp,n = 0,91440 M 1 M =1,0936 Hp,n
1 MHlliI = 1,6093 KM 1 KM =0,62137 MHlliI
Macca
1 YHUIDI =28,350 f 1 f =0,035274 YHUIDI
1 <PYHT =0,453 59 Kr lKr =2,2046 <PYHT
1 aHfJI. ueHTHep =50,802 Kr lKr =0,019684 aHfJI. ueHTHep
1 aHfJI. TOHHa =1,0161 TOHHa 1 TOHHa =0,98421 aHfJI. TOHHa
MOMeHT CHJIbI
1 <PYHT-CHJIa <PYT 1= 1,3558 H M 11 H M 1=0,73756 <PYHT-CHJIa <PYT
II.JJOCKHH yroJi
1 0 =0,01745 pan 1 pan =57,296 0
MOIIUIOCTh
1 <PYT <PYHT-CHJIa/ C =1,3558 BT 1 BT =0,73756 <PYT <PYHT-CHJIa/c
1 JI.C. =0,745 70 KBT 1 KBT =1,3410 JI.C.
,J.J;aBJIeHHe H uanpJDKeUHe
1 ,nIOHM pT.CT. =33,864 M6ap 1 M6ap =0,02953 ,nIOHM pT.CT.
1 <PYHT-CHJIa/,nIOHM =6,8948 Kna 1 KIla =0,14504 <PYHT-CHJIa/,nIOHM
1 aHfJI. TOHHa-CHJIa/,nIOHM =15,444 H/MM 1 H/MM =0,064749 aHfJI. TOHHa-CH-
JIa/,nIOHM
1.5. IIpeono'lmume/lbHble 'IuCIla
O"OH"taHue
E.zunutnw H3MepelllDl cJ}cJ}C 8 e,lUllllllOtl CII E.zunutnw H3MepelllDl CII 8 e,lUllllllOtl cJ}cJ}C
Y.n;eJlhHaJI TelIJIoeMKOCTh
1 BpHTaHCKaH TennOBaH 1=4,1868 /(KI' 0c) 11 /(KI' 0c) 1=0,23885 BplrnUlcKaH Ten-
e,lJ;HHHua/ (<pYUT OF) JIOBaH e,lJ;HHHua/( <PYHT OF)
CKOpoCTh
1 <PYT/c =0,30480 M/e 1 M/e =3,2808 <PYT/e
1 MHlliI/q =1,6093 KM/q 1 KM/q =0,62137 MHJIb/q
Ooo.eM
1 ,lJ;IOHM =16,387 eM lcM =O,061024,lJ;IOHM
1 <PYT =0,028317 M 1M =35,315 <PYT
hlp,lJ; =0,76456 M 1M =1,3080 Hp,lJ;
1 nHHTa =0,56826 JI 1 JI =1,7598 nHHTa
1 raJIJIOH =4,5461 JI 1 JI =0,21997 raJIJIOH
1.5. npeAnO'lTMTenbHble 'IMCna
Kor,na qeJIOBeK nOKYIIaeT, HanpHMep, 3JIeKTpHqecKYIO JIaMrry .rum HCnOJIb30BaHIDI B
6bITY, 06bIqHO B HaJIHqHH HMeIOTC.H JIaMnbI MOII(HOCTblO 15, 25, 40, 60, 100 BT H
T.,n. 3TH 3HaqeHIDI MOII(HOCTH CJIe,n)'lOT O,nHO 3a ,npyrHM npHMepHO B reOMeTpHqe-
CKOH lIporpeCCHH, np eM OTHOCHTeJIbHbIe H3MeHeHIDI CBeTOBoro H3.rryqeHIDI Me)l{-
l1Y coce,nHHMH 3HaqeHIDIMH MOII(HOCTeH B 3TOH nOCJIe,nOBaTeJIbHOCTH OCTaIOTC.H
npH6JIH3HTeJIbHO lIOCTO.HHHbIMH. KaK npaBHJIO, COOTHorneHIDI Me:>I<nY napaMeTpaMH
H3,neJIHH He c.rryqaHHbI, a OCHOBaHbI Ha CHCTeMe npeono"tmumeAbHblX "tuceA. (napa-
MeTp npO,nyKUHH - 3TO KOJIHqeCTBeHHIDI xapaKTepHCTHKa ee CBOHCTB. HaH60JIee
BIDKHbIMH napaMeTpaMH .HBJUIIOTC.H pa3MepHbIe, BeCOBbIe, 3HepreT eCKHe xapaKTe-
pHCTHKH npO,nyKUHH. - llpUMe"t. nep.)
IIpe,nnOqTHTeJIbHbIe qHCJIa 6a3Hp)'lOTC.H Ha R-"tUCAax, H306peTeHHbIX nOJIKOB-
HHKOM IllapJIeM PeHapOM. B OCHOBHOM HCnOJIb3)'1OTC.H p.H,LJ;bI - R5, RIO, R20, R40
H R80 H no,nrpynnbI 3THX p.H,LJ;OB. 3HaqeHIDI B KIDK,lJ;OM P.H.nY npe,nCTaBJUIIOT C060H
npH6JIH3HTeJIbHbIe reOMeTpHqeCKHe nporpeCCHH co 3HaMeHaTelliIMH ViQ, 1\¥iQ,
2\¥iQ, 4\¥iQ H 8\¥iQ, npH 3TOM 3HaqeHIDI ByrpH p.H,LJ;OB H3MeIDIIOTC.H Ha 58 % .rum p.H,LJ;a
R5, Ha 26% .rum p.H,LJ;a RIO, Ha 12% .rum R20, Ha 6% .rum R40 H Ha 3% .rum p.H,LJ;a
R80.
bOJIee no,np06HyID HH<popMaUHIO 0 3HaqeHIDIX H HCnOJIb30BaHHH npe,nnOqTHTe-
JIbHbIX qHCeJI MO)I{HO HaHTH B BS (British Standards) 2045:1965. (B HaCTO.H ee Bpe-
M.H ,neHcTByeT fOCT 8032-84 «IIpe,nnOqTHTeJIbHbIe qHCJIa H p.H,LJ;bI npe,nnOqTHTeJIb-
HbIX qHCeJI». YTBep)l(,L(eH: fOCCTaH,L(apT CCCP, 09.08.1984. B HeM npe,nYCMOTpeHbI
pR,nbI - R5, RIO, R20, R40. - llpuMe"t. nep.) AmI p.H,LJ;a R5 oKpyrJIeHHbIe 3HaqeHIDI
paBHbI 1,00, 1,60, 2,50, 4,00, 6,30 H 10,00; TaKHM 06pa30M, npHBe,neHHbIe BbIrne
3HaqeHIDI HOMHHaJIbHbIX MOII(HOcTeH 3JIeKTP eCKHX JIaMn 6a3HpyroTC.H Ha p.H,LJ;e
R5. bOJIbIIIHHCTBO HCnOJIb3yeMbIx CTaH,L(apTOB OCHOBaHO Ha p.H,LJ;ax lIpe,nnOqTHTeJIb-
HbIX qHCeJI; B TOM qHCJIe CTaH,L(apTbI Ha TOJIII(HHY JIHCTOBOro MeTaJIJIa H KaJIH6p
npOBOJIOKH, pa3MepbI raeK H 60JITOB, CTaH,L(apT 3JIeKTP eCKoro TOKa (A) H CKOpO-
CTH BpalI(eHH.H HHCTpyMeHTaJIbHbIX rnnHH,L(eJIeH B cTaHKax.
F/la8a 1. lfH:JICeHepHaJl MameMamUlCO
1.6. OnpeAeneHMe pa3MepoB
1.6. 1. nnOCKJfe cpJfryP&1
KBaLJ;paT
IIp.HMoyrOJIbHHK
.,
"
"
"
"
b
"
h
"
"
"
"
"
I"
I
I-
-I
b
CTopoHa b
IIJIolI(aLJ;b = b 2
):LrrHHa ,lJ;HarOHaJIH = ..fi x b
b
CTopoHa b, BbICOTa h
nJIOII(aLJ;b = b x h
):LrrHHa ,lJ;HarOHaJIH = .J b 2 + h 2
napaJIJIeJIorpaMM
TpalIeUIDI
a
I"
b
"I
I..
b
..I
CTopOHa b, BbICOTa h
IIJIolI(aLJ;b = b x h
OCHOBaHIDI a H b, BbICOTa h
1
llrrOII(aLJ;b = - x (a + b) x h
2
TpeyroJIbHHK
Kpyr
I.
b
I
CTopOHa b, BbICOTa h
1
nJIOII(aLJ;b = - x b x h
2
PaLJ;HYC r
nJIOII(aLJ;b = 1t X r 2
nepHMeTp = 2 x 1t x r
1.6. OnpeOe/leHUe pQ3Mep08
CeKTOp Kpyra
s
3JIJIHnC
i
I.
a
..I
P8)J;HYC r, ueHTpaJIbHbIH yrOJI 9, ,nyra s
1
llrrOII(an;b = - x r 2 x 9
2
):lrrHHa ,nyrH S = r x 9 (9 B pan;HaHax)
Pan;HYCbI a H b
nJIOII(an;b = 1t x a x b
nepHMeTP = 1t X (a + b)
HenpaBHJIbHbIH MHoroyrOJIbHHK
PI
I
I
I
I
t
YpoaeHb
OTC"IeTa
X 1
d
CylI(eCTByeT HeCKOJIbKO MeTo,nOB onpe,neJIeHIDI IIJIOII(an;H 3allITpHXOBaHHoH 06-
JIaCTH. ,[lJrn 3Toro HCnOJIb3yroTC.H lIpaBHJIO cpe,nHHX np.HMoyrOJIbHHKOB, npaBHJIO
TpaneUHH H npaBHJIO CHMncoHa. B KaqeCTBe lIpHMepa npHBe,neM <popMY.1IY CHMn-
COHa. Pa3,neJIHM OTpe30K XtX2 Ha qeTHOe KOJIJI1IeCTBO paBHbIX OTPe3KOB ,lUIHHOH d
K3.}K)J;bIH. nYCTb p, q, r, ... - ,lUIHHbI BepTHKaJIbHbIX JIHHHH, H3MepeHHbIe OTHOCH-
TeJIbHO HeKOToporo ypOBIDI OTCqeTa H nyCTb A - lIpH6JIH3HTeJIbHasI IIJIOII(8)J;b He-
lIpaBHJIbHOrO MHoroyrOJIbHHKa, BbI,l(eJIeHHOrO llITpHXOBKOH. B TaKOM c.rryqae:
d d
A = -[(p + t) + 4(q + s) + 2r] - -[(p + t) + 4(u + w) + 2v].
3 3
B 061I(eM, npaBHJIO CHMncoHa <POPMYJIHPyeTC.H CJIe,nyroII(HM 06pa30M:
.
lIpH6JIH3HTeJIbHasI IIJIOII(an;b =
= (%) x [(lIepBasI + nOCJIe,nHIDI) + 4(cyMMa qeTHbIX) + 2(cyMMa HeqeTHbIx)],
r,ne nepBasI, lIOCJIe,nHIDI, qeTHbIe H HeqeTHbIe - 3TO ,lUIHHbI COOTBeTCTB)'IOlI(HX Bep-
THKaJIbHbIX JIHHHH, a d - ,lUIHHa paBHbIX OTpe3KOB Ha ypOBHe JIHHHH OTCqeTa.
F/la8a 1. HH:JICeHepHaR MameMamU1CO
1.6.2. 06.eMH&le cpJfrYP&1
np.HMoyrOJIbHIDI npH3Ma
QHJIHH,L(P
hI
h ·
-- --,
,
06'beM = bhl
nJIOII(aLJ;b nOBepXHOCTH = 2(bh + hi + Ib)
06'beM = 1tr 2 h
nJIOII(aLJ;b nOBepXHOCTH = 21tr(r + h)
KoHYc
Y CeqeHHbIH KOHYC
h
06'beM = ! 1tr 2 h
3 1
lliolI(a,nb IIOBepXHOCTH = Ttr(1 + r) 06'beM = 3 rrh(R2 + Rr + r 2 )
lliolI(a,nb nOBepXHOCTH = 1t/(R + r) + 1t(R2 + r 2 )
C<pepa
nO.HC c<pepbI
\
\
4
06'beM = - 1tr 3
3
nJIOII(aLJ;b nOBepXHOCTH = 41tr 2
1th
06'beM = -(h 2 + 3R2 + 3 2)
6 1
lliOII(8)J;b lIOBepXHOCTH = 21trh + 1t( R 2 + 'i 2 ),
r,ne r - PaLJ;HYC C<pepbI
1.6. OnpeOeJleHUe p03Mep08
IIHpaMH)];a
TBep,nbIe TeJIa lIpaBHJIbHOH <pOpMbI
h
1
06'beM = - Ah
3 '
r,ne A - IIJIOII(an:b OCHOBaHH.H,
h - BbICOTa lIHpaMH)];bI
06'beM JII06oro TBep,noro TeJIa npaBHJIbHOH
<pOpMbI MO)I{HO HaHTH lIPH lIOMOII(H <POPMY-
JIbI CHMncoHa. YqHTbIBaIOTC.H TPH lIapaJI-
JIeJIbHbIe IIJIOCKOCTH C IIJIOII(a)J;.HMH AI' A3 H
A 2 , COOTBeTCTBeHHO pacnOJIOXeHHbIe Ha Kpa-
.HX H B n;eHTpe TBep,noro TeJIa. T or,na:
I
06'beM = -(AI + 4A 2 + A 3 ),
6
r,ne I - MHHa TBep,noro TeJIa.
TBep,nbIe TeJIa HelIpaBHJIbHOH <pOpMbI
I
,\ I
I \ I
I \ I \ ,
I \, \'
, 'I , ,
I .4_ , I .4 _ II .4
1'""'511 II
, , I , I
, I, , I
\ I , "
\' \ I ,
\' \
\
\
):lIDI OlIpe,neJIeHIDI 06'beMa TeJIa HelIpaBHJIbHOH <pOpMbI MO)I{HO HClIOJIb30BaTb
pa3JIJI1IHbIe MeTo,nbI; O,nHH H3 HHX OCHOBaH Ha npHMeHeHHH <pOPMYJIbI CHMlICOHa
(CMOTPH paHee B 3TOM pa3,neJIe). TBep,noe TeJIO CJIe,nyeT pa3,neJIHTb Ha qeTHOe KOJIH-
qeCTBO ceKUHH lIapaJIJIeJIbHbIMH IIJIOCKOCT.HMH, paClIOJIOXeHHbIMH Ha paBHbIX pac-
CTO.HHIDIX d o,nHa OT ,npyrOH H HMelOlI(HMH IIJIOII(an:H AI' A 2 , A 3 , ... . ECJIH HClIOJIb-
3yeTC.H, HalIpHMep, ceMb TaKHX IIJIOCKOCTeH, TO:
IIpH6JIH3HTeJIbHbIH 06'beM = d [(AI + A 7 ) + 4(A 2 + At + ) + 2(A 3 + As)].
3
F/la8a 1. HH:JICeHepHaJI MameMamUlCO
1.7. CTeneHM, KOpHM M o6paTHbie BenM'IMHbl
n n 2 .In .JIOn n 3 (n)x (IOn )X (lOOn )X
1 1 1,000 3,162 1 1,000 2,154 4,642 1,00000
2 4 1,414 4,472 8 1,260 2,714 5,848 0,50000
3 9 1,732 5,477 27 1,442 3,107 6,694 0,33333
4 16 2,000 6,325 64 1,587 3,420 7,368 0,25000
5 25 2,236 7,071 125 1,710 3,684 7,937 0,20000
6 36 2,449 7,746 216 1,817 3,915 8,434 0,16667
7 49 2,646 8,367 343 1,913 4,121 8,879 0,14286
8 64 2,828 8,944 512 2,000 4,309 9,283 0,12500
9 81 3,000 9,487 729 2,080 4,481 9,655 0,11111
10 100 3,162 10,000 1000 2,154 4,642 10,000 0,10000
11 121 3,317 10,488 1331 2,224 4,791 10,323 0,09091
12 144 3,464 10,954 1738 2,289 4,932 10,627 0,08333
13 169 3,606 11,402 2197 2,351 5,066 10,914 0,07692
14 196 3,742 11,832 2,744 2,410 5,192 11,187 0,07143
15 225 3,873 12,247 3375 2,466 5,313 11,447 0,06667
16 256 4,000 12,649 4096 2,520 5,429 11,696 0,06 50
17 289 4,123 13,038 4913 2,571 5,540 11,935 0,05882
18 324 4,243 13416 5832 2,621 5,646 12,164 0,05556
19 361 4,359 13784 6859 2,668 5,749 12,386 0,05263
20 400 4,472 14,142 8000 2,714 5,848 12,599 0,05000
21 441 4,583 14,491 9261 2,759 5,944 12,806 0,04762
22 484 4,690 14832 10648 2,802 6,037 13,006 0,04545
23 529 4,796 15, 166 12167 2,844 6,127 13,200 0,04348
24 576 4,899 15492 13824 2,884 6,214 13,389 0,04167
25 625 5,000 15,811 15625 2,924 6,300 13,572 0,04000
26 676 5,099 16,125 17576 2,962 6,383 13,751 0,03846
27 729 5,196 16,432 19683 3,000 6,463 13,925 0,03704
28 784 5,292 16,733 21952 3,037 6,542 14,095 0,03571
29 841 5,385 17,029 24389 3,072 6,619 14,260 0,03448
30 900 5,477 17,321 27000 3,107 6,694 14,422 0,03333
31 961 5,568 17,607 29791 3,141 6,768 14,581 0,03226
32 1024 5,657 17,889 32768 3,175 6,840 14,736 0,03125
33 1089 5,745 18,166 35937 3,208 6910 14,888 0,03030
34 1156 5,831 18,439 39304 3,240 6,980 15,037 0,02941
35 1225 5,916 18,708 42875 3,271 7,047 15,183 0,02857
36 1296 6,000 18,974 46656 3,302 7,114 15,326 0,02778
37 1369 6,083 19,235 50653 3,332 7,179 15,467 0,02703
38 1444 6,164 19,494 54872 3,362 7,243 15,605 0,02632
39 1521 6,245 19,748 59319 3,391 7,306 15,741 0,02564
40 1600 6,325 20,000 64000 3,420 7,368 15,874 0,02500
41 1681 6,430 20,248 68921 3,448 7,429 16,005 0,02439
42 1764 6,481 20,494 74088 3,476 7,489 16,134 0,02381
43 1849 6,557 20,736 79,507 3,503 7,548 16,261 0,02326
44 1936 6,633 20,976 85184 3,530 7,606 16,386 0,02273
45 2025 6,708 21,213 91125 3,557 7,663 16,510 0,02222
46 2116 6,782 21,448 97,336 3,583 7,719 16,631 0,02174
47 2209 6,856 21,679 103823 3,609 7,775 16,751 0,02128
48 2304 6,928 21,909 110592 3,634 7,830 16,869 0,02083
49 2401 7,000 22,136 117649 3,659 7,884 16,985 0,02041
1. 7. CmeneHu, KOpHU U o6pamHble 8eJlU'IUHbl
O"OH"taHue
n ,;z .In oJlOn n 3 (n)X (lOn)X (lOOn)X
50 2500 7,071 22,361 125000 3,684 7,937 17,100 0,02000
51 2601 7,141 22,583 132651 3,708 7,990 17,213 0,01961
52 2704 7,211 22,804 140608 3,733 8,041 17,325 0,01923
53 2809 7,280 23,022 148877 3,756 8,093 17,435 0,01887
54 2916 7,348 23,238 157464 3,780 8,143 17,544 0,01852
55 3025 7,416 23,452 166375 3,803 8,193 17,652 0,01818
56 3136 7,483 23,664 175616 3,826 8,243 17,758 0,01786
57 3249 7,550 23,875 185193 3,849 8,291 17,863 0,01754
58 3364 7,616 24,083 195112 3,871 8,340 17,967 0,01724
59 3481 7,681 24,290 205379 3,893 8,387 18,070 0,01695
60 3600 7,746 24,495 216000 3,915 8,434 18,171 0,01667
61 3721 7,810 24,698 226981 3,936 8,481 18,272 0,01639
62 3844 7,874 24,900 238328 3,958 8,527 18,371 0,01613
63 3969 7,937 25,100 250047 3,979 8,573 18,469 0,01587
64 4096 8,000 25,298 262144 4,000 8,618 18,566 0,01562
65 4225 8,062 25,495 274625 4,021 8,662 18,663 0,01538
66 4356 8,124 25,690 287496 4,041 8,707 18,758 0,01515
67 4489 8,185 25,884 300763 4,062 8,750 18,852 0,01493
68 4624 8,246 26,077 314432 4,082 8,794 18,945 0,01471
69 4761 8,307 26,268 328,509 4,102 8,837 19,038 0,01449
70 4900 8367 26,458 343000 4,121 8,879 19,129 0,01429
71 5041 8,426 26,646 357911 4,141 8,921 19,220 0,01408
72 5184 8,485 26,833 373,248 4,160 8,963 19,310 0,01389
73 5329 8,544 27,019 389017 4,179 9,004 19,399 0,01370
74 5476 8,602 27,203 405224 4,198 9,045 19,487 0,01351
75 5625 8,660 27,386 421875 4,217 9,086 19,574 0,01333
76 5776 8,718 27,568 438976 4,236 9,126 19,661 0,01316
77 5929 8,775 27,749 456,533 4,254 9,166 19,747 0,01299
78 6084 8,832 27,928 474552 4,273 9,205 19,832 0,01282
79 6241 8,888 28, 107 493039 4,291 9,244 19,916 0,01266
80 6400 8,944 28,284 512,000 4,309 9,283 20,000 0,01250
81 6561 9,000 28,460 531441 4,327 9,322 20,083 0,01235
82 6724 9,055 28,636 551368 4,344 9,360 20,165 0,01220
83 6889 9,110 28,810 571787 4,362 9,398 20,247 0,01205
84 7056 9,165 28,983 592,704 4,380 9,435 20,328 0,01190
85 7225 9,220 29,155 614125 4,397 9,473 20,408 0,01176
86 7396 9,274 29,326 636056 4,414 9,510 20,488 0,01163
87 7569 9,327 29,496 658503 4,431 9,546 20,567 0,01149
88 7744 9,381 29,665 681472 4,448 9,583 20,646 0,01136
89 7921 9,434 29,833 704969 4,465 9,619 20,724 0,01124
90 8100 9,487 30,000 729000 4,481 9,655 20,801 0,01111
91 8281 9,539 30,166 753,571 4,498 9,691 20,878 0,01099
92 8464 9,592 30,332 778688 4,514 9,726 20,954 0,01087
93 8649 9,644 30,496 804357 4,531 9,761 21,029 0,01075
94 8836 9,695 30,659 830584 4,547 9,796 21 , 105 0,01064
95 9025 9,747 30,822 857375 4,563 9,830 21,179 0,01053
96 9216 9,798 30,984 884736 4,579 9,865 21,253 0,01042
97 9409 9,849 31, 145 912673 4,595 9,899 21,327 0,01031
98 9604 9,899 31,305 941192 4,610 9,933 21,400 0,01020
99 9801 9,950 31,464 970299 4,626 9,967 21,472 0,01010
2-3255
F/la8a 1. HH:JICeHepHaJI MameMamUlCO
1 .8. nporpeccMM
IIocJIe,noBaTeJIbHOCTb qHCeJI, B KOTOpOH KIDK)];Oe qHCJIO CB.H3aHO co lIOCJIe,nyroII(HM
qHCJIOM B COOTBeTCTBHH C KaKHM-JIH60 3aKOHOM, Ha3bIBaeTC.H npozpeccueu.
1.8. 1. ApJfcpMeTJflfeCKSfI nporpeccJffl
IIOCJIe,nOBaTeJIbHbIe qHCJIa apH<pMeTJI1IeCKOH lIporpeCCHH CB.H3aHbI o6lI(eit pa3HO-
CTblO. KIDK)];bIH H3 qrreHOB lIOCJIe,nOBaTeJIbHOCTH 3, 6, 9, 12, 15, ... lIo.rryqeH lIpH6aB-
JIeHHeM qHCJIa 3 K lIpe,nbl.nYlI(eM)' qrreHy lIOCJIe,nOBaTeJIbHOCTH, T .e. pa3HOCTb lIpO-
rpeCCHH paBHa 3. B o6IUeM c.rryqae, eCJIH a - lIepBbIH qrreH lIporpeCCHH, a d - ee
pa3HOCTb, apH<pMeT}lqeCKa.H lIporpeCCIDI HMeeT CJIe,nyIOIUHH BIf,l(:
qJIeH nporpeCCHH
3HaqeHHe
I-H
a
2-H
a+d
3-H
a + 2d
4-H
a + 3d, ...
lIOCJIe,nHHH
a + (n - I)d
r,ne n - KOJIHqeCTBO qrreHOB lIporpeCCHH.
CYMMa Sn Bcex qrreHOB lIporpeCCHH onpe,neillIeTC.H KaK cpe,nHee 3HaqeHHe qrre-
HOB, YMHoxeHHoe Ha KOJIJI1IeCTBO qrreHOB nporpeCCHH, T.e.:
Sn = [(lIepBbIH + lIOCJIe,nHHH) / 2] x (qHCJIO qrreHOB) =
= [(a + a + (n - I )d) / 2] x n = (n / 2) [2a + (n - I )d].
1.8.2. reOMeTpJflfeCKSfI nporpeCCJffl
IIOCJIe,nOBaTeJIbHbIe qHCJIa reOMe1pHqeCKOH lIporpeCCHH CBR3aHbI 06W,UM 3HaMeHa-
melleM. Kax,nbIH H3 qrreHOB nOCJIe,nOBaTeJIbHOCTH 3, 6, 12, 24, 48, ... lIo.rryqeH YM-
HoxeHHeM lIpe,nbl.nYlI(ero qrreHa nOCJIe,nOBaTeJIbHOCTH Ha 2. B 06lI(eM CJIyqae, eCJIH
a - lIepBbIH qrreH lIporpeCCHH, a r - 3HaMeHaTeJIb, TO reOMe1pHqeCKa.H lIporpec-
CIDI HMeeT BIf,l(:
qJIeH lIporpeCCHH I-H
3HaqeHHe a
2-H
ar
3-H
ar 2
4-H
ar3, ...
lIOCJIe,nHHH
ar"-I
r,ne n - KOJI}lqeCTBO qrreHOB lIporpeCCHH.
CYMM)' Sn Bcex qrreHOB lIporpeCCHH MO)I{HO HaHTH CJIe,nyIOII(HM 06pa30M:
Sn = a + ar + ar 2 + ar 3 + ... + ar n -I . ( I)
YMHOXa.H KIDK)];bIH qrreH ypaBHeHIDI (I) Ha r, lIo.rryqaeM
rS n = ar + ar 2 + ar 3 + ... + ar n - 1 + ar n . (2)
BbIqHTaHHe ypaBHeHIDI (2) H3 ypaBHeHIDI (I) lIpHBO,nHT K pe3YJIbTaTY:
Sn(1 - r) = a - ar n ,
Sn = [a(1 - r n )] / (I - r). (3)
fuH xe, YMHOXa.H qHCJIHTeJIb H 3HaMeHaTeJIb lIOCJIe,nHero ypaBHeHIDI Ha -I,
lIOJIyqaeM:
Sn = [a(r n - I)] / (r -I).
(4)
1.9. TpuzoHoMempu'teclCue fjJopMY/lbl
06bIqHO HClIOJIb3yeTC.H ypaBHeHHe (3), Kor,n;a r < 1, H (4), Kor,n;a r > 1.
Kor,n;a -1 < r < 1, KIDK,D;bIH qrreH reOMe1pHqeCKOH nporpeCCHH MeHbIIIe, qeM
lIpe,n;bI):(ylI(HH; B 3TOM c.rryqae rOBOp.HT, qTO lIOCJIe,n;OBaTeJIbHOCTb cxooumcJl. MO)I{HO
HaHTH CYMM)' Bcex qrreHOB CXO,lUIIUeHC.H lIOCJIe,n;OBaTeJIbHOCTH. TaKYK> CYMM)' Ha3bI-
BalOT CYMMOH 6eCKOHeqHOH reOMe1p eCKOH lIporpeCCHH. qJIeH a(l - r n ) / 1 - r
MO)I{HO nepelIHcaTb B Blf,l(e [a / (1 - r)] - [ar n / 1 - r]. IIOCKOJIbKY r MeHbIIIe 1, r n
CTaHOBHTC.H Bce MeHbIIIe H MeHbIIIe lIPH B03paCTaHHH n. Kor,n;a n CTaHOBHTC.H OqeHb
60JIbIIIHM, 3HaqeHHe r n lIpaKT eCKH paBHO HyJIIO, H TaKHM o6pa30M [ar n / 1 - r]
CTaHOBHTC.H paBHbIM HyJIIO. OTclO,n;a CJIe,nyeT, qTO CYMMa 6eC"OHeltItOU zeOMempUlte-
CKOU npozpeccuu paBHa a / (1 - r) wrn c.rryqa.H -1 < r < 1.
1.8.3. rSpMOHJflfeCKSfI nporpeCCJffl
fapMOHHqeCKYK> lIporpeCCHIO o6pa3yroT qHCJIa, o6paTHbIe lIOCJIe,n;OBaTeJIbHbIM qrre-
HaM apH<pMeT eCKOH lIporpeCCHH. TaK, wrn apH<pMeT eCKOH lIporpeCCHH 1, 2, 3,
4, 5, ... COOTBeTCTByrolI(a.H rapMOH eCKa.H lIporpeCCIDI HMeeT BIf,l(: 1, 1/2, 1/3, 1/4,
1/5, ... .
1.9. TpMrOHOMeTpM'IeCKMe cl>opMynbl
1.9. 1. OCHOSH&le onpeAeneHJffl
B np.HMoyrOJIbHOM 1peyrOJIbHHKe, lIOKa3aHHOM HIDKe, a - CTopOHa, npomU80lleJICa-
U4aR yr.rry A (oPP), b - rHlIOTeHY3a 1peyrOJIbHHKa (hyp), a C - CTopOHa, npU/leJICa-
U4aR yr.rry A (adj). IIo OlIpe,n;eJIeHHIO:
sin A = opp / hyp = a / b
cos A = adj / hyp = C / b
tgA = opp / adj = a / C
cosecA = hyp / opp = b / a = 1 / sin A
secA = hyp / adj = b / C = 1 / cos A
ctgA = adj / opp = c / a = 1 / tgA,
c
A
80pp
r,n;e opp - CTopOHa, lIpOTHBOJIeXalI(a.H
yrJIY A, adj - CTopOHa, lIpHJIeXalI(a.H K
yr.rry A, hyp - rHnOTeHy3a.
B
Cadi
1.9.2. TOJK,qeCTSS
sin 2 A +cos 2 A =1
1 +tg 2 A =sec 2 A
1 + ctg 2 A = cosec 2 A
sin(-A) = -sin A
cos( -A) = cos A
tg( -A) = -tgA
F/la8a 1. HH:JICeHepHaJI MameMamUlCO
1.9.3. COCTSSH&le cpopMyn&1 Jf cpopMyn&1 AsoMHoro yrns
sin( A + B) = sin A cos B + cos A sin B
sin( A - B) = sin A cos B - cos A sin B
cos(A + B) = cos AcosB - sin A sinB
cos( A - B) = cos A cos B + sin A sin B
tg(A + B) = (tgA + tgB) / (1 - tgA . tgB)
tg(A - B) = (tgA - tgB) / (1 + tgA . tgB)
sin2A = 2 sin A cos A
cos 2A = cos 2 A - sin 2 A = 2 cos 2 A-I = 1 - 2 sin 2 A
tg2A = (2tgA) / (1 - tg 2 A)
1.9.4. tPopMynw «npOJf3seAeHJfe-cYMMS»
sinAcosB = l[sin(A + B) + sin(A - B)]
2
1
cos A cos B = - [cos( A + B) + cos( A - B)]
2
cos A sinB = l[sin(A + B) - sin(A - B)]
2
sinAsinB =l[cos(A + B) -cos(A -B)]
2
1.9.5. tPopMyn&1 TpeyrOn&HJfKS
C yqeToM 0603HaqeHHH, YKa3aHHbIX Ha pHCYHKe:
TeopeMa CHHyOB:
a / sin A =b / sinB =e / sinC.
c
TeopeMa KOCHHYCOB:
a 2 =b 2 +e 2 -2becosA
b 2 = a 2 + e 2 - 2aecosB
e 2 = a 2 + b 2 - 2abcosC.
8
c
IlrrOlI(aab:
IIJIolI(aab = lab sinC = lbe sin A = lea sinB
222
TaIOKe:
IIJIolI(aab = .J s(s - a)(s - b)(s - e),
r,n;e s - lIOJIyrrepHMe1'p, T.e. s = (a + b + e) / 2.
1 .10. Kpyr M OKPY>KHOCTb: HeKOTopble onpeAeneHMSI
-
M CBOMCTBa
):LIDI Kpyra ,n;HaMe1'pOM d II paaHYCOM r.
,l/;AuHa O"PY:>ICHOemU paBHa 1td HJIH 21tr.
llllOUl,aOb "pyza paBHa 1td 2 / 4 HJIH 1tr 2 .
1.9. TpuzoHoMempu'IecICue rjJOPMY/lbl
)];yra OKpyxHOCTH - 3TO ee qaCTb.
KacamellbHou K OIq)yxHOCTH Ha3bIBalOT np.HMyIO JIH-
HHIO, cOlIpHKaCalOlI(yroC.H C OIq)yxHOCTblO TOJIbKO B o,n-
HOH TOqKe. Pan;HYc, lIpoBe,neHHbIH B TOqKY KacaHIDI, 06-
pa3yeT C KaCaTeJIbHOH IIp.HMOH yrOJI.
CeKmopoM Iq)yra Ha3bIBalOT 06JIaCTb, orpaH eHHyIO
.nyfOH OIq)yxHOCTH H .D:BywI PMHYCaMH. IIrrOII(a,nL ceKTopa
1
paBHa - r 29, r,ne 9 - yrOJI Me:>K:,ny pan;HYcaMH B pan;HaHax.
2
XopiJou Ha3bIBalOT IIp.HMyIO JIHHHIO, coe,nHlUllOlI(yro
,nBe TOqKH OKpyxHOCTH. IIpH lIepeCeqeHHH ,nBYX Xop,n
lIpOH3Be,neHHe MHH qaCTeH O,nHOH XOp,nbI paBHO lIpOH3-
Be,neHHIO MHH qaCTeH BTOpOH XOp,nbI. Ha pHC. 1
AE x BE = CE x ED.
CeZMeHmoM Iq)yra Ha3bIBalOT 06JIaCTb, orpaH eH-
HyIO XOp,nOH H ,nyr<>H OIq)yxHOCTH. YrJIbI, lIOC1'poeHHbIe
Ha O,nHOM H TOM xe cerMeHTe, paBHbI: Ha pHC. 2 yroJI A =
= yroJI B.
A
1
1. 10. 1. Kpyr: nnOIl.4SA& Jf ,qJIJfHS OKpyJlCHOCTJf
,lI;HUeTp fiJIOIna.zn. ,lI;Jnma ,lI;HaMeTp fiJIouuw. ,lI;Jnma ,lI;HUeTp fiJIouuw. ,lI;Jnma
Olq)ymlOCTH Olq)ymlOCTH Olq)ymlOCTH
1 0,7854 3,142 24 452,39 75,40 47 1734,9 147,7
2 3,1416 6,283 25 490,87 78,54 48 1809,6 150,8
3 7,0686 9,425 26 530,93 81,68 49 1885,7 153,9
4 12,566 12,57 27 572,56 84,82 50 1963,5 157,1
5 19,635 15,71 28 616,75 87,96 51 2042,8 160,2
6 28,274 18,85 29 660,52 91,11 52 2123,7 163,4
7 38,485 21,99 30 706,86 94,25 53 2206,2 166,5
8 50,265 25,13 31 754,77 97,39 54 2290,2 169,6
9 63,617 28,27 32 804,25 100,5 55 2375,8 172,8
10 78,540 31,42 33 855,30 103,7 56 2463,0 175,9
11 95,033 34,56 34 907,92 106,8 57 2551,8 179,1
12 113,10 37,70 35 962,11 110,0 58 2642, 1 182,2
13 132,73 40,84 36 1017,9 113,1 59 2734,0 185,4
14 153,94 43,98 37 1075,2 116,2 60 2827,4 188,4
15 176,71 47,12 38 1134, 1 119,4 61 2922,5 191,6
16 201,06 50,27 39 1194,6 122,5 62 3019, 1 194,8
17 226,98 53,41 40 1256,6 125,7 63 3117,2 197,9
18 254,47 56,55 41 1320,3 128,8 64 3217,0 201 , 1
19 283,53 59,69 42 1385,4 131,9 65 3318,3 204,2
20 314,16 62,83 43 1452,2 135,1 66 3421,2 207,3
21 346,36 65,97 44 1520,5 138,2 67 3525,7 210,5
22 380,13 69, 11 45 1590,4 141,4 68 3631,7 213,6
23 415,48 72,26 46 1661,9 144,5 69 3739,3 216,8
F/la8a 1. HH:JICeHepHaJI MameMamU1Ca
O"OH"taHue
,lI;HaMeTp fiJIOIQa.zn. ,lI;Jnma ,n;HaMeTp fiJIOIQa.zn. ,lI;Jnma ,n;HaMeTp fiJIOIQa.zn. ,lI;Jnma
OKpymtOCTH Olq)ymtOCTH Olq)ymtOCTH
70 3848,5 219,9 80 5026,5 251,3 90 6361,7 282,7
71 3959,2 223,1 81 5153,0 254,5 91 6503,9 285,9
72 4071,5 226,2 82 5381,0 257,6 92 6647,6 289,0
73 4185,4 229,3 83 5410,6 260,8 93 6792,9 292,2
74 4300,8 232,5 84 5541,8 263,9 94 6939,8 295,3
75 4417,9 235,6 85 5674,5 267,0 95 7088,2 298,5
76 4536,5 238,8 86 5808,8 270,2 96 7238,2 301,6
77 4656,6 241,9 87 5944,7 273,3 97 7389,8 304,7
78 4778,4 245,0 88 6082, 1 276,5 98 7543,0 307,9
79 4901,7 248,2 89 6221,1 279,6 99 7697,7 311,0
1 . 11. KBaApaTHbie ypaBHeHMSI
PeIIIeHHeM (KopHeM) KBaapaTHoro ypaBHeHIDI:
ax 2 + bx + c = 0
.HBillI eTC.H:
-b + .J b 2 - 4ac
x=
2a
1 . 12. HaTYpanbHble norapMcI>Mbl
HaTYPaJIbHbIH JIOrapH<pM ,neHCTBHTeJIbHOrO qHCJIa x 0603HaqaeTC.H KaK In x. IIo
OlIpe,neJIeHHIO, OH paBeH TaKOM)' qHC.rry, qTO:
e 1n x = X
,
r,ne e = 2,1782 .HBillIeTC.H OCHOBaHHeM HaTYPaJIbHOrO JIOrapH<pMa.
HaTYPaJIbHbIH JIOrapH<pM 06JIaaaeT CJIe,nyroII(HMH CBOHCTBaMH:
In(xy) = In x + lny
In(x / y) = In x -lny
In(yx) = xlny
1. 13. CTaTMCTMKa: BBeAeHMe
1. 13. 1. OCHOSH&le nOHflTJffl
B 60JIbIIIHHCTBe PYKOBO,nCTB, HMelOlI(HX OTHOIIIeHHe K BOlIpocaM KOHTpOillI KaqeCT-
Ba, npe,nlIOJIaraeTC.H HeKoTopbIH 6a30BbIH ypOBeHb 3HaHHH no CTaTHCTHKe, He06xo-
,nHMbIH .n.rnI ,nOJDKHoro nOHHMaHHH yr.rry6JIeHHOH CTaTHCTHKH, JIeXalI(eH B OCHOBe
3Toro lIpe,nMeTa. B KpaTKOM BBO,nHOM Kypce, lIpeMaraeMOM ,naJIee, co,nepxaTC.H
CBe,neHH.H, KOTopbIe lIoTpe6yroTC.H qHTaTeJI.HM npH lIOCJIe,nyIO eM H3yqeHHH pa3-
JIHqHbIX PYKOBO,nCTB, CB.H3aHHbIX C KOHTpOJIeM KaqeCTBa.
1.13. CmamucmU1CO: 88eoeHue
CpeiJHee apurjJMemu"teCKoe HJIH npOCTO cpeiJHee - 3TO cpe,nHee 3HaqeHHe Ha60pa
,naHHbIX. QT06bI ero HaHTH, JIy}KH0 CJIO)I{HTb BMeCTe 3HaqeHIDI Bcex qrreHOB Ha60pa
,naHHbIX H 3aTeM pa3,neJIHTb CYMM)' Ha KOJIHqeCTBO qrreHOB B Ha60pe. MaTeMaTHqe-
CKH 3TO MO)I{HO BbIpa3HTb CJIe,nyroII(HM 06pa30M:
X=(X 1 +X 2 +...+XN)/N
TaKHM 06pa30M, cpe,nHee apH<pMeTHqeCKOe Ha60pa qllceJI 4, 6, 9, 3 II 8 6y,neT
(4 + 6 + 9 + 3 + 8)/5 = 6.
MeiJuaHa - 3TO RTIH cepe,nIlHHoe 3HaqeHlle, HJIII cpe,nHee ,nBYX cepe,nIlHHbIX
3HaqeHHH lIOCJIe,nOBaTeJIbHOCTII qHCeJI, paClIOJIOXeHHbIX B lIOp.H,Z:l:Ke B03paCTaHIDI.
TaK, Me,nHaHa lIOCJIe,nOBaTeJIbHOCTII 3, 4, 5, 6, 8, 9, 13 II 15 paBHa (6 + 8)/2 = 7, a
Me,nHaHa lIOCJIe,nOBaTeJIbHOCTII 4, 5, 7, 9, 10, 11, 15, 17 II 19 paBHa 10.
MoiJa - 3TO 3HaqeHHe, KOTopoe Hall60JIee qaCTO BC1'peqaeTC.H B Ha60pe qllceJI.
TaKHM 06pa30M, Mo,na Ha60pa 2, 3, 3, 4, 5, 6, 6, 6, 7, 8, 9 II 9 paBHa 6.
Pa3Max Ha60pa qHCeJI - 3TO pa3HOCTb Mex,ny MaKCIIMaJIbHbIM II MIIHHMaJIb-
HbIM 3HaqeHIDIMH B Ha60pe. TaK, pa3Max Ha60pa qllceJI 3, 2,9, 7,4, 1, 12, 3, 17 II
4paBeH 17-1 = 16.
CmaHiJapmHoe omKIlOHeHue, IIHor,na Ha3bIBaeMoe cpeiJHeK6aiJpamu"tecKUM omKIlO-
HeHueM, OlIpe,neillIeTC.H KaK:
S= [(XI -X)2 +(X 2 -X)2 +",+(X N -X)2]/ N.
TaK, ,nJUI qHCeJI 2, 5 II 11 cpe,nHee 3HaqeHHe paBHO (2 + 5 + 11 )/3 = 6. CJIe,noBa-
TeJIbHO, CT aH,l(apTHOe OTKJIOHeHlle:
s = [(2 - 6)2 + (5 - 6)2 + (11 - 6)2] / 3 = (16 + 1 + 25) / 3 = Jl4 3,74.
06WqHO S HClIOJIb3yeTC.H ,nJUI 0603HaqeHIDI CTaH,l(apTHOro OTKnOHeHIDI reHe-
paJIbHOH COBOKYIIHOCTII (lIOJIHOrO Ha60pa qHCeJI), a 0 IIClIOJIb3yeTC.H ,nJUI 0603Haqe-
HIDI CTaH,l(apTHOro OTKJIOHeHIDI BbI60pKH.
1.13.2. BepoflTHOCT&
IIycTb x - KOJI eCTBO 3JIeMeHTapHbIX C06bITIIH, 6JIarOlIpIDITHbIX ,nJUI HeKOToporo
C06bITIDI A, a n - lIOJIHOe KOJI eCTBO Bcex B03MO)I{HbIX II paBHOBepO.HTHbIX 3JIeMeH-
TapHbIX C06bITIIH; Tor,na BepO.HTHOCTb C06bITIDI A OlIpe,neillIeTC.H KaK p = x/no BepO.HT-
HOCTb C06bITHH eCTb qHCJIO OT 0 ,no 1. ECJIH q - BepO.HTHOCTb Toro, qTO ,naHHoe co-
6bITlle He IIp 0113 oi1,z:(eT , TO H3 CKa3aHHoro paHee CJIe,nyeT, qTO p + q = 1. TaK, lIpll
6pocaHHII lIpaBHJIbHOH IIIecrn:rpaHHoH IIrpaJIbHOH KOCTH (T.e. KY6HKa C H<ppaMII),
BepO.HTHOCTb BbIrran;eHIDI orrpe,neJIeHHOrO qHCJIa, HalIpHMep 1'pex, paBHa 1/6, TaK KaK
y KY6HKa IIIeCTb rpaHeH H qHCJIO 3 lIpllcyrcTByeT TOJIbKO Ha O,nHOH H3 HHX.
1.13.3. 5JfHOMJfSn&HOe pscnpeAeneHJfe
DUHOMUaIlbHOe pacnpeiJelleHue lIpHMeHHTeJIbHO K KOH1'pOJIIO KaqeCTBa MoxeT 6bITb
OlIpe,neJIeHO CJIe,l(ylOII(IIM 06pa30M. BepO.HTHOCTb lIO.rryqHTb 0, 1, 2, 3, ..., n ,ne<peKT-
HbIX H3,neJIHH B BbI60pKe H3 n H3,neJIHH, lIo.rryqeHHoH c.rryqaHHbIM 06pa30M H3 reHe-
paJIbHOH COBOKYIIHOCTH, ,l(JIH KOTOpOH BepOHTHOCTb lIO.HBJIeHIDI ,ne<peKTHOrO H3,ne-
JIIDI paBHa p, a He,ne<peKTHoro - q, OlIpe,neillIeTC.H lIOCJIe,nOBaTeJIbHbIMH qrreHaMH
pa3JIOXeHIDI (q + p)n HaqllHa.H C lIpaBoro qrreHa pa3JIOXeHIDI.
F/la8a 1. HH:JICeHepHaJI MameMamU1Ca
TaK, eCJIH BbI6opKa, COCTOIIT, HalIpHMep, H3 qeTbIpex ,neTaJIeH, BbI6paHHbIX c.rry-
qaHHbIM 06pa30M H3 rrpO,LJyKIJ;HH CTaHKa, lIpOH3BO,lUI ero B Cpe,lUleM 5 % ,ne<peKTHbIX
,neTaJIeH, TO BepOHTHOCTb lIOnyqlITb 0, 1, 2, 3 H.JIH 4 ,ne<peKTHbIe ,neTaJIH B BbI60pKe MO-
xeT 6bITb orrpe,neJIeHa CJIe,nyIOII(HM 06Pa30M. IIOBTOpHbIM YMHoxeHHeM lIonyqaeM:
(q + p)4 = q4 + 4q3 p + 6q2 p2 + 4 qp 3 + p4.
3HaqeHIDI q H P paBHbI COOTBeTCTBeHHO 0,95 H 0,05. Tor,na:
(0,95 + 0,05)4 = 0,95 4 + 4 x 0,95 3 x 0,05 + 6 x 0,95 2 x 0,05 2 + 4 x 0,95 x 0,05 3 +
+ 0,05 4 = 0,8145 + 0,1715 + 0,011354 + ...
3TO 03HaqaeT, qTO:
1) 81 % BbI6opOK, BepO.HTHO, He co,nep)I{HT ,ne<peKTHbIX ,neTaJIeH;
2) 17% BbI6opOK, BepO.HTHO, co,nep)I{HT O,nHY ,ne<peKTHyro ,neTaJIb;
3) 1 % BbI6opOK, BepO.HTHO, co,nep)I{HT ,nBe ,ne<peKTHbIe ,neTaJIH;
4) MaJIOBepO.HTHO, tffO B BbI60pKe lIOlIa,nyTC.H 1'pH HJIH qeTbIpe ,ne<peKTHbIe ,neTaJIH.
qTO KaCaeTC.H KOH1'pOillI KaqeCTBa, TO, eCJIH lIPH lIOBTOpHbIX BbI60pKax TaKoe
lIpOn;eHTHoe COOTHOIIIeHHe lIpH6JIH3HTeJIbHO coxpalUleTC.H, KOH1'pOJIep MoxeT c,ne-
JIaTb BbIBO,n, qTO CTaHOK lIpo,nOJDKaeT lIpOH3BO,nHTb OKOJIO 5 % ,ne<peKTHbIX ,neTaJIeH.
O,nHaKo eCJIH lIpOn;eHTHoe COOTHOIIIeHHe H3MelUleTC.H, TO, BepO.HTHO, lIpOn;eHT 6pa-
Ka TaIOKe H3MelUleTC.H. T OqHO TaK xe lIOKYIIaTeJIb, lIo.rryqalOlI(HH 60JIbmyIO lIapTHIO
H3,neJIHH, MoxeT, HClIOJIb3Y.H c.rryqaHHbIe BbI6oPKH, no,nCqHTaTb KOJIJI1IeCTBO ,ne<peK-
THbIX H3,neJIHH B BbI60PKax H C nOMOlI(blO 6HHOMHaJIbHOrO paclIpe,neJIeHIDI on;eHHTb
BepO.HTHOe KOJI}lqeCTBO ,ne<peKTHbIX H3,neJIHH BO BceH lIapTHH.
1.13.4. PscnpeAeneHJfe nYSCCOHS
BbIqHCJIeHIDI C HClIOJIb30BaHHeM 6HHOMHaJIbHOrO paClIpe,neJIeHIDI MOryT OKa3aTbC.H
OqeHb 1'py,noeMKHMH, eCJIH KOJIHqeCTBO n ,neTaJIeH B BbI60pKe 60JIbIIIe IIIeCTH HJIH
ceMH. B 3TOM c.rryqae pacnpeiJe.n.eHue llyaccoHa .HBlliIeTC.H XOpOIIIHM npH6JIIDKeHHeM
6HHOMHaJIbHOrO paClIpe,neJIeHIDI. OHO OlIpe,neJIeHO CJIe,nyroII(HM o6pa30M.
ECJIH BepO.HTHOCTb HaCTYTIJIeHIDI C06bITIDI B JII060H MOMeHT lIOCTO.HHHa H MaTe-
MaTHqeCKOe OXll,lJ;aHHe np HaCTYTIJIeHIDI C06bITIDI paBHO A, Tor,na BepO.HTHOCTb Ha-
CTYTIJIeHIDI C06blTIDI 0, 1, 2, 3, 4, ... pa3 OlIpe,neillIeTC.H KaK:
e-A., ')..,e-A., ')..,2e-A. / 2!, ')..,3e-A. / 3!, ')..,4e-A. / 4!,... ,
r,ne e - KOHCTaHTa 2,71828... H 2! = 2 x 1, 3! = 3 x 2 x 1, 4! = 4 x 3 x 2 x 1, H T.,n.
(3,necb 4! qHTaeTC.H KaK «qeTbIpe <paKTOpHaJI»).
IIpHMeHeHHe paClIpe,neJIeHIDI IIyaccoHa K HCnOJIb30BaHHOM)' BbIIIIe .n.rnI HJIJIIO-
C1'pan;HH lIpHMeHeHIDI 6HHOMHaJIbHOrO paClIpe,neJIeHIDI npHMepy co CTaHKOM, lIpO-
H3BO,lUI HM 5 % ,ne<peKTHbIX ,neTaJIeH, ,naeT:
MaTeMaT}lqeCKOe OXll,lJ;aHHe np = 4 x 0,05 = 0,2
BepO.HTHOCTb OTCyrCTBIDI ,ne<peKTHbIX ,neTaJIeH paBHa e-A. = e- O ,2 = 0,8187
BepOHTHOCTb HaJI}lqIDI O,nHOH ,ne<peKTHOH ,neTaJIH paBHa Ae-A. = 0,2e- O ,2 = 0,1637
BepOHTHOCTb Ha.rrwnm,nBYX ,ne<peKTHbIX ,neTaJIeH paBHa ')..,2e-A. j2! = 0,2 2 e-O,2 /2 = 0,0164.
MO)I{HO Blf,l(eTb, qTO BepO.HTHOCTH, lIpH6JIH3HTeJIbHO paBHbIe 82, 16 H 2 %, xo-
pOllIO COrJIacyroTC.H C pe3YJIbTaTaMH, no.rryqeHHbIMH paHee.
1.13. CmamucmuKa: 88eoeHue
1.13.5. HOpMSn&HOe pscnpeAeneHJfe
,n;aHHbIe, CBR3aHHbIe C H3MepeHHeM TaKHX BeJlHqHH, KaK Macca ,nJIHHa, BpeM.H H
TeMlIepaTYPa, Ha3bIBalOTCR HelIpepbIBHbIMH, TaK KaK OHH MOryr lIpHHHMaTb JlI06bIe
3HaqeHIDI B 3a,naHHOM ,nHalIa30He. npe,nlIOJlO)I{HM, qTO paClIpe,neJleHHe ,nJIHH ,ne-
TaJIeH, lIpOH3Be,neHHbIX HeKOTopbIM CTaH-
KOM, 6y,neT lIpe,nCTaBJIeHO B BH,[(e rpa<pH-
Ka, KaK lIOKa3aHO Ha pHCyHKe; Tor,na <poPMY
,naHHoro rpa<pHKa MO)I{HO OlIpe,neJlHTb MaTe-
MaTWleCKH. OHa OlIpe,neJI.HeTCR <POPMYJlOH
y = (1/ cr)e Z , r,ne Z = -x 2 / 2cr 2 , cr - CTaH-
,napTHoe OTKJIOHeHHe Ha60pa ,naHHbIX; x -
qaCTOTa, C KOTOpOH ,naHHOH 3HaqeHHe BC1'pe-
qaeTCR. TaKa.H KPHBa.H Ha3bIBaeTCR 2parjJUKOM
6epORmHocmu HOpMaJlbH020 pacnpeOe/leHUR
HJIH KPU80U HOpMaJlbH020 pacnpeOe/leHUR.
HaH60Jlee BIDKHbIMH ,[(.IDI KOH1'pOJI.H Kaqe-
CTBa RB.IDIIOTCR CJle,nyroII(He CBOHCTBa ,naHHOH KpHBOH.
1. nJlOII(a,nb 06J1aCTH, orpaHWleHHoH KpHBOH H ,nBywI BepTHKaJIbHbIMH JlHHIDI-
MH, OTCTORII(HMH Ha + 1 CTaH,[(apTHOe OTKJIOHeHHe OT cpe,nHero 3HaqeHIDI, COCTaB-
JI.HeT lIpHMepHO 67 % 06lI(eH IIJIOma,nH.
2. nJlOII(a,nb 06J1aCTH, orpaHWleHHoH KpHBOH H BepTHKaJIbHbIMH JlHHIDIMH, OT-
CTORII(HMH Ha + 2 CTaH,[(apTHbIX OTKJIOHeHIDI OT cpe,nHero 3HaqeHIDI, COCTaB.IDIeT
lIpHMepHO 95 % 06lI(eH IIJIOII(a,nH.
3. lliOII(a,nb 06J1aCTH, orpaHHqeHHOH KpHBOH H BepTHKaJIbHbIMH JlHHIDIMH, OT-
CTORII(HMH Ha + 3 CTaH,[(apTHbIX OTKJIOHeHH:SI OT cpe,nHero 3HaqeHIDI, COCTaBJI.HeT
lIpHMepHO 99,75 % 06meH IIJIOII(a,nH.
4. 06J1aCTb, orpaHWleHHa.H KpHBOH, lIpOlIOPUHOHaJIbHa IIJIOTHOCTH BepORTHO-
CTH B reHepaJIbHOH COBOKyIIHOCTH
,n;JI.H HJIJIIOC1'paUHH HClIOJlb30BaHIDI ,naHHbIX CBOHCTB paCCM01'pHM BbI60PKY, co-
COTORI.l(yID H3 30 KpyrJlbIX ,neTaJIeH, lIo.rryqeHHyID c.rryqaHHbIM 06pa30M H3 lIapTHH B
1000 ,neTaJIeH, lIpOH3Be,neHHbIX CTaHKOM. 11:3MepeHHeM 6blJI0 YCTaHOBJleHO, qTO
cpe,nHHH ,nHaMe1'p 06pa3uoB B BbI60pKe paBeH 0,503 CM, a CTaH,[(apTHOe OTKJIOHe-
HHe BbI60pKH COCTaBJI.HeT 0,0005 CM.
ECJlH ,nOrryCTHMbIMH RB.IDIIOTCR, HalIpHMep, TOJlbKO ,neTaJIH ,nHaMe1'pOM
0,502-0,504 CM, TO TeopeTWlecJ<yIO KpHByro HOpMaJIbHOrO paClIpe,neJleHIDI MO)I{HO
HClIOJlb30BaTb ,[(.IDI lIpe,nCKa3aHIDI lIpoueHTa 6paKa. ,n;OrryCTHMbIH pa36poc ,nHaMeTPoB
,neTaJIeH COCTaB.IDIeT 0,504-0,502 = 0,002 CM. TaK KaK CTaH,[(apTHOe OTKJIOHeHHe paB-
HO 0,0005 CM, ,naHHbIH pa36poc COOTBeTcTByeT + 2 CTaH,[(apTHbIM OTKJIOHeHIDIM. 11:3
CBoHcTBa (2), lIpHBe,neHHoro BbIIIIe, CJle,nyeT, qTO 95 % ,neTaJIeH yKJIaLJ:bIBaIOTCR B ,no-
rryCTHMbIH ,nHalIa30H, T.e. B BbI60pKe co,nep)I{HTCR 28 HJIH 29 ,nOrryCTHMbIX ,neTaJIeH, a
B lIapTHH, BepORTHO, co,nep)I{HTCR 95 % OT 1000, T. e. 950 ,nOrryCTHMbIX ,neTaJIeH.
,n;aHHbIH lIpHMep 6bIJI BbI6paH TaK, qTO pa36poc 6bIJI paBeH TOqHO + 2 CTaH,[(apT-
HbIM OTKJIOHeHIDIM. O,nHaKo CylI(eCTByroT Ta6J1HUbI qaCTHqHbIX IIJIOII(a,neH lIO,n KPH-
BOH HOpMaJIbHOrO paClIpe,neJIeHIDI, KOTopbIe lI03BOJI.HIOT CBR3aTb JlI060e CTaH,[(apT-
Hoe OTKJIOHeHHe C IIJIOII(a,nblO lIO,n KpHBOH. (06bJqHO TaKaR Ta6J1Hua Ha3bIBaeTCR
«<I>yHKUIDI paClIpe,neJleHIDI HOpMHpOBaHHoro H ueHTPHpOBaHHoro HOpMaJIbHOrO
paClIpe,neJleHIDI». - IlpuMe"Lf,. nep.)
F/la8a 1. HH:JICeHepHaJI MameMamUKa
1. 14. AMcI>cI>epeHu.ManbHoe MC'IMCneHMe (npoM3BoAHble)
ECJlH y = xn
ECJlH y = ax n
ECJlH f(x) = ax n
ECJlH y = sin e
ECJlH Y = cos e
ECJlH Y = tge
ECJlH Y = ctge
ECJlH Y = seee
ECJlH Y = eosece
ECJlH Y = sin -1 X
a
X
ECJlH Y = COS-1 -
a
ECJlH Y = tg-1 X
a
X
ECJlH Y = ctg- 1 -
a
X
ECJlH Y = see- 1 -
a
X
ECJlH Y = cosec -1 -
a
ECJlH Y = ex
ECJlH Y = e ax
ECJlH Y = ax
ECJlH Y = In X
TO dy = nx n - 1
dx
TO dy = anxn-1
dx
TO f'(x) = anx n - 1
TO dy = cose
de
TO dy = -sine
de
TO dy = see 2 e
de
TO dy = cosec 2e
de
dy sin e
TO - = tgeseee =
de COS2 e
dy Cose
TO - = -ctgecosece = -
de sin 2 e
dy 1
TO -
dx .J a 2 - x 2
dy 1
TO -
dx .J a 2 - x 2
dy a
TO -
dx a 2 + x 2
dy a
TO -
dx a 2 + x 2
dy a
TO -
dx x .J x 2 -a 2
dy a
TO -
dx x .J x 2 -a 2
TO dy = ex
dx
TO dy = ae ax
dx
TO dy =a X lna
dx
TO dy =l
dx X
IIpoH3Bo,n;uaB npOH3Be eHHB
dy dv du
ECJlH Y = UV, r,ae U H V - <PYllKUHH OT X, Tor a - = U - + v -
dx dx dx
1.14. ,4ufjJfjJepeHlJ,UOJlbHOe UC"tUCileHue (npoU36ooHble) 43
IIpoH3Bo,n;uaB qaCTHOro
du dv
v- -u-
ECJIH y = u / V, r.n;e U H V - cPyHKIJ;HH OT x, Tor.n;a dy = dx dx
dx v 2
IIpoH3Bo,n;uaB CJIOlKHOH fj)YUKD;llH
dy dy du
ECJlH y eCTb <PYllKUIDI OT x, Tor,na - = - x -
dx du dx
IIocJIe,n;oBaTeJILHoe ,n;Hfj)fj)epeHD;HpoBaHHe
ECJlH y = f(x), Tor,na ee lIepBa.H lIpOH3Bo,nHaR 3alIHCbIBaeTCR B BH)];e dy HJIH f'(x).
dx
ECJlH 3TO BbIpIDKeHHe lIpo,nH<p<pepeHUHpoBaTb BTOpOH pa3, TO lIOJlyqHTCR BTOpaR
d 2 y
lIpOH3BO,nHa.H, KOTOpaH 3aIIHCbIBaeTCR B BH)];e - HJIH f"(x).
dx 2
1 . 15. MHTerpanbHoe MC'IMCneHMe
(HeonpeAeneHHble MHTerpanbl)
3,neCb C - lIOCTORHHa.H HHTerpHpOBaHIDI; n * -1.
J xn+l
xndx = + C
n+l
J sin9d9 = -cos9 + c
J sec 2 9d9 = tg9 + c
J tg9sec9d9 = sec9 + c
J dx . I x
= sm - - + C
-J a 2 - x 2 a
J adx =tg- 1 X + C
a 2 + x 2 a
J adx = sec- 1 X + C
x -J x 2 - 0 2 a
J exdx = ex + s
J axn+l
axndx = + C
n+l
J cos9d9 = sin 9 + c
J cosec9d9 = -<:tg9 + c
J ctg9cosec9d9 = -<:osec9 + c
J -dx =cos- 1 X + C
-J a 2 - x 2 a
J -adx = ctg- 1 X + C
a 2 + x 2 a
J -adx = cosec-l X + C
x -J x 2 - 0 2 a
J eaxdx = eax + s
a .
J dx =lnx+c
X
J coshxdx = sinh x + s
f "
)
J axdx = ax + s
lna
J sinh xdx = cosh x + s
J sech 2 xdx = tghx + s
J dx = sinh-I x +c'
-J a 2 + x 2 a
J = COSh-I x + c
.JX2 a 2 a
J dx =!tgh- 1 X +c
a 2 - x 2 a a
HJIH
In[ x + .Jx a 2 + a 2 ] + c
[ X + -J x 2 -0 2 ]
In + C
a
1 1 (a + x)
- n +c
2a (a - x)
HJIH
HJIH
(::, F/la8a 1. HH:JICeHepHaJI MameMamUKa
1. 15. 1. HHTerpJfpOSSHJfe no IfSCTflM
J udv = uv - J vdu + c
1.15.2. OnpeAeneHH&le JfHTerpSn&1
BbIIIIeOlIHcaHHbIe HHTerpaJIbI co,n;epxaT npOH3BOJlbHyID KOHCTaHTY C H Ha3bIBalOTCR
HeOnpeOe/leHHblMU UHmeZpaJlaMu. OlIpe,n;eJleHHbIMH HHTerpaJIaMH Ha3bIBalOT HHTer-
paJIbI, ,lI;illI KOTOpbIX lIpe,n;eJlbI 3a.naHbI TaK: [x] = (b) - (a), CJle,n;OBaTeJlbHO:
3 [ 3 ] 3 [ 33 ] [ 13 ] ( 1 ) 2
y = f x 2 dx = x 3 + c 1 = 3 + c - 3 + c = (9 + c) - 3 + c = 8 3 ,
OTMeTHM, qTO lIOCTORHHbIe HHTerpHpOBaHH.H C B OlIpe,n;eJleHHOM HHTerpaJIe
B3aHMHO yHHqTOXaIOTCR.
1 . 16. &MHOM HblOTOHa (6MHOMManbHaR TeopeMa)
n(n -1) n(n -1)(n - 2)
(a + x)n =a n + nan-Ix + a n - 2 x 2 + a n - 3 x 3 +... + x n
2! 3! '
r,n;e 3! eCTb <t>aKTOpHaJI qHCJla 3 H paBH.HeTCR 1 x 2 x 3.
1 . 17. Pa3nO)l(eHMe B PRA MaKnOpeHa
x 2
f(x) = f(O) + xf'(O) + - f"(O) + ... .
2!
1.18. Pa3nO)l(eHMe B PRA TeMnopa
h 2
f(x + h) = f(x) + hf'(x) + - f"(x) + ... ·
2!
,n;OIIOJlHHTeJlbHyro HH<popMaUHIO lIO HIDKeHepHoH MaTeMaTHKe qHTaTeJlb MoxeT
lIOJIyqHTb, 06paTHBIIIHcb K cJle,n;yIOlI(eMY ClIpaBOqHHKY: ,lbKOH Bep,n; «ClIpaBOqHHK
lIO HIDKeHepHoH MaTeMaTHKe», «Newnes», TpeTbe H3,n;aHHe (Newnes Engineering
Mathematics Pocket Book, Third Edition, John Bird, 0750649925).
rnABA 2
MH>KEHEPHASI
CTATMKA
2.1. MH)I(eHepHaR CTaTMKa
HIDKeHepHYIO MexaHHKY MO)I{HO pa3,neJlHTb Ha cmamUKY H iJUHaMUKY. CTaTHKa B
OCHOBHOM H3yqaeT CHJIbI H pe3YJlbTaTbI HX B03,neHCTBIDI B COCTORHHH paBHOBeCIDI,
Tor,na KaK ,nHHaMHK:l H3yqaeT 06'beKTbI B ,nBIDKeHHH.
2.2. Macca, CMna M Bee
2.2. 1. Msccs
. Macca - 3TO Mepa KOJlWleCTBa BelI(eCTBa B TeJle; 061I(a.H C)'MMa Macc Bcex
cy6aToMHbIX qaCTHU, H3 KOTOpbIX COCTOHT ,naHHoe TeJlO. .
. BelI(eCTBO 3alIOJlHReT lIpOC1'paHCTBO H MoxeT HaxO,nHTbCR B TBep,nOM, )I{H)J;-
KOM HJIH ra3006pa3HoM COCTORHHH.
. ECJlH BelI(eCTBO He ,n06aBlliIeTCH K Te.rry HJIH He y,naJI.HeTCR H3 Hero, Macca
3Toro TeJla He MeH.HeTCR. OHa OCTaeTCR lIOCTORHHOH lIPH JII06bIX 06CTORTeJlb-
CTBax. B O,nHOM KHJIorpaMMe, HarrpHMep, MeTaJIJIa Ha JIyHe co,aep)I{HTCR CTO-
JlbKO xe aTOMOB, CKOJlbKO H B KHJIorpaMMe TaKoro xe MeTaJIJIa Ha f3eMJIe.
O,nHaKO KHJIorpaMM MeTaJIJIa Ha JIyHe 6y,neT BeCHTb MeHbIIIe, qeM Ha 3eMJIe
(CM. pa3,neJl 2.2.4).
. OCHOBHa.H e,nHHHua H3MepeHIDI MaCCbl - KWl02paMM (Kr). CaMa.H paClIpOCTPa-
HeHHa.H KpaTHa.H e,nHHHua,lJ)Ul 3TOH OCHOBHOH e,nHHHUbI - TOHHa (1000 Kr);
CaMa.H paClIpOCTPaHeHHa.H ,nOJlbHasI e,nHHHua - rpaMM (0.001 Kr).
(TaKoe OlIpe,aeJleHHe 6billO lIpHH.HTO B KJIaCCHqeCKOH <pH3HKe H HClIOJlb30Ba-
JlOCb, HalIpHMep, HbIOTOHOM. OHO HMeeT CMhICJI TOJlbKO AJUI O,nHOpO,nHbIX TeJl H
lI03BOJI.HeT BBeCTH rrOHRTHe IIJIOTHOCTH. Macca - 3TO <pH3W1eCKa.H BeJlHqHHa, o,nHa
H3 xapaKTepHCTHK MaTepHH, OlIpe,neJI.HlOlI(a.H ee HHepUHOHHbIe H rpaBHTaUHOHHbIe
CBOHCTBa. OlIbIT lIOKa3aJI, qTO HHepTHa.H H rpaBHTaUHOHHa.H MaCCbI lIPOlIopUHQHa-
JlbHbI o,nHa ,npyrOH. 3TOT <pYJI,LI;aMeHTaJIbHbIH 3aKOH lIpHpO,nbI Ha3bIBaeTCR lIPHHUH-
lIOM 3KBHBaJIeHTHOCTH.
npHpo,na MaCChI - o,nHa H3 BIDKHeHIIIHX elI(e He pelneHHbIX 3a,naq <pH3HKH.
npHHRTO CqHTaTb, qTO Macca 3J1eMeHTapHOH «<cy6aToMHOH») qaCTHUbI OlIpe,neJI.H-
eTCH lIOJI.HMH, KOTopbIe C HeH CBR3aHbI (3J1eK1'pOMarHHTHbIM, .H,L(epHbIM H IIp.). O,n-
HaKO KOJlHqeCTBeHHasI TeopIDI MaCCbI elI(e He C03,naHa.
11:3 CTaTbH Macca, <l>H3W1ecKHH 3HUHKJIOlIe,nHqeCKHH CJlOBapb. - IlpUMe"Lf,. nep.)
F/la8a 2. HHJlCeHepHaJI cmamU1CO
2.2.2. CJfns
QT06bI lIOH.HTb, KaK CBR3aHbI Macca H 8ec TeJla, He06xo,n;HMO paCCM01'peTb lIOH.HTHe
CUJlbl. CaMY lIO ce6e CHJIy HJIH CHCTeMY CHJI YBHJJ:eTb HeJlb3R; MO)I{HO 06Hap'YXHTb
TOJlbKO B03,n;eHcTBHe CHJIbI HJIH CHCTeMbI CHJI. HalIpHMep:
. CHJIa MoxeT H3MeHHTb HJIH lIOlIbITaTbCR H3MeHHTb <poPMY 06'beKTa.
. CHJIa MoxeT lIepeMeCTHTb HJIH lIOlIbITaTbCR lIepeMeCTHTb lIOKORlI(eeCR TeJlO.
ECJlH BeJlHqHHa CHJIbI ,aOCTaTOqHO 60JlbIIIa.H, TO 3TO lIpHBe,n;eT K lIepeMelI(e-
HHIO TeJla B HalIpaBJleHHH lIpHJIOXeHIDI CHJIbI. ECJlH BeJlWlHHa CHJIa He,n;OCTa-
TOqHa, qT06bI lIpeo,n;OJleTb COlIpOTHBJleHHe ,n;BIDKeHHIO, CHJIa Bce xe nonblma-
emCR C,n;BHHYTb TeJlO, XOTH H 6e3YClIeIIIHO.
. CHJIa MoxeT H3MeHHTb HJIH rrorrbITaTbCR H3MeHHTb ,n;BIDKeHHe TeJla, KOTopoe
yxe lIepeMelI(aeTCR. HalIpHMep:
- CHJIa BC1'peqHOrO Be1'pa MoxeT )'MeHbIIIHTb CKOpOCTb CaMOJleTa OTHOCH-
TeJlbHO 3eMJIH, Tor,n;a KaK CHJIa lIolIyrHoro Be1'pa MoxeT YBeJlWlHTb CKO-
pOCTb CaMOJleTa OTHOCHTeJlbHO 3eMJIH;
- CHJIa 60KOBoro Be1'pa MoxeT 3aCTaBHTb aBTOM06HJIb OTKJIOH.HTbCR OT KYPca.
. B03,l(eHCTBHe JlI060H CHJIbI 3aBHCHT OT:
- BeJlWlHHbI (pa3Mepa) CHJIbI, H3MepReMOH B HblOTOHax (H);
- HalIpaBJleHIDI CHJIbI;
- TOqKH lIpHJIOXeHIDI CHJIbI;
- clIoc06HOCTH TeJla COlIpOTHBJI.HTbCR B03,n;eHcTBHIO CHJIbI.
. KaK yxe 6billO CKa3aHO, CHJIY HeJlb3R YBHJJ:eTb; o,n;HaKO OHa MoxeT 6bITb
rrpe,aCTaBJleHa BeKTOpOM.
2.21'3. BeKTop&1
<l>H3HqeCKHe BeJlHqHHbI MO)I{HO pa3,aeJlHTb Ha ,n;Be KaTeropHH:
. CKaJI.HpHbIe BeJlHqHHbI;
. BeKTopHbIe BeJlHqHHbI.
CKaJIHpHbIe BeJlWlHHbI OlIpe,n;eJlRIOTCR TOJlbKO qHCJlOBbIM 3HaqeHHeM (pa3-
MepoM). HanpHMep:
. CKOpOCTb aBTOM06HJI.H MO)I{HO OlIpe,n;eJlHTb KaK 50 KHJIOMe1'pOB B qac (KM/q).
. MOII(HOCTb ,aBHraTeJI.H MoxeT 6bITb oueHeHa KaK 150 KHJIOBaTT (KBT).
. TOK, TeKYIIJ:HH B 3J1eKlpWleCKOH uelIH, MoxeT 6bITb paBeH 12 aMlIepaM (A).
BeKTopHbIe BeJlHqHHbI OlIpe,n;eJl.HIOTCH KaK qHCJlOBbIM 3HaqeHHeM, TaK H Ha-
rrpaBJleHHeM. HalIpHMep, CKOpOCTb aBTOM06HJIR - 50 KM/q TOqHO Ha ceBep H3
JIOH.nOHa. CKOpOCTb - BeKTOpHa.H' BeJlHqHHa, TaK KaK Y Hee eCTb H qHCJlOBOe 3Ha-
qeHHe (CKOpOCTb); H HarrpaBJleHHe (TOqHO Ha ceBep).
TOqHO TaK xe BeKTOpbI MO)I{HO HCrrOJlb30BaTb ,lJ;illI lIpe,n;CTaBJIeHHH CM H CHC-
TeM CHJI. Ha pHCyHKe 2.1 lIOKa3aHO, KaK MO)I{HO HCnOJlb30BaTb BeKTOp ,lJ;illI rrpe,n;-
CTaBJleHIDI CHJIbI (F) BeJlHqHHOH 150 HblOTOHOB (H), ,n;eHcTByrolI(eH Ha TOqKY (P) B
HarrpaBJIeHHH, COCTaBJlHlOlI(eM 30° C ropH30HTaJIblO. BeKTopHbIe ,n;HarpaMMbI 6y,ayr
no,ap06HO paCCMOTpeHbI B pa3,aeJle 2.3.
QT06bI lIpe,nCTaBHTb CHJIy BeKTO-
pOM, He06xo,nHMa cJle,nyrolI(a.H HH<pOP-
MaUIDI.
. T OqKa lIpHJIOXeHIDI CHJIbI.
. BeJl HHa (pa3Mep) CHJIbI.
. JIHHIDI B03,neHCTBIDI CHJIbI.
. HalIpaBJleHHe, B KOTOpOM ,neH-
cTByeT CHJIa (YKa3aHO cTpeJl-
KOH). OHa MoxeT HaxO,nHTbCR B
KOHue BeKTopa HJIH B cepe,nHHe
BeKTOpa, KaK 60Jlee y,n06HO.
2.2.4. Bec
2.2. Maeea, eU/la u 8ee
F = 150 H
p
Puc. 2.1. BeKTopHoe npe,n;CTaBJIeHHe CHJIbI
TBep,noe TeJlO, XH,llKOCTb HJIH ra3 MaCCOH 1 Kr 6y.nyr BeCHTb 9,81 H 6J1aro,napR rpa-
BHTaUHOHHOMY lIpHTIDKeHHIO IIJIaHeTbI 3eMJUI. TaK KaK IIJIaHeTa 3eMJIR He H)];eaJIb-
Ha.H c<pepa, TeJlO MaCCOH 1 Kr 6y,neT BeCHTb HeMHoro 60JlbIIIe Ha lIOJlIOCaX H HeMHO-
ro MeHbIIIe Ha 3KBaTope. O,nHaKo AJUI lIpaKT eCKHX ueJleH cpeoHuu 8ee MaCCbI 1 Kr
Ha IIJIaHeTe 3eMJUI CqHTaeTCR paBHbIM 9,81 H:
. rpaBHTaUHOHHa.H CHJIa rrpHTRrHBaeT Maccy JlI060ro TeJla (TBep,noro, )l{lf)]:KOrO
HJIH ra3006pa3Horo) K ueHTpy IIJIaHeTbI 3eMJUI;
. Bec TeJla - 3TO rpaBHTaUHOHHa.H CHJIa (cHJIa TIDKecTH), ,neHcTByrolI(a.H Ha 3TO
TeJIO;
. lI03TOMY Bec - 3TO CHJIa, H3MepHeMa.H B HbIOTOHax;
. K03<P<PHUHeHT 9,81 - 3TO YCKopeHHe cB060,nHoro lIa,neHIDI TeJla, 06YCJlOB-
JleHHOe CHJIOH TIDKeCTH, OHO paBHo 9,81 MeTPa Ha ceKJH,ll;Y B KBa,npaTe
(M/C 2 ). YCKopeHHe, 06YCJlOBJleHHOe CHJIOH TIDKeCTH, 06Cy)I(,l(aeTCR ,naJIee B
pa3,aeJle 3.6. 7; (
. XOTR Bec TeJla MaCCOH 1 Kr paBeH lIpH6J1H3HTeJlbHO 9,81 H (cpe,nHee 3Haqe-
HHe) Ha IIJIaHeTe 3eMJUI, Bec ,naHHoro TeJla H3MeHHTCR Ha IIJIaHeTe, HMelO-
lI(eH HHYIO CHJIy rpaBHTaUHOHHoro rrpHTRxeHHR, HJIH lIPH rrepeMelI(eHHH B
KOCMoce. HarrpHMep, rpaBHTaUHOHHoe lIpHTIDKeHHe JIYHbI COCTaBlliIeT lIPH-
6J1H3HTeJlbHO 1/6 lIO cpaBHeHHIO C IIJIaHeTOH 3eMJUI. n03TOMY Macca 1 Kr 6y-
,aeT BeCHTb Ha JIYHe )i x 9,81 = 1,64 H.
2.2.5. Msccs HS eAJfHJfqy 06"heMS (nnoTHOCT&)
I1YCTb TBep,aoe TeJlO HMeeT 06'beM 60 CM 3 . ECJlH Macca 3Toro TeJla COCTaBJlHeT
600 rpaMMOB (r), TO MO)I{HO BbIqHCJlHTb
Macca 1 CM 3 = 600 r/60 CM 3 = 10 rpaMMOB B CM 3 (10 r/cM 3 )
TaK KaK 1 CM 3 B 3TOM cJlyqae - e,nHHHQHbIH 06'beM, TO Macca e,nHHHUbI 06'beMa
,[(aHHoro TeJla COCTaBJI.HeT 10 r/cM 3 . Maccy e,nHHHUbI 06'beMa JlI060ro TeJla TaIOKe
F/la8a 2. HH:JICeHepHaJI cmamUl€a
Ha3bIBaIOT IIJIOTHOCTblO 3Toro TeJla. I1JIOTHOCTb 0603HaqaeTCR rpeqeCKOH 6yKBOH
«PO» (p). 061I(a.H <poPMYJla AJUI MaCCbI e,nHHHUbI 06'beMa (IIJIOTHOCTH):
p = m/V,
r,ne: p = IIJIOTHOCTb, m = Macca, V = 06'beM.
I1JIOTHOCTH HeKoTopbIX paclIpoc1'paHHbIX TBep,nbIX TeJl, )l{H)J;KOCTeH H ra30B, HC-
lIoJlb3yeMbIX B TeXHHKe, lIpHBe,aeHbI B Ta6J1Hue 2.1.
Ta6J1. 2.1. llJIOTHOCTb pacnpOCTpaHHbIX BerneCTB.
II.11OTHOCTh II.11OTHOCTh
BeIQeCTBO Kr/M 3 r/cM 3 BeIQeCTBO Kr /M 3 r/cM 3
AAIOMHHHH 2720 2,72 CnHPT 800 0,80
JIaTyHb 8480 8,48 PryTb 13590 13,59
Me,n;b 8790 8,79 llapa<p HH 800 0,80
qyryH 7200 7,20 BeH3HH 720 0,72
CBHHeI( 11350 11,35 Bo,n;a (qHCTaH npH 4 °C) 1000 1,10
HeHJIOH 1120 1,12 Au;eTHJIeH 1,17 0,1017
llOJIHBHHHJIXJIOPH.n (llBX) 1360 1,36 B03,ZJ;yX (CYXOH) 1,30 0,1013
Pe3HHa 960 0,96 YrJIeKHCJIbIH ra3 1,98 0,10198
CTaJIb 7820 7,82 Bo,n;opo,n; 0,19 0,10009
OJIOBO 7280 7,28 A30T 1,25 0,10125
QHHK 7120 7,12 KHcJIopo,n; 1,43 0,10143
2.2.6. Bec s eAJfHJfqsx 06"heMS
Bec e,nHHHUbI 06'beMa BelI(eCTBa MoxeT 6bITb OlIpe,neJleH:
a) lIpRMbIM H3MepeHHeM,
6) lIpe06pa30BaHHeM IIJIOTHOCTH BelI(eCTBa.
a) Orrpe,neJleHHe Beca e,nHHHUbI 06'beMa lIpRMbIM H3MepeHHeM:
Bec e,nHHHUbI 06'beMa (H/M 3 ) = Bec (H) / 06'beM (M 3 ) = W/
6) OlIpe,neJleHHe Beca e,nHHHUbI 06'beMa lIpe06pa30BaHHeM:
Bec e,nHHHUbI 06'beMa = W/V
nJlOTHOCTb (p) = m/V
Bec = m x 9,81
nO,acTaBJI.H.H ypaBHeHHe (3) B ypaBHeHHe (2):
Bec e,nHHHUbI 06'beMa = (m x 9,81) / V
m/V=p
Bec e,nHHHUbI 06'beMa = p x 9,81
(1)
(2)
(3)
Ho:
n03TOMY:
IlpuMettanue:
. 3TO lIpe06pa30BaHHe lIpHMeHHMO TOJlbKO Ha IIJIaHeTe 3eMJI.H. B ,npyrHX Mec-
Tax KOCMoca CJle,nyeT HClIOJlb30BaTb JlOKaJIbHOe 3HaqeHHe rpaBHTaUHOHHoro
YCKopeHH.H g.
. 3HaqeHHe IIJIOTHOCTH ,n0JI)I{H0 6bITb BbIpIDKeHO B KHJIorpaMMax Ha e,nHHHIfj'
06'beMa.
2.2. Maeea, eU/la u 8ee
2.2.7. OTHOCJfTen&HSfI nnOTHOCT&
OTHOCHTeJlbHa.H IIJIOTHOCTb BelI(eCTBa MoxeT 6bITb olIpe,n;eJleHa KaK OTHOIIIeHHe:
(nrrOTHOCTb BelI(eCTBa) / (IIJIOTHOCTb qHCTOH BO,n;bI lIpH 4°C)
HJIH
(Macca BelI(eCTBa) / (Macca paBHoro 06'beMa qHCTOH BO,n;bI lIpH 4°C)
TaK KaK OTHOCHTeJlbHa.H IIJIOTHOCTb lIpe,n;CTaBJI.HeT C060H OTHOIIIeHHe, OHa RB-
JI.HeTCR 6e3pa3MepHOH BeJlWlHHOH.
OTHOCHTeJlbHbIe IIJIOTHOCTH HeKOTopbIX paClIpOC1'paHeHHbIX BelI(eCTB, HClIOJlb-
3yeMbIX B TeXHHKe, lIpHBe,n;eHbI B Ta6J1Hue 2.2.
Ta6J1. 2.2. OTHOCHTeJIbHbIe llJIOTHOCTH HeKOTopbIX pacnpOCTpaHeHHbIX BeIIJ;eCTB.
BeIQecTBO OmOCHTeJlhHaJI BeIQeCTBO OmOCHTeJlhHaJI
WlOTBOCTh (d) WlOTBOCTh (d)
ArrIOMHHHH 2,72 CnHpT 0,80
JIaTYHb 848 Pryrb 13,95
KanMHH 8,57 llapa<pH H 0,80
XpOM 7,13 BeH3HH 0,72
Me,n;b 8,79 Bo,n;a (qHCTaH npH 4 °C) 1,10
qyryH 7,20 Bo,n;a (MOpCKaH) 1,12
CBHHeI( 11,35
HHKeJIb 8,73 Au;eTHJIeH 0,1017
HeHJIOH 1,12 B03,ZJ;yX (CYXOH) 0,1013
llOJIHBHHHJIXJIOPH.n (llBX) 1,36 YrJIeKHCJIbIH ra3 0,10198
Pe3HHa 0,96 YrapHbIH ra3 0,10126
CTaJIb 7,82 Bo,n;opo,n; 0,10009
OJIOBO 7,28 A30T 0,10125
QHHK 7,12 KHcJIopo,n; ( 0,10143
2.2.8. p,SSneHJfe ()lCJfAKOCTJf)
,n;aBJIeHHe, ,n;eHcTByrolI(ee Ha IIJIOII(a,nb lIOBepXHOCTH ,n;aHHoro TeJla, OlIpe,n;eJI.HeTCR
KaK HOpMaJIbHa.H CHJIa Ha e,n;HHHIfj' IIJIOII(a,nH, ,n;eHcTByrolI(a.H Ha lIOBepXHOCTb. Hop-
MaJIbHaR CHJIa 03HaqaeT CHJIY, ,n;eHcTByrolI(yro lIO,n; lIpRMbIM yrJlOM K lIOBepXHOCTH.
B CM e,n;HHHueH ,aaBJleHIDI KOCTH RBJI.HeTCR lIaCKaJIb (Ila). 1 Ila paBeH 1 H/M 2 .
,n;aBJIeHHe (P) = F/ A,
r,n;e: p - ,n;aBJleHHe B rraCKaJUIX; F - CHJIa B HbIOTOHax, ,n;eHcTByrolI(a.H lIO,n; rrpHMbIM
yrJlOM (IIO HOpMaJIH) K lIOBepXHOCTH; A - IIJIOII(a;J:b lIOBepXHOCTH B KBa,npaTHbIX
Me1'pax.
TaK xe:
1 MIla = 1 MH/M2 = 1 H/MM 2 .
TaK KaK naCKaJIb OqeHb MaJIaH e,n;HHHua, Ha lIpaKTHKe qalI(e HClIOJlb3yeTcR 6ap:
1 6ap = 10 5 lIaCKaJIeH.
F/la8a 2. HH:JICeHepHaJI cmamwco
llpUMe"taHue.
. ATMoc<t>epHoe ,naBJleHHe 06bJqHO BbIpIDKalOT B MHJIJIH6apax.
. MaHoMe'rpHqeCKOe ,naBJleHHe - 3TO ,naBJleHHe )lQf)];KOCTH, H3MepReMoe 'rpy6-
qaTbIM MaHoMe'rpoM, U-06pa3HbIM MaHoMe'rpoM HJIH aHaJIOrHqHbIM YC'rpOH-
CTBOM, TaK qTO H3MepReMoe ,naBJleHHe RBJlReTCR ,n06aBOqHbIM K aTMoc<t>epHo-
MY ,naBJleHHIO.
. A6coJIIOTHOe ,naBJleHHe, HClIOJlb3yeMoe B <pH3HKe H TepMo,nHHaMHKe, - 3TO
,naBJleHHe OTHOCHTeJlbHO a6COJllOTHOrO BaKY}'Ma, lI03TOMY:
a6coJllOTHoe ,aaBJIeHHe = aTMoc<PePHoe ,naBJIeHHe + MaHOMerp ecKoe ,naBJIeHHe.
2.3. BeKTOpHbie AMarpaMMbl CMn:
rpacl>M'IeCKOe peweHMe
KaK yxe 6billO OTMeqeHO, CHJIbI HeJlb3R }'BHJJ:eTb, lI03TOMY HX HeJlb3R HapHCOBaTb;
o,nHaKO B03,neHCTBHe CHJI H CHCTeM CHJI MO)I{HO rrpe,nCTaBHTb BeKTopaMH. BeKTopbI
6billH OlIpe,neJleHbI B pa3,neJle 2.2.2.
2.3. 1. PssHoAejfcTsYIO Jfe CJfn&1
CHJIa, KOTopaR MoxeT 3aMeHHTb ,nBe
HJIH 60Jlee CHJI H OKa3aTb TaKoe xe
B03,neHcTBHe, Ha3bIBaeTCR pe3YJlbTHPy-
IOlI(eH HJIH paBHo,neHcTByromeH CHJIOH.
HarrpHMep, CHJIbI Fl H F 2 , ,neHcTByro-
II(He B O,nHOM H TOM )l(e HalIpaBJleHHH
Ha TOqKY P B,nOJlb O,nHOH H TOH xe JlH-
HHH ,neHCTBH.H, MO)I{HO 3aMeHHTb e,nHH-
CTBeHHOH CHJIOH, oKa3bIBalOlI(eH Ta-
Koe )l(e B03,neHCTBHe, KaK rrOKa3aHO Ha
pHC. 2.2, a.
I10CKOJlbKY 06e CHJIbI Fl H F 2 HMe-
lOT 06lI.(yIO JlHHHIO ,aei1cTBHH H ,aeHcT-
BYIOT B O,nHOM H TOM )l(e HalIpaBJleHHH,
qT06bI lIOJlyqHTb BeJlHqHJIy BeKTopa
e,nHHCTBeHHOH CHJIbI, KOTopaR MoxeT
3aMeHHTb HX, ,nJIHHbI BeKTOpOB 3THX
CHJI MO)I{HO lIpOCTO CJlO)I{HTb. I10.rry-
qHBIIIaRCR CHJIa F R rrOKa3aHa Ha pHC.
2.2, 6. Ee Ha3bIBalOT paBHo,aeHcTByro-
meH CHJIOH. OTMeTHM, qTO BeKTOp paB-
Ho,neHcTBYlOmeH CHJlbI HMeeT ,aBOHHyID
pa3MepHYlO c'rpeJIKY, QTO rr03BOJlHeT
OTJlHqHTb ero OT ,apyrHX CHJI, ,aeHcTBY-
IOmHX B CMCTeMe.
B MaclIlTa6e 1 CM = 5 H BeKTOp,
0603HaqalOlI(HH F 1 , 6y,aeT HMeTb ,nJIHHY
4 CM, a BeKTOp, 0603HaqalOlI(HH F 2 , -
4 CM 5 CM
r F 1 = 20 H -r F 2 = 25 H -I
P . . .
a
9 CM
- -
F R = 45 H
P
6
4 CM
[ F 1 = 20 H T
P
I
B .
5 CM
F 2 = 25 H :I
F R = 5 H
..
Puc. 2.2. PaBHo,n;eHcTBYIOll(He CHJIbI:
a - CM.JIbI Fl H F 2 , ,n;eHCTByIOIl(He Ha TOtIKy P;
6 - paBHo,n;eHcTByrornaH CHJI Fl H F 2 ;
B - paBHo,n;eHcTBYIOInaH CHJI Fl H F 2 , ,n;eH-
CTBYIOInHX B npOTHBOnOJIO)l(HbIX HanpaB-
JIeHHHX.
MacllITa6: 1 CM = 5 H
2.3. BelCmopHble OUaZpaMMbl CUll: zparjJu'teclCoe peUleHue
AJIHHY 5 CM. B pe3YJIbTaTe CJIOXeHIDI, BbIlIOJIIDIeMOrO, qT06bI lIO.JIyqHTb ,nJIHHY BeK-
Topa pe3YJIbTHpyrolI(eH CHJIbI (F R ), lIOJIyqaeTC.H e,l(HHCTBeHHbIH BeKTOp ,nJIHHOH
4 CM + 5 CM = 9 CM, lIpe,l(CTaBIDIIOII(HH CHJIy B 45 H, ,l(eHcTByrolI(yID Ha TOqKy P.
ECJIH 6bI CHJIbI ,l(eHCTBOBaJIH B lIpOTHBOlIOJIO)I{HbIX HalIpaBJIeHIDIX B,l(OJIb TOH xe
JIHHHH ,l(eHCTBIDI, TO paBHO,l(eHCTByrolI(yID CHJIy (F R ) MO)I{HO 6 bill 0 6bI OlIpe,l(eJIHTb,
BbIqHTasI ,nJIHH)' BeKTOpa FI H3 ,nJIHHbI BeKTOpa F 2 , KaK lIOKa3aHO Ha pHC. 2.2, B.
2.3.2. nspsnnenorpsMM CJfn
Kor,l(a Ha 0,l(H)' TOqKy P ,l(eHcTByroT ,l(Be HJIH 60JIee CHJI, JIHHHH ,l(eHCTBIDI KOTOpbIX
JIeXaT lIO,l( yrJIOM ,l(pyr K ,l(pyry, me pe3YJIbTHpyrolI(yro CHJIy HeJIb3R orrpe,l(eJIHTb
rrpOCTbIM apH<pMeTHqeCKHM CJIOXeHHeM HJIH BbIqHTaHHeM. ECJIH ,l(eHcTByroT TOJIbKO
,l(Be CHJIbI, KaK lIOKa3aHO Ha pHC. 2.3, BeJIWlHHY H HalIpaBJIeHHe paBHO,l(eHcTByro-
eH CHJIbI MO)I{HO OlIpe,l(eJIHTb lIOC1'poeHHeM B MacIIITa6e lIapaJIJIeJIorpaMMa CHJI.
Ha pHC. 2.3, a lIOKa3aHbI BeKTOpbI ,lI)UI ,l(BYX CHJI, ,l(eHcTByroII(HX iIa TOqKy P,
rro,l( yrJIOM 60° O,l(Ha K ,l(pyrOH. Ha pHC. 2.3, 63TH BeKTOpbI 06pa3yroT ,l(Be CMe)I{HbIe
CropOHbI lIapaJIJIeJIorpaMMa P ABC. BeKTop P A COOTBeTcTByeT CHJIe F I , a BeKTOp
PC COOTBeTcTByeT CHJIe F 2 . QT06bI ,l(OCTpOHTb lIapaJIJIeJIorpaMM, lIPRMasI AB rrpOBe-
,neHa lIapaJIJIeJIbHO BeKTOpy PC, a rrpRMasI CB lIpOBe,l(eHa lIapaJIJIeJIbHO BeKTOpy
PA. TOqKa B JIeXHT Ha lIepeCeqeHHH IIp.HMbIX AB H CB. Pe3YJIbTHpyrolI(a.H CRJIa F R ,
,neHcTByrolI(aR Ha TOqKy P, RBJI.HeTCR ,l(HarOHaJIblO lIapaJIJIeJIorpaMMa PABC. BeJIH-
qHHY pe3YJIbTHpyrolI(eH CHJIbI F R MO)I{HO OlIpe,l(eJIHTb, H3MepHB ,nJIHHY ,l(HarOHaJIH
PB H YMHOXHB ee Ha MacIIITa6 ,l(HarpaMMbI (1 CM = 10 H B ,l(aHHOM c.JIyqae). YroJI a
MO)I{HO OlIpe,l(eJIHTb lIpH rrOMOII(H 1'paHClIopTHpa. ,n:JIR pHC. 2.3 TIOJIyq HOTCR CJIe.ny-
IO He 3HaqeHIDI : F R = 87 H H a = 23° (6JIl:OKaHIIIee ueJIoe qHCJIO).
B
'I
I
(
I
I
I
R = 87 HI
I
I
I
I
I
p
a
F 2 = 50 H
p
6
F 2 = 50 H
c
Pac. 2.3. naparrJIeJIOrpaMM CHJI.
MacllITa6: 1 CM = 10 H
2.3.3. YpSSHOSeWJfSSIOUCSfI CJfns
CRJIa, KOTOpasI ypaBHOBeIIIHBaeT ,l(eHCTBHe ,l(pyrOH CRJIbI HJIH CHCTeMbI CRJI, Ha3bI-
BaeTCR ypaBHOBeIIIHBalOlI(eH CHJIOH (FE)' YpaBHOBeIIIHBalOlI(aR CHJIa:
. HMeeT 1)' xe caMyro BeJIHqHHY, qTO H paBHO,l(eHCTByrolI(aR cRJIa;
. HarrpaBJIeHa B,l(OJIb TOH xe caMoH JIHHHH ,l(eHCTBIDI, qTO H paBHO,l(eHCTByro-
lI(aR cRJIa;
. ,l(eHcTByeT B HalIpaBJIeHHH, rrpoTHBOlIOJIO)I{HOM paBHO,l(eHCTByrolI(eH cl1JIe.
F/la8a 2. HH:JICeHepHaJl cmamUlCa
Ha pHC. 2.4 lIOK83aHa ypaBHOBeIIIHBalOlI(asI CHJIa (FE)' paBHasI lIO BeJI}fqHHe H
lIpOTHBOlIOJIO)I{HasI lIO HalIpaBJIeHHIO paBHO,l(eHcTByrolI(eH CHJIe (F R)' OlIpe,l(eJIeHHOH
Ha pHC. 2.3, lI03TOMY OHa ypaBHOBeIIIHBaeT B03,l(eHCTBHe CHJI FI H F 2 Ha TOqKy P.
A
B
FE = 87 H
Pac. 2.4. YpaBHoBellIHBaIOlI(aH CHJIa.
MacllITa6: 1 CM = 10 H
2.3.4. PS3nOJICeHJfe CJfn
Pa3JI0XeHHe CHJI - 3TO 06paTHasI OlIepaUIDI K HaxO)l{)J;eHHIO paBHO,l(eHcTByrolI(eH
CHJIbI. To eCTb pa3JIOXeHHe CHJIbI - 3TO 3aMeHa ,l(aHHOH e,l(HHCTBeHHoH CHJIbI ,l(BY-
M.H HJIH 60JIee CHJIaMH, ,l(eHcTByroII(HMH B TOH xe caMOH TOqKe B yxa3aHHbIX Ha-
lIpaBJIeHIDIX.
PaCCM01'pHM e,l(HHCTBeHHyIO CHJIy Fs, paBHyIO 50 H, ,l(eHcTByrolI(yID lIO,l( yrJIOM
30° K ropH30HTaJIH, KaK lIOKa3aHO Ha pHC. 2.5, a. QT06bI pa3JIO)I{HTb 31)' CHJIy Ha ee
ropH30HTaJIbHyIO H BepTHKaJIbHyIO COCTaBJI.HIOII(He, BHaqaJIe HapHcyeM JIHHHH ,l(ei1:-
CTBIDI 3THX CHJI, KaK lIOKa3aHO Ha pHC. 2.5, 6. 3aTeM ,l(OC1'pOHM lIapaJIJIeJIorpaMM
CRJI, KaK lIOKa3aHO Ha pHC. 2.5, 6. BeJIHqHHbI CHJI Fv H F H MO)I{HO lIOJIyqHTb H3Me-
peHHeM pHCYHKa B MacIIITa6e (BeKTOpHasI ,l(HarpaMMa) HJIH lIpH lIOMOII(H 1'pHrOHO-
Me1'pHqeCKHX <PYHKUHH.
Fv = 50 H x sin 30° = 25 H
F H = 50 H x cos 30° = 43,3 H
Fs = 50 H
p
a
=50H
------------- 5
I
Fv I
I
I
I
I
I
p
6
F H
Pac. 2.5. Pa3JIOXeHHe CHJI.
MacllITa6: 1 CM = 10 H
2.3. BelCmopHble OUaZpaMMbl CUll: zparjJu'teclCoe peUleHue
2.3.5. PSSHOSeCJfe Tpex CJfn (TpeyronbHJfK cJfn)
. BeKTOpbI 1'pex CHJI, ,l(eHcTByroII(HX Ha TeJIO B O,l(HOH H TOH xe TIJIOCKOCTH,
MOXHO HapHCOBaTb Ha JIHCTKe 6YMarH.
. CHJIbI, KOTopbIe ,l(eHcTByroT B O,l(HOH TIJIOCKOCTH, H83bIBaIOTCR KOMTIJIaHap-
HbIMH.
., . ECJIH 1'pH CHJIbI, ,l(eHcTByroII(He Ha TeJIO, HaxO,lUlTC.H B paBHOBeCHH, JII06asI
CHJIa ypaBHOBeIIIHBaeT B03,l(eHCTBHe ,l(BYX ,l(pyrHX CHJI. TpH CHJIbI MOryr 6bITb
rrpe,l(CTaBJIeHbI 1'peyrOJIbHHKOM, CTOpOHbI KOToporo RBJI.HIOTC.H BeKTOpaMH
3THX CHJI.
. ECJIH JIHHHH ,l(eHCTBIDI 1'pex CHJI lIepeceKalOTCR B O,l(HOH TOqKe, TO OHH 06pa-
3yroT CHCTeMY CXO,lUlII(HXCR CHJI.
Ha pHC. 2.6 lIOKa3aHbI 1'pH KOMTIJIaHapHbIe CHJIbI, ,l(eHcTByroII(He Ha TeJIO. Mx
JIHHHH ,l(eHCTBIDI lIpO,l(OJDKeHbI Ha38)J;, ,l(0 lIepeCeqeHIDI B TOqKe P. ToqKy P Ha3bIBa-
lOT TOqKOH lIepeCeqeHIDI CHJI. (Ee TaIOKe Ha3bIBalOT 06lI(eH TOqKOH lIpHJIOXeHIDI
CRJI. K HeH BCer,l(a MO)I{HO lIpHBR3aTb cHcTeMY KOOp,l(HHaT. - llpUMe"t. nep.) ECJIH
CRJIbI HaxO,lUlTC.H B paBHoBecHH:
. HX B03,l(eHCTBIDI ypaBHoBeIIIHBaIOTcR;
. TeJIO, Ha KOTopoe OHB ,l(eHCTByroT, OCTaHeTCR HelIO,l(BIDKHbIM;
. BeKTOpbI CHJI 06pa3yroT 3aMKJIyTbIH 1'peyrOJIbHHK;
. BeKTOpbI CJIe,l(ylOT ,l(pyr 3a ,l(pyrOM lIO 3aMKJIyT0MY KOHTYPY.
Ha pHC. 2.7 lIOKa3aH ,l(OlIOJIHHTeJIbHbIH lIpHMep C peIIIeHHeM. ToqHOCTb OTBe-
TOB 3aBHCHT OT TOqHOCTH pHCYHKa. ToqHOCTb pHCYHKa ,l(OJDKHa 6bITb KaK MOXHO
BbIIIIe, qT06bI lIOMOqb H3MepeHHIO.
F 2 = 20 H
F3 = 35 H
6
a
Pac. 2.6. TpeyrOJIbHHK CHJI:
a - cxeMa KOHC'rpYKI(HH;
6 - ,n;HarpaMMa YCHJIHH.
MacllITa6: 1 CM = 5 H
CVlJ1a B OTT5I)I(-
K = 20 KH
(
Ha-
rpY3Ka
20 KH
\
CVlJ1a B CTpeJ1e
KpaHa = 34,6
6
Pac. 2.7. CHJIbI B npOCTOM CTpeJIOBOM KpaHe.
a - cxeMa KOHC'rpYKI(HH;
6 - ,n;HarpaMMa YCHJIHH.
MacllITa6: 1 CM = 5 KH
F/la8a 2. HH:JICeHepHf1Jl cmamUica
2.3.6. MHoroyronbHJfK CJfn: nOCTpOeHJfe
AJfSrpSMMbl MaKcsenns-KpeMOH&1
MHoroyrOJIbHHK CHJI HClIOJIb3yeTC.H JVUI HaxO)l{)J;eHIDI paBHO,l(eHcTByrolI(eH JII060ro
KOJII-NeCTBa KOruIaHapHbIX CRJI C nepeceKalOmHMHC.H JIHHIDIMH .n.eHCTBIDI, B03.n.eHCT-
ByrolI(HX Ha TOqKy P. 3TH CHJIbI RBJI.HIOTCR lIepeCeKaIOII(HMHC.H, lIOCKOJIbKy ,l(eHCTBY-
lOT Ha e,l(HHCTBeHHyIO TOqKy P. OHH RBIDIIOTCR KOTIJIaHapHbIMH, TaK KaK JIeXaT B O -
HOH H TOH xe TIJIOCKOCTH. Ha pHC. 2.8, a lIOKa3aHa cxeMa KOHC1'pYKUHH, lIpWleM 06-
JIaCTH, orpaHWleHHbIe JIHHIDIMH ,l(eHCTBHH CHJI, 0603HaqeHbI 3arJIaBHbIMH 6yJ(BaMH.
CooTBeTcTByrolI(asI ,l(HarpaMMa YCHJIHH (,l(HarpaMMa MaKCBeJIJIa-KpeMoHbI) lIOKa3a-
Ha Ha pHC. 2.8, 6. CRJIbI 0603HaqeHbI C1'pOqHbIMH 6yJ(BaMH. 3TO rpa<pWlecKHH cno-
c06 paCqeTa YCHJIHH lIOC1'poeHHeM ,l(HarpaMMbI MaKCBeJIJIa- KpeMoHbI:
F 1 = 40 H
A
F 2 = 50 H
b
c
D
B
p
F3 = 30 H
c
d'
a
6 d
Pac. 2.8. MHoroyrOJIbHHK CHJI (HaKJIOHHbIe 0603HaQeHHH):
a - cxeMa KOHCTpYKI(HH (He B MacllITa6e);
6 - ,n;HarpaMMa YCHJIHH (MacllITa6: 1 CM = 10 H)
. CRJIbI, ,l(eHcTByroII(He Ha TOqKy P, CJIe,l(yeT lIpe,l(CTaBHTb BeKTOpaMH, ,l(JIHHbI
H yrJIbI KOTOpbIX ,l(OJDKHbI 6bITb Hap:ucoBaHbI C C06JIIO,l(eHHeM MacIIITa6a Ha-
CTOJIbKO TOqHO, HaCKOJIbKO 3TO B03MO)I{H0. 06JIaCTH, orpaHHqeHHble JIHHIDI-
MH ,l(eHCTBHH CHJI, 0603Haqa1OTC.H 3arJIaBHbIMH 6yJ(BaMH. OTlIpaBHasI TOqKa
He BaxHa, HO 6yJ(BbI ,l(OJDKHa CJIe,l(OBaTb BOKpyr lIO nop5JJJ;Ky, 06bIqHO B Ha-
npaBJIeHHH lIO qaCOBOH C1'peJIKe.
. ,n:HarpaMMa YCRJIHH ,l(O]I)I{Ha 6bITb HapHCOBaHa c1'poro B MaCIIITa6e, HaqHHasI C
rrO,l(XO,l(RlI(ero BeKTOpa. HanpHMep, MO)I{HO HaqaTh C BeKTopa BepTIlKaJIbHOH
CRJIbI Fl. TaK KaK 3TOT BeKTOp HaxO,l(HTCR Me)K,l(y 06JIaCT.HMH D H A, OH Map-
KHpOBaH da. TIoMHHTe, qTO 06JIaCTH npHH.HTO 0603HaqaTb 3arJIaBHbIMH 6yJ(Ba-
MH, TOr,l(a KaK CHJIbI 0603HaqalOT COOTBeTCTByrolI(HMH C1'pOqHbIMH 6yJ(BaMH.
,n:06aBbTe c1'peJIKy, qT06bI yKa3aTb, B KaKOM HalIpaBJIeHHH ,l(eHcTByeT CHJIa.
. CJIe,l(yIDlI(aR CRJIa (F 2 ) paClIOJIOXeHa Me)K,l(y 06JIaCTRMH A H B. OHa HapHCO-
BaHa B MaCIIITa6e, HaqHHaR OT KOHua lIepBoro BeKTOpa, H 0603HaqeHa ab.
CHOBa ,l(06aBbTe c1'peJIKy, qT06bI yKa3aTb, B KaKOM HalIpaBJIeHHH ,l(eHcTByeT
CRJIa.
. AHaJIOrHqHbIM ClIoc060M ,l(06aBbTe OCTaJIbHbIe CRJIbI TaK, qT06bI OHH CJIe,l(O-
BaJIH no nopMKy B COOTBeTCTBHH C 6yJ(BeHHbIMH 0603HaqeHIDIMH.
. HaKOHeu, pe3YJIbTHpyroII(yID CRJIY (FR) MO)I{HO onpe,l(eJIHTb, COe,l(HHeHIDI
TOqKH d H d' Ha ,l(HarpaMMe YCRJIHH. 06paTHTe BHHMaHHe, qTO pe3YJIbTHpyro-
2.3. BeICmopHble OUll2pflMMbl CUll: zparjJu'tecICoe peUleHue
IUasI CHJIa HalIpaBJIeHa rrpoTHB 06lI(ero HalIpaBJIeHIDI CHJI, 3an;aHHbIX Ha ,[(Ha-
rpaMMe YCHJIHH. llpH He06xo,[(HMOCTH pe3YJIbTHpyroII(yID CHJIY Terrepb MOXHO
rrepeHecTH Ha cxeMY KOHCTPYKUHH, qT06bI lIOKa3aTb ee BeJIHqHIfY H HarrpaB-
JIeHHe OTHOCHTeJIbHO TOqKH P.
. lloMHHTe, qTO pe3YJIbTHpyrolI(asI CHJIa MoxeT 3aMeHHTb Bce 3an;aHHbIe CHJIbI
H Bce xe OKa3bIBaTb TO xe caMoe B03,[(eHCTBHe Ha TOqKy P.
. ECJIH 6bI 1'pe60BaJIOCb HaHTH ypaBHOBeIIIHBalO1I(yID CHJIy, TO ee BeJIHqHHa
paBH.HJIaCb 6bI BeJIHqHHe pe3YJIbTHpyrolI(eH CHJIbI, HO ,[(eHCTBOBaJIa 6bI 3Ta
CHJIa B lIpOTHBOlIOJIO)I{HOM HalIpaBJIeHHH. OHa 6bma 6bI HalIpaBJIeHa B 06-
lI(eM HalIpaBJIeHHH Bcex 3an;aHHbIX CHJI Ha ,[(HarpaMMe YCHJIHH.
2.3.7. HenepeCeKSIOUCJfeCfI KonnSHspHble CJfnbl
(sepesolfHblH MHoroyrOn&HJfK)
KaK CJIe.nyeT H3 Ha3BaHIDI, HelIepeCeKalOlI(HeCR KOIIJIaHapHbIe CHJIbI JIeXaT B O,[(HOH
IIJIOCKOCTH, HO B03,[(eHCTByroT He Ha 0,[(1fY H 1)' xe TOqKY (T.e. HeT 06lI(eH TOqKH rrpH-
JIOXeHIDI CHJI). llpHMep lIOKa3aH Ha pHC. 2.9, a. ECJIH lIpHMeHHTb MeTO,[( lIOC1'poeHIDI
,[(HarpaMMbI MaKCBeJIJIa- KpeMOHbI, TO Ha OCHOBaHHH cxeMbI KOHC1'pYKUHH pe3YJIb-
mpyrolI(asI CHJIa (FR) MoxeT 6bITb OlIpe,[(eJIeHa 06bIqHbIM ClIoc060M H3 ,[(HarpaMMbI
YCHJIHH, KaK lIOKa3aHO Ha pHC. 2.9, 6. O,[(HaKO,LVIR Toro, qT06bI OlIpe,[(eJIHTb lIOJIOXe-
HHe H JIHHHIO ,[(eHcTBIDI pe3YJIbTHpyrolI(eH CHJIbI, He06xo,[(HMO rrOC1'pOHTh BepeBOq-
HbIH MHoroyrOJIbHHK, KaK lIOKa3aHO Ha pHC. 2.9, B, CJIe,ayroII(HM 06pa30M:
F3
d
c
c
A
F3
b
a
D
F R - pe3YJ1bTVlpYIOw.a51 CVI-
J1a. Ee BeJ1V1"1V1Ha OnpeAeJ1f1-
eTCfI Vl3 AViarpaMMbl YCVI-
J1V1 , a ee n0J10)l(eHVle VI
J1V1HVl5I Ae CTBVl5I OnpeAeJ1f1-
IOTC5I Vl3 BepeBO"lHOrO MHO-
royrOJ1 bH VI Ka.
a
w ------
\
\
(, \
\
\ I
\ / ' y
\ /
\ //
\ /
\ /
F3
.
B
Pac. 2.9. BepeBOqHbIH MHoroyrOJIbHHK:
a - cxeMa KOHCTPYKUHH;
6 - ,n;HarpaMMa YCHJIHH (HapHcoBaHa B MacllITa6e);
B - BepeBOqHbIH MHoroyrOJIbHHK (HapHcoBaH B MacllITa6e)
. HapHCyHTe ,[(HarpaMMY CHJI (pHC. 2.9, 6) 06bIqHbIM crroc060M H HaH.nHTe Be-
JIHqHHY H HarrpaBJIeHHe pe3YJIbTHpyroI.l..(eH CHJIbI (F R ), orrpe,[(eJIReMbIe BeKTO-
pOM ad.
. BbI6epHTe TOqKy rrOJIIOCa 0 TaK, qT06bI OHa HaXO,[(HJIaCb BHYTPH HJIH cHapy-
)l(H ,[(HarpaMMbI YCHJIHH, H coe,[(HHHTe 31)' TOqKy rrOJIlOca 0 C KIDK.n;bIM H3 yr-
F/la8a 2. HH:JICeHepHaJl cmamU1ca
JIOB ,l(HarpaMMbI YCHJIHH, KaK lIOKa3aHO Ha pHC. 2.9, 6. TIOJIOXeHHe TOqKH
lIOJIIOCa 0 He HMeeT lIpHHUHlIHaJIbHOrO 3HaqeHIDI, H OHa MoxeT 6bITb pa3Me-
lI(eHa TaM, r,l(e 3TO HaH60JIee Y,l(06HO.
. 113 JII060H TOqKH W, JIeXalI(eH Ha JIHHHH ,l(eHCTBIDI CHJIbI F 1 , lIpOBe,l(HTe lIP.H-
MyIO qepe3 06JIaCTb A, lIapaJIJIeJIbHO IIp.HMOH Oa Ha ,l(HarpaMMe YCHJIHH. 3Ta
IIp.HMasI lIOKa3aHa Ha pHC. 2.9, B.
. 113 TOqKH W qepe3 06JIaCTb B lIpOBe,l(HTe IIp.HMyIO WX, lIapaJIJIeJIbHyIO IIp.HMOH
Ob Ha ,l(HarpaMMe YCHJIHH H lIepeceKalO1I(yID JIHHHIO ,l(eHCTBIDI CHJIbI F 2 B
TOqKe X. 3Ta JIHHIDI lIOKa3aHa Ha pHC. 2.9, B.
. TIpO,l(OJDKaHTe lIOC1'poeHHe, lIOKa IIp.HMbIe He 6y,l(yr lIpOBe,l(eHbI qepe3 Bce 06-
JIaCTH; lIO.JIyqHBIIIasIC.H 06JIaCTb ,l(OJDKHa TelIepb HalIOMHHaTb pHC. 2.9, B.
TIpRMbIe, lIapaJIJIeJIbHbIe Oa HOd, TelIepb MO)I{HO lIpO,l(JIHTb ,l(0 me lIepeCeqe-
HIDI B TOqKe Z. TIpoBe,l(HTe qepe3 TOqKy Z IIp.HMyIO, lIapaJIJIeJIbHyIO ad Ha ,l(Ha-
rpaMMe YCHJIHH, qT06bI lIpe,l(CTaBHTb JIHHHIO ,l(eHCTBIDI BeKTOpa pe3YJIbTHpy-
IOlI(eH CHJIbl FR'
CJIe.nyeT oTMeTHTb, qTO, XOT.H p83JIOXeHHe CHJI H CHCTeM CHJI rpa<pWleCKHMH
MeTO,l(aMH .HBJI.HeTCR lIpOCTbIM H lIpRMbIM ClIoc060M, TOqHOCTb 3Toro clIoc06a 3aBH-
CHT OT MacIIITa6a pHcYHKa H KaqeCTBa lIoc1'poeHIDI. ECJIH 1'pe6yroTCR 60JIee TOqHbIe
pe3YJIbTaTbI, me MO)I{HO lIO.JIyqHTb MaTeMaTWleCKHMH BbNHCJIeHIDIMH, HClIOJIb3YR
TpHroHoMe1'pHIO.
2.4. MOMeHTbl CMn, u.eHTp TR>KeCTM
M u.eHTpbl TR>KeCTM nno aAeM
2.4. 1. MOMeHTbl CJfn
Ha pHC. 2.10, a lIOKa3aHO, KaK raeqHbIH KJIlOq HClIOJIb3yeTC.H ,l(JUI lIOBopOTa raHKH.
CHJIa (F) He ,l(eHcTByeT HelIOCpe,l(CTBeHHO Ha raHKy, BMeCTO 3Toro OHa ,l(eHcTByeT
Ha paCCTO.HHHH (d) OT OCH raHKH. TIPH 3TOM C03,l(aeTCR BpalI(alOlI(ee YCHJIHe, KOTO-
poe Ha3bIBaeTCR MOMeHTOM CHJIbI OTHOCHTeJIbHO OCH raHKH. Ero TaIOKe Ha3bIBalOT
BpalI(alOlI(HM MOMeHTOM HJIH lIapoH CHJI, HO Bce 3TH TepMHHbI 03HaqalOT O,l(HO H TO
xe. PaCCTORHHe (d) Ha3bIBaeTCR TIJIeqOM CHJIbI HJIH ,l(JIHHOH pbIqara, 06a TepMHHa
RBJI.HIOTCR B3aHM03aMeH.HeMbIMH. MaTeMaTHqeCKH 3TO MO)I{HO BbIpa3HTb CJIe,l(yID-
II(HM 06pa30M:
M = F x d,
r,l(e: M - MOMeHT CHJIbI (HM); F - lIpHJIOXeHHasI CHJIa (H); d - TIJIeqo CHJIbI
(,l(JIHHa pbNara) (M).
llpUMe"laHue.
CYIUeCTBeHHo, qTO TIJIeqo CHJIbI (d) H3MepReTC.H lIeplIeH;:I;HKyJI.HpHO JIHHHH ,l(eii-
CTBIDI CRJIbI. ECJIH CHJIa HarrpaBJIeHa lIO,l( yrJIOM, KaK lIOKa3aHO Ha pHC. 2.10, 6, 3<p-
<peKTHBHasI ,l(JIHHa raeqHOrO KJIlOqa YMeHbIIIaeTCR. B 3TOM c.JIyqae ypaBHeHHe 6Y,l(eT
BbIr.JUl)]:eTb CJIe,l(yIDII(HM 06p830M:
M = F x de'
r,l(e: M - MOMeHT CHJIbI (HM); F - lIpHJIOXeHHasI CHJIa (H); de - 3<p<peKTHBHOe
IIJIeqo CHJIbI (,l(JIHHa pbIqara) (M).
a
6
2.4. MOMeHmbl CWl, eHmp mJI:JICecmu u eHmpbl mJI:JICecmu fl./lOU4aOeU
F
rae"lHblVi KJ11O"I
I
I
d
I ·
AnVlHa (d)
rae"lHblH KJ11O"I
I
/
Puc. 2.10. nOBOpaQHBaIOII(He MOMeHTbI
(,
.
2.4.2. npJfHqJfn MOMeHTOB (JfCnOn&3yeMsfI TepMJfHOnOrJffl)
Toqu onopld
UJIeqo CHJILI
MOMeHT no
qaCOBOH CTJ)eJIKe
MOMeHT npOTHB
qaCOBOH CTpeJiKH
Pe3YJILTHPYJOIIUlH
MOMeHT
ToqKa (ueH1'p) HJIH OCb lIOBopOTa, BOKpyr KOTOpOH lIpOHCXO,l(HT
HJIH MoxeT lIpOHCXO,l(HTb BpalI(eHHe.
PaCCTORHHe Me)K,[{y JIHHHeH ,l(eHCTBIDI lIpHJIOXeHHOH CHJIbI H
TOqKOH OlIOpbI, H3MepeHHoe lIO,l( lIpRMbIM yrJIOM K JIHHHH ,l(eH-
CTBIDI CHJIbI. ( \
JII060H MOMeHT CHJIbI, KOTOpblli IIOBOpaqllBaeT HJIII CT:p(¥IITCSI
lIOBepHYTb TeJIO BOKpyr ero TOqKH OlIOpbI B HalIpaBJIeHHH lIO qa-
COBOH C1'peJIKe. MOMeHTbI lIO qaCOBOH C1'peJIKe lIpHH.HTO CqHTaTb
lIOJIO)I{HTeJIbHbIMH (+), KaK lIOKa3aHO Ha pHC. 2.11.
JII060H MOMeHT CHJIbI, KOTOpbIH lIOBOpaqHBaeT HJIH C1'peMHTCR
lIOBepHYTb TeJIO BOKpyr ero TOqKH onopbI B HanpaBJIeHHH lIpO-
THB qaCOBOH C1'peJIKH. MOMeHTbI lIpOTHB qaCOBOH C1'peJIKH lIPH-
H.HTO CqHTaTb 01'pHuaTeJIbHbIMH (-), KaK lIOKa3aHO Ha pHC. 2.11.
Pa3HocTb no BeJIHqHHe Me)l{)J;Y CYMMapHbIM MOMeHTOM lIO qaco-
BOH C1'peJIKe H CYMMapHbIM MOMeHTOM lIpOTHB qaCOBOH C1'peJIKH.
F/la8a 2. HH:JICeHepHaJl cmamUKa
I
A- TO'lKa onopbl
npOTVlB "IaCOBO CTpeJ1KVI
(-)
no "IaCOBO CTpeJ1Ke
(+)
Pac. 2.11. MOMeHTbI no qaCOBOH H npOTHB qaCOBOH CTpeJIKH
2.4.3. npJfHqJfn MOMeHTOB
Arrre6paWleCKa.H CYMMa MOMeHTOB HeCKOJIbKHX CHJI, ,neHcTByroII(HX OTHOCHTeJIbHO
JII060H TOqKH, paBHa pe3YJIbTHpyrolI(eMY MOMeH1)' CHJIbI OTHOCHTeJIbHO 3TOH TOqKH.
MaTeMaTWleCKH 3TO MO)I{HO BbIpa3HTb CJIe,l(yIDI.I..(HM 06pa30M:
M R =Ml +M 2 +(-M3)+...+Mn'
r,ne: M R - pe3YJIbTHpyrolI(HH MOMeHT CHJIbI; M I , ..., M n - JII060e KOJIHqeCTBO MO-
MeHTOB, ,neHcTByroII(HX OTHOCHTeJIbHO O,nHOH H TOH xe TOqKH OlIOpbI.
IIoMHume. TIOJIO)I{HTeJIbHbIe MOMeHTbI 6y,nyr ,neHCTBOBaTb B HalIpaBJIeHHH lIO
qaCOBOH C1'peJIKe, Tor,na KaK OTpHuaTeJIbHbIe MOMeHTbI (TaKHe KaK -M 3 ) 6y.nyr ,neH-
CTBOBaTb B HalIpaBJIeHHH lIpOTHB qaCOBOH CTpeJIKH.
TIpHMeH.H.H BbIIIIeynOM.HHYTbIe lIpHHU;HlIbI K pbIqary Ha pHC. 2.12, a, BbIqHCJIHM:
1. BeJIHqHHY pe3YJIbTHpyrolI(eH CHJIbI.
2. BeJIHqHHY pe3YJIbTHpyrolI(erO MOMeHTa.
3. TIOJIOXeHHe JIHHHH ,neHcTBIDI pe3YJIbTHpyrolI(eH CHJIbI.
1. TIOCKOJIbKy JIHHHH ,neHcTBIDI lIpHJIOXeH-
HbIX CHJI, ,neHcTByroII(HX Ha pbIqar, lIOKa3aHHbIH
Ha pHC. 2.12, a, lIapaJIJIeJIbHbI o,nHa ,npyrOH, pe-
3YJIbTHpyrolI(asI CHJIa (F R ) MoxeT 6bITb lIo.rryqeHa
lIpOCTbIM CJIOXeHHeM H BbJqHTaHHeM:
2M
2M
F 1 = 25 H
F 2 = 40 H
. CHJIbI FI H F 2 CTpeM.HTCR lIepeMeCTHTb
pbIqar BBepx. OHH ,neHCTByroT B O,nHOM H
TOM xe HalIpaBJIeHHH, rr03TOM)' HX MOXHO
CJIO)I{HTb.
. CHJIa F3 ,neHcTByeT B lIpOTHBOlIOJIO)I{HOM
HalIpaBJIeHHH, CJIe,nOBaTeJIbHO, ee CJIe.nyeT a
BbIqeCTb H3 CYMMbI FI H F 2 .
TI03TOMY:
F R = FI + F 2 + F3 = 25 H + 40 H + 50 H = 15 H.
2. HaitneM BeJIHqHHY pe3YJIbTHpyrolI(erO MO-
MeHTa (M R ).
MOMeHTbI lIO qaCOBOH CTpeJIKe (+):
TO"lKa onopbl .
F 2 = 50 H
3 M
2M
6
F R = 15 H
M I = FI x (2 M + 2 M) = 25 H x 4 M = 100 HM.
Pac. 2.12. npHMeHeHHe npHHUH-
na MOMeHTOB
2.4. MOMeHmbl CUll, Z4eHmp mJI:JICecmu u Z4eHmpbl mJI:JICecmu n./loU(aoeu
M 2 = F 2 x 2 M = 40 H x 2 M = 80 HM.
MOMeHT lIpOTHB qaCOBOH CTpeJIKH (-):
M3 = F3 x 3 M = 50 H x 3 M = 150 HM.
Pe3YJIbTHpyrolI(HH MOMeHT:
M R = M I + M 2 - M3 = 100 HM + 80 HM - 150 HM = 30 HM.
3. QT06bI HaHTH lIOJIOXeHHe JIHHHH ,l(eHCTBIDI pe3YJIbTHpyrolI(eH CHJIbI (F R ),
06'be,l(HHHM pe3YJIbTaTbI 1 H 2. 06paTHMcR K pHC. 2.12, 6.
M R = F R x d = 30 HM.
II03TOMY:
30 HM = 15 H x d,
d = 30 HM/15 H = 2 M.
TaKHM 06pa30M, CHJIbI F I , F 2 H F3 MOryr 6bITb 3aMeHeHbI O,l(HOH CHJIOH F R ,
.neHcTByrolI(eH Ha paCCTO.HHHH 2 M OT TOqKH OlIOpbI. TIOCKOJIbKy M R lIOJIO)I{HTeJIeH,
CHJIa F R 6Y,l(eT lIepeMelI(aTbCR HJIH C1'peMHTbC.H lIepeMeCTHTb pbIqar B HalIpaBJIeHHH
no qaCOBOH C1'peJIKe, TaKHM 06pa30M, CHJIa F R 6Y,l(eT ,l(eHCTBOBaTb B HalIpaBJIeHHH
BBepx, KaK lIOKa3aHO Ha pHCYHKe.
B lIpHMepe H3 lIpe,l(bl,l(ylI(ero pa3,l(eJIa MOMeHTbI, ,l(eHcTByroII(He B lIpOTHBOlIOJIOX-
HbIX HanpaBJIeHIDIX, He 6billH paBHbI. B HTore 3TO lIpHBO,l(HJIO K TOMY, qTO pe3YJIb-
THpyrolI(asI CRJIa CTaHOBHJIaCb HJIH C1'peMHJIaCb CTaTb lIPHqHHOH B lI(eHIDI OTHOCH-
TeJIbHO ueH1'pa BpalI(eHIDI (TOqKH OlIOpbI).
Ha pHC. 2.13 lIOKa3aHbI lIpOCTbIe BeCbI, B qaIIIKax KOTOpbIX MaCCbI M I H M 2
paBHbI, TaK qTO BeCbI HaxO,l(HTCR B COCTORHHH paBHOBeCIDI, KOpOMbICJIO BeCOB - B
ropH30HTaJIbHOM lIOJIOXeHHH. TIOCKOJIbKy CHJIa TIDKeCTH ,l(eHcTByeT O,l(HHaKOBO Ha
M I H M 2 , CHJIbI FI H F 2 TaIOKe paBHbI. CHJIa peaKUHH OlIOpbI (R) paBHa CYMMe Ha-
npaBJIeHHbIX BHH3 CHJI.
CHJIbI paBHOY,l(aJIeHbI OT TOqKH OlIOpbI, TaK qTO lIOBOpaqHBalOlI(He MOMeHTbI TaK-
xe paBHbI. TIOCKOJIbKy lIOBOpaqHBalOlI(He MOMeHTbI ,l(eHcTByroT B lIpOTHBOlIOJIO)I{HbIX
HanpaBJIeHIDIX, 3TH MOMeHTbI TaIOKe HaxO,l(HTC.H B paBHOBeCHH. OHH ypaBHOBeIIIHBa-
lOT ,lij)yr ,l(pyra, H KOpOMbICJIO BeCOB He C1'peMHTCR lIoBepHyrbCR. 3TO MO)I{HO c<pop-
MyJIHpOBaTb CJIe,ayrolI(HM 06pa30M.
ECJIH TeJIO no,n; B03,n;eicTBHeM MHOrux CHJI
HaxO,ZJ;HTCJI B COCTOJlHHH paBHOBeCHJI (c6aJIaHCH-
pOBaHHoM COCTOJlHHH), TO OTHOCHTeJILHO JII060i
TO'lKH MOMeHTLI no 'IaCOBOH CTpeJiKe paBHLI MO-
MeHTaM npoTHB qacoBoi CTpeJiKH OTHOCHTeJILHO
TOH )Ke caMOH TO'lKH.
DOJIee KpaTKO MO)I{HO CKa3aTb TaK.
AJIre6paH'leCKaB cYMMa MOMeHTOB OTHOCH-
TeJlLHO JII060H TOqKH paBHa HyJIIO.
2.4.4. PSSHOSeCJfe
"
F 1
F 2
F R
Pac. 2.13. npOCTbIe BeCbI
(::, F/la8a 2. HH:JICeHepHf1Jl cmamUlCa
,lVrn TeJIa, HaxO,lUllI(eroc.H B COCTORHHH paBHoBecIDI, ,l(OJDKHbI BbIlIOJIH.HTbC.H CJIe-
,l(yK>II(He YCJIOBIDI.
. Arrre6paWlecKasI cYMMa ropH30HTaJIbHbIX CHJI, ,l(eHcTByroII(HX Ha TeJIO,
,l(OJDKHa paBH.HTbC.H H)'JIIO, L F H = O.
. Arrre6pawIecKasI cYMMa BepTHKaJIbHbIX CHJI, ,l(eHcTByroII(HX Ha TeJIO, ,l(OJDKHa
paBH.HTbCR H)'JIIO, L Fv = O.
. Arrre6paWlecKasI cYMMa MOMeHTOB CHJI, ,l(eHcTByroII(HX Ha TeJIO, ,l(OJDKHa paB-
H.HTbC.H H)'JIIO, LM = O.
Ha pHC. 2.14 lIOKa3aH pbJqar, 3a-
KpeTIJIeHHbIH B ueH1'pe Ha OCH. JIHHIDI
,l(eHCTBIDI CHJIbI F 1 CMelI(eHa OT ueH1'pa
Ha 2 M BJIeBO H C1'peMHTCR C006lI(HTb
Teny MOMeHT lIpOTHB qaCOBOH c1'peJI-
KH. JIHHIDI ,l(eHCTBIDI CHJIbI F 2 CMelI(e-
Ha OT UeH1'pa Ha 3 M BlIpaBO H c1'pe-
MHTC.H C006lI(HTb TeJIY MOMeHT lIO qa-
COBOH C1'peJIKe. ECJIH BeJIWlHHa F 2
paBHa 20 H, BbIqHCJIHM:
F 1
F 2 = 20 H
F R
Puc. 2.14. CHJIbI B paBHOBeCHH
1. BeJIWlHHY CHJIbI F 1 , He06xo,l(HMyID ,l(JUI Toro, qT06bI pbJqar HaxO,l(HJIC.H B co-
CTO.HHHH paBHOBeCIDI.
2. BeJIHqHH)' CHJIbI peaKUHH (F R ) B TOqKe OlIOpbI.
,lVrn paBHOBeCIDI:
MOMeHTbI lIO qaCOBOH C1'peJIKe = MOMeHTbI lIpOTHB qaCOBOH C1'peJIKH
(20 H x 3 M) = (F) x 2 M)
F 1 = (20 H x 3 M)/2 M = 30 H
CHJIa peaKUHH F R , ,l(eHcTByrolI(asI BBepx, paBHa lIO BeJIWlHHe H lIPOTHBOlIOJIO)l{-
Ha lIO HalIpaBJIeHHIO CYMMe CHJI F 1 H F 2 , ,l(eHcTByroII(HX BHH3. TI03TOMY:
R = F 1 + F 2 = 20 H + 30 H = 50 H
Ha pHC. 2.15 lIOKa3aHa lIpOCTasI 6aJIKa Ha ,l(BYX OlIOpax, paClIOJIOXeHHbIX C ,l(BYX
KOHUOB. TIOCKOJIbKy OHa HaxO,l(HTCR B paBHOBeCHH, BpalI(alOlI(HH MOMeHT OTCyrCT-
ByeT H CHJIbI peaKUHH OlIOp R A H R B MOryr 6bITb BbJqHCJIeHbI C lIOMOlI(blO lIPHHUH-
lIa MOMeHTOB. 3TO MOXHO BbIlIOJIHHTb, BbJqHCJI.H.H MOMeHTbI OTHOCHTeJIbHO KIDK;J;OH
H3 OlIOp lIOOqepe,l(Ho.
3M
4M
3 M
600 H
500 H
R A
R B
Puc. 2.15. BbIqHCJIeHHe CHJI peaKI(HH onopbI
2.5. Pa3H06uonocmu pbl'laZ06
QT06bI HaHTH BeJIHtlHHY R A , onpe,n;eJIHM MOMeHTbI OTHOCHTeJIbHO TOqKH npHJIo-
xeHIDI R B , C TeM qT06bI YC1paHHTb 31)' CHJIy H3 paCCM01peHIDI npH nepBOHaqaJIb-
HbIX BbIqHCJIeHIDIX. nOCJIe 3Toro OCTaeTC.H TOJIbKO o,n;Ha HeH3BeCTHasI BeJIHtlHHa,
KOTOpyro MO)I{HO BbJqHCJIHTb CJIe,n;yroII(HM 06pa30M:
MOMeHTbI no qaCOBOH C1peJIKe = MOMeHTbI npOTHB qaCOBOH C1peJIKH
R A x 10 M = (600 H x 7 M) + (500 H x 3 M)
R A x 10 M = 4200 HM + 1500 HM
R A x 10 M = 5700 HM
R A = 5700 HM/I0 M
R A = 570 H
AHaJIOrHtlHO, qT06bI HaRTH BeJIHtlHHY R B , onpe,n;eJIHM MOMeHTbI OTHOCHTeJIbHO
TO'IKH npHJIOXeHIDI R A , C TeM qT06bI YC1paHHTb 31)' CHJIy H3 paCCM01peHIDI npH
nepBOHaqaJIbHhIX BbIqHCJIeHIDIX. nOCJIe 3Toro OCTaeTC.H TOJIbKO o,n;Ha HeH3BeCTHasI
BeJIH1IHHa, KOTOpyro MO)I{HO BbJqHCJIHTb CJIe,n;yrom:HM 06pa30M:
MOMeHTbI no qaCOBOH c1peJIKe = MOMeHTbI npOTHB qaCOBOR C1peJIKH
(600 H x 3 M) + (500 H x 7 M) = R B x 10 M
1800 HM + 3500 HM = R B x 10 M
5300 HM = R B x 10 M
R B = 5300 HM/I0 M
R B = 530 H
nOCKOJIbKY CHCTeMa CHJI HaxO,n;HTC.H B paBHOBeCHH, CyMMa CHJI, HanpaBJIeHHbIX
BHH3, ,n;OJDKHbI 6bITb paBHa CyMMe CHJI, HanpaBJIeHHbIX BBepx.
CJIe,n;oBaTeJIbHo:
R A + R B = 600 H + 500 H
570 H + 530 H = 600 H + 500 H
1100 H = 1100 H
()
nOJIyqHBIIIeeC.H TO)l{,l(eCTBO no,n;TBep)l{,l(aeT KOppeKTHOCTb BbIqHCJIeHHH R A H R B . He
COIq>am:aHTe BbfqHCJIeHIDI, onpe,n;e.rnrn CHJIy pea HH TOJIbKO O,n;HOH onopbI H BbIqH-
TasI ee H3 CyMMbI CHJI, HanpaBJIeHHbIX BHH3. JII06asI oIIIH6Ka, BHeceHHasI B nepBO-
Haq8JIbHbIe BbIqHCJIeHIDI, nOBJIIDIeT Ha Bce ,n;aJIbHeHIIIHe paCqeTbI, H BbI.HBHTb ee 6y-
.neT HeB03MO)I{HO.
B BbIIIIenpHBe,n;eHHbIX npHMepax He ytlHTbIBaJIC.H Bec KOpOMbICJIa BeCOB H 6aJIKH.
Bec O,ZJ;HOpO,ZJ;HOH 6aJIK11 (KopOMLlCJIa) M01KllO paCCMaTpHBaTL KaK cocpe,n;OTO'leH-
nyIO CBJIY, JIHHHJI ,n;eacTBHJI KOTopoa npe,znIOJIaraeTCJI npoxo,ZJ;JIInea '1epe3 cepe,ZJ;HHy
,ZJ;JlllllLI 6UD.
2.5. Pa3HOBMAHOCTM pbl'larOB
PbIqarH no,n;pa3,n;eillIIOTC.H Ha pbJqarH nepBoro, BToporo H 1peTbero po,n;a (pHC. 2.16).
(QacTo BbI,ll;eillIlOT TOJIbKO pbJqarH nepBoro H BToporo po,n;a, npHHHMasI BO BHHMa-
HHe JIHIIIb B3aHMHoe pacnOJIOXeHHe TOqKH onopbI H TOqeK npHJIOXeHIDI CHJI. -
IIpUMe"t. nep.) B COOTBeTCTBHH C npHHnHnOM MOMeHTOB COOTHOIIIeHHe Me)l{){y Ha-
rpY3KOR (W), paCCTO.HHHeM OT HarpY3KH .no TOqKH onopbI (d 1 ), npHJIOXeHHOH CH-
JIOR (F) H paCCTO.HHHeM OT TOqKH npHJIOXeHIDI CHJIbI,n;O TOqKH onopbI (d 2 ) o,n;HHa-
F/la8a 2. HH:JICeHepHaR cmamU1ca
d 1
_1 4
.1
1 4
TO"lKa onopbl n pVlJ1araeMa51
HarpY3Ka (w) CVlJ1a (F)
a
I: .1
d 1 -I
npVlJ1araeMa51
CVlJ1a (F)
TO"lKa onopbl
6 HarpY3Ka (w)
d 1
npVlJ1araeMa51 CVlJ1a (F)
TO"lKa onopbl
HarPY3Ka (w)
B
PRC. 2.16. PblqarH:
a - nepBoro po,n;a;
6 - BToporo po,n;a;
B - TPeTbero po,n;a
KOBO ,l(.IDI Bcex pO.n;OB pbIqarOB H MoxeT 6bITb BbIpaxeHo MaTeMaTHqeCKH CJIe.nyro-
IUHM 06pa30M:
Wx d J = Fx d 2 .
CJIe.n;OBaTeJIbHO:
W=Fxd 2 /d l
H:
F= Wx d l /d 2 .
2.5. 1. P&llfSrJf nepsoro POAS
. TOtIKa orropbI HaxO,ll;HTC.H Mex.ay TOqKOH rrpHJIOXeHIDI CHJIbI H HarpY3KoH.
. I1pHJIaraeMasI CHJIa MeHbIIIe, qeM HarpY3Ka.
. TOqKa lIpHJIOXeHIDI CHJIbI rrpOXO,ll;HT 60JIbIIIHH rryTb, qeM HarpY3Ka.
. Pb:Nar lIepBoro pO,ll;a MO)I{HO paCCMa1pHBaTb KaK YBeJIHqHTeJIb CHJIbI.
2.6. I(eHmp tn.R:JICecmu, zeOMempU'IeCKUU 14eHmp tjJUZYPbl U pa8H08ecue
2.5.2. P&llfSrJf SToporo POAS
. TOtIKa rrpHJIOXeHIDI CHJIbI H HarpY3Ka pacrrOJIOXeHbI rro o,n;HY H TY xe CTOpO-
HY OT TOqKH orropbI, HO CHJIa ,n;eHcTByeT B HarrpaBJIeHHH, rrpOTHBOrrOJIO)I{HOM
HarpY3Ke.
. HarpY3Ka pacrrOJIOXeHa Me)l{){y TOqKOH rrpHJIOXeHIDI CHJIbI H TOtIKOM OrrOpbI.
. I1pHJIaraeMa.H CHJIa MeHbIIIe, qeM HarpY3Ka.
. TOqKa rrpHJIOXeHIDI CHJIbI rrpoxo,nHT 60JIbIIIHM rryrb, tIeM HarpY3Ka.
. PbItIar BToporo po,n;a MO)I{HO paCCMaTpHBaTb KaK YBeJIHqHTeJIb CHJIbI.
2.5.3. P&llfSrJf TpftT&erO POAS
. TOqKa rrpHJIO}l(eHIDI CHJIbI pacnOJIOXeHa Me)l(,l(y HarpY3KoM H TOtIKOH OnOpbI.
. I1pHJIaraeMaH CHJIa 60JIbIIIe, qeM HarpY3Ka.
. HarpY3Ka rrpoxo,n;HT 60JIbIIIHH rryTb, qeM TOqKa rrpHJIOXeHIDI CHJIbI.
. PbIqar 1'peTbero po,n;a MO)I{HO paCCMa1'pHBaTb KaK YBeJIHqHTeJIb paCCTO.HHIDI.
2.6. LJ.eHTp TSI>KeCTM, reOMeTpM'IeCKMM LJ.eHTp cl>Mrypbl
M paBHOBeCMe
2.6.1. LleHTp TflJlCeCTJf (TsepAoe Teno)
fpaBHTan;HOHHoe rrpHTIDKeHHe ,n;eHcTByeT Ha Bce qaCTHn;bI TBep,n0F TeJIa, )I{H,l(KO-
cm HJIH ra3a, KaK rrOKa3aHO Ha pHC. 2.17. I1pe,n;rrOJIaraeTCH, qTO JIHHHH ,neHcTBIDI
CRJI rrpHTIDKeHIDI OT,n;eJIbHbIX qaCTHn; rrapaJIJIeJIbHbI. ,l(aJIee rrpe.n;rrOJIaraeTC.H, qTO
3TH OT,n;eJIbHbIe CHJIbI rrpHTIDKeHIDI rrpH BbJqHCJIeHIDIX MO)I{HO 3aMeHHTb O,n;HOH pe-
3YJIbTHpyrom:eH CHJIOH, paBHoM CyMMe CHJI rrpHTIDKeHIDI OT,neJIbHbIX qaCTHn;. U;eH1'p
TIDKeCTH (G) TBep,n;oro TeJIa - 3TO TOqKa rrpHJIOXeHIDI pe3YJIbTHpyrom:eH rpaBHTa-
n;HOHHOH CHJIbI, T.e. TOtIKa rrpHJIOXeHIDI Beca
TeJIa. HarrpHMep, n;eH1p TIDKeCTH n;HJIHH,lI;pa C
rrOCTOHHHbIM rrOrrepeqHbIM CeqeHHeM JIe)I{HT
Ha ero OCH rrocepe,n;HHe Me)l(,l(y ,n;ByM.H OCHO-
BaHIDIMH. 3TOT H HeKOTopbIe ,n;pyrHe rrpHMe-
pbI rrpe,n;CTaBJIeHbI Ha pHC. 2.18. (nOIDITHe
n;eH1pa TIDKeCTH HMeeT CMbICJI TOJIbKO ,l(.IDI
TBep,n;oro TeJIa, HaXO,lUIm:eroc.H B O,n;HOpO,n;HOM
rrOJIe TIDKeCTH; ,l(.IDI rrpOH3BOJIbHOH MeXaHHqe-
CKOH CHCTeMbI BBO,n;HTC.H rrOIDITHe l(eH1pa
HHepn;HH, He CBH3aHHoe C CHJIOBbIM rrOJIeM.
,lLJm TBep,n;oro TeJIa rrOJIOXeHIDI n;eH1pa TIDKe-
cm H n;eHTpa HHepn;HH COBrran;aIOT. - IIpu- PRC. 2.17. l(eHTP TH)I{eCTH
Me . nep.)
\. \
JlIiIHIiISI, CTBIiISI_
pe3YJ1 bTVI PYIO w.e VI
CVlJ1b1 (Bec W)
CVlJ1a, AeVl-
CTBYIOw.a51
Ha "IaCTVlu.bl
w
F/la8a 2. HH:JICeHepHaR cmamU1ca
opMa TBep oro TeJIa
nMo.eDe a (
(pacCTOJlHHe x, n0K838HHoe
Ha pHCyuKe)
061.eM
IJ;HJIHH.D:P
h(2
1tr 2 h
C<pepa
R
41tr 3 /3
lloJIyc<pepa
3r,/8
21tr 3 /3
KoHYc
h
h/4
1tr 2 h /3
llHpaMH,lI;a
h/4
abh /3
Pac. 2.18. llOJIOXeHHe I(eHTPa TH)I{eCTH (G) ,lI;JIH HeKOTopbIX 06w;epacnpOCTPaHeH-
HbIX TBep,n;bIX TeJI
2.6.2. LleHTp TflJlCeCTJf HeOAHOpOAH&IX
Jf COCTSSH&IX TSepA&IX Ten
Ha pHC. 2.19 rrOKa3aH n;HJIHH,D;pWIeCKHH BaJI C ,n;BywI ,n;HaMe1paMH:
. G} - n;eH1p TIDKeCTH n;HJIHH,D;pa C 60JIbIIIHM ,n;HaMe1pOM, OH pacrrOJIOXeH Ha
OCH rrocepe,n;HHe Me)l(,l(Y OCHOBaHIDIMH 3Toro n;HJIHH,D;pa;
. G 2 - n;eH1p TIDKeCTH n;HJIHH,lI;pa C MeHbIIIHM ,n;HaMe1pOM; OH pacrrOJIOXeH Ha
OCH rrocepe,n;HHe Me)l(,l(Y OCHOBaHIDIMH 3Toro n;HJIHH,lI;pa;
. G - n;eH1p TIDKeCTH COCTaBHoro TBep,n;oro TeJIa KaK e,n;HHoro IJ;eJIoro; OH pac-
rrOJIOXeH Ha paCCTOHHHH d OT 6a30Boro TOpn;a BaJIa. Ero rrOJIOXeHHe MO)I{HO
orrpe,n;eJIHTb, rrpHMemrn rrpHHn;Hrr MOMeHTOB.
1. CYMMapHbIH Bec BaJIa paBeH CyMMe BeCOB ,n;BYX IJ;HJIHH,lI;pOB. To eCTh 10 KH +
+ 5 KH = 15 KH.
2.6. I(eHmp mH:JICecmu, zeOMempU'IeCKUU u,eHmp rjJUrypbl U pa8H08ecue
2M 2M
G1 G
--4----.- ----4---
1 M
10 KH
d
( 1 0 + 5) KH
5 KH
3M
PRC. 2.19. Onpe,n;eJIeHHe I(eH1'pa TH)I{eCTH Heo,n;Hopo,n;Horo TBep,n;oro TeJIa
2. CYMMapHbIH Bec B 15 KH 6y,n;eT npHJIOXeH B n;eH1pe TIDKeCTH G BaJIa, KaK
e)];HHOrO n;eJIoro, Ha HeKOTopOM paCCTOHHHH d OT TOtIKH OTCtIeTa P Ha 6a30BOM
TOpn;e B8JIa, OTHOCHTeJIbHO KOTOpOH onpe,n;eillIIOTC.H MOMeHTbI.
3. B 3TOM BbIqHCJIeHHH YCJIOBHO npe,n;nOJIaraeTCH, qTO MOMeHT G OTHOCHTeJIbHO
roqKH P npOTHBOnOJIOXeH no HanpaBJIeHHIO MOMeHTaM G l H G 2 , XOT.H Ha caMOM
)];eJIe Bce OHH ,n;eHCTByroT no qaCOBOH C1peJIKe.
MOMeHTbI no qaCOBOH C1peJIKe = MOMeHTbI npOTHB qaCOBOH C1peJIKH
(G} x 1 M) + (G 2 x 3 M) = (G x d)
(10 KH x 1 M) + (5 KH x 3 M) = (15 KH x d)
10 KHM + 15 KHM = 15 KH x d
25 KHM = 15 KH x d.
(',
II03ToMY:
d = 25 KHM/15 KH = 1,67 M.
TaKOH xe MeTO,n; MO)I{HO HCnOJIb30BaTh ,l(.IDI COCTaBHbIX TBep,n;bIX TeJI, eCJIH
TIJIOTHOCTH HX pa3JIHqHbIX 3JIeMeHTOB OTJIH'laIOTCH.
2.6.3. LleHTp TflJlCeCTJf (TOHKSfI nnSCTJfHs)
ECJIH 3JIeMeHTbI H3 TOHKoro JIHCTOBOro MeTaJIJIa HJIH xeCTKoro JIHCTOBOro IIJIaCTH-
Ka HMelOT nOCTOHHH)'IO TOJIIUHHY (ToHKHe IIJIaCTHHbI) H 3Ta TOJIIUHHa He3HatIH-
TeJIbHa no cpaBHeHHIO C IIJIOIUaL(blO, TO MO)I{HO nOJIaraTb, qTO HX n;eH1p TIDKeCTH
pacnOJIOXeH B n;eH1paJIbHOH TOqKe IIJIOII(aL(H.
. U;eH1p TIDKeCTH G np.HMoyrOJIbHOH TOHKOH IIJIaCTHHbI pacnOJIOXeH B TOqKe
nepeCeqeHIDI ,n;HarOHaJIeH IIJIaCTHHbI.
. U;eHTp TIDKeCTH G KpyrJIOM TOHKOH IIJIaCTHHbI pacnOJIOXeH B n;eH1pe Kpyra.
3-3255
F/la8a 2. HH:JICeHepHaJI cmamU1ca
2.6.4. reOMeTpJflfeCKJfe qeHTp&1 cpJfryp
I10IDITHe reOMe1pHqeCKOrO ueH1'pa OTHOCHTC.H K ,n;ByMepHOH IIJIOCKOH <pHrype, He
HMelOIUeti TOJIII(HHbI. Y Hee eCTb TOJIbKO IIJIOIUaLJ:b. TaK KaK IIJIOIUaLJ:b He HMeeT
TOJIIUHHbI, Y Hee HeT MaCCbI, Ha KOTOpyro MOrJIa 6bI ,n;eHCTBOBaTb CHJIa rpaBHTan;HH.
CJIe,n;OBaTeJlbHO, Y Hee HeT Beca. TepMHH «reOMe1pHtleCKHH n;eHTp» MO)I{HO HC-
rrOJIb30BaTb rrpHMeHHTeJIbHO K IIJIOIUaLJ:H ,n;ByMepHOH IIJIOCKOti <pHrypbI, aHaJIOrHtlHO
TOMY, KaK rrOIDITHe n;eH1'pa TIDKeCTH HCrrOJIb3yeTC.H ,l(.IDI TBep,nbIX IIJIaCTHH. I103TOMY
reOMe1pHqeCKHH n;eH1p <pHrypbI - 3TO TOqKa Ha IIJIOCKOH <pHrype, B KOTOpOti, KaK
rrpe,n;rrOJIaraeTCH, cocpe,n;OTOqeHa BC.H IIJIOIUaLJ:b. KaK H n;eH1p TIDKeCTH, reOMe1pHtle-
CKHH n;eH1'p <pHrypbI TaIOKe 0603HaqaeTC.H 6YKBOH G. I1pHMepbI rrOJIOXeHHH reo-
Me1pHqeCKHX n;eH1'pOB ,l(.IDI HeKOTopbIX <pHryp rrpHBe,n;eHbI Ha pHC. 2.20.
opMa WIOUWUI
a
KBa,npaT
a
IIpHMoyrOJIbHHK
Kpyr
IIoJIyKpyr
.c::
IIPHMOyrOJIbHbIH TpeyrOJlbHHK
b
PRC. 2.20. feOMeTpHqeCKHe I(eHTpbI <pHryp
2.6.5. PSSHOSeCJfe
PaCCTOJlHHe x PaCCTOJlHHe y lIJIoma,zu.
a/2
a 2
a/2
a/2
b/2
ab
r
1tr 2
r
4r/3n
nr 2 /2
r
b/3
h/3
bh/2
nOH.HTHe paBHOBeCIDI 6billO BBe,n;eHO B pa3,n;eJIe 2.4.4. Ha pHC. 2.21, a rrOKa3aH Me-
TaJIJIHqeCKHH CTepxeHb C rrOCTO.HHHbIM CeqeHHeM, 3aKpeIIJIeHHbIH Ha OCH, rrpoxo-
,lUIIUeH qepe3 ero n;eH1p, TaK, qTO CTepxeHb MoxeT cBo6o.ll;HO BpaIUaTbC.H, a TaIOKe
2.6. I(eHmp mR:JICecmu, zeOMempU'IeCKUU u,eHmp rjJU Pbl u pa8H08ecue
1 4
_I. 4
p
d 1
-I
o
/......
/; / )
I I
I I
I I
I I
Y I I
/ f ll
I I
II G
P
o
o
OCb Bpa-
w.eHVlS1
M 1
M 2
G
a
6
PRC. 2.21. PaBHoBecHe:
a - 6e3pa3JIHqHOe HJIH YCTOHqHBOe paBHoBecHe;
6 - HeycTOHqHBOe paBHoBecHe;
B - YCTOHqHBOe paBHOBeCHe
/
/
/ /1
/ /
// 1 //
/ /
\ //G
/ /
/0/
l.. /
....j
B
nOKa3aHO, qTO MOMeHTbI Bpam:eHIDI, ,n;eHcTByrom:He Ha K oe IIJIeqo CTep)l{ID(
BCJIe,n;CTBHe CHJIbI TIDKecTH, paBHbI rro BeJIHtlHHe H rrpoTHBOrrOJIO)I{HbI rro HarrpaBJIe-
HHIO. I103TOMY H,ZJ;eaJIbHO ypaBHoBeIIIeHHbIH cTepxeHb OCTaHeTCH B JII060M rrOJIO-
xeHHH, B KOTopoe 6y,n;eT rroBepHYT. B TaKOM cJIyqae rOBopHT, qTO cTepxeHb Haxo-
)];HTCH B COCTO.HHHH 6e3pa3JIHtlHOrO paBHoBecIDI.
Ha pHC. 2.21, 6 TaKoH xe CTepxeHb 3aKpeIIJIeH Ha OCH, He rrpOXO,lUIm:eH qepe3
ero n;eH1p, TaK, qTO O,n;HO IIJIeqo LUIHHHee, qeM ,n;pyroe. npH BepTHKaJIbHOM rrOJIO-
xeHHH CTep)l{ID(, KaK rrOKa3aHO Ha pHC. 2.21, 6, JIHHIDI ,n;eifcTBIDI BeKTO rrpe,n;-
CTaBJUIIOm:ero CHJIy TIDKeCTH, rrpoxo,n;HT qepe3 TOqKY orropbI H MOMeHT BpalI(eHIDI
OTcyrcTByeT. O,n;HaKo Terrepb CTepxeHb HaxO,n;HTC.H B COCTO.HHHH HeycTOHqHBOrO
paBHOBeCIDI, TaK KaK MaJIeHIIIHH rrOBopOT CTep)l{ID( rrpHBe,n;eT K CMem:eHHIO n;eH1'pa
TIDKeCTH B CTOPOHY OT BepTHKaJIH, KaK rrOKa3aHO Ha pHCyHKe. B pe3YJIbTaTe B03-
HHKHeT MOMeHT Bpam:eHIDI H CTepxeHb rrpH,ZJ;eT B ,n;BIDKeHHe, KOTopoe 6y,n;eT rrpo-
)];OJl)l{aTbC.H ,n;o Tex rrop, rrOKa n;eH1p TIDKeCTH 60JIee LUIHHHoro IIJIetIa He OKIDKeTC.H
Herrocpe,n;CTBeHHO rro,n; TOqKOH OrrOpbI. Tor,n;a MOMeHT Bpam:eHIDI HCqe3HeT H 6aJIKa
OCTaHOBHTC.H.
Ha pHC. 2.21, B rrOKa3aH CTepxeHb, y KOToporo n;eH1'p TIDKeCTH 60JIee LUIHHHO-
ro TIJIeqa pacrrOJIOXeH TOqHO rro,n; TOtIKOM OrrOpbI. CJIe,n;oBaTeJIbHO, MOMeHT BltClm:e-
u \ /
HID! OTcyrcTByeT, CTepxeHb He rro,n;BepraeTCH ero B03,n;eHCTBHIO H OCTaeTC.H a no-
)];BH)I{HbIM. Ha pHCyHKe TaIOKe rrOKa3aHO, qTO rrpH JII060M OTKJIOHeHHH CTep)l{ID( OT
BepTHKaJIH C03,n;aeTCH MOMeHT, rrpHBO,lUIm:HH CTepxeHb B ,n;BIDKeHHe, KOTopoe 6y,n;eT
npo,n;OJl)l{aTbCH ,n;o Tex rrop, rrOKa n;eH1p TIDKeCTH 60JIee LUIHHHoro IIJIeqa CHOBa He
OKIDKeTCH Herrocpe,n;CTBeHHO rro,n; TOqKOH orropbI. I103TOMY B TaKOM CJIyqae
rOBopHT, tITO CTepxeHb Haxo,n;HTCH B COCTO.HHHH YCTOHqHBOrO paBHOBeCIDI.
IIpuMe"taHue.
I1pH MaJIOM B03MYlI(eHHH TeJIO Bcer,n;a rrepexo,n;HT HJIH C1'peMHTCH lIepeHTH 113
COCTOHHHH HeYCTOHqHBOrO paBHOBeCIDI B COCTOHHHe YCTOHqHBOrO paBHOBeCID!.
F/la8a 2. HH:JICeHepHaR cmamU1ca
2.7. TpeHMe
BC.HKHH pa3, Kor,n;a O,n;HO TeJIO CKOJIb3HT HJIH KaTHTC.H rro ,n;pyrOM)', eM)' rrpOTHBO-
,n;eHcTByeT CHJIa COrrpOTHBJIeHIDI, KOTOpasI Ha3bIBaeTC.H CHJIOH 1peHIDI CKOJIbXeHIDI
(,n;BIDKeHIDI). ,l(axe Kor,n;a ,n;BIDKeHIDI He rrpOHcxo,n;HT, Ha TeJIO ,n;eHcTByeT CKpbITasI
CHJIa corrpOTHBJIeHIDI, CHJIa 1peHIDI rrOKOH. TpeHHe rrOKO.H, KaK rrpaBHJIO, 60JIbIIIe,
qeM 1peHHe CKOJIbXeHIDI. ,l(.mI rrpeo,n;OJIeHIDI 1peHIDI rrOKOH Me)l{){y ,n;BywI ,n;aHHbIMH
MaTepHaJIaMH H HaqaJIa ,n;BIDKeHIDI H}')I{Ha 60JIbIIIasI CHJIa, qeM ,l(.IDI rrO,LUJ;epXaHIDI
,n;BIDKeHIDI C rrOCTO.HHHOH CKOpOCTblO.
2.7. 1. CMS3KS
TpeHHe Me)l{){y rrOBepXHOCT.HMH CKOJIbXeHIDI HJIH KaqeHIDI H H3HOC rroBepXHocTeH
MO)I{HO cyw;eCTBeHHO yMeHbIIIHTb, eCJIH o,n;HY rrOBepXHOCTb MaTepHaJIa OT,n;eJIHTb OT
,n;pyrOH cooTBeTcTByroIUeH IIJIeHKOH CMa3KH. ,l(.mI CMa3KH 6bIC1p0 ,n;BIDKYID:HXC.H rro-
BepXHocTeH, rro,n;BepraIOIUHXC.H OTHOCHTeJIbHO MaJIbIM HarpY3KaM, 06bIqHO HCrrOJIb-
3yroTC.H MaCJIa, a ,l(.IDI CMa3KH Me,n;.rreHHO ,n;BIDKYID:HXC.H rroBepXHocTeH, rro,n;BepralO-
IUHXCH 60JIbIIIHM HarpY3KaM, KaK rrpaBHJIO, HCrrOJIb3yroTC.H )l{HpbI. ECJIH 3a30p Mex-
l1.Y rrOBepXHOCT.HMH 3arrOJIHeH, TO cyxoe 1peHHe YC1paHeHO, H rrpeo,n;OJIeBaTb rrpHXO-
,n;HTCH TOJIbKO )l{H)];KOCTHoe 1peHHe, T.e. BHYTPeHHee 1peHHe Te eH cpe,n;bI, HJIH
B.H3KOCTb CMa3KH. CMa3Ka He TOJIbKO yMeHbIIIaeT H3HOC H 1peHHe, HO TaIOKe 3aIUH- I
IUaeT CKOJIb3.HIUHe rrOBepXHOCTH OT KOpp03HH H yMeHbIIIaeT TeIIJIOBbI,lI;eJIeHHe, a
3HaqHT, rrOTepH 3HeprHH. JII060e BbI,ll;eillIlOIUeeC.H TeIIJIO pacceHBaeTC.H CMa3KOH.
2. 7.2. 3SKOH&1 TpeHlffl
Ha BeJIHqHHY 1peHIDI Me)l{){y ,n;BywI rrOBepXHOCT.HMH CKOJIbXeHIDI HJIH KaqeHIDI
BJIIDIIOT CJIe,n;yroIUHe <paKTOpbI.
. C1pYKTYPa corrpHKaCalOIUHXC.H rroBepXHocTeH. fJI8)];KOCTb rroBepXHocTeH
yMeHbIIIaeT 1peHHe; HepOBHOCTH YBeJIHtlHBalOT 1peHHe.
. BH,lI; MaTepHaJIOB, HaxO,lUIIUHXC.H B KOHTaKTe (HarrpHMep, CTaJIb CKOJIb3HT rro
HeHJIOHY HaMHoro JIerqe, qeM rro pe3HHe).
. BeJIHqHHa HOpMaJIbHbIX (HarrpaBJIeHHbIX rro,n; rrp.HMbIM yrJIOM) CHJI rrpOTHBO-
,n;eHCTBIDI Me)l{){y rrOBepXHOCT.HMH.
. TpeHHe He 3aBHCHT OT IIJIOIU8)];H.
2.7.3. KoacpcpJfq1AeHT TpeHJffl
K03<P<P H D;HeHT 1peHIDI (J..1) ,l(.IDI rrapbI rroBepXHocTeH, HaxO,lUIII(HXC.H B KOHTaKTe,
orrpe,n;eillIeTC.H BbIpaxeHHeM:
J..1 = (cHJIa 1peHIDI Fj)/(cHJIa HOpMaJIbHOH peaKUHH orropbI Fn).
3TO rrOKa3aHO Ha pHC. 2.22. nOCKOJIbKY Fj H Fn BbIpaxalOTC.H B O,n;HHX H Tex xe
e,n;HHHD;ax H3MepeHIDI, HX OTHOIIIeHHe J..1 OKa3bIBaeTC.H 6e3pa3MepHOH BeJIHtlHHOH.
2. Z TpeHue 69'
CJIY'laH 1.
BJIOK BeCOM W T.HHyr no ropH30H-
TaJIbHOH nOBepXHOCTH, npHKJIaL(bIBasI
CHJIy BeJIHtlHHOH Fa, KaK nOKa3aHO Ha
pHC. 2.22. ECJIH 6JIOK ,n;BIDKeTC.H C no-
CTOHHHOH CKOpOCTblO HJIH Heno,n;BIDKeH,
TO Ha Hero ,n;eHcTByeT CHJIa conpOTHBJIe-
HID!, paBHasI no BeJIHqHHe H npOTHBO-
nOJIO)I{HasI no HanpaBJIeHHIO npHJIOXeH-
HOH CHJIe Fa. 3Ta CHJIa conpOTHBJIeHIDI
H eCTb CHJIa 1peHIDI Fj. CHJIa 1peHIDI
Bcer,n;a HanpaBJIeHa B CTOpOHY, npOTH-
BOnOJIO)I{Hyro ,n;BIDKeHHIO. TaKHM 06pa-
30M, B 3TOM c.rryqae:
Bec (W)
CVlJ1a Tpe-
HVl5I (F,)
npVlJ10)l(eH-
Ha51 CVlJ1a (Fa)
CVlJ1a HopMaJ1bHOVI
peaKu.VIVI onopbl (F n )
PRC. 2.22. TpeHHe
J.1 = FJFn = Fa/
. ECJIH CHJIa 1peHIDI paBHa npHJIOXeHHOH cHJIe, 6JIOK Heno,n;BIDKeH HJIH paBHo-
MepHo ,n;BIDKeTC.H H ,n;eHcTByroIUHe Ha Hero CHJIbI HaxO,ll;HTCH B paBHOBeCHH.
. ECJIH 6JIOK ,n;BIDKeTC.H C YCKopeHHeM, TO npHJIOXeHHasI CHJIa 60JIbIIIe, qeM
CHJIa 1peHIDI.
. CHJIa 1peHIDI MoxeT 6bITb MeHbIIIe HJIH paBHa npHJIOXeHHOH CHJIe. OHa HH-
Kor,n;a He MoxeT 6bITb 60JIbIIIe npHJIOXeHHOH CHJIbI. To eCTb CHJIa Fj paBHa
HJIH MeHbIIIe Fa H Fn paBHa HJIH MeHbIIIe
C.nyqaH 2.
ECJIH CHJIa (Fa) npHJIOXeHa K CKOJIb3.HIUeMy 6JIOKY no,n; yrJIOM 0, KaK nOKa3aHO
Ha pHC. 2.23, Tor,n;a CHJIa 1peHIDI Fj 6y,n;eT paBHa no BeJIHqHHe H npoTHBOnoJI6XHa
no HanpaBJIeHHIO ropH30HTaJIbHOH cocTaBillIlOIUeH CHJIbI (F h ), r,n;e Fh = Fa cosO.
BepTHKaJIbHasI COCTaBillIIOIUa.H CHJIbI Fv = Fa sinO. 3Ta CHJIa HanpaBJIeHa npOTHBO-
nOJIO)I{HO Becy W H, CJIe,n;OBaTeJIbHO, yMeHbIIIaeT HOpMaJIbH)'lO CHJIy pea HH ono-
pbI Fn. n03TOMY:
J.1 = Ff / Fn = (Fa cosO) / (W - Fa sinO).
TaK, eCJIH npHJIOXeHHasI CHJIa Fa ,n;eHcTByeT BHH3 no OTHOIIIeHHIO K ropH30HTa-
JIbHOH nOBepXHOCTH, Tor,n;a Fh 6y.neT YBeJIHtlHBaTb CHJIy HOpMaJIbHOH pea HH ono-
phI Fn. n03TOMy B 3TOM CJIyqae:
J.1 = Ff / Fn = (Fa cosO) / (W + Fa sinO).
Bec (W)
CVlJ1a TpeHVl5I (F,)
npVlJ10)l(eHHa51
CVlJ1a (Fa)
(
"- /;
BepTVlKaJ1bHa51 COCTaBJ151-
lOw.a51 CVlJ1bl Fv = Fa sine
Fn
PRC. 2.23. TpeHHe - CHJIa npHJIOXeHa no,n; yrJIOM
F/la8a 2. HH:JICeHepHaR cmamU1ca
B Ta6JIHD;e 2.3 rrpHBe,n;eHbI HeKOTopbIe THrrHqHbIe 3HaqeHIDI K03<P<PHD;HeHTa
1peHIDI ,lUIH pa3JIHqHbIX COqeTaHHM rroBepxHocTeH CKOJIbXeHIDI.
Ta6JI. 2.3. THrrHqHbIe 3HaqeHIDI K03<P<PHD;HeHToB TpeHIDI.
MarrepHaJIhI (cyxHe) p. MarrepH8JIhI (cyxHe) p.
CTaJIb no qyryHy 0,20 T OpM03HasI KOJIo,n;Ka no qyryHy 0,60
CTaJIb no JIa1)THH 0,15 Pe3HHa no aC<paJIbTy 0,65
qyryH no JIa1)THH 0,15 Pe3HHa no 6eTOHY 0,70
Koxa no qyryHy 0,55
2.7.4. Yron TpeHJffl
I10CKOJIbKy 06e CHJIbI Fj H Fn rrpHJIOXeHbI K CKOJIb3HIUeMY
6JIoKY, KOTOpbIH HaxO,n;HTCH B KOHTaKTe C ropH30HT8JIb-
HOM rrOBepXHOCTblO, B pe3YJIbTaTe BeKTOpHOrO CJIOXeHIDI
3THX CHJI, KaK rrOKa3aHO Ha pHC. 2.24, MO)I{HO rro.rrytIHTb
pe3YJIbTHpyrolI(ylO CHJIy peaKIJ;HH rrOBepXHOCTH Fro
TaK KaK CHJIbI Fj H Fn HarrpaBJIeHbI rro,n; rrp.HMbIM yr-
JIOM o,n;Ha K ,n;pyrOH:
tgq> = Ff / Fn,
HO
fl = Ff / Fn,
CJIe,n;OBaTeJIbHO:
tgq> = fl
YroJI <I> ,n;OCTHraeT MaKCHMaJIbHOrO 3HaqeHIDI rrpH
MaKCHMaJIbHOM 3HaqeHHH Fj. 3TO MaKCHMaJIbHOe 3Haqe-
HHe <I> Ha3bIBaeTCH yrJIOM 1peHIDI.
2.7.5. TpeHJfe HS HSKnOHHOH nnOCKOCTJf
Orrpe,n;eJIHM CHJIY Fa, lIpHJIOXeHH)'IO K TeJIY
BeCOM W, KOTOpas! T.HHeT ero BBepx rro IIJIOC-
KOCTH, HaKJIOHeHHOH rro,n; yrJIOM 0 K ropH-
30HT8JIH, eCJlH Fa ,n;eHcTByeT rro,n; yrJIOM <I> K
HaKJIOHHOH IIJIOCKOCTH, KaK rrOKa3aHO Ha
pHC. 2.25.
CHJIa Fa ,n;eHcTByeT rro,n; yrJIOM <I> K IIJIOC-
KOCTH, KaK rrOKa3aHO Ha pHC. 2.25, H Fn -
HOpMaJIbHas! peaKIJ;ID1 IIJIOCKOCTH, ,n;eMCTByro-
IUas! Ha TeJIO. I1pHpaBHHBaH KOMrrOHeHTbI
CHJI, lIeprreH,ll;HKyJI.HpHbIe HaKJIOHHOM IIJIOC-
KOCTH, rrOJIyqHM:
Fn + Fa sinq> = W cosO
Fn = W cosO - Fa sinq>
Fr
Fn
F,
PRC. 2.24. YroJI 1'peHHH
w
"
PRC. 2.25. TpeHHe Ha HaKJIOHHOH
nJIOCKOCTH:
Fa - npHJIOXeHHasI CHJIa; Fn - HOp-
MaJIbHaH peaKI(HH onopbI; Fj - npo-
THBo,n;eHCTBYIOw;aH CHJIa TpeHHH; W-
Bec TeJIa; fl - K03<P<PHI(HeHT 1'peHHH
2. 7. TpeHue 71
CHJIa TPeHIDI, lIpoTHBo,n;eHCTBYIOIUa.H ,n;BJDKeHHIO TeJIa, paBHa:
Ff = JJFn = J.l{W cose - Fa sin<p) (1)
IIpHpaBHHBa.H KOMlIOHeHTbI CHJI, lIapaJIJIeJIbHbIe HaKJIOHHOH IIJIOCKOCTH, lIO.rry-
qHM:
Fa COs<p = Ff + W sine
IIocJIe lIo,n;CTaHOBKH Fj H3 ypaBHeHIDI (1) lIo.rryqaeM:
Fa cos<p = J.l{W cose - Fa sin<p) + W sine
Fa cos<p = W(f.lCOSe + sin<p) - JJFa sin<p
Fa(f.l sin<p + cos <p) = W(f.lCOS e + sin<p)
Fa = [W(f.lCOSe + sin<p)] / [(f.lsin<p + cos<p)]
(2)
1. ECJIH Fa lIpHJIOXeHa lIapaJIJIeJIbHO IIJIOCKOCTH, TO <p = O. CJIe,n;OBaTeJIbHO,
sin <p = 0 H COS <p = 1. IIo,n;cTaBJIIDI 3TH 3HaqeHIDI B ypaBHeHHe (2), lIOJIyqHM:
Fa = [W(f.lCOS e + sine)] / (1 + 0)
Fa = W(f.lCOSe + sine)
2. ECJIH Fa lIpHJIOXeHa ropH30HTaJIbHO, TaK qTO OHa lIOMoraeT TeJIy,n;BHraTbC.H
BBepx lIO IIJIOCKOCTH, TO <p = -e. CJIe,n;OBaTeJIbHO:
cos <p = cos( -e) = cos e H
sin<p = sin(-e) = -sine
IIo,n;cTaBJI.H.H B ypaBHeHHe (2):
Fa = [W(f.lCOSe + sine)] / (cose + sine)
)
2.7.6. Yron TpeHJffl nOKOfl
TeJIo, HaxO,lUIIUeeC.H Ha IIIepoxoBaToH IIJIOCKOCTH, paClIOJIOXeHHOH lIO,n; yrJIOM e
K ropH30HTaJIH, KaK lIOKa3aHO Ha pHC 2.26, Haxo,n;HTC.H B COCTO.HHHH paBHOBeCIDI,
eCJIH rpaBHTaUHOHHa.H CHJIa, BbIffY)K,lI;alOIUa.H TeJIO CKOJIb3HTb BHH3 lIO HaKJIOHHOH
w
,
..
,# .. ..
W sin 8
/
" I\.
PRC. 2.26. YrOJI TpeHHH IIOKOH
F/la8a 2. HH:JICeHepHQJl cmamUica
IIJIOCKOCTH, ypaBHoBeIIIHBaeTC.H paBHoH lIO BeJIHqHHe H lIpOTHBOlIOJIO)I{HOH lIO Ha-
lIpaBJIeHHIO CHJIOH TPeHIDI, ,n;eHcTByrolI(eH BBepx lIO HaKJIOHHOH IIJIOCKOCTH. YroJI
HaKJIOHa IIJIOCKOCTH, lIPH KOTOpOM BbIlIOJIIDIIOTC.H YCJIOBIDI paBHOBeC:mI, olIpe,n;eIDI-
eTC.H Y2.ll0M mpeHUJl nOKOJl.
fpaBHTaUHOHHyIO cHJIY, ,n;eHCTBYIO Ha TeJIO (W), MO)I{HO pa3JIOXHTb Ha co-
cTaBIDIIOII(He; lIPH 3TOM COCTaBJI.HIOII(a.H, lIeplIeH,nHKYIDIpHa.H HaKJIOHHOH IIJIOCKO-
CTH, 6y,n;eT paBHa W cos 9, H COCTaBIDIIOII(a.H, lIapaJIJIeJIbHa.H HaKJIOHHOH IIJIOCKOCTH,
6y,n;eT W sin 9. B YCJIOBIDIX paBHOBeCIDI, lIPH KOTOpOM TeJIO yxe lIOqTH COCKaJIb3bI-
BaeT C HaKJIOHHOH IIJIOCKOCTH:
Jl = Ff / Fn = (W sin 9) / (W cos 9) = tg{}
B pa3,n;eJIe 2.7.4 yrOJI TPeHIDI OlIpe,n;eJIeH KaK Jl = tg<p; lIO 3TO MY , qT06bI TeJIO Ha-
XO,n;HJIOCb B COCTO.HHHH lIOK05.l, He06xo,n;HMO 9 = <po ECJIH 9 > <p, TeJIO 6y,n;eT CKOJIb-
3HTb BHH3 lIO HaKJIOHHOH IIJIOCKOCTH. ECJIH yrOJI 9 < <p, TeJIO 6y,n;eT OCTaBaTbC.H B
COCTO.HHHH lIOKO.H, nOKa BHeIIIH.IDI CHJIa He lIpHBe,n;eT ero B ,n;BJDKeHHe.
2.8. HanpR>KeHMe M Aecl>opMaLJ.MR
2.8. 1. HOpMan&HOe HanpflJICeHJfe
Ha pHC. 2.27, a lIOKa3aH UHJIHH,npHqeCKHH CTepxeHb C IIJIOIUMblO lIOlIepeqHOrO
CeqeH:mI A lIPH paCmJl:JICeHUU, a Ha pHC. 2.27, 6 lIOKa3aH TOT xe CTepxeHb lIPH c:JICa-
muu. IIpHJIoxeHHa.H CHJIa F HalIpaBJIeHa lIO OCH CTep)I{IDI H HOpMaJIbHa (lIeplIeH,nH-
KYIDIpHa) ero lIOlIepeqHOMY CeqeHHIO. B 3TOM CJIyqae rOBOp.HT, qTO CTepxeHb lIO,n;-
BepraeTC.H HOpMaJIbHOMY HalIp.HXeHHIO. HOpMaJIbHOe HalIp.HXeHHe 0603HaqaeTC.H
CHMBOJIOM cr (rpeqeCKa.H 6yxBa CHrMa).
HOpMaJIbHOe HalIp.HXeHHe cr =
= lIpHJIOXeHHa.H CHJIa F /IIJIOIUMb lIOlIepeqHOrO CeqeHIDI A.
A
F
F
a
F
+ =----.:_-=+
I
I
F
6
PRC. 2.27. HOpMaJIbHOe HarrpHxeHHe:
a - CTepxeHb rrpH paCTH)I{eHHH - HarrpHxeHHe paCTHxeHHH;
6 - CTepxeHb rrpH cxaTHH - HarrpH)l{eHHe cxaTHH
2.8. HanpJl:JlCeHUe u iJerjJopMal(UR
2.8.2. HSnpflJICeHJfe CASJfrS
Ha pHC. 2.28 lIOKa3aHO 33KJIelIOtffiOe coe,n;HHeHHe. IIoCKOJIbKY lIpHJIOXeHHbIe CHJIbI Q
CMelI(eHbI OTHOCHTeJIbHO OCH, B 3TOM c.rryqae rOBOp.HT, qTO 3aKJIelIKa lIo,n;BepraeTC.H
HarrpIDKeHHIO c,n;BHra, KOTopoe 0603HaqaeTC.H CHMBOJIOM 't (rpeqeCKa.H 6yxBa Tay).
HalIpIDKeHHe c,n;BHra 't = c,n;BHraIOIUa.H CHJIa Q/IIJIOII(a;:r;b c,n;BHra A.
HOpMaJIbHOe HalIpIDKeHHe H HalIpIDKeHHe c,n;BHra 06bIqHO ,n;OCTaTOqHO BeJIHKH
H n03TOMY H3Mep.HIOTC.H B MH/M2.
Q
Q
PRC. 2.28. HarrpH)l{eHHe c,n;BHra
2.8.3. OTHOCJfTen&HSfI nJfHeHHSfI AecpopMsqJffl
CR1IbI, ,n;eHcTByroII(He Ha TeJIO TaK, qTO B03HHKaeT HOpMaJIbHOe HalIpIDKeHHe, TaK-
xe RBIDIIOTC.H lIpWlHHOH H3MeHeHHH pa3MepOB TeJIa. HalIpHMep, paCT.HrHBaIOIUa.H
HarpY3Ka C03,n;aCT HalIpIDKeHHe paCTIDKeHIDI, a TaIOKe lIpHBe,n;eT K y,nJIHHeHHIO-- teJIa,
KaK lIOKa3aHO Ha pHC. 2.29, a. AHaJIOrHqHO, C)l{HMaIOIUa.H HarpY3Ka lIpHBe,n;eT K
)'KopOqeHHIO TeJIa, KaK lIOKa3aHO Ha pHC. 2.29, 6. OTHOCHTeJIbHa.H JIHHeHHaR ,n;e-
<l>opMaUIDI 0603HaqaeTC.H CHMBOJIOM E (rpeqeCKa.H 6yxBa 3lICHJIOH).
OTHOCHTeJIbHa.H JIHHeHHa.H ,n;e<popMaUIDI E = H3MeHeHHe ,nJIHHbI X/HCXO,n;Ha.H ,nJIHHa /.
F ..
. I .. F
I_ x .1- I .1 -J
;; )
,)
a
F
..
I: x .1
F
I
I-
.1
6
PRC. 2.29. OTHOCHTeJIbHaH JIHHeHHaH ,n;e<p0pMaI(HH:
a - B03HHKaIOInaH rrpH paCTHrHBaIOIneM HarrpH)l{eHHH;
6 - B03HHKaIOInaH rrpH C)l{HMaIOIneM HarrpHxeHHH
F/la8a 2. HH:JICeHepHQR cmamU1ca
IIOCKOJIbKY H3MeHeHHe ,1J)IHHbI H HCXO,n;Ha.H ,1J)IHHa H3Mep.HIOTC.H B o,n;HHaKOBbIX
e,n;HHHuax, TO OTHOCHTeJIbHa.H JIHHeHHa.H ,n;e<popMaUIDI, OlIpe,n;eIDIeMa.H KaK HX OTHO-
IIIeHHe, .HBillIeTC.H 6e3pa3MepHOH BeJIHqHHOH.
2.8.4. p,ecpopM8qJffl CASJfrS
,lJ:e<l>opMaUIDI c,n;BHra lIOKa3aHa Ha pHC. 2.30. IIpHJIoxeHHa.H CHJIa Q cMerueHa H
lIpHBO,n;HT K ,n;e<l>opMaUHH MaTepHaJIa. ,lJ:e<l>opMaUIDI c,n;BHra 0603HaqaeTC.H CHMBO-
JIOM Y (rpeqeCKa.H 6yxBa raMMa).
,lJ:e<l>opMaUH.H c,n;BHra y = BeJIHqHHa ,n;e<l>opMaUH.H X/HCXO,n;HbIH pa3Mep I.
3TO OII.HTb OTHOIIIeHHe, a CJIe,n;OBaTeJIbHO, 6e3pa3MepHaR BeJIHqHHa.
Q
n
\
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Q
PRC. 2.30. ,LJ;e<popMaI(HH c,n;BHra
2.8.5. MOAyn& ynpyroCTJf (3SKOH rYKS)
3aKOH fyJ(a YCTaHaBJIHBaeT, qTO B 06JIaCTH yrrpyrHX ,n;e<p0pMaUHH ,n;aHHoro MaTepH-
aJIa ,n;e<l>opMaUIDI lIpOlIOPUHOHaJIbHa lIpHJIOXeHHOH CHJIe, C03,n;aIOrueH 3TY ,n;e<l>op-
MaUHIO. ECJIH rrpHMeHHTb 3TOT 3aKOH K rrpyxHHe:
)l(ecTKocTb lIpyxHHbI =
= HOpMaJIbHOe HalIpIDKeHHe cr/OTHoCHTeJIbHa.H JIHHeHHa.H ,n;e<p0pMaUIDI E.
MO,LJ;yJIb yrrpyrOCTH E MO)I{HO rrOJIyqHTb H3 3aKOHa fyJ(a. HalIpIDKeHHe IIp.HMO
lIporrOpUHOHaJIbHO Y,1J)IHHeHHIO, lIOKa MaTepHaJI lIo,n;BepraeTC.H HalIpIDKeHHIO B 06-
JIaCTH yrrpyrHX ,n;e<l>opMaUHH, rr03TOMY:
HalIpIDKeHHe - ,n;e<l>opMaUIDI.
IIo3TOMY:
HalIp.H)I{eHHe = ,n;e<l>opMaUH.H x KOHCTaHTa.
CJIe,n;OBaTeJIbHO:
HalIpIDKeHHe/,n;e<l>opMaUIDI = KOHCTaHTa.
3Ta KOHCTaHTa (0603HaqaeMaR E) Ha3bIBaeTC.H Mo,n;YJIeM yrrpyrOCTH (KJIH MO,n;y-
JIeM IOHra) H H3Mep.HeTCR B fH/M2.
E = HalIpIDKeHHe cr/,n;e<l>opMaUIDI E.
2.8. HanpJl:JICeHUe u iJetjJoPMlll(UJI
2.8.6. MOAyn& CASJfra
MO.nyJIb c,n;BHra G CB.H3bIBaeT ,n;e<l>opMaUHIO c,n;BHra H HalIpIDKeHHe c,n;BHra CJIe,l(ylO-
lI(HM 06pa30M:
MO,n;YJIb c,n;BHra G = HalIpIDKeHHe c,n;BHra 't/,n;e<l>opMaUIDI c,n;BHra y.
MO.nyJIb c,n;BHra TaIOKe H3Mep eTC.H B fH/M2. B Ta6JIHue 2.4 lIpHBe,n;eHbI MO.nyJIb
c,n;BHra H MO,n;YJIb yrrpyrOCTH ,lJ;JUI HeKOTopbIX THlIHqHbIX MaTepHaJIOB.
Ta6JI. 2.4. MO,ZJ;yJIb ynpyrocm H MO,ZJ;yJIb C,lI;BHra ,lI)UI HeKoropbIX 'fHIIHqJIbIX MaTepHaJIOB
MO,ZJyJlh Mo,ZJy JIb Mo,ZJy JIb Mo,ZJy JIb
MaTepHaJI ynp E, c.ura G, MaTepHaJI ynpyroCTH E, c.ura G,
fH/M fH/M2 fH/M 2 fH/M2
ArrIOMHHHH 70 26 CBHHeu 16 6
JIaTyHb (70/30) 101 37 CTaJIb (MHrKaH, HH3- 212 82
KoyrJIepo,n;HCTaH)
KanMHH 50 19 OJIOBO 50 18
XpOM 279 115 THTaH 116 44
Me,n;b 130 48 BOJIb<ppaM 411 161
)l(eJIe30 ('IyryH) 152 60 QHHK 108 43
( '1
2.8.7. HSnpflJlCeHJfe KpYlfeHJffl
Ha pHC. 2.31, a MO)I{HO 3aMeTHTb, qTO, KOr,lIa Ha BaJI KpyroBoro rrOlIepeqHOrO ceqe-
HID! ,n;eHcTByeT MOMeHT KpyqeHIDI (3aKpyqHBaIOIUHH MOMeHT) T:
. Bce CeqeHIDI Barra OCTaIOTC.H KpyrOBbIMH H HX ,n;HaMeTP He H3MeIDIeTC.H;
. IIJIOCKOCTb lIOlIepeqHOrO CeqeHIDI OCTaeTC.H IIJIOCKOCTbID (TOJIbKO KpyroBa.H)
lIPH YCJIOBHH MaJIOCTH yrJIa lIOBopOTa.
TopueBbIe lIOBepXHOCTH H30JIHpOBaHHoro UHJIHH,lJ;pHqeCKOrO 3JIeMeHTa BaJIa,
nOKa3aHHoro Ha pHC. 2.31, 6, OCTaIOTC.H IIJIOCKHMH, H JII060H rrp.HMoyrOJIbHbIH 3JIe-
MeHT lIOBepXHOCTH abcd 6y,n;eT Haxo,n;HTbC.H B COCTO.HHHH qHCTOrO c,n;BHra. jIalIp.H-
xeHIDI C,l(BHra B,n;OJIb ad H bc BbI30Byr ,n;OlIOJIHHTeJIbHbIe HalIpIDKeHHe c,n;BIf B,n;OJIb
ab H cd. IIpoHcxo,n;HT lIpO,n;OJIbHOe cKpyqHBaHHe BaJIa TaK, qTO oTPe3KH\")Gib H cd
CMeIUaIDTC.H Ha yrOJI OTHOCHTeJIbHO JIHHHH AB, KaK lIOKa3aHO Ha pHC. 2.31, B.
IIpH qHCTOM c,n;BHre H MaJIbIX yrJIOB cKpyqHBaHIDI yrOJI lIpe,n;CTaBIDleT yrJIOBYIO
,n;e<l>opMaUHIO, a -r - KaCaTeJIbHOe HalIpIDKeHHe Ha lIOBepXHOCTH BaJIa. II03ToMY:
MO,n;YJIb c,n;BHra G = KaCaTeJIbHOe HalIpIDKeHHe -r/yrJIOBa.H ,n;e<l>opMaUIDI ; (1)
,l];JIHHa n;yrH BBI = I , lIPH YCJIOBHH, qTO ,n;OCTaTOqHO MaJIO;
,l];yra BB 1 = re,
r,n;e r - Pa)J;HYC BaJIa, e - yrOJI cKpyqHBaHIDI Ha BceH ,1J)IHHe BaJIa I.
II03TOMY:
I = ,lLrrHHa ,[(yrH BB I = re,
<p = re / I.
F/la8a 2. HH:JICeHepHQJl cmamU1CO
d
a
6
A
PRC. 2.31. HarrpHxeHHe H ,n;e<popMaI(HH
rrpH KpyqeHHH:
a - cKpyqHBaHHe KpyroBoro Bana;
6 - H30JIHpOBaHHbIH 3JIeMeHT abcd;
B - ,n;e<popMaI(HH KpyroBoro Bana
BCJIe,n;CTBHecKpyqHBaHHH
B
IIo,lJ;cTaBJI.H.H B ypaBHeHHe (1), lIo.rryqaeM:
G = 't / (re / I) HJIH 't / r = Ge / I.
IIpUMettaHue. IIoCKOJIbKY G H I .HBJI.HIOTC.H KOHCTaHTaMH AIDI JII060ro ,lJ;aHHOrO
BaJIa H e - KOHCTaHTa AIDI Bcex PMHYCOB JII060ro KOHKpeTHoro lIOlIepeqHOrO ce-
qeHIDI, TO:
't/r = KOHCTaHTa.
TaKHM 06pa30M, KaCaTeJIbHOe HalIpIDKeHHe B JII060H TOqKe ,lJ;aHHOrO lIOlIepeq-
Horo CeqeHIDI lIpOlIOPUHOHaJIbHO PMHYCY, H HalIpIDKeHHe YBeJIHqHBaeTC.H paBHO-
MepHO OT HYJIR Ha OCH BaJIa ,lJ;0 MaKCHMYMa Ha ero BHeIIIHeM PMHyce. II03TOMY
OqeBH,LI;HO, qTO lIOJIbIH BaJI MoxeT lIepe,lJ;aBaTb 60JIbIIIHH MOMeHT KpyqeHIDI, qeM
CTIJIOIIIHOH BaJI C TaKOH xe TIJIOII(MbIO lIOlIepeqHOrO CeqeHIDI.
2.8.8. Kon&qesoe HanpflJICeHJfe s TOHKJfX
qJfnJfHAPJflfeCKJfX 060nOlfKax
113 pHC. 2.32 lIOIDITHO, qTO ,lJ;aBJIeHHe P CTPeMHTC.H YBeJIHqHTb ,lJ;HaMeTP UHJIHH,lJ;pa.
OHO paCTRrHBaeT CTeHKH UHJIHH,lJ;pa lIO BceH ,lJ)IHHe OKpy:>KHOCTH H C03,lJ;aeT paCT.Hrn-
BaIOlI(ee HanpIDKeHHe, KOTopoe Ha3bmaeTCR KOJIbueBbIM (OKpyxHbIM) HanpIDKeHHeM crh'
CHJIa, B03HHKalOlI(a.H BCJIe,lJ;CTBHe BHyrpeHHero ,lJ;aBJIeHIDI P, ypaBHOBellIHBaeTCR
KOJIbueBbIM HalIpIDKeHHeM crh' OTCIO,lJ;a:
KOJIbueBOe HarrpIDKeHHe x TIJIOruMb = ,lJ;aBJIeHHe x lIpoeKUIDI lIOBepXHOCTH.
crh x 21t = Pdl.
crh=Pd/2t.
2.9. DOJIICU
npOeKu.Vl5I nOBepXHOCTVI
PRC. 2.32. KOJIbI(eBOe HarrpH)l{eHHe B TOHKHX I(HJIHH,lI;pHqeCKHX 060JIOqKax.
P - ,n;aBJIeHHe, ,n;eHcTBYKnnee PaLI.HaJIbHO Ha TOHKYIO 060JIoqKY
2.8.9. npO.ROn&HOe HanpflJICeHJfe S TOHKJfX
qJfnJfHAPJflfeCKJfX 060nOlfKax
Ha pHC. 2.33 MO)I{HO 3aMeTHTb, qTO BHyTpeHHee ,n;aBJIeHHe P C03,n;aeT paCT.HrHBalO-
mee HalIp.HXeHHe TaIOKe B lIpO,n;OJIbHOM HalIpaBJIeHHH, 3TO HalIpIDKeHHe 0603Haqa- (
eTC.H a[. CJIe,n;oBaTeJIbHO, ,n;aBJIeHHe P, ,n;eHcT-
BYIOlI(ee Ha IIJIOIIJ;a;:r;b nd 2 /4, ypaBHOBeIIIHBa-
eTC.H lIpO,n;OJIbHbIM (oceBbIM) HalIpIDKeHHeM
CJb ,n;eHCTBYIOIIJ;HM Ha IIJIOIIJ;a;:r;H ndt. (CTPoro
roBOp.H, ,n;OJDKeH HCnOJIb30BaTbC.H cpe,n;HHH
,n;HaMeTP, o,n;HaKO lIPH YCJIOBHH, qTO TOJIIIJ;H-
Ha CTeHKH t MaJIa lIO cpaBHeHHIO C ,n;HaMeT-
pOM, ,n;aHHoe lIpH6JIJDKeHHe .HBIDleTC.H KOp-
peKTHbIM.) TaKHM 06pa30M:
P x (1td 2 / 4) = a[ x 1tdt.
a[ = (nPd 2 ) / (41tdt).
a[ = Pd / 4t.
PRC. 2.33. npO,n;OJIbHOe HarrpH)l{eHHe B
TOHKHX I(HJIHH,lI;pHqeCKHX 060JIOqKax
IIpUMettaHue.
lIpaKTHqeCKHX ueJIeH B ypaBHeHIDIx ,LJ;.IDI a h Hal HalIpIDKeHIDI IIp e,n;lIOJIara -
IOTC.H lIOCTORHHbIMH lIO BceH TOJIIIJ;HHe CTeHOK. 3TO ClIpaBe,1J)lHBO TOJIbKO B TOM
c.rryqae, Kor,n;a OTHOIIIeHHe TOJIII(HHbI K BHyTpeHHeMY ,n;HaMeTPY MeHbIIIe 1:20.
2.9. &anKM
2.9.1. YCJfnJfe CASJfra
,lLJrn paBHOBeCIDI 6aJIKH CHJIbI, ,n;eHCTBYIOII(He CJIeBa OT JII060ro CeqeHIDI X, KaK rro-
Ka3aHO Ha pHC. 2.34, a, ,n;OJDKHbI ypaBHOBeIIIHBaTbC.H CHJIaMI1, ,n;eHCTBYIOIIJ;HMH
F/la8a 2. HH:JICeHepHQJl cmamU1ca
nOAAep)I(Ka
nOAAep)l(Ka
, F
" F
'F
HarPY3Ka
HarPY3Ka
Mx
M'
x
" F
a
6
B
PRC. 2.34. CHJIbI, ,n;eHcTByK>InHe Ha 6aJIKY:
a - CHJIbI, ,n;eHcTByK>InHe Ha 6aJIKY;
6 - rrOJIO)I{HTeJIbHaH rrOrrepeqHaH CHJIa;
B - OTpHI(aTeJIbHaH rrOrrepeqHaH CHJIa
ClIpaBa OT CeqeHIDI X. MOMeHTbI CHJI OTHOCHTeJIbHO CeqeHIDI X CJIeBa TaIOKe ,n;OJI-
)l{HbI ypaBHoBeIIIHBaTbC.H MOMeHTaMH CHJI OTHOCHTeJIbHO CeqeHIDI X clIpaBa.
HeCMOTp.H Ha TO qTO B COCTO.HHHH paBHOBeCIDI, CHJIbI H HX MOMeHTbI B3aHMHO
KOMlIeHCHpYIOTC.H, BeJIHqHHa H lIpHpo,n;a 3THX CHJI H MOMeHTOB HMelOT 3HaqeHHe,
lIOCKOJIbKY OHH OlIpe,n;eIDIIOT HalIpIDKeHIDI B CeqeHHH X, a TaIOKe KPHBH3HY H lIpO-
fH6 6aJIKH. Pe3YJIbTHPYIOIUa.H CHJIa CJIeBa OT X H pe3YJIbTHpYIOIUa.H CHJIa ClIpaBa OT
X (CHJIbI HJIH KOMlIOHeHTbI CHJI, rreplIeH,lJ;HKYillIpHbIe 6aJIKe) COCTaBillIlOT lIapy CHJI,
cTPeM.HIUYIOC.H C03,n;aTb C,n;BHf B 3TOM CeqeHHH 6aJIKH. ITolIepeqHa.H CHJIa OlIpe,n;eilll-
eTC.H KaK CHJIa, lIeplIeH,lJ;HKYIDIpHa.H K 6aJIKe H ,lJ;.IDI JII060fO 3aL(aHHOfO CeqeHIDI
lIpHBO,n;.HIUa.H K C,n;BHry B 3TOM CeqeHHH.
ECJIH C,n;BHf lIpOHCXO,n;HT, KaK lIOKa3aHO Ha pHC. 2.34, 6, TO lIOlIepeqHa.H CHJIa
YCJIOBHO CqHTaeTC.H lIOJIOXHTeJIbHOH (T.e. +F); eCJIH c,n;BHr lIpOHCXO,n;HT, KaK lIOKa-
3aHO Ha pHC. 2.34, B, CHJIa CqHTaeTC.H 0TPHuaTeJIbHOH (T.e. -F).
2.9.2. 1f3rJf6alOUlJfH MOMeHT
H3fH6aIOIUHH MOMeHT B ,n;aHHOM CeqeHHH 6aJIKH OlIpe,n;eIDIeTC.H KaK pe3YJIbTHPYIO-
IUHH MOMeHT OTHOCHTeJIbHO 3Toro CeqeHH.H HJIH Bcex CHJI, lIpHJIOXeHHbIX CJIeBa OT
CeqeHIDI, HJIH Bcex CHJI, lIpHJIOXeHHbIX ClIpaBa OT CeqeHIDI. Ha pHC. 2.34, a H3fH-
6alOIUHH MOMeHT - 3TO HJIH M x, HJIH M . 3TH MOMeHTbI 6y,n;yr HalIpaBJIeHbI lIO
qaCOBOH CTPeJIKe CJIeBa OT CeqeHIDI H lIpOTHB qaCOBOH CTpeJIKH - ClIpaBa OT ceqe-
HIDI. H3-3a HHX 6aJIKa 6y,n;eT lIporH6aTbC.H. Y CJIOBHO TaKOH lIpOfH6 CqHTaeTC.H lIO-
JIO)l{HTeJIbHbIM lIPOfH60M, T. e. lIOJIOXHTeJIbHbIe H3fH6alOIUHe MOMeHTbI C03,n;aIOT
lIOJIOXHTeJIbHbIH H3fH6 (lIpOfH6). AHaJIOfHqHO, OTpHuaTeJIbHbIe H3rH6aIOIUHe MO-
MeHTM CTaHOB.HTC.H lIPHqHHOH H3fH6a 6aJIKH B lIpOTHBOlIOJIO)I{HOM HalIpaBJIeHHH,
T. e. 0TPHuaTeJIbHbIe H3rH6alOIUHe MOMeHTbI C03,n;a1OT OTpHuaTeJIbHbIH H3fH6 (BbI-
rH6). Pa3HHua Me)l{)];y lIpOfH60M H BbIfH60M lIOKa3aHa Ha pHC. 2.35.
ITepefH6 B03HHKaeT, KOf,n;a BbIfH6 H lIporH6 lIpO.HBJIRIOTC.H B 6aJIKe o,n;HOBpe-
MeHHO, KaK lIOKa3aHO Ha pHC. 2.35, B. ITo,n; B03,n;eHcTBHeM HarpY3KH, lIOKa3aHHOH
Ha pHC. 2.35, a, 6aJIKa lIpOfHeTC.H BHH3 Me)l{,lJ;Y TOqKaMH B H C, a lIO,n; B03,n;eHCTBH-
eM HarpY3KH, lIOKa3aHHOH Ha pHC. 2.35, 6, 6aJIKa BbIfHeTC.H BBepx Me)l{,lJ;Y TOqKaMH
AH B.
2.9. DOJIICU
F L
Fs
Fs
a
6
Fs
Fs
B
PRC. 2.35. BbIrH6, rrporH6 H rreperH6:
F L - HarpY3Ka, Fs - orropa;
a - rrporH6;
6 - BbIrH6;
B - rreperH6
BeJIWlHHa lIOlIepeqHOH CHJIbI H BeJIWlHHa H3fH6alOIUefo MOMeHTa 06bIqHO H3-
MeH.HIOTC.H B,n;OJIb JII060H 6aJIKH. fpa<l>HKH, lIOKa3bIBalOIUHe lIOlIepeqHbIe CHJIbI H
H3fH6alOlI(He MOMeHTbI ,lJ;.IDI Bcex CeqeHHH 6aJIKH, Ha3bIBaIOTC.H 3lIIOpOH lIOlIepeq-
HbIX CHJI H 3lIIOpOH H3fH6alOIUHx MOMeHTOB COOTBeTCTBeHHO.
IIOlIepeqHbIe CHJIbI H 3lIIOpbI lIOlIepeqHbIX CHJI HMelOT MeHbIIIee 3HaqeHHe, qeM
H3fH6alOIUHe MOMeHTbI H 3lIIOpbI H3fH6alOIUHx MOMeHToB; o,n;HaKO OHH lIOJIe3HbI,
1l0CKOJIbKY yJ(33bIBaIOT Ha caMbIe Ba)l{HbIe aClIeKTbI 3lIIOpOB H3fH6alOIUHX MOMeH-
TOB HalIpHMep, TaM, f,n;e lIOlIepeqHa.H CHJIa paBHa HYJIIO, H3fH6alOIUHH MOMeHT
6y,n;eT MaKCHMaJIbHbIM HJIH MHHHMaJIbHbIM.
2.9.3. p,JfSrpSMM&1 YCJfnJffl CASJfrS
Jf Jf3rJf6slOIJ.4erO MOMeHTS
( ,
((J
)
//
PaCCMOTPHM 311lOpbI lIOlIepeqHOH CRJIbI H H3fH6alOIUefo MOMeHTa .l(JI.H CHCTeMbI
CM, ,n;eHcTByroIUHX Ha 6aJIKY, Ha pHC. 2.36. ,lI;JI.H MOMeHTa 6y,n;eT paCCMOTpeHa TOJIb-
KO lIpOCTa.H CHCTeMa H3 Tpex cocpe,n;OTOqeHHbIX HarpY30K.
IIpe)l{,lJ;e BcefO, He06xo,n;HMO paCCqHTaTb peaKUHH OlIOp B TOqKaX A H B, KaK
6bIJIO OlIHcaHO paHee B pa3,n;eJIe 2.4.4. OlIOpbI B TOqKaX A H B lIpOCTO lIO,LJJJ;ep)J{HBa-
lOT 6aJIKY. 3TO 03HaqaeT, qTO OHa rrOKOHTC.H Ha orropax H B 3THX TOqKaX ,n;eHcTByeT
24 KH
C"
A
B
5M
3 M
-
R A
R B
PRC. 2.36. CHJIbI, ,n;eHcTBYIOIUHe Ha 6aJIKY
F/la8a 2. HH:JICeHepHQJl cmamwco
BepTHKaJIbHa.H peaKII;lUl OlIOp. ,[LrnI BbIlIOJIHeHIDI YCJIOBHH paBHoBecIDI TPe6yeTC.H,
qT06bI pe3YJIbTHPYIOIUHH MOMeHT OTHOCHTeJIbHO JII060H TOqKH paBHIDIC.H HYJIIO H
cYMMa CHJI, ,n;eHcTByroIUHX BBepx, paBHIDIacb cYMMe CHJI, ,n;eHcTBYIOIUHX BHH3. IIo-
3TOMY, eCJIH olIpe,n;eIDITb MOMeHTbI OTHOCHTeJIbHO TOqKH A, MOMeHT, c03,n;aBaeMbIH
CHJIOH peaKII;HH RB, ,n;OJDKeH ypaBHOBeIIIHBaTb MOMeHT, c03,n;aBaeMbIH HarpY3KoH B
TOqKe C:
R B x 8 M = 24 KH x 5 M.
R B = (24 KH x 5 M) /8 M.
R B = 15 KH.
AHaJIOfWlHO:
R A = 24 KH - 15 KH = 9 KH.
HelIocpe,n;CTBeHHO ClIpaBa OT TOqKH A lIOlIepeqHa.H CHJIa OlIpe,n;eIDIeTC.H peaK-
UHeH R A H, CJIe,n;OBaTeJIbHO, paBHa 9KH. IIoCKOJIbKY 3Ta CHJIa lIpHJIOXeHa CJIeBa OT
paCCMaTpHBaeMOfO CeqeHIDI H HalIpaBJIeHa BBepx, OHa .HBIDIeTC.H lIOJIOXHTeJIbHoit.
IIOlIepeqHa.H CHJIa 6y,n;eT lIOCTO.HHHOH ,LJ;.IDI Bcex TOqeK Me)l{,LJ;y A H C, lIOCKOJIbKY
Me)l{,LJ;y 3THMH TOqKaMH Ha 6aJIKY He ,n;eHCTBYIOT HHKaKHe ,n;pyrHe CHJIbI.
IIpH paCCMOTPeHHH TOqKH ClIpaBa OT C CJIe,n;yeT lIpHHHMaTb BO BHHMaHHe Ha-
rpY3KY B TOqKe C, TaK xe KaK H CHJIY peaKII;HH R B . B KaqeCTBe aJIbTepHaTHBbI peaK-
l.(HIO R B MO)I{HO paCCMOTPeTb caMY lIO ce6e. IIOlIepeqHa.H CHJIa paBHa 15 KH. 3TO
3HaqeHHe R B BbNHCJIeHO paHee; OHO TaIOKe MoxeT 6bITb lIo.rryqeHO ,LJ;.IDI ,n;aHHOH Ha-
rpY3KH C - R A = 24 KH - 9 KH = 15 KH. ,[LrnI JII060H TOqKH Me)l{,LJ;y C H B CHJIa
lIpHJIOXeHa ClIpaBa H HalIpaBJIeHa BBepx, lI03TOMY lIOlIepeqHa.H CHJIa 0TPHuaTeJIb-
Ha, KaK 6bIJIO lIOKa3aHO paHee Ha pHC. 2.34. Hy:>KHo oTMeTHTb, qTO BeJIWlHHa lIO-
lIepeqHOH CHJIbI pe3KO H3MeIDIeTC.H B TOqKe C. 3TO lIOKa3aHO Ha pHC. 2.37, a.
CooTBeTCTBYIOIUHe H3rH6alOIUHe MOMeHTbI lIOK33aHbI Ha pHC. 2.37, 6. M3fH6a-
IOIUHH MOMeHT B TOqKe A paBeH HYJIIO, lIOCKOJIbKY HeT CHJI, lIpHJIO)l{eHHbIX CJIeBa
OT TOqKH A. B TOqKe, cMeIUeHHoH BlIpaBO Ha 1 M OTHOCHTeJIbHO TOqKH A, ,n;eHcTBY-
eT MOMeHT TOJIbKO O,n;HOH CHJIbI R A , lIPH-
JIO)l{eHHOH CJIeBa OT 3TOH TOqKH; OH paBeH
R A x 1 M = 9 KHM. IIoCKOJIbKY 3TOT MO- a
MeHT OTHOCHTeJIbHO TOqKH A HalIpaBJIeH
lIO qaCOBOH CTPeJIKe, OH lIOJIO)I{HTeJIeH
(+9 KHM). B TOqKax, CMeIUeHHbIX Ha 2, 3,
4 H 5 M BlIpaBO OT TOQKH A, H3fH6alOIUHe
MOMeHTbI COOTBeTCTBeHHO paBHbI:
A
9 KH
C
B
R A x 2 M = 9 KH x 2 M = 18 KHM.
R A x 3 M = 9 KH x 3 M = 27 KHM.
R A x 4 M = 9 KH x 4 M = 36 KHM.
R A x 5 M = 9 KH x 5 M = 45 KHM.
-15 KH
I 45 KH
6
IIOCKOJIbKY Bce 3TH MOMeHTbI HalIpaB-
JIeHbI lIO qaCOBOH CTPeJIKe, Bce OHH .HB.IDI-
IOTC.H lIOJIO)I{HTeJIbHbIMH H3fH6alOIUHMH
MOMeHTaMH. ,l);ID1 TOqeK lIpaBee C CJIe,n;yeT
yqHTbIBaTb HarpY3KY B TOqKe C, TaK xe
PRC. 2.37. 3IIIOpbI IIOIIepeqHOH CHJIbI H
H3rH6aIOInerO MOMeHTa.
a - 3IIIOpa IIOIIepeqHOH CHJIbI;
6 - 3IIIOpa H3rH6aIOInerO MOMeHTa
2.9. IiOJl1(,u
KaK H CIDIy peaKIJ;HH R B , HJIH, lIpOlI(e, KaK 6billO lIOKa3aHO paHee, MO)I{HO HClIOJIb-
30BaTb B BbIqHCJIeHlUIX TOJIbKO R B . B TOqKax, CMelI(eHHbIX Ha 5, 6 H 7 M OT TOq-
KH A, H3rH6alOlI(He MOMeHTbI COOTBeTCTBeHHO paBHbI:
R B x 3 M = 15 KH x 3 M = 45 KHM.
R B x 2 M = 15 KH x 2 M = 30 KHM.
R B x 1 M = 15 KH x 1 M = 15 KHM.
TaK KaK 3TH MOMeHTbI C03,n;aHbI CHJIOH, lIpHJIOXeHHOH ClIpaBa OT paCCMa1pHBa-
eMbIX TOqeK, H HalIpaBJIeHbI lIpOTHB qaCOBOH C1peJIKH, BCe OHH .HBJUIIOTCH nOJIO)I{H-
TeJIbHbIMH. B TOqKe B H3rH6alOlI(HH MOMeHT paBeH HYJIIO, TaK KaK HeT CHJI, lIpHJIO-
XeHHbIX ClIpaBa OT Hee. Pe3YJIbTaTbI CBe,n;eHbI B Ta6JIHUY 2.5.
Ta6J1. 2.5. 3HaqeHHH nOnepeqHOH CHJIbI H H3rH6aIOIIJ;erO MOMeHTa AJlH pHC. 2.37.
PaCCTOHHHe OT TOqI{H A (M) 0 1 2 3 4 5 6 7 8
Y CHJIHe c,n;BHra (KH) +9 +9 +9 +9 +9 +9 -15 -15 -15
H3m6aIOIIJ;HH MOMeHT (KHM) 0 +9 +18 +27 +36 +45 +30 +15 +15
WCnOJIb3YH pe3YJIbTaTbI H3 Ta6JIHUbI 2.5, MO)I{HO HapHCOBaTb 3lIIOpbI lIOlIepeq-
nOH CHJIbI H H3rH6alOlI(erO MOMeHTa, KaK lIOKa3aHO Ha pHC. 2.37. Kor,n;a 6aJIKa He-
ceT Ha ce6e TOJIbKO CKOHueH1pHpOBaHHyIO B TOqKax HarpY3KY, CTYIIe aTaH 3lIIOpa
nOnepeqHOH CHJIbI COCTOHT TOJIbKO H3 ropH30HTaJIbHbIX H BepTHKaJIbHbIX lIPHMbIX:-)
CKaqK006pa3Hoe H3MeHeHHe lIOlIepeqHOH CHJIbI lIpOHCXO,n;HT B Tex TOqKaX, r,n;e co-
cpe,n;OTOqeHa HarpY3Ka, B TOM qHCJIe B TOqKax lIpHJIOXeH:IDI peaKIJ;HH onop. ,lLJrn
3TOro npOCToro BH,l(a HarpY3KH 3lIIOpa H3rH6alOlI(erO MOMeHTa TaIOKe COCTOHT H3
npHMbIX JIHHHH, 06bIqHO HaKJIOHHbIX. Pe3KHX H3MeHeHHH H3rH6aJplI(ero MOMeHTa
06bflIHO He lIpOHCXO,n;HT, HCKJIlOqaH He06bIqHbIe YCJIOB:IDI, Kor,n;a K 6)mKe lIpHJIOXeH
... /
MOMeHT, OTJIHqHbIH OT HarpY3KH.
Ha caMOM ,n;eJIe, B peaJIbHOCTH He MoxeT cym;ecTBoBaTb 6aJIKa, Hecym;aH e,n;HH-
CTBeHHyIO HarpY3KY, cocpe,n;OTOqeHHyIO B O,n;HOH TOqKe. DaJIKa caMa lIO ce6e HMeeT
Maccy H, CJIe,n;OBaTeJIbHO, Bec. ECJIH lIOlIepeqHOe CeqeHHe 6aJIKH lIOCTOHHHO, Ha-
rpY3Ka paClIpe,n;eJIeHa paBHOMepHO lIO BceH A1IHHe 6aJIKH. PaCCM01pHM TelIepb
B03,n;eHCTBHe paBHOMepHO paClIpe,n;eJIeHHOH HarpY3KH.
Ha pHC. 2.38, a lIOKa3aHa paBHOMepHO HarpyxeHHaH 6aJIKa A1IHHOH 1 H Be-
COM Cocpe,n;OTOqeHHaH HarpY3Ka 3,n;eCb lIpHcyrcTByeT TOJIbKO B BH,l(e peaKIJ;HH
onop R A H R B . TaK KaK HarpY3Ka CHMMe1pHqHa, H R A , H R B paBHbI W12. M3 3nlOpbI
nOnepeqHOH CHJIbI BH,l(HO, qTO MaKCHMaJIbHbIe 3HaqeH:IDI ,n;OCTHraIOTCH B TOqKax
onopbI, a lIocepe,n;HHe YCHJIHe c,n;BHra paBHO HYJIIO. O,n;HaKO Ha 3TOT pa3 lIPHMaH,
onpe,n;eJI.HlOlI(aH BeJIINHHY lIOlIepeqHOH CHJIbI, HBJI.HeTCH HaKJIOHHOH JIHHHeH, npo-
XO,lUI eH qepe3 cepe,n;HHY.
PaCCMOTpHM CeqeHHe XX, paClIOJIOXeHHOe Ha paCCTOHHHH a OT JIeBOH OlIOpbI,
B03,n;eHCTByIOlI(eH Ha 6aJIKY C CHJIOH peaKIJ;HH R A :
IIOlIepeqHaH CHJIa, ,n;eHCTByrolI(aH Ha CeqeHHe .IT" = (WI I 2) - (W x a).
F/la8a 2. HH:JICeHepHOR cmamUlCO
a
x
PaBHOMepHa51 HarpY3Ka (WjL)
WI
R A =-
2
x
Rs= WI
2
I
a
WI
-
2 B
A
WI
-
2
6
A
B
B
PRC. 2.38. oarrKa c paBHOMepHO pacnpe,n;eJIeHHOH HarpY3KoH (UDL):
a - 3nIOpa pacnpe,n;eJIeHHH HarpY3KH;
6 - 3nIOpa YCHJIHH c,n;BHra;
B - 3nIOpa H3rH6aIOm;ero MOMeHTa
3TO ypaBHeHHe lIpe,n;cTaBJISIeT lIpSIMyro JIHHHIO, H 3lIIOpa lIOlIepeqHOH CIDIbI lIO-
Ka3aHa Ha pHC. 2.38, 6. B OTJIHqHe OT lIpe,nbl)];yw;ero lIpHMepa, Ha 3TOT pa3 3lIIOpa
H3rH6alOm;ero MOMeHTa COCTOHT He H3 lIpSIMbIX JIHHHH, a lIpe,nCTaBJI.HeT C060H He-
npepbIBHyIO KPHByIO C MaKCHMYMOM lIocepe,n;HHe.
W3rH6alOlI(HH MOMeHT Mx B CeqeHHH XX = [(wi / 2) x a] - [W x a x (a / 2)].
fI03ToMY:
Mx = W / 2(la - a 2 ).
(1)
3TO ypaBHeHHe lIapa60JIbI, MaKCHM)'M KOTOpOH MO)I{HO HaRTH, HClIOJIb3Y.H lIep-
BYIO npOH3BO,LJ;HyIO, H3 YCJIOBIDI:
dM x / da = O.
fIpo,nH<p<pepeHUHpyeM ypaBHeHHe (1):
dM x / da = W / 2(1 - 2a) = O.
OTKY,na:
a = I / 2.
2.9. EaIllCU
W3rH6alOlI(HH MOMeHT MaKCHMaJIeH B ueH1pe lIapa60JIbI, KaK H CJIe,n;OBaJIO
O)l{H,lJ;aTb lIPH cHMMeTpHqHOH HarpY3Ke. CJIe,n;oBaTeJIbHO, lIo,n;CTaB.IDI.H a = 1/2 B
ypaBHeHHe (1):
M max = W /2[(/ 2 /2) -(1 2 / 4)] = Wl2 /8.
3lIIOpa H3rH6alOlI(erO MOMeHTa lIOKa3aHa Ha pHC. 2.38, B. KpoMe CJIyqaH, lIOKa-
3aHHoro Ha pHC. 2.38, a, Kor,n;a paBHOMepHaH HarpY3Ka B03HHKaeT B pe3YJIbTaTe
.neiicTBIDI rpaBHTaUHH Ha Maccy caMo 6aJIKH, e,n;HHcTBeHHbIH CJIyqaH, Kor,n;a 6aJIKa
raIOKe paBHOMepHO HarpyxeHa, 3TO eCJIH OHa SIBJI.HeTCSI qaCTblO KapKaca H HeceT Ha
j
ce6e TIDKeCTb KHPlIHqHOH KJI3)(KU.f
EOJIee qaCTO, BC1peqaeTCSI COqeTaHHe cocpe,n;OTOqeHHbIX HarpY30K C paBHOMep-
HO paclIpe,n;eJIeHHOH HarpY3KoH, KaK lIOKa3aHO Ha ,n;HarpaMMe paClIpe,n;eJIeHIDI Ha-
rpY3KH, lIpHBe,n;eHHoH Ha pHC. 2.39, a.
45 KH
24 KH
UDL = 125 KHM
A B
2M
9M
R A
a
81 KH
D
3 M
Rs
A
24 KH
24 KH
c
D
6
- 72 KH
144 KHM
(' '\
\" )
/
!
c
B
3 M
T 0"1 Ka
neper 6a
7,9 M
-72 KHM
B
PRC. 2.39. EarrKa c cocpe,n;oTOqeHHOH H paBHoMepHoH HarpY3KoH:
UDL - paBHOMepHO pacnpe,n;eJIeHHaH HarpY3Ka;
a - ,n;HarpaMMa pacnpe,n;eJIeHHH HarpY3KH;
6 - 3nIOpa nOnepeqHOH CHJIbI;
B - 3nIOpa H3rH6aIOw;ero MOMeHTa
F/la8a 2. HH:JICeHepHtlH cmamU1ca
1. PaCCqHTaeM peaK«HH OlIOp R A H R B , OlIpe,n;e.IDI.H MOMeHTbI OTHOCHTeJIbHO A:
(45 x 2) + (12 x 9) x 4,5 + (24 x 12) = 9Rc
TaKHM 06pa30M: Rc = 96 kN H R A = 81 KH.
2. fIOlIepeqHbIe CHJIbI (eCJIH x 6y,n;eT paCCTO.HHHe OT TOqKH A):
,lLJrn 0 x 2, lIOlIepeqHaH CHJIa = (81 - 12x) KH (1)
,lLJrn 2 x 9, lIOlIepeqHaH CHJIa = (81 - 12x - 45) = (36 - 12x) KH
,lLJrn 9 x 12, lIOlIepeqHaH CHJIa = (81 - 12 x 9 - 45 + 96) = +24 KH
3TH pe3YJIbTaTbI MO)I{HO lIpe,n;CTaBHTb IIp.HMbIMH JIHHIDIMH, KaK lIOKa3aHO Ha
pHC. 2.39, 6.
3. W3rH6alOlI(He MOMeHTbI (eCJIH x - paCCTO.HHHe OT TOqKH A):
,lLJrn 0 x 2, M = 81x -12(x 2 / 2) = 81x - 6x 2 KHM.
fI03ToMY: B TOqKe A x = 0 H M A = 0
B TOqKe B x = 2 H M B = 162 - 24 = 138 KHM
,lLJrn 2 x 9, M = 81x - (12x 2 / 2) - 45(x - 2) = 36x - 6x 2 + 90 KHM. (2)
fIpH x = 2 H M B = 72 - 24 + 90 = 138 KHM (KaK BbIIIIe)
fIpH x = 9 H Me = 324 - 486 + 90 = -72 KHM
113rH6alOlI(HH MOMeHT MaKCHMaJIeH Me TOqKaMH B H C, TaM r,n;e dM/dx = O.
OTMeTHM, qTO 3TO Ta xe CaMaH TOqKa, B KOTOpOH lIOlIepeqHaH CHJIa paBHa JIy-
JIIO. 113 ypaBHeHIDI (2):
dM/dx = 36 - 12x = O.
CJIe,n;OBaTeJIbHO:
x = 3 M.
fIo,n;cTaBJUISI x = 3 M B ypaBHeHHe (2):
(36 x 3) - (6 x 3 2 ) + 90 = 144 KHM.
TaKHM 06pa30M, MaKCHMYM H3rH6alOlI(erO MOMeHTa paBeH 144 KHM H OH ,no-
CTHraeTCSI B TOqKe, CMelI(eHHOH Ha 3 M OT TOqKH A.
fIeperH6 lIpOHCXO,n;HT B TOqKe, r,n;e H3rH6alOIUHH MOMeHT paBeH JIyJIIO. qT06bI
HaHTH 311' TOqKY, ypaBHeHHe (2) CJIe,nyeT lIpHpaBHSITb HYJIIO H HaHTH ero lIOJIOXH-
TeJIbHbIH KopeHb.
36x - 6x 2 + 90 = O.
OTCIO,na:
x = 7,9 M (e,n;HHcTBeHHoe lIOJIO)I{HTeJIbHOe peIIIeHHe)
fI03ToMY lIeperH6 lIpOHCXO,n;HT B TOqKe, paClIOJIOXeHHOH Ha paCCTOSIHHH 7,9 M OT
TOqKH A.
2.9.4. BSnKJf (KoHCOn&)
KpOMe lIpOCTbIX 6aJIOK, cB060,n;HO JIeXalI(HX Ha Ollopax, HClIOJIb3yroTC.H 6aJIKH, BbI-
CTYIIalOlI(He B BH,l(e KOHCOJIH. B 3TOM c.rryqae TOJIbKO O,n;HH KOHeu 6aJIKH HMeeT
OlIOPy, B TO BpeM.H KaK ,naJIbHHH OT OlIOpbI KOHeu 6aJIKH OCTaeTCSI He3aKpeIIJIeH-
2.9. IiOJlKU
HbIM, KaK lIOKa3aHO Ha pHC. 2.40, a. 3aKpeIIJIeHHbIH KOHe 6aJIKH MoxeT 6bITb
BCTPoeH B KHplI HyID KJIMKY HJIH lIpOCTO lIpe,n;CTaB.IDITb C060H BbICTYIIalOlI(yIO
qaCTb 6aJIKH, JIeXalI(eH Ha Ollopax. THlIHqHbIe 3lIIOpa lIOlIepeqHOH CHJIbI H 3lIIOpa
H3rH6aIOlI(erO MOMeHTa ,nmI KOHCOJIbHOH 6aJIKH C cocpe,n;OTOqeHHbIMH TOqeqHbIMH
HarpY3KaMH lIOKa3aHbI Ha pHC. 2.40, 6, B.
W 1 W 2 w 3
I I
a
W 1
(W 1 + W 2 )
-(W 1 + w 2 + w:J
6
( '\
j'J
(
-51W 1 - 41W 2 - 31W 3
B
PRC. 2.40. KOHCOJIb - TOJIbKO cocpe,n;OTOqeHHble HarpY3KH:
a - ,n;HarpaMMa pacnpe,n;eJIeHHH HarpY3KH;
6 - 3nIOpa nOnepeqHOH CHJIbI;
B - 3nIOpa H3rH6aIOm;ero MOMeHTa
Ha pHC. 2.41 lIOKa3aHbI ,n;HarpaMMa paClIpe,neJIeHIDI HarpY3KH, 3lIIOpa lIOlIe-
peqHOH CHJIbI H 3lIIOpa H3rH6alOlI(erO MOMeHTa ,nmI KOHCOJIbHOH 6aJIKH lIPH 60JIee
peaJIbHOM COqeTaHHH paBHOMepHO paclIpe,n;eJIeHHOH H TOqeqHOH HarpY30K.
F/la8a 2. HH:JICeHepHtlH cmamUK.a
40 KH
3 M
UDL = 125 KHM
2M
a
I
-90 KH
-130 KH
6
-190 KH
-455 KHM
Pac. 2.41. KOHCOJIb - COqeTaHHe cocpe.aoTOqeHHOH H pacnpe,n;eJIeHHOH HarpY30K: '
a - ,n;HarpaMMa pacnpe,n;eJIeHHH HarpY3KH;
6 - 3nIOpa nOnepeqHOH CHJIbI;
B - 3nIOpa H3rH6aIOw;ero MOMeHTa
2.10. HanpSI>KeHMe, Aecj)opMau.MSI M M3rM6 6anoK
2. 10. 1. H3rJf6slO ee HSnpflJICeHJfe Jf HeHTpSn&HBfI nJfHJffl
I
Ha pHC. 2.42, a lIOKa3aHO, qro lIpOHCXO,n;HT, Kor,n;a cB060,n;HO OlIepTaSI 6aJIKa, HMe-1
IOlI(aSI lIpSIMoyrOJIbHOe CeqeHHe, H3rH6aeTcSI (lIporH6aeTcSI) lIO,n; B03,n;eHcTBHeM I
lIpHJIOXeHHOH HarpY3KH. BHyrpeHHHe CJIOH 6aJIKH C)l{HMaIOTCSI, a BHeIIIHHe - pac-
TSIrHBaIOTCSI. B HeKoTopoH TOqKe Me)l()];Y 3THMH lIpOTHBOlIOJIO)I{HOCTSIMH paClIOJIO-
xeHa HeH1paJIbHaH JIHHIDI, KOTOpaH He HalIpIDKeHa, TaK KaK He cxaTa H He paCTH- I
Hyra. 3lIIOpa HalIpIDKeHHM A1ISI 6aJIKH lIOKa3aHa Ha pHC. 2.42, 6. MO)I{Ho BH,l(eTh'l
qTO HalIpIDKeHHe MaKCHMaJIbHO BBepxy H BHH3Y 6aJIKH H paBHO HYJIIO Ha HeH1paJIh.:
HOM JIHHHH.
2.10. HanpJl:JICeHUe, oetjJopMa1.4UJl U U3zu6 60Jlo"
F
R A 'B Ra
,
a PaCT5I HYTbl t1 MeTaJ1J1
MaKc MYM C)l( MalO-
w.ero Hanp5l)l(eH 5I
- Het1TpaJ1bHa51 J1 H 5I (J = 0 5 PRC. 2.42. H3rH6alOw;ee HanpHxeHHe
H HeHTpaJIbHaH JIHHH:
a - ,n;HarpaMMa pacnpe,n;e-
MaKc MYM paCT5Ir Ba- JIeHHH HarpY3KH;
6 O't B lOw.ero Hanp5l)l(eH 5I 6 - 3nlOpa HanpHxeHHH
fI03TOMY TBep,l(a.H IIp.HMOyrOJIbHa.H 6aJIKa MeHee 3<p<peKTHBHa, qeM THlI Ha.H
.n;ByraBpOBa.H 6aJIKa, Y KOTOpOH OTHOIIIeHHe lIPOqHOCTH K Becy HaMHoro 60JIbIIIe.
B .n;ByraBpoBoH 6aJIKe MaKcHM)'M HalIpIDKeHIDI HClIbITbIBaIOT BepXHIDI H HIDKIDI.H lIOJI-
KH 6aJIKH, a 06JIerqeHHa.H CTeHKa Me)l(,l(y lIOJIKaMH 6aJIKH lIo.n;BepraeTC.H TOJIbKO He-
60JIbIIIOMY HalIpIDKeHHIO. <l>aKT eCKH, qT06bI eme 60JIbIIIe YMeHbIIIHTb Maccy 6aJIKH
6e3 OII(yTHMOH lIoTepH lIPOqHOCTH, 3aqacTYIO B lIOJIKaX MO)I{HO lIpO,l(eJIaTb oTBepcTIDI.
B lIpaKTHqeCKHX YCJIOBIDIX 06bIqHO HClIOJIb3yIOTC.H CJIe.n;yrolI(He .n;orryI.l(eHIDI.
. 113rH6 MaJI lIO cpaBHeHHIO C pa3MepaMH lIOlIepeqHOrO CeqeHIDI 6aJIKH, T. e.
PMJIyC H3rH6a BeJIHK lIO cpaBHeHHIO C pa3MepaMH lIOlIepeqHOrO CeqeHIDI
6aJIKH.
. fIpe,l(lIOJIaraeTCSI, tITO 6aJIKa CJIaraeTCSI H3 6eCKOHe1ffioro KOJIH1IeCTBa lIpO.n;OJIbHbIX
CJIOeB, KOTOpbIe COrrpHKaCaIOTCSI rrpH H3rn6e, HO He3aBHCHMbI ,npyr OT .n;pyra.
. fIaJIKa no.n;BepraeTcSI TOJIbKO lIpO.n;OJIbHOMY HalIpIDKeHHIO. He cym;ecTByeT pe-
3YJIbTHpyrolI(eH lIpO.n;OJIbHOH CIDIbI, .n;eHCTByIOlI(eH Ha KaKOe-JIH60 CeqeHHe
6aJIKH.
. HarpY3Ka Ha 6aJIKY Ha,n,e)I{HO Haxo.n;HTCSI B lIpe.n;eJIax ynpyrOCTH MaTepHaJIa,
TaK qTO HalIpSI)J{eHHe lIpOlIOPUHOHaJIbHO .n;e<popMaUHH.
. MO,l(YJIb ynpyrOCTH MaTepHaJIa 6aJIKH OCTaeTCSI lIOCTOSIHHbIM KaK lIPH paCTSI-
)J{eHHH, TaK H lIPH C)J{aTHH. L \ )
. fIOlIepeqHbIe CeqeHIDI, IIJIOCKHe .n;o H3rn6a, OCTaIOTCSI IIJIOCKHMH lIOCJI€t -:tI3rH6a.
. HeHTpaJIbHa.H JIHHIDI lIpOXO.n;HT qepe3 reOMeTpHqeCKHH ueHTp CeqeHIDI He3a-
BHCHMO OT <pOpMbI lIOlIepeqHOrO CeqeHHSI 6aJIKH.
OCHoBHoe ypaBHeHHe ,l(JUI H3rH6a 6aJIKH:
(J / y = M / I = E / R = Mil = EIR,
r.n;e (J - HalIpIDKeHHe, 06YCJIOBJIeHHOe H3rH60M, Ha paCCTOSIHHH Y OT HeHTpaJIbHOH
OCH; y - paCCTO.HHHe OT HeHTpaJIbHOH OCH; M - H3rH6alOlI(HH MOMeHT; I - MO-
MeHT HHepUHH ,l(JISI CeqeHHSI 6aJIKH; E - MO.n;YJIb ynpyrOCTH (MO.n;YJIb IOHra); R -
pan;HYC KpHBH3HbI 6aJIKH.
<l>OPMYJIbI ,l(JUI CeqeHHH, BKJIlOqaSI MOMeHT HHepUHH, MOMeHT COlIpOTHBJIeHIDI
CeqeHHSI H PMHYC HHepUHH, lIpe,l(CTaBJIeHbI Ha pHC. 2.43 BMeCTe C lIOlIepeqHbIMH
CeqeHIDIMH HaH60JIee paClIpOCTpaHeHHbIX 6aJIOK.
F/la8a 2. HH:JICeHepHtlH cmamUico
Ce1leHHe
MOMeHT
WIOIIWUI
lu
qf : d!
bd 3
12
y
d
bd 3
3
x x
; A-=r t
bd 3
36
!l !l
2 2
BD3 -bd 3
12
D
2
D
2
D
reD 4
32
y
nD4
64
D
y
d
D
re(D4 - d 4 )
64
PRC. 2.43. <l>OPMYJIbI CeKI(HH
MOMeHT cOllpOTllBJlelllDl
Ce1lelllDl
z = I/y
bd 2
6
bd 2
3
bd 2
Zl=-
24
bd 2
Z2=-
12
BD3 -bd 3
6D
reD 3
16
nD3
32
re(D4 - d 4 )
32D
P8)OO'C
HHepQIIII
k = Ji7A
d
Jfi
d
J3
d
J18
BD3 -bd 3
12(BD - bd)
D
J8
D
4
.J D2 -d 2
4
2.11. (/JePMbl
2. 11. cDepMbl
Pa3pa60TKa TaKHX KOHC1'pyxI.J;HH, KaK C1'pOlIHJIbHa.H <pepMa HJIH lIpOC1'paHCTBeHHa.H
KOHCTPyxI.J;IDI, COCTOSIII(HX H3 HeCKOJIbKHX 3JIeMeHTOB, coe,n;HHeHHbIX CBOHMH KOHua-
MH, BKJIlOqaeT B ce6SI OlIpe,n;eJIeHHe YCHJIHH B KIDK,l(OM 3JIeMeHTe lIPH ,n;aHHOH CHCTe-
Me HarpY30K. B 3TOM pa3,n;eJIe 6y,nyT paCCM01'peHbI TOJIbKO «lIpOCTbIe <pepMbI», T.e.
<pepMbI, 3JIeMeHTbI KqTOpbIX coe,n;HHeHbI IIIapHHpHO. Ha pHC. 2.44, a lIOKa3aHbI xeCT-
KO coe,n;HHeHHbIe 3JIeMeHTbI, Tor,n;a KaK 3JIeMeHTbI, lIOKa3aHHbIe Ha pHC. 2.44, 6, co-
e.nHHeHbI IIIapHHpHO H MOryI' cB060,n;HO BpalI(aTbC.H OTHOCHTeJIbHO TOqKH P. ,L(.mI
npocToH <pepMbI lIpe,n;lIOJIaraeTC.H, qTO:
)
. Bce 3JIeMeHTbI coe,n;HHeHbI Me C060H IIIapHHpaMH;
. lIOCKOJIbK)' 3JIeMeHTbI MOryI' cB060,n;HO BpalI(aTbCSI, B IIIapHHpax He 6y,n;eT MO-
MeHTOB H He 6y,n;eT H3rH60B 3JIeMeHTOB;
. BHeIIIHHe HarpY3KH lIpHJIOXeHbI TOJIbKO K IIIapHHpHbIM coe,n;HHeHIDIM. IIo-
3TOMY OT,n;eJIbHbIe 3JIeMeHTbI <pepMbI lIo,n;BepraIOTC.H TOJIbKO paCTSIrHBalOlI(HM
HJIH C)l{HMalOlI(HM HarpY3KaM;
)
o 0 0 0 0,'
p
WapH pHoe
coeA HeH e
F 1
,
,
,
,
,
,
,
,
,
,
,
- - --,
,
,
,
,
,
,
,
,
" F 2
..
a
6
B
F 2
R A
Ra
..
r
A
(' " I
(/ ->.
I
PRC. 2.44. <l>epMbI:
a - xeCTKoe 3aKJIenOqHOe coe,n;HHeHHe;
6 - no,n;BIDKHoe mapHHpHoe coe,n;HHeHHe;
B - coe,n;HHeHHbIH mapHHpaMH npHMoyrOJIbHbIH MO,n;YJIb <pepMbI He 06-
JIa,n;aeT BHYTpeHHe npHcyw;eH xeCTKOCTbIO;
r - coe,n;HHeHHbIH mapHHpaMH TPeyrOJIbHbIH MO,l(yJIb <pepMbI HBJIHeTCH
xeCTKHM no caMOH CBoeH npHpo,n;e;
,n; - <pepMa Y oppeHa, COCTOHm;aH H3 CBH3aHHbIX napa.rr.n:eJIbHbIMH nOHca-
MH TPeyrOJIbHbIX Mo,n;YJIeH
F/la8a 2. HH:JICeHepHOR cmamUlCO
. 3aTIDKKa - 3TO 3JIeMeHT, pa60TalOlI(HH Ha paCTIDKeHHe B KIDK,l(OM KOHue, T.e.
BOClIpHHHMalOlI(HH paCT.HrHBalOlI(yIO HarpY3KY, KOTopaSI CTpeMHTCSI YA1IHHHTb
3JIeMeHT;
. paClIopKa - 3TO 3JIeMeHT, pa60TalOlI(HH Ha cxaTHe B KIDK,l(OM KOHue, T.e.
BOClIpHHHMalOlI(HH C)l{HMalOlI(yro HarpY3KY, KOTOpaH C1peMHTCSI YKOpOTHTb
3JIeMeHT.
DOJIbIIIHHCTBO <pepM OCHOBaHO Ha 1peyrOJIbHHKe HJIH 1peyrOJIbHOH peIIIeTKe.
fIpHqHHY 3Toro MO)I{HO lIOIDITb H3 pHC. 2.44, B, r. MO)I{Ho BH,l(eTb, qTO eCJIH coe,n;H-
HeHHbIH IIIapHHpaMH lIpSIMOyrOJIbHHK lIo,n;BeprHeTCSI B03,n;eHcTBHIO CHJI FI H F 2 , TO
OH lIpOH3BOJIbHO ,n;e<popMHpyeTCSI. O,n;HaKO, eCJIH coe,n;HHeHHbIH IIIapHHpaMH 'rpe-
yrOJIbHHK lIo,n;BeprHeTC.H B03,n;eHCTBHIO Tex xe CHJI, ero <popMa He H3MeHHTC.H ,n;o Tex
nop, lIOKa He H3MeHHTCSI A1IHHa XOT.H 6bI o,n;Horo H3 ero 3JIeMeHTOB. TpeyroJIbH3j{
peIIIeTKa SIBJI.HeTCSI xeCTKOH lIO caMOH CBoeH lIpHpo,n;e. Ha pHC.. 2.44, ,n; lIOKa3aHa
THlIHqHaH CKB03HaH <pepMa, COCTO.HlI(aH H3 1peyrOJIbHHKOB. 3Ta KOHKpeTHaH CKB03-
HaH 6aJIOqHaSI <pepMa Ha3bIBaeTC.H <pepMoH C lIapaJIJIeJIbHbIMH lIO.HCaMH H 1peyrOJIb-
HOH peIIIeTKoH (<pepMoH YoppeHa).
2.11.1. MeToA CelleHJfH
OCHOBHoe lIpeHMym;ecTBo MeTo,n;a CeK«HH 3aKJIIOqaeTCSI B TOM, qTO YCHJIHe lIOqTH B
JII060M 3JIeMeHTe 06bIqHO MO)I{HO lIOJIyqHTb, pacceKaSI <pepMY lIO 3TOMY 3JIeMeHTY If I
lIpHMeH.H.H lIpHHUHlI MOMeHTOB. HalIpHMep, paCCMOTpHM, KaK, HClIOJIb3Y.H MeTO,n;
CeqeHHH, MO)I{HO OlIpe,n;eJIHTb YCHJIHSI B 1pex 3JIeMeHTax, paCCeqeHHbIX Bo06paxae- I
MOH IIJIOCKOCTblO XX Ha pHC. 2.45, a.
CeKyIUaH IIJIOCKOCTb XX ,n;eJIHT <pepMY Ha ,n;Be qaCTH. fIpe,n;lIOJIO)I{HM, qTO lIpaBWI
qaCTb <pepMbI y,n;aJIeHa. 3TO lIpHBe,n;eT K TOMY, qTO JIeBaH qaCTb lIOTepSIeT YCTOHqH-
BOCTb OTHOCHTeJIbHO coe,n;HHeHIDI Rl, eCJ1H Ha paCCeqeHHbIe 3JIeMeHTbI He 6y,n;yr
,n;eHCTBOBaTb BHeIIIHHe CHJIbI F BF , FFE H FED' KaK lIOKa3aHO Ha pHC. 2.45, 6. TaKHM I
06pa30M, 3TH BHeIIIHHe CHJIbI, lIOKa3aHHbIe Ha pHC. 2.45, B, Ha caMOM ,n;eJIe lIpe,n;- '
CTaB.1UIIOT C060H BHYTPeHHHe CHJIbI, KOTopbIe HYXHO OlIpe,n;eJIHTb B 3TOM lIpHMepe.
PaCCMo1pHM YCJIOBIDI paBHOBeCIDI JIeBOH qaCTH <pepMbI. BHeIIIHHe CHJIbI, lIpH-
JIOXeHHbIe K OTCeqeHHOMY <pparMeHTY, ,n;OJDKHbI HJIH TOJIKaTb, HJIH TSIH)'Tb IIIapHHp-
HbIe coe,n;HHeHIDI, paClIOJIOXeHHbIe CJIeBa OT CeqeHIDI XX. fIpHIDITo lIpe,n;lIOJIaraTh I
3apaHee, qTO Bce OTCeqeHHbIe 3JIeMeHTbI HaXO,lJ;.HTCSI B COCTO.HHHH paCTIDKeHIDI, TOf- I
,n;a lIOJIO)I{HTeJIbHbIH OKOHqaTeJIbHbIH pe3YJIbTaT lIo,n;TBep)l()];aeT, qTO 3JIeMeHT pa60-
TaeT Ha paCTIDKeHHe (3aTIDKKa), B TO BpeM.H KaK 01pHuaTeJIbHbIH pe3YJIbTaT:
lIo,n;pa3YMeBaeT, qTO 3JIeMeHT pa60TaeT Ha cxaTHe (paClIopKa).
JIeBaH qaCTb <pepMbI TelIepb HaxO,n;HTCSI B COCTOSIHHH paBHOBeCIDI lIO,n; ,n;eHCTBH- I
eM CHJIbI peaK«HH OlIOpbI R I , HarpY3KH BeJIWIHHOH 20 KH H 1pex HeH3BeCTHbIX CKJI I
F BF , FFE H FED' OlIpe,n;e.IDI.H MOMeHTbI OTHOCHTeJIbHO JIeBOH OlIOpbI (TOqKH lIpHJIO- I
xeHIDI Rl H o,n;HOBpeMeHHO TOqKH lIepeCeqeHIDI ,n;BYX HeH3BeCTHbIX CHJI FFE H FED)'
MO)I{HO JIerKO HaHTH 3HaqeHHe F BF . AHaJIOrWIHO, BeJIHqHHY FED MO)I{HO HaHTH,
OlIpe,n;e.IDI.H MOMeHTbI OTHOCHTeJIbHO TOqKH (1) (pHC. 2.46, 6). HaKoHeu, OlIpe,n;eJIe- I
HHe MOMeHTOB OTHOCHTeJIbHO TaKOH TOqKH, KaK P, lI03BOJIHT HaHTH BeJIHqHHY YCH- I
JIIDI B FE. !
2.11. tPepMbl
2,4 M 3 M
20 KH 30 KH
B
x
9 M D
R 1
fJ
a
20 KH
x
F BF
------.....--.
I ",
I "" F.
,,' FE
p
,,------------
,
,
,
\Q
,
,
,
FeD
. - - - - - - ..,- - -
Puc. 2.45. MeTo,n; CeqeHHH:
a - THnHqHaH <pepMa )];JIH
aHaJIH3a MeTo,n;OM CeqeHHH;
6 - JIeBaH qaCTb - paBHO-
BeCHe no,n;,n;epXHBaeTCH CH-
JIaMH F BF , FFE H FED
x
R 1
6
ITpe)l{)J;e qeM lIpHCTYIIaTb K HaxO)l{)J;eHHIO BbIIIIeyrrOM.HHYTbIX CHJI, He06xo,nHMO
paCCqHTaTb BeJIHqHHbI Rt H R 2 , HCnOJIb3YR npHHUHn MOMeHTOB, 06cyx,n;aBIIIHHCR
paHee.
Onpe,neJIHM MOMeHTbI OTHOCHTeJIbHO Rt:
(20 x 2,4) + (30 x 5,4) = 9R 2 .
CJIe,nOBaTeJIbHO:
Rz = 23,33 KH.
R 1 = 26,67 KH.
YCHJIHe B DF (pHC. 2.46, a)
CeKyI.I.J;a.H IIJIOCKOCTb XX:
Onpe,neJUIeM MOMeHTbI OTHOCHTeJIbHO TOqKH lIpHJIOXeHIDI R t :
C \ \ I
(
20 x 2,4 + FBFx 2,4 = O.
II03TOMY:
F BF = -20 KH.
ITOCKOJIbKY 3HaqeHHe F BF RBJlReTCR OTpHuaTeJIbHbIM, BF - pacnopKa.
F/la8a 2. HH:JICeHepHaJI cmamUica
2,4 M 20 KH
20 KH
3M
20 KH
F ED = 35 KH
p
r---------
"
, \1#
Q
, \
,
,
I
I
,
.
-...
xF ED = 35 KH
x F BF = -20 KH
----..
x
D
26,67 KH
R 1
-------,-,-,-(1)
"
x
26,67 KH
R 1
x
a
6
B
F AF = -28,3 KH
Y
p
:'; ::A5; - - - -, FFE = -16,4 KH
,R 1/
, \ '
: Q\ I
: FED = 35 KH
..
2,4 M
..
..
..
..
..
..
...."...... h EC = -4 2 KH
J!!!I z '
,
,
,
,'8
,
,
,
,
,
,
,
-------- .
z
36M
D
r
A
R 2 = -23,33 KH
Puc. 2.46. Y CHJIHH B 3JIeMeHTax <pepMbI:
a - YCHJIHe B BF; 6 - YCHJIHe BED; B - YCHJIHe B FE;
r - YCHJIHe B AF; ,n; - YCHJIHe B EC
YCHJIHe B ED (pHC. 2.46, 6)
CeK}'IUa.H IIJIOCKOCTb XX:
Onpe.neJUIeM MOMeHTbI OTHOCHTeJIbHO TOqKH (1):
(26,67 x 5,4) - (20 x 3) - FED x 2,4 = O.
IT03TOMY:
FED = 35 KH.
ITOCKOJIbKY 3HaqeHHe FED .HBJUIeTC.H nOJIO)I{HTeJIbHbIM, ED - 3aTIDKKa.
YCHJlHe B FE (pHC. 2.46, B)
CeK}'IUa.H IIJIOCKOCTb XX:
Onpe.neJUIeM MOMeHTbI OTHOCHTeJIbHO TOqKH P:
(20 x 2,4) - FEE x XX - FED x 2,4 = O.
48 - FEE x 2,4cos9 - 35 x 2,4 = o.
r.ne:
9 = 24°.
II03ToMY:
FEE = -16,4 KH.
IIoCKOJIbKY 3HaqeHHe FEE .HBJUIeTC.H OTpHuaTeJIbHbIM, FE - paClIopKa.
YCHJIHe B AF (pHC. 2.46, r)
CeK}'IUa.H IIJIOCKOCTb XX:
Onpe.neJUIeM MOMeHTbI OTHOCHTeJIbHO TOqKH P:
16,4 xx - FAExy - 35 x 2,4 = O.
2.11. (/)ePMbl
II03ToMY:
F AF = -28,3 KH
ITOCKOJIbKY 3HaqeHHe F AF RBJUIeTCR OTpHuaTeJIbHbIM, AF - paClIopKa.
YCHJIHe B EC (pHC. 2.46, ,n;)
Ce a.H IIJIOCKOCTb zz:
Onpe,neJUIeM MOMeItTbI OTHOCHTeJIbHO TOqKH (2):
23,33 x 3,6 + F EC x Z = 0
II03TOMY:
F EC = -42KH
ITOCKOJIbKY 3HaqeHHe FK RBJUIeTC.H OTpHuaTeJIbHbIM, EC - pacnopKa.
OTMeTHM, qTO BO Bcex paCCMOTpeHHb.x BbIIIIe c.rryqa.HX ,no Tex nop, nOKa YCH-
J
JIID! B 3JIeMeHTax HeH3BeCTHbI, npe,nnOJIaraJIOCb, qTO 3JIeMeHTbI HaxO,lUITCR B COCTO-
HHHH paCTIDKeHIDI.
2. 12. rJfAPOCTBTJflfeCKOe ABSneHJfe
)KH,nKOCTb B cocy,ne, lIOKa3aHHa.H Ha pHC. 2.47, a, OKa3bIBaeT ,naBJIeHHe Ha CTeHKH H
,ZJ;HO cocy,na. aBJIeHHe, OKa3bIBaeMoe )l{H)J;KOCTblO, 3aBHCHT OT:
. llJIOTHOCTH )l{H)J;KOCTH (p);
. BbICOTbI cToJI6a )l{H)J;KOCTH, ,neHCTByrolI(eH Ha TeJIO (h);
. rpaBHTaUHoHHoH lIOCTORHHOH (g).
- BbiCOTa
rViAPOCTaTVI"Ie-
CKoro Hanopa
a
6
Puc. 2.47. rH.D:pOCTaT ecKoe ,n;aBJIeHHe:
a - ,n;aBJIeHHe B cocy,n;e, co,n;epXalI(eM )f{H)J;KOCTb;
6 - ,n;aBJIeHHe PI = P 2 H 3aBHCHT OT h. ,n;aBJIeHHe He 3aBHCHT OT llJIOII(3)J;H.
Ha pHC. 2.47, 6 lIOKa3aHbI ,nBa cocy,na A H B, B KOTOpbIX BbICOTa cToJI6a )l{H)J;KO-
CTH (h) o,nHHaKOBa. IIpH YCJIOBHH, qTO IIJIOTHOCTb )l{H)J;KocTeH B 060Hx C.rrYqa.HX
O,ZJ;HHaKOBa, H nOCKOJIbKY rpaBHTaUHOHHa.H nOCTORHHa.H B 060HX C.rrYqa.HX o,nHHaKO-
Ba, ,naBJIeHIDI PI H P2 6y.nyT o,nHHaKOBbI, HeCMOTpR Ha TOT <paKT, qTO IIJIOII(a,zJ;H
OCHOBaHIDI KOHTeHHepOB pa3JIWIHbI. BbICOTa cToJI6a )l{H)J;KOCTH h OTHOCHTe!lpf!O
( -"
,ZJ;aHHOH TOqKH TaIOKe Ha3bIBaeTC.H: \
. BbICOTa rH;:J;pOCTaTWIeCKoro Hanopa;
. BbICOTa ,naBJIeHIDI.
F/la8a 2. HH:JICeHepHaJI cmamUica
aBJIeHHe (P) B )I{H,l(KOCTH onpe,n;eJUIeTCR CJIe,nyIOII(HM BbIpaxeHHeM:
P = P x g x h,
r,ne P - ,naBJIeHHe (ITa); h - r.rry6HHa, Ha KOTOpOH H3MepReTcR ,naBJIeHHe (M);
p _ IIJIOTHOCTb )I{H,l(KOCTH (Kr/M 3 ); g - rpaBHTaUHOHHa.H nOCTORHHa.H (9,81 M/C 2 ).
llpHMep
Ha pHC. 2.48 nOKa3aH KOHTeHHep, 3alIOJIHeHHbIH napa<pHHoM ,no BbICOTbI 2 M.
OlIpe,neJIHTb ,naBJIeHIDI PI H P2, eCJIH H3BeCTHO, qTO IIJIOTHOCTb napa<p HHa paBHa
800 Kr/M 3 H g = 9,81 M/C 2 .
PI = hI x P x g = 2 M x 800 Kr / M 3 x 9,81 M / c 2 = 15696 ITa HJIH 15,696 KITa.
P2 = h 2 x P x g = 1 M x 800 Kr / M 3 x 9,81 M / C 2 = 7848 lla HJIH 7,848 KITa.
B TOqKe Ha nOJIOBHHe r.rry6HHbI ,naBJIeHHe paBHO
nOJIOBHHe OT 3HaqeHIDI ,naBJIeHIDI Ha ,nHe cocy,na. Ha
nOBepXHOCTH ,naBJIeHHe paBHO HYJIIO, nOCKOJIbK}' r.rry-
6HHa OTCyTCTByeT. CJIe,noBaTeJIbHO, ,naBJIeHHe npo-
lIOPUHOHaJIbHO r.rry6HHe, Ha KOTOpOH OHO H3MepR-
eTCR.
2M
1 M
Puc. 2.48. <l>aKTopbI, BJIHSI-
IOIJJ;He Ha ,n;aBJIeHHe
2. 12. 1. p,SSneHJfe HS nosepXHOCT&,
HSXOAR YIOCR S JlCJfAKOCTJf
PaccMoTpHM npRMoyrOJIbHbIH KOHTeHHep, nOKa3aHHbIH Ha pHC. 2.49. B npe,nbI,ny-
lI(eM npHMepe 6bmo nOKa3aHO, qTO lIOJIOBHHa ,naBJIeHIDI ,nOCTHraeTC.H Ha lIOJIOBHHe
rJIy6HHbI. ITOCKOJIbKY ,naBJIeHHe H3MeIDIeTCR OT HYJUI Ha lIOBepXHOCTH ,no MaKCHMa-
JIbHOrO 3HaqeHIDI Ha lIOJIHOH r.rry6HHe, ,naBJIeHHe Ha nOJIOBHHHOH r.rry6HHe RBJUIeT-
CR cpe,nHHM ,naBJIeHHeM (PA). TaK:
PA =(PI + P2) /2 = P2 /2 (TaK KaKPI = 0)
2 M
Puc. 2.49. ,n;aBJIeHHe Ha nOBepXHOCTb, Haxo,n;}JIJJ;yroCSI B XH,lI;KOCTH
2.11. f/>epMbl
n03TOM)' CHJIa (Hanop), ,neHcTBYIOII(a.H Ha cTeHKY KOHTeHHepa 6y,neT paBHa
rrpoH3Be,neHHIO IIJIOII(a,zJ;H Haxo,lUIlI(eHCR B )l{H)J;KOCTH CTeHKH (As) Ha cpe,nHee ,naB-
JIeHHe (p A) . To eCTb:
Fs = PAX As ·
r,n;e FS - CHJIa (HanOp), ,neHCTByrolI(aR Ha CTeHKY KOHTeHHepa (H); PA - cpe,n;Hee
,n;aBJIeHHe (ITa); As - llJIOII(a,zJ;b HaxO,lUIlI(eHCR B )l{H)J;KOCTH CTeHKH KOHTeHHepa (M 2 ).
IIpuMe"taHue.
1. ITpe,nnOJIaraeTCR, qTO CHJIa npHJIOXeHa B ueHTpe llJIOII(a,zJ;H CTeHKH KOHTeH-
Hepa.
2. CHJIa, ,neHcTByrolI(a.H Ha ,nHO KOHTeHHepa, BbIqHCJUIeTCR qepe3 MaKCHMaJIb-
Hoe, a He qepe3 cpe,nHee ,naBJIeHHe.
IIpHMep , (
Ha pHC. 2.49 nOKa3aH npRMoyrOJIbHbIH pe3epByap C IIJIOma,zJ;blO ,nHa 9 M 2 . OH
HanOJIHeH BO,nOH ,no BbICOTbI 2 M. MCnOJIb3YR g = 9,81 M/C 2 , BbJqHCJIHM:
1) ,naBJIeHHe, ,neHcTByrolI(ee Ha ,nHO pe3epByapa;
2) CHJIY, ,neHcTByroll(yIO Ha ,nHO pe3epByapa;
3) cpe,nHee ,naBJIeHHe, ,neHcTByrolI(ee Ha CTeHKH pe3epByapa;
4) CHJIY (F s ), ,neHcTByroll(yIO Ha CTeHKY pe3epByapa;
5) BbICOTY (h) OT OCHOBaHIDI pe3epByapa, Ha KOTOpOH ,neHCTByeT CHJIa (Fs);
6) P B = h x p x g = 2 M x 1000 Kr / M 3 x 9,81 M/ C 2 = 19220 ITa = 19,22 KIT a;
7) F B = PB x A B = 19220 ITa x 9 M2 = 172980 H = 172,98 KH;
8) P A = (Ps + PB) / 2 = (0 ITa + 19220 ITa) / 2 = 9600 ITa = 9,6 KITa;
9) Fs =PA +As =9600ITax6M2 =57600H=57,6KH (r,ne As - IIJIOII(a,zJ;b
HaxO,lUIlI(eHCR B )l{H)J;KOCTH cTeHKH);
10) CHJIa Fs ,neHcTByeT Ha ueHTp IIJIOII(a,zJ;H Haxo,nRlI(eHCR B )l{H)J;KOCTH CTeHKH
pe3epByapa, T. e. Ha >i x 2 M = 1 M BblIIIe OCHOBaHIDI pe3epByapa.
2.12.2. 3SKOH nSCKsnR
3aKOH ITaCKaJI.H YTBep)K)];aeT, qTO:
,n:aBJIeHHe, OKa3LIBaeMoe Ha 1KII,ZJ;KOCTL B KOHTeHHepe, nepe,n;aeTCJI 1KII,ZJ;K0CTLIO
O,lUlHaKOBO BO Bcex HanpaBJIeHHJIX.
3TO lIOKa3aHO Ha pHC. 2.50, a. aBJIeHHe (P), KOTopoe RBJUIeTCR o,nHHaKOBbIM B
rrpe,neJIax 3aMKH)'Toro npOCTpaHCTBa, MoxeT 6bITb BbJqHCJIeHO CJIe,nyroII(HM 06pa-
30M:
,D:aBJIeHHe (P) = CHJIa (F)/IIJIOII(a,zJ;b (A) = 100 H/0,5 M 2 = 200 H/M2 = 200 ITa.
B COOTBeTCTBHH C 3aKOHOM ITaCKaJI.H ,naBJIeHHe B 200 ITa ,neHcTByeT o,nHHaKOBO
Ha Bce lIOBepXHOCTH. OHO ,neHcTByeT Ha lIopIIIeHb, Ha CTeHKY UHJIHH,l(pa H Ha
KpbIIIIKY UHJIHH,l(pa. ITOCKOJIbKY Macca )l{H)J;KOCTH MaJIa, B 3TOM npHMepe rHJJ;pOCTa-
TWleCKHM ,naBJIeHHeM H COOTBeTCTByrolI(HMH CHJIaMH MO)I{HO npeHe6peqb.
Ha pHC. 2.50, 6 nOKa3aHbI ,nBa UHJIHH,l(pa pa3JIHqHOH nJIOII(a,zJ;H, coe,nHHeHHbIe B
o,n;Hy CHCTeM)' H HanOJIHeHHbIe BO,nOH HJIH rHJJ;paBJIHqeCKOH )l{H)J;KOCTblO. aBJIeHHe
F/la8a 2. HH:JICeHepHaJI cmamUlCO
.. CVlJ1a (F) = 100 H
)KVlAKOCTb
nJ10W.aAb (A) = 0,5 M 2
a
HarpY3-
Ka
CVlJ1a (F 1 ) = 200 H
t C..m8 (F 2 )
nJ1ow.aAb (A 1 ) = 0,5 M 2
nJ10W.aAb (A 1 ) = 0,1 M 2 I
6
CoeAVlHVlTeJ1bHa51 )KVlAKOCTb
Tpy6a
Puc. 2.50. 3aKoH llaCKaJIH:
a - ,n;aBJIeHHe, ,n;eitcTByK>lI(ee Ha )f{H)J;KOCTb B 3aMKH)'TOM 06'beMe;
6 - CHCTeMa C0061I(aIOII(HXCH COCy,n;OB
B CHCTeMe BbIqHCJUIeTCR npH nOMOIl(H paHee npHBe,neHHoH <pOPMYJIbI p = FlA.
AmI MeHbIIIero UHJIHH,l(pa ,naBJIeHHe paBHO:
p = Fi I At = 200 N 10,1 M 2 = 2000 HI M 2 = 2000 ITa HJIH 2 KITa.
O,nHaKo ,nBa UHJIHH,l(pa coe,nHHeHbI BMeCTe, 06pa3YR o,nHY CHCTeMY, CJIe,nOBa-
TeJIbHO, B COOTBeTCTBHH C 3aKOHOM ITaCKaJI.H cyw:eCTByeT 06lI(ee ,naBJIeHHe B 2 KITa,
,neHcTByrolI(ee BO BceH CHCTeMe. IT03TOMY CHJIa, ,neHcTByrolI(a.H co CTOpOHbI 60JIb- i
IIIero nopIIIIDI Ha HarpY3KY, 6y,neT paBHa:
F 2 = P x A 2 = 2 KITa x 0,5 M2 = 1000 H HJIH 1 KH.
CHJIa F 2 B IDITb pa3 60JIbIIIe, qeM CHJIa Ft, lIOCKOJIbKY IIJIOII(a;:J;b lIOpIIIIDI A 2 B I
nRTb pa3 60JIbIIIe IIJIOII(a,zJ;H lIOpIIIIDI At. TaKa.H B03MO)I{HOCTb YBeJIWIHBaTb CHJIbI,
npHMemrn rHJJ;pOCTaTHqeCKHe lIpoueCCbI, HCnOJIb3yeTC.H B TaKHX YCTpOHCTBax, KaK
rHJJ;paBJIWIeCKHe npeCCbI, rH;ipaBJIWIeCKHe ,nOMKpaTbI H fHJJ;paBJIHqeCKHe TOpM03-
HbIe CHCTeMbI cpe,nCTB nepe,nBIDKeHID!. O,nHaKo CJIe.nyeT OTMeTHTb, qTO, XOT.H 60JIb-
IIIHH nopIIIeHb ,neHcTByeT C CHJIOH, B IDITb pa3 60JIbWeH, qeM CHJIa, ,neilcTByrolI(asI ,
Ha MeHbIIIHH nopIIIeHb, 60JIbIIIHH lIopweHb npoxo,nHT TOJIbKO IDITyID qaCTb paCCTO-
RHID!, npeo,nOJIeBaeMOro MeHbIIIHM nopIIIHeM.
rnABA 3
MH>KEHEPHASI
AMHAMMKA
3.1. MH>KeHepHaSi AMHaMMKa
KaK CKa3aHO B HaqaJIe BTOpOH fJIaBbI, HIDKeHepHa.H MexaHHKa MO:>KeT 6bITb pa3,ne-
JIeHa Ha CTaTHKY H ,nHHaMHKY. fJIaBa 3 onlfcbIBaeT ,nHHaMHKY, B KOTOpOH H3yqa1OT-
CR 06'bCKTbI B ,nBIDKeHHH. '
3.2. Pa60Ta
Kor,na npHJIOXeHHa.H K TeJIY CHJIa npHBo,nHT ero B ,nBIDKeHHe, rOBOp.HT, qTO CHJIa
COBepIIIaeT pa60TY. BbInOJIHeHHaR pa60Ta onpe,neJIReTCR KaK npOH3Be,neHHe npOH-
.n;eHHoro paCCTO.HHIDI B MeTpax (M) Ha BeJIHqHHY npHJIOXeHHOH CHJIbI B HblOTOHax
(H), H3MepeHHoH B HanpaBJIeHHH ,nBIDKeHHR. II03ToMY BbIlIOJIHeHHa.H pa60Ta
H3MepReTC.H B HbIOTOHaX-MeTpax, a e,nHHHueH pa60TbI RBJUIeTCR ,lCKOYJIb (,l(:>K),
1 H M = 1 ,[bK.
Ha pHC. 3.1, a lIOKa3aHO TeJIO, ,nBIDKYJI.(eeCR no,n ,neHcTBHeM CHJIbI F no fOpH-
30HTaJIbHOH IIJIOCKOCTH. IIoCKOJIbKY CHJIa ,neHcTByeT Ha TeJIO napaJIJIeJIbHO fOpH-
30HTaJIbHOH IIJIOCKOCTH, BbInOJIHeHHa.H pa60Ta paBHa npOH3Be,neHHIO CHJIbI F (H)
F = 50 H
.- - - - - - --.
. .
. .
----- . .
. .
a
1 4
S=3M
I
.- - - - - - - -
.
.
I
.
F H = 50 cos 30 0
6
1 4
S=3M
.1
Puc. 3.1. Pa60Ta:
a - BbInOJIHeHHaH CHJIOH F;
6 - BbInOJIHeHHaH CHJIOH F H
4.3255
(:;, F/la8a 3. HH:JICeHepHlUl OUHaMUlCa
Ha paccToRHHe S (M). ECJIH CHJIa paBHa 50 H, a paCCTORHHe 3 M, TO BbIlIOJIHeHHasI
pa60Ta paBHa:
50 H x 3 M = 150 H · M = 150 ,L(x.
Ha pHC. 3.1, 6 CHJIa HalIpaBJIeHa no,n yrJIOM K HanpaBJIeHHIO ,nBIDKeHHR TeJIa.
B 3TOM c.rryqae BeKTOp CHJIbI CJIe.nyeT pa3JIO)I(HTb Ha BepTHKaJIbHyro H ropH30HTaJIb-
HyID COCTaBIDIIOII(He, KaK nOKa3aHO Ha pHCyJlKe. COCTaBJUIIOII(a.H CHJIbI, HanpaBJIeH-
Ha.H lIapaJIJIeJIbHO ,nBIDKeHHIO TeJIa, paBHa F cos a.. TI03TOMY BbInOJIHeHHa.H pa60Ta
paBHa S x F cos a. ,l(x. ECJIH CHJIa (F) BHOBb paBHa 50 H, paCCTORHHe (s) CHOBa paB-
HO 3 M H yrOJI a. paBeH 30°, BbInOJIHeHHa.H pa60Ta 6y,neT paBHa:
W = 3 M x 50 H x 0,866 = 129,9 H · M = 129,9 ,L(x.
3.3. 3HeprMSI
ECJIH TeJIO cnoc06HO COBepIIIaTb pa60TY, rOBopRT, qTO OHO 06JIa,naeT 3HeprHeH.
3HeprIDI cyw:ecTByeT B pa3JIHqHbIX <popMax, H ee MO)I{HO paccMaTpHBaTb KaK «3a-
naceHHyID pa60TY», o)l{H)J;alOmyIO CBoero HCnOJIb30BaHIDI. HanpHMep:
. XHMWIeCKaR 3HeprIDI norJIolI(aeTCR HJIH BbICB060)K)];aeTCR B npouecce peaK-
UHH (HalIpHMep, lIpH cropaHHH HCKonaeMoro TOIIJIHBa);
. aTOMHa.H 3HeprIDI BbICB060)K)];aeTCR npH paClI(eIIJIeHHH HJIH coe,nHHeHHH
aTOMHbIX qaCTHU. PaClI(eIIJIeHHe aTOMHbIX qaCTHI( Ha3bIBaeTCR ,neJIeHHeM, a
coe,nHHeHHe aTOMHbIX qaCTHU Ha3bIBaeTCR CHHTe30M. TIpH 3THX peaKI(IDIX
BbI,neJUIeTCR 60JIbIIIOe KOJIHqeCTBO TeIIJIOBOH 3HeprHH;
. TellJIOByro 3HeprHIO MO)I{HO pa3,neJIHTb Ha RBHyID (OlI(yTHMyIO) H CKpbITYIO
TeTIJIoTY. .HBHa.H TeIIJIOTa onpe,neJUIeTCR KOJIWIeCTBOM 3HeprHH, oT,naBaeMoH
HJIH nOJIyqaeMoH npH HarpeBe HJIH OCTbIBaHHH TBep,noro TeJIa, )l{H)J;KOCTH HJIH
ra3a. CKpbITa.H TeTIJIOTa - 3HeprHR, He06xo,nHMa.H .nIDI H3MeHeHIDI arperaT-
Horo COCTORHIDI TBep,noro TeJIa, )l{H)J;KOCTH HJIH ra3a lIPH lIOCTORHHOH TeMne-
paTYPe;
. MeXaHlNeCKa.H 3HeprIDI MoxeT 6bITb no,npa3,neJIeHa Ha nOTeHUHaJIbHyID 3Hep-
rHIO, KHHeTHqecKyID 3HeprHIO H 3HeprHIO ,ne<p0pMaUHH.
1. TIoTeHUHaJIbHa.H 3HeprIDI (B KOHcepBaTHBHoH cHcTeMe) - 3TO 3HeprIDI,
KOTOpOH 06JIa,naeT TeJIO BCJIe,nCTBHe CBoero nOJIOXeHIDI B npOCTpaHCTBe.
HanpHMep, lIOCJIe BbInOJIHeHIDI CBaHHbIM KOlIpOM pa60TbI no no,nIDITHIO
MOJIOTa, 3Ta pa60Ta coxpaIDIeTCR B MOJIOTe KaK lIOTeHUHaJIbHa.H 3HeprIDI.
2. KHHeTHqeCKa.H 3HeprIDI - 3TO 3HeprIDI, KOTOpOH 06JIa,naeT TeJIO 6JIaro,na-
pR CBoeH CKOpOCTH. HanpHMep, lIpH na,neHHH MOJIOTa CBaHHoro Konpa ero
nOTeHUHaJIbHa.H 3HeprIDI YMeHbwaeTCR lIpRMO lIponOpUHOHaJIbHO lIOTepe
BbICOTbI. KHHeTHqeCKa.H 3HeprIDI npH 3TOM YBeJIWIHBaeTCR npRMO npo-
nOpUHOHaJIbHO B03paCTaHHIO CKOpOCTH. TIoTeHUHaJIbHa.H 3HeprIDI npe06-
pa3yeTcR B KHHeTHqecKyID 3HeprHIO BCJIe,nCTBHe ,nBIDKeHIDI MOJIOTa. B MO-
MeHT y,napa MOJIOTa 0 CBalO BCR lIOTeHUHaJIbHaR 3HeprIDI yxe npe06pa30-
BaHa B KHHeTHQecKyID 3HeprHIO, KOTOpa.H H HClIOJIb3yeTcR .nIDI COBepIIIe-
HIDI pa60TbI, a KOHKpeTHO .nIDI Toro, qT06bI 3a6HTb CBalO B 3eMJIIO.
KHHeTHqeCKa.H 3HeprIDI paBHa .!. m V 2 .
2
3.4. MOll/llocmfJ
3. 3HeprIDI ,ne<popMaUHH (B KOHcepBaTHBHoH cHcTeMe) - 3TO 3HeprIDI, Ha-
KOIIJIeHHa.H B HanpIDKeHHOM yrrpyrOM MaTepHaJIe. HanpHMep, eCJIH MeTaJI-
JIHqeCKHH CTepxeHb y.n.rrHHeH pacTRrHBalOlI(eH CHJIOH, Han CTep)I{HeM co-
BepIIIeHa pa60Ta. IIpH YCJIOBHH, qTO ,ne<popMaUIDI He BbIIIIJIa 3a npe,neJIbI
06JIaCTH yrrpyrHX ,ne<popMaUHH .nIDI ,naHHoro MaTepHaJIa, BbInOJIHeHHaB pa-
60Ta coxpaIDIeTCR B paCT.HHYTOM CTep)I{He B BH)];e 3HeprHH ,ne<popMaUHH.
3Ta 3HeprIDI MoxeT 6bITb BbICB060)l{)];eHa nOCJIe YCTpaHeHIDI ,ne<popMHPY-
IOlI(eH CHJIbI. TaKHe xe paccyx,neHIDI npHMeHHMbI H B TOM c.rryqae, Kor,na
CTepxeHb 3aKpyqeH, KaK TOpCHOHHbIH BaJI.
3.3. 1. COXpSHeHJfe 3HeprJfJf
3aKOH coxpaHeHIDI 3HeprHH 3aKJIIOqaeTCR B CJIe.nyIOlI(eM: 3HeprIDI He MoxeT 6bITb
C03,naHa HJIH yJlHqTOXeHa, OHa TOJIbKO npe06pa30BbIBaeTC.H H3 O,nHOH <pOpMbI B
)
,n;pyryIO. 5
HanpHMep, Ha 3JIeKTpOCTaHUHH XHMHqeCKa.H 3HeprIDI roplOqero BbICB060)l{)];a-
eTCH npH C)l{HraHHH H npe06pa3yeTC.H B TeIIJIOByro 3HeprHIO, KOTOpa.H, B CBOIO oqe-
pe,n;b, C03,naeT nap B KOTJIe. IIap BpalI(aeT TYP6HHY, KOTOpa.H npe06pa3yeT 3HeprHIO
napa B MeXaHHqecKYIO 3HeprHIO. 3Ta MeXaHHqeCKa.H 3HeprIDI npe06pa3Y TCR B
3JIeKTIlWlecKYIO 3HeprHIO reHepaTopOM nepeMeHHoro TOKa, npHBo,nHMbIM B ,nBIDKe-
HHe Typ6HHOH. Bo Bcex 3THX npoueccax npe06pa30BaHIDI npOHCXO,lUIT nOTepH
3HeprHH BCJIe,nCTBHe HeCOBepIIIeHCTBa HClIOJIb3yeMoro 060Py,nOBaHHR. «IIOTepRH-
HaR» 3HeprIDI He HCqe3aeT (3aKOH coxpaHeHIDI 3HeprHH), HO OHa npe06pa3yeTcR B
Tame <pOpMbI 3HeprHH, KOTopbIe He BHOCRT BKJIan B nOJIe3HyID pa60TY. HanpHMep,
B pe3YJIbTaTe pa60TbI, BbInOJIIDIeMOH .nIDI npeo,nOJIeHIDI TpeHIDI, HarpeBalOTCR
pa60qHe nOBepXHOCTH H CMa30qHbIe MaTepHaJIbI.
3.4. MO HOCTb
MOII(HOCTb - 3TO CKOpOCTb BbInOJIHeHIDI pa60TbI, H MaTeMaTHqeCKH ee MO)I{HO
BbIpa3HTb CJIe,nyroII(HM o6pa30M:
MOII(HOCTb (BT) = BbIlIOJIHeHHa.H pa60Ta (,L(x)/3aTpaqeHHOe BpeM.H (c) =
= CHJIa (H) x CKOpOCTb (M/C).
E,nHHHua MOII(HOCTH BaIT (BT), r,ne 1 BT paBeH pa60Te B 1 ,L(x, BbInOJIHeHHOH
3a 1 c.
npHMep.
TeJIo BeCOM 5 KH HyxHO no,nIDITb Ha BbICOTY 15 M 3a 10 c. Onpe,neJIHTb Tpe6ye-
MyIO MOII(HOCTb.
BbInOJIHeHHa.H pa60Ta = CHJIa (Bec TeJIa) x npOH,neHHOe paCCTORHHe =
= 5 KH x 15 M = 75 KH M = 75 .
Tpe6yeMaR MOII(HOCTb = BbInOJIHeHHa.H pa60Ta/BpeMR = 75 K,[(x/l0 C =
= 7,5 KBT (lIpH 100% K03<P<PHUHeHTe nOJIe3HOrO ,neHcTBIDI).
(::: F/la8a 3. HH:JICeHepHaJI OUHaMUlCa
3.5. KOsct>ct>MLJ.MeHT none3Horo AeMcTBMSI
K03<P<PHUHeHT nOJIe3HOrO ,neHCTBIDI (KII ) - 3TO Mepa «nOJIe3HOCTH» MaIIIHHbI,
lIpouecca HJIH onepaUHH.
KII,LJ; (,,) = [BbIXO,nHasI pa60Ta (HJIH MOII(HOCTb)/BXO,nHasI pa60Ta (HJIH MOII(HOCTb)].
KII,LJ; MO)I{HO BbIpaxaTb B lIpoueHTax (%) HJIH B ,neCRTWIHbIX ,nOIDIX OT 1. Ha
npaKTHKe Krr YCTpoHCTBa HHKor,na He MoxeT ,nOCTHraTb 100% HJIH 1.
npHMep.
ECJIH Krr lIo,n'beMHHKa B npe,nbI.D;ylI(eM lIpHMepe paBeH 80%, Tpe6yeTcR BbI-
qHCJIHTb <paKTWIeCKYIO Tpe6yeMyID MOII(HOCTb.
KII,LJ; (%) = (BbIXO,nHasI MOII(HOCTb x 100)/Bxo,nHasI MOII(HOCTb.
CJIe,noBaTeJIbHO 80% = 7,5 KBT/BXO,nHasI MOII(HOCTb
OTclO,na BXO,nHasI MOII(HOCTb = (7,5 x 100)/80 = 9,375 KBT.
3.6. CKOPOCTb M YCKopeHMe
. MO.D;yJIb CKOpOCTH - 3TO CKaJI.HpHasI BeJIHqHHa, lIOCKOJIbK}' HMeeT TOJIbKO
qHCJIOBOe 3HaqeHHe (HalIpHMep, 30 KM/q).
. CKOpOCTb - 3TO BeKTOpHasI BeJIWIHHa, nOCKOJIbKY HMeeT H qHCJIOBOe 3Haqe-
HHe, H HalIpaBJIeHHe (HanpHMep, 30 KM/q Ha ceBep).
. Y CKopeHHe - 3TO 6bICTpoTa H3MeHeHIDI CKOpOCTH.
3.6.1. Mo,qyn& CKOpOCTJf
MO.D;yJIb CKOpOCTH - 3TO 6bICTpOTa H3MeHeHIDI npOH,neHHOrO paCCTORHIDI. To eCTb
MO.D;yJIb CKOpOCTH = paccToRHHe/BpeM.H. 06bIqHO MO.D;yJIb CKOpOCTH H3MepReTCR B
KHJIOMeTpax B qac (KM/q) HJIH B MeTpax B ceKYH.D;Y (M/C).
3.6.2. CKOPOCT&
CKOpOCTb - 3TO 6bICTpOTa H3MeHeHIDI paCCTORHIDI, npoH,neHHoro B onpe,neJIeHHOM
HanpaBJIeHHH. 0 TeJIe, ,nBIDKyI.I:(eMCR C nOCTORHHOH CKOpOCTblO lIO lIpRMOH JIHHHH,
rOBopRT, qTO OHO ,nBIDKeTC.H paBHOMepHO H np.HMOJIHHeHHO. TeJIo ,nBIDKeTCR C no-
CTORHHOH CKOpOCTblO, eCJIH 3a paBHbIe npOMexyrKH BpeMeHH OHO lIpOXO,nHT
paBHbIe paCCTORHIDI B,nOJIb lIpRMOH JIHHHH.
CKOpOCTb = ds/dt B 3a,naHHOM HanpaBJIeHHH.
3.6.3. YCKopeHJfe
YCKopeHHe - 3TO 6bIcTpoTa H3MeHeHIDI CKOpOCTH TeJIa:
. TeJIO ,nBIDKeTCR paBHOYCKopeHHO, T.e. C nOCTORHHbIM YCKopeHHeM, eCJIH 3a
paBHbIe lIpOMexyrKH BpeMeHH CKOpOCTb TeJIa H3MeIDIeTCR Ha O,nHY H 11' :>Ke
BeJIWIHHY. YCKopeHHe H3MepReTCR B M/C 2 ;
. TopMoxeHHe HJIH 3aMe.n.rreHHe ,nBIDKeHIDI - lIpouecc 06paTHbIH YCKopeHHIO.
Ero qaCTO onpe,neJUIIOT KaK OTpHuaTeJIbHOe YCKopeHHe.
3.6. C1copocmb u YCICopeHue
3.6.4. YpssHeHJffl, OTHOCfI JfeCfI K CKOpOCTJf Jf YCKopeHJfIO
B npHBe,n;eHHbIX HIDKe ypaBHeHIDIX HCnOJIb3yroTC.H CJIe,n;yrolI(He CHMBOJIbI:
VI - HaqaJIbHa.H CKOpOCTb B Me1pax B ceKYH.nY (M/c);
V2 - KOHeqHa.H CKOpOCTb B MeTpaX B ceKYH.nY (M/c);
a - YCKopeHHe B Me1pax Ha ceKYH.nY B KBMpaTe (M/c 2 );
s - npoaneHHbIH rryTb B Me1pax (M);
t - BpeWl, B3.HTOe B ceKYJl,l(ax (c).
(Bce npHBe,n;eHHbIe ,n;aJIee <pOPMYJIbI OTHOC.HTC.H HCKJIIOqHTeJIbHO K paBHOYCKO-
peHHOMY ,n;BIDKeHHIO. - llpUMett. nep.)
1. Cpe,n;HIDI CKOpOCTb = (VI + V 2) I 2
2. KOHeqHa.H CKOpOCTb V2 = VI + at
3. IIpoaneHHbIH lIYTb S = (VI + V2)t I 2
4. llpoaneHHbIH rryTb S = Vit + at 2 I 2
5. YCKopeHHe a = (V2 - VI) I t
6. YCKopeHHe a = (vi - vl) I 2s
)
)
3.6.5. HMnyn&C
KOJIWleCTBO ,n;BIDKeHIDI HJIH HMrryJIbC TeJIa OlIpe,n;eJUIeTC.H CJIe,l(yIOII(HM 06pa30M:
HMrryJIbC = Macca x CKOpOCTb = mv.
OCHOBHa.H e,n;HHHQa H3MepeHIDI HMrryJIbCa Kr M/c.
3.6.6. 3SKOH&1 MeXSHJfKJf H&IOTOHS
IIepBbIH 3aKOH HbIOTOHa YTBep)l{)];aeT, qTO TeJIO coxpaIDIeT COCTO.HHHe nOKO.H IDIH
paBHOMepHoro np.HMOJIHHeHHOro ,n;BIDKeHIDI ,n;o Tex lIOp, nOKa pe3YJIbTHpyrolI(aR
Bcex CHJI, ,n;eHcTByroII(HX Ha TeJIO, paBHa HYJIIO. 3TO 03HaqaeT, qTO TeJIO He HaqHeT
,lJ;BIDKeHHe, He H3MeHHT HanpaBJIeHHe HJIH CKOpOCTb CBoero ,n;BIDKeHIDI ,n;o Tex lIOp,
nOKa ero He lIpHHY,n;HT K 3TOMY HeKOTOpa.H BHeIIIHIDI CHJIa. ll03TOMY CHJIY MO)I{HO
onpe,n;eJIHTb KaK HeqTO H3MeIDIIOlI(ee HJIH lIbITaIOlI(eeC.H H3MeHHTb ,n;BIDKeHHe TeJIa
nyTeM B03,n;eHCTBIDI Ha Hero.
BTopOH 3aKOH HbIOToHa YTBep)l{)];aeT, qTO CKOpOCTb H3MeHeHIDI HMrryJIbCa TeJIa
nponOPQHOHaJIbHa pe3YJIbTHpyrolI(eH CIDIe, ,n;eHcTByrolI(eH Ha 3TO TeJIO, H H3MeHe-
HHe lIpOHCXO,n;HT B TOM HalIpaBJIeHHH, B KOTOpOM npIDIoxeHa CHJIa.
TpeTHH 3aKOH HbIOTOHa YTBep)l{)];aeT, qTO ,lI;IDI KIDK,lI;OH ,n;eHCTByrolI(eH CHJIbI CY-
m;ecTByeT paBHa.H no BeJIHqHHe H lIpOTHBOnOJIO)I{Ha.H lIO HanpaBJIeHHIO CHJIa npOTH-
Bo,n;eHCTBH.H (CM. pa3,n;eJI 3.6.8).
H3 BToporo 3aKOHa ,n;BIDKeHIDI HbIOToHa CJIe,n;yeT, qTO:
llpHJIOXeHHaR CHJIa ,., 6bIC1poTa H3MeHeHIDI HMrryJIbca.
llpHJIOXeHHa.H CHJIa ,., H3MeHeHHe B HMnYJIbC/BpeWl.
CJIe,n;oBaTeJIbHO, eCJIH CHJIa F ,n;eHcTByeT Ha TeJIO MaCCOH m, TaK qTO ero CKO-
pOCTb H3MeIDIeTC.H OT VI ,n;o V2 3a BpeWl t, TO:
F ,., (mV2 - mVI) I t
F ,., m(V2 - VI) I t
F'" ma, r,n;e a =(V2 - VI) I t
F/la8a 3. HH:JICeHepHaJI OUHllMUICa
ll03TOMY
F = ma x const
llpH BbI60pe B KaqeCTBe e,n;HHHU;bI H3MepeHIDI CHJIbI (H), e,n;HHHQbI H3MepeHIDI
MaCCbI (Kr) H e,n;HHHQbI H3MepeHIDI YCKopeHIDI (M/C 2 ), const CTaHOBHTC.H paBHoH 1:
F=ma
DpHMep
CKOpOCTb JlerKOBOro aBTOM06HJI.H MaCCOH 4000 Kr 3a 10 C YBeJlHqHBaeTC.H OT 10
,n;o 60 KM/q. Onpe,n;eJlHTb BeJlHqHHY CHJIY, KOTOpyro TPe6yeTC.H npHJIOXHTb, qT06bI
06eClIeqHTb TaKoe YCKopeHHe.
V2 = VI + at (ypaBHeHHe (2), pa3,n;eJl 3.6.4),
r,n;e: V2 = 60 KM/q = 16,67 M/C, VI = 10 KM/q = 2,78 M/C, t = 10 C
T or,n;a:
a = (V2 - VI) / t = (16,67 - 2,78) / 10 = 1,39 M/C 2
CJle,n;OBaTeJlbHO:
F = ma = 4000 Kf x 1,39 M/C 2 = 5,56 KH.
.
3.6. 7. rpSSJfTsqJffl
Bec - 3TO CHJIa. HMeHHO lIO,n; BJIIDIHHeM CHJIbI T.HXeCTH, ,n;eHcTByrolI(eH Ha Maccy,
TeJlO ,n;BIDKeTC.H HJIH CTPeMHTC.H ,n;BHraTbC.H C YCKopeHHeM. OTMeTHM, qTO BeJlHqHHa
YCKopeHIDI 9,81 M/C 2 .HBJUIeTC.H cpe,n;HHM 3HaqeHHeM ,lI;IDI HaIIIeH nnaHeTbI. OHa
CJlerKa MeIDIeTC.H B 3aBHCHMOCTH OT MeCTOlIOJlOXeHH.H, o,n;HaKO 3HaqeHHe 9,81 M/C 2
lIpHMeHHMO ,lI;JI.H JlI06bIX lIpaKTHqeCKHX u;eJleH. YCKopeHHe, 06ycJloBJleHHoe CIDIOH
T.HXeCTH, 0603HaqaeTC.H CHMBOJlOM g, n03TOMY BbIpIDKeHHe F = ma npe06pa3yeTC.H B
F = mg npH BbIqHCJleHIDIX, CB.H3aHHbIX C CIDIOH T.HXeCTH.
(Ha nnaHeTe 3eMJISI CHJIa F ,n;eHcTByeT Ha Maccy 5 Kf = 5 x 9,81 = 49,05 KH. llo-
CKOJlbKY CHJIa TIDKeCTH Ha JIYRe COCTaBJUleT lIpH6J1H3HTeJlbHO 1/6 CHJIbI T.HXeCTH Ha
3eMJIe, Ha JIYRe CIDIa F ,n;eHcTByeT Ha Maccy 5 Kf = 5 x (9,81/6) = 8,175 KH.)
3.6.8. COXpSHeHJfe JfMnyn&CS
3aKOH coxpaHeHIDI KOJlHqeCTBa ,n;BIDKeHIDI HJlH HMrryJlbCa CJle,n;yeT H3 TPeTbero 3a-
KOHa HbIOTOHa: ,lI;IDI K3.)I{,lI;0H ,n;eHcTByrolI(eH CHJIbI CylI(eCTByeT paBHa.H lIO BeJlWlHHe
H npOTHBOnOJlO)I{HaSI no HanpaBJleHHIO CHJIa lIpoTHBo,n;eHcTBH.H. 3aKOH coxpaHeHIDI
HMrryJlbCa YTBep)l{)];aeT, qTO lIOJlHblH HMnYJlbC CHCTeMbI B ,n;aHHOM HalIpaBJIeHHH
OCTaeTCSI nOCTO.HHHbIM ,n;o Tex nop, rtoKa HHKaKHe BHeIIIHHe CIDIbI He ,n;eHCTByroT Ha
CHCTeMY B 3TOM HalIpaBJleHHH. 3TOT 3aKOH lI03BOJl.HeT JlerKO peIIIaTb 3a;:J;aqH, B KO-
TOpbIX ytIHTbIBaIOTC.H TOJlbKO BHyrpeHHHe CHJIbI.
PaCCMOTPHM cHapM, BbmeTalOlI(HH H3 opy,n;IDI. PaBHbIe H lIpOTHBOlIOJlOXHO
HanpaBJleHHbIe CHJIbI, ,n;eHCTByro He Ha CHapM H Ha opy,n;He, npHBO,nRT K TOM}',
qTO CHapM ,n;BIDKeTC.H BlIepe,n;, a opy,n;He ,n;BIDKeTC.H Ha3a;:J;. llOCKOJlbKY BHeIIIHHe
CHJIbI OTCYTCTByroT, eCJlH 6bI opy,n;He H CHapM HMeJlH paBHbIe MaCCbI, OHH ,n;BHra-
3.6. C1copocmb u YCICopeHue
JlHCb 6bI C o,n;HHaKOBbIMH CKOpOCT.HMH. K CqaCTbIO, Ha rrpaKTHKe Macca opy,n;IDI Ha-
MHoro 60JIbIIIe MaCCbI CHapg,na, rr03TOMY CKOpOCTb OTKaTa HaMHoro MeHbIIIe, qeM
CKOpOCTb ,n;BIDKeHIDI cHapg,na Brrepe,n;.
DpHMep.
TeJIo P MaCCOH 15 Kr, ,n;BIDKYIUeeC.H co CKOpOCTbIO 30 M/c, CTaJIKHBaeTC.H co
BTOpbIM TeJIOM Q MaCCOH 5 Kr, ,n;BIDKYIUHMC.H B TOM xe HarrpaBJIeHHH CO CKOpOCTbIO
5 M/c. Orrpe,n;eJIHTb 06lI(y1O CKOpOCTb ,n;BYX TeJI lIOCJIe CTOJIKHOBeHIDI.
COrJIaCHO 3aKOHY coxpaHeHIDI HMrrYJIbca:
HMrryJIbC ,n;o CTOJIKHOBeHIDI = HMrrYJIbC nOCJIe CTOJIKHOBeHIDI
Macca x CKOpOCTb ,n;o CTOJIKHOBeHIDI = Macca x CKOpOCTb lIOCJIe CTOJIKHOBeHIDI
15 Kr x 30 M/c + 5 Kr x 5 M/c = (15 Kr + 5 Kr)v,
r,ne v - CKOpOCTb rrOCJIe coy,n;apeHIDI.
v = 23,75 M/c.
Ha pHC. 3.10, a lIOKa3aHbI ,n;Ba TeJIa, ,n;BIDKYIUHeC.H ,n;o CTOJIKHOBeHIDI B lIpOTHBO-
rrOJIO)I{HbIX HalIpaBJIeHIDIX. ll03TOMY CKOpOCTb BToporo TeJIa Q CqHTaeTC.H 0TPHIJ;a-
TeJIbHOH BeJIHtlHHOH. BbIqHCJIeHIDI BbIlIOJIIDIIOTC.H CJIe,n;yroII(HM 06pa30M:
HMrryJIbC ,n;o CTOJIKHOBeHIDI = HMrryJIbC lIOCJIe CTOJIKHOBeHIDI
15 Kr (+ 30 M/c) + 5 Kr (-5 M/c) = (15 Kr + 5 Kr)v.
v = 21,25 M/c.
3.6.9. B03,qeiicTSJfe CTPYJf JlCH,qKOCTJf HS HenOASJfJICHOe Teno
. ECJIH CTPY.H OTKJIOIDIeTC.H OT CBoeH JIHHHH ,n;BIDKeHIDI, TO H3 rrepBoro 3aKOHa
HbIOTOHa CJIe,n;yeT, qTO Ha Hee ,n;eHcTByeT CHJIa.
. ECJIH CHJIa, ,n;eHCTByrolI(a.H Ha CTPyro, rrporrOPQHOHaJIbHa 6bICTPOTe H3MeHe-
HIDI HMlIYJIbCa H ,n;eHcTByeT B HarrpaBJIeHHH H3MepeHIDI HMrrYJIbCa, TO lIpHMe-
HHM BTOpOH 3aKOH HbIOTOHa.
. ECJIH CHJIa, C KOTOpOH TeJIO ,n;eHcTByeT Ha CTPyro, H3MeIDIeT ee HMrrYJIbC, TO
3Ta CHJIa ,n;OJDKHa 6bITb paBHa lIO BeJIHqHHe H lIpOTHBOrrOJIO)I{Ha lIO HarrpaB-
JIeHHIO CHJIe, C KOTOpOH CTPY.H ,n;eHcTByeT Ha TeJIO.
IIOCKOJIbKY ,n;aHHbIH rrpHMep BKJIIOqaeT Harrop CTPYII )l{Jl)];KOCTH, TO OH CBSl3aH
CO CKOpOCTbIO rrOTOKa CTPYII, H BTOpOH 3aKOH HbIOTOHa MO)I{HO 3arrHcaTb KaK:
CHJIa = CKOpOCTb H3MeHeHIDI HMIIyJIbCa =
= (Macca x H3MeHeHHe CKOpOCTH)/3a1paQeHHOe BpeWI =
= MaCCOBaH CKOpOCTb nOTOKa x H3MeHeHHe CKOpOCTH B HanpaBJIeHHH CHJIbI.
npHMep
CTPY.H Bo,n;bI,n;HaMeTpOM 50 MM co CKOpOCTbIO 75 M/c rreplIeH)J;HKYJI.HpHO y,n;ap.H-
OT B Herro,n;BIDKHoe TeJIO. OlIpe,n;eJIHTb CHJIY, ,n;eHcTByrolI(ylO Ha TeJIO.
IIycTb CTPY.H BO,n;bI pa36pbI3rHBaeTC.H lIpH CTOJIKHOBeHHH C TeJIOM pan;HaJIbHO,
-T.e. OHa OTKJIOIDIeTC.H OT lIepBOHaqaJIbHOrO HalIpaBJIeHIDI ,n;BIDKeHIDI Ha yrOJI 90°.
CJIe,noBaTeJIbHO, CTPY.H Tep.HeT BeCb CBOH HMrrYJIbC B HalIpaBJIeHHH, rreprreH)J;HKY-
IDIpHOM TeJIy, KaK lIOKa3aHO Ha pHC. 3.2.
F.na8a 3. HH:JICeHepHaJI OUHllMUlCa
050 MM
)l(ecTKa51
nJ1aCTVlHK8
Puc. 3.2. Hanop XH,lI;KOCTH Ha Heno-
,n;BHXHoe TeJIO
75 M/C
llJIOII(Mb CTPYII = (1t I 4) x (50 I 1000)2 M2 = 6,251t X 10-4 M 2 .
061>eMHaR CKOpOCTb lIOTOKa = 6,251t X 10-4 M 2 x 75 MI C = 0,0471t M3 I c.
MaCCOBa.H CKOpOCTb lIOTOKa (Bo,n;a) = 061>eMHaR CKOpOCTb lIOTOKa x
x IIJIOTHOCTb BO,n;bI = 0,0471t M 3 I s x 10 3 Kr/M 3 = 471t MKrI C.
CHJIa, ,n;eHCTByrolI(aR Ha TeJIO = MaCCOBaR CKOpOCTb lIOTOKa x H3MeHeHHe CKOpOCTH.
llpUMettaHue.
llpH CTOJIKHOBeHHH CTPYII )I{H,lI;KOCTH C TeJIOM rrpOHcxo,n;HT MrHOBeHHoe H3Me-
HeHHe CKOpOCTH OT 75 ,n;o 0 M/c.
ll03TOMY:
CIDIa, ,n;eHcTByrolI(a.H Ha TeJIO = 471t Kr/c X 75 M/c = 3525 H = 3,525 KH.
3.6. 10. HHepqJffl
llepBbIH 3aKOH ,n;BIDKeHH.H HbIOTOHa YTBep)l{)];aeT, qTO TeJIO coxpaIDIeT COCTO.HHHe
rrOKO.H HJIH paBHOMepHoro rrp.HMOJIHHeHHOro ,n;BIDKeHIDI, rrOKa Ha Hero He ,n;eHCTBY-
eT BHeIIIIDI.H CHJIa. 3TO corrpOTHBJIeHHe H3MeHeHHIO COCTO.HHIDI Ha3bIBaeTC.H HHep-
QHeH TeJIa, H BeJIHqHHa HHepIJ;HH 3aBHCHT OT MaCCbI TeJIa. ll03TOMY, qT06bI lIPH-
,n;aTb YCKopeHHe HaXO,nRlI(eMYcSI B COCTO.HHHH lIOKO.H lIOJIHOCTbIO 3arpyxeHHoMY T.H-
XeJIbIM 6arIDKoM aBToM06IDIIO, TPe6yeTC.H HaMHoro 60JIbIIIaR cHJIa, qeM cIDIa, He-
06XO,n;HMaR ,lI;IDI C006lI(eHIDI TaKoro xe YCKopeHIDI HaXo,nRlI(eMYc.H B COCTO.HHHH
rrOKO.H BeJIOCHne,n;y.
3.6. 11. COnpOTJfSneHJfe ASJfJICeHJfIO
MCrrOJIb3Y.H BbIpIDKeHIDI F = ma, CJIe,n;yeT 06palI(aTb BHHMaHHe Ha CJIe,l(yIOlI(ee.
. F MoxeT 6bITb KaK YCKOp.HIOlI(eH CHJIOH, TaK H 3aMe,ll;IDIIOlI(eH (TOpM03.HlI(eH).
. llpH BbIlIOJIHeHHH HH)I{eHepHbIX paCqeTOB qaCTO lIpHXO,n;HTC.H OlIpe,n;eJUITb Be-
JIHqHJIy YCKopeHIDI HJIH 3aMe,ll;JIeHIDI, HCrrOJIb3Y.H ypaBHeHIDI ,n;BIDKeHIDI pac-
CMOTPeHHbIe BbIIIIe.
. Kor,n;a CIDIe, BbI3bIBaIOlI(eH YCKopeHHe TeJIa, rrpoTHBo,n;eHcTByeT ,n;pyraR CHJIa,
cTPeMSllI(a.HC.H 3aMe,ll;JIHTb (3aTopM03HTb) ,n;BIDKeHHe TeJIa, TO rOBOp.HT, qTO
,n;BIDKeHHe TeJIa BCTpeqaeT COlIpOTHBJIeHHe.
Ha pHC. 3.3, a nOKa3aHa CIDIa P, ,n;eHCTByro aR Ha TeJIO MaCCOH m, TaK qTO OHO
,n;BIDKeTC.H C YCKopeHHeM a, rrpeo,n;OJIeBaR rrpOTHBOrrOJIO)I{HO HarrpaBJIeHHOe COlIPOTHB-
JIeHHe R. YCKOp.HIOlI(aR CIDIa Fa = (P - R) H Fa = ma, CJIe,n;OBaTeJIbHO, P - R = ma.
Ha pHC. 3.3, 6 rrOKa3aHO lIo,n;BeIIIeHHoe TeJIO MaCCOH m. llYCTb P - HaT.HXeHHe
BepeBKH, Ha KOTOpOH no,n;BeIIIeHO TeJIO.
3.6. C"opocmb u yc"opeHue I 05
HaT5I)I(eHVle (P) H
YCKopeHVle (a) M/C 2
C na conpOTVlB-
neHVl5I (R) H
Macca (m) Kr
YCKopeHVle
(a) M/C 2
f 1
Macca (m) Kr
CVlJ1a(P)H
Bec W = mg H
I
a
6
YCKopeHlile (a) M/C 2 \
)
'\
/
Bec W = mg H
B
Puc. 3.3. ConpOTHBJIeHHe ,n;BH)I{eHHIO:
a - Ha ropH30HTaJIbHOH llJIOCKOCTH;
6 - no,n;BemeHHoro TeJIa;
B - Ha HaKJIOHHOH llJIOCKOCTH
1. llpH ,n;BIDKeHHH BBepx HJIH BHH3 C IIOCTO.HHHOH CKOpOCTbIO HJIH eCJIH TeJIO
HaxO,n;HTC.H B COCTO.HHHH IIOKO.H YCKopeHHe paBHO HYJIIO; II03TOMY YCKOp.HIOlI(aR
CHJIa (F) TaIOKe paBHa HYJIIO.
2. llpH ,n;BIDKeHHH BHH3 C YCKopeHHeM a W 60JIbIIIe, qeM P, r,n;e W = mg. Tor,n;a
YCKOp.HIOlI(aR CHJIa F = (W - P), lI03TOMY (W - P) = ma.
3. llpH ,n;BIDKeHIDI BBepx C YCKopeHHeM a F = (P - W), II03TOMY (P - W) = ma.
Ha pHC. 3.3, B IIOKa3aHO TeJIO, paCIIOJIOXeHHOe Ha rJIa;:J;KoH HaKJIOHHOH IIJIOCKO-
CTH. B 3TOM lIpHMepe JII06bIM TPeHHeM IIpeHe6peraeM. KOMIIoHeHTa Beca TeJIa W;
.neHCTByIOlI(aR BHH3 B,n;OJIb IIJIOCKOCTH, paBHa Wsin8, r,n;e W = mg (H):
1. ECJIH P 60JIbIIIe W sin 8, TeJIO ,n;BIDKeTC.H BBepx lIO IIJIOCKOCTH C YCKopeHH-
eM a. YCKOP.HIOlI(aR CHJIa F = P - W sin 8, II03TOMY P - W sin 8 = ma.
2. ECJIH W sin 8 60JIbIIIe P, TeJIO ,n;BIDKeTC.H BHH3 lIO IIJIOCKOCTH C YCKopeHHeM a.
Tor,n;a YCKOp.HIOlI(aR CHJIa F = W sin 8 - P, II03TOMY W sin 8 - P = ma.
(::: F/la8a 3. HH:JICeHepHaJl OUHaMUlCa
DpHMep
Ha TeJIO MaCCOH 600 Kf ,n;eHcTByeT CHJIa corrpOTHBJIeHH.H 400 H. OlIpe,n;eJIHTb,
KaKYJO lIOJIHyIO CHJIY He06xo,n;HMO rrpHJIOXHTb K Te.rry, qT06bI OHO ,n;BHraJIOCb C rro-
CTO.HHHbIM YCKopeHHeM 3 M/c 2 .
llYCTb HCKOMaR rrOJIHa.H CIDIa = P.
Tor,n;a: YCKOp.HIOlI(aR CHJIa F = (P - 400).
TaK KaK F = ma, TO: (P - 400 H) = 600 Kr x 3 M/c.
ll03TOMY: P = 400 H + 1800 H = 2200 H.
DpHMep
llaccIDKHpcKHH JIH<pT MaCCOH 1500 Kr HaqHHaeT ,n;BIDKeHHe H3 COCTO.HHIDI rro-
KOSI H, ,n;BHraSiCb BBepx, Qepe3 10 M ,n;OCTHraeT CKOpOCTH 5 M/c. Onpe,n;eJIHTb HaTSI-
)KeHHe TPoca JIH<pTa, eCJIH YCKopeHHe nOCTO.HHHO. llpHMHTe g = 9,81 M/c 2 .
QT06bI HaHTH YCKopeHHe, HClIOJIb3yeM BbIpIDKeHHe (V 2 )2 = (Vi)2 + 2as.
ll03TOMY: (5 M 2 /c 2 )2 = 0 + 2 x a x 10 M.
TaKHM o6pa30M: a = 25/(2 x 10) = 1,25 M/C 2 .
lloKa JIH<pT Haxo,n;HTC.H B COCTO.HHHH rroKo , HaT.HXeHHe B TPoce 06YCJIOBJIeHO
TOJIbKO ,n;eHcTByromeH Ha JIH<pT CHJIOH T.HXeCTH (mg), paBHoH 1500 Kr x 9,81 M/c 2 =
= 14715 H. llOCKOJIbKy JIH<pT ,n;BIDKeTC.H C YCKopeHHeM BBepx, HaT.HXeHHe P 60JIbme
14715 H.
llYCTb P = HaTIDKeHHe B rro,n;'beMHOM Tpoce.
Tor,n;a YCKOpSiIOmaR CIDIa F = P - 14715 = ma = 1500 x 1,25 M/c 2 .
ll03TOMY: P = 14715 + 1500 x 1,25 = 16590 H = 16,59 KH.
3.7. Bpaw.aTenbHoe ABM>KeHMe
Kor,n;a xeCTKoe TeJIO BpamaeTC.H BOKpyr <pHKcHpoBaHHoH OCH, Bce TOqKH 3TOro
TeJIe BbIHyx,n;eHbI ,n;BHraTbCSI lIO KpyrOBbIM TPaeKTopIDIM. ll03TOMY 3a JII060H rrepH-
o,n; BpeMeHH Bce TOqKH TeJIa COBepIIIaT O,n;HO H TO )Ke KOJIHqeCTBO 060pOTOB BOKpyr
OCH BpaIl(eHIDI; TaKHM 06pa30M, CKOpOCTb BpaII(eHIDI MO)KHO orrpe,n;eJIHTb qepe3
060POTbI B MHHyry (06/MHH). O,n;HaKO ,lI;IDI MHorHX HH)I{eHepHbIX 3Maq qaCTO 6bI-
BaeT He06xo,n;HMO BbIpa3HTb CKOpOCTb BpaII(eHIDI Qepe3 yrOJI rrOBopOTa B PMHaHax
B e,n;HHHn;y BpeMeHH.
3. 7. 1. PSAJfSH&1
PMHaH - 3TO n;eHTpaJIbHbIH yrOJI, CTSlrHBaeMbIH ,n;yrOH, ,lI;JIHHa KOTOpOH paBHa ee
PMH)'CY. 3TO lIOKa3aHO Ha pHC. 3.4, a. CooTHoIIIeHHe Mex,n;y ,lI;JIHItOH ,l(yrH, PMHY-
COM H yrJIOM B PMHaHax rrOKa3aHO Ha pHC. 3.4, 6.
M3 orrpe,n;eJIeHIDI PMHaHa:
rr03TOMY
sir = 8,
s = reo
3.7. Bpaw,ame.tlbHOe 06UJlCeHUe 107"
r
s
a
Puc. 3.4. a - PMHaH (r - PMHYC Kpyra); 6 - COOTHOIIIeHHe Me)l{,ll;Y ,lI;JIHHOH (s),
PMHYCOM (r) H yrJIOM (9) B PMHaHax;
S - ,lI;JIHHa ,n;yrH; - yrOJI B PMHaHax; r - pa,n;HYC OKpyxHOCTH
(
/
ECJIH B BbIpIDKeHHe s = re 1I0,n;CTaBHTb s, paBHoe ,lI;JIHHe OKpyxHOCTH Kpyra, Tor,n;a:
21tr = re,
1I03TOMY 21t = e.
To eCTb 1 060POT = 21t panHaH (= 360°)
AHaJIOrWlHO 1 panHaH = 360/21t = 57,3° (lIpH6JIH3HTeJIbHo).
3. 7.2. Yron nosopOTS
IIpH 1I0CTYIIaTeJIbHOM ,n;BIDKeHHH CHMBOJIOM S 0603HaqaeTC.H paCCTO.HHHe, lIpOMeH-
Hoe 110 IIp.HMOH JIHHHH, T.e. JIHHeHHOe lIepeMelI(eHHe. llpH BpalI(aTeJIbHOM ,n;BIDKe-
HHH yrJIOBOe lIepeMelI(eHHe (HJIH yrOJI 1I0BopOTa), H3MepeHHoe B panHaHax, 060-
3HaqaeTC.H rpeqeCKOH 6)'KBOH e.
3.7.3. YrnossfI CKOPOCT&
TBep,n;oe TeJIO BpalI(aIOlI(eeC.H BOKpyr <pHKcHpoBaHHoH OCH 0 C lIOCTO.HHHOH CKOpO-
CTbIO n 06./c, 1I0BOpaqHBaeTC.H Ha 21t panHaH (pan) 3a K3.)I{,lI;bIH 060pOT. ll03TOMY
yrJIOBaR CKOpOCTb ro (rpeqeCKa.H 6)'KBa oMera) Ollpe,n;eJI.HeTC.H BbIpIDKeHHeM:
ro = 21tn pan/c
,lJ;aJIee, eCJIH TeJIO 1I0BOpaqHBaeT Ha yrOJI e panHaH 3a BpeWl t (c) H eCJIH ,n;BH-
xeHHe paBHOMepHoe, Tor,n;a
YrJIOBa.H CKOpOCTb ro = e / t pan/c.
OTMeTHM, qTO yrJIOBaR CKOpOCTb He HMeeT JIHHeHHbIX pa3MepHOCTeii.
F/la8a 3. HH:JICeHepHaJI OUHllMUICa
3. 7.4. CooTHOWeHJfe MeJICAY yrnosoH Jf nJfHeHHOH
CKOpOCTflMJf
PaCCMOTPHM TOqKY A Ha HapyxHOM 060,n;e TBep,n;o-
ro TeJIa, rrOKa3aHHoro Ha pHC. 3.5.
llYCTb TeJIO nOBOpaqHBaeTC.H Ha yrOJI e (pan) 3a
BpeWl t (c). HCrrOJIb3yeM <poPMY.rry: ,lI;JIHHa ,l(yrH =
= yrOJI B panHaHax x panH)'C, T.e.
s = reo
T errepb, qT06bI rrOJIyqHTb cpe,n;HIOIO CKOpOCTb,
rro,n;eJIHM 06e qaCTH BbIpIDKeHIDI Ha t Tax:, qTO:
sit = r(e It),
HO
s It=v He/t=OO.
v
s
Puc. 3.5. COOTHOIIIeHHe Me)l{,ll;Y
yrJIOBOH H JIHHeHHOH CKOpO-
CTHMH
n03TOMY:
V = roo HJIH JIHHeHHaR CKOpOCTb = yrJIOBaR CKOpOCTb x panH)'c.
llpUMettaHue.
1. ToqKa TeJIa B HMeeT TaKYIO xe yrJIOByro CKOpOCTb, KaK H TOqKa A, HO ee !lH-
HeHHaR CKOpOCTb MeHbIIIe, rrOCKOJIbKY eH COOTBeTcTByeT MeHbIIIHH panH)'C.
2. ECJIH panH)'C r BbIpIDKaeTC.H B MeTPax H yrJIOBaR CKOpOCTb BbIpIDKaeTC.H B
panic, Tor,n;a JIHHeHHaR CKOpOCTb v BbIpIDKaeTC.H B M/c. HHor,n;a yrJIOBa.H CKO-
pOCTb BbIpIDKaeTC.H B 06./MHH. Tor,n;a He06xo,n;HMO lIpe06pa30BaTb 06./MHH.
B panic ,n;o lIo,n;CTaHOBKH B TaKHe BbIpIDKeHIDI, KaK v = roo.
N (06/MHH) = 21tN (pan/MHH) = 21tN I 60(pan/c).
3. 7.5. Yrnosoe YCKopeHJfe
COOTHOIIIeHHe, aHaJIOrHqHOe TOMY, KOTopoe CB.H3bIBaeT JIHHeHHyro H yrJIOByro CKO-
pOCTH, CylI(eCTByeT ,lI;IDI JIHHeHHOro H yrJIOBOrO YCKopeHHH. TaKHM 06pa30M:
a = ra,
r,n;e a - JIHHeHHOe YCKopeHHe, r - panH)'C, a (rpeqeCKaR 6)'KBa aJIb<pa) - yrJIOBOe
YCKopeHHe.
B pa3,n;eJIe 3.6.4 rrepeqHCJIeHbI BbIpIDKeHIDI, CB.H3bIBaIOII(He JIHHeHHbIe CKOpOCTb
H YCKopeHHe. AHaJIOrHqHO, CylI(eCTByeT Ha60p BbIpIDKeHHH, CB.H3bIBaIOII(HX yrJIO-
BbIe CKOpOCTb H YCKopeHHe:
002 = 001 + at
e =[(001 + (02) I 2] x t
e = 001 t + at 2
00 2 = 00 2 + 2ae
21,
e = 002 t - 11 at 2
001 = HaqaJIbHaR yrJIOBaR CKOpOCTb
002 = KOHeqHaR yrJIOBaR CKOpOCTb
a = yrJIOBOe YCKopeHHe
e = yrOJI rrOBopOTa
t = 3aTpaqeHHOe BpeMSI
3. 7. Bpaw,ame.tlbHOe 06UJlCeHUe I 09'
3. 7.6. MOMeHT SpS eHJffl
MOMeHT BpaII(eHIDI - 3TO BpalI(aIOIUHH MOMeHT CHJIbI. ECJIH CHJIa npHBo,n;HT K
BpalI(eHHIO TeJIa lIPH OTCYTCTBHH nOCTYITaTeJIbHOrO ,n;BIDKeHIDI, ,n;OJDKHa CylI(eCTBO-
BaTh BTOpaR CHJIa, ,n;eHCTByrolI(aR Ha TeJIO, paBHaR no BeJIWlHHe H lIpOTHBOlIOJIOX-
Hag lIO HanpaBJIeHHIO nepBOH, TaK qT06bI pe3YJIbTHpyrolI(a.H CHJIa paBHIDIaCb HYJIIO.
Tame CHJIbI HaxO,nRTC.H B paBHOBeCHH. PaCCMOTPHM raeqHbID KJIIOq H raHKY, lIOKa-
3aHHbIe Ha pHC. 3.6, a. Kor,n;a CHJIa Fl npHJIOXeHa K KOH:Qy raeqHOrO KJIIOqa, paB-
Hag no BeJIHqHHe H lIpOTHBOnOJIO)I{HaR no HalIpaBJIeHHIO CHJIa F 2 B03HHKaeT B raD-
Ke. ECJIH 6bI 3TO 6billO He TaK, HaqaJIOCb 6bI nOCTYITaTeJIbHOe ,n;BIDKeHHe B HanpaB-
JleHHH CHJIbI F I _ Kor,n;a ,n;Be paBHbIe lIO BeJIWlHHe H lIpOTHBOnOJIO)I{HO HalIpaBJIeH-
HbIe CHJIbI ,n;eHcTByroT Ha TeJIO, rOBOp.HT, qTO OHH 06pa3yroT napy.
a
Puc. 3.6. a - MOMeHT Bpam;eHHH (Bpam;aIOm;HH MOMeHT);
6 - pa60Ta, BbInOJIHeHHaH MOMeHTOM Bpam;eHHH
o
s
6
MOMeHT BpaII(eHIDI (1) = BeJIHqHHa npHJIOXeHHOH CHJIbI (F I ) x ,lI;JIHHa IIJIeqa (d),
r,ne T - MOMeHT Bpa eHH.H (HM), F - CIDIa (H), d - IIJIeqo CHJIbI (M).
13. 7. 7. PS60TS MOMeHTS SpS eHJffl
PaCCMOTPHM pa60TY, BbInOJIHeHHyIO CHJIOH F (H), ,n;eHcTByrolI(eH lIO,n; np.HMbIM yr-
JlOM K IIJIeqy CHJIbI OA ,lI;JIHHOH r (M) H cOBepIIIHBIIIeH lIOBOpOT Ha yrOJI e pan, KaK
nOKa3aHO Ha pHC. 3.6, 6.
BbmOJIHeHHaR pa60Ta = JIHHeHHOe paCCTO.HHHe, lIpOH,n;eHHoe lIO,n; ,n;eHCTBHeM CHJIbI =
= s x F (HM HJIH ,l];x).
Ho: s = re (M).
II03TOMY:
BbInOJIHeHHaR pa60Ta = re x F = Fr x e.
F/la8a 3. HH:JICeHepHaJI OUHaMUICa
Ho:
ll03TOMY:
MOMeHT BpaII(eHIDI T = Fr.
BbIlIOJIHeHHaR pa60Ta = 10 (HM HJIH )];)K:).
Pa6oTa, BLlnOJIHeHHaJi Bpam:alOlIUIM MOMeHTOM =
= Bpam:alOlIUIH MOMeHT x yroJi nOBopOTa B pa.zntaHax.
npHMep
MaxOBHK BpalI(aeTC.H co CKOpOCTbIO 2400 06/MHH. B pe3YJIbTaTe HeO)l{H)];aHHoro
B03,n;eHcTBIDI TOpM03Horo MOMeHTa B03HHKaeT yrJIOBOe TopMoxeHHe (3aMe,ll;JIeHHe)
paBHoe 10 pan/c 2 . BbIqHCJIHTe:
1) BpeWl, 3a KOTopoe CKOpOCTb MaxoBHKa }'MHbIIIHTC.H ,n;o 600 06/MHH;
2) yrJIOByro CKOpOCTb MaxoBHKa qepe3 300 060pOTOB C MOMeHTa HaqaJIa TOpMO-
xeHIDI.
1. llpHMeHHM ypaBHeHHe:
002 = 001 + at (pa3,n;eJI 3.7.5),
r,n;e 001 = HaqaJIbHaR yrJIOBaR CKOpOCTb = (2400 06/MHH x 21t)/60 panic;
002 = yrJIOBaR CKOpOCTb qepe3 BpeWl t = (600 x 21t)/60 panic;
a = yrJIOBOe YCKopeHHe = -10 pan/c 2 (3HaK MHHYC yKa3bIBaeT Ha TopMoxeHHe).
ll03TOMY:
CJIe,n;OBaTeJIbHO:
2. npHMeHHM ypaBHeHHe:
oo = 001 + 2aa (pa3,n;eJI 3.7.5),
r,n;e 002 = yrJIOBaR CKOpOCTb qepe3 300 060pOTOB;
001 = (2400 06/MHH x 21t)/60 = 251,33 panic; a = -10 pan/c 2 ; a = 300 x 21t pan.
T or,n;a:
oo = 251,332 + 2 x (-10) X 6001t = 63166,8 - 37699,1 = 159,6 pan/c.
oo = (159,6 X 60)/21t = 1524 06/MHH.
(600 x 21t)/60 = (2400 06/MHH x 21t)/60 + (-10)t.
lOt = (1800 x 21t)/60.
t= 18,8 c.
HJIH
3.7.8. LleHTpOCTpeMJfTen&HOe YCKopeHJfe
Jf qeHTpoCTpeMJfTen&HSfI CJfns
COrJIaCHO CJIOBapIO, QeHTPOCTPeMHTeJIbHOe YCKopeHHe - 3TO YCKopeHHe, HanpaB-
JIeHHOe K n;eHTPY KpHBH3HbI TPaeKTOpHH TeJIa, ,lI;BIDKYIUerOC.H no TPaeKTOpHH C no-
CTO.HHHOH no MO,IJ;yJIIO CKOpOCTbIO. qHCJIeHHO OHO paBHO v 2 /r, r,n;e v - CKOpOCTb,
r - panHYC KpHBH3HbI, ero TaIOKe MO)I{HO BbIpa3HTb qepe3 yrJIOByro CKOpOCTb 00,
KaK 00 2 r.
Ha pHC. 3.7, a lIOKa3aHO TeJIO MaCCOH m, ,n;BIDKYIUeeC.H C nOCTO.HHHOH yrJIOBOH
CKOpOCTbIO 00 lIO KpyrOBOH TPaeKTOpHH panHYCOM r C n;eHTPOM B TOqKe O. Kor.na
TeJIO Haxo,n;HTC.H B TOqKe P, ero MrHOBeHHaR JIHHeHHaR CKOpOCTb v HanpaBJIeHa no
KaCaTeJIbHOH K OKpyxHOCTH, B,n;OJIb KOTOpOH OHO ,n;BIDKeTC.H. 3a npOMexyrOK Bpe-
3. Z Bpa14ameJlbHOe 08U:JICeHUe II
o
p
q
r
o
a
)
)
6
Puc. 3.7. a - JJ;eHTpOCTPeMHTeJIbHOe YCKopeHHe;
6 - nHarpaMMa H3MeHeHHH CKOpOCTH npH ,n;BH)I{eHHH no OKp)')KHOCTH C
I(eHTpOCTpeMHTeJIbHbIM YCKopeHHeM
MeHH ot TeJIO lIepeMemaeTcH no OKpyxHOCTH H3 TOqKH P B TOqKY Q. CooTBeTcTBY-
IOm;asI 3TOMY nepeMemeHHIO ,nyra PQ CT.HrHBaeT yrOJI oe. XOT.H TeJIO ,nBH)I{eTC.H C
nOCTO.HHHOH no MO,!{yJIIO CKOpOCTblO, HanpaBJIeHHe ero ,nBH)I{eHIDI He OCTaeTC.H no-
CTO.HHHbIM. TI03TOMY BeKTOp CKOpOCTH TeJIa H3MeH.HeTC.H; a nOCKOJIbKY BeKTOp CKO-
pOCTH H3MeH.HeTC.H co BpeMeHeM, TeJIO, no onpe,neJIeHHIO, ,nBH)I{eTC.H C YCKopeHHeM.
Ha pHC. 3.7, 6 nOKa3aHa BeKTOpHa.H ,nHarpaMMa CKopocTeit, r,ne:
. CKOpOCTb B TOqKe P (MO,!{yJIb CKOpOCTH H HanpaBJIeHHe) npe,nCTaBJIeHa BeKTO-
pOM Op;
. CKOpOCTb B TOqKe Q npe,nCTaBJIeHa BeKTopOM Oq;
. pa,nHaJIbHOe H3MeHeHHe CKOpOCTH npH nepeMemeHHH TeJIa H3 TOqKH P B TOq-
KY Q npe,nCTaBJIeHO BeKTopOM pq.
Pa,nHaJIbHOe H3MeHeHHe CKOpOCTH = pq = v x oe.
O,nHaKO:
e = rot.
TI03TOMY:
oe = ro x ot = (v / r) x ot.
TaKHM 06pa30M:
M3MeHeHHe BeKTOpa CKOpOCTH = (v 2 x ot) / (r x ot) = v 2 / r = ro 2 r.
,lI0 CHX nop MbI paCCMa1pHBaJIH Te.rry MaCCOH m, L(BIDICylI(eeC.H C ueH1pOC1peMH-
TeJlLHbIM YCKopeHHeM. 1f3 BToporo 3aKOHa MexaHHKH HblOTOHa CJIe,nyeT, qTO TeJIO
He MoxeT ,nBHraTbC.H C YCKopeHHeM, eCJIH Ha Hero He ,neitcTByeT BHeIIIHIDI CHJIa.
IT03TOMY C03,nalOma.H YCKopeHHe ueH1pOC1peMHTeJIbHa.H CHJIa = Macca x YCKope-
HHe. MaTeMaTHqeCKH 3TO MO)I{HO BbIpa3HTb:
o;eHTpOCTpeMHTeJILHaJi CHJIa = m x (V 2 / r) = mm 2 r.
F/la8a 3. HH:JICeHepHaJI OUHaMUKa
3. 7. 9. eHTpo6eJKHafl CHna
TpeTHH 3aKOH HblOTOHa )'TBep)l{)J;aeT, qTO ,l(lliI KaJK,l(OH ,neHcTByroIUeH CHJIbI cym;ecr-
ByeT paBHa.H no BeJIHqHHe H lIpOTHBOnOJIO)I{Ha.H lIO HalIpaBJIeHHIO CHJIa lIpOTHBO-
,neHCTBIDI. n03TOMY ,nOJDKHa cym;ecTBoBaTb CHJIa lIpoTHBo,neHcTBIDI, paBHa.H lIO Be-
JIWIHHe H npOTHBOnOJIO)I{Ha.H lIO HalIpaBJIeHHIO ueH1pOc1peMHTeJIbHOH CHJIe. 3ra
CHJIa npoTHBo,neHcTBIDI HalIpaBJIeHa lIO pa,nHYCY OT ueH1pa KpHBH3HbI 1paeKTOpHH
H Ha3bIBaeTC.H n;eH1p06e)I{HOH CHJIOH. PaccM01pHM noe3,n, ,nBIDICylI(HHC.H no 3aKpyr-
JIeHHOMY yqaCTKY rryTH. Pe60p,nbI KOJIeC noe3,na ,naB.HT Ha peJIbCbI B HanpaBJIeHHH
OT ueH1pa KpHBH3HbI 3aKpyrJIeHIDI (ueH1p06e)I{Ha.H cHJIa); B TO xe BpeM.H peJIbCbI e
CHJIOH, paBHOH lIO BeJIWIHHe, B03,neHCTByroT Ha KOJIeCa noe3,na B HalIpaBJIeHHH K
ueH1py KpHBH3HbI 3aKpyrJIeHIDI (ueH1pOC1peMHTeJIbHa.H CHJIa). ToqHO TaK xe, Kor-
,na rHpbKa, y,nep)I(HBaeMa.H IIIHypOM, BepTHTC.H BOKpyr OCH, ueH1p06e)I{Ha.H CHJIa TH-
HeT rHpbKY Hap)')I{Y, B TO BpeM.H KaK ueH1pOC1peMHTeJIbHa.H CHJIa T.HHeT ee BHYTPb;
npH 3TOM IIIHyp OCTaeTC.H HaT.HHYTbIM. (HeJIb3.H )'TBep)l{)J;aTb, qTO «ueH1p06e)I{HaH
CHJIa T.HHeT rHpbKY», lIOCKOJIbKY ueH1p06e)I{Ha.H CHJIa Bcer,na ,neHcTByeT Ha CBH3H, a
He Ha ,nBIDICylI(eeC.H TeJIO. npaBHJIbHO CKa3aTb MO)I{HO TaK: «ToqHO TaK xe, Kor,na
rHpbKa y,nep)I(HBaeMa.H IIIHypOM, BepTHTC.H BOKpyr OCH, ueH1p06e)I{Ha.H CHJIa ,neHcr-
ByeT Ha IIIHyp, HaT.HrHBa.H ero, B TO BpeM.H KaK ueH1pOC1peMHTeJIbHa.H CHJIa T.HHer
rHpbKY BHYTPb». - llpUMe"t. nep.)
3.8. YpaBHOBewMBaHMe BpaLQalOLQMXCR Mace
QT06bI MexaHH3MbI MOrJIH pa60TaTb nrraBHo, 6e3 BH6paUHH, He06xo,nHMO, qT06bI
Bce BpaIUaIOIUHeC.H MaCCbI HaxO,nHJIHCb B COCTO.HHHH paBHoBecIDI.
(MexaHH3M CqHTaeTC.H nOJIHOCTblO ypaBHoBeIIIeHHbIM, eCJIH CHJIa ,naBJIeHIDI Ha
onopbI OCTaeTC.H lIOCTO.HHHOH npH ,nBlUKeHHH 3BeHbeB. Y CJIOBHeM CTaTWIeCKoro
paBHoBecIDI .HBJI.HeTC.H nOCTO.HHHOe nOJIOXeHHe ueH1pa Mace MexaHH3Ma. ,[(HHaMH-
qeCKOe ypaBHOBeIIIHBaHHe - 3TO ypaBHOBeIIIHBaHHe peaKUHH, B03HHKalOIUHX npH
BpaIUeHHH TeJIa, T.e. o,nHOBpeMeHHO CTaTWIeCKoe H MOMeHTHoe ypaBHOBeIIIeHHe.
ECJIH OCb BpaIUeHIDI npoxo,nHT qepe3 ueH1p Macc TeJIa H COBna,naeT C W(HOH H3 ero
rJIaBHbIX oceH HHepUHH, TO rOBOp.HT, qTO BpaIUalOIUeeC.H TeJIO ,nHHaMWIeCKH ypaB-
HOBeIIIeHO Ha OCH BpaIUeHIDI. - llpUMe"t. nep.)
3.8. 1. YpasHosewHsaHHe KOMnnSHapH&IX Macc
(CTaTHlfeCKoe pasHoseCHe)
KOMnrraHapHbIMH 6y,neM Ha3bIBaTb MaCCbI, paClIOJIOXeHHbIe B O,nHOH nrrOCKOCTH.
QT06bI TeJIO HaxO,nHJIOCb B COCTO.HHHH CTaTWIeCKoro paBHOBeCIDI, pe3YJIbTHpyroIUaH
Bcex CHJI, ,neHcTByroIUHX Ha TeJIO, H aJIre6paWIeCKa.H CYMMa MOMeHTOB ,nOJDKHbI
paBH.HTbC.H HYJIIO. Ha pHC. 3.8, a nOKa3aHbI 1pH KOMnrraHapHbIe MaCCbI, paClIOJIO-
xeHHbIe BOKpyr TOqKH O. Bo Bcex CJIyqasIX ,l(lliI Bcex lIpaKTHqeCKHX ueJIeH Ha 3eM-
JIe MO)I{HO CqHTaTb, qTO rpaBHTan;HOHHa.H CHJIa, ,neHcTByroIUa.H Ha Maccy, paBHa
9,81 x Macca.
QT06bI CHCTeMa Macc, lIOKa3aHHa.H Ha pHCYHKe, 6bma ypaBHoBeIIIeHHoH, OHa
,nOJDKHa HaxO,nHTbC.H B COCTO.HHHH CTaTWIeCKoro paBHOBeCIDI H, CJIe,nOBaTeJIbHO, aJI-
3.8. Ypa6Ho6eUlu6aHue 6paUl,alOUI,UXCJl Mace 113
c
a
b
9,81 Ins
a
c
a
9,81 m 2
6
Puc. 3.8. CTaTHqeCKOe paBHOBeCHe KOMnJIaHapHbIX Macc:
a - KOMnJIaHapHbIe MaCCbI B nepBOM yrJIOBOM nOJIOXeHHH;
6 - KOMnJIaHapHbIe MaCCbI nOCJIe nOBopOTa Ha 90 0 BO BTOpOM yrJIOBOM
nOJIOXeHHH
re6palNeCKa.H C)'MMa MOMeHTOB OTHOCHTeJIbHO UeH1pa BpameHIDI 0 ,nOJDKHa paB-
HHThC.H HYJIIO. MaTeMaTWIecKH 3TO MO)I{HO BbIpa3HTb CJIe,nyromHM 06pa30M:
9,81mlrl COSel + 9,81m2r2 Cose 2 + 9,81m3r3 Cose 3 = o.
ECJIH pa3,neJIHTb KIDK,ZJ;Oe H3 CJIaraeMbIX Ha 9,81, lIOJIyqHTC.H:
mlrl COSel + m2 r 2 Cose 2 + m3 r 3 Cose 3 = O.
F/la8a 3. HH:JICeHepHaJI OUHaMUICll
O,nHaKO 3Toro e,nHHCTBeHHoro YCJIOBIDI He,nOCTaTOqHO, qT06bI CHCTeMa Macc
6bma ypaBHoBeIIIeHHoH npH Bcex yrJIOBbIX nOJIOXeHIDIX. ECJIH Tenepb nOBepJIyTb CH-
cTeMy Ha 90°, KaK nOKa3aHO Ha pHC. 3.8, 6, aJIre6paHqeCKa.H C)'MMa MOMeHTOB OTHO-
CHTeJIbHO TOqKH 0 CHOBa ,nOJDKHa paBH.HTbC.H HYJIIO.
9, 81m lrl sin9 1 + 9,81m2r2 sin9 2 + 9,81m3r3 sin9 3 = o.
CHOBa pa3,neJIHM KIDK,ZJ;Oe H3 CJIaraeMbIX Ha 9,81 H nOJIy1IHM:
mlrl sin9 1 + m2 r 2 sin9 2 + m3 r 3 sin9 3 = o.
ECJIH CHCTeMa ypaBHOBeIIIeHa B JII06bIX ,nBYX yrJIOBbIX nOJIOXeHIDIX, COCTaBJI.HIO-
IUHX Me)l{)J;Y C060H np.HMOH yrOJI, TO OHa TaIOKe 6y,neT ypaBHOBeIIIeHa B JII06bIX npo-
MexyTOqHbIX nOJIOXeHIDIX. CJIe,nOBaTeJIbHO, npHBe,neHHbIX BbIIIIe ypaBHeHHH ,no-
CTaTOqHO ,l(lliI npOBepKH ypaBHOBeIIIeHHOCTH CHCTeMbI. ECJIH CHCTeMa He ypaBHOBe-
IIIeHa, Tor,na Te xe caMbIe ypaBHeHHH n03BOJI.HT onpe,neJIHTb BeJIHqHHY H nOJIoxe-
HHe ypaBHOBeIIIHBalOIUeH MaCCbI.
3.8.2. YpasHosewHsaHHe KOMnnaHapH&IX Macc
(AHHaMHlfecKoe pasHosecHe)
BonpOCbI ,nHHaMHqeCKOrO ypaBHOBeIIIHBaHH.H OqeHb CJIO)I{HbI, H eCJIH nonbITaTbCjI
HCCJIe,nOBaTb HX ,nOCTaTOqHO rJIY60KO, TO B 3TOM CnpaBOqHHKe npOCTO He XBaTHT
MeCTa. O,nHaKO paCCMOTpHM npocTyro KOMllJIaHapHylO CHCTeMY CHJI, ,neHCTByIO-
IUHX B CHCTeMe npH BpaIUeHHH Macc OTHOCHTeJIbHO TOqKH 0, KaK nOKa3aHO Ha
pHC. 3.9, a. B npouecce BpaIUeHH.H KIDK,ZJ;OH H3 Macc Ha TOqKY 0 (OCb HJIH BaJI) ,neH-
cTByeT ueH1p06e)I{HaH CHJIa mr0)2. CKOpOCTb BpalI(eHH.H 0) BbIpaxeHa 3,neCb B pa,n/c.
KaK H paHee, aJIre6paHqeCKaH C)'MMa MOMeHTOB OTHOCHTeJIbHO TOqKH 0 ,noJI)I{Ha
paBH.HTbC.H HYJIIO B ,nBYX HanpaBJIeHH.HX, COCTaBJIHIOIUHX Me)l{)J;Y C060H np.HMOH yrOJI
(x H y), KaK nOKa3aHO Ha pHC. 3.9, a.
CJIe,noBaTeJIbHO, YCJIOBIDI ,nHHaMHqeCKOrO paBHOBeCIDI onHCbIBaIOTC.H ,nBywI
ypaBHeHIDIMH:
mlrl0)2 cos9 1 + m2r20)2 cos9 2 + m3r30)2 cos9 3 = o.
ml1i0)2 sin9 1 + m2r20)2 sin9 2 + m3r30)2 sin9 3 = o.
nOCne ,neJIeHH.H Ha 0)2 (nOCTOHHHOH BeJIHqHHbI ,l(lliI JII060H 3a,naHHOH CKOpOCTIi :
BpaIUeHIDI) ypaBHeHH.H CTaHOB.HTC.H H,neHTHqHbIMH npe,nbI,nylI(HM ypaBHeHIDIM, onH-
CbIBalOIUHM CTaTHqeCKOe paBHOBeCHe. CJIe,nOBaTeJIbHO, ,l(lliI JII060H KOMllJIaHapHOH
CHCTeMbI CM YCJIOBH.H CTaTHqeCKOrO H ,nHHaMHqeCKOrO paBHOBeCIDI o,nHHaKOBbI Ii
He 3aBHC.HT OT CKOpOCTH BpaIUeHIDI. Ha pHC. 3.9, 6 nOKa3aHa BeKTOpHa.H ,nHarpaM-
Ma CHJI, HJIJIIOC1pHpyroIUa.H npe,nbI,LJ;ylI(He ypaBHeHH.H.
. ECJIH MHoroyrOJIbHHK 3aMKHYT, KaK nOKa3aHO Ha pHCYHKe, TO MaCCbI ypaB-
HOBeIIIeHbI.
. ECJIH MHoroyrOJIbHHK He 3aMKHYT, TO MaCCbI He ypaBHOBeIIIeHbI, H 3aMbIKa-
IOIUHH BeKTOp nOKa3bIBaeT yrJIOBOe nOJIOXeHHe H 3HaqeHHe mr ,nJI.H MaCCbI,
He06xo,nHMOH, qT06bI ypaBHOBeCHTb CHCTeMy.
3.9. OmHocume.nbHble cICopocmu
x
.-------
IY
.
I
.
I
.
x
------
.
I
.
I
.
S Iy
a 9,81 I7Js
6
PRC. 3.9. a - ,n;HHaMHqeCKOe (B npOI(eCce Bpam;eHHH) paBHOBeCHe KOMnJIaHapHbIX
Macc;
6 - BeKTopHaH ,n;HarpaMMa CHJI ,lI;JIH KOMnJIaHapHbIX Macc
3.9. OTHOCMTenbHble CKOpOCTM
3.9.1. OTHOCHTen&H&le CKOpOCTH (HecoeAHHeHH&le Tena)
YTBep)f{)];eHHe, qTO TeJIO ,nBH)I{eTC.H co CKOpOCTblO 50 KM/q, 03HaqaeT, qTO TeJIO ,nBH-
)KerCH co CKOpOCTblO 50 KM/q OTHOCHTeJIbHO KaKorO-TO ,npyroro TeJIa, TaKoro, Ha-
npHMep, KaK nOBepXHOCTb nrraHeTbI 3eMJI.H. Ho Kor,na rOBOp.HT, qTO CKOpOCTb caMO-
JIera B B03,nyxe paBHa 300 KM/q, Ha caMOM ,neJIe yKa3bIBalOT CKOpOCTb CaMOJIeTa OT-
HOCHreJIbHO CKOpOCTH B03,nynIHbIX lIOTOKOB, CKB03b KOTopbIe OH JIeTHT. MCTHHHa.H
CKOpOCTb CaMOJIeTa OTHOCHTeJIbHO 3eMJIH MoxeT 6bITb 60JIbIIIe, qeM ero CKOpOCTb
F/la8a 3. HH:JICeHepHaJI OUHaMU1Ca
OTHOCHTeJIbHO B03,nyxa, eCJIH BeTep nonyrHbIH, HJIH MeHbIIIe, eCJIH BeTep
BC1peqHbIH.
Ha pHC. 3.10, a nOKa3aHbI ,nBa Hecoe,nHHeHHbIX TeJIa, 0603HaqeHHbIe TOqKaMH P
H Q. 3TH TeJIa ,nBIDKyrC.H B npOTHBOnOJIO)I{HbIX HanpaBJIeHIDIX co CKOpOCT.HMH 3 If
5 M/c COOTBeTCTBeHHO. By,neM CqHTaTb HanpaBJIeHHe ,nBH)I{eHIDI CJIeBa HanpaBO no-
JIO)I(HTeJIbHbIM, a cnpaBa HaJIeBO - 01pHuaTeJIbHbIM.
P 3 M/C
. ..
(+)
....
5 M/C a
.
(-)
P 3 M/C
.
(+)
..
. 5 M/C
(+)
a
6
;/ p a7
P a " "
" _ Vi p ',- Vp
, ,
, ,
, ,
, ,
, ,
Va
a
,
,
,
,
,
, /"
, ,
\ /"
'",
-Vp
R
B
r
A
Puc. 3.10. OTHOCHTeJIbHbIe CKOpOCTH Hecoe,n;HHeHHbIX TeJI:
a - OTHOCHTeJIbHbIe CKOpOCTH ,n;BYX Hecoe,n;HHeHHbIX TeJI, ,n;BIDJCYII(HXC$I B
npOTHBOnOJIOXHbIX HanpaBJIeHHHX;
6 - OTHOCHTeJIbHbIe CKOpOCTH ,n;BYX Hecoe,n;HHeHHbIX TeJI, ,n;BHXYIQHXC$I B
O,n;HOM HanpaBJIeHHH;
B - OTHOCHTeJIbHbIe CKOpOCTH ,n;BYX Hecoe,n;HHeHHbIX TeJI, ,n;BHxyIIJ;HXCH
no pa3JIHqHbIM TpaeKTopHHM;
r - MeTO,n; OCTaHOBKH P H BJIHHHHe Ha Q;
,n; - CKOpOCTb Q OTHOCHTeJIbHO P (pe3YJIbTHPYlOIQaH CKOpOCTb QR)
CKOpOCTb Q OTHOCHTeJIbHO P = CKOpOCTb Q - CKOpOCTb P =
= (-5 M/c) - (+3 M/c) = -8 M/c.
CKOpOCTb Q OTHOCHTeJIbHO P 01pHuaTeJIbHa, nOTOMy qTO TeJIO Q ,nBH)I{eTCjI
cnpaBa HaJIeBO.
AHaJIOrHqHo:
CKOpOCTb P OTHOCHTeJIbHO Q = (+3 M/c) - (-5 M/c) = +8 M/c.
CKOpOCTb P OTHOCHTeJIbHO Q nOJIO)I(HTeJIbHa, nOCKOJIbKY TeJIO P ,nBH)I{eTC.H CJIe-
Ba HanpaBO. B ,naHHOM CJIyqae BbI60p nOJIO)I(HTeJIbHOrO H 01pHuaTeJIbHOrO HanpaB-
JIeHHH 6bill c,neJIaH npOH3BOJIbHO. OTHOCHTeJIbHbIe HanpaBJIeHH.H H pacnOJIOXeHlfe
nOJIO)I(HTeJIbHbIX H 01pHuaTeJIbHbIX 3HaqeHHH ,nOJDKHbI YCTaHaBJIHBaTbC.H nepe,n;
HaqaJIOM peIIIeHIDI KIDKJJ:OH KOHKpeTHoH 3a,n;aqH.
ECJIH TeJIa ,nBIDKyrC.H B npOTHBOnOJIO)I{HbIX HanpaBJIeHH.HX HaBC1peqy ,npyr ,npy-
ry, HX OTHOCHTeJIbHa.H CKOpOCTb - 3TO CKOpOCTb C6JIH)I{eHIDI. nYCTb Tenepb 3TH
,nBa TeJIa ,nBIDKyrC.H B O,nHOM H TOM xe HanpaBJIeHHH, KaK nOKa3aHO Ha pHC. 3.10,6.
CKOpOCTb Q OTHOCHTeJIbHO P = +5 M/c - (+3 M/c) = +2 M/c.
3.9. OmHOCUmetlbHble Clwpocmu
ECJIH ,nBa TeJIa ,nBIDKyTC.H He no O,nHOH H TOH xe 1paeKTOpHH, HX OTHOCHTeJIb-
Hble CKOpOCTH HeJIb3.H onpe,neJIHTb npOCTbIM CJIOXeHHeM HJIH BbIqHTaHHeM. Ha
pHC. 3.10, B nOKa3aHbI ,nBa TeJIa P H Q, ,nBIDICylI(HeC.H B pa3JIHqHbIX HanpaBJIeHIDIX
IIO pa3JIINHbIM 1paeKTOpIDIM B O,nHOH llJIOCKOCTH. CKOpOCTb TeJIa P paBHa V p , a
CKOpOCTb TeJIa Q - V Q .
QT06bI HaHTH CKOpOCTb TeJIa Q OTHOCHTeJIbHO P, He06xo,nHMO HaHTH Kaxyw;y-
IOC.H CKOpOCTb Q, MbICJIeHHO OCTaHOBHB TeJIO P. ,l:LrnI 3Toro lfY)KH0 npH6aBHTb CKO-
pOCTb -VP K CKOpOCT.HM 060HX TeJI, KaK nOKa3aHO Ha pHC. 3.10, r, B pe3YJIbTaTe
qero CKOpOCTb P CTaHeT paBHoH HYJIIO. 113 BeKTOpHOH ,nHarpaMMbI (pHC. 3.10, ,n)
MO>KHO BH,neTb, qTO Tenepb CKOpOCTb TeJIa Q COCTOHT H3 ero c06CTBeHHOH CKOpO-
CTH VQ H nepeHocHoH CKOpOCTH (-VP). (nepeHocHoH Ha3bIBalOT CKOpOCTb no-
,lJ;BIDKHOH CHCTeMbI OTCqeTa no OTHOIIIeHHIO K OCHOBHOH CHCTeMe OTCqeTa. -
llpUMe"t. nep.) Pe3YJIbTHpyromasI CKOpOCTb TeJIa Q npe,nCTaBJIeHa BeKTOpOM QR, KO-
TOpbIH COOTBeTcTByeT CKOpOCTH Q OTHOCHTeJIbH P. I1MeHHo TaK BbIrJIR,nHT ,nBlUKe-
HHe TeJIa Q ,l(lliI Ha6JIIO,naTeJI.H, CB.H3aHHOro C TeJIOM P. Ha6JIIO,naTeJIb, CB.H3aHHbIH C
TeJIOM Q, 6y,neT BH,neTb TeJIO P, ,nBIDICylI(HMC.H B npOTHBOnOJIO)I{HOM HalIpaBJIeHHH,
HO C TaKOH xe CKOpOCTblO. TaKHM 06pa30M, 3HaK pe3YJIbTHpyromero BeKTOpa CKO-
pOCTH CJIe,nyeT H3MeHHTb Ha npOTHBOnOJIO)I{HbIH.
3.9.2. OTHOCHTen&H&le CKOpOCTH (coeAJfHeHH&le Tena)
B OTJIINHe OT npe,nbI,nylI(erO pa3,neJIa, B 3TOM pa3,neJIe 6y,neM HMeTb ,neJIO C OTHOCH-
TeJIbHbIMH CKOpOCT.HMH TeJI, coe,nHHeHHbIX Me)l{)J;y C060H. Ha pHC. 3.11, a nOKa3aHbI
,lJ;Ba TeJIa P H Q, coe,nHHeHHbIe xeCTKHM 3BeHOM ,nJIHHbI I. CKOpOCTH coe,nHHeH-
HbIX TeJI P H Q paBHbI COOTBeTCTBeHHO v;, H V q H HanpaBJIeHbI, KaK nOKa3aHO Ha
pHCyJIKe.
Va
a
o
p
6
Puc. 3.11. OTHOCHTeJIbHbIe CKOpOCTH (coe,n;HHeHHbIe TeJIa):
a - ,n;Ba TeJIa (P H Q), coe,n;HHeHHbIe xeCTKHM 3BeHOM;
6 - BeKTopHaH ,n;HarpaMMa CKopocTeH
F/la8a 3. HH:JICeHepHaJI OUHaMUICa
nOCKOJIbKY paccToHHHe / Mex.n.y TeJIaMH P H Q <pHKCHpOBaHO, He MoxeT c}'Ine-
CTBOBaTb KOMlIOHeHTa CKOpOCTH, HanpaBJIeHHa.H B,nOJIb 3BeHa, coe,nHH.HlOmerO P Ii
Q. TaKHM 06pa30M, JI106a.H OTHOCHTeJIbHa.H CKOpOCTb 6y,neT neplIeH;J;HKYJI.HpHa 3Be-
HY, coe,nHH.HlOmeMY P H Q, nOCKOJIbKY 3TO e,nHHCTBeHHoe HalIpaBJIeHHe, B KOTOpOM
OTcyrcTByeT KOMnOHeHTa, HalIpaBJIeHHa.H B,nOJIb 3BeHa, coe,nHH.HlOmerO P H Q. H3
BeKTOpHOH ,nHarpaMMbI CKopOCTeH, lIOKa3aHHOH Ha pHC. 3.11, 6, MO)I{HO BH,Z:(eTb,
qTO BeKTOp pq nepneH;J;HKYJI.HpeH 3BeHY, coe,nHH.HlOmeMY TeJIa P H Q. n03TOMY
OqeBH,Z:(HO, qTO P BpamaeTC.H C TaHreHUHaJIbHOH CKOpOCTblO pq OTHOCHTeJIbHO Q.
CJIe,noBaTeJIbHo:
YrJIOBa.H CKOpOCTb 3BeHa = (TaHreHUHaJIbHa.H CKOpOCTb)/(Pa,nHYc).
ro = (BeKTOp pq)//.
BbNHCJIeHHe CKOpOCTH Q OTHOCHTeJIbHO P npHBeJIO 6bI K TOMY xe pe3YJIbTaTY, Tal{
KaK 3BeHO, coe,nHIDIlOmee TeJIa P H Q, MoxeT HMeTh TOJIbKO 0,l(Hy yrJIOByro CKOpOCTh.
3.10. KMHeM8TMK8
KHHeMaTHKa H3yqaeT ,nBIDKeHHe TeJI, He paCCMa1pHBa.H CHJIbI, HBJI.HlOmHeC.H nplNH-
HOH ,nBIDKeHID!. JIHHeHHa.H CKOpOCTb - 3TO 6bIC1pOTa H3MeHeHID! MO,Z:(yJI.H BeKTOpa
nepeMemeHID! no OTHOIIIeHHIO KO BpeMeHH, H ee MO)I{HO BbIpa3HTb KaK:
CKOpOCTb = ds / dt.
(BeKTOp lIepeMemeHIDI - 3TO BeKTOp, HaqaJIbHa.H TOqKa KOToporo COBna,naeT C
HaqaJIbHOH TOqKOH ,nBIDKeHID!, a KOHeu - C KOHeqHOH. Cpe,nHIDI CKOpOCTb - OT-
HOIIIeHHe MO,nyJI.H BeKTOpa lIepeMemeHIDI K lIpOMexyrKY BpeMeHH, B TeqeHHe KOTO-
poro 3TO lIepeMemeHHe lIpOH30IIIJIO. MrHOBeHHa.H CKOpOCTb (CKOpOCTb, 0 KOTOpOH
3,neCb rOBOpHTC.H) - lIpe,neJI OTHOIIIeHIDI BeKTOpa lIepeMemeHID! K npOMexyrKY
BpeMeHH, 3a KOTOpbIH 3TO lIepeMemeHHe lIpOH30IIIJIO, Kor,na MHTeJIbHOCTb lIpOMe-
xyrKa BpeMeHH C1peMHTCH K HYJIIO. - llpUMe"t. nep.)
nOMHHTe, qTO CKOpOCTb TeJIa xapaKTepH3yeTC.H KaK Mo,nYJIeM CKOpOCTH, TaK Ii
HalIpaBJIeHHeM. QHCJIeHHOe 3HaqeHHe CKOpOCTH paBHO ee MO,nYJIIO. nepeMemeHHe
paBHO llJIOma,nH no,n rpa<pHKOM 3aBHCHMOCTH CKOpOCTH OT BpeMeHH. TaK KaK:
v = ds / dt,
TOr.n;a f tis = f vdt.
AHaJIOr HO, JIHHeHHOe YCKopeHHe - 3TO 6bIC1pOTa H3MeHeHIDI CKOpOCTH:
Y CKopeHHe = H3MeHeHHe CKOpOCTH/BpeM.H = dv / dt HJIH d 2 S / dt 2
OTMeTHM, qTO YCKopeHHe - 3TO, KpOMe Toro, BTOpa.H npOH3Bo,nHaH nepeMem;e.
HID! no BpeMeHH. CKOpOCTb paBHa llJIOma,nH no,n rpa<pHKOM 3aBHCHMOCTH YCKope.
HID! OT BpeMeHH. TaK KaK:
Tor,na
a = dv / dt,
f da = f adt.
AHaJIOrINHO, yrJIOBOe YCKopeHHe - 3TO 6bIC1pOTa H3MeHeHIDI yrJIOBOH CKOpOCTII
a. = dq,/ dt HJIH a. = d 2 e / dt 2 .
3.10. KUHeMamUlCO
3. 10. 1. 6annHcTHKa
Ha pHC. 3.12 nOKa3aHa 1paeKTOpIDI CHap.H,na, BbIrryI.l(eHHoro C HaqaJIbHOH CKOpO-
CTblO v, M/C, npH TOM qTO yrOJI B03BbIIIIeHIDI Opy,nIDI paBeH e. Tor,na BepTHKaJIbHa.H
COCTaBIDIIOIUa.H CKOpOCTH V v = vlsine H ropH30HTaJIbHa.H COCTaBlliIIOIUa.H CKOpOCTH
VB = VIcose. ECJIH npeHe6peqb conpOTHBJIeHHeM B03,nyxa, e,nHHCTBeHHOH CHJIOH,
,lI;eHCTByroIUeH Ha CHapM, 6y,neT CHJIa TIDKeCTH, co06IUalOIUa.H Macce cHapMa rpa-
BHTaUHOHHoe YCKopeHHe (9,81 M/C 2 ) B HanpaBJIeHHH BHH3. nOCKOJIbKY He CYIneCT-
ByeT ropH30HTaJIbHO HanpaBJIeHHOH CHJIbI, ,neHCTByroIUeH Ha CHapM, ropH30HTaJIb-
HWI COCTaBJUlIOIUa.H CKOpOCTH OCTaHeTC.H nOCTO.HHHOH Ha npOTIDKeHHH Bcero nOJIe-
Ta. (B peaJIbHOCTH OHa 6y,neT nOCTeneHHO )'MeHbIIIaTbCH 3a CqeT COnpOTHBJIeHIDI
B03,nyxa. )
v sin 8
MaKCH bHaR BbiCOTa nOAbeMa h
I.
TpaeKTopVl51 CHap5lAa
s
I
· v cos 8
Puc. 3.12. TpaeKTopHH CHapH,n;a
COrJIaCHO CooTHoIIIeHHIO, npHBe,neHHoMy B pa3,neJIe 3.6.4, nOJIHOe BpeMH nOJIe-
Ta MOXHO nOJIyqHTb, HCnOJIb3Y.H BbIpaxeHHe s = VI t + 1 / 2at 2 . nOCKOJIbKY npe,nno-
JIaraeTC.H, qTO cHapM CTapTYeT C ypOBH.H 3eMJIH, ,nOCTHraeT MaKCHMaJIbHOH BbICO-
TbI h, KaK nOKa3aHO Ha pHCYHKe, H CHOBa B03BpaIUaeTC.H Ha ypOBeHb 3eMJIH, TO pe-
3YJIbTHpyro:w;ee paCCTO.HHHe, npOH,neHHOe CHapMOM B BepTHKaJIbHOM HanpaBJIe-
HHH, 6y,neT paBHO HYJIIO. n03TOMy:
s = 0, V v = VI sin e H a = -g.
TIOCKOJIbKY:
o = (VI sine)t - gt 2 / 2.
t = (2VI sin e) / g.
Tor,na
TaK KaK ropH30HTaJIbHa.H COCTaBJI.HIOIUa.H CKOpOCTH cHapMa OCTaeTCH nOCTO.HH-
HOH, paCCTO.HHHe s, npOH,neHHOe CHapMOM B ropH30HTaJIbHOM HanpaBJIeHHH (,na-
JIbHOCTb), MO)I{HO paCCqHTaTb CJIe,nyroIUHM 06pa30M:
TIpoi!f,neHHoe paCCTO.HHHe HJIH ,naJIbHOCTb (s) =
= ropH30HTaJIbHa.H KOMnOHeHTa CKOpOCTH x BpeM.H nOJIeTa.
S = (VI cos e) x (2VI sin e) / g = [(VI)2 sin 2e] / g (TaK KaK sin 28 = 2 sin ecos e).
MaKCHMaJIbHyro BbICOTY (h), ,nOCTHraeMyID CHapMOM B nOJIeTe, MO)I{HO HaHTH
H3 BbIpaxeHIDI:
h = [(VI)2 sin 2 e] / 2g.
F/la8a 3. HH:JICeHepHaJI OUHaMU1Ca
3.11. KMHeTMKa
KHHeTHKa HCCJIe,nyeT npWIHHbI B03HHKHOBeHIDI ,nBH)I{eHIDI, B OTJIHqHe OT KHHeMa-
THKH, KOTOpa.H H3yqaeT TOJIbKO reOMe1pHIO ,nBH)I{eHIDI. CJIe,noBaTeJIbHO, B KHHeMa-
THKe lIpHMeH.HIOTC.H 3aKOHbI MexaHHKH HbIOTOHa.
3. 11. 1. BceMHpHoe TflrOTeHHe
3aKOH, onHcbIBalOIUHH B3aHMHoe npHTIDKeHHe TeJI, 06JIa,naIOIUHX MaccoH, Ha3bIBa-
eTCH 3aKOHOM BceMHpHoro T.HrOTeHIDI. 3TOT 3aKOH 6bill C<POpMyJIHpOBaH C3pOM
McaaKOM HbIOTOHOM, H OH yrBepx.n;aeT, qTO KIDIQ:J:Oe TeJIO BO BCeJIeHHOH lIpHT.HrH-
BaeTC.H K JII060MY ,npyroMy TeJIY C CHJIOH, KOTopaH IIp.HMO nponOpUHOHaJIbHa npo-
H3Be,neHHIO Macc 3THX TeJI H 06paTHO lIpOlIOPUHOHaJIbHa KBa,npaT}' paCCTO.HHIDI
Mex.n;y HHMH. MaTeMaTWIeCKH 3TO MO)I{HO C<POpMyJIHpOBaTb CJIe,nyIOIUHM 06pa30M:
F =( Gm lm2) / d 2 ,
r,ne F - B3aHMHa.H CHJIa npHTIDKeHIDI Mex.n;y MaccaMH ml H m2; d - paCCTO.HHHe
Mex.n;y MaccaMH; G - rpaBHTaUHOHHa.H nOCTO.HHHa.H (He 3aBHCHT OT B3aHMo,neHCT-
ByroIUHX Macc)
,l:LrnI JII06bIX ,nBYX Macc Ha JII060H nrraHeTe, BKJIlOqa.H nrraHeT}' 3eMJI.H, CHJIa B3a-
HMHoro npHTIDKeHIDI Mex.n;y MaccaMH F npeHe6pe)I(HMO MaJIa lIO cpaBHeHHIO C CH-
JIOH npHTIDKeHIDI Mex.n;y KIDIQ:J:OH H3 Macc H nrraHeTOH, Ha KOTOpOH 3TH MaCCbI Ha-
XO,lUITC.H. TIOCKOJIbKY CHJIa npHTIDKeHIDI nJIaHeTbI 3eMJI.H ,neHcTByeT Ha Bce OCTaJIb-
HbIe TeJIa, TO H3 BToporo 3aKOHa MexaHHKH HblOTOHa CJIe,nyeT, qTO 3Ta CHJIa coo6-
IUaeT HM YCKopeHHe g (M/C 2 ). TaK KaK
(GMoM)/ r 2 = F = Mg.
TI03TOMy:
g = (GM 0)/ r 2 = 9,81m / s 2 ,
r,ne G - rpaBHTaUHOHHa.H nOCTO.HHHa.H (6,668 x 10- 11 M 3 /KrC 2 ); Mo - Macca nrraHe-
TbI 3eMJI.H (5,98 x 10 24 Kr) npe,nlIOJIaraerc.H cocpe,nOTOqeHHOH B ueH1pe nrraHeTbI;
r - cpe,nHHH pa,nHYC nJIaHeTbI 3eMJI.H (6,375xl0 6 M); g - cpe,nHee YCKopeHHe CBO-
60,nHoro na,neHIDI Ha nJIaHeTe 3eMJI.H; F = B3aHMHa.H CHJIa npHTIDKeHIDI.
3. 11.2. nJfHeHHOe nepeMe eHHe
JII060e TeJIO, Ha KOTopoe ,neHcTByeT HeCKOJIbKO BHeIIIHHX CHJI TaK, qTO pe3YJIbTHPY-
IOIUaH 3THX CHJI npoxo,nHT qepe3 n;eH1p Macc TeJIa, 6y,neT ,nBHraTbC.H nOCTYIIaTeJIbHO.
KpoMe Toro, lIOCKOJIbKY pe3YJIbTHpyroIUa.H CHJIa npHJIOXeHa K ueH1py Macc TeJIa,
MOMeHT BpaIUeHIDI He B03HHKHeT, If TeJIO He 6y,neT BpaIUaTbC.H. TI03TOMy JII060e
TaKoe ,nBH)I{eHHe 6y,ner nOCTYIIaTeJIbHbIM, H TeJIO 6y,neT nepeMeIUaTbC.H HJIH c1pe-
MHTbC.H nepeMeCTHTbC.H C o,nHoro MeCTa B ,npyroe no np.HMOH JIHHHH. (TIpH nocTY-
naTeJIbHOM ,nBH)I{eHlfH Bce TOqKH TeJIa ,nBIDKyTC.H o,nHHaKOBO, Hero MO)I{HO pac-
CMa1pHBaTb KaK MaTepHaJIbHyro TOqKY. - llpUMe"t. nep.)
11. KUHemu a
3. 11.3. nepeMeU,f,eHJfe no KpJfSOnJfHeHHOH TpSeKTOpJfJf
Kor,na TeJIO lIepeMelI(aeTCR lIO KpHBOJIHHeHHOH 1paeKTOpHH PMHYca r C lIOCTORH-
HOD lIO MO.l(yJIIO CKOpOCTblO v, 3TO 03HaqaeT, qTO OHO ,nBIDKeTcR C YCKopeHHeM v 2 /r,
HanpaBJIeHHbIM lIO PMHYCY K n;eH1pY KpHBH3HbI TpaeKTOpHH, KaK 06Cy:>K,ZJ;aJIOCb B
pa3,neJIe 3.7.8. 3TO YCKopeHHe Ha3bIBaeTCR n;eH1pOC1peMHTeJIbHbIM. COrJIaCHO BTO-
poMy 3aKOH)' MexaHHKH HblOToHa, TeJIO He MoxeT ,nBHraTbCR C YCKopeHHeM, eCJIH
OHO He rro,nBepraeTCR B03,neHCTBHIO BHeIIIHeH CHJIbI. TaKHM 06pa30M:
:QeH1pOCTpeMHTeJIbHaR CHJIa = Macca x n;eH1pOC1peMHTeJIbHOe YCKopeHHe =
= (mv 2) / r.
ITOCKOJIbKY rrpH paBHOMepHOM )J;BIDKeHHH rro, OI(P}')KHOCTH v = !to, n;eHTPOCTPe-
MIITeJIbHaR CHJIa = mro 2 r.
:QeHlpOC1peMHTeJIbHaR CHJIa ,nOJDKHa 6bITb lIpHJIOXeHa K Te.rry H3BHe; HalIpHMep,
B c.rryqae aBTOM06HJI.H 3T0 CHJIa 1peHIDI IIIHH, COlIpHKaCalOlI(HXCR C ,noporOH, HJIH B
cJIy'lae lIoe3,na - 60KOBoe ,naBJIeHHe peJIbC Ha pe60p,nbI KOJIeC lIo,nBIDKHoro COCTaBa.
COrJIaCHO 1peTbeMY 3aKOH)' HbIOTOHa, AJUI KIDK.nOH aKTHBHOH CHJIbI CylI(eCTByeT CHJIa
peaKIJ;HH, paBHaR eH lIO BeJIHqHHe H lIpOTHBOlIOJIO)I{HasI lIO HalIpaBJIeHHIO. TI03TOMY
,ZJ;OJDKHa CylI(eCTBOBaTb CHJIa, paBHaR lIO BeJIINHHe H lIpOTHBOlIOJIO)I{HaR lIO HalIpaB-
JIeHllIO n;eH1pOC1peMHTeJIbHOH CHJIe. 3TO - n;eH1p06e)I{HaR CHJIa, H OHa ,neHcTByeT
no PMHYCY B HalIpaBJIeHHH OT n;eH1pa Iq)HBH3HbI 1paeKTOpHH. B c.rryqae aBTOM06HJI.H
ero WHHbI TOJIKalOT ,nopo)I{Hoe lIoIqJbITHe OT n;eH1pa KpHBH3HbI (n;eIITp06e)I{HaR
CHJIa), a ,nopora TOJIKaeT IIIHHbI aBTOM06HJI.H B lIpOTHBOlIOJIO)KHOM HalIpaBJIeHHH
(u;eIITpOCTPeMHTeJIbHaR cHJIa) ,no Tex lIOp, lIOKa CHJIa 1peHIDI Me)l{,[(y IIIHHaMH H ,no-
porOD OCTaeTCR ,nocTaTOqHOH, qT06bI aBTOM06HJIb He HaqaJI CKOJIb3HTb.
3.11.4. KOHJflfeCKJfH MSflTHJfK
ECJIII TBep,noe TeJIO MaCCOH m lIo,nBeIIIeHO K TOq-
Ke P Ha HHTH (JIerKOM CTep)I{He) .n.rrHHOH I TaK,
QTO OHO OlIHCbIBaeT OKpyxHOCTH PMHYca r C
nOCTORHHOH CKOpOCTblO <0, KaK lIOKa3aHO Ha
pllC. 3.13, TO AJUI JII060H 3MaHHOH CKOpOCTH
BpaIneHIDI yrOJI OTKJIOHeHIDI OT BepTHKaJIbHOH
OCII, rrpOXO,nRlI(eH qepe3 TOqKY lIo,nBeca, e H pa-
,ZJ;HYC BpalI(eHIDI r 6y,nyr BlIOJIHe OlIpe,neJIeHHbIMH
II B3aHMOCBR3aHHbIMH BeJIHqHHaMH. MMeHHO
npllHn;HlI KOHlNeCKOrO MaRTHHKa, TaK xe KaK H
npllHn;HlI peryJUlTOpa, HClIOJIb3yroTCR AJUI ynpaB-
JIeHIDI CKOpOCTblO ,nBHraTeJIeH. B lIOCJIe,nHeM
cJIy'lae, eCJIH HarpY3Ka Ha ,nBHraTeJIe YMeHbIIIaeT-
CH, TaK qTO CKOpOCTb ,nBHraTeJUI HaqHHaeT B03pa-
CTaTb, BeJIHqHHbI r H e TaIOKe YBeJIHqHBaIOTCR, H
PbIqIDKHbIH MexaHH3M, K KOTOpOMY lIpHcoe,nHHe-
Ha Macca m, 3aKpbIBaeT ,npOCCeJIbHyID 3aCJIOHKY
TaK, qT06bI CKOpOCTb ,nBHraTeJUI CHOBa CHH3H-
h
,
I ,
.... ""
I .........__...-'
I
,
9,81 m
Puc. 3.13. KOHHqeCKHH MaHTHHK
j
F/la8a 3. HH:JICeHepHaJI OUHaMUlCa
JIaCb ,no HOpMaJIbHOH (6e30rracHoH) BeJIHqHHbI. Ha060poT, eCJIH HarpY3Ka YBeJIINII-
BaeTCR TaK, qTO CKOpOCTb ,nBHraTelliI HaqHHaeT YMeHbIIIaTbcR, Tor,na r H e YMeHb-
IIIaIOTCR, H PbJqIDKHbIH MexaHH3M, K KOTOpOMY rrpHcoe,nHHeHa Macca m, OTKpbIBa-
eT ,npoCCeJIb H BOCCTaHaBJIHBaeT rrpaBHJIbHyID pa60qyro CKOpOCTb ,nBHraTelliI. TaKHM
06pa30M 06eCrreqHBaeTCR rrOCTORHHaR CKOpOCTb pa60TbI ,nBHraTelliI.
TIYCTb T - CHJIa HaT.HXeHIDI HHTH, Ha KOTOpOH rro,nBeIIIeHa Macca m; Tor,na
IJ;eH1poc1peMHTeJIbHaR CHJIa, rro.z:r.n;ep)I(HBalOlI(aR ,nBH)I{eHHe lIO O:KpyxHOCTH, 06ec-
lIeqHBaeTCR ropH30HTaJIbHOH cOCTaBlliIlOlI(eH CHJIbI T.
fOpH30HTaJIbHaR COCTaBlliIlOlI(aR CHJIbI T paBHa:
T sin a = mrro 2
TIOCKOJIbKY CHCTeMa Haxo,nHTCR B paBHoBecHH, BepTHKaJIbHaR COCTaBlliIlOlI(WI
CHJIbI T AJUI paBHoBecIDI paBHa:
TI03TOMY:
T cos a = 9,81m.
sin a / cos a = tg(}.
tg(} = (rro 2 ) / 9.81.
tg(} = (rro 2 ) / 9,81 H tg(} = r / h,
r / h = (rro 2 ) / 9,81.
h = 9,81 / 00 2 .
r = I sin a.
I = r / sin a.
T = m / 00 2 .
TIOCKOJIbKY:
To:
TaK KaK
TO
3. 11.5. BpSUf,eHJfe Tens sOKpyr HenOASJfJICHOH OCJf
Kor,na pe3YJIbTHpyrolI( BHeIIIHHX CHJI, ,neHCTByroII(HX Ha TeJIO, lIpHJIOXeHa K ero
IJ;eH1pY Macc, TeJIO ,nBH)I{eTCR TOJIbKO lIOCTYIIaTeJIbHO, H BpalI(eHIDI He B03HHKaeT (CM.
p33,neJI 3.11.4). O,nHaKo Kor,na pe3YJIbTHpyrolI(aR CHJIa lIpHJIOXeHa He K IJ;eHTPY Mace
TeJIa, B03HHKHeT MOMeHT BpalI(eHIDI, H TeJIO HaqHeT BpalI(aTbCR. Ha pHC. 3.14 lIOKa-
3aHO TeJIO, BpalI(alOlI(eeCR BOKpyr OCH P lIO,n B03,neHcTBHeM MOMeHTa BpalI(eHIDI T.
MrHOBeHHaR yrJIOBaR CKOpOCTb TeJIa paBHa 00, a ero yrJIOBOe YCKopeHHe - a.
YCKopeHHe, C KOTOpbIM ,nBIDKYTCR MaTepHaJIbHbIe TOqKH, HMeIOII(He MaccbIom,
8m! H 8m2, MO)I{HO pa3JI0)I(HTb Ha ,nBe cOCTaBlliIIOII(He: TaHreHIJ;HaJIbHyID COCTaBJUI-
IOIUyIO ar H IJ;eH1poc1peMHTeJIbHyID COCTaBlliIlOlI(yro 00 2 r, KOTopaR HalIpaBJIeHa no
PMHYCY KOCH P, BOKpyr KOTOpOH BpalI(aeTCR TeJIO. TIOCKOJIbKY IJ;eHTPOCTPeMllTe-
JIbHbIe COCTaBlliIlOlI(He AJUI KIDK,ZJ;OH H3 MaTepHaJIbHbIX TOqeK HalIpaBJIeHbI K OCII P,
COOTBeTCTByrolI(He CHJIbI He C03,na1OT MOMeHTOB OTHOCHTeJIbHO 3TOH OCH. O,nHaKO
CHJIbI, 06eClIeqHBalOlI(He TaHreHIJ;HaJIbHbIe COCTaBlliIlOlI(He AJUI KIDK,ZJ;OH H3 3JIeMeH-
TapHbIX MaCC (8mar 2 ), ,neHCTBHTeJIbHO C03,na1OT BpalI(alOlI(HH MOMeHT OTHOCHTeJIL-
HO OCH P. TI03TOMY lIOJIHbIH MOMeHT BpalI(eHIDI OTHOCHTeJIbHO OCH P paBeH:
21.8mar 2) = alJ..8mr 2 ),
TaK KaK Bce MaTCpHaJIbHbIe TOqKH BpalI(alOTCR BOKpyr P C O,nHHaKOBOH CKOpOCTblO.
3.11. KUHemUK,a
\00 -yrnoBaSi CKOpOCTb
) IX - yrnoBoe YCKopeHHe
TaHreHu.VlaJ1bHa51 (KacaTeJ1bHa5l)
COCTaBJ151IOw.a51 YCKopeHVI
J
PRC. 3.14. BpalI(eHHe TeJIa BOKpyr <pHKcHpoBaHHoro I(eHTpa
CYMMa lIpoH3Be,neHHH Macc Bcex MaTepHaJIbHbIX TOqeK TeJIa Ha KBan;paTbI HX
paccToRHHH ,no paccMaTpHBaeMoH OCH P lJ...omr 2 ) Ha3bIBaeTCR MOMeHTOM HHepIJ;HH.
TaKHM 06pa30M:
MOMeHT HHepIJ;HH I p = lJ...omr 2 )
MOMeHT BpalI(eHIDI T OTHOCHTeJIbHO P = I pa.
E,nHHHIJ;bI H3MepeHIDI: T (HM), Ip (KrM 2 ) H a (pan;/c 2 ).
3. 11.6. PSAJfYC KpJfSJf3H&1
TIOCKOJIbKY C)'MMa 3JIeMeHTapHbIX Macc paBHa 06lI(eii Macce TeJIa (m = Lom), eCJIH
k - 3TO paCCTORHHe OT BbI6paHHoH OCH ,no TOqKH, B KOTOpOH, KaK lIpe,ZJ;lIOJIaraeT-
CH, cocpe,nOTOqeHa C)'MMapHaR Macca, TaK qTO lIPH 3TOM MOMeHT HHepIJ;HH OTHOCH-
reJIbHO 3TOH OCH paBeH MOMeHTY HHepIJ;HH TeJIa mk 2 = lJ...omr 2 ), Tor,na MOMeHT
HHepUHH MO)I{HO BbIpa3HTb KaK:
Ip == mk 2 ,
r,n;e k - pan;HYC HHepIJ;HH OTHOCHTeJIbHO KOHKpeTHoH OCH BpalI(eHIDI.
3. 11. 7. LleHTp CTonKHOSeHJffl
TIpH peIIIeHHH 3an;aq, CBR3aHHbIX C BpalI(eHHeM, qaCTO 6bIBaeT He06xo,nHMO OlIpe-
,n;eJIHTb JIHHHIO ,neiicTBIDI pe3YJIbTHpyrolI(eH CHJIbI F (KaK lIOKa3aHO Ha pHC. 3.15}, I
r,n;e F paBIDIeTCR Macce TeJIa, )'MHOXeHHoii Ha YCKopeHHe IJ;eH1'pa Macc. TIpe,nlIOJIO-
)l{HM, qTO 3Ta JIHHHR ,neHcTBIDI pe3YJIbTHpyrolI(eii CHJIbI F lIpOXO,nHT qepe3 HeKOTO-
PYlO TOqKY P Ha JIHHHH RGP, r,ne R - OCb BpalI(eHIDI H G - IJ;eH1'p Macc. KaK 06-
Cyx,zJ;aJIOCb B pa3,neJIe 3.11.6, TOJIbKO TaHreHIJ;HaJIbHaR COCTaBIDIlOlI(aR CHJIbI F MO-
xeT C03,naBaTb MOMeHT BpalI(eHHR OTHOCHTeJIbHO R. P - 3TO TOqKa TeJIa, r,ne MO-
MeHTbI Bcex BHeIIIHHX CHJI ypaBHOBeIIIeHbI, H HX C)'MMa paBHa H)'JIIO. TOqKa P
Ha3bIBaeTCR IJ;eH1pOM y,napa. ,[L1rn Tex CJIyqaeB, Kor,na TeJIO BpalI(aeTCR BOKpyr CBoe-
ro n;eH1'pa Macc (R H G cOBlIan;aIOT), MO)I{HO 3alIHcaTb:
F/la8a 3. HH:JICeHepHaR OUHaMUlCa
(0 - yrJ10Ba51 CKOpOCTb
T aHreHu.VlaJ1bHa51 (KacaTeJ1 bHa5l)
COCTaBJ151IOw.a51 F = ma.t
- yrnoBoe YCKopeHloIe
PRC. 3.15. QeHTp Y,lJ;apa
MOMeHT BpalI(eHIDI T = m(kG)2a = IGa,
r,ne kG - panHYC HHepn;HH OTHOCHTeJIbHO G.
Kor,na TeJIO BpalI(aeTCR BOKpyr OCH, lIpOXO,nRlI(eH qepe3 ero n;eH1p Macc, panHYC
HHepn;HH MHHHMaJIeH H, CJIe,nOBaTeJIbHO, MOMeHT BpalI(eHIDI, He06xo,nHMbIH ,nmI
BpalI(eHIDI TeJIa, TaIOKe MHHHMaJIeH.
(EcJIH TeJIO, 3a:KpeIIJIeHHOe Ha OCH BpalI(eHIDI, HClIbITbIBaeT y,nap, TO ,neHCTBHe
y,napa B 06lI(eM c.rryqae lIepe,naeTcR H Ha OCb. Ho eCJIH y,nap HaHeceH CTporo B
n;eH1p y,napa, TO OCb He HClIbITbIBaeT HHKaKHX ,nOlIOJIHHTeJIbHbIX HarpY30K, CBR3aH-
HbIX C y,napOM. B 3TOM c.rryqae CKOpOCTb lIOCTYIIaTeJIbHOrO ,nBH)I{eHIDI, lIpH06peTae-
Moro TOqKOH BMeCTe C n;eH1pOM Macc, KOMlIeHcHpyeTcR JIHHeHHOH CKOpOCTblO Bpa-
lI(aTeJIbHOrO ,nBH)I{eHIDI BOKpyr n;eH1pa Macc (06a 3TH ,nBH)I{eHIDI HHHIJ;HHpyroTCR
CHJIOH F H lIpOHCXO,nRT o,nHOBpeMeHHO). - llpUMett. nep.)
3. 11.8 MOMeHT JfMnyn&CS
M3 pa3,neJIa 3.6.8 H3BeCTHO, qTO HMlIYJIbC TeJIa paBeH Macce TeJIa, YMHOxeHHoH Ha
ero JIHHeHHyID CKOpOCTb. MOMeHT HMrryJIbCa BpalI(alOlI(erOCR TeJIa - 3TO MOMeHT
ero HMrryJIbCa OTHOCHTeJIbHO TOqKH BpalI(eHIDI. Ha pHC. 3.16 lIOKa3aHO TeJIO, Bpa-
lI(alOlI(eeCR BOKpyr OCH P C yrJIOBOH CKOpOCTblO ro (pan/c). PaCCM01pHM MaTepH-
aJIbHyro TOqKY MaCCOH 8m, paClIOJIOXeHHyID Ha paCCTORHHH r OT OCH P, CKOpOCTb
KOTOpOH paBHa v M\C.
MMrryJIbC MaTepHaJIbHOH TOqKH = 8mv = 8mrro.
MOMeHT HMrryJIbCa OTHOCHTeJIbHO P = r(8mrro) = 8mr 2 ro.
MOMeHT HMrryJIbCa OTHOCHTeJIbHO P AJUI Bcero TeJIa = L8mr 2 ro.
L8mr 2 = I,
Ho:
r,ne I - MOMeHT HHepn;HH (CM01pH pa3,neJI 3.11.5).
TaKHM 06pa30M:
MOMeHT HMrryJIbCa OTHOCHTeJIbHO P = lro.
3.12. IIpocmoe zapMOHU'teCK,Oe 08U:JICeHUe
(0 - yrJ10Ba51 CKOpOCTb
,
,
,
,
,
", V - reo- J1V1HeVlHa51 CKOpOCTb
,
)
)
PRC. 3.16. MOMeHT HMnyJIbCa
ECJIH rrpoHcxo,nHT H3MeHeHHe yrJIOBOH CKOpOCTH, BbIpaxeHHe, lIpHBe,neHHoe
BbIwe, lIpe06pa3yeTcR KaK:
M3MeHeHHe MOMeHTa HMrryJIbCa = 1(002 - (01)'
CJIe,nOBaTeJIbHO: BpalI(aTeJIbHbIH HMrryJIbC Tt = 1(002 - (01),
r,ne T - MOMeHT BpalI(eHIDI (HM); t - BpeM.H (ATIHTeJIbHOCTb HMrryJIhCa B ceKYJI,ZJ;ax).
KHHeTlNeCKaR 3HeprIDI, KOTOpOH 06JIMaeT BpalI(alOlI(eeCR TeJIO = 1 p002 ,
r,n;e Ip - MOMeHT HHepIJ;HH OTHOCHTeJIbHO OlIOpHOH TOqKH P.
KHHeTHqeCKaR 3HeprIDI TeJIa, KOTopoe o,nHOBpeMeHHO H BpalI(aeTCR, H lIepeMe-
m;aeTCR = KHHeTHqeCKaR 3HeprIDI BpalI(eHIDI + KHHeTlNeCKaR 3HeprIDI lIepeMelI(e-
HID! = /002 + mv2.
3.12. npOCToe rapMOHMl.leCKOe ABM>KeHMe
)];BIDKeHHe, KOTopoe lIOBTopReTCR qepe3 HeKOTopbIe HHTepBaJIbI BpeMeHH, Ha3bIBaeT-
/
CH nepHo,nlNeCKHM. HalIpHMep, eCJIH ,nepHYTb TaKoe ynpyrde TeJIO, KaK cTPYHa My-
3bIKaJIbHOrO HHC1pyMeHTa, HJIH y,napHTb lIO HeH, TO OHa 6y,neT CB060,nHO KOJIe6aTbCR
OKOJIO cpe,nHero lIOJIOXeHIDI. ECJIH B03HHKIIIHe 3ByKOBbIe KOJIe6aHIDI HaxO,nRTCR B
npe,neJIax 06JIaCTH CJIbIIIIHMOCTH qeJIOBeqeCKOrO yxa, pO)l{)];aeTCR My3bIKaJIbHbIH 3ByK;
n03TOMy TaKHe KOJIe6aHIDI xapaKTepH3yroTCR KaK rapMOHlNeCKHe. TaKoe lIepHo,nH-
qeCKOe ,nBH)I{eHHe, lIOpO)l{)];alOlI(ee 3ByKOBbIe KOJIe6aHIDI, He lIpO.ZJ;OJDKaeTCR 6ecKo-
HeqHO, a B KOHIJ;e KOHIJ;OB 3aT}'XaeT. Ero «raCHT» BHYTPeHHee COlIpOTHBJIeHHe C1pYHbI
Ii BHeWHee COlIpOTHBJIeHHe B03,nyxa, oIqJ)')I{alOlI(ero CTPYHY.
TIpocToe rapMOHlNeCKOe .ZJ;BH)I{eHHe olIpe,nelliIeTcR KaK ,nBH)I{eHHe TOqKH B,nOJIb
npRMoH JIHHHH, TaK qTO YCKopeHHe TOqKH Bcer,na HalIpaBJIeHO K <PHKcHpOBaHHOH
TOQKe Ha 3TOH JIHHHH H lIpOlIOpIJ;HOHaJIbHO ee CMelI(eHHIO OT 3TOH TOqKH. Ha
pliC. 3.17 lIOKa3aHa Bo06paxaeMaR TOqKa P, BpalI(alOlI(aRCR lIO OKpyxHOCTH C PMHY-
COM r H IJ;eH1pOM B TOqKe 0 C lIOCTORHHOH yrJIOBOH CKOpOCTblO (0. ECJIH ClIPO UHpO-
BaTh TOqKy P Ha ,nHaMeTP OIqJyxHOCTH AB, TO ,nBH)I{eHHe TOqKH Q BlIepe,n-Ha3M lIO
I
,n;HaMeTpY AB 6y,neT lIpOCTbIM rapMOHlNeCKHM ,nBH)I{eHHeM. To eCTb, Kor,na T01JKa P
F/la8a 3. lfH:JICeHepHaJl OUHaMUlCa
AMnJ1V11)'Aa
AMnJ1V11)'Aa
PRC. 3.17. npOcToe rapMOHHqeCKOe ,nBH-
xeHHe.
COBepIIIHT O,nHH lIOJIHbIH 060POT, TOqKa Q
cOBepIIIHT lIOJIHOe KOJIe6aHHe OT A ,no B Ii
06paTHo K A. TI03TOMY BpeM.H o,nHoro
lIOJIHOrO 060poTa P paBHO BpeMeHH O,nHO-
ro lIOJIHOrO KOJIe6aHIDI Q. PaccToRHHe AO
(HJIH BO) Ha3bIBaeTCR aMIIJIHTY,noH KOJIe-
6aHHH.
1. qacTOTY KOJIe6aHHH B repn;ax (fu)
MO)I{HO HaHTH H3 BbIpaxeHIDI:
f = 1 / T = ro / 2TC,
r,ne f - qaCTOTa KOJIe6aHHH, T - lIepHO,lJ;,
ro - yrJIOBaR CKOpOCTb.
2. MaKCHMaJIbHyID CKOpOCTb Q ,no-
CTHraeT B cpe,nHeH TOqKe, Kor,na P HaxO-
,nHTCR HelIocpe,nCTBeHHO Han HJIH lIO,n
n;eH1pOM 0 H YCKopeHHe P paBHO H)'JIIO.
TI03TOMY:
V max = (J)T.
3. MaKCHMaJIbHOe YCKopeHHe Q paBHO YCKopeHHIO P H ,nOCTHraeTCR B KpaHHHX
TOqKax A H B, Kor,na CKOpOCTb Q paBHa HYJIIO. TI03TOMY:
a max = ro 2 r.
npHMep
TeJIo COBepIIIaeT lIpOCToe rapMOHlNeCKOe ,nBIDKeHHe C aMIIJIHTY,noH 50 MM H qac-
TOTOH 2 fn;.
TIOCKOJIbKy qaCTOTa f = ro / 2TC, Tor,na ro = f X 2TC = 2 X 2TC = 12,566 pan / c.
a) MaKCHMaJIbHaR CKOpOCTb = ror = 12,566 x 50 = 0,628 M/C B cpe,nHeit TOqKe.
6) MaKCHMaJIbHOe YCKopeHHe = ro 2 r = 12,566 2 x 50 = 7,895 M/C 2 B IqJaHHHX TOqKax.
3. 12. 1. MSTeMSTJflfeCKJfH MSflTHJfK
rpY3
mg
PRC. 3.18. MaTeMaTHqeCKHH MaHTHHK
MaTeMaTHqeCKHH MaRTHHK COCTOHT H3 He-
60JIbIIIOrO MaCCHBHoro rpY3a, lIo,nBeIIIeHHO-
ro Ha HIDKHeM KOHn;e JIerKOrO CTep)J{}UI.
BepXHHH KOHen; CTep)I{H.H 3aKpeIIJIeH TaK,
qTO CTepxeHb H rpY3 MOryr KOJIe6aTbCR B
BepTHKaJIbHOH IIJIOCKOCTH, KaK lIOKa3aHO
Ha pHC. 3.18.
PaCcM01pHM lIpOCTOH MaRTHHK co
CTep)I{HeM ATIHHOH I H rpY30M MaCCOH m,
OTKJIOHeHHbIH Ha yrOJI 9. TaK KaK rpY3 Mac-
COH m ,nBIDKeTCR lIO KpyrOBOH 1paeKTOpHH
panHYca I, e,nHHCTBeHHbIe CHJIbI, ,neHcTByK>-
II(He Ha Hero, 3TO CHJIa T.HXeCTH mg H CHJIa
HaT.HXeHIDI CTep)I{H.H T. TIpH OTKJIOHeHHIi,
3.12. llpocmoe zapMOHU'teCK,oe 08UJICeHUe
nOKa3aHHOM Ha pHCYHKe, CHJIa T.HXeCTH C03.n;aeT MOMeHT BpalI(eHIDI OTHOCHTeJIbHO
TOqKH P, C1peM.HII(HHCR B03BpaTHTb rpY3 B ero paBHoBecHoe lIOJIOXeHHe, T.e. B lIO-
JIO:>KeHHe, Kor.n;a MaRTHHK BHCHT BepTHKaJIbHO H rpY3 HaxO.n;HTCR HelIocpe.n;cTBeHHo
no,lJ; TOqKOH lIo.n;Beca (P). CJIe.n;oBaTeJIbHo:
B03BpalI(alOlI(HH MOMeHT = -mgl sin 9 = -mgl9 (LtIDI MaJIbIX 3HaqeHHH 9).
,[lJm rpY3a MaCCOH m MOMeHT HHepIJ;HH OTHOCHTeJIbHO P paBeH I p = ml 2 .
TIpHMeHHM BTOpOH 3aKOH MexaHHKH HblOToHa K BpalI(eHHIO MasITHHKa BOKpyr P:
T = I pa,
r,lJ;e T - lIepHO.n; \)
./
TaKHM 06pa30M: -mgl9 = ml 2 a r.n;e a = (-g(}) / I.
TI03TOMY YCKopeHHe = CMelI(eHHe x KOHCTaHTa H, lIPH YCJIOBHH, qTO CMelI(eHHe
MaJIO, KOJIe6aHIDI MaRTHHKa 6y.n;yr rapMOHlNeCKH M .n;B H)I{eHHeM. TI03TOMY:
1. TIepHo.n; T = 21t / ro = 21t ..J( 1 / g) ce KYH.ZJ;.
2. qacToTa f = 1 / T = (1 / 21t) ..J( 1 / g) fIJ;.
TaK KaK lIepHO.n; KOJIe6aHHH MaRTHHKa (H, COOTBeTCTBeHHO, qaCTOTa ero KOJIe6a-
HHH) 3aBHCHT TOJIbKO OT ero ATIHHbI H MeCTHoro YCKopeHIDI cB060.n;Horo lIan;eHIDI,
OTCIO,na CJIe.nyeT, qTO MaRTHHK - H,lJ;eaJIbHOe cpe.n;CTBO ynpaBJIeHIDI MeXaHlNeCKHMH
qaCaMH, lIPH YCJIOBHH, qTO CTepxeHb, Ha KOTOpOM lIo.n;BeIIIeH rpY3, H3rOTOBJIeH H3
MaTepHaJIa C OqeHb HH3KHM K03<P<PHIJ;HeHTOM paCIIIHpeHIDI lIpH H3MeHeHIDIX TeMne-
paTYPbI.
3.12.2. Co6CTSeHH&le Kone6sHJffl
C06CTBeHHbIe (cB060.n;HbIe) KOJIe6aHIDI lIPH-
6JIIDKalOTCR K lIpOCTOMY rapMOHlNeCKOMY
,lJ;BIDKeHHIO, Kor.n;a OHH B03HHKalOT B TeJIaX,
H3rOTOBJIeHHbIX H3 ynpyrHX MaTepHaJIOB,
nO,ZJ;TIHIDIIOII(HXCR 3aKOH)' fyKa. Ha pHC. 3.19
nOKa3aHa lIpyxHHa paCT.HXeHIDI, K KOTOpOH
no,nBeIIIeH rpY3 MaCCOH m. B lIOKoe lIOJIOXe-
HHe rpY3a 6y.n;eT 3aBHceTb OT xeCTKOCTH lIPY-
:>KHHbI H CHJIbI T.HXeCTH, .n;eHcTByrolI(eH Ha
rpY3. 3TO 03HaqaeT, qTO .n;Be 3TH CHJIbI lIpO-
THBo,neHCTByroT o.n;Ha .n;pyrOH, H rpY3 Haxo-
,lJ;HTCR B COCTORHHH paBHOBeCIDI. ECJIH CMec-
THTb rpY3 BHH3 Ha paCCTORHHe x H OTrryC-
THTb, TO no.n; B03.n;eHCTBHeM lIpyxHHbI OH
HaqHeT KOJIe6aTbCR C qaCTOTOH U0 B BepTH-
KaJIbHOH IIJIOCKOCTH.
TIYCTb S - xeCTKOCTb lIpyxHHbI (CHJIa
Ha e,nHHHIJ;y H3MeHeHIDI ATIHHbI), a x - Be-
npy)I(VlHa
Macca (paBHOBecVle VI
n0J10)l(eHVle «nOK05l») ,
x
, ,
, m
'T
PRC. 3.19. C06cTBeHHbIe KOJIe6aHHH
F/la8a 3. HH:JICeHepHaJI OUHaMUlCa
JIINHHa CMelI(eHIDI OT lIOJIOXeHIDI paBHoBecIDI; Tor,na H3MeHeHHe CHJIbI B lIpyxHHe
lIOCJIe paCT.HXeHIDI paBHo sx. 3TO H eCTb YCKOpRlOlI(IDI CHJIa F, ,neHcTByroII(IDI Ha
Maccy m, TaK qTO F = sx. CJIe,noBaTeJIbHo:
Y cKopeHHe Q = f I m = sx I m.
3HaqHT, YCKopeHHe lIpRMO lIpOlIOpU;HOHaJIbHO BeJIHqHHe CMelI(eHIDI MaCCbI m
OT lIOJIOXeHIDI paBHoBecIDI, H ,lJiBH)I{eHHe RBlliIeTCR lIpOCTbIM rapMOHHqeCKHM ,nBH-
xeHHeM. TIepHo,n KOJIe6aHHH T B ceKYJI,na x olIpe ,nelliIeTcR BbIpaxeHHeM:
T = 21t .J( m I s)
qacToTa KOJIe6aHHH B repu;ax = 1 I T
npHMep
K lIpyxHHe, pa60TalOlI(eH Ha paCT.HXeHHe, lIo,nBeIIIeH rpY3 MaCCOH 5 Kr, B co-
CTORHHH paBHOBeCIDI YATIHIDIIOII(HH ee Ha 12 MM. fpY3 CMeCTHJIH BHH3 elI(e Ha
15 MM H 3aTeM OTrryCTHJIH. TIpeHe6peraR lIOTepRMH Ha COlIpOTHBJIeHHe B03,nyxa Ii
lIOTepRMH Ha rHCTepe3HC B MaTepHaJIe lIPyxHHbI, OlIpe,neJIHTb: a) qaCTOTY KOJIe6a-
HHH, 6) MaKCHMaJIbHyID CKOpOCTb rpY3a, B) MaKCHMaJIbHOe YCKopeHHe rpY3a.
a) Bec rpY3a paBeH mg = 5 Kr x 9,81 M/c 2 = 49,05 H.
)l(ecTKocTb lIpyxHHbI S = CHJIa/YATIHHeHHe = 49,05 H/15 MM = 3,27 H/MM.
llpUMettQHue. 3,27 H/MM = 3,27 KH/M.
qacToTa KOJIe6aHHH f = 1 I T = 1 I 21t .J( s 1m).
TI03TOMY:
f = 1 I 21t .J [(3,27 x 103) I 5] = 4,07 fu;.
6) MaKCHMaJIbHaH CKOpOCTb HarpY3KH =
= <OX = 21tfx = 21t x 4,07 x 15 = 383,59 MMI c.
B) MaKCHMaJIbHOe YCKopeHHe HarpY3KH =
= ro 2 x = (21Cf) 2 X = (21C x 4,07)2 x 15 = 9809,3 MMI c 2 HJIH 9,81 MI c 2 .
3. 13. rMAPOAMH8MMK8
BOlIpOCbI rH,lJ;pOCTaTHKH 06Cy:>K,ZJ;aJIHCb B pa3,neJIe 2.13. B ,naHHOM pa3,neJIe 06cy:>K,ZJ;a-
IOTCR Te He cpe,nbI ()l{H)J:KOCTH HJIH ra3bI) B ,nBH)I{eHHH (,nHHaMHKa )l{H)J:KOCTeH Ii
ra30B). TIo CylI(eCTBY, lIpe,nlIOJIaraeTCR, qTO B YCTaHOBHBIIIeMCR paBHOMepHOM lIO-
TOKe MOJIeKyJIbI )l{H)J:KOCTH ,nBIDKYTCR lIO lIapaJIJIeJIbHbIM TPaeKTOpIDIM, a ,naBJIeHHe
H CKOpOCTb B cpe,ne He H3MeIDIIOTCR B 3aBHCHMOCTH OT BpeMeHH. TaKHe YCJIOBIDI
06bIqHO lIpHMeHHMbI K MeATIeHHOMY lIOTOKy B rJIMKOCTeHHbIX U;HJIHH,npHqeCKHX
TPy6ax C ,nOCTaTOqHO 60JIbIIIHM lIOlIepeqHbIM CeqeHHeM.
YCTaHoBHBIIIHHCR HepaBHoMepHbIH lIOTOK B03HHKaeT, Kor,na )l{H)J:KOCTb (HJIIi
ra3) TeqeT lIO KOHHqeCKOH TPy6e. TIo Mepe Toro KaK lIOlIepeqHOe CeqeHHe TPy6bI
CTaHOBHTCR MeHbIIIe, CKOpOCTb MOJIeKyJI )l{H)J:KOCTH HJIH ra3a YBeJIHqHBaeTCR TaK,
qT06bI TOT xe caMbIH 06'beM )l{H)J:KOCTH HJIH ra3a Mor lIpOHTH qepe3 )'MeHbIIIeHHoe
3.13. ruiJpoiJuHllMU"a 129
IIOrrepeqHOe CeqeHHe 3a ,naHHOe BpeM.H. O,nHaKo lIOCKOJIbKY CKOpOCTb H ,naBJIeHHe
HBJUIIOTCR lIOCTORHHbIMH B JII060M KOHKpeTHOM CeqeHHH Tpy6bl, 3TOT c.rryqaH Bce
:>Ke paCCMaTpHBaeTCR KaK YCTOHqHBbIH lIOTOK, HeCM01'pR Ha TO, qTO lIOTOK HepaB-
HOMepeH lIO .n.rrHHe KOHHqeCKOH TPy6bI.
(06 H3MeHeHIDIX CKOpOCTH MOJIeKYJI ra3a MO)I{HO Cy,nHTb, TOJIbKO ytlHTbIBaR
TaIOKe H ,naBJIeHIDI B CeqeHIDIX, KOTopbIe MOryr CylI(eCTBeHHO pa3JIlNaTbCR. -
l1pUMeli. nep.)
3. 13. 1. CKOPOCT& TelfeHJffl
f
/"
CKOPOCTb TeqeHIDI HJIH pacxo,n )l{H)J:KOCTH, lIpOXO,nRlI(eH qepe3 TPy6y, MO)I{HO OlIpe-
,n;eJIHTb H3 CJIe,nyrolI(ero BbIpaxeHIDI:
Q = Av,
r,ne Q - pacxo,n )l{H)J:KOCTH (M 3 /C); A - IIJIOII(Mb lIOlIepeqHOrO CeqeHIDI TPy6bI;
v - CKOpOCTb lIOTOKa.
Y,neJIbHbIH MaCCOBbIH pacxo,n MO)I{HO OlIpe,neJIHTb CJIe,nyrolI(HM 06pa30M:
pQ = pAv,
r,ne p - IIJIOTHOCTb )l{H)J:KOCTH; pQ - y,neJIbHbIH MaCCOBbIH lIOTOK (Kr/c).
3.13.2. Henpep&ISHOCT& TelfeHJffl
BbIwe lIpHBe,neHHbIe <pOPMYJIbI OTHOCRTCR K YCTaHOBHBIIIeMYCR lIOTOKY B Tpy6ax C
IIOCTORHHbIM CeqeHHeM. TIpH YCTaHOBHBIIIeMCR lIOTOKe B KOHlNeCKOH (cyxalOlI(eH-
CR) 1'py6e y,neJIbHbIH MaCCOBbIH pacxo,n, lIPOXO,nRII(HH qepe3 JII060e ,naHHoe lIOlIe-
peqHOe CeqeHHe, OCTaeTCR lIOCTORHHbIM. TI03TOMY:
pQ=PIAIvi =P2 A 2 V 2,
r,ne pQ - y,neJIbHbIH MaCCOBbIH pacxo,n; Al H A 2 - MaKCHMaJIbHaR H MHHHMaJIbHaR
llJIOInMH lIOlIepeqHOrO CeqeHIDI (M 2 ) COOTBeTCTBeHHO; VI - CKOpOCTb lIOTOKa )I{H)J:-
KOCTH B lIOlIepeqHOM CeqeHHH Al (M/C); v2 - CKOpOCTb lIOTOKa )l{H)J:KOCTH B lIOlIe-
peQHOM CeqeHHH A 2 (M/C); PI - IIJIOTHOCTb )l{H)J:KOCTH B lIOlIepeqHOM CeqeHHH AI;
P2 - IIJIOTHOCTb )l{H)J:KOCTH B lIOlIepeqHOM CeqeHHH A 2 .
3T0 BbIpaxeHHe Ha3bIBaeTCR ypaBHeHHeM Hepa3pbIBHOCTH, H OHO lIpHMeHHMo
KO BceM TeKyqHM cpe,naM, KaK K )l{H)J:KOCTRM, TaK H K ra3aM.
,[lJm HeC)l(HMaeMbIX TeKyqHx cpe,n ()l{H)J:KOCTeH) P RBlliIeTCR KOHCTa )0ID,nmI
Bcex lIOlIepeqHbIX CeqeHHH, lI03TOMY:
Q=AIvi =A 2 V 2.
5-3255
F/la8a 3. HH:JICeHepHaJI OUHaMUlCa
3.13.3. 3HeprJffl ASJfJKYU,f,eHCfI TeKYlfeH CpeA&1
(YPssHeHJfe 6epHynnJf)
HeC)l(HMaeMbIe Te He cpe,nbI ()l{H)J:KOCTH) 06JIan;a1OT 'rpeM.H BH,lJ;aMH 3HeprHH, a
HMeHHO:
. lIOTeHIJ;HaJIbHOH 3HeprHeH: mgZ, r,ne m - Macca (Kr), g - 9,81M/c 2 H Z -
BbICOTa )l{H)J:KOCTH Han; 3an;aHHbIM ypOBHeM OTCqeTa. TIoTeHIJ;HaJIbHIDI 3Hep-
rIDI B e,lJ;HHHIJ;y MaCCbI = gZ ( /Kr);
. KHHeTlNecKOH 3HepmeH: mv2, r,ne m - Macca (Kr) H V - lIOCTO.HHHasI CKOpocTb
)l{H)J:KOCTH (M/C). KHHeTlNeCKIDI 3HeprIDI Ha e,nHHHIJ;Y MaCCbI = v2 UJ:x/Kr);
. 3HeprHeH ,naBJIeHIDI: Kor,na )l{H)J:KOCTb TeqeT lIO Tpy6e lIO,n ,lJ;aBJIeHHeM, lIPIl
,nBIDKeHHH )l{H)J:KOCTH qepe3 KIDK,ZJ;Oe CeqeHHe TPy6bI BbIlIOJIIDIeTCR pa60Ta no
lIpeo,nOJIeHHIO rH,lJ;pOCTaTlNeCKOrO ,naBJIeHIDI, lIpHcyrcTByrolI(erO B 3TOM ce-
qeHHH. CJIe,noBaTeJIbHo:
BbIlIOJIHeHHIDI pa60Ta Ha e,nHHHIJ;Y MaCCbI = pQ / pQ = p / P ( /Kr),
r,lJ;e p - ,lJ;aBJIeHHe, p - IIJIOTHOCTb )l{H)J:KOCTH, Q - CKOpOCTb lIOTOKa, a p / p -
3HeprIDI ,naBJIeHIDI Ha e,nHHHIJ;y MaCChI )l{H)J:KOCTH.
CJIe,nOBaTeJIbHO, C)'MMapHIDI 3HeprIDI, KOTOpOH 06JIan;aeT e,nHHHIJ;a MaCCbI )I{Jf)];-
KOCTH, 6y,neT C)'MMOH ee lIOTeHIJ;HaJIbHOH 3HeprHH, KHHeTHqeCKOH 3HeprHH II
3HeprHH ,naBJIeHIDI.
C)'MMapHIDI 3HeprIDI Ha e,lJ;HHHIJ;y MaCCbI UJ:X/Kr) = gZ + v 2 / 2 + p / p.
B YCTaHoBHBIIIeMcR nOTOKe HeC)l(HMaeMOH Te eH cpe,nbI ()l{H)J:KOCTH) lIOTeH-
IJ;HaJIbHIDI, KHHeTlNeCKIDI H 3HeprIDI ,naBJIeHIDI MOryr pa3JIINaTbCR B pa3HbIX Mec-
Tax B,nOJIb lIOTOKa, o,nHaKO COrJIaCHO lIpHHIJ;Hrry coxpaHeHIDI 3HeprHH lIOJIHWI
3HeprIDI 6y,neT OCTaBaTbCR lIOCTORHHOH. TI03TOMY COrJIaCHO ypaBHeHHIO BepHYJIJIH:
gZ + v 2 / 2 + p / p = KO,HCTaHTa(K) HJIH Z + v 2 / 2g + p / W = KOHCTaHTa (K),
r,ne W - Bec e,lJ;HHHIJ;bI 06beMa (y,neJIbHbIH Bec).
3. 13.4. TelfeHJfe lfepe3 oTSepCTJfe
C60KY H3 6aKa Bo,na BbITeKaeT B BH,lJ;e ropH30HTaJIbHOH C'rpYH lIO,n HalIopOM; CKO-
pOCTHOH HallOp HJIH ,nHHaMHqeCKHH HallOp - pa3JIHqHbIe Ha3BaHIDI o,nHoro H Toro
xe lIOIDITIDI. BO,l(a B pe3epByape HMeeT HaqaJIbHbIH lIOTeHIJ;HaJIbHbIH HalIOp, 3aBH-
CRII(HH TOJIbKO OT BbICOTbI h OTHOCHTeJIbHO ypOBIDI OTCqeTa HJIH cpe,nHero ypOBIDI
OTBepCTIDI. TI03TOMY:
V 2 / 2g = h .
v = ,J( 2gh).
TIOCKOJIbKY HeKOTopoe KOJIlNeCTBO 3HeprHH TepReTCR H3-3a TPeHIDI, CTPYR
)l{H)J:KOCTH, BbITeKalOlI(IDI H3 OTBepCTIDI, 6y,neT HMeTb HeMHoro MeHbIIIyro CKOpOCTb,
qeM TeOpeTHqeCKHH MaKCHMyM.
,l(eHcTBHTeJIbHIDI CKOpOCTb CTPYH/TeopeTlNeCKIDI CKOpOCTb CTPYH =
= K03<P<P H IJ;HeHT (lIoTepH) CKOpOCTH (C v )'
3.13. FuopoiJuHaMUICa
h
.....
---.. -....
"... ....--..........:-:.:-...- -.
.......... ---....-.
- - - - - - ..... .... - -- - -t- -
- - - - - - - - - - - - -4.-.
.. :..-....-.,.,. .- --.....-..-...- :---; -:r:- -:
:...-::........- I '
....'
,
I
, ,
: I
. ,
L.. CY>I(eHVle (AVIaMeTp J
CTPYVI MeHbwe) "IeM
AViaMeTp 0:raepCTVl5I)
Pac. 3.20. TeqeHHe qepe3 OTBepCTHe
,lJ;HaMeTP cTPYH :>KH,ZJ;KOCTH, BbITeKalOlI(eH H3 oTBepcTIDI C OCTPOH ,nHa<pparMoH,
Ha npaKTHKe 6y,neT MeHbIIIe, qeM ,neHcTBHTeJIbHbIH ,nHaMeTP oTBepcTIDI, KaK nOKa-
3aHO Ha pHC. 3.20. 3TO TaIOKe Ha3bIBaeTC.H cyxeHHeM.
IIno a,nb nonepetffioro CeqeHIDI cTPYH/nrrOII(a,n;b nonepetffioro CeqeHIDI OTBepCTIDI =
= K03<p<pmnIeHT cyxeHIDI (C c )'
AHaJIOIWIHO:
,n;eHCTBHTeJIbHbIH pacxo,n :>KH,ZJ;KOcTH/TeopeTHqeCKHH pacxo,n =
= K03<P<PH:QHeHT pacxo,na (Cd)'
II03TOMy:
Cd = C v x C c .
3.13.5. Bfl3KOCT&
ConpHKaCaBCb C nOBepXHOCTblO, :>KH,ZJ;KOCTb KaK 6bI npHJIHnaeT K HeH. Y,n06HO pac-
CMaTpHBaTb :>KH,ZJ;KOCTb COCTO.HlI(eH H3 CJIOeB TaK, qTO CJIOH, conpHKaCalOII(HHC.H C
rrOBepXHOCTblO TPy6bI, Haxo,nHTC.H B nOKoe, a OCTaJIbHbIe CJIOH CKOJIb3.HT O,nHH no
,n;pyroMy C nOCTeneHHO YBeJIWIHBalOlI(eHC.H CKOpOCTblO, BIIJIOTb ,no HaH60JIee y,na-
JleHHOrO OT nOBepXHOCTH TPy6bI CJIO.H, ,nBIDKyIIJ;erOC.H C MaKCHMaJIbHOH CKOpOCTblO.
TaKOH nOTOK Ha3bIBaeTC.H JIaMHHapHbIM, H TaKoe npH6JIIDKeHHe npHMeIDIeTC.H, Kor-
,n;a )J{Jf)(KOCTb no,nBepraeTC.H B03,neHCTBHIO nOnepeqHOH CHJIbI. HanpHMep, CMa3Ka B
rro,n;mHnHHKe, OT,neJI.HlOlI(aB BpalI(alOII(HHC.H BaJI OT BKJIa,n;bIIIIeH no,n;IIIHnHHKa. TIpo-
THBo,n;eHcTByrolI(aB CHJIa - 3TO B.H3KOCTb :>KH,ZJ;KOCTH, H3-3a KOTOpOH B03HHKaeT co-
rrpOTHBJIeHHe cpe,nbI, HanpHMep eCJIH ,nBHraTeJIb TPaHcnopTHoro cpe,nCTBa 3aBo,nHT-
CH B XOJIO,nHyID noro,ny, Kor,na B.H3KOCTb CMa3KH YBeJIHqHBaeTC.H. ECJIH CKOpOCTb
rrpeBbImaeT HeKOTopoe KpHTHqeCKOe 3HaqeHHe, JIaMHHapHbIH nOTOK pa3pyrnaeTC.H
H CTaHOBHTC.H TYP6YJIeHTHbIM. AHaJIOrIDI co CJIO.HMH Tor,na yxe 60JIbIIIe He npHMe-
HHMa.
F/la8a 3. HH:JICeHepHaR OUHaMUKa
B JIaMHHapHoM nOTOKe KaCaTeJIbHOe HanpIDKeHHe Mex.ny JII06bIMH ,nBYM.H co-
ce,nHHMH CJIO.HMH paBHo FIA, r,ne A - nJIOII(a,nb COlIpHKOCHOBeHIDI Mex.ny CJIO.HMH
H Av / Ay - rpa,nHeHT CKOpOCTH. CJIe,noBaTeJIbHO, nOCKOJIbKY KaCaTeJIbHOe Hanp.H-
xeHHe H3MeIDIeTC.H nponop:QHOHaJIbHO rpa,nHeHTY CKOpOCTH:
F / A =(Av / AY)l1,
r,ne 11 - KOHCTaHTa, Ha3bIBaeMaB K03<P<PH:QHeHToM B.H3KOCTH.
TaKHM 06pa30M:
11 =(F / A) / (A v / Ay),
r,ne e,nHHH:QbI H3MepeHH.H B.H3KOCTH paBHbI H/CM 2 (TIac) HJIH Kr/MC, TaK KaK 1 H =
= 1 KrM/C 2 .
3.13.6. tPopMyns nys3eRnfl
,[lJrn JIaMHHapHoro TeqeHIDI B rJIa,nKOCTeHHOH KpyrJIOH TPy6e 06'beM npoTeKalOlI(eH
:>KH,ZJ;KOCTH (V) B ceK}'H,nY onpe,neJI.HeTC.H <pOPMYJIOH TIya3eHmI:
v = (1tpr 4 ) / (811/),
r,ne p - pa3HOCTb ,naBJIeHHH Ha KOH:Qax TPy6bI; r - BHyrpeHHHH pa,nHYC TPy6bI (M);
1 - ,nJIHHa TPy6bI (M); 11 - B.H3KOCTb :>KH,ZJ;KOCTH, TeKYlI(eH no TPy6e.
3. 13. 7. 3SKOH CTOKCS
3aKOH CTOKca HCnOJIb3yeTC.H ,l(IDI onpe,neJIeHIDI CHJIbI F, B03HHKalOIUeH H3-3a B.H3-
KOCTH :>KH,ZJ;KOCTH; C TaKOH CHJIOH np.HMOJIHHeHHO ,nBIDKyIUHHC.H nOTOK B03,neHcTByeT
Ha rJIa,nKYIO c<pepy. <l>oPMYJIa npHMeIDIeTC.H, JIH60 Kor,na c<pepa ,nBIDKeTC.H CKB03b
:>KH,ZJ;KOCTb, JIH60 Kor,na :>KH,ZJ;KOCTb 06TeKaeT c<pepy.
CHJIa F = 61t11rv,
r,ne r - pa,nHYC C<pePbI (M).
rnABA 4
KPEnE>KHbIE
AETAnM
, X /
4. 1. BMHToBble Kpene)l(Hble M3AenMSI
4. 1. 1. Pa3Mep&1 Jf COOTHOWeHJffl Ha lfepTeJICaX
BOJITY H BHHTLI
1,5D Me)I(AY
napaJ1J1eJ1bHbIMVI
rpaH5IMVI
AnVlHa pe3b6bl
( 60J1T)
5D
HOMVlHaJ1bHa51 AJ1V1Ha
illUHJILKH
\
/
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nOCaAO
KOH
- -
-
D ,
- - .
\ J
"IHbIVi 1,5D - 2,5D CT5I
eu. - . -
-
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HOMVlHaJ1bHa51 AJ1V1Ha
D
)l(HOVI (rae"lHbIVl)
KOHeu.
r J1aAKa51 "IaCTb
CTeP)l(H51
D
F/la8a 4. Kpene:JICHble iJemOJlu
CTaH)l;apTHaJi raiiKa
1,50
napaJ1J1eJ1bHble
nJ10CKOCTVI
HH3KaJI raio (KoHTpraio)
.1 O,5D I.
.0
"
)
,
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J
"
-
-
0,150
0.80
npOCTaJI mal6a
--I I... O,15 D
.D
4.1.2. PS3nJflfH&le rOnOSKJf SJfHTOS
nOTaVlHa51
r0J10BKa
yrOJ1 90 0 ,
co WJ1V1u.eM
n0J1YKpyrJ1a51
r0J10BKa co
WJ1V1u.eM
nJ10CKa51 U.VI- KBaApaTHa51
J1V1HAPVl"leCKa51 r0J10BKa
r0J10BKa co
WJ1V1u.eM
KpyrJ1a51 U.VI-
J1 VlHAPVl"le-
CKa51 r0J10BKa
co WJ1V1u.eM
nOJ1ynoTa .
Ha51 nJ1OC-
KOBblnYKJ1a
r0J10BKa co
WJ1 VI u.eM
o
@
r 0J10BKa C
KpecTo06pa3-
HblM WJ1V1u.eM
r0J10BKa co
WJ1 VI u.eM
@
LJ.VlJ1 VI HAPVl"leCKa51
r0J10BKa C weCTVI-
rpaHHblM OTBepCTVleM
4.1. BUHm08ble "pene:JICHble U3iJeJlWl
4.1.3. PS3nJflfH&le KOHq&1 SJfHTOS
-a- -a=t 1- - -a- -a-
nJ10CKVlVI
LJ.VlJ1V1HA- KOHVI"IecKVlVI Cct>epVl-
pVl"leCKVlVI "IeCKVlVI
3acBepJ1eHHblVi
4. 1.4. BJfHT&1 C WeCTJfrpSHH&IM yrny6neHJfeM S ronOSKe
Yr J1y6J1eHVle
nOA KJ11O"I
AViaMeTp
CTep)l(H5I
AViaMeTp
r0J10BKVI
Pa3Mep weCTVI-
yrOJ1 bHoro
OTBepCTVl5I
J
4. 1.5. npSKTJflfeCKOe npJfMeHeHJfe SJfHTOS&IX
KpeneJICH&IX Jf3AenJfH
60nT AOJ1)1(eH 6blTb BCTaBJ1eH
TaK, "IT06b1 OH He Mor BblnaCTb,
ecn raViKa He3aT5IHYTa
nOBepXHOCTb CTblKa AOJ1)1(Ha
npVlxOAVlTbC5I Ha rJ1aAKYIO "IaCTb
CTep)l(H5I 60J1Ta VI HViKorAa He
panOJ1araTbC5I nonepeK pe3b6bl
DOJ1T AOJ1)1(eH npoxo-
AVlTb "Iepe3 OTBepCTVle
C rapaHTVlpOBaHHblM
3a30pOM
l.IT06b1 06eCne"lVlTb nJ10CKYIO
nOCSAKY B Hecyw.VlX CTaJ1bHbIX
KOHCTPYKU.Vl5IX, CJ1eAyeT VlC-
n0J1b30BaTb KOCble waVl6bl
LlT06bl rapaHTVlpOBaTb nOJ1HOe
3au.enJ1eHVle 3aT5IHYTOVI raVlKVI,
3a ee npeAeJ1aMVI AOJ1)1(Hbl 6blTb
BVlAHbl no KpaVlHeVi pe ABa
BVlTKa pe3b6bl. )
4. 1.6. TpsneqeJfASn&HSfI pe3&6s
0, 3707 P I
l ·
War pe3b6b1 P "I
f
0,5P + 0,01
I. .1
0.3707 P
F/la8a 4. Kpene:JICHble iJemOJlu
4. 1. 7. npflMoyrOn&HSfI pe3&6s
I'" P/2 "I" War pe3b6bl P ..I
P/2
4. 1.8. YnopHSfI pe3&6s
O 7 __
War pe3b6bl P
O,245P
P/2
4. 1.9. OCTpoyrOn&HSfI pe3&6s
YrOJ1 npoct>VlJ151 pe3b6bl
O,1395P
BblCOTa npoct>VlJ151 pe3b6bl
OCb pe3b6bl
J5
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Q) a.
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::I:
4.1. BUHm06ble "peneJICHble U30e.tlUR I 37
4. 1. 10. OCHOSHSfI AIOHMOSSfI pe3&6s (55°):
qJfnJfHAPJflfeCKSfI pe3&6s
3TO OCHOBHMI <popMa pe3b6bI ,l(IDI BSW (6pHTaHCKMI ,nIOHMOBMI pe3b6a), BSF
(6pHTaHCKMI MeJIKMI ,nIOHMOBMI pe3b6a) H BSP (6pHTaHCKMI TPy6HMI KOHWIeCKM
pe3b6a) BHHTOBbIX pe3b6.
Hie
H h
War P
H = 0,960 491 P
h = 0,640 327 P
r = 0,137 329P
H'6
4. 1. 11. tPOPM&1 ISO MeTpJflfeCKOH Jf ISO 60°
YHJfcpJfqJfPOSSHHOH pe3&6&1
War pe3b6bl P
PaAVlYC BnaAVlHbl npoct>VlJ151
pe3b6bl raVlKVI
a..
,...
o
J5
\0
.0
(t)
Q)
a.
a.
j5
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co )s .0
S (t)
S :I: Q)
C[ :I: a.
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:I: S Q)
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m co
a. s
co a. C[
::I: U
a..
o
a..
<0
<0
co
o
0,217P
II BHYTpeHH5I5I pe3b6a (raVlKa)
HapY>KHa51 pe3b6a (60J1T)
4. 1. 12. BseAeHJfe S SJfHTOS&le KpeneJICH&le Jf3AenJffl
XOT.H B CJIe.nyro:m;HX Ta6JIH:Qax BHHTOBbIX pe3b6 pa3MepbI npHBe,neHbI B ,nIOHMax
(pa3,n;eJIbI 4.1.38-4.1.43), OHH He nOTepIDIH CBoero 3HaqeHIDI B KaqeCTBe ,naHHbIX
wm TeXHHqeCKOrO 06CJIy)l{HBaHIDI H aHaJIOrWIHbIX npHJIOXeHHH. BHHTOBbIe Kpe-
ne)I{HbIe H3,neJIIDI COrJIaCHO 3THM cne:QH<pHKa:QIDIM ,no CHX nop npOH3BOMTC.H:
4.1.39. opHTaHCKMI ,nIOHMOBMI pe3b6a (BSW) 60JITbI H raHKH
4.1.40. opHTaHCKMI MeJIKa.H ,nIOHMOBMI pe3b6a (BSF) 60JITbI H raHKH
F/la8a 4. Kpene:JICHble oemOJlu
4.1.41 ISO YHH<pH:QHpoBaHHMI TOqHOCTb BHyrpeHHeH pe3b6bI: PM C KpynHOH
pe3b60H (UNC) (aMepHKaHCKMI YHH<pH:QHpOBaHHMI KpynHMI pe3b6a)
4.1.42 ISO YHH<pH:QHpoBaHHaH TOqHOCTb HapyxHoH pe3b6bI: PM C KpynHOH pe-
3b60H (UNC) (aMepHKaHCKa.H YHH<PH:QHpOBaHHM KpynHMI pe3b6a)
4.1.43 ISO YHH<pH:QHpoBaHHMI TOqHOCTb BHyrpeHHeH pe3b6bI: PM C MeJIKOH
pe3b60H (UNF) (aMepHKaHCKa.H YHH<pH:QHpOBaHHMI TOHKa.H pe3b6a)
4.1.44 ISO YHH<pH:QHpoBaHHMI TOqHOCTb HapyxHoH pe3b6bI: PM C MeJIKOH pe-
3b60H (UNF) (aMepHKaHCKMI YHH<PH:QHpOBaHHMI TOHKMI pe3b6a)
XOT.H cJIe,nyrolI(MI Ta6JIH:Qa BHHTOBbIX pe3b6 (pa3,neJI 4.1.45) H YCTapeJIa, OHa CO-
xpaHeHa no TeM xe npHqHHaM, qTO lIpHBe,neHbI BbIIIIe:
4.1.45 DpHTaHcKM aCCO:QHa:QIDI TeXHHqeCKHX CTaH,napTOB (BA): 6pHTaHcKHe
CTaH,napTHbIe BHyTpeHHHe H HapyxHbIe BHHTOBbIe pe3b6bI
Ta6JIH:QbI, OCHOBaHHbIe Ha CTaH,napTax PMa BS EN 24 000, 3aMeHeHbI TeKY-
HM PMOM BS EN ISO 4000 ,lW.H BHHTOBbIX Kpene)I{HbIX H3,neJIHH C MeTPHqeCKHMH
pa3MepaMH. TIpHBe,neHbI CJIe,nyro He HOBbIe CTaH,napTbI (pa3,neJIbI 4.1.13-4.1.21):
4.1.13 BS EN ISO 4014: 2001 DOJITbI C IIIecTHrpaHHoH rOJIOBKOH - KJIaCCbI H3-
,neJIHR A H B
4.1.14 BS EN ISO 4016: 2001 DOJITbI C mecTHrpaHHoH rOJIOBKOH - KJIacc H3-
,neJIHR C
4.1.15 BS EN ISO 4017: 2001 BHHTbI C mecTHrpaHHoH rOJIOBKOH - KJIaCCbI H3-
,neJIHR A H B
4.1.16 BS EN ISO 4018: 2001 BHHTbI C IIIecTHrpaHHoH rOJIOBKOH - KJIacc H3-
,neJIIDI C
4.1.17 BS EN ISO 4032: 2001 IllecTHrpaHHbIe raHKH HCnOJIHeHHH 1 - KJIaCCbI
H3,neJIIDIAH B
4.1.18 BS EN ISO 4033: 2001 IllecTHrpaHHbIe raHKH HCnOJIHeHIDI 2 - KJIaCCbI
H3,neJIIDIAH B
4.1.19 BS EN ISO 4034: 2001 IllecTHrpaHHbIe raHKH HCrrOJIHeHIDI 1 - KJIacc
H3,neJIIDI C
4.1.20 BS EN ISO 4035: 2001 IllecTHrpaHHbIe HH3KHe raHKH (c <pJIaH:QeM) -
KJIaCCbI H3,neJIHH A H B
4.1.21 BS EN ISO 4036: 2001 IllecTHrpaHHbIe HH3KHe raHKH (6e3 <pJIaH:Qa) -
KJIacc H3,neJIIDI B
Bce BbImeyrrOM.HHyrbIe CTaH,napTbI OTHOC.HTCH K BHHTOBbIM Kperre)I{HbIM H3,ne-
JIHRM C MeTpHQeCKHMH pa3MepaMH H pe3b6e C KpynHbIM marOM. CTaH,napTbI ,[(JHI
MeJIKOrO IIlara pe3b6bI 6y,nyr npHBe,neHbI ,naJIee.
IIpUMeltaHue.
a) BS EN ISO 4015 KacaeTCR 60JITOB C IIIecTHrpaHHoH rOJIOBKOH, CTep)I{HH KO-
TOpbIX YMeHbIIleHbI ,no cpe,nHero ,nHaMeTpa HX pe3b6bI. OHH rrpe,nHa3HaQeHbI
LUIR CneUHaJIbHbIX rrpHJIOXeHHH H He BKJIlOqeHbI B 3TOT ClIpaBOqHHK.
6) CTaH,napTbI MeXaHHqeCKHX CBOHCTB, KOTopbIe co,nepXaJIHCb B rrpe,neJIax BS
4190 H BS 3692, MO)I{HO Tenepb HaH,nTH B BS EN 20898 qacTb 1 (60JITbI) H
qacTb 2 (raHKH).
Krracc H3,[(eJIIDI 03HaqaeT CJIe,nyro ee:
. TIpoaHaJIH3HpyHTe Ta6JIHUY H3 pa3,neJIa 4.1.13.
. ,lJ:HaMeTPY CTep)I{H.H (d s ) COOTBeTCTBYIOT MaKCHMaJIbHbIH ,nHaMeTp, paBHbIH
80 MM, HOMHHaJIbHbIH ,nHaMeTp, a TaIOKe MHHHMaJIbHbIH ,[(HaMeTp.
4.1. BUHmo6ble "peneJICHble U30e.tlUR 139
. Y MHHHMaJIbHOrO ,nHaMel'pa MoxeT 6bITb ,nOrryCK H3,neJIIDI KJIacca A HJIH ,no-
rryCK H3,neJIIDI KJIacca B. ,nOrryCK KJIacca A 60JIee xeCTKHH (60JIee TOqHbIH),
qeM ,nOrryCK KJIacca B.
. ,nOrryCKH H3,neJIHH KJIacca A OTHOC.HTC.H K KpelIe)I{HbIM H3,neJIIDIM C pa3Mepa-
MH B ,nHana30He OT Ml.6 ,no M24 BKJIlOqHTeJIbHO.
. ,nOrryCKH H3,neJIHH KJIacca B OTHOC.HTC.H K Iq>elIe)I{HbIM H3,neJIIDIM C pa3Mepa-
MH B ,nHana30He OT M16 ,no M64.
. II03ToMY pa3MepbI OT M16 ,no M24 BKJIlOqHTeJIbHO MOryr HMeTb ,nOrryCKH H3-
,neJIIDI KJIacca A HJIH B H CJIe.nyeT onpe,neJIHTb l'pe6yeMbIH ,nOrryCK.
. 06paTHTe BHHMaHHe Ha TO, qTO KJIaCC H3,neJIIDI 3aBHCHT He TOJIbKO OT ,nHa-
Mel'pa, HO TaIOKe H OT ,nJIHHbI.
npHMep 1
BOJIT C IIIecTHrpaHHoH rOJIOBKOH M5 npHaaMe)I{HT KJIaccy TOqHOCTH A H ,nHa-
MeTp ero CTep)I{H.H 6y,neT Haxo,nHTbC.H B ,nHana30He Mex.ny 5,00 H 4,82 MM BKJIlOqH-
TeJlbHO.
npHMep 2
BOJIT C IIIecTHrpaHHoH rOJIOBKOH M36 npHH3A1Ie)I{HT KJIaccy TOqHOCTH B H ,nHa-
MeTp ero CTep)I{H.H 6y,neT HaxO,nHTbC.H B ,nHana30He Mex.ny 36,00 H 35,38 MM BKJIIO-
QHTeJIbHO.
npHMep 3
Y 60JITa C IIIecTHrpaHHoH rOJIOBKOH M16 ,nHaMel'p CTep)I{IDI 6y,neT JIeXaTb B
,ZJ;Hana30He Mex.ny 16 H 15,73 MM BKJIlOqHTeJIbHO, eCJIH 3TO H3,neJIHe KJIacca TOqHO-
CTH A. ECJIH 3TO H3,neJIHe KJIacca TOqHOCTH B, TO ,nHaMel'p CTep)I{IDI 6y,neT JIeXaTb B
,ZJ;Hana30He Mex.ny 16 H 15,57 MM BKJIlOqHTeJIbHO.
llpUMettaHue.
BbIIIIeH3JIOXeHHaB CHCTeMa ,nOrryCKOB OTHOCHTCR H KO BceM ,npyrHM pa3MepaM
:Kpene)I{Hb!X H3,neJIHH B 3THX Ta6JIH:Qax.
. TIpoaHaJIH3HpyHTe Ta6JIHU}' B pa3,neJIe 4.1.14. Bce pa3MepbI B 3TOH Ta6JIHQe
OTHOC.HTC.H K BHHTOBbIM Kpene)I{HbIM H3,neJIIDIM KJIacca TOqHOCTH C. CpaBHe-
HHe 3TOH Ta6JIH:QbI C lIpe,nbmyIl(HMH nOKa3bIBaeT, qTO Kpene)I{HbIe H3,neJIIDI,
H3rOTOBJIeHHbIe COrJIaCHO Te \ecKHM YCJIOBIDIM KJIacca TOqHOCTH C, HMe-
lOT HaMHoro 60JIee rpy6bIe ,nOrryCKH, qeM H3,neJIIDI, H3rOTOBJIeHHbIe B COOT-
BeTCTBHH C l'pe60BaHIDIMH KJIaCCOB TOqHOCTH A H B.
. Y 60JITa M12 KJIacca TOqHOCTH A ,nHaMel'p CTep)I{H.H (ds) MoxeT HaxO,nHTbC.H B
,nHana30He Mex.ny 12 H 11,73 MM (,nOrryCK COCTaBJI.HeT 0,27 MM); Tor,na KaK y
60JITa M12, H3rOTOBJIeHHOrO B COOTBeTCTBHH C l'pe60BaHIDIMH KJIacca TOqHO-
CTH C, ,nHaMel'p CTep)I{H.H (ds) MoxeT Haxo,nHTbC.H B ,nHana30He Mex.ny 12,77 H
11,3 MM (,nOrryCK - 1,4 MM). .n:OrryCKH H3,neJIHH KJIacca B He npHMeIDIIOTC.H K
3TOMY pa3Mepy 60JITa.
CTapa.H TepMHHOJIOrIDI «qepHbIe 60JITbI» (rop.HqaB IIITaMnoBKa) H «qHCTbIe/HOp-
MaJIbHOH TOqHOCTH 60JITbI» (XOJIO,nHaB BbIca,nKa HJIH MamHHHaB 06pa60TKa) K 60JI-
TaM H raHKaM 60JIbIIIe He lIpHMeIDIeTC.H. O,nHaKO 60JITbI H raHKH, H3rOTOBJIeHHbIe
no cne:QHaJIbHOMY 3aKa3Y MeTo,nOM rOp.HqeH IIITaMnOBKH (qepHbIe, HeOT,neJIaHHbIe),
MOryT OTHOCHTbC.H TOJIbKO K KJIaccy TOqHOCTH C.
Bce npe,nbmyIl(He npHMeqaHIDI OTHOC.HTC.H K 60JITaMH H BHHTaM C IIIeCTHrpaH-
BOH rOJIOBKOH H K IIIeCTHrpaHHbIM raHKaM C KpynHbIM IIIarOM pe3b6bI. Y 60JITOB
F/la8a 4. Kpene:JICHble oemallu
qaCTb CTep)I{IDI Mex.ny pe3b60H H rOJIOBKOH OCTaeTC.H rJIa,nKoH, Tor,na KaK Ha BHHTe
pe3b6a Hape3aeTC.H <paKTWIeCKH no BceH ,nJIHHe BIIJIOTb ,no rOJIOBKH. CJIe,nyroI.U;He
Ta6JIH:QbI H CTaH,napTbI (pa3,neJIbI 4.1.22-4.1.26) OTHOC.HTC.H K COOTBeTCTByrolI(HM
p.SI,ll;aM BHHTOBbIX Kpene)I{HbIX H3,neJIHH C MeJIKHM marOM pe3b6bI. 3TH p.SI,ll;bI BHHTO-
BbIX Kpene)I{HbIX H3,neJIHH C MeJIKHM IIIarOM pe3b6bI H3rOTaBJIHBaIOTC.H TOJIbKO B
COOTBeTCTBHH C l'pe60BaHIDIMH KJIaCCOB TOqHOCTH A H B.
4.1.22 BS EN ISO 8765: 2001 DOJITbI C mecTHrpaHHoH rOJIOBKOH C Mel'pHqe-
CKOH pe3b60Hc MeJIKHM IIIarOM - KJIaCCbI H3,neJIIDI A H B
4 1.23 BS EN ISO 8676: 2001 BHHTbI C IIIecTHrpaHHoH rOJIOBKOH C Mel'pHqe-
CKOH pe3b60Hc MeJIKHM IIIarOM - KJIaCCbI H3,neJIIDI A H B
4.1.24 BS EN ISO 8673: 2001 IllecTHrpaHHbIe raHKH HCnOJIHeHIDI 1 C Mel'pHqe-
CKOH pe3b60H C MeJIKHM IIIarOM - KJIaCCbI H3,neJIH.H A H B
4.1.25 BS EN ISO 8674: 2001 IllecTHrpaHHbIe raHKH HCnOJIHeHIDI 2 C Mel'pHqe-
CKOH pe3b60H C MeJIKHM IIIarOM - KJIaCCbI H3,neJIIDI A H B
4.1.26 BS EN ISO 8675: 2001 IllecTHrpaHHbIe HH3KHe raHKH C MeTPHqeCKOH
pe3b60H C MeJIKHM marOM - KJIaCCbI H3,neJIIDI A H B
4. 1. 13. BS EN ISO 4014: 2001. 60nT&1 C WeCTJfrpSHHOH
ronOBKOH - KnSCC&1 Jf3AenJffl A Jf B
Pa3MepLI
llpUMettaHue. CHMBOJIbI H 0603HaqeHIDI pa3MepOB ,naHbI B COOTBeTCTBHH C ISO 225.
KOHeu. AOJ1)1(eH 6blTb C
ct>acKoVi VlJ1V1 AJ151 pe3b6
M4 MO)l(eT 6blTb 6e3
X ct>acKVI (cpe3HoVi 60J1T)
(CM. ISO 4753)
Pa3Mepbl B MVlJ1J1V1MeTpax
Is U(1) S
l (b)
k
X
k' I, MaKCVlMa11bHOe YTOJ1w.eHVle
nOA rOJ1oBKoVi BVlHTa
"tf-d
(1) HelIOJIHa.H pe3b6a (c6er pe3b6bI) u 2P
TIpHMep 0603HaqeHIDI 60JITa C IIIecTHrpaHHoH rOJIOBKOH C pe3b60H M12, HO.
MHHaJIbHOH ,nJIHHOH 1 = 80 MM H KJIaCCOM npOqHOCTH 8.8:
60JIT C mecTllrpaHHOH rOJIOBKOH ISO 4014 - M12 x 80 - 8,8.
4.1. BUHm06ble "peneJICHble U30eJl!J.R 14.
\0 \0 \0 V)
00 V) V) 00
("r') ("r') ....-4 N... ....-4 ("r') 0 ... ... \0... V) N'"
\0 , , V) ... ....-4 I ... , , , 0\ 0 , N ,
::a 0 t"-- \0 ("r') 00 ....-4 t"-- 0\
....-4 0 ("r') 0\
\0 00 ....-4 N
'oC \0 \0 \0 V) V"l V) 00
V) V"l t"-- ("r') ("r') \0 N \0... V) N V) ... ....-4 V) N
, , ("r') ... ....-4 ... , , ... , , , N ,
::a V) 0 \0 V) V) 00 ("r') ....-4 ("r') V) 00
....-4 ("r') ("r') 00
V) t"-- 0\ N
00 \0 00 V) \0 00 N ....-4 ....-4
00 ....-4 ("r') N'" 00 ("r') ... N 0 0 V) t"-- V) ...
V) , 0 N ... ....-4 ... , , , , ... , ... I ("r')
::a 0 t"-- 0\ ....-4 ("r') 0\ 0 0 ....-4 t"--
....-4 ....-4 V) 00 t"--
\0 N ("r') N
N \0... 00 V) ("r') 00 N ....-4 ....-4
V) \0 0\ N ("r') ... \0 V) ... V) ...
... , 0 ....-4 ... , , 00 I , ... , , ("r')
0\ 0 V) ....-4 0\ ....-4 N V) \0 t"-- ....-4 \0
....-4 t"-- \0
V) N N ....-4
'oC ... 00 ....-4 0\ V) 00 N \0
ff') t"-- N 00 \0 ("r') ....-4 t"--... N'" 0 0\ V)
, ... ... ... , ... , \0 , , N'" N'" , ....-4 I
::a 00 0\ 0 0 0\ ("r') V) ....-4 0 V) V) ("r')
("r') ("r') V) \0 N N N ....-4 V)
= ... 00 V) V) t"--... 00 N 00
ff') V"l \0 N V) N 00 0 ... t"-- 00... N... ....-4 N'" \0 V)
... 0 , N'" , \0 00 , , ... , ....-4 ,
::a ("r') \0 t"-- 00 0 ("r') ("r') 0\ 0 00 0\
("r') N V) ....-4 ....-4 ....-4 ....-4
t"-- 00 ....-4 V) 00 V) J V) V) V) V) V) \0 00
... 00 ....-4
0 ("r') N 00 \0... ... N V)- V) t"-- N \0 ("r') ("r') N... 00... \0 ("r') V)
("r') 0'" ... ... ... ... ... ...
::a V) \0 t"-- 0 \0 N ("r') ("r') ("r') ("r') 0\ 0\ ....-4 ... ... V) 0 0 0 ("r') V) ("r')
N N N ("r') ("r') ("r') ("r') V) ....-4 ....-4 ....-4 ....-4 ("r')
....-4 ....-4
t"-- 00 0\ ("r') V) V) V) V) V) t"-- \0
= t"-- V) 00 ....-4 ....-4
N V) \0 N N 00 N'" 0 ....-4 ... V) N N t"-- ....-4 00 \0... V) 00 0 \0... ....-4
N , ... ... t"-- ... N'" N 0 a\
::a V) 0 0 N 0\ 0\ 00 ("r') N N N'" 00 ... ("r') 0\
N ....-4 ....-4 N N ("r') ("r') ....-4 ....-4 ....-4 00 N N
....-4 ....-4
'oC t"-- ("r') t"-- 0\ V) t"-- N 00 ....-4 0\ t"-- t"-- \0
.,.,.,.. 00 N 00 ... \0 t"-- V) N t"--... ....-4 0 00 ....-4 t"--... N 00 00 \0 ....-4
N , ... ... N ("r') ... ... ... 0 ...
::a ("r') 0 0 t"-- ....-4 V) V) N \0 \0 ....-4 ... 0 0 ... \0 N ("r') ("r')
....-4 ....-4 ....-4 N N N 0\ ....-4 0\ ....-4 \0 N N
N V) V) t"--... ("r') ("r') ("r') N 00 N ("r')
.,.,.,.. t"--... 0 ....-4 \0... N t"--... \0... 0... ("r') V) ("r') \0... ....-4 \0... 00 t"--
I , , , , ... , , , ,
::a ("r') 0 0 ("r') ....-4 ....-4 \0 0 t"-- ... ... 0 ....-4 t"--
....-4 ....-4 ....-4 ....-4 N t"-- t"-- V) ....-4
= V) N 00 ("r') t"-- N 00 V) ("r')
.,.,.,.. V"l \0 ....-4 \0... ... 0 t"--... \0 t"--... N N V) ("r') \0 t"--...
, , ... I , \0'" , , , 0 ,
::a ....-4 N ... 0 ....-4 ....-4 t"-- ... ... ... ....-4 V)
0 ....-4 0\ ....-4 ....-4 \0 \0 ....-4
V) V) 00 ("r') 00 V) V) ....-4 ("r')
00 \0 N \0... ("r') ("r') t"--
::a N N , , ....-4 0'" ... 00 t"--... , I , N ... ....-4 ... , , \0... , ("r') N I
... N ... 0\ ....-4 V) ... 0 ....-4
....-4 0 t"-- ....-4 ....-4 V) V) ("r') ....-4
'oC V) N 00 V) V) V) V) 00
V) 00 0 ... t"-- 0
::a ....-4 00 I I ....-4 ... ... \0 00 , 00 , , 00 ....-4 I , N , N... t"--... ,
....-4 ... 0 \0 ... ... ....-4 ....-4 ... ....-4
0 V) 00 ....-4 ("r') 0 0\
V) 00... V) V) t"--... N 00 0\ N V) V) V) V) N 00
::a \0 , , ....-4 0 V) 00 , 00 , t"--... I ... ... ("r') \0... , , ("r') , ... 00 t"--... ,
0 ....-4 ... V) ... ... ....-4 ("r') ... ... 0
0 \0 00 ("r') ("r') N t"--
V) N 00 \0 V) V) t"-- 00
t"--... ... t"-- N 00 t"-- N N
::a , , ....-4 ... 00 , 00 I \0... , ... ... \0 0\ , , 00 , 0'" t"-- t"--... I
0 ....-4 ... 0 ... ... ....-4 N ...
0 ("r') V) t"-- N'" N'" ....-4 \0
V) \0 \ ....-4 V) V) ....-4 N
i V) ... \0... t"-- N ....-4 V)
... N , I ....-4 ("r') 00 L , 0 ....-4 N 00 ....-4 , I ("r') , ... ... ("r') I
0 ....-4 ... 0 ("r') N'" \0'" 0 V) ...
0 ... N ....-4 V)
....-4
V) V) V) \0 t"-- V) V) V) N
., ....-4 ....-4 V) t"--... t"-- N ....-4 ....-4
N ... , , ... N ... N'" ("r') 0 , ... , ....-4 V"l 00 , I ... I ... V) 00 ,
::a 0 0 0'" ("r') N ... V) ....-4 ... ....-4 0 ...
....-4 ....-4
V) \0 t"-- N V) V) 0\ N
N 0 ....-4 \0 00 t"-- N ....-4
::a I , 0'" N N'" N 00 I q I I ... V) I I 00 I ... 00 ,
0 ....-4 ... ... 0 ....-4 ... 0 ...
0 ....-4 ("r') ... 0 ("r')
....-4 ....-4
'oC V) V) \0 t"-- ....-4 V) V) 00 N
...;' ("r') ....-4 \0... N ... \0 ....-4 t"-- N \0 ....-4 0...
0\ , I ... N , , , 0 ... N... , , I 0 I
::a 0 0 0 ....-4 ....-4 N'" ("r') ....-4 0 ("r') ("r')
0 ....-4
.0 1 (,.) = = = :i = = = =
I I == == == 0 == == == ==
=
:i II I II
1 <1j:Q <1j:Q C"') « <1j:Q <1j:Q
:i == :i
0 <1j:Q 0
= (,.) (,.) (,.) (,.) (,.) = (,.)
t (,.) 5 (,.) 5 (,.) 5 (,.) 5 (,.) 5 (,.) 5
I g
== == == == == ==
c...;
"'r:;jr:::J "'r:;jl",,) ...c:u
..c::) c:J <u "" ,
F/la8a 4. Kpene:JICHble oemOJlu
P83Mep pe3h6w, d Ml,6 M2 M2,S M3 M4 MS M6 M8
KJIacc H3 eJIIUI I H I f, g
A B s g
ROM. MHH. MHC. MHH. MaKe. . . . . . . . .
:I :I :I :I :I :I :I :I
_fIJ ...... tIC _fIJ ...... tIC _fIJ ...... tIC _fIJ ...... tIC _fIJ ...... tIC _fIJ ...... tIC _fIJ ...... tIC _fIJ .....'C
12 11,65 12,35 - - 1,2 3 ,l:lrnI pa3MepOB BbIme cTYIIelf1la-
16 .15,65 16,35 - - ,.7. .7. 4 6 2,75 5 TOB JIHHHH, 0603HaQeHHOB KaK
20 '19,58 20,42 - - :8 10 6,75 9 5,5 8 _, peKoMeaayeTCH ISO 4017
1 . . . . . .
25 24,58 25,42 - - : \ t ,.7.5. .\4 10,5 13 7,5 11 5 9
30 29,58 30,42 - - : \ ,.5. .\& 12,5 16 10 14 7 12
35 34.5 35.5 - - : 17.5 21 15 19 12 17
.40 39,5 40,5 1 . 20 24 22 18
- - 122 5 17 11,75
. .'. .
45 44,5 45,5 - - : 25 29 22 27 16,75 23
50 49.5 50.5 - - :30 34 27 32 21.75 28
55 54,4 55,6 - - : 32 37 26,75 33
60 59,4 60,6 - - : 37 42 31,75 38
65 64.4 65.6 - - : 36.75 43
70 69,4 70,0 - - :41,75 48
80 79,4 80,6 - - :51 75 .
..'...
90 89.3 90.7 - -
100 99,3 100,7 - -
110 109,3 110,7 108,25 111,75
120 119.3 120.7 118.25 121..75
130 129,2 130,8 128 132
140 139,2 140,8 138 142
150 149.2 150.8 148 152
160 - - 158 162
180 - - 178 182
200 - - 197.7 202.3
220 - - 217,7 222,3
240 - - 237,7 242,3
260 - - 257.4 262.6
280 - - 277,4 292,6
300 - - 297,4 302,6
320 - - 317.15 322.85
340 - - 337,15 342,85
360 - - 357,15 362,85
380 - - 377.15 382.85
400 - - 397,15 402,85
420 - - 416,85 423,15
440 - - 436.85 443.15
460 - - 456,85 463,15
480 - - 476,85 483,15
500 - - 496.85 503.15
ap - mar pe3b6bI; b ,lI;IDI ,nJIHH I HOM . 125 MM;
C ,lI;IDI ,nJIHH 125 MM < I HOM . 200 MM; d ,nJIH ,nJIHH IHoM. > 200 MM;
e k'min = 0,7 k min ; f I gmaks = I HOM - b; I smin = I gmaks - 5P;
gig - MHHHMaJIbHaH ,nJIHHa ,nJIHHa rJI3):(KoH QaCTH CTep)I{IUI.
4.1. BUHmo6ble "peneJICHble U30eJlUR 143:::
OK,OH"taHue
MIO M12 M16 M20 M24 M30 M36 M42 M48 M56 M64
I H I I, g
s g
i . . . . . . . . . .
.
:I :I :I :I :I :I :I :I :I :I :I
..... GI'J ..... ..... GI'J ..... b. ..... GI'J ..... tJ( .....(0) ..... .....(0) ..... .....(0) ..... .....GI'J ..... .....(0) ..... tJ( .....(0) ..... tJ(I .....(0) ..... tJ( .....(0)
,n;m pa3MepOB BbIllie
warOBOH JIHHHH, 060-
3HaQeHHbIX TaK _, pe-
KOMeHn VeTCH ISO 4017
J
(
)
11,5 19
16 5 24 11 25 20
21,5 29 16,25 25
26,5 34 21,25 30
31,5 39 26 25 35 17 27
36,5 44 31,25 40 22 32
46,5 54 41,25 50 32 42 21,5 34
56.5 64 51.25 60 42 52 31.5 44 21 36
6.6., 7 61,25 70 52 62 41,5 54 31 46
:71,25 80 62 72 51,5 64 41 56 : 26,5 44
1 61.5 I
181.25 90 72 82 74 51 66 1 36.5 54
: 76 86 65,5 78 55 70 : 40,5 58
:86 1
96 75,5 88 65 80 : 50,5 68 36 56
1
: 96 106 98 I 78 46 66
85.5 75 90 I 60.5
106 116 95,5 108 85 100 70,5 88 56 76 41,5 64
115,5 128 105 120 90,5 108 76 96 61,5 84 47 72
135.5 148 125 140 110.5 128 96 116 81.5 104 67 92
132 147 117,5 135 103 123 88,5 III 74 99 55,5 83
152 , \137,5 155 123 143 108,5 131 94 119 75,5 103
\ 157.5 175 143 163 128.5 151 114 139 95.5 123 77 107
177,5 195 163 183 148,5 171 134 159 115,5 143 97 127
197,5 215 183 203 168,5 191 154 179 135,5 163 117 147
203 223 188.5 211 174 199 155.5 183 137 167
223 243 208,5 231 194 219 175,5 203 157 187
243 263 228,5 251 214 239 195 5 223 177 207
248.5 271 234 259 215.5 243 197 227
268,5 291 254 279 235,5 263 217 247
288,5 311 274 299 255,5 283 237 267
308.5 331 294 319 275.5 303 257 287
314 339 295,5 323 277 307
334 359 315,5 343 297 327
335.5 363 317 347
llpUMe"taHue. PacnpocTpaHeHHbIe ,nJIHHbI 0603HaQeHbI Is H I g:
113,n;eJIHH KJlacca A BbIllIe CTYIIeHqaTOH JIHHHH, 0603HaqeHHOH KaK ----
113,n;eJIHH KJlacca B HHxe 3TOH CTYIIewraToH JIHHHH.
F/la8a 4. Kpene:JICHble oemOJlu
::a
C"')
= \0 ....c ....c V') V') V') 00
\0 V) V') ("f"') t- o N .. N N 00 .. .. N 0 ..
::a .. I I 0" ....c \0 \0 I .. I I 0\ ....c ("f"') I I t- oo I \0" N 0\ I t-
V') ....c 0\ ("f"')
V') 00 0\ ("f"') ("f"') N 00
N \0 0\ \0 \0 N V') V') V') V') .-4
It') ("f"') \0" N N .. N 0 ("f"') .. .. t- \0.. 0 ..
V') I ....c N 0" ....c I .. I I .. I I N ("f"') I .. I 00
....c .-4 V') .-4 00 ....c ("f"') N ....c 00
V') V') t- oo ("f"') ("f"') N t-
It') \0.. 00 t- V') 00 .-4 ....c
V') N V') ("t") \0 ("f"') .. 0\ 00 V') .. ("f"') N 0 ..
::a .. I 0 .-4 .. ....c 00 I .. I I .. 00 N I I .. I .. .. t- I 00
....c ....c 0 \0 \0 t- oo 0\ ....c \0
t- N N ....c
CJ\ .. 00 \0 .. 00 N ....c 00
ff') 0 ("f"') ("f"') 0\ ("f"') 00 V') V') .. N 0 ..
I 0 .-4 N I .. I .. I \0 I I .. I .. ....c I 00
::a 0\ 0 ("f"') 00 V') \0 N V') t- \0
....c V')
("f"') V') \0 N N ....c
ff') 00 V') t- oo N ....c
ff') V') 00 ....c N 00 \0" ("f"') ("f"') V') ("f"') \0 .-4 V') .. 0 0\
::a .. I t- 0\ 0" 0" ("f"') I .. I \0" I .. N I I 0" I .. ....c V') I
("f"') ("f"') N \0 ....c
("f"') V') N N ....c
I' 00 N V') V') \0
N 0 \0 0\ N 00 0" t- 00 .. \0 t- \0 ("f"') \0 ....c 0
::a ("f"') \0 \0 t- o" 0" N I \0" I ("f"') I V') ....c I I \0" .. I .. ....c I
("f"') t- ....c
N ....c ....c ....c
t- oo ....c V') N 0\ V') V') V') V') 00
N V') N 00 \0 .. t- ("f"') t- N 00 ....c \0.. ("f"') V') \0 00 ("f"')
N .. 0 \0 0\ .. .. .. N .. .. .. .. .. t- N .. \0 V') .. .. ("f"')
::a N V') V') \0 0 0 N ....c ....c ....c ....c t- t- ....c .. .. ("f"') .. .. 0 ("f"') ("f"') ("f"')
N N N ("f"') ("f"') ("f"') ("f"') ("f"') ....c ....c 0\ 0\ ("f"')
....c ....c
("f"') t- V') \0 V') V') V') V') t- \0
00 N V') 00 t- ....c
.,.,.,.. V') N 00 N 00 .. 00 t- V') ("f"') 00 ....c V') .. N ....c .-4 00 0\ 00 \0.. t- \0 ....c
::a .. I 0" 0" 0 ....-4 .. .. .. .. 0" 0\ ("f"') ....c .. .. .. .. .. .. N \0" \0"
N N t- t- V') ....c ....c ....c ....c ....c t- t- o
.-4 ....c N N ("f"') N ....c ....c ....c ....c N N
V') t- ("f"') t- \0 N 00 ("f"') t-
.,.,.,.. N 0 ....c \0.. .. t- ("f"') ("f"') ("f"') 00 \0.. 0\ 0.. \0.. ....c \0
::a ("f"') I .. V') ....c .. I .. I .. I .. .. I I I N 0" I
0 0 ....c ("f"') 0\ ("f"') 00 00 00 \0 0
....c ....c N N
It') V') N t- oo V') V') 0\ N
\0 ("f"') ....c V') .. t- N ....c
0" I I ....c 0" .. .. ("f"') I 0.. I V') I ....c N V') I I V') I 0" \0 00 I
::a ....c 0" ("f"') .. .. N .. ..
("f"') V') \0 .. .. .-4 V')
N N
,.01 0 1 "'C) == == :i == ==
=: 0 =: =:
«S =
II < II
:i <IIXI <IIXI <IIXI <IIXI :i <IIXI
.,
:3 0 0
= 5 5 5 5 = 5
i
t =: =: == =: =: =: =:
I 0 0 0 0 0 0 0
0 0 0 0 0 0 0
«S «S «S «S «S «S «S
1-4 ...c:u
..t::) c:J &... CI'J
::a
\0
..Q
C"')
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=
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z
CJ'.)
4. 1. BuHm08ble Kpene:JICHble U30eJlUR
-- V') V')
0\ ....c
I ....c
:I
-- . V') V')
.. ..
t"- t"-
\0 00
-- ....c ....c ....c
00 0\ ....c ("f"')
:I ....c .-4
- . 0\ \0 \0 \0
V') \0 00 0
....c
-- t"- V') V')
....c 00 00 V')
0 t"- 0\ 0 M
:I .. ....c .-4 ....c
- . O V') \0.. V') V') V')
5a .. M" M" M"
r 1/ V') V') 0 M
V') t"- oo
t::5 .-4 ....c
-- ):s: 0 0 0 0 t"- t"- t"-
oG) \0 t"- 0'\ ....c ....c ("f"') V')
:I t; ....c ....c .-4 ....c
-- . G) 0 0 0 0 t"- t"- t-
G) V') t- 0\ 0\ ....c ("f"')
....c ....c
-- N N 0'\ 0\ 0\
() N N N N
V') \0 t- oo 0 N M \0
G) 1 ....c ....c .-4 ....c ....c
:I
. -- . V') V') V') V') V') V') V') V') V')
.. .. .. ..
...: .. .. .. .. .. ....c ....c ....c
..... ("f"') V') \0 00 0 ....c ("f"') V')
II & ....c ....c .-4 ....c
....rIj -- 0 0 0 .-4 ....c ....c
G)):s: V') \0 \0 t- oo 0\ ....c ("f"') \0 00
:I o ....c ....c ....c ....c ....c
=
-- . = V') V') V') 0\ 0\ 0\ 0\ 0\ 0\ \0 \0 \0
j N ("f"') V') \0 t"- 0'\ ....c N \0
.-4 ....c ....c .-4
-.......- ------...
-- C"') 0 0 0 0 : ....c
0 N V')
\0 V') \0 t- t- oo 0\.0 ....c ....c ....-4
:I 0 . .-4
-- . V') V') V') V') V') V') V').V') V') V') V')
.. .. ..
.. .. .. .. .. .. ..' .. V') ....c 00
t- t- t- t- ....c ....c ....c. ....c
N ("f"') V') \0 t- 00:0\ ....c ("f"') ("f"')
....-4 ....c ....c
U 00 00 00 00 00 00 N N N:N M
__I.\C)= N ("f"') V') \0 t- oo 0\ o.....c ("f"')
:I ....c. ....c ....c
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. . . . . . . . .
HOM. MHH. MaKC.
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60 58,5 61,5 16 26 ,[(JIR R-a epOB BbIllie CTYTIeHqaTOM JIHHHH,
65 63,5 66,5 21 31 0603HaQeHHOM KaK ,
peKOMeH,[(yeTCR ISO 4018
70 68,5 71,5 26 36
80 78,5 81,5 36 46 25,5 38
90 88,25 91,75 46 56 35,5 48 27,5 40
100 98,25 101,75 56 66 45,5 58 37,5 50
110 108,25 111,75 66 76 55,5 68 47,5 60 35 50
120 118,25 121,75 76 86 65,5 78 57,5 70 45 60
130 128 132 80 90 69,5 82 61,5 74 49 64 34,5 52
140 138 142 90 100 79,5 92 71,5 84 59 74 44,5 62
150 148 152 89,5 102 81,5 94 69 84 54,5 72 40 60
160 156 164 99,5 112 91,5 104 79 94 64,5 82 50 70
180 176 184 119,5 132 111,5 124 99 114 84,5 102 70 90 55,5 78
200 195,4 204,6 131,5 144 119 134 104,5 122 90 110 75,5 98 59 84
220 215,4 224,6 138,5 151 126 141 111,5 129 97 117 82,5 105 66 91
F/la8a 4. Kpene:JICHble oemOJlu
O"OHllaHue
Pa3Mep pe3L6hI, d MI4 MI8 M22 M27 M33 M39 M45 M52 M60
K.JJacc npo,ZJyKT8 I Hlf,g
A B s g
HOM. MHH. MaKe.
:I :I :I :I :I :I :I :I :I
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240 235,4 244,6 146 161 131,5 149 117 137 102,5 125 86 111 67,5 95
260 254,8 265,2 166 181 151,5 167 137 157 122,5 145 106 131 87,5 115
280 274,8 285,2 171,5 189 157 177 142,5 165 126 151 107,5 135
300 294,8 305,2 191,5 209 177 197 162,5 185 146 171 127,5 155
320 314,3 325,7 211,5 229 197 217 182,5 205 166 191 147,5 175
340 334,3 345,7 217 237 202,5 225 186 211 167,5 195
360 354,3 365,7 237 257 222,5 245 206 231 187,5 215
380 374,3 385,7 257 277 242,5 265 226 251 207,5 235
400 394,3 405,7 277 297 262,5 285 246 271 227,5 255
420 413,7 426,3 282,5 305 266 291 247,5 275
440 433,7 446,3 302,5 325 286 311 267,5 295
460 453,7 466,3 306 331 287,5 315
480 473,7 486,3 326 351 307,5 335
500 493,7 506,3 346 371 327,5 355
a P - mar pe3b6bI.
b ,LUUI ATlHH I HOM . :::; 125 MM.
C ,LUUI ATlHH 125 MM < I HOM :::; 200 MM.
d ATlH ATlHH 1 HoM . > 200 MM.
e k ' . - 0 7k .
mm- . rom
f/pnaks =/ HOM -b; I smin =Igmaks -5P.
gig - MHHHMaJIbHaH ATlHHa rJIa,nKoH qaCTH cTepXHH
llpUMellaHue. PacnpocTPaHeHHbIe ATlHHbI 0603HaqeHbI JIHHHeH Is H I g'
4.1. BUHmo8ble "pene:JICHble U30e.tlWl
4.1.15. BS EN ISO 4017: 2001. BJfHT&I C WeCTJfrpSHHOii
ronoBKoii - KnSCC&1 Jf3AenJffl A Jf B
Pa3MepLl
llpUMellaHue. CHMBOJlbI H 0603HaqeHH.H pa3MepOB ,naHbI B COOTBeTCTBHH C
ISO 225.
k
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ct>acKoVi VlJ1V1 AJ151 pe3b6
M4 MO)l(eT 6blTb 6e3
ct>acKVI (cpe3HoVi 60J1T)
(CM. ISO 4753)
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MHHaJIbHOH ,nJIHHOH I = 80 M H KJIaCCOM npOqHOCTH 8.8:
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F/la8a 4. Kpene:JICHble oemOJlu
BS EN ISO 4017: 2001. Ta6JI. 2. CneI(HaJIbHbIe pe3b6bI. Pa3MepbI B MM
P83Mep pe3L6hI, d M3,5 MI4 MI8 M22 M27 M33 M39 M45 M52 M60
pi! 0,6 2 2,5 2,5 3 3,5 4 4,5 5 5,5
MaKc. b 1,8 6 7,5 7,5 9 10,5 12 13,5 15 16,5
a
MHH. 0,6 2 2,5 2,5 3 3,5 4 4,5 5 5,5
MHH. 0,15 0,15 0,2 0,2 0,2 0,2 0,3 0,3 0,3 0,3
c
MaKC. 0,4 0,6 0,8 0,8 0,8 0,8 1 1 1 1
d a MaKC. 4,1 15,7 20,2 24,4 30,4 36,4 42,4 48,6 56,6 67
KJIacc 5,07 19,37 25,34 31,71 - - - - - -
d w H3,n;eJIHH MHH.
- - 24,85 31,35 38 46,55 55,86 64,7 74,2 83,41
KJIacc 6,58 23,36 30,14 37,72 - - - - - -
e H3,n;eJIHH MHH.
- - 29,56 37,29 45,2 56,37 66,44 76,95 88,25 99,21
HOM. 2,4 8,8 11,5 14 17 21 25 28 33 38
KJIacc MHH. 2,275 8,62 11,285 13,785 - - - - - -
k H3,n;eJIHHA MaKC. 2,525 8,98 11,175 14,215 - - - - - -
KJIacc MHH. - - 11,15 13,65 16,65 20,58 24,58 27,58 32,5 37,5
H3,n;eJIHH B MaKC. - - 11,85 14,35 17,35 21,42 25,42 28,42 33,5 38,5
KJIacc 1,59 6,03 7,9 9,65 - - - - - -
k'e H3,n;eJIHH MHH.
- - 7,81 9,56 11,66 14,41 17,21 19,31 22,75 26,25
r MHH. 0,1 0,6 0,6 0,8 1 1 1 1,2 1,6 2
HOM. = MaKC. 6 21 27 34 41 50 60 70 80 90
s KJIacc 5,82 20,67 26,67 33,38 - - - - - -
H3,n;eJIHH MHH. 26,16 33 40 49 58,8 68,1 78,1 87,8
- -
4.1. BUHmo8ble "pene:JICHble U30e.tlWl
O"OHliaHue
P83Mep pe3hOhI, d M3,5 MI4 MI8 M22 M27 M33 M39 M45 M52 M60
K.JJacc H eJJHJI
A B
[d
80M. MHB. MaKe. MHH. MaKe.
r ./
-'
8 7,71 8,29 - -
10 9,71 10,29 - -
12 11,65 12,35 - -
16 15,65 16,35 - -
20 19,58 20,42 - -
25 24,58 25,42 - -
30 29,58 30,2 - -
35 34,5 35,5 - -
-----
40 39,5 40,5 .
- - .
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45 44,5 45,5 .
- - .
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65 64,4 65,6 63,5 66,5 . .
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150 149,2 150,8 148 152 . .
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160 - - 158 162
180 - - 178 182
200 - - 197,7 202,3
a P - war pe3b6bI.
b 3HaqeHHH, COOTBeTCTByJOll(He a MaKc ., HOpMaJIbHOrO pH,ZJ;a, B ISO 3508.
C k:nm = 0,7 k min .
d )];Hana30H pacnpOC'rpaHeHHbIX .lUIHH pacnOJIOXeH Mex.ny CTYTIeHqaTbIMH JIHHHHMH:
Krracc H3,n;eJIHH A BbIwe cTYTIeHqaTOH JIHHHH, 0603HaqeHHOH KaK
Krracc H3,n;eJIHH B HHXe 3TOH cTYTIe aToH JIHHHH.
F/la8a 4. Kpene:JICHble oemOJlu
4. 1. 16. BS EN ISO 401 B: 2001. BJfHT&1 C WeCTJfrpSHHOH
ronoBKoii - KnSCC Jf3AenJffl C
Pa3MepLl
llpUMellaHue. CHMBOJIbI H 0603HaqeHH.H pa3MepOB ,naHbI B COOTBeTCTBHH C
ISO 225.
Cneu.VlanbHble Tpe-
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MHHaJIbHWI ,lUIHHa I = 80 MM H KJIacc lIPOqHOCTH 4.6:
BHHT C meCTHrpaHHOH rOJIOBKOH ISO 4018 - M12 X 80 - 4,6.
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oV')V') t'-t'-t'-NNN
' V') 00 V')V')V')V')V')V')V')V')
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NNNNN V')
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.. .. N .. N .. - 00 00 - - ." ._ ._ ....; - t'- 0- -- -
- V')t'- , , ,
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_ , 00 _ 0 ........ _, _, _, -, \J' , \J' , \J'
\J' ........ N
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= NNNNN V')
.
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4.1. BUHmo6ble "peneJICHble U30eJlUR 161
BS EN ISO 4018: 2001. Ta6JI. 2. CneI(HaJIbHbIe pe3b6bI. Pa3MepbI B MM
Pa3Mep pe3hOhl, d MI4 MIS M22 M27 M33 M39 M45 M52 M60
pa 2 2.5 2.5 3 3.5 4 4.5 5 5.5
a MaKC. 6 7,5 7,5 9 10,5 12 13,5 15 16,5
MHH. 2 2.5 2.5 3 3.5 4 4.5 5 5.5
c MaKC. 0.6 0.8 0.8 0.8 0.8 1 1 1 1
d.. MaKC. 16.7 21.2 26.4 32.4 38.4 45.4 52.6 62.6 71
d... MHH. 19.15 24.85 31.35 38 46.55 55.86 64.7 74.2 83.41
e MHH. 22.78 29.56 37.29 45.2 55.37 66.44 76.95 88.25 99.21
HOM. 8,8 11,5 14 17 21 25 28 33 38
k MHH. 8,35 10,6 13,1 16,1 19,95 23,95 26,95 31,75 36,75
MaKC. 9.25 12.4 14.9 17.9 22.05 26.05 29.05 34.25 39.25
k'e MHH. 5.85 7.42 9.17 11.27 13.97 16.77 18.87 22.23 25.73
r MHH. 0.6 0.6 0.8 1 1 1 1.2 1.6 2
HOM. = MaKC. 21 27 34 41 50 60 70 80 90
S MHH. 20,16 26,16 33 40 49 58,8 68,1 78,1 87,8
IC
HOM. MHH. MaKC.
30 28,95 31,05
35 33,75 36,25
40 38.75 41.25
45 43,75 46,25
50 48,75 51,25
55 53.5 56.5
60 58,5 61,5
65 63,5 66,5
70 68.5 71.5
80 78,5 81,5
90 88,25 91,75
100 98.25 101.75
110 108,25 111,75
120 118,25 121,75
130 128 132 /
140 138 142 \.._-
150 148 152 I
\
160 156 164
180 176 184
200 195,4 204,6
220 215.4 224.6
240 235,4 244,6
260 254,8 265,2
280 274.8 285.2
300 294,8 305,2
320 314,3 325,7
340 334.3 345.7
360 354,3 365,7
380 374,3 385,7
400 394.3 405.7
420 413,7 426,3
440 433,7 446,3
460 453.7 466.3
480 473,7 486,3
500 493,7 506,3
a P - mar pe3b6bI. b ktMHHo = 0,7 k MHHo
c )];Hana30H pacnpOC'rpaHeHHbIX,lI)IHH Mex.ny cTYIIe aTbIMH JIHHIDIMH, 0603HaQeHHbIMH KaK -.
6-3255
F/la8a 4. Kpene:JICHble OemOJlu
4. 1. 17. BS EN ISO 4032: 2001. WeCTJfrpSHH&le rSHKJf
JfCnOnHeHJffl 1 - KnSCC&1 Jf3AenJffl A Jf B
Pa3MepLI
30 0
7S o
...:
e
m'
c
CbOPMY BblCTYna
nOA wat16y CJ1e-
AyeT orOBap -
BaTb OTAeJ1bHO
o 0
i
.....
"tJ "tJ t
\
mil
m
- .
- -
CD
s
m
IIpHMep 0603HaqeHIDI IIIecTHrpaHHoH raHKH HCrrOJIHeHIDI I, C pa3MepOM pe3b-
6bI d = MI2 H KJIaCCOM rrpOqHOCTH 8:
lliecTHrpaHHaJi raHKa ISO 4032 - MI2 - 8.
BS EN ISO 4032: 2001. Ta6JI. 1. CTaH,l(apTHbIe pa3MepbI. Pa3MepbI B MM
Pa3Mep pe3hOhl, d MI,6 M2 M2,5 M3 M4 M5 M6 M8 MIO MIl
pa 0,35 0,4 0,45 0,5 0,7 0,8 1 1,25 1,5 1,75
MaKC. 0,2 0,2 0,3 0,4 0,4 0,5 0,5 0,6 0,6 0,6
c
MIIH. 0,1 0,1 0,1 0,15 0,15 0,15 0,15 0,15 0,15 0,15
MHH. 1,6 2 2,5 3 4 5 6 8 10 12
d a
MaKC. 1,84 2,3 2,9 3,45 4,6 5,75 6,75 8,75 10,8 13
d w MHH. 2,4 3,1 4,1 4,6 5,9 6,9 8,9 11,6 14,6 16,6
e MHH. 3,41 4,32 5,45 6,01 7,66 8,79 11,05 14,38 17,77 20,03
MaKC. 1,3 1,6 2 2,4 3,2 4,7 5,2 6,8 8,4 10,8
m 6,44
MHH. 1,05 1,35 1,75 2,15 2,9 4,4 4,9 8,04 10,37
m' MHH. 0,8 1,1 1,4 1,7 2,3 3,5 3,9 5,2 6,4 8,3
m" MHH. 0,7 1 1,2 1,5 2 3,1 3,4 4,5 5,6 7,3
HOM. = MaKC. 3,2 4 5 5,5 7 8 10 13 16 18
s 3,02 3,82 4,82 5,32 6,78 7,78 9,78 12,73 15,73 17,73
MHH.
4.1. BUHmo6ble "peneJICHble U30eJlUR 163"
O"OH'taHue
P83Mep Pe3hOhl, d MI6 M20 M24 M30 M36 M42 M48 M56 M64
pa 2 2,5 3 3,5 4 4,5 5 5,5 6
MaKC. 0,8 0,8 0,8 0,8 0,8 1 1 1 1
C
MHH. 0,2 0,2 0,2 0,2 0,2 0,3 0,3 0,3 0,3
d a MHH. 16 20 24 30 36 42 48 56 64
MaKC. 17,3 21,6 25,9 32,4 38,9 45,4 51,8 60,5 69,1
d w MHH. 22,5 27,7 33,3 42,8 51,1 60 69,5 78,7 88,2
e MHH. 26,75 32,95 39,55 50,85 60,79 71,3 82,6 93,56 104,86
MaKC. 14,8 18 21,5 25,6 31 34 38 45 51
m
MHH. 14,1 16,9 20,2 24,3 29,4 32,4 36,4 43,4 49,1
m' MHH. 11,3 13,5 10 -1 19,4 23,5 25,9 29,1 34,7 39,3
m" MHH. 9,9 11,8 14,1 17 20,6 22,7 25,5 30,4 34,4
HOM. = MaKC. 24 30 36 46 55 65 75 85 95
s 23,67 29,16 35 45 53,8 63,1 73,1 82,8 92,8
MHH.
a P - mar pe3b6bI.
BS EN ISO 4032: 2001. Ta6JI. 2. CneI(HaJIbHbIe pa3MepbI. Pa3MepbI B MM
P83Mep pe3hOhl, d M3,5 MI4 MI8 M22 M27 M33 M39 M45 M52 M60
pa 0,6 2 2,5 2,5 3 3,5 4 4,5 5 5,5
MaKC. 0,4 0,6 0,8 0,8 0,8 0,8 1 1 1 1
C
MHH. 0,15 0,15 0,2 0,2 0,2 0,2 0,3 0,3 0,3 0,3
d a MHH. 3,5 14 18 22 27 33 39 45 52 60
4 15,1 (19,5 23,7 29,1 35,6 42,1 48,6 56,2 64,8
MaKC.
d w MHH. 5 19,6 ( .4,9 31,4 38 46,6 55,9 64,7 74,2 83,4
e MIIH. 6,58 23,35 29,56 37,29 45,2 55,37 66,44 76,95 88,25 99,21
MaKC. 2,8 12,8 15,8 19,4 23,8 28,7 33,4 36 42 48
m
MHH. 2,55 12,1 15,1 18,1 22,5 27,4 31,8 34,4 40,4 46,4
m' MHH. 2 9,7 12,1 14,5 18 21,9 25,4 27,5 32,3 37,1
m" MHH. 1,8 8,5 10,6 12,7 15,8 19,2 22,3 24,1 28,3 32,5
HOM. = MaKC. 6 21 27 34 41 50 60 70 80 90
s 5,82 20,67 26,16 33 40 49 58,8 68,1 78,1 87,8
MHH.
a P - mar pe3b6bI.
F/la8a 4. Kpene:JICHble oemOJlu
4. 1. 18. BS EN ISO 4033: 2001. WeCTJfrpSHH&le rSHKJf
JfCnOnHeHJffl 2 - KnSCC&1 Jf3AenJffl A Jf B
Pa3MepLI
...:
i!!
b
C\I
g
o
c
AonYCT Ma
aJ1bTepHaT BHa51
ct>opMa BblCTYna
nOA wat16y
CD
1:) -d
3t
1:)
s
m
m
IIpHMep 0603HaqeHIDI IIIecTHrpaHHoH raHKH C pa3MepOM MeTPHqeCKOH pe3b6bI
d = MI2 H KJIaCCOM rrpOqHOCTH 9:
lliecTHrpaHHaJi raHKa ISO 4033 - MI2 - 9.
Pa3MepHOCTH B MM
Pa3Mep pe3hohl, d M5 M6 M8 MIO Ml2 (MI4) Ml6 M20 M24 M30 M36
pa 0,8 1 1,25 1,5 1,75 2 2 2,5 3 3,5 4
c MaKC. 0,5 0,5 0,6 0,6 0,6 0,6 0,8 0,8 0,8 0,8 0,8
d a MHH. 5 6 8 10 12 14 16 20 24 30 36
MaKC. 5,75 6,75 8,75 10,8 13 15,1 17,3 21,6 25,9 32,4 38,9
d w MHH. 6,9 8,9 11,6 14,6 16,6 19,6 22,5 27,7 33,2 42,7 51,1
e MHH. 8,79 11,05 14,38 17,77 20,03 23,35 26,75 32,95 39,55 50,85 60,79
MaKC. 5,1 5,7 7,5 9,3 12 14,1 16,4 20,3 23,9 28,6 34,7
m
MHH. 4,8 5,4 7,14 8,94 11,57 13,4 15,7 19 22,6 27,3 33,1
m' MHH. 3,84 4,32 5,71 7,15 9,26 10,7 12,6 15,2 18,1 21,8 26,5
HOM. = MaKC. 8 10 13 16 18 21 24 30 36 46 55
s 7,78 9,78 12,73 15,73 17,73 20,67 23,67 29,16 35 45 53,8
MHH.
Pa3MepOB B cK06Kax CJIe,n;yeT no B03MO)I{HOCTH H36eraTb.
a p - mar pe3b6bI.
4.1. BUHmo6ble "peneJICHble U30eJlUR 165"
BS EN ISO 4033: 2001. Ta6JI. 1.
HOMHH8JIh1lhlii ,lUIaMeTp Pa3Mep raiiKH llJIom;a,zu. KOJlhneBOii ropneaoii onopHoii nOBepXHOCTH/
pe3hOW (MM) no KJII01f (MM) HOMHH8JIhHaJI DJI0m;a,zu. Ce1felllDl no pe3..oe *
5 8 1,08
6 10 1,44
8 13 1,23
15 0,90
10 16 1,30
17 1,73
18 0,91
12
19 1,16
21 0,96
14 /
22 - 1,24
.J I
16 24 1,02
20 30 0,95
24 36 0,86
30 46 1,02
36 55 1,04
* BbIQHCJIeHHH OCHOBaHbI Ha 3HaqeHHHX .LJ)UI oTBepcTHH C rapaHTHpOBaHHbIM 3a30pOM B
COOTBeTCTBHH C ISO 273 (HcnpaBJIeHHbIM), cpe,n;HHH cepHH.
BS EN ISO 4033: 2001. Ta6JI. 2.
P83Mep pe3how, d MIO MI2 MI4
pa 1,5 1,75 2
d w MHH. 13,6 (15,6 17,4 20,4
e MHH. 16,64 90 21,10 24,49
MaKC. 10 8,8 11,3 13,13
m
MHH. 9,64 8,44 10,87 12,7
m' MHH. 7,7 6,75 8,7 10,2
MaKC. 15 17 19 22
s 14,73 16,73 18,67 21,67
MHH.
a P - mar pe3b6bI.
r--
F/la8a 4. Kpene:JICHble iJemOJlu
4. 1. 19. BS EN ISO 4034: 2001. WeCTJfrpSHH&le rSHKJf
JfCnOnHeHJffl 1 - KnSCC Jf3AenJffl C
Pa3MepLI
30°
15°
.,J
AonYCT Ma
3eHKOBKa s
B Ha"laJ1e
pe3b6bl
IIpHMep 0603HaqeHIDI IIIecTHrpaHHO:H ra:HKH C pa3MepOM pe3b6bI d = MI2 II
KJIaCCOM rrpOCqHOCTH 5:
illecTHrpaHHaJi raHKa ISO 4034 - MI2 - 5.
BS EN ISO 4034: 2001. Ta6JI. 1. CTaH,n;apTHbIe pa3MepbI. Pa3MepbI B MM
Pa3Mep pe3hohl, d M5 M6 M8 MIO MI2 MI6 M20
pa 0,8 1 1,25 1,5 1,75 2 2,5
d w MHH. 6,7 8,7 11,5 14,5 16,5 22 27,7
e MHH. 8,63 10,89 14,20 17,59 19,15 26,17 32,95
MaKC. 5,6 6,1 7,9 95 12,2 15,9 19
m 4,6 6,4 16,9
MHH. 4,4 8 10,4 14,1
m' MHH. 3,5 3,7 5,1 6,4 8,3 11,3 13,5
s HOM. = MaKC. 8 10 13 16 18 24 30
MHH. 7,64 9,64 12,57 15,57 17,57 23,16 29, 16
Pa3Mep pe3how, d M24 M30 M36 M42 M48 M56 M64
pa 3 3,5 4 4,5 5 5,5 6
d w MHH. 33,3 42,8 51,1 60 69,5 78,7 88,2
e MHH. 39,55 50,85 60,79 72,02 82,6 93,56 104,86
MaKC. 22,3 26,4 31,5 34,9 38,9 45,9 52,4
m 36,4 49,4
MHH. 20,2 24,3 28 32,4 43,4
m' MHH. 16,2 19,5 22,4 25,9 29,1 34,7 39,5
HOM. = MaKC. 36 46 55 65 75 85 95
s 35 45 53,8 63,1 73,1 82,8 92,8
MHH.
a p - mar pe3b6bI.
4. 1. BUHm08ble 1(;pene:JICHble U3Oe.nUR
BS EN ISO 4034: 2001. Ta6JI. 2. CneI(HaJIbHbIe pa3MepbI. Pa3MepbI B MM
Pa3Mep pe3hOhl, d MI4 MI8 M22 M27 M33 M39 M45 M52 M60
pa 2 2,5 2,5 3 3J 4 4,5 5 5,5
d w MHH. 19,2 24,9 31,4 38 46,6 55,9 64,7 74,7 83,4
e MHH. 22,78 29,56 37,29 45,7 55,37 66,44 76,95 88,25 99,21
MaKC. 13,9 16,9 20,2 24,7 29,5 34,3 36,9 42,9 48,9
m 12,1 15,1 18,1 22,6 27,4 31,8 34,4 40,4 46,4
MHH.
m' MHH. 9,7 12,1 14,5 18,1 21,9 25,4 27,5 32,3 37,1
s HOM. = MaKC. 21 27 34 41 50 60 70 80 90
MHH. 20,16 26,16 33 40 49 58,8 68,1 78,1 87,8
a P - mar pe3b6bI.
4.1.20. BS EN ISO 4035: 2001. WeCTJfrpaHH&le HJf3KJfe
raHKJf (c cpnaHqeM) - lUJaCC&1 Jf3AenJffl A Jf B
Pa3MepLi
ai
...
fa
.....
s
IIpHMep 0603HaqeHIDI HH3KO:H raHKH C <pJIaHueM C pa3MepOM pe3b6bI d = MI2
H KJIaCCOM rrpOqHOCTH 05: (-
illeCTHrpaHHaJI HH3KaJl raHKa ISO 4035 - MI2 - 00.5
BS EN ISO 4035: 2001. Ta6JI. 1. CTaH,l(apTHbIe pa3MepbI. Pa3MepbI B MM
P83Mep pe3hohl, d MI,6 M2 M2,5 M3 M4 M5 M6 M8 MIO MI2
pa 0,35 0.4 0,45 0,5 0,7 0.8 1 1,25 1,5 1,75
d a MHH. 1,6 2 2,3 3 4 5 6 8 10 12
1,84 2,3 2,9 3,45 4,6 5,75 6,75 8,75 10,8 13
MaKC.
d w MHH. 2,4 3,1 4,1 4.6 5,9 6,9 8,9 11,6 14,6 16,6
e MHH. 3,41 4,32 5,45 6,01 7,66 8,79 11,05 14,38 17,77 20,03
MaKC. 1 1,2 1,6 1,8 2,2 2,7 3,2 4 5 6
m 0,75 0,95 1,35 1,55 1,95 2,45 2,9 3,7 4,7 5,7
MHH.
m' MHH. 0,6 0,8 1,1 1,2 1,6 2 2,3 3 3,8 4,6
HOM. = MaKC. 3,2 4 5 5,5 7 8 10 13 16 18
s 3,02 3,82 4,82 5,32 6,78 7,78 9,78 12,73 15,73 17,73
MHH.
F/la8a 4. Kpene:JICHble OemOJlu
O"OH"taHue
Pa3Mep pe3hohl, d MI6 M20 M24 M30 M36 M42 M48 M56 M64
pa 2 2,5 3 3,5 4 4,5 5 5,5 6
d a MHH. 16 20 24 30 36 42 48 56 64
17,3 21,6 25,9 32,4 38,9 45,4 51,8 60,5 69,1
MaKC.
d w MHH. 22,5 27,7 33,2 42,8 51,1 60 69,5 78,7 88,2
e MHH. 26,75 32,95 39,55 50,85 60,79 71,3 82,6 93,56 104,86
MaKC. 8 10 12 15 18 21 24 28 32
m 7,42 9,10 10,9 13,9 16,9 19,7 22,7 26,7 30,4
MHH.
m' MHH. 5,9 7,3 8,7 11,1 13,5 15,8 18,2 21,4 24,3
HOM. = MaKC. 24 30 36 46 55 65 75 85 95
s MHH. 23,67 29, 16 35 45 53,8 63,1 73,1 82,8 92,8
a p - mar pe3b6bI.
BS EN ISO 4035: 2001. Ta6JI. 2. CneI(HaJIbHbIe pa3MepbI. Pa3MepbI B MM
Pa3Mep pe3how, d M3,5 MI4 MI8 M22 M27 M33 M39 M45 M52 M60
pa 0,6 2 2,5 2,5 3 3,5 4 4,5 5 5,5
d a MHH. 3,5 14 18 22 27 33 39 45 52 60
4 15,1 19,5 23,7 29,1 35,6 42,1 48,6 56,2 64,8
MaKC.
d w MHH. 5,1 19,6 24,9 31,4 38 46,6 55,9 64,7 74,2 83,4
e MHH. 6,58 23,35 29,56 37,29 45,2 55,37 66,44 76,95 88,25 99,21
MaKC. 2 7 9 11 13,5 16,5 19,5 22,5 26 30
m 1,75 6,42 8,42 9,9 12,4 15,4 18,2 21,2 24,7 28,7
MHH.
m' MHH. 1,4 5,1 6,7 7,9 9,9 12,3 14,6 17 19,8 23
HOM. = MaKC. 6 21 27 34 41 50 60 70 80 90
S MHH. 5,82 20,67 26,16 33 40 49 58,8 68,1 78,1 87,8
a p - mar pe3b6bI.
4.1.21. BS EN ISO 4036: 2001. WeCTJfrpaHH&le HJf3KJfe
raHKJf (6e3 cpnaHqa) - IUJBCC Jf3AenJffl B
Pa3MepLI
Pa3Mepbl B M J1J1 MeTpax
1:)
m
s
IIpHMep 0603HaQeHIDI IIIecTHrpaHHoH
HH3KOH raHKH C MeTPHQeCKOH pe3b6oH
d = M6, H3rOTOBJIeHHOH H3 CTaJIH C TBep-
,nOCTblO IIO BHKKepcy MHH. 110 HV (CT.):
lliecmrpaHHaJI raiiKa ISO 4036 - M6 CT.
4.1. BUHmo6ble "peneJICHble U30eJlUR 169
BS EN ISO 4036: 2001. Ta6JI. 1.
HOMHH8JIh1lhli ,lUIaMeTp Pa3Mep raiKH llJIOIQa,ZU. KOJlhneBOH TOpu;eBOH onopHOH nOBepxeOCTH/
pe3hO'" (MM) no KJII01f (MM) HOMHH8JIhHaJI DJI0m;a,zu. Ce1felllDl no pe3hoe *
5 8 1,08
6 10 1,44
8 13 1,23
15 0,90
10 16 1,30
17 1,73
* BbIQHCJIeHHH OCHOBaHbI Ha 3HaQeHHHX ,L(JIH oTBepcTHH C rapaHTHpOBaHHbIM 3a30pOM B
COOTBeTCTBHH C ISO 273 (HcnpaBJIeHHbIM), cpe,n;HHH) cepHH.
BS EN ISO 4036: 2001. Ta6JI. 2.
Pa3Mep Pe3hOW, d MIO
pa 1,5
e MHH. 16,46 18,73
MaKC. 5 5
m 4,52 4,52
MHH.
MaKC. 15 17
s MHH. 14,57 16,57
a p - mar pe3b6bI.
4. 1.22. BS EN ISO 8765:r.. OO 1. 50RThI C WeCTlffrpaHHOH
ronosKoif C MeTp...;:ecKoif MenKoH pe3&6oif -
KnSCC&1 Jf3AenJffl A Jf B
Pa3MepLI
llpUMe"taHue. CHMBOJIbI H 0603HaqeHIDI pa3MepOB .naHbI B COOTBeTCTBHH C
ISO 225.
KOHeu. AOJ1)1(eH Pa3Mep B M J1J1 MeTpax X MaKC MaJ1bHOe
6blTb C ct>acKot1 YTOJ1w.eH e
(CM. ISO 4753) k' I, nOA rOJ10BKot1
X c B HTa
-- Q)
I. U(1) S
Ig (b)
k I
(1) HerrOJIHa.H pe3b6a (c6er pe3b6bI) u 2P.
F/la8a 4. Kpene:JICHble OemOJlu
:a
Q)
M
\0 \0 \0 V)
x 00 V) V) 00
N w.. 0 w.. ow.. \Ow.. V) w..
I I V) ow.. I w.. I w.. I I I I N I
\C \0 00 0\ 0\
\0 00 0 N 0\
\0 \0 \0 V)
x V) V) 00
\C \0 N \Ow.. V) N V) w.. w.. V) w..
tn I I w.. \0 V) I w.. I I w.. I I V) I w.. N 00 I
0 V) 00
V) 0\ N 00
tf') 00 V) 00 N
X 00 \Ow.. w.. \Ow.. V) w.. \Ow.. ,....c
QO 00 0 0 V) ...
I 0 N ow.. N I w.. I I N I I w.. I ow.. I
0\ 0\ 0 M
V) \0 00 N N ['...
tf') 00 V) 00 N
X 0\ \Ow.. ,....c
N \0 N w.. \0 V) w.. N V) ...
I 0\ 0 ow.. V) I w.. I I 00 N I I w.. I w.. \0 I M
0\ V) \0
V) N N \0
tf') 0\ 00 N \0
x 00 V) 00
\C N 00 0\ \0 w.. w.. Ow.. w.. V) ...
tf') I 00 0\ ow.. ow.. I V) I w.. I ow.. \0 N I I I V) I M
N N V)
V) \0 N N N t/")
N 00 V) V) 00 N
X ... w.. 00
= \0 N V) N 00 0 w.. 00 N w.. \0 t/")
tf') \0 00 ... w.. I 0\ I I w.. \0 00 I I w.. w.. I N I
0 0 N 0 00 0\
N V)
N 00 V) 00 V) V) V) V) V) V) \0 00
x w.. 00
0 N 00 \0 \Ow.. N 0\ V) V) N \0 N 00 \0 t/")
w.. ow.. \0 w.. w.. w.. w.. w.. w.. w.. ow.. ow.. w..
V) \0 0 N 0\ 0\ w.. w.. V) 0 V) M
N N N V)
tn V) V)
00 0\ V) V) V) \0
...-4 w.. V) 00
x \0 N N 00 0 \Ow.. w.. w.. V) w.. N 00 \Ow.. V) 00 0 \Ow.. ......-I
= V) I w.. w.. N N w.. w.. N w.. w.. ow.. ...
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171
u
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00 0
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X / V) \0 t"-- 0\ ....... N
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ff') --- i :I: 1-4 M M
:S:t:J:: \0 \0 \0 \0 \0 0 N
u M V) t"-- 0\ ....... .......
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F/la8a 4. Kpene:JICHble oemOJlu
::s
:t:
:t:
C
U t"-- t"-- t"-- t"-- t"-- t"-- t"-- t"-- t"-- t"-- t"-- t"-- t"--
X --- = 0 N \0 00 0 N \0 00 0 N
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t:C
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CIS
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= 'I') I"- 0 N... ... N N 00 ... N 0
'..c I I ... t-4 \0 \0 I I I ... I I I"- 00 I ... N 0\ I I"-
t-4 0 0\ 0\ t-4 \0
'I') 00 0\ N 00
\0 'I') 'I')
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N ... N N ... N 0 ... ... I"- \0 0 ...
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t-4 t-4 0 t-4 00 N t-4
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ff') 00 'I') 00 N t-4
X \0... 1"-... t-4
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I 0 t-4 ... t-4 00 I I I 00 M I I ... ... I ... ... l"- I 00
t-4 t-4 0 \0 \0 I"- 00 0\ t-4 \0
l"- N N t-4
ff') 00 \0 00 N t-4
X ... 00
0'\ 0 0\ 00 'I') 'I') ... N 0 ...
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t-4 t-4
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0 t-4 0\ t-4 t-4 \0 \0 t-4
I .D 1 0 1 := 0 :i := 0 := 0 := := 0 :=
:= 0 := := := := :=
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x 00 0\
N ...
In
0\ \0
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M . 0 0 0 0 t---
0\0
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N :s:"'o N N N N 0 N N
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o 0 .......
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0 ....... N M V) \0 00 0 N
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V) V) V) V) V) V) V) V) V) V) V)
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V) V) V) V) V) V) V) V) V) V) V)
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KnSCC&1 Jf3AenJffl A Jf B
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c
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d a 32,4
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d w MHH. 11,63 14,63 16,63 22,49 27,7 33,25 42,75 51,11
e MHH. 14,38 17,77 20,03 26,75 32,95 39,55 50,85 60,79
MaKC. 7,5 9,3 12 16,4 20,3 23,9 28,6 34,7
m
MHH. 7,14 8,94 11,57 15,7 19 22,6 27,3 33,1
m' MHH. 5,71 7,15 9,26 12,56 15,2 18,08 21,84 26,48
m" MHH. 5 6,26 8,1 10,99 13,3 15,82 19,11 23,17
HOM. = MaKC. 13 16 18 24 30 36 46 55
s 12,73 15,73 17,73 23,67 29,16 35 45 53,8
MHH.
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BS EN ISO 8674: 2001. TaoJI. 2. CneI(HaJIbHble pe3b6bI. Pa3MepbI B MM
P83Mep pe3how, dxP MI0xl,25 M12xl,25 M14x 1,5 M18xl,5 M20x2 M22xl,5 M27x2 M33x2
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c
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MHH. 10 12 14 18 20 22 27 33
d a 21,6 35,6
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d w MHH. 14,63 16,63 19,64 24,85 27,7 31,35 38 46,55
e MHH. 17,77 20,03 23,36 29,56 32,95 37,29 45,2 55,37
MaKC. 9,3 12 14,1 17,6 20,3 21,8 26,7 32,5
m
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m' MHH. 7,15 9,26 10,72 13,52 15,2 16,4 20,32 24,72
m" MHH. 6,26 8,1 9,38 11,83 13,3 14,35 17,78 21,63
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s
MHH. 15,73 17,73 20,67 26,16 29,16 33 40 49
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PHC. 2. Pa3MepbI KOpOHqaTbIX raeK
4.1. BUHmo8ble K.pene:JICHble U30eJlUR
BS 7764:1994. TaoJI. 1. Pa3MepHocTH meCTHrpaHHbIX rrpope3HbIX H KOpOHqaTbIX raeK.
Pa3MepbI B MM
d M4 M5 M6 M8 MIO MI2 (MI4) MI6 (MI8) M20 (M22) M24
p 0,7 0,8 1 1,25 1,5 1,75 2 2 2,5 2,5 2,5 3
c MaKC. 0,4 0,5 0,5 0,6 0,6 0,6 0,6 0,8 0,8 0,8 0,8 0,8
d a MHH. 4 5 6 8 10 12 14 16 18 20 22 24
MaKC. 4,6 5,75 6,75 8,75 10,8 13 15,1 17,3 19,5 21,6 23,7 25,9
de MaKC. - - - - - l?J 19 22 25 28 30 34
( 24,16 27, 16 29,16
MHH. - - - - - 15,57 18,48 21 ,48 33
d w MHH. 5,9 6,9 8,9 11,6 14,6 16,6 19,6 22,5 24,8 27,7 31,4 33,2
e MHH. 7,66 8,79 11,05 14,38 17,77 20,03 23,36 26,75 29,58 32,95 37,29 39,55
MaKC. 5 6 7,5 9,5 12 15 16 19 21 22 26 27
m 4,7 5,7 7,14 9,14 11,57. 14,57 15,57 18,48 21,48 21,48 25,48 25,48
MHH.
m' MHH. 2,32 3,52 3,92 5,15 6,43 8,3 9,68 11,28 12,08 13,52 14,48 16,16
MHH. 1,2 1,4 2 2,5 2,8 3,5 3,5 4,5 4,5 4,5 5,5 5,5
n 1,45 1,65 2,25 2,75 3,05 3,8 3,8 4,8 4,8 4,8 5,8 5,8
MaKC.
MaKC. 7 8 10 13 16 18 21 24 27 30 34 36
s 6,78 7,78 9,78 12,73 15,73 17,73 20,67 23,67 26,16 29, 16 33 35
MHH.
MaKC. 2,9 4 5 6,5 8 10 11 13 15 16 18 19
w 3,2 3,7 4,7 6,14 7,64 9,64 10,57 12,59 14,57 15,57 17,57 18,48
MHH.
KJIacc H3,n;eJIHH A KJIacc H3,n;eJIHH B
CMO'rpH B Ta6JI. 2 CMO'rpH B Ta6JI. 2
d (M27) M30 (M33) M36 (M39) 42 (M45) M48 (M52) M56 (M60) M64
TJ 3 3,5 3,5 4 4 -4,5 4,5 5 5 5,5 5,5 6
c MaKC. 0,8 0,8 0,8 0,8 1 1 1 1 1 1 1 1
d a MHH. 27 30 33 36 39 42 45 48 52 56 60 64
MaKC. 29,1 32,4 35,6 38,9 42,1 45,4 48,6 51,8 56,2 60,5 64,8 69,1
de MaKC. 38 42 46 50 55 58 62 65 70 75 80 85
MHH. 37 41 45 49 53,8 56,8 60,8 63,8 68,8 73,8 78,8 83,8
d w MHH. 38 42,7 46,6 51,1 55,9 59,9 64,7 69,4 74,2 78,7 83,4 88,2
e MHH. 45,2 50,85 55,37 60,79 66,44 71,3/ ,.16,95 82,6 88,25 93,56 99,21 104,86
MaKC. 30 33 35 38 40 46 48 50 54 57 63 66
m .
MHH. 29,48 32,38 34,38 37,38 39,38 45,38 47,38 49,38 53,26 56,26 62,26 65,26
m' MHH. 18 19,44 21,92 23,52 25,44 25,92 27,52 29, 12 32,32 34,72 37,12 39,3
MIIH. 5,5 7 7 7 7 9 9 9 9 9 11 11
n 5,8 7,36 7,36 7,36 7,36 9,36 9,36 9,36 9,36 9,36 11,43 11,43
MaKC.
MaKC. 41 46 50 55 60 65 70 75 80 85 90 95
s 40 45 49 53,8 58,8 63,1 68,1 73,1 78,1 82,8 87,8 92,8
MHH.
MaKC. 22 24 26 29 31 34 36 38 42 45 48 51
w 21 ,48 23,48 25,48 28,48 30,38 33,38 35,38 37,38 41,38 44,38 47,38 50,26
MHH.
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llpUMe"taHue.
1. CneHaJIbHble pa3MepbI rrOKa3aHbI B cKo6Kax.
(2\KopOHqaTbIe raHKH HaqHHaIOTCH C pa3Mepa M12.
\ 3. KOpOHqaTbIe raHKH 60JIbme M39 HMeIOT BoceMb rpaHeH.
F/la8a 4. Kpene:JICHble oemOJlu
BS 7764:1994 TaoJI. 2. XapmcrepHCTHKH mecrnrpaHHbIX npOpe3HbIX H KOpO aThIX raeK
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TIOJIe ,n;onycKa pe3b6bI CooTBeTCTBYI<>IUee KJIaccy 6H B BS 3643: qacTb 1:1981 H BS 3643:
qacTb 2: 1981
npOqHOCTHble CooTBeTCTBYI<>IUHe CooTBeTCTBYI<>IUHe CooTBeTCTBYI<>I.U;He
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TepHaJIa 6, 8 HJIH 10 B MaTepHaJIa A2- 70
BS EN 20898-2: 1992 B BS 6105: 1981
B03MO)I{Hble OTKJIOHeHHH B COOTBeTCTBHH C KJIaCCOM H3,n;eJIHH A B BS 6322: qaCTh 1: 1982
pa3MepOB H <l>opMbI ,lI)UI pa3MepOB pe3b6bI M16
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4. 1.29. BS EN ISO 898-1: 1999. MSpKJfPOSKS
38am
3HaKH MapKHpOBKH npHBe,n;eHbI B BS EN ISO 898-1: 1999. Ta6JI. 1.
MapmpOBKa
J
\
bOAmbl U 8UHmbi c lUecmuzpaHHoii ZOA08KOii
BOJITbI H BHHTbI C IllecTHrpaHHoH rOJIOBKOH ,n;OJI)I{HbI MapKHpOBaTbCH 3HaKaMH
KJIacca npOqHOCTH, onHcaHHbIMH B nYHKTe 3.
f' """'" ,,-- ---... ""'"
8.8
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PHC. 1. npHMepbI MapKHpOBKH 60JITOB H BHHTOB
C mecTHrpaHHoH rOJIOBKOH
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apKHpOBKa 06H3aTeJIbHa
Bcex KJIaCCOB npOqHOCTH; npe,n;noq-
THTeJIbHO HaHOCHTb yr.rry6JIeHHbIe
HJIH BbInyKJIbIe 3HaKH MapKHpoBKH
Ha TOpueByID nOBepXHocTb rOJIOBKH
HJIH yr.rry6JIeHHbIe - Ha 60KOByID
lIoBepXHocTb rOJIOBKH (CM. pHC. 1).
apKHpoBKa TPe6yeTcH
60JITOB H BHHTOB C IllecTHrpaHHoH
rOJIOBKOH C HOMHHaJIbHbIM ,n;Ha-
MeTpOM d 5 MM, TaM, r,n;e <popMa
H3,n;eJIIDI 3TO n03BOillIeT, npe,n;noq-
THTeJIbHO Ha rOJIOBKe.
BUHmbl c lUecmUZpaHHbLM YZJly6AeHUeM 8 ZOA08Ke
BHHTbI C IlleCTHrpaHHbIM yr.rry6JIeHHeM B rOJIOBKe ,n;OJI)I{HbI MapKHpOBaTbCH 3Ha-
KaMH KJIaCca npOqHOCTH, onHcaHHbIMH B rryHKTe 3.
MapKHpoBKa 06H3aTeJIbHa ,lJ;IDI KJIaCCOB npOqHOCTH, paBHbIX HJIH 60JIbIllHX 8.8;
npe,nnOQTHTeJIbHO HaHOCHTb yrJIy6JIeHHbIe 3HaKH MapKHpOBKH Ha 60KOByID no-
BepXHOCTb rOJIOBKH HJIH yr.rry6JIeHHbIe HJIH BbInyKJIbIe - Ha TopueByID nOBepXHOCTb
rOJIOBKH (CM. pHC. 2).
I I i I I
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12.9
PHC. 2. llpHMepbI MapKHpOBKH BHHTOB C lUec-
THrpaHHbIM yrJIy6JIeHHeM B rOJIOBKe
apKHpOBKa TPe6yeTcH ,lLIDI
BHHTOB C IllecTHrpaHHbIM yr.rry6JIe-
HHeM B rOJIOBKe C HOMHHaJIbHbIM
,n;HaMeTPoM d 5 MM, r,n;e <popMa H3-
\
,n;eJIIDI 3TO n03BOillIeT, npe,n;nOqTH-
TeJIbHO Ha rOJIOBKe.
,l:LJrn MaJIeHbKHX BHHTOB C Illec-
THrpaHHbIM OTBepCTHeM B rOJIOBKe B
KaqeCTBe aJIbTepHaTHBbI ,n;orrycKaeTcH
HCnOJIb30BaHHe UH<pep6JIaTHOH Map-
KHpOBKH, peKoMeH,l(yeMoH ,lLIDI raeK
B ISO 898- 2.
F/la8a 4. Kpene:JICHble oemOJlu
BS EN ISO 898-1:1999. Ta6J1. 1. MapKHpOBOqHbIe 3HaKH
Krracc npOqHOCTH 3.6 4.6 4.8 5.6 5.8 6.8 8.8 9.8 10.9 12.9
MapKHpOBOqHbIH 3HaK a,b 3.6 4.6 4.8 5.6 5.8 6.8 8.8 9.8 10.9 12.9
a TOqKa B CHMBOJIe MapKHpOBKH MoxeT 6bITb onymeHa.
b Kor,n;a ,lI)UI KJIacca npOqHOCTH 10.9 (CMO'rpH BS EN ISO 898-1: 1999. Ta6JIHI(a 2) HC-
nOJIb3yK>TCH HH3KoyrJIepo,n;HCTbIe MapTeHCHTHbIe CTaJIH, 3HaK 10.9 ,n;OJDKeH 6bITb no,n;qepK-
JIyT: .
BS EN ISO 898-1: 1999. Ta6J1. 2. H,n;eHTH<pHKaI(HOHHbIe 3HaKH )];JIH illnHJIeK
Krracc npOqHOCTH 8.8 9.8 10.9 12.9
H,neHTH<pHKaI(HOHHaH MeTKa 0 + 0
mnUllbKU
IllnHJIbKH ,lI;OJI)I{HbI MapKHpOBaTbCR 3HaKaMH KJIacca npOqHOCTH, onHcaHHbIMH
B nyHKTe 3.
MapKHpOBKa 06R3aTeJIbHa ,lI;IDI KJIaCCOB npOqHO-
CTH, paBHbIX HJIH 60JIbIllHX 8.8; npe,ll;nOqTHTeJIbHO
HaHOCHTb yr.rry6JIeHHbIe 3HaKH MapKHpOBKH Ha TOp-
ue C pe3b60H (CM. pHC. 3). Y IllnHJIeK C HenO,ll;BIDK-
HOH nOC8)];KOH MapKHpOBKa ,lI;OJDKHa pacnOJIaraTbCg
Ha CTIDKHOM (raeqHOM) KOHue.
MapKHpOBKa TPe6yeTcR ,lI;IDI IllnHJIeK C HOMH-
HaJIbHbIM ,lI;HaMeTPOM paBHbIM HJIH 60JIbIllHM 5 MM.
CHMBOJIbI BS EN ISO 898-1: 1999. Ta6JIHua 2
Pac. 3. MapKHpOBKa illnHJIbKH ,lI;onYCTHMbI ,lI;IDI H,lJ;eHTH<pHKaUHH B KaqeCTBe aJIbTep-
HaTHBbI.
J(pyzue munbl 60/lm08 U 8UHm08
CHCTeMa MapKHpOBKH, aHaJIOrHqHa.H onHcaHHOH B pa3,l1;eJIaX «BOJITbI H BHHTbI C
IlleCTHrpaHHOH rOJIOBKOH» H «BHHTbI C IlleCTHrpaHHbIM yr.rry6JIeHHeeM B rOJIOBKe»,
,lI;OJDKHa HCnOJIb30BaTbCR ,lI;IDI ,lI;pyrHX THnOB 60JITOB H BHHTOB KJIaCCOB npOqHOCTH
4.6, 5.6 H Bcex KJIaCCOB, paBHbIX HJIH 60JIbIllHX 8.8, KaK onHcaHO B COOTBeTCTByro-
m;HX Me)l{J(YHapO,ll;HbIX CTaH)l;apTaX (ISO) HJIH ,lI;IDI CneUHaJIbHbIX KOMnOHeHTOB no
COrJIaCOBaHHIO Me)l{J(Y 3aHHTepeCOBaHHbIMH CTopOHaMH.
MapKHpoBKa JIeBOH pe3L6LI
BOJITbI H BHHTbI C JIeBOH pe3b60H ,lI;OJDKHbI MapKHpOBaTbCR CHMBOJIOM, nOKa3aH-
HbIM Ha pHC. 4, HaHeceHHbIM Ha TopueByIO nOBepXHOCTb rOJIOBKH HJIH KOHua.
MapKHpoBKa TPe6yeTcR ,lLIDI 60JITOB H BHHTOB C HOMHHaJIbHbIM ,lI;HaMeTPOM pe3b-
6bI d 5 MM.
,[{JIR 60JITOB H BHHTOB C IlleCTHrpaHHOH rOJIOBKOH ,lI;orrycKaeTC.H HCnOJIb30BaHHe
aJIbTepHaTHBHOH MapKHpOBKH JIeBOH pe3b6bI, KaK nOKa3aHO Ha pHC. 5.
4.1. BUHmo8ble Kpene:JICHble U30e.tlUR
k
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J
PHC. 4. MapKHpoBKa JIeBOH pe3b6bI Puc. 5. A.n:bTepHaTHBHaH MapKHpOBKa JIeBOH pe3b6bI:
S - illHpHHa Me)K)J;Y napaJIJIeJIbHbIMH rpaHHMH;.
k - BbICOTa rOJIOBKH
AJILTepHaTHBHaJiMapKHpOBKa
HaHeceHHe aJIbTepHaTHBHoH HJIH He06R3aTeJIbHOH ,lI;OrryCTHMOH MapKHpoBKH,
KaK 3a.HBJIeHO B pa3,l1;eJIaX «3HaKH», «MapKHpoBKa» H «0603HaqeHHe JIeBOH pe3b-
6bl», MoxeT 6bITb OCTaBJIeHO Ha YCMoTPeHHe H3rOTOBHTeillI.
ToprOBaJi (H,ZJ;eHTH4JHKaD;HJI) MapKHpOBKa
HaHeceHHe KJIeHMa (ToBapHoro 3HaKa H3foToBHTeillI) RBillIeTCR 06R3aTeJIbHbIM
,lUUI Bcex npo,[(yKToB, MapKHpoBaHHbIx KJIaCCOM npOqHOcTH.
4.1.30. BS EN 20898-2: 1994. MeXSHJflfeCKJfe CSOHCTSS
KAeneJICH&IX Jf3AenJfH: rs C YCTSHOSneHH&IMJf
'aHslfeHJfflMJf npo6HOH HS 3KJf - KpynHsfI pe3&6s
BS EN 20898-2:1994. Ta6J1. 1. MeXaHHqeCKHe CBOHCTBa
KJIacc np01JHOCTH
04 05
Pe3hoa
)= TBep ocTh T8ep OCTh )= TBep oCTh
e e
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Ii! Kepcy HV i! Kepcy HV Kepcy HV
S S
rI1 HC- rI1 HC- rI1 HC-
I COCTO- nOJl- I COCTO- nOJl- I COCTO- nOJl-
OT o = MHH. MaKC. JIHIIe He- = MHH. MaKe. JIHIIe He- = MHH. MaKe. JIHIIe He-
r! r! r! \
HHe HHe HUe
== == ==
- M4
M4 M7
M7 MI0 6e3 TOH- 353 3/0 b TOH- - - - - -
380 188 302 3/0 a KaH 500 272 KaH
M10 M16
M16 M39 510 117 302 6e3 1
3/0 a
F/la8a 4. Kpene:JICHble oemOJlu
llpoiJollJICeHUe
KJIacc np01JHOCTH
Pe3hoa 5 c 6
HanpJDKeHHe TBep oCTh no faiiKa HanpJDKeHHe TBep ocTh no faiiu
BHKKepcy HV BHKKepcy HV
OT npooHoii OT npooHoii
HarpY3KH Sp COCTO- HCnOJl- HarpY3KH Sp COCTO- HCnOJl-
OT o (H/MM2) MHH. MaKC. (H/MM2) MHH. MaKe.
JIHIIe HeHHe JIHIIe HeHHe
- M4 520 600
M4 M7 580 670
130 6e3 150 6e3
M7 MI0 590 302 3/0 a 1 680 302 3/0 a 1
MI0 M16 610 700
M16 M38 630 146 720 170
KJIacc npo1JHOCTH
Pe3hoa 8
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BHKKepcy HV BHKKepcy HV
OT npooHoii OT npooHoii
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OT o (H/MM2) MHH. MaKe. (H/MM2) MHH. MaKe.
JIHIIe HeHHe JIHIIe HeHHe
- M4 800 180
M4 M7 855 6e3
302 3/0 a - - - - -
M7 MI0 870 200 1
MI0 M16 880
M16 M38 920 233 353 3/0 b 990 180 302 6e3 2
3/0 a
KJIacc np01JHOCTH
Pe3hoa 9 10
HanpJDKeHHe TBep oCTh no faiiu HanpJDKeHHe T8ep OCTh no faHKa
BHKKepcy HV BHKKepcy HV
OT npooHoii OT npooHoii
Harp)'3KH Sp COCTO- HCnOJl- Harpy:JKH Sp COCTO- HcnWl-
OT (H/MM2) MaKe. (H/MM2) MHH. MaKe.
O MHH. JIHIIe HeHHe JIHIIe HeHHe
- M4 900 170 1040
M4 M7 915 1040
M7 MI0 940 302 6e3 2 1040 272 353 3/0 b 1
188 3/0 a
MI0 M16 950 1050
M16 M38 920 1060
4.1. BUHmo6ble "peneJICHble U30eJlUR 20 I
OKOHltaHUe
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Pe3b6a 12
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OT DpoOHoii OT Jt'6HOi
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JlHHe HeHHe BIllIe HeHHe
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M4 M7 1140 1150
295 353 3/0 b 1
M7 MI0 1140 1160 272 353 3/0 b 2
M10 M16 1170 1 190
M16 M38 - - - - - 1200
a Be3 30 - 6e3 3aKaJIKH H oTnycKa.
b 30 - 3aKaJIeHHble H oTnyrn;eHHble.
C MaKCHMaJIbHaSl TBep,n;OCTb 60JITOB KJlaCCOB npOQHOCTH 5.6 H 5.8 6y,neT H3MeHeHa Ha
3HaQeHHe 220 HV B CJIe,nyroIUeH pe,naKI(HH ISO 896-1: 1988. 3TO - MaKCHMaJIbHCUI TBep-
,l(OCTb 60JITa B 06JIaCTSlX 3aI(enJIeHHH pe3b6bI, Tor,na KaK TOJIbKO KOHIJ.bI pe3b6bI HJIH rOJIOBKa
MOryr HMeTb MaKCHMaJIbHyro TBep,nOCTb 250 HV. n03TOMY BeJIHQHHbI HanpH)l{eHHH OT np06-
HOB HarpY3KH OCHOBaHbI Ha MaKCHMaJIbHOH TBep,nOCTH 60JITa 220HV.
llpUMe'taHUe. "\
MHHHMaJIbHble 3Ha IJ:jlSI TBep,nOCTH YCTaHOBJIeHbI TOJIbKO J:wSl TepMHqeCKH 06pa6oTaH-
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):(Jrn Bcex OCTaJIbHbIX raeK MHHHMaJIbHCUI TBep,nOCTb He 06S13aTeJIbHa, a npHBe,neHa npOCTO
,l(IDI cnpaBKH.
):Lrrn raeK 6e3 3aKaJIKH H OTnYCKa, BbI,LJ;epXaBllIHX HCITbITaHHe np06HOH HarpY3KOH, MH-
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BeJIIf1IHHLI npo6HOH HarpY3KH
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\
BeJIMqMHbI lIp06HO:H HarpY3KH lIpMBe,ll;eHbI B BS EN 20898-2: 1994. Ta6JI. 2.
HOMMHaJIbHa5I IIJIOrn;anb CeqeHH.H lIO pe3b6e As BbJt:lMClliIeTCH lIO <popMyJIe:
2
A = 1t ( d 2 + d 3 )
s 4 2 '
f,ne d 2 - HOMMHaJIbHbI:H Cpe,ll;HM:H ,lI;MaMeTp HapyxHO:H pe3b6bI (CMOTpM ISO 724);
d 3 - BHYTpeHHM:H ,lI;MaMeTP HapyxHO:H pe3b6bI lIO ,lI;HY BlIanMHbI:
H
d 3 = d l - 6'
f,ne d 1 - BHYTpeHHM:H ,lI;MaMeTP HapyxHO:H pe3b6bI; H - BbICOTa MCXO,ll;HOrO TPe-
yrOJIbHMKa pe3b6bI.
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4.1. BUHmo6ble "peneJICHble U30eJlUR 203
BS EN 20898-2:1994. TaoJl. 3. 3HaKH MapKHpOBKH )].JHI raeK C KJIaCCaMH npOqHOCTH
B COOTBeTCTBHH C BS EN 20898-2 nYHKT 3.1
KJIacc npo1fHOCTH
= JII060e 0603HaqeHHe CHMBOJIa
==
!
&1 i H.rrH 3HaK MapKHpOBKH, RJIH KO,nO-
f c=.. BbIH 3HaK (I( H <pep6JIaTHCUI CHCTeMa
I MapKHpoBKH)
4
4
5
5
6
6
8
8
KJIacc Dp01fHOCTH
= JII060e 0603HaQeHHe CHMBOJIa
==
!
&1 i H.rrH 3HaK MapKHpOBKH, HJIH KO,nO-
c=.. BbIH 3HaK (QH<pep6JIaTHCUI CHCTeMa
I MapKHpoBKH)
9
9
10
10
12 8
12
a TOQeqHaH MapKHpOBKa He MO>KeT 6bITb 3aMeHeHa MapKHpOBKOH H3rOTOBHTeJISI.
BS EN 20898-2:1994 TaoJl. 4. 3HaKH MapKHpOBKH )J)ISI raeK C KJIaCCaMH npOQHOCTH
B COOTBeTCTBHH C BS EN 20898-2 nyHKT 3.2
KJIacc Dp01fHOCTH
04
05
)
MapKHpOBKa
MapmpOBKa JIeBOH pe3LoLI
faMKH C JIeBOM pe3b60M ,nOJDKHbI MapKHpoBaTbcH, KaK lIOKa3aHO Ha pMC. 1, yr-
JIy6JIeHHbIM 3HaKOM Ha OlIOpHOH IIOBepXHOCTM raMKH.
MapKHpoBKa TPe6yeTC.H ,lLJUI raeK C pe3b60M M5. /
,lJ;orrycKaeTcH TaIOKe MClIOJIb30BaHMe aJIbTepHaTMBHoM MapKHpOBKH JIeBOM pe3b-
6bI, KaK lIOKa3aHO Ha pRC. 2.
CI)
1\
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pe3b6bI. s - paCCTOSlHHe Me:>K.LJ:Y rrapaJIJIeJIb-
HbIMH rpaHSlMH
F/la8a 4. Kpene:JICHble oemOJlu
AHLTepHaTHBHaJi MapKHpoBKa
HaHeceHMe aJIbTepHaTMBHoH IDIM He06H3aTeJIbHOH ,nOrryCTMMOH MapKHpoBKH,
KaK 3aHBJIeHO B pa3,neJIaX «3HaKH», «MapKHpOBKa» M «0603HaqeHHe JIeBOH pe3b-
6bI», MoxeT 6bITb OCTaBJIeHO Ha YCMoTPeHMe M3rOTOBMTelliI.
ToprOBLIe (If)J;eHTH HKanaoHHLIe) 0603Ha'leHIUI
HaHeceHMe KJIeHMa (ToBapHoro 3HaKa M3roToBMTelliI) HBlliIeTCH 06H3aTeJIbHbIM
,LUISI Bcex lIpO,nyJ(TOB, MapKHpOBaHHbIX KJIaCCOM lIPOqHOCTM, npM HaJIWIMM TeXHlflIe-
CKOH B03MO)I(HOCTH. YnaKOBKH, TeM He MeHee, ,nOJDKHbI 6bITb npOMapKHpOBaHbI B
JII060M CJIyqae.
4.1.31. BS EN ISO 898-6: 1996. MeXSHJflfeCKJfe CSOHCTsa
KpeneJICH&IX Jf3AenJfH: rSHKJf C YCTSHOSneHH&IMJf
3HSlfeHJfflMJf npo6HoH HsrPY3KJf - MenKSfI pe3&6a
BS EN ISO 898-6:1996. TaoJl. 1. CHCTeMa 0603HaQeHHH ,l(JISI raeK C HOMHHaJIbHOH
BbICOTOH 0,8 d
faiKII
KJIacc CODpSlfaeMhIH 60JIT
Dp01fHOCTH HCDOJIHeHHe 1 HCDOJIHeHHe 2
raiiKH
KJIacc 1Ip01JH0CI1I ,lI;HaD83oH HOMHHaJIbHhIX aMeTp08 pe3bOhl (MM)
5 3.6, 4.6, 4.8 d 39 d39 -
5.6, 5.8
6 6.8 d 39 d 39 -
8 8.8 d 39 d 39 d 16
10 10.9 d 39 d 16 d 39
12 12.9 d 16 - d 16
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KH 60JIee HH3Koro KJIacca npOqHOcTH. TaKaH 3aMeHa peKOMeH,nyeTcH ,lLJUI coe,nMHe-
HMH 60JIT/raHKa, HalIpIDKeHMe B KOTOpbIX 6y,neT BbIme, qeM H:IDKHMH npe,neJI TeKY-
qeCTH HJIM HanpIDKeHMe 60JITa OT lIp06HOH HarpY3KM.
ECJIM xe coe,nMHeHMe 6y,neT 3aTHHyro BbIme lIp06HOH HarpY3KH 60JITa, TO KOH-
CTpyKUMH raHKH ,nOJDKHa 6bITb paCCqMTaHa TaK, qT06bI B pe3YJIbTaTe nepe3aTIDKKH
06eClIeqMTb no KpaHHeH Mepe 10 % nOBpe)l(,[{eHMH no CTep)I(H1O 60JITa ,lLJUI lIpe,ay-
npe)l(,[{eHHSI nOTpe6MTeJISI 0 HenpaBHJIbHOH YCTaHOBKe Kpene)I(HOro coe,nMHeHMSI.
IIpuMettaHue.
BOJIee nO,lI,p06HYIO MH<p0pMaUMIO 0 ,norrycKaeMbIX HarpY3Kax B pe3b60BbIX coe-
,nMHeHMSlX, a TaIOKe 0 BapMaHTax MClIOJIHeHIDI raeK CMOTpM B ISO 898-2: 1992,
TIpHJIOXeHMe A.
4.1. BUHmo8ble ICpene:JICHble U30e.tlUJI
faiiKH C HOMHHaJILHOH BLICoroH O,5d H < O,8d (a4KIJeKTHBHaJI AJIHHa pe3LOLI O,4d
H <O,6d)
faHKH C HOMMPIaJIbHOH BbICOTOH O,5d M <O,8d (3<p<peKTMBHaH ,[(JIMHa pe3b-
6bI O,4d M <O,6d) 0603HaqalOTCH KOM6MHaUMeH ,nBYX UM<PP: BTopaH YKa3bIBaeT
HOMMHaJIbHOe HalIp.HXeHMe OT lIp06HOH HarpY3KM B 3aKaJIeHHOH MClIbITaTeJIbHOM
onpaBKe, B TO BpeMH KaK lIepBaH YKa3bIBaeT Ha TO, qTO HarpY30QHaH ClIoc06HOCTb
COe,[(MHeHMH raHKM C 60JITOM HIDKe, qeM C 3aKaJIeHHOH OlIpaBKOH, M HIDKe, qeM Y
COe,n:MHeHMH, OlIMCaHHbIX B pa3,neJIe 3.1. <l>aKTMqeCKaH HeCYIIJ;aH clIoc06HOCTb
raRKH orrpe,l(eJISleTCSI He TOJIbKO TBep,lI,OCTblO raH -lI 3<p<peKTMBHOH ,[(JIMHOH pe3b-
6bI, HO TaIOKe lIPOqHOCTblO Ha paCT.HXeHHe 60JITa, C KOTOpbIM COlIpHraeTCH raHKa.
Ta6JIMue 2 BS EN ISO 898-6: 1996 lIpMBe,neHa CMCTeMa 0603HaqeHMH M HalIpSl-
:>KeHIDI OT lIp06HOH HarpY3KM. TIp06HbIe HarpY3KM ,naHbI B BS EN ISO 898-6:
1996 Ta6JIMua 3. B BS EN ISO 898-6: 1996 Ta6JIHua 4 lIpMBe,neHbI ,lI,illI ClIpaBOK
MHHMMaJIbHbIe pa3pymalOIIJ;Me (lIpMBo,nHrn;Me K CPbIBY pe3b6bI) HarpY3KH ,[(JISI coe-
,[(HHeHMH raeK C 60..1TaMH pa3JIMQHbIX KJIaCCOB lIPOQHOCTM.
BS EN ISO 898-6:1996. TaoJl. 2. CHcTeMa 0603HaqeHHH H HanpH)l{eHHSI OT npo6-
HOH HarpY3KH ,lI;JIH raeK C HOMHHaJIbHOH BbICOTOH 0,5d H < 0,8d
KJIacc HOMHHaJIbHOe eHHe AKTyJlbHOe aBJIeHHe
CBOHCTB raiiKH DO TeCTOBOH HarpY3KoH (H/MM 2 ) DO TeCTOBOH HarpY3KoH (H/MM 2 )
04 -, 400 380
05 U 500 500
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4.1. BUHmo8ble Kpene:JICHble U30e.tlUR
BS EN ISO 898-6:1996 TaoJl. 4. MHHHMaJIbHbIe pa3pymaIOm;He (npHBo,nSlIUHe K
CPbIBY pe3b6bI) HarpY3KH,lI;JIH coe,n;HHeHHH raeK C 60JITaMH B % np06-
HOH HarpY3KH 60JITOB
KJIacc MHHHMaJlbHOe HanpSDKeHHe B CTepmte 60JITa DpH cphme pe3bOW,
% DpofiHOH HarpY3KH 6oJlTOB KJlaCCOB Dp01fHOCTH
Dp01fllOCTH raeK 6,8 8,8 10,9 12,9
04 85 65 45 40
05 100 85 60 50
MaTepHaJILI
faHKH KJIaCCOB lIPOqHOCTM 05, 8 (MclIOJIHeHMe 1), 10 H 12 CJIe,nyeT lIo,nBepraTb
3aKaJIKe M OTrryCKY.
faHKH CJIe,nyeT M3rOTOBlliITb M3 CTaJIeH, XHMMqeCKHH COCTaB KOTOpbIX COOTBeT-
cTByeT BS EN ISO 898-6: 1996 Ta6JIMua 5. XMMMqeCKHH COCTaB He06xo,nMMO aHa-
JIH3MpOBaTb B COOTBeTCTBMM C cymecTByroIIJ;HMM Me)l()];YHapo,nHbIMM CTaH,napTaMM.
BS EN ISO 898-6:1996. TaoJl. 5. XHMHqeCKHH COCTaB CTaJIeH
KJIacc npe eJIbHOe CO ep]K3HHe 3J1eMeHTOB (KOIITpOJlhHWH aH8JlH3) %
Dp01fHOCTH C MaKC. Mn MHH. P MaKC. S MaKC.
5 a : 6 - 0 50 - o 060 O 150
8 b 04 a 0..58 0..25 0..060 0..150
lOb 05 b 0..58 0..30 0..048 0..058
12 b - 0..58 0..45 0..048 0..058
a faHKH 3THX KJIaCCOB npOqHOCTH ,nonycKaeTcSI H3rOTaBJIHBaTb H3 aBTOMaTHOH CTaJIH,
eCJIH HeT HHoro COrJIallIeHHSI Mex.ny nOTpe6HTeJIeM H H3rOTOBHTeJIeM. B TaKHX CJIyqaSlx ,n;o-
nycKaeTcH CJIe,l(yIOm;ee MaKCHMaJIbHOe co,nepxaHHe cepbI, <poc<popa H CBHHI(a: cepa 0,34 %;
4>OC<pOP 0,11 %; CBHHeQ 0,35 %.
b TIpH He06xo,nHMOCTH YJIyqmeHHH MeXaHHqeCKHX CBOHCTB raeK B03MO)I(H0 npHMeHeHHe
CTaJIH C ,n06aBKaMH JIerHpyrom;HX 3JIeMeHTOB.
MeXaHHlJeCKHe CBOHCTBa
TIpM lIpOBepKe MeTo,naMM, OIIMcaHHbIMM B rryHKTe 8, MeXaHMqeCKHe CBOHCTBa
raeK ,nOJDKHbI COOTBeTCTBOBaTb BS EN ISO 898-6: 1996 Ta6JIMua 1 C yqeToM pa3,ne-
JIa 4.1.30.
BeJIHlJHHLI npOOHOH HarpY3KH
BeJIMqMHbI lIp06HOH HarpY3KH lIpMBe,neHbI B BS EN 898-6: 1996. Ta6JI. 3.
HOMMHaJIbHaH IIJIOII(Mb CeqeHMH lIO pe3b6e As BbIqMClliIeTCH lIO <pOpMYJIe:
2
A = 1t ( d 2 + d 3 )
s 4 2 '
r,ne d 2 - HOMMHaJIbHbIM cpe,nHMH ,nMaMeTP Hap)')KHOH pe3b6bI (CMOTpM ISO 724);
d 3 - BHyrpeHHMH ,nMaMeTP Hap)')KHOH pe3b6bI lIO ,nHY BlIMMHbI:
H
d 3 = d} --,
6
r,ne d l - BHYTpeHHMH ,nMaMeTp Hap)')KHOH pe3b6bI; H - BbICOTa Mcxo,nHero Tpe-
yrOJIbHMKa pe3b6bI.
F/la8a 4. Kpene:JICHble oemOJlu
4.1.32. BS EN 20898-7: 1995. MeXSHJflfeCKJfe CSOHCTSS
KpeneJICH&IX Jf3AenJfH: JfCn&ITSHJfe HS KPYTflUCJfH
MOMeHT Jf MJfHJfMSn&H&le KPYTflUCJfe MOMeHT&1
Anfl 6onTos Jf SJfHTOS C HOMJfHSn&H&IMJf
AJfSMeTpSMJf 1-10 MM
BS EN 20898-7:1995. TaoJl. 1. K03<P<PHI(HeHT 3anaca npOqHOCTH X
Krracc 3anaca npOQHOCTH 8,8 9,8 10,9 12,9
K03<P<PHUHeHT X 0,84 0,815 0,79 0,75
BS EN 20898-7:1995. TaoJl. 2. MHHHMaJIbHbIH pa3pymaIOIUHH KpyrSlIUHH MOMeHT
MlmHMaJlhllhlii p83pymaIOlIUIii KPYTJIIIUIH MOMe...ra M B miD (11M)
Pe3boa mar (MM) KJIacc Dp01fHOCTH
8,8 9,8 10,9 12,9
M1 0,25 0,033 0,036 0,040 0,045
M1,2 0,25 0,075 0,082 0,092 0,10
M1,4 0,3 0,12 0,13 0,14 0,16
M1,6 0,35 0,16 0,18 0,20 0,22
M2 0,4 0,37 0,40 0,45 0,50
M2,5 0,45 0,82 0,90 1,0 1,1
M3 0,5 1,5 1,7 1,9 2,1
M3,5 0,6 2,4 2,7 3,0 3,3
M4 0,7 3,6 3,9 4,4 4,9
M5 0,8 7,6 8,3 9,3 10
M6 1 13 14 16 17
M7 1 23 25 28 31
M8 1,25 33 36 40 44
M8xl - 38 42 46 52
M10 1,5 66 72 81 90
M 10xl - 84 92 102 114
M10x1,25 - 75 82 91 102
a 3TH MHHHMaJIbHbIe 3HaQeHHSI pa3pymaIOIUHx KpyrSlIUHX MOMeHTOB OTHOCSlTCSI K 60JI-
TaM H BHHTaM C ,nonYCKaMH pe3b6bI 6g, 6f H 6e.
4. 1.33. BS EN ISO 4762: 2004. MeTpJflfeCKHH SJfHT
C qJfnHHAPJflfeCKOH ronosKOH Jf WeCTJfrpSH&IM
yrny6neHJfeM nOA KnIOIf
ISO 10683, KpeIIe)I(HbIe M3,neJIIDI - He3JIe:KTpOJIMTMQeCKHe UMHKOBbIe IIOKpbITIDI.
ISO.23429, KaJIM6pOBKa meCTMrpaHHbIX yrJIy6JIeHMH.
CMOTpM pMC. 1 M BS EN ISO 4762: 2004. Ta6JI. 1.
4.1. BUHmo8ble "pene:JICHble U30e.nUR
Pa3MepLI
IIpUMettaHue. CMMBOJIbI M 0603HaQeHHH pa3MepoB ,naHbI B ISO 225.
t
b
C\I
'r'"
AI
x
(1 )
1J
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4
CD
'T!
CI) -e-
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U(3)
Is
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(b)
J
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)
orrYCTHMaH aJIbTepHaTHBHaH <pOpMa yrJIy6JIeHHH
t
BepXHHH H HIDKHHH KPaH rOJIOBKH
o
o
C\I
AI
ri = t r tl
(5)
V
612
An nOJ1Y"leHHbIX paaBepTKO yrJ1y6J1eHVI
Ha 60J1bWerO npeAellbHOrO paaMepa aapea,
nOJlY"l BWVlVlC51 npVl CSepJ1eHVlVI, He AOJ1)1(eH
npeBblwaTb 1/3 AJ1V1Hbl J1t060 rpaHVI yrJ1y6-
neH , KOTOpa51 paBHa e/2.
( 612)/3
Puc. 1.
(1) ,lJ;OrryCTHMO He3HaQHTeJIbHOe cKpyrJIeHHe HJIH 3eHKOB Bxo,!:{a yrJIy6JIe-
HIDI.
(2) KOHeu ,nOJDKeH 6bITb C <paCKO:H HJIM ,lLJUI pe3b6 M4 MO)l(eT 6bITb 6e3 <pac-
KIf B COOTBeTCTBMM C ISO 4753.
(3) HeIIOJIHa5I pe3b6a u 2P.
(4) d s MCIIOJIb3yeTcH, eCJIM 3HaQeHHH Is min OIIpe,neJIeHbI.
,
(5) BepXHM:H KpaH rOJIOBKH MO)l(eT 6bITb cKpyrJIeH HJIM MMeTb <paCKY, KaK IIOKa-
3aHO, no BbI60py M3rOTOBMTelliI.
(6) HIDKHM:H Kpa:H rOJIOBKH MO)l(eT 6bITb cKpyrJIeHHbIM IDIM CKomeHHbIM ,no d w ,
HO B JII060M c.rryqae He ,nOJDKHO 6bITb 3ayceHueB.
MaKCMMaJIbHOe yrOJIIIJ;eHMe IIO,n rOJIOBKO:H BMHTa:
If,max =1,7r max '
da,max - ds,max
r nlax =
2
'min CM01'pH BS EN ISO 4762: 2004. Ta6JI. 1, pMC. 1.
F/la8a 4. Kpene:JICHble oemOJlu
BS EN ISO 4762: 2004. TaoJl. 1. Pa3MepbI B MM
P83Mep pe3hOW, d MI,6 M2 M2,5 M3 M4 M5 M6 M8 MIO MI2
pa 0,35 0,4 0,45 0,5 0,7 0,8 1 1,25 1,5 1,75
bb 15 16 17 18 20 22 24 28 32 36
MaKCC 3,00 3,80 4,50 5,50 7,00 8,50 10,00 13,00 16,00 18,00
dk MaKcd 3,14 3,98 4,68 5,68 7,22 8,72 10,22 13,27 16,27 18,27
MHH. 2,86 3,62 4,32 5,32 6,78 8,28 9,78 12,73 15,73 17,73
d a MaKC. 2 2,6 3,1 3,6 4,7 5,7 6,8 9,2 11,2 13,7
d s MaKC. 1,60 2,00 2,50 3,00 4,00 5,00 6,00 8,00 10,00 12,00
MHH. 1,46 1,86 2,36 2,86 3,82 4,82 5,82 7,78 9,78 11,73
ee,f MHH. 1,733 1,733 2,303 2,873 3,443 4,583 5,723 6,863 9, 149 11,429
If MaKC. 0,34 0,51 0,51 0,51 0,6 0,6 0,68 1,02 1,02 1,45
k MaKC. 1,60 2,00 2,50 3,00 4,00 5,00 6,0 8,00 10,00 12,00
MHH. 1,46 1,86 2,36 2,86 3,82 4,82 5,7 7,64 9,64 11,57
r MHH. 0,1 0,1 0,1 0,1 0,2 0,2 0,25 0,4 0,4 0,6
HOM. 1,5 1,5 2 2,5 3 4 5 6 8 10
sf MaKC. 1,58 1,58 2,08 2,58 3,08 4,095 5,14 6,14 8,175 10,175
MHH. 1,52 1,52 2,02 2,52 3,02 4,020 5,02 6,02 8,025 10,025
t MHH. 0,7 1 1,1 1,3 2 2,5 3 4 5 6
v MaKC. 0,16 0,2 0,25 0,3 0,4 0,5 0,6 0,8 1 1,2
d w MHH. 2,72 3,48 4,18 5,07 6,53 8,03 9,38 12,33 15,33 17,23
w MHH. 0,55 0,55 0,85 1,15 1,4 1,9 2,3 3,3 4 4,8
Ig Aruma CTep1KllJl/ s H ,lI,JIHHa rJla,nKoii 1faCTH CTep1KllJl Ig
HOM. MUH. MaKC. - - - - - - - - - -
_fIJ J -1 J J J J J J J -1 J J J fIJ "..,p. fIJ J J J
- -
2,5 2,3 2,7
3 2,8 3,2
4 3,76 4,24
5 4,76 5,24
6 5,76 6,24
8 7,71 8,29
10 9,71 10,29
12 11,65 12,35
16 15,65 16,35
20 19,58 20,42 2 4
25 24,58 25,42 5,75 8 4,5 7
30 29,58 30,42 9,5 12 6,5 10 4 8
35 34,5 35,5 11,5 15 9 13 6 11
40 39,5 40,5 16,5 20 14 18 11 16 5,75 12
45 44,5 45,5 19 23 16 21 10,75 17 5,5 13
50 49,5 50,5 24 28 21 26 15,75 22 10,5 18
55 54,4 55,6 26 31 20,75 27 15,5 23 10,25 19
60 59,4 60,6 31 36 25,75 32 20,5 28 15,25 24
65 64,4 65,6 30,75 37 25,5 33 20,25 29
4.1. BUHmo6ble "peneJICHble U3iJeJlUR 211'
llpoiJollxeHue
P83Mep pe3b6w, d MI,6 I M2 I M2,S I M3 I M4 I MS M6 I M8 I MIO I MI2
Ig ,lI;JIHHa CTep1KllJl/ s H .zuoma rJla,nKoA 1faCTH CTep1KllJlI g
HOM. MHH. MaKe. - - - - - - - - - -
J J -1 ""., J ...I J ...I J J J J J J. J ,.,JI. J J. J "",p.
70 69,4 70,6 35,75 42 30,5 38 25,25 34
80 79,4 80,6 45,75 52 40,5 48 35,25 44
90 89,3 90,7 -- 50,5 58 45,25 54
100 99,3 100,7 ,. 60,5 68 55,25 64
110 109,3 110,7 65,25 74
120 119,3 120,7 75,25 84
130 129,2 130,8
140 139,2 140,8
150 149,2 150,8
160 159,2 160,8
180 179,2 180,8
200 199,075 200,925
220 219,075 220,925
240 239,075 240,925
260 258,95 261,05
280 278,95 281,05
300 298,95 301,05
P83Mep pe3b6bI, d (MI4)h MI6 M20 M24 M30 M36 M42 M48 MS6 M64
PI 2 2 2,5 3 3,5 4 4,5 5 5,5 6
bb CCbillKa 40 44 52 60 72 84 96 108 124 140
MaKCC 21 ,00 24,00 30,00 36,00 45,00 54,00 63,00 72,00 84, 3,6,00
/
dk MaKcd 21,33 24,33 30,33 36,39 45,39 54,46 63,46 72,46 84,54 96,54
MHH. 20,67 23,67 29,67 35,61 44,61 53,54 62,54 71 ,54 83,46 95,46
d a MaKC. 15,7 17,7 22,4 26,4 33,4 39,4 45,6 52,6 63 71
d s MaKC. 14,00 16,00 20,00 24,00 30,00 36,00 42,00 48,00 56,00 64,00
13,73 15,73 19,67 23,67 29,67 35,61 41,61 47,61 55,54 63,54
MHH.
ee,f MHH. 13,716 15,996 19,437 21,734 25,154 30,854 36,571 41,131 46,831 52,531
If MaKC. 1,45 1,45 2,04 2,04 2,89 2,89 3,06 3,91 5,95 5,95
k MaKC. 14,00 16,00 20,00 24,00 30,00 36,00 42,00 48,00 56,00 64,00
MHH. 13,57 15,57 19,48 23,48 29,48 35,38 41,38 47,38 55,26 63,26
r MHH. 0,6 0,6 0,8 0,8 1 1 1,2 1,6 2 2
HOM. 12 14 17 19 22 27 32 36 41 46
sf MaKC. 12,212 14,212 17,23 19,275 22,275 27,275 32,33 36,33 41,33 46,33
MHH. 12,032 14,032 17,05 19,065 22,065 27,065 32,08 36,08 41,08 46,08
t MHH. 7 8 10 12 15,5 19 24 28 34 38
v MaKC. 1,4 1,6 2 2,4 3 3,6 4,2 4,8 5,6 6,4
d w MHH. 20, 17 23,17 28,87 34,81 43,61 52,54 61,34 70,34 82,26 94,26
w MHH. 5,8 6,8 8,6 10,4 13,1 15,3 16,3 17,5 19 22
F/la8a 4. Kpene:JICHble oemOJlu
O"OHltaHUe
P83Mep pe3b6w, d (M14)h M16 M20 M24 M30 M36 M42 M48 M56 M64
Ig ,lI;JntHa XBOCTOBHKa Is H .zuoma 3aXBaTa Ig
HOM. MMH. MaKe. - - - - - - - - - -
J J J J J ,..",. J ,..",. J ,..",. J J. J J J J J J J ,..II-
2..5 2..3 2..7
3 2..8 3..2
4 3,76 4,24
5 4,76 5,24
6 5..76 6..24
8 7..71 8..29
10 9,71 10,29
12 11,65 12,35
16 15,65 16,35
20 19..58 20..42
25 24,58 25..42
30 29,58 30,42
35 34,5 35,5
40 39..5 40..5
45 44,5 45,5
50 49,5 50,5
55 54,4 55,6
60 59..4 60..6 10 20
65 64.4 65..6 15 25 11 21
70 69,4 70,6 20 30 16 26
80 79,4 80,6 30 40 26 36 155 28
90 89,3 90,7 40 50 36 46 255 38 15 30
100 99..3 100.7 50 60 46 56 35..5 48 25 40
110 109.3 110..7 60 70 56 66 45..5 58 35 50 .5 38
120 119,3 120,7 70 80 66 76 55.5 68 45 60 30..5 48 16 36
130 129,2 130,8 80 90 76 86 65,5 78 55 70 40,5 58 26 46
140 139,2 140,8 90 100 86 96 75,5 88 65 80 50,5 68 36 56 215 44
150 149.2 150..8 96 106 855 98 75 90 ffi..5 78 46 66 31.5 54
160 159,2 160,8 106 116 95,5 108 85 100 70.5 88 56 76 41,5 64 27 52
180 179,2 180,8 1155 128 105 120 ,5 108 76 96 61,5 84 47 72 28,5 56
200 199,075 200,925 1355 148 125 140 110..5 128 96 116 81,5 104 67 92 48,5 76 30 60
220 219.075 220.925 101,5 124 87 112 68,5 96 50 80
240 239..075 240,925 121.5 155 107 132 88..5 116 70 100
260 258,95 261,05 141.5 164 127 152 108.5 136 90 120
280 278.,95 281,05 161,5 184 147 172 128..5 156 110 140
300 298.95 301,05 181,5 204 167 192 148,5 176 130 160
a P - mar pe3b6bI. b ,lJ.JHI ,lLJIHH Mex.ny )l(HpHbIMH cTYIIeHqaTbIMH JIHHH$lMH B He3aTeHeH-
HOH 06JIaCTH. C ,lLrrn rJIa,nKHX rOJIOBOK. d ,lJ..rrH rOJIOBOK C pH<pJIeHHeM. e e min = 1,14 smin
f npOBe,L(eHHe COBMeCTHOH KaJIH6pOBKH pa3MepOB yrJIy6JIeHH$I e H S CM. B ISO 23429.
g ,lJ..rrHHbI H3,n;eJIHH CTaH,ZJ;apTHOro HCnOJIHeHH$I pacnOJIaraIOTC$I Me)l(,l(y )l(HpHbIMH CTYTIeH-
qaTbIMH JIHHH$lMH. Pe3b6a Ha H3,n;eJIIDIX, ,lLJIHHbI KOTOpbIX pacnOJIaraIOTC$I B 3aTeHeHHOH 06-
JIaCTH, ,n;OXO,n;HT ,n;o rOJIOBKH B npe,n;eJIax 3P. ,lJ..rrH ,lLJIHH, pacnOJIOXeHHbIX HHXe 3aTeHeHHoH
06JIaCTH, Ig H Is npHHHMaIOT 3HaqeHHH B COOTBeTCTBHH co CJIe,n;yIOI.QHMH <popMYJIaMH:
I g max = I HOM - b; Is nun = I g max - 5P.
, "
h Pa3MepoB B cK06Kax CJIe,n;yeT no B03MO)l(HOCTH H36eraTb.
4.1. BuHmo8ble "pene:JICHble U3iJe/lUR
4. 1.34. BS EN ISO 10642: 2004. BJfHT&1 C nOTsHHoH
ronosKoH Jf WeCTJfrpSH&IM yrny6neHJfeM
nOA KnIOIf
Pa3MepLI H KaJIHOpOBKa rOJIOBKH
CMOTPH pHC. 1 H 2 H BS EN ISO 10642: 2004. Ta6JI. 1.
Pa3MepLI
IIpUMe'1.aHue. CHMBOJIbI H 0603HaQeHIDI pa3MepOB ,naHbI B ISO 225.
i J
/(
t w
AonYCTLflMa aJ1bTepHaTLflB-
Ha51 ct>opMa yrJ1y6J1eHLfl5I
t
o
o
N
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(2)
Q)
o
o
C\I
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AI
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's
Ig
U(5)
s
(b)
l
- /
e/2
(e/2)/3
An51 nOJ1Y"leHHbIX pa3BepTKOVI yrJ1y6J1eHLflVI HaLfl60J1bWerO npeAeJ1bHOrO
pa3Mepa 3ape3, nOJ1Y"lLflBWLflVlC5I npLfl CBepJ1eHLflLfI, He AOJ1)1(eH npeBblwaTb
1/3 AJ1Lf1Hbl J11060Vl rpaHLfi yrJ1y6J1eHLfl5I, KOTOpa51 paBHa e/2.
PRC. 1. BHHT C nOTaHHOH rOJIOBKOH H H llIeCTHrpaHHbIM yrJIy6JIeHHeM no,n; KJIIOq
(1) ,l(OrryCTHMO He3HaQHTeJIbHOe cKpyrJIeHHe HJIH 3eHKOBKa y Bxo,na yrJIy6JIe-
HHR.
(2) KOHeu ,nOIDKeH 6bITb C <pacKoH HJlH ,lUIR pe3b6 M4 MO)l{eT 6bITb 6e3 <pac-
KH B COOTBeTCTBHH C ISO 4753.
(3) KpaH rOJIOBKH MO)l{eT 6bITb cpe3aHHbIM HJlH cKpyrJIeHHbIM.
(4) a = 90° - 92°
(5) HeIIOJIHaR pe3b6a u 2P.
(6) d s HCIIOJIb3yeTcR, eCJIH 3HaQeHHR Is min OIIpe,neJIeHbI.
,
F/la8a 4. Kpene:JICHble iJemOJlu
KaJIHopoBKa roJIOBKH
BepXHIDI IIoBepXHocTb BHHTa ,nOJDKHa 6bITb paCIIOJIO)l{eHa Me)l{)];Y KOHTaKTHbIMH
IIOBepXHOCTRMH A H B.
90°-0°30 1
AonYCKLfI B MM
A
o a
; D-0,05
B
;d a
PUC. 2. npOBepKa 1lJI0CKOCTHOCTH
a D - dk.Teop. max (CMOTPH BS EN ISO 10642: 2004 Ta6JIHua 1).
b F - ,nOIIYCK Ha IIJIOCKOCTHOCTb rOJIOBKH (CMOTpH BS EN ISO 10642: 2004
Ta6JIHua 1).
BS EN ISO 10642: 2004. Ta6JI. 1. Pa3MepbI B MM
Pa3Mep pe3b6w, d M3 M4 MS M6 M8 MtO Mt2 (Mt4 Mt6 M20
pa 0,5 0,7 0,8 1 1,25 1,5 1,75 2 2 2,5
bb 18 20 22 24 28 32 36 40 44 52
d a MaKC. 3,3 4,4 5,5 6,6 8,54 10,62 13,5 15,5 17,5 22
Teope'I'JNe- 6,72 8,96 11,20 13,44 17,92 22,40 26,88 30,8 33,60 40,32
dk CKHH MaKC.
Cl>aKTJf1Ie- 5,54 7,53 9,43 11,34 15,24 19,22 23,12 26,52 29,01 36,05
CKHH MHH.
d s MaKC. 3,00 4,00 5,00 6,00 8,00 10,00 12,00 14,00 16,00 20,00
2,86 3,82 4,82 5,82 7,78 9,78 11,73 13,73 15,73 19,67
MHH.
ec,d MHH. 2,303 2,873 3,443 4,583 5,723 6,863 9,149 11,429 11,429 13,716
k MaKC. 1,86 2,48 3,1 3,72 4,96 6,2 7,44 8,4 8,8 10,16
Fe MaKC. 0,25 0,25 0,3 0,35 0,4 0,4 0,45 0,5 0,6 0,75
MHH. 0,1 0,2 0,2 0,25 0,4 0,4 0,6 0,6 0,6 0,8
r 6
HOM. 2 2,5 3 4 5 8 10 10 12
sd MaKC. 2,08 2,58 3,08 4,095 5,14 6, 140 8,175 10,175 10,175 12,212
MHH. 2,02 2,52 3,02 4,020 5,02 6,020 8,025 10,025 10,025 12,032
t MHH. 1,1 1,5 1,9 2,2 3 3,6 4,3 4,5 4,8 5,6
w MHH. 0,25 0,45 0,66 0,7 1,16 1,62 1,8 1,62 2,2 2,2
4.1. BUHmo6ble "peneJICHble u3deJlUR 215:::
O"OHttaHUe
Pa3Mep pe3b6w, d M3 M4 M5 M6 M8 MtO Mt2 (Mt4 Mt6 M20
If ,lI;JIHHa cTep1KllJl/ s H .zuoma rJla,nKOH 1faCTH CTep1KllJl Ig
HOM. MHH. MaKe. - - - - - - - - - -
fI.I J J J J J J J J J J J fI.I J J J J J J J
- -
8 7,71 8,29
10 9,71 10,29
12 11,65 12,35 (J
)
16 15,65 16,35
20 19,58 20,42
25 24,58 25,42
30 29,58 30,42 95 12 6,5 10
35 34,5 35,5 11,5 15 9 13
40 39,5 40,5 16,5 20 14 18 11 16
45 44,5 45,5 19 23 16 21
50 49,5 50,5 24 28 21 26 15,75 22
55 54,4 55,6 26 31 20,75 27 15,5 23
60 59,4 60,6 31 36 25,75 32 20,5 28
65 64,4 65,6 30,75 37 25,5 33 20,25 29
70 69,4 70,6 35,75 42 30,5 38 25,25 34 20 30
80 79,4 80,6 45,75 52 40,5 48 35,25 44 30 40 26 36
90 89,3 90,7 50,5 58 45,25 54 40 50 36 46
100 99,3 100, 7 60,5 68 55,25 64 50 60 46 56 35,5 48
a P - mar pe3b6bI.
b ,D;JIH ,lLJIHH Me)l()]:Y )l(HpHbIMH cTyrreHqaTbIMH JIHHHSlMH B He3aTeHeHHoH 06JIaCTH.
C e min = 1, 14s min .
d npoBe,n;eHHe COBMeCTHOH KaJIH6pOBKH pa3MepOB yrJIy6JIeHIDI e H S CMOTpH B
ISO 23429.
e F - nJIOCKOCTHOCTb rOJIOBKH, CMOTpH pHC. 2. llIa6JIoH ,lI;JUI H3MepeHHH F HMeeT ,n;o-
nYCK O.
f ,D;JIHHbI H3,n;eJIHH CTaH,n;apTHoro HCnOJIHeHHSI pacnOJIaraIOTCH Me)l(,l(y )l(HpHbIMH C1)'neH-
qaTbIMH JIHHHSlMH. Pe3b6a Ha H3,n;eJIHHX, ,lLJIHHbI KOTOpbIX pacnOJIaraIOTCH B 3aTeHeHHOH 06-
JIaCTH, ,n;OXO,nHT ,n;o rOJIOBKH B npe,n;eJIax 3P. ,D;JIH ,lLJIHH, pacnOJIO)l(eHHbIX HH)I(e 3aTeHeHHOH
06JIaCTH, Ig H Is npHHHMaIOT 3HaQeHHSI B COOTBeTCTBHH co CJIe,n;yIDI.QHMH <popMYJIaMH:
I g,max = I HOM - b; Is ,nun = I g,max - 5P.
g Pa3MepoB B cK06Kax CJIe eT no B03MO)I{HOCTH H36eraTb.
TpeOOBaHHB H COOTBeTCTBHe Me}K,ll;yllapo,n;HLIM CTaH,ZJ;apTaM
CMOTpH BS EN ISO 10642: 2004 Ta6JIHUbI 2 H 3.
F/la8a 4. Kpene:JICHble oemOJlu
BS EN ISO 10642: 2004. Ta6JI. 2. Tpe60BaHHH H COOTBeTCTBHe Me)l()];)'Hapo,n;HbIM
CTaH,ZJ;apTaM
MaTepHaJI
OCHoBHble T e60BaHIDI Me a
Pe3b6a )].OnyCK
CT8JIh
IIpHeMKa
ISO 8992
6g ,lLJIH KJIaCCOB npOqHOCTH 8.8 H 10.9;
5 6 ,lI,JUI KJIacca n OQHOCTH 12.9
I ISO 261 ISO 965-2 ISO 965-3
8 8 10 9 12 9
ISO 898-1
A
ISO 4759-1
Be3 CneI(HaJIbHOH 06pa60TKH
Tpe60BaHHH K raJIbBaHOnOKpbITIDIM
onpe,n;eJIeHbI B ISO 4042
Tpe60BaHIDI K He3JIeKTPOJIHTH'IeCKHM
I(HHKOBbIM nOKpbITHHM onpe,n;eJIeHbI B
ISO 10683
)].onycKaeMble npe,n;eJIbHble BeJIWlHHbI
HeCllJIOlliHOCTH nOBepXHOCTH onpe.ne-
JIeHbI B ISO 6157-1 H ISO 6157-3 ,[(JUI
KJIacca n OqHOCTH 12.9
IIpoI(e.nypa npHeMKH onHcaHa B 180
3269
MexaHWleCKHe
CBOHCTBa
)].OnyCKH
HeCllJIOlliHOCTH nOBepXHOCTH
a J13-3a KOH<pHrypaI(HH rOJIOBKH 3TH BHHTbI MOryr He y,n;OBJIeTBOpHTb Tpe60BaHIDIM no
MHHHMaJIbHbIM pa3pynIaIOI.QHM HarpY3KaM ,lI,JUI KJIaCCOB npOqHOCTH 8.8, 10.9 H 12.9, onpe.ne-
JIeHHbIX B ISO 898-1, npH TeCTHpOBaHHH B COOTBeTCTBHH C nporpaMMoH HcnbITaHHH B. OHM
,n;OJDKHbI, TeM He MeHee, y,n;OBJIeTBOpHTb ,n;pyrHM TPe60BaHHHM K MaTepHaJIaM H npOqHOCTM
,lLJIH KJIaCCOB npOqHOCTH 8.8, 10.9 H 12.9, onpe,n;eJIeHHbIX B ISO 898-1. KpoMe Toro, npH Ha-
rpY3Ke ueJIbIX BHHTOB, Kor,n;a rOJIOBKa nOMep)I(HBaeTCH Ha no,U,Xo,n;HIUeM xOMyre (c KOHHqe-
CKOH onopHoH nOBepxHocTbIO) C nOMOIUbIO npHcnoc06JIeHHH ,lUll[ HcnbITaHHH, onHcaHHoro
B ISO 898-1, OHH ,n;OJDKHbI BbI,n;ep)I(HBaTb 6e3 pa3pynIeHHH MHHHMaJIbHyro pa3pynIaIOI.QyIO
HarpY3K)' B COOTBeTCBHH C BS EN ISO 10642: 2004 Ta6JIHI(a 3. IIpH HcnbITaHHH ,n;o pa3py-
llIeHIDI pa3pymeHHe MO)l(eT npoH30HTH B pe3b60BoH qaCTH, rOJIOBKe, CTepXHe HJIH B MeCTe
coe,n;HHeHIDI rOJIOBKH co CTepXHeM.
BS EN ISO 10642: 2004. Ta6JI. 3. MHHHMaJIbHble pa3pynIaIOI.QHe HarpY3KH ,lI,JUI BHH-
TOB C nOTaHHOH rOJIOBKOH H llIeCTHrpaHHbIM yrJIy6JIeHHeM no,n; KJIlOq
KJIacc Dp01fHOCTH
P83Mep pe3hOW, d 8,8 10,9 12,9
MHHHM8JIhHaJI p83pymalOInaJI HarpY3K8 (H)
M3 3220 4180 4190
M4 5620 7300 856
M5 9080 11800 13800
M6 12900 16700 19600
M8 23400 30500 35700
M10 37100 48200 56600
M12 53900 70200 82400
M14 73600 96000 112000
M16 100000 130000 154000
M20 162000 204000 239000
80% 3HaqeHHH COOTBeTCTByroT ISO 898-1.
4.1. BUHmo8ble "pene:JICHble U3iJeJlUR
0003HaQeHHJI
llpHMep. BHHT C IIoTaHHoH rOJIOBKOH C IIIecTHrpaHHbIM yrJIy6JIeHHeM IIO,n; KJIIOq
C pe3b60H M12, HOMHHaJIbHOH ,lUIHHOH I = 40 MM H KJIaCCOM IIPOqHOCTH 12.9 060-
3HaQaeTCR CJIe,n;yroII(HM 06pa30M:
BHHT C IIoTaHHoH rOJIOBKOH C IIIeCTHrpaHHbIM yr.rry6JIeHHeM IIO,n; KJIIOq
ISO 10642-M12 x 40-12,9
HH<popMaUHIO, KacaIOlI(yIOCR BHHTOB C IIOTaHHOH rOJIOBKOH C IIIeCTHrpaHHbIM
yrny6neHHeM IIO,n; KJIIOq C pa3MepaMH B ,lI;IOHMaX, MO)I{HO HaHTH B BS2470.
4.1.35. 854827 ISO MeTpJflfeCKJfe SJfHTOS&le pe3&6&I,
MJfHJfSTlOpHSfI cepJffl
War e3b6bl P :z: /
It)
0,125P C\I
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0
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(1) ('f) co
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co II
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s:
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co ct 0
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a. OCb pe3b6bl ('f)
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Pa3MepbI B MM
HOMHllaJlhllhli p83Mep Hap)')KHhli Cpe.znmi Buyrpellllllii
mar pe3b6w P (HOMHH8JIhIlhIii)
1-1 PBA 2-ii PBA .1nfaMeTp .1nfaMeTp .1nfaMeTp
8-0 3 0,080 0,300000 0,248038 0,223200
,
8-0,35 0,090 0,350000 0,291543 0,263600
8-0 4 0, 100 0,400000 0,335048 0,304000
,
8-0,45 0,100 0,450000 0,385048 0,354000
8-0 5 0,125 0,500000 0,418810 0,380000
,
8-0,55 0,125 0,550000 0,468810 0,430000
8-0 6 0, 150 0,600000 0,502572 0,456000
,
8-0,7 0,175 0,700000 0,586334 0,532000
8-0,8 0,200 0,800000 0,670096 0,608000
8-0,9 0,225 0,900000 0,753858 0,684000
8-1 0,250 1 ,000000 0,837620 0,760000
8-1 1 0,250 1,100000 0,937620 0,860000
,
8-1 2 0,250 1 ,200000 1,037620 0,960000
,
8-1 4 0,300 1,400000 1,205144 1,112000
,
Donee IIOJIHyro HH<popMaUHIO CMOTPH B BS 4827.
F/la8a 4. Kpene:JICHble iJemOJlu
4.1.36. 853643-1/2 ISO MeTpJflfeCKJfe SJfHTOS&le pe3&6b':
cepJffl C nOCTOflHH&lM wsrOM
Pa3MepbI B MM
HapymrLli (HOMHH8JIhHLIi) .1nfaMeTp Cpe,lUflli BuyrpellllHii .1nfaMeTp
mar pe3b6w .1nfaMeTp
I-ii p 2-ii p 3-ii p DO .lUIY BD8,lUIIIbI BuyrpH
0,25 2,0 - - 1,84 1,69 1,73
0,25 - 2,2 - 2,04 1,89 1,93
0,35 2,5 - - 2,27 2,07 2,12
0,35 3,0 - - 2,77 2,57 2,62
0,35 - 3,5 - 3,27 3,07 3,12
0,50 4,0 - - 3,68 3,39 3,46
0,50 - 4,5 - 4,18 3,86 3,96
0,50 5,0 - - 4,68 4,39 4,46
0,50 - - 5,5 5,18 4,86 4,96
0,75 6,0 - - 5,51 5,08 5,19
0,75 - - 7,0 6,51 6,08 6,19
0,75 8,0 - - 7,51 7,08 7,19
0,75 - - 9,0 8,51 8,08 8,19
0,75 10,0 - - 9,51 9,08 9,19
0,75 - - 11,0 10,51 10,08 10,19
1,0 8,0 - - 7,35 6,77 6,92
1,0 - - 9,0 8,35 7,77 7,92
1,0 10,0 - - 9,35 8,77 8,92
1,0 - - 11,0 10,35 9,77 9,92
1,0 12,0 - - 11,35 10,77 10,92
1,0 - 14,0 - 13,35 12,77 12,92
1,0 - - 15,0 14,35 13,77 13,92
1,0 16,0 - - 15,35 14,77 14,92
1,0 - - 17,0 16,35 15,77 15,92
1,0 - 18,0 - 17,35 16,77 16,92
1,0 20,0 - - 19,35 18,77 18,92
1,0 - 22,0 - 21,35 21,77 21,92
1,0 24,0 - - 23,35 22,77 22,92
1,0 - - 25,0 24,35 23,77 23,92
1,0 - 27,0 - 26,35 25,77 25,92
1,0 - - 28,0 27,35 26,77 26,92
1,0 30,0 - - 29,35 28,77 28,92
1,25 10,0 - - 9,19 8,47 8,65
1,25 12,0 - - 11,19 10,47 10,65
1 25 a - 140 a - 13,19 12,47 12,65
, ,
4.1. BUHlTl08ble "pene:JICHble U3iJe.tlUR
llpoiJollxeHue
HapYJKllhIi (HOMHH8JIhHhIi) .1nfaMeTp Cpe,lUflli BuyrpellllHii .1nfaMeTp
mar pe3hOW
I-ii PBA 2-ii PBA 3-ii PBA .1nfaMeTp DO .lUIY BD8,ZUIIIW BllyrpH
1,5 12,0 - - 11,03 10,16 10,38
1,5 - 14,0 - 13,03 12,16 12,38
1,5 - - 15,0 14,03 13,16 13,38
1,5 16,0 - - 15,03 14,16 14,38
1,5 - - 17,0 16,03 15,16 15,38
1,5 - 18,0 - 17,03 16,16 16,38
1,5 20,0 - - 19,03 18,16 18,38
1,5 - 22,0 - 21,03 20,16 20,38
1,5 24,0 - - 23,03 22,16 'I 22,38
1,5 25,0 24,03 23,16 I 23,38
- -
1,5 - - 26,0 25,03 24,16 24,38
1,5 - 27,0 - 26,03 25,16 25,38
1,5 - - 28,0 27,03 26,16 26,38
1,5 30,0 - - 29,03 28,16 28,38
1,5 - - 32,0 31,03 30,16 30,38
1,5 - 33,0 - 32,03 31,16 31,38
1,5 - - 35,0 34,03 33,16 33,38
CepUJl C UlaZOM 1,5 MM npoiJollxaemCJl iJo MaKCUMOJlbHOZO iJullMempa 80 MM
2,0 18,0 16,70 15,55 15,84
2,0 20,0 - - 18,70 17,55 17,84
2,0 - 22,0 - 20,70 19,55 19,84
2,0 24,0 - - 22,70 21,55 21 ,84
2,0 - - 25,0 23,70 22,55 22,84
2,0 - - 26,0 24,70 23,55 23,84
2,0 - 27,0 - 25,70 24,55 24,84
2,0 - - 28,0 26,70 25,55 25,84
2,0 30,0 - - 28,70 27,55 27,84
2,0 - - 32,0 30,70 29,55 29,84
2,0 - 33,0 - 31,70 30,55 30,84
2,0 - - 35,0 33,70 32,55 32,84
CepUJl C UlaZOM 2 MM npoiJollxaemcJl iJo MaKCUMaJlbHOZO iJullMempa 150 MM
3,0 30,0 - - 28,05 26,32 26,75
3,0 - 33,0 - 31,05 29,32 29,75
3,0 36,0 - - 34,05 32,32 32,75
3,0 - - 38,0 36,05 34,32 34,75
3,0 - 39,0 - 37,05 35,32 35,75
3,0 - - 40,0 38,05 36,32 36,75
F/la8a 4. Kpene:JICHble iJemOJlu
OKOHttaHUe
HapYJKllhIi (HOMHH8JIhHhIii) .1nfaMeTp Cpe.znmii BuyrpeHHHii .1nfaMeTp
mar pe3b6w .1nfaMeTp
I-ii p 2-ii p 3-ii p DO .lnIY BD8,lUIIIbI BIfYTPH
3,0 42,0 - - 40,05 38,32 38,75
3,0 - 45,0 - 43,05 41,32 41,75
3,0 48,0 - - 46,05 44,32 44,75
3,0 - - 50,0 48,05 46,32 46,75
3,0 - 52,0 - 50,05 48,32 48,75
3,0 - - 55,0 53,05 51,32 51,75
CepUR C UlaZO.M 3 JAM npOaOJl:JICaemCJl ao .MaKCUMaJlbHOZO aUa.Mempa 250.M.M
4,0 42,0 - - 39,40 37,09 37,67
4,0 - 45,0 - 42,40 40,09 40,67
4,0 48,0 - - 45,40 43,09 43,67
4,0 - - 50,0 47,40 45,09 45,67
4,0 - 52,0 - 49,40 47,09 47,67
4,0 - - 55,0 52,40 50,09 50,67
4,0 56,0 - - 53,40 51 ,09 51,67
4,0 - - 58,0 55,40 53,09 53,67
4,0 - 60,0 - 57,40 55,09 55,67
4,0 - - 62,0 59,40 57,09 57,67
4,0 64,0 - - 61 ,40 59,09 59,67
4,0 - - 65,0 62,40 60,09 60,67
CepUR C UlaZO.M 4,0.M.M npOaOJl:JICaemcJl ao .MaKCUMaJlbHOZO aUa.Mempa 300 .M.M
6,0 - - 70,0 66,10 62,64 63,50
6,0 72,0 - - 68, 10 64,64 65,50
6,0 - 76,0 - 72,10 68,64 69,50
6,0 80,0 - - 76,10 72,64 73,50
6,0 - 85,0 - 81,10 77,64 78,50
6,0 90,0 - - 86,10 82,64 83,50
6,0 - 95,0 - 91,10 87,64 88,50
6,0 100,0 - - 96,10 92,64 93,50
6,0 - 105,0 - 101,10 97,64 98,50
6,0 110,0 - - 106, 10 102,64 103,50
6,0 - 115,0 - 111,10 107,64 108,50
6,0 - 120,0 ' - 116,10 112,64 113,50
6,0 125,0 - - 121,10 117,64 118,50
CepUR C UlaZO.M 6,0 JAM npOaOJl:JICaemCJl ao .MaKCUMaJlbHOZO aUa.Mempa 300 JAM
a 3TOT pa3Mep npHMeHHeTCH TOJIbKO .lUIH CBeqeH 3aJKHraHHH.
,[(aJIbHeHmyIO HH<popMaUHIO CMOTPH B BS 3643.
4.1. BUHm06ble "peneJICHble U30eJlUJl 221
4. 1.37. BS EN ISO 228-1: 2003. Tpy6H&le pe3&6&1,
He o6ecnelfJfSSIO Jfe repMeTJflfHOCT& COeAJfHeHlAfI
Pa3MepLI, ,n;OnyCKH H 0003Ha1JeHHJI
06JlaCmb npUMenenUR
3Ta qaCTb ISO 228 onpe,neJUIeT TPe60BaHlUI K npo<pHJIIO, pa3MepaM, ,norrycKaM
H 0603HaqeHlUIM TPy6HOH pe3b6bI ,l(JUI pe3b60BbIX coe,nHHeHHH C pa3MepaMH pe3b-
6bIOT 1/16 ,no 6 BKJIlOqHTeJIbHO. H BHyrpeHHHe, H Hap)')KHbIe [(HJIHH):(pHqeCKHe pe-
3b6bI npe,nHa3HaqeHbI ,l(JUI MexaHWIeCKHX coe,nHHeHHH ,neTaJIeH <pHTHHroB, KpaHOB
H BeHTHJIeH, BcnOMOraTeJIbHOrO 060py,noBaHIDI H T.,n.
3TH pe3b6bI He IIO,nXO,n.HT B KaqeCTBe coe,nHIDIIOIUHX, eCJIH pe3b60Boe coe,nH-
HeHHe ,nOJDKHO 6bITb repMeTHqHbIM. ECJIH coe,nHHeHHe C HCnOJIb30BaHHeM Ta-
KHX pe3b6 ,nOJDKHO 6bITb repMeTHqHbIM, CJIe,nyeT YCTaHOBHTb ,nBe CTonopHbIe IIJIac-
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/
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ISO 7 -1.
. B ISO 228-2 no,np06HO OIIHcaHbI MeTo,nbI npOBepKH pa3MepOB H npo<pIDIeH
Kpene)I{HOH pe3b6bI, a TaIOKe peKOMe eMbIe KaJIH6pbI.
HOpMaTHBHLIe CCLIJIKH
HIDKeCJIe,ayroIUHH HopMaTHBHbIH ,nOJ<yMeHT co,nep)I{HT nOJIOXeHlUI, KOTopbIe,
Qepe3 CCbillKH B TeKCTe, .HBJUlIOTC.H IIOJIOXeHlUIMH cooTBeTcTByroIUeH qaCTH ISO
228. LVrn ,naTHpOBaHHbIX CCbillOK He npHMeHHMa JII06aH H3 rry6JIHKa[(HH C nOCJIe.ny-
IOInHMH nonpaBKaMH HJIH B ,npyrOH pe,naKUHH. O,nHaKO yqacTHHKH COrJIaIIIeHlUI,
OCHOBaHHoro Ha 3TOH qaCTH ISO 228, nO,lI,l(ep)I{HBaIOT HCCJIe,nOBaHlUI, HanpaBJIeH-
HbIe Ha B03MO)I{HOCTb npHMeHeHlUI HOBeHllIHX BbIrryCKOB HopMaTHBHoro ,nOJ<yMeH-
Ta, YKa3aHHoro HIDKe. He,naTHpOBaHHbIX CCbIJIOK npHMeIDIeTC.H IIOCJIe,nHHH BbI-
rrYCK HopMaTHBHoro ,nOJ<yMeHTa, 0 KOTOpOM eT peqb. qJIeHbI ISO (MelK.UYHapo,n-
Hag opraHH3a[(IDI no CTaH):(apTH3a[(HH) H IEC (MelK.UYHapo,nHaH 3JIeKTpOTeXHlNe-
CKaH KOMHCClUI, M3K) IIO,lI,l(ep)I{HBaIOT peeCTpbI ,neHCTBHTeJIbHbIX B HaCTO.HIUee
BpeWI MelK.UYHapo,nHbIX CTaH):(apTOB.
ISO 7-1 1994, Tpy6HbIe pe3b6bI, 06eCneqHBalOIUHe repMeTHqHOCTb coe,nHHe-
HIDI. qacTb 1. Pa3MepbI, ,nOrryCKH H 0603HaqeHHe.
CHMBOJILI
B 3TOH qaCTH ISO 228 HCnOJIb3yroTC.H CJIe,ayroIUHe 0603HaqeHlUI:
A Krracc C xeCTKHMH ,norrycKaMH Ha Hap)')KHbIe TPy6HbIe pe3b6bI, He 06ecne-
qHBalOIUHe repMeTHqHOCTb coe,nHHeHlUI.
B Krracc C 60JIee IIIHpOKHMH ,norrycKaMH Ha Hap)')KHbIe Tpy6HbIe pe3b6bI, He
06eCneqHBalOIUHe repMeTHqHOCTb coe,nHHeHlUI.
F/la8a 4. Kpene:JICHble oemOJlu
D = d; Hap)')KHbIH JJ;HaMeTP BHYTPeHHeH pe3b6bI.
D} = D - 1,280 654 P = d}; BHYTPeHHHH JJ;HaMeTP BHYTpeHHeH pe3b6bI.
D 2 = D - 0,640 327 P = d 2 ; cpeJJ;HHH JJ;HaMeTPa BHYTPeHHeH pe3b6bI.
d Hap)')KHbIH JJ;HaMeTP Hap)')KHOH pe3b6bI.
d} = d - 1,280 654 P; BHYTPeHHHH JJ;HaMeTP Hap)')KHoH pe3b6bI.
d 2 = d - 0,640 327 P; CpeJJ;HHH JJ;HaMeTPa Hap)')KHOH pe3b6bI.
G Tpy6Ha.H pe3b6a, He 06eCIIeqHBaIOIUa.H repMeTINHOCTb coeJJ;HHeHlUI.
H BbICOTa HCXOJJ;Horo TPeyrOJIbHHKa pe3b6bI.
h Pa60qa.H BbICOTa IIPO<pHJI.H pe3b6bI (c 3aKpyrJIeHHbIMH BepIIIHHaMH H Bna-
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P IIIar.
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T Dt ,lJ;OrryCK Ha BHYTPeHHHH JJ;HaMeTP BHYTPeHHeH pe3b6bI.
T D2 ,lJ;OrryCK Ha CpeJJ;HHH JJ;HaMeTPa BHYTpeHHeH pe3b6bI.
Td ,lJ;OrryCK Ha Hap)')KHbIH ,ZJ;HaMeTPa Hap)')KHOH pe3b6bI.
T d2 ,lJ;OrryCK Ha cpeJJ;HHH JJ;HaMeTPa Hap)')KHoH pe3b6bI.
Pa3MepLI
IIpo<pHJIb 3THX pe3b6 H,LJ;eHTlNeH IIpO<pHJIIO :QHJIHH):(pHqeCKOH pe3b6bI, OIIpe,D;e-
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peHHHe, TaK H Hap)')KHbIe pe3b6bI.
ECJIH He orOBopeHO HHoe, pe3b6a, COOTBeTCTByroIUa.H 3TOH qaCTH ISO 228, SIB-
JUIeTC.H IIpaBoH pe3b60H (CMOTpH TaIOKe rryHKT 5).
BepIIIHHbI pe3b6bI 06bIqHO BbIIIOJIIDIIOTC.H C IIJIOCKHM cpe30M B IIpeJJ;eJIax JJ;ony-
CKa, KaK yx:a3aHO B KOJIOHKax 14 H 15 BS EN ISO 228-1: 2003 Ta6JIH[(a 1. MCKJlIO-
qeHHe COCTaBJUIIOT BHYTPeHHHe pe3b6bI, eCJIH CylI(eCTyeT B03MO)I{HOCTb HX coe,D;H-
HeHlUI C BHeIIIHHMH pe3b6aMH B COOTBeTCTBHH C ISO 7-1, H B 3TOM c.rryqae ,lJ)IHHa
pe3b6bI JJ;OJDKHa 6bITb paBHoH HJIH 60JIbIIIeH, qeM onpeJJ;eJIeHa B ISO 7-1.
,lJ;OrryCK Ha CpeJJ;HHH JJ;HaMeTP BHYTPeHHHX pe3b6 COOTBeTcTByeT nOJIO)I{HTeJIbHO-
MY OTKJIOHeHHIO JJ;OrryCKOB JJ;HaMeTPa B ISO 7-1, 3a HCKJIlOqeHHeM Tex pe3b6 C pa3-
MepaMH 1/16, 1/8, 1/4 H 3/8, ,l(JUI KOTOpbIX onpeJJ;eJIeHbI HeMHoro 60JIee BbICOKHe
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,lJ;.mI Hap)')KHbIX pe3b6 OIIpeJJ;eJIeHbI JJ;Ba KJIacca JJ;OrryCKOB Ha CpeJJ;HHH JJ;HaMerp
(CMOTPH BS EN ISO 228-1: 2003 Ta6JIH[(a 1).
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KIDK;:(bIH H3 KOTOpbIX 3KBHBaJIeHTeH COOTBeTCTByroIUeMY JJ;orrycKy Ha BHYT-'
peHHIOIO pe3b6y.
. Krracc B (KOJIOHKa 11) COCTOHT H3 nOJIHOCTbIO OTPH[(aTeJIbHbIX JJ;OrryCKOB,
KIDK;:(bIH H3 KOTOpbIX paBeH yJJ;BoeHHOMY 3HaqeHHIO COOTBeTCTyIDIUero ,ZJ;onyc-
Ky Ha BHYTPeHHIOIO pe3b6y.
BbI60p Me KJIaCCOM A H KJIaCCOM B 3aBHCHT OT YCJIOBHH npHMeHeHIDI Ii
JJ;OJDKeH 6bITb CJJ;eJIaH B CTaH):(apTaX Ha npO,nyK[(HIO, ,l(JUI KOTOpOH pe3b6bI onpeJJ;eJIe-
HbI B COOTBeTCTBHH C 3TOH qaCTbIO ISO 228.
Pa3MepbI TPy6HbIX pe3b6, B MHJIJIHMeTPax, JJ;aHbI B BS EN ISO 228-1: 2003
Ta6JIH[(a 1.
4.1. BUHmo6ble "peneJICHble U30eJlUJl
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I ...-4 ...-4 V) V) 00 00 00 00 \0 \0 \0 \0 \0 \0 M M M M M M M M M M
N N N N C'! N N C'! M M M M M M v
= 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
I I I I I I I I I I I I I I I I I I I I I I I I
It N N V) V) ...-4 ...-4 ...-4 ...-4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
S- 00 00 v v v v v v v v v v v v v v v v v v v v v
i i :;: N N V) V; V; V) d d \0 \0 d d ; d \0 d d d d d d
0 0 0 0 0 0 0 0 0 0 0 0
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t = v v 0 0 v v v v 0 0 0 0 0 0 v v v v v v v v v
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i ! ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 C'! C'! C'! C'! C'! C'! C'! C'! C'! C'!
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S- ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 ...-4 C'! C'! C'! C'! N N C'! C'!
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Ha pRC. 1 nOKa3aHa KpeIIe)I{H8j{ pe3b6a C nOJIHbIM npo<pHJIeM R noJUI ,norrycKa.
Ha pRC. 2 nOKa3aH npo<pHJIb Kpene)I{HOH pe3b6bI C IIJIOCKOCpe3aHHbIMH BepmH-
HaMR H noJUI ,norrycKa.
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(1) H = 0,960491P.
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4.1. BUHmo8ble "pene:JICHble U30eJlUJI
0003Ha1JeHHJI
0603HaqeHHe pe3b6bI ,nOJDKHO COCTO.HTb H3 CJIe,ayroIUHx 3JIeMeHTOB B ,u;aHHoH
rrocne,nOBaTeJIbHOCTH:
1. OnHCaTeJIbHbIH 6JIOK: Tpy6HaH pe3b6a.
2. DJIOK, yx:a3bIBaIOIUHH Ha HOMep Me)l()];yJIapo,nHoro CTaH):(apTa: ISO 228.
3. DJIOK, oIIpe,neJUIIOIUHH KOHKpeTHyIO pe3b6y (O,nHH H3 CJIe,n;yIOIUHX, B 3aBHCH-
MOCTH OT CJIytIaH):
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BS EN ISO 228-1: 2003 Ta6JIH[(a 1 ,l(JUI BHyrpeHHHX pe3b6 (TOJIbKO O,nHH
KJIacc TOqHOCTH); HJIH
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H3 BS EN ISO 228-1: 2003 Ta6JIH[(a 1 H 6yxBa A,l(JUI KJIacca TOqHOCTH A
Hap)')KHbIX pe3b6; HJIH
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H3 BS EN ISO 228-1: 2003 Ta6JIH[(a 1 H 6YKBa B ,ZJ;JI.H KJIacca TOqHOCTH B
Hap)')KHbIX pe3b6.
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Krracc TOqHOCTH B
Tpy6HbIe pe3b6bI ISO 228 - G 1 1/2
Hap)')KHaH pe3b6a
Tpy6HbIe pe3b6bI ISO 228 - G 1 1/2 A
Tpy6HbIe pe3b6bI ISO 228 - G 1 1/2 B
C01JeTaHHJI c COe,ZJ;llHHTeJILHLIMH pe3LoaMH
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COOTBeTcTByroIUeH C ISO 228-1, H BHYTpeHHeH [(HJIHH):(pHqeCKOH pe3b6bI Rp, COOT-
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8-3255
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OCHOSH&le pS3Mep&l
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(AI1 Ha cnonb3yeMoH pe3b6bl 3a OCHOBHOH
nnOCKOCTblO, He06xOA Ma , "IT06bl 06ecne-
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HOMHH8JIb1lhIi p83Mep 1'py6hI a qHCJIO mar Pa601faJI ,lI;HaMeTp pe3h6hI B OCHOBHOA DJIOCKOCTH (0)
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25,4 MM (MM)
1/8 6 28 0_907 0_581 9_728 9_147 8_566
1/4 &- 19 1_337 0_856 13_157 12_301 11_445
3/8 10 19 1_337 0_856 16_662 15_806 14.950
1/2 15 14 1.814 1.162 20.955 19.793 18.631
3/4 20 14 1.814 1.162 26.441 25.279 24.117
1 25 11 2.309 1.479 33.249 31.770 30_291
1 1/8 32 11 2_309 1_479 41_910 40_431 38_952
1 1/8 40 11 2_ 309 1_479 47 _803 46_324 44.845
2 50 11 2309 1_479 59_614 58.135 56.656
2 1/8 65 11 2.309 1_479 75.184 73.705 72.226
3 80 11 2309 1.479 87.884 86.405 84.926
4 100 11 2.309 1.479 113.030 111.551 110_072
5 125 11 2_309 1_479 138_430 136_951 135_472
6 150 11 2_309 1_479 163_830 162_351 160_872
a 3KBHBaJIeHTbI HOMHHaJIbHbIX ,lI;HaMeTpOB 'rpy6, a He pe3YJIbTaTbI npe06pa30BaHHH.
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Ta6JI. 2.
HOMH- Aruma HapymtoA pe3h6hI Aruma ,n;OnyCK
B8Jlb1lhdi Pa601faJI ,lUIIIIIa pe3h6hI Ha npa- Ha DO-
p83Mep OT ropna .no OCHOBHOA (MHH.) c60PKY nyCK JI01Ke- ,n;OnyCK
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1/8 6 4 3/8 1 5 3/8 3 3/8 7 1/8 8 1/8 6 1/8 2 1/2 1 1/2 1 1/4 0,071
(4,0) (0,9) (4,9) (3,1) (6,5) (7,4) (5,6) (2,5) (1,4) (1,1)
1/4 8 4 1/2 1 5 1/2 3 1/2 7 1/4 8 1/4 6 1/4 2 1/2 1 1/2 1 1/4 0,104
(5,0) (1,3) (7,3) (4,7) (9,7) (11,0) (8,4) (3,7) (2,0) ( 1 , 7)
3/8 10 4 1/2 1 5 1/2 3 1/2 7 1/2 8 1/2 6 1/2 2 1/2 1 1/2 1 1/4 0,104
(6,4) (1,3) (7,7) (5,1) (10,1) (11,4) (8,8) (3,7) (2,0) ( 1 , 7)
1/2 15 4 1/2 1 5 1/2 3 1/2 7 1/4 8 1/4 6 1/4 2 1/2 1 1/2 1 1/4 0,142
(8,2) (1,8) (10,0) (6,4) ( 13,2) (15,0) (11,4) (5,0) (2,7) (2,3)
1/2 20 5 1/4 1 6 1/4 4 1/4 8 9 7 2 1/4 1 1/2 1 1/4 0,142
(9,5) (1,8) (11,3) (7,7) (14,5) ( 16,3) (12,7) (5,0) (2,7) (2,3)
1 25 4 1/2 1 5 1/2 3 1/2 7 1/4 8 1/2 6 1/4 2 1/2 1 1/2 1 1/4 0, 180
(10,4) (2,3) (12,7) (8,1) (16,8) (19,1) (14,5) (6,4) (3,5) (2,9)
11/4 32 5 1/2 1 6 1/2 4 1/2 8 1/4 9 1/4 7 1/4 2 1/2 1 1/2 1 1/4 0, 180
(12,7) (2,3) (15,0) (10,4) (19,1) (21,4) (16,8) (6,4) (3,5) (2,9)
11/2 40 5 1/2 1 6 1/2 4 1/2 8 1/4 9 1/4 7 1/4 2 3/4 1 1/2 1 1/4 0,180
(12,7) (2,3) ( 15,0) (10,4) (19,1) (21,4) (16,8) (6,4) (3,5) (2,9)
2 50 6 7/8 1 7 7/8 5 7/8 10 1/8 11 1/8 9 1/8 3 1/4 2 1 1/4 0, 180
(15,9) (2,3) (18,2) (15,6) (23,4) (25,7) (21,1) (7,5) (4,6) (2,9)
2 1/2 65 7 9/16 1 1/2 9 1/16 6 1/16 11 9/16 13 1/16 10 1/16 4 2 1/2 1 1/2 0,216
(17,5) (3,5) (21,0) (14,0) (26,7) (30,2) (23,2) (9,2) (5,8) (3,5)
3 80 8 15/16 1 1/2 10 7/16 7 7/16 12 15/16 14 7/16 11 7/16 4 2 1/2 1 1/2 0,216
(20,6) (3,5) (24,1) (17,1) (29,8) (33,3) (26,3) (9,2) (5,8) (3,5)
4 100 11 1 1/2 12 1/2 9 1/2 15 1/2 17 14 4 1/2 3 1 1/2 0,216
(25,4) (3,5) (28,9) (21,9) (35,8) (19,3) (32,3) (10,4) (6,9) (3,5)
5 125 12 3/8 1 1/2 13 7 /8 10 7 /8 17 3/8 18 7/8 15 7/8 5 3 1/2 1 1/2 0,216
(28,6) (3,5) (32,1) (25,1) (40,1) (43,6) (36,6) (11,5) (8,1) (3,5)
6 150 12 3/8 1 1/2 13 7 /8 10 7 /8 17 7 /8 18 7/8 15 7 /8 5 3 1/2 1 1/2 0,216
(28,6) (3,5) (32,1) (25,1) (40,1) (43,6) (36,6) (11,5) (8,1) (3,5)
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M48 43,00 - 50,0 52,0 56,0
M52 4 7 00 - 54_0 56_0 62 0
F/la8a 4. Kpene:»cHble oemOJlu
4. 1.49. PS3Mep&1 csepn Anfl oTSepCTJfH nOA
ISO MeTpJflfeCKYIO pe3&6y Jf Anfl CKS03H&IX
oTSepCTJfH C 3S30pOM: PflA C KpynHoH pe3&6oif
HOMHHaJIh.....H Pa3Mep CBepJla DO pe3WY (MM) P83Mep CBepJla .zum CKB03HhIX OTBepcTHii (MM)
p83Mep PeKOMeu.nyeMoe AJIhTepHaTHBHoe nOC8,lI,K8 C nepexo.lUlaJI noc8,ll,K8c
80% 3aQeDJIeHHe 70% 3aQeDJIeHHe HaTJlroM (1 PB.lO DOC8,ll,K8 (2 PW 3a30pOM (3 pJiJQ
M6 5,20 5,30 6,4 6,6 7,0
M8 7,00 7,10 8,4 9,0 10,0
MI0 8,80 8,90 10,5 11,0 12,0
M12 10,80 10,90 13,0 14,0 15,0
M14 12,50 12,70 15,0 16,0 17,0
M16 14,50 14,75 17,0 18,0 19,0
M18 16,50 16,75 19,0 20,0 21,0
M20 18,50 18,75 21,0 22,0 24,0
M22 20,50 20,75 23,0 24,0 26,0
M24 22,00 22,25 25,0 26,0 28,0
M27 25,00 25,25 28,0 30,0 32,0
M30 28,00 28,25 31,0 33,0 35,0
M33 31,00 31,25 34,0 36,0 38,0
M36 33,00 - 37,0 39,0 42,0
M39 36,00 - 40,0 42,0 45,0
M42 39 00 - 43 0 45 0 48 0
4. 1.50. PS3Mep&1 csepn p,nfl oTSepCTJfH nOA
ISO YHJfcpJfqJfPOSSHHYIO pe3&6y Jf Anfl CKS03H&IX
oTSepCTJfH C 3S30pOM: pe3&6s C MenKJfM wsrOM
HOMHHaJIhllhlii P83Mep CBepJla DO pe3hOY Pa3Mep CBepJla .zum CKB03....1X OTBepcTHii
p83Mep, ,lJ.IOHM MM ,lJ.IOHM MM oyua HJIH ,lJ.IOHM
1 5,20 13 6,50 17
-x20 - A HJIH -
4 64 64
5 6,60 17 8,00 21
-x18 - o HJIH -
16 64 64
3 8,00 5 9,80 25
-x16 - W HJIH -
4 16 64
7 9,40 3 11,30 33
-x14 - -
16 8 64
1 10,80 27 13,00 33
-x13 - -
2 64 64
9 12,20 31 14,75 37
-x12 - -
16 64 64
5 13,50 17 16,25 41
-xlI - -
8 32 64
3 16,50 21 19,50 47
-x10 - -
4 32 64
7 19,25 49 20,25 51
-x9 - -
8 64 64
4.1. BUHmo8ble Kpene:JICHble U30e.tlUJI
OKoH"taHue
HOMHH8JIh1lldi Pa3Mep CBepJIa DO pe3hoy P83Mep CBepJIa .n;JUI CKB0311h1X OTBepcTHii
p83Mep, ,lJ.IOHM MM ,lJ.IOHM MM oyua HJIH ,lJ.IOHM
1x8 22,25 7 25,75 1-.L
-
8 64
1 25,00 63 26,00 1
1-x7 -
8 64 64
1 28,25 a 1 28,25 1 17
1-x7
4 64 64
3 30,50 a III 30,75 1 25
l-x6
8 64 64
1 34,00a 1 21 34,00 1 33
1-x6
2 64 64
3 39,50 a 1 35 45,00 1 49
1-x5
4 64 64
1 45,50 a 1 25 52,00 2-.L
2x4-
2 64 64
a DJIHXaHIlIHH CTaH,lJ;apTHbIH MeTpHQeCKHH pa3Mep: npH6JIH3HTeJIbHO Ha 0,25 MM 60JIb-
me peKOMeH,l(yeMoro ,lI;IOHMoBoro pa3Mepa.
4.1.51. PS3Mep&1 csepn Anfl OTSepCTJfH nOA
ISO YHJfcpJfqJfpOSSHHYIO pe3&6y Jf Anfl CKS03H&IX
OTSepCTJfH C 3S30pOM: pe3&6s C MenKJfM warOM
HOMHHaJIhHhlH p83Mep Pa3Mep CBepJIa DO pe3hOY Pa3Mep CBepJIa .n;JUI CKB0311h1X oTBepCTHii
,lJ.IOHM MM oyua HJIH ,lJ.IOHM MM oyua HJIH ,lJ.IOHM
)
1/4x28 5,50 7/32 6,50 F
5/16x24 6,90 I 8,00 0
3/8x24 8,50 R 9,80 W
7/16x20 9,90 25/64 11 ,30 29/64
1/2x20 11,50 29/64 13,00 33/64
9/16x18 12,90 33/64 14,75 37/64
5/8x18 14,50 37/64 16,50 41/64
1/2x 16 17,50 11/16 19,50 49/64
7/8x14 20,50 13/16 22,75 57/64
1x12 23,25 59/64 25,80 1 1/64
1 1/8x 12 26,50 1 3/64 29,00 1 9/64
1 1/4x12 29,50 ] 11/64 32,50 1 17/64
1 3/8x 12 33,00 1 19/64 35,50 1 25/64
] 1/2x 12 36,00 1 27 /64 38,50 1 33/64
F/la8a 4. Kpene:JICHble oemOJlu
4. 1.52. PS3Mep&1 csepn p,nfl oTSepCTJfH nOA
ISO MeTpJflfeCKYIO pe3&6y Jf Anfl CKS03H&IX
oTSepCTJfH C 3S30pOM: MJfHJfSTlOpHSfI cepJffl
HOMHH8JIhHhIii p83Mep mar Pa3Mep CBepJIa DO pe3hOY P83Mep CBepJIa JUUI
BHTKH CKB03HhIX OTBepcTHii
Ha ,lJ.IOHM
ISO MM ASA Bl.10 MM MM MM 1fHCJIO HJIH OOh MM 1fHCJIO HJIH p06h
S-O 3 0,30 unm 0,080 318 0,25 - 0,32 -
,
(S-0,35) (0,35 unm) 0,090 282 0,28 - 0,38 79
S-O 4 0,40 unm 0,100 254 0,35 80 0,45 77
,
(S-0,45) (0,45 unm) 0,100 254 0,38 79 0,50 76
S-O 5 0,50 unm 0,125 203 0,42 78 0,55 75,74
,
(S-0,55) (0,55 unm) 0,125 203 0,45 77 0,60 73
s-o 6 0,60 unm 0,150 169 0,50 76 0,65 72
,
(S-0,7) (0,70 unm) 0,175 145 0,58 74 0,78 1/32 ,lI;IOHMa
S-O 8 0,80 unm 0,200 127 0,65 72 0,88 66,65
,
(S-0,9) (0,90 unm) 0,225 113 0,72 70 0,98 62
S-10 1,00 unm 0,250 102 0,80 1/32 ,lI;IOHMa 1,10 57
,
(5-1,1) (1,10 unm) 0,250 102 0,90 65 1,20 3/64 ,lI;IOHMa
S-12 1,20 unm 0,250 102 1,00 61 1,30 55
,
(S-1,4) (1,40 unm) 0,300 85 1,15 3/64 ,lI;IOHMa 1,50 53
4. 1.53. PS3Mep&1 csepn p,nfl OTSepCTJfH nOA SSW pe3&6y
Jf p,nfl CKS03H&IX OTSepCTJfH C 3S30pOM pe3&6&I,
HSpe3H&le Jf npOlfJf SIO Jfe MeTlfJfKJf
Pa3Mep BHTKH no ,lI;mI CKB03HhIX Pa3Mep BUTKH no ,lI;mI CKB03HhIX
Ha ,lJ.IOHM pe3hOY OTBepcTHii Ha ,lJ.IOHM pe3hOY OTBepcTHii
1/16 60 58 49 1/4 20 7 G
3/32 48 49 36 5/16 18 F P
1/8 40 38 29 3/8 16 0 W
5/32 32 31 19 7/16 14 U 29/64
3/16 24 26 9 1/2 12 27/64 33/64
7/32 24 15 1
4. 1.54. PS3Mep&1 csepn p,nfl OTSepCTJfH nOA SSF pe3&6y
Jf p,nfl CKS03H&IX OTSepCTJfH C 3S30pOM pe3&6&I,
HSpe3H&le Jf npOlfJf SIO Jfe MeTlfJfKJf
Pa3Mep BUTKH no ,lI;mI CKB03HhIX Pa3Mep BHTKH no ,lI;mI CKB03HhIX
Ha ,lJ.IOHM pe3hOY OTBepcTHii Ha ,lJ.IOHM pe3hOY OTBepCTHii:
7/32 28 14 1 3/8 20 21/64 W
1/4 26 3 G 7/16 18 W 29/64
9/32 26 C M 1/2 16 7/16 33/64
5/16 22 H P
4.1. BUHmo6ble "peneJICHble U30eJlUR 23 9
4.1.55. nnOCKJfe WSH6&I, IfJfCT&le: MeTpJflfeCKJfH PflA
Pa3MepbI B MM
d 1
d 2
-!s
BuyrpeHHHH BHeIlIllllii TOJIDUllla s
0603Ha'leHHe aM d t aMeTp d z
WtaMeTp TOJiCThie (HopMaJIhHLIe) TOHKHe
Pe3hOhl)8 I
MaKe. MHH. MaKe. MHH. MaKe. MHH. MaKe. MHH.
M1..0 1..25 1.1 2.5 2.3 0.4 0.2 - -
M1.2 1..45 1.3 3.0 2.8 0.4 0.2 - -
(M1.4) 1..65 1.5 3.0 2.8 0.4 0.2 - -
M1.6 1.85 1..7 4.0 3.7 0.4 0.2 - -
M2,0 2.35 2.2 5.0 4.7 0.4 0.2 - -
(M2,2) 2.55 2.4 5.0 4.7 0.6 0.4 - -
M2,5 2,85 2,7 6.5 6.2 0.6 0.4 - -
M3 3,4 3,2 7,0 6,7 0.6 0.4 - -
(M3,5) 3,9 3,7 7,0 6,7 0,6 0,4 - -
M4 4.5 4.3 9,0 8,7 0,9 0,7 - -
(M4.5) 5.0 4.8 9,0 18,7 0,9 0,7 - -
M5 5.5 5.3 10.0 9.7 1.1 0.9 - -
M6 6.7 6.4 12.5 12.1 1.8 1.4 0.9 0.7
(M7) 7,7 7,4 14.0 13.6 1.8 1.4 0.9 0.7
M8 8,7 8.4 17.0 16.6 1..8 1..4 1.1 0.9
MI0 10,9 10,5 21,0 20.5 2.2 1.8 1.45 1.05
M12 13,4 13,0 24,0 23.5 2.7 2.3 1..8 1.4
(M14) 15,4 15,0 28,0 27,5 2,7 2,3 1..8 1,4
M16 17.4 17.0 30,0 29,5 3,3 2,7 2,2 1,8
(M18) 19.5 19.0 34,0 33,2 3,3 2,7 2,2 1,8
M20 21.5 21.0 37.0 36.2 3,3 2,7 2,2 1,8
(M22) 23.5 23.0 39.0 38.2 3,3 2,7 2,2 1,8
M24 25.5 25.0 44.0 43.2 4.3 3.7 2.7 2.3
(M27) 28.5 28.0 50.0 49.2 4.3 3.7 2.7 2.3
M30 31,6 31.0 56.0 55.0 4.3 3.7 2.7 2.3
(M33) 34,6 34.0 60.0 59.0 5.6 4.4 3.3 2.7
M36 37,6 37,0 66,0 65.0 5.6 4.4 3.3 2.7
(M39) 40,6 40,0 72,0 71,0 6.6 5.4 3.3 2.7
a CneI(HaJIbHbIe pa3MepbI yJ<a3aHbI B cK06Kax ().
DOJIee nOJIHyID HH<popMaI(HIO CMOTpH B BS 4320.
F/la8a 4. Kpene:JICHble oemOJlu
4. 1.56. nnOCKJfe waH6&I, lfepH&le: MeTpJflfeCKJfH PflA
d 1
Pa3MepbI B MM
d 2
s s
0003Ha'leHHe Buyrpellllllii: )UlaMeTp d 1 BHeIlIllllii )UlaMeTp d z TOJIDUllla s
()UlaMeTp
pe3hohl)8 MaKe. MHH. MaKC. MUH. MaKe. MHH.
M5 5,8 5,5 10,0 9,2 1,2 0,8
M6 7,0 6,6 12,5 11,7 1,9 1,3
(M7) 8,0 7,6 14,0 13,2 1,9 1,3
M8 9,4 9,0 17,0 16,2 1,9 1,3
MI0 11,5 11,0 21,0 20,2 2,3 1,7
M12 14,5 14,0 24,0 23,2 2,8 2,2
(M14) 16,5 16,0 28,0 27,2 2,8 2,2
M16 18,5 18,0 30,0 29,2 3,6 2,4
(M18) 20,6 20,0 34,0 32,8 3,6 2,4
M20 22,6 22,0 370 35,8 3,6 2,4
(M22) 24,6 24,0 39,0 37,8 3,6 2,4
M24 26,6 26,0 44,0 42,8 4,6 3,4
(M27) 30,6 30,0 50,0 48,8 4,6 3,4
M30 33,8 33,0 56,0 54,5 4,6 3,4
(M33) 36,8 36,0 60,0 58,5 6,0 4,0
M36 39,8 39,0 66,0 64,5 6,0 4,0
(M39) 42,8 42,0 72,0 70,5 7,0 5,0
M42 45,8 45,0 78,0 76,5 8,2 5,8
(M45) 48,8 48,0 85,0 83,0 8,2 5,8
M48 53,0 52,0 92,0 90,0 9,2 6,8
(M52) 57,0 56,0 98,0 96,0 9,2 6,8
M56 63,0 62,0 105,0 103,0 10,2 7,8
(M60) 67,0 66,0 110,0 108,0 10,2 7,8
M64 71,0 70,0 115,0 113,0 10,2 7,8
(M68) 75,0 74,0 120,0 118,0 11,2 8,8
a CneUHaJIbHbIe pa3MepbI yJ<a3aHbI B cK06Kax ().
Donee nOJIHyID HH<popMaUHIO CMOTpH B BS 4320.
4.1. BUHmo6ble "peneJICHble U30eflUR 241
4.1.57. YCTpOHCTBS Anfl cTOnOpeHJffl,
OCHOBSHH&le HS TpeHJfJf
CTOnOpHaJi raiKa
CaMOCTOnOpJlInaJlCJI raiiKa
(c KOJILD;eBOi BCTaBKoi)
rat1Ka nOJ1-
HOt1 BblCOTbl
BCTaBKa 3 Het1J10-
Ha J1 nJ1aCT Ka
CTonopHa J1
3a)l( MHa rat1Ka
nJ10CKa wat16a
nJ10CKa
wat16a
CaMOCTOnOpJlInaJlCJI raHKa (IneJIeBaJi rOJIOBKa)
nJ10CKa
wat16a
eJ1eBa51 r0J10BKa
(c AByxcerMeHTHblM
npOn J10M)
eJ1eBa r0J10BKa
(c KOJ1bu.eBbIM npOn J10M)
nJ10CKa
wat16a
3YO'laTan nPY1KHHHaJi maHoa
/
Cn0J1b30BaH e 3y6"1aTot1
np HHot1 (3aw. w.eHHot1
OT caMOOTB H"I BaH 5I np
COTp5lCeH X) wat16bl
CMOTPH npo CTOIIopHbIe IIIai1:6bI:
IIp)')KHHHa.H maH6a 4.1.59,4.1.60,4.1.61
IIp)')KHHHa.H maH6a C 3y6bHMH 4.1.62
CTOIIOpHa.H maH6a C 3y6bHMH 4.1.63
IIp)')KHHHIDI BOJIHHCTaSI IIIaH6a 4.1.64
F/la8a 4. Kpene:JICHble oemOJlu
4. 1.58. YCTpOHCTBS,lInfl CTOnOpeHJffl, OCHOBSHH&le
HS MeXSHJflfeCKOH cpJfKCSqJfJf
npOpe3HaJi raHKa
CTOnOpHaJi
DJIaCTHHa
BJl3Ka
npOBOJIOKOH
KOpOJl1laTaJI ranKa
CTOnOpHaJI manoa
(c JIanKaMH HJIH HOCKOM)
KOHLJ.bl npOBOAa
CKPY"IeHbl BMeCTe
aaKpenJ1eHbl
4.1. BUHmo8ble Kpene:JICHble U30e.tlUR
4. 1.59. npyJKJfHHSfI wsii6s C KBSAPSTH&IM nonepelfH&lM
CelfeHJfeM: MeTpJflfeCKJfii PflA, TJfn A
1 s r-
,
I
Ce"leHVle xx
h = 2s :!:: 15%
Pa3MepbI B MM
HOMHHaJILHai BuyTpeHHHi BHemHHi P8,lUIycr
p83Mep H ,lUIaMeTp ,lUIaMeTp d t TOJIIIUIHa ,lUIaMeTp d 2
pe3L6Ll a d H IIIIIpHHa s
MaKC. MHH. MaKC. MaKC.
M3 3,3 3,1 1 :to, 1 5,5 0,3
(M3,5) 3,8 3,6 1 :to, 1 6,0 0,3
M4 4,35 4,1 1 2 :to, 1 6,95 0,4
M5 5,35 5,1 1,5 :to, 1 8,55 0,5
M6 6,4 6,1 1,5 :to, 1 9,6 0,5
M8 8,55 8,2 2 IO, 1 12,75 0,65
MIO 10,6 10,2 2,5 :to, 15 15,9 0,8
M12 12,6 12,2 2,5 :to, 15 17,9 0,8
(M 14) 14,7 14,2 3 :to, 2 21,1 1,0
M16 16,9 16,3 3,5 :t 0,2 24,3 1,15
(M 18) 19,0 18,3 3,5 :to,2 26,4 1,15
M20 21,1 20,3 4,5 :t 0,2 30,5 1,5
(M22) 23,3 22,4 4,5 :t 0,2 32,7 1,5
M24 25,3 24,4 5 :to, 2 35,7 1,65
(M27) 28,5 27,5 5 :to, 2 38,9 1,65
M30 31,5 30,5 6 :to, 2 43,9 2,0
(M33) 34,6 33,5 6 :to, 2 47,0 2,0
M36 37,6 36,5 7 :t 0,25 52,1 2,3
(M39) 40,8 39,6 7 :t 0,25 55,3 2,3
M42 43,8 42,6 8 :t 0,25 60,3 2,65
(M45) 46,8 45,6 8 :t 0,25 63,3 2,65
M48 50,0 48,8 8 :t 0,25 66,5 2,65
a B cK06Kax )'Ka3aHbI cneQHaJIbHbIe, pe,ll;KO BCTpeqaIOID;HeCH pa3MepbI.
,lJ.aJIbHeHrnyIO HH<popMaQHIO CMOTpH B BS 4464.
F/la8a 4. Kpene:JICHble oemOJlu
4. 1.60. npyJKJfHHSfI wsif6s C npflMoyrOn&H&IMJf KOHqSMJf:
MeTpJflfeCKSfI CepJffl, TJfn&1 B Jf BP
k
WTpVlx-nYHKTVlpOM
nOKaaaHa np VlHHa
wat16a C nJ10CKVlM
KOHU.OM
YBeJ1V1"1eHHblt1 ct>parMeHT A
McnonHeHMe BP
h 1 = (28 + 2k) :t 15%
McnonHeHMe B
Ce"leHVle XX
h 2 = 28 :t 15%
Pa3MepbI B MM
HOMHHaJlbHLIH BuyrpelUllfii BHeomHii P8,lUIyC , k (TOJlbKO
pa3Mep ,lUI8MeTp d t illHpHHa b TOJlllUllla s ,lUI8MeTp d 2 .lJ,JUI THDa
H ,lUIaMeTp BP)
pe3L6 y a d MaKC. MHH. MaKC. MaKC.
Ml,6 1,9 1,7 0,7:t 0,1 0,4 :t 0,1 3,5 0,15 -
M2 2,3 2,1 0,9 :t 0,1 0,5 :t 0,1 4,3 0,15 -
(M2,2) 2,5 2,3 1,0 :t 0,1 0,6 :t 0,1 4,7 0,2 -
M2,5 2,8 2,6 1,0 :t 0,1 0,6 :t 0,1 5,0 0,2 -
M3 3,3 3,1 1,3 :t 0,1 0,8 :t 0,1 6,1 0,25 -
(M3,5) 3,8 3,6 1,3 :t 0,1 0,8 :t 0,1 6,6 0,25 0,15
M4 4,35 4,1 1,5 :t 0,1 0,9 :t 0,1 7,55 0,3 0,15
M5 5,35 5,1 1,8 :t 0,1 1,2:t 0,1 9,15 0,4 0,15
4.1. BUHmo6ble "peneJICHble U30eJlUR 245
O"OHltaHUe
HOMHHaJlbllhlii BuyrpelUllfi BHeDIHHH P8,lUIyC , k (TOJlhKO
p83Mep ,lUIaMeTp d t illupHHa b TOJlllUllla s ,lUIaMeTp d 2 .lJ,JUI TUDa
H 8MeTp BP)
pe3L6 y a d MaKC. MHH. MaKC. MaKC.
M6 6,4 6,1 2,5 :t 0,15 1,6 :t 0,1 11,7 0,5 0,2
M8 8,55 8,2 3 :t 0,15 2 :t 0,1 14,85 0,65 0,3
MI0 10,6 10,2 3,5 :t 0,2 2,2 :t 0,15 18,0 0,7 0,3
M12 12,6 12,2 4 :t 0,2 2 5 :t 0,15 21,0 0,8 0,4
(M14) 14,7 14,2 4,5 :t 0,2 3 :t 0,15 24,1 1,0 0,4
M16 16,9 16,3 5 :t 0,2 3,5 :t 0,2 27,3 1,15 0,4
(M18) 19,0 18,3 5 :t 0,2 3,5 :t 0,2 29,4/ I 1,15 0,4
M20 21,1 20,3 6 :t 0,2 4 :t 0,2 33,5 1,3 0,4
(M22) 23,3 22,4 6 :t 0,2 4 :t 0,2 35,7 1,3 0,4
M24 25,3 24,4 7 :t 0,25 5 :t 0,2 39,8 1,65 0,5
(M27) 28,5 27,5 7 :t 0,25 5 :t 0,2 43,0 1,65 0,5
M30 31,5 30,5 8 :t 0,25 6 :t 0,25 48,0 2,0 0,8
(M33) 34,6 33,5 10 :t 0,25 6 :t 0,25 55,1 2,0 0,8
M36 37,6 36,5 10 :t 0,25 6 :t 0,25 58,1 2,0 0,8
(M39) 40,8 39,6 10 :t 0,25 6 :t 0,25 61,3 2,0 0,8
M42 43,8 42,6 12 :t 0,25 7 :t 0,25 68,3 2,3 0,8
(M45) 46,8 45,6 12 :t 0,25 7 :t 0,25 71,3 2,3 0,8
M48 50,0 48,8 12 :t 0,25 7 :t 0,25 74,5 2,3 0,8
(M52) 54,1 52,8 14 :t 0,25 8 :t 0,25 82,6 2,65 1,0
M56 58,1 56,8 14 :t 0,25 8 :t 0,25 86,6 2,65 1,0
(M60) 62,3 60,9 14 :t 0,25 8 :t 0,25 90,8 2,65 1,0
M64 66,3 64,9 14 :t 0,25 8 :t 0,25 93,8 2,65 1,0
(M68) 705 69,0 14 :t 0,25 8 :t 0,25 99,0 2,65 1,0
a B cK06Kax )'Ka3aHbI cneQHaJIbHble, pe,ll;KO BC'rpeqaIOID;HeCH pa3MepbI.
,lJ.aJIbHeHrnyIO HH<popMaQHIO CMO'rpH B BS 4464.
4. 1.61. npyJKJfHHSfI ASYXSJfTKOSSfI WSM6s
C npflMoyrOn&H&IM nonepelfH&IM CelfeHJfeM:
MeTpJflfeCKJfM PflA, JfCnOnHeHJfe D
'j'
r r
Ce"leH Vie XX
F/1080 4. Kpene:JICHble oemOJlu
Pa3MepbI B MM
HOMHHaJlbllhlii BuyrpellllHii ,lUIaMeTp BHelllllHii P8,lUIycr
p83Mep IIIHpHHa b TOJlllUllla s ,lUIaMeTp d 2
H,lUIaMeTp
pe3L6 y a d MaKC. MHH. MaKC. MaKC.
M2 2,4 2,1 0,9 :t 0,1 0,5 :t 0,05 4,4 0,15
(M2,2) 2,6 2,3 1,0 :t 0,1 0,6 :t 0,05 4,8 0,2
M2,5 2,9 2,6 1,2:t 0,1 0,7 :t 0,1 5,5 0,23.
M3,0 3,6 3,3 1,2:t 0,1 0,8 :t 0,1 6,2 0,25
(M3,5) 4,1 3,8 1,6 :t 0,1 0,8 :t 0,1 7,5 0,25
M4 4,6 4,3 1,6 :t 0,1 0,8 :t 0,1 8,0 0,25
M5 5,6 5,3 2 :t 0,1 0,9 :t 0,1 9,8 0,3
M6 6,6 6,3 3 :t 0,15 1 :t 0,1 12,9 0,33
M8 8,8 8,4 3 :t 0,15 1,2 :t 0,1 15,1 0,4
MI0 10,8 10,4 3,5 :t 0,20 1,2 :t 0,1 18,2 0,4
M12 12,8 12,4 3,5 :t 0,2 1,6 :t 0,1 20,2 0,5
(M 14) 15,0 14,5 5 :t 0,2 1,6 :t 0,1 25,4 0,5
M16 17,0 16,5 5 :t 0,2 2 :t 0,1 27,4 0,65
(M18) 19,0 18,5 5 :t 0,2 2 :t 0,1 29,4 0,65
M20 21,5 20,8 5 :t 0,2 2 :t 0,1 31,9 0,65
(M22) 23,5 22,8 6 :t 0,2 2,5 :t 0,15 35,9 0,8
M24 26,0 25,0 6 5 :t 0,2 3,25 :t 0,15 39,4 1,1
(M27) 29,5 28,0 7 :t 0,25 3,25 :t 0,15 44,0 1,1
M30 33,0 31,5 8 :t 0,25 3,25 :t 0,15 49,5 1,1
(M33) 36,0 34,5 8 :t 0,25 3,25 :t 0,15 52,5 1,1
M36 40,0 38,0 10 :t 0,25 3,25 :t 0,15 60,5 1,1
(M39) 43,0 41,0 10 :t 0,25 3,25 :t 0,15 63,5 1,1
M42 46,0 44,0 10 :t 0,25 4,5 :t 0,2 66,5 1,5
M48 52,0 50,0 10 :t 0,25 4,5 :t 0,2 72,5 1,5
M56 60,0 58,0 12 :t 0,25 4,5 :t 0,2 84,5 1,5
M64 70,0 67,0 12 :t 0,25 4,5 :t 0,2 94,5 1,5
a B cK06Kax )'Ka3aHbI cneQHaJIbHbIe, pe,ll;KO BCTpeqaIOID;HeCH pa3MepbI.
IIpuMettaHue. BbICOTa ,L(ByxBHTKOBOH maH6bI B CB060,L(HOM COCTO.HHHH rrepe,n
cxaTHeM 06blqHO rrpH6JIH3HTeJIbHO B II.HTb pa3 60JIbllIe ee TOJIII(HHbI, HO eCJIH rpe-
6yroTCH llIai1:6bI C ,L(pyrOH BbICOTOH B CB060,L(HOM COCTO.HHHH, OHH MOryr 6bITb rrony-
qeHbI B COOTBeTCTBHH C ,L(orOBopeHHOCTbIO Me)l{,L(Y rroTpe6HTeJIeM H H3rOTOBHTeJIeM.
)];aJIbHeHmyIO HH<popMaUHIO CMOTPH B BS 4464.
4.1. BUHmo8ble "pene:JICHble U30e.tlUR
4.1.62. npyJKJfHH&le wsii6&1 C 3y6&flMJf, MeTpJflfeCKJfe
HCnOJIHeHHe A C Hap)T)Kllh.MH ay6hSlMH
HCnOJIHeHHe J C BHyrpeHHHMH ay6hBMH
81
min. 2B.t
min. 28 1
HCnOJIHeHHe V C ay6hBMH noon BHHTh. C nOTaHHOH rOJIOBKOH
90°
IlapaMeTpbI, He orrpe,L(eJIeHHble TeXHHqeCKHMH YCJIOBH.HMH, ,L(OJDKHbI 6bITb rrpo-
pa60TaHbI COOTBeTCTByrolI(HM 06pa30M. )
0603HaqeHHe 3y6qaTOH rrp)')KHHHOH rnaH6bI THna J C ,L(HaMeTpOM OTBepCTIDI
d] = 6,4 MM, H3rOTOBJIeHHotf H3 rrp)')KHHHoH CTaJIH, C <poc<paTHbIM nOKpbITHeM ,L(JI.H
3a HTbI OT KOpp03HH: 3y6qaTaH IIp)')KHHHIDI maH6a J 6.4 DIN 6797 - XHM. <l>oc.
npM.
0603HaqeHHe 3y6qaTbIX rrpYXHHHbIX IIIatf6 ,L(JIH 60JITOB C JIeBotf pe3b60tf qHTa-
eTCH: 3y6qaTIDI rrp)')KHHHa.H rnatf6a J 6.4 JIeBa.H DIN 6797- XHM. <l>oc. rrpM.
F/la8a 4. Kpene:JICHble oemOJlu
Pa3MepbI B MM
qHCJIO 3yOheB Bee (7,85 Kr/JJ.M 3 ) ,lI;mI
d d d3 sl s2 MHH. Kr/lOOO DJTYK a-
(HI3) (1\14) MeTpa
AHJ V A J V pe3bOw
1..7 3,6 - 0,3 - 6 - 0,01 - - 1..6
1,8 3,8 - 0,3 - 6 - 0,015 - - 1,7
1,9 4 - 0,3 - 6 - 0,02 0,03 - 1,8
2,2 4,5 4,2 0,3 0,2 6 6 0,025 0,04 0,02 2
2,5 5 - 0,4 0,2 6 6 0,03 0,025 - 2,3
2,7 5,5 5,1 0,4 0,2 6 6 0,04 0,045 0,025 2,5
2,8 5,5 - 0,4 0,2 6 6 0,04 0,045 - 2,6
3,2 6 6 0,4 0,2 6 6 0,045 0,045 0,025 3
3,7 7 7 0,5 0,25 6 6 0,075 0,085 0,04 3,5
4,3 8 8 0,5 0,25 8 8 0,095 0,1 0,05 4
5,l a 9 - 0,5 - 8 - 0,14 0,15 - 5
5,3 10 98 0,6 0,3 8 8 0,18 0,2 0,12 5
6,4 11 11,8 0,7 0,4 8 10 0,22 0,25 0,2 6
7,4 12,5 - 0,8 - 8 - 0,3 0,35 - 7
8,2 a 14 - 0,8 - 8 - 0,4 0,45 - 8
8,4 15 15,3 0,8 0,4 8 10 0,45 0,55 0,4 8
10,5 18 19 0,9 0,5 9 10 0,8 0,9 0,7 10
12,5 20,5 23 1 0,5 10 10 1..1 1,3 1..2 12
14,5 24 26,2 1 0,6 10 12 1,7 2 1,4 14
16,5 26 30,2 1,2 0,6 12 12 2,1 2,5 1,4 16
19 30 - 1,4 - 12 - 3,5 3,7 - 18
21 33 - 1,4 - 12 - 3,8 4,1 - 20
23 36 - 1,5 - 14 - 5 6 - 22
25 38 - 1,5 - 14 - 6 6,5 - 24
28 44 - 1,6 - 14 - 8 8,5 - 27
31 48 - 1,6 - 14 - 9 9,5 - 30
a TOJIbKO ,lI)UI 60JITOB C llieCTHyrOJIbHOH rOJIOBKOH.
,lJ.JIH ,lI;aJIbHeHlliHX ,lI;eTaJIeH CMOTpH DIN 6797.
4. 1.63. CTonopHSfI Wsif6&1 C 3y6&flMJf, MeTpJflfeCKJfe
HCnOJllleHHe A c Hap)T)KllhlMH 3y6hBMH
HCnOJlHeHHHe J C BuyrpeHHHMH 3y6bBMH
51
3S1
:==38 1
4.1. BUHmo6ble "peneJICHble U30eJlUR 249
HCnOJlHeHHHe V C 3y6hBMH
DO)); BHHTh. C nOTaHHOH
rOJIOBKOH
d:3
90°
IlapaMeTPbI, He orrpe,L(eJIeHHble TeXHHqeCKHMH YCJIOBH.HMH, ,L(OJDKHbI 6bITb rrpo-
pa60TaHbI COOTBeTCTByrolI(HM 06pa30M.
0603HaqeHHe CTonopHOH maif6bI C 3y6b.HMH HCHOJlHeHH.H J C ,L(HaMeTPOM OT-
BepCTIDI d l = 6,4 MM, H3rOTOBJIeHHOH H3 rrpyxHHHOH CTaJIH, C <poc<paTHbIM rrOKpbI-
THeM AIDI 3alUHTbI OT KOpp03HH: CTOrrOpHa.H C 3y6b.HMH maH6a J 6.4 DIN 6797 -
XHM. <Doc. rrpM.
0603HaqeHHe CTOIIOpHbIX maH6 C 3y6b.HMH AIDI 60JITOB C JIeBoif pe3b60if qHTa-
eTCH: 3y6qaTIDI rrpyxHHHIDI rnaH6a J 6.4 JIeBaH DIN 6797 - XHM. <Doc. rrpM.
Pa3MepbI B MM
qHCJIO 3yOheB MHH. Bec (7,85 KI'/JUl3) ,lI;mI
d d d KI' /1000 DJTYK ,lUI8 -
(HI3) (1\14) 3 Sl S2 MeTpa
A J V AHJ V pe3L6w
1,7 3,6 0,3 - 9 7 - 0,02 - 1,6
1,8 3,8 0,3 - 9 7 - 0,02 - 1,7
1,9 4 0,3 - 9 7 - 0,025 - -
2,2 4,5 4,2 0,3 0,2 9 7 10 0,03 0,025 2
2,5 5 0,4 0,2 9 7 10 0,04 - 2,3
2,7 5,5 5,1 0,4 0,2 9 7 10 0,045 0,03 2,5
2,8 5,5 0,4 0,2 9 7 10 0,05 - 2,6
3,2 6 6 0,4 0,2 9 7 12 0,06 0,04 3
3,7 7 7 0,5 0,25 10 8 12 0,11 0,075 35/
,
4,3 8 8 0,5 0,25 11 8 14 0,14 0,1 4
5 l a 9 0,5 - 11 8 - 0,22 - 5
,
5,3 10 9,8 0,6 0,3 11 8 14 0,28 0,2 5
6,4 11 11,8 0,7 0,4 12 9 16 0,36 0,3 6
7,4 12,5 0,8 - 14 10 - 0,5 - 7
82 a 14 0,8 - 14 10 - 0,75 - 8
,
8,4 15 15,3 0,8 0,4 14 10 18 0,8 0,5 8
10,5 18 19 0,9 0,5 16 12 20 1,25 1 10
12,5 20,5 23 1 0,5 16 12 26 1,7 1,5 12
14,5 24 26,2 1 0,6 18 14 28 2,4 2 14
16,5 26 30,2 1,2 0,6 18 14 30 3 2,4 16
19 30 - 1,4 - 18 14 - 5 - 18
F/la8a 4. Kpene:JICHble oemOJlu
OKOH"taHue
qHCJIO 3y6heB MHH. Bee (7,85 KI' / 3)
d d d3 KI' /1000 DJTYK ,lUIa-
(HI3) (1\14) St s2 MeTpa
A J V AHJ V pe3L6w
21 33 - 1,4 - 20 16 - 6 - 20
23 36 - 1,5 - 20 16 - 7,5 - 22
25 38 - 1,5 - 20 16 - 8 - 24
28 44 - 1,6 - 22 18 - 12 - 27
31 48 - 1,6 - 22 18 - 14 - 30
a TOJIbKO ,lI)UI 60JITOB C meCTHrpaHHOH rOJIOBKOH. DOJIee nO,ll;p06HO CMOTpH B DIN 6797.
4. 1.64. ISO MeTpJflfeCKSfI npyJKJfHHSfI BOnHJfCTSfI wsii6a:
o6tqee MSWJfHOCTpOeHJfe
d 2 d 1
--L
h
f
Pa3MepbI B MM
HOMHHaJlbHhIii Buyrpelllllli aMeTp d t BHelIllllli aMeTp d 2 BhlCOTa h
(pe3hOOBoii) TOJIDUDlas
aMeTpa MaKC. MHH. MaKC. MHH. MaKC. MHH.
MI,6 1,8 1,7 3,7 3,52 0,51 0,36 0,16
M2 2,3 2,2 4,6 4,42 0,53 0,38 0,16
M2,5 2,8 2,7 5,8 5,62 0,53 0,38 0,16
M3 3,32 3,2 6,4 6,18 0,61 0,46 0,16
M4 4,42 4,3 8,1 7,88 0,84 0,69 0,28
M5 5,42 5,3 9,2 8,98 0,89 0,74 0,30
M6 6,55 6,4 11,5 11,23 1,14 0,99 0,40
M8 8,55 8,4 15,0 14,73 1,40 1,25 0,40
MI0 10,68 10,5 19,6 19,27 1,70 1,55 0,55
M12 13,18 13 0 22,0 21,67 1,90 1,65 0,55
,
(M14) 15,18 15,0 25,5 25, 17 2,06 1,80 0,55
M16 17,18 17,0 27,8 27,47 2,41 2,16 0,70
(M18) 19,21 19,0 31,3 30,91 2,41 2,16 0,70
M20 21.21 21.0 34.7 34.31 2.66 2.16 0.70
a BTOpOH PH.D: pa3MepOB B cK06Kax.
DOJIee nOJIJIyIO HH<popMaQHIO CMOTpH BS 4463.
4.1. BUHmo6ble "peneJICHble U30eJlUJl 25 I
4.1,,65. npocpJfn& nS30B nOA T-06pS3HYIO ronoBKY 60nTs
r
YAaJU1Tb OCTpbl
yrOJ1
0.3 x 45° max.
K
H
G
Pa3MepbI B MM
mllpHHa fnyfiHHa nOJIHaJI 4>acKa x 45 0 PacCTOJllllle Me
mllpHHa ropJlOBHHhI At D83a Bt Da3a C t rJIyOHHa HJIH P8.ZUIYC D838MH P (H36eraiiTe
0603ua- T-D83a H 3Ha1feHHii mara B
qeHHe ,lI;JuI HCDOJll»30- CKoOK8X, DOCKOJlh&y
T-0838 Ho- 00""- BaIllUl B Ka1fe- OHH MOryr CTaTh
MH- HhIii . . . :I :I :I Dpll'llllloii
HaJJ (H 12) CTBe IIIIIIIJIhKH t.::) Henp01lllOCTH)
(HB) :I :I :I
M4 5 +0,12 +0,018 10 11 3,5 4,5 8 10 20 25 32
M5 6 0 0 11 12,5 6,7 5 11 13 25 32 40
M6 8 +0,15 +0,022 14,5 16 7 8 15 18 1,0 0,6 1,0 32 40 50
M8 10 0 0 16 18 7 8 17 21 40 50 63
MI0 12 +0,18 +0,027 19 21 8 9 20 25 (40) 50 63 80
- -
M12 14 0 0 23 25 9 11 23 28 (50) 63 80 100
-
M16 18 30 32 12 14 30 36 1,6 1,6 (63) 80 100 125
M20 22 +0,21 +0,033 37 40 16 18 38 45 (80) 100 125 160
1,0 2,5
M24 28 0 46 50 20 22 48 56 100 125 160 200
-
M30 36 +0,25 +0,039 56 60 25 28 61 71 125 160 200 250
M36 42 0 0 68 72 32 35 74 85 2,5 1,6 4,0 160 200 250 320
M42 48 80 85 36 40 84 95 200 250 320 400
M48 54 +0,30 +0,046 90 95 40 44 94 106 2,0 6,0 250 320 400 500
0 0
,lJ;OnyCKH Ha paCCTOJlHHJI Me1K,ZJ;y oa3aMB p ,ZJ;JIJI T -oa30B
mar (MM) ,n;OnyCK (MM)
Or 20 ,lI;0 25 :to,2
OT 32 ,lI;0 100 :to, 3
OT 125 ,lI;0 250 :to,5
OT 320 ,lI;0 500 :to,8
)];a.rrbHeHIIIyro HH<popMaUHIO CM01'pH B BS 2485.
F/la8a 4. Kpene:JICHble oemOJlu
4.1.66. PS3Mep&1 6onToB Jf rseK K T-06pS3H&IM nS3SM
T -raMKa
T -6onT
K A aMeTp
pe3b6bl
K A aMeTp
pe3b6bl
-1
B.2
M
L
PaBHbie
paCCT05lH 5I
A A a-
MeTp
C 2
F
t
f
N
F
R
E
8 2
E
C 2
B.2
Ta6JI. 1.
0603Ha- IIIHpHHa BWCOTa ,n;Ha- <l>aCKa Pa;ntyc illHpHHa BWCOTa <l>acu
1feHHe I'OJlOBKH BWCOTa CTYDeHH MeTp E r T -raiiKII G T -raiiKH F
T -ooJlTa H (KBa.npaT) B 2 I'OJlOBKH c CTyIIeHH H
;ntaMeTpa ,lI;oD.:tO,2 CTep1KllJl CTep1KllJl
Pe3hOW K HOM. ,lI;OD. N A 2 MaKe. MaKe. HOM. ,lI;OD. MaKe. MaKC.
M4 9 2 5 - 4 5 6
M5 10 4 - 5 6 -0 3 8
M6 13 6 - 6 8 -0 5 10
M8 15 6 8 1,0 10 12
-
MI0 18 0 7 - 10 12 16
M12 22 -0 5 8 - 12 14 -0 3 19
M16 28 10 - 16 18 -0 6 25
M20 34 14 20 1,0 22 30 0,3x45°
-
M24 43 18 20 26 1,5 28 40
M30 53 23 20 33 36 -0 4 45
M36 64 28 25 39 42 -0,7 55
M42 75 32 25 46 48 65
M48 85 36 30 52 2,5 54 -0,4 75
-0,8
aJIbHeHmyIO HH<p0pMaUHIO CMOTpH B BS 2485.
4.1. BUHm06ble "peneJICHble U30eJlUJl 253
Ta6JI. 2.
Pa3MepbI B MM
,[(HaMeTp PeKOMeH,ZJ;OBaHHaJI .zunma CTep1KllJl OOJITa L Aruma Pe3hOhI Ha
pe3hOhI K CTep1Klle 60JITa M
M4 30 40 50 60 70 80 100 ,[(IDI L 100 M = 0,5L
M5 30 40 50 60 70 80 100
M6 60 70 80 100
M8 60 70 80 100
MI0 60 70 80 100 125 160 180 / I
M12 70 80 100 125 160 180 ,[(IDI L > 100 M = 0,3L
M16 70 80 100 125 160 180 200 250 300
M20 70 80 100 125 160 180 200 250 300
M24
M30
M36 100 125 160 180 200 250 300
M42
M48
)];aJIbHeiimyIO HH<popMaUHIO CM01'pH B BS 2485.
4. 1.67. PS3Mep&1 wnOHOK AJlfl T-06pS3H&IX nS30B /
M- Ad!a.
B dia.
1
L
j
w
E
p
Q
1
D
B.2
E
F/la8a 4. Kpene:JICHble iJemOJlu
=
::is
c.
Q)
M
t'<S
Q...
I =;
1- t "! V) V) V) V)
c:t.. 8u «I e= .., .., .., ..,
c:t.. + N \0 00
t!1I ):I1u
i
I ::II
81 0.., 0
c:t.. I Q == 0... ...
i i ! ... \0 ......c
......c ......c
i= =&i
8
i = i
1°-1= ... ... \0 0
it = \0'" 0\
e 5 i; = N
I f'11!!0
= u
iill;li N \0 00
i....fl..
::I IIQ
i" ..
!!I iE! !!I
U IIQ c:t..:11 IIQ
i \0 0... V)
... ...
0 ......c ......c
::I
! V) 0 0 0
N \0
i Q, 0 N 0 0
eue ......c ......c
=
«I ;
S eO V) V) V) V)
... ......c N
a V)
.-..
«I roo- 00 ......c V) 0
..c:: ......c N N
I --- 0 0... 0 0... 0 0... 0 0...
i; =1 0 0 0 0
I I I I
=e
ia :i \0 0 0 0
e e ......c V)
= =
.-..
a roo- N V) 00 ......c V) 0
..c:: ......c ......c ......c N N
--- 0 0 0 0 q 0 0... 0 0... 0 0...
0
i 0'" 0'" 0 0 0 0
I I I I I I
, :i V) \0 00 0 N 00 N 00 \0 N 00
i ......c ......c ......c ......c N N V)
I
ia
'r 0 N \0 0 0 \0 N 00
o E-4 V) \0 00 ......c ......c ......c N N
.
f'.
00
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00
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:=
o
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:=
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:=
:=
i
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4.2. 3a1(,Jleno"tHble coeOUHeHUJl 255"
4.2. 3aKnenO'lHble coeAMHeHMH
4.2.1. TJfnJflfH&le rOnOBKJf Jf CTepJICHJf 3SKJlenOK
<l>D
2D
D
HHa [
3 D
2
f
nOJ1YKpyr J1a51
J1 n0J1YKpyrJ1a51
3aKJ1aAHa51 r0J10BKa
U. J1 HAPVl"leCKa51
cKpyrJ1eHHa51
r0J10BKa
H 3Ka51
nOJ1YKpyr J1 a51
r0J10BKa
2D
KOHycoo6pa3Ha51
r0J10BKa
nJ10CKa51
r0J10BKa
nOTaVlHa51
r0J10BKa
yrOJ1 90°
U. J1 HAP "IeCK V1
J1 cnJ10WHOVi
CTep)l(eH b
nOJ1ynycTOTeJ1bIVi
CTep)l(eHb
nYCTOTeJ1blVI
CTep)l(eH b
J1 n CTOH
Pa3ABoeHHblVi
(B J1b"laTbIVl)
CTep)l(eHb
CTe )l(eHb
AJ151 M5IrK X
MaTep aJ10B
F/la8a 4. Kpene:JICHble iJemOJlu
4.2.2. TJfnJflfH&le 3aKJIenOIfH&le COeAJfHeHJffl BHaxnecTKY
O,ZJ;llopJl,ZJ;Hoe COe,ZJ;HHeHHe BHaxJIeCTKY
M. r-I'" 3D _I. 3D _I D - AlllaMeTp CTep)l(HSI 3aKJ1enKIII
W
, , , ,
BeJ1 "I Ha Ha-
XJleCTK 30 Q
..-
,[(BYXPJl,ZJ;HOe COe,ZJ;HHeHHe BHaxJIecTKY (,ZJ;Be D;enO'lKH)
M. r -I'" 3D _I. 3D -I
PaCCT05lH e Me)I(AY WBa ,
p5lAaM 3aKJ1enOK ' , ,
- -- --- -----
BeJ1 "I Ha Ha- Q
XJleCTK 60 c-)
Q
..-
,[(BYXPJl,ZJ;HOe coe,n;HHeHHe BHaXJIecTKY (3Hr3ar)
1.5D
3D
ar
3D
3D
PaCCT05lH e Me)I(AY
p5lAaM 3aKJ1enOK
BeJ1 "I Ha Ha-
XJleCTK 60
Q
c-)
Q
....
3D 3D
4.2. 3a1(,Jleno"tHble coeOUHeHUJl 257
4.2.3. TJfnJflfH&le CT&IK08&le 3SKhenOlfH&le COeAJfHeHJffl
3aKJIenO'IHOe CTLIKOBoe COe,ZJ;HHeHHe C O,ZJ;llOH HaKJIa;ncOH (o,ZJ;llop.H,ZJ;IIoe)
1.5D 3D 3D 3D D - A aMeTp CTep)l(H5I 3aKJ1enK
War
W p Ha
HaKJ1aAK
6D
i
(CTbIKOBa5l)
HaKJ1aAKa
IlpUMettanue. 3TO coe,nHHeHHe TaIOKe MoxeT 6bITb BbInOJIHeHO ,nBOHHbIM
pH,Il;OM 3aKJIenOK, uenOqKaMH HJIH 3Hr3arOM. IllHpHHa HaKJIa,nKH = 12D npH
,IJ;BOHHOM pR,LI.e 3aKJIenOK (IIIar Me)l{)(y pR,LI.aMH = 3D).
3aKJIenO'IHOe CTLIKOBoe COe,ZJ;HHeHHe C ,ZJ;BYMJI HaKJIa)Q(aMH (,ZJ;BYXPJl)l;Hoe)
1.5D 3D
3D
3D
W p Ha
(CTbIKOBO )
HaKJ1aAK
12D
Q
.....
PaCCT05lH e Me)I(AY
p AaM 3aKJ1enOK
IIpuMettanue. 3TO coe,nHHeHHe TaIOKe MOxeT 6bITb BbInOJIHeHO ,nBOHHbIM pR,LI.OM
3aKJIenOK, pacnOJIOXeHHbIX 3Hr3arOM (CM01'pH pa3,neJI 4.2.2), MH o,nHHapHbIM P.H-
,aOM 3aKJIenOK, CM01'pH BbIIIIe.
9-3255
F/la8a 4. Kpene:JICHble OemOJlu
4.2.4. CooTHOWeHJffl MeJKAY AJfaMeTpOM oTSepCTJffl
Jf A/lJfHoii 3aKJIenKJf
1.0625D
1 D r
4.2.5. 3aKJIenKJf C nonYKPyrnoif 3aKJIaAHOif ronosKoif,
Jf3rOTOSneHH&le xonoAHoif wTaMnosKoif
D
I-
I
-I
K
npH d = 16 MM HJlH MeHbme
D=1,75d
K = 0,6 d
L = ,lI;JIHHa
L
LJ
p
a3Mepbl B MM
HOMHH8JIhllblH ,n;OnyCK Ha HOMHH8JIh1lblH ,n;OnyCK Ha HOMHH8JIhHaJI ,n;OnyCK Ha ,n;OnyCK HI
;ntaMeTp ;ntaMeTp d ;ntaMeTp ;ntaMeTp D BMCOTa BMCary ,zuumy L
CTep1KllJl a d I'OJIOBKH D I'OJlOBKH K I'OJlOBKH K
1 1..8 0..6 +0,2
1..2 2..1 :f:0,2 0..7
-0,0
1..6 2..8 1..0
2..0 :f:0,07 3..5 1..2
2..5 4..4 :f:0,24 1..5 +0,24 +0,5
-00
3..0 5..3 1..8 , -0,0
(3..5) 6..1 2..1 +0,29
4 7..0 :f:0,29 2..4
:f:0,09 -0,0
5 8..8 3..0
6 10..5 3..6 + 0,35
(7) 12..3 :f:0,35 4..2
-0,0 +0,8
8 :f:0,11 14..0 4..8
-0,0
10 18..0 6..0
12 21..0 :f:0,42 7..2 + 0,42 + 1,0
(14) :f:0,14 25..0 8..4 -00
, -00
16 28..0 9..6 ,
a B cKo6Kax y:Ka3aHbI CneUHaJIbHbIe pa3MepbI 3aKJIenOK.
,LJ;aJIbHeHmyIO HH<popMaI(HIO CMOTpH B BS 4620: 1970.
4.2. 3aK./leno"tHble coeiJuHeHUR 259
4.2.6. 3aKJIenKJf C nonYKpyrnoH 3aKJIaAHOif ronoBKoif,
Jf3rOTOSneHH&le ropfllfeif wTaMnosKoif
D
K
L
ITpH d = 14 MM HJlH 60JIbme
D = 1,6 d
K = 0,65 d
L = )];JIHHa
Pa3MepbI B MM
HOMHllaJlbllblH ,n;OnyCK Ha HOMHHaJlbHWi ,n;OnyCK Ha HOMHHaJlbHaJI ,n;OnyCK Ha ,n;OnytK
ABaMeTp ;ntaMeTp d ;ntaMeTp ;ntaMeTp D BMCOTa BMCary Ha MIlBY L
CTeJUKlUla d I'OJlOBKH D I'OJlOBKH K I'OJlOBKH K
(14) 22 9 + 1,0
16 :1:043 25 :I: 1,25 10 + 1,00 -0,0
-00
,
18 28 11,5
20 32 13 + 1,6
(22) :f:0,52 36 + 1,8 14 + 15 -00
,
-00
,
24 40 16
(27) 43 17
30 48 :f:2,5 19 + 2,0
-0,0
(33) :f:0,62 53 21 + 3,0
-0,0
36 58 23 + 2,5
62 :f:3 ,0 25 -00
39 ,
a B cKo6Kax y:Ka3aHbI CneI(HaJIbHbIe pa3MepbI 3aKJIenOK.
)];a.rrbHeiimyIO HH<popMaUHIO CM01'pH B BS 4620: 1970.
F/la8a 4. Kpene:JICHble oemOJlu
4.2. 7. npeAnonaraeM&IH Alfana30H HOMJfHan&H&IX ,qJJJfH,
CBfl3aHH&IX C AJfaMeTpOM CTepJICHeH
Pa3MepbI B MM
HOMHHaJlbHWi HOMHHaJlbHaJI MIIIIa a L
,lUIaMeTp
CTep1KllJl* d 3 4 5 6 8 10 12 14 16 (18) 20 (22) 25 (28) 30 (32) 35 (38) 40 45 50 55
1,0 x x x x x x x x x x
1,2 x x x x x x x x x x
1,6 x x x x x x x x x x x x
2,0 x x x x x x x x x x x x
2,5 x x x x x x x x x x x X
I
3,0 x x x x x x x x x x x X
I
(3,5) I
4,0 x x x x x x x x x
5,0 x x x x x x x x x x x x x x
6,0 x x x x x x x x x x x x x x x
a Pa3MepbI H ,lI;JIHHbI, y:Ka3aHHbIe B cKo6Kax, HBIDIIOTCH CneI(HaJIbHbIMH H HX cne.nyeT no'
B03MO)l{}{OCTH H36eraTb. BKJIlOqeHHe B Ta6nHI(bI ,lI;aHHbIX 0 pa3Mepax He 03HaQaeT, QTO Bce
onHcaHHbIe H3,l1;eJIHH BXO,ll;HT B accopTHMeHT BbInYCKaeMOH npO,n;yKUHH. nOTpe6HTeJIIO CJIe-
,n;yeT npOKOHCYJIbTHpOBaTbCH C H3rOTOBHTeJIeM OTHOCHTeJIbHO cnHCKa HMeIO HXCH B HaJIH-
QHH pa3MepOB H3,l1;eJIHH.
nOJIHbIH ,lI;Hana30H THnOB H pa3MepOB rOJIOBOK, BKJIIOQ3jl ,lI;HaMe'rp 39 MM npH ,nJIHHe
CTepXHH 60 MM, CMO'rpH B BS 4620: 1970.
4.2.8. POFJf8J 3aKJIenKJf
POP@ HJIH O,nHOCTOpOHHIDI KJIenKa - 3TO MeTO,n, KOTOpbIH n03BOJUIeT BbInOJIIDITb
MeXaHlNeCKHe coe,nHHeHHH, Kor,na ,nOC1)'I1 orpaHlNeH TOJIbKO O,nHOH CTOpOHOH co-
e,nHH.HeMbIX qaCTeH; HO 6JIaro,nap.H Ha,ne)I{JIOCTH, npe,nCKa3yeMocTH, HH3KOH CTOH-
MOCTH C60PKH H npOCTOTe npHMeHeHHH O,nHOCTOpOHHAA KJIenKa IIIHpOKO HCnOJ!bool
3yeTC.H TaIOKe H Tor,na, Kor,na ,nOC1)'I1HbI 06e CTOpOHbI coe,nHHeHHH. PO P@, KaK If,
,npyrHe BH.l(bI CHCTeM O,nHOCTopoHHeH KJIeIIKH, onpe,neJUIeTC.H ,nBywI 3JIeMeHTaMH -
BbITIDKHOH 3aKJIenKOH H BbI6paHHbIM YCTPOHCTBOM ,l.(JUI YCTaHOBKH 3aKJIenOK (3a-
KJIenOqHHKoM).
BbITIDKHa.H 3aKJIenKa - 3TO MeXaHHqeCKOe Kpene)I{JIOe cpe,nCTBO, COCTO.Hru;ee H3!
,nBYX qaCTeH. OHa npe,nCTaBJUIeT C060H TPy6qaTbIH KOprryC C 60PTHKOM, 3apaHee 3a-
Be,neHHbIH B cTepxeHb, KOTOpbIH 06JIa,naeT CBOHMH OC06bIMH CBoHcTBaMH. Kor,n;a B
npouecce YCTaHoBKH ero BTHrHBaIOT B TeJIO 3aKJIenKH, npoHcxo,nHT pacIIIHpeHHe
Tpy6qaTOrO Kopnyca H <pOpMHpOBaHHe 3aMbIKaIOII(eH rOJIOBKH, qTO npHBo,nHT K CO-
e,nHHeHHIO cKpeIIIDIeMbIx ,neTaJIeH. 3aKJIenOqHHK 06bIqHO BKJIIOqaeT B ce6.H ynop,.
KOTOpbIH y,nep)I{HBaeT 60pTHK 3aKJIenKH, H 3IDKHM, KOTOpbIH 3axBaTbIBaeT H BhITjf-
rHBaeT cTepxeHb, B pe3YJIbTaTe qero 3aKJIenKa YCTaHaBJIHBaeTC.H, a 3aTeM, npH'
3apaHee onpe,neJIeHHOH HarpY3Ke, cTepxeHb pa3pbIBaeTC.H.
CyIUeCTByeT MHoxeCTBO pa3JIHqllbIX BHJ(OB BbIT.H)l{JIbIX 3aKJIenOK, HO HaH6o-
JIee IIIHpOKO pacnpocTpaHeHbI CTaH.napTHbIe (c OTKpbITbIM TOpUOM) 3aKJIenKH.
4.2. 3aKlleno"tHble coeOUHeHUJl 261
B BS EN ISO 14588: 2000 TaKaH 3aKJIenKa onpe,neJIeHa TaK: «BbIT.H)I{HaH 3aKJIenKa,
nycTOTeJIaH no BceH ,nJIHHe, C KOTOpOH MO)I{HO HCnOJIb30BaTb CTaH,[(apTHbIH CTep-
xeHb». IIpHHIJ;HI1 O,nHOCTopoHHeH KJIenKH npH HOMOII(H 3aKJIenOK C OTKpbITbIM
KOHn;OM I1pe,nCTaBJIeH Ha CJIe.nyrolI(eM pHCYHKe.
CTepxeHb 3aKpeIlIDIIOT B 3aKJIenOqHHKe H TeJIO 3aKJIenKH BCTaBJI.HIOT B npe,nBa-
pHTeJIbHO np06HToe HJIH npOCBepJIeHHOe OTBepCTHe B coe,nHH.HeMbIX ,neTaJI.HX. 3a-
KJrenOqHHK THHeT CTepxeHb, BTHrHBaH ero rOJIOBKY B TeJIO 3aKJIenKH, qTO BbIH)'X-
,naeT ee paCIIIHpHTbCH Ha HIDKHeH CTopOHe coe,nHHeHIDI, B TO xe BpeM.H B I1pOn;eCce
YCTaHOBKH CTHrHBaH ,neTaJIH BMeCTe H YCTPaH.HH JII06bIe 3a30pbI Me)l()(y HHMH.
B onpe,neJIeHHbIH MOMeHT, Kor,na 3aMbIKalOIUaH rOJIOBKa Ha HIDKHeH CTopOHe nOJI-
HOCTblO C<P0PMHpOBaJIaCb, ,naJIbHeHIIIee BbITHrHBaHHe CTep)I{IDI 3aKJIenOqHHKOM
HpHBO,nHT K pa3pbIBY CTep)I{IDI. OTPa60TaHHyID qaCTb CTep)I{IDI BbIHHMaIOT, H YCTa-
HOBKa 3aKJIenKH 3aBepIIIeHa.
3aKpbITaH 3aKJIenKa (c 3aKpbITbIM Topn;OM) onpe,neJIeHa B BS EN ISO 14588:
2000 TaK: «BbIT.H)I{HaH 3aKJIeI1Ka, KOTOpa.H 3aKpbITa H OCTaeTCH 3aKpbIToH nOCJIe
YCTaHOBKH». 3TOT BH,l( 3aKJIenOK TaIOKe IIIHpOKO H3BeCTeH KaK «repMeTHqHbIH». 3a-
KpbITWI 3aKJIenKa npe,nOTBpalI(aeT nonanaHHe napa HJIH BJIarH qepe3 OTBepCTHe B
YCTaHOBJIeHHOH 3aKJIenKe, a TaIOKe rapaHTHpyeT Y).J;epxaHHe roJIOBKH CTep)I{IDI, qTO
oco6eHHO BaxHO, HanpHMep, B 3JIeKTp eCKOM 060Py,noBaHHH.
3aKJIaLJ;HbIe 3aKJIenKa POP@ ,nOCTYIIHbI BO MHoxeCTBe MaTepHaJIOB, <pOPM KY30-
B8. H B03rJIaBJI.HIOT <pOPMbI, qT06bI 06eCneqHTb BapHaHTbI 3aKpeIIJIeHIDI ,lLillI IIIHpO-
Koro CneKTPa c06paHIDI H 3KOJIOrHqeCKHX TPe60BaHHH OT JIOMKHX H XpynKHX MaTe-
pHaJIOB, TaKHX KaK aKpHJIOBbIe IIJIaCTMaCCbI K HepXaBelOlI(eH CTaJIH. Pe310Me nOKa-
3bIBalOT B pa3,neJIe 4.2.9. 3TOT pHCyJlOK H CJIe.nyrolI(He Ta6JIHn;bI B3HTbI H3 ny6JIH-
IGlI HH Emhart Teknologies (Tucker Fasteners Ltd.). A,npec 3TOH KOMnaHHH ,naH B
IIpHJIoxeHHH 3.
F/la8a 4. Kpene:JICHble oemOJlu
4.2.9. 0630P SMAOS POpIJ 3alUJenOK
CTaHAapTHa51 (OTKpbITa5l) aaK11enKa
aK
3aKpblTa51 (repMeTH"IHa5l) 3aK11enKa
JlenecTKOBa51 3aK11enKa
I(
c:.u III po Kill A Alllana30HQaKJ1enOK' nplllroAH blX AIlS! nplllMe-
HeHVl5I B Tex npHnO)l(eHH5IX, rAe He npeAb5lBJ151IOTC5I BbI-
COKVle Tpe6oBaHVl5I K pa60"lHM HarpY3KaM
S! nplllnO)KeHIIIA, BQOTOPblX Tp e6YIOTCS! BOAOHenpOHM-
u.aeMble, repMeTH"IHble coeAHHeHH5I HJ1V1 B KOTOpblX
Tpe6yeTc5I YAep)I(aHHe CTep)I(H5I
riPIIIMeHIIIMa AIlS! CO IIIHeHIIIS! nn aCTMaCCbI, pe3l11HbI,
ApeBeCHHbI, CTeK110nJ1aCTHKa HJ1V1 J1aMHHaTOB
MHor03IDKVlMHa51 3aK11enKa
tc
IIIPOKIIIA Alllana30H p eKPaCHO nOAXOAIIIT ATlSI
HCn0J1b30BaHH5I npH HeCOBnaAalO HX OTBepCTVl5IX
PaCnOpHa51 aJ1IOMHHHeBa51 3aK11enKa
0tC
aKJ1enKa C pacnpeineHllleM H arpY3KIII nOAXOAIIIT ATlSI
HCn0J1b30BaHVl5I C M5IrKHMH, J10MKHMH HJ1H xpynKHMVI
MaTepHaJ1aMH
Cl)OPMLI 60p'rHKOB
3aKJIenKH C HH3KHM K:yIIOJI006pa3HbIM 60pTHKOM (CTaH,[(apTHbIe) no,nXO)UT JI.IDI
npHMeHeHIDI B 60JIbIIIHHCTBe npHJIOXeHHH, o,nHaKO, eCJIH M.HrKHe HJIH xpynKHe
MaTepHaJIbI 3a:KpeII.IDIIOTCH Ha xeCTKOH OCHOBe, CJIe,nyeT paCCMOTPeTb B03MO)I{HOCTb
HCnOJIb30BaHIDI 3aKJIenOK C YBeJIHqeHHbIMH 60pTHKaMH. 3aKJIenKH C nOTaHHbIM
(yrOJI 120°) 60pTHKOM CJIe,nyeT HCnOJIb30BaTb B Tex CnytlaHX, Kor,na TPe6yeTcH POB-
HaH nOBepXHOCTb.
B I cTeplKHei
CTaH,[(apTHbIe POP@ 3aKJIenKH (c OTKpbITbIM TopnoM) 06bIqHO cHa6xalOTcB
CTep)I{IUIMH, 0603HaqaeMbIMH BS «<pa3JIaMbIBaIOII(HHCH cTepxeHb») H pa3pa60TaH-
HbIMH TaK, qT06bI rOJIOBKa CTep)l{}ffi y,nep)J{HBaJIaCb npH YCTaHOBJIeHHOH 3aKJIenKe.
CTep)l{}ffiMH C 0603HaqeHHeM BH «<Pa3JIaMbIBalOlI(aHCH rOJIOBKa»), pa3pa60TaHHbI-
MH TaK, qTO rOJIOBKa H3BJIeKaeTCH H3 TeJIa 3aKJIenKH, MoxeT 6bITb cHa6xeHo 60Jlb-
IIIHHCTBO OTKpbITbIX 3aKJIenOK, HO oc06eHHo TaKHe CTep)KHH nOJIe3HbI I1PH npe,nBa-
pHTeJIbHOH c60pKe 3JIeIcrpHqeCKHX MOHTaxHbIX IIJIaT.
nOKpLlTHe
. CmaHoapmHoe nOKpblmue Kopnyca 3aK./lenKU. CTaJIbHbIe H HHKeJIb-Me,nHbIe
(MoHeJIb) 3aKJIenKH 06biQHO nOCTaBJI.HIOTCH OUHHKOBaHHbIMH.
. OKpawu6aHue U opyzue 6UObl o6pa6omKu n06epXHocmu. 110 TPe60BaHHIO MOryT
I10CTaBJI.HTbCH 3aKJIenKH C pa3JIHqHbIMH BH,l(aMH nOKpbITHH nOBepXHOCTH H
OKpaIIIeHHbIe B pa3JIHqHbIe nBeTa. 3aKJIenKH H3 aJIlOMHHHeBbIX CIIJIaBOB MO-
ryT 6bITb aHo,nHpOBaHHbIMH H OKpaIIIeHHbIMH, MaTOBbIMH HJIH 6JIeCTHlI(HMH B
3aBHCHMOCTH OT 3CTeTHqeCKHX Tpe60BaHHH H npe,nnOJIaraeMbIX BHeIIIHID
YCJIOBHH npH 3Kcrr.rryaTaUHH.
4.2. 3aKlleno"tHble coeouHeHUR 26
4.2.10. npaKTHlfeCKHe peKoMeHAaqHH
no HCnOn&30SaHHIO KpenneHHH
O,lJ;HOCTOPOHH.H.H KJIenKa - 3TO BbICOKOHan;e)f{HbIH H npoBepeHHbIH MeTO,n BbII1OJI'
HeHIDI Hepa3'beMHbIX coe,nHHeHHH. QT06bI nonyqHTb HallJI)"lIIIee coe,nHHeHHe, CJIe.
,nyeT npH,ll;ep)I{HBaTbCH CJIe,nyroII(HX npHHUHI1OB.
MaTepHaJILi COe,ZJ;HHJleMLIX ,n;eTaJIei
IIpH coe,nHHeHHH MarepHaJIOB pa3JIHqHOH TOJIII(HHbI H npOqHOCTH 60JIee npoq.
HbIH MaTepHaJI no B03MO)I{HOCTH CJIe,nyeT pacnOJIaraTb C HIDKHeH CTOpOHbI. Hal1pH'
Mep, npH coe,nHHeHHH IIJIaCTHKa H MeTaJIJIa IIJIaCTHKOBbIH JIHCT ,nOJl)l{eH panOJIaraTh'
CR I1O,n 60pTHKOM 3aKJIe11KH, a MeTaJIJI eCKaH ,neTaJIb ,noJI)I{Ha 6bITh CHH3Y.
Pa3Mep OTBepCTHJI H no,n;rOTOBKa
IIoJIyqeHHe xopOIIIero coe,nHHeHIDI 3aBHCHT OT xopoIIIeH no,nrOTOBKH OTBep'
CTIDI, npe,nnOqTHTeJIbHO np06HToro H npH He06xo,nHMOCTH paCTOqeHHOrO ,no pa3'
MepOB, peKOMeH,nyeMbIX B Ta6JIHUax ,naHHbIX 110 BbITIDKHbIM 3aKJIenKaM.
,l);HaMeTP 3aKJIenKH
COrJIaCHO CnpaBOqHHKY no Hecyru;HM HarpY3KY coe,nHHeHIDIM, ,nHaMelp 3a-
KJIenKH ,nOJl)l{eH 6bITb no KpaHHe Mepe paBHbIM TOJIII(HHe caMoro TOJICTOrO JIHCTa I'
He 60JIee qeM B TPH I1peBbIIIIaTb TOJIIUHHy JIHCTa, Haxo,nHlI(erOCH Henocpe,nCTBeaH(
no,lJ; 60pTHKOM 3aKJIenKH. 06paTHTecb K Ta6JIHn;aM ,naHHbIX 110 xapaKTepHCTHKa
npOqHOCTH 3aKJIenOK.
PaCCTOJlHHe OT 3aKJIenOK ,n;o KpaJi 3JIeMeHTa
OTBepcTIDI ,l.(.illI 3aKJIenOK ,nOJDKHbI 6bITb npOCBepJIeHHbI HJIH np06HTbI Ha pac-
CTOHHHH He MeHbIIIe ,nBYX ,nHaMeTPOB OT KpaH, HO He ,naJIee qeM B 24 ,nHaMeTpax 01
3TOro KpaH.
mar mBa
COrJIaCHO CnpaBOqHHKY paCCTOHHHe MelK,l(y 3aKJIenKaMH B cnyqae Hecyru;HX Ha-
rpY3KY coe,nHHeHHH HHKor,na He ,nOJl)l{O npeBbIIIIaTb TPex ,nHaMeTPOB 3aKJIenKH
IIpH pa3pa60TKe CTbIKOBbIX coe,nHHeHHH ueJIeC006pa3HO BKJIlOqHTb YCHJIeHHyID Ha-
KJIMKY, npHKpenHB ee K JIexalI(eMy BHH3Y JIHCTY 3Hr3aro06pa3HbIM 3aKJIeIIOqHbI
mBOM.
MaTepHaJI 3aKJIenOK
BbI60p MaTepHaJIa 3aKJIenOK 06bIqHO 3aBHCHT OT Tpe6yeMoH npOqHOCTH 3aKJIe-
nOQHOrO coe,nHHeHIDI. ECJIH npHxo,nHTCH HCnOJIb30BaTb 3aKJIel1KH H3 MaTepHaJIa
OTJIHqalOlI(erOCH OT MaTepHaJIa coe,nHH.HeMbIX JIHCTOB, BaxHO 3HaTb, qTO 3JIeIcrpO-
JIHTlNeCKOe B03,neHCTBHe MoxeT CTaTb I1p HHOH KOpp03HH (CMOTpH pa3,neJ
4.2.12).
Y CTaHOBKa H 6e30nacHocTL
3aKJIenOqHHK 06bNHO BbI6HpalOT B COOTBeTCTBHH C YCJIOBIDIMH npOH3Bo,nCTBa
IIepe,n YCTaHoBKoH CJIe,nyrolI(eH 3aKJIenKH HHCTpYMeHT ,nOJl)l{eH 6bITb OqHlI(eH 01
OTpa60TaHHbIX MaTepHaJIOB. 3JIeIcrpHqeCKHH 3aKJIenOqHHK He ,nOJl)l{eH HCnOJIb30Ba-
!bCH 6e3 ,ne<pJIeKTOpa CTep)KHeH HJIH YCTaHOBJIeHHOrO KOHTeHHepa ,l.(.illI c60pa OTpa-
60TaHHbIX 3aKJIenOK. Bcer,na CJIe,nyeT nOJIb30BaTbCH 3aIUHTHbIMH OQKaMH.
F/la8a 4. Kpene:JICHble oemOJlu
4.2.11. B&160p POpIJ (HnH B&ITflJlCH&IX) 3alUJenOK
np01JHOCTL COe,ZJ;HHeHHJI
IIpe)l{,L(e Bcero CJIe,nyeT On;eHHTb TPe6yeMYlO npOqHOCTb coe,nHHeHIDI Ha pa3pbIB
H Ha c,nBHr. QT06bI y,nOBJIeTBOpHTb 3THM TPe60BaHIDIM, He06xo,nHMO npaBHJIbHO
BbI6paTb KOJIHqeCTBO KpenexeH H paCCTOHHHe Me HHMH, a TaKXe MaTepHaJI 3a-
KJIenOK H HX ,nHaMeTp. ,lI;aHHbIe 0 npOqHOCTH, npHBe,neHHbIe Ha COOTBeTCTByroIIJ;:HX
CTPaHHn;ax, n03BOJI.HIOT BbI6paTb 3aKJIenKH TPe6yeMoH npOqHOCTH.
TOJIDJ;HHa COe,lUfHeHHJI
Ha CJIe,nyIOlI(eH CTa,rJ;HH He06xOHMO onpe,neJIHTb CYMMaplfYIO TOJIIIJ;HJIy coe,nHIDIe-
MbIX MaTepHaJIOB, He 3a6bIBaH yqHTbIBaTb JII06bIe B03,l(yll1HbIe 3a30pbI HJIH npOMe-
xyrOqHbIe CJIOH, TaKHe KaK ynnoTHHTeJIH (repMeTHKH). Tenepb onpe,neJIHTe p33Mep
BbI6paHHOH 3aKJIenKH C He06xo,nHMOH ,l.(JIHHOH 33XBaTa, 06paTHBIIIHCb K COOTBeTCT-
ByIOII(eH CTPaHHl(e C ,naHHbIMH. 3TO BaxHO c,neJIaTb, nOCKOJIbKY npH HenpaBHJIbHOM
BbI60pe ,l.(JIHHbI 33XBaTa 3aKJIenKa He CMoxeT y,nOBJIeTBOpHTeJIbHO 3aXBaTHTb 06paT-
IfYIO CTOpOJIy 3arOTOBKH HJIH naKeTa.
YCHJIeHHe KOpp03HH (CBOHCTBa MaTepHaJIOB)
HaKOHen;, CJIe,nyHTe 06lI(eMy npaBHJIY, qTO BbI6paHHaH 3aKJIenKa ,noJDKHa HMeTb
TaKHe xe <pH3 eCKHe H MeXaHHqeCKHe CBOHcTBa, KaK H 3arOTOBKa. 3aMeTHoe pa3-
JIHqHe B CBOHCTBax MoxeT CTaTb np HHOH pa3pyrneHIDI coe,nHHeHIDI B pe3YJIbTaTe
B03HHKHOBeHIDI YCTaJIOCTH MeTaJIJIa HJIH KOHTaKTHOH KOpp03HH. KOPp03IDI YCKO-
pHeTcH npH onpe).J;eJIeHHbIX COqeTaHH.HX MaTepHaJIOB H B03,neHcTBIDI OKpyxalOru;eit
cpe,nbI. KaK npaBHJIO, CJIe,r(yeT H36eraTb KOHTaKTa Me)l{,L(y pa3Hopo,nHbIMH MeTaJIJIa-
MH. By-KBbI A, B, C H D B Ta6JIHue 03HaqalOT CJIe.nyrolI(ee:
A KOpp03IDI paCCMaTpHBaeMoro MeTaJIJIa He YCHJIHBaeTCH npH KOHTaKTe C ,npy-
rHM MeTaJIJIOM.
B KOpp03IDI paCCMaTPHBaeMoro MeTaJIJIa MoxeT CJIerKa YCHJIHTbCH npH KOH-
TaKTe C ,npyrHM MeTaJIJIOM.
C KOpp03IDI paCCMaTPHBaeMoro MeTaJIJIa MO)l{eT 3aMeTHO YCHJIHTbCH npH KOH-
TaKTe C ,npyrHM MeTaJIJIOM.
D B YCJIOBIDIX BJIaxHOCTH KOM6HHan;IDI paCCMaTPHBaeMoro MeTaJIJIa C KOHTaK-
THpyrolI(HM MeTaJIJIOM Hen;eJIeco06pa3Ha; ,nIDKe B 60JIee M.HrKHX YCJIOBIDIX He-
06XO,nHMbI COOTBeTCTByIOlI(He 3aIIJ;HTHbIe MepbI.
ECJIH npHBe,neHbI ,nBa CHMBOJIa (HanpHMep, B HJIH C), TO 3TO 03HaqaeT, qTO YCH-
JIeHHe, BepOHTHO, H3MeHHTCH npH H3MeHeHHH BHeIIIHHX YCJIOBHH HJIH COCTOHHIDI
MeTaJIJIa.
KOHTaKTHPYJOIQHi MeTaJJJI
MaTepH8JI
3aKJIeDKH HHKeJJh- Hep1K88elO- Me CT8JIh AmoMHIIIfii IJ;HHK
Me,lJ,llhlii CDJIU OUUI CT8JIh H CDJlULI
HHKeJIb- Me,ll;HbIH CllJIaB - A A A A A
HepXaBeIOIIJ;aH CTaTlb A - A A A A
Me,ll;b B HJIH C B HJIH C - A A A
CTaJIb C C C - B A
ArrIOMHHHH H CllJIaBbI C B HJIH C D B HJIH C - A
IJ;HHK C C C C C -
4.2. 3aKlleno"tHble coeOUHeHUR 265
4.2. 12. PeKoMeHAaqHH no npOeKTHpOSaHHIO
npHCOe,ZJ;HHeHHe MJlfKoro MaTepHaJIa K TBep,n;oM)'
ECJIH 60pTHK 3aKJIenKH HaxO,nHTCH co CTOpOHbI WIrKoro MaTepHaJIa, MO)I{HO
HCnOJIb30BaTb 3aKJIenKY C YBeJIHqeHHbIM 60pTHKOM. Ii Ha060poT, paCnOpHaH 3a-
KJIenKa pacnpe,neJI.HeT C)J{HMalOlI(yID HarpY3KY no 60JIbIIIeH 06JIaCTH, qTO n03BOJI.HeT
H36exaTb nOBpe)K,l(eHIDI M.HrKOrO MaTepHaJIa.
YBeJ1V1"1eHHblt1 60pTiI1K
PacnopHa aa KnenK a
TBePA b t It
MflrK1II1II -
nJiaCTHKH H xpynKHe MaTepHaJILI
,[LrnI JIOMKHX TIJIaCTMaCC H XpynKHX MaTepHaJIOB POP@ KJIenKa npe,l(JlaraeT MHO-
xeCTBO pa3Ho06pa3HbIx peIIIeHHH. JIerKo YCTaHaBJIHBaeMbIe aJIlOMHHHeBbIe 3aKJIeI1-
KH ,norrycKalOT HH3KHe HarpY3KH I1PH YCTaHOBKe, B TO BpeM.H KaK H JIeneCTKOBbIe, H
pacnopHbIe 3aKJIenKH 06eCI1eqHBa1OT YBeJIHqeHHe TIJIOIIJ;Cl,l.(H 0I10pbI Ha coe,aHIDIe..
MbIe MaTepHaJIbI. ,[LITH 60JIee npOqHbIX TIJIaCTMaCC MO)I{HO HCI10JIb30BaTb CTaH,l(apT-
HbIe BbITH)l{HbIe 3aKJIeIIKH - C OTKpbITbIM HJIH 3aKpbITbIM TOpUOM.
JlerKa YCTaHoBKa (PAD) YBeJ1i11"1eH- JlenecTKoBa PacnopHa
AAIOMiI1HiI1V1 (AD/ASS) Hblt1 60pTiI1K aaKnenKa aaKJ1enKa
MaTepHaJI c Ce1JeHHeM, HanOMHHalOIIUlM 6YKBY «n» (mBeJlJIep)
QT06bI ,nOCTHqb ,nHa Y3Koro CeqeHIUI, MO)f{HO HCnOJIb30BaTb YMHHeHHyID Ha-
Caru(y (A) (CMOTPH pHCYHOK HHXe). IIpH 3TOM CJIe,nyeT HCI10JIb30BaTb 60JIee ,l(JIHH-
HbIH CTepxeHb 3aKJIeI1KH, H MaKCHMaJIbllbIH ,nHaMeTp HaCan;KH ,nOJl)l{eH 6bITb paBeH
.D;HaMeTPY 60pTHKa 3aKJIeilKH. B KaqeCTBe aJIbTepHaTHBbI 3aKJIeilKY MO)I{HO YCTaHO-
BHTb C ,npyrOH CTOpOHbI (B) IDIH paCIIIHpHTb KaHaJI, QT06bI npHMeHHTb CTaH,[(apT-
HyIO 3aKJIeilKY H 3aKJIeI10qHHK(C).
YAJ1i11HeHHa51
HaCSAKa
A
B
c
F/la8a 4. Kpene:JICHble oemOJlu
TOJICTLIe/TOHKHe JIHCTLI
IIpH coe,nHHeHHH MaTepHaJIOB pa3JIWlHOH TOJIII(HHbI JIyqIIIe paCnOJIO)J{HTb 60-
JIee TOJICTYIO TIJIaCTHJIy co CTOpOHbI 3aMbIKalOlI(eH fOJIOBKH (A) (CMOTPH pHCyJlOK
HIDKe). ECJIH ,nHaMeTp OTBepCTIDI B 60JIee TOHKOH TIJIaCTHHe BeJIHK, CJIe,nyeT HC-
nOJIb30BaTb 3aKJIenKY C YBeJIHqeHHbIM 60PTHKOM (B). ECJIH 60JIee TOHKaH IIJIaCTHHa
pacnOJIO)l{eHa co CTOpOHbI 3aMbIKalOlI(eH rOJIOBKH, Hy)KH0 JIH60 HCnOJIb30BaTb
onopHyro IIIaH6y (C), JIH60 06eCneqHTb, qT06bI ,nHaMeTP OTBepCTIDI B 60JIee TOJI-
CTOH TIJIaCTHHe 6bill MeHbIIIe, qeM B 60JIee TOHKOH TIJIaCTHHe (D).
A
B
c
D
fJIYXlle OTBepCTHJI H na3LI
YCTaHoBKa POP@ HJIH BbITIDKHOH 3aKJIenKH B rJIyxoe OTBepCTHe HJIH B npo<ppe-
3epoBaHHbIH na3, nepeCeKalOlI(HH OTBepCTHe HJIH BHYTpeHHlO1O nOJIOCTb, B03MOlKHa
6JIaro,napR paCIIIHpeHHIO TeJIa 3aKJIenKH npH YCTaHOBKe.
A
B
c
illapHHpHoe COe,ZJ;HHeHHe
HCnOJIb30BaHHe Cnen;HaJIbHOH HaCan;KH 06eCneqHBaeT He60JIbIIIOH 3a30p Mex,ny
60pTHKOM 3aKJIenKH H naKeTOM, TaKHM 06pa30M 06eCneqHBaR no,nBIDKHOCTb co-
e,nHHeHIDI. HacaAKa, o6ec-
ne"lil1BalOw.a
t wapHVlpHoe
coeAVlHeHiI1e
AeTaJ1b
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XOTR CTaH,[(apTHbIe ,nHaMeTpbI oTBepcTHH paBHbI ,nHaMeTpy Koprryca 3aKJIenKH
IIJIIOC 0, 1 MM, pa3MepbI oTBepcTHH B coe)J;HH.HeMbIX ,neTaJI.HX He Bcer,na MOryT 6bITb B
TOQHOCTH paBHbIMH 3an;aHHOMY 3HaQeHHIO, HanpHMep eCJIH OTBepCTHR np06HTbI B
,neTaJUIX 3apaHee. B Tex CJIyqaRx, KOf,na OTBepCTHe Ha HIDKHeH CTopOHe (co CTOpO-
HbI 3aMbIKalOIIJ;eH rOJIOBKH) 60JIbIIIe, CJIe,nyeT BbI6paTb MHor03IDKHMHyIO 3aKJIenKY
4.2. 3aKlleno"tHble coeOUHeHUR 267'
H3-3a ee HCKJIlOqHTeJIbHOrO CBOHCTBa 3anOJI-
IDITb OTBepCTHe. JIenecTKoBbIe H pacnopHbIe 3a-
KJIeilKH TaIOKe MOryT CTaTb aJIbTepHaTHBHbIMH
perneHIDIMH npH 3THX 06CTOHTeJIbCTBax, oco- MHOr03a)l(VlM-
6eHHo npH pa60Te C JIOMKHMH HJIH XpynKHMH Ha 3aK11enKa
MaTepHaJIaMH. Ii Ha060poT, eCJIH OTBepCTHe 60-
JIbme co CTOpOHbI 60pTHKa, CJIe,r(yeT BbI6paTb 3aKJIeilKY C
)'BeJIWleHHbIM 60pTHKOM.
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50 100 150 200 °C
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4.2.17. 3aKnenOlfH&le raNKJf (<<raelfH&le 3aKnenKJf»)
3aKJIeIIOqHbIe raHKH pa3pa60TaHbI CIIeI..J;HaJIbHO, qT06bI 06eCIIeqHTb 60JIee IIpOqHOe
pe3b60Boe coe,nHHeHHe JIHCTOB (CTaJIH) H ,npyrHX MaTepHaJIOB, aHaJIOrHqHO BbITIDK-
HbIM 3aKJIeIIKaM, TaM, r,ne ,[(JI.H YCTaHOBKH B03MoxeH ,nOCTYII TOJIbKO K O,nHOH CTO-
pOHe H3,neJIIDI. OHH He TOJIbKO <pOpMHpyroT HaKH)];Ilyro raHI{)', HO, B OTJIWIHe OT He-
KOTOpbIX ,npyrHX BH,nOB, TaIOKe ,noIIycKalOT CKJIeIIbIBaHHe KOMIIoHeHToB, 3ao,nHO
06eCIIeQHBa.H 3aKpeIIJIeHHe BHHTOBOH pe3b6bI. IIpHHUHII HX HCIIOJIb30BaHIDI nOKa-
3aH HIDKe.
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YCTaHOBOQHOrO HHc1]JYMeHTa ( «3aKJIenOQHHKa ,[(lliI 3aKJIeIIOQHbIX
raeK», «pe3b60Boro 3aKJIenOqHHKa»), KOTOpbIH 3aTeM BCTaBJI.HeTC.H B
npOCBepJIeHHOe HJIH IIp06HToe oTBepcTHe.
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BasI HX BMeCTe.
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or M3 ,no M12, IIPH 3TOM B03MO)KHbI caMbIe pa3Ho06pa3HbIe COqeTa-
HIUI <pOPMbI 60pTHKa, <pOpMbI KopIIyca H MaTepHarra. BbI,l(eJI.HIOT TPH
THna 60pTHKOB - CTaH,[(apTHbIH, IIOTaHHOH (yrOJI 90°) H ,[(lliI TOHKHX
MaTepHaJIOB YMeHbIIIeHHbIH 60PTHK, KOTOpbIH 06eCIIeQHBaeT YCTa-
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CTaH,[(apTHbIH KOPIIYC - KpyrJIbIH OTKpbITbIH HJIH 3aKpbITbIH. 3a-
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rpaHHbIe KopIIyca (YCTaHOBJIeHHbIe B IIIeCTl1yrOJIbHbIe OTBepcTIDI) HJIH Koprryca co
IllJIHl(aMH (YCTaHOBJIeHHbIe B KpyrJIOe oTBepCTHe).
4.2. 18. POP@ pe3&6os&le 3aKnenKJf: npJfMeHeHJfe
POP@ pe3b60BbIe 3aKJIenKH 06eCIIeqHBalOT npocToH H
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3<p<peKTHBHbIH CIIoco6 coe,nHHeHHR aTepHaJIOB, n03B( f '
JUIIOmHH B pa3JIHqHbIX IIpHJIO)f(eHHRX H IIOJIb30BaTb npe-
HMyIneCTBO BHyrpeHHeH pe3b6bI.
POP@ pe3b6oBbIe 3aKJIenKH .HBJl.HIOTC.H IIpeKpaCHbIM
pemeHl1eM ,[(.JlSI <pOpMHpoBaHIDI BbICOKOKaqeCTBeHHbIX, Ha-
rpyxeHHbIX pe3b60BbIX coe,nHHeHHH B pa3JIHqHbIX MaTepH-
arrax TaM, r,ne B ,npyrHe coe,nHHeHIDI, He C03,na101I(He Bpa-
m;aIOIIJ;erO MOMeHTa, He MOryT y,nepxaTb BbInOJI3alOII(yro
HarpY31{)'. POP pe3b60BbIe 3aKJIenKH IIO,nxOMT ,nIDKe ,[(.JlSI
o,nHHapHbIX JIHCTOB TOJIII(HHOH He 60JIee 0,5 MM.
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IIpHJIOXeHHH, B KOTOpbIX ,nocTYIIHa TOJIbKO o,nHa CTOpO-
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IIOBpe)l(,[(a.H IIpe,nBapHTeJIbHO o6pa6oTaHHyro OKpyxalO1I(yIO IIOBepXHOCTb HJIH TOH-
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B COBpeMeHHbIX YCJIOBH-RX IIpOH3Bo,nCTBa:
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. IllHpoKoe pa3Hoo6pa3He BH,l.(OB
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KJIeIIKH C)l{HMaeTC.H, <POpMHPY.H 6ypT Ha HIDKHeH CTopOHe IIaKeTa, H CHJIbHO CXH-
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4.2. 3aK./leno"tHble coeOUHeHUJl 279"
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HOrO 3JIeMeHTa KpeIIJIeHH.H rrpH rrOCJIe,nyroII(HX C60POqHbIX pa6oTax.
4.2.20. PO raHKa: CTan&
OTKpLITaJl, CTaH,ZJ;apTHLIH OOpTHK (c pH4JJIeHHeM)
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d 0003Ha1feHHe (MM) DaKeTa e OTBepCTHJI CTep1KllJl OOPTHKa OOpTHKa BO B KOH- CTBO B
L (MM) (MM) (MM) D (MM) B (MM) S TeiHepe KopoOKe
M4 PSFON430 10,0 0,3-3,0 10000 500
PSFON440 11,5 3,1-4,0 6,0 5,9 9,0 1,0 10000 500
M5 PSFON530 12,0 0,3-3,0 8000 500
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M6 PSFON630 14,5 0,5-3,0 4000 500
PSFON645 16,0 3,1-4,5 9,0 8,9 12,0 1,5 4000 500
M8 PSFON830 16,0 0,5-3,0 2000 250
PSFON855 18,5 3,1-5,5 11,0 10,9 15,0 1,5 2000 250
MI0 PSFONI030 17,0 0,5-3,0 1500 200
PSFONI060 22,0 3,0-6,0 12,0 11,9 16,0 2,0 1500 200
M12 PSFON1240 23,0 1,0-4,0 16,0 15,9 22,0 2,0 1500 200
F/laBa 4. Kpene:JICHble oemOJlu
3aKpLITaJI, cTau,napTHLIH OOPTHK (c pH4JJIeHHeM)
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d 0003Ha1feHHe (MM) DHeTa e OTBepCTHJI cTep1KllJl oOpTHKa 60pTHKa 80 8 KOH- CTBO B
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M5 PSFCN530 18,0 0,3-3,0 7,0 6.,9 10,0 1,0 5000 500
M6 PSFCN630 20,5 0,5-3,0 9,0 8,9 12,0 1,5 2000 500
M8 PSFCN830 25,0 0,5-3,0 11,0 10,9 15,0 1,5 1500 250
OTKPLITaJI, CTaH,ZJ;apTHLlH OOPTHK, meCTHrpaHHHK
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d 0003Ha1feHHe (MM) DaKeTa e OTBepCTHJI CTep1KllJl OOp1'HKa 6op1'HKa 80 8 KOH- CTBO B
L (MM) (MM) (MM) D (MM) B (MM) S TeiHepe Kopo6Ke
M4 PSFOH430 11,5 0,5-3,0 6,1 6,0 9,3 1,0 10000 500
MS PSFOH530 13,5 0,5-3,0 7,1 7,0 10,3 1,0 8000 500
M6 PSFOH630 15,5 0,5-3,0 9,1 9,0 12,3 1,5 4000 500
MB PSFOH830 17,5 0,5-30 11,1 11,0 14,3 1,5 2000 250
MI0 PSFOHI040 22,0 1,0-4,0 13,1 13,0 16,3 2,0 1500 200
4.3. (/JQJlbu,e6ble coeouHeHUR 281
OTKpLITaJl, nOTaHHoH OOpTHK (c pHfj)JIeHHeM)
goo
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d 0003H81feHHe (MM) DHeTa e OTBepCTHJI crrep1KllJl oOpTllKa 60pTllKa 80 8 KOH- cTB08
L (MM) (MM) (MM) D (MM) B (MM) S rreiHepe KopOOKe
M4 PSKON435 11,5 2,0-3,5 6,0 59 9,0 1,5 10000 500
M5 PSKON540 13,5 2,0-40 7,0 69 10,0 1,5 8000 500
M6 PSKON645 16,0 2,0-4,5 9,0 89 12,0 1,5 4000 500
MS PSKON845 19,0 2.CM,5 11,0 10,9 14,0 1,5 2000 250
MI0 PSKONI045 21,0 2,0-4,5 12,0 11,9 14,7 1,5 1500 200
,D;aJIbHeHmyIO HH<popMaUHIO MO)I{HO HaHTH BO MHoxeCTBe rry6JIHKaUHH, rrOCB.H-
m;eHHbIX POP KJIerrKe, BbIrryI.l(eHHbIX Emhart Teknologies (Tucker Fasteners Ltd) -
CMOTpH rrpHJIOXeHHe 3.
4.3. Cbanbu.eBble coeAMHeHMSI
4.3. 1. C/)sn&qes&le COeAJfHeHJffl
Jle)KaqHH 4JaJILD;
/j-
/
,[(BOHHOH JIe)Ka'lHH 4JaJILD;
Pila8a 4. Kpene:JICHble oemOJlu
npocToi yrJIOBoi 4JaJILD;
KOMOHHHpOBaHHLIH yrJIOBoi 4JaJILn
nOCJIe,n;OBaTeJILHOCTL 4JopMHpOBaHHJI JIe1Ka'lero 4JaJILna
np cnOC06J1eH e c
KaHaBKoVi AJ151 06-
)I( Ma coeA HeH
) (
OTr 6 KpOMK AJ151 ct>OpM pOBaH 5I
OA HapHoro J1 e)l(a"lero ct>aJ1bu.a
)
CoeA HeHVle J1 CTOB OA HapHbIM
J1e)l(a"lViM ct>aJ1bu.eM
CTau.VlOHapHa51 J1 ne-
peHOCHa51 HaKOB J1bH
OKOH"IaTeJ1bHOe ynJ10THeH e coeA HeH 5I np
nOMow. np cnOC06J1eH 5I AJ151 06)1( Ma C Ka-
HaBKoVi cooTBeTcTBYIOw.eVl W pVlHbl
4.3.2. npJfnycKJf HS cpsn&qes&le COeAJfHeHJffl
Jle)Ka'lHH 4JaJILD;
1
w
T
w
w
4.4. PQ3Jlu"tHble "peneJICHble U30eJlUR 283
npOCTOH yrJIOBOH 4JaJILD;
KOMOHHHpOBaHHLIH yrJIOBOH 4JaJILn
T
W - IIIHpHHa OTOrHYTOH KpOMKH
G - IIIHpHHa JIexaqero <paJIbua
L - IIIHpHHa <pHKcHpyrolI(eH rrOJIOCKH
P - IIIHpHHa rrpOCToro yrJIOBOrO <paJIbua
K - IIIHpHHa KOM6HHHpoBaHHoro yrJIOBOrO <paJIbua
T - TOJIII(HHa MeTaJIJIa
THo coe,znmelllDl
npHMepHlde
onyIQelllDl
npHMepHbIe npHnycKH
CYMMapHbIH npHnycK = 3G-4T paCnpe,ll;eIDIeTCH:
(a) nOpOBHY Mex.ny ,lI;BYMH KOHI(aMH 1 H 2; HJIH
(b) ,lI;Be 'rpern - KOHeI( 1 H O,ll;Ha 'rpeTb - KOHeI( 2, eCJIH BIDKHO
nOJIOXeHHe eH a coe HHeHHHeHH n03H HH
BOHHOH JIeXaqHH <PaJIbI( ,LJ;o6aBHTb W - T K Iq>OMKe KIDK,ZJ;OH H3 COe,ll;HIDIeMbIX 3arOTOBOK.
llIH HHa HKCH eH nOJIOCKH = 4W + 4T Tor a L = 2W + 4T
ITpOCTOH yrJIOBOH <paJIbI( ,LJ;o6aBHTb W ,lI)UI O,ll;HHapHOH Iq>OMKH K KOH
3.
,LJ;o6aBHTb 2W + T ,lI)UI ,lI;BOHHOH Iq>OMKH K KOH
4.
P = 2W + 2T
,LJ;o6aBHTh W ,lI)UI O,ll;HHapHOH Iq>OMKH K KOH
5.
,LJ;o6aBHTb 2W+ T ,lI)UI ,lI;BOHHOH Iq>OMKH K KOH
6.
K = 2W + 3T
JIe:>KaqHH <PaJIbI(
KOM6HHHpOBaHHbIH
yrJIOBOH <paJIbI(
4.4. Pa3nM'IHble Kpene>KHble M3AenMSI
4.4. 1. KOHJflfeCKJfe WTJfcpT&I, He3SKSneHH&le
Pa3MepLI
Krracc A (IIIJIH<p0BaHHbIe IIITH<pTbI): IllepoxoBaTocTb Ra = 0,8 MKM
Krracc B (o6TOqeHHbIe IIITH<pTbI): IllepoxoBaTocTb Ra = 3,2 MKM
1:50
r2
a + d + (0,02/)2
2 8a
1J
a
a
FII060 4. KpeneJICHble iJemOllu
Pa3MepbI B MM
d hl0 a 0,6 0,8 1 1,2 1,5 2 2,5 3 4 5 6 8 10 12 16 20 25 30 40 50
a :=::: 0,08 0,1 0,12 0,16 0,2 0,25 0,3 0,4 0,5 0,63 0,8 1 1,2 1,6 2 2,5 3 4 5 6,3
lb
HOM. MHH. MaKC.
2 1,75 2,25
3 2,75 3,25
4 3,75 4,25
5 4,75 5,25
6 5,75 6,25
-
8 7,75 8,25
10 9,75 10,25
12 11,5 12,5 -
--
14 13,5 14,5
16 15,5 16,5
- -
18 17,5 18,5 ,L(Hana30H
20 19,5 20,5
22 21,5 22,5
24 23,5 24,5 -
-
26 25,5 26,5
28 27,5 28,5
30 29,5 30,5 npOMbIlliJIeHHbIX
-
32 31,5 32,5
35 34,5 35,5
-
40 39,5 40,5
-
45 44,5 45,5
50 49,5 50,5
-
55 54,25 55,75 ,l(JIHH -
-
60 59,25 60,75
65 64,25 65,75
70 69,25 70,75
75 74,25 75,75
80 79,25 80,75
85 84,25 85,75
90 89,25 90,75
95 94,25 95,75
100 99,25 100,75
120 119,25 120,75
140 139,25 140,75
160 159,25 160,75
180 179,25 180,75
-
200 199,25 200,75
a ,L(pyrHe ,n:OnyeKH, HanpHMep all, ell, f8, B eOOTeTeTBHH e eOfJIaWeHHeM Me
110-
Tpe6HTeJIeM H 110eTaBIl(HKOM
b ,L(JHI HOMHHaJIbHbIX ,l(JIHH eBbIwe 200 MM mafH 20 MM.
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3:
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FII060 4. KpeneJICHble iJemOllu
r.Q
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p,.
I .-..
)1 Q. t 8Cu N 00 \C .-4 0 N \C'" \C'" \C'" \C'" 00 0 N \C'" 00 00 0", N '"
0'" '" '" '" '" '" '" '" '" '" '"
!ei '" '" N V") \C f' 00 0'\ 0 N V") \C f' 0'\ 0 .-4 N
I f' 00 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 N N N N N N N N M
=
11 Q,) \J
I= \C N 00 .-4 0;, 0 N N .-4 .-4 N '" V") \C'" 00 00 00 0", N '" \0
'" '" '" '" '" '" '" '" '" '" '" '" 0
= '" '" '" .-4 N V") \C f' 00 0'\ 0 .-4 N V") f' 00 0'\
\C 00 0'\ .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 N N N N N N N N N M
=
I 00 0", 0", V") N N N V") V") f'", f' f' f' f' f' 0", 0", 0 0 0 q
I ii '" .-4 '" '" '" '" '" '" '" '" '" '" '" '" '"
0 .-4 .-4 '" .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 N N N N N N
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'" '" M '" '" '" '" '" '" '" '" '" '" '" '"
.-4 N N
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c i i ii 00 0;, '" V") f' 00 00 00 0", .-4 N N '" V") \C'" f' 00 0\
'" '" '" '" '" '" '" '" '" '" M '" '" '" '" '"
0 0 .-4 .-4 .-4 .-4 .-4 .-4 .-4 N N N N N N N N N N
= = '-"
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0 0",
0 0'" 0 0
I I
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= '" '" \C'" f' 00 0 0", 0", 0", 0", 0 0 0 0", N N N", N N
'" '" '" '" '" '" '" '" '" '"
0 0 0 0 0 0 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4
\C V") 0'\ 00 00 \C
0 .-4 0 .-4 .-4
'" '" <;'" '" '" '"
0 0 0 <; 0
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t \C V") V") V") V") 0 0", 0;, 0;, 00 f' f' V") V'l V") V") V) "1
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N V") \C f' 00 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 N N
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! fl '" '" \C'" \C \C'" f' f'", 0'\ 0;, .-4 N N V") V") V") V") "1- 'i')
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0 0 0 0 0 0 0 0 0 0 0 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4
i .-4
<;'" 0
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\C V") 0'\
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t 00 00 00 f' f' \C'" \C'" \C'" V") V") '" '" N", N", 0", 0", 0", 0", q
I\:) '" '" '"
'" '" '" '" '" 0 .-4 N V") \C f' 00 0'\ 0 .-4 N
N V") \C f' 00 0'\ .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 N N N
t 0 N 0 N M
I- V") \C f' 00 0'\ .-4 V") \C f' 00 0'\ .-4
i .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 N N N N
&rill
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C U 0 0 0 0 0 0 0 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 N N N N
u
= te I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
rJ'.) rJ'.) rJ'.) rJ'.) rJ'.) rJ'.) rJ'.) rJ'.) rJ'.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) 00 00
4.4. P03IIulfHble Kpene:JICHble U3iJeJ1UJ/
00 00 0 N '" \C 0", N '" 00 N N '" \C'" 00 q N 0", N N '" '" \C.. 00 00 00 0",
M '" '" '" '" '" '" v-) '" '" '" '" .. '" N '" '"
\C f' 00 0'\ .-4 N f' 00 0'\ 0 .-4 \C f' 00 0'\ 0 .-4 f'
M V") V") V") V") V") V") V") V") \C \C \C \C \C \C
'- " /
t--. f' 0'\ 00 0", N \C'" V") f'", 0;, .-4 N N \C'" 00 V") f' V") f' f' 0'\ 0'\ 00 0",
'" '" '" '" '" '" '" '" '" '" '" '" '" '" '" '" '" '" 0 ..
N \C f' 00 0'\ 0 .-4 V") \C f' 00 0'\ 0 N V") \C 00 0'\ 0
M V") V") V") V") V") V") V") V") \C \C \C
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N N N N N N N N N N N N N N N N N N N N N N N N N N N N
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P""4 N V") 0 0'\ 00
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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N N N N N N V") V")
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
00 00 00 C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) C/.) 00 C/.) C/.) C/.) C/.) C/.)
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4.4. P03IIU'IHble ICpene:JICHble U3iJeIIUJ/
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N V") V") \C f' 00 00 0'\ 0 N N V") f' 00 0 .-4 N V") V") \C f' f'
. N N N N N N N N
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. . . . . . . . . . . . . . . t; f' f' f' f' f' f' f' f' f' N N N
1"'"4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 . . . . . . . . .
.-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4
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. . .r) ...0 . . . N .r) ...0 r..: 00 0\ d N .r) ...0 r..: 00 0\ d . N .r) \0
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.-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 .-4 N N N
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N 0 N N
d d 0 d 0 d 0
+ + + +
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0 N .r) \0 r---: N .r) . N .r) \0 r---: 00 0\ d .
00 0'\ 0 .-4 f' 00 0'\ 0 .-4 .-4
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0 .-4 N V") \C f' 00 0'\ 0 .-4 N V") \C f' 00 0'\ 0 .-4 N V") \C f' 00 0'\ 0 .-4 N
N N N N N N N N N N V") V") V")
::E ::E ::E ::E ::E ::E ::E ::E ::E ::E ::E ::E ::E
0\ 0 .-4 N V") \C f' 00 0'\ 0 .-4 N V") \C f' 00 0'\ 0 .-4 N V") \C f' 00 0'\ 0 .-4 N
N N N N N N N N N N V") V") V")
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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FII060 4. Kpene:JICHble iJemOllu
4.5. CKneMBaHMe MeTannOB
4.5. 1. AHBapo6Hble KneJf
CyrueCTByIOT BbICOKOnpOqHble KJIeH, mHpOKO HCnOJIb3yeMble B MamHHOCTpoeHHH.
AHa3po6Hble KJIeH - O,n;HOKOMnOHeHTHble MaTepHaJIbI, KOTopble OCTalOTCR HeaK-
THBHbIMH B YCJIOBHRX KOHTaKTa C KHCJIOpO,n;OM. ,[LJrn OTBepX,ll;eHHR 3THM KJleRM He-
06XO,n;HMO BblnOJIHeHHe o,n;HOBpeMeHHO ,n;BYX YCJIOBHH: OTC)'TCTBHe KHCJIOpo,n;a H Ha-
JIJ{qHe MeTaJIJIJ{qeCKHX ,n;eTaJIeH. TaKHe KJIeH mHpOKO HCnOJIb3yIOTCR ,nJIR <pHKca:U;HH
H repMeTH3aU;HH pe3b6oBbIX coe,n;HHeHHH, yruIOTHeHIDI H y,n;ep:>KaHIDI (IUIH coe,n;H-
HeHIDI) ,n;eTaJIeH U;IUIHH,lJ;p:uqecKoH <pOpMbI npH KOMHaTHOH TeMnepaType, Kor,n;a cy-
IUeCTByIOT :u,n;eaJIbHbIe YCJIOBIDI ,LLJUI OTBepX,ll;eHHR KJIeR, KaK nOKa3aHO Ha pHC. 1.
PUC. 1. K.1IeH 3aTeKaeT B 3a30pbI Me)K,[(Y rneCTepHeH H BaJIOM, r,n:e cyru;eCTByroT H,ZJ;e-
aJIbHbIe YCJIOBHH ,l(JUI ero OTBep)K,[(eHHH (OTcyrcTBHe KHCJIOpo,n:a H aKTHBHbIe
MeTaJlJIHQeCKHe ,n:eTaJIH)
Me,n;b, JIaTYHb H HeJIerHpOBaHHaR yrJIepo,n;HCTaR CTaJIb «aKTHBHbI» no OTHome-
HHIO K aHa3po6HbIM KJIeRM, nOCKOJIbKy B HX npHc)'TcTBHH KJIeH 6bICTPO oTBep,n;eBaIOT
npH KOMHaTHoH TeMnepaType. Hep:>KaBelOIUaR CTaJIb, aJIlOMHHHH H aJIlOMHHHeBbIe
CTIJIaBbI, a TaIOKe MeTaJIJIbI C nOIqJbITHRMH - «naCCHBHbI» H, qTo6bI o6eCneqHTb nOJI-
Hoe OTBep,n;eHHe, TPe6yIOT HCnOJIb30BaHHR aKTHBaTopa. TaK KaK KJIeH :>KJf,l:I;KHH, OH
3aTeKaeT B MeJIbqaHmHe IUeJIH Me BCTaBJIeHHbIMH o,n;Ha B ,n;pyryro KOMnOHeHTa-
MH, r,n;e, B OTC)'TCTBHH aTMoc<pepHoro KHCJIOpo,n;a, 3aTBep,n;eBaeT H OKa3bIBaeTCR «3a-
nepTbIM» Me HepOBHOCTRMH nOBepXHOCTH. TIpo:Qeccy OTBepX,ll;eHIDI TaIOKe cno-
co6cTByeT KOHTaKT KJIeR C MeTaJIJI:uqeCKOH nOBepXHOCTblO, KOTOpaR ,n;eHcTByeT KaK
KaTaJIH3aTOp B TOM cJIyqae, eCJIH MeTaJIJI «aKTHBeH». ECJIH nOCJIe OTBepX,ll;eHIDI a,n;re-
3HB ,n;OCTHraeT BR3KOCTH TepMOpeaKTHBHOH TIJIaCTMaCcbI, OH o6eCneqHBaeT BTIJIOTb ,n;o
60% npOqHOCTH coe,n;HHeHIDI npH IqJyqeHHH, KaK nOKa3aHO Ha pHC. 2. QTo6bI rapaH-
THpOBaTb npOqHOCTb coe,n;HHeHIDI, conpHKacalOIUHeCR nOBepXHOCTH CJIe,n;yeT Mexa-
HJ{qeCKH H XHMJ{qeCKH OqHCTHTb nepe,n; HaHeceHHeM KJIeR H JII06oro Heo6xo,n;HMoro
aKTHBaTOpa - ,LLJUI y,n;o6cTBa ero 06b}qHO HaHOCRT Ha OXBaTbIBaeMYIO qaCTb coe,n;HHe-
HHR. BpeWi <pHKcaU;HH COCTaBillIeT 10-20 MHH)'T, a OKO aTeJIbHaR npOqHOCTb ,n;o-
CTHraeTCR 3a 4-24 qaca B 3aBHCHMOCTH OT BeJIJ{qHHbI 3a30pa Me ,n;eTaJIRMH, Ma-
TepHaJIOB conpHKacalOIUHXCR nOBepXHocTeH H TeMnepaTypbI. OTBep,n;eBmHe a,n;re3H-
BbI cnoco6HbI BbI,lJ;ep:>KHBaTb TeMnepaTypy BTIJIOTb ,n;o 150°C, a. TaIOKe RBJlRIOTCR
CTOHKHMH K 60JIbmHHcTBY XHMJ{qecKHX B03,n;eHcTBHH, o,n;HaKO cyrueCTByIOT a,n;re3H-
4.5. CKJleU60HUe MemOJlll06
- 60 DonT M10
J: 50
-
as
CD
Ji 40
a.
0
30
:r:
Q)
20
0
10
0
40 HM YCVlnVle
OTBOpat.lVlBaHVlS1
B OT-
CYTCT-
BVIVI
KJ1 eS1
Kne Kne BbICOKO-
HVl3KO cpeAHe npOt.lHbl
npot.l- npot.l- KJ1e
HOCTVI HOCTVI
PUC. 2. fpa<pHK, nOKa3bIBalO HH MOMeHT cpbIBa ,l(JUI 60JITa M lOB 3aBHCHMOCTH OT
KJIaCCa KJIeH, npH YCHJIHH OTBOpaQHBaHHH paBHOM 40HM
BbI, CnOC06Hble BbI,lJ;ep:>KaTb H 60JIee BbICOKHe TeMnepaTypbI. THnJ{qHble aHa3po6Hble
KJIeH H3 aCCOpTHMeHTa Loctite H HeKOTOpble HX npHMeHeHHR nepeqHCJIeHbI B Ta6JI. 1.
Ta6J1. 1. )];aHHbIe 0 npO,n:yKUHH Loctite (JIoKTaHT)
ARas o611Ye Meu
KJIeu ,lUIJI
660
HaMe aJIbHbIH 3a30
II 01JHOCTb BbICOKCUI BbICOKCUI C e,l(IDUI
BpeWi <pHKca HH npH 23 °C (MHH.) 10 10 30 10
Te MOCTOHKOCTb °C
150
150
150
175
KJIeu ,lUIJI
e3hOOBbIX coe.znmeHHii
243 2701
)];0 0,15 )];0 0,15
3a30p B
HH3KCUI C e,l(IDUI BbICOKCUI
15 10 10
150 150 150
577
542
C e,l(IDUI
30
150
napa BTIJIOTb ,l(0 ,l(aBJIeHIDI
pa3pbIBa TPy6bI I1PH
fH,lJ;paBJIWleCKHX coe-
,l(HHeHIDIX
FII060 4. Kpene:JICHble iJemOllu
4.5.2. KneJf YcP-oTSepJlCAeHJffJ
CyrueCTByIOT KJIeH, KOTopble OTBepX,ll;alOTCR no,n; B03,n;eHcTBHeM YJIbTPa<pHOJIeToBoro
(Y<I» H3JIyqeHHR. BpeMR OTBepX,ll;eHHR 3aBHCHT OT HHTeHCHBHOCTH H ,nJIHHbI BOJI-
HbI Y<I>-H3JIyqeHHR, KOTopoe HHH:QHHpyeT nOJIHMepH3a:QHIO.
IIpuMel.taHue. TIPH pa60Te C Y<I>-H3JIyqeHHeM Heo6xo,n;HMO Bcer,n;a HCnOJIb30BaTb
COOTBeTCTByIOIUHe cpe,n;CTBa 3aIUHTbI rJIa3.
K.JIeH, KOTopble OTBepX,ll;alOTCR no,n; B03,n;eHcTBHeM Y<I>- H3JIyqeHHR, RBillIlOTCR
BbICOKOnpOqHbIMH, 06JIa,n;a1OT xopomeH 3anOJIIDIIOIUeH cnoco6HoCTblO, xapaKTepH-
3yIOTCR He60JIbmHM BpeMeHeM <pHKcaO;HH, npORBillIlOT BbICOKyIO YCTO:HqHBOCTb K
B03,n;eHCTBHIO BHemHHX YCJIOBHH H JIerKO ,n;03HpyIOTCR aBTOMaTHqeCKHMH CHCTeMa-
MH, nOCKOJIbKy RBillIlOTCR O,n;HOKOMnOHeHTHbIMH.
MCTOqHHK Y<I>-H3JIyqeHHR RBillIeTCR BIDKHOH COCTaBillIlOIUeH npoo;ecca. Hana-
30H 3THX YCTPOHCTB npOCTHpaeTCR OT npOCTbIX pyqHbIX JIaMn ,n;o nOJIHOCTblO aBTO-
MaTH3HpOBaHHbIX KOHBeHepoB C HeCKOJIbKHMH Y<I>-npo:>KeKTOpaMH, BKJIlOqalOII(HX
B ce6R cne:QHaJIbHble KpeTIJIeHHR, y,n;ep:>KHBaIOIUHe KOMnOHeHTbI BMeCTe B npoo;ecce
OTBepX,ll;eHHR. ,[LITR MaJIeHbKHX KOMnOHeHTOB peKOMeH,lJ;yeTcR HCnOJIb30BaTb CBeTO-
BO,n;bI, TaK KaK 3TH YCTPOHCTBa 06eCneqHBalOT BbICOKyIO HHTeHCHBHOCTb H3JIyqeHIDI
Ha TIJIOIUa,n;H ,n;HaMeTPOM OKOJIO 10 MM. TaKHe CBeTOBO,n;bI rapaHTHpyIOT, qTO Y<I>-
H3JIyqeHHe HanpBJIeHO TOqHO Ha 06JIaCTb nOJIHMe-
pH3aO;HH, qTO n03BOJIReT MHHHMH3HpOBaTb MOm;-
HOCTb Y<I>-H3JIyqeHHR HerO pacceRHHe. CBeTOBO,l(
nOKa3aH Ha pHC. 1.
B HeKOTopbIX CJIyqaRX He Bcer,n;a MO:>KHO rapaH-
THpOBaTb, qTO BeCb KJleH no,n;BeprCR Y<I>-o6.rryqe-
HHIO, n03TOMY pa3pa6oTaHbI KJleH, KOTopble OTBep-
,n;eBalOT nOCJIe O;HKJla Y<I>-06JIyqeHHR. CyrueCTByeT
HeCKOJIbKO BapHaHTOB BTopJ{qHoro OTBepX,ll;eHIUI.
nO)l;orpeB
BTopJ{qHoe OTBepX,ll;eHHe no,n; B03,n;eHCTBHeM
TeTIJIa rapaHTHpyeT nOJIHOe OTBepX,ll;eHHe ,LLJUI MHO-
rHX BH,lJ;OB Y<I>-KJIeeB. TeMnepaTypbI OTBepX,ll;eHIDI
06bIQHO JIe:>KaT B ,n;Hana30He 100-150°C.
OTCYTCTBHe KHCJIOpO)l;a
Y<I> aHa3po6Hble copTa npHMeIDIIOTCR B Tex
npIUlO:>KeHHRX, r,n;e Tpe6yeTcR OTBepX,ll;eHHe B 06-
JIaCTH TeHH. TaKHe aHa3po6Hble KJIeH OTBep,n;eBaIOT
PUC. 1. rH6KHH Y<I>-cBeTOBO,n: Ha rJIy6HHe 0,2 MM BCJIe,n;CTBHe KOHTaKTa C MeTaJI-
,l(JUI OTBep)K,[(eHHH Y<I>-KJIeH.
JIOM H OTC)'TCTBIDI KHCJIOpo,n;a.
BJImKHOCTb
Y<I> CIUIHKOHOBble KJleH CXBaTbIBalOTCR B pe3YJIbTaTe Y<I>-nOJIHMepH3aO;HH, H
3aTeM OTBepX,ll;eHHe npo,n;OJI:>KaeTCR B TeqeHHe 24 qaCOB 6JIaro,n;apR BJIIDKHOCTH
OKpyxalOIUero B03,n;yxa.
nOBepxnocTHaB BJImKHOCTb
Y<I> O;HaHoaKplUlaTHble KJIeH OTBepX,ll;alOTCR Ha HeCKOJIbKO MHJIJIHMeTPOB no,n
B03,n;eHCTBHeM Y<I>-06JIyqeHHR, HO OHH TaIOKe OTBepX,ll;alOTCR 6JIaro,n;apR nOBepXHO-
CTHOH BJIIDKHOCTH B 3aTeHeHHbIX 06JIaCTRX.
4.5. C1(;JleU8aHUe Mematll108 2.
O,n;HOH H3 OCHOBHbIX npJ{qHH HCnOJIb30BaHHR Y<I>-KJIeeB RBJlReTCR npeHMYIUec
BO «OTBepX,ll;eHHR no TPe60BaHHIO» (T. e. cnoco6HoCTb OTBepX,ll;aTbCR TOqHO B JIy)
HbIH MOMeHT, TOJIbKO nOCJIe Toro KaK KOMnOHeHTbI 6y,n;yT nOJIHOCTblO BblpoBHeHbI)
4.5.3. LlJfBHOBKpJfnBTHble KneJf -
BHJfOHHBfJ nOnJfMepJf3BLlJffJ
O,n;HOKOMnOHeHTHble U;HaHoaKplUlOBble KJIeH nOJIHMepH3HpyIOTCR B KOHTaKTe c
CJIerKa IUeJIOqHbIMH nOBepXHOCTRMH. KaK npaBIUIO, BJIIDKHOCTH oKpyxalOIUeH Cpt
,[(bI H BJIIDKHOCTH nOBepXHOCTH coe,n;HHeHHR ,n;OCTaTOqHO, qTo6bI HaqaJIOCb OTBep)J
,[(eHHe H B TeqeHHe HeCKOJIbKHX ceKyH,lJ; 6bma ,n;OCTHrHYTa <pHKCaU;HR. HalUlyqml1
pe3YJIbTaTbI MO:>KHO nOJIyqHTb npH OTHOCHTeJIbHOH BJIIDKHOCTH B03,n;yxa 40-60
rrpH KOMHaTHOH TeMnepaType B pa60qeM nOMeIUeHHH. EOJIee HH3KaR BJIIDKHOCl
rrpHBo,n;HT K 60JIee Me,nJIeHHOMY OTBepX,ll;eHHIO, 60JIee BbICOKaR BJIIDKHOCTb YCKOp5.1
eT OTBepX,ll;eHHe, HO B KpaHHHX CJIyqaRX MO:>KeT OCJIa6HTb OKOHqaTeJIbHYIO npotJ
HOCTb coe,n;HHeHHR.
IToCJIe HaHeCeHHR KJIeR qaCTH CJIe,n;yeT 6bICTPO coe,n;HHHTb, TaK KaK nOJIHMepH
3a:U;HR HaqHHaeTCR yxe qepe3 HeCKOJIbKO ceKyH,lJ;. BpeMR ,n;o HaqaJIa nOJIHMepH3a
nHH 3aBHCHT OT OTHOCHTeJIbHOH BJIIDKHOCTH B03,n;yxa, BJIIDKHOCTH coe,n;HIDIeMbIX no
BepXHocTeH H TeMnepaTypbI oKpyxalOIUeH cpe,n;bI. M3-3a 6bICTPOTbI OTBepX,ll;eHID
nHaHoaKplUlaTHble KJIeH oco6eHHO nO,llXOMT ,lI)IR CKJleHBaHHR MeJIK.HX ,n;eTaJIeH
TalOKe cyrueCTByIOT BH,lJ;bI KJIeR Y<I>-oTBepX,ll;eHHR, n03BOillllOIUHe YJIyqmHTb OTBep.
:>K.LJ;eHHe no BceH rJIy6HHe KJIeR, a TaIOKe cnoC06CTByIOIUHe OTBepX,ll;eHHIO JII06bD
H3JIHmKOB KJIeR. l(HaHoaKplUlaTHble KJleH CJIe,n;yeT HaHOCHTb TOJIbKO Ha o,n;HY no-
BepXHOCTb, npHqeM JIyqmee coe,n;HHeHHe no.rryqaeTCR, TOJIbKO eCJIH HaHeCTH ,n;OCTa-
TOqHO KJIeR, qTo6bI 3anOJIHHTb Bce 3a30pbI B coe,n;HHeHHH. AIcrHBaTopbI MOryr HC-
rrOJIb30BaTbCR ,LLJUI YCKopeHHR npou;ecca OTBepX,ll;eHHR, a TaIOKe ,LLJUI OTBepX,ll;eHID]
JII06bIX H3JIHmKOB KlIeR. ,LJ;onOJIHHTeJIbHOe npeHMyrueCTBO U;HaHoaIqJlUlaTHbIX KJleeE
3aKJIIOqaeTCR B TOM, qTO HX MO:>KHO HCnOJIb30BaTb KaK rpYHTOBKy (npaHMep) npl1
coe,n;HHeHHH TaKHX MRrKHX TIJIaCTHKOB, KaK nOJIHnpOnlUleH H nOJIH3TlUleH.
,LJ;OCToHHCTBa :QHaHoaIqJlUlaTHbIX KlIeeB:
. OqeHb BbICOKaR npOqHOCTb Ha paCTR:>KeHHe H KpyqeHHe;
. OqeHb BbICOKaR CKOpOCTb OTBepX,ll;eHHR (CKopee ceKyH,lJ;bI, qeM MHHYTbI);
. MHHHMaJIbHbIH pacxo,n; KJIeR;
. coe,n;HHeHHe nOqTH Bcex BH,lJ;OB MaTepHaJIOB;
. JIerKaR ,n;03HpOBKa 6JIar,n;apR xopomeMY COnpOTHBJIeHHIO CTapeHHIO O,n;HOKOM-
nOHeHTHbIX KJIeeB;
. o,n;HOBpeMeHHbIH 3<p<peKT repMeTH3aU;HH.
4.5.4. MOAJfCPJfLlJfPOSBHHble BKpJfnOSble KneJf -
OTSep eHJfe C JfCnOnb30SBHJfeM BKTHSBTOpOS
OTBepX,ll;eHHe 3THX KlIeeB npOHcxo,n;HT npH KOMHaTHOH TeMnepaType B npHC)'TCT-
BHH aKTHBaTopOB. K.JIeH H aKTHBaTOp OT,n;eJIbHO HaHOCRTCR Ha coe,n;HIDIeMbIe no-
BepXHOCTH. KOMnOHeHTbI 3TOH CKJleHBalOIUeH CHCTeMbI 3apaHee He nepeMemHBa-
IOTCR, n03TOMY HeT Heo6xo,n;HMOCTH 6ecnOKOHTbCR 0 «:>KH3HeCnoco6HOCTH» KJIeR.
rl1060 4. Kpene:JICHble iJemOllu
Mo,n;H<pHnHpOBaHHble aKplUloBble KJIeH 06JI8JJ:a1OT CJIe,n;yIOIUHMH xapaKTepHbIMH
CBoHcTBaMH:
. OqeHb BblCOKaR npOqHOCTb Ha pacTIDKeHHe H Ha c,n;BHr;
. xopomaR y,n;aponpOqHOCTb H cOnpOTHBJIeHHe OTCJIaHBaHHIO;
. mHpoKHH ,n;Hana30H pa60qHX TeMnepaTYP (-55 ... +120°C);
. coe,n;HHeHHe nOqTH Bcex MaTepHaJIOB;
. BbICOKaR 3anOJIIDIIOIUaR cnoco6HoCTb;
. XopomaR YCTOHqHBOCTb K B03,n;eHcTBHIO oKpyxalOIUeH cpe,n;bI.
4.5.5. KneJf, OTsepJK,qeHJfe KOTOpblX npoJfCXOAJfT
nOA s03AeiicTSJfeM SnSJlCHOCTJf
3TH KJIeH/repMeTHKH nOJIHMepH3HpyIOTCR (B 60JIbmHHCTBe CJIyqaeB) 3a CqeT KOH-
,n;eHcanHH, KOTOpaR BKJIlOqaeT peaKI.J;HIO C BJIarOH H3 B03,n;yxa. B 3TOH KaTeropHH
cyrueCTByeT TpH THna KJIeeB, a HMeHHO:
. CIUIHKOHOBble;
. nOJIHypeTaHOBble;
. Mo,n;H<pHnHpOBaHHble ClUlaHOBble.
CHJlHKOHOBble
BYJIKaHH3anIDI (OTBep)l{,lJ;eHHe) npOHcxo,n;HT npH KOMHaTHOH TeMnepaTYPe B pe-
3YJIbTaTe peaKI.J;HH C BJIarOH H3 B03,n;yxa. MOHOJIHTHaR pe3HHa H3 CIUIHKOHa OTJI:uqa-
eTCR CJIe,n;yIOIUHMH CBOHCTBaMH:
. npeBocxo,n;HaR TepMOCTOHKOCTb;
. 3JIaCTHqHOCTb, npOqHOCTb, HH3KHH MO,n;yJIb ynpyrOCTH H 60JIbmOe OTHOCH-
TeJIbHOe y,nJIHHeHHe;
. 3<p<peKTHBHbIH repMeTHK,LLJUI pa3JI:uqHblx BH,lJ;OB )I{H,lJ;KOCTH.
nOJluypeTaHOBble
MexaHH3M 06pa30BaHIDI nOJIHypeTaHOB OCHOBaH Ha peaKI.J;HH BO,n;bI (B 60JIb-
mHHCTBe CJIyqaeB) C BeIUeCTBaMH, co,n;ep:>KaIUHMH rpynnbI H30IJ;HaHaTa. 3TH KJIeH
OTJIHqalOTCR CJIe,n;yIOIUHMH CBOHCTBaMH:
. npeBocxo,n;HaR npOqHOCTb H 3JIaCTHqHOCTb;
. npeBocxo,n;Hoe 3anOJIHeHHe 3a30pOB (,n;o 5 MM);
. nOCJIe OTBep)l{,lJ;eHIDI nOMalOTCR OKpaCKe;
. MO:>KeT HCn0JIb30BaThCR C npaHMepaMH (rpYHTOBKOH) ,nmI yJIyqmeHHR anre3HH.
MO.znt4»HIUlpoBaHHble CHJlaHOBhIe
OTBep)l{,lJ;eHHe MO,n;H<pHIJ;HpOBaHHblx ClUlaHOB TaIOKe npOHcxo,n;HT qepe3 peaK-
IJ;HIO C BJIarOH H3 B03,n;yxa. OHH 06JI8JJ:a1OT CJIe,n;yIOIUHMH CBOHCTBaMH:
. nOCJIe OTBepX,ll;eHIDI nOMalOTCR OKpaCKe;
. xopomo coe,n;HHRIOTCR C mHpOKHM ,n;Hana30HOM oCHoBaHHH;
. OTCYTCTBHe H30nHaHaTOB;
. npeBocxo,n;HaR npOqHOCTb H 3JIaCT:uqHOCTb.
3,n;ecb npe,n;CTaBJIeH Bcero JIHmb KpaTKHH 0630P OCHOBHbIX BH,lJ;OB 3THX cnenHa-
JIH3HpOBaHHblX KJIeeB, H qHTaTeJIb MO:>KeT o6paTHTbcR K TeXHHqeCKOH JIHTepaTYPe,
H3,n;aHHoH Henkel Loctite Adhesives Limited, qTo6bI nOJIyqHTb 60JIee no,n;po6JIYIO
HH<popManHIO 0 BH,lJ;ax KJIeeB H HX npHMeHeHHH.
4.5. CKJleU60HUe MemOl/l106
4.5.6. 3nOKCJfAHble KneJf
3nOKCH,lJ;Hble KJIeH OCHOBaHbI Ha CMOJIax, no eHHbIX H3 3nHXJIOprH,lJ;pHHa H 6HC-
<l>eHoJI'il-AJ OHH xapaKTepH3yIOTCR HH3KOH YC8JJ:KOH npH nOJIHMep 3anHH, BbICOKOH
a):{re3HeH H xopomeH MexaH:uqeCKOH npOqHOCTblO. 06bIHO 3TH KJIeH ,n;ByxKOMnO-
HeHTHble, H OTBep)l{,lJ;eHHe HaCTYIIaeT B pe3YJIbTaTe CMemHBaHIDI KJIeR C KaTaJIH3a-
TOpOM (OTBep,n;HTeJIeM) HenOCpe,n;CTBeHHO nepe,n; HCnOJIb30BaHHeM. OTBepX,ll;eHHe
HaqHHaeTCR C MOMeHTa ,n;06aBJIeHIDI KaTaJIH3aTOpa. O,n;HaKO B HeKOTOpbIX CJIyqaRX
OTBep,n;HTeJIb CMemHBaeTCR C KJIeeM B npOnecce H3rOTOBJIeHIDI, a aKTHBH3HpyeTcR
COCTaB HarpeBaHHeM (06blqHO) ,n;o 150°C B TeqeHHe 30 MHHYT. B accopTHMeHe
Loctite@ Hysol@ npHCYTCTByIOT Bce THn:uqHble 3nOKCH,lJ;Hble KJIeH. PyxOBO,n;CTBO no
BbI60py KJIeR B 3aBHCHMOCTH OT OCHOBaHIDI npe,n;CTaBJIeHO Ha pHC. 1.
CyruecTByIOT CJIe.l(ylOIUHe THn:uqHble Hysol@ 3nOKCH,lJ;Hble KJIeH:
1. 3nOKCH,lJ;ble KJIeH o6IUero Ha3HaqeHIDI:
. YHHBepCaJIbHble KJIeH,LLJUI coe,n;HHeHHH o6IUero Ha3HaqeHIDI.
. YJIbTpanp03paqHble KJIeH ,LLJUI np03paqHbIX mBOB.
. 3JIaCTHqHble KJIeH ,LLJUI CJIa60HanpIDKeHHbIX coe,n;HHeHHH, TIJIaCTMaCC H Heo,n;-
HOpO,n;HbIX OCHOBaHHH
2. DbICTPonOJIHMepH3yIOIUHeCR 3nOKCH,lJ;Hble KJIeH:
. DbICTPOe OTBep)l{,lJ;eHHe B TeqeHHe KopOTKoro BpeMeHH <pHKcanHH.
. YJIbTpanp03paqHble KJIeH,LLJUI 6bICTPOro np03paQHOrO coe,n;HHeHIDI.
. CpOQHbIH peMOHT MeTaJIJI:uqecKHX QaCTeH, TaKHX KaK TPy6bI H 6aKH.
3. BblcOKOnpOQHble 3nOKCH,lJ;Hble CMOJIbI:
. BbICOKaR npOQHOCTb Ha c,n;BHr H OTCJIaHBaHHe.
. TIpeBocxo,n;HaR y,n;aponpOQHOCTb.
. CKJIeHBaHHe CJIO:>KHbIX KOMn03HTOB, TaKHX KaK CTeKJIOTIJIaCTHK H yrJIeTIJIac-
THK (TIJIaCTHK, apMHpoBaHHbIH yrJIepo,n;HbIM BOJIOKHOM).
4. TepMocToHKHe 3nOKCH,lJ;Hble CMOJIbI:
. Y CTOHqHBOCTb npH BbICOKHX pa60QHX TeMnepaTYPax.
. CooTBeTcBHe UL94- VO ,LLJUI orHeynopHbIX ,n;eTaJIeH.
. BblcoKaR TeTIJIOnpOBo,n;HOCTb.
5. MeTaJIJIOHanOJIHeHHble 3nOKCH,lJ;Hble CMOJIbI:
. PeMoHT H BOCCTaHOBJIeHHe H3HomeHHbIX H nOBpe)l{,lJ;eHHbIX MeTaJIJI:uqecKHX
,n;eTaJIeH.
. PeMoHT MeTaJIJI:uqecKHX TPy6 H OTJIHBOK.
. M3rOTOBJIeHHe <pOPM, HHCTPYMeHTa H apMaTYPbI.
. CHIDKeHHe H3Hoca ,n;BIDKYIUHXCR QaCTeH npH TpeHHH CKOJIb:>KeHIDI.
THnHQHbIe pa60QHe xapaKTepHCTHKH npHBe,n;eHbI Ha pHC. 2. qHTaTeJIb MO:>KeT
o6paTHTbcR 3a HCQepnbIBalOIUeH HH<popManHeH K ,n;aHHbIM, ony6JIHKOBaHHbIM Hen-
kel Loctite Adhesives Limited, CBR3aTbCR C KOTOpOH MO:>KHO no 8JJ:pecy, npHBe,n;eH-
HOM)' B npIUlO:>KeHHH 3.
4.5.7. BOCCTSHOSJfTenbHblH npOLf,eCC
MeTo,n;, pa3pa6oTaHHbIH ,LLJUI coe,n;HHeHHR HCXO,n;HbIX JIHCTOB MeTaJIJIa B CaMOJIeTOCT-
poeHHH C nOMOIUblO ,n;ByxKOMnOHeHTHoro KJIeR, npH TIUaTeJIbHOM KOHTPOJIe 3a
TeMnepaTYPOH H ,n;aBJIeHHeM.
FII060 4. Kpene:JICHble iJemOllu
@)
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o
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@)
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o t;:(I:S r.Q:= - ............ 0
e a
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sag s g1 C!Sg gJ
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0 ..,Q Q $Q
cd cd:= cd E-t':' p,. o M
o ogog 20S2 O
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4.5. CKJleU60HUe MemO/lJl06 2 -1
a,)g e
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ci o
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FII060 4. Kpene:JICHble iJemOllu
4.5.8. Kneesoe COeAJfHeHJfe
KaK yxe 6billO CKa3aHO, ,nJIR OnTHMaJIbHOrO coe,n;HHeHHR Heo6xo,n;HMa npaBlUlbHasI
no,n;rOTOBKa nOBepXHOCTH. TIpOqHOCTb coe,n;HHeHHR B 3HaqHTeJIbHOH CTeneHH onpe-
,n;eJIReTCR CneTIJIeHHeM MeX,ll;Y KJIeeM H OCHOBaHHeM. TI03TOMY npH no,n;rOTOBKe c
MeCTa coe,n;HHeHHR CJIe,n;yeT y,n;aJIHTb MaCJIO, CMa3Ky, OKHCHble TIJIeHKH H rpR3L,
qTo6bI 06eCneqHTb XHMHqecKyIO H MexaH:uqecKyIO qHCTOTY. MeXaHHqeCKaR o6pa-
60TKa nOBepXHOCTH 06,n;YBKOH CTaJIbHOH KpomKoH IUIH npOBOJIOqHOH IUeTKOH ra-
paHTHpyeT xopomee CneTIJIeHHe.
KpoMe Toro, Heo6xo,n;HMO npaBlUlbHO CnpOeKTHpOBaTb coe,n;HHeHHe. Conpo-
THBJIeHHe KJIeeB paCTIDKeHHIO If C,n;BHry OTHOHTeJIbHO BeJIHKO no cpaBHeHHIO C HX
conpOTHBJIeHHeM CKaJIbIBaHHIO H OTCJIaHBaHHIO. 3TO Heo6xo,n;HMO yqecTb npH npo-
eKTHpOBaHHH coe,n;HHeHHR, a TaIOKe npe,n;yCMOTPeTb ,n;OCTaTOqHYIO nOIU8JJ:b nOBepx-
HOCTH Me coe,n;HIDIeMbIMH qaCTRMH, qTo6bI 06eCneqHTb TPe6yeMYIO npOqHOCTb.
TaKHM o6pa30M, coe,n;HHeHHe C caMoro HaqaJIa CJIe,n;yeT npOeKTHpOBaTb C yqeToM
HCnOJIb30BaIDI KJIeR, a He npOCTO npHcnoca6JIHBaTb cyrueCTByIOIUee MexaH:uqe-
CKoe/CBapHoe coe,n;HHeHHe. Ha pHC. 1 nOKa3aHO HeCKOJIbKO npaBlUlbHO H Henpa-
BlUlbHO CnpOeKTHpOBaHHblX coe,n;HHeHHH, no,n;xoAAIUHX,LLJUI CKJleHBaHHR.
ABTOP 6JIaro,n;apHT MHCTepa Bo6a rocca, CTapmero CnenHaJIHCTa no TeXHOJIO-
rHH B Henkel Loctite Adhesives Limited 3a ero nOMomb B no,n;rOTOBKe BblmeH3JlO-
:>KeHHOH HH<popManHH 0 KJleeBbIX coe,n;HHeHIDIX.
npaBMnbHO
AnbTepHaTHBHble BapHaHTbl npOCToro
COe,D,HHeHHR BHaxnecTKY
HenpaBMnbHO
nepeKawHBaHHe H pa3pyweHHe
npOCToro COe,D,HHeHHR BHaxnecTKY
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c -.
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B03HVlKHOBeHVle pa3pyweHVlS1 OTpblBOM
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1 HarPY3Ka
HarpY3Ka
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arpY3Ka
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CoeAVlHe-
HVie npVI
C)f(aTVIVI
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PUC. 1. npeKTHpOBaHHe KJIeeBbIX coe,n:HHeHHH
rnABA 5
MEXAHM'tECKME
nEPEAA'tM
5.1. MeXaHM"IeCKMe nepeAa"lM: 3y6"1aTbie nepeAa"lM
5. 1. 1. HeKoTopble TJfnJfI.fHble 3y61.fsTble nepeASI.fJf
npRMo3y6aR
MnMHAPM'IeCKaR 3y6'1aTaR nepeAa'la
Pee'tHaR nepeAa'la: npeo6pa30BaHMe Bpal1.\aTenbHoro ABM)I(eHMR B nOCTYnaTenbHoe
3y6t.1aToe Koneco
I
/
3y6t.1aTas:a pe
Ka
Dla8a 5. MexaHulteclCue nepeiJaltu
Koco3y6aR 3y6'taTaR nepeAa'ta
WeBpOHHaR 3y6'taTaR nepeAa'ta
npRMo3y6aR KOHM'teCKaR 3y6'taTaR nepe.qa'l8
'fepBRK M 'tepBR'tHoe Koneco
5.1. MexaHUlteC1(,Ue nepeoaltu: 3y6ltamble nepeoaltu 30 I:::
5.1.2. npOCTble npflMo3y6ble LfJfnJfHAPJflleCKJfe nepe,q8l1Jf
BeAy a weCTepH
npOMe)K}'TOYHOe KOl1eco
BeAOMoe KOl1eco
IIpocTaJl nepe,ZJ;a1fa
1. Be,n; (UI rneCTepIDI H Be,n;OMoe KOJIeCO BpalI..(alOTCR B rrpOTHBOrrOJIO)I(HbIX
HanpaBJIeHHRX.
2. OTHollIeHHe qaCTOTbI BpalI..(eHHR Be,n; eit llIeCTepHH K qaCTOTe BpalI..(eHHR
Be,nOMoro KOJIeCa HJIH rrepe,n;aTOqHOe OTHOllIeHHe (oTHollIeHHe yrJIOBbIX CKopocTeH
Be,nyIUeH llIeCTepHH H Be,n;OMoro KOJIeca) BbIqHCIDIeTCR no CJIe.nyIDlI..(eH <popMYJIe:
06/MHH Be,LJylI(ee _ qHCJlO 3y6beB B Be,nOMOM
06/MHH Be,nOMoe - qHCJlO 3y6beB B Be,LJylI(eM.
(BbIpaxeHHe crrpaBa OT 3HaKa paBeHCTBa Ha3bIBaeTCR rrepe,n;aTOqHbIM qHCJIOM. -
llpUMett. nep.)
IIpHMep.
PaCCqHTaTb qaCTOTY BpalI..(eHIDI Be,n;OMoro KOJIeCa, eCJIH qaCTOTa BpalI..(eHIDI Be.ny-
meH llIeCTepHH COCTaBJUleT 120 06/MHH. Be,n;oMoe KOJIeCO HMeeT 150 3y6beB, a Be.ny-
mWI llIeCTepIDI - 50 3y6beB:
120 150
06/MHH Be,nOMoe - 50 '
120 x 50
06/MHH Be,nOMoe = = 40 06/MHH.
150
Dla8a 5. MexaHulteCK,Ue nepeiJaltu
npOCTaJI nepe,ZJ;a1fa C npOMe1K)'T01fHbIM KOJleCOM
1. Be,l YIIUUl meCTepIDI II Be,ZJ;OMoe KOJIeCO BpalI..(alOTCR B O,n;HOM HanpaBJIeHHH,
eCJIII KOJIlftleCTBO rrpOMexyrOqHbIX KOJIeC HeqeTHOe, H B npOTIIBOrrOJIO)KHbIX Ha-
rrpaBJIeHIDIX, eCJIII HX KOJIlftleCTBO qeTHO.
2. npoMexyrOqHbIe KOJIeCa HCrrOJIb3yroTCR .nIDI 113MeHeHIDI HarrpaBJIeHIDI Bpa-
lI..(eHIDI II/R1I11 .nIDI YBeJIllqeHIDI MexoceBoro paCCTORHIDI Me y Be.nyIneit
mecTepHeH Be,n;OMbIM KOJIeCOM.
II'
3. KOJIlftleCTBO rrpOMexyrOqHbIX KOJIeC II qHCJIO 3y6beB Ha rrpOMexyrOqHbIX KO-
JIecax He BJIIDIIOT Ha o61I..(ee nepe,n;aTOqHOe OTHomeHlle.
4. 061I..(ee nepe,n;aTOqHOe OTHomeHlle MO)KHO BbIqllCJIIITb no <poPMYJIe:
06/MHH Be,nyInHH _ qHCJIO 3y6beB B Be,nOMOM
06/MHH Be,nOMbIH - qHCJIO 3y6beB B Be,nyIneM'
5. 1.3. CTyneHII8T8f1 npflMo3y68f1 3y6118T8f1 nepeA8118
npOMe)l(YTOYHOe KOl1eco '1
npOMe)l(YTOYHOe KOl1eco '2
BeAy aS1 weCTepHS1
1. B OTJIllqlle OT npOMexyrOqHOrO KOJIeCa npocToH rrepe,n;aqll, rrpOMexyrOqHbIe
KOJIeCa cTYIIeHqaTOH nepe,n;aqll BJIIDIIOT Ha o61I..(ee rrepe,n;aTOqHOe OTHOllIeHlle (nOJI-
Hoe OTHOllIeHlle yrJIOBbIX CKopOCTeH Be,n;yII..(eH llIeCTepHII II Be,n;OMoro KOJIeca).
2. 06a npOMexyrOqHbIX KOJIeCa (It II 1 2 ) YCTaHOBJIeHbI Ha O,n;HOM II TOM xe BaJIe
II IIMelOT o,n;HY II TY xe qaCTOTY BpalI..(eHIDI.
3. Be.nyIn(UI llIeCTeplUl II Be,n;OMoe KOJIeCO BpalI..(alOTCR B O,n;HOM HanpaBJIeHIIII. qTO-
6bI 113MeHIITb HanpaBJIeHlle BpalI..(eHIDl, Heo6xo,n;IIMO YCTaHOBIITb rrpOMexyrOqHOe KO-
JIeco JIII60 Me Be.nyIneH llIecrepHeH II II' JIII60 Me Be,n;oMbIM KOJIeCOM II 1 2 ,
5. 1. MexaHUlteCKUe nepeiJaltu: 3y6ltamble nepeiJaltu 3
4. 061I..(ee rrepe,n;aTOqHOe OTHOllIeHHe MO)J(}lO BbIqHCJIHTb no <popMyJIe (T.e. KaK
rrpoH3Be,n;eHHe rrepe,n;aTOqHbIX qHCeJI):
06/MHH Be,LJyI.QHH _ qHCJlO 3y6beB B /} qHCJlO 3y6beB B Be,nOMOM
- x .
06/MHH Be,nOMbIH qHCJlO 3y6beB B Be,LJyI.QeM qHCJlO 3y6beB B /2
npHMep
PaCCqHTaTb qaCTOTY BpalI..(eHIDI Be,n;OMoro KOJIeCa, eCJIH H3BeCTHO: Be.nyIUIDI llIe-
CTepIDI BpalI..(aeTCR C qaCTOTOH BpalI..(eHIDI 600 06/MHH H HMeeT 30 3y6beB; II HMeeT
60 3y6beB; 1 2 HMeeT 40 3y6beB; a Be,n;OMoe KOJIeCO HMeeT 80 3y6beB:
06/MHH Be,LJyI.QHH = 60 x 80 = i
06/MHH Be,noMbIH 30 x 40 1
Ho qaCTOTa BpalI..(eHIDI Be,n;yII..(eH llIecTepHH = 600 06/MHH
TI03TOMy
600 06/MHH Be,LJyI.QHH = i
06/MHH Be,noMbIH 1
600 x 1
qacToTa Bpa eHHH Be,nOMoro = = 150 06/MHH.
4
5. 1.4. 3sonbseHT8 KpJfsoif
C
/
/
/
/
I
OSOl1bseHTa ---,
I
I
A I //
--f--
rV16KV1 HepaCT )I(V1MblVi WHYP
T(TOYKa KacaHV1 )
OCHOSHa OKpY)I(HOCTb
B
I
3BOJIbBeHTa HCnOJIb3yeTcR ,L(JIR npo<pHJIeH 3y6beB 60JIbllIHHCTBa cepHHHo H3ro-
TaBJIHBaeMbIX npRMo3y6bIX n;HJIHH,L(pHqeCICHX 3y6qaTbIX nepe,n;aq. Ha pHCYHKe nOKa-
3aHa 3BOJIbBeHTa, no.rryqeHHIDI npH CMaTbIBaHHH Boo6paxaeMoro TYI'0 HaTRHyroro
illHypa BTC C OCHOBHOH OKpyxHOCTH C n;eHl'pOM B TOqKe 0, Ha'lHHaR C TOqKH A.
KpHBIDI AC, KOTOpyro onHCbIBaeT KOHen; llIHypa C, HMeeT <POPMY 3BOJIbBeHTbI.
KpHBH3Ha C 3aBHCHT OT pa.nHYca OCHOBHOH OKpyxHOCTH. ECJIH pa.nHYC
OCHOBHOH OKpyxHOCTH YBeJIHqHBaeTCR, KpHBH3Ha 3BOJIbBeHTbI YMeHbllIaeTCR. ,lJ;JIR
OCHOBHOH OKpyxHOCTH 6eCKOHeqHOrO p.a.nHYca JIHHIDI AC nepeCTaeT 6bITb KpHBOH
H CTaHOBHTCR npRMOH JIHHHeH. TaKHM 06pa30M, peeqHIDI nepe,n;aqa HMeeT 3y6bR C
Dla8a 5. MexaHulteclCue nepeiJaltu
npRMbIMH cTopoHaMH, nOCKOJIbKy 3y6qa1)1O peHKy MO:>KHO paccMal'pHBaTb, KaK
qaCTb OKpyxHOCTH 3y6qaTOrO KOJIeCa 6eCKOHeQHOrO pa.n:M)'ca. n03TOMY 3y6qaTWI
peHKa C npRMbIMH cTopoHaMH 3y6beB Bcer,n;a y,n;oBJIeTBOpHTeJIbHO BXO,n;HT B 3a en-
JIeHHe C 3y6qaTbIM KOJIeCOM C npRMbIMH 3y6bRMH B <popMe 3BOJIbBeHTbI.
<l>opMa 3BOJIbBeHTbI ,L(IDI 3y6beB npRMo3y6oH :U;R1IHH,L(pHtleCKOH 3y6qaTOH nepe-
,n;aqH HMeeT CJIe.nyIDII..(He npeHMYII..(eCTBa.
1. 3BOJIbBeHTHbIe 3y6bR npe,n;OCTaBIDIIOT rrepe,n;aTOqHOMY MexaHH3MY B03MO)l{-
HOCTb I1JIaBHO nepe,n;aBaTb 60JIbllIHe HarpY3KH rrpH rrOCTORHHOH CKOpOCTH.
2. npH corrpIDKeHHbIX 3y6bRX C npo<pR1IeM, OqepqeHHbIM no 3BOJIbBeHTe, B03-
HHKaeT npeHMYII..(eCTBeHHO KOHTaKT KaqeHIDI Mex.ny HO)l{l(aMH 3y6beB, Kor,n;a OHH
BXO,nRT H BbIXO,nRT H3 3a:u;eIIJIeHIDI. nOCKOJIbKy KOHTaKT CKOJIbXeHIDI MHHHMaJIeH,
CTHpaHHe H H3HOC HoxeK 3y6beB TalOKe MHHHMaJIbHbI.
3. oJIaro,n;apR COOTHOllIeHHIO Mex.ny 3BOJIbBeHTHbIMH 3y6bRMH H 3y6bRMH C
npRMbIMH CTopOHaMH 3y6qaTOH peHKH, 3y6bR 3y6qaTOrO KOJIeCa MO:>KHO 6bICTPO H
aKKYPaTHO Hape3aTb C nOMOlI..(blO <ppe3bI B BH.l(e peHKH C JIerKO H3rOTaBJIHBaeMbIMH
pexyII.J;HMH 3y6bRMH C npRMbIMH CTopOHaMH. OT 3Toro, OqeBH.l(HO, BbIHrpbIBaer
CTOHMOCTb HHCl'pYMeHTOB.
5. 1.5. OCHOBbl reOMeTpJfJf 3y6118Toro KoneC8
QTo6bI Ha npaKTHKe nOCl'pOHTb npo<pR1Ib 3y6a 3y6qaTOrO KOJIeCa Ha OCHOBaHHH 6a-
30BOH 3BOJIbBeHTbI, onHcaHHOH B pa3,n;eJIe 5.1.4, Heo6xo,n;HMO paCCMOl'peTb ,n;Ba CJIe-
,n;YIOII..(HX reOMel'pHqeCKHX COOTHOllIeHHR.
1. KaCaTeJIbHaR K 3BOJIbBeHTe B JII060H TOqKe Bcer,n;a rrepneH,L(HKyIDIpHa K Kaca-
TeJIbHOH K OCHOBHOH OKpyxHOCTH, npoBe,n;eHHoH H3 TOH xe caMOH TOqKH. B paJ,n;e-
JIe 5.1.4 nOKa3aHO, qTO npRMIDI CT RBIDIeTCR KaCaTeJIbHOH K OCHOBHOH OKpyxHO-
CTH H qTO 3Ta KaCaTeJIbHaH nepneH,L(HKyIDIpHa KaCaTeJIbHOH, npoBe,n;eHHoH K 3BOJIb-
BeHTe B TOqKe C. oy,n;eT nOKa3aHO, qTO Ka-
CaTeJIbHaR CT RBIDIeTCR TalOKe JIHHHeH
3a:u;eIIJIeHIDI 3y6beB KOJIeca.
2. ,LLrrHHa npRMoH CT TalOKe paBHa .nnH-
He ,L(yrH AT.
PaCCMOl'pHM ,n;Be OKpyxHOCTH, KacalOlI(H-
eCR B TOqKe P, KaK nOKa3aHO Ha pHCyHKe.
T OqKa P Ha3bIBaeTCR nOJIIOCOM 3a ellJIeHIDI,
a OKpyxHOCTH Ha3bIBalOTCR HaqaJIbHbIMK
OKpyxHOCTRMH. ECJIH 6bI HaqaJIbHbIe OIq)YJK-
HOCTH 6billH <ppHK:QHOHHbIMH ,n;HCKaMH, T0
OHH KaTHJIHCb 6bI O,ZJ;HH no ,n;pyrOMY C TPe6ye-
MbIM OTHOllIeHHeM CKopocTeH B 3aBHCHMocm
OT COOTHOllieHIDI HX ,n;HaMel'pOB. O,n;HaKo Boa-
MO:>KHOCTH MexaHH3MOB, B KOTOpbIX nepe aqa
MOIIJ;HOCTH 3aBHCeJIa 6bI HCKJIlOqHTeJIbHO OT
CR1IbI l'peHIDI, 6billH 6bI CR1IbHO orpaHWleHLI.
Ha npaKTHKe, qTo6bI npe,n;OTBpaTHTb rrpOCKa-
Ha al1bHaS1 JIb3bIBaHHe, ,n;HCKH coe,n;HIDIIOT 3a:u;eIIIDIIOII(H-
OKPY>KHOCTb 2 MHCR 3y6bRMH. ECJIH HCnOJIb3yroTCR 3BOJIb-
Ha al1bHaS1
OKPY?KHOCTb 1
/
5.1. MexaHulteclCue nepeiJaltu: 3y6ltamble nepeiJaltu 3
BeHTHbIe 3y6bR, TO Ha pHCYHKe rrpH.l(eTCR ,n;06aBHTb ,n;Be ,n;OrrOJIHHTeJIbHbIe OKpyxHO-
cm. 3TH ,n;orrOJIHHTeJIbHbIe OKpyxHOCTH RBIDIIOTCR OCHOBHbIMH OKpyxHOCTRMH, ,L(JUI
KOTOpbIX Cl'pORTCR 3BOJIbBeHTbI (p83,n;eJI 5.1.4). Terrepb 3BOJIbBeHTbI Cl'pORTCR, HCXO,nR
H3 3THX OCHOBHbIX OKpyxHOcTeH, TaK, qTo6bI OHM KaCaJIHCb Ha JIHHHH 3a:u;ellJIeHIDI.
3m JIHHIDI 3aueIIJIeHIDI - 061I..(aR KaCaTeJIbHaR K OCHOBHbIM OKpyxHOCTRM H RBIDleT-
CH npo,n;OIDKeHHeM rrpRMoH CT (pa3,n;eJI 5.1.4).
YroJI 3an;eIIJIeHIDI , rrOKa3aHHbIH Ha pHCYHKe, 3TO yrOJI Mex.ny JIHHHeH 3a:u;eI1JIe-
HID! H 061I..(eH KaCaTeJIbHOH K OCHOBHbIM OKpyxHOCTRM, rrpOBe,n;eHHbIM Qepe3 TOqKY
P. OrrbIT rrOKa3aJI, qTO = 20° 06eCrreQHBaeT OrrTHMaJIbHYK> CR1IY B COQeTaHHH C
IDIaBHbIM XO,n;OM. 3Ta BeJIHtlHHa rrpHHRTa B 60JIbllIHHCTBe COBpeMeHHbIX MexaHH3-
MOB.
Ha al1bHaS1
OKPY>KHOCTb 1
0 1
ConpVlKOCHO-
BeHHe ay6beB
Ha l1V1HVIVI aa-
u,enl1eHVlS1
I
nMHHS1 aau,enl1eHVlS1
Ha al1bHaS1
OKPY>KHOCTb 2
,
OCHOBHa
I OKPY>K-
HOCTb 2
°2
BblCOTa
ay6a
.........
.........
.........
.........
.........
--- .........
-
Add. - BbiCOTa rOl1OBKVI ay6a
Oed. - BblCOTa HO)l(KVI ay6a
. - yrol1 aau,enl1eHVlS1
P - nOl1lOC aau,enl1eHVlS1
T - TO'iKa KacaHVlS1
Dla8a 5. MexaHUlteCKUe nepeiJaltu
QT06bI CrrpOeKTHpOBaTb pa60qHH rrpo<pHJIb 3y6a Ha OCHOBaHHH a6Cl'paKTHOH
3BOJIbBeHTbI, He06xo,n;HMbI CJIe,nyIOmHe ,n;orrOJIHHTeJIbHbIe rrocl'poeHIDI.
OKPYJKHOCTb roJlOBOK 3y6beB
Y CTaHaBJIHBaeT BbICOTY 3y6a, TaK qT06bI rrpH 3a:QeIIJIeHHH rrpe,n;oTBpaTHTb ero
CTOJIKHOBeHHe C Brr3.,L(HHOH 3y6a rrapHoH rnecTepHH.
OKPYJKHOCTb BDa;ntH 3y6beB
Y CTaHaBJIHBaeT rrOJIOXeHHe ,n;Ha HJIH Brr3.,L(HHbI 3y6a H TaKHM 06pa30M YCTaHaB-
JIHBaeT rJIy6HHY, ,n;o KOTOpOH rrpo<pHJIb 3y6a BbIpe3aeTcR H3 3arOTOBKa ,nmI
3y6qaTOrO KOJIeca.
BblcoTa roJlOBKH 3y6a
P3.,L(HaJIbHOe paccToRHHe Me OKp OCTbID rOJIOBOK 3y6beB H HaqarrbHOH
OKp OCTbID.
BblcoTa HO)KKH 3y6a
P3.,L(HaJIbHOe paccToRHHe Me y OKp OCTbID Brr3.,L(HH 3y6a H HaqarrbHOH
OKp OCTbID.
----
---
---
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
, .
. .
. .
. .
. .
. .
. .
. I .
f 0 2
OBOl1bBeHT-
_ .. .. Ha 4>opMa
.... T. OCHOBHO
o KpY)I(HOCTVI
AO OKPY>KHO-
oCTVI rOl1OBOK
ay6beB
3aKPyrl1eHHa
4>opMa OT
OCHOBHO
OKPY>KHOCTVI AO
OKPY>KHOCTVI
Bnap.VlH ay6beB
Add. - BblCOTa
rOl1OBKVI ay6a
Oed. - BblCOTa
HO)l(KVI ay6a
BblCOTa ay6a
Add.
Ded.
BblCOTa 3y6a
P3.,L(HarrbHOe paCCTORHHe Mex.ny
OKp OCTbID rOJIOBOK 3y6beB H OIq)YX-
HOCTbID BII3.,L(HH 3y6beB. II03TOMY' BbICO-
Ta 3y6a = BbICOTa rOJIOBKH 3y6a + BbICO-
Ta HOXKH 3y6a.
OTMeTHM, qTO rrpO<pHJIb 3BOJIbBeHT-
Horo 3y6a 3y6qaTOrO KOJIeCa OqepqeH no
3BOJIbBeHTe OT OCHOBHOH OKp OCTH
,n;o OKp OCTH rOJIOBOK 3y6beB, o,n;HaKO
HMeeT 3aKpyrJIeHHyIO <POPMY' OT OKPYX-
HOCTH Brr3.,L(HH 3y6beB ,n;o OCHOBHOH OK-
p OCTH, KaK rrOKa3aHO Ha pHCYHKe.
npocIJHJlb 3y6beB peRKH
Ha pHCYHKe rrOKa3aHO, KaK COOTHO-
rneHIDI 3BOJIbBeHTbI rrpHMeIDIIDTCR ,lQUI
3y6beB peHKH. PeHKa RBJIReTCR OCHOBOH
JIID60H CHCTeMbI 3y6qaTbIX rrepe,n;aq II
rr03TOMY CJIy)KHT HaqarrbHOH TOqKOH, OT
KOTOpOH Cl'pOHTCR rrOCJIe,n;OBaTeJIbHOCTb
3y6qaTbIX rrepe,n;aq.
....
HaYal1bHa np Ma
Add. - BblCOTa rOl1OBKVI ay6a
TeOpeTVlYeCKVI npo4>Vll1b ay6a pe KVI Oed. - BblCOTa HO)l(KVI ay6a
5.1. MexaHUlteC1(,Ue nepeoaltu: 3y6ltamble nepeoaltu 307
1 ,5708
1 ,5708
.
0,02 max. } AOn Y CTHMaS1 MOAH4>HKa-
0,6 max. HS1 npo4>HnS1 rOl1OBKH
1
\.L}
_ HC! anbHaS1 (Ael1V1-
Tel1bHaS1) l1V1HHS1
1,25
"
1,00
} Pap.VlYC
0,39 max. OKPY>KHOCTH
0,25 max. Bnap.HH ay6a
BpHTaHCKHH CTaH,ll;apT rrpO<pHJIR 3y6a peHKH
(pa3MepbI npHBe,n;eHbI ,L(JIR MO,n;YIDI 3y6beB, paBHOrO e,n;HHHue)
KaK nOKa3aHO Ha pHCYHKe, TeOpeTlftleCKHH rrpO<pHJIb 3y6a peHKH HMeeT npR-
Mble 60Ka H qeTKO 0603HaqeHHbIe yrJIbI. H3 npaKTHqeCKHX co06paxeHHH TaKOH
rrpO<pHJIb 3y6a MO,n;H<pHUHpyeTcR rryreM cKpyrJIeHIDI y BepllIHHbI 3y6a H 3aMeHbI
qeTKO 0603HaQeHHbIX yrJIOB BO Brra,nHHe 3aKpyrJIeHHeM.
PeaJIbHbIH rrpO<pHJIb 3y6a peHKH COrJIaCHO BS 436 (Mel'plftleCKHe e,n;HHHUbI) no-
Ka3aH BbIllie. 3T0 OCHOBHOH rrpo<pHJIb 3y6beB peHKH, cooTBeTCTByIDI.l(HH 6pHTaHcKo-
MY CTaH,ll;apTY; pa3MepbI yJ(a3aHbI ,L(JUI MO,L(yIDI 3y6beB paBHoro e,n;HHHue. AmI JII060ro
3HaqeHIDI MO,L(yIDI, OTJIIftIHOrO OT e,n;HHHUbI, p83MepbI 3y6a onpe,n;eIDIIOTCR YMHoxe-
HHeM yJ(83aHHbIX QHCeJI Ha BeJIIftIHHY MO,L(yJUl. H3 rrpaK1'J{qeCKHX co06paxeHHH ,n;aH-
HbIH OCHOBHOH npo<pHJIb MoxeT 6bITb ,n;aJIee MO,n;H<pHUHpoBaH CJIe,L(yIDI.l(HM 06pa30M.
1. OTKJIOHeHIDI nOJIHOH BbICOTbI B npe,n;eJIax 2,25-2,40 3HaqeHIDI MO,n;YIDI.
2. OrKJIOHeHIDI pa,nHYca OKp)')KHOCTH Bna,nHH 3y6a B npe,n;eJIax 0,25-0,39 3Ha-
qeHIDI MO,L(yIDI.
illecTepHH pa36HTbI Ha 10 KJIaCCOB TOqHOCTH, KaK yJ(a3aHO B BS 436.
5. 1.6. War 3aqenneHJffl 3y6bes
c _v-'
'3y6bR npRM03y60ro UHJIHH,lI;plftleCKOrO 3y6qaTOrO KOJIeCa pacnOJIOXeHbI B,n;OJIb Ha-
1JaJIbHOH OKp)')KHOCTH qepe3 paBHbIe npOMexyrKH, KOTopbIe Ha3bIBalOTCR llIaraMH.
C ecTByeT l'pH pa3JIHQHbIe CHCTeMbI ,L(JUI onpe,n;eJIeHIDI llIarOB.
OKPYJKHoi mar (p)
3ro paCCTORHHe Me cepe,n;HHaMH ,n;BYX coce,n;HHX 3y6beB Ha KOJIeCe (B 06-
U(eM CJIyqae Me y o,n;HOHMeHHbIMH TOQKaMH ,n;BYX coce,n;HHX npo<pHJIeH), H3Me-
peHHoe no HaqaJIbHOH OKp)')KHOCTH. (no 3TOH npHQHHe HaQaJIbHbIH Kpyr TaIOKe
Ha3bIBaIOT «llIarOBbIH» Kpyr. - llpUMett. nep.) ECJIH llIHpHHa 3y6a H paccToRHHe
Mex,ny ,n;ByMR coce,n;HHMH 3y6bRMH paBHbI (npeHe6perIDI 3a30pOM), Tor,n;a TOJII.l(HHa
KaXC,noro 3y6a (H3MepeHHaR no HaQaJIbHOH OKp)')KHOCTH) paBHa nOJIOBHHe OKPYX-
Horn llIara.
,n;HaMeTpaJlbHhlH mar (P)
31'0 «,n;IOHMOBIDI» CHCTeMa ,L(JUI orrpe,n;eJIeHIDI llIara 3y6beB 3y6QaTOrO KOJIeca:
qHCJlO 3y6beB
AHaMeTpaJIbHbIH war P = .
,nHaMeTp HaqaJIbHOH OKpyxHOCTH B ,lUOHMax
Dla6a 5. MexaHU'IeCKUe nepeiJa'lu
MO Jlb 3y6beB (m)
3TO cOBpeMeHHbIH Me)l{)];)'Hapo,n;HbIH MeTpWIecKHH rrapaMe1p ,L(JUI orrpe,n;eJIeHIDI
mara. BbIqHCIDIeTCR OH aHaJIOrHqHO ,n;HaMe1paJIbHOMY mary:
M 6 ,l(HaMeTp HaqaJIbHOH OKpyxHOCTH B MHJIJIHMeTpax
O.nyJlb 3Y beB m = .
qHCJlO 3y6beB
5. 1. 7. BblCOT8 3y6bes KoneC8
Ha al1bHble
OKPY>KHOCTVI
/
/
CYMMapHaS1 BblCOTa
(2 x aaaop)
(BblcoTa rOl1OBKVI ay6a +
+ BblCOTa HO)l(KH ay6a)
/
AKTVlBHaS1 BblCOTa
(2 x BblCOTa
rOl1OBKVI ay6a)
PaAVlal1bHbl
aaaop
-+-
1 02
Ha pHC)'HKe rrOKa3aHO, qTO rrpH Cu;eI1JIeHHH ,n;BYX 3y6beB HaqaJIbHbIe OKpyxHO-
CTH KacalOTCR o,n;Ha ,n;pyrOH, H rOJIOBKa 3y6a o,n;Horo KOJIeCa BBO,n;HTCR B rrpOMexy-
TOK Me HO)I(KaMH 3y6a corrpIDKeHHoro 3y6qaTOrO KOJIeca. IIOCKOJIbK}' ,n;OJDKeH
c eCTBOBaTb 3a30p Me)l{)];Y rOJIOBKOH (rpe6HeM) o,n;Horo 3y6a H BIIa,n:HHOH rrpOMe-
xyTKa Me)l{)];y 3y6bRMH, B KOTOpyro OH BCTaBJIReTCR, BbICOTa HO)I(KH 3y6a 60JIbme,
qeM BbICOTa ero rOJIOBKH Ha BeJIHqHHY 3a30pa.
TaKHM 06pa30M, aKTHBHaR BbICOTa 3y6a paBHa y,n;BoeHHOMY 3HaqeHHIO BbICOTLI
rOJIOBKH 3y6a, B TO BpeMR KaK rrOJIHIDI BbICOTa 3y6a paBHa y,n;BoeHHOMY 3HaqeHHIO
BbICOTbI rOJIOBKH 3y6a I1JIIOC BeJIHqHHa pa,n:HaJIbHOrO 3a30pa (T. e. BbICOTa rOJIOBKH
3y6a IIJIIOC BbICOTa HO)I(KH 3y6a). ECJIH BepHyrbcR K 3y6qaTOH peHKe (pa3,n;eJI 5.1.5),
TO MOXHO YBH.D;eTb, qTO 3a30p paBeH pa,n:HYCY Brra,n:HHbI. B H.D;eaJIe, 3TO COCTaBIDIeT
0,25-0,39 3HaqeHIDI MO,n;yJUI 3y6beB. CJIe,n;oBaTeJIbHo:
BbICOTa rOJIOBKH 3y6a = 1,00 m; BbIcoTa HO)J(l(a 3y6a = 1,25 m;
BbIcoTa 3y6a (rny6HHa pe3aHHR) = BbICOTa rOJIOBKa 3y6a + BbICOTa HO)I(KH 3y6a =
= 1,00 m + 1,25 - 1,39 m = 2,25-2,39 m;
AKTHBHIDI BbICOTa = BbICOTa rOJIOBKH 3y6a + BbICOTa rOJIOBKa 3y6a = 2,00 m,
f,n;e m - MO,n;YJIbHbIH mar.
(OKpyxHOCTb, KOTOpIDI ,n;eJIHT 3y6 Ha rOJIOBK}' H HOXKy, Ha3bIBaeTCR ,n;eJIHTeJIb-
HOH OKpyxHOCTblO. ,[LJrn HYJIeBbIX (HeKoppHrHpoBaHHbIx) KOJIeC HaqaJIbHIDI H ,n;eJIH-
TeJIbHIDI OKpyxHOCTH COBIIa,n:aIOT. - llpUMett. nep.)
5. 1. MexaHUlteCfWe nepeiJaltu: 3)'6ltamble nepeiJaltu 3
5. 1.8. 3neMeHTbl CT8HA8pTHoro 3y6118Toro KoneC8 (AIOHMbl)
.
HOpM8JlbHwii HOpMaJlb- CTa ap1'llU CTaIWlPT- CTaIWIPT- MHHH- MHHHMaJlb- nOJIHYii npHDYCK
' 8MeTp8Jlb- ,HWi OKPY1K- Otq)ymtU HU BblCO- HU aKTHB- MaJlbHwii HU nOJIHU no,n meBHHI'OBaHHe
Ta roJlOBKH
HWii IIIIT'I HoA mar TOJlllUllla 3y6a 3y6a HU BbiCOTa 3830p* BbiCOTa * TOJUIUIIIbI 3y6a
2,5 1,256637 0,6283 0,4000 0,8000 0,090 0,890 0,0040/0,0050
3 1,047198 0,5236 0,3333 o 6666 0,083 0,750 0,0040/0,0050
3,5 0,897598 0,4488 0,2857 0,5714 0,074 0,645 0,0040/0,0050
4 0,785398 0,3927 0,2500 0,5000 0,068 0,568 0,0035/0,0045
4,5 0,698132 0,3491 0,2222 0,4444 0,060 0,504 0,0035/0,0045
5 0,628319 03142 0,2000 0,4000 0,056 0,456 0,0035/0,0045
6 0,523599 0,2618 o 1667 0,3334 0,050 0,383 0,0030/0,0040
7 0,448799 02244 0,1429 0,2858 0,044 0,330 0,0030/0,0040
8 0,392699 0, 1963 0,1250 0,2500 0,040 0,290 0,0030/0,0040
9 0,349066 0,1745 0,1111 0,2222 0,038 0,260 0,0025/0,0035
10 0,314159 0,1571 0, 1000 0,2000 0,035 0,235 0,0025/0,0035
11 0,285599 0,1428 0,0909 0,1818 0,032 0,214 0,0020/0,0030
12 0,261799 o 1309 0,0833 0, 1666 0,030 0, 197 0,0020/0,0030
14 0,224399 0,1122 0,0714 0,1428 0,026 0,169 0,0020/0,0030
1'6 0,196350 0,0982 0,0625 0,1250 0,023 0, 148 0,0015/0,0025
18 0,174533 0,0873 0,0556 0,1112 0,021 0,1 32 0,0015/0,0025
* OCHoBaHo Ha CTaH,napTHOM PMHYCe 3aKpyrJleHHH pe eH KpOMKH rrpH o6pa6oTKe
tlepBjJqHoH <ppe30H rro,l( meBHHfOBaHHe H 3y6ope3HbIM ,l(OJl6HKOM. nOJlHaR BbICOTa )'BeJlH-
tlUTCH rrpH6J1H3HTeJlbHO Ha 0,005-0,010 ,l(IOHMa rrpH 60QKOo6pa3HoM meBHHfOBaHHH.
5. 1.9. 3neMeHTbl MenKoMoAynbHoro 3y6118Toro KoneC8
(AIOHMbl)
HOpMaJlbHblH HOpM8JIb- CTalWlp1'llU CTaIWlPT- CTaIWlPT- MHHH- MHHHM8JIb- nOJOlWH npHDYCK
8MeTp8Jlb- Hhm OKPY1K- Otq)ymtU HU BblCO- HU aKTHB- MaJlbHhIH HU nOJIHaSi no,n meBHHfOBaHHe
Ta roJlOBKH
HWii IIIIT'I HOH mar TOJIlIUlHa 3y6a 3y6a HU BblCOTa 3a30p* BbiCOTa * TOJiIIUlHbI 3y6a
(- " ,
20 0,157080 0,0785 0,0500 0, 1000 0,020 0,120
22 0,142800 0,0714 0,0454 0,0908 0,020 0, III
24 0,130900 0,0654 0,0417 0,0834 0,020 0,103
26 0,120830 0,0604 0,0385 0,0770 0,019 0,096
28 0,112200 0,0561 0,0357 0,0714 0,019 0,090
30 0,104720 0,0524 0,0333 0,0666 0,018 0,085 0,0005-0,0015
32 0,098175 0,0491 0,0312 0,0624 0,018 0,080
36 0,087266 00436 0,0278 o 0556 0,016 0,072
40 0,078540 0,0393 0,0250 0,0500 0,015 0,065
44 0,071400 0,0357 0,0227 0,0454 0,014 0,059
48 0.065450 0.0327 0.0208 0.0416 0.013 0.055
52 0,060415 0,0302 0,0192 0,0384 0,012 0,050
56 0,056100 0,0281 0,0178 0,0356 0,011 0,047
60 0,052360 0,0262 0,0167 0,0334 0,010 0,043 0,0003-0,0007
64 0,049087 0,0245 o 0156 0,0312 0,010 0,041
72 0,043633 0,0218 0,0139 0,0278 0,010 0,038
* OCHoBaHo Ha CTaH,napTHOM PMHYCe 3aKpyrJleHIDI pe eH KpOMKH rrpH o6pa6oTKe
qepBHQHOH <ppe30H rro,l( meBHHfOBaHHe H 3y6ope3HbIM ,l(OJl6HKOM. nOJlHaR BbICOTa )'BeJlH-
tlUTCH rrpH6J1H3HTeJlbHO Ha 0,005-0,010 ,l(IOHMa rrpH 60QKOo6pa3HoM meBHHfOBaHHH.
Dla8a 5. MexaHultecICue nepeiJaltu
5. 1. 10. 3neMeHTbl CTSH,qspTHoro 3y6lfSTOrO Konecs
C YKopolfeHHblMIA 3y6bflMIA (,qIOHMbl)
l
CTaQapr- I
HOpMaJIh.....A HOpMam.- CTBIItUip1'llU CTall,lUtpr- MJout- MHHHMam.- DoJIIIYI DPHOyCI I
.lUIaMeTpam.- HWii OJq)yK- OJq)yJKllU BU BhlCO- BU aKTHB- Mam.HWii BU DOJIHU DO meBHHI'OBIIOIe
Ta roJlOBKH
HWii IIJI'n BoA mar TOJIIIJ,IIIIa 3,oa 3,oa BU BMcara 3830P* BMcara* TOJIIQIIIIY 3168
,
3/4 1,047198 0,5236 0,2500 0,5000 0,083 o 583 0,0040/0,0050' "
4/5 0,785398 0,3927 0,2000 0,4000 0,068 0468 0,0035/0,0045 I
5/7 o 628319 03142 0,1429 02858 0056 o 342 0,0035/0,0045 I
6/8 0,523599 02618 0,1250 0,2500 0,050 0300 0,0030/0,0040
7/9 0448799 0,2244 0,1111 0,2222 0,044 0,266 0,0030/0,0040 '
8/10 0,392699 0,1963 0,1000 0,2000 0,040 0240 0,0030/0,0040 'I
0,349066 0,038 0,0025/0,0035 I
9/11 0,1745 0,0909 0,1818 0,220
t
10/12 0,314159 01571 0,0833 o 1666 0,035 0,202 0,0025/0,0035
12/14 o 261799 0,1309 0,0714 01428 0,030 0,173 0,0020/0,0030
I
14/18 0224399 01122 0,0556 0,1112 0,026 0,137 0,0020/0,0030
16/21 0,196350 00982 0,0476 00952 0023 0118 0,0015/0,0025
18/24 0,174533 o 0873 0,0417 00834 o 021 0,104 0,0015/0,0025
20/26 0,157080 00785 0,0385 0,0770 0,020 0,097 0,0010/0,0015
I
22/29 0,142800 0,0714 0,0345 0,0690 0,020 0089 0,0010/0,0015
24/32 0,130900 0,0654 0,0313 0,0626 0,020 0,083 0,0010/0,0015
2635 0,120830 0,0604 00286 0,0572 0,019 0,076 0,0010/0,0015
2837 0,112200 0,0561 0,0270 0,0540 0,019 0,073 0,0010/0,0015
30/40 0,104720 00524 0,0250 00500 0,018 0,068 0,0010/0,0015
32/42 0,098175 0,0491 0,0238 0,0476 0,018 0,066 0,0010/0,0015
34/45 0,092400 0,0462 0,0222 0,0444 0,017 0,061 0,0010/0,0015
36/48 0,087266 0,0436 0,0208 0,0416 0,016 0,058 0,0010/0,0015
38/50 0,082673 0,0413 00200 0,0400 0,016 0,056 0,0010/0,0015
40/54 0,078540 00393 00185 0,0370 0015 0,052 o 0010/0 0015
* OCHoBaHo Ha CTaH,napTHOM patl:HYce 3aKpyrJIeHIDI pexyIl(eH KpOMKH npH o6pa6oTKe
qepBgqHOH <ppe30H no,D; weBHHfOBaHHe H 3y6ope3HbIM ,D;OJI6HKOM. llOJIHaH BbICOTa yBeJIM-
qHTCH npH6JIH3HTeJIbHO Ha 0,005-0,010 ,D;IOHMa npH 60QKOo6pa3HoM weBHHfOBaHHH.
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OOMOON \O v)OV)O'\ OOMOON \O OO'\OO \O
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OoO NNNNNNNMMMMM v)\O
000000000000000000000000000
\Ov) MN OO'\OO \O\Ov) MMN OOO\OV)NOO
M V)\O OOO'\O NNM v)\O OOO'\O N v) O'\M\O
Nv)OO O OM\OO'\Nv)OO OO O\ONOO M
NNNMMM v)V)v)\O\O\O OOOOO'\O'\ N
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OOM OO'\O MOV) O N M \O ONO
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O'\0o_o_o0O'\00 _OON N N NNN
00 \0 N \0 N _ V) N M 00 0'\ V) \ \0 00 0'\ 0 N
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O'\OO\O NO'\\ONO'\v) \ONf'.N N N\O NNN
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N NOOMO'\ O'\V)O\O \ON MOOMOO OO NM \O
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MM v)\O OOO'\ NNNNNM
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Dla8a 5. MexaHu'IecICue nepeiJa'lu
5. ,. 12. ISYKseHHble o603HalfeHlfR A,nR pa3MepHocTeH
3y6lfaToro Koneca If SbllflfcneHlfR
a BbICOTa rOJIOBKH 3y6a
b BbICOTa HO)I{KH 3y6a
B 60KOBOH 3a30p
Bn HOpMaJIbHbIH OKpyxHOH 3a30p
c PMHaJIbHbIH 3a30p
C MexoceBoe paCCTOHHHe
d ,lI;HaMeTp H3MepHTeJIbHbIX pOJIHKOB (mapHKoB)
D ,lI;eJIHTeJIbHbIH ,lI;HaMe1'p
Db OCHOBHOH ,lI;HaMe1'p
Dc ,lI;HaMe1'p KOHTaKTa
Dr ,lI;HaMe1'p rpaHHqHbIX TOqeK
D F ,lI;HaMeTp HaqaJIa BnMHH
D i BH)'TpeHHHH ,lI;HaMeTp (3y6qaTOe KOJIeCO C BH)'TpeHHHMH 3y6bHMH)
Dm ,lI;HaMeTp no IJ;eHTpy H3MepHTeJIbHbIX pOJIHKOB (mapHKoB)
D Me pa3Mep no pOJIHKaM (mapHKaM)
DMi pa3Mep Me)l{,ll;y pOJIHKaMH (mapHKaMH)
Do BHemHHH ,lI;HaMeTp BepmHH
Dr HaqaJIbHbIH ,lI;HaMeTp
DR ,lI;HaMe1'p BnMHH
Ds ,lI;HaMe1'p meBHHrOBaHIDI
F mHpHHa 3y6qaTOrO BeHIJ;a
h k pa60qaH rny6HHa 3axO,ll;a 3y6beB
ht nOJIHWI BbICOTa 3y6a
L mar BHHTa
LA fIOJIHaH AJIHHa JIHHHH 3aIJ;enJIeHIDI
m MO,ll;YJIb 3y6beB (MeTp.uqeCKaH cHcTeMa)
mF K03<P<P H IJ;HeHT nepeKpbITIDI 3y6a (K03<P<PHIJ;HeHT oceBoro nepeKpbITIDI)
m n HOpMaJIbHbIH MO,ll;YJIb 3y6beB
mp K03<P<PHIJ;HeHT KOHTaKTa 3BOJIbBeHT (3BOJIbBeHTHoe nepeKpbITHe)
mt OKpyxHOH MO,LJ;yJIb 3y6beB
N qHCJIO 3y6beB B 3y6qaTOM KOJIeCe (N G ) HJIH B meCTepHe (N p )
P OKpyxHOH mar
Pb OCHOBHOH mar 3aIJ;enJIeHIDI
Pn HOpMaJIbHbIH OKpyxHOH mar
Pt TOpIJ;OBbIH OKpyxHOH mar
Px oceBOH mar
P ,lI;HaMeTpaJIbHbIH fIHTq
P n HOpMaJIbHbIH ,lI;HaMe1'paJIbHbIH nHTq
Pt TOpIJ;OBbIH: ,lI;HaMe1'paJIbHbIH nHTq
SAP HaqaJIO aKTHBHOrO npo<pHlliI
5.1. MexaHUlteCKUe nepeoaltu: 3y6ltamble nepeoaltu 3 13
S IIIHpHHa BnMHHbI OKpyxHIDI
SRP HaqaJIO 3aKpyrJIeHHOrO npo<pHlliI
Sn IIIHpHHa BnMHHbI HOpMaJIbHaH ,[(eJIHTeJIbHIDI
St IIIHpHHa BnMHHbI TOpU;OBIDI OKpyxHIDI
t TOJIII(HHa 3y6a (In' It, H T.,[(.) OKpyxHaH
t. c TOJIII(HHa 3y6a no xop,[(e (Inc, ltc, H T.,[(.)
Z JIHHIDI 3au;enJIeHIDI
YrJIhI
cP yrOJI npo<p HlliI
I
CPm yrOJI rrpo<pHlliI no u;eHTpy H3MepHTeJIbHbIX pOJIHKOB (IIIapHKoB)
CPn yrOJI npo<pHJIH B HOpMaJIbHOM CeqeHHH
CPr HaqaJIbHbIH yrOJI rrpO<pHlliI (<Pnr' <Ptr H T .,[(.)
CPt TOpU;OBbIH yrOJI rrpO<pHJIH
CPto TOpU;OBbIH yrOJI npo<pHlliI no BHeIIIHeMY ,[(HaMeTpy BepIIIHH
CPx oceBOH yrOJI npo<p HIDI
\IJ yrOJI HaKJIOHa JIHHHH 3y6a
ItIJ b OCHOBHOH yrOJI HaKJIOHa JIHHHH 3y6a
r HaqaJIbHbIH yrOJI HaKJIOHa JIHHHH 3y6a
ltIJ o yrOJI HaKJIOHa JIHHHH 3y6a no BHeIIIHeMY ,[(lIaMe1'py BepIIIHH
X MexoceBOH yrOJI
npHMe1JaHHe.
1. CHMBOJI ,[(yrH ( ), ,[(o6aBJIeHHbIH K 0603HaqeHHIO yrJIa, YKa3bIBaeT Ha TO, qTO
yrOJI H3MepHeTCH B PMHaHax, a He B rpanycax.
2. HIDKHHe HH;J;eKCbI, HCrrOJIb3yeMbIe C CHMBOJIaMH, n03BOllillOT rrpOBeCTH pa3-
JIHtlHe Me pa3Hoo6pa3HbIMH ,[(HaMe1'paMH H yrJIaMH, a TaK)l{e YKa3aTb, qTO pac-
CMa'rpHBaIOTCH xapaKTepHCTHKH IIIeCTepHH HJIH 3y6qaTOrO KOJIeca.
TepMHHOJIOrHJI
TOpu;oBbIe xapaKTepHCTHKH (HIDKHHH HH;J;eKC t) OTHOCHTCH K IIJIOCKOCTH Bpa-
m;eHIDI, napaJIJIeJIbHOH TOpU;Y KOJIeCa H neprreH;J;HKYlliIpHOH ,K OCH.
HOPMaJIbHbIe xapaKTepHCTHKH (HIDKHHH HH;J;eKC n) OTHOCHTCH K pa3MepaM B
CeqeHHH 3y6a nJIOCKOCTblO, HOpMaJIbHOH K JIHHHH 3y6a, npH ,[(aHHOM ,[(HaMe1'pe.
XapaKTepHCTHKH oceBOH nJIOCKOCTH (HIDKHHH HH;J;eKC x) HaXO,[(HTCH B IIJIOCKO-
CTH, rrpOXO,[(HlI(eH qepe3 3y6 H OCb KOJIeCa, rrepneH;J;HKYlliIpHOH K TOpU;Y IIIeCTepHH.
HaqaJIo aKTHBHOrO npo<pHJIH (SAP) - 3TO caMIDI HJI)I(HIDI TOqKa KOHTaKTa C
conpIDKeHHbIM 3y6qaTbIM KOJIeCOM, B ,[(IOHMax, H3MepeHHaH B,[(OJIb JIHHHH 3au;enJIe-
HID!, HJIH B rpMycax, KaK yrOJI rrOBopOTa OT HYillI (OCHOBHOH ,[(HaMeTp).
)];HaMeTp KOHTaKTa (Dc) - 3TO ,[(HaMe1'p OKpyxHOCTH, rrpoBe,[(eHHoH qepe3 ca-
MyIO HIDKHIOIO TOqKY KOHTaKTa C conpIDKeHHbIM 3y6qaTbIM KOJIeCOM.
)];HaMeTp rpaHHqHbIX TOqeK (Dt) - 3TO ,[(HaMe1'p OKpyxHOCTH, npoBe,[(eHHoH
Qepe3 CaMyIO HIDKHIOIO TOqKY npo<pHlliI KOJIeCa, HaqHHWI C KOTOpOH OqepTaHHe
npocPHJIb nepeXO,[(HT B 3MaHHyIO 3BOJIbBeHTY.
HaqaJIo 3aKpyrJIeHHOrO npo<pHIDI (SRP) - 3TO BbICOTa HaqaJIa 3aKpyrJIeHIDI Bna-
,nHH Ha KOJIeCe, H3MepeHHWI B,[(OJIb JIHHHH 3au;enJIeHIDI OT OCHOBHoro ,[(HaMe1'pa.
Dla8a 5. MexaHU'IeCKUe nepeoa'lu
,n;HaMe1'p HaqaJIa BnMHH (DF) - 3TO ,[(HaMeTp OKpyxHOCTH, npoBe,[(eHHOH: qe-
pe3 HaqaJIO 3aKpyrJIeHIDI BnMHH.
,n;HaMeTp meBHHrOBaHIDI (DS) - 3TO ,[(HaMe1'p OKpyxHOCTH, npoBe,[(eHHOH: qe-
pe3 caMyIO HIDKHIOIO TOqKY corrpHKOCHOBeHIDI C meBepoM; T. e., HaqaJIO npocPHIDI
meBHHrOBaHIDI KOJIeca.
MeXOCeBOH: yrOJI (X) HBlliIeTCH C)'MMOH: HJIH pa3HOCTblO yrJIOB HaKJIOHa BHHTO-
BOH JIHHHH meCTepHH H meBepa, B 3aBHCHMOCTH OT HanpaBJIeHIDI BHHTOBOH JIHHHH
CnHpaJIH H MexoceBoro paCCTOHHIDI. ECJIH HanpaBJIeHIDI npOTHBOnOJIO)I(HbIe, TO
MexoceBOH yrOJI 6y,[(eT paBeH pa3HOCTH Me yrJIaMH HaKJIOHa; eCJIH HanpaBJIe-
HIDI O,[(HHaKOBbI, TO OH 6y,[(eT paBeH C)'MMe.
5. ,. 13. OCHoBHble cpopMynbl AJlR npRMo3y6oro
qJfnlAHAPJflfeCKOro 3y6lfaToro Koneca
napaMeTp .IUOAM MM I
,lJ;eJIHTeJIbHbIH ,D;HaMe1'p D NIP mN
BbICOTa rOJIOBKH 3y6a 0 liP MO,l(yJIb m I
CTaH,napTHbIH BHeWHHH ,D;HaMeTp D + 2a D+2m
I
OKpyxHOH war p Tt/P Ttm
Cpe,D;HHH 3a30p B IIape B O,040/P O,040m I
,lJ;HaMe1'p BIIatJ:HH DR Do- 2h t
OCHOBHOH ,D;HaMe1'p Db Dcos cp
CTaH,napTHaH OKpyxHaH TOJImHHa 3y6a t p/2
llpeoopa30BaHHJI
,n;HaMe1'paJIbHbIH nHTq P = 25,4/m
MO,[(YJIb 3y6beB m = 25,4/P
MHJIJIHMe1'pbI = ,[(IOHMbI/0,03937 = 25,4 ,[(IOHMbI
,n;IOHMbI = 0,03937 MM = MM/25,4
5. 1. 14. OCHoBHble ypaBHeHlAR Koco3y6oro
qJfnJfHAPJflfeCKOro 3y6lfaToro Koneca
T OPU;OBbIH ,[(HaMe1'paJIbHbIH nHT'I l't = 1'" cos 'I'
,n;eJIHTeJIbHbIH ,[(HaMe1'p D = N / l't
CTaH;J;apTHaH BbICOTa rOJIOBKH 3y6a = 1 / 1'"
BHemHHH ,[(HaMe1'p Do = D + 2a
TOPU;OBbIH yrOJI npo<pHlliI tg<Pt = tg<Pn / cos'l'
OCHOBHOH ,[(HaMe1'p Db = Dcos<Pt
llIar BHHTa L = TtDctg\V = TtD / tgv
HOPMaJIbHbIH OKpyxHOH mar Pn = Tt / 1'"
CTaH;J;apTHaH HOpMaJIbHaH OKpyxHaH TOJIII(HHa 3y6a t n = Pn / 2
OceBoH mar Px = Tt / 1'" sin 'I' = Pn / sin 'I' = L / N
Topu;eBoH OKpyxHOH mar Pt = Tt / l't = Pn / cOS'l'
5.1. MeXaHUlteCKUe nepeiJaltu: 3y6ltamble nepeiJaltu 315
5. 1. 15. BcnoMoraTenbHble ypasHeHJfR
AJlR 3y6lfaroro Koneca
1. YroJI HaKJIOHa JIHHHH 3y6a '1', Kor,na 3anaHHoe Me:>KOCeBOe paCCTOHHHe HBJUI-
eTCH CTaH;J;apTHbIM:
N +N o
cos 'I' = p .
2Pn C
2. HaqaJIbHbIH (,neJIHTeJIbHbIH) ,nHaMe1'p (KOJIeco) npH HeCTaH;J;apTHOM Me:>KOCe-
BOM paCCTOHHHH C: v
Drp = 2CN p .
N p +N o
3. HaqaJIbHbIH yroJI np<><pH.IDI cj)rt npH HeCTaH,ZJ;apmOM Me:>KOCeBOM paCCTOHHHH C:
Do + DG
cos + rt = P b .
2C
4. HOpMaJIbHbIH ,nHaMe1'paJIbHbIH nHT'I:
Pn=Ptsect/J.
5. YroJI HaKJIOHa JIHHHH 3y6a '1':
N
cOS'l' = -,
DP n
. TtN
sIn 'I' = -,
Pn L
llpH JII060M ,D;HaMe1'pe D 2 tan'l'2 = D 2 tan'l'l .
D}
6. TOPU;OBbIH OKpyxHOH mar Pt2 npH JII060M ,nHaMeTpe D 2 . (- -I /
D 2
Pt2 = N '
7. 3BOJIbBeHTHbIH yrOJI npo<pHJIH (<pYHKIJ;IDI Ta6YJIHpOBaHa):
inv <p = tan <p - <po
8. HOpMaJIbHbIH yrOJI npo<pH.IDI:
tan CPn = tan CPt - COS "'.
9. TOPU;OBbIH yrOJI npo<pHlliI cj)t npH JII060M ,nHaMe1'pe D 2 :
COS+t2 = Do .
D 2
10. OCHOBHOH yrOJI HaKJIOHa JIHHHH 3y6a 'l'b:
_ COS'l' cos +n _ sin +n
cos 'I' b - -,
cos +t sin +t
sin t/J.o = sin t/J cos <Pn' tan t/J.o = tan t/J cos CPt.
11. OCHOBHOH mar:
Pb = TtDo = pcos+.
N
Dla8a 5. MexaHultecICue nepeiJaltu
5. ,. 16. TepMlfHonorlfR npRMo3y6oM KOHlAlfeCKOH
3y61f8TOM nepe,qalflf
6aaOBoe paCCTO H e
PaCCTO H e OT Bep HbI AO nIlOCKOCT
BHeWHe OKpy)l(HOC BepW H (ay6beB
YrOIl
BepW Ha Aell TellbHoro rOIlOBK ay6a
KOHyca (Ha aIl0 OTc eTa) Y
rOIl HO)l(-
o 1 K ay6a
PaCCTO H e OT
aaOBO nIl0CKOCTM
AO nIl0CKOCT
BHeWHe OKpy)l(HO-
CT BepW H ay6bes
1 - yroll BHyrpeH-
Hero AonOIlH Tellb-
Horo KOHyca
rOIl BHeWHer
AonOIl H Tellb-
Horo KOHyca
CpeAHee KOHYCHoe pac-
CTO H e no BHeWHeMY
AonOIlH TellbHOMY KOHYCY
5. 1. 17. TepMlfHonorlfR lfepSRIfHoro 3aqenneHMR
(lfepSRK If lfepSfllfHoe Koneco)
c
d a
d r
WHeK
Da D. Dr -
C - MexoceBoe paCCTOHHHe; Da - ,D;HaMeTp BepWHH qepBHqHOrO KOJIeCa (HaH6oJIbWHH);
d a - ,D;HaMeTp BepWHH BHTKOB (HaH6oJIbWHH); Dr - ,D;HaMeTp BIIa,nHH qepBHqHOrO KOJIeCa;
Dt - ,D;HaMeTp ,D;O BbIeMKH IIOBepXHOCTH BepWHH 3y6beB KOJIeCa;
d r - ,D;HaMeTp BIIa,nHH qepBHKa
5.2. MexaHUlteCKUe nepeoaltu: peMeHHble nepeoaltu 317
06/MHH WHeKa _ qHCJIO 3y6beB qepBHqHoro KOJIeCa
06/MHH qepBHqHoro KdJIeca qHCJIO 3axO,nOB qepBHKa
llpHMep
PaCCqHTaTb CKOpOCTb qepBWlHOro KOJIeCa B 06/MHH, 3HaH, qTO IIIHeK BbInOJIIDI-
eT 500 06/MHH, qTO qepBHqHOe KOJIeCO HMeeT 50 3y6beB H qTO IIIHeK HMeeT ,[(Be OT-
CeqKH.
500 06/MHH _ 50 3y6beB
06/MHH qepBHqHoro KOJIeCa 2 3axo,na
500 x 2'
06/MHH qepBHqHOrO KOJIeCa = = 20 06/MHH.
50
5.2. MeX8HM'IeCKMe nepeA8'1M: peMeHHble nepeA8'1M
5.2. 1. npOCTble nnocKopeMeHHble nepe,qalfJf
llepe,ll;a1Ja C OTKphlThIM peMHeM
....
BeAyw.lII WKlIIB
BeAOMbl WKlIIB
.-/1
/
1. Be.nyw;HH H Be,[(oMbIH IIIKHBbI Bpa:w;aIOTCH B O,[(HOM HanpaBJIeHHH.
2. OTHoIIIeHHe qaCTOTbI Bpa:w;eHIDI Be.nyw;ero IIIKHBa K qaCTOTe Bpa:w;eHIDI Be-
,nOMoro HJIH nepe,[(aTOqHOe OTHOIIIeHHe (oTHoIIIeHHe yrJIOBbIX CKopocTeH Be.nyw;ero
H Be,[(OMoro IIIKHBOB) BbIqHClliIeTCH no CJIe :w;eH <popMYJIe:
06/MHH Be.nyIUHH = ,lUiaMeTp DN Be,nOMoro
06/MHH Be,noMbIH ,nHaMeTp DR Be.nym:ero
llpHMep
PaCCqHTaTb qaCTOTY Bpa:w;eHIDI Be,[(OMoro IIIKHBa B 06/MHH, eCJIH qaCTOTa Bpa-
w;eHIDI Be.nyw;ero IIIKHBa COCTaBlliIeT 200 06/MHH. ,lJ.HaMeTp DR paBeH 500 MM H
,nHaMeTp DN paBeH 800 MM.
200 06/MHH
06/MHH . Be,noMbIH
800 MM
=
500 MM
200 x 500
06/MHH Be,noMbIH = = 125 06/MHH.
800
Dla8a 5. MexaHU'IeCKUe nepeiJa'lu
llepeKpeCTHaJl peMeHHaJI nepeAa1Ja
BeAyw.lII WKlIIB
BeAoMbl WKlIIB
1. Be,nyw;Hii H Be,[(OMhIH IIIKHBbI BpCilUalOTCH B rrpOTHBOnOJIO)f{HbIX HanpaBJIeHIDIX.
2. TIepeKpecTHWI peMeHHWI nepe,[(aqa MoxeT HCnOJIb30BaTbCH TOJIbKO C IIJIOC-
KHMH peMIUIMH (60JIbIIIHe MexoceBbIe paCCTOHHID!) HJIH peMIUIMH KpyrJIOrO ceqe-
HID! (MaJIeHbKHe MexoceBbIe paCCTOHHID!).
3. OTHOIIIeHHe qaCTOTbI BpalI(eHID! Be,[(ylI(ero IIIKHBa K qaCTOTe BpalI(eHID! Be-
,[(OMoro HJIH nepe,[(aTOqHOe OTHOIIIeHHe (oTHoIIIeHHe yrJIOBbIX CKopocTeH Be,nyrnero
H Be,[(OMoro IIIKHBOB) BbIqHClliIeTCH no CJIe,[(ylOlI(eH <poPMYJIe:
06/MHH Be.nyIlUfH = ,lUiaMeTp DN Be,n;OMoro
06/MHH Be,n;OMbIH ,n;HaMeTp DR Be,nyI.Qero
llpHMep
Be,[(YIUHH IIIKHB HMeeT qaCTOTY BpalI(eHID! 500 06/MHH H ,[(HaMeTP 600 MM.
PaCCqHTaTb ,[(HaMeTP Be,[(OMoro IIIKHBa, eCJIH ero qaCTOTa BpalI(eHID! COCTaBIDIeT
250 06/MHH.
500 06/MHH = ,n;HaMeTp.D N
250 06/MHH 600 MM
500 x 600
,[(HaMeTJ) DN = = 1200 MM.
250
5.2.2. CTYneHlfaTwe nnOCKopeMeHHble nepe,qalfJf
-
...
1
npOMe>KYTO"lHbl
eAOMbl WKlIIB I
BeAyw.lII WKlIIB
npOMe>KyrO"lHbl Ban
n pOMe>KyrO"l H bl
BeAyw.lII WKlIIB
BeAOMbl WKHB
5.2. MeXaHUlteCKUe nepeoaltu: peMeHHble nepeoaltu 3 19
1. ,lJ.lliI onpe,[(eJIeHIDI HanpaBJIeHIDI BpalI(eHIDI npHMelUllOTCH npaBHJIa ,lJ)UI ne-
pe,[(aq C OTKpbITbIM peMHeM H nepeKpecTHbIX nepe,[(aq (pa3,[(eJI 5.2.1).
2. OTHoIIIeHHe qaCTOTbI palI(eHIDI Be.nyw;ero IIIKHBa K qaCTOTe BpalI(eHIDI Be-
,nOMoro HJIH nepe,[(aTOqHOe OTHOIIIeHHe (oTHoIIIeHHe yrJIOBbIX CKopocTeH Be.nyw;ero
H Be,[(OMoro IIIKHBOB) BbIqHClliIeTCH no CJIe,[(ylOlI(eH <poPMYJIe:
06/MHH Be.nyIlUfH = ,lUiaMe1'p.D 1 x ,nHaMe1'p.D N .
06/MHH Be,nOMbIH ,nHaMe1'p.D R ,lUiaMe1'p.D 2
llpHMep
PaCCqHTaTb qaCTOTY BpalI(eHIDI B 06/MHH Be,[(OMoro IIIKHBa, eCJIH qaCTOTa BpalI(e-
HID! Be.nyw;ero IIIKHBa COCTaBllileT 60006/MHH. ,lJ.HaMeTpbI IIIKHBOB: DR = 250 MM,
Dl = 750 MM, D 2 = 500 MM, DN = 1000 MM.
600 06/MHH
06/MHH Be,noMbIH
750 MM 1000 MM
= x
250 MM 500 MM
600 x 250 x 500
06/MHH Be,noMbIH = = 100 06/MHH.
750 x 1000
5.2.3. TJfnJflfHble HBTRJlCHble YCTPOHCTSB
YCTPOiCTBO HaTSDKeHHJI C nOBopoTHOi paMoii
HaTJDKlloii pOJIHK
BeAYw.
WK B
BeAOMbl
WK B
BeAOMbl
WK B
BeAYw. .,
WK B
PeMeHb
PeMeHb
YBel1 ...eH e
HaTSI)I(eH SI ..
nOBOpOTHaSl
paMa
YBel1 ...eH e
aTSI)I(eH SI
\ B HT, pery-
I1 PYIOW.
HaTSI)I(eH e
CTaH Ha
¥cTpoicTBO HaTSDKeHHJI C peJIhCOBhIMH HanpaBJUlIODUlMH
PeMeHb
B HT, pery-
I1 PYIOW.
HaTSI)I(eH e
MOTOP
Pe11bCOBbie
HanpaBI1S1IOw. e
5.2.4. TlAnlAlIHble nplANleHeHlAfI KnIAHOBblX IA CIAHXPOHHblX
npHMeHeHHe
C'rpOHTeJlbHbIe MaWHHbI
fOPHasI npOMbIllIJIeHHOCTb
O<pHCHoe o6opy,u;oBaHHe
Pe.nyKTOpbI peryJlHpYIOIUHe CKOpOCTb
neqaTHOe o6opy,u;oBaHHe
BbIpa60TKa 3J1eIcrp03HeprnH
3J1eIcrpWIeCKHe HH'rpYMeHTbI
KOHBeHepHWI ,u;OCTaBKa
npOMbIllIJIeHHbIe npHBo,u;bI
FO@-Z
MOllUlLle ay01faThie 003 o6eJ)TKII
60KOBhIX rpaHeii KJlHHOBWe peMHH
ULTRAFLEx<ID
KJlHHOBWe peMHH
C 06ePTKoii 60KOBYX
rpaHeii H Y30M
Ce1feHHeM
fpyHTOyruIOTIDIIOIUee o6opy- DeTOHOMeWaJIKH
,u;OBaHHe
H3MeJlbqHTeJlH 6YMarH
npHMeHeHHe Ha
nO,u;3eMHbIX pa60Tax
POTaU;HOHHbIe neqaTHbIe Ma-
WHHbI
CHCTeMbI aBapHHHOrO pe3ep-
BHpOBaHIDI
lIInH<pOBaJIbHbIe CTaHKH
npHBO,u;bI KOHBeHepa
MeXaHWIeCKHe npHBO,u;bI
DOJlbWHe 6bITOBbIe npH60pbI
MaJIbIe 6bITOBbIe npH60pbI MHKCepbI
,LJ;epeBoo6pa6aTbIBalOIUee o6opy,u;OBaHHe C'rpOraJIbHbIe CTaHKH
06pa6oTKa pe3HHbI H nrraCTHKa
Cpe,u;CTBa nepe,u;BIDKeHIDI
KOMnpeCCOpbI
3KC'rpy,u;epbI
BCnOMOraTeJlbHbIe Cpe,u;CTBa
nOpWHeBbIe KOMnpeCCOpbI
CeJlbCKOX03HHCTBeHHoe o6opy,u;OBaHHe B03,l(yXO,u;yBKH
MOTOI.J:HKJlbI
DyMaro,u;eJlaTeJlbHbIe MaWHHbI
HaCOCbI
06opy,u;OBaHHe .nIDI yxo,u;a 3a ra30HaMH
TeKCTHJIbHOe 060pO,u;yBaHHe
BeHTH.JUITOpbI
,LJ;BHraTeJlH BJIyTpeHHerO CrOpaHIDI
MeTaJlJIOo6pa6aTbIBalOIUHe CTaHKH
H3MeJlbqHTeJlH/llIJIH<p 0BaJIb IUHKH
CymHJIbHbIe 6apa6aHbI
Pa,nHaJIbHO-OCeBbIe HaCOCbI
QHJIHH.npWIeCKHe CymHJIbHbIe
annapaTbI
OCeBbIe BeHTH.JUITOpbI
BCnOMOraTeJlbHbIe MeXaHH3MbI
TOKapHbIe CTaHKH
P336paCbIBaTeJlH
peMeHHblX nepeASII
MULTIFLE
KJDIIIOBWe peMHH C ooepTKoii
6oKoBhIX rpaHeii H KJlaCCll'lecKHM
Ce1feHHeM
Y,napHbIe ,u;P06HJUlli
npHMeHeHHe Ha nO,u;3eMHbIX
pa60Tax
BapHaTopbI
KOBWOBbIe KOHBeUepbI
MeXamrqeCKHe npHBO,u;bI
npHcnoco6J1eHIDI .nIDI no,u;'be-
Ma CBeKJIbI (B npOH3BO,u;CTBe
caxapa)
11-3255
CONTI-V MULTIRIB@
nOJIHKJIHHOBWe
peMHH
VARIDUR@-Z
3y01faTble 6e3 OOOpnot 6oKoBhIX
rpaHeii BapHaropHlde peMHH
<l>paHKHpOBaJIbHabIe MaWHHbI KOMnaKTHbIe 6JIOKH
O<pceTHbIe neqaTHbIe MaWHHbI MHOrOI.J:BeTHbIe O<pCeTHbIe
neqaTHbIe MallIHHbI
PyqHbIe py6aHKH
MeXaHH3M ,u;BepeU JIH<pTa
CTlipaJIbHbIe MaWHHbI
nOJlOrepbI
<l>pe3epHbIe CTaHKH
BcnOMOrareJlbHbIe Cpe,lJ;CTBa
PeryJlHPYIOIUHe nOJlHCnaCTbI
MOJlOTHJlbHbIe 6apa6aHbI
ABToMaTWIeCKHe nepe,u;aqH
npHBO,nbIraJOHOKOCHJlOK
HaMOTO'tJHbIe MeXaHH3MbI
BcnOMOrareJlbHbIe MeXaHH3MbI
fJlaBHbIe npHBO,u;bI CTaHKa TOKapHbIe CTaHKH
(WnHH,lJ;eIDI)
illpe,u;epbI
C Dla8a 5. MexaHu'IecICue nepeiJa'lu
OKOHllaHue
npHMeHeHHe
VARIFLEX@-Z
3y01faThie
BapHaropllWe
peMHH
SYNCHROBELT* H
SYNCHROFORCE*
npHBO;nlLle peMHH
BhI,l1ep1KllB8lODOIe BhlCOKHe
MOMeHTlIWe HarpY3KH
SYNCHROBELT*
clUIXpOllHhle
DpHBO,lUlhle
peMHH
O<pHCHoe o6oPy,u;oBaHHe
06pa6oTKa ,u;aHHbIX
Pe.nyKTOphI peryJlHpYJOIUHe
CKOpOCTb
<l>oToKonHpOBanbHbIe
YC'rpoHcTBa
llpHHTepbI
llHmyuIHe MaWHHKH
llJIOTIepbI
lleqaTHoe o6oPy,u;oBaHHe
MaWHHbI ,nmI POTaUHoHHbIe
BbICOKOH neqaTH HhIe MaJ.IIHHbI
neqaT-
3J1eKTP eCKHe HHC'rpY-
MeHTbI
KHHOnpOeKTOpbI
KOHBeHepHWI ,u;OCTaBKa
JIeHTOqHO-llIJIH<P0Ba-
JlbHbIe CTaHKH
"PHBO,u;bI nepeMO-
TOqHOrO YC'rpOHCTBa
CHCTeMbI ynpaBJIe-
HIDI no,u;'beMOM
DbITOBbIe npHJIOXeHIDI MexaH eCKHe IUeT-
06oPy,u;oBaHHe ,nmI coe- KH
,u;HHeHIDI CKJleHBaHHeM "PHBO,u;hI ICyJlaqKO-
"PHBO,u;bI ICyJlaqKOBOrO Born HJlH pacnpe,ne-
HJlH pacnpe,u;eJlHTeJlb- JlHTeJlbHOrO Bana
Horo Bana II pHBO,u; neTJlHTeJUI
PyqHbIe Py6aHKH
llpOMbIllIJIeHHbIe npHBo,u;bI PeryJlHPYIOIUHe
ManbIe 6bITOBbIe npH60pbI nOJlHCnaCTbI
,LJ;epeBoo6pa6aTbIBalOIUee
o6opy,u;OBaHHe
Cpe,u;CTBa nepe,u;BIDKeHIDI
llIBeHHbIe MaWHHbI
06opy,u;OBaHHe .nIDI yxo,u;a 3a
raJOHaMH
Po60TOTeXHHKa
TeKCTHJIbHOe o6opy,u;OBaHHe
BeHTHIDlTopbI
,LJ;BHraTeJlH BHYTPeHHero
cropaHIDI
YnaKOBOqHbIe MaWHHbI
MeTaJlJIOo6pa6aTbIBalOIUHe
CTaHKH
KYJl bTH BaropbI
llPHBO,n n03HI.J:HOHHpO- llpHBO,u; n03HUHOHH-
BaHIDI pOBaHIDI
TKaI.J:KHe CTaHKH
fJlaBHbIH npHBO.n llpHBO.nbI ICyJlaqKO-
"PHBO,u;bI ICyJlaqKOBOrO Boro HJlH pacnpe,ne-
HJIH pacnpe,neJlHTeJlb- JlHTeJlbHOrO Bana
Horo Bana CqeTHbIe YC'rpOHCTBa
llpHBO,u; MexaHWIeCKOH
no,u;aqH
Bce .naHHbIe rrpe.nOCTaBJleHbI KOMrraHHeH ContiTech P.T.S. Ltd, C TeXHHqeCKH-
MH rry6J1HKaIJ;IDIMH KOTOpOH MOXHO 03HaKOMHTCR ,l(.IDI rroJlyqeHIDI rrOJlHOrO rrepe-
qIDI H3.neJlHH, rrpHMeHeHHH H TeXHINeCKHX .naHHbIX. (BoJlee rrOJlHyK> HH<popMaIJ;HIO
CMOTPH B rrpHJIOXeHHH 3.)
llpUMeltaHue. CONTICORD@ IUIOCKHe peMHH H CON-FLEX@ rrpHBo.nHbIe
peMHH 60Jlbme He rrpOH3BO,lUlTCR.
5.2. MexaHu ec"ue nepeoa'lu: peMeHHble nepeoa u 32
5.2.5. ULTRAFLEX(I) IUJIAHOBble peMHIA C o6epTKoR
60KOBbiX rpsHeR IA Y3KlAM CelleHlAeM
.
b o
..
b o
...
bw
...
1 4
I
I
bw
.1
I
I
.--r---
----
I
-1
.----t---
I
I
I
I
-::--1
.c:
.c:
DIN CHMBOJI SPZ SPA SPB SPC 19
Ce1feHHe peMHJI
BS/ISO CHMBOJI SPZ SPA SPB SPC -
illHpHHa 60JlbllierO OCHOBaHIDI peMIDI ho MM 9,7 12,7 16,3 22 18,6
PaCqeTHasI lliHpHHa peMIDI bw MM 8,5 11 14 19 16
illHpHHa MeHblliero OCHOBaHIDI peMIDI hu MM 4 5,6 7,1 9,3 8
BbIcoTa peMIDI h MM 8 10 13 18 15
BbIcoTa peMIDI Ha,L( paCqeTHOH llilipHHOH hw MM 2 2,8 3,5 4,8 4
PaCqeTHbIH MHH. ,lJ;HaMe'rp lliKHBa d WMHH MM 63 90 140 224 180
MaKc. qaCTOTa H3rn6a !BMaKc j) B ceK)'II.nY 100 100 100 100 100
/
MaKc. CKOpOCTb peMIDI V MaKc M/C 40 40 40 40 40
Macca Ha Me'rp KI/M 0,073 0,100 0,178 0,380 0,360
Hana30H paCqeTHbIX MHHbI Lw:
Or MM 512 647 1250 2000 1175
)];0 MM 3550 4500 8000 1225 5000
0
BeJlI[qHHa OTKJIOHeHIDI MHHbI OT Lw: MM 13 18 22 30 25
AL = La - Lw
ULTRAFLEX@ KJIHHOBbIe peMHH C o6epTKoH 60KOBbIX rpaHeH H Y3KHM ceqe-
HHeM, cooTBeTcTByK>IIJ;He BS 3790 H CTaH,napTY DIN 7753 qacTb 1, BocTPe6oBaHbI
BO Bcex 06JIaCTRX MaillHHOCTPoeHIDI. OHH rr03BOlliIIOT rrepe.naBaTb 60JlbillHe MOIIJ;-
HOCTH, 3KOHOMHQeCKH 3<p<peKTHBHbI H 06J1ana1OT 60JIbillHM 3KcrmyaTaIJ;HOHHbIM
pecypCOM.
rAa8a 5. MexaHu'IeclCue nepeiJa'lu
5.2.6. FO(j)-Z MO Hble 3y6l1aTble KnJfHOBble peMHJf
6e3 06epTKJf 60KOBblX rpaHeH
b o b o
bw ! I . bw ..I
I I
.t! I
1
.c: .c::
-t!-
b u
DIN CHMBOJI 5 6 SPZ SPA SPB
Ce1feHHe peMHJI
BS/ISO CHMBOJI - Y SPZ SPA SPB
llIHpHHa 60JIbwero OCHOBaHIDI peMIDI ho MM 5 6 10 13 16,3
PaCqeTHWI WHpHHa peMIDI hw MM 4,2 53 8,5 11 14
BbICOTa peMIDI h MM 3 4 8 9 13
BbIcoTa peMIDI Han paCqeTHOH WHpHHOH hw MM 1,3 16 2 28 35
PaCqeTHbIH MHH. )];HaMe'rp WKHBa d WMHH MM 16 20 50 63 100
MaKc. qaCTOTa H3rn6afBMaKC B ceK)'II.nY 120 120 120 120 120
MaKc. CKOpOCTb peMIDI V MaKc M/C 50 50 50 50 50
Macca Ha Me'rp KI/M 0,015 0,023 0,073 0, 100 0,178
,lJ;Hana30H paCqeTHbIX MHHbI Lw:
OT MM 171 295 590 590 1250
)];0 MM 611 865 3550 3550 3550
BeJlH'lHHa OTKJlOHeHIDI MHHbI OT Lw: MM 11 15 - - -
AL = La - Lw
FO@-Z MOIIJ;HbIe 3y6qaTbIe KJIHHOBbIe peMHH rrpOH3BO,lUlTCR 6e3 o6epTKH 60KO-
BbIX rpaHeH H ,l(orrOJlIDIIOT rrpoBepeHHbIH accopTHMeHT Bcex KJIHHOBbIX peMHeit
CONTI@. I1x pa3MepbI KaK KJIHHOBbIX peMHeH C Y3KHM CeqeHHeM cooTBeTcTByJOT
CTaH,napTaM DIN 7753 qacTb 1 H BS 3790, a KaK CTaH,napTHbIX KJIHHOBbIX peM-
HeH - CTaH,napTaM DIN 2215 H BS 3790.
5.2. MeXaHUy,ecKue nepeoay,u: peMeH":ble nepeoay,u 32
5.2. 7. MUL TIFLEXfI) KnIAHOBble peMHIA C o6epTKoR
60KOBblX rpBHeR H KnBCClAlleCKHM celleHHeM
b o
b o
..c:
bw
bw
.
--T
I
--T--
.c:
b u
DIN 8 10 13 17 20 22 25 32 40
CHMBOJI
Ce1feHHe peMU
BS/ISO - z A B - C - D E
CHMBOJI
illHpHHa 60JIbWerO OCHOBa- MM 8 10 13- 17 20 22 25 32 40
HID! peMIDI ho ::=:
PaCqeTHasI IIIHpHHa peMIDI hw MM 6,7 8,5 11 14 17 19 21 27 32
illHpHHa MeHbwero OCHOBa- MM 4,6 5,9 7,5 9,4 11,4 12,4 14 183 228
HID! peMIDI hu::=: I
BbICOTa peMIDI h i 6 16
MM 1/ 5 8 11 125 14 20 25
BbIcoTa peMIDI Ha,L( paCqeT- MM 2 2,5 3,3 4,2 4,8 5,7 6,3 8,1 12
HOB WHpHHOB hw
PaCqeTHbIB MHH. ,lJ;HaMe'rp MM 40 50 80 125 160 200 250 355 500
illKHBa d WMHH
MaKc. qaCTOTa H3rn6a B ce- 60 60 60 60 60 60 60 60 60
faMaKc K)1II.nY
MaKC. CKOpOCTb peMIDI M/C 30 30 30 30 30 30 30 30 30
V MaKC
Macca Ha Me'rp KI/M 0,040 0,060 0,105 0,170 0240 0300 0,430 0,630 0,970
)];HanaJoH paCqeTHbIX MHHbI
Lw: MM 160 375 400 615 900 1150 1400 2080 5080
Or
,LJ;o MM 1250 2500 5000 8763 8000 8000 9000 13460 11280
BeJlWIHHa OTKJIOHeHIDI MH- MM 19 22 30 43 48 52 61 75 82
HbI OT Lw: AL = La - Lw
MUL TIFLEX* KJIHHOBbIe peMHH C o6epTKoH 60KOBbIX rpaHeH H KJIaCCINeCKHM
CeqeHHeM, cooTBeTcTByroIIJ;He BS 3790 H CTaH,napTY DIN 2215, pa3pa6oTaHbI ,lWI
JIIo6bIX rrpOMbIII1JIeHHbIX rrpHMeHeHHH OT BbICOKOTOqHOH HIDKeHepHH .no TIDKeJlOrO
MamHHOCTPoeHIDI.
rAa8a 5. MexaHU'IecKue nepeiJa'lu
5.2.8. MULT/BELT MHorOPY"beBble KnIAHOBble peMHIA
f>
Pa3Mepbl peMH.R
MHoropyqbeBbIe KJIHHOBbIe peMHH MUL TIBEL T <pOpMHPYI<>T rrpHBO.n;, COqeTa-
IOIIJ;HH B ce6e rrpeHMYIIJ;eCTBa e.n;HHCTBeHHoro peMIDI C YBeJlHqeHHeM rrepe.n;aBaeMoH
MOIIJ;HOCTH 6J1aro.n;apR MHorOKaHaBOqHbIM mKHBaM AID! KJIHHOBbIX peMHeH. 3TOT
rrpHBO.n; rrOMoraeT pemHTb Te rrp06J1eMbI, CBR3aHHbIe C rrpHBo.n;aMH, KOTopbIe rrpex-
.n;e rrpHBo.n;HJIH K 3aMeTHbIM 3aTPaTaM rrpH KOHCTPYHpOBaHHH.
Pa3MepHbIe ,lJ;aHHbIe
DIN/ISO 9J SPA 15J 17/B 19 SPC
CHMBOJI
Ce1feHHe peMHJI
RMAjASAE 3V - 5V BIBB - -
CHMBOJI
llIHpHHa npo<pHIDI BBepxy ho :=:: MM 9 12,5 15 16 19 22
BbICOTa peMIDI h MM 11 12 15 13 21 23
PaccToHHHe Me OCHMH pe6ep, e MM 10,3 15 17,5 19,05 22 25,5
PaCqeTHbIH MHH. ,lJ;HaMe'rp WKHBa deMuH MM 67 95,6 180 100 188 265
MaKC. qaCTOTa H3fH6a/BMaKc B ceK:YJI.nY 60 60 60 60 60 60
MaKC. CKOpOCTb peMIDI V MaKc M/C 30 30 30 30 30 30
Macca Ha KaHaBKY Ha Me'rp KI/M 0,115 0,170 0,250 0,240 0,405 0,505
L'(HanaJOH paCqeTHbIX MHH Lw:
OT MM 750 1350 1350 1350 2500 2500
,lJ;O MM 2800 2800 5600 5600 5600 5600
BeJlWIHHa OTKJlOHeHIUI ,lLJIHHbI OT Lw: * - * - - -
-
AL = La - L; MM - - - 62
AL = La - Lw MM - 18 - - 25 30
* HCXO,lJ;HWI MHHa La HBJlHeTCH onpe.neIDIeMOH MHHOH .nIDI pa3,lJ;eJlOB 9J H 15J.
5.2. MexaHulfeclCue nepeiJalfu: pe.MeHHble nepeiJalfu 3
5.2.9. WKIASbl KnlfHOBblX peMHeH, COOTseTCTSYIO lAe
CTaHAapTBM BS 3790 IA DIN 2211
Anfl peMHeH FO(j)-Z If UL TRAFLEX(j).
Rz xx o603HallaeT wepoxosaTOCTb nosepXHOCTIf
OAHOKaHaBOYHbl
WK B
MHorOKaHaBOYHbl WK B
3aKpyrneHHbie
yrnbl (KpOMK )
,J
8
N
It
N
It
I Ce1feHHe peMHJI
DIN 7753 1faCTh 1 DIN CHMBOJI SPZ SPA SPB SPC 19
BS 3790 BS/ISO CHMBOJI SPZ SPA SPB SPC -
DIN 2215 DIN CHMBOJI 10 13 17 22 -
BS 3790 BS/ISO CHMBOJI z A B C -
PaCqeTHWI wHpHHa KaHaBKH bw 8,5 11 14 19 16
I
, illHpHHa KaHaBKH BBepxy bl 9,7 12,7 16,3 22 18,6
I
C j 2 2,8 3,5 4,8 4
Ij
llapaMe'rpbI KaHaBKH e 12:to.3 15:to.3 19:tO.4 25,5:to.5 22:to.4
f 8:t:O.6 IO:tO.6 12,5:to.8 17:tt 14,5:tO.8
fJIy6HHa KaHaBKH HIDKe t 11 +0,6 14 +0,6 18+ 0 ,6 24 +0,6 20+ 0 ,6
paCqeTHOH WHpHHbI 0 0 0 0 0
34 d w 80 118 190 315 250
x "PH paCqeTHOM
38 >80 >118 >190 >315 >250
,lJ;HaMe'rpe WKHBa
OnyCK ,nmI yrJla KaHaBKH :f:l° :f:l° :f:l° :f:0,5° :f:l°
a = 34-38
illHpHHa WKHBa b2 "PH 1 16 20 25 34 29
'IHCJle KaHaBOK z: 2 28 35 44 59,5 51
b2 = (z - l)e + 21
3 40 50 63 85 73
4 52 65 82 110,5 95
5 64 80 101 136 117
6 76 95 120 161,5 139
7 88 110 139 187 161
(3,necb H ,lJ;anee: a - yroJl 8 100 125 158 212,5 183
KaHaBKH WKHBa, 1 - pac- 9 112 140 177 238 205
croHHHe Me OCblO KpaH- 10 ' 124 155 196 263,5 227
HeR KaHaBKH H 6J1IDKaHWHM
roPU:OM WKHBa. - llpUMey,. 11 136 170 215 289 249
nep. ) 12 148 185 234 314,5 271
Dla8a 5. MexaHulfeclCue nepeoalfu
5.2.10. WKIABbl KnJfHOBblX peMHeH, cooTBeTcTBYIO lAe
cTaHAapTY DIN 2217 '1acTb 1 Anfl peMHeR
FO@-Z IA MUL TIFLEX@
OAHOKaHaBO"iHbl
WK B
3aKpyrneHHbie
yrnbl (KpOMK )
II:
MHorOKaHaBO"iHblt1 WK B
b 2
Ce'leHHe peMHJI
DIN
DIN 2215:* CHMBOJI 5 6 (8) 10 13 17 (20) 22 (25) 32 40
BS/ISO - Y - Z A B - C - D E
CHMBOJI
AATepHaTHBHoe BS/ISO
Ce'leHHe (DIN 2211 - - - SPZ SPA SPB - SPC - - -
qaCTh 1) BS 3790 CHMBOJI
PaCqeTHasI wHpHHa bw 4,2 5,3 6,7 8,5 11 14 17 19 21 27 32
KaHaBKH
IIIHpHHa KaHaBKH bl 5 6,3 8 20 25 32 40
BBepxy
C 1,3 1;6 2 5,1 6,3 8,1 12
napaMeTPbI KaHaBKH e 6:1:0.3 8:1:0.3 10:1:0.1 23:1:0.4 29::1::0.5 37:1::0.6 44,5:1::0.1
f 5:1:0.5 6:1::0.5 7 :1:0.6 15::1::0.& 19:1::1 24:1::2 29:1::2
f.rry6HHa KaHaBKH t 6+0,6 7+0,6 9+0,6 18+0,6 22+0,6 28 +0,6 33+0,6
0 0 0 0 0 0 0
HIDKe paCqeTHOH
WHpHHbI
32
34 npH pacqer -
x HOM ,u;HaMe'rpe d w 50 63 75 - - - -
36 - - - 250 355 - -
WKHBa >50 >63 75 500 630
38 - -
- - - >250 >355 >500 >630
,LJ;OrryCK .nIDI yrJla :t:l :t:l :t:l :t:l 30° :1:30 0 :t:30°
KaHaBKH a = 34-38
IIIHpHHa WKHBa b2 1 10 12 14 30 38 48 58
npH qHCJle KaHaBOK 2 16 20 24 53 67 85 102,5
z: b2 = (z - l)e + 2 3 22 28 34 76 96 122 147
4 28 36 44 99 125 159 191,5
5 34 44 54 122 154 196 236
6 40 52 64 145 183 233 280,5
7 60 74 168 212 270 325
8 84 191 241 307 369 5
9 214 270 344 414
10 237 299 381 458,5
11 260 328 418 503
12 283 357 455 547,5
* 3HaqeHIDI B cKo6Kax He CJle,u;yeT HCnOJlb30BaTb B HOBbIX pa3pa6oTKax.
5.2. MexaHUy,eCKue nepeoay,u: peMeHHble nepeoay,u 329
5.2. 11. WKIABbl C rny60KlAMIA KBHBBK8MJf
MHorOKaHaBO'"lHbl WK""B
) C)
(
\
r
3aKpyrneHH ,J
yrnbl (KpOMK
8
8
rr:."
Ce1feHHe peMHJI
DIN 7753 qaCTh 1 DIN CHMBOJI SPZ SPA SPB SPC 19
BS 3790 BS/ISO CHMBOJI SPZ SPA SPB SPC -
DIN 2215 DIN CHMBOJI 10 13 17 22 -
BS 3790 BS/ISO CHMBOJI z A B C -
PaCqeTHWI WHpHHa KaHaBKH bw 8,5 11 14 19 16
YBeJlWIeHHWI WHpHHa KaHaBKH (X, = 34° 11 15 18,9 26,3 22,1
BBepxv b 1 (X, = 38° 11,3 15,4 19,5 27,3 22,9
J 4 6,5 8 12 10
C /
fIapaMeTPbI KaHaBKH e 14+0 l 18+0 l 23+0 4 31+0 27 +0 "
f 9+0 (\ 11,5+0 (\ 14,5+0 R 20+1 17+1
YBeJlHtIeHHWI r.rry6HHa KaHaBKH t MHH 13 18 22,5 31,5 26
HIDKe paCqeTHOH WHpHHbI
34° npH paCqeTHOM ,nHaMeTpe
a 63-80 90-118 140-190 224-315 180-250
38° llIKHBa d w c peMIDIMH
tDIN 7753 1 H BS 3790 >80 >118 >190 >315 >250
34° npH paCqeTHOM ,[(HaMeTpe
a 50-80 71-118 112-190 180-315 -
38° WKHBa d w c peMIDIMH
DIN 2215 H BS 3790 >80 >118 >190 >315 >250
onycK .nIDI yrJla KaHaBKH :1:1 ° :1:1° :1:1 0 :1:0,5° :1:1 °
a = 34°-38°
IDHpHHa WKHBa b2 npIDI tIHCJIe 1 18 23 29 40 34
KaHaBOK z: b2 = (z - l)e + 2f 2 32 41 52 71 61
3 46 59 75 102 88
4 60 77 98 133 115
5 74 , ) 95 121 164 142
6 88 113 144 195 169
7 102 131 167 226 196
8 116 149 190 257 223
9 130 167 213 288 250
10 144 185 236 319 277
11 158 203 259 350 304
12 172 221 282 381 331
CJle,nyeT CTporo npH.nepXHBaTbCH MHHHMaJIbHOrO ,nHaMeTpa WKHBa. He HCnOJIb30BaTb
.nmI MHoropyqbeBbIx KJIHHOBbIX peMHeH.
330 rAa8a 5. MexaHu"tecKue nepeiJa"tu
5.2. 12. CHHXpoHHb,e peMeHHwe nepe,qalfH: BBe,qeHHe
CHHXpOHHbIe (3y6qaTbIe) peMeHHbIe nepe,n;aqH B HaCTOj)J.u;ee BpeMH mHpOKO HC-
nOJIb3YJOTCH BO MHorHX npHJIOXeHJUlX BMeCTO TPanH HOHHbIX, enHbIX pOJIHKOBO-
BHHTOBbIX nepe,n;aq. B OTJIWlHe OT nrrOCKHX HJIH KJIHHOBbIX peMHeH, 3y6qaTbIH pe-
MeHb He npOCKarrb3bIBaeT H n03TOMY MoxeT HCnOJIb30BaTbCH TaM, r,n;e BpaI.u;eHHe
BXO,n;HbIX (Be HX) H BbIXO,n;HbIX (Be,n;OMbIX) 3JIeMeHTOB CHCTeMbI Bcer,n;a ,n;OJDKHO
6bITb CHHXpOHH3HpOBaHO.
fJIaBHbIe npeH ecma CHHXPOHHbIX peMeHHbIX npHBo,n;OB no cpaBHeHHIO C
TpanH HOHHbIMH pOJIHKOBO- BHHTOBbIMH enHbIMH nepe,n;aqaMH CJIe I.u;He.
1. Cyn:(ecTBeHHo 60JIee HH3KWI CTOHMOCTb.
2. MarrOmYMHbIH Xo,n;.
3. B03MO)I{HOCTb <PYllKI.J:HOHHpOBaHJUI BO BHemHHX YCJIOBJUlX, KOTopbIe 6bIJIH
6bI He6JIarOnpHHTHbIMH u;enHbIX pOJIHKOBO-BHHTOBbIX nepe,n;aq.
4. OTcyrcTBHe He06xo,n;HMOCTH CMa3KH nepe,n;aqH.
5. MaTepHaJI 3JIaCTOMepa, H3 KOToporo H3rOTOBJIeHbI peMHH, B 60JIbmeH CTene-
HH norJIOI.u;aeT KOJIe6aHHH, qeM nepe,n;aeT HX.
CHHXpoHHbIe peMHH HaxO,nRT npHMeHeHHe TaM, r,n;e BocTPe60BaHbI HX oco6LIe
CBOHCTBa. HanpHMep:
1. O<pHcHoe 060py,n;oBaHHe, r,n;e BIDKHbI Marro
CMa3KH.
2. 060pY,lJ;OBaHHe J(IDI npOH3Bo,n;CTBa nHI.u;eBbIX npo TOB, r,n;e 06bIqHWI CMa3-
Ka, He06xo,n;HMWI enHbIX nepe,n;aq, MOrJIa 6bI HcnopTHTb 06pa6aTbIBaeMLIe
nHI.u;eBbIe npO,lJ;yJ(TbI.
3. TIpHBO,n; pacnpe,n;eJIHTeJIbHOrO Barra B aBTOM06HJUIX, r,n;e Tpe6YJOTCH CHHXPOH-
HOCTb, HanexHOCTb, OTCyrcTBHe CMa3KH, a TaIOKe 6ec HbIH H nrraBHbIH XO,lJ;.
4. COBO HOCTb marOBbIX ,n;BHraTeJIeH H cepBonpHBo,n;OB no,n;aIOI.u;HX MexaHH3-
MOB B ynpaBJIHeMbIX KOMnbIOTepaMH MeXaHHqeCKHX CTaHKax, r,n;e TPe6yJOTCH CHH-
XpOHHOCTb, Hane)I{HOCTb, 6e3BH6pa HOHHbIH H nrraBHbIH XO,lJ;.
CJIe,lJ;YJOIUHe Ta6JIH bI ,n;aHHbIX no 3y6qaTbIM peMIDIM H COOTBeTCTBYJOI.u;HM HM
3y6qaTbIM IllKHBaM BbI6paHbI TaK, qT06bI OKa3aTb nOMOI.u;b npH pa3pa60TKe CHH-
XpOHHbIX peMeHHbIX nepe,n;aq.
u
HbIH XO,lJ; H OTcyrcTBHe
KOBCTp
OCHOBa 1113 nOJ1I11XllOpOnpeHa
KOPAbl 1113 CTeKnOBonOKHa
3y6b 1113 nOJ1I11XllOpOnpeHa
BHeWHII1H cnOH nOnll1aMII1AHOH TKaH
CHHXpOHHbIe (3y6qaTbIe) peMHH COCTOHT H3:
. 110JIHXJIOpOnpeHOBbIX 3y6beB H OCHOBbI,
u
e Hapyx<:Horo nOKpbITHSI H3 nOJIHaMHAHOH TKaHH,
e KOp,lJ;OB H3 CTeKJIOBOJIOKHa.
5.2. MexauUlI,eCKUe nepeiJolI,u: peMeUUble nepeiJolI,u 331
DOJIHXJIoponpeHOBwe 3y6.B H OCHOBa
3y6b.Sl H OCHOBa peMIDI H3rOTOBJIeHbI H3 cnoc06Horo BbI,Z(ep)l{JfBaTb BbICOKHe
HarpY3KH OCHOBaHHoro Ha nOJIHXJIOpOnpeHe 3JIaCTOMepa, xeCTKO coe,nHHeHHoro C
3JIeMeHTOM, pa60TaIOm;HM Ha paCTIDKeHHe, H TKaHbIO Hap oro nOKphITWI.
Hap oe nOKpYTHe H3 nOJiHaMH)Uloi maHU
I
Ha.n:e:>KHaH H ,nOJIrOBeqHaH 3am;HTa 3y6beB I BWKHoe YCJIOBHe .nmI nrraBHOH pa60-
ThI H ,lJ)IHTeJIbHOrO cpOKa C 6bI peMIDI. TaKWI 3am;HTa 06eCneqHBaeTC.SI HCnOJIb30-
BaHHeM nrroTHoH, H3HOCOYCTOittlHBOH TKaHH C HH3KHM K03<1><I>HI.J;HeHTOM TPeHWI.
Kop.lUtl H3 CTeKJIOBOJlOKHa
CHHXpoHHbIe npHBo,n;bI Tpe6YJOT OT peMHeH MaKCHMaJIbHOH cTa6HJIbHOCTH no
,lUIHHe H npOqHOCTH Ha paCTIDKeHHe. 3THM TPe60BaHWlM OnTHMaJIbHO y,n;OBJIeTBO-
pHIOT MaJIOpaCTIDKHMbIe KOp,nbI H3 CTeKJIOBOJIOKHa, CnHpaJIbHO npOJIOXeHHbIe no
BceR lliHpHHe peMIDI. IIonepeqHoe CMem;eHHe MHHHMH3HpOBaHO 6J1aro,n;apH HC-
nOJIb30BaHHIO KOp,n;OB, COCTO.Slm;HX H3 ,n;BYX OB, cKpyqeHHbIx H3 CTeKJIOBOJIOKHa
B npOTHBOnOJIO:>KHbIX HanpaBJIeHWlX
Csoiiem SQ
nOCToBHHaB yrJlOBaJI CKOpOCT. H paBHOMepHaB nepe,lJ.aqa CKOpoCTH
IIpHMepHo TaK xe, KaK 3y6b.Sl 3y6qaTOrO KOJIeCa, 3y6bH peMIDI 06pa3YJOT np.Sl-
Moe CI.J;enrreHHe C npOMe KaMH Me)KJ(y 3y6b.SlMH «conpIDKeHHoro» lliKHBa. IIpHH-
nm nepe,n;aqH C npHMbIM coe,n;HHeHHeM 06eCneqHBaeT CHHXpOHHOCTb pa60TbI H
nOCTO.SlHHYJO CKOpOCTb ,nBIDKeHWI no OKp OCTH.
OTCYTCTBHe CBJIhHOro HaTJDKeHIUI -
npHHI.J;Hn KOHCTp HH 3y6beB TPe6yeT OqeHb He60JIblliOrO HaTIDKeHWI peMIDI,
H, CJIe,n;OBaTeJIbHO, HarpY3Ka Ha BMbI H n WHrrHHKH CBO,n;HTC.SI K MHHHMYMY.
nepe,lJ.aqa 60JIhmoi MOIQIIOCTH (
IIepe,n;aqa 60JIbIllOH MOm;HOCTH rapaHTHpyeTc.SI COqeTaHHeM qpe3BbIqaHHO xe-
CTKHX 3y6beB H H3HOCOYCTOHqHBOH TKaHH, a TaIOKe BbICOKHM conpOTHBJIeHHeM K
,lJ;HHaMHqeCKHM HarpY3KaM 3JIeMeHTa, pa60TaIOm;ero Ha HarrpIDKeHHe.
))oJI.moe nepe,lJ.aTOqHOe OTHomeHHe
Ha.n:e:>KHoe <l>YHKI.J;HOHHpOBaHHe nepe,naqH ,nIDKe rrpH He60JIbIllHX ,n;yrax 06XBaTa
H MarreHbKHX ,nHaMeTpax IllKHBa ,n;OCTHraeTC.SI 6JIaro,n;ap.Sl npHMOMy CQenrreHHIO.
MHHHMaJI.Hhle Tpe60BaHHB K npOCTpaHCTBY
BbIcoKoe COnpOTHBJIeHHe K ,n;HHaMWleCKHM HarpY3KaM H cnoc06HoCTb nepe,na-
BaTh 60JIblliYJO MOm;HOCTb II03BOIDIIOT HCnOJIb30BaTb lliKHBbI C MMeHbKHMH ,nHa-
Me1paMH H KopOTKHe MexoceBbIe paCCTOHHHH. 3TO rr03BOJIHeT HIDKeHepaM pa3pa-
6aTbIBaTb 3KOHOMWlHbIe nepe,n;aqH He TOJIbKO KOMrraKTHbIe, HO H JIerKHe.
BhlCOKaB CKOpOCT. peMHB
He60JIblliHe CHJIbI HHepI.J;HH H qpe3BbIqaHHO 60JIbIllOH CpOK CJIyx6bI npH H3rH-
6e 06eCneqHBaIOT Ha.n:e)I{HOe <l>YHKI.J;HOHHpOBaHHe nepe,n;aq npH CKOpOCTHX peMIDI
BnJIOTb ,n;o 60 M/c.
MaJIO HaB pa60Ta
3JIaCTHqHaH KOHCTp WI peMIDI C nOKpbITbIMH TKaHbIO Ka OBbIMH 3y6b.Sl-
MH B COqeTaHHH C MeTaJIJIHqeCKHMH HJIH nrraCTMaCCOBbIMH lliKHBaMH,no MHHHM)'Ma
CHIDKaeT ypOBeHb a.
OTCYTCTBHe Heo6xo,lUlMOCTH B CMa3Ke H o6c BaBHH
CHHXpoHHbIe peMHH S CHROBELT@ He TPe6YJOT TeXHHqeCKOrO 06CJI -
BaHIDI. OHH He aIOTC.SI B CMa3Ke HJlH B nOBTopHOM HaTIDKeHHH. IIocToHHHoe
/
...
HaTIDKeHHe peMIDI rapaHTHpyeTcH HCnOJIb30BaHHeM B KaqeCTBe CHJIOBbIX 3JIeMeHTO
BbICOKOnpOqHbIX KOp,n:OB H3 CTeKJIOBOJIOKHa.
BhlCOKaJI 34J4JeKTHBHOCTh
fH6KWI H 3JIaCTWlHWI KOHCTP JUI peMHeH, a TaIOKe OnTHMaJIbHOe COOTBeTC'I
BHe pa3MepOB 3y6beB peMIDI C npOMe KaMH Mex.ny 3y6bHMH mKHBa ,norrycKalO
KOHCTPYlfpOBaTb rrepe,n:aqH npaKTHQeCKH 6e3 TPeHJUI, C 3<1><I>eKTHBHOCTbIO 98%.
CO I S CHROBELT@ CHUXpOHHhle npHBO)Ulhle peMHH
CONTI S CHROBELT@ CHHXpOHHbIe npHBo,n:HbIe peMHH 06JIa.n:aIOT CJIe.ny'
IOII.(HMH KaqeCTBaMH. OHH YCTOWIHBbI K:
e onpe,n:eJIeHHbIM MaCJIaM
e 030HY
. TeMrrepa e B ,n:Hana30He OT 40,n:0 1 00 °C H K TOM}' xe
. He no,nBepxeHbI BJIHHHHIO TPonH1leCKHX YCJlOBHH
u
e He CTBHTeJIbHbI K npHpo,n:HbIM B03,n:eHCTBJUlM.
Oco6eHHOCTH KOHCTp H
OnHcaHHe CHHXPOHHbIX npHBo,n:HbIX peMHeH S CHROBELT@ nOJIHOCTbIO
COOTBeTcTByeT CTaH,n:apTY, OCHOBaHHOMY Ha DIN ISO 5296, qTO 03HaqaeT:
. PaCqeTHaH ,lI)IHHa H3MepHeTCH B ,n:eCHTbIX ,n:OIDIX ,n:IOHMa.
. PaCqeTHWI ,lI)IHHa CHHxpOHHoro rrpHBo,n:Horo peMIDI paBHa ero nOJIHOH ,lI)IHHe
u u u u
no 3aM OH KpHBOH, H3MepeHHOH no ypOBHIO paCqeTHOH JIHHHH, H He H3-
MeIDIeTCH npH H3rH6aHHH peMIDI. PaCqeTHWI JIHHJUI npoxo,n:HT nOcepe,n:HHe
3JIeMeHTa, pa60TaIOII.(erO Ha paCTIDKeHHe, H MoxeT 6bITb TOqHO JIOKaJIH30Ba-
Ha TOJIbKO npH rrOMOm;H COOTBeTCTBYIOII.(eH H3MepHTeJIbHOH annapaTYpbI. DO-
JIee no,np06HO CMOTPH pa3,neJI 2.17 «M3MepeHHe ,lI)IHHbI».
. llIar 3y6beB.
. llIar 3y6beB 3TO paCCTOHHHe Me ,nBYMH coce,n:HHMH 3y6bHMH no pac-
v
qeTHOH JIHHHH.
. llIHpHHa peMIDI B COTbIX ,nOIDIX ,nIOHMa.
. IIIHpHHa peMIDI H 0603HaqaeMaH mHpHHa peMIDI MeHTWlHbI.
DpHMep
CHHXpOHHbIH rrpHBo,nHOH peMeHb S CHROBELT@ 1100 H 100
1100 ,lI)IHHa no paCqeTHOH JIHHHH 110 ,nIOHMOB 2794,0 MM
H mar 3y6beB 0,5 ,nIOHMa 12,7 MM
100 mHpHHa peMHH I,nIOHM 25,4 MM
qHCJIO 3y6beB Z 3aBHCHT OT ,lI)IHHbI no paCqeTHOH JIHHHH Lw H mara t:
Lw
z=
t
BwnycKaeMhle pa3Mephi
y
t
t
..
.r:
s
5.2. MexaHU'IeCKUe nepeiJa'lu: peMeHHble nepeiJa'lu 3
nOnepe1JHOe Ce1JeHHe CHHXpOHHOro npHBO}Uloro peMHH
IlIalu 3y6beB
CHHXpoHHbIe npHBO.ll.HbIe peMHH SYNCHROBELT@ nOCTaBJISlIOTCSI C lleCTblO
pa3MepaMH llarOB 3y6beB. OHH COOTBeTCTBYIOT DIN ISO 5296 H Mex,aYHapO.ll.HbIM
CTaH.ll.apTaM. 0603HaQeHHSI H pa3MepbI pacnpOCTpaHeHHbIX llarOB npHBe.ll.eHbI B
ra6JIHue.
HapaMempbl
DIN ISO
P83Mep 0603Ha- MXL XL L H XU XXH
'IeHHe
llIar 3y6beB t MM 2,032 5,080 9,525 12,700 22,225 31 ,750
,lUOHMbI 0,080 0,200 0,375 0,500 0,875 1,250
YroJI KJIHHa y rpa,ayCbI 40 50 40 40 40 40
TOJIIl(HHa peMHH h I MM 1,14 2,3 3,6 4,3 11,2 15,7
BblcoTa 3y6a hI MM 051 1,27 1,91 2,29 6,35 9,53
llIHpHHa 3y6a nOBepxy s MM 1 14 2,57 4,65 6,12 12,57 19,05
PanHYc 3aKpyrJIeHIDI BepxHeH MM 0,13 0,38 051 1,02 1,19 1,52
KpOMKH ra
PanHYc 3aKpyrJIeHHH yrJIa MM 0,13 0,38 051 1,02 1,57 229
BHH3Y rr
BbICOTa paCqeTHOH JIHHHH U MM 0,254 0,254 0,381 0,686 1,397 1,524
Bec (peMeHb llIHpHHOH Kr/M 0,013 0,016 0,089 0,117 0,235 0,321
25,4 MM)
L{Mana30H ,lJ)IHH no paCqeTHOH
JIMHHH Lw:
01 MM 109,73 152,40 314,33 609,60 1289,05 1778,00
.lI0 MM 920 50 1473,20 1524,00 4318,00 4445,00 4572,00
PacnpOCl'paHeHHaH IIIHpHHa b:
01 MM 3,18 6,35 12,7 19,05 50,8 50,8
.lI0 MM 6,35 25,4 76,2 127,0 177,8 127,0
UHbl
CHHXpoHHble npHBO.ll.Hble peMHH SYNCHROBEL T@ BblnycKalOTcSI C .IJ.JIHHaMH,
OXBaTbIBalOll(HMH llHpOKHH .lI.Hana30H npHJ10)l(eHHH. KpoMe Toro, peMHH co cneUH-
aJIbHbIMH ,lJ.JIHHaMH MOryr nOCTaBJISlTbCSI Ha 3aKa3. PacnpocTpaHeHHble .IJ.JIHHbI npH-
BelleHbI B Ta6JIHUax llJIR llarOB 3y6beB MXL, XL, L, H H XH B pa3.l1.eJIe 5.2.13.
IlIupuHa peMHeii
PacnpocTpaHeHHaSl lllHpHHa peMHeH npHBe.ll.eHa B Ta6JIHuaX BMeCTe C pacnpo-
CJpaHeHHbIMH .IJ.JIHHaMH. PeMHH C HepacnpocTpaHeHHoH llHpHHOH TalOKe MOryr
6blTb nOCTaBJIeHbI no Tpe60BaHHIO.
PeMHu co cneu,UtlAbHblMU xapaKmepUCmUKaMU
CHHXpoHHble npHBO.ll.Hble peMHH SYNCHROBEL T@ HMelOT CTaH.lI.apTHble
CBoHcTBa, nepe\:fHCJIeHHble B n}'HKTe 1.5. no BonpocaM HCnOJIb30BaHHSI CneUHaJIb-
HbIX THnOB peMHeH npoKoHcYJIbTHPYHTecb C HallHMH HH)I(eHepaMH.
Dla8a 5. MexaHu'tecICue nepeiJa'tu
5.2. 13. CHHXpoHHble peNleHHble nepe,qS'IH:
THnbl H pS3Mepbl peMHeR
Pa3Mep MXL
mar 3y6beB 2,032 MM (0,080 JJ;IOHMa)
PacnpoCTpue......e ,lUDIIIhI
0603Ha1leHHe ,nmma DO paC1leT- 1JHCJlO 0603Ha1leHHe ,n.r.HHa DO paC1IeT- 1JHCJlO
,lUDIIIhI Hol JIHHHH Lw (MM) 3yOheB Z ,lUDIIIhI Hol JIHHHH Lw (MM) 3yOheB Z
43,2 MXL 109,73 54 91,2 MXL 231,65 114
44,0 MXL 111,76 55 96,0 MXL* 243,84 120
44,8 MXL * 113,79 56 97,6 MXL 247,90 122
46,4 MXL* 117,86 58 98,4 MXL* 249,94 123
48,0 MXL 121,92 60 100,8 MXL 256 06 126
54,5 MXL 138,18 68 112,0 MXL* 284,48 140
56 0 MXL* 142,24 70 120,0 MXL* 304,80 150
56,8 MXL 144,27 71 132,0 MXL* 335,28 165
57,6 MXL* 146,30 72 136,0 MXL 345,44 170
60,0 MXL* 152,40 75 140,0 MXL 355,60 175
64,0 MXL * 162,56 80 144,0 MXL 36576 180
65 6 MXL* 166,62 82 147,2 MXL 37389 184
67 2 MXL 170,69 84 180,0 MXL* 457,20 225
68 0 MXL* 172,72 85 188,8 MXL* 47955 236
70 4 MXL* 178,81 88 200,8 MXL* 510,03 251
72 0 MXL 182,88 90 204,8 MXL * 520 19 256
75,2 MXL 191,01 94 238 4 MXL* 605 54 298
77 6 MXL* 197,10 97 277 6 MXL 705,10 347
80 0 MXL* 203,20 100 282,4 MXL * 71730 353
80,8 MXL* 205,23 101 292,0 MXL* 741 68 365
J
82,4 MXL* 209,30 103 320 0 MXL* 81280 400
84,0 MXL 213,36 105 347,2 MXL* 881,89 434
84 8 MXL* 215,39 106 362 4 MXL* 92050 453
88,0 MXL 223,52 110 370,4 MXL* 940 82 463
89,6 MXL* 227,58 112 398,4 MXL * 1011,94 498
90 4 MXL 229,62 113 404 0 MXL* 1026 16 505
* PeMHH Ha 3aKa3.
PacnpocrpaHeHHaH UlHpHHa
0603HaQaeMaH llIHpHHa 0,12 0,19 0,25
IllHpHHa (MM) 3,18 4,76 6,35
5.2. MexaHUy,ecKue nepeoay,u: peMeHHble nepeoay,u 335
Pa3Mep XL
llIar 3y6beB 5,080 MM (0,200 ,luoHMa)
PaCDpocTpaHeHHhle AJIHHhI
0603Ha- ,n.r.HHa DO pac- 1JHCJlO 0603Ha- ,n.r.HHa DO pac- 1JHCJlO 0603Ha- ,ltJIHHa DO pac- 1JHCJlO
qeHHe qeTIIOH JlHHHH 3y6beB qeHHe qeTIIOH JlHHHH 3y6beB qeHHe qeTIIOH JlHHHH 3y6beB
AJIIfHY Lw (MM) Z ,lUIIIIIhI Lw (MM) Z NlHHhI Lw (MM) Z
60 XL 152,40 30 156 XL* 396 24 78 280 XL* 711,20 140
70 XL 177,80 35 160 XL 406 40 80 286 XL * 726,44 143
80 XL 203,20 40 162 XL* 411,48 81 290 XL * 73660 145
86 XL * 218,44 43 168 XL* 426,72 84 296 XL * 751 84 148
90 XL 228,60 45 170 XL 431,80 85 300 XL * 762,00 150
92 XL* 233,68 46 174 XL* 441,96 87 306 XL * 777 24 153
94 XL* 238,76 47 176 XL* 447,04 88 316 XL* 802,64 158
96 XL* 243,84 48 178 XL * 452,12 89 322 XL* 817 88 161
100 XL 254,00 50 180 XL 457,20 90 330 XL* 838,20 165
'102XL* 259 08 51 182 XL* 462,28 91 340 XL * 863 60 170
106 XL* 269,24 53 184 XL" 467 36 92 344 XL * 87376 172
108 XL* 274,32 54 188 XL* 477,52 94 350 XL* 889 00 175
110 XL 279,40 55 190 XL 482 60 95 380 XL* 96520 190
112 XL* 284,48 56 196 XL* 497,82 98 382 XL* 97028 191
116 XL* 294 84 58 200 XL 508,00 100 388 XL* 98552 194
118 XL * 299,72 59 210 XL 53340 106 392 XL* 995,68 196
120 XL 304,80 60 220 XL 55880 110 412 XL* 1046,48 206
124 XL* 314,96 62 230 XL 584,20 115 414 XL* 1051,56 207
126 XL* 320,04 63 240 XL 609,60 120 438 XL* 1112,52 219
130 XL 330,20 65 244 XL * 619,76 122 460 XL * 1168,40 230
134 XL* 340,36 67 248 XL * 62992 124 498 XL * 1264,92 249
136 XL* 34544 68 250 XL 63500 125 506 XL * 1285 24 253
138 XL* 350 62 69 260 XL 660,40 130 514 XL* 1305,56 257
140 XL 355,60 70 270 XL* 68580 135 580 XL * 1473,20 290
148 XL* 37692 74 272 XL* 690,88 136 630 XL* 1600 20 315
150 XL 381 00 75 274 XL* 695,96 137
* PeMHH Ha 3aKa3.
PaCnpOCTPaHeHHaamHpHHa
0603HaQaeMasI llIHpHHa 10,25 0,31 0,37 0,50 0,75 1,00
illHpHHa (MM) 6,35\ 7,94 9,53 12,7 19,05 25,4
fJla8a 5. MexaHU'IeCKUe nepeiJa'lu
Pa3Mep L
llIar 3y6beB 9,525 MM (0,375 ,luoHMa)
9,525
.....
ot
.....
PacnpocTPaHeHHhle ,lUIIIHId I
,n.,.HHa DO pac- ,nmma DO pac- I
0603HaqeHHe 1JHCJlO 0603HaQeHHe 1JHCJlO I
I
QeTIIOH JlHHHH QeTIIOH JIHHHH I
3yOheB Z AJIHHhI 3y6heB Z I
,lUIIIHId Lw (MM) Lw (MM) I
124 L 314,33 33 322 L 819,15 86
150 L 381,00 40 345 L 876,30 92 I
187 L 476,25 50 367 L 93345 98
210 L 533,40 56 390 L 990,60 104 I
I
225 L 571,50 60 420 L 1066 80 112 !
236 L 600,70 63 450 L 1143 00 120 I
I
I
240 L 609,60 64 454 L* 1152,53 121 I
255 L 647,70 68 480 L 1219,20 128
270 L 685,80 72 510 L 1295 40 136
285 L 723,90 76 540 L 137160 144
300 L 762,00 80 600 L 1524 00 160 r
I
I
* PeMHH Ha 3aKa3.
PacllpOCTpaHeHHaJI DIHPHHa
0603HaQaeMasI WHpHHa 0,50 0,75 1,00 1,50 2,00 3,00
IIIHpHHa (MM) 12,7 19,05 25,4 38,1 50,8 76,2
5.2. MeXaHUy,eCKue nepeoay,u: peMeHHble nepeoay,u 3
Pa3Mep H
mar 3y6beB 12.700 MM (0.500 ,IUOHMOB)
I. 12,700
I
PaCDpocTpUeHHhle ,lUIIIIIW
0603Ha1leHHe ,n.r.HHa DO pac- 1JHCJlO 0603Ha1leHHe ,ltJIHHa no pac- tbtCJIO
,lUIIIIIW 1IeT110ii JIHHHH 3yOt.eB Z ,lUIIIIIW 1IeT110ii JIHHHH 3yOt.eB Z
Lw (MM) Lw (MM)
240 H 609 60 48 600 H 1524,00 120
'255 H* 647 70 51 630 H 1600 20 126
,270 H 685 80 54 660 H 1676,40 132
300 H 782,00 60 700 H 1778,00 140
330 H 838,20 66 730 H* 1854 20 146
335 H* 850,90 67 750 H 1905 00 150
360 H 91440 72 800 H 2032 00 160
370 H* 939,80 74 850 H 2159,00 170
390 H 990,60 78 900 H 2286 00 180
420 H 1066,80 84 1000 H 2540,00 200
450 H 1143,00 90 1100 H 2794,00 220
480 H 1219,20 96 1250 H 3175,00 250
510 H 1295,40 102 1400 H 3556,00 280
540 H 1371,60 108 1700 H 4318,00 340
570 H 1447,80 114
* PeMHH Ha 3aKa3.
PaCllpOCTpaHeHHaJI IDHpHHa
0603HaQaeMaH llIHpHHa 0,75 1,00 1,50 2,00 3,00 4,00 5,00
illHpHHa (MM) 19,05 25,4 38,1 50,8 76,2 101,6 127,0
Dla8a 5. MexaHU'IeCKUe nepeoa'lu
Pa3Mep XH
llIar 3y6beB 22,275 MM (0,875 ,luoHMa)
22,225
PacnpoCTpUeHHhle AJIHHhI
0603Ha1leHHe ,ltJIHHa no pac- 1JHCJlO 0603Ha1leHHe ,n.,.HHa no pac- 'IHCJlO
AJIHHhI 1IeT110H JlHHHH 3yOheB Z .zunmhl 1IeT110H JIHHHH 3yOheB Z
Lw (MM) Lw (MM)
507 XH 1289,05 58 980 XH 2489,20 112
560 XH 1422,40 64 1120XH 2844,80 128
630 XH 1600,20 72 1260XH 3200,40 144
700 XH 1778 00 80 1400XH 3556,00 160
770 XH 1955,80 88 1540XH 3911,60 176
840 XH 2133,60 96 1750XH 4445,00 200
PacnpOCTpaHeHHaJI DIHPHHa
0603HaQaeMaH llIHpHHa 2,00 3,00 4,00 5,00 6,00 7,00
IllHpHHa (MM) 50,8 76,2 101,6 127,0 152,4 177,8
Pa3Mep XXH
llIar 3y6beB 31,750 MM (1,250 ,IUOHMa)
31,750 .
D 19,05
Pacnpoc'rpaHeHHhle ,lUIIIIIhI
0603Ha1leHHe ,l\JIHHa no pac- 1JHCJlO KOA ,n.,.HHa DO pac- 1JHCJlO
,nJIHHhI 1Ie1110H JlHHHH 3y6heB Z ,nJIHHhl 1IeT110H JlHHHH 3yOheB Z
Lw (MM) Lw (MM)
700 XXH 1778,00 56 1200 XXH 3048,00 96
800 XXH 2032,00 64 1400 XXH 3556 00 112
900 XXH 2286,00 72 1600 XXH 4064,00 128
1000 XXH 2540,00 80 1800 XXH 4572,00 144
PacnpOCTpaHeHHU DlHpHHa
0603HaQaeMaH llIHpHHa 2,00 3,00 4,00 5,00
llIHpHHa (MM) 50,8 76,2 101,6 127,0
5.2. MexaHUy,eC1(,Ue nepeoay,u: peMeHHble nepeoay,u 33
5.2.14. CHHXpo",Hble peMeHHble nepe,qS'IH: WKIfBbl
, )
\ Ha.n;n:exaIUee KaqeCTBO H npaBH.1ILHbIH BbI60p mKHBOB - BIDKHeHu.me <paKTOpbI
BJIIDIIOIUHe Ha pa60Ty CHllXpOHHOH peMeHHoH nepe,naqH. llIKHBbI H3roTaBJIHBalOTCSI C
BbICOKOH roqHOCThIO H o6pa6aThIBaIOTCSI CneUHaJThHbIMH <ppe3aMH roqHO B COOTBeTCT-
BHH C KIDK,l,(bIM H3 pa3MepoB, tffO rapaHTHpyeT roqHoe CueIIJIeHHe mKHBOB C 3y6bSlMH.
llIKHBbI ,nmI CHHXpOHHbIX peMeHHbIX rrepe,naq ,nOJDKHbI H3rOTaBJIHBaTbCSI B co-
OTBeTCTBHH co crreUH<pHKaUHeH DIN ISO 5294 H MOryr 6bITb nOJIy'leHbI H3 6JIH-
:>KaitmeH K BaM <PHPMbI C 3anacaMH rOTOBOH npO,nyKUHH mKHBOB.
HeKoTopasI nOJIe3HaSI HH<popMaUIDI no mKHBaM npHBe,neHa HIDKe.
0603Ha1feHHe
llIKHBbI SYNCHROBELT@ HMeIOT CJIe,nYX>Iuee 0603HaqeHHe:
. qHCJIO 3y6beB
. qHCJIO 3y6beB BbNHCJUIeTCSI qepe3 ,n.n:HHY OKpyxHOCTH H Illar 3y6beB CJIe,nyIO-
IUHM o6pa30M:
U w 7t .d w
Z ---
- -
t t
mar 3y6heB
llIar 3y6beB - 3TO paCCTOSlHHe no OIqJyxHOCTH paCqeTHoro ,nHaMeTPa Me)l{,[(y
,l(BywI KOHTPOJIbHbIMH TOqKaMH Ha coce,nHHX 3y6bSIX. PaCqeTHbIH ,nHaMe1p 60JIbme,
qeM HaH60JIbmHH BHemHHH ,nHaMeTP IllKHBa, Ha y,nBoeHHYID BbICOT)' paCqeTHOH
JIHHHH COOTBeTCTByIOIUero peMIDI H COBna,naeT C paCqeTHOH JIHHHeH peMHSI.
mHpHHa mKHBa B COThIX OJIJIX lOiiMa
0603HaqaeMaSl mHpHHa YKa3bIBaeT Ha mHpHHY COOTBeTCTByIOIUero peMIDI.
TOqHbIe 3HaqeHIDI IllHpHHbI mKHBa H cooTBeTcTByIOIUeH eM IllHpHHbI peMIDI co,nep-
:>KaTCSI B Ta6JIHue Ha CTPaHHue 343.
UpHMep " j')
SYNCHROBELT@ mKHB 28 H 100
28 28 3y6beB
H mar 3y6beB 0,500 ,nIOHMa = 12,700 MM
100 0603HaqaeMaSI IllHpHHa 1 ,nIOMM = 25,4 MM IllHpOKHM CHHXPOHHbIM npH-
BO,nHOH peMeHb.
MaTepHaJIhI
BbI60p MaTepHaJIa 3aBHCHT OT pa3Mepa IllKHBa H nepe,naBaeMoH MOIUHOCTH.
HaH60JIee mHpOKO pacrrpOCTpaHeHbI CJIe,L(y1OIUHe MaTepHaJIbI:
. ArrIOMHHHeBbIH CIIJIaB: AlCuMgPb F 36 HJlH F 38
. CTaJIb: ST 9 S20K
. CepbIH qyryH: GG- 25
. IlrracTHK: IIoJIHaMH,LJ; 6 H 6,6, nOJIHaueTaJIb (POM), nOJIH6yrHJIeHTepe<pTaJIaT
(PBTP), nOJIHKap6oHaT
1I3MepeHHJI Bna,aHHhI Me 3y6hJlMH
CHHXpoHHbIe rrpHBo,nHbIe peMHH MOryr rro,nxo,nHTb K mKHBaM C rrpSlMbIM npo-
qnrneM 3y6beB HJlH C 3BOJIbBeHTHbIMH 3y6bSlMH. THn IllKHBa orrpe,neillIeTCSI rrpouec-
COM npOH3Bo,nCTBa H npe,nnOJIaraeMbIM rrpHMeHeHHeM.
B Ta6JIHue Ha CTPaHHue 341 npHBe,neHbI pa3MepbI Brra,nHHbI Me)l{,[(Y 3y6bSlMH AJUI
illKHBOB C rrpSlMbIM 60KaMH 3y6beB. B HaCTOSlIUee BpeMSl OHH IllHpOKO He HCrrOJIb3Y-
IOTCSI.
Dta8a 5. MexaHultecICue nepeiJaltu
qTO KacaeTCR 3y6beB C 3BOJIbBeHTHbIM rrpo<tnrneM, B 3TOM cJIyqae pa3MepbI Brra-
,nHHbI Me)l{,[(Y 3y6bRMH MOryr CIDIbHO 3aBHceTb OT ,nHaMeTpa IllKHBa; rro3ToMY ,l(lliI
orrpe,neJIeHIDI pa3MepoB Brra,nHHbI 3BOJIbBeHTHoro 3y6a CJIe,nyeT rrOJIb30BaTbCR crre-
UHaJIbHbIMH Ta6JIHuaMH. TaKHM o6pa30M, B Ta6JIHue Ha C1paHHue 342 npHBe,neHbI
pa3MepbI qepBRQHOH <ppe3b1 ,nmI IllKHBOB C 3BOJIbBeHTHbIMH 3y6bRMH.
illKHBhI c npJlMhIMH 60KaMH 3y6heB ..
Bna,aHHa c npJlMhIMH 60KaMH
Pa3MepbI B MM
0603H811eHHe MXL XL L H XII XXII
lIIar 3y6beB, t 2,032 5,080 9,525 12,700 22,225 31,750
lIIHpHHa ,LJ;Ha BIH1,lJ;HHbI 0, 84 :f:0 05 1 ,32:f:O 05 3,05:f:O 10 4, 19:f:0 13 7, 90 :f:0 15 12,17 :f:0,18
Me)K,l(y 3y6bHMH, b w , , , , ,
f.rry6HHa BIH1,lJ;HHbI 0,69 0,05 1 , 65 0,08 2,67 0 10 3,05 0 13 7 , 14 o 13 10,31 13
Me)K,l(y 3y6bHMH, hg , , , ,
Y rOJI BIH1,lJ;HHbI Me)K,l(y 4O:f:3 5O:f:3 40:1:3 4O:t:3 4O:f:3 4O:f:3
3y6bHMH Y B rpa,nycax
Pa.nHYc 3aKpyrJIeHHH 0,25 0,41 1,19 1,60 1,98 3,96
yrJIa BHH3Y r bMaKC
Pa.nHYc 3aKpyrJIeHHH o 13+ 0 ,05 o 64 +0,05 1 17+{),13 1 60 +0,13 2 39+ 0 ,13 318+0,13
BepxHeH KpOMKH rt ' 0 ' 0 ' 0 ' 0 ' 0 0
2. BbICOTa paCqeTHOH 0,508 0,508 0762 1,372 2,794 3,048
JIHHHH U
illKHBhI c 3BOJIhBeHTHhIM 3y6oM
qepBJI'IHaJl tj)pe3a ,nJIJI 3BOJIbBeHTHoro 3y6a
5.2. MexaHu",eC1(,Ue nepeda"'u: peMeHHble nepeda"'u 341
Pa3MepbI B MM
mar MXL XL L H XII XXII
illar 3y6beB t 2,032 5,080 9,525 12,700 22,225 31,750
qHCJIO 3y6beB llIKHBa I 10-23 IO 10 14-19 18 18
2 24 >19
YroJI, 06pa30BaHHbIH 60- I 56 50 40 40 40 40
KaMH 3y6a 2. B rpa,nycax 2 40 40
illHpHHa 3y6a BHH3Y hg I o 61 +0,05 I 27+0,05 3 10+0,05 4 24+ 0 ,05 7 59+0,05 II 61 +0,05
2 ' 0 ' 0 ' 0 ' 0 ' 0 , 0
o 67+ 0 ,05
, 0
BbIcOTa 3y6a h r o 64+ 0 ,05 1 40+ 0 ,05 2 13+0,05 2 59+ 0 ,05 6 88+0,05 1 0,29 0,05
, 0 ' 0 ' 0 ' 0 ' 0
P HYc 3aIq)yrJIeHIDI yrJIa 0, 3O :t:O,03 0, 61 :t:o,03 0, 86:t:o,03 1, 47 :tO 03 2,01:t:o,03 2, 69 :t:o,03
,
BHH3Y rbmax
,
P HYc 3aKpyrJIeHIDI 1 0, 23 :tO,03 0, 61 :t:003 0, 53 :t:003 1 ,04:t:o 03 1, 93 :t:o,03 2, 82 :t:o,03
BepXHeH KpOMKH 1L. , , ,
2 0, 23 :t:o,03 1,42
2. BbICOTa paCqeTHOH JIH- 0,508 0,508 0,762 1,372 2,794 3,048
HHH U MM
,lJ;OrryCK ,lUHI Bcex llIarOB 3y6beB :to,003.
illHpHHa mKHBOB
0603HaQaeMa5I IIIHpHHa, HOMHHaJIbHa5I IIIHpHHa H MHHHMaJIbHa5I IIIHpHHa 3y6b-
eB ,WUI Ill, OB C <pJIaHuaMH H 6e3 <pJIaHueB rrepeQHCJIeHbI B CJIe,nyIOm;eH Ta6JIH e.
TIpH HCnOJIb30BaHHH IllKHBOB C O,nHHM <!>JIaHueM peKoMeH)fj'eTcSI BbI6HpaTb MHHH-
MaJIbHYIO IIIHpHHY 3y6beB AJUI IllKHBOB C ,nBYMH <!>JIaHuaMH.
mHpHHhl DlKHBOB (Bee p83Mep'" B MM)
0603Ha'iaeMaaJI HOMHH8JlbHaJI MHHHM8JlhHaJi UlHpHHa 3y6heB
mar
mHpHHa IDHpHHa e c1maunaMH fie3 cl»JIauneB
I MXL 012 3,2 3,8 5,6
I 018 4,8 5,3 7,1
\
I 025 6,4 7,1 8,9
1 'XL 025 6,4 7,1 8,9
031 7,9 8,6 10,4
, 037 9,5 10,4 12,2
IH 075 19,1 20,3 24,8
I 100 25,4 26,7 31,2
150 38,1 39,4 43,9
200 50,8 52,8 57,3
300 76,2 79,0 83,5
XH 200 50,8 56,6 62,6
I 300 76,2 83,8 89,8
I 400 101,6 110,7 116,7
'XXH 200 50,8 56,6 64,1
300 76,2 83,8 91,3
400 101,6 110,7 118,2
500 127,0 137,7 145,2
1
fJl(l8a 5. MexaHu'tecICue nepeiJa'tu
,n:HaMeTphl mKHBOB
8JIee rrpHBe,neHbI paCqeTHbIH H BHeIIIHHH ,nHaMeTPbI ,l(JUI IIIKHBOB
SYNCHROBELT@, a TaIOKe KOJIlftIeCTBO 3y6beB.
IDKHBhI Synchrobelt@ (pa3Mep MXL)
OT 10 3y6beB p.,n. 6.47 MM, B.,n. 5.96 MM
,no 150 3y6beB p.,n. 97.02 MM, B.,n. 96.51
MM C rnarOM B 1 3y6
IDKHBhI Synchrobelt@ (pa3Mep XL)
OT 10 3y6beB p.,n. 16.17 MM, B.,n. 15.66
MM ,no 150 3y6beB p.,n. 242.55 MM, B.,n.
242.04 MM C IIIarOM B 1 3y6
IDKHBhI Synchrobelt@ (pa3Mep L)
OT 12 3y6beB p.,n. 36.38 MM, B.,n. 55.62
MM ,no 150 3y6beB p.,n. 454.78 MM, B.,n.
454.02 MM C rnarOM B 1 3y6
IDKHBhI Synchrobelt@ (pa3Mep H)
OT 16 3y6beB, p.,n. 64.88 MM, B.,n. 63.61\
MM ,no 150 3y6beB p.,n. 606.38 MM, B.)];.
605.01 MM C IIIarOM B 1 3y6
IDKHBhI Synchrobelt@ (pa3Mep XII)
OT 20 3y6beB, p.,n. 141.49 MM, B.)];.
138.69 MM ,no 150 3y6beB p.,n. 1061.17
MM, B.,n. 1058.37 MM C rnarOM B 1 3y6
IDKHBhI Synchrobelt@ (pa3Mep XXII)
OT 22 3y6beB, p.,n. 222.34 MM, B.)];.
219.29 MM ,no 120 3y6beB p.,n. 1212.79
MM, B.,n. 1209.71 MM C rnarOM B 1 3y6
5.2. 15. SYNCHROBEL T@ HTD KOHCTPYKl,fHR
KOPAbl 1113 CTeKJIOBOJlOKHa, I
pa60TalOIl.\Vle Ha paCTs:I)KeHVle
nOJlVlaMVlAHas:l TKaHb
nOJlVlXJlOpOnpeH
3y6MI H BepXIDISI qaCTb peMHett H3fOTOBJIeHbI H3 crroco6Horo BbJ)J:ep:X{JmaTh
60JIbIIIHe HarpY3KH, OCHOBaHHoro Ha rrOJIHXJIOpOrrpeHe 3JIaCTOMepHoro COe,lJ;HHe-
HIDI. OHH rrpeBOCXO,lJ;HO CKpeIIJIeHbI KaK C 3JIeMeHTOM, pa6OTaIOIIJ:HM Ha paCTIDKe-
HHe, TaK H C Hap)')KHbIM rrOKpbITHeM H3 TKaHH.
Ha,n;e)KHaSI H ,lJ;OJIroBeqHaSI 3aIIJ:HTa 3y6beB - BIDKHOe YCJIOBHe ,l(JUI IIJIaBHott pa-
60TbI H MHTeJIbHOro CpOKa CJIyx6bI peMHSI. TaKaSI 3aIIJ:HTa 06eCrreqHBaeTCSI rrpHMe-
HeHHeM oco6eHHO H3HOCOYCTOHqHBOH rrOJIHaMH,lI;HOH TKaHH C HH3KHM K03$$HlI;H-
eHTOM TpeHIDI.
CHHXpOHHbIe rrpHBo,nbI TPe6yroT OT peMHeH MaKCHMaJIbHOH cTa6HJIbHOCTH no
,lLJIHHe H rrpOqHOCTH Ha paCTIDKeHHe. 3THM Tpe60BaHIDIM OnTHMaJIbHO y,nOBJIeTBO-
pRIOT MaJIOpaCTIDKHMbIe KOp,nbI H3 CTeKJIOBOJIOKHa, CIIHpaJIbHO npOJIOXeHHbIe no
BceH II1HpHHe peMIDI. JII060e IIpO,nOJIbHOe nepeMem;eHHe npe,nOTBpam;aeTCR Hcno-
JIb30BaHHeM KOp,nOB, COCTORm;HX H3 ,nBYX )KIj'TOB, cKpyqeHHbIX H3 CTeKJIOBOJIOKHa B
rrpOTHBOIIOJIO)KHbIX HarrpaBJIeHIDIX.
PeMHH TaIOKe YCTOHqHBbI K ycnlJIOCTHoMy paJpYIIIeHHIO, TeMrrepaTYPHbIM H3-
MeHeHIDIM, CTapeHHIO, ,ne<l>opMa HH H IIIHPOKOMy ,nHana30HY BHernHHX YCJIOBHit
5.2. MexaHu",ecKue nepeoa",u: peMeHHble nepeda"'u 34
0603HaQeHHe
SYNCHROBELT@ HTD peMHH 0603HaqaIOTCR CJIe,nyIOInHMH xapaKTepHCTIlKaMH
PacqeTHaJl ,nJIHHa (MM). PaCqeTHaR ,lLJIHHa peMIDI paBHa ero 1I0JIHOM ,lLJIHHe lIt
3aMKHyTOH KpHBOH, H3MepeHHoH 110 ypOBHIO cpe,nHeH paCqeTHOH JIHHHH. PaCqeT
HaH JIHHIDI IIpOXO,nHT 1I0cepe,nHHe 3JIeMeHTa, pa60TalOInerO Ha paCTIDKeHHe. Toq
HaH paCqeTHaR ,lLJIHHa MoxeT 6bITb TOqHO Ollpe,neJIeHa (CMOTpH pa3,neJI 5.2.4).
mar 3y6heB (MM). llIar 3y6beB - 3TO paCCTORHHe Mex.ny ,nBYMR coce,nHHMH 3Y,
6bRMH 110 paCqeTHOH JIHHHH.
mHpHHa peMHJI (MM). llIHpHHa peMHSI H 0603HaqaeMaR IIIHpHHa peMHR H,LJ;eH-
THqHbI.
HallpHMep, peMeHb SYNCHROBELT@ HTD 960 8M 50 HMeeT paCqeTHYK
,nJIHHY 960 MM, Illar 3y6beB 8 MM, mHpHHY 50 MM.
qHCJIO 3y6beB Z 3aBHCHT OT ,lLJIHHbI 110 paCqeTHOH JIHHHH H Illara: Z = Lw/t.
BwnYCKaeMhIe pa3MephI
PeMHH SYNCHROBELT@ HTD nOCTaBJIRIOTCR C qeTbIpbMR pa3MepaMH IllaroE
3y6beB.
HTD-3M: 3 MM Illar 3y6beB
HTD-5M: 5 MM Illar 3y6beB
HTD-8M: 8 MM Illar 3y6beB
HTD-14M: 14 MM Illar 3y6beB
HTD-20M: 20 MM Illar 3y6beB
Pa3MepbI ,lLJIHHbI H III HpHHbI BbInycKaeMbIX peMHeH rrpHBe,neHbI B pa3,neJIe
5.2.11. Harra30H IllKHBOB rrpe,nCTaBJIeH B pa3,neJIe 5.2.16.
tj
"
)
5.2.16. SYNCHROBELTD> HTD CIfHXpOHHble (3y6lfsTblej
peMHIf: npocplfnlf pscnpe,qeneHIfR 3y6&es
mar 3y6heB 3 MM
--------------
12 N
TI
CTau.napTHhIe ,nJIHHhI
0603Ha1leHHe PaC1IeTllaJI qHCJlO 0603Ha1leHHe PaC1IeTllaJi qHCJIO
,nJIHHa Lw (MM) 3y6heB Z ,nJIHHa Lw (MM) 3y6heB Z
144-3M 144 48 420-3M 420 140
177-3M 177 59 474-3M 474 158
225-3M 225 75 513-3M 513 171
255-3M 255 85 564-3M 564 188
300-3M 300 100 633-3M 633 211
339-3M 339 113 711-3M 711 237
384-3M 384 128 1125-3M 1125 375
CTa apTHaR IIIHpHHa: 6, 9, 15 MM; npOMexyrOqHaR IIIHpHHa - no TPe60BaHHIO.
rAa8a 5. MexaHUtteCICue nepeiJattu
mar 3yfiheB 5 MM
l
---------------L <0
(f)
N
Tf
CTall)l;apTRbIe ,LUIHRhl
06038a- Pac'IeTllaJI 1JHCJlO 06038a- Pac'IeTllaJI 'lHCJlO
'IeHHe .zunma Lw (MM) 3y6heB Z 'IeHHe .zunma Lw (MM) 3y6heB Z
350-5M 350 70 800-5M 800 160
400-5M 400 80 890-5M 890 178
450-5M 450 90 1000-5M 1000 200
500-5M 500 100 1125-5M 1125 225
600-5M 600 120 1270-5M 1270 254
710-5M 710 142 1500-5M 1500 300
CTaH,LJ;apma5I lliHpHHa: 9, 15, 25 MM; npOMexyrOQHa5IlllHpHHa - no TPe6oBamno.
mar 3yfiheB 8 MM
L r
<0
. ..
-T-1
CTall)l;apTRhle MHRbI
06038a'leHHe Pac'IeTllaJI 1JHCJlO 06038a'le8He PaC'IeT8aJ1 1JHCJlO
.zunma Lw (MM) 3y6heB Z .zunma Lw (MM) 3y6heB Z
480-8M 480 60 1120-8M 1120 140
560-8M 560 70 1200-8M 1200 150
600-8M 600 75 1280-8M 1280 160 ,
640-8M 640 80 1440-8M 1440 180
656-8M 656 82 1600-8M 1600 200
720-8M 720 90 1760-8M 1760 220
800-8M 800 100 1800-8M 1800 225
880-8M 880 110 2000-8M 2000 250
960-8M 960 120 2400-8M 2400 300
1040-8M 1040 130 2800-8M 2800 350
CTa apTHaR lliHpHHa: 20, 30, 50, 85 MM; npOMexyrOQHa5I lliHpHHa - no TPe-
6oBaHHIO.
5.2. MexaHu"tecICue nepeiJa"tu: peMeHHble nepeiJa"tu 345
mar 3yfibeB 14 MM
---------------.
, It
,... 0
11
14,0
CTaH)l;apTHWe )\JIHHbI
j Pac'IeTllaJI 1JHCJlO Pac'IeTllaJI 'lHCJlO
J 0603ua'leHHe 0603ua'leHHe
i .zunma Lw (MM) 3y6heB Z AJDIua Lw (MM) 3y6heB Z
t
966-14M 966 69 2450-14M 2450 175
1190-14M 1190 85 2590-14M 2590 185
1400-14M 1400 100 2800-14M 2800 200
t 1610-14M 1610 115 3150-14M 3150 225
1778-14M 1778 127 3500-14M 3500 250
1890-14M 1890 135 3850-14M 3850 275
2100-14M 2100 150 4326-14M 4326 309
2310-14M 2310 165 4578-14M 4578 327
CTaH,n pTHWI lliHpHHa: 40,55,85, 115, 170 MM; npOMexyrOqHWI lliHpHHa - no
TPe6oBaH Io.
)
npo4»HJIb pacnpe,ZJ;eJleHHJI 3yfibeB HTD-20M
-'-'-'-'-'-'-'-'-'-'-'- -=r-
It"!.
o ('I)
11
20,0
CTaH,ZJ;apTHwe ,ZJ;JIIIHbI
Ofio3Ua'leHHe Pac'IeTllaJI 1JHCJlO 0603ua'leHHe Pac'IeTllaJI 1JHCJlO
.zunma Lw (MM) 3YOheB Z .zunma Lw (MM) 3YOheB Z
2000-20M* 2000 100 5400-20M* 5400 270
2500-20M* 2500 125 5600-20M* 5600 280
3400-20M* 3400 170 5800-20M* 5800 290
3800-20M* 3800 190 6000-20M* 6000 300
4200-20M* 4200 210 6200-20M* 6200 310
4600-20M* 4600 230 6400-20M* 6400 320
5000-20M* 5000 250 6600-20M* 6600 330
5200-20M* 5200 260
* OTcyrcTByJOm;He Ha CKJIan;e HaHMeHOBaHHH, ,nOCTaBKa no TPe60BaHHIO.
CTaH,LJ;apTHaR lliHpHHa: 115, 170, 230, 290, 340 MM; npOMexyrOqHaR lliHpHHa -
no Tpe6oBaHHIO.
IIpUMettaHue. Pa3MepbI lliKHBa npe,n;OCTaBIDIIOTCR TOJIbKO no 3arrpocy B KOMIIaHHIO.
Dla6a 5. MexaHuilecICue nepeiJailu
5.2.17. CJfHXpOHHble (3y6IfsTble) peNlHJf:
Jf3N1epeHJfe jJnJfHbl
PaCqeTHasI ,l(JIHHa RBlliIeTCR pemalOmHM napaMe1]>OM ,l(JIR BbIqHCJIeHHH H npHMeHe-
HID! CHHXPOHHbIX npHBO,n;HbIX peMHeH. TOqHOe H3MepeHHe MOXeT 6bITb BbInOJIHe-
HO TOJIbKO Ha COOTBeTCTByJOmeM H3MepHTeJIbHOM o6opy,n;OBaHHH.
PeMeHb HaTRrHBalOT Ha ,aBa H3MepHTeJIbHbIX mKHBa paBHblX pa3MepOB C O,n;HHa-
KOBbIMH paCqeTHbIMH ,n;HaMeTpaMH. IIO,n;BlUKHbIH H3MepHTeJIbHbIH mKHB HarpyxeH
TaKHM 06pa30M, qT06bI H3MepHTeJIbHOe YCHJIHe F ,n;eHcTByeT Ha peMeHb. QTo6bI ra-
paHTHpOBaTb npaBHJIbHOe nOJIOXeHHe peMIDI Ha mKHBax H paBHOMepHOe HaTIDKe-
HHe Ha 06eHX CTOpOHax peMIDI, peMeHb ,aOJDKeH COBepmHTb no KpaHHeH Mepe ,D;Ba
nOJIHbIX 060pOTa no,n; HarpY3KOH. 3aTeM H3MepReTCR paCCTORHHe a Me)l{)J;y OCRMH
,aBYX mKHBOB.
PaCqeTHasI ,l(JIHHa Lw paBHa y,n;BoeHHOMY paCCTORHHIO Me)l{,l(y OCRMH a I1JIIOC
paCqeTHasI ,l(JIHHa OKpyxHOCTH U w H3MepHTeJlbHbIX mKHBOB:
Lw = 2a + U w = 2a + Ttd w = 2a + zt
CxeMa KOH1]>OJIbHblX H3MepeHHH npHJIaraeTCR.
F
I
14
a
I
I
5.2. 18. SYNCHROBEL rm HTD 3y6lfsTble WKJfBbl:
npe,qnOIfTJfTenbHble pS3N1epbl
mar 3yobeB 3 MM
Pa3MepbI B MM
tJHCJlO Pac1IeTIIhIii Hap)']Kllhlii ,nuaMeTp lDKIIBa HMelOm,HHCJI .lUIaMeTp KOUe1l.....H .lUIaMeTp
3y6heB z .lUIaMeTp d w .lUIaMeTp d II C 4»Jl8IIIUlMH db OTBepcTHJI d v OTBepcTIUI d F max
10 9,55 8,79 12 3 3
12 11,46 10,70 14 3 4
14 13,37 12,61 16 3 6
15 14,32 13,56 16 3 6
16 15,28 14,52 18 3 8
17 16,23 15,47 20 4 8
18 17,19 16,43 20 4 8
19 18,14 17,38 21 4 8
20 19,10 18,34 23 4 10
22 21,01 20,25 25 4 10
24 22,94 22,16 26 4 12
26 24,83 24,07 28 4 14
5.2. M exaHu"teCICue nepeiJa"tu: peMeHHble nepeiJa"tu 3 4 7
OKoH"tQHUe
tJHCJlO Pac1IeTIIhIii Hapymu.di .nuaMeTp lDKIIBa HMelOlQIIicJI ,lUIaMeTp Koue1lHYi ,lUIaMeTp
3y6heB Z ,lUIaMeTp d w ,lUIaMeTp d II C 4m8IIU,8MH db OTBepcTIUI d v OTBepcTIUI d F max
28 26,74 25,98 30 4 15
30 28,65 27,89 33 6 17
32 30,56 29,80 34 6 19
34 32,47 31,71 36 6 20
36 34,38 33,62 38 6 20
38 36,29 35,53 42 6 25
40 38,20 37,44 42 6 25
44 42,02 41,26 47 8 28
50 47,75 46,99 51 8 32
56 53,48 52,72 59 8 36
62 59,21 58,45 64 8 42
72 68,75 67,99 73 8 50
COOTHomeHIDI Me)l{,l(y cTaH,lJ;apTHoH lliHpHHOH peMIDI H lliHpHHOH lliKHBa.
Pa3MepbI B MM
CTau,nap1'lWllUllpHua mllpHHa lDKHBa = IUllpHHa 3YOheB mllpHHa 3y6heB lDKHBa
peMBJIb lDKHBa fie3 4mauneB C 4m811Q8MH
\J/ 6 11 9
9 14 12
15 20 18
mar 3yoheB 5 MM
Pa3MepbI B MM
tJHCJlO ( , ) Hapymu.di ,ntIaMeTp lDKIIBa HMelOlQIIicJI ,lUIaMeTp Koue1fllhIii ,lUIaMeTp
Pac1IeTIIhIii
3y6heB Z ,lUIaMeTp d w ,lUIaMeTp d II C 4mUQaMH db OTBepcTIUI d v OTBepcTIUI d F max
14 22,28 21,14 26 4 / )12
15 23,87 22,73 28 4 14
16 2546 2432 30 4 14
17 27,06 2592 32 4 15
18 2865 27,51 33 6 17
19 3024 29, 10 34 6 18
20 31 83 30,69 36 6 20
22 3501 33,87 40 6 21
24 38 20 37,06 42 6 25
26 41 38 40,24 45 8 25
28 44,56 4342 48 8 30
30 47,75 4661 51 8 32
32 50,93 49,79 55 8 35
34 54,11 52,97 59 8 36
36 57,30 56,16 61 8 38
38 6048 59 34 64 8 40
DlO6a 5. MexaHuilecICue nepeiJailu
O"oHlfaHue
1JHCJlO Pac1IeTHLIii Hap)']KHYi .nuaMeTp lDKHBa HMelOlQIIicJI ;.utaMeTp Kone1fllhIii ,lUIaMeTp
3YOheB Z ,lUIaMeTp d w ,lUIaMeTp d II C cl»JlaunaMH db OTBepcTIUI d v OTBepcTIIJI d F max
40 63 66 62,52 67 8 45
44 7003 6889 73 8 50
50 79 58 7894 85 8 60
56 89 13 87 99 95 8 70
62 98 68 97,54 103 8 75
72 114,59 113,45 118 10 90
COOTHOllieHIDI Me)l{,l(y CTaIUJ:apTHOH lliHpHHOH peMIDI H lliHpHHOH lliKHBa.
Pa3MepbI B MM
CTau.napmaJI IUllpHHa mlipHna lDKHBa = DlHpHHa 3y6heB mHpHHa 3y6heB lDKIIBa
peMHJIb DIKHBa 003 cl»JlUQeB C cl»JlaHQaMH
9 14 12
15 20 18
25 30 28
mar 3yoheB 8 MM
Pa3MepbI B MM
1JHCJlO Pac1IeTllhlii Hap)']KHYi aMeTp lDKIIBa HMelOlQIIicJI ,lUIaMeTp Kone1fllhli ,lUIaMeTp
3y6heB Z ,lUIaMeTp d w ,lUIaMeTp d II C cl»JlaHQaMII db OTBepcTIUI d v OTBepcTIUI d F DIU
22 5602 54,65 61 8 38
24 61,12 59,75 67 8 45
26 6621 64,84 75 8 50
28 71,30 70,08 80 8 55
30 7639 75,13 82 8 60
32 81 49 80 16 86 8 60
34 86 58 85,22 95 8 70
36 91 67 90 30 99 8 75
38 9677 95 39 103 8 75
40 101 86 100,49 107 10 80
44 112 05 110,67 118 10 90
48 12223 120,86 127 10 98
56 142 60 141,23 150 10 124
64 162,97 161,60 168 16 138
72 18335 181 ,97 189 16 155
80 20372 20235 210 20 170
90 229,18 227,81 235 20 190
112 285,21 283 83 292 20 250
144 36669 365,32 - 30 300
168 427,81 42644 - 30 350
192 488 92 487 55 - 30 400
5.2. M exaHu"teCICue nepeiJa"tu: peMeHHble nepeiJa"tu 3
'\
COOTHomeHIDI Me)l{,l(y CTaIUJ:apTHOH lliHpHHOH peMIDI H lliHpHHOH lliKHBa.
Pa3MepbI B
CTalf,lJ,8pT118J1 DlHpHHa IIIHpHHa lDKIIBa = IIIIIpHHa 3y6heB IIIHpHHa 3y6heB lDKHBa
peMHJIb DIKHBa fie3 tlmaHueB C cl»JlallUaMH
20 26 22
30 38 34
50 58 54
85 94 90
mar 3yfiheB 14 MM
'lHCJlO
3y6heB Z
Pa3MepbI B M
Pac1IeTIIhIii Hapymu.di aMeTp lDKIIBa HMelOIQIIicJI ,lUIaMeTp KOHe'llDdii ,lUIaMeTJ
,lUIaMeTp d w ,lUIaMeTp d fl C cl»JlaHnaMH db OTBepcTIUI d v OTBepcTHJI d F max
28
29
30
32
34
36
40
48
56
64
72
gO
90
112
144
192
124,78
12923
13369
14260
151 52
160,43
178,25
213,90
24 !?5
85,21
320,86
356,51
401,07
499, 11
641 71
855,62
122 12
126,57
130,99
139,88
148,79
157,68
175,49
211,11
246,76
28241
318 06
35371
39828
496,32
63892
852 62
130
134
138
148
156
166
184
220
254
290
326
362
10
10
10'
10
16
16
16
20
20
20
30
30
30
30
30
30
95
100
100
110
120
130
145
180
210
240
260
290
330
420
550
750
/-,
/
)
COOTHomeHIDI Me)l{,l(y CTaH,LJ;apTHOH lliHpHHOH peMIDI H lliHpHHOH lliKHBa.
Pa3MepbI B MM
CTalf,lJ,8pT118J1 IIIIIpHHa IIIIIpHHa lDKIIBa == IIIIIpHHa 3y6heB IIIHpHHa 3y6heB DIKHB8
peMHJIb lDKHBa fie3 cl»JlaHQeB C tlmaHQaMH
40 54 47
55 70 63
85 102 95
--....... 115 133 126
170 187 180
DlO6a 5. MexaHUtteCICue nepeiJattu
5.3. MeX8HM'IeCKMe nepeA8'1M: enHble nepeA8'1M
CJIe IUaR HHcl>opMaUIDI no.rryqeHa B Renold Chain Designer Guide C pa3peme-
HHR KOMnaHHH.
5.3. 1. Pa60lfJfe xapaKTepJfCTJfKJf qeneH
H3,n;eJIIDI Renold Chain, no pa3MepaM COOTBeTCTBYIOIUHe CTaH,lJ;apTaM ISO, HaMHO-
fO npeBbImalOT 1]>e60BaHIDI ISO no MHHHMaJIbHOMY npe,n;e.rry npOqHOCTH Ha pa3-
pbIB. O,n;HaKo B KOMnaHHH He paCCMaTPHBalOT BeJIHqHHY pa3pymalOIUeH HarpY3KH
KaK KJIlOqeBOH nOKa3aTeJIb 3cl>cl>eKTHBHOCTH, nOCKOJIbKY B HeM He yqHTbIBalOTCR Ta-
KHe BIDKHbIe cl>aKTOpbI, KaK H3HOC H YCTaJIOCTb. B 3TOM OTHomeHHH H3,ZJ;eJIIDI Re-
nold pa3pa60TaHbI TaK, qTO ,n;OCTHfHYTbI HaHJIyqillHe B03MO)I{HbIe pe3YJIbTaTbI, H 3TO
no,n;TBepx.neHO He3aBHCHMbIMH HcnbITaHIDIMH.
,lJ;aJIee no TeKCTy TaM, r,n;e pa3pym IOIUasI HarpY3Ka ISO yJ{a3aHa, CJle.nyeT no-
MHHTb, qTO KOMnaHHeH Renold 3asIBJIeHO 0 TOM, qTO H3,n;eJIIDI Renold COOTBeTCTBY-
lOT MHHHMaJIbHOMY CTaH,lJ;apTy ISO. Pe3YJIbTaTbI He3aBHCHMbIX HcnbITaHHH nOKa3bI-
BaIOT, qTO MHHHMaJIbHasI (MHofHe KOMnaHHH CCbillalOTCR Ha cpe,n;H 10 10 ) pa3pymaIO-
IUasI HarpY3Ka HaMHOfO npeBbImaeT MHHHMYM ISO.
ECJIH pa3pymalOIUaR HarpY3Ka yJ{a3aHa 6e3 CCbillKH Ha ISO, 3TO 03HaqaeT, 1ff0
B ISO OTcyrcTByeT no,n;xo,nRIUHH CTaIUJ:apT. B TaKOM CJIyqae npHBo,n;HMaSI pa3pyma-
IOIUaR HarpY3Ka - 3TO fapaHTHpoBaHHbIH MHHHMYM.
3cl>cl>eKTHBHOCTb ueneH onpe,aeillleTCR HeCKOJIbKHMH KJIlOqeBbIMH cl>aKTOpaMH.
IIpoqHOCTb Ha pa3pbIB HaH60JIee OqeBHtJ;HbIH H3 HHX, nOCKOJIbKY HMeHHO no HeMY
opHeHTHpOBOqHO no,n;6HpalOT CHCTeMY uenH. O,n;HaKo, nOCKOJIbKY uenb CKOHCTPyH-
pOBaHa H3 CTaJIH, npe,n;eJI TeKytIeCTH KOTOpOH COCTaBIDIeT npHMepHO 65 % npe,n;eJIa
npOqHOCTH Ha pa3pbIB, JII06aR HarpY3Ka, npeBbImalOIUaR 3TOT npe,n;eJI, MoxeT CTaTb
np:HtIHHOH KaKOH-JIH60 OCTaTOQHOH ,n;ecl>opMaUHH, KOTOpaR nOBJIeQeT 3a C060H no-
CJIe IUee 6bIC1]>Oe nOBpex.neHHe.
IIpHBe,n;eHHasI HIDKe s-n KPHBasI nOKa3bIBaeT, qTO npH HarpY3Kax HIDKe ypOBIDI
65% MO)I{HO o aTb nOJIHyJO Hapa60TKy, H npH ,n;aJIbHeHmeM YMeHbmeHHH Ha-
rpY3KH o aeMbIH pecypc YBeJIHqHBaeTCR ,n;o Tex nop, nOKa He 6y,n;eT ,n;OCTHrnyT
npe,n;eJI YCTaJIOCTHOH BbIHOCJIHBOCTH, COCTaBJIRIOIUHH OKOJIO 8 000 000 onepaUHH.
HarpY3KH HIDKe YCTaJIOCTHOH CTOHKOCTH npHBO,nsIT K npaKT:HtIeCKH 6eCKOHeQHOH
Hapa60TKe ,n;o YCTaJIOCTHOfO pa3pymeHIDI. Tor,n;a np:HtIHHOH OTKa3a CTaHOBHTCR H3-
HOC, KOTOpbIH HaMHOfO 6e30naCHee, nOCKO-
JIbKY KOHTpOJIb paCTIDKeHIDI uenH ,n;OJDKeH
npOBo,n;HTbCR qepe3 COOTBeTCTBYIOIUHe nrra-
HOBbIe HHTepBaJIbI. Ha npaKTHKe, eCJIH BbI-
6paHO OTHOmeHHe npe,aeJIbHOH HarpY3KH Ha
pa3pbIB K MaKCHMaJIbHOH pa60QeH HarpY3Ke
KaK 8: 1, npe,n;eJI YCTaJIOCTH HHKor,n;a He 6y-
,n;eT npeBbImeH. CJIe.nyeT BHHMaTeJIbHO no.l1-
XO,n;HTb K paCCM01]>eHHIO MaKCHMaJIbHbIX
pa60qID{ HarpY30K, TaK KaK OHH qaCTO OKa-
3bIBalOTCR BbIme, qeM KOHC1]>YKTOp Mor
s
s-n KpHBaSi
to
(W)
>-
C.
L.
to
J:
OCTaTOYHaSi
Ae<l>opMaLJ.HSI 65%
npeAen YCTanOCTH
1 8.0 x 10 6 n
Hcno LJ.HKJ10B AO OTKa3a
5.3. MexaHu"teCICue nepeiJa"tu: l4enHble nepeiJa"tu 35
npe,n;rrOJIO)I{HTb! Heo6xo,n;HMbIM YCJIOBHeM TaIOKe RBIDIeTCR, qTo6bI JII060H naCCIDKHp'
CKHH JIHcl>T rrpOeKTHpOBaJICR C 3arraCOM rrpOqHOCTH He MeHbme 10: 1.
MHorHe rrpHJIOXeHIDI npOeKTHPYIOTCR TaK, qTo6bI rrp:HtIHHOH OTKa3a CTaHOBHJI-
CH H3HOC, H rr03TOMY HeKOTopbIe coo6pIDKeHIDI 0 rrOBe,aeHHH uerrH B 3TOM pe)I{HMf
npHBe,n;eHbI ,n;aJIee.
AHaJIH3 rpacl>HKa xapaKTepHCTHK H3Hoca, npHBe,n;eHHbIH HlDKe, rrOKa3bIBaeT.
1ffO uerrb rrpH6JIlDKaeTCR K COCTORHHIO H3Hoca 3a 1]>H 3Tarra. IIepBbIH 3Tan, Ha-
3BaHHbIH «rrpHpa6oTKa», - 3TO OqeHb 6bICTpO HaC1)'IIalOmee H3MeHeHHe ,l(JIHHb]
uerrH, CBR3aHHoe C rrpHcnoco6JIeHHeM KOMnOHeHTOB K HarpY3Ke, KOTOpOH OHI1
no,n;BepraIOTCR. CTerreHb rrepBOHaqaJIbHOrO H3MeHeHIDI 6y,n;eT C}'II(eCTBeHHO 3aBH-
ceTh OT KaqeCTBa HCrrOJIb3yeMoH uenH. HanpHMep, xopomeH rro,n;rOHKH KOMrrOHeH-
TOB, rrpe,n;BapHTeJIbHOrO HarpyxeHIDI B rrpouecce rrpOH3Bo,n;CTBa, IIJIaCTHH, co6paH-
HbIX rrpRMO H T.,a. I.J;enH Renold HMelOT MHoro oco6eHHocTeH, MHHHMH3HPYIOmHX
CTerreHb rrpHpa6oTKH.
XapaKTepMCTMKM M3Hoca
-
-
npHpa- npHcnoco6neHHe PaC'IeTHwi CpOK cnpd5bl 15000 'I
60TKa K HaTSI}I(eHHIO
+nePBOH -1- +- -
I Y; bIH I I I
_ 1 -'- -,- -,-
3HOC B YCTaHoBHB-
_ _ -! w C OC H
(I.)
s:
J:
(I.)
J:
s:
/ \
/ ,- ):>\
(
100 200
/
cTeKwee BpeMsV (Y)
BTOPYIO cl>a3Y, Ha3BaHHyK> «HaqaJIbHbIH H3HOC», MO)I{HO TaIOKe orrHcaTb KaK
BTOPHqHYio «rrpHpa6oTKY». Ee rrp:HtIHHOH cTaHoBHTcR, Bo-nepBbIX, HCTHpaHHe BbI-
,nalOmHXCR JIOKaJIbHbIX yqacTKoB Ha corrpHKacalOmHXCR rrOBepXHOCTRX BTYJIOK H Ba-
JIHKOB H, BO-BTOpbIX, cMemeHHe MaTepHaJIa Ha KOHUax BTYJIOK. QTo6bI 06'bRCHHTb
3TO 60JIee rromtTHo, ,n;aJIee rrpHBe,n;eHa cxeMa BHyrpeHHero YC1]>OHCTBa coe,n;HHeHIDI.
Ha HeH BHtJ;HO, qTO ,lUUI rapaHTHH xopomeH YCTaJIOCTHOH ,n;OJIrOBeqHOCTH BTYJIKa H
TIJIaCTHHa co6paHbI co 3HaqHTeJIbHbIM HaTRrOM, B pe3YJIbTaTe qero KOHUbI BTYJIKH
HeMHoro npOBaJIHBalOTCR BHyrpb. 3TOT JIOKaJIbHbIH
BbIC1)'II 6y,n;eT 6bIC1]>O H3HamHBaTbCR ,n;o Tex nop, rrOKa n t\
HarpY3Ka BaJIHKa He CTaHeT paBHOMepHOH rro BceH
,lUIHHe BTYJIKH. Renold orpaHHqHBaeT 3TOT 3cl>cl>eKT
npHMeHeHHeM CrreUHaJIbHOH TeXHOJIOrHH rrpOH3Bo,n;CT-
Ba. HeKoTopbIe rrpOH3Bo,n;HTeJIH nO,lJJ(ep)I{HBaIOT rrpaBH- >
JIbHyK> UHJIHH,lJ;p:HtIecKYIO cl>oPMY, CHIDKaR CTerreHb Ha-
THra ,n;o OqeHb HH3Koro ypOBIDI. 3TO yxy,amaeT YCTaJIO-
CTHbIe xapaKTepHCTHKH.
H3HOC B OKOHqaTeJIbHO YCTaHOBHBmeMCR COCTOR- CxaTHe KOHI.J;OB BTYJIKH
HHH pa3BHBaeTCR OqeHb Me,l(JleHHO ,ao Tex rrop, rrOKa npH c6opKe,
Tlla6a 5. MexaHu'IeclCue nepeiJailu
uenb He 6y,n;eT lfYX,l(aTbCR B peKOHC1]>YKUHH. ,[(mI npaBMbHO CnpOeKTHpOBaHHOH
CHCTeMbI npH COOTBeTCTByK>m;eM CMa3bIBaHHH HOpMaJIbHbIH CpOK C.rryx6bI COCTaB-
illIeT 15000 qaCOB HenpepbIBHoH pa6oTbI.
ITPHqHHbI, no KOTOpbIM Boo6m;e npOHcxo,n;HT H3HOC, HJIJIIOC1]>HpyeT KPHB8.SI
llITpH6eKa, nOKa3aHHaR Ha CJIe,n;yK>m;eM rpacl>HKe. 1f3 rpacl>HKa MO)I{HO Blf,l(eTh, qro
TaM, r,n;e ,n;Be conpIDKeHHbIe nOBepXHOCTH conpHKacalOTCR, K03cl>cl> H UHeHT 1]>eHIDI
OqeHb BbICOK B MOMeHT HaqaJIa ,n;BIDKeHIDI; OH 06YCJIOBJIeH 'rpeHHeM nOKOR. TIpH-
qHHa 3Toro 3aKJIIOqaeTCR B TOM, qTO HepOBHOCTH nOBepXHOCTeH ,n;BYX TeJI cueIIJllI-
IOTCR npH He6oJIbmOH TOJIm;HHe CJIOR pa3,n;eillllOm;eH CMa3KH MH nOJIHOM ee OTCyr-
CTBHH. ITo Mepe Toro KaK CKOpOCTH nOBepXHOCTeH YBeJI:HtIHBaIOTCR, CMa3Ka npo-
CaqHBaeTCR Mex.ny HHMH; HO TpeHHe OCTaeTCR Mex.ny HeKOTopbIMH 06JIaCTRMH
nOBepXHOCTH, npo,n;OJDKalOm;HMH conpHKacaTbCR. TaKoe 1]>eHHe Ha3bIBaeTCR «CMe-
maHHbIM» (rpaH:HtIHO-rlf,l(pO,l(HHaMHqeCKoe). 3TH ,n;Ba Blf,l(a 1]>eHIDI co BpeMeHeM
npHBO,[(RT K nOTepRM MaTepHaJIa. ITpH ,n;aJIbHeHmeM YBeJI:HtIeHHH CKOpOCTH nOBepx-
HOCTH HaqHHaeT npe06JIan;aTb rlf,l(po,n;HHaMHqeCKOe TpeHHe; conpHKOCHOBeHHe Me-
TaJIJIa C MeTaJIJIOM OTcyrcTByeT.
KpMB8R WTpM6eK8
g;
s:
J:
(I.)
a.
t-
t-
J:
(I.)
: CMe- :
s: : waHHoe:
.g. : eHH : rHAPoAHHaMHyeCKOe TpeHHe
.g.
(1)
o
. '\ TpeHH nOKOSi
. .
. .
t rpaHHY Oe TpeHLrte
'-IacToTa Bpa eHHSI
ECJIH paccMo1]>eTb B3aHMo,n;eHcTBHe conpIDKeHHbIx nOBepXHocTeH BTyJIOK H Ba-
JIHKOB B TeqeHHe o,n;Horo UHKJIa CHCTeMbI C ,n;ByMR 3Be3,n;OQKaMH, TO MO)I{HO 6bICTPO
nOIDITb, QTO 3TH KOMnOHeHTbI Heno,n;BIDKHbI O,n;HH no OTHomeHHIO K ,n;pyrOMY Ha
npOTIDKeHHH Bcero rryTH OT O,n;HOH 3Be3,n;OQKH ,n;o ,n;pyrOH H 6bIC1]>O YCKOPRIOTCg,
nOBOpaqHBasI Ha OQeHb MaJIbIH yrOJI, Kor,n;a BXO,nsIT B 3aueIIJIeHHe CO 3Be3,n;OQKOH,
npex.ne qeM CHOBa npHHTH B COCTORHHe nOKOR OTHOCHTeJIbHO ,n;pyr ,n;pyra. 3Te
03HaqaeT, qTO conpIDKeHHe BaJIHK/BTyJIKa cl>YJlKD:HOHHpyeT B YCJIOBIDIX MH 'rpeHIDI
nOKOR, MH CMemaHHoro TpeHHR; H, CJIe,n;OBaTeJIbHO, CMa3Ka OqeHb BIDKHbIH BO-
npoc npH npOeKTHpOBaHHH CHCTeMbI.
5.3.2. KoscpcpJfqJfeHT Jf3HOCa
KaK yxe nOKa3aHO, H3HOC 06'bRCHReTCR 1]>eHHeM Mex.ny conpIDKeHHblMH nOBepx-
HOCTRMH BaJIHKa H BTyJIKH. CKOpOCTb H3Hoca nepBOHaqaJIbHO onpe,n;eillleTCR IIJIO-
m;an;blO onopHbIX nOBepXHocTeit H y,l(eJIbHbIM ,n;aBJIeHHeM Ha 3TH nOBepXHOCTH.
YnpOqHeHHbIe CJIOH BaJIHKa H BTyJIKH nOCTeneHHO CTHpaIOTCR, H TaKHM 06pa30M
uenb YAJIHIDIeTCR.
5.3. MexaHu"teCICue nepeiJa"tu: l4enHble nepeiJa"tu 353
YAJIHHeHHe MoxeT COCTaBIDITb MaKCHMYM 2% HOMHHaJIbHOH AJIHHbI uerrH. IIpH
Y,1VIHHeHHH CBbIme 2% MOryT B03HHKHYTb rrp06JIeMbI H3-3a Toro, qTO uerrb 6y,n;eT
C'be3XaTb Ha60K H COCKaKHBaTb C 3y6beB 3Be3,n;OqKH.
YAJIHHeHHe ,n;OJDKHO 6bITb orpaHHqeHO ,n;o 1 %, Kor,l(a:
. 3Be3,n;OqKa B CHCTeMe HMeeT 90 3y6beB HJIH 6oJIee;
. T})e6yeTcR H.neaJIbHasI CHHxpOHH3aUIDI;
. paCCTORHHe Mex.ny ueHTpaMH 60JIbme, qeM peKOMeH,lJ;OBaHO H He HaC1]>aHBa-
eTCR.
ECJIH 1]>e60BaHIDI CHCTeMbI CTaHOBRTCR eme BbIme, Heo6xo,n;HMO eme 60JIbme
YMeHbmHTb ,l(OrryCTHMbIH rrpoueHT YAJIHHeHIDI.
M3HOC 3aBHCHT OT CJIe,nyIOmHX rrapaMe1]>oB rrpHBo,n;HOH CHCTeMbI.
. CKOpOCTb. qeM BbIme CKOpOCTb cHcTeMbI, TeM BbIme qaCTOTa rroBopoTOB
mapHHpoB, qTO YCKOpgeT H3HOC.
. KOJlH'lecTBO 3Be3,ZJ;OQeK. qeM 60JIbme 3Be3,l(OqeK HCrrOJIb3yeTcR B rrpHBo,n;e, TeM
qame mapHHpbI nOBOpaqHBaIOTcR.
. KOJlH'leCTBO 3YObeB. qeM MeHbme KOJIWleCTBO 3y6beB B 3Be3,n;OqKe, TeM
60JIbme CTerreHb rroBopoTa H TeM BbIme H3HOC.
. AnuRa neRU. qeM KOpOqe uerrb, TeM qame mapHHpaM uerrH rrpHXo,n;HTCR pa-
60TaTb, TeM 6bICT})ee H3HOC.
. CMa3IdBaRHe. KaK yxe 6billO rrOKa3aHO, HCrrOJIb30BaHHe COOTBeTCTByJOmeH
CMa3KH pemalOmHM 06pa30M BJIIDIeT Ha rrpOAJIeHHe cpOKa CJIy)I{6bI
5.3, . TJfnbl qeneif
y
KaK H Bce rtpOMbIIIIJIeHHbIe H3,neJIIDI, uerrb ,n;OJDKHa 6bITb H3rOTOBJIeHa B COOTBeTCT-
BHH C cl>OpMaJIbHbIMH CTaH,lJ;apTaMH. OCHOBHbIe CTaH,lJ;apTbI Ha uenHbIe nepe,n;aqH
H3JIOXeHbI B pa3,n;eJIax 5.3.4 H 5.3.5.
OAHOpRAH8R L\enb. CTaHAapT ISO 606, ANSI 829.1.
\ )
/
ABYXPRAH8R L\enb. CTaHAapT ISO 606, ANSI 829.
TpexpRAH8R L\enb. CTaHAapT ISO 606, ANSI 829.1.
12-3255
Dta8a 5. MexaHu'tecKue nepeiJa'tu
5.3.4. MeJICAYHspoAHb,e CTSHASpTbI
EBponeiicKHe CTa apTbi
U:errH H3rOTaBJIHBalOTCH B COOTBeTCTBHH co CTaH,l(apTaMH ISO 606 H DIN 8187.
3TH CTaH,l(apTbI rrpe,ayCMa1'pHBaIOT 1'pH BapHaHTa erreH:
. O,nHOPMHbIe errH
. ,l(BYXPMHbIe errH
. TpeXPMHbIe errH
,l(Harra30H p33MepOB IIlarOB MoxeT MeIDlTbCH OT 4 MM (0,158 ,nIOHMa) ,no 114,3 MM
(4,500,nIOHMa).
U:errH xapaKTepH3yIDTCH 60JIbIIlHM ,nHaMe1'pOM BaJIHKOB, oco6eHHO rrpH 60JIL-
IIlHX pa3Mepax IIlarOB. 3TO rrpHBo,nHT K JIytlIIleMy corrpOTHBJIeHHIO H3HOCY 6JIaro,n;a-
pH 60JIbIIleH IIJIOII(a;J:H OrrOpHOH rrOBepXHOCTH.
CTaH,l(apT ISO rrpe,n.rraraeT rrpocToH BH.n 0603HaqeHIDI erreH, HarrpHMep ,nBYX-
PMHIDI errb C IIlarOM 1/2 ,nIOHMa 0603HaqaeTCH KaK 08B-2.
. llepBbIe ,nBe H<l>PbI - pa3Mep IIlara B 1/16 ,nIOHMa, CJIe,nOBaTeJIbHO, 08 =
= 8/16 HJIH 1/2 ,nIOHMa.
. D)'KBa «B» yKa3bIBaeT Ha EBporreHcKHH CTaH,l(apT.
. llocJIe,nmrn H<l>pa yKa3bIBaeT KOJIWleCTBO PMOB B errH, B ,naHHOM c.rry-
qae - ,nBYXPMHIDI errb.
AMepHKaHcKHe CTa apTbi
AMepHKaHcKHe CTaH,l(apTbI co,nepxaTCH B ISO 606, ANSI B29.1 H DIN 8187.
3TH CTaH,l(apTbI rrpe,ayCMa1'pHBaIOT BoceMb BapHaHTOB erreH:
. O,nHOPMHbIe, ,nBYXPMHbIe H 1'peXPMHbIe B COOTBeTCTBHH C EBpOrreHCKHMH
CTaH,l(apTaMH.
. qeTbIpeXPMHbIe
. llHTHPMHbIe
. llIeCTHPMHbIe
. BOCbMHPMHbIe
. ,l(ecHTHPMHbIe
Pa3MepbI IIlarOB yKa3aHbI B CTaH,l(apTe B ,nHarra30He OT 1/4,no 3 ,nIOHMOB.
B COOTBeTCTBHH C AMepHKaHcKHM CTaH,l(apTOM errH HMelOT MeHbIIlHH ,nHaMerp
BaJIHKa, qeM 3KBHBaJIeHTHbIe HM errH B COOTBeTCTBHH C EBporreHcKHM CTaH.nap-
TOM. CJIe,nOBaTeJIbHO, HX H3HOCOCTOHKOCTb CHIDKeHa rro cpaBHeHHIO C eruIMH EB-
porreHCKoro CTaH,l(apTa 3a O,nHHM HCKJllOqeHHeM - 5/8,nIOHMa. B 3TOM CJIyqae ,n;Ha-
MeTp BaJIHKa H BTYJIKH 60JIbIIle B AMepHKaHcKoM CTaH,l(apTe.
B COOTBeTCTBHH C AMepHKaHcKHM CTaH,l(apTOM errH 06bIQHO 0603HaQalOTCH no
CTaH,l(apTY ANSI, HarrpHMep, ,nBYXPMHIDI errb C IIlarOM ,nIOHMa 0603HaQaeTCg
KaK ANSI 40-2.
CHcTeMa 0603HaQeHHH ANSI pa60TaeT CJIe,nyIDII(HM o6pa30M:
. llepBIDI H<l>pa - pa3Mep IIlara B 1/8 ,nIOHMa; T. e. 4/8 = 1/2,nIOHMa.
. BTopaH H<l>pa yKa3bIBaeT lia TO, QTO errb pOJIHKOBIDI; 0 - COOTBeTCTByeT
pOJIHKOBOH errH. ECJIH 6bI BMeCTO 0 6billO 5, 3TO 03HaQaJIO 6bI BTYJIOQIfYlO
errb.
5.3. MexaHUlf,eCKUe nepeoalf,u: u,enHble nepeoalf,u 355
. nOcJIe,nmrn UH<ppa, KaK H B EBporreHcKoM CTaH,l(apTe, 03HaqaeT KOJIWleCTBO
pR,nOB B uerrH, T. e. 2 - ,nBYXPMHIDI uerrb
B CTaH,l(apTe ANSI orrpe,neJIeH TaIOKe BapHaHT uerreH )])UI TIDKeJIbIX YCJIOBHH pa-
60TbI C 60JIee TOJICTbIMH IIJIaCTHHaMH (H) H C 3aKaJIeHHbIMH HaCKB03b BaJIHKaMH
(V). npH 0603HaQeHHH TaKHX uerreH 6)'KBbI ,no6aBIDIIOTcH B KOHeu 0603HaQeHIDI.
To eCTb
ANSI I40-2HV - ,l(BYXPHJJ;HIDI C TOJICTbIMH IIJIaCTHHaMH, 3aKaJIeHHbIMH Ha-
CKB03b BaJIHKaMH
ANSI 80H - O,nHOPHJJ;HIDI C TOJICTbIMH IIJIaCTHHaMH
)J;Hana30H B03M01KllbIX npHJI01KeHHH
MHPOBOH pbIHOK rrpHBo,nHbIX uerreH pa3,neJIeH B COOTBeTCTBHH C ,nBywI pa3HbI-
MH CTaH,l(apTaMH uerreH. TaKoe pa3,neJIeHHe HMeeT rro,n C060H KaK 3KOHOMHQecK}TIO,
TaK H HCTOpWlecK}TIO OCHOBY.
. U;errH, COOTBeTCTByIDlI(He AMepHKaHCKOMy CTaH,l(apTY, HCrrOJIb3yIDTCH rrpeH-
MYlI(eCTBeHHO B CllA, KaHane, ABCTPaJIHH, HrroHHH H HeKoTopbIX cl'paHax
A3HH.
. EBporreHcKHH CTaH,l(apT ,nOMHHHpyeT B EBporre, BpHTaHcKOM Co,npyxecTBe,
awpHKaHCKHX H a3HaTCKHX cTPaHax, B KOTOpbIX HCTopWlecKH CHJIbHO BJIIDI-
H e BpHTaHHH
) u
B EBporre OKOJIO 85% Bcero pbIHKa 3aIDITO ueruIMH EBporreHcKoro CTaH,l(apTa.
OCTaBIIlHecH 15% uerreH AMepHKaHcKoro CTaH,l(apTa rrpHXO,lUlTCH Ha:
. MaIIlHHHoe o6opy,noBaHHe, HMrropTHpyeMoe H3 CTPaH, r,ne ,nOMHHHpyeT AMe-
pHKaHcKHH CTaH,l(ap'r uerreH;
. MaIIlHHHoe o6opy,noBaHHe, H3rOTaBJIHBaeMOe B EBporre rro JIHueH3ID1M Tex
CTPaH, r,ne ,nOMHHHpyeT AMepHKaHcKHH CTaH,l(apT uerreH.
enH, He COOTBeTCTBytOllUle ISO CTa aPTaM
CyrQecTByIDT TaIOKe cta apTbI rrpOH3Bo,nCTBa Renold )])UI CrreUHaJIbHbIX H KOH-
CTp}'KTHBHO CJIO)l{}{bIX uerreA, pa3pa6oTaHHbIx Ha BbICOKOM TeXHWleCKOM ypOBHe.
Hx MO)l{}{O pa3,neJIHTb CJIe.nyIOlI(HM o6pa30M.
1. Uerr, C 60JIee BbICOKOH pa3pynIalOII(eH HarpY3KOH. 3TH uerrH 06bIQHO HMelOT
ITJIaCTHHbI, KOTopbIe rro,nBeprJIHCb CrreUHaJIbHOH o6pa6oTKe, 60JIee TOJICTbIe 60KO-
Bble nrraCTHHbI H/HJIH ,nHaMeTP BaJIHKOB, KOTOpbIH HeMHoro OTJIHQaeTCH OT CTaH-
,n;apTOB.
2. CrreUHaJIbHbIe pa3MepbI. Pa3MepbI HeKOTopbIX uerreH MOryr 6bITb CMeCblO
AMepHKaHcKHX H EBporreHcKHx CTaH,l(apTOB, HJIH MOryr BapbHpOBaTbCH BHYTPeH-
HID! IIlHpHHa H ,nHaMeTP pOJIHKOB, KaK, HarrpHMep, B ueruIX MOTOUHKJIOB.
3. CrreUHaJIbHbIe rrpHJIOXeHIDI. ,l(illI HCrrOJIb30BaHIDI B CrreUHaJIbHbIX rrpHJIoxe-
HIDIX H3rOTaBJIHBalOTCH CrreUHaJIbHbIe KOHCTPYKTHBHO CJIO)l{}{bIe uerrH, KaK, HarrpH-
Mep:
. U;errH H3 HepXaBelOlI(eH CTaJIH
. U;errH C UHHKOBbIM HJIH HHKeJIeBbIM rrOKpbITHeM
. U;errH C BTYJIKaMH C IIJIaCTHQHOH CMa3KOH
. U;errH C rrOJIbIMH BaJIHKaMH
. U;errH, KOTopbIe MOryr H3rH6aTbCH B60K
rAa8a 5. MexaHulteclCue nepeiJaltu
5.3.5. HOpMSTJfSHble CCblnKJf
THDbI DpHBO,lUlbIX neDeii
ISO ANSI ,lJ;pyrae
CTall,lJ;aJlTlal
npHBO,lJ;HaH u;eIIb C KOpOTKHM marOM H 3Be3,lJ;OqKaMH 606 B29,lM DIN 8187
DIN 8188
BTYJIOQHaH u;eIIb C KOpOTKHM marOM H 3Be3,lJ;OQKaMH 1395 DIN 8154
POJIHKOBaH u;eIIb C ,lJ;BOHHhIM marOM (,WIHHH03BeH- 1275 B29 3M DIN 8181
HaH) H 3Be3,lJ;OQKaMH
U;eIIH ,l])UI He<pTeIIpOMhICJIOBOrO o6oPY,lJ;OBaHIDI co 606 B29 1M API Spec
3Be3,lJ;OQKaMH 7F
BeJIOCHIIe,lJ;HbIe u;eIIH 9633
MOTOU;HKJIeTHhle u;eIIH 10190
U;eIIH C H30rHYThIMH IIJIaCTHHaMH H 3Be3,lJ;OQKaMH 3512 B29 1M DIN 8182
THDbI Do,n'beMHbIX (TBfOBbIX) neDeii
ISO ANSI ,lJ;pyme CTaIl,lJ;8p1'W I
n.rracTHHQaTaH u;eIIh, V -o6pa3HhIe 3BeHhH H mKHBhI 4347 B29,8M DIN 8152
POJIHKOBhle rpY30BhIe u;eIIH ,l])UI IIO,lJ;BeCHhIX TaJIeH B29,24M
5.3. 6. npeJfMy ecTss Lf,enHblX nepeASII
CTaJIbHble pOJIHKOBble rrpHBo,nHble uerrH H3rOTaBJIHBalOTCH C xeCTKHMH ,nonycKa-
MH, C rrpeBocxo,nHOH rro,nBIDKHOCTblO coe,nHHeHHH, qTO rr03BOJUleT IIJIaBHO H 3<1>-
<peKTHBHO rrepe,naBaTb rrOTOK MOII(HOCTH. KaKOe-JIH60 'rpeHHe Me)l{,Uy pOJIHKaMH
uerrH H 3y6bHMH 3Be3,nOqKH <paKTHqeCKH HCKJIlOqeHO, TaK KaK pOJIHKH BpalI(alOTCi
CHapyxH BTYJIOK He3aBHCHMO 01' rrOBopOTOB orropHbIX BaJIHKOB BHYTPH BTYJIOK.
B pe3YJIbTaTe OqeHb HeMHoro MOII(HOCTH TepHeTCH BrryCTYI<>, H HcrrbITaHIDI rrOKa3a-
JIH, qTO uerrH HMelOT K03<P<PHUHeHT rrOJIe3HOrO ,neHCTBIDI Me)l{.l(Y 98,4% H 98,9%.
TaKoH BbICOKHH ypOBeHb K03<P<PHUHeHTa rrOJIe3HOrO ,neHcTBIDI, rroJIyqaeMbIH
Ha CTaH,l(apTHbIX cepHHHo BblrrYCKaeMbIX ueillIX rrpH rrpaBHJIbHOM CMa3bIBaHHH H
YCTaHOBKe, MO)I{HO cpaBHHTb TOJIbKO C K03<P<PHUHeHToM rrOJIe3HOrO ,neHcTBIDI 3y6-
qaTbIX rrepe,naq BbICOqaHIIlerO CTaH,l(apTa C 3y6bHMH, OTIIIJIH<poBaHHbIMH B COOTBe1-
CTBHH C caMbIMH xeCTKHMH ,norrycKaMH.
POJIHKOBble uerrH rrpe,nOCTaBJUlIOT xeCTKoe, He rrpOCKaJIb3bIBalOII(ee rrpHBO,ll;HOe
YCTPOHCTBO. BJIaro,napH xeCTKOMy rrpHBO,ny, OHH 06eCrreqHBalOT TOqHOCTb mara,
qTO cym;ecTBeHHO )])UI CHHXpOHHbIX rrpHBo,nOB, HarrpHMep B pacrrpe,neJIHTeJIbHbIX
BaJIaX aBTOM06HJIbHbIX H Cy,nOBbIX ,nBHraTeJIeH, rraKeTHpOBOqHbIX MaIIlHHax H rreqa-
TalOIUHX YCTpOHCTBax. B YCJIOBIDIX BbICOKOH CKOpOCTH H rrHKOBOH HarpY3KH, Kor a
K TO My xe 'rpe6yeTcH BbICOKHH K03<P<PHUHeHT rrOJIe3HOrO ,neHCTBIDI, pOJIHKOBLIe
uerrH rrOCJIe,nOBaTeJIbHO ,nOK33aJIH CBOIO 6eCmyMHOCTb H Ha;J:e)I{HOCTb.
MexoceBoe paCCTORHHe BaJIOB MoxeT COCTaBJIHTb 01' 50 MM ,no 60JIee qeM 9 M B
OqeHb KOMrraKTHO c06paHHoH 060JIOqKe. npHBO,nbI MOryr 6bITb CrrpOeKTHpOBaHbI
TaK, qTO 3y6bH 3Be3,nOqKH 6y,nyr rrOqTH KacaTbCH O,nHH ,npyroro, HJIH TaK, qTO n;em
5.3. MexaHUlf,eCKUe nepeoalf,u: u,enHble nepeoalf,u 357
rrpeo,nOJIeeT 3HaqHTeJIbHOe paCCTOHHHe. KaK pa3 B 3TOH rrOCJIe,nHeH KaTeropHH
n;enH C ,nBOHHbIM IIlarOM rrOJIyqHJIH rrpH3HaHHe.
POJIHKOBbIM neruIM ,no orrpe,neJIeHHOH CTerreHH rrpHcym;a ynpyrOCTb, H 3TO
CBOHCTBO, BMeCTe C aMopTH3HpyIDII(HM ,neHcTBHeM MaCJUlHOH IIJIeHKH B MecTax coe-
,lUiHeHIDI nerrH, o6eCrreQHBaeT xopornee y,naporrOrJIOlI(eHHe. KpoMe Toro, HarpY3Ka
Me nerrblO H 3Be3,nOqKOH pacrrpe,neJUleTCH rro 60JIbIIlOMY KOJIWIeCTBY 3y6beB,
qTO crroco6cTByeT yMeHbIIleHHIO H3Hoca. l103TOMy Kor,na nOCJIe ,nJIHTeJIbHOrO cpOKa
CJIyJK6bI CTaHOBHTCH Heo6xo,nHMOH 3aMeHa nerrH, 3Ta rrpOCTCUI orrepanIDI 06bIQHO
He BJIeqeT 3a C060H 3aMeJIy 3Be3,nOqKH lUIH orrop.
POJIHKOBble nerrH MHHHMH3HpyIDT HarpY3KY Ha orropbI Be,nym;ero ,nBHraTeJUI H
Be,noMoro BaJIa, rrOCKOJIbKY HHKaKoH rrpe,nBapHTeJIbHOH HarpY3KH He l'pe6yeTcH ,[(illI
Toro, qTo6bI HaTHHyrb nerrb, YCTaHOBHB ee is CTaTWIeCKoe COCTOHHHe.
O,nHa nerrb MoxeT CJI)')KHTb rrpHBo,nOM )])UI HeCKOJIbKHX BaJIOB o,nHOBpeMeHHO,
rrpWIeM rrpH rrOQTH rrpOH3BOJIbHOM pacrrOJIOXeHHH H JII06bIX MexoceBbIX paCCTOH-
HIDIX. Ee rrpHcrroco6JIHeMOCTb He orpaHHQHBaeTCH B03MO)I{HOCTblO rrpHBo,nHTb B
;n;eHCTBHe O,nHH HJIH HeCKOJIbKO BaJIOB OT o,nHoro ,nBHraTeJUl. MoxeT HCrrOJIb30BaTb-
CR MHoxeCTBO pa3Hoo6pa3HbIX YCTPOHCTB, TaKHX KaK B03BpaTHO-rrOCTYTIaTeJIbHbIH
MexaHH3M; 3y6tfii peHKa; 3KCneHlpHKOBbIH 3eBoo6pa30BaTeJIbHbIH MexaHH3M;
3y6QaTaH rrepe,naQa C BHyrpeHHHM lUIH BHeIIlHHM 3aneIIJIeHHeM; rrpHcrroco6JIeHIDI,
06eCneQHBalOII(He ypaBHOBeIIlHBaHHe, rro,n'beM lUIH B3BeIIlHBaHHe. 3Be3,nOQKH C
OT,n;eJIbHbIMH 3y6QaTbIMH yqacTKaMH HJIH «oxepeJIbHble» 3Be3,nOQKH MOryr rrpHMe-
IUITbCH )])UI BpalI(eHIDI 60JIbIIlHX 6apa6aHOB.
llOCKOJIbKY B nelliIX OTCyrCTByIDT KaKHe-JIH60 KOMrrOHeHTbI H3 3JIaCTOMepOB,
OHH rrpHro,nHbI K HCrrOJIb30BaHJ;l1O B llIHpOKOM ,nHarra30He BHellIHHX YCJIOBHH,
BKJIIOQ3jI 3KCTpeMaJIbHble TeMrrepa bI. U:errH HCrrOJIb3yIDTCH B TaKHX He6JIarOrrpH-
iTHbIX BHeIIlHHX YCJIOBIDIX, KaK XHMWleCKoe rrpOH3Bo,nCTBO, ropHble pa60TbI, JIH-
TeHHoe rrpOH3Bo,nCTBO, 6ypeHHe rro rropo,ne H o6pa6oTKa ,npeBeCHHbI. CrrenHaJIbHble
IIOKpbITIDI elI(e 60JIbIIle paCIIlHpHIOT B03MO)I{JIOCTH nerreH.
POJIHKOBble nerrH TaIOKe MOryr 6bITb OCHalI(eHbI HaKJIa;J:KaMH C KpeIIJIeHIDIMH H
YMHHeHHbIMH BaJIHKaMH H T.rr., QTO rr03BOJIHT HCrrOJIb30BaTb HX MeXaHHQeCKHX
rpaHcrropTHbIX YClpOHCTBax H HCrrOJIHHTeJIbHbIX YClpOHCTBax.
llpHBO,nbI C pOJIHKOBbIMH QeruIMH MOryr HMeTb rrepe,naTOQHOe OTHomeHHe 3Ha-
qeHIDI 9: 1 H rrepe,naBaTb BIIJIOTb ,no 520 KBT rrpH 550 06/MHH. KpoMe Toro, QeTblpe
COrJIaCOBaHHble BeTBH lpexPMHOH nerrH MOryr ,nOCTWlb 3200 KBT rrpH 300 06/MHH.
POJIHKOBble nerrH He nopTHTCH co BpeMeHeM, e,nHHCTBeHHbIM CBH,neTeJIbCTBOM
cpOKa HX C.rryx6bI 6y,neT Y,nJIHHeHHe, 06YCJIOBJIeHHOe H3HOCOM, KOTOpbIH 06bIQHO
rrpOHCXO,nHT rrOCTerreHHO, H CHCTeMy MO)I{JIO K HeMY rrpHcrroco6HTb peryJIHpOBKOH
MexoceBoro paCCTOHHIDI lUIH HaClpOHKOH HaTIDKHOH 3Be3,nOQKH. llpH YCJIOBHH,
qTO nerrHOH rrpHBO,n BbI6paH npaBHJIbHO, COOTBeTCTByIDlI(HM 06pa30M YCTaHOBJIeH
H 06C.JIyXHBaeTCH, MO)I{HO nporH03HpOBaTb CpOK CJIyx6bI 15000 QaCOB 6e3 rrOBpex-
eHHH nerrH OT YCTaJIOCTH HJIH H3Hoca.
3ct>ct>eKTHBHOCTb neneH rapaHTHpOBaHa, H OHH MOryr rrpHMeIDITbCR B Tex rrpH-
JIOXeHIDIX, r,ne Ba)I{HbI a6COJIIOTHaH Ha;J:e)I{HOCTb H ,nJIHTeJIbHbIH CpOK CJIyx6bI, KaK,
HarrpHMep, rro,n'beM rpact>HToBbIX CTep)I{HeH B aTOMHbIX peaKTopax H CHCTeMbI
yrrpaBJIeHIDI B aBHanHH
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BeTCTBHH co CTaH,IJ;apTaMH ISO BO BceM MHpe. K TOMY xe OHH neJIHKOM MOryr 6bITb
rAa8a 5. MexaHu'tecKue nepeiJa'tu
rro,nBeprHYTbI rroBTopHOH o6pa6oTKe H He OKa3bIBalOT Bpe,nHoro B03,neHCTBIDI Ha
OKpyxalOIQy1O cpe,ny.
HIDKe rrpHBe,neHa Ta6JIH a cpaBHHTeJIbHbIX ,nOCTOHHCTB pa3JIHqHbIX CHCTeM ne-
pe,naQH rro,n'beMa.
KpaTKHH HTor nepe'lHCJleHHbIX Byrne npeHMYJQeCTB
XapaKTepHCT11K8 3yfi'laThie KaHaTHhle PeMeHHWe D;ellHJ.le
nepe,lUt'IH nepe,lUt'IH nepe,lUt'IH nepe,lUt'IH
K03<P<PHI(HeHT rrOJIe3Horo ,aeHcTBIDI A X B A
)l(eCTKHH npHBO,a A X B A
MexoceBoe paCCTORHHe C A B A
YrrpyrocTb C A A B
H3HOCOCTOHKOCTh A C B A
OrcYTCTBHe rrpe,aBapHTeJIhHOH HarpY3KH A C C A
06cJIy)KHBaHHe HeCKOJIhKHX YC'rpOHCTB C X C A
TepMocToHKOCTh B B C A
CTOHKOCTh K XHMH'IeCKOMY B03,aeHcTBHIO B A C A
MaCJIOCTOHKOCTh A A C A
npHcrroco6JU1eMOCTb C B C A
)];Harra30H MOW;HOCTH A X B A
npOCToTa 06CJIy)KHBaHIDI C B B A
CTaH,IJ;apTH3aI(IDI C B B A
BHemHHe YCJIOBIDI A A C A
A - OTJIH1IHO; B - xopomo; C - nJIOXO; X - HerrpHeMJIeMO.
llpUMe"laHue. QTo6bI rrOJIytlHTb ,naHHyIO o eHKY, rr01'pe60BaJIHCb 6bI pa3JIWlHbIe
BH,nbI peMHeH.
5.3.7. npeJfMYlJ.leCTSa qenHblx npJfSo,qos
3aMeQaHIDI, H3JIOXeHHble HIDKe, 3TO 061I(He peKOMeH,[(a HH, KOTOpbIM HyXHO CJIe-
,nOBaTb rrpH BbI60pe H YCTaHOBKe errHblX rrpHBo,nOB, QTo6bI 06eCrreQHTb y,nOBJIeTBO-
pHTeJIbHble 3KCIIJIyaTa HoHHbIe KaQeCTBa H ,nJIHTeJIbHbIH CpOK C.rryx6bI.
mar nenH
CxeMa o eHKH (pa3,neJIbI 5.3.12, 5.3.13) ,naeT aJIbTepHaTHBHble pa3MepbI erre:H,
KOTopble MOryr HCrrOJIb30BaTbCH )])UI rrepe,naQH HarpY3KH rrpH ,naHHoH CKOpOCTH.
ECJIH B03MO)I{JIO, CJIe,nyeT HCrrOJIb30BaTb HaHMeHbIIlHH IIlar O,nHOpHJ(HOH errH, rro-
CKOJIbKY 06bJtIHO 3TO HaH60JIee 3KOHOMHQHOe peIIleHHe. ECJIH O,nHOPMHIDI errb c
HaHMeHbIIlHM IIlarOM He y,nOBJIeTBOpHeT Tpe6oBaHIDIM, HaJIaraeMbIM orpaHHQeHIDI-
MH rro rrpOCTpaHCTBY, MaKCHMaJIbHOH CKOpOCTH, IIlyMOBbIM xapaKTepHCTHKaM HJIH
IIJIaBHOCTH xo,na, Tor,na CJIe,nyeT paCCMOTpeTb ,nBYXPMHble HJIH TpeXPMHble errH c
HaHMeHbIIlHM IIlarOM.
Kor,na l'pe60BaHIDI K MOII(HOCTH rrpH ,naHHOH CKOpOCTH rrpeBOCXO,lUlT B03MO)l{-
HOCTH O,nHOH BeTBH errH, HCrrOJIb30BaHHe MHorOBeTBeBoro rrpHBo,na rr03BOJIHT rre-
pe,naBaTb 60JIee BbICOKHe MOII(HOCTH
5.3. MexaHUlf,eCKUe nepeoalf,u: u,enHble nepeoalf,u 359
TaKHe rrpHBo,nbI MOryr 6bITb co6paHbI H3 HeCKOJIbKHX COrJIaCOBaHHbIX O,nHO-
pg,nHbIX, ,[(BYXPMHbIX MH TpeXPMHbIX uerreH rrpH HCrrOJIb30BaHHH CTaH,l(apTa ISO,
MH, B c.rryqae HCrrOJIb30BaHIDI uerreH rro CTaH,l(apTY ANSI, MOryr rrpHMeIDITbCH
MHorOPMHble uerrH, BIIJIOTb ,no ,neCHTHPMHbIX (10 BeTBeH).
,l(aJIbHeHrnyIO HH<popMaUHIO MO}J{HO rro.rryqHTb Y TeXHHqeCKOrO rrepCOHaJIa
Renold.
MaKCHMaJlbHaB paOO'laB CKOpOCTb MaKCVlMal1bHa pa6oLfa CKOpOCTb
,lLrr.sI 06blqHbIX rrpOMbIIIlJIeHHbIX rrpH _ 6000
BO,n;OB H3 orrbITa YCTaHOBJIeHO MaKCHMa- 5000
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JIbHOe qHCJIO 060pOTOB 3Be3,nOqKH)])UI \0
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n;erreH C KIDK,lJ;bIM IIlarOM. 3TH CKOpOCTH, In
OTHOCHII(HeCH K Be,nym;HM 3Be3,nOQKaM, S 3000
HMelOlI(HM 17-25 3y6beB BKJIIOQHTeJIbHO, g. 2000
rrpHBe,neHbI Ha tP'\'tbHKe; OHH rrpHMeHH- '8
o 1000
MbI TOJIbKO B TOM c.rryqae, Kor,na MeTO,n 5
CMa3bIBaHIDI 06eCrreQHBaeTCH B COOTBeT- 0 10 20 30 40 50 60 70 80
CTBHH C peKOMeH,l(aUIDIMH{' _ J War u.enVi (MM)
BJlHBHHe MHoroyrOJl,"oCTH
qeTblpe BroKHbIX e MYUJ:eCTBa .QerrHoro rrpHBo.n;a Herrocpe.n;CTBeHHO 3aBHCRT
OT KOJIWleCTBa 3y6beB B'iie eH 3Be3,nOQKe (Zl)'
3TH rrpeHMym;ecTBa - IIJIaBHaH paBHOMepHaH rrepe,naqa MOII(HOCTH, MaJIOmyM-
HOCTb pa60TbI, BbICOKHH K03<P<PHUHeHT rrOJIe3HOrO ,neHCTBHH H ,nJIHTeJIbHbIH CpOK
C.rryx6bI - 3aBHCHT OT 3Be3,nOQKH, TaK KaK uerrb o6pa3yeT Ha HeH MHoroyrOJIbHHK.
TaKHM 06pa30M, Kor,na QaCTOTa BpalI(eHIDI 3Be3,nOqKH rrOCTOHHHa, CKOpOCTb uerrH
(06YCJIOBJIeHHIDI ee TpaeKTOpHeH BOKpyr 3Be3,nOQKH B BH,ne MHoxeCTBa CTOpOH
MHoroyrOJIbHHKa) rro,nBepraeTCH peryJUlpHbIM UHKJIWleCKHM H3MeHeHIDIM. 3TH
n;HKJIHQeCKHe H3MeHeHIDI CTaHOBHTCH MeHee 3aMeTHbIMH rro Mepe Toro, KaK 1paeK-
TOpIDI uerrH CTpeMHTCH K rrpaBHJIbHOH OKpy:>KHOCTH, H <paKTWleCKH B 60JIbIIlHHCTBe
IIpHJIOXeHHH CTaHOBHTCH He3HaQHTeJIbHbIMH rrOCJIe Toro, KaK KOJIHQeCTBO 3y6beB
Be,nylI(eH 3Be3,nOQKH rrpeBbIIIlaeT 19.
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c.rryqaH - Be,l(ylI(yIO 3Be3,nOQKY C a6COJIIOTHO MHHHMaJIbHbIM KOJIWleCTBOM 3y6beB,
T. e. C lpeWI. B 3TOM rrpHMepe rrpH KIDK,lJ;OM o6opoTe 3Be3,nOQKH uerrb rrpoxo,nHT
rpex<pa3HbIH UHKJI; KIDK,lJ;IDI <pa3a CBH3aHa C 3auenrreHHeM o,nHoro 3y6a. Kor,na 3y6
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HOllIeHHe CKOpOCTb/MOII(HOCTb TaKOBbI, qTO MeHbIIlee KOJIWleCTBO 3y6beB (T.e. Me-
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KOJllf1leCTBO 3yfiheB ,lJ;OJUI B npou;eHTaX OT MaKCHMaJlhHOH ,lJ;OJUI B npou;eHTaX OT MaKCHMaJlhHOH
HOMHHaJIhHOH CKOpoCTH HOMHHaJlhHOH MOIQIIOCTH
11 20 30
13 30 40
15 50 60
17 80 90
5.3.8. COBMeCTJfMOCTb 3se3,qO'lKJf Jf LlenJf
B 60JIbllIHHCTBe rrpHBo,nOB errb COCTOHT H3 qeTHOrO KOJIWleCTBa 3BeHbeB, H 6JIaro-
,napH HCrrOJIb30BaHHIO Be,n eH 3Be3,nOqKH C HeqeTHbIM KOJIHqeCTBOM 3y6beB rapaH-
THpyeTcH O,nHopo,nHoe pacrrpe,neJIeHHe H3Hoca KaK errH, TaK H 3y6beB 3Be3,nOQKH.
Moryr HCrrOJIb30BaTbCH H Be aH, H Be,nOMaH 3Be3,nOQKH C qeTHbIM KOJIWleCTBOM
3y6beB, HO pacrrpe,neJIeHHe H3Hoca 3y6beB 06eHX 3Be3,nOqeK H errH 6y,neT HepaBHO-
MepHbIM.
KOJllf1lecTBO 3yobeB
MaKCHMaJIbHOe KOJIHQeCTBO 3y6beB JII060H Be,nOMOH 3Be3,nOQKH (Z2) He ,nOJDKHO
rrpeBbIIIlaTb 114. 3TO orpaHWleHHe 06YCJIOBJIeHO TeM <paKToM, QTO rrpH ,naHHOM y,n-
5.3. MeXaHUlf.eCKUe nepeoalf.u: u,enHble nepeiJalf.u 361
JIBHeHHH, enH, CBH3aHHblM C H3HOCOM, pa60qHH HaqaJIbHblH ,l(HaMeTP errH Ha
3Be3,nOqKe YBeJIHqHBaeTCH rro OTHOIIleHHIO K HOMHHaJIbHOMy HaqaJIbHOMy ,nHaMeT-
.
py, T. e. rrpe,nrrOJIaraeTCH 60JIee BblCOKoe pacrrOJIOXeHHe errH Ha 3y6e 3Be3,nOqKH.
CqHTaeTCH, qTO ,nOrryCTHMbIH 6e30rracHblH H3HOC errH ,nOJDKeH COCTaBJUlTb rrOPM-
Ka 2% y,nJIHHeH:IDI OT HOMHHaJIbHOH ,nJIHHbI.
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3Be3,nOqKa, MO)I{HO rro rrpocToH cPopMyJIe 200fN, r,ne N - KOJIWleCTBO 3y6beB MaK-
CBMaJIbHOH 3Be3,nOQKH B CHCTeMe rrpHBo,na.
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qeK, patfo II(HX C O,nHOH nerrblO, QTo6bl CyMMapHoe KOJIWleCTBO HX 3y6beB 6billO
He MeHbIIle 50; HarrpHMep, rrpH rrepe,naTOQHOM OTHOIIleHHH 1:1 o6e 3Be3,nOQKH Mor-
JIB 6bl HMeTb rro 25 3y6beB KIDK,LJ;aH.
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,l(BMOCTH CKOHCTPYHpOBaTb errb C paCCTOHHHeM Me y eHTPaMH, MeHbIIle QeM B
30 pa3 rrpeBblIIlalOlI(HM IIlar errH MH 60JIbIIlHM 2 M, peKOMeH)(yeM 06Cy,nHTb ,neTa-
JIB rrOCTPoeH:IDI errH C TeXHHQeCKHM nepCOHa-
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MHHHMaJIbHOe paCCTORHHe Me y eHTpaMH
BHor,na orrpe,neillIeTCH 06XBaTOM errblO Be,nym;eH
3Be3,nOQKH; B TaKHX CJIyqaHX Mbl peKOMeH,IJ;yeM,
qTo6bl He MeHbIIle 6 3y6beB o,nHOBpeMeHHO BXO-
,l(HJIO B 3a eIIJIeHHe C errblO.
PaCCTOHHHe Me y eHTPaMH TaIOKe orrpe,ne-
JUleTCH rrpHBJIeKaTeJIbHOCTblO HCrrOJIb30BaH:IDI e-
lIB C QeTHblM KOJIHQeCTBOM 3BeHbeB, QTo6bl H3-
6exaTb HctIOJIb30BaH:IDI rrepexo,nHoro 3BeHa, qTO
HBKor,na He peKOMeH,IJ;yeTcR, 3a HCKJIIOQeHHeM MVlH MYM weCTb 3y6beB
OC06blX 06CTOHTeJIbCTB.
B COOTBeTCTBHH C peKOMeH,IJ;yeMblM 06XBaTOM
n;errblO Be eH 3Be3,nOQKH )LIDI rrpHBo,nOB, pacrrOJIOXeHHbIX B ropH30HTaJIbHOH
IIJIOCKOCTH, ,nOJDKHO HCrrOJIb30BaTbCH KpaTtIaHIIlee paCCTOHHHe Me)I{,Uy eHTPaMH.
C!>OPMYJIbl BbIQHCJIeH:IDI ,nJIHHbI errH H paCCTOHH:IDI Me eHTpaMH ,nJIH rrpH-
BO,nOB C ,nByMR 3Be3,nOQKaMH rrpHBe,neHbl Ha CTPaHH e 368.
PeKOMeH,IJ;yeMble paCCTOHH:IDI Me y eHTPaMH )LIDI rrpHBo,nOB
liar LUOHMOB 3/8 1/2 5/8 3/4 1 11/4
MM 9,525 12,70 15,87 19,05 25,40 31,75
PaccToRHIDI Me)l{)Jy u;eH'rpaMH MM 450 600 750 900 1000 1200
liar LUOHMOB 1 1/2 1 3/4 2 2 1/2 3
MM 38,1 44,45 50,80 63,50 76,20
PaCCTORHHR Me)l{)Jy u;eH'rpaMH MM 1350 1500 1700 1800 2000
Dla6a 5. MexaHu'IeclCue nepeiJa'lu
PacnOJlO1KeUue npuBo,na
TIpHBO,nbI MOryr pacrrOJIaraTbC.H ropH30HTaJIbHO, HaKJIOHHO MH BepTHKaJIbHO.
KaK rrpaBHJIO, HarpyxeHHIDI BeTBb MoxeT pacrrOJIaraTbC.H KaK cBepxy, TaK H CHH3Y,
rro XeJIaHHIO. ECJIH rrpHBo,n pacrrOJIOXeH BepTHKaJIbHO HJIH rrOqTH BepTHKaJIbHO,
rrpe,nrrOqTHTeJIbHO, qTo6bI Be a.H 3Be3,nOQKa (Zl) 6bma pacrrOJIOXeHa BbIIIle Be,n;o-
MOH 3Be3,nOQKH (Z2); o,nHaKO ,nIDKe B rrpHBo,ne C BepTHKaJIbHbIM pacrrOJIOXeHHeM
BrrOJIHe B03MO)I{JIO paCrrOJIO)f{HTb Be.nyII.'(ylO 3Be3,nOQKY HIDKe, eCJIH rrpHIDITb MepbI K
TOMy, QTo6bI errb Bce BpeWI OCTaBaJIaCb rrpaBHJIbHO Ol'peryJIHpOBaHHoH.
I(enmpbl
MexoceBoe paCCTO.HHHe Mex.ny ,nBYM5I BaJIaMH HJIH 3Be3,nOQKaMH.
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Qepe3 eH'rpbI BaJIOB, C ropH30HTaJIblO.
BpaUl,enue
ECJIH cMoTpeTb B,nOJIb OCH Be,nOMoro BaJIa, BpameHHe MoxeT rrpOHcxo,nHTb no
QaCOBOH C'rpeJIKe MH rrpOTHB QaCOBOH Cl'peJIKH.
( J
5.3. MexaHUlf,eCKUe nepeoalf,u: u,enHble nepeoalf,u 36
5.3.9. PacnOnOJICeHJfe npJfso,qa
O,nHa errb MoxeT HCrrOJIb30BaTbCH )])UI rrpHBe,neHIDI B ,neHCTBHe HeCKOJIbKHX Ba-
JIOB, H 6JIaro,napH crroc06HOCTH pOJIHKOBOH errH BXO,nHTb B 3a eIIJIeHHe C JII06bIM
MexaHH3MOM OT,neJIbHble BaJIbI o,nHoro H Toro xe rrpHBo,na MOryr BpamaTbCH B 0)];-
HOM H TOM xe HJIH B rrpOTHBOrrOJIO)I{HbIX HarrpaBJIeHIDIX, eCJIH Be,nOMble 3Be3,nOQIGl
P33JIHQHbIMH crrOC06aMH BXO,lUlT B 3a enrreHHe C errblO. ,LJ;OrrycTHMoe KOJIHQeCTBO
Be.nyII(HX 3Be3,nOQeK B JII060M rrpHBO,ne 3aBHCHT OT paCrrOJIOXeHIDI.
BapHaHTbI B03MO)l{JlbIX paCrrOJIOXeHHH rrpHBO,na rrOKa3aHbI HIDKe.
npHBO,lUtI C nepeMeHHbIM nOJlO1KeHHeM BaJlOB
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c 27 HJIH 60JIee 3y6bHMH. U:eHTpbI: mar errH, YMHoxeHHbIH Ha 30-50.
npHBO,lUtI co CJlHmKOM OOJlbIUHM paCCTOBHHeM Me1K.nY neHTpaMH
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B03MO)KHO BBe,aeHHe rrpOMexyTOQHOrO Barra R1IH orropHhIX 3Be3,aOQeK;
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K1IH orropHhIX HarrpaBJHIIOW;HX.
364 fl108a 5. MexaHUy,ecKue nepeoay,u
npHBO,lUt1 C HeCKOJIhKHMH BaJIaMH (MHOrOBaJIhHhle)
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JUIeT npHMepHO 98%, npH coe,nHHeHHH nOCJIe,nOBaTeJIbHOCTH B3aHMOCB.SI3aHHbIX
npHBo,nOB, KaK B npHBo,nHOM pOJIHKOBOM KOHBeHepe, 06 HH K03<P<PHIJ;HeHT nOJIe3-
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-----------
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iJeuCm8UJl, HO c YMeHbUleHHblM KOHmaKmOM MeJICiJy 3y6bJlMU.
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XBaT u;enblO Be,nOMbIX 3Be3,nOQeK.
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c 27 HJIH 60JIee 3y6b MH.
UeHTPbI. HaHKpaT1.JaHmee B03MO)I(HOe paCCTO HHe.
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QenH, BbI6paHHbIe C HCnOJIb30BaHHeM 3Toro MeTo,aa, 6y,ayr HMeTb nporHo3Hpye-
MbIH CpOK CJI}')K6bI 15000 1.JaCOB npH YCJIOBHH npaBHJIbHOH YCTaHOBKH H o6cJIyxH-
BaHH .
Upe.nynpeJK.neHHe
CxeMbI oueHKH xapaKTepHCTHK, npHBe,aeHHbIe B pa3,aeJIaX 5.3.12, 5.3.13, npe-
BbIllIalOT MHHHMaJIbHbIe CTaH.aapTbI, H BbI60p uenH C HCnOJIb30BaHHeM 1.JHCeJI, npH-
BO,l{HMbIX B 3TOM pa3,aeJIe, no,axo,aHT TOJIbKO J])I ueneH Renold.
HCnOJIb3yHTe HHTepaKTHBHbIH BbI60p ueneH Renold Ha caHTe www.renold.com.
CHMBOJIbl, TepMHHbl H e.lnlHHl(b1
ZI - KOJIH1.JeCTBO 3y6beB Be,aymeH 3Be3,a01.JKH.
Z2 - KOJIH1.JeCTBO 3y6beB Be,aoMoH 3Be3,a01.JKH.
C - paCCTOSlHHe Me)l(.[\Y ueHTpaMH (Me)l(OCeBoe) (MM).
P - mar uenH (MM).
i - nepe,aaT01.JHOe OTHomeHHe.
L - J])IHHa uenH (marH).
QTo6bI BbI6paTb uenHoH npHBO,a, Heo6xo,aHMa CJIe,aYlOwa HH<p0pMaUHSI.
. nepe,aaBaeMaSi MOWHOCTb B KHJIOBarrax.
. qHCJIO 060pOTOB Be,aywero H Be,aOMoro BaJIOB.
. XapaKTepHCTHKH npHBo,aa.
. PaCCTO HHe Me)l(.[\y ueHTPaMH.
Ha OCHOBaHHH 3TOH 6a30BOH HH<popMaUHH H BapHaHTOB npHJIaraeMOH MOWHO-
fH nOCTpoeHbI cxeMbI oueHKH xapaKTepHCTHK.
Dla8a 5. MexaHU'lecICue nepeiJalfu
KpaTKHH 0030P MeTO,lJ;a Bwoopa
1. BbI60p nepe,naTO'lHOrO OTHomeHIDI H 3Be3,nO'leK npH MHHHMy-Me ZI = 193Y-
6beB - CTP. 366.
2. Onpe,neJIeHHe paC'IeTHOrO K03<P<PHUHeHTa BH,ZJ;a HarpY3KH II C yqeToM ,nHHa-
MH'IeCKOH HarpY3KH.
K03<P<PHUHeHT 3y6a/2 (19/Z I ) - CTP. 367.
3. BbJtlHCJIeHHe paC'IeTHOH MOInHOCTH = MOInHOCTb x fi x 12 (KBT) - CTP. 368.
4. BbI60p uenHoro npHBo,na.
MCnOJIb30BaHHe cxeM oueHKH xapaKTepHCTHK - CTP. 368, 372, 373.
5. BbI'IHCJIeHHe ,nJIHHbI uenH no <popMYJIe - CTP. 368.
6. BbI'IHCJIeHHe TO'lHOrO paCCTOHHIDI Me)l{,l(y ueHTPaMH - CTP. 369.
HaKoHeu, BbI60p MeTo,na CMa3bIBaHIDI.
Bwoop npHBO.lOl H nepe,lJ;aTO'IHoro OTHOmeHHJI
.IDI BbI60pa nepe,naTO'lHOrO OTHomeHIDI Ha OCHOBaHHH cepHHHo BbIrrycKaeMhIX
3Be3,nOqeK CTaH;J;apTHbIX pa3MepOB MO)I{HO HCnOJIb30BaTb Ta6JIHUY (CM. HIDKe). nyq-
me HCnOJIb30BaTb HeqeTHOe KOJIH'IeCTBO 3y6beB B CO'leTaHHH C 'IeTHbIM KOJIWleCT-
BOM 3BeHbeB uenH.
B H,ZJ;eaJIe CJIe,nyeT BbI6HpaTb uenHbIe 3Be3,nO'lKH KaK MHHHMYM C 19 3y6bHMH.
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HMeTb no Iq)aHHeH Mepe 25 3y6beB H 6bITb yrrpOqHeHHhI-
MH.
PeKOMeH;J;yeTcH, qTo6bI uenHbIe 3Be3,nO'lKH HMeJIH He
60JIee 114 3y6beB.
TIepe,naTO'lHOe OTHomeHHe B JII060M c.rryqae MO:>KHO
BbIqHCJIHTb no <poPMYJIe:
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min
Be,nyw:aH 3Be3,nOQKa (Zl)
TIpH 60JIbmHX nepe,naTO'lHbIX OTHomeHIDIX y6e,nH-
TeCb, 'ITO yrOJI OXBaTa AJUI ZI He MeHbme 120°.
PaCqeTHOe nepe,naTO'lHOe OTHomeHHe H 3Be3,nOQKH = Z 2 .
Zl
TIepe,naTO'lHbIe OTHomeHIDI AJUI uenH npH HCnOJIb30BaHHH 3Be3,nO'leK npe,nnoq-
THTeJIbHbIX pa3MepOB
qHCJlO 3y6heB qHCJlO 3y6heB ae eii: 3Be3.Il;O'IKII Z.
BeJJ;oMoH
3Be3JJ;O'IKH Zz 15 17 19 21 23 25
25 - - - - - 1,00
38 2,53 2,23 2,00 1,80 1,65 1,52
57 3,80 3,35 3,00 2,71 2,48 2,28
76 5,07 4,47 4,00 3,62 3,30 3,04
95 6,33 5,59 5,00 4,52 4,13 3,80
114 7,60 6,70 6,00 5,43 4,96 4,56
PeKOMeH;J;yeMbIe paCCTOHHIDI Mex,ny ueHTPaMH CMOTPH CTPaHHIJ;y 369.
5.3. MeXaHUlteCKUe nepedaltu: l(enHble nepedaltu 367
BeAy aSl 3Be3AO Ka Z1
BeAOMaSl 3Be3AO Ka Z2
C
PaCCTORHHe Mex,ny n;eHTPaMH
XapaK.TepHCTHKH
npHBO,lUlMhIX B ,aeiiCTBHe
ycrpoiiCTB
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KOMIIpeccopbI, IIeqaTHbIe Ma-
mHHbI, KarraH,D;pbI ,lUUI 6)'Ma-
rH, paBHOMepHO HarpyxeH-
HbIe KOHBeilepbI, 3CKaJIaTOpbI,
MemarrKH H MHKcepbI ,lUUI
KHX IIpO OB, 6apa6aH-
HbIe CyrnHJIKH, BeHTHIDITopbI
HaCOCbI H KOMIIpeccopbI (3 +
UHKJIOB), 6eToHoMemarrKH,
HepaBHOMepHO HarpyxeHHbIe
KOHBeilepbI, MemarrKH H MHK-
cepbI ,lUUI CbIrrytlHX IIpO OB
C1porarrbHbIe CTaHKH, 3KCKa-
BaropbI, BarrbUOBbIe H mapo-
BbIe ,nP06HJIKH, CTaHKH ,lUUI
o6pa6oTKH pe3HHbI, IIpeCCbI
H pe3aKH, HaCOCbI Ii KOMII-
peccopbI C 1 H 2 UliKJIaMH,
He<pTHHbIe 6ypbI
Onpe.n;eJIeHHe K034»4»HIUfeHTOB
CJIe.nyIOIUHe K03<P<PHUHeHTbI 6y,nyr HCIIOJIb30BaTbCH B .n;aJIbHeHmeM npH onpe-
,n;eJIeHHH paCqeTHOH MOIUHOCTH.
K034»4»lIIUIeHT Blf)J;a HarpY3KH Ii .
K03<P<PHUHeHT It yqHTbIBaeT .n;HHaMHqeCKHe HarpY3KH, 3aBHCHIUHe OT YCJIOBHH
pa60TbI uellH. 3HaqeHHe K03<P<PHUHeHTa fi MO)I{HO BbI6paTb HanpHMyro RJIH 110
aHaJIOrHH, HCIIOJIb3YH .n;aHHyro Ta6JIHUY.
XapaK.TepHCTHKH ,aBIll'aTeJIeii
lJJIaBIIhIii xo,a. Jlel1Wl y,aapnaJI
3J1eK'l'pO,aB1II'a - narpY3Ka.
TeJIH, napoBhle ,ZJ;BIll'aTeJIH Bnyr-
H ra30Bhle TYP- peBHero cropanlUl
OHllhl, ,aB1ll'a1'e- meCTHTaKTllhle H
JIB BHY'fpeBHero oOJlee, C MexanH-
cropaHHJI C qecKoii nepe,aaqeii,
I'It,ApaBJIJl'le- 3J1eup0,aBIll'aTeJIH
CKoii nepe,aaqeii C 1JaCTWMH nyCKaMII
YMepeBHaJI y,aap-
naJI narpY3Ka.
,ZJ;BIll'aTeJIH Bnyr-
peBHero cropa-
HHJI Menee qeM
meCTHTaKTllhle,c
MeXaHII'IecKoii
nepe,aaqeii
lliaBHbIH
xo,n
YMepeHHasI
y,napHasI
HarpY3Ka
TIDKeJIasI
y,napHaH
HarpY3Ka
1
1,1
1,3
1,4
1,5
1,7
1,8
1,9
2,1
Dla8a 5. MexaHU'lecKue nepeiJalfu
K034»4»HIUfeHT 3yoa h
TIpHMeHeHHe K03<P<PHUHeHTa 3y6a eIUe 60JIbme H3MeIDIeT OKOl{qaTeJIbJIYlO pac-
qeTHYID MOIUHOCTb. BbI60p 3Be3,nOqKH C MeHbmHM ,nHaMeTPoM npHBe,neT K CHIDKe-
HHIO MaKCHMaJIbHO B03MO)I{HOH nepe,naBaeMoH MOIUHOCTH, nOCKOJIbKY HarpY3Ka Ha
uenb 6y,neT BbIme.
19
K03<P<PHUHeHT 3y6a/2 BbJtlHC.IDleTCH no <poPMYJIe: /2 =-.
Zl
06paTHTe BHHMaHHe, qTO 3Ta <poPMYJIa nOJIy'laeTCH 6JIaro,napH TOMY, qTO KPH-
BbIe AJUI oueHKH xapaKTepHCTHK, npe,nCTaBJIeHHbIe Ha rpa<pHKax B rryHKTax 5.3.12,
5.3.13, nOCTPoeHbI AJUI 3Be3,nOqeK C 19 3y6bHMH.
K034» HIUfeHT 12 ,lUIJi CTaH.ZJ;apTHbIX pa3MepOB 3Be3,lJ;O'leK
z. Ii
15 1,27
17 1,12
19 1,00
21 0,91
23 0,83
25 0,76
BbJ1lHCJIeHHe paC'IeTHOH MOIU.HOCTH
YMHO)l{bTe MOIUHOCTb, KOTOPYID He06xo,nHMO nepe,naBaTb Ha K03<P<PHn.HeHThI,
nOJIyqeHHbIe Ha IIIare 2.
PacqeTHaR MOIUHOCTb - MOIUHOCTb, KoropYK> He06xo,l(HMO nepe,naBaTh x f} x f 2 (KBT).
PaCqeTJIYIO MOIUHOCTb Tenepb MO)I{HO HCnOJIb30BaTb AJUI BbI60pa n.enHoro npH-
Bo,na C nOMOIUhlO rpa<pHKoB B nyJiKTax 5.3.12, 5.3.13.
Bbloop nenHoro npHBO,lJ;a
Ha cxeMe BbI6epHTe O,nHOpH.n;JIYIO uenb C HaHMeHbIIIHM marOM, qTo6bI nepe,na-
BaTb paCqeTJIYIO MOIUHOCTb npH 3an;aHHOM qHCJIe 060pOTOB Be,ayII(eH 3Be3,nOqKH ZIt
3TO 06bIqHO npHBo,nHT K HaH60JIee 3KOHOMWlHOMY BbI60py npHBo,na. ECJIH
paCqeTHaH MOIUHOCTb 60JIbIIIe, qeM YKa3aHa AJUI O,nHOpH.n;HbIX ueneH, paCCMOTPHTe
MHOrOpH.n;HbIe n.enH C TeM )l(e pa3MepOM IIIara, KOTOpbIH no,np06HO onHcaHO B CO-
OTBeTCTBYIDIUeM pa3,neJIe.
BbJ1lHCJIeHHe ,lUIHObi nenH
QT06bI HaRTH AJIHJIy n.enH qepe3 ee IIIar (L) AJUI JII060ro npe,nnOJIaraeMOro pac-
CTOHHIDI Me)l{,l(y ueH1paMH AJUI npHBo,na C ,nB)'MH 3Be3,nOqKaMH, HCnOJIb3yHTe CJIe.ny-
IOIUYIO <POPMY.rry:
Z + Z 2C ( Z 2 2 Z\ ) 2 x P
ITTT L I 2
I-IfJIHHa = + - +
2 P C
BbIqHCJIeHHOe qHCJIO marOB CJIe,nyeT OKpyrJIHTb C nOBbIIIIeHHeM ,no 6JIIDKaRIIIe-
ro ueJIoro qeTHOrO qHCJIa marOB. HeqeTHOrO qHCJIa marOB CJIe,nyeT H36eraTb, no-
5.3. MeXaHUlteCKUe nepedaltu: l(enHble nepedaltu 36
CKOJIbKY B npoTHBHOM cnytIae npHIIIJIOCb 6bI HCnOJIb30BaTb nepexo,nHoe 3BeHO, qTC
He peKOMe eTCH. ECJIH ,nIDI peryJIHpOBKH HCnOJIb3yeTcH HaTHXHaH 3Be3,nOqKa, I<
.nnHHe uenH (L) CJIe,nyeT ,n06aBHTb ,nBa mara.
C - 3TO npe,nnOJIaraeMOe paCCTOHHHe Mex,ny ueHTPaMH H, KaK npaBRJIO, ,nOJI-
:>KHO nonan:aTb B ,nHana30H Mex,ny 30 H 50 maraMH.
HanpHMep, ,nIDI uenH C marOM I! ,nIOHMa C = 1,5 x 25,4 x 40 = 1524 MM.
2
BbJ1IHCJleHHe TO'lHOrO paCCTOJlHHJI Me n;eHTJ)aMH
<l>aKTWleCKOe paCCTOHHHe Mex,ny ueHTPaMH ,nIDI uenH AJIHHOH (L), BbIqHCJIeH-
HOB MeTo,noM, npeAJIO)l(eHHbIM BbIme, 6y,neT, KaK npaBRJIO, 60JIbIIIe, qeM npe,nno-
JIaraeMOe nepBOHaqarrbHo. MCnpaBJIeHHOe paCCTOHHHe Mex,ny ueHTPaMH MO)I(HO
BWlHCJIHTb no CJIe,nyroIUeH <poPMYJIe:
C= [2L-Z2 -z! + (2L-Z2 _Z!)2 -( 3, 8 (Z2 _Z!)2)J
r,ne P - mar uenH (MM), L - AJIHHa uenH (marH), Zl - qHCJIO 3y6beB Be,nYIUeH
3Be3,nOqKH, Z2 - qHCJIO 3y6beB Be,nOMOH 3Be3,nOqKH.
npHBO,lUJI C HeCKOJIbKHMH 3Be3.l1.0'lKaMH
llpH npOeKTHpOBaHHH npHBo,noB C HeCKOJIbKHMH 3Be3,nOqKaMH BbIqHCJIeHHe
,l(JIHHbI uenH CTaHOBHTCH HaMHoro CJIO)I(Hee. O,nHaKO 60JIbmHHCTBO CHCTeM CAD
MO)I(HO HCnOJIb30BaTb ,nIDI BbIqHCJIeHIDI AJIHHbI uenH, npOBe,I(H 3aMKIfYTYIO KpHByro
Ha paCCToHHHH ,nHaMeTPa HaqaJIbHOH OKpyxrnOCTH, TaK qT06bI OXBaTHTb KIDK,ZJ:yro
3Be3,nOqKY. TIpH BbInOJIHeHHH pHCyJiKa BpyqHyro pe3YJIbTaT TaIOKe 6y,neT ,l(OCTaTOq-
HO TOqHbIM H MO)l(eT BbIr.1UI,L(eTb CJIe,nyroIUHM 06pa30M:
/3 1
Ln
.
CQ. .
JU1Hbl Lr,
Yrnbl
/33
TeOpeTHqeCKYIO AJIHHY B marax Tenepb MO)I(HO BbIqHCJIHTb qepe3 L T H no
CJIe,l{ylOIUeH <poPMYJIe:
1 n n Z
qHCJIO IIIarOB = - L LT, + L I '
P ;=1 ;=1 360
r,ne P - mar uenH, Z; - KOJIHqeCTBO 3y6beB Be,nOMOH 3Be3,nOQKH.
3TOT MeTO,n BbIQHCJIeHIDI TaIOKe MO)I(HO npHMeIDITb AJIH CnytIaeB, Kor,na ueJIb
npOJIO)l(eHa no HanpaB.IDlIOIUHM nOJI03bHM RJIH BOKpyr HaTIDKHbIX 3Be3,nOqeK. I1x
CJIe.nyeT paCCMaTPHBaTb KaK 06bIqHbIe 3Be3,nOQKH.
Dla8a 5. MexaHU'lecKue nepeiJa'lu
3Be3.l1.0'lKH ,lUIJi n;enHbIX nepe.ll.a'l
TIpe,nnpHHTHe Renold nOCTaBIDleT HCqepnbIBaIOIUHH ,nHana30H 3Be3,nOqeK .wm
QeneH EBponeHcKHx CTaH;J;apTOB BITJIOTb ,no mara 2 ,nIOHMa.
3Be3,nOqKH ,npyrHX p3.3MepOB, BKJIIOQaH 3Be3,l(OQKH C pa3MepaMH, COOTBeTCTByro-
IUHMH AMepHKaHCKOMY CTaH;J;apTY, MO)I{HO nOJIyqHTb no cneQHaJIbHOMY 3aKa3Y.
CneQHaJIbHbIe 3Be3,l(OQKH, H3 cneQHaJIbHOrO MaTepHaJIa RJIH cneQHaJIbHOrO
BH)J;a, TaIOKe H3rOTaBJIHBaIOTCH Ha 3aKa3. 06bNHO OHH npHMeIDIIOTCH B cneQHaJIh-
HhIX npHJIO)l(eHHHX B He6JIarOnpIDITHbIX BHemHHX YCJIOBIDIX RJIH B YCJIOBIDIX orpa-
HHQeHHOrO npoCTPaHCTBa. BOT HeKoTopbIe npHMepbI:
. 3Be3,l(OqKH C BaJIOM.
. TIpHBapHbIe RJIH C'beMHbIe CTYTIHQbI.
. 3Be3,l(OQKH co cpe3HbIMH mTH<pTaMH.
. «O)l(epeJIbHbIe» 3Be3,l(OQI(H C QeI1HbIMH I1JIaCTHHaMH H OT,l(eJIbHbIMH 3y6QaTbIMH
yqaCTKaMH, npe,l(Ha3HaQeHHbIe MH BpaIUemrn 60JIbmHX 6apa6aHOB HJIH CTOJIOB.
. KOM6HHHpOBaHHbIe 3Be3,l(OQKH (COQeTaHHe ,l(BYX RJIH 60JIee 3Be3,l(OQeK C pa3-
JIHQHbIM marOM H QHCJIOM 3y6beB).
. 3Be3,l(OQKH, COcToHIUHe H3 ,l(BYX RJIH 60JIee OT,l(eJIbHbIX QaCTeH (pa3'beMHhle
RJIH cerMeHTHbIe).
BbIOOP MaTepHaJIOB 3Be3,lJ;O'leK
« Q)I(e pen bHaSl»
3Be3AOYKa
CerMeHTHaSl
3Be3AOYKa
BbI60p MaTepHaJIa H cnoco6a TenrroBoH o6pa6oTKH 3aBHCHT OT <pOPMbI, ,nHa-
MeTPa H MaCCbI 3Be3,l(OQKH. Ta6JIHl(y, npHBe,neHJIyIO HIDKe, MO)I{HO HCnOJIb30BaTb B
KaQeCTBe CnpaBOQHOH npH BbI60pe MaTepHaJIa 3Be3,l(OQeK.
3Be 01JK8 lJJIuHhlii xo,n; YMepeHHu y,n;apHU HarpY3Ka TJDKeJlU y.n;aPHU HarpY3Ka
JJ;o 29 3y6beB EN8 HJIH EN9 EN8 HJIH EN9 3aKaJIeHHasI OT eHHasI CTaJIb HJIH IIOBepx-
HOCTHO yrrpOqHeHHaH WIfKasI CTaJIb
30 H 60JIee qyryH MHfKasI CTaJIb HJIH MHxa- EN8 HJIH EN9 3aKaJIeHHasI OTny-
3y6beB HHT meHHasI CTaJIb HJIH IIOBepXHOCTHO
yrrpotJHeHHasI WIfKasI CTaJIb
5.3. MeXaHUlteCKUe nepeoaltu: u,enHble nepeoaltu
CxeMbI oueHKH MOIUHOCTH AJUI ueneH EBponeHcKoro CTaH;J;apTa H ANSI, 11
Be,neHHbIe B rryHKTax 5.3.12, 5.3.13, OCHOBaHbI Ha CJIe,nYIOIUHX npe,nnOJIO)l(eHIDU
1. K03<P<PHUHeHT YCJIOBHH 3KCIIJIyaTaUHH paBeH 1.
2. PaccToHHHe Mex,ny ueHTPaMH 3Be3,nOqeK COCTaBIDleT 30-50 marOB uenH.
3. CJIO o6opoTOB Be.nyw;eH 3Be3.f(Ot{I{H (Zl) HJIH Ha Be.nyw;eM, HJIH Ha Be,nOMOM Be
4. TIPHBo,nHoe YCTPOHCTBO COCTOHT H3 ,nBYX 3Be3,nOqeK.
5. PeryJIHpOBKa paCCTOHHIDI Mex,ny ueHTPaMH RJIH HaTIDKHOH 3Be3,nOqKOH ]
HeHarpyxeHHoH BeTBbIO.
6. Coe,nHHeHHaH 3aKJIenKaMH 6eCKOHeqHaH uenb (coe,nHHeHHe 3anpeccoBKoi
7. CooTBeTCTBYIOIUee CMa3bIBaHHe.
8. TOQHaH peryJIHpOBKa BaJI/3Be3,nOQKa
TIpH TaKHX YCJIOBIDIX O)l(H)];aeMbIH CpOK CJIy)K6bI 06bNHO COCTaBlliIeT npHMep
15000 QaCOB, Kor,na uenb <PYHKUHOHHPyeT npH nOJIHOH HarpY3Ke. MOIUHOCTb ,D
MHOrOPMHbIX ueneH no EBponeHCKOMY CTaH;J;apT}', BITJIOTb ,no 1peXPMHbIX, npHI
,neHa COOTBeTCTBeHHO BO 2 H 3 KOJIOHKax; AJUI ueneH ANSI, BITJIOTb ,no QeTbIpexpSl
HbIX, BO 2, 3 H 4 KOJIOHKax.
5.3. 11. OLleHKa xapaKTepHCTHK
CxeMbI oueHKH xapaKTepHCTHK Ha nepBbIH B3r.1UI,L( KIDK}TTCH CJIO)I(HbIMH, o,nHaJ
OHH CKOHCTPYHpOBaHbI Ha OCHOBe TPex npOCTbIX npHMbIX. 113 rpa<pHKa BH)J;HO, Qr
npH HH3KHX CKOpOCTHX COCTOHHHe OTKa3a
qaIUe Bcero 06YCJIOBJIeHO YCTaJIOCTbIO
DJIaCTHH, eCJIH npeBbImeHa MaKCHMaJIb-
HaH peKOMeH;J;yeMaH MOIUHOCTb. O,nHaKO
HcrnpaHHe BaJIHKOB B03HHKaeT H3-3a pa3-
pbIBa rpaHHQHOH CMa3KH npH BbICOKHX
CKOpOCTHX. EIUe ,no nepeCeQeHIDI 3THX
JIHHHH, Cpe3aH yrOJI, npoxo,nHT JIHHIDI,
xapaKTtpH3YIOIUaH YCTaJIOCTb BT}'JIOK H
pOJIHKOB.
OnopHoe ,lJ;aBJIeHHe
ECJIH uenb npaBRJIbHO BbI6paHa, npWlHHOH OTK3.3a Qepe3 AJIHTeJIbHbIH npOMe.
xyTOK BpeMeHH, CKopee Bcero, CTaHeT H3HOC.
BonpOCbI H3Hoca, KOTOpbIH 3aBHCHT OT MHorHX <paKTOpOB, 06Cy)I{)J;aJIHCb paHee
B 3TOM PYKOBo,nCTBe, o,nHaKO OQeHb BIDKHbIM nOKa3aTeJIeM, C xopomeH TOQHOCTbl()
xapaKTepH3YIOIUHM H3HamHBaHHe, MO)l(eT CJIy)KHTb BeJIHqHHa ,naBJIeHIDI Mex,ny
OCHOBHbIMH conpIDKeHHbIMH nOBepXHOCTHMH, T. e. BaJIHKOM H BT}'JIKOH.
3TO ,naBJIeHHe H3.3bIBaeTCH onopHbIM ,naBJIeHHeM H BbIQHC.IDleTCH ,neJIeHHeM pa-
60QeH HarpY3KH Ha onopHYIO IIJIOIUa;:J;b. OnopHbIe ITJIOIUa;:J;H AJUI CTaH;J;apTHbIX ue-
neH npHBe,neHbI B ,naHHbIx AJUI npOeKTHpOBaHIDI B KOHue 3Toro PYKOBo,nCTBa.
CJIe,nyIOIUaH Ta6JIHua ,naeT 06IUee npe,nCTaBJIeHHe 0 nOCJIe,nCTBIDIX HCnOJIb30Ba-
HID! pa3JIHQHbIX onopHbIX ,naBJIeHHH, HO OHa He ,nOJDKHa npHMeIDITbCH 6e3 yqeTa
,npyrHX MeTo,nOB BbI60pa ueneH, npeAJIaraeMbIX B 3TOM PYKOBo,nCTBe.
HH3KaH CKOpOCTb ,no 60% MaKCHMaJIbHOH ,nOrryCTHMOH CKOpOCTH.
Cpe,nHIDI CKOpOCTb 60-80% MaKCHMaJIbHOH ,[(OrryCTHMOH CKOpOCTH.
BbICOKaH CKOpOCTb CBbIllie 80% MaKCHMaJIbHOH ,nOrryCTHMOH CKOpOCTH.
YCTPOtiCTBO cxeMbl ou.eHOK xapaKTep CT
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no EsponeHcKoMY cTaH,qapTY
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5.3. MexaHu'tecKue nepeiJa'tu: l(enHble nepeiJa'tu
5.3.13. OLleHKa xapaKTepHCTHK LleneR,
H3rOTOSneHHIJIX no cTaH,qapTY ANSI
AMepHKaHCKHH CTaH;J;apT QerrHbIX rrpHBo,nOB
OQeHKa xapaKTepHCTHK.rvrn Be,n eH 3Be3,nOqKH C 19 3y6bRMH
.
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CleO 340 200
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m 2111 = ;= =
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OT 3T0ii1 npSlMoii1 npoKoHcynb-
>:: ...
TLt1pYLt1TeCb CO cneLJ.Lt1an CTaM
', Renold, T06bl nony Lt1Tb Lt1H-
, <t>opMaLJ.Lt11O 06 OnTLt1ManbHoii1
! '<' xapaKTepLt1CTLt1Ke npLt1BOAa.
o. 040 034 0.10 ,
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2
YpaBHeHHJI nepe,lJ;a'lH
CJIe :m:He ypaBHeHHR ,naIOT COOTHOllieHIDI Me)l()];Y MO:m:HOCTbIO, BpalI(aIOII(HM
MOMeHTdM H CKOpOCTbIO .rvrn pa3JIHQHbIX rrpHBo,nHbIX YCTPOHCTB.
Fi . d 1 9550 · Pr
BpamaIOIUHH MOMeHT Md = -
2000 nl
Md . n} Fi. V
MO:m:HOCTb Pr = = (KBT)'
9550 1000 '
CRJIa Fi = 1000 . Pr = 2000 . Md (H);
V d}
n} . Zl . P
CKOpOCTb V = (M/C),
60000
r,ne Md - BpalI(alOII(HH MOMeHT Be,n eH 3Be3,nOQKH (HM); Pr - MOII(HOCTb (KBT);
d 1 - HaqarrbHbIH ,nHaMel'p Be,n eH 3Be3,nOQKH (MM); n} - QHCJIO 060pOTOB Be,l(Y-
m;eH 3Be3,l(OQKH (06/MHH); Z} - QHCJIO 3y6beB Be,nym;eH 3Be3,nOQKH; Z2 - QHCJIO 3Y-
6beB Be,l(OMOH 3Be3,l(OQKH; V - JIHHeHHaJI CKOpOCTb QerrH (M/C); Fl - HaTR)I(eHHe
l(errH (H); P - war QenH (MM).
Dla8a 5. MexaHU'lecKue nepeiJalfu
QeHTpOCTJ)eMHTeJIbHOe YCKopeHHe
[(eHTPOCTPeMHTeJIbHOe YCKopeHHe, ,neHCTBYIDIUee Ha qaCTH uerrH, 3aueI1JleH-
HbIe Ha 3Be3,nOqKH, orrpe,ne.IDleTCH CJIe,nyIOIUeH <pOPMYJIOH:
F 2 = q · V 2 (H),
r,ne F 2 - CRJIa (H), q - Macca uerrH (K2/M).
113 3TOH <l>OPMYJIbI MO)I{HO BH)J;eTb, qTO rrpH BbICOKHX CKOpOCTHX 3TOH CHJIOH
HeJIb3H rrpeHe6peqb, H 3TO OCHOBHaH rrpWlHHa OrpaHWleHIDI CKOpOCTH.
5.3.14. npOsHcaHHe qenH
CRJIa, ,neHCTBYIDIUaH Mex,ny coce,nHHMH 3BeHbHMH, 6JIaro,napH Macce uerrH M8JIa H
BHYTPeHHe ypaBHOBemeHa B uerrH. E,nHHcTBeHHoe, Ha qeM CKa3bIBaeTCH Macca l(e-
rrH, 3TO rrpOBHcaHHe uerrH Mex,ny 3Be3,nOqKaMH.
TIpH YCTaHOBKe Heo6xo,nHMO c,neJIaTb rrpHrrycK C yqeToM Toro, qTO uerrb npH-
HHMaeT HeCKOJIbKO pa3JIWlHbIe <pOpMbI rrpH pa3JIWlHbIX HarpY3Kax OT JIy.IDI ,no MaK-
CHM}'Ma.
5.3.15. CMa3"/saHHe
[(enHbIe npHBo,nbI CJIe,nyeT rrpe,noxpaIDITb OT rrorranaHIDI rpH3H H BJIIDKHOCTH H
CMa3bIBaTb xopomero KaqeCTBa MaCJIOM Ha MHHepaJIbHOH OCHOBe, 6e3 ,neTepreHTOB.
)l(eJIaTeJIbHO rrepHo,nWleCKH MeIDITb MaCJIO. TIDKeJIbIe MaCJIa H rycTbIe CMa3KH, KaK
npaBRJIO, CJIHIIIKOM n.rrOTHbIe, QTo6bI 3arrOJIIDITb rrpOMexyrKH Mex,ny pa60QHMH
nOBepXHOCTHMH uenH, H HX He CJIe,nyeT HCrrOJIb30BaTb.
CJIe,nyeT npHHHMaTb MepbI, qTo6bI CMa3Ka ,nOCTHraJIa onopHbIX rrOBepXHOCTeA
uenH. 3Toro MO)I{HO ,n06HTbCH, HarrpaB.1IIDI MaCJIO B 3a30pbI Mex,ny BHyTpeHHHMH H
BHellIHHMH n.rraCTHHaMH, rrpe,nrrOqTHTeJIbHO Ha HIDKHeH BeTBH B TOQKe Bxo,na ueIIH
Ha 3Be3,nOqKY.
B CJIe,nyIOIUeH Ta6JIHue yx:a3aHa Ha)VIe)l(aIUaH BH3KOCTb CMa30QHbIX MaTepHaJIOB
AJIH pa3JIHQHbIX BHemHHX TeMrrepaTYP.
XapaKTepHCTIIKa CMa30'IHoro MaTepHaJla
BHellIlUlJl TeMDepaTY))a °C CTaIWlPT SAE (Acconaanu BS4231
HlDKeHepoB aBTOMOOHJIecTpoeHHJI)
OT -5 .no +5 20 OT 46 .no 68
OT 5 .no 40 30 100
OT 40 .no 50 40 Or 150 .no 220
OT 50 .no 60 50 320
JUI 60JIbIIIHHCTBa npRJIO)l(eHHH B BbImerrpHBe,neHHoM ,nHarra30He TeMnepaTYP
no,noit)J;eT yJiHBepCaJIbHOe MaCJIO SAE 20/50.
HCnOJIb30BaHHe ryCTOH CMa3KH
KaK yrrOMHHaJIOCb BbIIIIe, HCrrOJIb30BaHHe ryCTOH CMa3KH He peKOMeH,nyeTCg.
O,nHaKO, eCJIH HCrrOJIb30BaHHe CMa3KH HBJUIeTCH rrpHHUHrrHaJIbHbIM TPe60BaHHeM,
Heo6xo,nHMO 06paTHTb BHHMaHHe Ha CJIe,nYIDIUHe oco6eHHOCTH:
. CKOpOCTb ,nOJDKHa 6bITb orpaHHqeHa ,no 4 M/c.
5.3. MeXaHUlteCKUe nepedaltu: l(enHble nepedaltu 375
. & pe3YJIbTaTe npHMeHeHIDI 06bIqHOH CMa3KH C BHemHeH CTOpOHbI nOBepXHO-
CTH uenH CMa3Ka TOJIbKO 3arepMeTH3HpyeT onopHbIe nOBepXHOCTH H He 6y,neT
pa60TaTb Me)l{,l(y HHMH. 3TO CTaHeT npHqHHOH npex,neBpeMeHHoro pa3pyme-
HIDI. CMa3KY CJIe,nyeT no,norpeTb ,no :>KH)];KOrO COCTOHHIDI, a 3aTeM OKYHYTb B
Hee uenb H no,nox,naTb, nOKa CMa3Ka npOCOqHTCH BO Bce OTBepCTHH, T. e.
nOKa B03.nymHbIe rry3bIpH He nepeCTaH)'T no,nHHMaTbCH HaBepx. ECJIH 3Ta CH-
CTeMa HCnOJIb3yeTcH, uenb He06xo,nHMO pery.IDlpHO OqHlI(aTb H 3aHOBO CMa-
3bIBaTb qepe3 npOMexyrKH, 3aBHCHII(He OT MOII(HOCTH H CKOpOCTH npHBO,l(OB.
He06xo,nHMO TaIOKe OTMeTHTb, qTO npH TeMnepaTYPe CBbIme 80°C MHorHe
CMa3KH nopTHTCH, H HX 3<p<peKTHBHOCTb CHIDKaeTCH.
AHoMaJIbHble BHemHHe TeMnepaTYPbI
TIpH BbICOKHX TeMnepaTYPax, BIIJIOTb,nO 250°C, B 60JIbmeH CTeneHH npHMeHH-
MbI TBep,nbIe CMaJOqHbIe MaTepHaJIbI, TaKHe KaK KOJIJIOH)];HbIH rpa<pHT RJIH MOS2 B
yaHT-cnHpHTe RJIH npOH3Bo,nHbIe nOJIHaJIKRJIeHrJIHKO.IDl.
M Ha060poT, npH HH3KHX TeMnepaTYpax Me)l{,l(y -5°C H -40°C He06xo,nHMbI
CneuHaJIbHbIe HH3KOTeMnepaTYPHbIe nepBOHaqaJIbHO CMa3KH H 3aTeM MaCJIa. TIo-
CTaBII(HKH CMa30qHbIX MaTepHaJIOB MOryr ,naTb COOTBeTCTByrolI(He peKOMeH)J;aUHH.
5.3.16. MeTo,q1J1 CMa31J/SaHHfI
C ecTByeT qeTbIpe OCHOBHbIX cnoc06a CMa3bIBaHIDI uenHbIX npHBo,nOB. PeKOMeH-
,nyeMbIH MeTO,n CMa3KH OCHOBbIBaeTCH Ha CKOpOCTH uenH H nepe,naBaeMoH MOII(HO-
CTH H MO)l(eT 6bITb onpe,neJIeH no cxeMaM oueHKH xapaKTepHCTHK (CM. pa3,neJIbI
5.3.12, 5.3.13).
THO 1. PyqHoe CMa3b1BaHHe
MacJIo HaHOCHTCH nepHo,nWleCKH C nOMOlI(bIO KHCTOqKH RJIH MaCJIeHKH, npe,n-
nOqTHTeJIbHO KIDK,[(bIe 8 qaCOB pa60TbI. 06'beM CMa3KH H qaCTOTa ,nOJDKHbI 6bITb ,no-
CTaTOqHtI, qT06bI uenb 6bma BJIIDKHOH OT MaCJIa H qT06bI qHCTaH CMa3Ka MOrJIa
npOHHKHYTb B coe,nHHeHIDI uenH.
3AopOBbe M 6e30naCHOCTb
Y6eALt1TeCb, TO Bce MaWLt1HHOe
o6oPYAoBaHLt1e HenOABLt1 HO Lt1
OTKJ1IO eHO, npe*Ae eM HaHO-
CLt1Tb CMa3KY, - Tw.aTenbHO
cneAyii1Te Lt1HCTPYKLJ.Lt1S1M Lt13rO-
TOBLt1Ten 06oPYAoBaHLt1S1.
HaHeceHHe a3p030JIbHOH CMa3KH TaIOKe ,naeT y,noBJIeTBOpHTeJIbHbIH pe3YJIbTaT,
HO BIDKHO, qT06bI a3p030JIbHaH CMa3Ka no,nxo,nRJIa AJUI Tex npRJIO)l(eHHH, KOTopbIe
nOCTaB.IDleT Renold. 3TOT BH)]; CMa3KH npOHHKaeT B 3a30pbI Mex,ny BaJIHKOM/BTYJI-
KOH/pOJIHKOM, He KanaeT H He BbITeKaeT, Kor,na uenb Heno,nBIDKHa, If He BbI6paCbI-
BaeTCH ueH1p06e)I(HOH CHJIOH, Kor,na uenb ,l(BIDKeTCH.
Dla8a 5. MexaHUlteCKUe nepeiJaltu
THO 2. KaOeJlbHaJI oo a'la
MacJIo Hal1paBJIeHHO Kal1aeT Me)l{,[(y rpaIDIMH IIJIaCTHH H3 .ny6pHKaTopa C Kane-
JIbHOH l1o,naqeH MaCJIa. 06'beM CMa3KH H qaCTOTa ,nOJDKHbI 6bITb ,nOCTaTOqHbI, qTO-
6bI CMa3Ka MOfJIa l1pOHHKHyTb BO Bce coe,nHHeHIDI n;el1H.
THO 3. MaCJlJlHaJi BaHHa HJIH CMa3bIBaHHe C OOMOInbIO ,lUICKa-pa30pbI3rHBaTeJIJI
I1pH CMa3Ke B MaCJUIHOH BaHHe HH.}I{}IIDI BeTBb n;el1H l1pOXO,nHT qepe3 MaCIDI-
HYI<> BaHHY B Koprryce l1pHBO,nHOfO MexaHH3Ma. YpoBeHb MaCJIa ,nOJDKeH 6bITb Ta-
KHM, qTo6bI MaCJIO 110KpbIBaJIO n;el1b B ee HIDKHeH TOqKe B l1pOn;eCce pa60TbI.
I1pH CMa3bIBaHHH C 110MOlI(blO ,nHCKa HCIIOJIb3yeTCH MaC.IDIHasI BaHHa, HO n;el1b pa-
60TaeT BbIme ypOBIDI MaCJIa. Pa36pbI3rHBalOlI(He BbIC1)'IIbI ,nHCKa 110,D;XBaTbIBaIOT MaCJIO
113 MaC.IDIHOH BaHHbI, H C 110MOlI(blO OTPIDKalOlI(HX II(HTKOB OHO paCl1pe,ne.IDIeTCH no
n;el1l1. ECJIH HC110JIb3yroTCH pa36pbI3fHBalOII(He ,n:nCKH, OH:n ,nOJDKHbI 6bITb Cl1poeKTH-
pOBaHbI TaK, q'f06bI HX OIqJyxHasI CKOpOCTb COCTaBJUIJIa OT 180 ,no 2440 M/MHH.
THO 4. nOTOK MaCJIa
Hel1pepbIBHasI l1o,naqa MaCJIa n;:npKYJUIn;HOHHbIM HaCOCOM MH CHCTeMOH n;eHT-
paJIH30BaHHoH CMa3KH; CTPyH MaCJIa Hal1paBJIeHbI l1pHMO Ha n;el1b. BIDKHO o6ecl1e-
QHTb, QTo6bI OTBepCTJUI, H3 KOTOpbIX BbIXO,nHT MaCJIO, paC110JIafaJIHCb l1pHMO Ha,zJ;
5.3. MexaHullecKue nepeoallu: u,enHble nepeoallu 377
pe6paMH nrraCTHH. Pa36pbI3rHBaTeJIH ,nOJDKHbI pacrrOJIaraTbCH TaK, qT06bI MaCJIO
norra;J;aJIO Ha n;errb Herrocpe,nCTBeHHO rrepe,n TeM, KaK OHa BoitD;eT B 3an;enrreHHe C
Be.nyIIJ;eH 3Be3,nOqKOH.
3TO 06eCrreqHT pacrrpoc'rpaHeHHe CMa3KH rro,n B03,neHcTBHeM n;eH1'p06eXHoH
CHJIbI rro BceH n;errH H rrOMoxeT CMHftlHTb y,napbI pOJIHKOB 0 3y6bH 3Be3,nOQKH. 110-
TOK CMa3KH TaIOKe 06eCrreQHBaeT 3<p<peKTHBHOe OXJIIDK,lJ;eHHe H aMopTH3an;HIO y,na-
pOB rrpH 60JIbillHX CKOpOCTHX.
BJIHHHHe TeMneparrypbI
TeMrrepaT}'Pa n;errH H Koxyxa n;errH B rrpon;ecce pa60TbI rrpHBo,na HBlliIeTCH BIDK-
HbIM <l>aKTOpOM, Hy)K)J;aIOII(HMCH B rrOCTOHHHOM KOH'rpOJIe. I1pH HHTeHcHBHoH pa-
60Te rrpHBo,na, HerrpepbIBHoM HCrrOJIb30BaHHH H T.rr. MeTo,nbI CMa3KH MOryr rro'rpe-
60BaTb oc060ro BHHMaH:IDI.
M3-3a orpaHHQeHHH, HaKJI3J1bIBaeMbIX cMa3KoH, CJIe.nyeT rro B03MOXHOCTH H3-
6eraTb TeMrrepaT}'P CBbIille 100°C, XOTH caMH n;errH, KaK rrpaBHJIO, 06eCrreQHBalOT
llpH HeKOTOpbIX 06CTOHTeJIbCTBaX rrpHeMJIeMbIe xapaKTepHCTHKH BIIJIOTb ,no 250°C.
QTo6bI rrOBbICHTb 3<p<peKTHBHOCTb CMa3KH H ee OXJIIDK,lJ;aIOII(HH 3<p<peKT, CJIe.nyeT
}'BeJIWlHTb 06'beM MaCJIa (BIIJIOTb ,no 4,5 JI/MHH Ha BeTBb n;errH) H rrpHMeIDITb MeTO-
)J;bI BHeillHero OXJIIDK,lJ;eH:IDI MaCJIa.
5.3.17. nO,q-.eNlHlJle YCTPOHCTBB
3TOT pa3,neJI OXBaTbIBaeT rrpHJIOXeHIDI, TaKHe KaK rro,n'beM H rrepeMelI(eHHe, B KOTO-
pbIX rrpHJIaraeMaH HarpY3Ka, KaK rrpaBHJIO, HBlliIeTCH CTaTHQeCKOH. OQeB HO, ,nH-
HaMWIeCKHe HarpY3K.H TaIOKe rrpHcyrcTByroT B 60JIbillHHCTBe rrpHJIOXeHHH, H pa3-
pa60'f1IHKY He06xo,nHMO rrpHHHMaTb }IX BO BHHMaHHe. Pa3pa60'f1IHK MexaHH3MOB
)J;OJDKeH TaIOKe 03HaKOMHTbCH C DTI Publication INDY J1898 40M, B KOTOpOM
CYMMHpyroTCH H3MeHeHIDI B 3aKOHo,naTeJIbCTBe C 1 HHBapH 1993 ro,na rro 1 HHBapH
1995 ro,na, KacalOII(HeCH CTaH,l(apTOB Ha MaillHHbI H 060py,noBaHHe.
I.J;e _rrH ,D;.JUI rro,n'beMHbIX YC'rpOHCTB MOXHO pa3,neJIHTb Ha ,nBe KaTeropHH:
. nJIaCTHHQaTbIe n;errH.
. BTYJIOQHbIe H pOJIHKOBbIe n;errH.
nJiaCTHJI1IaTbIe nenH
I1JIaCTHHQaTbIe n;errH, KaK rrpaBHJIO, HCrrOJIb3yroTCH B rro,n'beMHbIX YC1'pOHCTBax
C BbIpaBHHBaHHeM HarpY3KH, KaK rrOKa3aHO Ha pHCyJlKe HIDKe. OHH ,nOJDKHbI 6bITb
3aKpenrreHbI Ha 060HX KOHn;ax, rrOCKOJIbKY Ha caMOH n;errH HeT HHKaKHX rrpHcrro-
C06JIeHHH ,D;.JUI 3y6QaTOrO 3an;enrreH:IDI.
K03fjJfjJuu,ueHm HaOeJICHOCmU
K03<P<PH:QHeHT Ha;J;eXHOCTH 7: 1 HBmIeTCH CTaH,l(apTHbIM ,D;.JUI cTa6HJIbHOrO pe-
XHMa B03BpaTHo-rrOCTYIIaTeJIbHOrO ,nBIDKeH:IDI, KaK, HarrpHMep, B rrorpY3QHKax C
BHJIOQHbIM 3aXBaTOM. I1pH YMepeHHbIX y,napHbIX HarpY3Kax K03<PcPH:QHeHT ,nOJDKeH
COCTaBlliITb 9: 1, a rrpH TIDKeJIbIX y,napHbIX HarpY3Kax - 11: 1.
Pa60ttaJl CKopocmb
MaKCHMaJIbHaH CKOpOCTb :QerrH He ,nOJDKHa rrpeBbIillaTb 30 M/MHH.
IIpUAoJICeHUJl
1. MeXaHHQeCKHe CTaHKH - C1'poraJIbHbIe, CBepJIHJIbHbIe CTaHKH, <ppe3epHbIe
rOJIOBKH, MHOrOn;eJIeBbIe CTaHKH.
Dltl8a 5. MexaHulleclCue nepeiJallu
2. I10rpY3qHKH C BIDIOqHbIM 3aXBaTOM, JIH<pTbI, rro,n'beMHHKH.
3. YpaBHoBemHBalOII(He rrpOTHBOBeCbI - ,nOMKpaTbI, ,nBepH, BopOTa H T.rr.
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BTYJIO'lHbIe H pOJIHKOBbIe nenH
BTYJIOqHbIe H pOJIHKOBbIe n;errH MOryr HCrrOJIb30BaTbCH ,D;.JUI rro,n'beMa H rrepe-
,nBIDKeH:IDI, H HX rrpeHMyII(eCTBOM, rro cpaBHeHHIO C IIJIaCTHH1IaTbIMH n;eIUlMH, HB-
lliIeTCH crroco6HoCTb BXO,nHTb B 3an;eIIJIeHHe C COOTBeTCTByrolI(HMH Be,nylI(HMH 3Be3-
,nOqKaMH. POJIHKOBbIe n;errH HMelOT .rrytIIIIyIO H3HOCOYCTOWIHBOCTb, qeM IIJIaCTHlPla-
TbIe, H MOryr HCrrOJIb30BaTbCH rrpH 60JIbmHX CKOpOCTHX.
K03fjJfjJuu,ueHm HaOeJICHOCmU
B 3aBHCHMOCTH OT rrpIDIoxeHHH B bI rrpIDIaraeMbIX HarpY30K MeIDIIOTCH B
mHpOKOM ,nHarra30He, H, CJIe,nOBaTeJIbHO, rrpH BbI60pe K03<P<PHn;HeHTa Ha;J;e)KJIOCTH
peKOMeH):(yeTcH ytlHTbIBaTb HeKOTOpyro CTerreHb HapymeH:IDI rrpaBIDI H HOpM 3Kcn-
.nyaTan;HH:
. K03<P<PHn;HeHT Hane)KJIOCTH 8: 1 ,D;.JUI rpY30BbIX rro,n'beMHbIX YCTPOHCTB.
. K03<P<PHn;HeHT Hane)KJIOCTH 10: 1 ,D;.JUI rraCCIDKHpcKHX rro,n'beMHbIX YCTPOHCTB.
K03<P<PHn;HeHT Ha;J;e)KJIOCTH MoxeT 6bITb CHIDKeH rro cpaBHeHHIO C peKOMeH)ijT-
eMbIM (3a HCKJIlOqeHHeM rraCCIDKHpcKHX rro,n'beMHbIX YCTPOHCTB) rrpH YCJIOBHH TIIJ;a-
TeJIbHOrO aHaJIH3a MaKCHMaJIbHbIX HarpY30K H B03MO)KJIbIX rrOCJIe,ncTBHH ,D;.JUI 3 O-
pOBbH H 6e30rracHocTH. KOMMeHTapHH Ha 3TY TeMY CMOTPH B pa3,neJIe «<I>aKTOpbI,
BJIHHlOlI(He Ha CpOK CJIy.}K6bI n;errH».
Paoo'laJi CKOpOCTb
MaKCHMaJIbHaH CKOpOCTb n;errH He ,nOJDKHa rrpeBbImaTb 45 M/MHH. ,[LmI 60JIee
BbICOKHX CKopocTeH rrpH BbI60pe n;errH IfY)KHO paCCMaTPHBaTb ee KaK rrpe,nHa3Ha-
qeHHYID .n.rrH rrepe,naqH MOII(HOCTH; HarpY3KY Ha n;errb MO)KJIO rrpeo6pa30BaTb B
MOII(HOCTb, HCrrOJIb3YH CJIe,nyromym <poPMY.ny:
MOII(HOCTb = FV (KBT),
r,ne F - HarpY3Ka (KH), V - CKOpOCTb n;errH (M/c).
3aTeM CJIe.nyeT orrpe,neJIHTb K03<P<PHn;HeHTbI ,D;.JUI paCqeTHOH MOII(HOCTH, KaK 3TO
orrHcaHO Ha BTOpOM mare B pa3,neJIe, rrOCBHlI(eHHOM BbI60PY rrpHBo,na.
BbIqHCJIHTe qHCJIO 060pOTOB B MHHYTY, HCrrOJIb3YH HaHMeHbIIIyIO 3Be3,nOqKY B
CHCTeMe, rro <poPMYJIe
CKOpOCTb = 60000 VI PZ,
r,ne P - mar n;errH (MM), Z - qHCJIO 3y6beB 3Be3,nOqKH.
MeTo,n CMa3bIBaH:IDI TaIOKe BbI6HpaHTe B COOTBeTCTBHH co cxeMaMH On;eHKH xa-
paKTepHCTHK.
5.3. MexaHullecKue nepeiJallu: u,enHble nepeiJallu 379
5.3.18. ANSI X-,lIHSnS30H
CTaH):(apTOM ANSI rrpe,nYCMOTpeHbI TaIOKe BapHaHTbI rrpHBo,nHbIX n;erreH .nIDI pa6o-
TLI B TIDKeJIOM peXHMe.
3TH n;errH rrpHMeHHMbI B YCJIOBIDIX qaCTbIX IDIH ,nHHaMHqHbIX H3MeHeHHH 3HaKa
HarpY3KH. THrrHqHOH 06JIaCTblO rrpHMeHeH:IDI TaK.HX n;erreH HBJUIIOTCH ,no6bIBalOlI(He
orpaCJIH rrpOMbIWJIeHHOCTH, TaKHe KaK ropHbIe pa60TbI, pa3pa6oTKa rrOJIe3HbIX HC-
KonaeMbIX OTKpbITbIM crroco60M, 6ypeHHe rro KopeHHbIM rropo,naM, a TaIOKe JIeCO-
TeXHHqeCKOe H C1'pOHTeJIbHOe o6oPy,nOBaHHe.
QTo6bI rrpHcrroco6HTb n;errH K 3THM 6bIC1'pO BbI3bIBalOII(HM YCTaJIOCTb HarpY3-
KaM, TOJIII(HHY BHYTPeHHHX H BHeillHHX IIJIaCTHH yBeJIHqHBalOT rrpHMepHO Ha 20%.
B pe3YJIbTaTe 3TOH Mo,nHcPHKan;HH rrpe,neJI rrpOqHOCTH Ha pa3pbIB He B03paCTa-
eT, rrOCKOJIbKY caMOH CJIa60H KOMrrOHeHTOH CTaHOBHTCH BaJIHKH. O,nHaKo cyII(ecT-
ByJOT H n;errH .nIDI TIDKeJIbIX peXHMoB C yBeJIHqeHHbIM rrpe,neJIOM rrpOqHOCTH Ha pa3-
pLlB. 3TO ,nocTHraeTcH HCrrOJIb30BaHHeM 3aKaJIeHHbIX HaCKB03b BaJIHKOB BMeCTO Ba-
JIHKOB, yrrpOqHeHHbIx rroBepXHocTHO. K COXaJIeHHIO, H3-3a CHIDKeH:IDI TBep,nocTH
BaJIHKOB rrpH 3TOM CHIDKaeTCH H3HOCOYCTO}iqHBOCTb.
Renold rrpe,n.rraraeT CJIe,nyroII(He n;errH ANSI X-,nHarra30Ha:
. H X-,nHarra30H - 60JIee TOJICTbIe IIJIaCTHHbI.
. V X-,nHarra30H - 60JIee 3aKaJIeHHbIe HaCKB03b BaJIHKH.
. HV X-,nHarra30H - 60JIee TOJICTbIe IIJIaCTHHbI H 3aKaJIeHHbIe HaCKB03b BaJIHKH.
:QerrH H H HV He rrpHMeHHMbI IDIH He rro,nxO,LOlT .nIDI rrpIDIoxeHHH C BbICOKHMH
CKOpOCTHMH.
Heo6xo,nHMO 06paTHTb BHHMaHHe Ha cJIe,nyrolI(ee:
. :QerrH V rrOJIHOCTblO B3aHM03aMeIDIeMbI co CTaH):(apTHbIMH ANSI n;eIDIMH.
. Bce pa3MepbI 3an;eIIJIeHHH o,nHOPMHbIX n;erreH H H HV rrOJIHOCTblO eHTWI-
HbI pa3MepaM CTaH):(apTHbIX n;erreH, H, CJIe,nOBaTeJIbHO, 3TH n;errH MOryr pa6o-
TaTb C TeMH xe caMbIMH 3Be3,nOqKaMH, qTO H 06bNHbIe n;errH. BOJIee illHpO-
KHe IIJIaCTHHbI 1'pe6yroT 60JIbillHX HarrpaBJUIIOII(HX YC1'pOHCTB, H XeJIaTeJIbHO
HCrrOJIb30BaTb 3Be3,nOqKH C 3y6bHMH rrOCJIe TepMoo6pa6oTKH. MHoroPMHbIe
n;errH 'rpe6yroT yBeJIHqeHHOrO rrOrrepeqHOrO illara 3y6beB, HO ,npyrHe pa3MepbI
3an;eIIJIeH:IDI OCTalOTCH CTaH):(apTHbIMH.
. E,nHHcTBeHHoH rrpHqHHOH HCrrOJIb30BaHIDI n;erreH H IDIH HV MOryr 6bITb
rrp06JIeMbI C YCTaJIOCTHOH ,nOJIrOBeqHOCTblO. ,[LmI 3Toro ,nHarra30Ha He H3ro-
TaBJIHBalOTCH rrepexo,nHbIe IDIH CKOJIb3HII(He coe,nHHHTeJIbHbIe 3BeHbH,
rrOCKOJIbKY OHH CHIDKalOT H3HOCOYCTOHqHBOCTb.
. Pa3'beMHbIe (KJIHHOBbIe) n;errH MOryr 6bITb H3rOTOBJIeHbI Ha 3aKa3 TaK xe,
KaK H 1'peXPMHbIe IDIH 60JIee illHpOKHe n;errH.
5.3.19. cPSKTOPW, SnlAfllOutlAe HS CpOK CnyJIC6bl LlenlA
CPaKTOPW oe30naCHOCTH
Bce n;errH Renold 0603HaqalOTCH rro CBoeMY MHHHMaJIbHOM)' rrpe,neJl)' rrpOqHOC-
TH Ha pa3pbIB. QTo6bI rrOJIyqHTb paCqeTHyIO pa6oqyro HarpY3KY, CJIe,nyeT HCrrOJIb30-
BaTb K03cPcPHn;HeHT Ha;J;e)KJIOCTH rro OTHomeHHIO pa3pymalOII(eH HarpY3Ke. O,nHa-
KO, rrpex,ne qeM rrepexo,nHTb K paCCMOTpeHHIO 3Toro Borrpoca, Heo6xo,nHMO o6pa-
THTb BHHMaHHe Ha CJIe,nyrolI(ee.
Dla6a 5. MexaHulleclCue nepeiJallu
. BOJIbillHHCTBO 60KOBbIX IIJIaCTHH 3BeHbeB H3rOTaBJIHBaeTCH H3 CTaJIeH C HH3-
KHM IDIH cpe,nHHM co,nepxaHHeM yrJIepo,na H HX pa3Mep no,n6HpaeTcH TaK,
qTo6bI rapaHTHpOBaTb, qTO OHH HMelOT cooTBeTcTByromym npOqHOCTb, TaIOKe
KaK BH3KOCTb, qTo6bI npoTHBoCTOHTb y,napHbIM HarpY3KaM.
. 3TH CTaJIH HMelOT npe,neJI TeK)'1IeCTH Ha ypOBHe npHMepHO 65% MX npe eJIa
npOqHOCTH Ha pa3pbIB. 3TO 03HaqaeT, qTO eCJIH n;enH no,nBepralOTCH 60JIb-
illHM HarpY3KaM B 3aBHCHMOCTH OT MaTepHaJIa, HCnOJIb3yeMoro ,lJ;.JUI 60KOBbIX
IIJIaCTHH, TO B pe3YJIbTaTe OCTaTOqHOH ,ne<;popMan;HH npOH30H.neT yBeJIHqeHHe
illara n;enH.
. B 60JIbillHHCTBe npIDIoxeHHH n;enH no,nBepralOTCH Iq>aTKOBpeMeHHbIM ,nHHa-
MHqeCKHM HarpY3KaM 3HaqHTeJIbHO npeBbIillalOlUHM MaKCHMaJIbHbIe CTaTlNe-
CKHe HarpY3KH, H 06brqHO 60JIbillHM, qeM no OIJ;eHKe pa3pa6oTQHKOB.
. ,[(BHraTeJIH, HanpHMep, ,nonYCKaIOT B TeqeHHe KopOTKoro BpeMeHH ,no 200%
nOJIHOrO BbIXo,nHoro KpYTHlI(erO MOMeHT HarpY3KH.
113 H3JIOXeHHOro BbIille CJIe.nyeT, qTO u;enb, yaepeHHo BbI6paHHaR C K03<;P<;PHIJ;H-
eHTOM Ha;J;e)KJIOCTH 8:1 no OTHOilleHHIO K pa3pymalOII(eH HarpY3Ke, <;paKTWleCKH
pa60TaeT npH K03<;p<;pHIJ;HeHTe Ha;J;e)KJIOCTH 5: 1 no OTHomeHHIO K npe,neJIY TeK)'1le-
CTH H elI(e HaMHoro MeHbilleM, eCJIH yqecTb MrHOBeHHbIe neperpY3KH npHBo,na.
,[(JUI ,naJIbHeHillero paCCMOTPeH:IDI HCnOJIb30BaHIDI K03<;p<;pHIJ;HeHTa Hane)KJIOCTH
Heo6xo,nHMO BBeCTH nOIDITHe cpOKa CJIyx6bI (pecypca) n;enH.
ECJIH npH COOTBeTCTByrolI(eM TeXHHqeCKOM 06CJIyxHBaHHH CpOK CJIy)K6bI co-
CTaBJUIeT 8 000 000 n;HKJIOB IDIH 15 000 qaCOB (B 3aBHCHMOCTH OT Toro, qTO paHbme
npOH3oH.neT), 3TO HOpMaJIbHO. I1PHqHHOH OTKa3a 6y,neT H3HOC.
B Tex npIDIoxeHlffiX, r,ne 'rpe6yeTcH HH3KHH K03<;p<;pHn;HeHT Ha;J;e)KJIOCTH, CpOK
CJIy)K6bI 6y,neT, COOTBeTCTBeHHO, MeHbille.
5.3. MexaHullecKue nepeoallu: u,enHble nepeoallu 381'
MaK.cHMaJIbHag pa60qag HarpY3Ka 110JIyqaeTcH ,neJIeHHeM MHHHMaJIbHOrO l1pe-
,l(eJIa l1pOqHOCTH Ha pa3pbIB Ha K03cPcPHI.J;HeHT Ha;J;eXHOCTH.
B CJIe,nyIOlI(eH Ta6JIHI.J;e l1pHBe,neHbI l1pHMepHbIe CpOKH CJIyx6bI ,D;illI pa3JIHQHbIX
K03cPcPHI.J;HeHTOB Ha;J;eXHOCTH.
Koacl»4»lII.UIeHT H8,AelKllOCTH MaKCHM8JlhHOe npHJI01KeHHe
KOJIll1leCTBO IUIKJIOB
OAHOpSWlhle MHoropJl,lUlWe
5,0 6,0 1000000 ,D;HHaMWleCKaJI HarpY3Ka He rrpeBbIlliaeT
pa60qyIO HarpY3KY
6,0 7,2 2000000
8,0 8,0 8000000 ,D;HHaMWleCKaJI HarpY3Ka HHor,n;a npe-
BbIlliaeT pa60qyIO HarpY3KY Ha 20%
10,0 10,0 8000000 Bce naCCIDKHpCKHe JIH<PTbI
CJIe,nyeT oTMeTHTb, QTO l1pH Bcex K03<PcPHI.J;HeHTaX, MeHbillHX 8: 1, 0110pHOe ,naB-
JIeHHe l1peBbIillaeT peKOMeH,D;yeMbIH MaKCH;MYM, B pe3YJIbTaTe Qero B03HHKaeT YCKO-
v 6 p
peHHbIH H3HOC, eCJIH He y,neJUITb OCO oro BHHMaH:IDI CMa3bIBaHHIO, Hal1pHMep:
. BOJIee QaCTOe CMa3bIBaHHe.
. BOJIee 3cPcPeKTHBHag CMa3Ka.
. JIyqillHe C110C06bI HaHeCeH:IDI CMa3KH.
BWKHoe 3aMe1faHHe
I1pH K03cPcPHUHeHTax, MeHbillHX 5: 1, 0110pHOe ,naBJIeHHe Ha 50% 60JIbille, QeM
peKOMeH,D;yeMoe, H H3HOC I.J;el1H, pa60TalOII(eH B TaKHX YCJIOBlffiX, 6y,neT l1pe)l{,D;eBpe-
MeHHbIM, KaKOH 6bI B CMa3KH HH l1pHMeIUIJICH.
)KecTKHe BHemHHe YCJIOBHH
I1pH JII06bIX BHeillHHX YCJIOBlffiX, KpOMe QHCTOTbI H xopoilleH CMa3KH, B K03cP-
cl>HUHeHT Ha;J;eXHOCTH CJIe.nyeT BHOCHTb 11011paBKH, eCJIH 1'pe6yeTcH H36exaTb He-
KOToporo YMeHbilleH:IDI cpOKa 3KCIIJIyaTaUHH I.J;el1H. HH3KHe TeMl1epaTYPbI TaIOKe
YMeHbillalOT CpOK CJIy}K6bI, oco6eHHO eCJIH l1pHC)'TCTByJOT y,napHbIe HarpY3KH.
B cJIe,nyrolI(eH Ta6JIHI.J;e l1pHBe,neHbI 061I(He peKOMeH,D;aI.J;HH OTHOCHTeJIbHO KO-
3<;PcPHI.J;HeHTOB Ha;J;eXHOCTH, COOTBeTCTByJOlI(HX pa3JIHQHbIM l1pIDIOXeH:IDIM, Heo6-
XO,nHMbIX ,D;illI ,nOCTIDKeHIDI cpOKa CJIy}K6bI 8 000 000 UHKJIOB.
QHCTOTa
CMa3Ka
CTO YMepelDlo qHCTO rpJl3h/a6pa3HBW
PeryIDIpHaH 8 10 12
HeperyIDIpHaJI 10 12 14
OTcVTcTBveT 12 12 14
CMa3Ka TeMDepaTYJ)a CC)
OT 10 o 150 OT 150 o 200 OT 200 o 300
PeryIDIpHaJI 8 10 12
HeperyIDIpHaJI 10 12 14
OTcVTcTBveT 12 12 14
TeMDepaTYJ)a CC) Pe1KllM HarpY30K
IIJJaBHhlH XO YMepelDlaJI YMPHaJI HarpY3Ka TSDKeJlaJl YMPHaJI HarpY3Ka
OT 10 ,n;o 150 8 11 15
OT 0 ,n;o 10 10 15 19
OT -20 ,n;o 0 12 20 25
OT -40 LIO - 20 15 25 33
Tlla8a 5. MexaHU'lecICue nepeiJa'lu
5.3.20. Y/VIIAHeHlAe LlenlA
I1pH pa3pa6oTKe no,n'beMHbIX YCT})OHCTB nOJIe3HO 3HaTb, HaCKOJIbKO n;enb MOIer
paCTHHYTbCH npH ,naHHOH HarpY3Ke.
I1pH6JIH3HTeJIbHO Y,nJIHHeHHe u;enH npH ,naHHOH HarpY3Ke MOXHO BbIqHCJIHTb
no CJIe,nyIOlI(HM cPoPMYJIaM:
(1451) .10- 5 · L
O,nHOpH,nHaH u;enb AL = ' Fi .
p2
(972) .10- 5 . L
)];BYXPMHtuI n;enb AL = ' Fi .
p2
(726) .10- 5 . L
TpexPMHtuI u;enb AL = ' Fi ,
p2
r,ne AL - H3MeHeHHe .n.rrHHbI u;enH (MM); L - nepBOHaqaJIbHtuI .n.rrHHa u;enH (MM);
P - mar u;enH (MM); F 1 - cpe,nHIDI HarpY3Ka Ha nenb.
5.3.21. CornSCOSSHlAe (SblpSSHIASSHlAe) LleneR
B JII060M npIDIoxeHHH, B KOTOpOM T})e6yeTcH, qTo6bI ,nBe IDIH 60JIee BeTBeH rrpH-
BO,nHbIX u;eneH cPYHK:QHOHHpOBaJIH o,nHa PMOM C ,npyrOH B 061I(eM npHBo,ne HJIH
KOHBeHepHoH YCTaHOBKe, MoxeT B03HHKH)'Tb Heo6xo,nHMOCTb COCTaBJIeH:IDI nap
IDIH COrJIaCOBaH:IDI. TaKHe npIDIOXeH:IDI, KaK npaBIDIa, npHH8MexaT K O,nHOH H3
CJIe,nyIOlI(HX KaTeropHH.
COrJIaCOBaHHe ,ltJIHH ,nJIJI KOHBeiiepHoH YCTaHOBKH HJIH aHaJIOI1l'lHhIX npHJIo1KeHHi
f,ne 6bI HH T})e60BaJIOCb COrJIaCOBaHHe ,nJIHHbI npHBo,nHbIX n;eneH, HMeTb ,neJIO
np eTCH co CJIe,nyIOII(HM.
. CHaqaJIa aKKYPaTHO H3MepHIOT TeXHOJIOrWlecKYK> ,nJIHHY no,nxO,lOlII(HX n;eneiI
Me)l{,lJ;Y 3 H 5 M H 3aTeM oT6HpalOT HX TaK, qTo6bI o6eCneqHTb ,nBe (IDIH 60-
JIee) BeTBH npHBo,na, pa3JIHq:IDI nOJIHOH ,nJIHHbI KOTOpbIX YKJI3JJ;bIBaIOTCH B Y3-
KHe npe,neJIbI. O,nHaKo TaKasI TOqHOCTb He 06H3aTeJIbHa .n.rrH JII06bIX npOMe-
xyrOqHbIX <pparMeHTOB u;enH, XOTH cPaKTHqeCKtuI ,nJIHHa Bcex npOMexy-
TOqHbIX cPparMeHTOB H B,nOJIb, H nonepeK npHBo,na He ,nOJDKHa H3MeHHTbCH
60JIbme, qeM ,nonycKalOT 06bIqHbIe npOMbIlUJIeHHbIe npe,neJIbI. O,nHaKo npH-
cnOC06JIeHHbIe npHBo,nHbIe n;enH 06bIqHO H3rOTaBJIHBalOTCH no CneU;HaJIb-
HbIM 3aKa3aM, KOTopbIe 3aBepmalOTcH, KaK npaBIDIo, nOCJIe O,nHOH cepHH
H3,neJIHH, TaK qTO ,nOnyCTHMO npe,nnOJIaraTb, qTO pa3HHn;a .n.rrHH npoMexy-
TOqHbIX cPparMeHToB 6y,neT He6oJIbmoH.
. l(enH nOCTaB.JUIIOTCH KOMlIJIeKTaMH, KOTopbIe O,nHOpO,nHbI no nOJIHOH .n.rrHHe
B ,nonycTHMbIX Y3KHX npe,neJIax H YKJI3J1bIBaIOTCH B 06bIqHbIe npOMbIlUJIeHHbIe
npe,neJIbI. CJIe,nyeT oTMeTHTb, qTO u;enH, KOTopbIe nOCTaBJUIIOTCH no pa3JIWI-
HbIM 3aKa3aM B pa3JIWIHOe BpeMH, MOryT He 6bITb TOqHO TaKOH xe .n.rrHHbI,
KaK nOCTaBJIeHHbIe nepBOHaqaJIbHO, HO 6y,n)'T OTJIWlaTbCH He 60JIbllIe, qeM B
npe,neJIax HOpMaJIbHOrO ,nonYCKa 0,0%, +0,15%.
5.3. MexaHullecKue nepeoallu: u,enHble nepeoallu 31
COrJIaCOBaHHe maroB neneii TpaHcMHccHoHHoro npHBO,lUl
l(enH C COrJIaCOBaHHbIMH maraMH HapalI(HBalOTCH H3 60JIee KOpOTKHX <ppa]
MeHTOB (06brqHO 300-600 MM ,nJIHHOH), KOTopbIe CHaqaJIa H3MepHIOT, a 3aTeM COt
THpyroT Ha KJIaCCbI no ,lL1IHHe. )];JIHHbI <pparMeHToB o,nHoro KJIacca ,nOJDKHbI 6bI1
6JIH3KHMH no 3HaqeHHIO, H <pparMeHTbI, o6pa3yJOII(He o,nHY rpyrrrry nonepeK KOMf
JIeKTa n;eneH, BbI6HpalOTcH H3 o,nHoro H Toro xe KJIacca ,lL1IHHbI.
Tpe6yeMoe KOJIHqeCTBO rpyrrn nOCJIe 3Toro coe,nHIDIIOT, qTo6bI C<pOpMHpoBa1
COfJIaCOBaHHbIH no mary KOMIIJIeKT I.J;eneH IDIH (eCJIH 3TO CJIHmKOM ,nOJIro H He
Y 06HO) B KaqeCTBe aJIbTepHaTHBbI - KOMIIJIeKT o6pa6oTaHHbIX <pparMeHTOB, qTO
6bI, 3aBepmaR YCTaHOBKY, 3aKa3qHK Mor co6paTb n;enb C COrJIaCOBaHHbIMH maraMI1
K n;elUlM npHKpeIIIDIIOTCH COOTBeTCTByJOlI(He 6Hpm, qTo6bI rapaHTHpOBaTb, qTt
nenH 6y,nYT co6paHbI B npaBIDIbHOH nOCJIe,nOBaTeJIbHOCTH.
lbeHTH4»HKan HH TexnOJIOl1l'lecK15 MHH
TexaOJlOl'll'leCKHe ,lUIHHhI
1 2 3
BeTBb A A-AI AI-A2 A2-A3
BeTBb B B-BI B 1- B2 B2-B3
BeTBb C C-CI CI-C2 C2-C3
)];JIHHHbIe n;enH HapalI(HBalOTCH H3 <pparMeHToB, nOCJIe,nHee 3BeHO KIDK,ZJ;oro
cl>parMeHTa cHa6xaeTcH HOMepoM. <l>parMeHTbI CJIe,nyeT co6HpaTb TaK, qTo6bI coe-
AHIDIJIHCb n(jCJIe,nHHe 3BeHbH C o,nHHaKOBbIMH HOMepaMH. ECJIH n;enb BXO,nHT B
KOMIIJIeKT H3 ,nBYX IDIH 60JIee BeTBeH, KIDK,ZJ;aR BeTBb 0603HaqaeTCH Ha nOCJIe,nHeM
3BeHe KIDK,ZJ;orO <pparMeHTa 6yxBOH, B ,nonOJIHeHHe K HOMepy. <l>parMeHTbI KIDK,ZJ;OH
BeTBH ,nOJDKHbI 6bITb eHTH<pHn;HpoBaHbI no nOCJIe,nHHM 3BeHbHM H B npaBIDIbHoH
nOCJIe,noBaTeJIbHOCTH, KaK )'Ka3aHo, c06paHbI.
COrJIaCOBaHHwe no mary no oruaHHbIe npHBO)UlbIe nenH (nenH, OCHameHHbIe co-
e,lUlHeHHJIMH)
3a e,nHHCTBeHHbIM HCKJIlOqeHHeM n;eneH C y,lL1IHHeHHbIMH onopHbIMH BaJIHKa-
MH, BbIpOBIDITb mar oTBepcTHH caMHX coe,nHHeHHH B OqeHb Y3KHX npe,neJIax HeB03-
MO)KHO H3-3a Toro, qTO npHXo,nHTCH 60pOTbCH C ,nonOJIHHTeJIbHbIMH ,norrycKaMH
(H3rH6, npOCBepJIHBaHHe oTBepcTHH H T.n.).
QBeTOBoe KO,lUlpOBaHHe
)];JUI nOKYITaTeJIeH, KOTopbIe caMH XOTHT BbIpaBHHBaTb CBOH n;enH, B03MO)KHO
OCHaCTHTb HX Cnen;HaJIbHbIMH coe,nHHeH:IDIMH Ha MeCTe. Renold BbIrrycKaeT KOPOT-
KHe n;enH C n;BeTOBbIM KO,nOM C OC06bIMH nOJUIMH ,norrycKa. l(BeTOBaR MapmpoBKa
06bIqHO 6bIBaeT KpacHoH, XeJITOH IDIH 3eJIeHOH, qTO )'Ka3bIBaeT Ha HIDKHIOIO, cpe,n-
HIOIO IDIH BepXH1010 1'peTb noJUI ,norrycKa. )];JUI 60JIee TOqHbIX nOJIeH ,norrycKa MOryr
HCnOJIb30BaTbCH ,nonOJIHHTeJIbHbIe I.J;BeTa, HO 06brqHO 60JIee qeM ,nOCTaTOqHO MaK-
CHMYM IUITH I.J;BeTOB.
Dla8a 5. MexaHulleclCue nepeiJallu
l(BeT
KpaCHbIH
)l(eJITbIH
3 eJIeHbIH
CHHHH
BeJIbIH
0,05%
0,10%
0,15%
,[LmI MeJIKHX TOqHbIX
,nOnyCKOB
5.3.22. IA3N1epeHlAe 1A3HOCa LlenlA
Henocpe,nCTBeHHOH MepoH H3Hoca n;enH HB.JUIeTCH yBeJIHqeHHe ee .n.rrHHbI no CPaB-
HeHHIO C HOMHHaJIbHOit CJIe,noBaTeJIbHO, H3HOC n;enH MOXHO BbUIBHTb, H3MepIDI ee
.n.rrHHY B COOTBeTCTBHH C npHBe,neHHbIMH ,naJIee peKOMeH):(an;:IDIMH.
. PaCnOJIO}J(HTe n;enb, o6a KOHn;a KOTOpOH ,nOJDKHbI 3aKaWlHBaTbCH BHYTPeHHH-
MH 3BeHbHMH (,neTaJIb NQ 4), Ha IIJIOCKOH nOBepXHOCTH H, 3aIq)enHB ee 3a
O,nHH KOHen;, npHcoe,nHHHTe K ,npyrOM)' KOH:Qy CTIDKHOH 3aMOK H npyxHHHbIe
BeCbI, COOTBeTCTByIOm;HM 06pa30M 3aKpeIIJIeHHbIe.
. I1pH nOMOm;H YCTaHOBJIeHHOrO CTIDKHoro 3aMKa npHJIO}J(HTe CHJIy HaTIDKeHIDI:
O,lJ;HOPMHaH n;enb p2 x 0,77 (H).
)];BYXPMHaH n;enb p2 x 1,56 (H).
TpeXPMHaH n;enb p2 x 2,33 (H),
r,ne P - mar n;enH B MM.
K ,l(JIHHH03BeHHOH n;enH (T.e. n;enH, xapaKTepH3YIOm;eHCH TaKOH xe, KaK H
06b:NHaH n;enb, pa3pymaIOlI(eH HarpY3KOH, HO C y,nBoeHHbIM marOM) npH H3MepeHHH
npHJIaraHTe TaKYIO xe CHJIy, KaK H K 3KBHBaJIeHTHOH n;enH C KOpOTKHM marOM.
B KaqeCTBe aJIbTepHaTHBbI n;enb MOXHO rto,nBeCHTb BepTHKaJIbHO H 3KBHBaJIeHT-
HbIH Bec npHcoe,nHHHTb K HIDKHeM)' KOH:Qy.
M
r "I
. H3MepbTe .n.rrHHY «M» (CM01'pH cxeM)' BbIme) B MHJIJIHMe1'pax H qepe3 Hee
BbIqHCJIHTe OTHOCHTeJIbHOe Y,nJIHHeHHe no CJIe,nyIOm;eH <;popMYJIe:
M - (N · P)
OTHOCHTeJIbHOe y.n.rrHHeHHe = x 100,
N.P
r,ne N - qHCJIO marOB B H3MepHeMoH n;enH; P - mar.
. KaK npaBHJIO, CpOK nOJIe3HOrO HCnOJIb30BaHIDI n;enH 3aKaWlHBaeTCH H n;enb
Tpe6yeT 3aMeHbI, Kor,na OTHOCHTeJIbHOe y,l(JlHHeHHe ,nOCTHraeT 2% (1 % B CJIY-
qae .n.rrHHH03BeHHbIX n;eneH). ,[LmI npHBo,nOB, He cHa6xeHHbIX peryJIHpYIOInH-
MH YC1'pOHCTBaMH, KpHTWleCKaH rpaHHn;a HIDKe H 3aBHCHT OT CKOpOCTH H
pacnOJIOXeHIDI. 06bflIHO 3TO 3HaqeHHe pacnOJIaraeTCH B ,nHana30He Mex.ny
0,7% Ii 1,0%.
5.3. MexaHullecKue nepeoallu: u,enHble nepeoallu 385
CnpaBOlJllHK no H3HOCY Renold
)];OCTYTIHbIH CnpaBOqHHK no H3HOCY n;eneH .nIDI n;eneH C HaH60JIee nonYlliIpHbI-
MH pa3MepaMH marOB BbI MoxeTe nOJIyqHTb, o6paTHBmHcb B KOMMepqeCKOe npe,n-
CTaBHTeJIbCTBO.
5.3.23. PeNlOHT If 3BNleHB
3Be3 01fKH
AHaJIH3 06eHX 60KOBbIX nOBepXHocTeH ,naCT npe,nCTaBJIeHHe 0 CTeneHH c eCT-
ByJOlI(erO H3Hoca. I1pH HOpMaJIbHbIX 06CTOHTeJIbCTBax 3aMeTHa OTnOJIHpOBaHHaR
rrpOTepmaHCH nOJIoca Ha ypOBHe HaYa.rrbHOH OIq)yxHOCTH 3y6a 3Be3,nOqKH.
ECJIH r.ny6HHa H3Hoca «x» ,nOCTHrJIa 10% 3HaqeH:IDI «Y», Heo6xo,nHMO npHIDITb
MepbI no 3aMeHe 3Be3,nOqKH. Xo,n HOBOH n;enH no 3Be3,nOQKaM, HMelOlI(HM TaKOH
H3HOC 3y6beB, npHBe,neT K 6bIC1'pOM)' H3HOCY n;enH.
AH8MeTp H8l18nbH0ii1 OKPY'KHOCTVI
rny6V1H8 Vl3HOC8
y
x=-
10
y
:- ..:
CJIe,nyeT OTMeTHTb, QTO npH HOpMaJIbHbIX YCJIOB:IDI pa60TbI H npaBIDIbHOM CMa-
3bIBaHHH BeJIWlHHa H3Hoca «X» ,nOCTHraeT TaKoro 3HaQeHIDI TOJIbKO nOCJIe Toro,
KaK 6y,neT 3aMeHeHO HeCKOJIbKO n;eneH.
Qenb
KaK npaBIDIO, He B03HHKaeT Heo6xo,nHMOCTH B peMOHTe n;enH. I1paBHJIbHO BbI-
6paHHaR H 06C.JIy)KHBaeMaR n;enb 6y,neT nOCTeneHHO H3HamHBaTbCH B TeQeHHe ,nJIH-
TeJIbHOrO nepHo,na BpeMeHH (npH6JIH3HTeJIbHO 15 000 QaCoB), HO He JIOMaTbCSI. 06-
pa aHTecb B OT,neJI YCTaHOBKH H TeXHWleCKoro 06C.JIy)KHBaH:IDI 3a KOHCYJIbTan;IDIMH
no BonpocaM OCTaBmerOCH 3KcIIJIyaTan;HOHHoro pecypca.
ECJIH npHBo,nHaR n;enb nOBpex.neHa npH neperpY3Kax H 3aKJIHHHBaeT IDIH 3a-
crpeBaeT npH npoxo,ne no 3Be3,nOQKe, ee CJIe.nyeT aKKYPaTHO CIDITb C npHBo,na H
rro,nBeprHYTb BH3YaJIbHOMY OCM01'pY. QTo6bI 06JIeftlHTb pa6oTY, y,naJIHTe KOHCH-
CTeHTHYID CMa3KY H MaCJIO.
B 3aBHCHMOCTH OT nOBpe)l{,D;eH:IDI, B03MO)KJIO, np eTCH npOH3BeCTH BpeMeH-
HbIH peMOHT 3aMeHOH 3BeHa. O,nHaKo 3TO He rapaHTHpyeT, QTO n;enb CHOBa He no,n-
BepFHeTCH neperpY3KaM, a TaKOH peMOHT c,neJIaeT ee YH3BHMOH K nOJIOMKaM B 6y-
,nyw;eM. CJIe,nOBaTeJIbHO, .rryqmee, QTO MO)KJIO c,neJIaTb, 3TO YC1'paHHTb HCTOQHHK
HeHcnpaBHOCTeH H YCTaHOBHTb HOBYIO n;enb. 3TO CJIe,nyeT c,neJIaTb no CJIe,nyIOlI(HM
nplf1lHHaM.
1. CTOHMOCTb npOCTOH CHCTeMbI HJIH CTaHKa QaCTO npeBbImaeT CTOHMOCTb 3a-
MeHbI n;enH.
2. HOBaH HJIH ,nIDKe 6bIBmaH B yrr01'pe6JIeHHH QaCTb n;enH mIH mapHHpa, coe-
,lUIHeHHaR C nOBpe)l{,D;eHHOH n;enblO, CTaHeT npHQHHOH 6:ueHHH :u rryJIbCan;HH Ha-
13-3255
Dl08a 5. MexaHu'tecICue nepeiJa'tu
rpY3KH. C 60JIbWOH BepoHTHoCTblO 3TO rrpHBe,neT K 6bIC1'pOH rrOJIOMKe o;enH, H
YCKOPHT H3HOC KaK o;errH, TaK H 3Be3,nOqeK.
ECJIH rrOJIOMKH o;errH rrpoHcxo,n;HJIH ,nBa pa3a HJIH 6oJIee, orrpe,neJIeHHO MO)I{HO
YTBep)l{,LJ;aTb, qTO qepe3 HeKoTopoe BpeWl o;errb CHOBa CJIOMaeTCH. ECJIH HeMe,l(JIeH-
HaH 3aMeHa o;errH HeB03MO)I{Ha, rrOqHHHTe ee, HO 3aMeHHTe rrpH rrepBoH xe
B03MO)I{HOCTH.
5.3.24. PerynlfpoBKB qenlf
QTo6bI 06eCrreQHTb rrOJIHbIH CpOK C.rryx6bI o;errH, Heo6xo,nHMO rrpOBo,nHTb HeKOTO-
pyIO peryJIHpOBK}' o;errH, rrpe,nrrOQTHTeJIbHO c,nBHraH O,nHH H3 BaJIOB. ECJIH nepe-
,n;BIDKeHHe BaJIa HeB03MO)I{HO, peKOMeH,IJ;yeTCH HCrrOJIb30BaTb peryJIHpyeMYlO Ha-
TIDKHyIO 3Be3,nOQK}', TaK QTo6bI OHa Bxo,nHJIa B 3ao;eIIJIeHHe C HeHarpyxeHHOH
BeTBblO o;errH. KaK rrpaBHJIO, HaTIDKHaH 3Be3,nOQKa ,nOIDKHa HMeTb TaKoe xe QHCJIO
3y6beB, KaK H Be,nyruaH 3Be3,n;OQKa. CJIe,nyeT y6e,nHTbCH, QTO CKOpOCTb He rrpeBbI-
CHT MaKCHMYM, YKa3aHHblH B cxeMe oo;eHKH xapaKTepHCTHK (CMOTpH CTpaHHIJ;bI
368 H 369).
:Qerrb peryIDIpHo CJIe.nyeT HaCTpaHBaTb TaK, QTo6bI rrpH O,nHOH HaTHHYTOH :HeTBH
HeHaTHHYTYIO BeTBb MO)I{HO 6billO CMeCTHTb Ha paCCTOHHHe «A» rrocepe,nHHe Mex.ny
o;eH1'paMH (CMOTpH cxeMY HIDKe). npHHHMasI BO BHHMaHHe B03MO)l{HyIO Heo;eHrpH-
pOBaHHOCTb KpeIIJIeHHH, CJIe,nyeT HcrrbITaTb peryJIHpOBK}' Ha rrpOTIDKeHHH rrOJIHOrO
o6opoTa 60JIbWOH 3Be3,n;OQKH.
A - rrOJIHOe CMem;eHHe
C - paCCTOHHHe Me)l{,LJ;y o;eHTpaMH rro rOpH30HTaJIH
C (MM)
nOJIHOe CMem;eHHe 'A' (MM) = ,
K
r,ne K = 25 ,IJ;JUI rrpHBo,nOB rrpH IIJIaBHOM xo,ne;
K = 50 ,IJ;JUI rrpHBo,nOB B YCJIOBIDIX y,napHbIX HarpY30K.
A
..
...............f-----------
c
.--------- -..-....
o peryJIHpOBKe BepTHKaJIbHO pacrrOJIOXeHHbIX rrpHBo,n;OB 60JIee rro,npo6HO rrpo-
KOHCYJIbTHpyHTeCb B OT,n;eJIe YCTaHOBKH H TeXHHQeCKOrO 06CJIy)KHBaHIDI.
5.3. MexaHulteCK,Ue nepeiJaltu: u,enHble nepeiJaltu 387
5.3.25. KOHCTPYlCTopcKlfe If,qelf
Pa3Hooopa3Hhle npHJI01KeHHJI.
KOHBeHepHasI ,nOCTaBKa, rrepHo,nHqeCKasI Iq)yrOBasI rro,naqa, rro,n'beM, rrepe,naqa
MOII(HOCTH H CHHxpOHH3anIDI.
..
"t
--
Pa3Hooopa3Hhle OTpaCJlH npoMhiIDJieHHocTH.
ABHacTpoeHHe, aBToMo6unecTPOeHHe, cy,nOCTPoeHHe, rro,n'beMHO-TPaHcrropTHoe
o6opy,noBaHHe, MOTOnHKJI, Hecl>THHoH rrpOMbICeJI.
C:,;:;1
Dla8a 5. MexaHu'teclCUe nepeiJa'tu
5.3.26. Ts6nJfqs KoaCPCPJfqJfeHTOB ,lIJfSMeTpS
HSlfsnbHOH OKpyJlCHOCTJf
QTo6bI rrOJIyqHTb ,IJ;HaMe1'p HaqarrbHOH OKp)')KHOCTH JII060H 3Be3,IJ;OQKH C KOJIHQeCT-
BOM 3y6beB OT 9 ,no 150, YMHO:>KbTe war nerrH Ha cooTBeTCTByIOlI(HH K03c1>cI>HnHeHT.
HarrpHMep, ,nHaMeTp HaQarrbHOH OKp)')KHOCTH 3Be3,IJ;OQKH C 38 3y6bHMH rrpH
ware 3/4,nIOHMa (19,05 MM) = 19,05 x 12,110 = 230,70 MM.
qHCJlO Ko3CjMJ)lIIUfeHT AHaMeTpa
3y6heB Ha'laJlhHOH OK})ymtOCTH
9 2,924
10 3,236
11 3,549
12 3,864
13 4,179
14 4,494
15 4,810
16 5, 126
17 5,442
18 5,759
19 6,076
20 6,392
21 6,709
22 7,027
23 7,344
24 7,661
25 7,979
26 8,296
27 8,614
28 8,931
29 9,249
30 9,567
31 9,885
32 10,202
33 10,520
34 10,838
35 11 , 156
36 11,474
37 11,792
38 12,110
39 12428
40 12,746
41 13,063
42 13382
43 13,700
44 14,018
qHCJlO Ko34»4»lIIUfeHT ,lUIaMeTpa
3y6heB Ha'laJlhHOH OK})ymtOCTH
45 14,336
46 14,654
47 14,972
48 15,290
49 15,608
50 15,926
51 16,244
52 16,562
53 16,880
54 17,198
55 17,517
56 17,835
57 18,153
58 18,471
59 18,789
60 19, 107
61 19,426
62 19,744
63 20,062
64 20,380
65 20,698
66 21,016
67 21,335
68 21,653
69 21 ,971
70 22,289
71 22,607
72 22.,926
73 23,244
74 23,562
75 23,880
76 24,198
77 24,517
78 24,835
79 25,153
80 25,471
1IHCJlo K03"lIIUfeHT ,lUIaMeTpa
3y6heB Ha'laJlhHOH OK})ymtOCTH
81 25,790
82 26,108
83 26,426
84 26,744
85 27,063
86 27,381
87 27,699
88 28,017
89 28,335
90 28,654
91 28,972
92 29,290
93 29,608
94 29,927
95 30,245
96 30,563
97 30,881
98 31,200
99 31,518
100 31,836
101 32, 154
102 32,473
103 32,791
104 33, 109
105 33,428
106 33,746
107 34,064
108 34,382
109 34,701
110 35,019
111 35,337
112 35,655
113 35,974
114 36,292
115 36,610
116 36,928
5.3. MexaHUlteCK,Ue nepeiJaltu: u,enHble nepeiJaltu 389
OK,OHltaHUe
qHCJlO Ko3CjMJ)lIIUfeHT ,lUIaMeTpa
3y6heB HaqaJlhHOH OK})ymtOCTH
117 37,247
118 37,565
119 37,883
120 38,202
121 38,520
122 38,838
123 39,156
124 39,475
125 39,793
126 40,111
127 40,429
128 40,748
qHCJlO Koa"lIIUfeHT ,lUIaMeTpa
3y6heB HaqaJlhHOH OK})ymtOCTH
129 41,066
130 41,384
13t? 41,703
132 42,021
133 42,339
134 42,657
135 42,976
136 43,294
137 43,612
138 43,931
139 44,249
140 44,567
qHCJlO Koa"HlUleHT ,lUIaMeTpa
3y6heB HaqaJlhHOH OKp)']KHOCTH
141 44,885
142 45,204
143 45,522
144 45,840
145 46,159
146 46,477
147 46,795
148 47,113
149 47,432
150 47,750
5 3.27. nplfBO,llb' war 3a warOM: nplfMep nepBb'H
CJIe,[(ylOIIJ;He pa60qHe rrpHMepbI rrpe,ncTaBIDlIOT C060H rrpocToe rrowarOBoe PYKO-
BO,nCTBO rro BbI60PY pa3JIHqHbIX CHCTeM nerrHbIX rrpHBo,noB. CJIy)K6a TeXHlNeCKOH
nO,lI,D;ep)I{KH Renold 06eCrreQHT KOHcYJIbTanHH ,IJ;JUI peweHIDI JII06bIX rrp06JIeM BbI-
60pa nerrHbIX rrpHBo,noB.
nO,np06Hee 06 ypaBHeHIDIX rrepe,naQH CM01'pH B pa3,neJIe 5.3.13.
npHMep 1. npHBO.a pOTaIUlOHHoro Hacoca
,n;aHo:
qHCJIO 060POTOB Hacoca
norJIO aeMasI MOII(HOCTb
npHBO,n
OrpaHINHBalO He YCJIOBIDI
360 06/MHH.
7,5 KBT
3JIeIcrpHQeCKHH MOTOp Ha 1440 06/MHH.
PaccToHHHe Me)K)fjT neH1'paMH rrpHMepHO 458 MM
PeryJIHpOBKa ,nBIDKeHHeM Barra
Bbl60p napaMemp08
KOJIHQeCTBO 3y6beB Zl = 19T
HeT 3c1>cI>eKTa MHoroyrOJIbHHKa
nO,nXO,nHT ,IJ;JUI rrpHBo,noB C IIJIaBHbIM XO,nOM
BbIQHCJIHM rrepe,naTOQHOe OTHoweHHe rro CJIe,[(ylOIIJ;eH <!>0PMYJIe:
IIepe.naTo'lHoe OTHoweHHe i = Z 2 = N 2 = 1440 = 4.
Zl N 1 360
CJIe,noBaTeJIbHO, QHCJIO 3y6beB Be,noMoH 3Be3,nOQKH:
Z2 =4xZI =4xI9=76T.
K03tPtPuijueHmbl iJJlJl onpeiJeAeHUJl MOU4Hocmu
K03<!>cI>HnHeHT BH,IJ;a HarpY3KH fi = 1 (IIJIaBHbIH XO,n Be,nYIUeH II Be,noMoH 3Be3-
,nOQeK) :
19 19
K03c1>cI>HUHeHT 3y6a 12 = - = - = 1.
Zl 19
PaCQeTHaH MOIIJ;HOCTb = 7,5 x 1 x 1 = 7,5 KBT.
Dla6a 5. MexaHU'IeCKUe nepeiJa'lu
Bbl60p ijenu
Tenepb u;enb MO)I{HO BbI6paTb, HCnOJIb3YH cxeMbI 3 H 4 (pa3,neJIbI 5.3.12 H 5.3.13).
nepeCeqeHIDI 3a,naHHbIX MO HOCTH H qHCJIa 060pOTOB ,nalOT CJIe.nyIO He B03MO)l{-
HOCTH:
0,5" BS O,nHOPMHCUI u;enb
0,375" BS ,nBYXPMHCUI u;enb
0,5" ANSI O,nHOPMHCUI u;enb
0,375" ANSI ,nBYXPMHCUI u;enb
(npH6JIH3HTeJIbHO 81 % HOMHHaJIbHOH MOInHOcm)
(npH6JIH3HTeJIbHO 98% HOMHHaJIbHOH MO HOCTH)
(npH6JIH3HTeJIbHO 83% HOMHHaJIbHOH MOInHOcrn)
(npH6JIH3HTeJIbHO 84% HOMHHaJIbHOH MOInHOCTH)
0,375" ANSI ,nBYXPMHCUI o;enb HenpHMeHHMa, TaK KaK OHa HBIDleTCH BTYJIOq-
HOH u;enblO.
llpUMer.taHue. npH6JIH3HTeJIbHbIH npou;eHT HOMHHaJIbHOH MOInHOCTH BbJ1IHCIDI-
eTCH ,neJIeHHeM BbI6paHHOH MO HOCTH npH 1440 06/MHH Ha MaKCHMaJIbHYIO MO -
HOCTb u;enH npH 1440 06/MHH.
,[LrnI 3Toro npHMepa MbI BbI6epeM 0,5" O,nHOPMHYIO u;enb no EBponeHCKOMY
CTaH,napTY .
llapaMempbl ycmaHo8KU
CMa3hlBaHHe. EBponeHcKCUI cxeMa ou;eHKH xapaKTepHCTHK u;eneH (CM01'pH Pa3-
,neJI 5.3.12) HCHO yx:a3bIBaeT, qTO CMa3bIBaHHe u;enH ,nOJDKHO BbInOJIIDITbCH C Hcno-
JIb30BaHHeM MaCIDIHOH BaHHbI. :Qenb ,nOJDKHa 6bITb nOMe eHa B MaCIDIHYIO BaHHY
H npoxo,nHTb qepe3 Hee B npou;ecce pa60TbI.
BbJ1IHCJIHM Tenepb ,n.rrHHY u;enH:
P ( Z2 -Zl ) 2
L= Zl+Z2 + 2C + 21t =
2 P C
2
127 ( 76 -19 )
19 + 76 + 2 x 458 + ' 21t = 121,9.
2 12,7 458
OKpyrJIIDI ,no 6JIIDKaHWero qeTHOrO qHCJIa waroB, no.rryqaeM 122.
Bblr.tucAeuue paCCmOJlHUJl MeJICoy ijeHmpaMU
PaccToHHHe Me o;eH1'paMH npHBo,na MoxeT 6bITb Tenepb BbIqHCJIeHO no
cl>oPMYJIe, npHBe,neHHoH HIDKe:
= P ( 2L -Z2 -ZI + 1 (2L -Z2 -ZI)2 - (Z2 -ZIP J =
8 3 8
= 12.7 ( (2 x 122) -76 -19) + «2 x 122) -76 _19)2 - x (76 -19)2 J = 458,6 MM.
8 3 8
PeZYAup08Ka
npH YCJIOBHH, qTO H3HOC u;enH COCTaBillIeT 2% MH ,nBa wara (B 3aBHCHMOCTH
OT Toro, qTO MeHbwe), B 3TOM CJIyqae no.rryqaeM (122 x 1,02) - 2,44 wara
CJIe,noBaTeJIbHO, HCnOJIb3yeM ,nBa mara: L = 124.
nOcJIe no,nCTaHOBKH 3Toro 3HaqeHIDI B ypaBHeHHe H HOBbIX BbJ1IHCJIeHHH
no.rryqaeM: C = 471,7 MM,
n03TOMY nOJIHCUI peryJIHpOBKa ,nOIDKHa COCTaBIDlTb 13,1 MM.
OTMeTHM, qTO Ha npaKTHKe HeKOTopbIe 01'pHu;aTeJIbHbIe peryJIHpOBKH 06JIerqaT
c60PKY H 6y,nyr Heo6xo,nHMbI, eCJIH npe,nnOJIaraeTCH c60pKa u;enH, 3apaHee coe,nH-
HeHHoH B 6eCKOHeqHyIO neTJIIO.
5.3. MexaHulteCK,Ue nepeiJaltu: u,enHble nepeiJaltu 39
,l(pyzue iJaHHble
C N x P x ZI = 1440 x 12,7 x 19 = 579 M I. C.
KOpOC nerrH 60000 60000 ' I
HarpY3Ka B uerrH BCJIe,nCTBHe rrepe,naBaeMoH 3HeprHH
= Q x 1000 = 7,5 x 1000 = 1295 H,
v 5,79
r,ne Q - BbI6paHHCUI MOInHOCTb (KBT).
HarpY3Ka B nerrH BCJIe,nCTBHe neH1'pOC1'peMHTeJIbHOrO YCKopeHIDI
= IJ;errb . Macca / Me1'p x CKOpOCTb 2 = 0,68 x 5,79 2 = 23 H.
CYMMapHCUI pa60qCUI HarpY3Ka nerrH = 1318 H.
OTMeTHM, qTO HarpY3Ka B nerrH, .06YCJIOBJIeHHaH neHTpOCTpeMHTeJIbHblM YCKO
peHHeM, CTaHeT HaMHoro 60JIee cyruecTBeHHoH rrpH BbICOKHX CKOpOCTHX, rrOCKOJIb
KY B ypaBHeHHe BXO,nHT KBa,npaT CKOpOCTH nerrH:
OceBCUI pa3pymalOInaH HarpY3Ka nerrH = 19000 H
1900
K03c1>cI>HnHeHT Ha,nelKHOCTH nerrH = - = 14,4
1318
OrropHaH IIJIO a,nb nerrH = 50 MM 2
OrropHoe ,naBJIeHHe = Pa60qCUI HarpY3Ka = 1318 = 23,36 H/MM2.
IIrrOIna,nb 50
5.3.28. nplfSO,llbl war 3a warOM: nplfMep sTopoR
CJIe,l(ylOInHe pa60QHe rrpHMepbI rrpe,nCTaBIDlIOT C060H rrpOCToe rrowarOBoe PYKO.
BO,nCTBO rro BbI60py pa3JIHQHbIX CHCTeM nerrHblX rrpHBo,nOB. CJIy)K6a TeXHlNeCKO
nO,lI,D;ep)I{KH Renold 06ecrreQIIT KOHCYJIbTanHH ,IJ;JUI peweHIDI JII06bIX rrp06JIeM Bbl-
60pa nerrHbIX rrpHBo,nOB.
nO,np06Hee 06 ypaBHeHIDIX rrepe,naQH CM01'pH pa3,neJI 5.3.13.
npHMep 2. 4-IUfJIHH;J:plf1leCKHH KOMDpeccop
,lJ;aHo:
qHCJIO 060pOTOB
norJIOInaeMCUI MOInHOCTb
npHBO,n
OrpaHHBalO He YCJIOBIDI
Bbl60p napaMemp08
HCrrOJIb3yeTcH 3Be3,nOQKa C 25 3y6bHMH ,IJ;JUI rrpHBo,na B YCJIOBIDIX ,nHHaMINHb
H3MeHeHHH HarpY3KH (CM01'pH C1'paHHny 366 BbI60pa rrepe,naTOQHOrO OTHoweHIDI Ii
3Be3,nOQeK):
250 06/MHH
250 KBT
3JIeIcrpINeCKHH ,nBHraTeJIb C 960 06/MHH
PaCCTOHHHe Me)l{)];Y neH1'paMH rrpHMepHO 1500 MM.
IIepe.n;aTOtlHoe OTHoweHHe = Z 2 = N 2 = 960 = 3,84
ZI N I 250
qHCJIO 3y6beB Z2 = 3,84 x ZI = 3,84 x 25 = 95T
Dla8a 5. MexaHu'tecKue nepeiJa'tu
K03fjJfjJuu,ueHmbl iJJlJl onpeiJeAeHUJl MOU4Hocmu
K03c1>cI> H nHeHT BH,[(a HarpY3KH fi = 1,5 (cpe,nHeH CTerreHH ,nHHaMINHCUI HarpY3-
Ka Ha Be.nyII(ylO H Ha Be,noMYIO 3Be3,nOqKH):
19 19
K03c1>cI>HnHeHT 3y6a 12 = - = - = 0,76
Zl 25
PaCqeTHCUI MO:rn;HOCTb = nepe,naBaeMCUI MO:rn;HOCTb xfi x 12 (KBT)
PaCqeTHaH MO:rn;HOCTb = 250 x 1,5 x 0,76 = 285 KBT.
Bbl60p u,enu
:Qerrb MOlKeT 6bITb Bbl6paHa rrpH rrOMOIIJ;H EBporreHcKoH cxeMbI OneHKH xapaKTe-
pHCTHK nerreH (CM01'pH pa3,neJI 5.3.12) Ha rrepeCeqeHHH 3a,naHHoH MO:rn;HOCTH
(285 KBT Ha BepTHKaJIbHOH OCH) H CKOpOCTH (960 06/MHH Ha ropH30HTaJIbHOH OCH).
,[LrnI rro.rryqeHHH rrepe,naTOqHOrO OTHoweHIDI 3,8: 1 MOryT HCrrOJIb30BaTbCH ,nBe
COrJIaCOBaHHbIX BeTBH 1peXPMHbIX nerreH EBporreHcKoro CTaH,D;apTa C warOM 1,25"
BMeCTe C TepMHqeCKH o6pa6oTaHHbIMH CTaJIbHOH Be,nyIneH C 25 3y6bHMH H Be,no-
MOH C 95 3y6bHMH 3Be3,nOqKaMH.
llapaMempbl ycmaHo8KU
EBporreHcKCUI cxeMa OneHKH xapaKTepHCTHK nerreH (CM01'pH pa3,neJI 5.3.12)
HCHO YKa3bIBaeT, qTO CMa3bIBaHHe nerrH ,nOJDKHO BbIrrOJIIDITbCH C HCrrOJIb30BaHHeM
MaCIDIHOH BaHHbI. :Qerrb ,nOJDKHa 6bITb rrOMe:rn;eHa B MaCIDIHYIO BaHJIy H rrpOXO,ZJ;HTb
qepe3 Hee B rrponecce pa60TbI.
BbIqHCJIHM Terrepb .n.rrHHY nerrH:
317 1 95 _ 25 ) 2
L = 25 + 95 + 2 x 1500 + ' \.. 21t = 157 12.
2 31,75 1500 '
OKpyrJIIDI ,no 6JIIDKaHWero qeTHOrO qHCJIa waroB, rro.rryqaeM 158.
Bbl"tUCJleHUe P4CCmOJlHUJl MeJICiJy u,eHmpaMU
PaccToHHHe Me)l{){y neH1'paMH rrpHBo,na MoxeT 6bITb Terrepb BbIqHCJIeHO no
CTaH.napTHOH cl>oPMYJIe, rrpHBe,neHHoK HIDKe: = 1514,44 MM
C = 31,75 ( (2 x 158) - 95 - 25) + 1 «2 x 158) - 95 - 25) 2 - (95 - 25)2 ) .
8 88
PeZYAup08Ka
960 x 31 75 x 25
CKOpOCTb nerrH ' = 12,7 M/C.
60000
HarpY3Ka B nerrH 285 x 1000 = 22440 H.
12,7
HarpY3Ka B nerrH BCJIe,nCTBHe neH1'pOC1'peMHTeJIbHOrO YCKopeHIDI =
= 11,65 x 2 x 12,7 x 12,7 = 3758 H.
nOJIHCUI pa60qCUI HarpY3Ka nerrH = 26027H.
OrropHoe ,naBJIeHHe = Pa60qCUI HarpY3Ka = 23272 = 14,7 H/MM2.
llrrO:rn;a,nb orropbI 885 x 2
MaKCHMaJIbHCUI HarpY3Ka 294200
K03c1>cI>HnHeHT Ha,ne)I{HOCTH nerrH = = x 2 = 22,6.
Pa60qCUI HarpY3Ka 26027
5.3. MexaHu'teCKue nepeiJa'tu: l(enHble nepeiJa'tu
MHOrOBaJlOBhle npHBO,zu.l
-.J}
IIoClleiJo8ameAbHo paCnOAOJICeHHble 8MbI
Ha cxeMe rrOKa3aHO rrpHBe eHHe B eHcTBHe rrpHBo Horo ponHKoBoro KOH-
BeHepa.
BbI60p nerrH OCHOBbIBaeTCSI Ha MOMeHTe rrpOCKaJIb3bIBaHIDI Me ponHKaMH H
rpaHcrropTHpyeMblM MaTepHaJIOM. 06bIqHO AJUI 3Toro THrra rrpHBo oB K03<P<PHnH-
eHT Ha,ne)I{HOCTH orrpe eIDIeTcSI cne yJO HM o6pa30M:
K03c1>cI>HUHeHT Ha,ne)I{HOCTH = 5 AJUI O HOHarrpaBJIeHHbIX rrpHBO OB
K03c1>cI>HnHeHT Hane)I{HOCTH = 8 AJUI peBepCHBHbIX rrpHBO OB
K3.)K)J;bIH ponHK, HCKJIIOqasI rrocne HHH, 3aKJIIOqaeT B ce6e Be rrpOCTbIe 3Be3-
,n;OqKH HJIH O HY CrrenHaJIbHyIO 3Be3 OqKY, KOTOpasI MoxeT Hcrronb30BaTbCSI C BY-
MSI rrpOCTbIMH neIDIMH. npH HH3KHX CKOpOCTSlX H B peBepCHBHbIX rrpHBo ax on-
XHbI rrpHMeIDITbCSI 3Be3 OqKH C yrrpOqHeHHbIMH 3y6bSlMH.
PonHKoBbIe KOHBeHepbI MeHee qeM C 10 ponHKaMH MOryr rrpHBO HTbCSI B .n;eH-
CTBHe C O Horo H3 KOHnOB neHTbI KOHBeHepa. EcnH qHCnO ponHKOB 6onbme, AJUI
YJIyqmeHIDI pacrrpe eneHIDI MOIIJ;HOCTH H HaH60nbmeH CYMMapHOH 3c1><peKTHBHO-
CTH peKOMeH.nYeTCSI, qTo6bI rrpHBO,L(Sl ee B eHcTBHe YC1]JOHCTBO HaxO.n;HJIOCb B
cepe HHe KOHBeHepa.
EcnH rrpe rronOXHTb, qTO rrpHBO , pa60TalOIIJ;HH B HJJ:eaJIbHbIX ycnoBIDIX, TaKHX
KaK qHCTasI BHemHIDI cpe a H COOTBeTCTByJOIIJ;ee CMa3bIBaHHe, HMeeT K03c1>cI>HnHeHT
none3Horo eHcTBIDI R%, Tor.n;a rronHbIM K03c1>cI>HnHeHT rrone3Horo eHcTBIDI
ponHKOBoro KOHBeHepa C X ponHKaMH 6y.n;eT paBeH:
100 ( ) X = RX
100 100(X -1) ·
EcnH K03<PcI>HnHeHT rrone3Horo eHcTBIDI oT enbHoro rrpHBo.n;a R paBeH 98%,
Tor a rrpHBO ponHKOBoro KOHBeHepa C 30 ponHKaMH 6y.n;eT HMeTb, cne OBaTenbHO,
nonHbIH K03<P<PHnHeHT rrone3Horo eHcTBIDI Bcero 55%.
CooTBeTcTBeHHo, He peKOMeH.nYeTCSI HCrrOnb30BaTb B O HOM rrpHBo.n;e 60nee
30 ponHKOB. ,[LrnI ponHKOBbIX KOHBeHepoB 60nee qeM C 30 ponHKaMH Hcrronb3yJOTCSI
HeCKonbKO rrpHBO OB.
npHBO OJDKeH 6bITb B COCTOSlHHH pa3BHTb MOMeHT, cooTBeTcTByJO HH MO-
MeHTy rrpOCKaJIb3bIBaHIDI HarpyxaeMbIX ponHKOB.
Dla8a 5. MexaHu'tecICue nepeiJa'tu
5.3.29. nplfBO,qbl war 3a warOM: nplfMep TpeTIfH
CJIe,l(ylO He pa60qHe rrpHMepbI rrpe,nCTaBIDlIOT C060H rrpOCToe rrowarOBoe pyKo-
BO,nCTBO rro BbI60PY pa3JIHQHbIX CHCTeM I(errHbIX rrpHBo,nOB. CJIy)K6a TeXHlNeCKOH
rrO,lI,D;ep)I{I(H Renold 06eCrreQHT KOHCYJIbTanHH AIDI peweHIDI JII06bIX rrp06JIeM BbI-
60pa nerrHbIX rrpHBo,nOB.
nO,np06Hee 06 ypaBHeHIDIX rrepe,naQH CM01'pH B pa3,neJIe 5.3.10.
npHMep 3.
,lJ;aHo:
nepeMe eHHe rraKeTa CTaJIbHbIX JIHCTOBbIX 3arOTOBOK.
20 pOJIHKOB C ,nHaMe1'pOM 150 MM.
BaJIbI ,nHaMe1'pOM 60 MM Ha wapHKorro,nWHrrHHKax.
Bec o,nHoro pOJIHKa paBeH 1900 H.
Ha KOHBeHepe o,nHOBpeMeHHO HaXO,nHTCH ,nBa rraKeTa.
Bec o,nHoro rraKeTa COCTaBIDIeT 17500 H rrpH .n.rrHHe 1500 MM.
CYMMapHCUI rrOJIe3HaH HarpY3Ka: 35000 H (,nBa rraKeTa).
PaccToHHHe Me)l(,lJ;Y neH1'paMH pOJIHKOB: 300 MM.
JIHHeHHCUI CKOpOCTb: 15 M/MHH.
,lJ;HaMeTp HaQaJIbHOH OKpyxHOCTH 3Be3,nOQeK: 140 MM.
,lJ;HHaMHQeCKCUI HarpY3Ka: 30 rryCKOB B Qac, B O,nHOM HarrpaBJIeHHH.
llpeOnOAOJICeHUR
npHBO,n pacrrOJIaraeTCH rrocepe,nHHe C 10 pOJIHKaMH C KIDK,IJ;OH CTOpOHbI.
CorrpOTHBJIeHHe KaQeHIDI pOJIHKOB paBHO 0,05.
CorrpOTHBJIeHHe TpeHIDI Me)l(,lJ;Y pOJIHKaMH H HarpY3KoH paBHO 0,25.
K03c1>cI>HnHeHT rrOJIe3HOrO ,neHcTBIDI OT,neJIbHOrO rrpHBo,na paBeH 98%.
Bbl"tUC./leHUR OAR 8bl6opa npU800a
KIDK,IJ;bIH rraKeT JIHCTOB CTaJIH BeCOM 17500 H rrepeMew;aeTCH Ha:
,l];.rrHHa rraKeTa 1500 5
= - = pOJIHKOB,
PaccToHHHe Me)l{){y neH1'paMH pOJIHKOB 300
HJIH 10 pOJIHKOB rrOJIHOH rrOJIe3HOH HarpY3KH.
ECJIH rrOJIe3HYJO HarpY3Ka 35000 H CJIOXHTb C CYMMapHbIM BeCOM 10 orropHbIX
pOJIHKOB (19000 H), TO rrOJIyqHTCH, QTO 06w;aH HarpY3Ka paBHa 54000 H. TaHreH-
nHaJIbHCUI CHJIa rrpH 10 pOJIHKaX paBHa: 54000 x 0,05 = 2700 H, H COOTBeTCTByro-
HH MOMeHT paBeH:
006
F x d (cHJIa x paCCTOHHHe )2700 x = 81 HM,
2
r,ne d - ,nHaMe1'p BaJIa.
,[LrnI KIDK,IJ;OH rpyrrrrbI H3 10 pOJIHKOB K03c1>cI>HnHeHT rrOJIe3HOrO )];eHCTBIDI paBeH:
98 10
= 81,7%.
100 9
3c1>cI>eKTHBHbIH MOMeHT CHJI B 3TOM CJIyqae 6y)];eT paBeH:
<l>aKTHQeCKHH MOMeHT CHJI = 81 = 99 HM.
K03c1>cI>HI(HeHT rrOJIe3Horo )];eHCTBHH 0,817
5.3. MexaHUlteCK,Ue nepeiJaltu: u,enHble nepeiJaltu 39!
.....J} u
3Be3,nOqeK C ,nHaMe1'poM HaqaJIbHOH OIq)yxHOCTH 140 MM THrOBoe YCHJIH'
n;errH 6y,neT paBHO:
2000 x Md = 2000 x 99 = 1414 H.
d 1 140
CHJIa 1'peHIDI rrpH K03c1>cI>HnHeHTe 1'peHIDI 0,25 paBHa 35000 x 0,25 = 8750 H.
CooTBeTCTBYI<> HH MOMeHT paBeH:
015
F x d(CHJIa x paccToHHHe) = 8750 x -2- = 656 HM,
2
r,ne d - pa,nHYC BaJIa.
nOJIHblH MOMeHT rrpHBo,na paBeH 656 + 81 = 737 HM.
3c1>cI>eKTHBHbIH MOMeHT, CJIe,nOBaTeJIbHO, paBeH:
737 = 902 HM.
0,817
Tor,na THrOBoe YCHJIHe nerrH CTaHOBHTCH paBHbIM:
2000 x Md = 2000 x 902 = 12886 H.
d 1 140
Terrepb MO)I{HO OneHHTb nerrb ,IJ;JUI o,nHoro rrpHBo,na; MO)I{HO HCrrOJIb30BaTI
n;errH ISO 16B-l HJIH Renold 1 10 088 BMeCTe C ,nBywI 3Be3,nOQKaMH C 17 3y6bHMI-
H ,nHaMe1'pOM HaQaJIbHOH OKpyxHOCTH 138 MM.
npH 06bJ1IHOM HCrrOJIb30BaHHH:
K OCeBCUI p 3pymalOInCUI CHJIa 67000 47 4
03'¥'¥HnHeHT Ha,ne)I{HOCTH = =,
Pa60QCUI HarpY3Ka 1414
O Pa60QCUI HarpY3Ka 1414 6 83 HI 2
rrOpHOe ,naBJIeHHe = - =, MM .
OrrOpHCUI IIJIO a,nb 207
npH rrpOCKaJIb3bIBaHHH:
K OceBaH pa3pymalOInaH CHJIa 67000 5 2
03'¥'¥HnHeHT Ha,ne)I{HOCTH = = ,
THroBoe YCHJIHe nerrH 12886
O THroBoe YCHJIHe nerrH 12886 62 26 HI 2
rrOpHOe ,naBJIeHHe = =, MM .
OrrOpHCUI IIJIO a,nb 207
JIHHeHHCUI CKOpOCTb nerrH paBHa:
CKOpOCTb rraKeTa x d 1 ( l.. ) = 15 x 0,138 = 0,23 M/c,
,n;HaMe1'p pOJIHKa 60 0,15 x 60
r,ne d 1 - ,nHaMe1'p HaQaJIbHOH OKpyxHOCTH 3Be3,nOQKH B Me1'pax.
Fi.V
):LrnI KIDK,IJ;OH rpyrrrrbI H3 10 pOJIHKOB MO HOCTb paBHa: .
1000
npH HOpMaJIbHbIX pa60QHX YCJIOBIDIX
Pa60QaH HarpY3Ka x JIHHeHHCUI CKOpOCTb _ 1414 x 0,23 = 0 33 KBT.
1000 1000'
Dla8a 5. MexaHU'IeCKUe nepeiJa'lu
T5IroBoe YCHJIHe IJ;errH x JlHHeHHasI CKOpOCTb = 12886 x 0,23 = 2 96 KBT
1000 1000' ,
Kor,na pOJlHKH rrpOCKaJIb3bIBa1OT.
. IIpHHHMasI BO BHHMaHHe K03<P<PHIJ;HeHT rrOJle3HOrO ,neHcTBIDI rrpHBo,na, KO-
TOpbIH ,no CHX rrop He 6bill yqTeH, CJle,nyeT ,n06aBHTb 25% K rrOJlHOH MOInHO-
CTH, qTO ,naCT 3,7 KBT.
llpUMe"laHue. IIpH 60Jlee BbICOKHX JlHHeHHbIX CKOpOCT5IX, CJIe,nyeT rrpHIDITb BO
BHHMaHHe TaIOKe H ,npyrHe ,norrOJIHHTeJlbHbIe <paKTOpbI, TaKHe KaK MOMeHT HHep-
IJ;HH pOJlHKOB H MOIIJ;HOCTb, He06xo,nHM)'IO ,nIDI YCKopeHIDI pa3JIHqHbIX KOMrrOHeH-
TOB CHCTeMbI.
napaJlJleJlbHO pacnOJlO1KeHHbIe BaJIbI
TIpHBOJJ:bI 3Toro THrra HCrrOJlb3yIOTCR TOJlbKO B c.rryqae BbIrrOJlHeHIDI CJle,l(yIOInHX
YCJlOBHH.
. CyruecTByeT rrOCTORHHasI Ha-
rpY3Ka, rrpe,nrrOQTHTeJlbHO
pa3,neJleHHasI paBHOMepHO Ha
CHCTeMY' 3Be3,nOQeK.
. JIHHeHHbIe CKOpOCTH He rrpe-
BbIIIlalOT 1,5 M/c.
. ,lJ;BIDKeHHe rrp Hcxo,nHT TOJlb-
KO B O,nHOM HarrpaBJleHHH.
K03<P<PHIJ;HeHT rrOJle3Horo ,n;eHcTBIDI TaKoro rrpHBo,na BbIIIle, QeM rrpH rrOCJle,nOBa-
TeJlbHOM pacrrOJlOXeHHH BaJIOB, rrOCKOJlbKY YMeHbillaeTCR corrpHKOCHOBeHHe 3y6beB.
KIDK,LJ:bIH rrpHBO,n 1'pe6yeT oc060ro BHHMaHIDI B TOM, QTO KacaeTCR pacrroJloxe-
HHR rro OTHOIIleHHIO K Be,nyrueH 3Be3,nOQKe, HaTIDKHOH 3Be3,nOQKe H peBepCHBHOH
meCTepHe.
PacrrOJlOXeHHe 3Be3,nOQeK, orropa H HarrpaBJUIIOInasI IJ;errH B 3HaQHTeJlbHOH CTe-
rreHH orrpe,neJUIIOT CpOK CJIy)K6bI IJ;errH.
IJ;errb B 60JIbIIlHHCTBe cJlyqaeB ,nOCTaTOqHO AJIHHHasI, H XOpOIIlHH OXBaT Be,ny-
IneH 3Be3,nOQKH B03MoxeH TOJlbKO rrpH HeKOTopOH CTerreHH rrpe,nBapHTeJlbHOrO Ha-
TIDKeHIDI. OH HHKor,na He ,nOJDKeH rrpeBbIIIlaTb rrOJlOBHHbI HOpMaJIbHOrO TRrOBoro
YCHJlIDI B rrpHJIOXeHHH.
MeTO,n BbI60pa IJ;errH TaKOH xe, KaK H rro,np06HO orrHcaHHbIH B pa3,neJle «IIo-
CJle,nOBaTeJlbHO pacrrOJlOXeHHbIe BaJIbI».
IIPHBO,nbI, YCTaHOBJleHHbIe, KaK rrOKa3aHO Ha pHCYHKe BbIIIle, rrpH HOpMaJIbHbIX
YCJlOBIDIX HMelOT K03<P<PHIJ;HeHT rrOJle3HOrO ,neHCTBIDI:
. 94% rrpH 5 pOJlHKaX
. 89% rrpH 10 pOJlHKaX
. 84% rrpH 15 pOJlHKaX
. 79% rrpH 20 pOJlHKaX
. 75% rrpH 25 pOJlHKax.
5.3. MexaHU eCl(,Ue nepeiJa u: u,enHble nepeiJa u 3
. 3. 30. npe,qocTepeJICeHlffl
Coe.lUlHeHHe 3BeHbeB
Coe,nHHeHIDI NQ 11 RJlH 26 (CKOJlb3Rm;asI noca,n;Ka) He CJle,nyeT HCnOJlb30Ba'
npH BbICOKHX CKOpOCTRX RJlH B TIDKeJlbIX YCJlOBHRX. IIpH TaKHX RJlH 3KBHBaJIeH'
HbIX 06CTORTeJlbCTBax, Kor,na BIDKHa 6e30naCHOCTb, CJle,nyeT HCnOJlb30BaTb 3aKJIt
nOqHOe coe,nHHeHHe NQ 107 (noca,n;Ka C HaTRroM).
ECJlH TOJlbKO B03MO)K}lO, npHBo,nHOH MexaHH3M ,nOJDKeH HMeTb ,nOCTaTOqHY
nOJlHyIO peryJlHpOBKY, qTo6bI rapaHTHpOBaTb HCnOJlb30BaHHe qeTHOrO qHCJla 3y6bf
Ha npOTIDKeHHH Bcero cpOKa nOJle3HOrO HCnOJlb30BaHIDI l..{enH. Coe,nHHeHHe nept
XO,nHbIM 3BeHOM (NQ 12 RJlH 30) CJle,nyeT HCnOJlb30BaTb TOJlbKO B KpaHHeM cnytlae
TOJlbKO B JlerKOM peXHMe B HeKpHTWIeCKHX npRJIOXeHIDIX.
TeXJlll1leCKOe 06CJIY1KHBaHHe neOH
CJle,nyIOIIJ;He npe,nOCTOpO)K}lOCTH Heo6xo,nHMO C06J1IO,naTb npH OTcoe,nHHeHHH
CIDITHH l..{enH C npHso,na ,lUUI 3aMeHbI, peMOHTa RJlH nepe,neJlKH AJIHHbI.
1. Bcer,na OTKJIIOqaH're HCTOqHHK HanpIDKeHIDI OT npHBo,na RJlH o6opy,noBaHIDI
2. Bcer,na HOCHTe 3aW;HTHbIe OqKH.
3. Bcer,na HOCHTe COOTBeTCTByIOIl(yIO 3am;HTHyIO cnel..{o,ne)K)];y, rOJlOBHOH y6o{
nepqaTKH H 3am;HTHyIO 06YBb, 06oCHOBaHHyIO 06CTORTeJlbCTBaMH.
4. Bcer,na npoBepRHTe, qTO HHCTPYMeHT HaxO,nHTCR B xopomeM pa60qeM co
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cm nop Ha paCCMOTpeHHH ISO. nO,np06HOCTH nOKa He,nOCTyIIHbI.
,LJ;HaMeTp (d l > ,lI;.Jomw (II>
HOM. ;(on. Aruumoe KopoTKoe
HCnOJIHeHHe HCnOJlHeHHe
+0,006
j6
6 -0,002 16 -
7
+0,007
8 j6 20 -
9 -0,002
10 23 20.
11
Pa3MepbI B MM
,lI;HaMeTp (d l > ,lI;.Jomw (II>
HOM. ;(on. Aruumoe KopoTKoe
HCnOJlHeHHe HCnOJlHeHHe
100 +0035
110 m6 210 165
+0013
120
125
130 +0040
140 m6
150 +0,015 250 200
160
170
180
\ ')
,lbtaMeTp (d l > Ammw (II>
HOM. ;(On. Aruumoe KopoTKoe
HCnOJlHeHHe HCnOJIHeHHe
12 +0,008 30 25*
14 j6
16 -0,003
18 40 28
19 LJ
20 +0,009
22 50 36
24 j6
-0,004
25 60 42
28
-
30
32 80 58
35
38 +0,018
40 k6
+0,002 /"
42 C -
45
48 110 82
50
55
56
60 +0,030
63 m6
65 +0,011 140 105
70
71
75
80
85 +0,035
90 m6 170 130
95 +0,013
5.4. MexaHUlI,eCK.Ue nepeoall,u: 8QJlbl 411
O"Olf,lI,aHUe
,lbtaMeTp (d I> Ammw (II>
HOM. ;(on. ,nm.HHoe KOpoTKoe
HCnOJIHeHHe HCnOJlHeHHe
190
200 +0046 300 240
220 m6
240 +0,017
250 350 280
260 +0052
280 m6
300 +0020 410 330
320
340 +0,057
m6
360 +0,021 550 450
380
400
420
/ '440 +0,063 650 540
/ m6
) 450 +0,023
460
480
500
530 +0,070
560
600 m6 800 680
630 +0,026
* YKa3aHHbIe TaK pa3MepbI He COfJIaCyJOTCH C COOTBeTCTByJOmHMH pa3MepaMH KOHH'Ie-
CKHX KOHUOB Barra B ,nJIHHHOM HCnOJIHeHHH. CMOTPH B84506 Ta6JIHua 2 H TIYHKT 2.
Dla8a 5. MexanUlteCKUe nepeiJaltu
5.4.9. Pa3Mepbl KOHlflfeCKIfX KOHqos sanos
C nplf3MaTlflfecKlfMIf wnOHKaMIf,
nlfHHoe IfcnonHeHlfe
d 3
b
' 2
\ I
1
'3
A
'-/2 I '-/2
1
d 4
-
YB8nM 8HHa. A8Tanb
B C8't8HMM A-A
llInOHOQHbIH na3 MO)l{eT HMeTb cPOPMY, OTJIWIHyID OT nOKa3aHHOH
KOHYCHOCTb 1:10 03HaQaeT (d 1 - d2)/(12/2) = 1/10
t
A
Ce\4eHHe A-A
1-/2
A
1 2
1 2
II = d 1 - d 2
+ I.
2
Pa3MepbI B MM
,lbtaMe'I'p a llinOHKH BHelUHJUl BuyrpellllJUl
H DlDOHO'lllhle nuy pe3hfia pe3.oa
d l II 1 2 13 d 2 bxh I II d 3 d 4
6 16 10 6 5,5 - - - M4 x 0,7 -
7 6,5 - - - M4 x 0,7
8 20 12 8 7,4 - - - M6 x 1 -
9 8,4 - - - M6 x 1
10 23 15* 8 9,25 2 x 2 1,2 1,6 M6 x 1 -
11 10,25 M6 x 1
12 30 18* 12 11,1 2 x 2 1,2 1,7 M8 x 1 M4 x 0,7
14 13,1 3 x 3 1,8 2,3 M8 x 1 M4 x 0,7
16 40 28 12 14,6 3 x 3 1,8 2,5 M10 x 1,25 M4 x 0,7
18 16,6 4x4 2,5 3,2 M10 x 1,25 M5 x 0,8
19 17,6 4x4 2,5 3,2 M10 x 1,25 M5 x 0,8
5.4. MexaHUlI,6CKUe nepeoall,u: 8QJlbl 413
OKOHlI,QHUe
aMeTp a llinOHKH BHeUDUIJI BII)'1'PeHIUUI
H DlDOHO'lllhle na3h1 pe3h6a pe3h6a
4. II 1 2 13 4 2 bxh I 'I 4 3 4 4
20 50 36 14 l ) 18,2 4x4 2,5 3,4 M12 x 1,25 M6 x 1
22 20,2 4x4 2,5 3,4 M12 x 1,25 M6 x 1
24 22,2 5 x 5 3,0 3,9 M12 x 1,25 M6 x 1
25 60 42 18 22,9 5 x 5 3,0 4,1 M16 x 1,5 M8 x 1,25
28 25,9 5 x 5 3,0 4,1 M16 x 1,5 M8 x 1,25
30 80 58 22 27,1 5 x 5 3,0 4,5 M20 x 1,5 MI0 x 1,5
32 29,1 6 x 6 3,5 5,0 M20 x 1,5 MI0 x 1,5
35 32,1 6 x 6 3,5 5,0 M20 x 1,5 MI0 x 1,5
38 35,1 6 x 6 3,5 5,0 M24 x 2,0 M12 x 1,75
40 110 82 28 35,9 10 x 8 5,0 7,1 M24 x 2,0 M12 x 1,75
42 37,9 10 x 8 5,0 7,1 M24 x 2,0 M12 x 1,75
45 40,9 12 x 8 5,0 7,1 M30 x 2,0 M16 x 2,0
48 43,9 12 x 8 5,0 7,1 M30 x 2,5 M16 x 2,0
50 )5 12 x 8 50 7,L M36 x 3,0 M16 x 2,0
55 ( 50,9 14 x 9 5,5 7,6 M36 x 3,0 M20 x 2,5
56 51,9 14 x 9 5,5 7,6 M36 x 3,0 M20 x 2,5
60 54,75 16 x 10 6,0 8,6 M42 x 3,0 M20 x 2,5
63 57,75 16 x 10 6,0 8,6 M42 x 3,0 M20 x 2,5
65 140 105 35 59,75 16 x 10 6,0 8,6 M42 x 3,0 M20 x 2,5
70 64,75 18 x 11 7,0 9,6 M48 x 3,0 M24 x 3,0
71 6575 18 x 11 7,0 96 M48 x 3,0 M24 x 3,0
75 69,75 18 x 11 7,0 9,6 M48 x 3,0 M24 x 3,0
80 73,50 20 x 12 75 10,8 M56 x 4,0 M30 x 3,5
85 170 130 40 78,50 20 x 12 7,5 108 M56 x 4,0 M30 x 3,5
90 83,50 22 x 14 90 123 M64 x 4,0 M30 x 3,5
95 88,50 22 x 14 90 12,3 M64 x 4,0 M36 x 4,0
100 91,75 25 x 14 90 13 1 M72 x 4,0 M36 x 4,0
110 210 165 45 101,75 25 x 14 9,0 13,1 M80 x 4,0 M42 x 4,5
120 111,75 28 x 16 10,0 14,1 M90 x 4,0 M42 x 4,5
125 116,75 28 x 16 100 14,1 M90 x 4,0 M48 x 5,0
130 120,0 28 x 16 10,0 15,0 MI00 x 4,0 -
140 250 200 50 130,0 32 x 18 11,0 16,0 MI00 x 4,0 -
150 140,0 32 x 18 11,0 16,0 MIlO x 4,0 -
160 1480 35 x 20 12,0 18,0 M125 x 4,0 -
170 300 240 60 158,0 36 x 20 12,0 180 M125 x 4,0 -
180 168 0 40 x 22 13,0 190 /M140 x 60 -
176,0 20,0 ) , /
190 40 x 22 130 M140 x 6,0 -
200 350 280 70 186,0 40 x 22 13,0 20,0 M160 x 6 0 -
220 206,0 45 x 25 15,0 22,0 M160 x 6 0 -
* YKa3aHHbIe TaK pa3MephI He COfJIaCyIDTCH C COOTBeTCTByIDIUHMH pa3MepaMH KOHHtle-
CKHX KOHUOB BaJla B ,lUIHHHOM HCnOJIHeHHH. CMOTPH BS4506 Ta6JIHua 2 H II}'HKT 2.
,IJ;aJIbHeitillyro HHcP0pMaJJ;HIO CMOTpH BS 4506.
TIla8a 5. MexaHu'IecICue nepeiJa'lu
5.4.10. Pa3Mephl KOHlflfeCKIfX KOHqos san os
C AlfaMeTpaMIf CShlwe 220 MM C na3aMIf
,lVIfI wnOHOK, napannenhHhlMIf nosepxHocTIf
sana, ,lVIIfHHOe IfcnonHeHlfe
h
m
t
1/2 1/2
/2
I
Ce\4eHHe A-A
KOHYCHOCTb 1:10 03HaQaeT (d t - d2)/(12/2) = 1/10
Pa3MepHOCTH B MM
,lbtaMeTp a llInOHKH H IDDOHO'lllhle BUY BHelUHJUl pe3t.6a
4 1 11 1 2 13 4 2 bxh t 4 3
240 223,5 50 x 28 17 M180 x 6
250 410 330 80 233,5 50 x 28 17 M180 x 6
260 243,5 50 x 28 17 M200 x 6
280 261,0 56 x 32 20 M220 x 6
300 470 380 90 281,0 63 x 32 20 M220 x 6
320 301,0 63 x 32 20 M250 x 6
340 317,5 70 x 36 22 M280 x 6
360 550 450 100 337,5 70 x 36 22 M280 x 6
380 357,5 70 x 36 22 M300 x 6
400 373 0 80 x 40 25 M320 x 6
420 3930 80 x 40 25 M320 x 6
440 413,0 80 x 40 25 M350 x 6
450 650 540 110 423,0 90 x 45 28 M350 x 6
460 433,0 90 x 45 28 M380 x 6
480 453,0 90 x 45 28 M380 x 6
500 473,0 90 x 45 28 M420 x 6
530 496,0 100 x 50 31 M420 x 6
560 800 680 120 526,0 100 x 50 31 M450 x 6
600 566,0 100 x 50 31 M500 x 6
630 5960 100 x 50 31 M550 x 6
,[Lng 60JIbmeH HHcPopMaJJ;HH CMOTpH BS 4506.
5.4. MexaHUlI,eCKUe nepeoall,u: 8QJlbl 415
( )
5.4. 11. Pa3Meph' KOHlflfeCKIfX KOHqos sanos
C nplf3MaTlflfeCKlfMIf wnOHKaMlf,
KopOTKoe IfcnonHeHlfe
b
' 2
I
YBenH eHHa aCTb
AeTanH B CeYeHH X A-A
llInOHOqHbIH na3 MoxeT HMeTb cP0PMY, OTJIHqlfYlO OT nOKa3aHHoH
KOHYCHOCTb 1:10 03HaqaeT (d 1 - d 2 )/(IJ2) = 1/10
t
A
T
d 1
1
'-/2 1 2
' 2
11 = d l - d 2 + 1
2
Pa3MepbI B MM
,lbta'MeTp a llinOHKH BHelUHJUl BayrpeHIUUI
H DlDOHO'lllhle naay pe3h6a pe3h6a
4 1 II 1 2 13 4 2 bxh t 4 3 4 4
16 15,2 3 x 3 1,8 MI0 x 1,25 M4 x 0,7
18 28 16 12 17,2 4x4 2,5 MIO x 1,25 M5 x 0,8
19 18,2 4x4 2,5 MI0 x 1,25 M5 x 0,8
20 18,9 4x4 2,5 M12 x 1,25 M6 x 1,0
22 36 22 14 20,9 4x4 2,5 M12 x 1,25 M6 x 1,0
24 22,9 5 x 5 3,0 M12 x 1,25 M6 x 1,0
25 42 24 18 23,8 5 x 5 3,0 M16 x 15 M8 x 1,25
28 26,8 5 x 5 3,0 M16 x 1,5 M8 x 1 25
rAa8a 5. MexaHUlteCKUe nepeiJaltu
O"OHItDnUe
aMeTp ,nmnta llInOHKH BHeDIHJUI BayrpelllDDl
H WDOHO......e 883M pe3h6a pe3h6a
d 1 '1 '2 '3 d 2 bxll t d 3 d 4
30 ,j ) 28,2 5 x 5 3,0 M20 x 1,5 M lOx 1,5 I
32 58 36 22 30,2 6x6 3,5 M20 x 1,5 MI0 x 1,5
35 33,2 6x6 3,5 M20 x 15 MI0 x 1,5
38 36,2 6x6 3,5 M24 x 2 0 M12 x 1,75
40 37,3 10 x 8 5,0 M24 x 2 M12 x 1,75
42 39,3 10 x 8 5,0 M24 x 2 M12 x 1,75
45 42,3 12 x 8 5,0 M30 x 2 M16 x 2,0
48 82 54 28 45,3 12 x 8 5,0 M30 x 2 M16 x 2,0
50 47,3 12 x 8 5,0 M36 x 3 M16 x 2,0
55 52,3 14 x 9 5,5 M36 x 3 M20 x 2,5
56 53,3 14 x 9 5,5 M36 x 3 M20 x 2,5
60 56,5 16 x 10 6,0 M42 x 3 M20 x 2 5
63 59,5 16 x 10 6,0 M42 x 3 M20 x 2,5
65 105 70 35 61,5 16 x 10 6,0 M42 x 3 M20 x 2,5
70 66,5 18 x 11 7,0 M48 x 3 M24 x 3,0
71 67,5 18 x 11 7,0 M48 x 3 M24 x 3,0
75 71,5 18 x 11 7,0 M48 x 3 M24 x 3,0
80 75,5 20 x 12 7,5 M56 x 4 M30 x 3,5
85 130 90 40 80,5 20 x 12 7,5 M56 x 4 M30 x 3,5
90 85,5 22 x 14 9,0 M64 x 4 M30 x 3,5
95 90,5 22 x 14 90 M64 x 4 M36 x 4,0
100 94,0 25 x 14 9,0 M72 x 4 M36 x 4,0
110 165 120 45 104,0 25 x 14 90 M80 x 4 M42 x 4,5
120 1140 28 x 16 10,0 M90 x 4 M42 x 4,5
125 119,0 28 x 16 10,0 M90 x 4 M48 x 5,0
130 122,5 28 x 16 10,0 MI00 x 4 -
140 200 150 50 132,5 32 x 18 11,0 MI00 x 4 -
150 142,5 32 x 18 11,0 MIlO x 4 -
160 151,0 36 x 20 12,0 M125 x 4 -
170 240 180 60 161,0 36 x 20 12,0 M125 x 4 -
180 171,0 40 x 22 13,0 M125 x 6
190 1795 40x22 13 0 M140 x 6 -
200 280 210 70 189,5 40 x 22 13,0 M160 x 6 -
220 209,5 45 x 25 15 0 M160 x 6 -
,lJ;arrblfeHmyIO HH$opMaUHIO CMOTPH BS 4506.
5.4. MexaHu"teCK:Ue nepeda"tu: 801lbl 417'
5.4.12. ,QonycKaeMb,e Bpa alO He MOMeHTb'
8MeTp ,lI;onycaeMYe .pam,aJO.....e
KOJ1Q8 B8J1a MOM T (8M)
d 1 (MM) (a) ( J (c)
6 \) 0,307 0,145
7 0,53 0,25
8 0,85 0,4
9 1,25 0,6
10 1,85 0,875 I
11 2,58 1,22
12 3,55 1,65
14 6,00 2,8
16 9,75 4,5
18 14,5 6,7
19 I /17,5 8,25
20 -- / 21,2 9,75
22 29,0 13,6
24 40,0 18,5
25 46,2 21,2
28 69,0 31,5
30 206 87,5 40,0
32 250 109,0 50,0
35 325 150,0 69,0
38 425 200,0 92,5
40 487 236,0 112
42 560 280 132
45 710 355 170
48 850 450 212
50 950 515 243
55 1280 730 345
- 56 1360 775 355
60 1650 975 462
63 1900 1150 545
65 2120 1280 600
( 70 2650 1700 800
71 2780 1800 825
75 3250 2120 1000
80 3870 2650 1250
85 4750 3350 1550
14-3255
,lI;HaMeTp ,lI;onycaeMYe .palQalO.....e
KOHQa B8J1a MOMe........ T (HM)
d 1 (MM) (a) (b) (c)
90 5600 4120 1900
95 6500 4870 2300
100 7750 5800 2720
110 10300 8250 3870
120 13700 11200 5150
125 15000 12800 6000
130 17000 14500
140 21200 19000
150 25800 24300
160 31500 30700
170 37500 37500
180 45000
190 53000
200 61500
220 82500
240 106000
250 118000
260 136000
280 170000
300 206000
320 250000
340 300000
360 355000
380 425000
400 487000
420 560000
440 650000
450 690000
460 750000
480 850000
500 950000
530 1150000
560 1360000
600 1650000
630 1900000
\ I;Jla8a 5. MexaHUfteCKUe nepeiJaftu
3HaqeHIDI BpaIUalOIUero MOMeHTa paCCqHTaHbI no CJle.nyIOru;HM $oPMYJlaM H
oKpyrJleHbI,n;o 3HaqeHHH PMa R80 (npe,n;nOqTHTeJlbHbIe qHCJla):
1. nepe,n;aeTCH BpaIUalOIUHH MOMeHT npH q}fCTOM K:pyqemm:
T = 2,451661t x 10- 3 x d l 3 HM.
2. nepe,n;aeTcH H3BeCTHbIH BpaIUalOIUHH MOMeHT C H3rH6alOIUHM MOMeHTOM H3-
BeCTHOH BeJlWIHHbI: T = 58,8399 x 10- 5 x d/,5 HM.
3. nepe,n;aeTcH H3BeCTHbIH BpaIUalOIUHH MOMeHT C Heonpe,n;eJleHHbIM H3rH6aIO-
IUHM MOMeHTOM: T = 27,45862 x 10- 5 x d/,5 HM.
3TH 1'pH $OPMYJlbI npe,n;nOJlaralOT HCnOJlb30BaHHe CTarrH C npe,n;eJlOM npOqHOC-
TH Ha pa3pbIB OT 490 ,no 590 H/MM 2 . 3TH 3HaqeHIDI 06eCneqHBalOT B03MOXHOCTb
6bIC1'pOrO cpaBHeHIDI BarrOB pa3J1WIHbIX pa3MepOB, o,n;HaKO OHH He npe,n;Ha3HaqeHbI
,LI;lliI HCnOJlb30BaHIDI B KaqeCTBe 6a30BbIX ,n;aHHbIX ,LI;lliI npoeKTHpOBKH. BpalI(alOII(HH
MOMeHT npe,n;nOJlaraeTCH HeH3MeIDIIOIUHMCH.
5.4.13. npflM06ollHb,e wnH b'lUIfI Lf,HnHHAPHlieCKHx
sanos, MeTpHlieCKHe eAHHHLf,b'
0603HaQeHHJI: HOMHHaJlbHhle pa3Mephi
npO<pRTIb IIIJIHueBOro Barra RTIH BTYJlKH 0603HaqaeTCH BbIpaxeHHeM, co,n;epxa-
IUHM CJle,n;yK>IUHe BeJlWIHHbI no nOPMKY:
qHCJlO IIIJIHueB N
BHYTPeHHHH ,n;HaMe1]) d
HapyxHbIH ,n;HaMe1'p D
HanpHMep, Barr (RTIH BTYJlKa) 6 x 23 x 26
D
aJ
(-
(/
d JIefIWI ceplUl Cpe,lUUlJl ceplUls
(MM) o603Ha'leHHJI N D (MM) B (MM) o603Ha'leHHJI N D (MM) B (MM)
11 6 x 11 x 14 6 14 3
13 6 x 13 x 16 6 16 3,5
16 6 x 16 x 20 6 20 4
18 6 x 18 x 22 6 22 5
5.4. MeXaHUlteCKUe nepedaltu: 801lbl 419
O"OHltaHUe
d ' JIefIWI cepHJI cpe,lUUlJl cepHJIs
(MM) ( 5 o&;3Ha'leHHJI N D (MM) B (MM) 0003Ha'leHHJI N D (MM) B (MM)
21 6 x 21 x 25 6 25 5
23 6 x 23 x 26 6 26 6 6 x 23 x 28 6 28 6
26 6 x 26 x 30 6 \ 6 6 x 26 x 32 6 32 6
30
28 6 x 28 x 32 6 32 7 6 x 28 x 34 6 34 7
32 8 x 32 x 36 8 36 6 8 x 32 x 38 8 38 6
36 8x36x40 8 40 7 8 x 36 x 42 8 42 7
42 8 x 42 x 46 8 46 8 8 x 42 x 48 8 48 8
46 8x46x50 8 50 9 8x46x54 8 54 9
52 8 x 52 x 58 8 58 10 8 x 52 x 60 8 60 10
56 8 x 56 x 62 8 62 10 8 x 56 x 65 8 65 10
62 8 x 62 x 68 8 68 12 8 x 62 x 72 8 72 12
72 \- 10 x\72 x 78 10 78 12 lOx 72 x 82 10 82 12
/
82 lOx 82 x 88 10 88 12 lOx 82 x 92 10 92 12
92 lOx 92 x 98 10 98 14 lOx 92 x 102 10 102 14
102 lOx 102 x 108 10 108 16 10 x 102 x 112 10 112 16
112 10 x 112 x 120 10 120 18 10 x 112 x 125 10 125 18
,n;OnyCKH DB OTBepCTHJI H BMY
OTBepCT e
Ban
(YCT8HO,K8 CHM3Y)
B
Q
,lJ;onyCKH Ha OTBepCTHJI
,lJ;OnyCKH
Be3 o6pafioTKH 06pa6oTKa Ha Ba.1IY B coe eHHJI
DOCJIe DpcmII1IIUUIIUI DOCJIe DpoTJII1IB8HHJ1
B 0 d B D d B D d
H9 HIO H7 Hl1 HIO H7 dl0 all f7 CKOJIb3Rw.ee
f9 all g7 CKOJIb3Rw.ee C OqeHb
MaJIeHbKHM 3a30pOM
HI0 all h7 Heno.nBIDKHoe
' 'fJl08a 5. MexaHUfteClCUe nepeiJaftu
,n;OnyCKH HB cHMMeTpHIO
Pa3MepbI B MM
llillpHHa DlJIHQa B 3 3,5 4 5 6 7 8 9 10 12 14 16 18
,[(OnyCK Ha t 0,010 0,012 0,015 0,018
CHMMe1'pHIO (IT7) (IT7) (IT7) (IT7)
,[(OnyCKH, onpe,neJIeHHbIe B B, BKJIIOtIaIOT HaKOIIJIeHHyIO norpemHOCTb (H H3MeHeHIDI
cHMMeTpHH).
IIpuMellaHUJl.
1. C orrpe,n;eJIeHHbIMH $pe3aMH ,lI;lliI CrreUHaJIbHbIX rrpRTIOXeHHH B03MO)I{HO BbI-
TaqHBaTb IIIJIHUbI 6e3 HIDKHero 3a30pa Me)l{,ll;y HHCTPYMeHTOM H 3arOTOBKOH C CHJIb-
HO YMeHbIIIeHHbIM Pa)];HYCOM 3aKpyrJIeHIDI Me)l{,ll;y 60KOBOH CTOpOHOH IIIJIHua H
BHYTPeHHHM ,n;HaMeTPOM d (HarrpHMep, $pe3a C <pHKcHpoBaHHbIM pa60qHM rrOJIO-
xeHHeM) .
2. )];OnyCKH Ha pa3MepbI oTBepcTHH H BaJIbI OTHOCHTCH K rrOJIHOCTblO o6pa6o-
TaHHbIM ,n;eTamIM (BaJIaM H BTYJIKaM). n03TOMY HHCTPYMeHTbI ,lI;lliI Heo6pa6oTaHHbIX
,n;eTaJIeH RTIH ,n;eTaJIeH, o6pa6oTaHHbIX ,n;o MaIIIHHHOH o6pa6oTKH, H ,n;eTaJIeH, rrpo-
IIIe,n;IIIHX MaIIIHHHYIO o6pa6oTKY, ,n;OJDKHbI pa3JIJ1tIaTbCH.
3. )];aJIbHeH:rnyIO HH$opMaUHIO, KacalO:rnyIOCH rrpHM060qHbIX IIIJIHUOB H H3Me-
pHTeJIbHbIX rrpH6opoB ,lI;lliI rrpOBepKH TaKHX IIIJIHUOB, CMOTPH B BS5686: 1986
3BOJIbBeHTHbIe IDJIHQbI
TaKHe IIIJIHUbI HMelOT rrpo$RTIb, aHaJIOrJ1tlHbIH rrpo$RTIIO 3y6beB rrpHMo3y6oro
URTIHH,lI;pHQeCKOrO KOJIeca. OHH HMelOT ropa3,n;o 60JIb:rnyIO rrpOQHOCTb, QeM rrpHMO-
60QHbIe IIIJIHUbI, H MOryT rrpOH3Bo,n;HTbCH Ha 3y6oo6pa6aTbIBalOIUHx CTaHKax co
CTaH,ll;apTHbIMH $pe3aMH. O,n;HaKo HX reOMeTPIDI H rrOBepKa HaMHoro CJIO)I{Hee,
QeM y rrpHM060QHbIX IIIJIHUOB, QTO BbIXO,n;HT ,n;aJIeKO 3a paMKH 3TOH KHHrH. CM01'pH
BS 3550 (AIOHMbI) H BS 6186 (MeTpH'leCKHe eAHHHIJ;bI).r
5.5. KOHYCbl 421
a.
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S 0
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HJIH no,n'beMHbIX MOCTOB, HCnOJIb3yeMbIX npeHM)'IIJ;eCTBeHHo Ha cHcTeMax KaHaJIOB H
BO,nHbIX nyTRX KOHTHHeHTaJIbHOH EBpOnbI. O,nHaKO B cHcTeMax ,l(JUI npOMbIllIJIeHHO-
ro npHMeHeHIDI B KaqeCTBe pa60qeH )l{Jf)(KOCTH npeHM)'IIJ;ecTBeHHo HCnOJIb3yeTcR
MaCJIO, 06eCneqHBaIOm;ee caMocMa3Ky H He npHBOMm;ee K KOpp03HH.
5.6. 1. TJfnJf..,HBII nHeSMaTJf..,eCKBII CJfCTeMB
Ha CJIe.nymm;eM pHCyJlKe npe,nCTaBJIeHa cxeMa nHeBMaTHqeCKOH CHCTeMbI. B03,nyx
nOCTYIIaeT H3 aTMoc<l>epbI qepe3 B03,nymHbIH cPHJIb1p; B03,nymHbIH KOMnpeccop
no,nHHMaeT ,naBJIeHHe ,no 1pe6yeMoro ypOBIDI. KOMnpeccop 06bIqHO npHBo,nHTCR B
,neHcTBHe 3JIeKlpOMOTOpOM (B nepe,nBIDKHbIX KOMnpeccopHbIX YCTaHOBKax, HanpH-
Mep TaKHX, KOTopbIe HCnOJlb3yIOTCR B cTpOHTeJIbHOH npOMbIIIlJIeHHOCTH, B03,l(y111-
HbIH KOMnpeccop npHBo,nHTCR B ,neHcTBHe ,nH3eJIbHbIM ,nBHraTeJIeM). B npon;ecce
KOMnpeCCHH TeMnepaTYPa B03,nyxa no,nHHMaeTCR. B03.ZJ;yX TaIOKe co,nep)I{HT 3HaqH-
TeJIbHOe KOJIHqeCTBO BO,lUIHOrO napa. IIpeX,ll;e qeM cxaTbIH B03.ZJ;yX nona,n;eT B npH-
eMHbIH pe3epByap (eMKOCTb,l(JUl xpaHeHIDI cxaToro B03.ZJ;yXa), OH ,nOJDKeH 6bITb ox-
JIIDK,L(eH, B pe3YJIbTaTe qero BeCb npHcyrcTByIOrn;HH BOMHOH nap CKOH,LJ:eHcHpyeTCR.
KOH,ZJ;eHCaT ,nOJDKeH 6bITb y,naJIeH, npe)l{,ZJ;e qeM B03.ZJ;yX ,nOCTHmeT pe3epByapa. PeJIe
Dla8a 5. MexaHu'IecICue nepeiJa'lu
r --- - ---- -- 1
EMKOCTb I
AJ1R xpa- I BblKJ1lO-..eHO
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HCTO'lHHK: PHCyJlOK 1.3 B Hydraulics & Pneumatics, 2 H3,l(aHHe Andrew Parr: B/Heinemann.
peryJUlTOpa ,naBJIeHIDI BKJIIOqaeT ,nBHrareJIb, Kor,na ,naBJIeHHe B pe3epByape n3).J;aer,
H BbIKJIIOqaeT, Kor,na ,naBJIeHHe ,nOCTHraeT onpe,neJIeHHOrO ypOBIDI. Pe3epByap TaK-
xe OCHaIIJ;eH npe,n;oxpaHHTeJIbHblM KJIanaHOM Ha cJIytlaH HeHcnpaBHocTH peJIe pery-
JIRTopa. 3TOT npe.aoxpaHHTeJIbHbIH KJIanaH ,nOJDKeH 6bITb cnoco6eH BblnycKaTb BeCh
nOCTYTIaIOIIJ;HH OT KOMnpeccopa B03.nyx. 3a pe3epByapoM 06}dqHO CJIe,nyeT
MaCJIOpaCnbillHTeJIb, qepe3 KOTOpbIH MacIDIHbIH T}'MaH nOCTYTIaeT B nOTOK cxaTOfO
B03.nyxa H 3aTeM CMa3bIBaeT nHeBMopacnpe,neJIHTeJIb H HCnOJIHHTeJIbHbIH Mexa-
HH3M. B npocTeHmHX cHcTeMax B03.ZJ;yX npoxo,nHT qepe3 nHeBMopacnpe,neJIHTeJIb, 38
KOTOpbIM CJIe,nyeT HCnOJIHHTeJIbHbIH MexaHH3M, KaK npaBHJIO, nopmeHb H IJ;H-
JIHH,ZJ;p, 06eCneQHBaIOIIJ;HH JIHHeHHOe nepeMeIIJ;eHHe.
Pa60QHe ,naBJIeHIDI B nHeBMaTWlecKHX CHCTeMax HIDKe, QeM B rH,ZJ;paBJIWlecKHX.
06bJ1lHO ,naBJIeHHe B nHeBMaTWleCKOH CHCTeMe COCTaBllileT nOpR,lJ;Ka 10 6ap, qro
o6eCneQHBaeT YCHJIHe 98,1 KH/CM 2 II.1IOIIJ;3).J;H nopmIDI. CJIe,noBaTeJIbHO, HCnOJIHHTe-
JIbHble MexaHH3MbI nHeBMaTHQeCKHX CHCTeM ,nOJDKHbI 6bITb 60JIbme, QeM HCnOJIb3ye-
Mble B fH,ZJ;paBJIHQeCKHX CHCTeMax AJUI nepeMeIIJ;eHIDI TaKHX xe HarpY30K. CXHMae-
MOCTb raJa npHBo,nHT K Heo6xo,nHMOCTH xpaHeHIDI 60JIbmOrO 06'beMa ra3a B pe3epBY-
ape, qTo6bI OH Mor 6bITb noJIytleH HCnOJIHHTeJIbHbIM MexaHH3MOM cpa3Y xe, KaK TO-
JIbKO nOTPe6yeTcR. Be3 TaKoro pe3epByapa no,n'beM ,naBJIeHIDI 6bIJI 6bI Me.nn:eHHbIM H
nYJIbCHpymIIJ;HM, ,naBJIeHHe B03paCTaJIO 6bI no 3KCnOHeHIJ;HaJIbHOMY 3aKOHY. COOT-
BeTCTBeHHO, TaKHM xe Me.nn:eHHbIM H nyJIbCHpymIIJ;HM 6billO 6bI ,nBIDKeHHe nopmHSI
cpa3Y xe nOCJIe Toro, KaK peryJIHpymIIJ;HH KJIanaH 6y,neT OTKpbIT. ,[lJm 60JIbmHHCTBa
npOMbIIIlJIeHHbIX YCTaHOBOK TPe6yeTcR, QTo6bI cxaTbIH H KOH,ZJ;HIJ;HOHHpOBaHHblH
B03,nyx H3 pe3epByapa pacnpOCTPaIDIJICR no TPy6onpoBo.ny, OXBaTbIBaIOIIJ;eMY BCIO
TeppHTOpHIO 3aBo,na, Ha pa3JIWlHble yqacTKH npOH3Bo,nCTBa, r,ne OH MoxeT nOTPe6o-
BaTbCR. CMeHHble nHeBMaTWleCKHe pa3'beMbI 06eCneQHBaIOT B03MO)I{HOCTb no,nco-
e,nHHeHIDI K mTYIJ;epy KaJK,lJ;Oro BblnyCKHOro OTBepCTIDI IIlJIaHra YCTPOHCTBa (,npeJIH,
KJIenaJIbHOrO MOJIOTKa, Bblpy6HOro YCTPOHCTBa H T.,n.). Pa3'beM caMorepMeTH3Hpym-
IIJ;HHCR, npH OTcoe,nHHeHHH IIlJIaHra He npOHcxo,nHT nOTepb B03.nyxa HJIH ,naBJIeHIDI.
5.6. CUCme.Mbl 06oe.MHOU nepeoallu
5.6.2. TJfnJf..,HBfI rJfAPBSnJf..,ecKBfI CJfCTeMB
Ha CJIe,nyIOm;eM pHCyJlKe npe,nCTaBJIeHa cxeMa THnHqHOH fH,ZJ;paBJIHqeCKOH CHCTe-
MM. B KaqeCTBe aKTHBHpyrom;eH )l{Jf)(KOCTH, KaK npaBHJIO, HCnOJIb3yeTcR MaCJIO
(BO,na HCnOJIb3yeTcR TOJIbKO B qpe3BbIqaHHO IqJYIIHOMaCmTa6HbIX CHCTeMaX). B OT-
JIHqHe OT nHeBMaTHqeCKHX CHCTeM, 06Cyx,naBmHXCR B pa3,neJIe 5.6.1, rH,ZJ;paBJIH-
qeCKasI CHCTeMa o6pa3yeT 3aMKHYTbIH KOHTytJ, TaK qTO nOCJIe npOXO)l{,ZJ;eHIDI qepe3
HCnOJIHHTeJIbHbIH MexaHH3M MaCJIO B03Bpam;aeTCR B pe3epByap .nmI nOBTopHoro HC-
nOJIb30BaHIDI. ,n;aJIee, rH,ZJ;paBJIHqeCKHe CHCTeMbI - 3TO 06bIqHO CnenHaJIH3HpOBaH-
HbIe, HHTerpHpOBaHHbIe CHCTeMbI, KOTopbIe pa6oTaIOT C O,nHHM YC1pOHCTBOM, Ha-
npHMep nepe,nBIDKHoH CTOJI .nmI TIJIOCKOIIlJIH<l>oBaJIbHOrO CTaHKa HJIH no,n'beMHbIH
MexaHH3M no,nBIDKHoro rpY30no,n'beMHOrO KpaHa. Pa60qasI )l{Jf)(KOCTb HHKor,na He
no,naeTCR no TPy6aM no BceMY 3aBO.ny, qTo6bI 06eCneqHTb «nHTaHHe no 1pe60Ba-
HHIO CHCTeMbI», KaK cxaTbIH B03,nyx. fH,ZJ;paBJIHQeCKHe CHCTeMbI pa60TaIOT npH Ha-
MHoro 60JIee BbICOKHX ,naBJIeHIDIX, 06bIQH 150 6ap, no cpaBHeHHIO C ,naBJIeHHeM B
nHeBMaTWleCKHX cHcTeMax (10 6ap), H, CJIe,nOBaTeJIbHO, HCnOJIHHTeJIbHbIH Mexa-
HH3M (nHJIHH.np H nopmeHb HJIH rH,ZJ;paBJIHQeCKHH ,nBHraTeJIb) MoxeT 6bITb
CYIUeCTBeHHO MeHbme, qeM ero nHeBMaTHQeCKHH aHaJIOr .nmI ,naHHoro npHJIoxe-
HIDI. K TOMY xe, nOCKOJIbKy MaCJIO HJIH Bo,na npaKTHQeCKH HeC)l{HMaeMbI, rH,ZJ;paB-
JIINeCKHe CHCTeMbI 60JIee xeCTKHe, QeM nHeBMaTHQeCKHe CHCTeMbI.
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)l(H,ZJ;KOCTb (MaCJIO HJIH Bo,na) nOCTyrraIOT H3 pe3epByapa .nmI xpaHeHIDI Qepe3
<j;)HJIbTP K Hacocy, npHBOMm;eMYcR B ,nBIDKeHHe ,nBHraTeJIeM. Ha cTaHKax Hacoc npH-
BO,nHTCR B ,neHcTBHe 3JIeKlpo,nBHrareJIeM, B TO BpeWI KaK Ha KpaHax H ,npyrnx nepe-
)];BIDKHbIX YC1pOHCTBax OH npHBo,nHTCR B ,neHCTBHe ,nH3eJIbHbIM ,nBHrareJIeM. B OTJIH-
qHe OT KOMnpeccopa, Hacoc pa60TaeT Bce BpeWl, KOTopoe HCnOJIb3yeTcR CTaHOK.
ECJIH ,naBJIeHHe MaCJIa npeBbImaeT 3apaHee YCTaHOBJIeHHOe npe,neJIbHOe 6e30naCHoe
3HaQeHHe, Qepe3 KJIanaH peryJIHpOBaHIDI ,naBJIeHIDI H36bITOK MaCJIa B03Bpam;aeTCR B
F/la6a 5. MexaHu'IeclCue nepeiJa'lu
pe3epByap. ECJIH CHCTeMa He OCHam;eHa MaCJIOOXJI3).J;HTeJIeM, eMKOCTb pe3epByapa
,nOJDKHa 6bITb TaKOH, qTo6bI MaCJIO ycneBaJIO OXJI3).J;HTbCR, H ero BR3KOCTb He n3).J;an:a.
KaK nOKa3aHO Ha cxeMe, ,nBIDKeHHeM nopmIDI yrrpaBllileT lpexno3HIJ;HOHHbIH Ha-
npaBIDIIOm;HH rH,ZJ;popacnpe,neJIHTeJIb. MacJIo nOCTyrraeT qepe3 OTBepcrne A, KOf,n;a
H)')KHO no,nIDITb nopmeHb (H HarpY3Ky W). MacJIo, KOTopoe yxe HaxO,nHTCR B H-
JIHH.LJ;pe, MoxeT BbITeqb qepe3 OTBepCTHe B H qepe3 KJIanaH B03BpaTHTbCR B pe3epBY-
ape MacJIo nOCTyrraeT qepe3 OTBepCTHe B, Kor,na H)')KHO OnyCTHTb HarpY3Ky, H MaCJlO,
KOTopoe yxe Haxo,nHTCR B IJ;HJIHH.LJ;pe, MoxeT BbITeqb qepe3 OTBepCTHe A H B03Bparn-
TbCR B IJ;HJIHH,LJ:p. CKOPOCTbIO ,nBIDKeHIDI MO}l{HO yrrpaBllilTb, H3MeHIDI o6DeMHYIO CKO-
pOCTb TeqeHIDI, T. e. pa3Mep npoxo,nHoro OTBepCTIDI KJIanaHa onpe,neIDIeTCR onepaTO-
pOM. 3Ta B03MO)I{HOCTb 06eCneqHTb TOqHYIO peryJIHpOBKy npH MaJIeHbKHX CKOpO-
CTRX, O,nHO H3 OCHOBHbIX npeHM)'IIJ;eCTB rH,ZJ;paBJIWleCKHX CHCTeM. IIpH IJ;eHlpaJIbHOM
nOJIOXeHHH KJIanaH 6JIOKHpyeT )l{Jf)(KOCTb B IJ;HJIHH.LJ;pe no pa3HbIe CTOpOHbI nopmIDI,
TaK qTO nopmeHb He MoxeT nepeMem;aTbCR, eCJIH HeT npOTeqKH. PeryJUlTOp OTBO,n;HT
H36bITOK MaCJIa, npo,nOJDKaIOm;ero nOCTyrraTb B pe3YJIbTaTe pa60TbI Hacoca, o6paTHo
B pe3epByap. Kor,na B KaqeCTBe B03,neHCTByIOm;eH cpe,nbI HCnOJIb3yeTcR MaCJIO,
CHCTeMa RBlliIeTCR caMocMa3bIBaIOm;eHcR.
B KpyrrHoMacmTa6HbIx CHCTeMax, oco6eHHo eCJIH .nmI CHIDKeHIDI CTOHMOCTH
HCnOJIb3yeTcR Bo,na, 1pe6yIOTCR OqeHb 60JIbmHe 06'beMbI BO,nbI npH OqeHb BbICOKHX
,naBJIeHIDIX, HanpHMep qTo6bI no,nIDITb H OnyCTHTb TaY3pcKHH MOCT B JIOH.LJ;OHe.
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Henocpe,nCTBeHHO rH,ZJ;pOno,n'beMHHKH. KaK nOKa3aHO Ha CJIe.nymm;eM pHCyJlKe, pe-
meHHe 3aKJIIOqaeTCR B YCTaHOBKe rH,ZJ;paBJIWleCKOro aKKyMYIDITopa Me HaCOCOM
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o6eCneqHBaIOrn;HH TPe6yeMoe ,naBJIeHHe rH,ZJ;paBJIHqeCKOH KOCTH, HO C HH3KOH
no,naqeH. CaM aKKyMyIDITOp 06eCneqHBaeT ,naBJIeHHe KOCTH no TPe60BaHHIO,
Qro6bI npHBeCTH B ,neHCTBHe CHJIOBbIe IJ;HJIHH,lI;pbI.
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CTYITaTb H3 IJ;HJIHH,lI;pa B B IJ;HJIHH,lI;p E. OHa nepeMem;aeT BBepx nO,ZJ;'beMHHK F H c,naB-
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HbKHX CHCTeM. IIOCKOJIbKy B03.ZJ;yX 6e3MaCIDIHbIH, OHH llIHpOKO HCnOJIb3yIOTCR B
He60JIbllIHX pacnbillHTeIDIX IqJaCKH H KpacKonyJIbTax. OHH 06bJ1lHO HCnOJIb3yIOTCR
B nepeHOCHbIX OT,neJIbHO pa60TaIOm;HX KOMnpeccopax, HanpHMep, no,npR)];qHKaMH
Ha CTPOHTeJIbHbIX TIJIOm;a,n;Kax AIDI nHTaHIDI TaKHX YCTPOHCTB, KaK KaHIJ;eJIRpCKHH
nHCTOJIeT AIDI CKpenOK.
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peccopax. Heo6xo,nHMoe CMa3bIBaHHe KpaeB TIJIaCTHH 06eCneqHBaeTCR CHCTeMOH
nHpKyIDIIJ;HOHHoro CMa3bIBaHIDI; H3 BbIXOMm;ero B03.ZJ;yXa MaCJIO y,n8.IDleTCR. IIpH He-
06XO,nHMOCTH B MHorOCTYIIeHqaTbIX TIJIaCTHINaTbIX KOMnpeccopax npHMeIDIeTCR
npOMexyrOqHOe OXJIIDK,L(eHHe, qTO n03BOIDIeT nO.JIyqHTb 60JIee BbICOKoe ,naBJIeHHe H
YBeJIH1IHTb 06'beM B03,nyxa. IIpHHIJ;Hn pa60TbI nOKa3aH Ha CJIe,nymm;eM pHCyJlKe.
BHHTOBOH KOMDpeccop
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IOTCR AIDI nHTaHIDI KpyrrHoMacllITa6HbIX npOMbIllIJIeHHbIX YCTaHOBOK. IIpHHIJ;Hn HX
4 Dla8a 5. MexaHU'IeCKUe nepeiJa'lu
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nJlaCTHHtfaTLIH KOMnpeccop
HCTO'lHHK: PHCyJlOK 5.27 (ananTHpoBaHHbIH) B Hydraulics & Pneumatics, 2 H3,l(aHHe And-
rew Parr: B/Heinemann.
pa60TbI TIOKa3aH Ha pHCyJlKe «BHHTOBOH KOMTIpeCcop». MoXHo BH)];eTb, qro BbI-
CTYTIbI o,nHoro pOTopa Cn;eIIIDIIOTCR co BTI3).J;HHaMH pOTopa MeHbmero ,nHaMeTPa.
MacJIo He TOJIbKO CMa3bIBaeT pa60qHe TIOBepXHOcTH, HO H repMeTH3HpyeT 3a30pbI
MeX,ll;y pOTopaMH H OXJI3.)I{,L(aeT B03.nyx, TIOCJIe qero y,namIeTCR H3 B03.nyxa TIepe,n BbI-
nyCKHbIM oTBepcTHeM. Ha pHCYHKe «THTIbI KOMTIpeCCopoB: THTIWlHbIe c<l>epbI TIPH-
MeHeHIDI» TIOKa3aHbI 06JIaCTH TIpHMeHeHIDI KOMTIpeCCOpoB, OTIHCaHHbIX BbIme.
,
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HCTO'lHHK: PHCyJlOK 5.27 (ananTHpoBaHHbIH) B Hydraulics & Pneumatics, 2 H3,l(aHHe And-
rew Parr: B/Heinemann.
5.6. CucmeMbl 06lJeMHOU nepeiJaIt.
1000
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THUW KOMupeccopOB: THUIf1IHWe ccI»epw upHMeHeHHB
HCTO'lHHK: PHCyJlOK 4.2 B Hydraulics & Pneumatics, 2 H3,l(aHHe Andrew Parr: BjHeinema
5.6.4. rJfApaBnJf..,eCKJfe HaCOCh'
meCTepeHHh.e HaCOCh.
3TO caMbIe npOCTbIe H HaH60JIee H3).J;e)I{HbIe 06'beMHbIe HaCOCbI, BKJIIOqaIOW;J
B ce6R Bcero ,nBe ,nBIDKYJ.UHeCR qaCTH, KaK nOKa3aHO Ha pHCyJlKe «illecTepeHH:b
HaCOCbI». TOJIbKO O,nHO 3y6qaTOe KOJIeCO npHBo,nHTCR B ,neHCTBHe HCTOqHHKOM nl
TaHIDI. CJIe.nyeT o6paTHTb BHHMaHHe Ha HanpaBJIeHHe ,nBIDKeHIDI KOJIeC, nOCKOJIbI<
OHH C03,naIOT qaCTWlHbIH BaK}'YM, BbIXOM H3 3an;enrreHIDI, H BTRfHBaIOT )f(H)];KOC1
B KaMepy BcaCbIBaHIDI. MacJIo nepeHOCHTCR no Kpyry Me)K,ZJ;y 3y6bRMH KOJIeC
CTeHKaMH Kopnyca Hacoca, 6JIaro,napR qeMY OHO HenpepbIBHO nOCTYTIaeT B HarHe
TaTeJIbHYIO KaMepy. IIo,naqa Hacoca, T.e. 06'beM nepeKaqHBaeMOH )f(H)];KOCTH, onpe
,neIDIeTCR 06'beMOM )f(H)];KOCTH MeX,ll;y KIDK,l(OH napoH 3y6beB H CKOpOCTbIO Bpaw;e
HIDI. 3a KIDK,l(bIH 060POT Hacoc HameTaeT <l>HKcHpoBaHHbIH 06'beM )f(H)];KOCTH, ];
,naBJIeHHe B BbInyCKHOM KaHaJIe onpe,neIDIeTCR «npOTHBo,naBJIeHHeM», npOTHBOCTOR-
IUHM nOTOKy B OCTaJIbHOH qaCTH CHCTeMbI. 3TOT THn Hacoca npHMeIDIeTCR BnrrOTI
,no ,naBJIeHHH OKOJIO 150 6ap H OKOJIO 6750 JI/MHH. 90% 06'beMHOH npOH3Bo,nHTeJIb-
HOCTH (o6'beMHOrO Knn) - 3TO HaHxy,nmHH nOKa3aTeJIb H3 Bcex THnOB HaCOCOB,
onHcaHHbIX B 3TOM pa3,neJIe. Cym;ecTByeT MHoxeCTBO BapHaHTOB meCTepeHHbIX Ha-
COCOB, BKJIIOqasI mecTepeHHbIH Hacoc C BHYTPeHHHM 3an;eTIJIeHHeM H TIJIaCTHHqa-
TbIH Hacoc. IIJIaCTHINaTbIH Hacoc nOKa3aH Ha pHCyJlKe «IlJIacTHINaTbIH Hacoc».
Dla8a 5. MexaHU'leCKUe nepeiJa'lu
60KosaR HarpY3Ka
)l(HAKOCTb nOA SbiCOKHM
AasneHHeM
)KHAKOCTb, nepeHOCH-
MaR Me)I(AY 3y6bRMH
H KopnYCOM
60KosaR HarpY3Ka
Ha saJl-WeCTepHIO
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HH3KHM AasneHHeM
BcaCblsaHHe
meCTepeHHble HaCOCbI
HCTO'lHHK: PHCyJlOK 2.7 B Hydraulics & Pneumatics, 2 H3,l(aHHe Andrew Parr: B/Heinemann.
BblnYCK
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':: ::':.' :::::"
; ;: ; f:; ; ;: :!;j :1!1 ; \; k.:::- f::;:;i.::;.;::::..
;i :: !;: ; i :: ::1 !: ; ; ; :; t f::::;: :':" .': f: ::.
: :?/ =:T:: .
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BcaCblBaHHe
llJIaCTHJI1IaTblH Hacoc
HCTO'lHHK: PHCyJlOK 2.8 B Hydraulics & Pneumatics, 2 H3,l(aHHe Andrew Parr: B/Heinemann.
nJlaCTIfII1IaTble (JlOnaCTHble) HaCOCbI
IIp:nqHHOH OTHOCHTeJIbHO HH3KOH 06'beMHOH npOH3BO,LJ;HTeJIbHOCTH (KII,lI;) me-
cTepeHHbIx HaCOCOB RBIDIIOTCR 3a30pbI Me 3y6bRMH H Me 3y6qaTbIMH KOJIe-
caMH H CTeHKaMH Kopnyca. 3TH HCTOqHHKH yreqeK npeHMYIneCTBeHHO YCl'paHeHbI
B TIJIaCTHHqaTbIX Hacocax 6JIarO,LJ;apR HCnOJIb30BaHHIO npyxHH, npIDKHMaIOm;HX
TIJIaCTHHbI, KaK nOKa3aHO Ha pHCYHKe «HeypaBHOBemeHHbIH TIJIaCTHHqaTbIH Ha-
COC». npHHIJ:Hn ,LJ;eHCTBIDI rH)];paBJIHqeCKHX HaCOCOB TIJIaCTHHqaTOrO THna aHaJIOrn-
qeH npHHIJ:Hny ,LJ;eHCTBIDI TIJIaCTHHqaTbIX KOMnpeccopOB, onHcaHHbIX B pa3,LJ;eJIe
5.6. CucmeMbl o6oeMHou nepeoalfu 447
BcaCblBaHHe
BblnYCK
CTaTopHoe KonbUO
npy*HHa HnH nHeBMaTHyeCKOe
AaBneHHe npH)KHMaIOT nnaCTHHbl
K CTaTopHOMY KonbUY
HeypaBHoBeweHHblH nnaCTHHyaTbli71 Hacoc
BblnYCK
f
BnYCKHoi71 KaHan
BblnYCKHoi71 KaHan
.- BcaCblBaHHe
3nnHnTHyeCKOe
CTaTopHoe KonbUO
YpaBHOBeweHHbli7I nnaCTHHyaTbli71 Hacoc
llJlaCTHJI1IaTLIe HaCOCLI
HcrOtfilHK: PHCYHOK 2.10 B Hydraulics & Pneumatics, 2 H3,l(aHHe Andrew Parr: B/Heinemann.
5.6.3, 3a HCKJIIOqeHHeM Toro, qTO npH nepeKaqHBaHHH MaCJIa OHH RBlliIIOTCR caMO-
CMa3bIBaIOm;HMHCR. ArrbTepHaTHBHOe pemeHHe nOKa3aHO Ha pHCyJlKe «YpaBHoBe-
meHHbIH II.1IaCTHHqaTbIH Hacoc».
nOpmHeBLIe HaCOChI
B03BpaTHo-nocTYJIaTeJIbHbIe HarHeTaTeJIbHbIe HaCOCbI HCnOJIb3yIOTCR TOJIbKO B
KpyrrHoMacmTa6HbIX npHJIOXeHIDIX B COqeTaHHH C aKK}'MYIDITopaMH, He06xo,nHMbI-
MH, qT06bI CrJIa,nHTb nyJIbCaIJ:HH. B HaCTORm;ee BpeWI B 60JIbmHHCTBe npHJIoxe-
HHH, Kor,na TPe6yeTcR MHoxeCTBO nopmHeBbIX HaCOCOB, nopmHH H IJ:HJIHH.npbI
pacnOJIaraIOT p3).J;HaJIbHO, KaK nOKa3aHO Ha pHCyJlKe «Pan;HaJIbHO-nOpmHeBoH Ha-
COC». Hacoc COCTOHT H3 HeCKOJIbKHX nOJIbIX nopmHeH BHYTPH CTaIJ:HOHapHoro 6JIO-
Ka IJ:HJIHH.npOB. KIDK,l(bIH nopmeHb HMeeT Hanp.IDKeHHYIO npyxHHY, BnyCKHOH H
BbInyCKHOH KJIanaHbI. IIpH Bpam;eHHH pOTopa KOCTb OTHOCHTeJIbHO II.1IaBHO ne-
(::: Dla8a 5. MexaHu'IeclCue nepeiJa'lu
HenOABH>KHblH 6nOK
Ll,HnHHAPOB
Bpaw.alOw.HHCSI pOTOp
Konb3S1w.HH nopweHb
BnYCKHOH KJ1anaH
BblnYCKHOH KJ1anaH
Pa.z.HaJlhHO-DOpmHeBoi Hacoc
BcaCblBaHHe Macna H3
06naCTH HH3Koro AaBneHHSI
BblnYCK Macna nOA
BbiCOKHM AaBneHHeM
HenOABH>KHblH Kopnyc
BcaCblBaHHe
HenOABH>KHblH pOTOp
Bpaw.alOw.HHCSI
6nOK Ll,HnHHAPOB
nonblH nopweHb
C nPY>KHHHblM
B03BpaTOM
nOpmHeBoi Hacoc c HeDO lDKHhlM pOTOpOM H BpaInalOIQIIMCJl 6J10KOM IUfJlHtmPOB
HCTotJHHK: PHCyJIKH 2.12 H 2.13 B Hydraulics & Pneumatics, 2 H3,naHHe Andrew Parr: B/
Heinemann.
5.6. CUCmeMbl 06lJeMHOU nepeiJallu
peHOCHTCB OT BnycKHoro K BbIrryCKHOM)' KaHarry. llpHHUHn Hacoca, nOKa3aJ
Ha pHcyJlKe «llopmHeBoH Hacoc C Heno,nBIDKHbIM pOTOpOM H Bpaw;alOW;HMC.f.
KOM UHJIHH)l:pOB», aHaJIOrHqeH, HO B HeM pOTOp CTaUHOHapeH, a Bpaw;aeTCB
UHJIHH)l:POB. B 3TOM cnytIae HCqe3aeT Heo6xo,nHMOCTb BO MHoxeCTBe BrryCKI
BhIrryCKHbIX KJIanaHOB, H, CJIe,nOBaTeJIbHO, TaKaH KOH<pHrypaUIDI BBillIeTCB
npOCTOH, Ha,ne)I{HOH H ,nemeBOH C TOqKH 3peHIDI KaK npOH3Bo,nCTBa, TaK H C
)l{HBaHIDI. l1031;:OM)' 3TOT THn BBJUleTCB 60JIee pacnpOCTpaHeHHbIM.
I
OceBble (c HaKJIOHHblM ,lUICKOM) HaCOCbI
3TO TaIOKe MHoronopmHeBOH Hacoc. llopmHH pacnOJIOXeHbI BO Bpaw;al()
CB 6JIOKe UHJIHH.npOB, TaK qTO OHH napaJIJIeJIbHbI OCH Be,nyIUero BaJIa, KaK nc
HO Ha CJIe,nyIOw;eM pHCyJlKe. XO,nOM nopmIDI ynpaBJUleT HaKJIOHeHHbIH no,n
,l{HCK, KaK nOKa3aHO Ha pHCyJlKe. KIDK,lJ;bIH nopmeHb nO,ZJJJ;epXHBaeT KOHTaKT
KJIOHHbIM ,nHCKOM C nOMOW;blO npIDKHMHOH npyxHHbI HJIH Bpaw;alOw;eHC$I Ha]
HOH maH6bI, CBB3aHHOH C HaKJIOHHbIM ,nHCKOM. K03<P<PHUHeHTOM no,naqH H
MO)I{HO ynpaB.IDITb, H3MeIDUI yrOJI HaKJIOHa ,nHCKa. qeM 60JIbme yrOJI, TeM 6c
CKOpOCTb nOTOKa npH ,naHHOH CKOpOCTH Bpaw;eHIDI. MaKCHMaJIbHbIH yrOJI Hal
,l{HCKa orpaH eH MaKCHMaJIbHOH npe,nYCMOTpeHHOH KOHCTPYKUHeH ,nJIHHOH
nopWIDI. HYJIeBOH pacxo,n ,nOCTHraeTCB, Kor,na HaKJIOHHbIH ,nHCK nepneH)l:HK}'J
Be,nYII.J;eM)' BaJIY. H3MeHeHHe yrJIa HaKJIOHa ,nHCKa Ha npOTHBOnOJIO)I{HbIH H3MI
HanpaBJIeHHe nOTOKa )lGf)J;KOCTH qepe3 Hacoc.
BcacbI-
BaHHe
HaKJloHeHHblH
nOA yrnoM
KpyrnblH AHCK
HaKJloHHaR
waH6a Hal
Hbll
AH(
BblnYCK
nOpweHb
nOpWHH, nepe-
Mew.aeMble wa-
pHKaMH, ABH)I(y-
Bpaw.alO- W.HMHCR no Ha-
W.HHCR KJlOHHOMY AHCKY
6noK
Ll,HnHHAPoB
Yron HaKJlOHa AHCK
onpeAenReT XOA
HenOABH>KHbIH
6noK
OceBble HaCOCbI C HaKJIOHHhlM ,lUICKOM
I1cTotJHHK: PHCyJIOK 2.14 B Hydraulics & Pneumatics, 2 H3,naHHe Andrew Parr: B/I-
mann.
Bce BH,nbI nopmHeBbIx HaCOCOB HMelOT OqeHb xoponryIO 06'beMHYIO npoH31
TeJIbHOCTb (Kll ) H MOryr HCnOJIb30BaThCB npH caMbIX BhICOKHX rH,npaBJIHqe
,l{aBJIeHIDIX. OHH 60JIee CJIO)I{HbI, qeM TIJIaCTHHqaTbIe H mecTepeHHbIe HaCOC]
CJIe,noBaTeJIbHO, ,nopoxe C TOqKH 3peHIDI nepBOHaqaJIbHOH CTOHMOCTH H o6cJI
BaHIDI. B CJIe,nyIOw;eH Ta6JIHue conOCTaBillIlOTCB npeHMYIUeCTBa H orpaHH'I
Pa3JIHqHbIX THnOB rH,npaBJIHqeCKHX HaCOCOB.
15-3255
Dla6a 5. MexaHU'IeCKUe nepeiJa'lu
CpaBHeHHe THOOB rH,ZJ;paBJIlflieCKHX HaCOCOB
MUCHMaJlbHoe MUCHMaJlbHaJI PeryJIHPOBaIOIe DpDoe
THo )UlBJIeHHe npoH3BOAHTeJIhHOCTh (paoo'lero
(6ap) (no)Ul'la) (JI/MHH) 06wMa) BYTecHeHBe
:QeIITp06eXHbIH 20 3000 OTCYTCTByeT OrCYTCTByeT
llIecrepeHHbIH 175 300 OrCYTCTByeT HMeeTcB
IlrracTHH'laTbIH 175 500 HMeeTcB HMeeTCB
AKCHaJIbHO- nopwHeBoH 300 500 HMeeTcH HMeeTCB
(c nrrOCKHM pacnpe,neJIHTeJIeM)
AKCHaJIbHO- nopwHeBoH 700 650 HMeeTcH HMeeTcB
(c KJIanaHaMH)
MHoroPMHbIH Hacoc 1000 100 HMeeTcH HMeeTcR
C eCTBYI<>T CneI.J;HaJIbHbIe HaCOCbI ,l])UI ,naBJIeHHH BTIJIOTb ,no nOqTH 7000 6ap
npH CJIa60M nOTOKe. HarHeTaHHe ueHTpo6e)l{JlbIX H illeCTepeHHbIX HaCOCOB MO)l{HO
BapbHpOBaTb, H3MeIDUI CKOpOCTb ,nBHraTeillI Hacoca C qaCTOTHo-peryJIHpyeMbIM
3JIeK1ponpHBo,nOM.
HCTotJHHK: Ta6JIH a 2.1 B Hydraulics & Pneumatics, 2 H3,naHHe Andrew Parr: BjHeine-
mann.
5.6.5. HcnonHHTenbHble MexaHH3Mbl (nHHeHHble)
If B nHeBMaTlNeCKHX, H B rH.npaBJIlNeCKHX cHcTeMax HCnOJIb3YI<>TCB JIHHeHHhIe
HCnOJIHHTeJIhHbIe MexaHH3MbI, Kor,na 1pe6yeTcR ,nBIDKeHHe no npBMoH JIHHHH, KaK,
HanpHMep, B 3IDKHMHhIX CTOJIax H pa6oqill{ CTOJIax CTaHKOB. TaKHe YC1pOHCTBa HMe-
lOT nopilleHb H UHJIHH.nP C KOpOTKHM XO,nOM. OHH 06b:NHO aHaJIOrlNHbI H B nHeBMa-
TlNeCKHX, H B rH.npaBJIlNeCKHX cHcTeMax, 3a HCKJIlOqeHHeM Toro, qTO rH.npaBJIHtIe-
CKHe HCnOJIHHTeJIbHbIe MexaHH3MbI HMelOT 60JIee TIDKeJIyIO KOHC1pYKUHIO, n03BOIDI-
IOIIJ;He HM npOTHBOCTOBTh 60JIee BbICOKHM ,naBJIeHIDIM H CHJIaM BHYTPH rH.npaBJIHtIe-
CKHX CHCTeM. YCTPOHCTBa MOryr 6bITh O,nHOCTopOHHero ,neHCTBIDI, KaK nOKa3aHO Ha
pHC)'HKe «:QIDIHH.nP O,nHOCTopOHHero ,neHCTBIDI», ,nBYCTopOHHero ,neHCTBIDI, KaK no-
Ka3aHO Ha pHC)'HKe «:QHJIHH.nP ,nBYCTopOHHero ,neHCTBIDI», IDIH C HaC1paHBaeMhIM
nOrJIOIIJ;eHHeM, KaK nOKa3aHO Ha pHC)'HKe «YC1pOHCTBO C peryJIHpyeMbIM TopMoxe-
HHeM». fH.npaBJIlNeCKHe YCTPOHCTBa qaCTO 1pe6YI<>T HCnOJIHHTeJIbHbIX MexaHH3MOB C
60JIbillOH ,l(JIHHOH xo,na. B 3TOM c.rryqae nopillHH Ha3bIBalOTCB IIJIyfDKepaMH, a THnHtI-
HaR KOH<pHrypaI.J;IDI YC1pOHCTBa nOKa3aHa Ha pHC)'HKe «I1.rryIDKep C ,l(JIHHHbIM XO,nOM
H rH.np0I.J;IDIHH.nP». 3TO YC1pOHCTBO O,nHOCTopOHHero ,neHCTBIDI H OCHOBaHO Ha YCH-
JIHH npOTHBo,neHCTBIDI HarpY3KH, nepeMeIIJ;aeMOH 06paTHbIM XO,nOM. Hana30H Ta-
KHX YCTPOHCTB CJIHillKOM BeJIHK, qTo6hI nepeqHCJIHTb ill{ B 3TOH KHHre, H qHTaTeJIh
MoxeT 06paTHTbCB K npHJIOXeHHIO 3, qTo6bI no,npo6HO 03HaKOMHTbCB C nOCTaBIIJ;H-
KaMH, KOTophIe MOryr npe,l(JlOXHTb HCqepnbIBalOIIJ;He KaTaJIOrH. npH JII06bIX 06CTOB-
TeJIbCTBax nHeBMaTlNeCKHe HJIH rH,lI;paBJIlNeCKHe 3IDKHMHbIe npHcnoco6JIeHIDI ,nOJI-
)KHbI 6bITb CKOHC1pYHPOBaHhI TaK, qTo6bI YCIDIHe 3IDKHMa He )'MeHbillaJIOCh H He
CHHMaJIOCh (pa36JIOKHpOBKa) B c.rryqae nOJIOMKH CHCTeMhI.
5.6. CUCmeMbl o6oeMHOU nepeiJallu 451 ::
r=
UHnHHAP OAHOCTO-
pOHHero AeHCTBHR
(Bo3BpaT nOA AeHCT-
BHeM npY'KHHbI)
(
I
nOpWHeBOH KOnbLl,O A11R KOM-
WTOK neHCaLl,HH H3Hoca
Kopnyc Ll,HnHHApa BnYCKHOH
KaHan
B03Bpaw.alOw.aR
npY'KHHa
nepeAHRR KpblWKa
WTOKOBOH nonOCTH
Ll,HnHHApa
YnnOTHeHHe
nopWHR
3aAHRR
KpblWKa
D;HJlHImP O,lUlOCTOpOHHero eiiCTBHJI
OJ ..L
UHnHHAP ABYCTopOHHero
AeHCTBHR
nOpWHeBOH
WTOK
KOnbLl,O A11R KOM-
neHCaLl,HH H3Hoca
BnYCKHOH
KaHan
B-rynKa WTOKa
rpR3e-
CbeMHaR
MaH>KeTa
Kopnyc Ll,HnHHApa
nepeAHRR KpblWKa
WTOKOBOH nonOCTH
Ll,HnHHApa
YnnOTHeHHe
nopWHR
3aAHRR
KpblWKa
UenbHblH nopweHb
C ynnoTHeHHeM
D;HJlHImP .lUIYCTopOHHero eiiCTBHJI
fAa6a 5. MexaHu'IeclCue nepeiJa'lu
B03AYWHblH KaHaJ1
AeMncpHPYIOLJJ.HH nHeBMaTH e-
CKHH BHHTOBOH APOCCeJ1b
OrpaHH eHHoe ABH eHHe B03Ayxa
Orpa)KAeHHe B03AYWHOH nOAYWKH
HOpMaJ1bHOe ABH eHHe B03Ayxa
AeMncpHPYIOLJJ.HH APOCCeJ1b 1
3aXBa eHH H 06beM B03Ayxa
r L
U,HJ1 HHAP C
peryJ1HPyeMblM
TopMo eHHeM
. .
ApOCCeJ1HPYIOLJJ.He BTYJ1KH
YCTpOHCTBO C peryJlHpyeMblM TOpM01KeHHeM
U,HJ1HHAP
t!
nOpweHb
nJIyIDKep C ,lJ.JIHHHhIM XO OM H rHJJ;pOIUlJlHtmP
5.6.6. HcnonHHTenbHble MexaHH3Mbl (Bpa aTenbHble)
3TH HCnOJIHHTeJIhHhIe MexaHH3MbI aHaJIOrHqHbI no KOHC1pYKUHH KOMnpeccopaM H
HacocaM, onHcaHHhIM paHee. HanpaBJIeHHe Bpam;eHIDI 3aBHCHT OT HanpaBJIeHIDI
rrOTOKa )lGf)J;KOCTH.
nHeBMaTlflleCKHe
B npHJIOXeHIDIX 06m;ero Ha3HaqeHIDI, TaM r,ne 1pe6yeTcB BbICOKWI MOm;HOCTb
rrpH cpe,nHHX CKOpOCTBX, MOryr HCnOJIh30BaTbCB pa,n;HaJIbHO-nOpmHeBbIe rH,npo-
,nBHraTeJIH H rH,npOIJ;HJIHH)l:pbI, KaK nOKa3aHO Ha pHCyJlKe «nOpmHeBOH ,nBHra-
TeJIb». OHH rpOM03,nKHe, ,noporOCTOBm;He, myMHbIe H Tpe6YI<>T OCHam;eHIDI CHCTe-
MbI BbIrrycKa rJIYlIIHTeillIMH. DOJIee ,nemeBbIM H JIerKHM pemeHHeM ,l])UI Tex c.rryqaeB,
Kor,na 1pe6yeTcB 60JIee HH3KWI MOm;HOCTb npH BbICOKHX CKOpOCTID:, BBillIeTCB illH-
6epHhIH rH,npo,nBHraTeJIb, KaK nOKa3aHO Ha pHCyJlKe «mH6epHbIH rH,npo,nBHra-
TeJIb». ,[LrnI TaKHX npHJIOXeHHH, KaK He60JIhmHe nepeHOCHhIe ,npeJIH, CTaHKOB .nmI
3aTOQKH TIJIameK H 60pMamHH, npe,nHa3HaQeHHbIX ,l])UI TOQHOH pa60TbI, no,noH,nyT
TYP6HHHbIe nHeBMaTHQeCKHe ,nBHraTeJIH.
fHJJ;paBJllflleCKHe
HaH60JIee mHpOKO pacnpOCTpaHeHbI pe,nYKTopHbIe H mH6epHbIe ,nBHraTeJIH.
OHH aHaJIOrHQHbI meCTepeHHbIM H TIJIaCTHWlaTbIM HacocaM, onHcaHHbIM paHee.
HanpaBJIeHHe Bpam;eHHSI 3aBHCHT OT HanpaBJIeHIDI nOTOKa )lGf)J;KOCTH.
5.6. CucmeMbl 06'beMHOU nepeoallu 45
/
U.HJ1HHAPH eCKHH
pacnpeAeJ1HTeJ1b-
HblH KllanaH
KOJ1eH aTblH Ban
J].BHraTeJ1b (ABa
HanpaBJ1eHHSI )
nOpmHeBOH rH.npO,lJ;BHraTeJIb
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npY'KHHbl HJ1H ABY-
CTopOHHHe WTOKH,
To6bl YAep>KHBaTb
nJ1aCTHHbI CHapY'KH
B nYCKOBOM pe>KHMe
mH6epHbIH rH.npO,lJ;BHraTeJIb
nHeBMaTlflleCKHe BpatnaTeJlhHhle HCDOJlHHTeJlhHhle MeXaHH3MhI
HCTOtJHHK: PHCyJIKH 9.5, 9.6 B Practical& Pneumatics, eris Stacey, Newnes
fAa6a 5. MexaHu'IeclCue nepeiJa'lu
5.6. 7. HcnonHHTenbHble MexaHH3Mbl CMewaHHoro THna
B rH6pH.nHbIX ,nBHraTeillIX BpaIIJ;aTeJIbHOe ,nBIDKeHHe nHeBMaTHqeCKOrO HJIH rH.npaB-
JIHqeCKOrO ,nBHraTeillI npHBo,nHT B ,neHcTBHe MexaHH3M peeqHOH nepe,naqH, KOTO-
pbIH 06eCneqHBaeT JIHHeHHOe ,nBIDKeHHe. TaM r,ne Tpe6yeTcB 60JIbillWl ,l(JIHHa xo,n;a,
3y6qaTOe KOJIeCO MoxeT 6bITb 3aMeHeHO uenHoH 3Be3,nOQKOH, a peHKY - pOJIHKO-
BOH uenblO. If Hao6opOT, nHeBMaTHQeCKHH HJIH rH.npaBJIHQeCKHH ,nBHraTeJIb MoxeT
HCnOJIb30BaTbCB ,l])UI npHBe,neHIDI B ,neHcTBHe XO,nOBOH BHHT H XO,nOByIO raHKY.
5.6.8. 0603HalfeHHfI A,nfl rHApasnHlfeCKHX CHCTeM
CJIe,nyIOIIJ;He ,naHHbIe ,l])UI npOeKTHpOBaHIDI JII06e3HO npe,nOCTaBJIeHbI accoUHaU;HeH
British Fluid Power. HeKoTopbIe HaH60JIee illHpOKO pacnpOC1paHeHHbIe CHMBOJIbI
,l])UI m,npaBJIlNeCKHX CHCTeM nOKa3aHbI Ha CJIe,nyIOIIJ;eM pHCyJlKe. DOJIee nOJIHbIH Ha-
60p rpa<pHQeCKHX 0603HaQeHHH QHTaTeJIb CMoxeT HaHTH B CTaH,D;apTe ISO 1219-1,
npHIDITOM B 1991 ro,ny. npaBHJIa, OTHOCBIIJ;HeCB K npHHUHnHaJIbHbIM cxeMaM, CMOT-
pH B ISO 1219-2. 0603HaQeHIDI oTBepcTHH H MapKHpOBKY peryillITopoB CM01pH ISO
9461 (m,npaBJIHKa) HJIH CETOP RP68P (nHeBMaTHKa) HJIH ISO 5599 (nHeBMaTHKa).
CHMBOJI ODHCaHHe CHMBOJI ODHCaHHe
. HCTOtJHHK 3HeprHH - rH,ZJ;paBJIlNeCKHH UHJIHH.nP -
rH,lJ,paBJIlNeCKHH ,nBYXCTopOHHero ,neHCTBIDI
l>-- HCTotJHHK 3HeprnH - m nHeBMaTlNeCKHH UHJIHH.nP -
nHeBMaTlNeCKHH ,nBYXCTopOHHero ,neHCTBIDI
fH,lJ,paBJIlNeCKHH Hacoc W' QHJIHH.nP fH.npaBJIlNeCKHH
HeperyJIHpyeMbIH - ,nBYXCTopOHHero ,neHCTBIDI
C HepeBepCHBHbIM nOTOKOM - C ,nBYXCTOpOHHHM WTOKOM
rH,ZJ;paBJIlNeCKHH Hacoc nHeBMaTlNeCKHH UHJIHH.nP
Pe ryJIHpye MbIH QJ AA A - O,nHOCTopOHHero ,neHCTBIDI
C peBepCHBHbIM nOTOKOM '\'\' I - C B03BpaTOM WTOKa npyxHHOH
I v v
rH,ZJ;paBJIlNeCKHH MOTOp QHJIHH.nP
0\ HeperyJIHpyeMbIH - ,nBYXCTopOHHero ,neHCTBIDI
C HepeBepCHBHbIM nOTOKOM - C peryJIHpyeMbIM TOpMO:>KeHH-
eM B KOHue xo,na: C ,nBYX CTOpOH
- TIHeBMaTlNeCKHH
rH,ZJ;paBJIlNeCKHH MOTOp nOCTYIIaTeJIbHbIH npe06pa30Ba-
${ PeryJIHpyeMbIH TeJIb
C peBepCHBHbIM nOTOKOM - C O,nHHM BH,ZJ;OM pa60tJeH cpe-
,nbI
- rH,ZJ;paBJIlNeCKHH
KOMnpeccop =if nOBOpOTHbIH ,nBHraTeJIb
- ,nBYXCTopOHHero ,neHCTBIDI
- rH,ZJ;paBJIlNeCKHH
TIHeBMaTHtJeCKHH MOTOp TIOBOPOTHbIH ,nBHraTeJIb
HeperyJIHpyeMbIH j)= - O,nHOCTopOHHero ,neHCTBIDI
C HepeBepCHBHbIM nOTOKOM - C B03BpaTOM npyxHHOH
- TIHeBMaTlNeCKHH
CHMBOJI
e
\IJ)-t>-
em
DJlJ
OTIXJ
mr:m
[!DIIJ
1II:N
[{tY
dty
i
L_.J
ODHcaHHe
AKKyMyIDITOp -
3apMKa ra30M
B03,nyxonpHeMHbIH UHJIHH.nP
HanpaBIDllOII(HH 2/2 (.n;ByxJlH-
HeHHbIH .n;Byxn03HUHOHHbIH)
pacnpe.n;eJIHTeJIb
HanpaBIDllOII(HH 3/2 (TPeXJIH-
HeHHbIH .n;Byxn03HUHOHHbIH)
pacnpe.n;eJIHTeJIb
HanpaBIDllOII(HH 4/2 (qeTbI-
peXJIHHeHHbIH .n;Byxn03HUH-
OHHbIH) pacnpe.n;eJIHTeJIb
HanpaBIDllOII(HH 4/3 qeTbI-
peXJIHHeHHbIH TPexno3HIJ;H-
OHHbIH pacnpe.n;eJIHTeJIb
- C 3aKpbITbIM ueHTPOM
HanpaBIDllOII(HH 5/2 (IDITH-
JIHHeHHbIH .n;Byxn03HUHOH-
HbIH) pacnpe.n;eJIHTeJIb
KOHTPOJIHpyIOlI(HH HanpaB-
JIeHHe 3/3 3aTBOp
- c 3aKpbITbIM ueHTpOM npy-
XHHHOH
- C npyxHHHbIM BbIBO.n;OM
30JIOTHHKa B cpe.n;Hee nOJIO-
eHHe (npyxHHHOe ueHTPH-
pOBaHHe), c nHJIOTHbIM
ynpaBJIeHHeM
KnanaH c6poca .n;aBJIeHIDI
- o.n;HOCTYTIeHqaTbIH
- peryJIHpyeMoe .n;aBJIeHHe
Pe.nyKl(HOHHbIH KJIanaH
- co C6POCOM .n;aBJIeHIDI
- nHeBMaTH1IeCKHH
06paTHbIH KJIanaH
,[U>ocCeJIb c o6paTHbIM KJIana-
HOM HJIH C nepeMeHHbIM
.n;pOCCeJIHpOBaHHeM
5.6. CUCmeMbl 06'beMHOU nepeoallu 455
CHMBOJI
@:
--c
<t=
1=
czC
**
'--/
-9-
w-
-V-
OKOHl.f.aHUe
ODHcaHHe
TeJIeCKOnH1leCKHH UHJIHH.nP
- ,nBYXCTopoHHero ,ne HCTBIDI,ne H-
CTBIDI (c O.n;HOCTOpOHHHM BbI.nBH-
eHHeM)
- rH,ZJ;paBJIH1IeCKHH
3JIeIcrpH1leCKHH MOTOp
(OT IEC 617)
YnpaBJIeHHe pacnpe.n;eJIHTeJIeM -
.n;aBJIeHHeM
YnpaBJIeHHe pacnpe.n;eJIHTeJIeM
- pyqHoe, KHonKOH
- pOJIHKOM
- COJIeHOH,ZJ;OM
- HanpBMyIO
- COJIeHOH,ZJ;OM
- nHJIOTHOe ynpaBJIeHHe, C npH-
MeHeHHeM .n;aBJIeHIDI
- nHeBMaTH1IeCKOe
MY<PTa 6bICTPOrO paCueIIJIeHIDI
- C o6paTHbIM KJIanaHOM
- coe.n;HHeHHIDI
rH6KIDI JIHHIDI
- IIIJIaHr
Cl>HJIbTP
OXJIMHTeJIb
- c yKa3aHHeM JIHHHH .n;BIDKeHIDI
OXJI alOlI(eH )l{H)];KOCTH
BJIarOOT.n;eJIHTeJIb
b Dla8a 5. MexaHU'IeCKUe nepeiJa'lu
5.6.9. ,QaHHble A,nfl paClfeTOB o6.eMHoH rHAPonepeAalfH
(OCHoBHble cpopMynbl)
paBJIHKa
(a) HaCOCbl U Momopbl
D .n
CKOpOCTb nOTOKa (JI/MHH) Q =
1000
D.p
KpyrBIIJ;HH MOMeHT Ha BaJIY (HM) T =
20x
T .n
MOIIJ;HOCTb Ha Barry (KBT) P =
9554
fH.ll:paBJIlf1IecKaH MO HOCTb (KBT) P = Q · p
600
6bIC1pbIX BbItIHCJIeHHH
MOIIJ;HOCTb (KBT) · P = TOHHbI x MM / ceK
100
(6) I(UJlUHiJPbl
F
,!I;aBJIeHHe (H/M2) p = -
A
CKOpOCTb nOTOKa (I/MHH) Q = 60 . A . v . 10 3
F - CHJIa (H)
A - llJIOIIJ;an;b (M 2 )
V - CKOpOCTb (M/C)
p - ,naBJIeHHe (6ap)
D - 06'beMHWI npOH3Bo,nHTeJIbHOCTb Hacoca (o6'beM) (CM 3 /o6)
n - 06/MHH
(c) IIomoK
nOTOK (JI/MHH) Q ex: f¥J
Ap - H3MeHeHHe ,naBJIeHIDI (6ap)
To eCTb npH H3MeHeHHH nOTOKa B 2 pa3a .naBJIeHHe H3MeHHTCB B 4 pa3a.
nOTJlpJl aBJIeHHJI B TPy6ax
nOTOK BayrpelllDli ,lUIaMeTp 1'))y6 (MM)
B JI/MHH S 7 10 13 16 21 2S 30 36
1 0,69 0,22
2 1,38 0,44
3 2,07 0,66 0,17
5 4,14 1,24 0,24
7,5 6,55 1,72 0,31
5.6. CUCmeMbl 06oeMHOU nepeiJallu 457
I
/
O"OHl.f.aHUe
nOTOK BII)'TpeIllDli ,lUIaMeTp 1'))16 (MM)
B JI/MHH 5 7 10 13 16 21 25 30 36
10 3,10 0,38 0,14
15 5,38 0,69 0,21 0,08
20 1,10 0,30 0,14 -
30 2,21 0,69 0,25 0,04
40 1,17 0,45 0,08 0,04
50 0,59 0,12 0,07 0,03
75 1,31 0,23 0,14 0,06 0,02
100 0,41 0,22 0,13 0,03
150 0,45 0,23 0,06
200 0,41 0,10
250 0,16
3Ta Ta6JIHua npHMepHo ,naeT BeJIHqHHy na,neHIDI ,naBJIeHHe B rJIa,nKHX npBMbIX
TPy6ax, B 6apax Ha 3 Me1pa ,l(JIHHbI. H3rH6hI H CTbIKH YBeJIINHBalOT CYMMapHoe na-
,ZJ;eHHe ,naBJIeHIDI, n03TOMY npOH3Bo,nHTeillIM CJIe,nyeT o6paw;aThcSI K 60JIee TOqHbIM
D:H<ppaM.
nHeBMaTHKa
(a) Te'leHUe 8 mpy6ax
1,6 x 10 8 x (Q x 10- 3 )1,85 x L x 10- 3
f¥J = d 5 x P ,
r,ne Ap - na,neHHe ,naBJIeHIDI (6ap); Q - nOTOK aTMoc<pepHoro B03,nyxa (M 3 jC) =
= JIjc x 10-3; L - ,l(JIHHa 1py6bI (M); d - BHyTpeHHHH ,nHaMe1p TPy6bI
(6) CKopocmb me'leHUJl 8 mpy6ax
1273Q
v = ,
(p + l)d 2
r,ne v - CKOpOCTh nOTOKa (MjC); p - HaqaJIhHOe ,naBJIeHHe (6ap); d - BHyTpeHHHH
,ZJ;HaMeTP 1py6bI (MM)
ECJIH H3BeCTeH nOTOK aTMOC<pepHoro B03,nyxa, TO MHHHMaJIbHbIH BHyTpeHHHH
,ZJ;HaMe1p, Heo6xo,nHMhIH ,l])UI nO,ZJJJ;epxaHIDI CKOpOCTH nOTOKa HIDKe 6 MjC, MoxeT
6hITb Haif.neH no <poPMYJIe:
d(MM) = 212 x Q.
(p + 1)
,[{mI 06hIqHhIX YCTaHOBOK, ,naBJIeHHe B KOTOpbIX nOPMKa 7 6ap, BhIpIDKeHHe
MO)I{HO ynpOCTHTb:
,nHaMe1p d (MM) ,nOJDKeH 6hITb 60JIhme, qeM 5 x .jQ.
HCTOqHHK: CTPaHHD:bI 14 H 15 BFPA Data book.
Dta8a 5. MexaHU'IeCKUe nepeiJa'lu
5.6. 10. npoeKTHhle ,lIaHHhle o6-.eMHoH rJf,llponepe,llalfJf
(rJf,llpaSnJflfeCKJfe qJfnJfH,lIphl)
BhIXO.lUlOe YCHJlHe H MaKCHM8JlhHhIe ,nJIHHhI mTOKOB
UpHMep. ECJIH H3BeCTHO Tpe6yeMoe BbIxo,n;Hoe YCHJIHe (200 KH) H ,n;aBJIeHHe B
CHCTeMe (160 6ap), HaRTH no HOMorpaMMe ,n;HaMel'p HJIHH,ZJ;pa.
OTBeT: 125 MM
HaRTH MaKCHMaJIbHyJO ,lVIHBy mTOKa. ECJIH coe,n;HHHTb Ha HOMorpaMMe l'pe6ye-
Moe BbIxo,n;Hoe YCHJIHe (200 KH) H ,ZJ;HaMeTp mTOKa (70 MM), TO MO)I{HO HaRTH MaK-
CHMaJIbHyJO ,lVIHBy mTOKa (Lm).
OTBeT: 2800 MM.
QTo6bI HaRTH «paKTHqecKYK> ,lVIHBy xo,n;a (LA) ,ZJ;JUI KOHIqJeTHoro cnoco6a Kpen-
JIeH:IDI, BOCnOJIb3yHTeCb «pOPMYJIaMH, npHBe,n;eHHbIMH ,n;aJIee:
MaKCHM8JlhHaJl ,nJIHHa xo,na ,lUIJI KOHKpeTHhIX cnoco60B KpeDJIeHHJI
KpeDJIeHHe Ha JIanax, mTOK C npoymHHoR
KpeDJIeHHe Ha JIanax, xeCTKO onepTbIR mTOK
LA = Lm x 0,8
LA = Lm
15000
500
20
10000 400
25 9000
I
8000
30 m 4 300
7000
-35 co
)s
40 co2 6000
c;c:[
co s -
0. O)s 5000 200
50 50 )s
2
s c:[
c; e co
60 40. 100 4000 E
150
2.5 ...J
0. .
I- 70 3000 co
Q) -
80 2000
)s 3000 0
2 2 l-
S c:[ 3
E:{go 1000 :; E2500 100
co
100 ...J 90
500 o- s
1.5 I- co
400 3 2ooo 80
300 0.1-
200 I- 3 70
Q) co
150 1500 60
100 1 s
AaBneHHe o.gq: 50
200
40
250 35
1000 30
HCTO':lHHK: CTpaHHua 16 BFPA Data book.
5.6. CucmeMbl o6",eMHou nepeoaltu 459
IIepe,nHHH «pJIaHen;, IIITOK C npOYIIIHHOH
IIepe,nHHH «pJIaHen;, xeCTKO onepTbIH IIITOK
3 HHH «pJIaHen;, IIITOK C npOYIIIHHOH
3 HHH «pJIaHen;, xeCTKO onepTbIH IIITOK
KpeTIJIeHHe n;HJIHH,npa Ha npOYIIIHHe, «pJIaHen; C npOYIIIHHOH
Uan«pa Ha rOJIOBKe, IIITOK C npOYIIIHHOH
Uan«pa Ha CaJIbHHKe, IIITOK C npOYIIIHHOH
Uan«pa Ha CaJIbHHKe, xeCTKO onepTbIH IIITOK
LA = Lm x 0,8
LA = Lm
LA = Lm x 0,4
LA = Lm x 0,8
LA = Lm x 0,3
LA = Lm x 0,3
LA = Lm x 0,6
LA = Lm x 0,8
,[lrnI npOMexyrOqHbIX nOJIOXeHHH n;an«pbI CJIe,nyeT HCnOJIb30BaTb MacIIITa6Hpy-
IOInHH MHO)I{HTeJIb. KpeTIJIeHIDI C Y -o6pa3HoH H c«pepHqeCKOH npOYIIIHHOH HMelOT
TaKOH xe K03«P«PH HeHT, KaK H KpeTIJIeHIDI C npOYIIIHHoH.
UpHMep. HCnOJIb3YR HaH,neHHOe 3HaqeHHe Lm (2800 MM) ,nJUI KpeTIJIeHIDI 3an-
HHM «pJIaH eM H IIITOKa C npOYIIIHHOH, no.rryqaeM LA = Lm x 0,4 = 2800 x 0,4 =
= 1120 MM.
5.6.11. p,aHHhle ,lVIR paclfeToB o6.eMHoR rlf,llpOnepe,llalflf
(rlf,llpasnlflfecKlfe Tpy6hl If wnaHrlf)
400
,
300 ,
, 150
,
, 0,3
,
200 ,
, 100
, 0,4
,
150 , _ 0,5
,
- , o 0,6
} PeKOMeHAyeMbli'I AHa-
100 50 0,7
- _ 0,8 na30H CKopOCTeH
c. 40 0,9
- 0: 1 BcacblBalOw,eH nHHHH
l- S
S 0> 30
50 , 0>
"'- CO , ,7 1.5
c; 40 S 20 0>
- c:[ I- ,2
30 .0 ,
0 )s 15 I- } PeKoMeHAyeMbli'I AHa-
l- S 0 3
0 0 naaOH CKopOCTeH
r::: 20 C.
0> 10 0 4 HanopHOH nHHHH
15 c. 9
8 () 5
7
6 6
18 ca 7
5 8
8 4 9
7 10
6 3
5
4 2,5
3
2
HOMorpaMMa ,nJUI onpe,neJIeHIDI pa3MepOB TPy6 npH 3 aHHOM nOTOKe H peKO-
MeH,nyeMoM ,nHana30He CKopOCTeH
OCHOBaHa Ha «poPMYJIe:
Pacxo,n (JIjMHH) x 2122
CKOpOCTb KOCTH B TPy6e (M\C) = ' ,
d 2
r,ne d - BHyrpeHHHH ,nHaMeTP TPy6bI (MM).
r/la6a 5. MexaHu'tecKue nepeiJa'tu
PeKOMeH,n;yeMbIH ,n;Hana30H CKopocTeH OCHOBaH Ha CBoHcTBax MaCJIa, HMelOm;e-
fO MaKCHMaJIbHbIH K03«P<PH HeHT BR3KOCTH 70 CCT npH 40°C H «PYH HOHHpyIO-
m;efO npH TeMnepaTYPax OT 18 ,n;o 70°C.
llpuMeltanue. ,[lrnI yqacTKoB TPy6onpoBo,n;a OOJIbIIIe 10 M pa3Mep TPy6 ,nOJDKeH
6bITb COOTBeTCTBeHHO YBeJIHqeH. ,[lrrHHa BcacbIBalOmeH JIHHHH HHKOf,n;a He ,n;OJDKHa
npeBbIIIIaTb 1 M.
,lI;aJIbHeHIIIyIO HH<popMa HIO CMOTPH: BFPA/B7 PyKOBO,n;CTBO no BbI60py H
npHJIOXeHHRM CTbIKOB TPy6onpoBo,n;a ,nJllI HCnOJIb30BaHIDI B 06'beMHbIX cHcTeMax;
BFPA/B47 PyKOBO,n;CTBO no HCnOJIb30BaHHIO IIIJIaHfOB B c60pe C coe,n;HHeHIDIMH B
06'beMHbIX CHCTeMax.
HCTO':lHHK: CTPaHHua 17 BFPA design data book.
5.6.12. p,aHHhle p,nfl paCileTOB 06-.eMHOH rlf,llpOnepe,llaillA
(pa6o'llfe JlCIf,llKOCTIf, repMeTlfKIf
If KOHTponh 3arpfl3HeHHOCTIf)
OCTH
ISO KAaccufjJuKau,UJl pa60ltux :JICUOKOCmeu - BS ISO 6743
HH
HL
HM
HV
HFAE
HFAS
HFB
HFC
HFDR
OqHm;eHHbIe MHHepaJIbHbIe MaCJIa 6e3 HHfH6HTOpOB
OqHmeHHbIe MHHepaJIbHbIe MaCJIa C y.rryqIIIeHHbIMH aHTHKopp03HH-
HbIMH H aHTHOKHCJIHTeJIbHbIMH CBOHCTBaMH
MacJIa HL THna C YJIyqllIeHHbIMH npOTHBOH3HOCHbIMH CBOHCTBaMH
MacJIa HMTHna C yrryqllIeHHbIM nOKaJaTeJIeM BR3KOCTb/TeMTIepaTYPa
3MYJIbCHSI THna «MaCJIO B Bo,n;e»
XHMHqeCKHe paCTBopbI B Bo,n;e
3MYJIbCIDI THna «Bo,n;a B MaCJIe»
BO,n;HbIH paCTBOp nOJIHMepOB
CHHTeTWIecKHe )KJ.I,lI;KOCTH Ha OCHOBe 3<pHPOB «pOC«POpHOH KHCJIOTbI
3KOJl02UlteCKU npUeMileMble pa60ltue :JICUOKOCmu
HFTG TpHfJIH epH,ZJ;bI
HEPG TIOJIHfJIHKOJIH
HEES CHHTeTHqeCKHe 3<pHpbI
HEPR TIOJIHaJIb«paOJIe<pHHbI
KAaccufjJuKau,UJl 2UOpa8JlUlteCKUX :JICUOKOCmeu no 8Jl3KOCmU - ISO 3448 (BS 4231)
KIDK,nbIH K03«P«PH HeHT BR3KOCTH 0603HaQaeTCSI 6JIIDKaHllIHM l.(eJIbIM qHCJIOM K
ero cpe,n;HeH KHHeMaTHqeCKOH BSI3KOCTH B caHTHCTOKcax npH 40°C. COKpameHHo
ISO VG (T.e. K03«P«PHl.(HeHT BSI3KOCTH). K03«P«PHl.(HeHTbI o6m;epacnpOCTPaHeHHblx
pa60qHX )KJ.I,lI;KOcTei1: COCTaBJUIIOT VG5, 10, 22, 32, 46, 68, 100, 150, 220 H 320.
HM32 - 3TO MHHepaJIbHOe MaCJIO C YJIyqIIIeHHbIMH aHTHKopp03HHHbIMH, aH-
THOKHCJIHTeJIbHbIMH H npOTHBOH3HOCHbIMH CBoHcTBaMH, HMelOIl(ee K03<P«PH HeHT
BR3KOCTH npHMepHO 32 caHTHCTOKca npH 40°C.
DOJIee no,npo6HyIO HH<popMa HIO 0 Cne HaJIbHbIX )KJ.I,lI;KOCTSIX MO)I(HO HaHTH B
BFPA/PI2 - Cne H<pI1Ka IDI MHHepaJIbHbIX MaCeJI, BFPA/PI3 - Cnel.(H<pHKa HSI
HefOplOQHX )I(H,nKocTeH, BFPA/P67 - Cne H<pHKal.(HSI 3KOJIOfHQeCKH npHeMJIeMbIX
)KJ.I,lI;KOCTeH.
5.6. CucmeMbl 06lJeMHOU nepeoall-u 46
fepMeTHKH
MaTepH8JIhI repMeTHKOB
AKpHJIOHH1pHJI 6yra,nHeH
TIOJIHaKpHJIaTOBaSI CMOJIa
TIOJIHypeTaH
<l>TopnOJIHMep
_/
CHJIHKOH
CTHPOJI 6yra,nHeH
3THJIeHnpOnHJIe HeH
PeKOMeH,lQ'eTCB MB
B03,n;yx, MaCJIO, Bo,na, Bo,n;a/rJIHKOJIb
B03,n;yx, MaCJIO
B03.nyx, MaCJIO
B03,n;yx, MaCJIO, Bo,n;a, Bo,n;a/rJIHKOJIb, XJIOpHpO
BaHHbIH yrJIeBO,n;opo,n;, 1pHapHJIbHbIH <poC<paT
B03.nyx, MaCJIO, XJIOpHpOBaHHbIH yrJIeBO,n;opo,n;
B03,nyx, Bo,n;a, Bo,n;a/rJIHKOJIb
B03.nyx, Bo,n;a, Bo,n;a/rJIHKOJIb, 3<pHpOB <poc<pop
HOH KHCJIOTbI
B03.nyx, MaCJIO, Bo,na, Bo,n;a/rJII1KOJIb, 3<pHpO
<POC<pOpHOH KHCJIOTbI
n OJIHTe1pa<pTop3THJIeH
DOJIee no,n;p06HyIO HH<popMa HIO CM01pH ISO 6072: 06'beMHbIe rH,ZJ;pOnpHBo,n;bI
COBMeCTHMOCTb 3JIal;TOMepOB H )I(IiI,n;KocTeH HJIH BS 7714: PyKOBO,n;CTBO no OTBep)l(
,n;eHHIO H 06pa60TKe repMeTHKOB ,nJllI rH,ZJ;paBJIHqeCKHX npHJIO)l(eHHH. PeKoMe a
IJ;HH no yruIOTHHTeJIbHbIM KOJIbIJ;aM CM01pH BFPA/P22 TIpoMbIIIIJIeHHbIe CTa ap
TbI Ha yruIOTHHTeJIbHbIe KOJIh a - MeTpHqeCKHe H ,n;IOHMoBbIe.
HCTO':lHHK: CTpaHHUbI 18-20 BKJIIO':IHTeJIbHO BFPA Data book.
qHcToTa 1KII)J;KOCTH
TIpHcyrcTBHe 3arpR3HSIIOIl(HX qaCTH «<rpR3H») - 3TO e,n;HHcTBeHHbIH HaH60JIei
BIDKHbIH <paKTop, onpe,n;eJUIIOIl(HH CpOK CJIy)K6bI H Ha,ne)I(HOCTb rH,ZJ;paBJIHqecKH:
CHCTeM. Pa60Ta C qHCTbIMH XH,l(KOCTRMH KpaHHe BIDKHa. COBeTbI no KOH1pOJIIO 3a
rpR3HeHHocTH MO)I(HO HaHTH B BFPA/P5.
KOHTpOJIh 3arpB3HeHHocTH
Cne H<pHKa HSI TOHKOCTH <pHJIbTpa HH - ISO 4572 (BS 6275/1)
MHoronpoxo,n;HbIH TeCT ISO 4572 (BS 6275/1) 6bIJI BBe,neH, QT06bI npeo,n;OJIeT]
TPy,nHOCTH, CBSI3aHHbIe co cpaBHeHHeM 3<p<peKTHBHoCTH <pHJIbTpOB. B YCJIOBIDIX no.
CTOSIHHOH HPKYJUI HH MaCJIa qepe3 3JIeMeHT B TeqeHHe Bcero BpeMeHH TeCTa B Te
CTOBbIH MexaHH3M BBO,n;SITCSI HOBbIe 3arpSI3HeHHocTH (ISO TecToBaSI nbIJIb). 3arpSI3
HeHHOCTH, He y,n;arreHHbIe TecTHpyeMbIM 3JIeMeHTOM, 6y,n;yr npo,nOJDKaTb HPKYJIH
pOBaTb, TaKHM 06pa30M HMHTHPYSI YCJIOBHR 3KCIIJIyaTa HH.
K03<P<PH HeHT <pHJIbTpa HH ,nJllI <pHJIbTpa no.rryqaeTCSI B pe3YJIbTaTe aHarrH3,
06pa3 OB XH,l(KOCTH, H3BJIeqeHHbIX ,n;o H nOCJIe <pHJIb1pa, T. e.:
(3x=
KOJIH':IeCTBO ':IaCTHU 60JIbillHX x Ha BXO,l(e <pHJIbTpa
KOJIH':IeCTBO ':IaCTHU 60JIbUlHX x Ha BblXo,l(e <pHJIbTpa
KaqeCTBO <pHJIb1pyIOInerO 3JIeMeHTa onpe,nenSIeTCSI KaK pa3Mep B MHKpOHax
r,n;e x - 3TO BepXHee 3HaqeHHe (HanpHMep, 100 HJIH 200).
CTall,lJ;apThI ttHCTOThI 1KII)J;KOCTH
TIpe,n;nOqTHTenbHo o eHHBaTb KOJIHqeCTBO TBep,nbIX qaCTH 3arpSI3HeHHSI B 06.
pa3 e B COOTBeTCTBHH C BS ISO 4406.
Dla8a 5. MexaHu'teclCue nepeiJa'tu
Ko,n; C1pOHTCR Ha .0cHoBe COqeTaHIDI ,n;Hana30Ha Mex,ny ,n;B}'MR qHCJIaMH, BbI-
6paHHbIMH H3 cJIe,n;YX>II(eH Ta6JIH bI. TIepBoe qHCJIO ,n;Hana30Ha npe,n;cTaBIDIeT KO-
JIHqeCTBO qaCTHIJ; B MHJIJIHMe1pe o6pa3 a XH,nKOCTH, 60JIbIIIHX 5 MKM; BTopoe qHC-
JIO npe,n;CTaBIDIeT KOJIHqeCTBO qaCTH , 60JIbIIIHX 15 MKM.
KOJlll'lecTBO '1aC'I'IIQ Ba MHJJJIHMeTp 3BaMeBaTeJlh
OT AO H BKJIIO'IU MacIDT86a
10000 20000 21
5000 10000 20
2500 5000 19
1300 2500 18
640 1300 17
320 640 16
160 320 15
80 160 14
40 80 13
20 40 12
10 20 11
5 10 10
2,5 5 9
1,3 2,5 8
0.64 1.3 7
HanpHMep, KO,n; 18/13 )'Ka3bIBaeT, qTO npHcyrcTByeT OT 1300 ,n;o 2500 qaCTHI(,
60JIbIIIHX 5 MKM, H OT 40 .no 40 qaCTH , 60JIbIIIHX 15 MKM.
,lI;aJIbHeHIIIyIO HH<I>opMa HIO H cpaBHeHHe CTaH,napTa BS ISO 4406 C ,n;pyrHMH
KJIaCCaMH qHCTOTbI CM01pH BFP A/P5 PyKOBO,n;CTBO no KOHTpOJIIO 3arpSI3HeHHOCTH
B 06'beMHblX fH,npaBJIHqeCKHX cHcTeMax.
UpOMhIBKa
<l>oPMYJIa BeJIHqHHbI nOTOKa, He06xo.nHMOfO, qT06bI B ,n;ocTaTOqHOH Mepe npo-
MbITb CHCTeMY
Q > 0,189 vd (JI/MHH),
f,n;e Q - nOTOK (JI/MHH); v - KHHeMaTJ.I1IeCKIDI BSI3KOCTb (cCT); d - BHYTPeHHHH
,n;HaMeTp 1py6bI (MM).
aJIbHeHmyIO HH<I>opMa HIO 0 npOMbIBKe CM01pH BFPA/P9 PyKOBO,n;CTBO no
qHCTOTe 06'beMHblX fH,npaBJIHqeCKHX CHCTeM.
qHCTOTa KOMDOHeHTOB
TpH MeTo,n;a cyw;eCTByIOT ,nJllI TOfO, qTo6bI H3MepHTb qHCTOTY KOMnOHeHTOB:
npOBepbTe 6ypoByIO YCTaHOBK)', TeCT nOTOKa, nOJIOcy H MbITbe. YpoBeHb 1pe6yeMoH
qHCTOTbI ,n;OJDKeH 6bITb COfJIaCOBaH Me:>K,ZJ;y nOCTaBIIJ;HKOM H KJIHeHTOM, HO MeTo,n;bI
nOJIHOCTblO onHcaHbI B BFP A/P48 - PyKoBO,lUlII(He npHH HnbI K qHCTOTe fH,npaB-
JIJ.I1IeCKHX XH,nKHX KOMnOHeHTOB BJIaCTH.
5.6. CucmeMbl 06lJeMHOU nepedaltu 46:
5.6. 13. p,aHHh,e ,lVIfI \!'.fClfeToB o6-.eMHoH rJf,llponepe,llalfJf
(rJf,llpaBnJflfeC Jfe aKKYMynflToph')
UpHJlO]l(eHIUI, HCDOJlh3YJODUle HaKODJIeHIIYJO 3HeprHIO
llpHJlo1KeHHJI
cl»oPMYJIa onemm BeOOXO,lUlMOro ,lUUI npHJIO]KeHHJI o61.eMa au:yMyJUlTOpa
MeAJIeHHWI 3apMKa
MeAJIeHHWI pa3PMKa
V a X P2
V; - PI
1 -
1- P2
P3
BbIC1'pWI 3apMKa
BbIC1'pWI pa3PMKa
1
Va X ( P2 J I,4
Vi = PI
1
1_( ;:Y4
MeAJIeHHWI 3apMKa
BbIC1'pWI pa3PMKa
Va X P3
V; - PI
I-
I
( ;:Y4 -1
L
P2
V1CnOllb-
ayeMblH
o6beM
>KHAKOCTPI
,[J;aBJIeHHe npe,nBapHTeJIbHOH 3apMKH BbI6HpaeTCSI Ha ypOBHe 90% MHHHMaJIb-
Horo pa6oqero ,naBJIeHIDI, n H3MeIDIeTCSI Me)f{,lJ;y 1 H 1,4 B 3aBHCHMOCTH OT Toro, SIB-
IDIeTCSI JIH 3apMKa Me,nJIeHHOH (H30TepMJ.I1IeCKoH) HJIH 6bIC1pOH (anHa6aTHQeCKoH).
UYJlhCaQIUI Hacoca
TIYJIbCa HSI Hacoca H <popMYJIa pa3Mepa aKKYMYJUITOpa, Heo6xo,nHMoro, QTo6bI
YMeHbIIIHTb nyJIbCa HH Hacoca.
(a) MHHHMaJIbHbIH pa60QHH 06'beM (JI)
k.Q
Vi = .
n
llpUMettanue. CQHTaeTCSI TeXHJ.I1IeCKH rpaMoTHblM BbI60p aKKYMYJUITOpa C coe-
,nHHHTeJIbHbIM OTBepCTHeM, paBHbIM coe,nHHHTeJIbHOMY OTBepCTHIO Hacoca.
(::: Dta6a 5. MexaHu'tecKue nepeiJa'tu
(6) TIpoBepReM no.rryqeHHbIH ypOBeHb nyJIbCa HH.
06'beM )fGf)];KOCTH, nOCTYTIalOIneH B aKKYMYJUITOp = D . C
,[lrnI nO,ZJ;aBJIeHIDI nyJIbCa HH, eCJIH ,ZJ;aBJIeHHe npe,ZJ;BapHTeJIbHOH 3apsuurn
II = 0,7 . P 2 H npH YCJIOBHH, qTO H3MeHeHIDI OT PI ,ZJ;O P 2 RBJUIIOTCR H30TepMHtle-
CKHMH, nO.rryqaeM
V 2 = 0,7 . Vi.
V 3 = V 2 - (D · C).
( V2 ) 1.4
P3 = P 2 V 3 ·
CJIe,ZJ;OBaTeJIbHO, npO eHT nYJIbCa HH BbIIIIe H HIDKe cpe,ZJ;Hero paBeH
( P 2 P 3 )100.
3,neCb VI - pa60qHH 06'beM ra3a; V 2 - MHHHMaJIbHbIH o6DeM ra3a; V 3 - MaKCH-
MaJIbHbIH 06'beM ra3a; PI - ,ZJ;aBJIeHHe npe,ZJ;BapHTeJIbHOH 3apSl,l(KH; P2 - MHHHMaJIb-
HOe pa60Qee ,ZJ;aBJIeHHe; P3 - MaKCHMaJIbHOe pa60Qee ,ZJ;aBJIeHHe; = V 3 - V 2 - pa-
60QHH 06'beM ()fGf)];KOCTb); k - KOHcTaHTa*; Q - no,naqa Hacoca (JI/MHH); n - CKO-
pOCTb pa60TbI Hacoca (06/MHH), eCJIH n > 100 HCnOJIb3yeTcR 100; D - 06'beMHasI
npOH3Bo,nHTeJIbHOCTb Hacoca (JI/o6); C - KOHcTaHTa*.
* 3aBHcHT OT KOJIHqeCTBa nopIIIHeH. ,lI;JUI MHoronopIIIHeBbIX HaCOCOB > 3 nop-
IIIHeH k = 0,45 H C = 0,013.
HCTO':lHHK: CTpaHHua 21 BFPA data book.
5.6. 14. p,aHHh,e ,lVIR paClfeTOS 06-.eMHoii rlf,llpOnepe,llalllA
(rlf,llpaSnlflfeCKoe OXnaJKAeHJfe If Harpes)
OXJIaJK,lJ;eHHe
)KH;:J;KOCTb B pe3epByape OXJIIDK)];aeTCR 6JIaro,napSI H3JIyqeHHIO H KOHBeKIJ;HH.
1l . A . k
P=
1000 '
r,ZJ;e k = 12 npH HOpMaJIbHOM BeHTHIDI HOHHOM npOC1paHCTBe
k = 24 BT/M2 °C B YCJIOBIDIX npHHy,ZJ;HTeJIbHOH BeHTHIDI HH
k = 6 npH CJIa60H HPKYJUI HH B03 a
Tpe6yeMbIH nOTOK BO,ZJ;bI qepe3 OXJIa,rJ;HTeJIb:
Q 860 nOTepRHHaR MOInHOCTb /
= x JI qac.
T BO,ZJ;bI
HarpeR
HarpeB KpaHHe Heo6xo,ZJ;HM, eCJIH TeMnepa1'ypa OKpyxalOIneH cpe,ZJ;bI cyw;ecT-
BeHHO HIDKe O°C.
\
(
5.6. CucmeMbl 06lJeMHOU nepeoall-u 465
Tpe6yeMbIH 3<l><l>eKT HarpeBa:
p = V · T2 B KBT.
35 · t
3 Hepl1lJl
J = M · C . T
,
r,ne M - Macca (Kf); C - y,neJIbHIDI TeITJIOeMKOCTb ,lhK/Kf °C; 1i - pa3HOCTb TeM-
nepa1'yp (OC) KOCTb/B03,nyx; T2 - YBeJIHtleHHe TeMnepa1'ypbI KOCTH (OC);
t - BpeWI (MHH).
llpUMettaHue. 1 M)];x = 0,2777 KBT/qac.
TeDJIOBOH 3KBHBaJIeHT nu;paBJIll'leCKOH MOIQHOCTH
K,l:(x/c = llOTOK (JI/MHH) x MBJIeHHe (6ap) =KBT.
600
H3MeHeHHe 06'heMa DPH H3MeHeHHH TeMDepaTYJ)hl
H3MeHeHHe 06'beMa
V = 6,3 x 10-4 . V . T.
H3MeHeHHe ,naBJIeHIUI DPH H3MeHeHHH TeMDepaTYJ)h1
llpUMettaHue: B 6eCKOHeqHO xeCTKOM HJIHH,npe.
H3MeHeHHe ,naBJIeH:IDI = 11,8 · T (B 06IUeM 3aBHCHT OT MHorHX nepeMeH-
HbIX) .
UpHMep. H3MeHeHHe TeMnepa1'ypbI HJIHH,ZJ;pa C MaCJIOM OT HOqHOH (10°C) ,no
.nHeBHoH/cOJIHeqHOrO H3JIyqeH:IDI (50°C) ,naeT:
= 11,8 x 40 = 472bar,
r,ne T - H3MeHeHHe TeMnepa1'ypbI (OC); P - MOInHOCTb (KBT); k - K03<l><l>H H-
eHT HarpeBa (BT/M2 °C); A - llJIOInanb nOBepXHOCTH pe3epByapa, HCKJllOqIDI OCHO-
BaH:IDI (M 2 ); t - H3MeHeHHe BpeMeHH (MHH); - H3MeHeHHe ,naBJIeH:IDI (6ap);
C - y,neJIbHIDI TeITJIOeMKOCTb (,lJ;X/Kf °C); V - 06'beM (JI)
HCTO':lHHK: CTpaHHua 21 BFPA data book.
5.6.15. p,aHHhle ,lVIfI paClfeTOB 06-.eMHoii rJf,llponepe,llalfJf
(Kna na Hhl)
-
Pacxo,nHYIO xapaKTepHCTHKY KJlanaHa 06bIqHO }'Ka3bIBa1OT KaK HeKoTopbIH K03<l>-
<l>HIJ;HeHT nponycKHoH cnoc06HOCTH (pacxo,na), TaKoH, HanpHMep, KaK, C, b, Cv,
Kv H ,npyrHe.
TIpH HaH60JIee TOqHOM cnoc06e onpe,neJIeH:IDI pacxo,nHoH xapaKTepHCTHKH KJla-
rraHa HCnOJIb3yIOT 3HaqeH:IDI C (npoBo,nHMOCTb) H b (KpHTHqeCKOe OTHomeHHe ,naB-
JIeHHH) .
Dta6a 5. MexaHu'tecKue nepeiJa'tu
3TH H«PPbI onpe,n;eJUIIOTCR TeCTHpOBaHHeM KJlanaHa B COOTBeTCTBHH C peKO-
MeH,ZJ;a IDIMH CETOP RP50P.
Pe3YJIbTaTOM TeCTOB 06bIqHO 6bIBaeT Ha60p KpHBbIX, aHaJIOrHqHbIX nOKa3aH-
HbIM HIDKe.
113 HHX MO)I{HO HaHTH KpHTJ.I1IeCKOe OTHOmeHHe ,n;aBJIeHHH b. b npe,n;CTaBJUIeT
C060H OTHOmeHHe P 2 K PI' npH KOTOpOM CKOpOCTb nOTOKa CTaHOBHTCSI 3B}'KOBOH
(OrpaHHqeHHe CKOpOCTH B03,n;yxa). TIpOBO,n;HMOCTb C TaIOKe npe,n;CTaBJUIeT C060H
nOTOK «,n;M 3 /C/6ap (a6COJIIOTHOe») B 3TOH TOQKe.
ECJIH Ha60p KPHBbIX OTcyrcTByeT, 3HaQeHHe nOTOKa ,ZJ;.JllI ,n;pyrHX nepenan;OB
,n;aBJIeHIDI MO)I{HO BbIQHCJIHTb no «poPMYJIe:
P2 -b
Q = Cll 1 - _ b '
r,n;e PI - ,n;aBJIeHHe Ha Bxo,n;e KJlanaHa 6ap; C - npOBO,ZJ;HMOCTb ,n;M 3 /c/6ap (a6co-
JIIOTHoe); Q - nOTOK ,n;M 3 /C; P 2 - ,n;aBJIeHHe Ha BbIxo,n;e KJlanaHa 6ap; b - IqJHTII-
QeCKOe OTHOllIeHHe ,n;aBJIeHHH.
MeTO,n ISO 65238/CETOP RP50P
35
KpHTH eCKoe OTHoweHHe
AaBlIeHHH b = 0,36
P1 P 2
30
M
c:[ 25
o
b 20
E::
)s
J5 15
c.
0) 10
e-
o
o
5
<
npOBOAHMOCTb C = 4,0 AM 3 /c/6ap
(a6COllIOTHoe) TOllbKO AlISi ropH-
30HTallbHOH aCTH KpHBOH
o
o 1 2 3 4 5 6 7
AaBlIeHHe P2 noclIe K1IanaHa 6ap MaHOMeTpH eCKoro AaBlIeHHSI
HCTOQHHK: CTpaHHua 23 BFP A data book.
5.6. 16. p,aHHh,e ,ling paclfeTos o6.eMHoH rJf,llponepe,llaIfIA
(nHeSMaTJflfeCKJfe qJfnJfH,lIph')
HeKOTopbIe «paKTopbI, KOTopbIe CJIe,n;yeT ytIHTbIBaTb npH BbI60pe H HCnOJIb30Ba-
HHH nHeBMaTHQeCKHX JIHHeHHbIX HCnOJIHHTeJIbHbIX MexaHH3MOB - nHeBMO HJIHH-
,n;pOB.
\
5.6. CucmeMbl 061JeMHOU nepeoaltu 46
Pe]KlfM pa60Thl
TpH OCHOBHbIX THna
. O,ZJ;HOCTopoHHero ,neHcTBIDI, C B03BpaTOM mTOKa npyxHHoH: no,n B03,ZJ;eHc1
BHeM ,ZJ;aBJIeHIDI B03.nyxa npHKJI3J,J;bIBaeTCR YCHJIHe, H npOHCXO,ZJ;HT ,nBIDKeHHe
O,ZJ;HOM HanpaBJIeHHH; o6paTHoe ,ZJ;BIDKeHHe npOHCXO,ZJ;HT no,ZJ; B03,ZJ;eHcTBHel
BHYTPeHHeH CHJIbI npyxHHbI, 06bl'IHO oCBo6ox.naeMoH B nOJIOXeHHH XO,ZJ;
BbInycKa, HO HHor,na HMeeT MeCTO o6paTHbIH XO,ZJ;.
. ,lI;BYXCTopoHHero ,ZJ;eHcTBIDI: 11'e6yeTcR ,ZJ;aBJIeHHe B03.nyxa, qTo6bI C03,ZJ;aBaT
YCHJIIDI H BbInOJIHRTb ,ZJ;BIDKeHIDI B 060HX HanpaBJIeHIDIX xO,ZJ;a.
. ,lI;BYXCTopoHHero ,ZJ;eHcTBIDI, C ,ZJ;BYXCTOpOHHHH mTOKOM: ,ZJ;BYXCTOpOHHHi
mTOK «PYH HOHHPyeT TaK xe, KaK H 06bIqHbIH B HJIHH,npe ,nBYXCTopOHHer<
,ZJ;eHcTBIDI, HO MeXaHHqeCKOe coe,ZJ;HHeHHe B03MO)I(HO C 060HX KOH OB ,ZJ;BYX'
CTopOHHero mTOKa.
HCTO':lHHK: CTpaHHna 23 BFPA data book.
6ecmToKoBbie IUlJlHll)]:pbl
TaM, r,ZJ;e npoc11'aHcTBo nOJIb3yeTcR 60JIbmHM cnpocoM H cym;ecTByJOT nOTeH-
HaJIbHbIe np06JIeMbI C HarpY3KOH H peryJIHpOBKOH, MOryr HCnOJIb30BaTbCR pa3Ho-
06pa3Hble 6ecmToKoBbIe HJIHH,ZJ;pbI. ,lI;Hana30H B03MO)I(HbIX BHyrpeHHHX ,ZJ;HaMeT-
pOB TaKHX HJIHH,npOB orpaHl{qeH (HanpHMep, 16-100 MM).
KJIaccbl Ka1JeCTBa
Cyw;ecTByeT 11'H KJIacca KaqeCTBa
. 06JIeNeHHbIH pe)I{HM, KOMnaKTHbIe HJIHH,npbI: orpaHl{qeHHbIH ,ZJ;Hana30H
BHYTPeHHHX ,ZJ;HaMe11'OB. OTcyrcTByeT TopMoxeHHe B KOH e xO,ZJ;a HJIH eCTb
TOJIbKO no,nymKa. H3yqHTe PYKOBO,ZJ;CTBa npOH3BO,ZJ;HTeJUI, qTo6bI npOBepHTb
y,ZJ;06CTBO TeXHl{qeCKOrO o6cJIyXHBaHIDI H BOCnpHHMqHBOCTb K KOpp03HH.
. Cpe,ZJ;HHH pe)I{HM/cTaH,napTHbIe YCJIOBIDI: ,n.JllI CTaH,napTHOro npOH3Bo,nCTBeH-
Horo o6opY,ZJ;oBaHHIO. HeKoTopIDI CTeneHb YCTOHqHBOCTH K KOpp03HH. TIpH-
cnOC06JIeHbI K TeXHHqeCKOMY 06CJIyXHBaHHIO. TopMoxeHHe Ha 060HX KOH-
ax. 06bIQHO ,ZJ;BYCTopOHHero ,ZJ;eHcTBIDI. ,lI;Hana30H BHYTPeHHHX ,ZJ;HaMe11'OB
OT 32 MM H 6oJIee.
. TIDKeJIblH pe)I{HM: npOqHIDI KOHC11'yKIJ;IDI. TIpHcnoco6JIeHbI K TeXHHqeCKOMY
06cJIyXHBaHHIO. HepxaBelOInHe MaTepHaJIbI, ,nonOJIHHTeJIbHOe TopMoxeHHe,
60JIee TOJICTbIe CTep)I(HH H MOInHbIe KpeTIJIeHIDI ,n.JllI TIDKeJIbIX pe)I{HMOB pa6o-
TbI. ,lI;Hana30H BHYTPeHHHX ,ZJ;HaMe11'OB OT 32 MM H 6oJIee.
HH«popMa HIO no B3aHM03aMelffieMOCTH H CTaH,napTHbIX pa3Mepax KpeTIJIeHHH
CM011'H ISO 6432 ,n.JllI BHYTPeHHHX ,ZJ;HaMe11'OB 8-25 MM, ISO 6432 ,n.JllI BHYTPeH-
HHX ,nHaMe11'OB 32-320 MM: HOpMaJIbHbIH pe)I{HM, ,ZJ;BYXCTopOHHee ,ZJ;eHcTBHe, MeT-
plNeCKHe pa3MepbI.
CTall,lJ;apTHbie pa3Mepbl BHyTpeHHHX ,lUIaMeTpOB
. ,lI;BYXCTopoHHero ,ZJ;eHcTBIDI: 8, 10, 12, 16, 20, 25, 32, 40 50, 63, 80, 100, 125,
160, 200, 250 H 320 MM.
CTall,lJ;apTHbie MHHbI xo,na DopmHei
. ,lI;BYXCTopoHHero ,ZJ;eHcTBIDI: 25, 50, 80, 100, 125, 160, 200, 250 H 320 MM.
Dla8a 5. MexaHU.,ecKue nepeiJa.,u
OceBoe YCHJIHe IUIJIH pa
QT06bI BbIqHCJIHTb TeOpeTHqeCKOe oceBoe YCHJIHe UHJIHH,lJ;pa ,nBYCTopoHHero
,neHcTBIDI, BOCnOJIb3yHTeCb <POPMYJIOH:
( 1t D 2 x P )
OceBoe YCHJIHe = 4 H,
r,ne D - ,nHaMeTP nopmIDI (MM), P - MaHOMeTpHqeCKOe ,naBJIeHHe (6ap).
Tllra 6y,neT MeHbme H3-3a llJIOlI(anH mTOKa.
( 1t(D2 -d2)XP )
Tllra = H,
4
r,ne d - ,nHaMeTP nopmHeBoro npyra (MM).
IlpH CTaTlNeCKHX HarpY3Kax, TO eCTb eCJIH nOJIHOe oceBoe YCHJIHe TPe6yeTcH,
Kor,na UHJIHH,lJ;p Heno,nBIDKeH (HanpHMep, 3IDKHMaHHe, <pHKcanHll), HCnOJIb3yHTe
BbIllIenpHBe,neHHbIe paCqeTbI.
IlpH ,nHHaMHqeCKHX HarpY3Kax, TO eCTb eCJIH nOJIHOe oceBoe YCHJIHe TPe6yeTcH
B npouecce xo,na nopmHH, B paCqeTaX CJIe,nyeT yqecTb npOTHBo,naBJIeHHe B TPaKTe
BbInycKa, TPeHHe, H3MeHeHHll ,naBJIeHHe BbITeCHeHIDI H T.n. H ,n06aBHTb 30% K 3Ha-
qeHHIO Tpe6yeMoro YCHJIHll ,lUUI HOpMaJIbHbIX CKopocTeH. ,[LJm 60JIbmHX CKopocTeH
BllJIOTb,nO 100%.
CKOpOCTH D;HJlHH,ZJ;pa
IlpH HOpMaJIbHOH HarpY3Ke, KJIanaHHOH CHCTeMe H ,naBJIeHHH 5-7 6ap BIDKHO
COOTHomeHHe Me)l{,l{y llJIOlI(anbIO BHyrpeHHero CeqeHIDI UHJIHH,lJ;pa H <paKTlNeCKOH
llJIOlI(anbIO BHyrpeHHero CeqeHIDI Bxo,nHoro OTBepCTHll UHJIHH,lJ;pa. 06bIqHO 3TO co-
OTHomeHHe COCTaBIDIeT nOpll,lJ;Ka 100: 1 H n03BOIDIeT pa3BHBaTb CKOpOCTb 0,3-
0,5 M/c. ,n;IDI HOpMaJIbHbIX CKopocTeH HCnOJIb3yHTe HanpaBIDIIOII(HH nHeBMopacn-
pe,neJIHTeJIb H CHCTeMy TPy6 TaKoro )l(e pa3Mepa, KaK Bxo,nHoe OTBepCTHe UHJIHH,LJ;-
pa. ,n;IDI 60JIee BbICOKHX CKopocTeH HCnOJIb3yHTe UHJIHH,lJ;p 60JIbmerO BHyrpeHHero
,nHaMeTpa, qeM Heo6xo,nHMO, llJIIOC 60JIbmHe KJIanaHbI H TPy6bI, HO He 3a6bIBaHTe 0
np06JIeMaX TOpMO)l(eHIDI.
,lI;JlHHbI xo)];a
IlpH CTaTHqeCKHX HarpY3Kax HCnOJIb3yHTe 06bIqHbIe cTaH,napTHbIe AJlHHbI xo,na,
nOCKOJIbKY np06J1eMbI TOpMO)l(eHIDI He HBIDIIOTCll cymecTBeHHbIMH. IlpH ,nHHaMH-
qeCKHX HarpY3Kax 3aKIDKHTe YCTPOHCTBO C TPe6yeMoH no,nXO.lUllI(eH AJlHHOH xo,na,
nOCKOJIbKY HCnOJIb30BaHHe BHemHeH OCTaHOBKH BJIHlleT Ha B03MO)I{HOCTb TOpMO-
)l(eHHH. IlpH 60JIbII10H ,lI;JIHHe xo,na, TO eCTb 60JIbllIeH qeM 15 x BHyrpeHHHH ,nHa-
MeTp, He06xo,nHMO npHHHMaTb MepbI, QT06bI npe,nOTBpaTHTb 60KOByIO HarpY3KY Ha
onopbI H T.n.; HCnOJIb3yHTe mapHHpHbIe KpellJIeHIDI. IlpoKoHTpoJIHpyHTe ,nHaMeTp
mTOKa, qTo6bI npe,nOTBpaTHTb H3rH6 no,n HarpY3KoH. ECJIH Heo6xo,nHMO, HCnOJIb-
3yHTe UHJIHH,lJ;p 60JIbmerO BHyrpeHHero ,nHaMeTPa, qeM HOpMaJIbHbIH, H Y Hero, Be-
pOHTHO, 6y.nyr 60JIee AJlHHHbIe onopbI H 60JIee TOJICTbIH mTOK.
5.6. CucmeMbl o6oeMHou nepeiJaltu 46
5.6. 17. npoeKTHble .qSHHble o6heMHoii rff.qponepe.qslfff
(ynnoTHeHffe, cpffnbTpSLtffR ff CMS3KS)
fepMeTHKH
,lLrnI HeKOTopbIX MHHHaTlOpHbIX nHeBMaTHqeCKHX KOMnOHeHTOB H ,nIDI KJIana
HOB, pa60TalOII(HX B TIDKeJIOM pe)l{}lMe, npHMeIDIeTCll repMeTH3alUUl MeTaJIJI-Me
TaJIJI. B 60JIbmeH qaCTH o6opy,nOBaHIDI HCnOJIb3yIOTCll 3JIaCTHqHbIe repMeTHKH, H
rOTaBJIHBaeMbIe H3 CHHTeTHqeCKHX KayqyKOB. OHH Bbmep)l{}lBalOT BHelliHHe TeMne
paTypbI BllJIOTb ,nO 80°C. fepMeTHKH H3 <pTopnOJIHMepOB H CIDIHKOHa (BHTOH) He
nOJIb3yIOTCll npH TeMnepaTYPax ,nO 150°C.
CHHTeTHqeCKHe repMeTHKH YCTOHqHBbI K B03,n;eHcTBHIO rH.npaBJIHqeCKHX Mace
Ha MHHepaJIbHOH OCHOBe, HO 0 KOHKpeTHbIX BH.naX MaCeJI CJIe,nyeT KOHCYJIbTHpOB8
TbCll C npOH3Bo,nHTeIDIMH o6opy,n;OBaHIDI, qTo6bI H36e)KaTb np06J1eM C ,no6aBKaM
(CMOTPH pa3,neJI 5.6.12).
XopomasI H3HOCOCTOHKOCTb rapaHTHpyeT npHeMJIeMyIO 3<p<peKTHBHoCTb, ,nIDI{
npH pa60Te C OTHOCHTeJIbHO BJIIDKHbIM H 3arpll3HeHHbIM B03,nYXOM. O,nHaKo, qTO
6bI 06eCneqHTb 6e30naCHyIO 3KcruryaTaUHIO H y,noBJIeTBOpHTeJIbHbIH CpOK c.JIy)K61
CHCTeMbI, Heo6xo,nHMa CHCTeMa <pIDIbTPaUHH H KaKOH-TO BH.n CMa3KH.
Cl>HJlbTpanuB
XOpOlliasI <pIDIb1'paUIDI HaqHHaeTCll C KOMnpeccopa C npaBHJIbHO pa3MelI(eH
HbIM B03,nyxo3a6opHHKOM H BcaCbIBalOlI(erO <pHJIbTPa. OmH6KH B BbI60pe pa3MelI(e
HIDI Ha 3TOH CTanHH MOryT CTaTb npHqHHOH np06JIeM npH nOCJIe,l(yIOlI(eH YCTaHOB
Ke. XOTll OXJIanHTeJIH H BJIarOOT,neJIHTeJIH rapaHTHpyIOT, qTO BXO.lUlII(HH B03,ny
nonanaeT B 3aMKHYTYIO ceTb B COOTBeTCTByIOlI(eM COCTOHHHH, KOH,n;eHCaTbI H 3a
rpll3HeHIDI MOryT CHOBa nonaCTb B Hero Ha nyrH K MecT)' HCnOJIb30BaHIDI. Heo6
XO,nHMbI OT,neJIbHbIe <pHJIbTpbI BO Bcex OCHOBHbIX MeCTax npHMeHeHIDI.
B 061I(eM MamHHOCTpoeHHH ,nOCTaTOqHO <pHJIbTPOB C 40 MKM 3JIeMeHTaMH. ,l(m
nHeBMaTHqeCKHX HHCTpYMeHTOB, nHeBMaTHqeCKHX ,naT'IHKOB, paCnbIJIeHIDI H T.n
lpe6yIOTCll <pHJIbTp 0,5 MKM HJIH JIyqme. BbICOKOKaqeCTBeHHbIe <pHJIbTpbI qaCTO Ha
3bIBalOT KoaryIDITopaMH. CymecTByIOT <pHJIbTpbI C pyqHOH, aBTOMaTHqeCKOH H no
JIyaBTOMaTHqeCKOH CHCTeMOH OqHCTKH.
QTo6bI CrJIanHTb npo6JIeMy rpll3H, nOnanalOlI(eH B OTKpbITbIe BbInYCKHbIe KaHa
JlbI, HCnOJIb3yHTe rJIynIHTeJIH IIlYMa BbInycKa, KOTopbIe TalOKe nOMOryT H36e)l(aTJ
np06JIeM C llI)'MOM. ,lLrnI BbInYCKHbIX oTBepcTHH TaIOKe cymecTByIOT npOCTbIe <pHJIb
TPbI, o6eCneqHBalOII(He npHeMJIeMbIH ypOBeHb llI)'Mor.rrymeHHH npH He6oJIbmO
conpOTHBJIeHHH nOTOKY.
CMa3Ka/COBpeMeuuoe o6oPY,ZJ;oBauHe, 1faCTO npoeKTHpyeMoe )];JIB pa60TbI 6e
CMa3KH
O.nHaKO B 60JIbillHHCTBe CJIyqaeB B npOMbIllIJIeHHOCTH nOCTaBIDIeMbIH B03,nyJ
co,nep)I(HT HeMHoro BJIarH. Bce nHeBMaTHqeCKHe KOMnOHeHTbI npOMaCJIeHbI npl
c60pKe, eCJIH HeT CneUHaJIbHbIX TPe60BaHHH. 3TO 06eCneqHBaeT nOJIHOneHHYK
cMa3KY H rapaHTHpyeT HeCKOJIbKO MH.JIJIHOHOB UHKJIOB y,nOBJIeTBOpHTeJIbHOrO <pyH-
KIJ;HOHHpOBaHIDI o6opy,nOBaHHH, oco6eHHO npH qaCTOM HCnOJIb30BaHHH.
CMa3Ka B03,nYXOBO,nOB npe,nYCMOTpeHa BO MHorHX npOMbIllIJIeHHbIX npIDIO)l(e.
HIDIX.
Dla8a 5. MexaHulteclCue nepeiJaltu
CHCTeMWKO QHOHHpOBaHHR
COrJIaCHO oueHKe 90% nOJIOMOK nHeBMaTlNeCKHX CHCTeM 06YCJIOBJIeHO llJIO-
XHM KaqeCTBOM BcaCbIBaeMoro B03.ayxa. 3arp1l3HeHIDI nonanalOT B KOMnpeccop H3
aTMoc<pepbI. YpoBeHb 3arp1l3HeHHH cymecTBeHHO nOBbIillaeTCll npH C)KaTHH.
JII06bIe 3arp1l3HeHIDI pa3pymalOT KOMnOHeHTbI CHCTeMbI.
B COBpeMeHHbIe nHeBMaTlNeCKHe CHCTeMbI BXO,lUIT pa3JIHqHbIe YCTPOHCTBa
KOH,lJ;HUHOHHpOBaHIDI B03.ayxa, BKJIlOqalOlI(He B ce611 BJIarOOT,neJIHTeJIH, ,lI;IDI y,narre-
HIDI BJIarH, <pHJIbTPbI ,lI;IDI YCTPaHeHIDI 3arp1l3HeHHH H, B03MO)KH0, KaKOH-JIH60 BH)];
CMa3KH. ,[LJm K oro npIDIO)KeHIDI CJIe,nyeT TlI(aTeJIbHO BbI6HpaTb CHCTeMy KOH,lJ;H-
UHOHHpOBaHIDI, y,nOBJIeTBoplllO:rnyIO TPe6yeMbIM YCJIOBIDIM <PYHKnHOHHpoBaHIDI.
HCTOqHHK: C1'paHHQa 26 BFPA data book.
5.6.18. p,aHHble ,qJJR paClfeTOS 06heMHoii rlf.qponepe.qalfff
(S03AywHble KOMnpeccopbl)
Ha 60JIbillHHCTBe npOMbIWJIeHHbIX npe,nnpIDITHH H B MeXaHl{tleCKHX MaCTepcKHX
nHeBMaTHqeCKOe 060py,noBaHHe <PYHKnHOHHpyeT npH ,naBJIeHHH npHMepHO 6 6ap;
yqHTbIBasI nOTepH B TPy6ax, 06bIqHO BbI6HpalOT KOMnpeccoplfYlO YCTaHOBKY, 06ec-
neQHBalO:rnyIO ,naBJIeHHe 7 6ap.
THOLl KOMopeccopoB
. KOMnpeccopbI 06'beMHOrO THna: B03.ayx C)KHMaeTCll npH COKpalI(eHHH 06'be-
Ma, co,nepxalI(ero B03,nyx npH aTMoc<pepHOM ,naBJIeHHH (HanpHMep, nopillHe-
BbIe KOMnpeccopbI - nopillHeBoro IDIH ,nHa<pparMeHHoro THna; pOTanHOH-
HbIe KOMnpeccopbI - illH6epHbIe, illecTepeHHbIe, BHHTOBbIe). IIIecTepeWIa-
TbIe KOMnpeccopbI (PyTca).
. ,l(HHaMlNeCKHe KOMnpeccopbI: C)I(aTHe ,nocTHraeTcll npe06pa30BaHHeM CKO-
pOCTH BcaCbIBaeMoro B03,nyxa B ,naBJIeHHe (HanpHMep, ueHTP06eXHbIe KOMn-
peccopbI - TYP60KOMnpeccopbI C BpalI(alOlI(HMHCll JIOnaTKaMH, oceBbIe KOM-
npeccopbI).
qTO KacaeTCll ,nHana30HOB npOH3Bo,nHTCJIbHOCTH H ,naBJIeHIDI, pa3JIHQHbIe THnbI
KOMnpeccopOB QaCTHQHO COBnanaIOT. ECJIH TPe6yeTcll OQeHb BbICOKoe ,naBJIeHHe,
BllJIOTb ,no 1000 6ap, HCnOJIb3yIOTCll nopillHeBbIe KOMnpeCCOpbI. nJIaCTHHQaTbIe
KOMnpeccopbI HCnOJIb3yIOTCll npH cpe,nHHX ,naBJIeHIDIX, BllJIOTb ,no 7 6ap, eCJIH ,no-
CTaTOQHO HH3KOH npOH3Bo,nHTeJlbHOCTH. IIIecTepeWIaTbIe KOMnpeccopbI HCnOJIb3Y-
IOTCll npH 60JIbillHX 06'beMax H HH3KOM ,naBJIeHHH, ,no 1 6apa.
Pa3MepLI
KOMnpeccopbI npOMbIWJIeHHOrO Ha3HaQeHIDI MO)KHO KJIaCcH<pHUHpoBaTb CJIe-
,l(yIOII(HM 06pa30M:
MaJIbIe - ,n;o 40 JIfc
Cpe,nHHe - OT 40 ,no 300 JIfc
60JIbillHe - CBbIille 300 JIfc
KOMopeccopuLle CTaHQHH
B 3aBHCHMOCTH OT npHJIOXeHHH pa3JIHQalOT TPH BH,n;a cTaHUHH:
. nepeHocHbIe: paCnbIJIeHHe KpaCKH, HaKaQHBaHHe B03,nYXOM illHH H T.,n.
5.6. CucmeMbl o6oeMHou nepeoaltu 471
. Ilepe,nBIDKHbIe: nHeBMo6ypbI/nep<popaTopbI, lpaM6oBKH, aBapHHHbIe pe3epB.
Hble arperaTbI H T.,n.
. CTal(HOHapHbIe: CTaHKH, 3aBo,nbI, MeXaHHqeCKHe MaCTepCKHe H T.,n.
nepBII'IHhle HCT01fHHKH 3HepfHH
,[LJm no.rryqeHIDI 3<p<peKTHBHOH H 3KOHOMHqHOH no,naqH B03,IJ;yXa BIDKeH npa.
BHJIbHbIH BbI60p nepBINHOrO ,nBHraTeIDI. MCnOJIb3yIOTCll lpH OCHOBHbIX THna
3JIeK'rpo,nBHraTeJIH npHMeIDIIOTCll TaM, r,ne lpe6yIOTCll KOMnaKTHOCTb H npOCTOTc
yrrpaBJIeHIDI; ,nBHraTeJIH BHYTPeHHero cropaHIDI (Ha ,nH3eJIbHOM, 6eH3HHOBOM, ra.
30BOM TOllJIHBe) HCnOJIb3yIOTCll ,lJ;IDI nepe,nBIDKHbIX CTaHl(HH, aBapHHHbIX pe3epB-
HbIX arperaTOB HJIH TaM, r,ne 3JIeKlpOCHa6xeHHe OTcyrcTByeT; ra30TYP6HHHbIe ,nBH-
raTeJIH (ra3, nap) MOryr 6bITb BKJIlOqeHbI B o6:rnyro 3HepreTHqecKyIO CHCTeM)
3aBo,na H HCnOJIb30BaTb cymecTByIO:rnyro CHCTeMy no,naqH napa HJIH ra3a.
Cl>aKTOpw, BJlHJlIOJIUle Ha Bw60p KOMnpeccopa
. ,l(aBJIeHHe no,naqH: ,nOJDKHO 6bITb ,nOCTaTOqHbIM ,lJ;IDI Bcex cymecTByIOlI(HX 11
nOTeHl(HaJIbHbIX 1'pe60BaHHH. ECJIH cymecTByIOT oco6bIe lpe60BaHIDI K 60JIb-
lliOMY o6'beMy HJIH npH BbICOKOM, HJIH npH HH3KOM ,naBJIeHHH, .rryqllie YCTa-
HaBJIHBaTb ,lJ;IDI 3THX l(eJIeH OT,neJIbHbIe arperaTbI.
. IlpoH3Bo,nHTeJIbHocTb: CJIe,nyeT no,nCqHTaTb He TOJIbKO cpe,nHee nOTpe6JIeHHe
B03,IJ;yXa, HO TaIOKe H MaKCHMaJIbHbIe He3aMe,lJ;JIHTeJIbHbIe lpe60BaHHll, Ha-
npHMep l(HJIHH,lJ;pbI C 60JIblliHM BHYTPeHHHM ,nHaMelpOM H nHeBMo,nBHraTe-
JIH, pa60TalOII(He Ha 60JIblliHX CKOpOCTllX. Onpe,neJIHTe K03<P<PHl(HeHT HC-
nOJIb30BaHIDI. qacTo nOJIb30BaTeJIH Hepa36opqHBO ,no6aBIDIIOT MarHClpaJIM
no,nBo,na K yxe cymecTByIOlI(HM H BbInycKalOT B03,nyx.
. IloJIo)KeHHe B03,IJ;yX03a6opHHKa: ,lJ;IDI MaKCHMaJIbHOH 3<p<peKTHBHOCTH BcaCbI-
BaeMbIH B03,nyx ,nOJDKeH 6bITb HaCKOJIbKO B03MO)KHO qHCTbIM H XOJIO,nHbIM.
. BcaCbIBalOII(He <pHJIblpbI: BbICOKOMOII(HbIe, qTo6bI 3anep)I{HBaTb a6pa3HBHbIe
MaTepHaJIbI, KOTopbIe MOryr npHBeCTH K 6bICTpOMy H3HOCY.
. KaqeCTBO B03,nyxa: M3yqHTe Tpe60BaHIDI K KaqeCTBY B03,IJ;yXa BO BceH CHCTeMe
HJIH Ha BceM 3aBo,ne. ,l(OJDKHO 6bITb npaBMJIbHO onpe,neJIeHO COqeTaHHe nHeB-
MocenapaTopOB, BTOPHqHbIX OXJIanHTeJIeH (YCTaHaBJIHBaeMbIX nOCJIe KOMn-
peccopa), BbIXO,nHbIX <pHJIbTPOB H BJIarOOT,neJIHTeJIeH. Ilpo6JIeMa 06e3B0)l(l1-
BaHIDI He ,nOJDKHa OCTaBaTbCll <pHJIblpaM B03,IJ;yXOBO,nOB, CBll3bIBalOII(HM
KOHKpeTHbIH 3aBO,n HJIH CHCTeMy.
. Pe3epBHasI MOII(HOCTb: qTO npOH30H,neT B Henpe,nBM.neHHbIX aBapHHHbIX CHTY-
al(IDIX HJIH eCJIH OT,neJIbHbIe KOMnpeccopbI nOlpe6yIOT TeXHHqeCKOrO o6c.rry-
)l{HBaHIDI.
. B03,IJ;yXOc60pHHK: CHCTeMa ,noJDKHa HMeTb cooTBeTcTByIOlI(He xapaKTepHCTH-
KH HaKOllJIeHIDI, He TOJIbKO qTo6bI y,nOBJIeTBOpllTb lpe60BaHIDI, HO TaIOKe
qTo6bI rapaHTMpOBaTb 3<p<peKTHBHyIO pa60TY nepBHqHOrO ,nBHraTeIDI.
. IlponycKHasI cnoco6HOCTb nHeBMaTHqeCKOH ceTH: KOJIbl(eBOH MarHClpaJIb-
HbIH Tpy6onpOBO,n C 60JIblliHM BHYTPeHHHM ,nHaMelpOM ,neHcTByeT KaK no-
JIe3HbIH pe3epByap, YMeHbmaeT nepenanbI ,naBJIeHHll H TeKYlI(He pacxo,nbI.
CTOHMOCTb B03,IJ;yXOBo,na 60JIbllierO ,nHaMeTpa COCTaBIDIeT MarryIO qaCTb OT
3alpaT Ha YCTaHOBKY.
HCTOQHHK: CTpaHHQa 26 BFPA data book.
Dla8a 5. MexaHU.,eCKue nepeiJa.,u
5.6. 19. p,sHHble ,qJJR psclfeTos o6heMHoif rff.qponepeASlfJf
(Ts6nffLCbl If KoacpcpffLtffeHTbl nepeclfeTs
S nHesMsTffKe)
Ta6JIHUbI Ha 3TOH H nOCJIe,nyIOII(HX CTPaHHUax MOryT nOMOqb OTBeTHTb Ha qaCTO
B03HHKalOII(He B nHeBMaTHKe BonpOCbI, CBll3aHHbIe C KaqeCTBOM ,lJ;HHaMlNeCKHX H
H3rH6alOII(HX YCHJIHH Ha UHJIHH,lJ;pe, pacxo,ne B03,nyxa, IIJIIOC KJlanaHbI H CMa3Ka.
Ka1feCTBO B03 a
CTaH,lJ;apT ISO 8573-1 onpe,neIDIeT KJIaCCbI KaqeCTBa C)KaTOrO B03,nyxa. Knacc
KaqeCTBa CKJlanbIBaeTCll H3 KOHIq>eTHoro MaKCHMaJIbHO ,nonycTHMoro co,nep)KaHIDI
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32 12 0,00563 0,00484 0,01047
40 16 0,00880 0,00739 0,01619
50 20 0,01374 0,01155 0,02529
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80 25 0,03519 0,03175 0,06694
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125 32 0,08590 0,08027 0,16617
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BFPA/P3 1995 BFPA/P53 2002
BFPA/P4 1986 BFPA/P54 2003
BFPA/P5 1999 BFPA/P55 1993
BFPA/P7 2004 BFPA/P56 2004
BFPA/P9 1992 BFPA/P57 1993
BFPA/P12 1995 BFPA/P58 2003
BFPAlP13 1996 BFPA/P59 1993
BFPA/P22 2003 BFPA/P60 1994
BFPA/P27 1993 BFPA/P61 1998
BFP/P28 1994 BFPA/P65 1995
BFPA/P29 1987 BFPA/P66 1995
BFPA/P41 1995 BFPA/P67 1996
BFPA/P44 1995 BFPA/P68 1995
BFPA/P47 2004 BFPA/P83 2003
BFPA/P48 1998 BFPA/P95 2003
BFPA/P49 1995 BFPA/PI00 2003
BFPA/P52 1997 BFPDA/D2 1994
HCTOQHHK: CTpaHHQa 26 BFPA data book.
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6. 1.4. npOlfHOCTb npJf y,qape: y,qapHaSl BSl3KOCTb
3TO cnoco6HOCTb MaTepHaJIa npOTHBOCTOHTb pa3pymeHHIO npH y,n;ape. ECJIH MaTepH-
aJI pa36HBaeTcH Ha KYCKH, TO OH xpyrrKHH (HanpHMep, CTeKJIO). ECJIH MaTepHaJI He
pa36HBaeTCH, no,n;BepraJICb y,napHOH HarpY3Ke, TO OH 3JIaCTHQHbIH (HanpHMep, pe3H-
Ha). Y,n;aponpOQHOCTb (y,n;apHyIO BH3KOCTb) He CJIe,nyeT rryraTb C npOQHOCTblO. JII060H
MaTepHaJI, B KOTOpOM He npOHcxo,n;HT pacnpOCTPaHeHIDI TPeIUHH no nOBepXHOCTH
MH npOHcxo,n;HT TOJIbKO B orpaHWIeHHOH CTeneHH, Ha3bIBaeTCH y,n;aponpOQHbIM.
F - YAapHaH HarpY3Ka
THCKH
BH3KOCTb: MaTepHal1
crH6aeTCH npH YAape
6. 1.5. YnpyrocTb
3TO crroco6HOCTb MaTepHaJIa ,n;e<p0pMHpoBaTb-
CH rro,n; HarpY3KoH H B03BpaJnaTbCH K rrepBOHa-
qaJIbHbIM pa3MepaM H <popMe rrOCJIe YCTPaHe-
HIDI HarpY3KH. TaKHe MaTepHaJIbI Heo6xo,n;HMbI
,lJ)UI H3fOTOBJIeHIDI rrpyxHH (CM. Ha pHcYHKe).
6. 1.6. nnaCTJflfHOCTb
CBOHCTBO, rrpHMO rrpOTHBOrrOJIO)KHoe yrrpyrOCTH.
MMeHHO TaK peafHpyeT Ha HarpY3KY MaTepHaJI,
eCJIH HarpY3Ka rrpeBbICHJIa rrpe,n;eJI efO yrrpyrOCTH.
IIo,n; HarpY3KoH, rrpeBbIwalOJneH 11', KOTOpaJI BbI-
3bIBaeT yrrpyrHe ,ne<popMaUHH (T.e. rrpeBbIwalOJneH
rrpe,n;eJI yrrpyrOCTH), MaTepHaJI, 06JIa;:J:aIOJnHH IIJIac-
TWIHOCTblO, ,n;e<p0pMHpyeTcH Heo6paTHMo. OCTa-
TOqHaJI ,n;e<popMaUIDI CTaHOBHTCH rrpHqHHOH TOfO,
qTO MaTepHaJI He BOCCTaHaBJIHBaeTCH rrOCJIe YCTPa-
HeHIDI HarpY3KH.
6. 1. 7. BSl3KOCTb
6.1. MexaHUqeCKUe C80ucm8a 479
06pa3eLl
CJt3--TIiICKIiI
XPynKocTb: MaTepHal1 pa3pywa-
eTCH (pa36HBaeTCH) npH YAape
F
-+- I :s:
- - ill
Ao nOA nOCl1e
HarpY3KH HarPY3KH CHHTH
HarpY3KH
F
3TOT TepMHH HCrrOJIb3yeTcH, KOf,n;a IIJIaCTHqeCKaJI ,n;e<popMaUIDI B03HHKaeT B pe3Y-
JIbTaTe rrpHJIOXeHIDI paCTHfHBalOJneH HarpY3KH. BH3KHe MaTepHaJIbI COqeTalOT B
ce6e CBOHCTBa IIJIaCTHqHOCTH H rrpOqHOCTH
(rrpOqHOCTH Ha pa3pbIB), rr03TOMY HX MOX-
HO paCTHfHBaTb HJIH BOJIOqHTb, rrpH,n;aBaJI
HM <p0PMY, H OHH coxpaIDIT 311' <POPMY,
KOf,n;a ,n;e<popMHPYlOJnaJI CHJIa rrepeCTaHeT
,neHCTBOBaTb. HarrpHMep, rrpH BOJIOqeHHH
rrpOBOJIOKH OHa YMeHbwaeTCH B ,nHaMe1'pe
rrpH rrpOTHfHBaHHH ee qepe3 BOJIOKY.
-Q
Ao nOA nOCl1e
HarpY3KH HarpY3KH CH THH
HarpY3KH
MaTepHal1,
nOAQalOl1I.HHCH
o6pa6oTKe
B0110Ka
n pOB0110Ka
F
.
HanpaBl1eHHe
BOl1o...eHH
F - npH110)KeHHaH CHl1a (BbITH)KeHHe)
rAa8a 6. MalUuHocmpoumeJlbHble MamepUOIlbl
3TO cnoc06HoCTb MaTepHaJIa npOTHBO-
CTOHTb :QapanHHaM (cTHpaHHIO) HJIH B,n;aBJIH-
BaHHIO ,n;pyroro TBep,noro TeJIa. 3TO nOKa3a-
TeJIb H3HOCOCTOHKOCTH MaTepHaJIa.
npo:QeccbI, KOTopbIe YBeJIHqHBalOT TBep-
,nOCTb MaTepHaJIOB, TaIOKe YBeJIHqHBalOT HX
npe,neJI npOqHOCTH Ha pa3pbIB. B TO xe
BpeM.SI y,n;apHaH BH3KOCTb MaTepHaJIa YMeHb-
maeTCH, H OH CTaHOBHTCH 60JIee xpynKHM.
npOKaJIHBaeMOCTb He CJIe,n;yeT rryraTb C
TBep,n;OCTblO. npOKaJIHBaeMOCTb - 3TO cnoc06HOCTb MeTaJIJIa pearHpOBaTb Ha npo-
:Qecc TepMo06pa60TKH 3aKaJIKoit ,[LrnI 3aKaJIKH rOpHqHH MeTaJIJI ,n;OJDKeH 6bITb ox-
JIIDK,L(eH CO COpOCTblO, nepeBbImalOJneH KpHTWIecK}'IO CKOpOCTb OXJIIDK,L(eHIDI. no-
CKOJIbKY JII060H MaTepHaJI OXJIIDK,L(aeTCH Ha
nOBepXHOCTH 60JIee 6bICTPO, qeM B cepe,n;HHe,
CYIUeCTByIOT orpaHHqeHIDI Ha pa3Mep 6pyc-
Ka, KOTOpbIH MoxeT ,nOCTaTOqHO 6bICTPO ox-
JIa;:J:HTbCH B :QeHTpe, qT06bI ,n;OCTHrHYTaR
TBep,n;OCTb 6bIJIa O,n;HOpO,n;HOH no BceH rJIy6H-
He. 3TO :KpHTHqeCKOe CeqeHHe MaTepHaJIa.
qeM 60JIbme npOKaJIHBaeMOcTb, TeM 60JIbme
KpHTHqeCKOe CeqeHHe MaTepHaJIa.
6. 1.8. KOSKOCTb
I F 06)ICHMKa A11R 3aKJ1e-
f nOK Q>opMHpyeT rOI1OB-
KY 3aKJ1enKH, npHl1araR
C)lCHMalOl1I.YIO HarpY3KY
KnenanbHaR nOAAep)IC-
Ka YAep)ICHBaeT 3aKl1e-
nO'"lHYIO r0110BKY
F - npHl10)ICeHHas:l CHl1a (C)lCaTHe)
6. 1.9. Tsep,qocTb
3aAaHHaR HarpY3Ka
TBepAbl wapHK
cnblTbiBaeMbI
MaTepHal1
TBepAbl MaTepHan -
He6011bwoe yrl1y611eHHe
Ta )ICe caMaR 3aAaHHaR
HarpY3Ka
MRrKH MaTepHal1: 6011bwee yr-
l1y611eHHe npH TO )ICe HarpY3Ke
3TOT TepMHH HCnOJIb3yeTcH, Kor,n;a IIJIac-
THqeCKaH ,ne<popMa:QIDI B03HHKaeT B pe3YJIb-
TaTe npHJIOXeHIDI C)l{HMalOJneH HarpY3KH.
KOBKHe MaTepHaJIhI COqeTalOT B ce6e CBOHCT-
Ba IIJIaCTHqHOCTH H C)l{HMaeMOCTH, TaK qro
HM MO)J{HO npH,n;aTb <POp MY cxaTHeM B npo-
:Qecce TaKHX onepa:QHH, KaK KOBKa, npOKaTKa
H KJIenKa.
6. 1. 10. HcnblTaHJfe Ha paCTSlJlCeHJfe
McnbITaHHe Ha paCTIDKeHHe mHpOKO npHMeIDIeTCH ,l(JIH onpe,neJIeHIDI npOqHOCTH H
BH3KOCTH MaTepHaJIa. McnbITaHHe BKJIlOqaeT B ce6H HarpyxeHHe CTaH,n;apTHOro 06-
pa3:Qa B oceBOM HanpaBJIeHHH, KaK nOKa3aHO Ha pHCYHKe. HarpY3Ka MeXaHHqeCKH
HJIH rH,n;paBJIHqeCKH YBeJIHqHBaeTCH C nOCTOHHHOH CKOpOCTblO. ,[LrrHHa 06pa3:Qa
YBeJIWIHBaeTCH ,no Tex nop, nOKa OH, HaKOHe:Q, He pa3pymaeTCH. npH TeCTHpOBa-
HHH 06pa3e:Q 3aKpelIJUIeTCR B 3aXB3TbIBalOJneM npHcnoc06JIeHHH C 060HX KOH:QOB,
6.1. MeXaHUqeCKUe C80ucm8a 48
PSAHYC r
nl1oa.u.aAb nonepe"tHoro Ce'"leHHSI A
F
--.d
F
.
.
Lo
6aaoBaR A11HHa
F - npH110>KeHHaR HarpyaKc
Lc
MHHHMal1bHaR AJlHHa
HI1HHAPH'"IeCKO '"IaCTH
qTO 06eCneqHBaeT npHJIOXeHHe HarpY3KH TOJIbKO no O,n;HOH OCH H npe,n;OTBpaJnaeT
H3rH6. Y,l(JIHHeHHe H3MepHeTCH OTHOCTHTeJIbHO 6a3bI (6a30BOH ,l(JIHHbI). HaMeTP
cpe,n;HeH qaCTH 06pa3:Qa YMeHbmeH, KaK nOKa3aHO Ha pHCYHKe, qT06bI rapaHTHpo-
BaTb, qTO pa3pbIB npOH30H,n;eT B npe,neJlax 6a30BOH ,l(JIHHhI.
Pe3YJIbTaTbI HcnhITaHIDI npe,n;CTaBJIeHhI Ha rpa<pHKe B pa3,n;eJIe 6.1.11; 06hIqHO
npHJIOXeHlfYIO HarpY3KY oT06pIDKalOT Ha rpa<pHKe no BepTHKaJIH, a pe3YJIbTHPYI<>-
Jnee Y,l(JlHHeHHe - no ropH30HTaJIH. TOqHO TaK xe Ha rpa<pHKe 3aBHCHMOCTH ,n;e-
<popMa:QHH OT HanpIDKeHIDI HanpIDKeHHe oT06pIDKaeTcH no BepTHKaJIH, a pe3YJIbTH-
PYI<>JnaJI ,ne<popMa:QIDI - no ropH30HTaJIH. ,[LrnI ,n;aHHoro 06pa3:Qa MO)J{HO nocTPo-
IITb aHaJIOrHqHble KpHBhIe. CooTHomeHHe Me)J{,ll;Y HanpIDKeHHeM H ,n;e<popMa:QHeH:
HanpIDKeHHe = HarpY3Ka
nepBOHaqaJIbHaH IIJIOJna;:J:b nOnepeqHoro CeqeHHH
IT I'h YBeJIHqeHHe ,l(JIHHbI no,n HarpY3KoH
,L-tee'¥OpMa:QIDI = .
nepBOHaqaJIbHaH ,l])IHHa
Pa3MepbI nponop:QHOHaJIbHbIX 06pa3:QoB (BS EN 10002-1) onpe,n eJUIIOTCH COOT-
HomeHHeM La = 5,65JA. ITOCKOJIbKY A = 1td 2 / 4, TO .,fA = d ( 1t) / 2 = O,886d. ITo-
3TOMY Lo = 5,65 x 0,886 5d. CJIe,noBaTeJIbHO, 06pa3e:Q ,n;HaMe1'pOM 10 MM 6y,n;eT
HMeTb 6a30ByIO ,l(JIHHY 50 MM.
6. 1. 11. HHTepnpeTaLf,lffl IfcnblTaHlffl Ha paCTSlJlCeHlfe:
MaTeplfanbl C BblpaJICeHHblM npe,qenOM TeqlfecTIf
IIoKa3aHHaJI KpHBaH THnlf1:lHa ,l])IH BH3Koro MaTepHaJIa C BblpIDKeHHbIM npe,neJIOM
TeK}'tIeCTH (HanpHMep, OTO)lQl{eHHaJI HH3KoyrJIepo,n;HCTaH CTaJIb).
HaqaJIbHaJI qaCTb rpa<pHKa OT 0 ,n;o A HBJIHeTCH JIHHeHHOH, TaK KaK MaTepHaJI
npORBJUIeT ynpyrHe CBOHCTBa (3aKoH fYKa). ECJIH CIDITb HarpY3KY B 1I1060H TOqKe
Me)J{,ll;y 0 H A, TO 06pa3e:Q Be pH eTCH K CBoeH nepBOHaqaJIbHOH ,l(JIHHe. BOJIee KPY-
TOH HaKJIOH COOTBeTcTByeT 60JIee xeCTKOMY (Heno,n;aTJIHBoMY) MaTepHaJIY. ToqKY A
Ha3bIBalOT npe,n;eJIOM nponop:QHOHaJIbHOCTH.
B TOqKe A HeKOTopble MaTepHaJIhI MOryr npo,neMOHCTPHpOBaTb BHe3anHoe pac-
illHpeHHe 6e3 COOTBeTCTBYI<> ero YBeJIHqeHIDI HarpY3KJ;f. 3TY TOqKY Ha3bIBalOT npe-
,neJIOM TeK}'tIeCTH, H HanpIDKeHHe npH TeK}'tIeCTH B 3TOH TOqKe Bb}qHCJUIeTCH ,n;eJIe-
HHeM BeJIWIHHbI HarpY3KH Ha nepBOHaqaJIblfYlO IIJIOJna;:J:b nOnepeqHOrO CeqeHIDI.
16-3255
Dla8a 6. MalUuHocmpoumeJlbHble MamepUOIlbl
:J: ):5: I
o :5:
('t)X 1
I ('O I
1::>0.
0. 0
I::-e-
> I
I .. 0611aCTb nl1aCTH"'IeCKHX Ae<l>opMa Hi1I _ ,
PaBHoMepHaSl J1oKal1bHaSl nl1ac-
nl1aCTH"'IeCKaSl TH"'IeCKaSl Aecpop-
AecpopMa HR Ma HR (o6paaoBa-
I HHe wei1lKH)
B
('0
('t)
>
0.
L-
('0
:L
TO"'lKa TeKY"'IeCTH
o
YA/1HHeHHe
..
aJIee 3a TO'lKOH A rpa<PHK yxe He JIHHeHHbIH, nOCKOJIbKY Tenepb MaTepHaJI
npOHBJUIeT CBOHCTBa IIJIaCTHqHOCTH. ECJIH HarpY3KY CIDITb B KaKOH-JIH60 TOqKe 06-
JIaCTH IIJIaCTWIHOCTH, TO yrrpyrWl ,ne<popMa:QIDI BOCCTaHOBHTCH, o,nHaKO IIJIaCTWIHWI
COCTaBJUIIOIUWI ,ne<popMa:QHH coxpaHHTCH, H MaTepHaJI OCTaHeTCH paCTHHYTbIM, T.e.
coxpaHHT OCTaTOqHylO ,n;e<popMa:QHIO.
aJIee 3a TOqKOH B MaTepHaJI Y,l])IHIDIeTCH npH MeHbmeH HarpY3Ke. O,nHaKO
H3-3a JIOKaJIbHOrO YMeHbmeHIDI IIJIOIUa;:J:H nOnepeqHOrO Ce'leHIDI (06pa30BaHIDI
meHKH) HanpIDKeHHe (OTHomeHHe HarpY3KH K IIJIOIUa;:J:H nOnepeqHOrO CeqeHIUI) B
,neHCTBHTeJIbHOCTH YBeJIWIHBaeTCH BIIJIOTb ,n;o npe,n;eJIa npOqHOCTH. HanpIDKeHHe,
BbJqHCJIeHHOe B TOqKe B, Ha3bIBaeTCH npe,n;eJIOM npO'lHOCTH Ha paCTIDKeHHe (HJIH
BpeMeHHbIM COnpOTHBJIeHHeM Ha paCTIDKeHHe) MaTepHaJIa.
BH3KOCTb MaTepHarra onpe,n;eJUIIOT, IIJIOTHO CKJIa;:J:bIBWI BMeCTe 06e nOJIOBHHbI
pa3pymeHHoro 06pa3:Qa H H3MepHH YBeJIHqeHHe ero ,l])IHHbI no cpaBHeHHIO C
nepBOHa'laJIbHOH.
Tor,n;a:
Y (%) YBeJIH'IeHHe ,l])IHHbI 100
,l])IHHeHHe l) = x .
nepBOHaqaJIbHWI ,l])IHHa
npH YCJIOBIDIX 3KCIIJIyaTa:QHH MaTepHaJI HarpyxaeTCH B npe,n;eJIax 06JIaCTH OA.
06bJqHO HarpY3KH He npeBbImalOT 50% 3HaqeHIDI B TOqKe A, qTO n03BOJUIeT
C03,n;aTb 3anac npO'lHOCTH.
6. 1. 12. HHTepnpeTaLf,JfSl IfcnblTaHlfSl Ha paCTSlJlCeHlfe:
ycnoBHblii npe,qen TeKYlfeCTIf
Y MHorHX MaTepHaJIOB OTcyrcTByeT BbIpIDKeHHbIH npe,neJI TeK}'tIeCTH, H BMeCTO Hero
BBO,n;HTCH YCJIOBHbIH npe,n;eJI TeK}'tIeCTH. Y CJIOBHbIH npe,n;eJI TeK}'tIeCTH onpe,n;eJUIeT-
CH YCHJIHeM, KOTopoe He06xo,n;HMO npHJIO)I{HTb, qT06bI nOJIyqHTb 3a;:J:aHHyIO BeJIH-
qHHY IIJIaCTWIeCKOH ,ne<popMa:QHH.
6.1. MeXaHUqeCKUe C80ucm8a 4.
npHMaH BC rrpOBe,n;eHa rrapaJI.1IeJIbHO OA - JIHHeHHOH qaCTH rpa<pHKa, coo'
BeTcTByIDII.J;eH yrrpyrOH 06JIaCTH, TaK qTO rrepeceKaeT KpHByJO 3aBHCHMOCTH Y,l(JIHHC
HIDI OT HarpY3KH B TOqKe C. CMeII.J;eHHe rrpHMoH BC 3a;:J:aeTCH 3apaHee (06bIql]
0,1% HJIH 0,2% 6a30BOH ,l(JIHHbI).
YCJIOBHbIH rrpe,n;eJI TeK}'tIeCTH BbIqHCJUIeTCH KaK HarpY3Ka F} B TOqKe C, ,n;eJIel
HaJI Ha rrepBOHaqaJIbHyID IIJIOII.J;a;:J:b rrOrrepeqHOrO CeqeHIDI Ao. MaTepHaJI y,n;OBJIe1
BopHeT TeXHHqeCKHM YCJIOBIDIM, eCJIH rrOCJIe Toro, KaK K HeM)' rrpHJIOXeHO Harrp.f
xeHHe, COOTBeTCTByJOII.J;ee YCJIOBHOM)' rrpe,n;e.rry TeK}'tIeCTH, a 3aTeM CIDITO, OCTaTO
HaJI ,n;e<popMa:QIDI He rrpeBbImaeT 3a;:J:aHHoe CMeII.J;eHHe.
F 1
t
I
I
I
I
I
I
I
I
I
I
I
I
Y CJIOBHbIH rrpe,n;eJI TeK}'tIeCTH = Fi j Ao.
MO,n;YJIb yrrpyrOCTH = HaKJIOH BC.
Y AlU1HeHHe
..
6. 1. 13. HHTepnpeTBLf,JfSl IfcnblTaHJfSl HB paCTSlJlCeHJfe:
ceqUlJfii Mo,qynb
npH HcrrbITaHIDIX Ha paCTIDKeHHe HeKOTopbIX OqeHb BH3KHX MeTaJI.1IOB, TaKHX KaK
OTO)lQl{eHHaJI Me,n;b H HeKOTopbIe rrOJIHMepbI, 06JIaCTb JIHHeHHOH 3aBHCHMOCTH Ha
rpa<pHKe OTcyrcTByeT, ,n;eMOHCTPHpyJOT 3aBHCHMOCTH, H, CJIe,nOBaTeJIbHO, YCJIOBHbIH
npe,n;eJI TeK}'tIeCTH orrpe,n;eJIHTb HeB03MO)J{H0.
B 3THX CJIyqaJIX 3a;:J:31OT COOTBeTCTByIDII.J;ee pacmHpeHHe (06bIqHO 0,5 % 6a30-
BOH ,l(JIHHbI), H rrpe,neJI TeK}'tIeCTH orrpe,n;eJUIIOT KaK HarpY3KY, BbI3bIB31OIUYIO rrOJI-
Hoe pacmHpeHHe 0,5% 6a30BOH ,l(JIHHbI, ,n;eJIeHHyID Ha rrepBOHa'laJIbHyID IIJIOII.J;a;:J:b
nOrrepeqHOrO CeqeHIDI AO.
,[LrnI orrpe,neneHIDI yrrpyrOCTH MaTepHaJIa BMeCTO MO,nyJUI yrrpyrOCTH B TaKHX
c.rryqaHX HCrrOJIb3yeTcH ceKYII.J;HH MO,ZJ;yJIb.
F 1
t
co
('f)
a.
L-
eo
:J:
npe,n;eJI TeK}'tIeCTH Fi j Ao.
CeKYII.J;HH MO,nYJIb (Lo j Ao)S,
r,n;e S = OAjOB.
YA/1HHeHHe
..
rAa8a 6. MalUuHoCmpOUmeJlbHble MamepUOIlbl
6. 1. 14. HcnblTaHlfe Ha y,qapHYIO BSl3KOCTb: no H30,qy
B HcnbITaHHH no M30,ny HCnOJIb3YI<>T 10-MHJlJIHMeTPoBbIH KBa;:J:paTHbIH HcnbITa-
TeJIbHbIH 06pa3el( C Ha;:J:pe30M. OH 3aKpeIIllileTCH KaK KOHCOJIb B THCKax HcnbITa-
TeJIbHOH MamHHbI H no HeMY HaHOCHT y,n;ap C KHHeTWIeCKOH 3HeprHeH 162,72
IIPH CKOpOCTH 3,8 M/c. 3HeprIDI, nOrJIO eHHasI npH ,n;e4>opMa:QHH MH pa3py-
meHHH HcnbITaTeJIbHOrO 06pa3:Qa, - y,n;apHaJI npOQHOCTb (noKa3aTeJIb BH3KOCTH).
BS 131 (MeTaJI.1IbI), BS 2782-350 (IIJIaCTMaccbI).
cnbITaTel1bHbl
o6paae
50
PaaMepbl B MM
m o
T.
PSAHYC OCHOBaHHSI
HSApeaa 0,25
Cl>parMeHT
MeCTa
HRHO
CeL.leHHe HcnblTa-
Tel1bHoro o6paa-
a no paapeay
6. 1. 15. HcnblTaHlfe Ha y,qapHYIO BSl3KOCTb: no Wapnlf
B HcnbITaHHH no illapnH 10-MHJlJIHMeTPOBbIH KBa;:J:paTHbIH HCnbITaTeJIbHbIH 06pa-
3e:Q 3a:KpeIIllileTCH KaK 6aJIKa H no HeM)' HaHOCHT y,n;ap C KHHeTWIeCKOH 3HeprneH
298,3 Ax Ha CKOpOCTH 5 M/c. 3HeprIDI, nOrJIO eHHaJI npH H3rH6e MH pa3pymeHHH
HCIThrraTeJIbHoro 06pa3:Qa, - y,n;apHasI npo1ffiOCTh (noKa3aTeJIb BH3KOCTH). BS EN 10045
(MeTaJI.1IbI), BS 131-6 H BS 131-7 (MeTaJlJIbI), BS 2782-359 (IIJIaCTMaccbI).
PaaMepbl B MM
.10
I W CeL.leHHe HcnblTaTel1bHoro
o6paa a no paapeay
R1.o-1.5
60eK
cnbITaTel1bHbI
o6paae
o
J-C sor5 U-06pasHbI.;1 HaApea
R1.0
-==r or 5 HaApea B cj>OpMe WnOHO"lHOrO naaa
R 1.0
\! r 9.?2 O
. _ __ ..r-0 V-06paaHbI.;1 HaApeS
R1.0
CTaHAapTHble HSApeabi no WapnH
6.1. MeXaHUlf,eCKUe C80ucm8a 48,
6. 1. 16. HHTepnpeTaLf,JfSl pe3ynbTaToB JfCnblTaHJfSl
Ha y,qapHYIO BSl3KOCTb
XpynKHe MeTaJIJlbI. nOJIHbIH pa3pbIB npH He60JIbmOM YMeHbmeHHH IIJIOJna;:J:H none
peqHOrO CeqeHIDI. nOBepXHocTb H3JIOMa BbIrJUl):(HT KaK 3epHHCTaJI cTPYKTYPa.
BJl3KHe MeTaJIJlbI. M3JIOM HepoBHbIH H BOJIOKHHCTbIM. B O'leHb BH3KHX MeTaJIJIa
nepeJIOM MoxeT 6bITb He nOJIHbIM: HcnbITaTeJIbHaJI qaCTb H30rHeTCH H npo,n;eMOH
cTpHpyeT TOJIbKO He60JIbmOH pa3pbIB OT Ha;:J:pe3a. TaIOKe 6y,n;eT HeKOTopoe YMeHb
meHHe IIJIOJna;:J:H nOnepeqHOrO CeqeHHH 06JIaCTH B MeCTe nepeJIOMa MH H3rH6a.
XpynKHe nOJIHMepbI. Pa3pbIB nOJIHbIH, nOBepXHOCTb H3JI0Ma rJIa;:J:KaR, CTeKJIO
BH,lJ;HaR, C HeKOTopbIM paCJ.,UeIIJIeHHeM.
nJIaCTIfIIHble nOJIHMepw. He cyrueCTByeT xapaKTepHOrO BH,n;a H3JI0Ma, eCJIH 01
Bo06Jne npOHcxo,n;HT. 3Ha'lHTeJIbHOe YMeHbmeHHe IIJIOJ.,Ua;:J:H nOnepe'lHOrO Ce'leHH.5
06JIaCTH H HeKoTopbIH pa3pbIB B MeCTe Ha;:J:pe3a.
PacnpOCTpaHeHHe TpeUUlH. nOCKOJIbKY B HcnbITaHIDIX H no M30,n;y, H no illapnl
npHMeIDIIOTCH Ha;:J:pe3bI HcnbITaTeJIbHbIX 06pa3:QOB, MoxeT 6bITb nOnytleHa nOJIe3.
HaJI HH<!>opMa:QIDI OTHOCHTeJIbHO COnpOTHBJleHIDI MaTepHaJIa K pacnpOCTPaHeHHK
1'peJnHH. TaKaJI TPeJnHHa MoxeT B03HHKHYTb B TO'lKe KOH:QeHTPal(HH HanpIDKeHID
H YKa3bIBaeT Ha He06xo,n;HMOCTb H36eraTb OCTPbIX yrJIOB, no,npe30B, He3anHbIx H3-
......
MeHeHHH CeqeHHH H CJIe,n;OB 06pa60TKH.
6. 1. 17. Onpe,qeneHJfe TBep,qocTIf no 6plfHennlO
B 3TOM TeCTe xeCTKHH CTaJIbHOH mapHK B,naBJIHBaeTCH B nOBepXHOCTb TecTHpyeMOJ;
IIJIaCTHHbI, HCnOJIb3YH 3a;:J:aHH)'IO HarpY3KY. KOM6HHa:QIDI HarpY3KH H ,n;HaMe1'pc:
mapHKa ,n;OJDKHa COOTHOCHTbCH C TecTHpyeMbIM MaTepHaJIOM BO H36exaHHe no-
Bpe)J{,ll;eHIDI. )l(ecTKocTb l'eCTHpyeMoH IIJIaCTHHbI CJIe,n;yeT orpaHHqHTb Hb = 500, E
npOTHBHOM cnytlae mapHKoBbIH HaKOHeqHHK 6y,n;eT CTPeMHTbCH BbIpOBIDITbCH 11
BHeceT omH6KH (BS 240).
HarpY3Ka P
=k
D2 '
cnbITa-
Tel1bHblH
o6pa3e
r,n;e P - HarpY3Ka (lIT); D - ,nHaMe1'p HH,n;eHTepB
(MM); k = 30 ,lWI qepHbIX MeTaJIJIOB, k = 10 ,lI;.ID]
Me,nH H Me,nHbIX CIIJIaBOB, k = 5 ,lWI aJIlOMHHIDI 11
aJIlOMHHHeBbIX CIIJIaBOB, k = 1 ,lWI CBHH:Qa, OJIOBa,
6a66HTa.
HarpY3Ka
3HaqeHHe TBep,n;OCTH (H b ) =
c<!>epHqeCKaJI IIJIOJna;:J:b B,naBJIHBaHHH
P
-
1t(D / 2)[D - (D2 - d 2 )]
rAa8a 6. MalUuHocmpoumeJlbHble MamepUOIlbl
6. 1. 18. Onpe,qeneHJfe Tsep,qOCTJf no BJfKKepcy
npH 3TOM H3MepeHHH HCnOJIb3yeTcH aJIMa3HbIH HaKOHe'lHHK B <popMe npaBHJIbHOH
qeTbIpexrpaHHoH nHpaMH,lJ;bI C yrJIOM 136 0 Me rpaIDIMH. nOCKOJIbKY TBep,nOCTb
aJIMa3a no BpHHeJIJIIO paBHa 6000 HB, 3TO H3MepeHHe nO,l(Xo,n;HT ,n;IDKe )LJUI OqeHb
TBep,n;bIX MaTepHaJIOB. MCnOJIb3yeTcH TOJIbKO O,n;HH pa3Mep HaKOHeqHHKa, a HarpY3-
Ka BapbHpyeTCH. CTaH,n;apTHbIe HarpY3KH - 5, 10, 20, 30, 50 H 100 lIT. BMecTe c
'IHCJIOM TBep,n;OCTH no BHKKepcy He06xo,n;HMO YKa3bIBaTb TeCTOByJO HarpY3KY (Ha-
npHMep, H D (50) = 200).
D 2
p
3HaqeHHe TBep,nOCTH H D = 1,844 -,
D2
r,ne P - HarpY3Ka (lIT); D - )VIHHa HaKOHe'lHHKa no ,nHaro-
HaJIH (cpe,n;IDUI).
BS 427, BS EN 23878 (TBep,n;bIe CIIJIaBbI), BS 411-6 (Me-
TaJIJIWIeCKHe nOKpbITIDI),BS 6479 (noBepXHocTHo-yrrpOqHeH-
HbIe CTaJIH), BS 6481 (CTaJIb H HoHHO-BaKYYMHOH
BbIIIJIaBKH, ra30IIJIaMeHHOe nOKpbITHe H 3aKaJIeHHbIe CTaJIH,
BbIIIJIaBJIeHHbIe B H HOHHOH neqH), DD ENV 843-4
(MOHOJIHTHaJI KepaMHKa).
D 1
D 1 + D 2
D=
2
nOs:lBneHHe
yrny6neHHR
6. 1. 19. Onpe,qeneHJfe Tsep,qOCTJf no POKsenny
IIpH 3TOM H3MepeHHH HCnOJIb3yeTcH HJIH mapHK H3 3aKaJIeHHOH CTaJIH)LJUI 60JIee
M.SIrKHX MaTepHaJIOB, HJIH 120 0 aJIMa3HbIH KOHYCHbIH HaKOHeqHHK)LJUI 60JIee TBep-
,n;bIX MaTepHaJIOB. npH HcnbITaHHH cpaBHHBaeTCH pa3JIHqHe no r.rry6HHe npOHHKHO-
BeHIDI no,n; B03,n;eHcTBHeM npe,n;BapHTeJIbHOH HarpY3KH (98 H) H OCHOBHOH HarpY3-
KH. Pe3YJIbTaT H3MepeHIDI CqHTbIBaeTCH Henocpe,nCTBeHHO co mKaJIbI MamHHbI.
H R = E - e,
r,n;e E - KOHCTaHTa, 3aBHCHJnaJI OT HCnOJIb3yeMoro HaKOHeqHHKa; e - coxpaIDIIO-
JneeCH YBeJIHqeHHe rJIy6HHbI npOHHKHOBeHHR, 06YCJIOBJIeHHOe npHJIOXeHHeM
OCHOBHOH HarpY3KH
illKaJla HaKOHe'IHHK
OCHOBHaJI
HarpY3Ka, ill
llpHMeHeHIUI
A 120 0 aJIMa3HbIH KOH)'C-
HbIH HaKOHeqHHK
0,59
C 128 0 aJIMa3HbIH KOH)'C-
HbIH HaKOHe1.JHHK
1,47
JIHCTOBasI CTaJIb; fIOBepXHOCTHO yrrpOq-
HeHHble KOMfIOHeHTbI Her.rry6oKoro JIem-
pOBaHIDI
Me,nHble ClUIaBbI, aJIIOMHHHeBble ClUIaBbI,
OTO)l{)J{eHHbIe HH3KoyrJIepo,nHCTble CTaJIH
MCfIOJIb3yeTcH HaH60JIee mHpOKO; 3aKa-
JIeHHble CTaJIH; qyryHbI; r.rry6oKo yrrpOq-
HeHHble KOMfIOHeHTbI
TOHKHe, HO TBep,nbIe CTaJIH; KOMfIOHeHTbI
yrrpOqHeHHbIe Ha cpe,nHIOIO r.rry6HH)'
B map, 0 1,588 mm
0,98
D 120 0 aJIMa3HbIH KOH)'C-
HbIH HaKOHeqHHK
0,98
IDUJla HaKOHeqHHK
OCHOBHaJI
HarpY3Ka, ill
E map, 0 3,175 mm
0,98
F map, 0 1,588 mm
0,59
G map, 0 1,588 mm
1,47
H map, 0 3 175 mm
0,59
K map, 0 3,175 MM
L map, 0 6,350 MM
M map, 0 6,350 MM
P map, (2) 6,350 MM
R map, 0 12,70 MM
S map, (2) 12,70 MM
V map, (2) 12,70 MM
1,47
0,59
0,98
1,47
0,59
0,98
1,47
6.1. MexaHUlf,eCKUe C80ucm8a 48:
OKOHlf,aHUI
llpHMeHeHU
qyryH; aJIlOMHHHeBble CIDIaBbI; MafHHeBbIe
CIDIaBbI; Do,nmHDHHKOBble MeTaJlJIbI
OTToxeHHbIe Me,nHble CIDIaBbI; TOHKHe
MHfKHe JlHCTOBble MeTaJlJIbI
KOBKHe qyryHbI; <POC<pOpHCTasI 6poH3a;
nymeqHasI 6poH3a; Me,nHO- HHKeJleBbIe
CIDIaBbI H T .,n.
MHfKHe MaTepHaJIbI; BbICOKO <peppHTHble
COJIaBbI; aJIIOMHHHH; CBHHeu; UHHK
AnIOMHHHeBble H MafHHeBble CIDIaBbI
TepMoIDIacTbI
TepMoIDIacTbI
TepMOpeaKTHBHble IDIaCTMaCCbI
OqeHb MHfKHe IDIaCTMaCCbI H pe3HHbI
( -,
6. 1.20. Onpe,qeneHJfe Tsep,qoCTJf no POKsenny
(npJf YMeHbweHHb'x no cpaSHeHJfIO
C 06b'lfHb'MJf HarpY3KaMJf)
B 3TOM HcnbITaHHH npe,n;BapHTeJIbHaJI HarpY3Ka YMeHbmeHa C 98 .no 29,4 H H
OCHOBHaJI (fJIaBHaJI) HarpY3Ka TaIOKe YMeHbmeHa. TaKoH ,n;Hana30H HcnbITaHHH HC-
nOJIb3yeTcH ,n;.JUI H3MepeHIDI TBep,n;OCTH TOHKHX JIHCTOB H <pOJIbfH.
IDUJla HaKOHeQHHK ,lI;onOJlIIII'I'eJIhHaJl CHJla, ill
15-N 120 0 aJIM83HbIH KOH)'CHbIH HaKOHeqHHK 0,14
30-N 120 0 aJIMa3HbIH KOH)'CHbIH HaKOHetJHHK 0,29
45-N 120 0 aJIM83HbIH KOH)'CHbIH HaKOHetJHHK 0,44
15-T map, (2) 1,588 MM 0,14
30-T map, (2) 1,588 MM 0,29
45-T map, (2) 1,588 MM 0,44
BS 5600-4-5 (TBep,n;bIe CIIJIaBbI)
BS 891, 4175 (TBep,n;bIe CIIJIaBbI)
DD ENV 843-4 (MOHOJIHTHbIe KepaMHKH)
BS 2782-365C (IIJIaCTMaccbI).
rAa8a 6. MalUuHoCmpOUmeJlbHble MamepUOIlbl
6. 1.21. CpasHHTenbHafl WKana TsepAocTH
10000
10 AAMa3
5000
2000
1000 80
60
500
110 40
100
100
60
40
20
o
WKana B
POKBel1l1a
20
o
WKana C
POKBel1l1a
KOPYHA 11 }
9 can<1>Hp A30T pOBaHHble CTal1
8 TOna3
} Pe)l(\ll1.\l'Ie I'IHCTpYMeHTbI
} 3aKal1eHHbI AO TBepAOCT
Han l1bH Ka
} MeXaH ...eCK 06pa6aTblBa-
eMble CTal1 (np cnOl1b-
30BaH HHCTpYMeHTOB 3
} 6bICTpope)l(yw.e CTal1 )
J1al)lHHble anIOM H eBbie
cnl1aBbl
80
7 KBap
6 OpTOKna3
5 AnaT T
200
4 ct>11100p T
3 Kanb T
50
20
2 r nc
6011bW HCTBO nl1aCTMacc
10
5
TBepAOCTb
no 6p Hel1l1lO
MaW HOCTpO Tel1bHble
MaTep al1bl
1 Ta11bK
TBepAOCTb no Mocy
CpaBHHTeJIbHbIMH Ta6JIHuaMH H ,nHarpaMMaMH, B KOTOpbIX npHBo,ngTCR qHCJIa
TBep,nOCTH, nOnytleHHbIe pa3JIHqHbIMH MeTO,naMH, CJIe,nyeT nOJIb30BaTbCR OCMOTPH-
TeJIbHO, TaK KaK H3MepeHIDI BbInOJIIDIIOTCR B pa3JIHQHbIX YCJIOBIDIX. HanpHMep:
1. OTHOCHTeJIbHO 60JIbmOH ,nHaMeTp mapHKa (HH,neHTepa) npH onpe,neJIeHHH
TBep,nOCTH no BpHHeJIJIIO H B HeKOTopbIX CnytlaRX npH onpe,n;eJIeHHH TBep,no-
CTH no POKBeJIJIY nepeMem;aeT MeTaJIJI HcnbITaTeJIbHOrO o6pa3ua B pe3YJIbTa-
Te IIJIaCTHQeCKOH ,ne<p0pMaUHH.
2. OCTPbIe pe6pa H OCTPaR BepmHHa aJIMa3HOH nHpaMH;J;bI npH onpe,neJIeHHH
TBep,nOCTH no BHKepcy MOryr «Bpy6aTbcR» B HcnbITaTeJIbHbIH o6pa3eu B pe-
3YJIbTaTe ,ne<popMaUHH c,nBHra.
3. O,nHaKo npH onpe,neJIeHHH TBep,nOCTH no POKBeJIJIy HCnOJIb3yeTcR ,npyrasI
<popMa HH,neHTepa, a HMeHHO aJIMa3HbIH KOHYC C yrJIOM 120°. K TOMY xe
npH 3TOM H3MepeHHH cpaBHHBaeTCR YBeJIHQeHHe r.rry6HHbI npOHHKHOBeHIDI,
npH YBeJIHQeHHH HarpY3KH, Tor,na KaK B n. 1 H 2 06JIaCTb B,n;aBJIHBaHIDI H3-
MepReTCR ,lJ;lliI e,n;HHcTBeHHoH 3a,naHHoH HarpY3KH.
4. Onpe,neJIeHHe TBep,nOCTH C nOMOm;bIO CKJIepOCKOna (no illopy) - 3TO ,nHHa-
MHQeCKOe H3MepeHHe TBep,nOCTH KaK <PYHKUHH ynpyrOCTH. (BoeK C aJIMa3-
HbIM HJIH TBep,n;OCIIJIaBHbIM HaKOHeQHHKOM B <popMe mapHKa HJIH yceQeHHO-
ro KOHYca na,naeT C nOCTORHHOH BbICOTbI Ha nOBepXHOCTb o6pa3ua H TBep-
,n;OCTb no illopy onpe,neJUIeTCR no BbICOTe OTCKOKa. - IIpuMel/,. nep.)
6.2. lfepHble MemaJlllbl U C11Jla8bl 411
6.2. LlepHble MeTannbl M cnnaBbl
6.2. 1. "'epHb,e NleTannw: HenerHposaHHafl
yrnepoAHcTafl CTanb
OCHOBOH qepHbIX MeTaJlJIOB RBJIReTCR XeJIe30, XHMWleCKH 3JIeMeHT, oTHOCRm;HHC
K MeTaJlJIaM (JIaTHHCKoe ferrum - XeJIe30). )l(eJIe30 CBR3bIBaeTCR C yrJIepo,nOM, 06
pa3YR KaK TBep,n;bIH paCTBOp, TaK H XHMHqeCKOe coe,n;HHeHHe Kap6H;J; XeJIe3a (ue
MeHTHT). B c.rryqae qyryHOB HeKOTopoe KOJIWleCTBO yrJIepo,na MoxeT OCTaBaTbCR ,
HeCBR3aHHbIM (cB060,nHbIM) B BH,n;e qeillyitqaTOrO rpa<pHTa. KpoMe yrJIepo,n;a MOry
npHcyrcTBoBaTb TaIOKe H ,npyrHe 3JIeMeHTbI. Co,nepXaHHe oCJIa6mnOm;HX MeTaJIJ
npHMeceH, TaKHX KaK cepa H <poc<pop, CTapaIOTCR CBeCTH K MHHHMYMY. JIerHpyIO'
m;He 3JIeMeHTbI (HanpHMep, XpOM H HHKeJIb) ,n06aBJUIIOT, qT06bI y.rryqillHTb xapaK.
(
TepHCTHKH MeTaJlJIa. '\
HeJIerHpOBaHHbIe yrJIepo,nHCTbIe CTaJIH COCTORT rJIaBHbIM 06pa30M H3 XeJIe3a F
yrJIepo,na; 3TO caMbIe npOCTbIe H3 qepHbIX MeTaJlJIOB. MoxeT TaIOKe npHcyrcTBoBaTI
HeKOTopoe KOJIWleCTBO MapraHua ,l(JUI HeHTpaJIH3aUHH Bpe,nHoro BJIIDIHIDI cepbI 11
y.rryqmeHIDI 3epHHcToH CTPyKTypbI. npH 3TOM ero KOJIHqeCTBeHHoe co,n;epxaHHe
He,nOCTaTOqHO, qT06bI ero MO)I{HO 6billO paCCMaTPHBaTb KaK JIerHpyIOm;HH 3JIeMeHT.
B pa3,neJIe 6.2.2 nOKa3aHO, KaK KOJIHqeCTBO npHcyrCTByIOm;ero B CTaJIH yrJIepo-
,n;a BJIIDIeT Ha ee CBOHCTBa. MaKCHMaJIbHOe co,n;epxaHHe yrJIepo,na, npH KOTOpOM OH
MoxeT OCTaBaTbCR CBR3aHHbIM C XeJIe30M npH Bcex TeMnepaTYPax, COCTaBJUIeT
1,7 %. Ha npaKTHKe BepXHHH npe,neJI 1,2-1,4 % YCTaHaBJIHBaIOT TaK, qT06bI ra-
paHTHpOBaTb 3anac npOqHOCTH. CTaJIb, no onpe,neJIeHHIO, He ,nOIDKHa co,nepxaTb
CB060,nHbIH yrJIepo,n.
HH3KoyrJIepOJnlCTbie CTaJlH
Co,nepxaHHe yrJIepo,na B HHX COCTaBJUIeT 0,1-0,3 % IIJIIOC npHMeCH, IUlIOC HeKO-
Topoe KOJIWleCTBO MapraHua, qT06bI HeHTPaJIH30BaTb BJIIDIHHe JII060ro co,n;epxaHIDI
cepbI, oCTaIOm;eHcR nOCJIe npoueCCOB ee y,naJIeHIDI. TaKHe CTaJIH He MOryr 6bITb no,n;-
BepHyrbI Henocpe,nCTBeHHO TepMo06pa60TKe C ueJIbIO nOBbImeHIDI TBep,nOCTH, HO
OHH JIerKO MOryr 6bITb 3aKOKCOBaHbI H HayrJIepOXeHbI. HaH60JIee HH3KoyrJIepo,nH-
CTbIe CTaJIH 3TOH KaTeropHH, nOCKOJIbKY OHH HMeIOT BbICOKYIO BR3KOCTb, HCnOJIb3Y-
IOTCR ,l(JUI npOH3Bo,nCTBa CTaJIbHbIX JIHCTOB, H3 KOTOpbIX 3aTeM npeCCOBaHHeM H3ro-
TaBJIHBaIOTCR TaKHe KOMnOHeHTbI, KaK naHeJIH KY30Ba aBTOM06RJU1. HaH60JIee HH3-
KoyrJIepO,l1HCTbIe CTaJIH 3TOH KaTeropHH TaIOKe HCnOJIb3yIOTCR ,l(JUI BbITRrHBaHIDI 3a-
roTOBOK ,l(JUI npOBOJIOKH H TPy60K. CTaJIH 3TOH KaTeropHH C 60JIbillHM co,nepxaHHeM
yrJIepo,na, 60JIee xeCTKHe H MeHee BR3KHe, HCnOJIb3yIOTCR ,l(JUI H3rOTOBJIeHIDI CTaJIb-
Horo CopTOBoro npOKaTa, JIHCTOBOro npOKaTa H 6aJIOK (<paCOHHoro npOKaTa) 06lI(ero
Ha3HaQeHIDI. HH3KoyrJIepo,nHCTbIe CTaJIH cyru;eCTBeHHO 60JIee npOQHbI, QeM KOBKHH
qyryH, KOTOpbIH 60JIee He paCCMaTPHBaeTCR KaK KOHCTPYKUHOHHbIH MaTepHaJI.
Cpe.naeyrJIepOJnlCTble CTaJlH
1. Co,nepxaHHe yrJIepo,na 0,3-0,5%: TaKHe CTaJIH MOryr 6bITb ynpOqHeHbI Tep-
Mo06pa60TKoH (HarpeBaHHeM ,n;o TeMnepaTYPbI KpaCHoro KaJIeHIDI H 3aKaJIHBaHH-
eM - 6bICTPbIM OXJIIDK,l(eHHeM B Bo,ne). OHH HCnOJIb3yIOTCR ,l(JUI KOBKH KOJIeHqaTbIX
BaJIOB H oceH, r,ne BIDKHa CTOHMOCTb H3,neJIIDI, a 3KCIIJIyaTaUHoHHbIMH Tpe60BaHIDI-
MH He 060CHOBaHO HCnOJIb30BaHHe 60JIee npOqHbIX, HO 60JIee ,noporHX JIerHpOBaH-
HbIX CTaJIeH.
Dla8a 6. MalUuHoCmpOUmeJlbHble MamepUOIlbl
2. Co,aep)l{aHHe yrJIepo,aa 0,5-0,8%: 3TH CTaJIH HCnOJIb3yIDTCR ,nJUI JIHCTOBbIX
peccop B TPaHCnOpTHbIX Cpe,aCTBaX H B CaaOBOM HHBeHTape. TaKHe CTaJIH MOryr
nO,aBepraTbCR ynpOQHeHHIO 3aKaJIKOH C HCnOJIb30BaHHeM TepMOo6pa6oTKH
BblcoKoyrJIepO,lUlCTble CTaJlH
Bce BbIcoKoyrJIepO,aHCTbIe CTaJIH MOryr 6bITb ynpOqHeHbI ,aO BbICOKOH CTeneHH
TBep,aOCTH nyreM HarpeBa ,aO TeMHO-KpaCHOrO KaJIeHIDI H nOCJIe,ayIDm;eH 3aKaJIKH.
TBep,aOCTb H B03MO)I{HOe npHMeHeHHe 3aBHCRT OT cO,aepXaHIDI yrJIepo,aa, CKOpOCTH
OXJIa)I{,LJ:eHIDI OT TeMnepaTYPbI 3aKaJIKH H CTeneHH OTnYCKa nOCJIe 3aKaJIKH:
1. Co,aepxaHHe yrJIepo,aa 0,8-1,0 %; HCnOJIb3yeTcR ,l(JIR UHJIHH.LJ:pHQeCKHX BHH-
TOBbIX npyxHH H CTaMeCOK.
2. Co,aepxaHHe yrJIepo,aa 1,0-1,2 %; HCnOJIb3yeTcR ,l(JIR HanHJIbHHKOB, CBepJI,
MeTqHKOB H IIJIameK.
3. Co,aepxaHHe yrJIepo,aa 1,2-1,4 %; HCnOJIb3yeTcR ,nJUI HHCTPyMeHTOB C
OCTpbIMH JIe3BIDIMH (HO)J{H H T.,a.).
6.2.2. BnHflHHe COAepJlC8HHfI yrnepoA8 H8 CTPYKTYPY,
CSOiiCTS8 H npHNleHeHHe HenerHpos8HHblX
yrnepoAHcTblX CT8neii
1000
C\I
..........
:I: 800
m
::0
a.
('I)
co
a. 600
co
:s:
I-
0
0
400
J
0
a.
I::
Q)
c:[
Q)
a.
r::
.J1
I-
o
o
I-
200
70 a
60 :s:
I::
a.
50 3
o
40 I::
:s:
I-
30 g
('I)
20
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6.2.5. HeKOTophle THnHlfHhle CTanH H HX npHNleHeHHe
nJIOCKaJl yrJIepO,lUlCTaJi CTaJlb
THnJl1UlhIe MeXaHlf1IeCKHe
CBOHCTBa
I .
, (J
TlmIf1l- ! iN
TIm HWii co- TepMlf1lecKaJI - 1 HCnOJlL30BaHHe
CTaJIII CTaB (%) o6pafioTKa == i
a; i 'I
i'i Iii t
J 51 c:i&
! !
HH3KoyrJIe- 0,10 C TepMWleCKH He 06- - 230 28 - - llerKo HarpyxaeMbIe qa(
pO,lJ;HCTasI 0,40 Mn pa6aTbIBaeTcH, HCK- 0 TH, H3fOTaBJIHBaeMble xc
CTaJIb JIlOqasI rrpOIJ;ecc OT- JIO,lJ;HOH BbICa,nKOH (He
)I{liffa ,lI)UI HCKJIlOqe- rrpHMep, r.rry60KasI Bb
HIDI 3cPcP eKTOB Xo- TIDKKa H rrpeCCOBaHHe)
JIO,lJ;HOH o6pa60TKH
KOHCTpYX- 0,20 C TepMWleCKH He 06- 240 450 25 - - OCHOBHasI KOHCTpyxIJ;J'
IJ;HOHHasI 0,20 C pa6aTbIBaeTcH 350 325 20 - - OHHasI CTaJIb.
CTaJIb 1,50 Mn TepMHqeCKH He 06- BbIcOKOrrpOqHasI KOHC1
pa6aTbIBaeTcH pyxIJ;HOHHasI CTaJIb ,lJ;J1
CTpOHTeJIbCTBa MOCTOB
3,lJ;aHHH - KaqeCTBeHH3
CBapKa IIJIaBJIeHHeM
llHTasI CTaJIb 0,30 C TepMHqeCKH He 06- 265 500 18 20 150 llHTbe ,lI)UI WHpOKOI
pa6aTbIBaeTcH, HCK- ,lJ;HarraJOHa npHMeHeHI1
JIlOqasI OTIKHr,ll)Ul H3- B MaWHHOCTpoeHHH, Ta
MeJIbqeHHH 3epHa f,lJ; e Tpe6yIDTCH Cpe,lJ;ID
rrpOqHOCTb H XOpOllIe
o6pa6aTMBaeMocTb
KOHCTpYX- 0,40 C 06pa6aThIBaeTCH 33- 500 700 20 55 200 OCH KOJIelNaTbIX BaJIO
IJ;HOHHasI 0,80 Mn KaJIHBaHHeM rrpH TeM- llIrrHH,neJIH H T .,lJ;. rrI
CTaJIb (cpe,lJ;- rrepa-rype OT 830 ,lJ;0 Cpe,lJ;HHX HarpY3Kax
HeyrJIepO,lJ;H - 860°C. OrrryCK rrpH
CTasI) rrO,lJ;XO,lUlInHX TeMrre-
paTYPax Me 550 H
660°C
0,55 C 06pa6aThmaeTCH Ja- 550 750 14 - 250 nepe,lJ;aTOqHbIe MexaHH
0,70 Mn KaJIHBaHHeM rrpH TeM- Mbl, IJ;HJIHH.npbI H ,neTaJ
rrepa-rype OT 810 ,lJ;0 MaWHH, OT KOTOpbIX Tp'
840°C. OrrryCK rrpH 6yeTcH H3HOCOYCTOHq]
rrO,lJ;XO,lUlInHX TeMrre- BOCTb
paTYPax Me 550 H
666°C
Dla8a 6. MalUuHOCmpOUmeJlbHble MamepUOIlbl
OKOHl.f,aHUe
TlIIIII'IIIWe MexaHll'lecKHe
CaolCTBa
., I
i u
THIIIf1I- iN
Tan Hwii CO- TepMlf1lecKaJI - ! 1 HCnOJJh30B8HHe
CT8JIH CTaB (%) 06pa6oTKa == r
ar I 'J
i) [! 1
5
! =! ! !
HHCTpYMeH- 0,70 C Me.n.rreHHbIH HarpeB 780 CJIeCapHbIe 3y6HJIa, Iq>e-
TaJIbHasI 0,35 Mn ,IJ;O 790-810 °C H 3a- Ile)KH, YCTaHaBJIHBaeMbIe
CTaJIb KaJIKa B BO,IJ;e HJIH XOJIO,IJ;HbIM cIloco60M,
(BbICOKOyr- COIDIHOM paCTBope. C1]>OHTeJIbHble HHC1]>Y-
JIep0,IJ;HCTasI) OTrryCK IlPH 150- MeHThI, K}'3HetffibIe HHCT-
300 °C PYMeHThI, CTep)I(HH OTBep-
TOK, qeKaHOqHble WTaM-
1Ib1, KJIIOq}{, pexyIIUle
JIe3BIDI, CBepJIa ropHble,
HO)I{H ,lI)UI 6YMam
0,90 C Me.n.rreHHbIH HarpeB 800 IIpeccoBble WTaMnbl; rry-
0,35 Mn ,IJ;O 760-780 °C H 3a- aHCOHbI; MeTaJIJUNeCKHe
KaJIKa B BO,IJ;e HJIH <}>OpMbl; IlpeCCbl ,lI)UI xo-
COilllHOM paCTBope. JIO,IJ;HOH BbICa,nKH, llITaM-
OrrryCK npH 150- Ilbl ,lI)UI qeKaHKH MOHeT,
350 °C WTaMIlbI ,lI)UI THCHeHIDI;
HO:>KeBble IlOJIOTHa; HHCT-
PYMeHTbI ,lI)UI ,IJ;epeBoo6-
pa6oTKH; u;eHTpbl TOKap-
HbIX CTaHKOB; BOJIOqHJIb-
Hble ,IJ;OCKH
1,00 C Me.n.rreHHbIH HarpeB 800 Me'ftlHKH; KJIyIIIlbl; CIIH-
-
0,35 Mn ,IJ;O 770-790 °C H 3a- paJIbHbIe CBepJIa; pa3BepT-
KaJIKa B BO,IJ;e HJIH KH; 3eHKOBKH; Bblpy6HOH
COilllHOM paCTBope. HHC1]>YMeHT; llITaMIIbI,ll)lSl
OrrryCK IlPH 150- TIlCHeHIDI, qeKaHKH,
350 °C. WTaMIIbI ,lI)UI qeKaHKH
MOHeT, BbITIDKHble WTaM-
Ilbl, HroJIbqaTble WTaMlIb1
H KaHu;eilllpCKHe WTaM -
1Ib1; HO:>KeBble IlOJIorna,
HO)I{H; IlpeCCOBble WTaM-
Ilbl; KepHepbl; pe3tIHKH IlO
,IJ;epeBY; IlpaBHJIa, CTaMe-
CKH; nHeBMaTHtIeCKHe qe-
KaHbI; nyaHcoHbl
1,20 C Me.n.rreHHbIH HarpeB 800 fpaBHpOBaJIbHble pe3l(bI ;
0,35 Mn ,IJ;O 760-780 °C H 3a- HaIlHJIbHHKH; mpypIWIe-
KaJIKa B BO,IJ;e HJIH CKHe HHCTpYMeHThI; MeT-
COilllHOM paCTBope. qHKH; pe3b6oHape3Hble
OTrryCK IlPH 180- HHC1]>YMeHTbl
350 °C
6.2. lfepHble MemaJlllbl U C11Jla8bl 497
HH3KOJIempOBaHHble KOHCTpYKQlloHHble CTaJlH
(\ MexaHll'lecKHe CBolCTBa
.. I
i (J
-N
THo COCTaII COCTOJlHHe I ! llpHMeHeHHe
CT8JIH (%) = r TepMll'lecKaJI
Gf I 06pa6cmat
11 III ..
I 51 i
= ==
HH3Koe 0,28C HOPMaJIH30- 355 587 20 - 3aKaJIKa B MaCJIe ABToM06HJIbHbIe
CO,IJ;epXaHHe 1,50 Mn BaHHoe OT 860°C (3a- OCH, KOJIe}{qa -
MapraHu;a KaJIKa BO,IJ;Oit TbIe BaJlbI, coe-
npH CeqeHIDIX ,IJ;HHHTeJIbHbIe
60JIbllIe 38 MM B THm H T.,IJ;., TaM,
,IJ;HaMeTpe) . Or- r,IJ; e Tpe6yeTcH
rryCK rrpH He06- OTHOClITeJIbHO
XO,IJ;HMOCTH ,IJ;ellIeBasI CTaJIb
MapraHeu;- 0,40 C 3aKaJIKa H 494 695 25 91 3aKaJlKa B MaCJIe KOJIelNaTbIe
XpOM 0,90 Mn OmyCK rrpH .OT 850°C; OT- BaJIbI, OCH, coe-
1,00 Cr 600°C rryCK MeJK:.n}' 550 ,LJ;HHHTeJIbHbIe
H 660°C H ox- THrH, ,IJ;pyrHe ,IJ;e-
JIIDK,l(eHHe B TaJIH B aBTOMO-
MaCJIe HJIH Ha 6HJIbHOH rrpo-
B03.nyxe MbIllIJIeHHOCTH H
B 06w;eM MallIH-
HOCTpoeHHH
MapraHeu;- 0,38 C 28.5 MM 6pyc, 1000 1130 19 70 3aKaJIKa B MaCJIe 3aMeHHTeJIb 60-
MOJIH6,IJ;eH 1,50 Mn 3aKaJIKa B OT 830 ,IJ;O 850°C; JIee BbICOKOJIe-
0,50 Mo MaCJIe H OT- OmyCK Me mpOBaHHbIX HH-
rryCK npH 550 H 650°C H KeJIb- XpOM - MO-
600°C OXJIIDK,l(eHHe B JIH6,IJ;eHOBbIX
MaCJIe HJIH Ha CIIJIaBOB
B03.nyxe
HHKeJIb- 0,31 C 28,5 MM 6aJ1- 819 927 23 104 3aKaJIKa B MaCJIe BbIcoKorrpotJHbIe
XpOM 0,60 Mn Ka, rrOCJIe ra- OT 820 )];0 840 °C; tJacrn B aBTOMO-
3,00 Ni llIeHIDI OTIKHr OTrryCK Me 6HJIeCTpOeHHH H
1,00 Cr npH 600°C 550 H 650 °C. 06w;eM MalliH -
OXJIIDK,l(eHHe B HOCTpoeHHH
MaCJIe, tJT06bl ( HarrpHMep, OCb
H36exaTb OTrry- ,IJ;H<l><l>epeHU;Ha -
CKHOH xpynKO- JIa, nOBopOTHasI
crn u;arr<l>a, llIaT}'H,
BbICOKorrpOtJHbIe
rB03,IJ;H, 60JITbI
BHHTbI H T. ,IJ;.,
BaJI-llieCTepIDI)
rAa8a 6. MalUuHocmpoumeJlbHble MamepUOIlbl
THo
CTaJIH
COCTaB
(%)
CocroBHHe
I
11
=
OKOHltaHUe
exa eCKHe CBOHCTBa
I
(J
-N
:1
=
e
i
ii
=E-i
8
=,,-,
;i
ei
o ==
HHKeJIb- 0,40 C 3aKaJIKa B
XPOM- 0,55 Mn MaCJIe H OT- - 2010 14 27
MOJIH6,l(eH 1,50 Ni rryCK npH
1,20 Cr 200°C. 988 1080 22 69
0,30 Mo 3aKaJIKa B
MaCJIe H OT-
rryCK npH
600°C
MapraHeu:-
HHKeJIb-
XPOM-
MOJIH6,l(eH
0,30 C 3aKaJIKa Ha
0,55 Mn B03.nyxe H OT- 1470 1700 14
4,25 Ni rryCK npH
1,25 Cr 200°C
0,30 Mo
0,38C 28,5 MM 6pyc.
1,40 Mn 3aKaJIKa B 958 1040 21
0,75Ni MaCJIe lIPH
0,50 Cr TeMnepaTYPe
0,20 Mo OT 850°C H
OTrryCK npH
600°C
TepMll'leCKaJI
o6pa60TKa
npHMeHeHHe
3aKaJIKa B MaCJIe OCH ,l(H<p<pepeH-
or 830 ,l(0 850°C; U:HaJIa, KOJIeH1Ia-
HH3KHH OTrryCK TbIe BaJIbI II ,l(PY-
180-200°C; BbI- me BbICOKO-
COIrn" OTrryCK npotJHbIe ,l(eTa-
550-650 °C; ox- JIH, r,l(e BIDKHbI
JIax.n;eHHe B YCTaJIOCTHasI
MaCJIe HJIH Ha npOqHOCTb H
B03.nyxe Y,l(aponpotJ-
HOCTb; nOCRe
HH3Koro OTrryC-
Ka CTaJIb npH-
rO,l(Ha )])UI nepe-
,l(aTotJHbIX Mexa-
HH3MOB aBTOMO-
6HIDIX; nOBepx-
HOCTb MoxeT
6bITb yrrpotJHeHa
a30THpOBaHHeM
3aKaJIKa Ha B03- 06pa60TaHHasI
35 .nyxe OT 820 ,l(0 Ha B03,l(yXe
840°C; OTrryCK CTaJIb )])UI coe-
npH 150-200 °C ,l(HHHTeJIbHbIX
H OXJIax.n;eHHe TRr B aBHaU:HOH-
Ha B03.nyxe HbIX ,l(BHraTeIDIX,
KJIanaHHbIX Me-
xaHH3MOB, nepe-
,l(aTOqHbIX Mexa-
HH3MOB, Oce"
,l(H<p<pepe HU:HaJIa
H ,l(pyrHX BbICO-
KonpotJHbIX ,l(e-
TaJIeH; ,l(OrryCTH-
MO yrrpotJHeHHe
nOBepXHOCTH
U:HaHHpOBaHHeM
HJIH HayrJIepO-
)l(HBaHHeM
3aKaJIKa B MaCJIe KOMnoHeHTbI
85 or 830 ,l(0 850°C, aBTOM06HJIeCT-
OTrryCK npH poeHIDI H 06IUe-
550-660 °C, H ro MallIHHOC'TpO-
OXJIax.n;eHHe Ha eHHR C Tpe6ye-
B03,l(yXe MbIMH npotJHOC-
TRMH Ha paJpbIB
nOPMKa 700-
1000 H/MM2
6.2. l{epHble MemOJlJlbl U C11Jla8bl 4
HHCTPYMeHT8JIhHaJi H lDTaMDOBaJI CT8JIH (CMOTpH TalOKe pa3,neJl 6.2.6)
3aKaJIKa B MaCJIe OT 800 )(0 KY3HeqHbIe 3y6HJIa, 3y6HJIa KOTI
850°C. OmyCK: a) HHCTpYMeH- JIbIUHKa H )(pyrHe HHCTpYMeHTIJ
TbI )J)UI XOJIO,l(HOH 06pa60TKH CTpOHTeJIbHbIe HHCTpYMeHTbI
IIpH 200-300 °c. 6) HHCTpy- lUaxTHbIe HHCTpYMeHTbI; ry6K
MeHThI )])UI rOpHtleH 06pa60TKH THCKOB; rrpeCCbI )])UI ropHtle
rrpH 400-600°C IUTaMrrOBKH H KOBOqHbIe WTaMrrl
1 % yrJIepo)(- 1,00C 3aKaJIKa B MaCJIe OT 810°C; oT-llIapHKoBbIe H pOJIHKOBbIe rro,D
XpOM 0,45 Mn rryCK rrpH TeMrrepaTYPa rrpH 150 IUHrrHHKH; HHCTpYMeHTaJIbHbI
1 40 Cr °c. OCH; KYJIaqKH; He60JIblUHe BaJIbI
BbIcoKoyrJIepO- 2,10 C Me,l])leHHbIH HarpeB )(0 750- BbIpy6HbIe rryaHcoHbI, IUTaMrrbI I
)(HCTbIe, C BbI- 0,30 Mn 800°C H 3aTeM 6bICTpbIH )(0 HO>KeBbIe rrOJIOTHa )])UI TBep)(bD(
COKHM Co)(ep- 12,50 Cr 960-990°C. 3aKaJIKa B MaCJIe TOHKHX MaTepHaJIOB; MaTpHQI
:>KaHHeM xpOMa (rrpH MaJIbIX CeqeHIDIX B03MO:>K-)])UI <pOpMOBKH a6pa3HBHbIX rro
(HCCR) HO OXJIIDK,l(eHHe Ha B03.nyxe). pOIUKOB (HarrpHMep, KepaMH1Ie
OTrryCK rrpH 150-400 °c B Te- CKHX); KOHTpOJIbHbIe KaJIH6pbI
qeHHH 30-60 MHH. pe3b60HaKaTHbIe rOJIOBKH
3aKaJIKa B BO)(e OT 850°C; OT- MaTpHQbI )])UI XOJIO)(HOH BbITIDK.
rryCK rrpH He06xo)(HMOCTH KH H T.rr.
THo CTaJIH
60
XpOM
COCTaB, %
yrJIepo)(- 0,60 C
0,65 Mn
0,65 Cr
.! % BaHanIDI 1,00 C
4 0,25 Mn
0,20 V
4 % BaHanIDI 1,40 C
0,40 Mn
0,40 Cr
0,40 Mo
3,60 V
CTaJIb )])UI 0,35 C
IUTaMrrOB ropR- 1,00 Si
qero )(e<popMH - 5,00 Cr
pOBaHIDI 1,50 Mo
0,40 V
1,35 W
BbICOKOCKo/JocmHble cmaJlU
18 % BOJIb<ppaM 0,75 C
4,25 Cr
18,00 W
1,20 V
12% K06aJIbT 0,80 C
4,75 Cr
22,0 W
1,50 V
0,50 Mo
12,0 Co
TepMll'leclWl o6pa6oTKa
npHMeHeHHe
3aKaJIKa B BO)(e OT 770°C; OT- BbICanOqHbIe MaTpHQbI H T.rr.
rryCK rrpH 150-300 °C.
npe)(BapHTeJIbHbIH HarpeB )(03KCTpY3HoHHbIe MaTpHQbI,
800°C, BbI.nep:>KKa H 3aTeM 6bI - orrpaBKH H HaKOHeqHHKH ,l(lliI
CTpbIH HarpeB )(0 1020 °C H ox - aJIIOMHHHeBbIX H Me)(HbIX clIJIa-
JIIDK,l(eHHe Ha B03.nyxe. OrrryCK BOB; HHCTpYMeHTbI )])UI rOpRqeH
rrpH 540-620 °C B TeqeHHe lUTaMrrOBKH, rrpOIUHBHbIe (rrpo-
rroJIyTopa qaCOB. 6HBHbIe) HHCTpYMeHTbI, 3axBaTbI
H BbICanOqHbIe IUTaMrrbI; KOBOq-
HbIe IUTaMrrbI )])UI JIaTYHH H
ropHtlero rrpeCCOBaHHR
3aKaJIKa B MaCJIe HJIH B03.nym- TOKapHbIe, CTporaJIbHbIe pe3QbI H
Hoe .nyTbe OT 1290 )(0 1310 °C. rrpaBHJIa; <ppe3bI H )(OJI6RKH; PaJ-
,[(BOHHOH OTrryCK rrpH 565°C B BepTKH; rrpOTIDKKH; Me'NHKH;
TeqeHHe qaca. MaTpHQbI; CBepJIa; HO:>KOBOqHbIe
rrOJIOTHa; JIeHTOqHbIe rrHJIbI; po-
JIHKOBbIe rrO)(IUHrrHHKH )])UI BbI-
COKHX TeMrrepaTYP (raJoBbIe
TYP6HHbI)
3aKaJIKa B MaCJIe HJIH B03.nym- TOKapHbIe, CTporaJIbHbIe pe3QbI H
Hoe ,l(y'I'be OT 1300 )(0 1320 °C. rrpaBHJIa, <ppe3bI, CrrHpaJIbHbIe
,[(BOHHOH OTrryCK rrpH 565°C B CBepJIa H T.)(. )])UI HCKJIIOqHTeJIbHO
TeqeHHH qaca. TBep)(bIX MaTepHaJIOB; HMeIOT
MaKCH KpacHocToHKOCTH H
rrpOqHOCTH; rrpHrO)(HbI )])UI BbI-
rrOJIHeHIDI caMOH CJIO)KHOH Ma-
IUHHHOH 06pa60TKH (HarrpHMep,
MapraHQeBOH CTaJIH H CTaJIH C 60-
JIblUOH rrpOqHOCTbIO Ha pa3pbIB,
MeJIK03epHHCToro qyryHa)
Dla8a 6. MalUuHocmpoumeJlbHble MamepUOllbl
O"OHltaHUe
THo CTaJIH
COCTaB,%
TepMll'leclWl o6pa60TKa
npHMeHeHHe
MOJIH6,neH
'562'
0,83 C
4,25 Cr
6,50 W
1,90 V
5,00 Mo
9% MOJIH6,neH
8% K06aJIbT
1,00 C
3,75 Cr
1,65 W
1, 10V
9,50 Mo
8,25 Co
3aKaJIKa B MaCJIe HJIH B03,l(}'llI - npH6JIH3HTeJIbHbIH 3KBHBaJIeHT
Hoe .nyTbe OT 1250°C. ,[(BOHHOH CTaH.D:apTHOH 18-4-1 BOJIb<ppaMo-
OTrryCK npH 565°C B TeqeHHe BOH BbICOKOCKOpOCTHOH CTaJIH,
qaca o,nHaKO npOqHee; CBepJIa, pa3Bep-
TKH, Me'NHKH, <ppe3bI, rryaHcoHbI,
BHHTope3bI, Ma'TpHQbI ,lJ)UI
XOJIO,nHOH IUTaMnOBKH
3aKaJIKa B MaCJIe HJIH B03,l(}'llI- AHaJIOrH1lHO HCnOJIbJOBaHHIO
Hoe .nyTbe OT 1180 ,no 1210 °C. 12% Co-22% W BbICOKOCKOpOCT-
TPOHHOU: OTrryCK IIpH 530°C B HOU: CTaJIH.
TeqeHHe qaca
Hep1KaBelOID;He H 1KapOnpO'lHhle CTaJIH
1'HnJtqm,Je MeXaHH-
'IecKHe CBOHCTBa
... I
E u
THO CTaJlH COCTaB, COCTOJllllle IN TepMll'leclWI npHMeHeHHe
-! 1
% i 06pa6oTKa
==
e ...
iSM i r;i i
:JI is 51 a
=-= =
=
HepxaBelOIUasI 0,04 C MHrKasI 340 510 31 - He3aKaJIeHHasI, llIHpoKHH ,nHa-
CTaJIb ( <peppHT- 0,45 Mn 3a HCKJIIOqeHH- na30H npe,nMe-
HaR) 14,00 Cr eM XOJIO,nHOH TOB ,nOMalUHero
06pa60TKH 06Hxo,na, BHJI-
KH, JIO)f(KH ;
MO)KHO CKpyqH-
BaTb, BbITRfH -
BaTb H npecco-
BaTb
HepxaBeIOIUasI 0,30 C OTrryCK .lLIDI - 1670 - 534 3aKaJIKa B Bo,ne PexyII(He H 3a-
(HoxeBasI ) 0,50 Mn HoxeH HJIH B MaCJIe TOqeHHbIe HH-
CTaJIb (MapTeH- 13,00 Cr OTrryCK .lLIDI - 1470 - 450 ( HJIH B03,l(}'llI- C'TpYMeHTbI,
CHTHasI ) npyxHH Hoe OXJIIDK,ZJ;e- TaM r,ne 'Tpe6y-
HHe) OT 950 ,no eTCR KOpp03H-
1000 °C. OT- OHHasI CTOU:-
rryCK: .lLIDI HO- KOCTb; CTonop-
xeu: npH HbIe npyxHH -
150-180°C; HbIe KOJIbQa H
.lLIDI npyxHH T .,n.; nOtffH
npH 400- nepJIHTHasI no
450°C c'TpYKTYPe no-
CJIe HOPMaJIH-
3aQHH
6.2. lIepHble MemOJlJlbl U C11Jla8bl 50
O"oHllaHU
Tlunfqm.Je MexaHH-
qeCKHe CBOHCTBa
... I
u
THo CTaJIH COCTaB, COCTOJlHlle IN TepMJI1IecKaJI npHMeHeHHe
-! i 1
% i o6pa60TKa
== Ii
e ... i
iSM IIi
:JI is jl a
=- =
=
18/8 Hep:>KaBe- 0,05 C CWlftleHHasI 278 618 50 170 He3aKaJIeHHasI , OtJeHb BH3KaS1
IOIUasI CTaJIb 0,80 Mn XOJIO,LtHasI 803 896 30 - 3a HCKJIlOtJeHH- H JIerKO rrOMa-
(aycTeHHTHasI ) 8,50 Ni rrpOKaTKa eM XOJIO,l(HOH IOIUasICH 06pa-
18,00 Cr 06pa60TKH 60TKe CTaJIb,
( 6bIcTpoe ox- HMelOIUasI BbI-
JIax.n;eHHe OT COKyIO KOppO-
1050°C, tJT06bI 3HOHHYK> CTOH-
Y,l(ep:>KaTb yrJIe- KOCTb. llIHpoKo
pO,l( B TBep,l(OM HCrrOJIMyeTcH
COcToHHHe) )])UI KyXOHHbIX
rrpHH8Jl)Ie)KH0-
cTeH, paKOBHH,
B rrpOH3BO,l(CTBe
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qeHHe % % % % % % % % % % % % % %
BWCOKOCKODOCTHaJI HHCTDYMeHT8JILHaJI CTaJIL
BMI 0_75 0_85 - 0_40 - 0_40 - 0_035 - 0.035 3_75 4.5 8.0 9.0
BM2 0_82 0_92 - 0_40 - 0_40 - 0_035 - 0.035 3.75 4.5 4.75 5.5
BM4 1_25 L40 - 0_40 - 0_40 - 0_035 - 0_035 3_75 4_5 4_25 5.0
BM15 1_45 L60 - 0_40 - 0_40 - 0_035 - 0.035 4.25 5.0 2.75 3.25
BM35 0_85 0_95 - 0_40 - 0_40 - 0.035 - 0_035 3.75 4.5 4.75 5.25
BM42 1_0 1.10 - 0_40 - 0.40 - 0.035 - 0.035 3.5 4.25 9.0 10.0
BTI 0_70 0_80 - 0.40 - 0_40 - 0.035 - 0.035 3.75 4.5 - 0.70
BT4 0_70 0.80 - 0.40 - 0.40 - 0.035 - 0.035 3.75 4.5 - 1.0
BT5 0.75 0.85 - 0.40 - 0.40 - 0.035 - 0.035 3.75 4.5 - 1.0
BT6 0.75 0.85 - 0.40 - 0.40 - 0.035 - 0.035 3.75 4.5 - 1.0
BT15 1.40 1.60 - 0.40 - 0.40 - 0.035 - 0.035 4.25 5'10 - LO
BT21 0'160 0'170 - 0.40 - 0'140 - 0.035 - 0.035 3'15 4'125 - 0_7
BT42 1.25 1.40 - 0'140 - 0.40 - 0'1035 - 0.035 3.75 4_5 2.75 3.50
HHC10YMeHT8JILHaB CTaJIL .zvn I rooSf1leii: 06 pa60TKH
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BHI0A 0'130 0_40 0.75 LI0 - 0.40 - 0_035 - 0,035 2,8 3.2 2,65 2,95
BHll 0'132 0.42 0_85 L15 - 0_40 - 0..035 - 0,035 4,75 5,25 1.25 1,75
BH12 0..30 0_40 0..85 1..15 - 0,40 - 0.035 - 0,035 4,75 5,25 1.25 1,75
BH13 0..32 0.42 0..85 1.15 - 0..40 - 0,035 - 0.035 4,75 5.25 1,25 1,75
BH19 0,35 0,45 - 0,40 - 0,40 - 0,035 - 0,035 4,0 4.5 - 0.45
BH21 0.25 0.35 - 0.40 - 0,40 - 0,035 - 0,035 2,25 3,25 - 0,60
BH21A 0,20 0,30 - 0.40 - 0.40 - 0,035 - 0,035 2.25 3,25 - 0.60
CT8JIL II m MOJlOTOBhIX mTaMDOB
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i
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BD2A 1.60 1.90 - 0.60 - 0.60 - 0.035 - 0.035 12.0 13.0 0_70 0.90
BD3 1.90 2'130 - 0'160 - 0'160 - 0'1035 - 0_035 12'10 13.0 - -
BA2 0.95 1.05 - 0.40 0_30 0.70 - 0_035 - 0.035 4_75 5.25 0..90 Ll
BA6 0.65 . 1.6
0.75 - 0'140 1.8 2.1 - 0'1035 - 0'1035 0.85 1'115 1.2
BOI 0.85 1'10 - 0.40 I'll 1.35 - 0'1035 - 0'1035 0..40 0.60 - -
B02 0.85 0'195 - 0.40 1.5 1..8 - 0_035 - 0.035 - - - -
BSI 0.48 0'155 0.70 LO 0.30 0..70 - 0.035 - 0_035 1.2 1.7 - -
BLI 0.95 1_10 - 0.40 0_40 0.70 - 0.035 - 0.035 1.20 1.60 - -
BW2 0.95 I'll - 0.30 - 0.35 - 0.035 - 0.035 - 0,15 - 0.10
CT8JIH ,WIB H3roTOBJIeHHJI Doecc-cboPM,WIB DJIaCTMaCC
BP20 0,28 0,40 0.40 0,60 0'165 0'195 - 0'1025 - 0.025 1.50 1'180 0.35 0_55
BP30 0,26 0.34 - 0.40 0'175 0'170 - 0.025 - 0.025 1'110 1.40 0.20 0_35
* 3HaqeHHR TBep,l(OCTH ,l])IR BH224/5 OTHOCRTCR K 3aKaJIeHHOH H oTrrym:eHHoH CTaJIH.
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% % % % % % % % % % % % DB HV
- 0,40 - 1..0 - 0..20 - 0..05 1..0 1..25 1.0 2..0 241 823
- 0..40 - 1.0 - 0..20 - 0..05 1..75 2.05 6..0 6..75 248 836
- 0,40 - 1..0 - 0..20 - 0..05 3..75 4..25 5..75 6..5 255 849
- 0,40 4,5 5,5 - 0,20 - 0..05 4.75 5..25 6..25 7..0 277 869
- 0,40 4,60 5,20 - 0..20 - 0.05 1..75 2..15 6.0 6.75 269 869
- 0,40 7,5 8,5 - 0.20 - 0,05 1..0 1..3 1..0 2.0 269 897
- 0,40 - 1,0 - 0,20 - 0..05 1..0 1..25 17..5 18..5 255 823
- 0,40 4,5 5,5 - 0,20 - 0..05 1..0 1.25 17..5 18..5 277 849
- 0,40 9,0 10,0 - 0,20 - 0,05 1..75 2..05 18..5 19..5 290 869
- 0,40 11,25 12,25 - 0,20 - 0..05 1,25 1.75 20.0 21..0 302 869
- 0,40 4,5 5,5 - 0,20 - 0,05 4,75 5,25 12,0 13..0 290 890
- 0,40 - 1,0 - 0,20 - 0,05 0,40 0,60 13,5 14..5 255 798
- 0,40 9.0 10,0 - 0,20 - 0,05 2,75 3,25 8,5 9,5 277 912
- 0,40 - - - 0,20 - 0,05 0,30 0,50 - - 229 -
- 0.40 2..8 3,2 - 0.20 - 0.05 0.30 1,10 - - 241 -
- 0.40 - - - 0.20 - 0.05 0.30 0,50 - - 229 -
- 0.40 - - - 0.20 - 0.05 - 0.50 1,25 1.75 229 -
- 0.40 - - - 0.20 - 0.05 0.90 1.10 - - 229 -
- 0..40 4.0 4..5 - 0.20 - 0.05 2.0 2.4 4.0 4.5 248 -
- 0..40 - - - 0.20 - 0.05 - 0.40 8.5 10.0 235 -
2..0 2..5 - - - 0.20 - 0.05 - 0.50 8.5 10.0 255 -
1,25 1,80 - - - 0,20 - 0,05 - - - - A*444/447 -
A 401/249
B 363/388
C 331/352
D 302/321
E 269/293
- 0.40 - - - 0.20 - 0,05 0.25 1.00 - - 255 735
- 0.40 - - - 0.20 - 0,05 0.25 1.00 - - 255 763
- 0.40 - - - 0,20 - 0.05 - 0.50 - - 255 763
- 0.40 - - - 0.20 - 0.05 0.15 0.40 - - 241 735
- 0..40 - - - 0.20 - 0.05 - - - - 241 735
- 0.40 - - - 0.20 - 0.05 - 0.25 0.40 0.60 229 735
- 0.40 - - - 0.20 - 0..05 - 0.25 - - 229 735
- 0.40 - - - 0..20 - 0..05 0.10 0.30 2..0 2..5 229 600
- 0..40 - - - 0..20 - 0.05 - - - - 229 735
- 0..20 - - - 0..20 - 0..05 0..15 0..35 - - 207 790
- 0,40 - - - 0,25 - 0,05 & &
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KaK u;eMeHTHT (cBR3aHHbIH yrJIepo.n), HJIH Bbl,1.1;eJIHTbCR, KaK cBo6o.nHbIH yrJIepo.n, B
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f 3TO 3HaqeHHe BKJIIOqeHO KaK 60JIee HH3KHH npe,l(eJI ,l(Hana30Ha 3HaQHMOH TOJIIUHHbI
CTeHOK.
g 3HaqeHIDI KacalOTCR 06pa3QOB C ,l(HaMe1]>oM OTJIHBKH, B JIHTOM BH,l(e COCTaBJUIIOIUHM
30 MM, qTO COOTBeTcTByeT 3HaQHMOH TOJIIUHHe CTeHOK 15 MM.
IIpUMeltaHue.
1. H/MM2 3KBHBaJIeHTeH 1 MTIa.
2. C TOQKH 3peHIDI BbICOKOH ,l(eMn<pHpyIOIUeH cnoc06HoCTH H TeIIJIOnpOBO,l(HOCTH
EN-GJL-I00 (EN-JLlOI0) HaH60JIee nO,l(XO,l(RIInfe MaTepHaJIbI.
3. 0603HaQeHHR MaTepHaJIOB npHBe,l(eHbI B COOTBeTCTBHH C EN 1560.
4. qHCJIa, BbI.neJIeHHbIe )l(HpHbIM mpH<pToM, YKa3bIBaIOT MHHHMaJIbHbIH npe,l(eJI npOqHO-
CTH Ha pa3pbIB ,l])IR KJIaCca, 0603HaQeHHOfO 3THM CHMBOJIOM.
6.2. lIepHble MemOJlJlbl U C11Jla8bl 507
TBepJJ;OCTh no 6pHHeJIJIIO OTJlHBOK H3 ceporo 'lYfYHa, Tpe6yeMhle H 01Kll}J;aeMLIE
3Ha'leHHJI npH COrJIaCOBaHHoi JlOKaJIH3anaH npOBeJJ;eHHJI HCnhlTaHHJI
0OO3HaQeHHe 3Ha'lltMaJI TOJIllUlHa CTeHOK TBep.n;ocTh no BpHHeJIJIIO a,b
MaTepHaJIa (MM) (HB30)
063HaQeHHe HOMep Or )J.o H BKJDOQaJI MHH. MaKC.
EN-GJL-HBI55 EN-JL2010 40 c 80 - 155
20 40 - 160
10 20 - 170
5 10 - 185
25 5 - 210
EN-GJI-HBI75 EN-JL2020 40 c 80 100 175
20 40 110 185
10 20 125 205
5 10 140 225
2,5 5 170 260
EN-GJL-HBI95 EN-JL2030 40 c 80 120 195 I
I
I
20 40 135 210
10 20 150 230
5 10 170 260
4 5 190 275
EN-GJL-HB215 EN -JL2040 40 c 80 145 215
20 40 160 235
10 20 180 255
5 10 200 275
EN -GJL- HB235 EN-JL2050 40 c 80 165 235
20 40 180 255
10 20 200 275
EN-GJL-HB255 EN-JL2060 40 c 80 185 255
20 40 200 275
a AmI KIDK,noro KJIacca TBep,l(OCTb no BpHHeJIJIIO }'MeHbrnaeTCR npH YBeJIHqeHHH TOJIIUH-
HbI CTeHOK.
b no cOrJIarneHHIO Me)J{,l(Y H3rOTOBHTeJIeM H no.rryqaTeJIeM npH COrJIaCOBaHHOH JIOKaJIH-
3aQHH npOBe,l(eHIDI HcnbITaHIDI MO:>KeT 6bITb npHIDIT 60JIee Y3KHH ,l(Hana30H TBep,l(OCTH, npH
YCJIOBHH, qTO OH 6Y,l(eT COCTaBmITb He MeHee 40 e,l(HHHQ TBep,l(OCTH no BpHHeJIJIIo. npHMe-
pOM TaKHX 06CTORTeJIbCTB MO:>KeT 6bITb JIHTbe ,l])UI KpyrrHocepHHHoro npOH3BO,l(CTBa.
c OnOpHaR 3HaqHMaR TOJIIUHHa CTeHOK ,l])IR KJIacca.
IIpUMelfaHue.
1. HH<popMaQIDI 0 COOTHOlUeHHRX Mex,ny TBep,l(OCTbIO no BpHHeJIJIIO H npe,l(eJIOM npot.J-
HOCTH Ha pa3pbIB nOKa3aHa Ha HJIJIIOCTpaQHH B.1, a 0 COOTHOlUeHIDIX Mex,ny TBep,l(OCTblO no
EpHHeJIJIIO H 3HaQHMOH TOJIIUHHOH CTeHOK - Ha HJIJIIOC'TpaQHH C.2 ,[(onOJIHeHHH B H C,
COOTBeTCTBeHHO (CM.: BS EN 1561).
2. 0603HaQeHHR MaTepHaJIOB npHBe,l(eHbI B COOTBeTCTBHH C EN 1560.
3. qHCJIa, BbI,l(eJIeHHbIe )l(HpHbIM IUpH<pTOM, YKa3bIBalOT MHHHMaJIbHyIO H MaKCHMaJIb-
HYIO TBep,l(OCTb no BpHHeJIJIIO ,l])IR KJIaCca, 0603HaQeHHOrO COOTBeTCTByIOIUHM CHMBOJIOM, H
npe,l(eJIbI ,l(Hana30Ha onopHbIX ,l])UI ,l(aHHOrO KJIacca 3HaQHMbIX TOJIIUHH CTeHOK.
Dla6a 6. MalUuHOCmpOUmeJlbHble MamepUOIlbl
6.2.9. KOBKHe "'yrYHbl
BS EN 1562: 1997
CTaanapT BS EN 1562 orrpe,neillleT 1pe6oBaHIUI K KOBKHM qyryHaM. BH.n qyryHa
0603HaqaeTC.H CJIe,ZIylOIUHM o6pa30M:
EN-GJMW 6eJIoCep,neqHbIH KOBKHH qyryH
EN -GJMB qepHocep,neqHbIH KOBKHH qyryH
EyxBeHHOe 0603HaqeHHe COrrpOBO)l{)];aeTC.H ,nBYX3HaqHbIM KO,nOM, 0603HaqalO-
IUHM MHHHMaJIbHbIH rrpe,neJI rrpOqHOCTH Ha pa3pbIB B MIla ,[(lliI HcrrbITaTeJIbHOrO
06pa3IJ;a ,nHaMe1pOM 12 MM. JUI rrOJIyqeHIDI Ko,na pe3YJIbTaT HcrrbITaHIDI ,neJIHTC.H
Ha ,neCHTb. HaKOHeIJ;, eIUe ,nBe IJ;H<PPbI rrpe,nCTaBJUIIOT MHHHMaJIbHOe OTHOCHTeJIbHOe
y,n.rrHHeHHe B rrpOIJ;eHTaX,[(lliI 3an;aHHOH 6a30BOH ,n.rrHHbI.
TaKHM 06pa30M, rrOJIHOe 0603HaqeHHe KOBKoro qyryHa MoxeT BbIr.JUl)];eTb KaK
EN-GJMW-350-4; 3TO 6eJIOCep,neqHbIH KOBKHH qyryH C MHHHMaJIbHbIM rrpe,neJIOM
rrpOqHOCTH Ha pa3pbIB 350 H/MM2 ,[(lliI HcrrbITaTeJIbHOrO o6pa3IJ;a ,nHaMe1pOM 12 MM
H MHHHMaJIbHbIM OTHOCHTeJIbHbIM y,n.rrHHeHHeM 4 %.
qTO KaCaeTC.H cepbIX qyryHOB, HX CrreIJ;H<pHKaIJ;IDI He CB.H3aHa C COCTaBOM qyry-
Ha. BbI60p COCTaBa H TeXHOJIOrHqeCKHX rrpOIJ;eCCOB OCTaBJIeH Ha YCM01peHHe crre-
IJ;HaJIHCTOB JIHTeHHOro rrpOH3Bo,nCTBa rrOCJIe KOHCYJIbTaIJ;IDI C 3aKa3qHKOM.
PaCIIJIaBJIeHHbIH qyryH 1'1 H3rOTOBJIeHHbIe 1'13 Hero OTJIHBKH 6yJ(yT y,nOBJIeTBOp.HTb
TPe60BaHIDIM CTaanapTa BS 6681, eCJIH pe3YJIbTaTbI HcrrbITaHHH H o6IUee KaqeCTBO
OrJIHBOK COOTBeTCTByroT rrpHBe,neHHbIM B CTaanapTe TeXHWIeCKHM YCJIOBIDIM.
nponecc nOJIY1leHHSI 6eJIoCep,ne1JHOrO 1JYfYIIa
OTJIHBKH 1'13 6eJIoro qyryHa rrpOKaJIHBaIOTC.H B KOHTaKTe C OKHCJIHTeJIbHOH cpe-
,nOH rrpH TeMrrepaTYPe rrpH6JIH3HTeJIbHO 1000°C B TeqeHHe 70-100 qaCOB, B 3aBH-
CHMOCTH OT MaCCbI 1'1 TOJIIUHHbI OTJIHBOK. YrJIepo,n Bbl,L(eJUIeTC.H H3 OTJIHBOK H OKHC-
illIeTC.H, rrOCJIe qero OCTaIOTC.H OTJIHBKH C <peppHTHOH CTPYKTYPOH Ha rrOBepXHOCTH
H rrepJIHTHOH CTPYKTYPOH B IJ;eHTPe OTJIHBKH. Ey,nyr rrpHcyrcTBoBaTb HeKOTopbIe
OCTaTOqHbIe p03eTKH cBo6o,nHoro rpa<pHTa. XapaKTepHCTHKH 6eJIoCep,neqHbIX OTJIH-
BOK B 60JIbllIeH CTerreHH rroxo)l(lf Ha xapaKTepHCTHKH CTaJIbHbIX OTJIHBOK; HX rrpeH-
M)'IIJ;eCTBOM .HBJUIeTC.H 60JIee HH3Ka.H TOqKa IIJIaBJIeHIDI 1'1 60JIbilla.H TeKyqeCTb B rrpo-
IJ;eCce JIHTb.H.
IlpHJIoxeHIDI: CTyIIHIJ;bI KOJIeC, Y3JIbI paMbI MOTOIJ;HKJIOB H BeJIOCHrre,nOB; rraT-
py6KH B ra30-, BO,nO- H rraporrpOBo,nOB.
nponecc nOJIY1leHHSI 1JepHocep,ne1JHOrO 1JYfYIIa
OTJIHBKH H3 6eJIoro qyryHa rrpOKaJIHBaIOTC.H B KOHTaKTe C B03,[(yxOM rrpH TeM-
rrepaTYPe 850-950°C B TeqeHHe 50-170 qaCOB, B 3aBHCHMOCTH OT MaCCbI 1'1 TOJI-
IUHHbI OTJIHBOK. U:eMeHTHT pacrran;aeTC.H Ha MeJIKHe p03eTKH cBo6o,nHoro rpa<pHTa,
paCCe.HHHbIe B cTPYKTYPe <peppHTa. 3TO rrpHBo,nHT K YBeJIWIeHHIO KOBKOCTH,
B.H3KOCTH, rrpe,neJIa rrpOqHOCTH Ha pa3pbIB 1'1 y,naporrpOqHOCTH.
IlpHJIoxeHIDI: CTyIIHIJ;bI KOJIeC, TOpM03HbIe 6apa6aHbI, rraTPy6KH ,[(lliI Tpy6o-
rrpOBo,nOB, pyqKH yrrpaBJIeHIDI 1'1 rre,naJIH.
nponecc nOJIY1leHHJI nepJIHTHOrO 1JyryHa
3TOT rrpOIJ;eCC rro,no6eH rrpOIJ;eccy rro.rryqeHIDI qepHocep,neqHOrO qyryHa, o,nHaKO
COrrpOBO)l{)];aeTC.H 6bICTPbIM OXJIIDK,[(eHHeM. 3TO rrpe,nOTBpaIUaeT <POpMHpoBaHHe
<peppHTa H XJIOrrbeB rpa<pHTa, a BMeCTO 3Toro rrpHBo,nHT K o6pa30BaHHIO HeKOTOpo-
6.2. lfepHble MemOJlJlbl U C11Jla8bl 5(
ro KOJIHqeCTBa p03eTOK rpa<l>HTa, paCCe.HHHbIX B cTPYKTYPe rrepJIHTa. OTJIHBKH rr(
JIyqaIOTC.H 60JIee TBep,[(bIMH, y,[(aporrpOqHbIMH, C 60JIee BbICOKHM rrpe,[(eJIo
rrpOqHOCTH Ha pa3pbIB, HO MeHee KOBKHe H B.H3KHe.
IIpHJIOXeHIDI: IIepe,[(aTOQHbIe MexaHH3MbI, CIJ;eIIJIeHIDI, pacrrpe,[(eJIHTeJIbHb
BaJIbI, KapTepbI Be,[(yru;ero MOCTa, KapTepbI ,[(H<l><l>epeHIJ;HaJIa H KOMlIJIeKTy:IOIUHe.
MeXaHlf1IeCKHe CBoHcTBa 6eJIoCep,ne1JHLIX KOBKHX 1JYfYIIOB
0603Ha'leHHe MaTepHaJla HOMHHaJIh- npe.ZJ;eJI npo'l- OmOCH- 0,2% YCJlOB- TBep.ZJ;OC'r.
HYH ,lUIa- HOCTH Ha P83- HhIii npe.ZJ;eJI no BpH-
MeTp HCIIhI- pbIB Rm (Bpe- TeJlhHoe TeKY'leCTH HeJIJDO ('f(J
Y.ZJ;JIIIHe-
0603Ha'leHHe HOMep TaTeJlhHOrO MeHHoe co- HHe A3 4 (Jr 2) J1hKO,ll;JUl
06pa31(8 d npoTllB}leHHe) copaBU)
(MM) (H/MM2) MHH. (%) MaH. MHH. H B MaKC.
EN-GJMW-350-4 EN-JMI0I0 6 270 10 -
9 310 5 -
12 350 4 - 230
15 360 3 -
EN-GJMW-360-12 b EN -JM 1020 b 6 280 16 _a
9 320 15 170
12 360 12 190 200
15 370 7 200
EN-GJMW-400-5 EN-JMI030 6 300 12 _a
- '1
9 360 8 200 I
12 400 5 220 220
15 420 4 230
EN-GJMW-450-7 EN-JMI040 6 330 12 _a
9 400 10 230
12 450 7 260 220
15 480 4 280
EN-GJMW-550-4 EN-JMI050 6 - - _a
9 490 5 310
12 550 4 340 250
15 570 3 350
a BCJIe,nCTBHe CJIO)I{HOCTH onpe,neJIeHIDI YCJIOBHOrO npe,neJla TeKY'leCTH ,lUUI MaJIblX Hcnbl
TaTeJIbHblX 06Pa3 OB 3HaqeHIDI H MeTO,n H3MepeHIDI ,nOJDKHbI 6blTb COrJIaCOBaHbl Mex,ny H3
rOTOBHTeJIeM H nOJlyqaTeJIeM Ha MOMeHT 3aKJIIOqeHIDI ,norOBopa.
b MaTepHaJI HaH60JIee npHro,neH ,lUUI CBapKH.
llpUMellaHue:
1. 1 H/MM2 paBeH 1 Mna.
2. 0603HaQeHIDI MaTepHaJIOB npHBe,neHbl B COOTBeTCTBHH C EN 1560.
3. qHCJIa, BbI,LJ;eJIeHHble :>KHpHbIM WPH<pTOM, yJ<a3bIBaIOT MHHHMaJIbHblH npe,neJI npOQHOC
TH Ha pa3pblB H MHHHMaJIbHOe OTHOCHTeJIbHOe YWIHHeHHe A3,4 ,lUUI KJIaCca, 0603HaQeHHorc
COOTBeTCTByIOIUHM CHMBOJIOM, a TaIOKe npe,nn01JTHTeJIbHbIH HOMHHaJIbHbIH ,nHaMeTp HCnbITa
TeJIbHoro o6p33 a H cooTBeTCTByIOIUHH MHHHMaJIbHbIH YCJIOBHbIH npe,neJI TeKy'leCTH 0,2%.
rJl{l6a 6. MalUuHocmpoumeJlbHble MamepUOIlbl
MeXaHlf1IeCKHe CBoHcTBa 1JepHocep,ne1JHLIX KOBKHX 1JYfYIIOB
0603Ha'leHHe MaTepHaJla HOMHHaJlhHbrii npe.ZJ;eJI npo'l- Omo- 0,2% YCJlOB- TBep.ZJ;OCTIt
aMeTp HOCTH Ha P83- CIITeJIh- IIhrii npe.ZJ;eJI no BpHHeJI-
pbIB (BpeMeH- Hoe Y.ZJ;- TeKY'leCTH
HCnhlTaTeJlh- Hoe Conpo- JlHHeHHe Rpo JIIO (TOJlhKO
0603Ha'leHHe HOMep HOro 06p83na a THBJIeHHe) a... A 3t (%) (H/ 2) .ZJ;JUI cnpaa-
d(MM) (H/MM2) MHH. MHH. MHH. 0) H B
EN -GJMB-300-6b EN-JMIII0 b 12 WIH 15 300 6 - 150
MaKCHMYM
EN -GJMB-350-10 EN-JMI130 12 WIH 15 350 10 200 150
MaKCHMYM
EN -GJMB-450-6 EN-JMI140 12 WIH 15 450 6 270 150- 200
EN -GJMB-500-5 EN-JMI150 12 WIH 15 500 5 300 165-215
EN -GJMB-550-4 EN-JMI160 12 WIH 15 550 4 340 180-230
EN -GJMB-600-3 EN-JMI170 12 WIH 15 600 3 390 195-245
EN-GJMB-650-2 EN-JMI180 12 WIH 15 650 2 430 210-260
EN -GJMB-700-2 EN-JMI190 12 WIH 15 700 2 530 240-290
EN -GJMB-800-1 EN-JMI200 12 WIH 15 800 1 600 270-320
a ECJIH HcnbITaTeJIbHbIH 06pa3e ,nHaMeTPOM 6 MM npe,nCTaBIDIeT 3HaqHMYI<> TOJIID:HHY
CTeHOK OTJIHBKH, 3TOT pa3Mep HcnbITaTeJIbHOfO 06pa3 a MoxeT HCnOJIb30BaTbCB no COfJla-
meHHIO Me)K,l(Y H3fOTOBHTeJIeM H nOJIy'laTeJIeM Ha MOMeHT npHIUITIDI 3aKa3a. ,n;OJDKHbI npH-
MeHBTbCB MHHHMaJIbHbIe nOKa3aTeJIH, npHBe,neHHbIe B ,naHHoH Ta6JIH e.
b MaTepHaJI, npe,nHa3HaQeHHbIH oco6eHHO .nIDI Tex npWIoxeHHH, B KOTOpbIX HenpOHH-
aeMOCTb no,n ,naBJIeHHeM 60Jlee BIDKHa, QeM BbICOKaB CTeneHb npOQHOCTH H BB3KOCTH.
llpUMellaHue:
1. 1 H/MM2 paBeH 1 Mna.
2. 0603HaQeHH MaTepHaJIa npHBe,neHbI B COOTBeTCTBHH C EN 1560.
3. qHCJIa, BbI,LJ;eJIeHHbIe :>KHpHbIM mpH<pTOM, yx:a3bIBa1OT MHHHMaJIbHbIH npe,neJI npOQHO-
CTH Ha pa3pbIB H MHHHMaJIbHOe Y,lI)IHHeHHe A 3 ,4 ,lUUI KJIaCca, 0603HaQeHHOfO COOTBeTCTByIO-
ID:HM CHMBOJIOM.
6.2.10. '1yryH c wapOBHAHblM rpacpHTOM
qyryH C mapOBH,lJ;HbIM rpa<pHToM TaIOKe Ha3bIBalOT B.H3KHM qyryHOM, BbICOKOnpOq-
HbIM qyryHOM H T.,[(.
06aBJIeHHe MarHIDI HJIH u;epIDI B )l{}l)(KHH cepbIH qyryH npe,[(OTBpa:w;aeT <pop-
MHpOBaHHe qemyeK rpa<pHTa npH OXJIIDK,[(eHHH H 3aTBep,[(eBaHHH. BMeCTO 3Toro
HeCB.H3aHHbIH yrJIepo,[( pacnpe,[(eJUIeTC.H B BH,[(e MeJIbqaHmHX c<pepOH,lJ;OB no BceH
Macce OTJIHBKH. 3TO npHBO,[(HT K <pOpMHpoBaHHIO 60JIee O,[(HOpO,[(HOH CTPYKTYPbI,
HMelOIUeH 60JIbII.IyIO npOqHOCTb H B.H3KOCTb H MeHee nO,[(BepxeHHoH YCTaJIOCTHOMY
pa3pyrneHHIO.
BS EN 1563:1997: qyrya C mapOBH)UlhlM rpacl»HTOM
CTaanapT BS EN 1563 onpe,[(eJUIeT TPe60BaHIDI K qyryHaM C mapOBH,lJ;HbIM rpa-
<pHTOM. CTaanapT OIDITb He onpe,[(eJUIeT XHMHqeCKHH COCTaB qyryHa, MeTO,[( ero H3-
rOTOBJIeHIDI HJIH KaKYJO-JIH60 nOCJIe,ZIylOIUYIO TepMoo6pa60TKY. CTaanapT KaCaeTC.H
6.2. lfepHble MemOJlJlbl U C11Jla8bl 51
HCKJIlOqHTeJIbHO CBOHCTB, MeTO,[(OB HCIIbITaHHH H KOHlpOJUI KaqeCTBa rOTOBbIX T'
JIHBOK. BbI6paTb MeTO,[(bI ,[(OCTIDKeHIDI pe3YJIbTaTa ,[(OJDKHbI CIIeIJ;HaJIHCTbI JIHTeHHO.
ro IIpOH3BO,[(CTBa IIOCJIe KOHCYJIbTaIJ;IDI C 3aKa3qHKOM. CTaH,[(apT .HBJI.HeTC.H OqeHI
BCeCTOpOHHHM, H B paMKaX 3TOH rJIaBbI B03MO)I{HO TOJIbKO KpaTKO paCCMOTpeTb He.
KOTopble H3 HaH60JIee BIDKHbIX IIyHKTOB. DOJIee IIo,[(po6HyIO HH<popMaIJ;HIO MO)I{H(
IIOJIyqHTb H3 caMoro CTaH,[(apTa.
MexaHlf1Iecme cBoiicTBa, H3MepeHHhle Ha HCnhlTaTeJIhHhIX o6pa3nax, MeXaHlf1Ie.
cm nOJIY1leHHhIX H3 OT,neJIhHO OTJIHThIX 06pa3nOB
0603Ha'leHHe MaTepHaJla npe.ZJ;eJI npo'lHOCTH Ha 0,2% YCJlOBHWA npe- OmoCHTeJlhHOe
pa3pLm (BpeMeHHoe .ZJ;eJl TeK)"leCTH R,o 2 YNlHHeHHe A (%)
COnpoTllBJIeHHe) a...
0603Ha'leHHe HOMep (H/MM2) MHH. (H/MM2) MHH. ' MaH.
EN -GJS-350-22- LTa EN-JSI015 350 220 22
EN-GJS-350-22-RTb EN-JSI014 350 220 22
EN-GJS-350-22 EN-JSI010 350 220 22
EN-GJS-400-18-LTa EN-JSI025 400 240 18 I
EN -GJS-400-18- RTb EN-JSI024 400 250 18 I
I
EN-GJS-400-18 EN-JSI020 400 250 18 I
EN-GJS-400-15 EN-JSI030 400 250 15
EN-GJS-4 50-10 EN-JSI040 450 310 10
EN-GJS-500-7 EN-JSI050 500 320 7
EN-GJS-600-3 EN-JSI060 500 370 3
EN-GJS-700-2 EN-JSI070 700 420 2
EN-GJS-800-2 EN-JSI080 800 480 2
EN-GJS-900-2 EN-JSI090 900 600 2
a L T - ,lUUI HH3KOH TeMnepaTYPbI.
b RT - ,lUUI KOMHaTHOH TeMnepaTYPbI.
llpUMellaHue:
1. 3HaqeHIDI ,nIDI 3THX MaTepHaJIOB npHMeHHMbI ,lUUI OTJIHBOK, OTJIHTbIX B neCqaHbIX
<popMax co cpaBHHMOH TeMnepaTYPonpOBo,nHOCTblO. IIpH YCJIOBHH, qro nonpaBKH orOBope-
HbI B ,norOBope, 3HaqeHIDI MOryT npHMelUlTbCB K OTJIHBKaM, nOJIy'leHHbIM aJIbTepHaTHBHbI-
MH Mero,naMH.
2. KaKOH 6bI Mero,n HH HCnOJIb30BaJICB .nIDI nOJIy'leHIDI OTJlHBOK, KJIaCCbI OCHOBbIBalOTCB
Ha MeXaHH1IeCKHX CBOHCTBax, H3MepeHHbIX Ha HCIIbITaTeJIbHbIX 06pa3 ax, nOJlyqeHHbIx H3
06pa3 OB qyryHa, OT,neJIbHO OTJIHTbIX HJIH B neCqaHbIX <popMax, HJIH B <pOpMax C conOCTaBH-
MOH TeMnepaTYPonpOBo,nHOCTblO.
3. 1 H/MM2 paBeH 1 Mna.
4. 0603HaqeHHB MaTepHaJIOB npHBe,neHbI B COOTBeTCTBHH C EN 1560.
Dla8a 6. MalUuHocmpoumeJlbHble MamepUOIlbl
MHHHMaJlLHhle 3Ha1JeHHSI y,napHoH BSl3KOCTH, H3MepeHHhle Ha HCnbITaTeJIbHhIX 06-
pa3Qax C V -06pa3HhlM H8,lI;pe30M, MeXaHH1JeCKH n0JIY'leHHhIX H3 OT,neJIIdiO OTJIHTLIX 06-
pa3QOB
MHHHMaJIhHWe 3Ha'ielOOI YA8PHOii BR3KOCTH <,n1K)
0603Ha1JeHHe MaTepHaJla "pH KOMHamoii "IH "pH
TeMDepa (-20 ,2) °C (-40 :E 2) °C
(23 :f 5) C
Cpe ee Or.ZJ;eJIh- Cpe ee Or.ZJ;eA- Cpe ee Or.ZJ;eJIh-
0OO3Ha1JeHHe HOMep 3Ha'leHHe DO Hoe 3Ha'leHHe no Hoe 3H8'1eHHe no Hoe
'rpeM HCDW- 3Ha'le- TPeM Hcnw- 3Ha'le- 'rpeM HCDW- 3Ha'le-
TaIDUlM HHe T8HHJIM HHe T8IIIUIM HHe
EN-GJS-350-22-LTa EN-JSI015 - - - - 12 9
EN-GJS-350-22-FlTb EN-JSI014 17 14 - - - -
EN-GJS-400-18-LTa EN-JSI025 - - 12 9 - -
EN-GJS-400-18-FlTb EN-JSI024 14 11 - - - -
a LT - ,lI)UI HH3KOH TeMnepaTYPbI.
b FlT - ,lI)UI KOMHaTHOH TeMnepaTYPbI.
llpUMellaHue:
1. 3HaqeHIUI ,lUUI 3THX MaTepHaJIOB npHMeHHMbI .nIDI OTJIHBOK, OTJIHTbIX B neCqaHbIX
<pOpMax co cpaBHHMOH TeMnepaTYPonpOBo,nHOCTblO. npH YCJIOBHH, 'lTO nonpaBKH orOBope-
HbI B ,norOBope, 3HaqeHIDI MOryr npHMelUlTbCB K OTJIHBKaM, nOJIy'leHHbIM aJIbTepHaTHBHbI-
MH Mero,naMH.
2. KaKOH 6bI MeTO,n HH HCnOJIb30BaJICB .nIDI nOJIy'leHIDI OTJIHBOK, KJIaCCbI OCHOBbIBalOTCB
Ha MeXaHHqeCKHX CBOHCTBax, H3MepeHHbIX Ha HcnbITaTeJIbHbIX o6pa3 ax, nOJIy'leHHbIX H3
06pa3 OB qyryHa, OT,neJIbHO OTJIHTbIX HJlH B neCqaHbIX <popMax, HJIH B <POp Max C conOCTaBH-
MOH TeMnepaTYponpOBo,nHOCTblO.
3. 0603HaqeHHe MaTepHaJIa npHBe,neHO B COOTBeTCTBHH C EN 1560.
6.2.11. nerJfpOSaHHble "'yryHbl
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JI.HX.
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npOqHOCTb H cnoco6CTBOBaTb <}>OpMHpoBaHHIO cBo6o,[(Horo rpa<}>HTa. qyryH CTaHO-
BHTC.H 60JIee xeCTKHM.
XpOM cTa6HJIH3HpyeT npHcyrcTByIOIUHH CB.H3aHHbIH yrJIepo,[( (u;eMeHTHT) II, Ta-
KHM o6pa30M, YBeJIHqHBaeT TBep,[(OCTb H H3HOCOYCTOHqHBOCTb JIHTb.H. OH TaIOKe
y.rryqmaeT KOpp03110HJIyIO CTOHKOCTb JIHTb.H, oco6eHHO npH BbICOKHX TeMnepaTY-
pax. KaK H B JIerHpOBaHHbIX CTaJI.HX, HHKeJIb II XpOM 06bIqHO HCnOJIb3yIOTC.H BMec-
Te. 3To CB.H3aHO C TeM, qTO OHH HMelOT onpe,[(eJIeHHbIe He,[(OCTaTKH npH HCnOJIb30-
BaHHH HX no OT,[(eJIbHOCTH, KOTopble CBO,[(.HT Ha HeT HX npeHMYIUeCTBa. O,[(HaKo
npH HCnOJIb30BaHHH HHKeJUI H xpOMa BMeCTe He,[(OCTaTKH no,[(aBJUIIOTC.H, B TO
BpeM.H KaK npeHM)'IUeCTBa OCTaIOTC.H.
6.2. lfepHble MemOJlJlbl U C11Jla8bl 51
Me HCrrOJIb3yeTC.H OqeHb paCqeTJIHBO, rrOCKOJIbKY OHa MaJIOpaCTBopHMa B XI
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Kap6:u,nbI H }'MeHbmaeT HX TeaneHn;HIO pa3JIaraTbC.H rrpH BblCOKHX TeMrrepaTYPax.
MOJIH6,neH paCTBOp.HeTC.H B <}>eppHTe H, rrpH HCrrOJIb30BaHHH B MaJIbIX KOJIHqeC'
Bax (0,5 %) y.rryqmaeT y,napHYIO B.H3KOCTb JIHTb.H. OH TaIOKe rrpe,nOTBpaIUaeT pacrrc
rrpH BbICOKHX TeMrrepaTYPax B qyryHax, co,nepxaIUHX HHKeJIb H XpOM. Kor,na M(
JIH6,neH ,n06aBJI.HIOT B 60JIbmHX KOJIWIeCTBax, OH <}>opMHpyeT ,nBoHHble Kap6:u,n1
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HHKpOCHJIaJI - 3TO 60JIee ,noporoH CIIJIaB. OH rrpe,nCTaBIDIeT C060H aycTeHHTHbII
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· TpH THrrWIHbIX JIerHpOBaHHbIX qyryHa rrepeqHCJI HbI B pa3,neJIe 6.2.12 BMeCTe (
HX CBoHcTBaMH, COCTaBOM H HeKOTopbIMH 06JIaCT.HMH rrpHMeHeHIDI.
17-3255
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6.2.12. CocTas, CsoHcTsa H npHMeHeHHe
HeKoTopblX THnH'IHbIX 'IyryHOS
TIm 1fYI'YIIa
COCTaB
(%)
CepbIH qyryH 3,30 C
1,90 Si
0,65 Mn
0,10 S
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CepbIH qyryH 3,25 C
J 2,25 Si
0,65 Mn
0,10 S
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CepbIH qyryH 3,25 C
1,25 Si
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BbICOKHM co,nep- 1,75 Si
:>KaHHeM <l>oc<l>o- 0,50 Mn
pa (TOMacoB- 0,10 S
CKHH) 0,80 P
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2,10 Si
0,80 Mn
0,05 S
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H3HOCO- 2,90 C
H y,naponpOqHbIH 2,10 Si
0,70 Mn
0,05 S
0,10 P
1,75 Ni
0,10 Cr
0,80 Mo
0,15 Cu
HHpe3HcT 2,90 C
2,01 Si
1,00 Mn
0,05 S
0,10 P
15,00 Ni
2,00 Cr
6,00 Cu
XapaKTep....e Mexallll'lecKHe CBOHCTBa
Upe.ZJ;eJI npo'lllOCTH Ha
paCTJDKeHHe (BpeMeHHoe
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6.3. 8emHble MemOJlJlbl U C11Jla8bl 51
6.3. BeTHble MeTannbl M cnnaBbl
6.3. 1. LlseTHble MeTannbl H cnnaSbl. BseAeHHe
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B paMKax 3TOH KHHrH HeB03MO)I{H0 paCCMOTpeTb COCTaBbI H CBOHCTBa rpOMaD
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CYJIbTaIJ;HH HJIH 06paTHBillHCb K B eCTopOHHHM PYKOBO,[(CTBaM, orry6JIHKOBaHHbIM]
npOH3BO,[(HTeJUIMH MeTaJlJIOB H HX ToprOBbIMH aCCOIJ;HaIJ;IDIMH (HanpHMep, ACCOIJ;H
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6.3.2. Cnnasbl C SblCOKHM COAepJICaHHeM MeAH
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3BOJUIeT KOMnOHeHTaM H3 HarapToBaHHoH XOJIO,[(HOT.HHYTOH Me,[(H H36exaTb pa3Y-
npOqHeHIDI, Kor,[(a K HHM npHnaHBalOT npOBO,[(HHKH.
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6.3.3. KosaHafl MeAb H MeAHble cnnaSbl: KOA COCTOflHHfI
o MaTepHaJI B OTO)IQKeHHOM (pa3yrrpOqHeHHoM) COCTO.HHHH.
M MaTepHaJI, He rrO,[(BepraBmHHC.H HHKaKOH 06pa60TKe.
H MaTepHaJI, OTrryIIJ;eHHbIH Ha qeTBepTb TBep,[(ocTH (BCJIe,[(CTBHe XOJIO,[(HOH
06pa60TKH).
H MaTepHaJI, oTrryIIJ;eHHbIH Ha rrOJIOBHHY TBep,[(ocTH (B rronyTBep,[(OM CO-
CTO.HHHH) .
6. 3. 8emHble MemOJlJlbl U C11Jla8bl 5
H MaTepHaJI, OTrryIIJ;eHHbIH Ha MaKCHMaJIbHyro TBep,nOCTb (B TBep,n4
COCTO.HHHH).
EH MaTepHaJI B Oco6oTBep,noM COCTO.HHHH.
SH MaTepHaJI B rrpyxHHHOTBep,nOM COCTO.HHHH.
ESH MaTepHaJI B oco60 rrpyxHHHOTBep,nOM COCTO.HHHH.
TIpHBe,neHHble 0603HaqeHIDI rrepeqHCJIeHbI B rrOp.H,ZJ;Ke B03paCTaHH.H TBe
,nOCTH.
TBep,nocTb MaTepHaJIOB, KOTopble 6billH yrrpOqHeHbI XOJIO,nHOH o6pa6oTK<J
MOXHO }'MeHbillHTb, a HX B.H3KOCTb YBeJIWIHTb rrocpe,nCTBOM TepMoo6pa6oTKH (H
rrpHMep, OTIKHr HJIH o6pa6oTKoH pacTBopoM).
XHMWIecKHe 3JIeMeHTbI, HCrrOJIb3yeMble B rrOCJIe,nYIO:W;HX Ta6JIHIJ;ax:
AI aJIlOMHHHH Co Ko6aJIbT Ni HHKeJIb Si KpeMHHH
As Mblill'b.HK Cr XpOM P <poc<pop Sn OJIOBO
Be 6epHJIJIHH Cu Me,nb Pb CBHHeIJ; Te TeJIJIyp
Bi BHCM)'T Fe XeJIe30 S cepa Ti THTaH
Ca KaJIbIJ;HH Mg MarHHH Sb cypbMa Zn IJ;HHK
Cd K MHH Mn MapraHeIJ; Se CeJIeH Zr IJ;HPKOHHH
6.3.4. 6pHTaHcKHe CTaHAapTbl, OTHOCflUlHeCfI K MeAH
H MeAHblM cnnasaM
EpHTaHCKHH CTaanapT BS 2874: TIpyrKH H rrpO<pHJIH 1£3 Me,nH H ee cnrraBOB (XHMJ
qeCKHH COCTaB H MexaHWIeCKHe CBOHCTBa), KacalO:W;HHC.H Me,nH H Me,nHbIX CllJIaBC
B HaCTO.H:w;ee BpeM.H YCTapeBaeT Hero He CJIe,nyeT HCrrOJIb30BaTb ,[(.JUI HOBbIX pa3p.
60TOK, XOT.H MaTeplfaJIbI, rrepeqHCJIeHHble B paMKax ,naHHoro CTaanapTa, rrpo,nOJDKt
lOT 6bITb ,nOCTyrrHbIMH H 6y,nyr HCrrOJIb30BaTbC.H e:w;e B TeqeHHe HeKOToporo Bpi
MeHH.
3aMeIDIlOlQHe CTaanapTbI rrepeqHCJIeHbI ,naJIee. Bce OHH OqeHb rro,npo6Hble
BceCTopOHHHe, H <pH3HqeCKH HeB03MOXHO BocrrpOH3BeCTH HX B paMKax 3TOJ
CrrpaBOqHHKa.
. BS EN 12163: 1998 - Me,nb H Me,nHble CllJIaBbI. IIpyrKH o6lQero Ha3Haqi
HIDI .
. BS EN 12167: 1998 - Me,nb H Me,nHble CllJIaBbI.TIpo<pHJIH H rrp.HMoyrOJIbHb
CTepXHH o6lQero Ha3HaqeHIDI.
. BS EN 1652: 1997 - Me,nb H Me,nHble CllJIaBbI. IlrrHTbI, JIHCTbI, rrOJIOCbI
,nHCKH o6:w;ero Ha3HaqeHIDI.
. BS EN 1653: 1998 - Me,nb H Me,nHble CITJIaBbI. TIJIHTbI, JIHCTbI H ,nHCKH )J.J
KOTJIOB, COCy,nOB, pa60TalOlQHX rro,n ,naBJIeHHeM H pe3epByapoB ,[(.JUI XpaHeHI1
rOp.HqeH BO,nbI.
. BS EN 1982: 1998 - Me,nb H Me,nHble CllJIaBbI. CJIHTKH H OTJIHBKH.
CJIe,nyro:W;He ,naHHble, KaCalOlQHeC.H Me,nH H Me,nHbIX CllJIaBOB, rrpHBe,neHHble
pa3,neJIaX 6.3.5-6.3.26 HOC.HT HCKJIlOqHTeJIbHO CrrpaBOqHbIH xapaKTep.
rAa6a 6. MalUuHocmpoumeJlbHble MamepUOIlbl
6.3.5. npyrKH H npocpHnH H3 Me,qH H Me,qHbIX cnnssos
XuMH'IeCKHH COCTaB, TO'lHOCTh H3roTOBJIeHHJI H MeXaHlf1IeCKHe CBOHCTBa Me)UlLIX
XHMll'lecKHii COCTaB (%)
i
060- :s
3Ba'le- MaTepHaJI CYMMap-
HHe
HS Co So Pb Fe Ni As Sb S P Se Te Hi Bye
:I
i npHMecB
C 101 3JIeIcrpOJIH- I - 0,005 - - - - - - - - 0,0010 0,03
THqeCKag Tex- (HCKJIIO-
HHqeCKH qHC- qag 0
TaH MeAb C HAg)
BbICOKOH 99,90
3JIeIcrponpo- MHH.
BOAHOCTbIO (BKJIIO-
C 102 MeAb orHeBO- I qag - 0,005 - - - - - - - - 0,0025 0,04
ro pa<l>HHH - Ag) (HCKJIIO-
pOBaHIDI C qag 0
BbICOKOH Ii Ag)
3JIeIcrponpo-
BOAHOCTbIO
C 103 EeCKHCJIO- I 99,95 - 0,005 - - - - - - - - 0,0010 0,03
pOAHag MeAb MHH. (HCKJIIO-
C BbICOKOH (BKJIIO- qag 0
3JIeIcrpOnpo- qag HAg)
BOAHOCTbIO Ag)
C 106 PaCKHCJIeH- I 99,85 0,01 0,010 0,03 0,10 0,05 0,01 - 0,013- Se+ Te 0,0030 0,06
Hag <l>oc<l>o- MHH. 0,050 0,020- (HCKJIIO-
pOM MeAb (He (BKJIIO- 0,010 qag Ag,
COAep)I{HT qag As, Ni
MbIllI'bHK )** Ag) H P)
IIpUMettaHue:
,lI..rnI OCHOBHbIX 3JIeMeHTOB cnrraBa npe,n:eJIbI BbmeJIeHbI XHpHbIM mpH<pToM. ECJIH He
orOBopeHO HHoe, 3HaqeHHH B KOJIOHKe CYMMapHbIX npHMeceH BKJIIOqaIOT Te, KOTopbIe He
BbmeJIeHbI )l{HpHbIM mpH<pTOM. ECJIH He YKa3aHO HHaqe, Bce e,n:HHH'lHbIe npe,n:eJIbI COOTBeT-
CTByIOT MaKCHM}TMaM.
(**BapHaHT <poc<pop-,n;e30KCH,lI;HpOBaHHCUI. B03MO)KHO, He HMeeT YCTORBillerOCR
Ha3BaHIDI B PYCCKOM R3bIKe. MbIillbRK Boo6w;e He ynoMHHaeTCR, XOTR cyw;eCTByeT
aHarrOfHQHbIH CI1JIaB C MbIillbRKOM: CuAsP no ISO. - llpUMe"t. nep.)
(3,n;eCb H ,n;arree «OTHOCHTeJIbHOe Y,n;JIHHeHHe Ha» 03HaQaeT OTHOCHTeJIbHO Y,n;JIH-
HeHHe npH COOTBeTCTByrow;eH ,n;JIHHe 06pa3u;a. HanpHMep, «OTHOCHTeJIbHOe Y,n;JIH-
HeHHe Ha 50 MM». - llpuMe"t. nep.)
6.3. 8emHble MemOJlJlbl U C11Jla8bl
CDJlaBOB
MeXalllf1leCKHe CBOBCTBa
Pa3Mep npe)];eJI npo'IHOCTH ua paCTJDKeUHe OmOCHTeJlhBoe eBIIe
(BpeMeHHoe COllpOTHBJleHHe) (H/MM2) ua 5,65
BJDDKai
Co- paTHhlii npJIMo- DIHii
KB8,ZI;paTllWii Kpyr- aUUOJ
CTOS- )];0 H KpyrJIWii H mecTH- npJIMo- JlhlB U mecTH- yroJlh- ISO
HHe OT BKJIIO- yroJlhllhdi yroJlhHhlB (%) yronhUhlB UhlB
(MM) '10 (%) (%)
(MM)
MHH. MaKC. MHU. MaKC. MHH. MaKC. MHH. MHH. MHH.
0 4 6,3 - 260 - - - - 32 - - Cu-ET
6,3 10 - 250 - - - - 32 - -
10 12 - 240 - 240 - 240 40 40 40
12 50 - 230 - 230 - 230 45 45 45
50 80 - 230 - 230 - - 45 45 -
H 4 6,3 290 - - - - - 4 - - Cu-FRH
6,3 10 280 - - - - - 8 - -
10 12 260 - 260 - 250 - 12 12 12
12 25 250 - 250 - 230 - 18 18 18
25 50 230 - 230 - 230 - 22 22 18
50 80 230 - 230 - - -' 22 22 -
H 4 6,3 350 - - - - - - - - Cu-OF
6,3 10 350 - - - - - - - -
10 12 320 - 310 - 270 - 6 6 6
12 25 290 - 280 - 260 - 8 8 8
25 50 260 - 250 - 250 - 12 12 10
0 6 - 210 MHH. 33 Cu-DHI
M 6 - 230 MHH. 13
Dla6a 6. MalUuHocmpoumeJlbHble MamepUOIlbl
XitMJtqecKHi
0603ua- ;
'IeHHe MaTepuaJI
BS Co Ni P Te Cr Co Be Zr Bi Fe Sb
:I
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C 109 Me,n:b-TeJI - I OCT. - - 0,30- - - - - - - -
.rryp 0,70
C 111 Me,n:b-cepa I OCT. - - - - - - - - - -
C 112 Me,n:b- II OCT. Ni + Fe - - - 20- 04- - - 0,10 -
, ,
Ko6aJIbT- 0,5 2,8 0,7
6epHJIJlHH
C 113 Me,n:b- II OCT. 0,8-1,2 0,16- - - - - - - - -
HHKeJIb- 0,25
cPoc<pop
CC 101 Me,n:b- XpOM II OCT. 0,02 0,01 - 0,3- - - - 0,001 0,08 0,002
1,4
CC 102 Me,n:b-xpoM- II OCT. 0,02 0,01 - 0,5- - - 0,02- 0,001 0,08 0,002
:QHpKOHHH 1,4 0,2
IIpUMe"tQHue.
,LlJuI OCHOBHbIX 3JIeMeHTOB cnrraBa npe,n:eJIbI BbmeJIeHbI )l{HpHbIM mpH<pToM. ECJIH He
orOBopeHO HHoe, 3HaqeHIDI B KOJIOHKe CYMMapHbIX npHMeceH BKJIIOqaIOT Te, KOTopbIe He
BbmeJIeHbI )l{HpHbIM mpH<pTOM. ECJIH He YKa3aHO HHaqe, Bce e,n:HHH'lHbIe npe,n:eJIbI COOTBeT-
CTByIOT MaKCHM}TMaM.
6.3. #8emHble MemOllJlbl U CTlJla8bl 5
O"OH"IaHUe
COCTaB (%) MexaHll'lecKHe CBOiiCTBa
npeaeJI
opo'lllOC- OmOCH-
TH Ha 0,2% YCJlOB-
p83p'" TeJlhHOe
P83Mep (BpeMeH- uwA npe,ll;eJI YJlJllllle- 6.J00uA-
Co- Hoe CO- TeK)"lecTII HHe Ha DIHii
C)'MMapawe (H/MM2) 5,65 8BaJlor
Si S SO CTOJI- 1IpOTIIB- ISO
npHMecH HHe neHHe!
(H/MM )
OT ,lI;O H
(MM) BKJUO'IU MHH. MHB. MHB.
(MM)
- - - 0,2 0 6 - 210 - 28 CuTe
M 6 50 260 - 8
50 - 240 - 8
- 0,3- - 0,2 0 6 - 210 - 28 CuS
0,6 M 6 50 260 - 8
50 - 240 - 8
0,2 - - 0,05 (HCKJIIOqasJ TH - - 690 - 9 CuCo2Be
Fe, Ni H Si)
- 0,2 - 0,03 TH - 25 410 - 18
(HCKJIIOqasJ S) 25 - 390 - 20
0,2 0,08 0,008 0,05 (HCKJIIOqasJ TH - 25 410 - 15 CuCrl
Fe, Si H S) 25 - 370 - 15
0,2 - 0,008 0,05 (HCKJIIOqasJ TH - 25 410 - IS CuCrlZr
Fe H Si) 25 - 370 - 15
Dla8a 6. MalUuHocmpoumeJlbHble MamepUOIlbl
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0611U1e CBOBCTB8 NUl CIOI, CI02, CI03, CI04 H CI06, nepe1JllCJIellllblX BYllle
T Ha (MM) Dpe,ZJ;eJI DpO'IIIOCTH OruOCH- HCDYTaIOIe Ba H31116
Ba p83pwa Te.JD.Boe
Co- y.zuome- TBep- DOBepeqm.di Dpo,ZJ;oJIhBWI
CTOJI- ));0 H BUIO'IU EoJlee BHe Ba ,ZJ;OCTJ.
De ,ZJ;O H 450 MM IDH- 450 MM 50 MM HV H3m H31116
OT BKJIIO-
QU pllllY (MHB.) (MHB.) (MHB.) YroJI, YroJI,
(H/MM2) (H/MM2) (%) rp c.. Pa.zntYc rp c.. Pa.zntYc
0 0,5 10,0 210 210 35 55 180 )];0 co- 180 )];0 co-
(MaKc.) npH- npH-
M 3,0 10,0 210 210 35 65 180 KOCHO- 180 KOCHO-
(MaKc.) BeHIDI BeHIDI
H 0,5 2,0 240 240 10 70/95 180 t 180 t
2,0 10,0 240 240 15 70/95 180 t 180 t
0,5 2,0 310 280 - 90 MHH. 90 t 90 t
H 2,0 1,00 290 280 - - - - - -
(3,l(eCb H ,l(aJIee t - BH,l(HMO, HMeeTCR B BIf.nY TOJIIUHHa HcnbITaTeJIbHOrO 06pa3u;a. -
llpUMelf.. nep.)
OCHOBaH Ha BS 2870: 1980, K KOTOpOMY CJIe,nyeT 06paIUaTbcR ,l(IDI no.rryqeHIDI nOJIHoit
HH<popMaU;HH. )];.rnI OCHOBHbIX 3JIeMeHTOB CIDIaBa npe,l(eJIbI BbI.neJIeHbI )l(HpHbIM mpH<pToM.
ECJIH He oroBopeHo HHoe, 3HaqeHIDI B KOJIOHKe CYMMapHbIX npHMeceit BKJIIOqaIOT Te, KOTO-
pble He Bb:r,neJIeHbI )l(HpHbIM mpH<pTOM. ECJIH He yK3.3aHO HHaqe, Bce e,l(HHWIHbIe npe,l(eJIbI
COOTBeTCTByIOT MaKCHMy:MaM.
llpUMer.tanue: H/MM2 = Mna.
6.3.9. naTYHHble nlfCTbl, nonOCbl If cponbra:
IIBYXKOMnOHeHTHble (6IfHapHble) cnnaBbl Melilf
If qlfHKa
,l{IDI 0603HaQeHHH CZ125, CZIOI, CZI02, CZI03.
CyM- TOJIIQlllla (MM) Dpe,ZJ;eJI Dpo'lllOCTH
Ba p83pwa
CBH- Ie- Map- Co-
0603Ba- MarrepH3JI Me,ZJ;b Ben JIe:JO BLle CTOJI- ));0 H BKJIIO- 60JIee
'IeHBe (%) (%) (%) (%) DpH- HBe ,ZJ;O H 'IU 450 MM 450' MM DIH-
MecH OT BKJIIO- (MHB.) pHBLI (MHB.)
(%) 'IU (H/MM2) (H/MM2)
CZ125 KanCIOJIb- 95,0/98,0 0,02 0,05 OCT. 0,025 0 - 10 - -
HasI Me,l(b
CZI0l 90/10 89,0/91,0 0,05 0,10 OCT. 0,40 0 - 10,0 245 245
JIaTYHb JiH - 3,5 310 380
JiH 3,5 10,0
H - 10,,0 350 325
CZI02 85/15 84,0/86,0 0,05 0,10 OCT. 0,40 0 - 10,0 245 245
JIaTyHb JiH - 3,5 325 295
JiH 3,5 10,0
-
H 10,0 370 340
CZI03 80/20 79,0/81,0 0,05 0,10 OCT. 0,40 0 - 10,0 265 265
JIaTyHb JiH - 3,5 340 310
JiH 3,5 10,0
-
H 10,0 400 370
rAa8a 6. MaUluHoCmpOUmeAbHbte MamepU(JJlbl
OKOH"IaHUe
TBep,ZJ;OCTh no BlIKKepcy (H v ) HclDtlT8lllle Ba B3I1I6
OmOCH- COBII8JU1-
060- Te.JD.Boe )];0 B BKJIIO'IO 60Jlee Donepe'lBLlii Dpo,ZJ;oJlhIlLlii eT IIJD[
3Ba'le- y.zuome- 450 MM IIDIpIlllhl 450 MM B31116 B31116 Baxo
BHe BHe Ba CB B l
50 MM ,ZJ;eJJax
MHB. (%) MHB. MaKC. MHB. MaKC. YI'OJI Pa.AHY c YI'OJI Pa.AHYc ISO
(rpwc) (rpwc)
-.
CZ125 - - 75 - 75 180 )]:0 COnpH- 180 )]:0 COnpH- -
KOCHOBeHHH KOCHOBeHHH
, -
CZ101 35 - 75 - 75 180 )]:0 COnpH- 180 )]:0 COnpH- ISO
7 95 - 85 - 180 KOCHOBeHHH 180 KOCHOBeHHH 426/1
3 110 - 100 - 180 t 180 t CuZnlO
90 2t 90 t
-
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CZ102 35 - 75 - 75 180 )]:0 COnpH- 180 )];0 COnpH- ISO
7 95 - 85 - 180 KOCHOBeHHH 180 KOCHOBeHHH 426/1
3 110 - 100 - 180 t 180 t CuZn15
90 2t 90 t
CZ103 40 - 80 - 80 180 )];0 COnpH- 180 )];0 COnpH- ISO
10 95 - 85 - 180 KOCHOBeHHH 180 KOCHOBeHHH 42611
5 120 - 110 - 180 t 180 t CuZ O
.90 2t 90 t
,l{IDI 0603HaQeHHH CZI06, CZI07, CZI08.
TOJllQlllla Dpe,ZJ;eJI Dpo'lllOCTB Ba
CyM- (MM) p83pYB (BpeMeBBoe'
060- CBB- Ie- Map- Co- cOIlpOTHBJleBHe)
3Ba'le- MaTe- Me,ZJ;b Ben Jle30 BLle CTOB- - ,"'
BHe pBU DpB- BHe ,ZJ;O B )];0 B BKJIIO- BoJIee
MecB '10 450 MM 450 MM .....
(%) OT BKJIIO- (MHB.) pllllY (MIiB.)
'10 (H/MM2) (H/.2)
.
.. ",
CZ106 70/30 68,5/71,5 0,05 0,05 OCT. 0,30 0 - 10,0 280 280
naT- 1/4H - 10,0 325 325
POH- 1/2H - 3,5
HasI 1/2H 3,5 10,0 350 340
JIaTYHb H - 10,0 415 385
CZ107 2/1 JIa- 64,0/67,0 0,10 0,10 OCT. 0,40 0 - 10,0 280 280
TYHb 1/4H - 10,0 340 325
1/2H - 3,5
1/2H 3,5 10,0 385 350
H - 10,0 460 415
EH - 10,0 525
... .
....
CZ108 npo- 62,0/65,0 030 0,20 OCT. 0,50 0 - 10,0 280 280
,
CTasI (HCK- 1/4H - 10,0 340 325
JIaTYHb mo- 1/2H - 3,5
qasI 1/2H 3,5 10,0 358 350
CBH- H - 10,0 460 415
Hen;) EH - 10,0 525 -
6.3. l(8emHble MemOJl/lbl U Cnn.Q8bl
OKOH"IaHUe
OruOCH- TBep OCTh no BlIKKepcy (1Iy) Hcm.mume Ba H31116 COBna.na-
060- Te.JD.Boe ));0 H BKJII01IaJI EoJIee DonepetDlYi Dpo oJIhBWI eT HJIH
3Ba'le- y.zuome- 450 MM mHlum... 450 MM H31116 H31116 BaxO,lUlT-
BHe BHe Ba CB B npe-
50 MM YroJi YroJi eJlax
MHB. (%) MHB. MaKC. MHB. MaKC. (rpwc) Pa.zntYc (rpwc) Pa.zntYc ISO
CZI06 50 - 80 - 80 180 )];0 conpH- 180 )];0 conpH- ISO
35 75 - 75 - 180 KOCHOBe- 180 KOCHOBe- 426/1
20 100 - 95 - 180 HIDI 180 HID! CuZn30
5 125 - 120 - 180 t 180 t
90 2t 90 t
CZI07 40 - 80 - 80 180 )];0 corrpH- 180 )];0 conpH- ISO
30 75 - 75 - 180 KOCHOBe- 180 KOCHOBe- 426/1
15 110 - 100 - 180 HIDI 180 HIDI CuZn33
5 135 - 125 - 180 t 180 t
- 165 - - - 90 2t 90 t
- 90 2t
CZI08 1 2 3 4 5 6 7 8 ISO
426/1
CuZn37
OCHOBaH Ha BS 2870: 1980, K KOTOpOMY CJIe,nyeT 06pamaTbcR 3a nOJIHOH HH<popMa-
UHeH. ,lLrnI OCHOBHbIX 3JIeMeHTOB CIIJIaBa npe,l(eJIbI Bbl,l(eJIeHbI )l(HpHbIM mpH<pToM. ECJIH He
orOBopeHO HHoe, 3HaqeHIDI B KOJIOHKe CYMMapHbIX npHMeceH BKJIIOqaIOT Te, KOTopbIe He
Bbl,l(eJIeHbI )l{HpHbIM mpH<pTOM. ECJIH He yx:a3aHO HHaqe, Bce e,l(HHI{qHbIe npe,l(eJIbI COOTBeT-
CTByIOT MaKCHMYMaM. llpUMer.tanue: H/MM2 = MIla.
6.3.10. naTYHHble nlfCTbl, nonOCbl If cponbra:
cneqlfanbHble cnnaBbl If nerlfpOBaHHafl naTYHb
JKe- Amo- CyM- TOJIIQlllla
0603Ba- MaTepH3JI Me.zo, OJlOBO CBHHeu; Jle30 QHHK MIIIIIIii MI.nobn MapBLIe Cocro- o H
'IeBHe (%) (%) (%) (%) (%) (%) (%) npHMecH JlBHe BKJIIO'IaJI
(%) (MM)
CZII0 AJIIOMHHHeBasI 76,0/ - 0,04 0,06 OCT. 1,80/ 0,02/ 0,30 M 10,0
JIaTYHb 78,0 2,30 0,05 a 10,0
CZ112 CY,l(OC1pOH - 61,0/ 1,0/ - - OCT. - - 0,75 M 10,0
TeJIbHaH 63,5 1,4 HJIH a 10,0
JIaTYHb H
CZ118 CBHHIJ;OBasI 63,0/ - 0,75/ - OCT. - - 0,30 H 6,0
JIaTYHb 66,0 1,5 H 6,0
64%Cu I%Pb EH 6,0
CZ119 CBHHUOBasI 61,0/ - 1,0/ - OCT. - - 0,30 H 6,0
JIaTYHb 64,0 2,5 H 6,0
62% Cu 2% Pb EH 6,0
CZ120 CBHHIJ;OBasI 58,0/ - 1,5/ - OCT. - - 0,30 H 6,0
JIaTYHb 60,0 2,5 H 6,0
59% Cu 2% Pb EH 6,0
CZ123 60/40 JIaTYHb C 59,0/ - 0,3/ - OCT. - - 0,30 M 10,0
HH3KHM CO,l(ep- 62,0 0,8
)J(aHHeM CBHH-
ua: mTaMIIO-
BaHHasI JIaTYHb
rJla6a 6. MawuHocmpoUme.tlbHble MamepUOJlbl
OKOH"IaHUe
HCDhlT8BHe Ha H31116 ....,...,
Dpe eJI OraOCH- TBep OCTh DO
COBD8,lJ,aer
0003Ha- 8p01JIIOCTH Te.JD.Hoe BlIKKepcy (1Iy) DODepe'lBLlii H31116 Dpo OJIhIlLlii H3rH6 HJIH H&xoJOlftJl
1IeHHe Ha p83pYB y)J,JllllleHHe B npe eJIIX
(MHH.) Ha 50 MM YI'OJI, YroJI, ISO
(H/MM2) MHH. (%) MHH. MaKC. rp8,lQ"C Pa.zntYc rp8,lJyC Pa.zntYc
340 45 -
CZII0 - - - - - - ISO 462/2
310 50 - 80 180 )];0 00- 180 )];0 00- CuZn20/AI2
npHKOC- npHKOC-
HOBemm HOBemm
CZ112 340 25 180 180 -
- - t t -
400 20 - - - - 90 t
CZ118 370 10 110 140 '" ,
- - - - -
430 5 140 165 - - - -
510 3 165 190 - - - -
CZ119 370 10 110 140 - - - - -
430 5 140 165 - - - -
510 3 165 190 - - - -
CZ120 - 10 110 140 - - - - ISO 42612
510 5 140 165 - - - - CuZn39/Pb2
575 3 165 190 - - - -
CZ123 370 - 20 - - - - - ISO 426L2-
CuZn40/}'h
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<l>oc<l>op - 0,1 - 0,1 - - - 0,02 - 0,02
-
HHKeJIb - 2,0 - 2,0 - 1,0 5,25 5,75 5,25 5,75
-
)l(eJIe30 - - - - 0,15 b - _b - _b
AmoMHHHH - 0,5 - - - 0,01 - 0,01 - 0,01
MapraHe - - - - - - - 0,20 - 0,20
CypbMa - 0,02 - 0,5 - _b - _b - _b
-
MbIillbSIK - - - - - _b - _b - _b
KpeMHHH - 0,1 - 0,01 - 0,02 - 0,02 - 0,02
BHCMYT - - - - - 0,03 - 0,02 - 0,02
Cepa - 0,1 - - - 0,10 - 0,10 - 0,10
-
MafHHH - - - - - - - - - -
-
HH06HH + - - - - - - - - - -
TaHTaJI
-
YrJIepo,n - - - - - - - - - -
-
- -
XpoM - - - - - - - - - -
-"
:QlipKOHHH - - - - - - - - - -
KOOaJIbT - - - - - - - - - -
CyMMapHbIe - 0,30 - 0,30 - 0,50 - 0,50 - 0,50
npHMeCH .
6.3. I(8emHble MemaJ/JIbl U CfIIla8bl
,lI;o6aB01JllbIe Me,lUlbIe CDJIaBbI ,nJUI JIHTbJl
0603HalleBHe SCB4. CT2 AD3 CNI CN2
Cy.ll.oC'rp()llTeJlhHaJI AmoMHHHeBO- Me.ll.b- Me.ll.b-
MarepHaJI JIa'fYllh AJUI JIHThJl Me.ll.b-OJIOBO KpeMHHeBaJI 1IIIKem.- 1IIIKem.-
B nec1lalllde cI»oPMW 6poH3a xpoM 'BHo6Hii
HOMRHan- Cu Zo 36 So Cu So 12 Ni Cu AI 6 Si 2 Fe Cu Ni 30 Cr Cu Ni 30 NB
BYii COCTaa
3JIeMeHThI MRH. MaKC. MRH. MaKC. MRH. MaKC. MBH. MaKC. MRH. MaKC.
(%) (%) (%) (%) (%) (%) (%) (%) (%) (%)
Me,nb 60,0 63,0 85,0 87,0 OCT8TOK OCTaTOK OCT8TOK
OJIOBO 1,0 1,5 11,0 13,0 - 0,10 - - - -
[(HHK OCT8TOK - 0,4 - 0,40 - - - - -
CBHHe - 0,50 - 0,03 - 0,03 - 0,005 - 0,005
<l>oc<l>op - - 0,05 0,40 a - - - 0,005 - 0,005
HHKeJIb - - 1,5 2,5 - 0,10 29,0 33,0 28,0 32,0
)l(eJIe30 - - - 0,20 0,5 0,7 0,4 1,0 1,0 1,4
AAIOMIffiHH - 0,01 - 0,01 6,0 6,4 - - - -
MapraHe - - - 0,20 - 0,50 0,4 1,0 1,0 1,4
CypbMa - - - - - - - - - -
MbIIIIb.SlK - - - - - - - - - -
KpeMHHH - - - 0,01 2,0 2,4 0,20 0,40 0,20 0,40
BHCM)'T - - - - - - - 0,002 - 0,002
Cepa - - - 0,05 - - - 0,01 - 0,01
MarHHH - - - - - 0,05 - - - -
HH06MH + - - - - - - - - 1,20 1,40
TaHTaJI
YrJIepo,n - - - - - - - 0,02 - 0,02
XPOM - - - - - - 1,5 2,0 - -
[(HpKOHHH - - - - - - 0,05 0,15 - -
K06aJIbT - - - - - - - 0,05 - 0,05
C)'MMapHbIe - 0,75 - 0,80 - 0,80 - 0,20 - 0,30
npHMeCH
a AmI HenpepbIBHoro JIHTb.Sl co,nep:>KaHHe <l>oc<l>opa MO:>KeT 6bITb yBeJIHtIeHO MaKCHMYM
.no 1,5% H K 0603HaQeHHIO CruIaBa ,n06aBJIeHO fL.
b )l(eJIe30 + cypbMa + MbIWb.SlK MaKCHMYM 0,20%.
nOJIHbIH .D:Hana30H CruIaBOB H ,nonOJIHHTeJIbHYJO HH<l>opMa HIO CMOTPH BS 1400.
AmI OCHOBHbIX 3JIeMeHTOB CruIaBa npe,neJIbI BbI.neJIeHbI :>KHpHbIM mpH<l>ToM. ECJIH He
orOBopeHO HHoe, 3HaqeHIDI B KOJIOHKe C)'MMapHbIX npHMeceH BKJIIOqaIOT Te, KOTopbIe He
BbI.neJIeHbI :>KHpHbIM WPH<l>TOM. ECJIH He yxa3aHO HHaqe, Bce e,nHHHtIHbIe npe,neJIbI COOTBeT-
CTByIOT MaKCHMYMaM.
18-3255
fADea 6. MaUluHOCmpOUmeAbHble MamepUaJlbl
6.3.20. MeAHwe cnnaSbl,lUlfl nlfTbfl: TlfnH&fHble CsoMcTsa
If 3Ha&feHlffl JlCeCTKOCTIf
. -
npo1lll0CTh H& paCTJDKeHHe 0,2% YCJloBHWii npe.ll.eJJ Te&:y'leCTII
TIm 11II- (H/MM2) (H/MM2)
0603Ha- TepBaJla
lIeHHe KPHCTaJI- .JIaTbe B .JIaTbe B Henpe- D:ellTpo- .JIaTbe B .JIaTbe B Henpe- D:eHTpO-
JIII3aIUDI oec'l8lfYlO phIBHoe OOmloe necllauyJO phIBBoe 6e1uoe
cI»oPMT' KOKIIJIL JIIIThe JIIIThe cI»oPMY' KOKllJlb JIIIThe JDI'fJae
rpynna A
PB4 L 190-270 270-370 330-450 280-400 100-160 140-230 160-270 140-230
LPBl L 190-250 220-270 270-360 230-310 80-130 130-160 130-200 130-160
LB2 L 190-270 270-280 280-390 230-310 80-130 140-200 160-220 140-190
LB4 L 160-190 200-270 230-310 220-300 60-100 80-110 130-170 80-110
LGI L 180-220 180-270 270-340 220-310 80-130 80-130 - -
LG2 L 200-270 200-280 - - 100-130 110-140 100-140 110-140
SCBl S 170-200 - - - 80-110 - - -
SCB3 S 190-220 - - - 70-110 - - -
SCB6 S 170-190 - - - 80-110 - - -
DCBl S - 280-370 - - - 90-120 - -
DCB3 S - 300-340 - - - 90-120 - -
PCB 1 S - 280-370 - - - 90-120 - -
-
I'pynna B
HCCI S 160-190 - - - - - - -
CCI-TF S 270-340 - - - 170-250 - - -
PBl S 220-280 310-390 360-500 330-420 130-160 10-230 170-280 170-230
PB2 L 220-310 270-340 310-430 280-370 130-170 170-200 170-250 170-200
CTI L 230-310 270-340 310-390 280-370 130-160 140-190 160-220 180-190
LG4 L 250-320 250-340 300-370 230-370 130-140 130-160 130-160 130-160
ABI S 500-590 540-620 - 560-650 170-200 200-270 200-270
AB2 S 640-700 650-740 - 670-730 250-300 250-310 - 250-310
CMAI S 650-730 670-740 - - 280-340 310-370 - -
HTBI S 470-570 500-570 - 500-600 170-280 210-280 - 210-280
HTB3 S 740-310 - - 740-930 400-470 - - 400-500
-
rpynna C 130-160
LBI L 170-230 200-270 230-310 220-300 80-110 130-160 130-190
LBS L 160-190 170-230 190-270 190-270 60-100 80-110 100-160 80-116
Gl L 270-340 230-310 300-370 250-340 130-160 130-170 140-190 130-170
G3 L 280-340 - 340-370 - 140-160 - 170-190 -
G3-TF L 430-480 - 430-500 - 280-310 - 280-310 -
SCB4 S 250-310 - - - 70-110 - - -
CT2 L 280-330 - 300-350 300-350 160-180 - 180-210 180-21G
AB3 S 460-500 - - - 180-190 - - -
CNI S 480-540 - - - 300-320 - - -
CN2 S 480-540 - - - 300-320 - - -
- -
(BanHMO, L - ,lUIHHHbIH, S - KOpOTKHH. - IIpUMe't. nep.)
6.3. I{8emHble MemOJlllbl U C1IJla8bl
OKoH'taHue
OmOCHTeJILBoe Y)J)DllleHHe TBep.ll.OCTh no BpHBeJIJIIO (HS>
THo HR- Ba 5,65
5,65 (%)
0603B8- TepBaJIa
qeHHe KPHCTaJI- .Jbrn.e B Henpe- D:ellTpO- .Jbrn.e B Henpe- D:ellTpO-
JlH38nHB nec1l8JlYlO .Jbrn.e B phIBBoe OO]KJIoe necqaayJO Jbrn.e B phIBBoe 6emIoe
cI»oPMY' KOKllJlb JIIIThe JlllTheb cI»oPMY' KOKllJlb JIIIThe .JIIITheb
Fpynna A
PB4 L 3-12 2-10 7-30 4-20 70-95 95-140 95-140 95-140
LPBl L 3-12 2-12 5-18 4-22 60-90 85-110 85-110 85-110
LB2 L 5-15 3-7 6-15 5-10 65-85 80-90 80-90 80-90
LB4 L 7-12 5-10 9-20 6-13 55-75 60-80 60-80 60-80
LGI L 11-15 2-8 - - 55-65 65-80 - -
LG2 L 13-25 6-15 13-35 8-30 65-75 80-95 75-90 80-95
SCBl S 18-40 - - - 45-60 - - -
SCB3 S 11-30 - - - 45-65 - - -
SCB6 S 18-40 - - - 45-60 - - -
DCBl S - 23-50 - - - 60-70 - -
DCB3 S - 13-40 - - - 60-70 - -
PCB 1 S - 25-40 - - - 60-70 - -
Fpynna B
HCCI S 23-40 - - - 40-45 - - -
CCI-TF S 18-30 - - - 100-120 - - -
PBl L 3-8 2-8 6-25 4-22 70-100 95-150 100-150 25-150
PB2 L 5-15 3-7 5-15 3-14 75-110 100-150 100-150 100-150
CTI L 6-20 5-15 9-25 6-25 70-90 90-130 90-130 90-130
LG4 L 16-25 5-15 13-30 6-30 70-85 80-95 80-95 80-95
ABI S 18-40 18-40 20-30 90-140 130-160 - 120-160
AB2 S 13-20 13-20 13-20 140-180 160-190 - 140-180
CMAI S 18-35 27-40 20-38 160-210 - - -
HTBI S 18-35 18-35 13-21 100-150 - - 100-150
HTB3 S 11-18 - 150-230 - - 150-230
Fpynna C
LBI L 4-10 3-7 9-10 4-10 50-70 70-90 70-90 70-90
LB5 L 5-10 5-12 8-16 7-15 45-65 50-70 50-70 50-70
Gl L 13-25 3-8 9-25 5-16 70-95 85-130 90-130 70-95
G3 L 16-25 - 18-25 - 70-95 - 90-130 -
G3-TF L 3-5 - 3-7 - 160-180 - 160-180 -
SCB4 S 18-40 - - - 50-75 - 100-150 100-150
CT2 L 12-20 - 8-15 10-15 75-110 - -
AB3 S 20-30 - - - - - - -
CNI S 18-25 - - - 170-200 - - -
CN2 S 18-25 170-200
a Ha OT,neJIbHO OTJIHTbIX TeCTOBbIX CTep)KHID{
b 3HaqeHIDI npHMeHHMbI ,lUllI 06pa3
OB, Bblpe3aHHbIX H3 OTJIHBOK, no.nyqeHHbIX
eHTPO-
6eXHbIM JIHTbeM B MeTaJIJIu:qecKHX <pOpMax. MHHHMaJIbHble xapaKTepHCTHKH ,nIDI OTJIHBOK,
no.rryqeHHbIX
eHTPo6e)KHbIM JIHTbeM B neCqaHble <pOpMbI, Tame :>Ke, KaK H npH 06bJ1IHOM
JIHTbe B neCqaHble <l>OpMbI.
Dla8a 6. MaUluHocmpoumeJlbHble MamepUOIlbl
6.3.21. AnIONlIfHIfM If anlONlIfHlfeSble cnnaSbl
qHCTbIH aJJJOMHHHH HMeeT HH3KYK> MeXaHlNecKYK> npOqHOCTb H 06bPlHO HCnOJIL-
3yeTcH B BH,l(e CruIaBOB C ,npyrHMH MeTa.rr.rraMH, o6pa3yJOI.I.J;HMH IIIHpOKHH ,lJ;Han3.30Ii
nOJIe3HbIX, JIerKHX MaTepHaJIOB. AnIOMHHHeBbIe CruIaBbI MOryr 6bITb pa3,neJIeHbI Ha
qeTbIpe KaTeropHH:
. ,l];e<l>opMHpyeMbIe CruIaBbI, KOTopbIe MOryr no,nBepraTbCH TepMoo6pa6oTKe.
. ,l];e<l>opMHpyeMbIe CruIaBbI, KOTopbIe He MOryr no,nBepraTbCH TepMoo6pa6oTICe.
. JIHTeHHbIe CruIaBbI, KOTopbIe MOryr no,nBepraTbCH TepMoo6pa6oTKe.
. JIHTeHHbIe CruIaBbI, KOTopbIe He MOryr no,nBepraTbCH TepMoo6pa6oTKe.
KaK H 60JIbIIIHHCTBO BeTHbIX MeTaJlJIOB H HX CruIaBOB, aJIlOMHHHH H aJIIOMH-
HHeBbIe CruIaBbI 3aBHCHT OT npo eCCOB XOJIO,nHOH o6pa6oTKH MeTaJlJIa, TaKHX K8J{
npOKaTKa H BbITIDKKa, ,l{.JUI y.rryqIIIeHIDI HX CBOHCTB. TOJIbKO OTHOCHTeJIbHO He6oJI -
IIIoe KOJIlNeCTBO aJIlOMHHHeBbIX CruIaBOB, co,nep)KaI.I.J;HX Me,nb H ,npyrHe JIerHpYIO""
I.I.J;He 3JIeMeHTbI, MOryr no,nBepraTbCH TepMoo6pa6oTKe. IIpHMepoM JIerKOrO CITJI8.Ba
o6I.I.J;ero Ha3HaqeHIDI, nepBOHaqaJIbHO pa3pa6oTaHHoro ,l{.JUI no,nBepraeMbIX BbICO-
KHM HarpY3KaM ,neTaJIeH CaMOJIeTa, MO)KeT CJIy)KHTb ,nlOpaJIIOMHHHH. 3TOT CIm4
HMeeT CJIe,nyroI.I.J;HH COCTaB:
Me,nb (Cu) 4,0%
KpeMHHH (Si) 0,2%
MapraHe (Mn) 0,7%
MarHHH (Mg) 0 8%
AnIOMHHHH (AI) OCTaToK
3TOT CruIaB MO)KeT 6bITb pa3ynpOqHeH HarpeBOM ,no 480°C C nOCJIe,nyroI.I.J;HM O -
JI3.)K,lI;eHHeM. 3TOT npo ecc Ha3bIBaeTCH rOMoreHH3a HeH; JIerHpyJOI.I.J;He 3JIeMellThl
o6pa3yJOT TBep,nbIH paCTBOp C aJIIOMHHHeM, B pe3YJIbTaTe qero OH CTaHOBHTCH ITJIae
TINHbIM H npHro,nHbIM ,l{.JUI XOJIO,nHOH o6pa6oTKH 6e3 paC1'peCKHBaHIDI. O,lJ;HaKO OR
HeMe,aJIeHHO HaqHHaeT ynPOqIDIThCH 6JIaro,napH eCTecTBeHHoMY npo eccy, KOTO
pbIH Ha3bIBaeTCH cTapeHHeM, H nOJIHOCTblO BOCCTaHaBJIHBaeT TBep,nocTb CruIaBa TO-
JIbKO qepe3 4 ,nIDI. Bo BpeMH CTapeHIDI HeCTa6HJIbHbIH nepeHaCbII.I.J;eHHbIH pac ()p
JIernpyJOI.I.J;HX 3JIeMeHTOB pacna,n;aeTCH C BbIna,n;eHHeM B OCa,n;OK HHTepMeTa.rr.rrlNe
CKoro coe,nHHeHIDI CuAl 2 . OCa,n;OK BbIna,n;aeT B <l>opMe MeJIbqaHIIIHX qaCTH , pacce-
HHHbIX no BceH Macce MeTa.rr.rra, qTO npH,l(aeT eMY 60JIbIIfYlO npOqHOCTb H )KeCT
KOCTb.
,l];pyrOH CruIaB, eI.I.J;e 60JIee npOqHbIH, HMeeT CJIe,nyroI.I.J;HH COCTaB:
Me,nb (Cu) 1,6%
THTaH (Ti) 0,3%
MarHHH (Mg) 2,5%
QHHK (Zn) 0,2%
AnIOMHHHH (AI) Bce OCTaJIbHOe
-'
3TOT CruIaB TalOKe MO)KeT 6bITb pa3ynpOqHeH rOMoreHH3a HeH npH HarpeBe )];0
465°C H OXJI3.)K,lI;eHHH. IIoBTopHoe ynpOqHeHHe npOHcxo,nHT 3a CqeT eCTeCTBeHHoro
CTapeHIDI. ECJIH npo ecc eCTeCTBeHHoro CTapeHIDI YCKOPHIOT, nOBTopHO HarpeBWI
CruIaB ,no 165°C npH6JIH3HTeJIbHO B TeqeHHe 10 qaCOB, npo ecc Ha3bIBalOT ,nHcnep
CHOHHbIM TBep,neHHeM HJIH HCKYCCTBeHHbIM CTapeHHeM. IIpo ecc CTapeHIDI nocJle
rOMoreHH3a HH MO)KeT 6bITb 3aMeAJIeH OXJI3.)K,lI;eHHeM.
6.3. 8emHble MemQ/l/lbi U CfI./la8bl
6.3.22. 6plfTaHcKlfe CTaH,lIapTbl
HIDKe npHBe,neHbI HeKOTopbIe nOJIe3HbIe 6pHTaHCKHe CTaH,ll;apTbI, KacalOm;HeCH
aJIIOMHHIDI, a TalOKe ,ne<!>opMHpyeMbIX H JIHTeHHbIX aJIlOMHHHeBbIX CruIaBOB, KaK
TIo,nBepralOm;HXCH, TaK H He no,nBepralOm;HXCH TepMo06pa60TKe:
. BS EN 485-2: 2004 ArrIOMHHHH H aJIlOMHHHeBbIe CruIaBbI. JIHCTbI, nOJIOCbI H
ruIHTbI - XHMlNeCKHH COCTaB.
. BS EN 485-2: 2004 ArrIOMHHHH H aJIlOMHHHeBbIe CruIaBbI. JIHCTbI, nOJIOCbI H
ruIHTbI - MeXaHlNeCKHe CBOHCTBa.
. BS EN 573: 1995 (qeThIpe qaCTH) - ,ne<!>opMHpyeMbIe H3,neJIIDI:
qacTb 1: :QH<!>POBaH CHCTeMa 0603HaqeHIDI
qacTb 2: CHcTeMa 0603HaqeHHH, OCHOBaHHaH Ha XHMlNeCKHX CHMBOJIax
qacTb 3: XHMWIecKHH COCTaB.
qacTh 4: <l>OpMbI H3,neJIHH.
. BS EN 1559-4: 1999 JIHThe - ,nonOJIHHTeJIbHbIe 1'pe60BaHIDI K OTJIHBKaM H3
aJIlOMHHIDI H aJIlOMHHHeBbIX CruIaBOB
. BS 1706: 1998 ArrIOMHHHH H aJIlOMHHHeBbIe CruIaBbI. OTJIHBKH. XHMHqeCKHH
COCTaB H MeXaHlNeCKHe CBOHCTBa.
IlepeqHcJIeHHbIe CTaH,ll;apTbI OqeHb no,np06HbIe H BceCTopOHHHe, H <!>H31NecKH
HeB03MO)f{H0 BocnpOH3BeCTH HX B paMKax 3Toro CnpaBOqHHKa. O,nHaKo CJIe.nyeT 06-
pam;aTbCH K HHM npH BbI60pe MaTepHaJIOB npH pa3pa60TKe HOBbIX H3,neJIHH H HX
TIpOH3Bo,nCTBa.
HeKoTopbIe THTIINHbIe npHMepbI aJIIOMHHIDI, a TalOKe ,ne<!>0pMlfpyeMbIX H JIH-
TeHHbIX aJIlOMHHHeBbIX CruIaBOB npHBe,neHbI B Ta6JIH ax B CJIe,nyrom;HX pa3,neJIax.
OHH npHBe,neHbI TOJIbKO AJUI cnpaBKH.
6.3.23. nnlfTw, nlfCTbl If nonOCbl 1f3 .,IfCToro anlONlIfHlffl
COCTaB
0003ua- KpeMHHi IeJle30 Me. Map- Mar- Amo- QtmK faJlJlllii Tlrraa ,ZWyraeb
'IellHJl (%) (%) (%) raae.. HBii MIIIIIfiC (%) (%) (%)
MaTe- (%) (%) (%) I\uw.Ii Deero
pHaJlOB a (%) (%)
1080(A) 0,15 0,15 0,03 0,02 0,02 99,80 0,06 0,03 0,02 0,02 -
1050(A) 0,40 0,05 0,05 0,05 0,05 99,50 0,07 - 0,05 0,03 -
1200 1,0Si+Fe 0,05 0,05 - 99,00 0,10 - 0,05 0,05 0,15
CBOHCTBa
TOJllQlllla npe,ZJ;eJI npo'lllOCTH OruOCIlTeJIhHoe Y,lJ.JDIIIeHBe Ha 50 MM: OruOCIlTeJIhHoe
0003Ha- (MM) Ha pa3phIB (BpeMeH- MaTepHaJIW ro.mu;e, 'IeM Y)J.JllllleHBe Ha
'IeHBe 06pa- Hoe eOlIpOTllBJleHBe) 5,65..jS; 6o.JIee
MaTepHa- 60Tu d 6o.JIee 12,5 MM
JIOB (%) > MHH. MaKe. 0,5 MM 0,8 MM 1,3 MM 2,6 MM 3,0 MM IIIHIUUIY (MHH.)
(H/MM2) (H/MM2) (%) (%) (%) (%) (%) (%)
1080(A) F 3,0 25,0 - - - - - - - -
0 0,2 6,0 - 90 29 29 29 35 35 -
H14 0,2 12,5 90 125 5 6 7 8 8 -
H18 0,2 3,0 125 - 3 4 4 5 - -
19-3255
Dla8a 6. MaUluHocmpoumeJlbHble MamepUOJlbl
O"oHliaHue
TOJllQlllla npe.ZJ;eJI npO'lllOCTH OruoCHTeJIhHOe Y,lJ.JDIIIeHBe Ha 50 MM: OruOCHTeJJJ.BOe
0603Ha- (MM) Ha Jla3PhIB (BpeMeH- MaTepHaJIhI TOJDQe, 'IeM YNIHQeHBe aa
'IeHBe 06pa- Hoe CODpOTHBJIeBHe) S,6S 6o.Dee
MaTepHa- 60TKa d 6o.JIee 12,5 MM
JIOB (%) > MHH. MaKC. 0,5 MM 0,8 1,3 MM 2,6 MM 3,0 MM IIIIIpHBW (MBB.),.
(H/MM2) (H/MM2) (%) (%) (%) (%) (%) (%)
-
1050(A) F 3,0 25,0 - - - - - - - -
0 0,2 6,0 55 95 22 25 30 32 32 -
H12 0,2 6,0 80 115 4 6 8 9 9 -
H14 0,2 12,5 100 135 4 5 6 6 8 -
H18 0,2 3,0 135 - 3 3 4 4 - -
1200 F 3,0 25,0 - - - - - - - -
0 0,2 6,0 70 105 20 25 30 30 30 -
H12 0,2 6,0 90 125 4 6 8 9 9 -
H14 0,2 12,5 105 140 3 4 5 5 6 -
H16 0,2 6,0 125 160 2 3 4 4 4 -
H18 0,2 3,0 140 - 2 3 4 4 - -
-
a COCTaB B rrpoueHTax (M/M) COOTBeTCTByeT MaKCHMYMY, eCJIH HBHO He YKa3aH ,nHana3Q1;J
HJIH MHHHM}'M. b AHaJIH3 peryJUlpHO BblrrOJIIDIeTCH TOJIbKO ,l(JUI 3JIeMeHTOB, ,l(JUI KOTOpLIX
yKa3aHbI orrpe,neJIeHHbIe rrpe,neJIbI. ECJIH, o,nHaKO, 3arro,n03peHO rrpHC}'TCTBHe ,npyrHX SJIe:
MeHTOB HJIH peryJUlpHbIH aHaJIH3 yKa3aJI Ha HX rrpHC}'TCTBHe CBepx 3a,naHHbIX rrpe,neJIOB, ,n;a-
JlbHeHWHH aHaJIH3 CJle.nyeT BbIrrOJIIDITb, qTo6bI y6e,nHTbCR, qTO KOJIH'leCTBO 3THX 3JIeMemo)
He rrpeBbIwaeT 3a,naHHbIX rrpe,neJIOB. c Co,nepxaHHe amoMHHIDI B 1flICTOM aJIIOMHHHH, He no.
BepraBweMCH rrpoueccy 01fllCTKH, orrpe,neJUleTCH KaK pa3HHUa Me)l{)Jy 100% H CYMMOH 'WO-
ueHTOB Bcex OCTaJIbHbIX MeTaJIJIOB, KOJIH'leCTBO KIDK,lIOro H3 KOTOpbIX paBHO HJIH rrpeBbIIIIaT
0,10%, OKpyrJIeHHbIX rrepe,n HaxO)K,l(eHHeM C)'MMbI ,no BTOpOro 3HaKa rrOCJIe 3aIDITOH. d AnD-
TepHaTHBHbIH MeTO,n rrpOH3Bo,nCTBa, 0603HaQeHHbIH KaK H2, MoxeT HCrrOJIb30BaTbCH BMeCT0
TeXHOJIOIWIeCKOro Mapwp}'Ta HI, eCJIH ,nOCTHI'HyrO COrJIaWeHHe Mex.ny rrOCTaBII(HKOM II
rr01'pe6HTeJIeM H rrpH YCJIOBHH rro.rryqeHIDI Tex xe 3a,naHHbIX CBOHCTB.
6.3.24. nnlfTbl, nlfCTbl If nonOCbl 1f3 anlONlIfHlfeSOro
cnnasa: 6e3 TepNlIf.,eCKOM o6pa6oTKIf
COCTaB
, ,
060- ,ZWyraeh
3Ha'le- KpeM- Ie- Me. Map- Mar- XpoM Amo- ,ZWyrae TImm
HBe BBii JIe30 (%) raRe.. BHii (%) MIIIIIIii (%) orpaBll'le- (%) Ka1K- Bcero
MaTe- (%) (%) (%) (%) (%) IIHJI (%) .ZJ;Idi (%)
pHaJla a (%)
- -
. .,
3103 0,50 0,7 0,10 0,9/1,5 0,30 0,10 OCT. 0,20 0,10 - 0,05 o 15
,
Zr + Ti
'"
3105 0,6 0,7 0,3- 0,3/0,8 0,2/0,8 0,20 OCT. 0,40 - 0,01 0,05 O,
5005 0,3 0,7 0,2 0,2 0,5/1,1 0,10 OCT. 0,25 - - 0,05 011 5 ,
5083 0,40 0,40 0,10 0,4/1,0 4,0/4,9 0,05/0,25 OCT. 0,25 - 0,15 0,05 O l
5154 0,50 0,50 0,10 0,50 3,1/3,9 0,25 OCT. 0,20 0,10/0,50 0,20 0,05 0,15
Mn+Cr . . .
. .
5251 0,40 0,50 0,15 0,1/0,5 1,7/2,4 0,15 OCT. 0,15 - 0,15 0,05 o 15
, ,
5454 0,25 0,40 0,10 0,5/1,0 2,4/3,0 0,5/2,0 OCT. 0,25 - 0,20 0,05 0,t5.
-
6.5. Ilo/lUMepHble MamepUOIlbl (lIIlaCmMaCcbl)
O"oHlfaHue
npe,IJ;eJI DpO'IIIOC- OruOCHTeJIh-
060- 06- TOJllQlllla 0,2% TO Ha pat3phIB OruoCHTeJIhHOe Y,lJ.JDIIIeHBe Ha Hoe Y,lJ.JDIIIeHBe
3Ha'le- pa- (MM) YCJIOBIIhIii (BpeMeHHoe 50 MM: MaTepHaJI TOHLme, 'IeM Ha 5,65
HBe fioT.. npe,IJ;eJI cOlIpOTllBJleHBe)
MaTe- gC TeKY'leCTH 60JIee 12,5 MM
pHaJla a (%) (H/MM2) MHH. MaKC. 0,5 MM 0,8 MM 1,3 MM 2,6 MM 3,0 MM TO
> < (H/MM2) (H/MM2) (%) (%) (%) (%) (%) (MHH.) (%)
3103 F 0,2 25,0 - - - - - - - -
-
0 0,2 6,0 - 90 130 20 23 24 24 25 -
H12 0,2 6,0 - 120 155 5 6 7 9 9 -
H14 0,2 12,5 - 140 175 3 4 5 6 7 -
H16 0,2 6,0 - 160 195 2 3 4 4 4 -
H18 0,2 3,0 - 175 - 2 3 4 4 - -
3105 0 0,2 3,0 - 110 155 16 18 20 20 - -
H12 0,2 3,0 115 130 175 2 3 4 5 - -
H14 0,2 3,0 145 160 205 2 2 3 4 - -
H16 0,2 3,0 170 185 230 1 1 2 3 - -
H18 0,2 3,0 190 215 - 1 1 1 2 - -
5005 0 0,2 3,0 - 95 145 18 20 21 22 - -
H12 0,2 3,0 80 125 170 4 5 6 8 - -
H14 0,2 3,0 100 145 185 3 3 5 6 - -
H18 0,2 3,0 165 185 - 1 2 3 3 - -
5083 F 3,0 25,0 - - - - - - - - -
0 0,2 80,0 125 275 350 12 14 16 16 16 14
H22 0,2 6,0 235 310 375 5 6 8 10 8 -
H24 0,2 6,0 270 345 405 4 5 6 8 6 -
5154 0 0,2 6,0 85 215 275 12 14 16 18 18 -
H22 0,2 6,0 165 245 295 5 6 7 8 8 -
H24 0,2 6,0 225 275 325 4 4 8 6 5 -
5251 F 3,0 25,0 - - - - - - - - -
0 0,2 6,0 60 160 200 18 18 18 20 20 -
H22 0,2 6,0 130 200 240 4 5 6 8 8 -
H24 0,2 6,0 175 275 275 3 4 5 5 5 -
H28 0,2 3,0 215 255 285 2 3 3 4 4 -
5454 F 3,0 25,0 - - - - - - - - -
0 0,2 6,0 80 215 285 12 14 16 18 18 -
H22 0,2 3,0 180 250 305 4 5 7 8 - -
H24 0,2 3,0 200 270 325 3 4 5 6 - -
a COCTaB B rrpoueHTax (M/M) COOTBeTcTByeT MaKCHMYMY, eCJIH HBHO He yKa3aH ,nHarra30H
IDIH MHHHM)'M. b AHaJIH3 peryJUlpHO BbIrrOJIIDIeTCH TOJlbKO ,l(JUI 3JIeMeHTOB, ,l(JUI KOTOpbIX
yxa3aHbI orrpe,neJIeHHbIe rrpe,neJIbI. ECJIH, o,nHaKO, 3arro,n03peHO rrpHcyrcTBHe ,npyrHX 3JIe-
MeHTOB HJIH peryJUlpHbIH aHaJIH3 yKa3aJI Ha HX rrpHcyrcTBHe CBepx 3a,naHHbIX rrpe,neJIOB,
D:aJIbHeHmHH aHaJIH3 CJIe.nyeT BbIrrOJIIDITb, qTo6bI y6e,nHTbCH, qTO KOJIH'leCTBO 3THX 3JIeMeH-
TOB He rrpeBbImaeT 3a,naHHbIX rrpe,neJIOB. c Moryr HCrrOJIb30BaTbCH TeXHOJIOfH'leCKHe Mapm-
PYTbI HI HJIH H2, eCJIH ,nOCTHfuyrO COfJIameHHe Mex,ny rrOCTaBII(HKOM H rro'rpe6HTeJIeM H
IIPH YCJIOBHH rro.rryqeHIDI Tex xe 3a,naHHbIX CBOHCTB.
FilO8a 6. MalUuHoCmpOUmeJlbHble MamepUOJlbl
6.3.25. nnlfTbl, nlACTbl If nonoc., 1f3 anlONlIfHlAeSOrO
cnnasa: TepNlIA.,eCKafl o6pa6oTKa
COCTaB
-
OOO3Ha- KpeM- Ie- Me. Map- Mar- XpoM IIH- ,[Wyrae 1imm Amo- ,[Wyrae ·
'IeHBe HBii JIe30 (%) raae.. mdi (%) KeJD. (%) orpaHII- (%) MIOIIIi ...
MaTe- (%) (%) (%) (%) (%) 'IellHJl (%) IWK- Bcero
pHaJla a (%) .zu.Di (%)
(%)
--
2014A 0,5/ 0,50 3,9/ 0,4/ 0,2/ 0,10 0,10 0,25 0,20 Zr 0,15 OCT. 0,05 0,15
0,9 5,0 1,2 0,8 + Ti
Clad 0,5/ 0,50 3,0/ 0,4/ 0,2/ 0,10 0,10 0,25 0,20 Zr 0,15 OCT. 0,05 0,15
20 14Ac 0,9 5,0 1,2 0,8 + Ti
2024 0,50 0,50 3,8/ 0,3/ 1,2/ 0,10 - 0,25 - 0,15 OCT. 0,05 0,15
4,4 0,9 1,8 -
Clad 0,50 0,50 3,8/ 0,3/ 1,2/ 0,10 - 0,25 - 0,15 OCT. 0,05 0,15
2024 c 4,4 0,9 1,8
-
6082 0,7/ 0,50 0,10 0,4/ 0,6/ 0,25 - 0,20 - - OCT. 0,05 0,15
1,3 1,0 1,2 -
CBOHCTBa
TOJIIQIIIIa n eJI DpO'IIIOC- OmOCIlTeJIhHoe Y)J.JIlllleHBe Ha OraOCH-
(MM) 0,2% TH Ha pa3phIB 50 MM: MaTepHaJIhI 1'OJIIQe, 'IeM TeJlWloe
0OO3Ha- 06- YCJIOB- YAJDIBe-
IIhIii HBeD
'IeHBe pa- Dpe,ZJ;eJI 5,65J{
MaTe- 6oT-
pHaJla a u d > < TeKY- MHH. MaKC. 0,5 MM 0,8 MM 1,3 MM 2,6 MM 3,0 MM fiOJIee
'I (H/MM2) (H/MM2) (%) (%) (%) (%) (%) 12,5 MM
(H/MM2) TO.JIIQJIIIU
(....) (%)
2014A 0 0,2 6,0 110 - 235 14 14 16 16 16
T4 0,2 6,0 22 400 13 14 14 14 14
T6 0,2 6,0 380 440 - 6 6 7 7 8
T451 6,0 25,0 250 400 - - - - 14 12
25,0 40,0 250 400 - - - - - 10
40,0 80,0 250 395 - - - - - 7
T651 6,0 25,0 410 460 - - - - - 6
25,0 40,0 400 450 - - - - - 5
40,0 60,0 390 430 - - - - - 5
60,0 90,0 390 430 - - - - - 4
90,0 115,0 370 420 - - - - - 4
115,0 14.9,0 350 410 - - - - - 4
ft .
Clad
20 14AcT4 0 0,2 6,0 100 - 220 14 14 16 16 16 -
(nrraKH- 0,2 1,6 240 385 - 13 14 14 - - -
pOBaH- 1,6 6,0 245 395 - - - 14 14 -
HbIB)
T6 0,2 1,6 345 420 - 7 7 8 9 - -
1,6 6,0 355 420 - - - 9 9 - J..
6.5. IIo/lUMepHble MamepUQIlbl (f1.IIaCmMaCcbl)
OKOHlI.aHUe
TOJllQlllla npe,ZJ;eJI DpO'IIIOC- OraOCHTeJlhlloe YAJllllleHBe Ha OraOCH-
(MM) 0,2% TIi Ha pa3phIB 50 MM: MaTepHaJIhI TOJDQe, 'IeM TeJlhHoe
0603Ha- 06- YCJIOB- YNDlHe-
IIhIii HUe Ha
'IeHBe pa- npe,ZJ;eJI 5,65
MaTe- 00.....
pHaJla a u d > < TeKY- MHH. MaKC. 0,5 MM 0,8 MM 1,3 MM 2,6 MM 3,0 MM ooJlee
'I (H/MM2) (H/MM2) (%) (%) (%) (%) (%) 12,5 MM
(H/MM2) TO
(MHIL) (%)
2024 0 0,2 6,0 110 - 235 12 12 14 14 14 -
T3 0,2 1,6 290 440 - 11 11 11 - - -
1,6 6,0 290 440 - - - - 12 12 -
T351 6,0 25,0 280 430 - - - - - 10 10
25,0 40,0 280 420 - - - - - 9
40,0 60,0 270 410 - - - - - 9
90,0 115,0 270 400 - - - - - - 8
115,0 140,0 260 390 - - - - - - 7
Clad
2024 b 0 0,2 6,0 100 - 235 12 12 14 14 14 -
(DJIaKH- T3 0,2 1,6 270 405 - 11 11 11 - - -
pOBaH- 16 6,0 275 425 - - - - 12 12 -
HbIH)
6082 0 0,2 3,0 - 155 16 16 16 15 - -
-
T4 0,2 3,0 120 200 - 15 15 15 15 - -
3,0 25,0 115 200 - - - - - 15 12
T6 0,2 3,0 255 295 - 8 8 8 8 - -
3,0 25,0 240 295 - - - - - 8 -
T451 6,0 25,0 115 200 - - - - - - 15
25,0 90,0 115 200 - - - - - - 15
T651 6,0 25,0 240 295 - - - - - - 8
25,0 900 240 295 - - - - - - 8
90,0 115,0 230 285 - - - - - - 7
115,0 150,0 220 275 - - - - - - 6
a COCTaB B rrpou;eHTax (M/M) COOTBeTcTByeT MaKCHM}'MY, eCJIH HBHO He yKa3aH ,nHarra30H
IDIH MHHHMYM. b AHaJIH3 peryJUlpHO BbIrrOJIIDIeTCH TOJIbKO ,l(JUI 3JIeMeHTOB, ,l(JUI KOTOpbIX
yJ<a3aHbI orrpe,neJIeHHbIe rrpe,neJIbI. ECJIH, o,nHaKO, 3arro,n03peHO rrpHcyrcTBHe ,npyrHX 3JIe-
MeHTOB HJIH peryJUlpHbIH aHaJIH3 yKa3aJI Ha HX rrpHcyrcTBHe CBepx 3a,naHHbIX rrpe,neJIOB,
,naJIbHeHmHH aHaJIH3 CJle.nyeT BbIrrOJIIDITb, qTo6bI y6e,nHTbCH, QTO KOJIH'leCTBO 3THX 3JIeMeH-
TOB He rrpeBbImaeT 3a,naHHbIX rrpe,neJIOB. C (DJIaKHpOBaHHbIH) B KaqeCTBe MaTepHaJIa ,l(JUI rro-
KpbITIDI HCrrOJIb3yeTcH qHCTbIH aJIlOMHHHH copTa 1050A. TOJlII(HHa rrOKpbITIDI COCTaBJUleT
4% Ha KIDK,LIOH CTopOHe MaTepHaJIa rrpH TOJIII(HHe MeHbmeH HJIH paBHoH 1,6 MM, H 2% Ha
KIDK,lJ;OH CTopOHe MaTeparra rrpH TOJIII(HHbI CBbIme 1,6 MM. d 06pa6oTKa Tx51 (CIDITHe HarrpH-
)KeHHe paCTIDKeHHeM) rrpHMeIDIeTCR ,l(JUI DJIHT H JIHCTOB, KOTopbIe paCTHHyrbI rrOCJIe rOMore-
HH3aUHH,l(JUI rrpH.naHIDI HM OCTaTOqHOH ,ne<!>opMaUHH rrpH6JIH3HTeJIbHO 1,5-3,0%. e npHBe-
,neHbI MaKCHMaJIbHbIe 3HaqeHIDI YCJIOBHOrO rrpe,neJIa TeKY'leCTH ,l(JUI CDJIaBOB rrOCJIe o6pa6oT-
KH 0 H MHHHMaJIbHbIe 3HaQeHIDI ,l(JUI Bcex OCTaJIbHbIX CDJIaBOB.
FilO8a 6. MaUluHOCmpOUme.tlbHble MamepUOIlbl
6.3.26. npyrKIA, WTaNlnOSaHHble Tpy6bl IA npocplAnlA
Jf3 anlONlIfHlffl IA anlONlIfHlfeSOro cnnasa
- ,lInfl o6Lqero NlaWIAHOCTpoeHlffl:
6e3 TepNlIf.,ecKoM o6pa6oTKIf
COCTaB
"-
0OO3Ha'le- KpeM- Ie- Me. Map- Mar- XpOM ,[Wyrae Tlrraa ,IJ;pyraeb Amo-
HBe MaTe- HHii JIe30 (%) raae.. HHii (%) (%) orpaHH- (%) Ka1K,zu.Iii Dcero MIIBBI
pHaJla 8 (%) (%) (%) (%) '1elllUl (%) (%) (%) (%)
1050A 0,25 0,40 0,05 0,05 0,05 - 0,07 - 0,05 0,03 - 99,5Od
MHH.
1200 1,0 0,05 0,05 - - 0,10 - 0,05 0,05 0,15 99,0()d
Si+Fe MHH.
5083 0,4 0,4 0,10 0,40/ 4,0/ 0,05/ 0,25 - 0,15 0,05 0,15 OCT.
1,0 4,9 0,25
5154A 0,50 0,50 0,10 0,50 3,1/ 0,25 0,20 0,10-0,50 0,20 0,05 0,15 OCT.
3,9 Mn + Cr
5251 0,40 0,50 0,15 0,10/ 1,7/ 0,15 0,15 - 0,15 0,05 0,15 OCT.
0,5 2,4
....
CBOHCTBa
- -
-..
npe,ZJ;eJI npO'lllOCTH OmOCHTe.1lhHoe
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HJIH TOJlIQlllla (TPY- npe,ZJ;eJI TeKY-
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MaTepH8Jla 60TKa c (H/MM2) Ha 50 MM
...
> MHB. MHH. MaKC. MHH. (%) MHH. (%)
,
1050A F - - - (60) - (25) (23)
1200 F - - - (65) - (20) (18)
5083 a - 150 e 125 275 - 14 13
F - 150 ( 130) (280) - (12) (11)
5154A a - 150 e 85 215 275 18 16
F - 150 (100) (215) - (16) (14)
5251 F - 150 (60) ( 170) - (16) (14)
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,l])U( MaTepHaJIOB B COCTOHHHH F. YKa3aHHbIe B cKo6Kax 3Ha'leHIDI YCJIOBHOrO rrpe,neJIa TeI<.Y-
'leCTH, rrpe,neJla rrpO'lHOCTH Ha pa3pbIB H OTHOCHTeJIbHOrO YMHHeHIDI HBJUlIOTCH THrrWlHbIMH
xapaKTepHCTHKaMH H rrpHBe,neHbI TOJIbKO ,l])U( crrpaBKH. d Co,nepxaHHe aJIlOMHHIDI B 'lHCTOM.
MIOMHHHH, He rro,nBepraBmeMCH rrpoueccy O'lHCTKH, orrpe,neJUleTCH KaK pa3HHu;a Me)l{)Jy
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paBHO H.JIH rrpeBbImaT 0,10%, oKpyrJIeHHbIX rrepe,n HaxO)K,l(eHHeM CYMMbI ,no BToporo 3HaK&
rrocJle 3aIDIToH. e HHKaKHe MexaHWleCKHe CBOHCTBa He orrpe,neJIeHbI ,l])U( TPy6 H rrOJIbIX rrpo-
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6.3.27. npyrKIf, WTaNlnOSaHHble Tpy6bl If npocplfnlA
1A3 anlONlIAHlAeSOrO cnnasa IUJfI o6u.cero
MaWIAHOCTpoeHlffl: TepMlflfecKafl o6pa6oTKa
COCTaB
0OO3Ha'le- KpeM- Xe- Me. Map- Mar- XpOM
,[Wyrae Tlrraa ,[Wyrae b Amo-
HBe MaTe- HHii JIe30 (%) raae.. HHii (%) (%) orpaJIII- (%) KaQyi Dcero MIIIIIIii
pHaJla 8 (%) (%) (%) (%) '1ellHJl (%) (%) (%) (%)
2014A 0,5/ 0,50 3,9/ 0,4/ 0,2/ 0,10 0,25 0,20 0,15 0,05 0,15 OCT.
0,9 5,0 1,2 0,8 Zr + Ti
6060 0,3/ 0,1/ 0,10 0,10 0,35/ 0,05 0,15 - 0,10 0,05 0,15 OCT.
0,6 0,3 0,6
6061 0,4/ 0,7 0,15/ 0,15 0,8/ 0,04/ 0,25 - 0,15 0,05 0,15 OCT.
08 0,4 1,2 0,35
6063 0,2/ 0,35 0,10 0,10 0,45/ 0,10 0,10 - 0,10 0,05 0,15 OCT.
0,6 0,9
6063A 0,3/ 0,15/ 0,10 0,15 0,6/ 0,05 0,15 - 0,10 0,05 0,15 OCT.
0,6 0,35 0,9
6082 0,7/ 0,50 0,10 0,40/ 0,6/ 0,25 0,20 - 0,10 0,05 0,15 OCT.
1,3 1,0 1,2
6463 0,2/ 0,15 0,20 0,05 0,45/ - 0,05 - - 0,05 0,16 OCT.
0,6 0,9
CBOHCTBa
,LbtaMeTp (npyroK) npe,IJ;eJI DpO'lHOCTH OmOCHTeJlhHOe
HJIH TOJllQlllla 0,2% YCJIOBHLIi Ha pa3phIB (BpeMeH- YNlHlleHBe
0603Ha'leHBe 06pa- (1'py6a/npo4»HJIh l' npe,IJ;eJI TeKY- Hoe COnpOTHBJIeHBe)
MaTepHaJla OOTU c (MM) '1ecTH (H/MM2) (H/MM2) na 5,65
Ha 50 MM
>
MHH. MHH. MaKC. MHH. (%) MHH. (%)
2014A T4 - 20 230 370 - 11 10
20 75 250 390 - 8 11
75 150 250 390 - 8
T6 150 200 230 370 - 7
- 20 370 435 - 6
T6510 20 75 435 480 - 7
150 75 420 465 - 7
150 200 390 435 - 7
6060 T4 150 60 120 15
T5 150 100 145 8
T6 150 150 190 8
6061 T4 150 115 190 16 14
T6 150 240 280 8 7
T6510
DlO8a 6. MalUuHoCmpOUmeJlbHble MamepUOIlbl
O"oHliaHue
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eHBe)
MaTepll8JIa 60TKa c (MM) '1ecT11 (H/MM2) (H/MM2) Ha S,6S.[S; Ha 50 MIl
>
MHH. MHH. MaKC. MHH. (%) MHH. (%)
6063 0 200 - 140 15 13
F 200 - (100 ) (13) (12)
T4 150 200 70 130 16 14
150 70 120 13
T5 25 110 150 8 7
T6 150 200 160 195 8 7
50 130 150 6
6063A T4 - 25 90 150 - 14 12
T5 - 25 160 200 - 8 7
. ,
T6 - 25 190 230 - 8 7
6082 0 - 200 - - 170 16 14
F - 200 - (110) - (13) (12)
T4 - 150 120 190 - 16 14
150 200 100 170 13 -
T5 - 6 230 270 - - 8
- 20 255 295 8 7
T6 20 150 270 310 - 8 -
T6510 150 200 240 280 5 -
6463 T4 - 50 75 125 - 16 14
T6 - 50 160 185 10 9
a COCTaB B rrpoueHTax (M/M) COOTBeTcTByeT MaKCHM}'MY, eCJIH HBHO He yKa3aH ,nHarra30H
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,naHHbIX rrpe,neJIOB.
c HHKaKHe MexaHWleCKHe CBOHCTBa He orrpe,neJIeHbI ,l(JUI MaTepHaJIOB B COCTOHHHH F.
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pa3pbIB H OTHOCHTeJIbHOrO YMHHeHIDI HBJUlIOTCH THrrWlHbIMH xapaKTepHCTHKaMH H rrpHBe-
,neHbI TOJIbKO ,l(JUI crrpaBKH. 06pa6oTKa T6510 rrpHMeHHMa TOJIbKO,l(JUl rrpyrKoB (CM. pa3,l(eJt.
6.3.20).
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CD
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0
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6.3.31. nlfTeHHb,e anlOMlfHlfeSb,e cnnaSb':
MeXaHIf'leCKlfe CsoHcTsa
Dpe;J;eJI npolOlOCTH Ba pa3phIB OmOCHTeJIhBoe y
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OJIaBJIJIeMLIM MO;J;e- (H/MM2) DJIaBJUIeMLIM MO;J;e- MHH. (%)
JDIM MHH. (H/MM2) JDIM MHH. (%)
..,,::.
f))ynna A
LM2 M - 150 - -
LM4 M 140 160 2 2
TF 230 280
LM6 M 160 190 5 7
LM20 M - 190 - 5
LM24 M - 180 - 1,5
LM25 M 130 160 2 3
TE 150 190 1 2
TB7 b 160 230 2,5 5
TF 230 280 - 2
LM27 M 140 160 1 2 _.
-
f))ynna B
LMO M - -
LM5 M 140 170 3 5
LM9 M 170 190 1,5 3
TE 240 230 - 2
TF - 295 - -
LM13 c TE 170 210 - -
TF 140 280 - -
TF7 - 200 - -
LM16 TB 170 230 2 3
TF 230 280 - -
LM21 M 150 170 1 1
LM22 TB - 245 - 8
fJtynna C
LM12 M - 170 - -
LM26 c TE - 210 - -
L28 d TE 120 170 . -
TF - 190
LM29 d TE 120 190 - -
TF 120 190
LM30 M - 150 - -
TS - 160
LM31 e M 215 - 4 -
TE 215 - 4 -
a CBOHCTBa no.rryqeHbI.... AIDI OT,neJIbHbIX OTJIHTbIX HcnbITaTeJIbHbIX 06pa3
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qaHHe 5.4). e OTJIHBKH LM31 B M COCTOHHHH ,nOJDKHbI no,nBepraTbCH eCTeCTBeHHOMY crnpe-
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6.4. P03Mepbl MemaJlllUltecK,UX U3iJeJlUU 565
6.4. Pa3Mepbl MeTannM eCKMX' M3AenMM
6.4.1. Pa3N1epb' MeTannJflleCKJfX Jf3p,enJfH:
BBep,eHJfe 8 BS 6722:1986
BpHTaHCKHH CTaH,l(apT BS 6722 3aMeIDIeT BS 4229 qaCTH 1 H 2, BS 4391 H DD5,
....
KOTopbIe B HaCTOBIUHH MOMeHT OTMeHeHbI.
C asI rrpOBonOKH peKOMe eMbIMH OCTalOTCB pa3MepbI, KOTopbIe paHee
6bIJIH orrpe,neneHbI B BS 4391, rrOCKOJIbKY OHH c'rporo H norWlHO YCTaHaBnHBalOT
u
Bce, qTO KacaeTCB rrpOBonOKH H COOTBeTCTByIDIUeH 01paCTH rrpOMbInmeHHOCTH.
u v
,np H3,n:enHH, KOTOpbIX He cym;ecTByeT qeTKOH C1p bI pa3Me-
u
pOB, a npe,n.rroxeHHe H cnpoc Ha KOTopbIe H3MeIDIIOTCB OT O,nHOH 01pacnH npo-
MbInmeHHOCTH K ,npyrOH, rrpe,nrronaraeTCB, qTO ,nOIDKeH 6bITb YCTaHOBneH crrHCOK
peKOMe eMbIX pa3MepOB, OCHOBaHHbIX Ha O:KpyrneHHH cepHH R20 (BS 2045) 6e3
u
BCBKHX nonbITOK npOBeCTH pa3JIWlIDI no THIIaM H3,nenHH HJIH Me qepHbIMH H
UBeTHbIMH MeTaJIJIaMH. 3aTeM, qT06bI YCTaHOBHTh ,nHarra30H pa3MepOB, Ha llIHM
06pa30M y,nOBJIeTBOpBIOIUHH xapaKTepy crrpoca, H3 3Toro crrHCKa MOryr 6bITh BbI-
6paHbI rro,nxoAAIUHe pa3MepbI.
TaKHM 06pa30M, ,neTaJlbHbIe peKOMeH,l(aI(HH H3 CTaH,l(apTa BS 4229, KacalOIUHe-
CR <pOpMbI rrpyrKoB, B HOBbIH CTaH,l(apT He BKJIlOqeHbI. AHaJlOrHqHO, peKOMeH)J;a-
UHH H3 DD5, KacalOIUHeCB IIJIHT H nHCTOB, YCOBepllIeHCTBOBaHbI, H peKOMeH,na-
UHH OTHOCHTenbHO TonIUHHbI nHCTOB H llJIHT, TaK xe KaK H OTHOCHTenbHO pa3Me-
pOB rrpyrKoB, HOCBT Terrepb He06R3aTeJIbHbIH xapaKTep. TIO,n:p06HasI HH<popMaI(:IDI
o rrpe,n:rrOqTHTenbHbIX pa3Mepax rrpyrKoB llIeCT onbHoro CeqeHIDI rrpHBe,n:eHa B
BS 3692.
PeKOMe eTCB, qT06bI rrpHMeHHMbIe BpHTaHCKHe CTaH,l(apTbI Ha MeTaJIJIWle-
CKHe H3,nenIDI co,nepXaJIH COqeTaHIDI pa3MepOB, peKOMeH,l(OBaHHbIe B BS 6722:
1986. BS 6722 ,n:aeT peKOMe eMbIe pa3MepbI Hcrronb30BaHIDI HX B KaqeCTBe
OCHOBbI rrpH BbI60pe pa3MepOB TaKHX MeTaJIJIWleCKHX H3,nenHH, KaK rrpOBonKa,
rrpyrKH (HCKJIlOqaR rrpyrKH llIeCT onbHoro CeqeHIDI) H llJIOCKHe H3,nenIDI, BKJIIO-
qasI nHCThI H llJIHTbI.
npOBOJIOKa. )];HaMe1pbI rrpOBonOK cne,nyeT BbI6HpaTb H3 peKOMe eMbIX pa3-
MepOB, rrpHBe,n:eHHbIX B pa3,n:eJIe 6.4.2.
Up . )];HaMe'rpbI KpyrnbIX rrpyrKoB H TonIUHHa H llIHpHHa rrpyrKoB npBMO-
yronbHoro HJIH KB3,L{paTHOro CeQeH:IDI cne,nyeT BbI6HpaTb H3 peKOMe eMbIX pa3-
MepOB, npHBe,n:eHHbIX B pa3,n:eJIe 6.4.3.
UJIOCKHe H3,lJ.eJIIIJI. IIIHpHHa H/IDIH ,nJIHHa llJIOCKHX H3,neJIHH (llJIHThI, rronOCbI H
JIHCTbI) cne,nyeT BbI6HpaTb H3 peKOMeH,l(yeMbIX pa3MepOB, rrpHBe,neHHbIX B pa3,nene
6.4.4. TOnIUHHY llJIOCKHX H3,nenHH cne,nyeT BbI6HpaTh H3 peKOMe eMbIX pa3Me-
pOB, npHBe,n:eHHbIX B pa3,n:eJIe 6.4.3.
rAa6a 6. MamuHOCmpOUmeAbHbte MamepUaJlbt
6.4.2. PeKoNleH,qyeNlb,e ,qJfBNleTpb' npOBOnOKJf,
NleTpJf'leCKJfe
-'
p (3H8'1elllUl B MM)
--
nepBwH BTOpoi 1'peTHi nepBwH Bropoi TpeTBii nepBwH Bropoii nepBwH Bropo,
0,010 0, 100 1,0 10,0 -
0,011 0,112 1,12 11,2
0,012 0,125 1,25 12,5
0,013 0,132
0,014 0, 140 1,40 14,0
0,015 0,150
0,016 0, 160 1,60 16,0
0,017 0,170
0,018 0,180 1,80 18,0
0,019 0,190
0,020 0,200 2,00 20,0
0,021 0,212
0,022 0,224 2,25
0,024 0,236
0,025 0,250 2,50
0,026 0,265
0,028 0,280 2,80
0,030 0,300
0,032 0,315 3,15
0,034 0,335
0,036 0,355 3,55
0,038 0,375
0,040 0,400 4,00
0,042 0,425
0,045 0,450 4,50
0,048 0,480
0,050 0,500 5,00
0,053 0,530
0,056 0,560 5,60
0,060 0,600
0,063 0,630 6,30
0,067 0,670
0,071 0,710 7,10
0,075 0,750
0,080 -' 0,800 8,00
0,085 0,850
0,090 0,900 9,00
0,095 0,950 -
3KBHBaJIeHTHbIe Me'rpWIecKHM KaJIH6pbI npOBOJlOKH B ,l:UOHMax CMO'rpH B pa3-
,neJle 6.4.7.
6.4. P03Mepbl MemOJl.llU'IeCICUX U30e.nUU
6.4.3. PeKoMeH,qyeMwe pa3Mepbl npyrKoB
H nnOCKJfX Jf3,Q,enJfH
Pu (3Ba1felllUl B MM)
DepBwi Bropoi DepBWii Bropoii DepBwi BTOpoii DepBwH Bropoi
0,10 1,0 10,0 100
0,11 1,1 11,0 110
0,12 1,2 12,0 120
0,14 1,4 14,0 140
016 1,6 16,0 160
0,18 1,8 18,0 180
0,20 2,0 20,0 200
0,22 2,2 22,0 220
0,25 2,5 25,0 250
0,28 2,8 28,0 280
0,30 3,0 30,0 300
0,35 3,5 35,0
0,40 4,0 40,0
0,45 4,5 45,0
0,50 5,0 50,0
0,55 5,5 55,0
0,60 6,0 60,0
0,7(} 7,0 70,0
0,80 8,0 80,0
0,90 9,0 90,0
6.4.4. PeKoMeH,qyeMble WJfpJfHa fA ,lVIJfHa
nnOCKHX Jf3,Q,enJfH
I.IIHpHBa (MM) Amma (MM)
400 2500
500 3000-
600 4000
800 5000
1000 6000
1200 8000
1250 10000
1500
2000
(::: FAa8a 6. MaUluHoCmpOUmeJlbHble MamepUOJlbl
6.4.5. Macca Me Tplf.,eCKIf X npyrKos Kpyrnoro
If Ksa,qpaTHoro Ce'leHJffl
CT8JIh Me
JIa'fYllh OJIOBSIIIIICTIUI 6poB3a ,LJ;lOpamoMlllllli
Pa3Mep
(MM) Kpyr- KBa,n- Kpyr- KBa,n- Kpyr- KBa,n- Kpyr- KBa.npaT- Kpyr- KBa,n-
JIhIi paTBWii JIhIi paTIIhIH Ali paTIIhIH JIhIii HYi JIhIi paTIIYI
1,0 0,0062 0,0079 0,0071 0,0090 0,0065 0,0085 0,0069 0,0088 0,0023 0,0027
1,1 0,0075 0,0095 0,0085 0,0108 0,0081 0,0103 0,0084 0,0106 0,0029 0,0035
1,2 0,0089 0,0113 0,0101 0,0129 0,0096 0,0122 0,0100 0,0127 0,0032 0,0041
1,4 0,0120 0,0154 0,0137 0,0175 0,0130 0,0166 0,0134 0,0173 0,0044 0,0056
1,6 0,0160 0,0201 0,0181 0,024 0,0173 0,0217 0,0179 0,0225 0,0058 0,0073
1.8 0,020 0,0254 0,023 0,029 0,0216 0,0275 0,0224 0,0285 0,0073 0,0093
,
2,0 0,025 0,0314 0,028 0,036 0,027 0,034 0,028 0,035 0,0091 0,0114
2,5 0,039 0,0491 0,044 0,056 0,042 0,053 0,043 0,055 0,0142 0,0179
3,0 0,055 0,0707 0,063 0,080 0,060 0,076 0,062 0,079 0,0200 0,0257
3,5 0,076 0,0962 0,087 0,109 0,082 0,104 0,085 0,108 0,0277 0,0350
4,0 0,099 0,126 0,113 0,143 0,107 0,136 0,111 0,141 0,0360 0,0459 I
4,5 0,125 0,159 0,142 0,181 0,135 0,172 0,140 0,178 0,0455 0,0579
5,0 0,154 0,196 0,175 0,223 0,166 0,212 0,173 0,220 0,0560 0,0713
5,5 0,187 0,237 0,213 0,270 0,202 0,256 0,209 0,265 0,0680 0,0863
6,0 0,222 0,283 0,253 0,322 0,240 0,306 0,249 0,317 0,0808 0,1030
7,0 0,302 0,385 0,344 0,438 0,326 0,416 0,338 0,431 0,110 0,140 I
8,0 0,395 0,502 0,450 0,571 0,427 0,543 0,442 0,562 0,144 0,183
9,0 0,499 0,636 0,568 0,724 0,539 0,688 0,559 0,712 0,182 0,2
2
10,0 0,617 0,785 0,702 0,893 0,667 0,849 0,691 0,879 0,225 0,286
11,0 0,746 0,950 0,849 1,081 0,806 1,027 0,836 1,064 0,272 0,346
12,0 0,888 1,130 1,010 1,286 0,960 1,222 0,995 1,266 0,323 0,411
14,0 1,208 1,539 1,375 1,751 1,306 1,664 1,353 1,724 0,440 0,560
16,0 1,578 2,010 1,796 2,287 1,706 2,173 1,767 2,251 0,574 (),732
18,0 1,998 2,543 2,274 2,894 2,160 2,749 2,238 2,848 0,727 0,926
20,0 2,466 3,140 2,806 3,573 2,666 3,394 2,762 3,517 0,898 1,14a
25,0 3,853 4,906 4,385 5,583 4,165 5,303 4,315 5,495 1,402 1,786
30,0 5,158 7,065 5,870 8,040 5,876 7,637 5,777 7,913 1,878 2,572
35,0 7,553 9,616 8,595 10,943 8,165 10,395 8,459 10,770 2,749 3,500
40,0 9,865 12,56 11,23 14,29 10,66 13,58 11,05 14,07 3,590 4,572
45,0 12,48 15,90 14,20 18,09 13,49 17,19 13,98 . 17,81 4,542 5,788
50,0 15,41 19,63 17,54 22,34 16,66 21,22 17,26 21,99 5,609 7,145
55,0 18,65 23,75 21,22 27,03 20,16 25,67 20,89 26,60 6,789 8,645
60,0 22,20 28,26 25,26 32,16 24,00 30,55 24,86 31,65 8,081 10,29
70,0 30,21 38,47 34,38 43,78 32,66 41,59 33,84 43,09 11,00 14,00
80,0 39,46 50,24 44,91 57,17 42,66 54,31 44,20 56,27 14,36 18,29
90,0 49,94 63,59 56,83 72,37 53,99 68,74 55,93 71,22 18,18 23,15
100,0 61,65 78,50 10,16 89,33 66,64 84,86 69,05 87,92 22,44 28,57
120,0 88,78 113,04 101,03 128,64 95,97 122,20 99,43 126,60 32,32 41,15
160,0 167,84 200,96 191,00 228,69 181,44 217,24 187,98 225,08 61,09 73,15
200,0 246,60 314,00 280,63 319,36 266,58 339,43 276,19 351,68 89,76 114,30
250,0 385,31 490,63 438,48 558,34 416,52 530,37 431,55 549,51 140,25 178,59
300,0 554,80 706,50 631,36 804,00 599,74 763,73 621,38 791,28 201,95 257;17
3HaqeHIDI B Kr 1M.
6.4. P03Mepbl Mema/l/lU'IeC1CUX U3iJe.nuu
6.4.6. PS3Mepbl npyrKoB WeCTJfyronbHoro Ce'leHJffl
,qJJfI BJfHTOBblX KpeneJICeii, MeTpJf'leCKJfe
P83Mepw WecTHyI'OJlhHOH 6aJIKH (MM) Macca (KI'/M)
HOMHB8JIhHYi
Pu p83Mep p83Mep «DO)); KJII01f» Me1K)ly p83Mep «BO)); KJIIO'I» Me1K)ly (MaKC. pa3Mep
pe3h6w 1IpOTIIB000Jl0mu.IMII rp8IUIMII 1IpOTIIB0BOJIOmu.IMII yrJIaMII npyru:
CTaJIh)
MaKC. MHB. MaKC. MHB.
nepBbIH MI,6 3,2 3,08 3,7 3,48 0,07
(pacnpoc1'pa- M2 4,0 3,88 4,6 4,38 0,11
HeHHLIii) M2,5 5,0 4,88 5,8 5,51 0,17
M3 5,5 5,38 6,4 6,08 0,21
M4 7,0 6,85 8,1 7,74 0,33
M5 8,0 7,85 9,2 8,87 0,44
M6 10,0 9,78 11,5 11,05 0-,68
M8 13,0 12,73 15,0 14,38 1,15
MlO 17,0 16,73 19,6 18,90 1,97
M12 19,0 18,67 21,9 21,10 2,45
M16 24,0 23,67 27,7 26,75 3,62
M20 30,0 29,67 34,6 33,53 6,12
M24 36,0 35,38 41,6 39,98 8,81
M30 46,0 45,38 53,1 51,28 14,40
M36 55,0 54,26 63 5 61,31 20,52
M42 65,0 64,26 75,1 72,61 28,67
M48 75,0 74,26 86 6 83,91 35,15
M56 85,0 84,13 98 1 95,07 49,00
M64 95.0 94.13 109.7 106.37 61.22
BTOpOH M14 22,0 21,67 25,4 24,49 3,29
(Hepacnpo- M18 27,0 26,67 31,2 30,14 4,95
C1'paHeHHbIH) M22 32,0 31,61 36,9 35,74 6,96
M27 41,0 40,38 47,3 45,63 11,43
M33 50,0 49,38 57,7 55,80 17,00
M39 60,0 59,26 69,3 66,96 24,42
M45 70,0 69,26 80,8 78,26 32,23
M52 80,0 79,26 92,4 89,56 43,41
M60 90,0 89,13 103,9 100,72 55,00
M68 100.0 99.13 115 5 112.02 67.84
Maccy 06b:NHbIX rrpyrKoB mecTJIyTOJIbHOrO CeqeHIDI H3 UBeTHbIX CTIJIaBOB MOX-
HO orrpe,neJIHTb, yMHOXWI Maccy cooTBeTcTBYI<>IUero CTaJIbHOrO rrpyrKa Ha O,nHH H3
CJIe.nyIOIUHX K03<P<PHUHeHToB rrpeo6pa30BaHIDI:
JIaTYHb x 1,081. opoH3a x 1,120. ,lJ;lOpaJIIOMHHHH x 0,364.
HarrpHMep, Macca CTaJIbHOrO rrpyrKa meCTJIyTOJIbHOrO CeqeHIDI C paCCTO$lHHeM
Mex.ny rpaIDIMH 30 MM paBHa 6,12 KT/M. CJIe,noBaTeJIbHO, Macca JIaTYHHoro rrpyrKa
mecTJIyTOJIbHOrO CeqeHIDI C paCCTO$lHHeM Mex.ny rpaIDIMH 30 MM paBHa 6,12 x
x 1,081 = 6,616 KT/M.
20-3255
r/la8a 6. MaUluHoCmpOUmeJlbHble MamepUa/lbl
6.4. 7. PS3Mepbl Ksnlf6pos If If X 3KSlfssneHTbl
-
ISWG 6pHTallcKHii MeTIUlqe- Macca (KI'/M) ISWG 6pHTallcKHi MeTIUlqe- Macca (KI'/At)
(JnOiiMLt) cKHi (MM) ( CTaJIh) (JnOiiMLt) cKHi (MM) ( CTaA)
..
50 0,0010 0,025 0,0000044 21 0,032 0,8 0,0041
49 0,0012 0,030 0,0000057 20 0,036 0,9 0,0052
48 0,0016 0,040 0,0000102 19 0,040 1,0 0,0064
47 0,0020 0,050 0,000016 18 0,048 1,2 0,0092
46 0,0024 0,061 0,000023 17 0,056 1,4 0,0125
45 0,0028 0,071 0,000032 16 0,064 1,6 0,0163
44 0,0032 0,081 0,000041 15 0,072 1,8 0,0211
43 0,0036 0,091 0,000052 14 0,080 2,0 0,025
42 0,0040 0,101 0,000064 13 0,092 2,3 0,034
41 0,0044 0,112 0,000077 12 0,104 2,6 0,043
40 0,0048 0,122 0,000092 11 0,116 3,0 0,054
39 0,0052 0,127 0,000108 10 0,128 3,3 0,065
38 0,0060 0,152 0,000144 9 0,144 3,7 0,083
37 0,0068 0,172 0,000185 8 0,160 4,1 0,102
36 0,0076 0,177 0,000231 7 0,176 4,5 0,123
35 0,0084 0,203 0,000256 6 0,192 4,9 0,147
34 0,0092 0,230 0,000338 5 0,212 5,4 0,178
33 0,0100 0,254 0,000397 4 0,232 5,9 0,214
32 0,0108 0,27 0,000463 3 0,252 6,4 0,25
31 0,0116 0,28 0,000527 2 0,276 7,0 0,31
30 0,0124 0,32 0,000613 1 0,300 7,6 0,36
29 0,0136 0,35 0,000735 1/0 0,324 8,2 0,42
28 0,0148 0,37 0,00087 2/0 0,348 8,8 0,48
27 0,0164 0,4 0,00107 3/0 0,372 9,4 0,55
26 0,0180 0,45 0,00129 4/0 0,400 10,2 0,64
25 0,0200 0,5 0,00159 5/0 0,432 11,0 0,74
24 0,022 0,55 0,00192 6/0 0,464 11,8 0,86
23 0,024 0,6 0,0023 7/0 0,500 12,7 1,0
22 0,028 0,7 0,0031
. -
Maccy 06b:NHOH rrpoBOJIOKH 113 UBeTHoro CTIJIaBa MO)l{}{O orrpe,neJIIITb, yMHO)Ka61
Maccy COOTBeTCTByroIII;eH CTaJIbHOH rrpOBOJIOKH Ha O,nIlH 113 CJIe.nyroIII;HX K034><):«-
UlleHTOB rrpeo6pa30BaHHSI:
JIaTYHb X 1,081
opoH3a X 1,120
;::J;lOpaJIb X 0,364.
./
6.5. llOllUMepHble MamepUOJlbl (ntlacmMaccbI)
6.5. nonMMepHble MaTepManbl (nnacTMaccbl)
6.5. 1. nOnJfMepHble MSTepJfSnbl (nnscTMscCbl).
Bse,qeHJfe
TIOJIHMepHbIe MaTepHaJIbI 1pan;HnHOHHO Ha3bIBalOT TIJIaCTMaCcaMH, T.e.TIJIaCTlfqe-
CKHMH MaTepHaJIaMH. 3TO Ha3BaHHe KIDKeTC$I HerrpaBHJIbHbIM, rrOCKOJIbK}' rrOJIH-
MepHbIe MaTepHaJIbI B HX 3aKOINeHHOM B e pe,nKO ,neMOHC1pHpyIOT TIJIaCTlfqeCKHe
CBoHcTBa; <paKTlfqeCKH, MHorHe H3 HHX rrpe,nCTaBillIlOT C060H yrrpyrHe MaTepHaJIbI.
O,nHaKo B rrponecce OTJIHBKH, qTo6bI rrp aTb H3,neJIHIO Hy)KHyIO <p0PMY, rrOJIHMe-
pbI rrpHBOMTC$I B TIJIaCTlfqeCKOe COCTO$lHHe HarpeBaHHeM HX ,no TeMrreparypbI
BbIme TeMrreparypbI KHIDIII.J;eH BO,nbI, H HMeHHO OT 3Toro OHH rro.rryqHJIH o6II.J;ee Ha-
3BaHHe «TIJIaCTMaCCbI».
Cym;ecTByIOT ,nBe OCHOBHbIe rpyrrrrbI rrOJIHMepHbIX MaTepHaJIOB.
TepMODJIaCTHKH. OHH MOryT p83W1rqaTbC$I BC$lKHH pa3 rrpH HarpeBe. TepMOTIJIa-
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C <P0pMaJIb,nem.noM
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nOJIH3CTepbI (HeHaCbIIIJ;eHHbIe) 1,12 50-60 2,0 0,7 220
nOJIH3CTepbI (aJIKH,ZUIbIe CMOJIbI) 2,00 20-30 0,0 0,25 150
CHJIHKOHbI 1,88 35-45 30-40 0,4 450
a C HanOJIHHTe,neM H3 ,npeBeCHOH MYJGf.
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nOJIHTeYpa<pTop3THJIeH 90 2170 17-25 200-600 3-5 -126 327 260
(T e<pJIOH)
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(llJIeKCHrJIac) (nepcneKc)
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( CBOHCTBa ,lJ)UI Heitrro- MeH-
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nOIDIOKCHMeTHJIeH f 70-90 1410 60-70 15-70 0,5-2,0 -76 180 120
nOJIHKap6oHaT 0 1200 60-70 60-100 10-20 150 - 130
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HHTL paJMep BaJIa 06TOqKOH HJIH IlIJIH OBKOH.
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HCTOqHHK: Engineering Fundamentals: Timings: Elsevier (Newnes).
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6 10 +36 -25 +22 -13 + 15 -5 +15 -0 +15 +10 +15 +24
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18 30 +52 -40 +33 -20 +21 -7 +21 -0 +21 +15 +21 +35
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30 50 +62 -50 +39 -25 +25 -9 +25 -0 +25 +18 +25 +42
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50 80 +74 -60 +46 -30 +30 -10 +30 -0 +30 +21 +30 +51
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80 120 +87 -72 +54 -36 +35 -12 +35 -0 +35 +25 +35 +59
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120 180 +100 -85 +63 -43 +40 -14 +40 -0 +40 +28 +40 +68
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BaTb 6pOCOK (3Kcn:eHTpHCHTeT), Kor,na Barr BpamaeTCH.)
Ta .rum ,n;OnyCKOB, onpe,n;emIlO HX KOHueH1JlWIHOCTb OCTaJIbHbIX yqacTKoB Barra H
Bpa eHHe 6e3 6HeHHH onopHOH nOBepXHOCTH <pJIaHua. Ha pHC. 7.11, a TaIOKe nOKa-
3aHO, qTO 3aBHCHMbIe yqaCTKH BaJIa H Topeu HMelOT ,n;OnyCKH <pOpMbI, TaK xe KaK H
,n;OnyCKH pa3MepOB. B paMKax ,n;OnyCKOB YKa3aHbI: CHMBOJI KOHueH'IpH'IHOCTH, ,n;o-
nyCK KOHueHTPWIHOCTH H 6)'KBbI, 0603HaqaIO He 6a3Y. 3TH 6)'KBbI nOKa3bIBaIOT,
tJTO KOHueHTPHtlHOCTb OCTaJIbHbIX yqacTKoB BaJIa onpe,n;eIDIeTCH OTHOCHTeJIbHO 06-
eH OCH 6a30BbIX yqacTKoB X H Y. B paMKe ,n;onycKa, BbIHOCHWI JIHHIDI OT KOTOpOH
ynHpaeTcH B onopHYID nOBepXHOCTb <pJIaHua, YKa3aHO, tJTO 3Ta nOBepXHOCTb ,n;OJDKHa
Bpa aTbCH 6e3 6HeHIDI, B npe,n;eJIax 3a,naHHoro ,n;onycKa, Kor,n;a Barr Bpa aeTCH, onH-
pWICb Ha V-06pa3Hble onopbI B CeqeHIDIX X H Y, KaK nOKa3aHO Ha pHC. 7.11, 6.
3TH ,n;Ba npHMepa HeJIb3H paCCMaTPHBaTb KaK BceCTopOHHHH 0630p npHJIoxe-
HHH ,n;onycKa <pOpMbI, a TOJIbKO KaK BBe,neHHe B npe,n;MeT H KaK BBe,n;eHHe B BS ISO
1101:1983. B 3TOM EpHTaHcKoM CTaH,l(apTe no,n;p06HO onHcaH nOJIHbIH ,n;Hana30H
npHMeHeHHH H HX HHTepnpeTaUIDI. OH TaIOKe BKJIlOqaeT B ce6H MHoxeCTBO npHMe-
pOB qepTeXeH co BceMH pa3MepaMH H ,n;onycKaMH.
rfla8a Z Ha3Ha'teHUe flUHeUHbIX U ZeOMempU'teCICUX iJonycIC08
7.4. AeMcTBMTenbHblM pa3Mep
,l:lJrn rrOHHMaHIDI 3Toro pa3,n;eJIa Heo6xo,n;HMO BBeCTH rrOIDITIDI «rrpe,n;eJI MaKCHMyMa
MaTepHana» H «rrpe,n;eJI MHHHM)'Ma MaTepHana».
. ITpe,n;eJI MaKCHM)'Ma MaTepHana - TepMIIH, OTHOC.SIm;HHCH H K OTBepCTHIO, H
K BaJIy, Kor,n;a HaHMeHbmee KOJIWleCTBO MeTaJIJIa y,n;aneHO, HO KOMrrOHeHTa
Bce em;e YKJI3,lJ;bIBaeTCH B 33,lJ;aHHble rrpe,n;eJIbHble pa3MepbI, T.e. 3TO HaH6oJIb-
mHH Ban H HaHMeHbmee OTBepCTHe, ,L(IDI KOTOpbIX BCe em;e C06JIIO,n;eHbI 3a
,n;aHHble ,n;OrryCKH.
. ITpe,n;eJI MHHHM)'Ma MaTepHana - TepMHH, OTHOCHm;HHCH II K OTBepCTHIO, H K
BaJIy, KOr,n;a HaH60JIbmee KOJIWleCTBO MeTaJIJIa y,n;aneHO, HO KOMrrOHeHTa BCe
em;e YKJI3,lJ;bIBaeTC.SI B 33,lJ;aHHble rrpe,n;eJIbHble pa3MepbI, T.e. 3TO HaH60Jlbmee
OTBepCTHe H HaHMeHbmHH Ban, ,L(IDI KOTOpbIX BCe em;e C06JIIO,n;eHbI 33,lJ;aHHbIe
,n;OrryCKH.
Ha pHC. 7.12 rrOKa3aHO BJIIDIHlle H3MeHeHIDI <pOpMbI Ha rrOC3,lJ;KY CTepXIDI B OT-
BepCTHH. Ha pHC. 7.12, a rrOKa3aH H,ZJ;eanbHbIH CTepxeHb rrpHMoH OCblO. Ha pHCyJI-
Ke MO)I(HO BH,ZJ;eTb, cym;ecTByeT JIH 3a30p Me CTep)I(HeM H OTBepCTHeM. O,lUlaKQ
Ha pHC. 7.12, 6 CTepxeHb HCIq)HBJIeH, H Terrepb rrOC3,lJ;Ka B OTBepCTHe CTana lIJIot-
HOH, HeCMOTPH Ha TO qTO ,n;OrryCK pa3MepOB He H3MeHHJIC.SI.
CTep>KeHb
CTep>KeHb
--.........--...----...--.....
..---..-....----...--.----...--
a
6
Pac. 7.12. BJIIDIHHe <POpMLI Ha noc3.ll:KY. (a) CTepxeHL C npRMoH OCLIO: nOC3.lI:Ka C
3a30pOM H (6) CTepxeHL C HCKpHBJIeHHOH OCLIO: llJIOTHaR nOC3.lI:Ka B OT-
BepCTHH, HeCMOTpR Ha TO qTO pa3Mep He H3MeHHJICR
Ha pHC. 7.13, a rrOKa3aHbI Te xe CTepxeHb H OTBepcrne, TOJIbKO Ha 3TOT pa3,IUU1
CTep)l{ID[ orrpe,n;eJIeHbI ,n;OrryCKH pa3MepOB H <popMbI. ,l:lJrn rrpOCTOTbI OTBepcrne rrpH
IDITO reOMeTPlftIeCKH rrpaBHJIbHbIM. PaMKa ,n;orrycKa orrpe,n;eIDIeT ,n;orryCK Ha rrp.HMO-
JIHHeHHOCTb, paBHbIH 0,05 MM. 3TO 03HaqaeT, 1ffO OCb crep)l{ID[ MoxeT fHYTbCH B
rrpe,n;eJIax Boo6paxaeMoro l(HJIHH,l(pa ,lUfaMeTPOM Ha 0,05. ITpe,n;eJIbHble pa3MepbI CO
OTBeTCTByroT ,n;orrycKY 0,08 MM.,-HaHXY,n;mHe YCJIOBIDI,L(IDI C60PKH (nrroTHaH rroc )
B03HHKaIOT, Kor,n;a CTepxeHb H OTBepcrne HaxO,ZJ;HTCH B COCTOHHIDIX, COOTBeTCTByIO-i
m;HX HX rrpe,n;eny MaKCJIMyMa MaTepHana, II, Iq)OMe Toro, TaIOKe rrpHCYTCTByeT MaKCH..:
MaJIbHO ,n;orrycrnMoe HCKIDKeHHe -<}>oPMbl. Ha pHC. 7.13, 6 rrOKa3aHa rrOC3,lJ;Ka CTep
IDI B OTBepCTHe rrpH TaKHX YCJIOBIDIX.
B 3TOM c.rryqae CTepxeHb 6y,n;eT e,n;Ba BXO,n;HTb B ,n;eHCTBHTeJIbHO rrp.SlMOe H $-
JIHHJJ;pWleCKOe OTBepCTHe C ,n;HaMeTPOM, paBHbIM ,n;HaMeTPY CTep)l{ID[ B YCJIOBIDIX
rrpe,n;eJIa MaKCHM)'Ma MaTepHana (25,00 MM) nrrlOc ,n;orryCK <pOpMbI PaBHbIH 0,05 MM,
T.e. B OTBepCTHe C ,n;HaMeTPOM 25,05 MM. 3TOT TeopeTWleCKOH ,n;HaMeTP OTBepCTIDI
25,05 MM Ha3bIBaeTC.SI ,n;eHCTBHTeJIbHbIM pa3MepOM ,L(IDI CTep)l{ID[.
Z5. 3ICOHOMUlteCICUu 3l/JtjJeICm iJonyclCa tPoPMbI
025.00
1-100.051 M I
- -1-------+4
" 25.00
24.92
.L
It)
o
&ri
C\I
T
AeHCTB TenbHbIH
pa3Mep
nOlle AonYCKa
npeACTaBlls:leT
C060H U, ll HAP,
r COAep>Kaw. H B
--I - 0 ce6e OCb CTep-
t - >KHs:I 00,05 MM
a
0.05
6
024.92
A aMeTp cooTBeTcTBYIOw.ero nOlllO
AonycKa U, ll HApa, COAep>Kaw.ero
B ce6e OCb CTep>KHs:I, MO>KeT 6b1Tb
YBell eH AO 00, 13 MM B YCllOB s:lX
S npeAella M H MYMa MaTep ana
t O
.L
It)
o
an
C\I
T
AeHCTB TeJ1bHblH
pa3Mep
0.13
B
Pac. 7.13. ,D:eHcTBHTeJIbHbIH pa3Mep: (a) WTH<pT, ,lLJUI KOToporo onpe,n:eJIeHbI ,n:onyc-
KIf <pOpMbI H pa3MepOB; (6) ,n:eHcTBHTeJIbHbIH pa3Mep B YCJIOBIDIX npe,n:eJIa
MaKCHMYMa MaTepHaJIa (,n:HaMeTp wTH<pTa = 25,00 MM) H (B) ,n:eHCTBH-
TeJIbHbIH pa3Mep B YCJIOBHRX npe,n:eJIa MHHHMyMa MaTepHaJIa (,n:HaMeTp
WTH<pTa = 24,92 MM). Pa3MepbI B MM
B YCJIOBIDIX IIpe,neJIa MHHHM)'Ma MaTepHaJIa ,norrycK <pOpMbI ,L(IDI CTep)I{IDI MO-
xeT 6bITb YBeJIWleH 6e3 H3MeHeHIDI IIOC3,lurn CTep)I{IDI B oTBepcTHe. KaK IIOKa3aHO
Ha pHC. 7.13, B ,nOrryCK <pOpMbI MoxeT 6bITb YBeJIlftIeH ,no 0,13 MM 6e3 KaKOrO-JIH60
YBeJIlftIeHIDI ,neHcTBHTeJIbHOrO pa3Mepa HJIH H3MeHeHIDI IIOC3,lurn.
7.5. 3KOHOMM"IeCKMM 3c1>cI>eKT AonYCK8 cl>OpMbl
Ha pHC. 7.14 IIOKa3aHO THillftIHOe COOTHomeHHe Mex.ny ,nOrryCKOM H CTOHMOCTblO
IIpOH3Bo,ncTBa ,L(IDI JII060H H3rOTaBJIHBaeMOH KOMIIOHeHTbI. IIpH YMeHbmeHHH ,no-
nycKa CTOHMOCTb IIpOH3Bo,nCTBa HMeeT TeHJJ;eHl(HIO 6bICTPO B03paCTaTb. ,l];o6aBJIe-
HHe ,nOrryCKOB <pOpMbI K ,norrycKaM pa3MepOB yxy,nmaeT 3TY CHTYal(HIO em:e 60JIbme.
J5
::r
s
J:
SS
C[S
Q)::r
00
00.
t:
S
o
.-
U
Ha3Ha eH e o6o x AonYCKOB
Ha3Ha eH e AonYCKa Q>OPMbI
Ha3Ha eH e AonYCKa pa3MepOB
o
AonYCK
PRC. 7.14. CTOHMOCTb ,n:onycKa
rfla8a 7. H03Ha'teHUe flUHeUHbIX U ZeOMempU'teCICUX iJonycIC08
TaKHM 06pa30M, ,n;OrryCKH <pOpMbI IIpHMeIDIIOTCH TOJIbKO TOr,n;a, KOr,n;a <PYH HOHH-
pOBaHHe H B3aHM03aMeIDIeMOCTb KOMIIOHeHT HBIDIIOTCH KJIlOqeBbIMH H nOJIHOCTblO
3aBHCHT OT TOqHOCTH <pOPMbI. QTo6bI He YBeJIWlHBaTb CTOHMOCTb npO.nyKIJ;HH, qac-
TO MO)I(HO npe,n;nOJIaraTh, 1ffO CTaHOK RJIH npol(eCC 06eCneqHBalOT COOTBeTCTBYIO-
IUYIO <POPMY KOMnOHeHTbI, Ii 3an;aBaTb Ha qepTexax TOJIbKO .D;orryCKH pa3MepOB.
HanpHMep, npHIDITO CqHTaTb, qTO KOMnOHeHTa, o6pa6oTaHHaH Ha Iq)yrJIOIIIJIH<pO-
BaJIbHOM CTaHKe Me)l{.ll;y l(eHTPaMH, 6y,n;eT npHMOH H HMeTb l(HJIHHJ(pWlecK)'IO <pop-
MY C BbICOKOH CTeneHblO TOqHOCTH. O,n;HaKO COBpeMeHHbIe TeHJ(eHl(HH KOHTPOIDI
KaqeCTBa H pa60TbI cTPoro no rpa<pHKY (JIT) npHBO,ZJ;HT K B03paCTaHHIO TPe60Ba-
HHH OTHOCHTeJIbHO pa3MepOB H <pOPMbI, qTo6bI rapaHTHpOBaTb OTCYTCTBHe 3an;ep-
xeK B npOl(eCce C60PKH, a TaIOKe qTo6bI TPe60BaHIDI K KaqeCTBY y,n;OBJIeTBOpIDIHCb
C nepBoro pa3a, 6e3 Heo6xo,n;HMOCTH BHeceHIDI KOppeKTHB RJIH OTKJIOHeHIDI TOBapa
nOTPe6HTeJIeM.
rnABA 8
ABTOMATM3MPOBAHHOE
KOHCTPYMPOBAHME
8.1. "Iny TMna CNC
B. 1. 1. THnHlfHb'e o6nscTH npHMeHeHHfI
IfHcnosoro nporpsMMHoro ynpssneHHfI
qHCJIOBOe rrporpaMMHoe yrrpaBJIeHHe (qIIY) HCrrOJIb3yeTcR B mHpOKOM ,nHarra30He
TeXHOJIOrwIeCKHX rrpOl(eCCOB BO MHorHX 0TPaclliIX rrpOMbIIIDIeHHOCTH. B MamHHO-
CTPoeHHH OHO rrpHMeIDIeTCR rrpH BbIrrOJIHeHHH CJIe,l(YJOIUHX orrepal(Hit
1. MeTaJIJIOpexymHe CTaHKH, BKJIlOqaH:
- <ppe3epHbIe CTaHKH H l(eHTPbI MexaHH3HpoBaHHoH o6pa6oTKH;
- l(eHTPOBbIe TOKapHbIe CTaHKH H TOKapHbIe MHOrOl(eJIeBbIe CTaHKH;
- CBepJIbIe llIJIH4K>BaJIbHbIe CTaHKH;
- 3JIeIcrp03p03HOHHbIe CTaHKH (3JIeKTp03p03HOHHaH o6pa6oTKa);
- CTaHKHJIbHbIe CTaHKH;
- TOqHH ,L(IDI <ppe3epoBaHIDI mTaMrrOB.
2. CTaHKH ,L(IDI o6pa6oTKH JIHCTOBOro MeTaJIJIa, BKJIlOqaH:
- peBOJIbBepHbIe ,nbIporrpo6HBHbIe rrpeCCbI;
- KJIerraJIbHbIe CTaHKH;
- JIHCTOIIITaMIIOBOqHbIe rrpeCCbI.
3. 06opy,noBaHHe ,L(IDI o6pa6oTKH MeTaJIJIOB, BKJIlOqaH:
- ra30pe3qHKH;
- CBapOqHbIe arperaTbI;
- CTaHKH ,L(IDI rHYTbR TPy6.
4. Koop,nHHaTHo-H3MepHTeJIbHbIe MamHHbI ,L(IDI rrpOBepKH TPeXMepHbIX (3D)
KOMrrOHeHTOB.
B. 1.2. npeHMy ecTss H orpsHHlfeHHfI '1ny
illHpOKoe H rrOCTORHHO pacmHpRIOIUeeCR HCrrOJIb30BaHHe CTaHKOB C qIIY B o6pa-
6aTbIBalOIUeH rrpOMbIllIJIeHHOCTH rrOKa3bIBaeT, qTO rrpeHMYIIJ;eCTBa MeTo,na cym;ecT-
BeHHO rrepeBemHBalOT orpaHlftIeHIDI.
npeHMyIQecTBa
BbICOKaB npoH3Bo.znrreJIbHOCTh. XOTR CKOpOCTH pe3aHIDI H rro,naqH ,L(IDI CTaHKOB
C qIIY TaKHe xe, KaK H Y CTaHKOB C pyqHbIM yrrpaBJIeHHeM, MHoro BpeMeHH 3KO-
rfla8a 8. A8mOMamU3up08aHHoe KOHcmpyup08aHue
HOMHTCH 3a CqeT 6bIC1pOrO rrepeMem:eHIDI H rr03Hl(HOHHpOBaHIDI Mex.ny orrepaI(IDI-
MH. K TOMY xe Ha cTaHKax C qIIY BbIrrOJIIDIeTCR 60JIee mHpoKHH ,n;Harra30H orrepa-
l(HH, qTO rr03BOJUIeT H36exaTb He06xo,n;HMOCTH BbIrrOJIIDITb pa60TY Ha HeCKOJIbKHX
cTaHKax, HarrpHMep CBepJIHJIbHOM, <ppe3epHoM H paCTOqHOM. 3TO YMeHbmaeT rro-
1pe6HocTb B ,n;oporocToHm:HX 3IDKHMHbIX rrpHcrroc06JIeHIDIX H KpenrreHIDIX H YC1pa-
IDIeT He06xo,n;HMOCTb xpaHeHIDI 06pa6aTbIBaeMbIX H3,n;eJIHH Mex.ny Orrepal(IDIMH.
KpoMe Toro, CTaHKH C qIIY He YCTalOT H rro,z:r,nep)KJfBaIOT rrOCTOHHHyID rrpOH3Bo,n;H-
TeJIbHOCTb. IIpH aBTOMaTWleCKOM YC1pOHCTBe rro,n;aqH 3arOTOBOK OHH MOryr pa60-
TaTb 6e3 06CJIy)KHBaHIDI BCIO HOqb.
KOHCTPYKTHBHaJI m6KOCTh. CJIO)l{J{bIe <pOpMbI JIerKO BocrrpOH3BO,lUlTCH Ha CTaH-
Kax qIIY. KpOMe Toro, Ha cTaHKax qIIY MO)I(HO H3rOTaBJIHBaTb ,n;eTaJIH co CJIOX-
HbIM 06'beMHbIM KOHTYPOM, KOTopbIe HeB03MO)I(H0 H3rOTOBHTb Ha 06bPlHbIX CTaH-
Kax C pyqHbIM yrrpaBJIeHHeM.
34»4»eKTHBHOCTh ynpaBJIelllUl. IIpOH3Bo,n;HTeJIbHOCTb, YMeHbmeHHe OTXO,n;OB H
rrOBbImeHHe KaqeCTBa rrpOHCXO,lUlT rro,n; yrrpaBJIeHHeM qIIY H He 3aBHCHT OT 3<p-
<peKTHBHOCTH pa60TbI orrepaTopa.
KallecTBo. CTaHKH C qIIY 06eCrreqHBalOT 60JIee BbICOKOH TOqHOCTblO H .rryq-
myIO rrOBTopHeMOCTb, qeM 06bPlHbIe CTaHKH. ECJIH CTaHOK OCHam:eH CHCTeMoii
an;arrTHBHoro yrrpaBJIeHIDI, TO OH CMoxeT 06HapyxHTb rrOJIOMKY HHC1pYMeHTa HJDI
,n;pyrHe H3MeHeHIDI B pa60Te H JIH60 OCTaHOBHTbCH, JIH60, eCJIH OH OCHam:eH CHCTe:.:.
MOH aBTOMaTlftIeCKOH CMeHbI HHC1pYMeHTOB, BbI6paTb pe3epBHbIH HHC1pYMeHT H3
Mara3HHa YC1pOHCTBa aBTOMarnqeCKOH CMeHbI HHCTPYMeHTOB rrpe)K}J;e, qeM HaqHeT
rrpOH3Bo,n;HTb 6paK HJIH 6y,n;eT rrOBpe)K}J;eH.
YMeHbmeHHoe BpeMJI OCBoeHHH HOBOR npO,nyKUHH. BpeMH OCBoeHIDI HOBOH rrpo-
.nyKl(HH y CTaHKOB C qIIY HaMHoro MeHbme, qeM y ,n;pYfHX CTaHKOB-aBTOMaTOB. He
JIYXHO HHKaKHX CJIO)I(HbIX H ,n;oporOCTOHm:HX KYJIaqKOB H <pacoHHbIX pe3l(OB; He06-
XO,n;HMO rrpOCTO HarrHcaTb rrporpaMMY ,n;eTaJIH H 3arpY3HTb ee B'\ rraMHTb CTaHKa.
CJIO)I(HbIe rrpo<pHJIH rrpOH3BO,lUlTCH C HCrrOJIb30BaHHeM CTaHJJ;apTHbIX HHC1py-
MeHTOB.
Orpalllf1leHHH
KaDHT8JIbHbIe 3aTPaTbI. HaqaJIbHaH CTOHMOCTb CTaHKOB C qIIY cym;ecTBeHHO\
BbIme, qeM Y CTaHKOB C pyqHbIM yrrpaBJIeHHeM TaKoro xe THrra. O,n;HaKo B rrOCJIe,n;-
HHe ro,n;bI pa3HHl(a B CTOHMOCTH HeCKOJIbKO CHH3HJIaCb.
CTOHMOCTh HHCTPyMeHTOB. qT06bI HCrrOJIb30BaTb BeCb rrpoH3Bo,n;cTBeHHbIH rro
TeHl(HaJI CTaHKOB C qIIY, 1pe6yroTcH Crrel(HaJIH3HpOBaHHbIe pexym:He HHC1pYMeH
ThI. XOTH rrepBOHaqaJIbHaH CTOHMOCTb HX BbICOKa, OHa B 3HaqHTeJIbHOH CTerremt
KOMrreHcHpyeTcH CTOHMOCTblO XBOCTOBHKOB HHC1pYMeHTOB H HHC1pYMeHTaJIbHOH
OCHaCTKH, KOTopbIe He rrpHXo,n;HTCH 3aMeIDITb. CTOHMOCTb 3aMeHbI pexym:HX nrrac-
THH HHC1pYMeHTa He BbIme, qeM ,l(illI 06bPlHbIX CTaHKOB.
TeXlllf1leCKoe 06CJIY1KIIBaHHe. H3-3a CJIO)I(HOcrn CTaHKOB C qIIY JIHmb HeMHO-
rHe MeJIKHe H cpe,n;HHe KoMrraHHH HMelOT TeXHWlecK)'IO 6a3Y ,l(illI qerO-TO 60JIbme
ro, qeM caMoe rrpOCToe TeXHWleCKoe 06CJIy)KHBaHHe H peMOHT. II03TOMY He06xo
,n;HMJ>I KOH1paKTbI Ha TeXHWleCKoe 06CJIy)KHBaHHe. Hx CTOHMOCTb ,n;OCTaTOqHO Bht-
COKa H COCTaBIDIeT B ro,n; rrpH6JIH3HTeJIbHO 10% KarrHTaJIbHbIX 3a1paT.
06yqeHHe. Tpe6yeTcH 06yqeHHe rrporpaMMHcTajorrepaTopa. 06yqeHHe 06bAHP
06eCrreqHBaeTCH H3rOTOBHTeJIeM 060py,n;oBaHIDI, o,n;HaKO OHO 3aHHMaeT MHoro Bpe-
MeHH H HBIDIeTCH ,n;oporOCTOHm:HM.
8.1. lJIIY muna CNC
AMOpTll3aQIIJI. KaK If Bce YCTpOHCTBa, OCHOBaHHbIe Ha rrpHMeHeHHH BbPlHCJIH-
TeJIbHOH TeXHHKH, qIIY 6bICTpO YCTapeBaIOT. IIo3ToMY CTaHKH C qIIY CJIe,nyeT
crrHCbIBaTb 3a 60JIee KOpOTKHH rrepHo,n;, qeM CTaHKH C pyqHbIM ynpaBJIeHHeM, If 3a-
MeIDITh HX rrpH6JIH3HTeJIbHO KIDK,ZJ;bIe 5 JIeT.
B. 1.3. YnpBsnfleMble KOOp,qHHBTbl CTBHKOS
CYIneCTByeT MHoxeCTBO CHCTeM KOH<pHrypal(HH oceH ,l(illI CTaHKOB qIIY; caMbIe
pacrrpOCTpaHeHHbIe HCrrOJIb3YIOTCH B BepTHKaJIbHbIX/ropH30HTaJIbHbIX <ppe3epHbIX
cTaHKax H B TOKapHbIX cTaHKax, KaK rrOKa3aHO Ha pHCyJlKe. OTMeTHM, qTO:
1) OCb Z Bcer,n;a rJIaBHaJI IDrrHHJ(eJIbHaJI OCb;
2) OCb X Bcer,n;a ropH30HTaJIbHa H rreprreHJ(HKYIDIpHa OCH Z;
3) OCb Y rreprreMHKYIDIpa o6eHM OCHM X H Z.
BepTHKaJlbHblH 4»pe3epllYH CTaHOK:
ynpaBJUleMbie KOOPJnlllaTbI
fOpH30HTaJlbHblH 4»pe3epHbIH CTaHOK:
ynpaBJUleMbIe KOOp,lUlHaTbi
DCb Z
DCbY
DCb X
IJ;eHTJ)OBOH TOKapHbIH CTaHOK:
ynpaBJUleMbIe KOOp,lUlHaTbi
DCb X
DlO8a 8. A8moMamU3up08aHHoe KOHcmpyup08aHue
8. 1.4. CHcTeMbl ynpssneHHfI
CHCTeMbI ynpaBJIeHIDI CTaHKOB C qIIY MO)I(HO pa3,n;eJIHTb Ha ,n;Be KaTeropHH CJIe,n;y-
IOm:HM 06pa30M.
YnpaBJIeHHe 6e3 o6paTHoi CBB3H
KaK CJIe,n;yeT H3 Ha3BaHIDI, 06paTHasI CBR3b B 3TOH CHCTeMe OTcyrcTByeT, T. e. OT-
cyrcTByeT CBR3b Mex.ny BXO,n;OM H BhIXO,n;OM. ,n;m npHBe,n;eHIDI B ,n;eHCTBHe MexaHH3Ma
n03HUHOHHpOBaHIDI B CHCTeMe HCrrOJIb3yJOTCR maroBbIe ,l(BHrareJIH, H HX Bpam:alOnum
MOMeHT rrpOCTO orpaHINeH, no CpaBHeHHIO C 06b:NHbIMH cepBOMOTOpaMH. DoJIee
TOro, eCJIH H3-3a 1peHIDI B MexaHH3Me ,l(BHraTeJIb caMorrpOH3BOJIbHO OCTaHaBJIHBaeTCR
H rrporrycKaeT mar, CHCTeMa He rrpe,lU1pHMeT HHKaKHX KoppeKTIipyJOIUHX ,n;eHCTBHH.
BXOAHOt1 npeo6pa30BaHHblt1
c rHa.n c rHa.n
.... BxoAHOt1 .... C cTeMa .... Yc .n Te.nb
.... np 6op .... ....
ynpaB.neH s:I
I
BBOA AaHHblX BPYYHYIO M KPOKOHTpo.n.nep
i1HCTPYMeHTaJ1bHblX
nep<I>op poBaHHas:l neHTa ca.na30K
MarH THas:l .neHTa
BblXOA
,r
YnpaBJIeHHe C o6pamoi CBB3blO
CJIe.nyrom;aR cxeMa 06bRCIDIeT yC1pOHCrBO CHCTe:M:bI yrrpa.BJIeHIDI C 06paTHoH CBR3bIO.
BxoAHOt1 C rHaJ1
!
BxoAHOt1 BBOA AaHHblX BPYYHYIO
np 6op nepcI>op poBaHHas:l .neHTa
MarH THas:l .neHTa
\
npeo6pa30BaHHblt1 c rHa.n
.. .
C cTeMa Aet1cTB e Mi1KpOKOHTpo.n.nep BblXOA
... Yc .n Te.nb .... ....
ynpaB.neH s:I .... .... HcTPYMeHTa.nbHbIX ....
ca.na30K
!
.-
. 06paTHas:l CBs:l3b 1t13Mep Te.nbHoe
YCTPOt1CTBO
I
AaTY K no.nO)l(eH s:I
8.1. lfIIY muna CNC
B CHCTeMe ynpaBJIeHIDI C 06paTHoH CBR3b1O 06paTHaJI CBR3b HenpepbIBHo OKa-
3bIBaeT BJIIDIHHe Ha ,n;eHcTBIDI KOHTPOJIJIepa H HcnpaBlliIeT JII06bIe omH6KH n03Hl(H-
oHHpoBaHIDI. 3Ta CHCTeMa n03BOIDIeT HCnOJIb30BaTb cepBoMoTOpbI ,L(IDI npHBe,n;eHIDI
B ,n;eHcTBHe MexaHH3Ma n03 HoHHpoBaHIDI, H OHH HMelOT HaMHoro 60JIbmHH Bpa-
lUalOlUHH MOMeHT, qeM maroBbIe ,n;BHraTeJIH, HCnOJIb3yeMbIe B CHCTeMe yrrpaBJIeHIDI
6e3 06paTHOH CBR3H.
B. 1.5. tPOpMBT H TepMHHonorHfI nporpaMMbl
CHMBOJI
CHMBOJI - 3TO qHCJIO, 6YKBa HJIH ,n;pyrOH 3HaK, KOTOpbIH pacn03HaeTCR KOHT-
pOJIJIepOM. 061>e,n;HHeHHaJI rpynna CHMBOJIOB 06pa3yeT CJIOBO.
CJIOBO
CJIOBO 3TO rpyrrrra CHMBOJIOB, KOTOpaH onpe,n;eIDIeT O,n;HH 3JIeMeHT, co,n;epxa-
IUHH nOJIHyJO 3aKOffieHHyJO HH<popMal(HIO (HanpHMep, NlOO). Cym:ecTByeT ,n;Ba
THna CJIOB.
OnpeJJ;eJIeHHe nOJI01KeHH.H H nepeMem;eHH.H
3TO JII06bIe CJIOBa, HMelOlUHe OTHomeHIDI K JIHHeHHbIM paCCTORHIDIM, T. e. JIIO-
6bIe CJIOBa, HaqHHaIOIUHeCR C 6YKB X, Y, Z, I, J, K, HJIH JII06bIe CJIOBa, B KOTOpbIX
3TH CHMBOJIbI nO,n;pa3YMeBaIOTCR.
BYKBbI X, Y, Z OTHOCHrCR K paCCTORHIDIM, H3MepeHHbIM napaJIJIeJIbHO COOTBeT-
CTByrolUHM OCRM CTaHKa, OnHCaHHbIM B pa3,n;eJIe 8.1.3.
BYKBbI I, J, K OTHOCRTCR K ,n;yraM OKpyxHOCTeH. HaqaJIbHOe H KOHeqHOe nOJIO-
xeHIDI ,n;yr onpe,n;eIDIIOTCR 3HaqeHIDIMH X, Y, Z, a l(eHTP OKpyxHOCTH ,n;yrH onpe,n;e-
JUleTCR 3HaqeHIDIMH I, J, K CJIe,l(YJOIUHM 06Pa30M:
3HaqeHHe I COOTBeTcTByeT HanpaBJIeHHIO no X
3HaqeHHe J COOTBeTcTByeT HanpaBJIeHHIO no Y
3HaqeHHe K COOTBeTcTByeT HanpaBJIeHHIO no Z.
COBpeMeHHbIe CTaHKH no,z:r,neplKHBalOT HCnOJIb30BaHHe ,n;ecHTWlHoH TOqKH B
CJIOBax, onpe,n;eIDIIOIUHX paCCTOHHIDI. TaKHM 06pa30M, B pyKOBo,n;CTBe K CTaHKY MO-
xeT 6bITb orOBopeHO, qTO CJIOBO, onpe,n;eIDIlOlUee paCCTOHHHe X, HMeeT BH,l( X4, 3.
3TO 03HaqaeT, qTO CJIOBO, onpe,n;eIDIlOlUee paCCTOHHHe X, MoxeT co,n;epxaTb ));0
4 l(H<PP nepe,n; ,n;ecRTIftIHOH TOqKOH H ,n;o 3 l(H<PP nOCJIe ,n;ecHTWlHoH TOqKH. HeKo-
TopbIe 60JIee CTapbIe CHCTeMbI, Bce elUe mHpOKO HCnOJIb3yeMbIe, He no,z:r,neplKHBalOT
HCnOJIb30BaHHe ,n;eCHrWlHOH TOqKH, a BMeCTO 3Toro B HHX HCnOJIb3yIOTCR HaqaJIb-
HbIe H KOHeqHbIe HYJIH; HanpHMep, 3HaqeHHe 25,4 6y,n;eT 3anHcaHO KaK 0025400.
YnpaBJIJlIOlQlle CJIOBa
3TO mo6bIe CJIOBa, KOTopbIe He OTHOCHTCR K paCCTOHHIDIM, T. e. JII060e CJIOBO,
HaqHHaIOlUeeCH C CHMBOJIa N, G, F, S, T, M, HJIH JII060e CJIOBO, B KOTOpOM BbIme-
yrrOMHHYTbIe CHMBOJIbI no,n;pa3YMeBaIOTCH. IIpHMepaMH yrrpaBIDIIOlUHX CJIOB MOryr
6bITb CJIe,n;yroIUHe:
N4 IIOPMKOBbIH HOMep: CHMBOJI N, 3a KOTOpbIM CJIe,n;yeT BnrrOTb ,n;o qeTbIpex
l(H<pP (T. e. Nl... N9999).
G 2 IIo,n;roToBHTeJIbHaH <PYHKl(IDI: CHMBOJI G, 3a KOTOpbIM CJIe,n;yeT BnrrOTb ,n;o ,n;BYX
l(H<PP (T. e. GO... G99).
Dlaoa 8. A8moMamU3up08aHHoe KOHcmpyup08aHue
F4 Y CTaHOBKa CKOpOCTH rro,n;aqH: CHMBOJI F, 3a KOTOpbIM CJIe,n;yeT BnrrOTb ,n;o qe-
TbIpeX l(H<PP.
84 YCTaHoBKa CKOpOCTH Bpam:eHIDI illnHHJJ;e.IDI: CHMBOJI 8, 3a KOTOpbIM CJIe,n;yeT
BnrrOTb ,n;o qeTbIpex l(H<PP.
T2 H,n;eHTH<pHKaTop HHCTPYMeHTa: CHMBOJI T, 3a KOTOpbIM CJIe,n;yeT BnrrOTb ,n;o
,n;BYX l(H<PP.
M2 BcnoMOraTeJIbHbIe KOMaHJJ;bI: CHMBOJI M, 3a KOTOpbIM CJIe,n;yeT BnrrOTb ,n;o ,n;B)'X
l(H<PP.
OTMeTHM, qTO B HeKOTOpbIX CaMbIX CTapbIX, HO Bce em:e illHpOKO HCnOJIb3ye-
MbIX cHcTeMax npH BBo,n;e KOMaHJJ; N, G, T H M MOryr nOTPe60BaTbcH HaqaJIbHbIe
HYJIH (HarrpHMep, He GO, a GOO, BMeCTO Gl - GOI H T.,n;.).
B. 1.6. tPOpM8T C 8,l1peCOM B' K8J1C,l10M cnose
B HaCTOHm:ee BpeMH 3TO HaH60JIee illHpOKO HCnOJIb3yeMbIH <popMaT. K3)I{)J;0e CJIOBO
HaqHHaeTCH C 6YKBbI, KOTOpaH Ha3bIBaeTCH an;peCOM. CJIe,n;oBaTeJIbHO, CJIOBO onpe-
,n;eIDIeTCH 6YKBOH, a He ero nOJIOXeHHeM B 6JIOKe (B OTJIIftIHe OT CHCTeMbI C <pHKCH-
pOBaHHbIMH 6JIOKaMH, onHcaHHOH HIDKe). TaKHM 06pa30M, B <popMaTe C an;peCOM B
K3)I{)J;0M CJIOBe, HHCTPYKIJ;HH, KOTopbIe He H3MeHHJIHCb no cpaBHeHHIO C npe,n;bI,ny-
m:HM 6JIOKOM, B nOCJIe,l(YJOm:HX 6JIOKaX MOryr 6bITb rrporry:m;eHbI.
THrrWlHbIe KOMaHJJ;bI B <popMaTe C an;peCOM B K3)I{)J;0M CJIOBe, KOTopbIe rrpHBO-
,lUITCH B pyKOBo,n;CTBe rrpOH3Bo,n;HTeIDI, BbIrIDl,lI.RT CJIe,l(YJOm:HM 06pa30M:
MeTPWleCKaH CHCTeMa N4 G2 X4, 3 Y4, 3 Z4, 3 14, 3 J4, 3 K4, 3 F3 84 T2 M2
,l:(IOHMbI N4 G2 X3, 4 Y3, 4 Z3, 4 13, 4 J3, 4 K3, 4 F3 84 T2 M2
B. 1. 7. KO,llHpOS8HH8f1 HHcpOpM8L1HfI
IIporpaMMbI qIIY co,n;epxaT HH<popMan;HIO, He06xo,n;HMYIO ,L(IDI H3roTOBJIeHIDI ,n;eTa-
JIeH. KOHTPOJIJIep qIIY nOCJIe,n;OBaTeJIbHO HarrpaBlliIeT CHrHaJIbI K p33JIWlHbIM npH-
Bo,n;aM.
KO.nLI
HOMepa 6JIOKa N
IIo,n;roTOBHTeJIbHbIe <PYHKl(HH G
,l:(aHHbIe 0 paCCTOHHIDIX X, Y, Z, I, J, K
CKOpOCTb rro,n;aqH F
CKOpOCTb Bpam:eHIDI illrrHHJJ;eJIJI 8
HOMepa HHCTPYMeHTOB T
BcnoMOraTeJIbHbIe <PYHKIriIH M
IIpHMep rrporpaMMbI qIIY Mor 6bI BbIr.IDI.,D;eTb TaK:
N5
NI0
N15
G90 G71 GOO X25.0 Y25.0 TOI
XI00.0 YI00.0 81250
GOI Z25.0 F125 M03
M06
8.1. lfIIY mUM CNC
HOMepa fiJIOKa
HOMep 6JIOKa - 06bPlHO rrepBoe CJIOBO, KOTopoe rrOHBIDIeTCH B JII060M 6JIOKe.
BJIOKH npOJIyMepOBaHbI C marOM 5 HJIH 10 TaK, qTo6bI B c.rryqae OillH6KH MO)I(HO
6billO JIerKO BCTaBHTb ,n;orrOJIHHTeJIbHbIe 6JIOKH.
nO,nfOTOBHTeJIbHhle 4»YHKnHH (G)
ORK HCrrOJIb3yroTCH, QTo6bI C006m;HTb KOIITpOJIJIepy CTaHKa, KaKHe <PYH HH He-
06XO,n;HMbI ,L(IDI CJIe,n;yrom;eH orrepal(IDI. CTa.HJJ;apTH3HpoBaHHbIe no,n;rOTOBHTeJIbHbIe
<pyJIKl.(HH rrpHBe,n;eHbI B CJIe,n;yrom;eH Ta6JIHl(e. Ha rrpaKTHKe <paKTlftIeCKH HCrrOJIb3ye-
MbIe KO,n;bI 6y,l(yT 3aBHCeTb OT CHCTeMbI yrrpaBJIeHIDI H THrra CTaHKa. HcnOJIb3yeMbIe
KO,ZJ;bI MOryr MeIDITbCH npH rrepexo,n;e OT O,n;HOH CHCTeMbI K ,n;pyroH, n03TOMY Heo6xo-
,n;HMO o6pam;aTbcH Henocpe,n;CTBeHHO K COOTBeTCTByrom;eMY pyKOBO,n;CTBY no npo-
rpaMMHpOBaHHIO.
HOMep
KO
GOO
GOI
G02
G03
G04
G05
G06
G07
G08
G09
GIO
GII
Gl2
G13-G16
Gl7
Gl8
Gl9
G20
G21
G22
G23
G24
G25-G29
G30
G31
G32
G33
G34
G35
G36-G39
G40
G41
fl)ymanura
DbICTPOe n03HI010HHpOBaHHe, OT TOqKH K TOtIKe (M)
I103HI(HOHHpOBaHHe npH ynpaBJUIeMOH CKOpOCTH no,n:aqH, HOpM3JIbHbIe (M)
pac ToHHIDI
KpyrOBaH HHrepnOJUII(IDI, HOpM3JIbHbIe paCCTORHIDI (M)
KpyrOBaH HHTepnoJUII.(IDI cqeTtIHK npOTHB qaCOBOH CTPe1IKH, HOpM3JIbHbIe (M)
paCCTOHHIDI
OCTaHOBKa nporpaMMHpyeMoH AJIHTeJIbHOCTH
I1pHocTaHOBKa: ,n:o OTMeHbI onepaTopOM
3ape3epBHpoBaHo ,lJ)UI 6y.ZJYlI(HX CTaH,n;apTOB:
06bAHO He HCnOJIb3yeTcR
I1porpaMMHpyeMoe YCKopeHHe C3JIa30K
I1porpaMMHpyeMoe 3aMeAJIeHHe C3JIa30K
JIHHeHHaH HHTepnOJUII(IDI, AJIHHHbIe paCCTORHIDI (M)
JIHHeHHaH HHTepno.JUII(IDI, KOpOTKHe paCCTORHIDI (M)
TpeXMepHaH HHTepnO.JUII(IDI (M)
BbI60p OCH (M)
BbI60p IIJIOCKOCTH XV (M)
BbI60p IIJIOCKOCTH ZX (M)
BbI60p IIJIOCKOCTH YZ (M)
KpyrOBaH HHTepnoJUII.(IDI no qaCOBOH cTPeJIKe (CW), AJIHHHbIe paCCTORHIDI (M)
KpyrOBaH HHTepnO.JIHnIDI CW, KOpOTKHe paCCTORHIDI (M)
BKJIlOqeHHe orpaH:uqeHIDI nepeMelI(eHIDI
BbIKJIlOqeHHe orpaHWIeHIDI nepeMemeHIDI
3ape3epBHpOBaHO ,lJ)UI 6y.ZJYlI(HX CTaH,ZJ;apTOB
,D:OCTYJIHO ,lJ)UI HH,lUIBH,JJya.JThHOrO HCnOJlb30BaHIDI
KpyrOBaH HHrepnOJUII(IDI CCW, ,n:.JIHHHbIe paCCTORHIDI (M)
KpyrOBaH HHTepnOJUII(ID1 CCW, KOpOTKHe paCCTORHIDI (M)
3ape3epBHpOBaHO,lJ)UI 6y.ZJYlI(HX CTaH,ZJ;aprOB
Hape3aHHe pe3b6bI, nOCTORHHbIH war pe3b6bI (M)
Hape3aHHe pe3b6bI, YBeJIJI1IHBalOlI(HHCR war pe3b6bI (M)
Hape3aHHe pe3b6bI, YMeHbWaIOlI(HHCR war pe3b6bI (M)
,D:OCTYJIHO ,lJ)UI HH,ZJ;HBH,JJya.JThHOrO HCn0JIb30BaHIDI
KoppeKUIDI Ha pe)K}'IIUIH HHCTPYMeHT, OTMeHa
Ko eKI(IDI Ha e HH HHC eHT BJleBO
rMl8a 8. A8moMamU3upo8aHHoe lCOHcmpyup08aHue
O"oHIlDHue
HOMep a
KO
G42 KOPpeKUIDI Ha pe HH HHC1pYMeHT, BnpaBO (M)
G43 KOPpeKUIDI Ha pe HH HHC1pYMeHT, nOJlO)I(HTeJlbHaJI
G44 KoppeKQIDI Ha pe HH HHC1pYMeHT, 01pHI(aTeJIbHaJI
G45 KoppeKQIDI Ha pe HH HHC1pYMeHT +/+
G46 KoppeKUIDI H3 pexynntH HHC1pYMeHT +/-
G47 KoppeKQIDI Ha pe HH HHC1pYMeHT -/-
G48 KoppeKUIDI Ha pexynntH HHC1pYMeHT -/+
G49 KoppeKQIDI Ha pexynntH HHC1pYMeHT 0/+
G50 KoppeKQIDI Ha pe HH HHC1pYMeHT 0/-
G51 KoppeKQIDI Ha pexynntH HHC1pYMeHT +/0
G52 KoppeKQIDI Ha pe HH HHC1pYMeHT -/0
G53 TIpRMOJlHHeHHOecMe eHHe,oTMeHa (M)
G54 TIpRMOJIHHeHHOe CMe eHHe X (M)
G55 TIpHMOJlHHeHHOe CMe eHHe Y (M)
G56 TIpRMOJIHHeHHOe CMe eHHe Z (M)
G57 TIpRMOJlHHeHHOe CMe eHHe XV (M)
G58 TIpRMOJIHHeHHOe CMe eHHe XZ (M)
G59 TIpRMOJlHHeHHOe CMe eHHe YZ (M)
G60 TotJHoe n03HUHOHHpoBaHHe 1 (M)
G61 TotJHoe n03HUHOHHPOBaHHe 2 (M)
G62 BhIC1pOe n03Hl(HOHHpOBaHHe (M)
G63 )KecTKoe Hape3aHHe pe3b6hI
G64 H3MeHeHHeCKOpOCTH
G65-G79 3ape3epBHpOBaHO AID! 6y.nyIIUiX CTaH,LJ;aprOB
G80 OrMeHa nOCTORHHoro IUIKJIa (M)
G81-G89 nOCTORHHhIH nHKJI (M)
G90-G99 b 3ape3epBHpoBaHo .wm 6y.nyIQHX CTaH,LJ;aprOB
(M) }'Ka3hIBaeT Mo,naJIbHhIe KOMaH,LJ;bI G, KOTophIe OCTaIOTCR B CHJIe OT Ka,npa K Ka.npy,
nOKa He 6y.nyr OTMeHeHhI.
a Pa3JI}{tJIDI B CTaH,napTe KO,nHpOBaHIDI cym;ecTByIOT He TOJlbKO Mex.ny KOH1pOJIJIepaMH
Pa3JI}{tJHbIX npOH3Bo,nHTeJleH, HO H Mex.ny pa3JI}{tJHbIMH Mo,neIDIMH O,nHHX H Tex )ICe npOH3-
Bo,nHTeJleH H ,naxe Mex.ny pa3JI}{tJHbIMH THnaMH O,nHOH H TOH )ICe Mo,neJlH. TI03TOMY CHOBa
H)')KHO no,nqepKHyTb, qTO nporpaMMHCT/onepaTOp ,nOJDKeH pa60TaTb Ha OCHOBe npe,nOCTaB-
JleHHOrO H3rOTOBHTeJleM P}'KOBo,nCTBa, COOTBeTCTByIO ero ,naHHOMY COqeTaHHIO CTaHOK/
KOH1pOJIJIep.
b BOJlbIDHHCTBO 6J10KOB ynpaBJIeHIDI HCnOJlb3yIOT G90, qT06hI YCTaHOBHTb nporpaMMY B
peXHM HCnOJlb30BaHIDI a6COJlIOTHOrO n03HJJ;HOHHpOBaHIDI, H G91, qT06hI YCTaHOBHTb npo-
rpaMMY B peXHM OTHOCHTeJIbHOrO (HHK:peMeHTHoro) n03HnHOHHpOBaHIDI. O,nHaKO 6J10KH
ynpaBJIeHIDI FANUC HCnOJIb3yIOT G20 BMeCTO G90 H G21 BMeCTO G92.
n0311Q110HHpOBaHHe.
HHC'rpYMeHTbI CTaHKa C qny HMelOT OCH, KOTopbIe a,npeCYIOTCR 6YKBaMH (X,
Y, 'Z, H T..n.). nporpaMMa qny Bbl)];aeT KOH'rpOJIJIepy KOMaHJJ;bI nepeMeCTHTb COOT-
BeTCTBYIOIIJ;He 3neMeHTbI CTaHKa B 'rpe6yeMoe nonoxeHHe napaJIJIenbHO COOTBeTCT-
BYIOIIJ;HM OCRM, Hcnonb3YR cnOBa BHJ(a (X25.0 Y55.0), COCTORIIJ;He H3 6YKBbI, YKR-
3bIBalOIIJ;eH Ha OCb, llJIlOC paCCTORHHe. 3TO paCCTORHHe MoxeT 6bITb co 3HaKOM
(- HJIH +). EcnH 3HaK OTcyrcTByeT, KOH'rpOJIJIep CqHTaeT qHCnO nOnO)I{HTenbHbIM.
8.1. lfIIY muna CNC
3TO npHJ(aeT nporpaMMe qnY,n;onOnHHTenbHyro Han;e)KHOCTb, nOcKonbKY rapaHTH-
pyeT nepeMeru;eHHe HHcTPYMeHTa B 6e30nacHoe nonoxeHHe (KaK nOKa3aHO HIDKe),
ecnH nporpaMMHcT qny 3a6bill BBeCTH 3HaK «MHHyC» B KOMaH,l(y no OCH Z, T. e.
HHCTPYMeHT CMeCTHTCR OT 3arOTOBKH, KaK nOKa3aHO Ha cne,nyIOru;eM pHCyJlKe.
HCTPYMeHT +
HanpaBneH e AB eH R
HCTPYMeHTa BAonb OC Z
HCTPYMeHT 6YAeT OTBeAeH
Ha 30 MM OT CXOAHoro 30
YPOBHR, ecn 3a.QaHO Z30 +
6a3a OTc eTa
_ - HOpMMbHO ZO
HcTPYMeHT npOH KHeT
BHYTpb 3arOTOBKH Ha 30 MM 30 ------- : ::=-------_
ecn 3a.QaHO Z-30.0
PaCCMOTPHM cTPoKY nporpaMMbI (Kan;p) NIO GOI X25.0 Y25.0 Z30.0. Ee pe3Y-
nbTaTOM CTaJIO 6bI nepeMeru;eHHe HHcTPYMeHTa B nonoxeHHe C Koop,n;HHaTaMH X25,
Y25, Z30. O,n;HaKO, nocKonbKY YKa3aHo nOnO)I{HTenbHOe paccToRHHe no Z, HHCTPY-
MeHT 6y,n;eT nepeMeru;aTbcR BBepx He MeHee qeM Ha 30 MM OT nOBepXHOCTH. qT06bI
npOCBepnHTb 3aroTOBKY Ha r.ny6HHy 30 MM, CTPOKa nporpaMMbI ,n;OJDKHa BbIr.IDl)]:eTh
cne,nyIOru;HM 06pa30M NIO GOI X25.0 Y25.0 Z-30.0.
CKOPOCTh DO,lJ;a'lll (F)
CnoBa, HaqHHalOru;HeCR C F, YKa3bIBalOT KOIITpOIDIepy TPe6yeMYK> CKOpOCTb no-
,n;aqH ,lI)DI MeXaHlftleCKOH 06pa60TKH. ECTh HeCKonbKO crroc060B onpe,n;enHTh CKO-
pOCTb no,n;aqH.
I. MHJIJIHMeTPbI/MHHYTa: F30 = 30 MM/MHH.
2. MHJIJIHMeTPbI/060pOT: FO.2 = 0,2 MM/060pOT.
3. qHcno B ,n;Hana30He 1-20 YKa3bIBaeT o,n;Hy H3 npe,n;onpe,n;eneHHbIX H3rOTOBH-
TeneM CKopocTeH no,n;aqH B 060POTax/MHHyTy HJIH MM/MHHyTy, KaK rrpe,n;yCMOTPe-
HO. npH Hcnonb30BaHHH 3TOH CHCTeMbI KOMaHJJ;e YCTaHOBKH CKOpOCTH no,n;aqH
,n;OJDKeH npe,n;meCTBOBaTh KO,n; G. TonbKo B OqeHb HeMHOrHX CTapbIX cTaHKax Hcno-
JIb3yeTcR 3Ta CHCTeMa.
CKOpOCTh Bpam.eHHJI DIDlIII,1J;eJUI (8)
CnoBa, HaqHHalOru;HeCR C 6YKBbI S, YKa3bIBalOT KOHTPOIDIepy TPe6yeMYK> ,lI)DI
MeXaHlftleCKOH 06pa60TKH CKOpOCTb Bparu;eHIDI mnHHJJ;eIDI. CHOBa eCTb HeCKonbKO
cnoc060B onpe,n;enHTb CKOpOCTb Bparu;eHIDI mnHHJJ;eIDI; KIDK,lI;bIH H3 HHX BbI6HpaeT-
CR npH nOMoru;H COOTBeTCTBYIOmero Ko,n;a G.
I. CKOpOCTb BpameHIDI mnHHJJ;eIDI B 060poTax/MHHyTy.
2. CKOpOCTb pe3aHIDI B MeTPax/MHHyTy.
3. nOCTORHHasI CKOpOCTb pe3aHIDI B MeTPax/MHHyTy.
HOMepa HHCTpYMeHTOB (T)
KIDK,lI;bIH HHCTPYMeHT, Hcnonb3yeMbIH npH 06pa60TKe ,n;eTaJIH, HMeeT CBOH c06-
CTBeHHbIH HOMep (HanpHMep, TOI 03HaqaeT HHCTPYMeHTa I, TI9 - HHCTPYMeHT
19). BonbmHHCTBO KOHTpOIDIepOB CTaHKOB C qny MOryT XpaHHTh HH<popMaIJ;HIO 0
20 H 60nee HHCTPYMeHTax. TaKasI HH<popMaIJ;IDI 06 HHCTPYMeHTe co,n;ep)I{HT KOp-
21-3255
Dla8a 8. A8moMamU3upo8aHHoe 1COHcmpyup08aHue
pe HIO Ha MHHy HHc1pYMeHTa H KOMneHca HIO Ha ,n;HaMe1p/pa,nHyc HHc1pYMeHTa
(CM01pH pa3,n;enbI 8.1.9 H 8.1.10). EcnH CTaHOK OCHaIIJ;eH CHCTeMOH aBTOMaTWIe-
CKOH CMeHbI HHC1pYMeHTOB, OH TaIOKe MoxeT HJ(eHTH<pH HpoBaTb nonoxeHHe HH-
C1pYMeHTa B Mara3HHe YC1pOHCTBa aBTOMaTlftleCKOH CMeHbI HHC1pYMeHTOB.
BcnoMOraTeJIbHbIe cj)yuKQHH (M)
KpoMe no,n;rOTOBHTenbHbIX <PYHKI..J;HH, eCTb eIIJ;e MHoxeCTBO ,n;pyrHX <PYHKI..J;HH,
KOTopbIe 1pe6YIOTCR Ha npOTIDKeHHH BceH nporpaMMbI (HanpHMep, BKJIlOqHTb
mnHH,l(enb, BKJIlOqHTb no,n;aqy OXJIa,nHTeIDI H T .,n;.). 3TH <PYHKI..J;HH CTaH,l(apTH3HpOBa-
HbI; HX 06bPIHO Ha3bIBalOT M Ko,n;aMH. BYKBa M a,npeca COnpOBO)l{)];aeTCR ,n;ByMH
H<ppaMH. 06bPIHO HcnOnb3YIOTCR cne,nyIOIIJ;He M KO,n;bI:
MOO OCTaHoBKa nporpaM- M04 llInHH,l(enb npOTHB M08 BKJIlOqHTb no,n;a-
MbI qaCOBOH C1penKH qy OXJIa,nHTeIDI
MOl OCTaHoB no ,n;onon- M05 B])IKJIlOqHTb mnHH- M09 BbIKJIlOqHTb ox-
HHTenbHOM)' 3a,naHHIO ,n;enb nIDK;J;eHHe
M02 KOHe nporpaMMbI M06 CMeHa HHC1pYMeHTa M30 KOHe neHTbI
M03 llInHH,l(enb no qaco- M07 BKJIlOqHTb OXJIIDK;J;e-
BOH C1penKe HHe TYMaHOM
8. 1.8. Bxo,qHble ,qaHHble
,JJ:aHHbIe nporpaMMbI MOryr 6bITb BBe,n;eHbI B MaIIIHHY qIIY HeCKOJIbKHMH cnoc06aMH.
BBO)); ));aHHbIX BPyquyIO. 3TOT MeTO,n; 1pe6yeT BBo,n;a ,n;aHHbIX onepaTopOM Ha neH-
TOqHOM nep<popaTope (ceWIac YCTapeBmHH).
MarHllTllaB JIeHTa. Tpe6yeTcR KonHpOBaTb nporpaMM)' qny Ha MarHHTJIyIO
neH1)' HJIH Kap1p1UPK (ceWIac YCTapeBmHH).
ABToMam311poBaHHoe nporpaMMIipOBaHHe. nporpaMMHpoBaHHe Ha KOMnblOTepe
C Hcnonb30BaHHeM nporpaMMHoro 06eCneqeHIDI, KOTopoe He TonbKO reHepHpyeT
nporpaMM)', HO H Mo,n;eJIHpyeT ee onepa HH C enblO npOBepKH TOqHOCTH H 6e30-
naCHOCTH nporpaMMbI ,n;o ee 3arpY3KH B ynpaBIDIIOIIJ;HH Mo,n;ynb CTaHKa.
llpBMoe IUlcj)pOBoe ynpaBJIeHHe (llQY). nO,n;rOTOBneHJIyIO nporpaMMY qny 1pe-
6yeTcR coxpaHHTb Ha y,n;aJIeHHOM KOMnblOTepe. Tor,n;a ,lI;aHHbIe qny nepe,n;alOTcR
Henocpe,n;cTBeHHo Ha HIDKHHH ypoBeHb HHc1pYMeHToB CTaHKa qny nocpe,n;cTBoM
cooTBeTcTBYIOIUero KaHaJIa CBR3H.
,lJ;HaJIOrOBbm BBO)); ,naHHbIX. 3TO n03BOIDIeT onepaTopy 3arpY3HTb nporpaMM)' He-
nocpe,n;cTBeHHo B ynpaBIDIIOIIJ;HH 6noK cTaHKa, Hcnonb3YR KOHcynbTa HoHHbIe Me-
HIO, nORBIDIIOIUHecR Ha 3KpaHe 6noKa ynpaBneHIDI. KOH1pOIDIep HMeeT pa3,n;eneH-
JIyIO naWITb, TaK qTO npe,n;bl,L(ylUaR nporpaMMa MoxeT npo,n;OJDKaTb ynpaBIDITb 06-
pa60TKoH B npo ecce 3arpY3KH HOBOH nporpaMMbI.
8.1.9. KOppeKf.lHfI Ha ,qnHHY HHcTPYMeHTa: cppe3eposaHHe
BonbllIHHCTBO MamHHHbIX onepa HH 1pe6YIOT Hcnonb30BaHIDI HeCKonbKHX HHCT-
PYMeHTOB, KOTopbIe pa3nWIalOTCR no MHHe H ,lI;HaMe1pY. YqeCTb Bce 3TH pa3nWIIDI
n03BOIDIeT B03MO)I(IIOCTb KOppeKI..J;HH Ha MHHy HHC1pYMeHTa H KOMneHca HH Ha
,lI;HaMe1p HHC1pYMeHTa.
8.1. lfIIY muna CNC
KOppeKI..J;IDI Ha .n.rrHHY HHc'rpYMeHTa n03BOIDIeT nporpaMMHpoBaTb OnepaIJ;HH
HeCKOllbKHX HHc'rpYMeHToB C pa3llWIHbIMH .n.rrHHaMH, Hcnollb3YR o6J.UY1O 6a3Y OT-
CqeTa HJIH HOllb, KaK nOKa3aHO Ha pHCyJlKe.
37.98
37.84
061.1-'aS1 6aaa OTc eTa no Z
8. 1. 10. KOMneHcaLlHfI Ha ,qHaMeTp cppe3bl: cppe3eposaHHe
npH HcnOllb30BaHHH KOMneHCaIJ;HH Ha ,n;HaMe'rp HJIH Ha pa,nHyC, 06bNHO nporpaM-
MHPYIOT, npHHHMasI BO BHHMaHHe TOllbKO <paKTWIeCKHH pa3Mep KOMnOHeHTbI, a
3aTeM HcnOllb3YIOT B03MO)I(IIOCTb KOMneHCaIJ;HH Ha ,n;HaMe'rp, qTo6bI yqecTb pa,nHyC
pe3IJ;a. 3Ta B03MO)I(IIOCTb n03BOIDI.eT TaIOKe 3aMeHHTb O,l(HH HHC'rpYMeHT Ha ,n;pyrOH
C OTllWIalOIIJ;HMCR ,n;HaMe'rpOM, He H3MeHIDI qaCTb nporpaMMbI qny. KOMneHCaIJ;IDI
Ha ,n;HaMe'rp aKTHBH3HpyeTcR Clle IIJ;HMH no,n;rOTOBHTellbHbIMH Ko,n;aMH (CM. pa3-
,n;ell 8.1.7):
G41 KOMneHCaIJ;IDI pe3IJ;a ClleBa
G42 KOMneHCaIJ;IDI pe3IJ;a cnpaBa
G41 KOMDencanmI CJIeBa
Pe3eIJ; Bcer,n;a HaxO,n;HTCR ClleBa OT o6pa6aTbIBaeMoH nOBepXHOCTH, ecnH CMOT-
peTb B,n;Ollb HanpaBlleHIDI ,L(BIDKeHIDI pe3IJ;a, KaK nOKa3aHO CTpellKaMH Ha pHCyJlKe.
o - - - - - -- - - - Pe)l(}'ll.IIiIH IiIHCTPYMeHT
I "
I \
I \
I \
t
I I
I I
/
I - - - -- - .. ./ '>Z.
I ./ / 3arOTOBKa
G- - - - -- - - - -e - ./
.4
HanpaBneH e AB eH S1 HCTPYMeHTa
Dla8a 8. A8moMamU3upo8aHHoe 1COHcmpyup08aHue
G42 KOMDencaQIIJI cnpaBa
Pe3e BCer,lJ;a HaxO,lJ;HTCR cnpaBa OT o6pa6aTbIBaeMoH nOBepXHocTH, eCllH CMOT-
peTb B,lJ;Ollb HanpaBlleHIDI ,lI;BIDKeHIDI pe3 a, KaK nOKa3aHO cTpellKaMH Ha pHcyJlKe.
I
I
I
I
+
I
I
I
I
- --.-
Pe)f(}'LlI.LJlt1 LJlHCTPYMeHT
-----..----
I
I
t
I
I
- - -..... - -
3arOTOBKa
-----....---
.
HanpaBneHLJle ABLJI eHLJI LJlHCTPYMeHTa
G40 llepeKJIlO'IeHHe KOMDenCaQIIII
ECllM on HH G41 HJIH G42 aKTHBH3HpoBaHbI, ,lJ;HaMe'rp pe3 a KOMneHcHpyeTcR
Ha npoTIDKeHHH clle ru;ero ,lJ;BIDKeHIDI no OCRM X H Y, KaK nOKa3aHO Ha pHCyJI-
Ke. nO,lJ;rOTOBHTellbHoe ,lJ;BIDKeHHe pe3 a ,lJ;O HaqaJIa pe3KH Ha3bIBaeTCR «B'be3,lJ;».
n03LJ1 LJI 1
Pe)f(}'LlI.LJlt1 LJlHCTPYMeHT
n03LJ1 LJlS1 3
......
TpaeKTOpLJlS1 pe3 a C
eTOM KOMneHCa LJILJI
-'
-,-'
-,-'
3anpOrpaMMLJlpOBaHHa
TpaeKTOpLJI
«Bbe3A» Me)K.D.Y n03LJ1-
LJleH 1 LJI n03LJ1 LJlet1 2
3arOTOBKa
AHaJIOIWIHO KOMaH,ZJ;a G40 OTKJIIOqaeT KOMlleHCaIUflO npH clle IUHX nepeMeru;e-
HIDIX no OCRM X H Y, KaK nOK33aHO Ha pHcyHKe, H 3TO ,[(BIDKeHHe H33bIBaeTCR «C'be3,lJ;».
n03LJ1 LJlS1 22
TpaeKTOpLJlS1 pe3 a C /
eToM KOMneHCa LJILJI
3anpOrpaMMLJlpOBaHHaS1
TpaeKTOpLJlS1
n03LJ1 LJlS1 23
8.1. If/IY muna CNC
«B'be3,n;» H «C'be3,n;» n03BOIDIIOT cepBoMoTOPY no,n;aqH YCKOPRTbCR ,n;o Heo6xo,n;H-
MOH CKOpOCTH no,n;aqH H 3aMe,nJUITbCR B KOH e pe3aHIDI, B TO BpeMR nOKa pe3e
HaxO,n;HTCR Ha paCCTORHHH OT 3arOTOBKH. 113 3TOrO Cne,n;yeT, qTO KOMneHCa IDI Ha
,n;HaMeTp HHKor,n;a He MoxeT 6blTb BKJIlOqeHa HJIH OTKJIlOqeHa, Kor,n;a pe HH
HHCTPYMeHT HaxO,n;HTCR B npRMOM KOHTaKTe C 3arOTOBKOH.
8. 1. 11. MeTo,qbl nporpaMMHposaHHfI:
cppe3eposaHHe H csepneHHe
Cl>HKcHpoBaHHhIe QIIKJIbI
QTo6bI H36exaTb nOBTopHoro nporpaMMHpOBaHIDI aHaJIOfWIHbIX onepa HH,
MO)KHO Hcnonb30BaTb mHpoKHH ,n;Hana30H nOCTORHHbIX HJIH <pHKcHpoBaHHbIX HK-
nOB, npe.nnaraeMblH KOHTPOJIJIepaMH Qny. Heo6xo,n;HMO TonbKO 06eCneqHTb ,n;aH-
HOle 0 pa3Mepax TPe6YIOru;HMHCR G Ko,n;aMH. ,JJ:aJIee nepeqHCneHO HeCKonbKO
npHMepOB <pHKCHpOBaHHbIX HKJIOB ,nJUI <ppe3epOBaHIDI:
G80
G81
G82
G83
G84
G85
G86
G87/88
OTMeHa <pHKCHpOBaHHbIX HJIH nOCTORHHbIX HKJIOB
:QHKJIbl CBepneHIDI
:QHKJIbI CBepneHIDI C OCTaHOBKOH
:QHKJI r.rry6oKoro CBepneHIDI
:QHKJI Hape3aHIDI pe3b6bl
:QHKJI paCTaqHBaHIDI
:QHKJI paCTaqHBaHIDI C OCTaHOBKOH
:QHKJI r.rry6oKoro paCTaqHBaHIDI
G81 CBepJIellllJl
O,n;HHM H3 HaH60nee nonyIDIpHbIX <pHKCHpOBaHHbIX HKJIOB RBIDIeTCR HKJI
CBepneHIDI G81. ,JJ:BIDKeHIDI CTaHKa, BblnonIDIIOru;ero CBepneHHe PMa OTBepCTHH,
nOKa3aHbI Ha pHCYHKe H nepeqHCJIeHbl HIDKe:
lt1HcTPYMeHT
6b1CTpOe nepeMew,eHL<1e Ha BbI-
COTY 30Hbl 6e30naCHoro OTBOAa
I I 6blCTpoe nepeMew.eHL<1e
I II K CJ1eAYIOw,eMY OTBepCTL<11O
I I I ·
I I
",I BblCOTa 30Hbl 6e30-
I vI I naCHoro OTBOAa
l 6b1CTpoe nepe-
Mew.eHL<1e BBepx
6blCTpoe nepeMew,eHL<1e
K nepBOMY OTBepCTL<11O
..
nOAa a Ha
rJ1y6i4HY
3arOTOBKa
F/la8a 8. A8mOMmnU3Up08aHHoe 1COHcmpyup08aHue
1. BbIc'rpoe nepeMeru;eHHe K eH'rpY nepBoro OTBepCTIDI.
2. BbIc'rpoe nepeMeru;eHHe Ha BbICOTY 30HbI 6e30naCHoro OTBo,n;a.
3. llo,n;aqa Ha rny6HRY OTBepCTIDI.
4. BbIc'rpoe nepeMeru;eHHe BBepx Ha BbICOTY 30HbI 6e30nacHoro OTBo,n;a.
5. BbIc'rpoe nepeMeru;eHHe K eH'rpY cne,[{y1Oru;ero OTBepCTIDI.
6. lloBTopReTcR,lLJUI CTonbKHX oTBepcTHH, CKonbKO Tpe6yeTcR.
,JJ:aHHbIe, KOTopbIe ,n;OJDKHbI 6bITb 3anporpaMMHpOBaHbI:
HOMep HHC'rpYMeHTa
l103H IDI OTBepCTIDI (X, Y)
fny6HHa OTBepCTIDI (Z)
CKOPOCTb Bparu;eHIDI mnHH,l(eJUI (S)
CKOPOCTb no,n;aqH (F).
8. 1. 12. npHMep nporpaMMbl: cppe3eposaHHe
KOMDOHeHTa
0 '-"1-
{I I
.-+
I
I
I
.
0 ,r- i -
\._L
I
I
I
I
I
0 ,- -
{I :
.-..1-
MaTepHaJI: aJIlOMHHHeBbIH CllJIaB BS 1474: 1987 THn 5154(A) COCTORHHe o.
,lI;aHHhle,lUUI o6pa6oTKH
CKOpOCTh CKOpoCTh Do.n;a1fll (MM/MHH)
HOMep ODHcaBHe HHCTpYMeHTa BpmnellHJl
HHCTpYMeHTa IIIIIIfRJl e.1UI Bep11lIWIbHaJI fOpH30HTaJlhHaJI
(o6/MHH)
TOI CBepJIO .wm o6paJoBaHIDI na30B 1500 70 100
,ZJ;HaMeT}JOM 10 MM
T02 :QeHTpOBOQHOe CBepJIO N2 2 2500 40 -
T03 CnHpaJIbHOe CBepJIO .IJ:HaMeT}JOM 8 MM 1760 60 -
llonoxeHHe npH CMeHe HHc'rpYMeHTa 6y,n;eT X - 100,0, Y - 100,0. CooTBeTcT-
BYIOru;HH M-KO,n; B nporpaMMe nepe,n; CMeHOH HHC'rpyMeHTa nepeMeCTHT ero B 3TH
Koop,n;HHaTbI H OTBe,n;eT BBepx no OCH Z B Hcxo,n;Hoe nonoxeHHe Ha HeKOTopOM pac-
CTORHHH OT 3arOTOBKH, qTo6bI 06neNHTb HeaBTOMaTH3HpOBaHH)'IO CMeRY HHC'rpY-
MeHTa.
llporpaMMHpOBaHHe 6y,zi;eT OCyrI(eCTBIDITbCR ,lLJUI 'rpaeKTOpHH eH'rpOBOH nHHHH/
eH'rpa HHC'rpyMeHTa, H ,lLJUI npOCTOTbI B 3TOM npHMepe OTCYTCTByeT KaKa5I-nH60
KOMneHCa IDI Ha ,lI;HaMelp.
,lI;aHHhle 0 pa3Mepax
llOKa3aHHbIe Ha pHCyHKe pa3MepbI npe,n;CTaBJUIIOT C060M X, Y, Z, ,lI;aHHbIe ,lLJUI
na3a 10 MM mHpHHoM H 8 MM rny6HHoH H oTBepcTHH 8 MM ,lI;HaMeTpOM H 12 MM
8.1. lfIlY muna CNC
rny6HHoit qHcna B Kpyrax OTHOCRTCR K nonoxeHIDIM HHcTPYMeHTa, ynoMHHalO-
IIJ;HMCR B o6pa3 e nporpaMMbI, npHBe,n;eHHoM ,n;aJIee. Ba3a OTCqeTa Z (ZO) COBnana-
eT C BepXHeH nOBepXHocTblO 3arOTOBKH.
na3 10 MM WL<1pL<1Ha x
x 8 MM rJ1y6L-1Ha
o
N
Ha ano
pa60Tbi
TpL<1 npOCBepJ1eHHbiX OTBep-
CTL<1 08 MM x 12 MM rJly6L-1Ha
w
Pa3Mepbl B MM
06pa3eu npOrpaMMbI
<1>opMaT Cne IIJ;erO npHMepa npOrpaMMbI COBMeCTHM C npOrpaMMHbIM o6ec-
neqeHHeM Bridgeport BOSS 6. npH o eHKe 3TOH nporpaMMbI cne eT o6paTHTbcR
K HH<popMa HH 0 Ko,n;ax, npHBe,n;eHHoH B pa3,n;ene 8.1.7.
JlHCTHBf nporpaMMhl
,lJ.JUIqllY
%
N5 G90 G71 GOO G75
NIO X-IOO.O Y-100.0
S1500 T01 M06
N15 X50.0 Y30.0
N20Z1.0M03
N25 G01 Z-8.0
F70 M07
N30 G02 X50.0 Y90.0
150.0 J60.0 F100
N35 G01 X100.0 Y90.0
N40 G02 X100.0 Y30.0
100.0 J60.0
N45 G01 X50.0 Y30.0
N50 GOO Z1.0
ODHcaBHe
CHMBOJI npOneHTa = CTapT nporpaMMbI/JIeHTbI.
Y CTaHOBKa KO.u;OB no.u;roToBHTeJIbHOH <PYHKlurn no yMomaHHIO.
G75 - CnenHaJIbHO AIDI nporpaMMHoro o6eCneqeHIDI BOSS 6.
DbICT}JOe nepeMemeHHe B nOJIOXeHHe AIDI CMeHbI HHCT}JyMeHTOB
(Hcxo,nHoe). Y CTaHOBKa CKOpOCTH BpaIUeHIDI IIInMH,LJ;eIDI. BbI60p
T}Je6yeMoro HHCT}JyMeHTa, M BCTaBKa nepBoro MHCT}JyMeHTa (cBepJIO
AIDI o6pa30BaHIDI na30B). OCTaHOB ynpaBJIeHIDI AIDI CMeHbI MHCT}JY-
MeHTa.
B0306HOBJIeHMe ynpaBJIeHIDI. DbICT}JOe nepeMeIUeHMe B n03Ml(HIO 1.
DbICT}JOe nepeMeIUeHHe MHCT}JyMeHTa B nOJIOXeHMe Ha 1,0 MM
BblIIIe 3arOTOBKH. CTapT IIInMH,[(eIDI (CKOpOCTh BpaIUeHIDI IIInMH,ZJ;e-
IDI YCTaHOBJIeHa B 6JIOKe N10).
npRMOJIMHeHHOe nepeMeIUeHHe co CKOpOCTblO no.u;aqM (70
MM/MMH) Ha T}Je6yeMYJO r.rry6MHy. BKJIIOqeHMe OXJIIDK,D:eHIDI TYMa-
HOM.
KpyrOBIDI MHTepnO.1UIll:IDI no X M Y Koop.u;MHaTaM, 06eCneqJfBalO-
IUIDI nepeMeIUeHHe B n03Hnmo 2; B KaqeCTBe l(eHT}JOB HHTepnOIDI-
l(MM MCnOJIb3yIOTCR I M J Koop.u;MHaTbI. YBeJIWIeHHe CKOpOCTH
no.u;aqH (no rOpM30HTaJIM) .u;o 100 MM/MMH.
TIpRMOJIMHeHHOe nepeMeIUeHHe co CKOpOCTblO no,naqH, YCTaHOB-
JIeHHOH B 6JIOKe N30, B n03Hl(HIO 3.
KpyroBIDI MHTepnOIDInIDI no X M Y Koop,nMHaTaM, 06eCneqHBaIO-
IUIDI nepeMeIUeHMe B n03Hl(HJO 4, co CKOpOCTbIO no.u;aqM, YCTaHOB-
JIeHHOH B 6JIOKe N30.
TIpRMOJIMHeHHOe nepeMeIUeHHe co CKOpOCTbIO no.u;aqM, YCTaHOB-
JIeHHOH B 6JIOKe N30, B n03MUHIO 1.
EbIC oe ne eMeIUeHHe MHC eHTa OT 3arOTOBKH no OCM Z.
Dla8a 8. A8moMamU3up08aHHoe 1COHcmpyup08aHue
N55 X-100.0 Y-100.0 DhICT}JOe nepeMemeHHe B nOJIOXeHHe CMeHhI HHCT}JyMeHTa (HCXO,n-
82500 T02 M06 Hoe) H OCTaHOBKa IIInHH,ll;eIDI. Y,naJIeHHe HHCT}JyMeHTa 1 H BCTaBKa
HHCT}JyMeHTa 2 (neHT}JOBOqHOe CBepJIo). YCTaHoBKa CKOpOCTH Bpa-
meHIDI IIInHH,ll;eIDI 2500 o6/MHH .wm CBepJIeHIDl.
B0306HOBJIeHHe ynpaBJIeHIDI. DbIcT}JOe nepeMemeHHe B n03HnHIO 5.
DhIc'rpoe nepeMemeHHe HHCT}JYMeHTa B nOJIOXeHHe Ha 1,0 MM
BhIllIe 3arOTOBKH. CTapr mnHH,LJ;eIDI (CKOpOCTh BpameHIDI mnHH.ZJ;e-
IDI 2500 06/MHH YCTaHOBJIeHa B 6JIOKe N55).
N70 G81 X170.0 Y90.0 CTapT nHKJIa CBepJIeHIDI (CM. pa3,neJI 8.1.11) H CBepJIeHHe nepBoro
Z-5.0 F40 M07 nempOBoro OTBepCTIDI (no3HnIDI 5) ,no 3anaHHoH rny6HHbI co CKO-
pOCTbIO no,naq}f 40 MM/MHH. BKJIIOqeHHe OXJIIDK,IJ:eHIDI TYMaHOM.
N75 X170.0 Y60.0 CBepJIeHHe BToporo OTBepCTIDI (no3HnIDI 6).
N80 X170.0 Y30.0 CBepJIeHHe T}JeTberO OTBepCTIDI (no3HnIDI 7).
N85 G80 OrMeHa lUIKJIa CBepJIeHIDl.
N90 GOO-X100.0 DbICT}JOe nepeMemeHHe B nOJIOXeHHe CMeHbI HHCT}JYMeHTa (HCXO.n-
Y-100.0 81760 T03 M06 Hoe) H OCTaHOBKa mnHH,LJ;eIDI. Y,na.n:eHHe HHCT}JYMeHTa 2. BCTaBKa
HHCT}JyMeHTa 3 (cnHpa.n:bHoe CBepJIo). YCTaHOBKa CKOpOCTH Bpame-
HIDI mITHH,LJ;eIDI 1760 06/MHH.wm CBepJIeHIDl.
BbIcT}JOe nepeMemeHHe B n03HI(HIO 5.
DhICT}JOe nepeMemeHHe HHCT}JYMeHTa B nOJIOXeHHe Ha 1,0 MM
BhIme 3arOTOBKH. CTapT nmHH,ZJ;eIDI.
N105 G81 X170.0 Y90.0 CTapr nHKJIa CBepJIeHIDI H CBepJIeHHe nepBoro OTBepCTIDI,no rny6H-
Z-12.0 F60 M07 HbI (12 MM) B n03HnHH 5 co CKOpOCTbIO no,naqH 60 MM/MHH. BKJIIO-
qeHHe OXJIIDK,IJ:eHIDI TYMaHOM.
CBepJIeHHe BToporo OTBepCTIDI (no3HnIDI 6).
CBepJIeHHe T}JeTbero OTBepCTIDI (no3HnIDI 7).
BbIKJIIOqeHHe IIIITHH,LJ;eIDI.
B03BpameHHe HHCT}JYMeHTa B nOJIOXeHHe CMeHbI HHCT}JyMeHTa (HC-
xo,nHoe) H OCTaHOBKa mIIHH.LJ;eIDI. fOTOBHOCTh K nOBTOpy nporpaM-
MhI.
KOHen nporpaMMhI.
KOHen JIeHTbI.
JlHCTHBI' oporpaMMhl
,lJ.JUIqllY
N60 X170.0 Y90.0
N68 Z1.0 M03
N95 X170.0 Y90.0
N100 Z1.0 M03
N110 X170.0 Y60.0
Nl15 X170.0 Y30.0
N120 G80
N125 GOO X-100.0
Y-100.0 M06
N130 M02
N135 M30
O"oHIlDHue
ODHC8HHe
8. 1. 13. KoppeKLlHfI Ha HHCTPYMeHT:
o6pa6oTKa Ha TOKapHOM CTaHKe
Ha TOKapHOM CTaHKe C qny, ,lLJUI Toro q'f06bI coxpaHHTb o6 6a3Y OTCqeTa ,lLJUI
Bcex HHCTPYMeHTOB B peBonbBepHoH ronOBKe, KOppeKI..J;IDI Ha .n.rrHHy HHCTPYMeHTa
TPe6yeTcR no 06eHM X- H Z-OCRM, KaK nOKa3aHO Ha pHCyJlKe.
Ha eHTPOBOM TOKapHOM CTaHKe C qny B peBonbBepHoH ronOBKe 3aIq)enneHO
HeCKonbKO pa3nWIHbIX H crpYMeHTOB. ,[lmI KIDK.ZI:OrO HHCTPYMeHTa 3a,naHa CBOR
co6CTBeHHasI KOppeKI..J;IDI Ha ,l(JIHHy no X H no Z, ,n;eHcTBYIOru;asI Tor,n;a, Kor,n;a npo-
rpaMMa npHBo,n;HT B ,n;eHCTBHe 3TOT HHCTPYMeHT. Kor,n;a rOnOBKa C HH,l(eKCa HeH,
Bce HHCTPYMeHTbI 3aHMYT pa3nlftlHbIe nonoxeHIDI OTHOCHTenbHO 3arOTOBKH. KaK
MO)I(HO BHJ(eTb Ha cxeMe, TaK KaK pa3nWIHbIe HHCTPYMeHTbI BbICTyIlalOT H3 ronOBKH
Ha pa3nlftlHbIe paCCTORHIDI no OCRM X H Z, ,lLJUI KIDK.ZI:OrO HHCTPYMeHTa ,n;OIDKHa
6bITb YCTaHOBneHa CBOR KOppeKI..J;IDI Ha .n.rrHHy.
8.1. If/IY muna CNC
xO Ha ano pa60Tbi
zO
3arOTOBKa
KoppeK LJlS1
no Z
KoppeK LJlS1 no X
Pe)f(}'I.!-'LJlt1 LJlHCTPYMeHT
PeBOJ1bBepHaS1 r0J10BKa
n0J10)l(eHLJle CMeHbI LJlH-
CTPYMeHTa (LJlCXOAHoe)
HanpaBJ1eHLJle Bpaw.eHLJlS1
bBePHOA ronOBKH
lt1HcTPYMeHT HOMep 1
TOKapHblH pe3e AJlS1
LJlCTOBOH 06pa60TKLJI
lt1HcTPYMeHT HOMep 2
AJlS1 Hape3aHLJlS1 pe3b6b1
o
lt1HcTPYMeHT HOMep 4
oTpe3Hot1 pe3e
lt1HcTPYMeHT HOMep 3
TOKapHblH pe3e AJlS1
epHoBot1 06TO KLJI
8. 1. 14. KOppeKf.lHfI Ha pa,qHYC sepWHHbl pe3f.1a:
TOKapHblH CTaHOK
KOMneHCaIJ;IDI pa,nHyca 3aKpyrJIeHIDI BepmHHbI HHC'rpYMeHTa Hcnonb3yeTcR aHaJIO-
fWIHO KOMneHCaIJ;HH ,l(HaMe'rpa npH <ppe3epoBaHHH. Cne,lJ;OBaTenbHo, QTo6bI aKTH-
BH3HpOBaTb H ,lJ;e3aKTHBHpOBaTb KOMneHCaIJ;HIO pa,nHyca 3aKpyrneHIDI BepmHHbI HH-
C'rpYMeHTa, MOryr Hcnonb30BaTbCR Te xe caMbIe nO,lJ;fOTOBHTenbHbIe KO,lJ;bI (KO,lJ;bI
G). KOMneHCaIJ;IDI ynpOIIJ;aeT nOBTOpRIOIIJ;HeCR CnO)I(IIbIe BbNHcneHIDI, Heo6xo,lJ;H-
MbIe ,l(IDI onpe.aeneHIDI 'rpaeKTOpHH HHC'rpYMeHTa. TIporpaMMHcT MoxeT nHcaTb
nporpaMM)', CQHTasI, QTO Hcnonb3YIOTCR HHC'rpYMeHTbI C OC'rpbIM KOHIJ;OM. llpHMe-
IDIIOTCR cne,[{y1OIIJ;He KO,lJ;bI:
rAa6a 8. A6moMamU3upo6alllloe KOllcmpyup06allue
G41 KOMrreHcaUIDI Ha PMHYC 3aKpyrJIeHIDI BepllIHHbI HHcTPYMeHTa BJIeBO
G42 KOMrreHcaUIDI Ha PMHyca 3aKpyrJIeHIDI BepllIHHbI HHcTPYMeHTa BrrpaBo
G40 OTMeHa KOMrreHcaUHH Ha PMHYc 3aKpyrJIeHIDI BepllIHHbI HHCTPYMeHTa
G41 KOMOeHCaQHJI BJleBO
G42 KOMOeHCaQHJI BopaBo
I
- -
I
I
- -
I
8. 1. 15. MeTo,qbl nporpaMMHposaHHfI:
o6pa6oTKa Ha TOKapHoM CTaHKe
WHKCHpOBaHHble IUfKJIbl
,lJ;arree rrepeqHCJIeHO HeCKOJIbKO rrpHMepOB <pHKcHpoBaHHbIX UHKJIOB KOHTPOJI-
JIepa ueHTPOBoro TOKapHoro CTaHKa C qny:
G66/67
G68/69
G81
G82
G83
G84/85
G88
-'
[(HKJIbI KOHTypHOH o6pa6oTKH
[(HKJI qepHOBOH o6pa6oTKH
[(HKJI 06TOqKH
[(HKJI 06TOQKH JIHueBOH rrOBepXHOCTH
[(HKJI rrry6oKoro CBepJIeHIDI
[(HKJIbI Hape3KH UHJIHH,D;pJ11IeCKOH pe3b6bI
[(HKJI aBTOMaTlfleCKOH rrpOTOQKH
8.1. lfIlY muna CNC
G68. QHKJI lIepHoBoH o6pa6oTKH
3roT I(HKJI HCrrOJTh3YeTCSI IIpH CDeMe 6oJIbllIOro KOJIWIecma MeTaJIJIa. UHKJI aKTHBH-
pyeTCSI KO,r(OM G68. ,lJ;BIDKeHIDI CTaHKa rrOKa3aHbI Ha pHcYHKe H rrepeT.JHCJIeHbI ,n;aJIee.
\
1. BbIC1'pOe rrepeMem;eHHe B TOqKY CTapTcl.
2. HeCKOJIbKO rrpSIMOJIHHeHHbIX qepHoBbcl\ rrpOXO,r(OB (KOJIJ11IeCTBO 3aBHCHT OT
r.rry6HHbI cpe3a).
3. KOHT)'pHbIH rrpoxo,r(, rrOCJIe KOToporo OCTaeTCSI rrpHrrycK Ha qHCTOBYIO 06pa-
60TKY.
TIocJIe 3aBepllIeHIDI UHKJIa qepHOBOH 06pa60TIQI KOMrrOHeHTa MO)l{eT 6bITb 06-
TOqeHa ,r(0 OKOJItIaTeJIbHOrO p3.3Mepa. \
- - .- -
-------......-----
T O'-lKa CTapTa
G83. QaKJI rJl)'60KOrO CBepJleHIUI
l(HKJI r.rry60Koro CBepJIeHIDI HCrrOJIb3yeTcSI ,r(.JUI CBepJIeHIDI oTBepcTHH C 60JIb-
llIHM OTHOllIeHHeM r.rry6HHa /,r(HaMe1'p H 06eCrreqHBaeT OTcyrcTBHe CTPyxKH B OT-
BepCTHH Ha rrpOTIDKeHHH Bcero UHKJIa. l(HKJI aKTHBHpyeTcSI KO,n;OM G83. ,lJ;BlDKeHIDI
CTaHKa rrOKa3aHbI Ha pHC)'HKe H rrepeqHCJIeHbI ,r(aJIee.
1. BbIC1pOe rrepeMem;eHHe K TOqKe CTapTa.
2. TIo,r(aqa Ha r.rry6HJIy rrepBoro rrpoxo,r(a.
3. BbIC1'poe rrepeMem;eHHe Hapyxy K cTaproBoH TOqKe.
4. BbIc1'poe rrepeMem;eHHe BHyrpb, HeMHoro He ,r(OXO,lUI .n;o r.rry6HHbI rrepBoro
rrpoxo,r(a.
5. TIo,r(aqa Ha r.rry6HJIy BToporo rrpoxo,r(a.
6. TIoBTopeHHe ,r(BlDKeHHH (c)-(e) Ha r.rry6HJIy KIDK,L(OrO rrocJIe.nyIOlI(ero rrpoxo-
,r(a, rrOKa He 6Y,r(eT ,r(OCTHrHyra 1'pe6yeMaH r.rry6HHa.
3arOTOBKa
bblCTpoe ne p eMe -.
eHHe HapY'KY
CBepll0
, , , ,
, , , ,
, , , ,
, , , ,
" " "
" " "
" " "
" " "
-4
nOAa a BHyrpb
1-v. npoxOA H BblBOA CBeplla
2-v. npOXOA H BblBOA CBeplla
3-v. npOXOA H BblBOA CBeplla
4-v. npOXOA H BbiBOA CBeplla
5-v. npoxOA H 4>HHanbHa rlly6 Ha
T 0'-1 Ka CTapTa
rA060 8. A6moMomU3upo6oHHoe KOHcmpyupo6oHue
8. 1. 16. npHMep nporpaMMbl: o6pa6oTKa
Ha TOKapHOM CTaHKe
,lJ;aJIee CJIe.nyeT npHMep nporpaMMbI ,I:LJUI qTIY. TIporpaMMa 06eCneQHBaeT BbInOJI-
HeHHe CJIeJ\YIOIIJ;HX ,[(eHcTBHH:
1. qepHOBaH 06TOQKa, nOCJIe KOTOpOH OCTaeTCSI npHrrycK 0,5 MM Ha ,[(HaMe1'pbI
H rpaHH.
2. OKOHQaTeJIbHaH 06TOQKa ,[(eTaJIH ,[(0 pa3Mepa.
3. 01'pe3aHHe no ,[(JIHHe.
KOMDOHeHTa
-t
.
l
Stock
038
g Ha"lall0 pa60Tbi
I
./
036
034
031.5
\ -_/
15
30
Pa3Mepbl B MM
45
MaTepHaJI: aJIlOMHHHeBbIH crrrraB BS 1474: 1987 THn 5154(A) COCTOSIHHe O.
HaCTPYMeHThI H ,lI;aHHLIe ,l(JUI o6pa6oTKH
HOMep ODHCaHHe CKOpoCTb BpameHBJI CKOpoCTb DOJ,Ul1lll
HHCTp)'MeHTa HHCTp)'MeHTa eJIJI (MMj06)
T101 TOKapHbIH pe3eu .lWI rpy60H 130 M/MHH 0,2
o6pa6oTKH
T202 TOKapHbIH pe3eu .lWI OKOH- 2500 06/MHH 0,05
qaTeJlbHOH o6pa6oTKH
T303 HHc'rpYMeHT y,naJIeHIDI qaCTH 120 M/MHH 0,05
06pa3en DporpaMMbI
1. <l>opMaT nporpaMMbI COBMeCTHM C KOH1'pOJIJIepOM qTIY GE 1050.
2. B 3TOM npHMepe HCnOJIb3yeTcH nporpaMMHpOBaHHe ,[(HaMe1'pa.
-'
3. TIOJIOXeHHe CMeHbI HHC1'pYMeHTa (Hcxo,[(Hoe nOJIOXeHHe) X177.8 Z254.
JlHCTHHr DporpaMMW AJIJI qllY ODHcaHHe
% CTapT nporpaMMbI/JleHTbI.
N0010 G71 AIcrHBH3aUIDI peXHMa pa60TbI C Me'rpWleCKHMH ,naHHbIMH.
N0020 G95 YCTaHOBKa CKOpOCTH no,naqH B MM/o6.
JIHCTHBr nporpaMMY AJIJI qllY
N0030 G97 SIOOO M03
N0040 GOO M08
N0050 G53 XI77.8 Z254.0 TO
N0060 TIOO
N0070 G54 XOO Z2.0 TIOI
\
N0080 G92 RO S2000
N0090 G96 SI30
NOIOO GOI XO.O ZO.5 FO.2
NOIIO X36.5
NOI20 Z50.0
NOI30 GOO X37.0
NOI40 ZO.5
NOI50 X34.5
NOI60 GOI Z-29.5
NI70 GOO X35.0
NOI80 ZO.5
NOI90 X32.0
N0200 GOI Z-I4.5
NOI20 GOO
N0220 G53 XI77.8 Z254.0 TO
N0230 T200
N0240 G54 XIO.O ZIO.O T202
N0250 G4I XO.O ZO.05
N0260 G97 S2500
N0270 GOI ZOO FO.05
N0280 X3I.5
N0290 Z-I5.0
N0300 X34.0
N03IO Z-30.0
N0320 X36.0
8.1. If/IY muna CNC
llpoiJoA:JICeHUe
ODHCaHlle
IlpgMasI YCTaHOBKa B 06/MHH CKOpOCTH wnHH,ZJ;eIDI Ilepe-
KJllOqeHHe CKOpOCTH wnHH,ZJ;eIDI Ha 1000 06/MHH.
YCTaHoBKa 6bIC1'pOro nepeMe eHIDI. BKJIlOqeHHe no.n;aqH
OXJIa,nHTeIDI.
OTMeHa CMe eHIDI Ha 3arOTOBKY. IlepeMe eHHe rOJIOBKH B
Hcxo.n;Hoe nOJIOXeHHe. OTMeHa KOppeKiniH HHC1'pYMeHTa.
IloBopoT rOJIOBKH B nOJIOXeHHe 1.
Y CTaHOBKa CHCTeMbI Koop.n;HHaT 3aroToBKH. DbIc1'pOe .n;BIDKe-
HHe B Koop.n;HHaTbI. AIcrHBaUIDI KoppeKUHH HOMep 1 HHCT-
PYMeHTa C HOMepOM 1.
Y CTaHOBKa napaMe1'pOB ,nJUI nOCTOgHHOH CKOpOCTH cpe3aHIDI
nOBepXHOCTH (MaKCHMaJIbHO 2000 06/MHH).
AIcrHBaUIDI peXHMa nOCTOgHHOH CKOpOCTH cpe3aHIDI no-
BepXHOCTH Ha 130 M/MHH.
IlpRMoJIHHeHHoe nepeMe eHHe co CKOpOCTblO no.n;aqH
0,2 MM/06.
IlpgMoJIHHeHHoe nepeMe eHHe co CKOpOCTblO no.n;aqH
0,2 MM/06.
IloBopoT 3a npe.n;eJIaMH KOMnOHeHThI ,nJUI YMeHbweHIDI .n;Ha-
Mel'pa npH 01'pe3aHHH. IlpgMoJIHHeHHoe nepeMe eHHe co
CKOpOCTblO no.n;aqH 0,2 MM/06.
DbIC1'pOe nepeMe eHHe HHCl'pYMeHTa OT 3arOTOBKH.
DbIC1'pOe nepeMe eHHe HHC1'pYMeHTa OT 3arOTOBKH.
DbIc1'pOe nepeMe eHHe HHC1'pYMeHTa OT 3arOTOBKH.
IlpgMoJIHHeHHoe nepeMe eHHe co CKOpOCThIO no.n;aqH.
DbIc1'pOe nepe.n;BIDKeHHe.
DbIcl'poe nepeJ(BIDKeHHe.
DbIcl'poe nepe.n;BIDKeHHe.
IlpgMoJIHHeHHoe nepeMe eHHe co CKOpOCTblO no.n;aqH.
DbIcTPOe nepe.n;BIDKeHHe.
OTMeHa CMe eHIDI Ha 3arOTOBKY H OTMeHa KoppeKUHH HH-
C1'pYMeHTa, nepeMe eHHe rOJIOBKH B HCXO.n;uyIO n03HUHIO.
IloBopoT rOJIOBKH B n03HUmo 2.
Y CTaHOBKa CHCTeMbI Koop.n;HHaT 3arOTOBKH. DbIC1'pOe .n;BIDKe-
HHe B Koop.n;HHaTbI. AKTImaUIDI KoppeKUHH HOMep 2 HHCT-
PYMeHTa C HOMepOM 2.
IlepeMe eHHe B Koop.n;HHaTbI H aKTHBaUIDI KOMneHcaUHH
pa,nHYca 3aKPYTJIeHIDI BepWHHbI HHC1'pYMeHTa.
IlpgMasI YCTaHOBKa 2500 06/MHH.
IlpgMoJIHHeHHoe nepeMe eHHe co CKOpOCTblO no.n;aqH
0,05 MM/06.
IlpgMoJIHHeHHoe nepeMe eHHe co CKOpOCThIO no.n;aqH, qTO-
6bI 06TOqHTb KOHTYP .n;eTaJIH no pa3Mepy.
rAa6a 8. A6moMamU3upo6aHHoe KOHcmpyupo6aHue
JlHCTHBr nporpaMMW AJIJI qllY
N0330 Z-45.0
N0340 G40
N0350 GOO
N0360 G53 X177.8 Z254.0 TO
N0370 T300
N0380 G54 X38.0 Z-45 T303
N0390 G92 R38 S1000
N0400 G96 S120
N0410 GOI X-2.0 FO.05
N0420 GOO X38.0 M05
N0430 G53 X177.8 Z254.0 TO
N0440 M02
OKOH"laHUe
ODHCaHHe
OrMeHa KOMTIeHcaI.Urn panHYca 3aKPYTJIeHIDI BepWHHbI HH-
c'rpYMeHTa.
DbIc'rpoe nepeMe eHHe.
OrMeHa CMem:eHIDI Ha 3arOTOBKY. IlepeMem:eHHe roJIOBKH B
Hcxo,nHoe nOJIOXeHHe. OrMeHa KOppeKiniH HHC'rpYMeHTa.
IloBopoT rOJIOBKH B n03HIJ:HIO 3.
YCTaHOBKa CHCTeMbI Koop,nHHaT 3aroToBKH. DbIc'rpoe ,nBIDKe-
HHe B Koop,nHHaThI. AIcrHBaQIDI KOppeKI.(HH HOMep 3 HHCT-
PYMeHTa C HOMepOM 3.
YCTaHoBKa napaMe'rpOB AJUI nOCTOHHHOH CKOpOCTH cpe3aHIDI
nOBepXHOCTH (MaKCHMaJIbHO 2000 06/MHH).
AIcrHBaUIDI peXHMa nOCTOgHHOH CKOpOCTH cpe3aHIDI no-
BepXHOCTH Ha 130 M/MHH.
IlpSIMOJIHHeHHOe nepeMe eHHe co CKOpOCTblO no,natIH.
DbIc'rpoe nepeMe eHHe OT 3arOTOBKH. BbIKJIlOqeHHe
llIIIHH,l(eIDI.
OrMeHa CMem:eHIDI Ha 3arOTOBKY H OTMeHa KOppeKlJ;lm HH-
C'rpYMeHTa. DbIc'rpoe nepeMe eHHe rOJIOBKH B HCXO,nHyIO
n03HUHI<>.
KOHeu nporpaMMbI.
8. 1. 17. Cnosapb TepMHHos
MaDTHBHOe ynpaBJIeHHe
CHCTeMa yrrpaBJIeHIDI C BC1'poeHHhIMH ceHcopaMH, H3MeIDIIOIIJ;IDI CKopocThjrro-
,[(aqy rrpH H3MeHeHHH HarpY30K pe3aHIDI. TaIOKe 06eCrreQHBalOT KOH1'pOJIb B rrpo-
uecce o6pa6oTKH H KoppeKIJ;HIO pa3Mepa.
Mpec
B rrporpaMMHpOBaHHH CHMBOJI, KOTOphIH YK3.3hIBaeT 3HaQeHHe HH<popMaUHH,
Herrocpe,[(CTBeHHO 3a HHM CJIe,nyroIIJ;eH.
Mpec CJlOBa
BJIOK 3HaKOB, HaQHHalOIIJ;HHCSI C 6yxBeHHorO CHMBOJIa, KOTOphIH ero H,[(eHTH-
<pHUHpyeT.
Ba3a OTClIeTa
Mcxo,[(Hoe rrOJIOXeHHe, OT KOToporo OTCQHThIBalOTCSI Bce a6COJIIOTHhIe KOOp,[(H-
HaTh!.
BaHT
E,[(HHHI.J;a HH<popMaUHH, COCTOSIIIJ;IDI H3 BOChMH 6HT.
BUT
A66peBHaTYPa OT «,[(BOJ11IHIDI I.J;H<ppa (binary digit»).
BJlOK
C1'pOKa (K3)]:p) RJIH rpyrrrra CJIOB, co,[(epxaIIJ;IDI Bce HHC1'pYKUHH ,[(JUI O,nHOH
orrepaUHH.
8.1. If/lY muna CNC
6bICTpoe nepeMemeHHe
TIepeMem;eHHe C BbICOKOH CKOpOCTblO, 06bPIHO HCrrOJIb3yeMoH, qTo6bI C3KOHO-
MHTb BpeMH rrpH rro3HUHoHHpoBaHHH pe3ua rrepe,r( HaqaJIOM pe3aHIDI.
)];BOIf1lHOe qHCJlO
qHCJIO B CHCTeMe C OCHOBaHHeM 2.
)];BOIfIIHO- ,IJ;eCJlTIf1IHOe qHCJlO
Crroco6 rrpe,r(CTaBJIeHIDI ,r(eCSITWIHbIX qHCeJI qepe3 pH)]; ,r(BOJ11IHbIX qHCeJI.
HHKpeMeHTHaJi CHCTeMa
CHcTeMa, rrpH KOTOpOH KIDK,r(oe rrepeMem;eHHe H3MepHeTCSI OT rrpe,r(b ero
rrOJIOXeHIDI.
HHTepnoJIJIIUfJI
Coe,r(HHeHHe 3arrporpaMMHpOBaHHbIX TOqeK rrpH rrOMOm;H BbPIHCJIeHHH, TaK
1ff06bI rro.rryqHTb IIJIaBJIyIO KPHBYIO.
KO,IJ;HpOBIQHK
Y CTPOHCTBO, KOTopoe HCrrOJIb3yeTcH ,r(.JUI rrpeo6pa30BaHIDI rrOJIOXeHIDI ,r(BH)I{}'-
m;erocSI YCTPOHCTBa '3 3JIeIcrpOHHbIH CHrHaJI.
KOlITpoJlb B npon cce o6pa6oTKH
H3MepHTeJIbHaH CHCTeMa, BCTPoeHHaH B CTaHOK, KOTOpaH H3MepSIeT 3arOTOBKY
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HbIX OTCne)J(HBaeT rronoxeHHe aBTOMaTJI1IeCKH CKaHHpyID ero HJIH rrepe,nBHraeMoro
Bpyq copa. IIrraHmeT co,nep)J(HT 3ne OMarHHT , 3ne OCTaTHqeC
HJIH 3ne ope3HCTHB ceTKy, COOTBeTCTByID pa3pemeHHIO ,nHCWleB. TaKHM
06pa30M, Koop,nHHaThI X H Y C WlaHmeTa MOryr oT06paxaTbcB Herrocpe,nCTBeHHO
Ha 3KpaH.
j(JlCOUCmUK. 3TO YC1pOHCTBO ynpaBneH:IDI C ,nB OCBMH, 06eCrreqHBalO ee
6bIC1pOe ,nBIDKeHHe copa. OH 3HaKOM BceM, KTO HrpaeT B BH,neOHrpbI. npH HC-
nonb30BaHHH B CHCTeMe C OH rr03BOIDIeT 6bIC1pee nepe,nBHraTb cop, qeM 3TO
B03MO)l{}fO rrpH rrOMO H KJIaBHa bI. O,nHaKO TOqHOCTb rr03HI(HOHHpOBaH:IDI y
u
,lPKOHCTHKa HH3KasI H 3aBHCHT OT HaBbIKa onepaTopa.
MblWb. MbImb B HaCTOB ee BpeWl mHpOKO Hcrronb3yeTcB BMeCTO ,lPKOHCTHKa H
He06xo,nHMa rrpH Hcrronb30BaHHH rrporpaMMHoro 06eCrreqeH:IDI C B OrrepaI(HOH-
HOH CHCTeMe Windows. KaK TonbKO cop rrOMe eH B oe nonoxeHHe, en-
qOK KHorrKOH MbImH rr03BOIDIeT BBO,nHTb KOMaH,nbI 6bIC1p0 H nerKO.
Y cTJ)oiicTBa BhmO,lJ.a
HarreqaTaTb TBep.nyro KorrHIO OI(H<PPOBaHHbIX ,naHHbIX MO)l{}fO MHorHMH crroco-
6aMH.
IIAallwemllblU 2pafjJonocmpoumeAb (11Il0mmep). bYMara Herro,nB 0 3aKpeWleHa
Ha DJIOCKOM CTone. 3aKpeWleHHe 3ne OCTaTHqeCKOe HJIH Ba Hoe. qT06bI Ha-
pHCOBaTb H306paxeHHe, ronoBKa rrepeMe aeTCB B,nonb oceH X H Y. KapeTKa rrepe-
MelUaeTCB B,nonb OCH X, a ronOBKa rrepeMe aeTCB B,nonb OCH Y rro MOCTY, pacrrOJIO-
XeHHOMY Ha KapeTKe. CymecTByeT TaIOKe Hcxo,nHoe rronoxeHHe, B KOTopoe ronOB-
Ka YCTaHaBnHBaeTCB B HaqaJIe H KOHI(e pHCOBaH:IDI. 3TO rr03BOIDIeT BCTaBIDITb 6y-
622 r.l1080 8. A8moMomU3upo8oHHoe ICOHcmpyupo80Hue
Mary H BhIHHMaTb 3aKOINeHHbIH pHCyHOK, He 33J1;eBasI rrepo. fonOBKa TalOKe
B03Bpa aeTCR B Hcxo,nHoe rronoxeHHe, Kor,na 0 3aMeHHTb rrepo, tfr06hI 06ec-
rreqHTb ,np Ton HHY nHHHH H/HJIH I(BeT. nepbB pacrronoxeHbI B Mara3HHe H
BbI6HpalOTCR rro KOMaH,ne C KOMrrblOTepa.
Eapa6all1lblU UAU PYAOHHblU zpaf/JonocmpoumeAb. HOCHTeJIb Bpa aeTCB, 06ecrre-
qHBasI rrepeMe eHHe rro OCH X, a KapeTKa C rrepOM rrepeMe aeTCB TonbKO B,nOJIb
OCH Y, rrapaJI.1IenbHO OCH Bpa eHIDI 6apa6aHa. TaKoe YC1pOHCTBO rr03BOIDIeT BbI-
rronIDITb 60nbmHe pHCyHKH, XOTB caMO OHO 3aHHMaeT MeHbme MeCTa. 3TH llJIOTTe-
phI He HaCTonbKO TOqHbI, KaK llJIaHmeTHbIe, TaK KaK 6YMara paCTBrHBaeTCB H rrpo-
CKaJlb3bmaeT. )];Harra30H MaTepHaJlOB, C KOTOpbIMH OHH MOryr pa60TaTb, TaIOKe 60-
nee orpaHWleH.
He60nbmHX pHCyHKOB no,nxO,lUlT 06bl'IHbIe Ma1pWIHbIe, na3epHbIe H 3neKT-
pOCTaTWleCKHe rrpHHTepbI, KOTopbIe HcrrOnb3yIDTCR,lUUI 06bl'IHOro rreqaTaH:IDI TeK-
CTOB.
8.2.3. nporpsMMHoe o6eCnelfeHJfe CJfCTeMh' CAD
CymecTByeT MHoxeCTBO ,noc bIX rraKeTOB C . OHH MOryT 6bITb npe,nHa3Haqe-
HbI,lUUI pa60TbI B 2D H B 3D. KaK rrpaBHJIO, 2D rraKeT He ,nenaeT HHqerO TaKoro,
qTO He MoxeT 6bITb c,nenaHO Bpyq rrpH rrOMO H qepTe)I{HOH ,nOCKH H peHcmH-
HbI BMeCTe C 06bl'IHbIMH qepTe)I{HbIMH HHC1]>YMeHTaMH. BbI TaIOKe MOXeTe rroc1pO-
HTb H30Me1pWleCKHe H KOCbIe rpa<pWleCKHe rrpe,nCTaBneH:IDI. qT06bI C3KOHOMHTb
BpeMj{, MO)I{HO HTb 6H6nHOTeKH CTaH,napTHbIX CHMBonOB. HeKOTopbIe KOMrra-
HHH Ha ,nHCKe rrpe,nOCTaBIDIIOT CBOHM 3aK33qHKaM ,lUUI rronb30BaH:IDI 6H6nHOTeQ
HH<popMaI(HIO 0 CBOHX rrpo ax. HarrpHMep, H3rOTOBHTenH BaHHoro H OHHoro
060py,nOBaHIDI rrpe,nOCTaBIDIIOT apXllTeKTOpaM Ha ,nHCKe BeCb ,nHarra30H CBoeH rrpo-
HH B BH)(e qepTeXeH B MacmTa6e, qT06bI HX MO)I{HO 6blJI0 BCTaBlliITb Herro-
cpe,nCTBeHHO B HX rrpOeKTbI. HeKOTopbIe rronb30BaTenH C03,na1OT c06CTBeHHhIe 6H6-
nHOTeKH qaCTO Hcrronb3yeMbIX KOMITOHeHT, HCrrOnb3YB 6nOqHbIe KOMaH,nbI.
TpeXMepHoe rrporpaMMHoe 06eCrreqeHHe He06xo,nHMO, ecn:o BaM rr01pe6yeTCR:
. KapKaCHoe MO,lJ.eJIHpOBaHHe. II03BoIDIeT H306pIDKaTb yrnbI H pe6pa Mo,neJIH,
KaK rrOKa3aHO HIDKe. Pe3YJIbTaTOM TaKoro no,nxo,na MoxeT CTaTb H306pIDKe-
HHe, BbIr ee Heo,nH03HaqHO.
. MO,lJ.eJIH nOBepxaocTei. OHH 06bl'IHO Hcrronb3yIOTCB, Kor,na KOMrrOHeHThI
HMelOT cno rrOBepXHOCTb, Ta KaK rraHenH aBTOM06HID1 HJIH CaMOJIe-
Ta. HH<popMaI(:IDI, KacalO aBCB rrOBepXHOCTH, MOXeT 6bITb H3BneqeHa H3 3a-
u
TeHeHHOH Mo,nenH rrOBepXHOCTH.
. OO'beMHLIe MO,lJ.eJIH. OHH 06eCrreqHBaIOT rro,np06 HH<popMaI(HIO OTHOCHTe-
nbHO 06naCTeH, 06'beMgB H I(eH1]>OB TIDKeCTH KOMrrOHeHT. 06DeMHbIe Mo,ne-
.
nH MO)I{HO C1pOHTb H3 CTaH,napTHbIX 1peXMepHbIX <pOpM H MO,nH<pHI(HpOBaTb,
qT06bI rro HTb bIH pe3ynbTaT.
..
Bce Hcrronb3yeMoe B HaCTOB ee BpeWl rrporpaMMHoe 06eCrreqeHHe C MO-
xeT pa60TaTb B OrrepaI(HOHHOH CHCTeMe Windows, HO HeKOTopbIe BepCHH MOXHO
HCrrOnb30BaTb H Ha KOMrrblOTepax Mac · tosh. CymecTByeT mHpoKHH ,nHarra30H
rraKeTOB rrporpaMM, KOTopbIe MOryT 6bITb HaC1poeHbI ,lUUI Hcrronb30BaH:IDI TeXHWle-
8.2. A8moMomU3upo8oHHoe npoeICmupo8oHue (CAD) 623
CKHMH npOeKTHpOB HKaMH, apXHTeKTOpaMH, xy,nO)l{}fHKaMH-,neKopaTopaMH, KO-
pa6neC1pOHTellilMH H ,npyrHMH. TaKHe rraKeTbI Bcer,na MOryT 6bITb CKOH<pHrypHpO-
BaHbI rronb30BaTeneM TaK, qT06bI COOTBeTCTBOBaTb KOHKpeTHbIM rrpHJIOXeH:IDlM.
OHH 06eCrreqHBalOTCB 6H6nHoTeKaMH ,naHHbIX H cHMBonoB, KOTopbIe MOryT 6bITb
BbI6paHbI rro xenaHHIO. XOTB caMbIe rrocne,nHHe rraKeTbI 1pe6yIDT OT KOMrrblOTepoB
60nbmeH MO HOCTH, rro cpaBHeHHIO C paHHHMH BepC:IDlMH, cOBpeMeHHbIe HaCTO-
nbHbIe KOMrrblOTepbI H HOyr6 Bce xe rrO)J.l{ep)J(HBaIOT 60nbillHHcTBO HaH60nee
pacrrpOC1paHeHHbIX rraKeTOB.
8.2.4. ASTOM8TJf3JfPOS8HHoe npoeKTJfpOS8HJfe
Jf npOJf3s0,qCTSO
MHTerpaU:IDI C C aBTOMaTH3HpOBaHHbIM yrrpaBneHHeM npOH3Bo,nCTBOM BneqeT
3a C060H COBMeCTHoe Hcrronb30BaHHe 6a3bI ,naHHbIX 3THMH p3.3nWlHbIMH C1p -
paMH. npeH eCTBa TaKOH CHCTeMbI cne IUHe.
. Ha.n:e)I{Ho 06eCrreqHBaeTCB HerrpOTHBOpeqHBOCTb HH<p0pMaI(HH, KacalO eHCB
rrpOeKTHpOBaHRSI H rrpOH3Bo,nCTBa; OTcyrcTByeT B03MO)l{}fOCTb nOBTOpeH:IDI
omH60K.
. nporpaMMbI qny MOryT pa3pa6aTbIBaTbcB Herrocpe,nCTBeHHO Ha OCHOBaHHH
OI(H<ppoBaHHbIX ,naHHbIX qepTeXa B cymecTBeHHO 60nee KopOTKHe CpOKH.
. M3rOTOBneHHe CnO)I{HbIX ,neTaJleH MoxeT 6bITb 3arrporpaMMHpOBaHO 6e3 He-
06XO,nHMOCTH B ,nJIHHHbIX BbI'lHCJleHIDIX.
. npoBepKa Ha 3KpaHe 3arrporpaMMHpOBaHHbIX ,lUUI qny 1paeKTOpHH HHC1py-
MeHTOB YMeHbmaeT BepOBTHOCTb H3rOTOBneH:IDI 6paKoBaHHbIX ,neTaJIeH H rro-
Bpe eH:IDI pe HX HHCTpYMeHTOB.
. COKpa eHHe BpeMeHH OCBOeH:IDI HOBOR npo HH OT CT3JI;HH rrpoeKTa ,no
u
cepHHHoro rrpOH3Bo,nCTBa
624 r.lla80 8. A8moMomU3upo8aHHoe ICOHcmpyup080Hue
8.2.5. npeJfMy ecTsa Jf OrpaHJf'leHJffl CAD
npe eCTRa
. CymecTBeHHo rrOBbImaeTCR rrpOH3Bo,nHTenbHOCTb rrpoueCCOB pa3pa60TKH H
u
rro,nrOTOBKH qepTexeH.
. qepTe)I{JI MOryr 6bITb BbIrronHeHbI Ha OqeHb BbICOKOM ypOBHe TOqHOCTH B co-
OTBeTCTBHH C <pHpMeHHbIM CTHJIeM.
. npoeKT H3,nen:IDI MOXeT 6bITb Y meH.
. MO,l(H<pHKaI(HH nerKO BHeCTH, He rrepe,nenbIB8.SI qepTe)I{JI rronHOCTblO.
. no cpaBHeHHIO C KaJlbKaMH, XpaHHTb Ha ,nHCKe OI(H<PPOBaHHbIe ,naHHbIe rrpo-
e H OHH 3aHHMalOT MeHbme MeCTa.
. MoxeT 6bITb rro eHa TBep,nasI KOrr:IDI B I(BeTe, Tor,na KaK 06bl'IHbIe CBeTO-
KorrHH o,nHOI(BeTHhI.
. OI(H<PPOBaHHbIe ,naHHbIe MOryr Hcrronb30BaTbCR ,lUUI: KaJlbKyIDII(HH H OI(eH-
KH, 3a OK, llJIaHHpOBaH:IDI H yrrpaBJIeH:IDI rrpOH3Bo,nCTBOM, KOH1]>OIDI 1pY-
,nOBbIX 3a1paT, KOH1pOIDI KaqeCTBa.
. OI(H<PPOBaHHLIe ,naHHbIe C MOryr 6bITb 06'be,nHHeHhI CO CTaHKaMH qny
(C IC ), a TaIOKe C aBTOMaTWleCKHMH YC1pOHCTBaMH, 06Pa3YB rH6
rrpOH3Bo,nCTBe CHCTeMY.
OrpaHll'lelllUl
. CTOHMOCTb arrrrapaTHbIX H rrporpaMMHbIX cpe,nCTB ,lUUI C MoxeT 6bITb
OqeHb BbICOKa. XOTR CTOHMOCTb OT,nenbHbIX COCTaBIDIIO HX MoxeT 6bITb CHH-
v
xeHa, HerrpepbIBHbIH pOCT CnO)l{}fOCTH H COBepmeHCTBOBaHHe rrporpaMMHoro
06eCrreqeH:IDI 1pe6yIOT Bce 60nbmHX H 60nb o6DeMoB rraWlTH, 60JIbmeH
MO HOCTH H CKOpOCTH OT I(eH1paJIbHOrO rrpOI(eCcopa. Bce 3TO rrepeKpbIBaeT
nlO6hIe CHIDKeHIDI CTOHMOCTH OT,nenbHbIX COCTaBIDIIO HX.
. MO HbIe CHCTeMbI C 1pe6yIOT peryIDIpHoro 06c BaH:IDI, XOTB OHH
CTaJlH HaMHoro Ha.n;e)I{Hee, H B03MO)l{}fhI KO aKTbI Ha TeXHWleCKOe 06c.rry-
)J(HBaHHe.
. nepBOHaqaJIbHasI YCTaHOBKa H rro,nrOTOBKa K3Jl:pOB MOryr 6bITb ,noporOCTOB-
HMH, rrOKa 6H6nHOTeKH ycnoBHbIX CHMBonOB rro,nrOTaBnHBaIOTCB H OI(H<p-
pOBbIBaIOTCR, TaK qT06bI COOTBeTCTBOBaTb H3,nen:IDlM KOMnaHHH.
. He06xo,nHMbI COOTBeTCTByIO He 3prOHOMWlHbIe BHemHHe ycnOB:IDI, qT06bI
rrpe,nOTBpaTHTb YCTaJlOCTb orrepaTopa H rapaHTHpOBaTb 3KOHOMWlHOCTb HC-
IIonb30BaH:IDI CHCTeMbI.
8.3. npOMblwneHHble P060Tbi
8.3.1. Bse,qeHJlfe s po60TOTeXHJf
npOMbIllIJIeHHbIH P060T 3TO rrporpaMMHpyeMbIH CTaHOK 06 ero Ha3HaqeHIDI,
06na:nalO HH HeKOTopbIMH aH1pOrrOMop<pHbIMH oc06eHHOCTBMH (rro,n06HbIH qeno-
BeKy). CaMasI THrrWlHasI aH1pOrrOMop<pHasI oc06eHHOCTb p060Ta ero PYKa. 3Ta
PYKa, BMeCTe C B03MO)I{HOCTblO rrporpaMMHpOBaH:IDI p060Ta, ,nenaeT ero H)(eaJIbHO
rrO,[(XO,lUl HM ,lUUI pemeH:IDI MHoxeCTBa rrpOH3Bo,nCTBeHHbIX 3a,naq, BKJIlOqasI 3a-
rpY3Ky (pa3rpY3KY) CTaHKOB, TOqeq CBapKy, 0KPacKy paCrrbIJIeHHeM H c60pKy.
8.3. llpoMblUUleHHble po60mbl 625
P060T MOXeT 6bITb 3arrporpaMMHpoBaH Ha BbIrronHeHHe rrocne,nOBaTenbHOCTII Me-
v
xaHWlecKHX ,nBIDKeHHH, H OH MoxeT rrOBTopBTb 3Ty rrocne,nOBaTenbHOCTb ,l(BIDKe-
HHH Heorrpe,neneHHO ,nonro ,no Tex rrop, rrOKa He 6y,neT rrOBTopHO 3arrporpaMMHpo-
BaH BbIrrOnHeH:IDI KaKOH -TO ,npyrOH pa60TbI.
npOH3Bo,nHTenH HCrrOnb3yIDT P060TOB rnaBHhIM 06pa30M ,lUUI YMeHbmeH:IDI KO-
nWleCTBa 06e BalO ero rrepCOHaJIa. Y P060TOB, Hcrronb3yeMbIX BMeCTe C ,npy-
rnMH p060TaMH HJIH C ,npyrHMH CTaHKaMH, eCTb ,nBa OCHOBHbIX rrpeH eCTBa rro
cpaBHeHHIO C 1]>3Jl:HI(HOHHbIMH CTaHKaMH. Bo-rrepBbIX, OHH rr03BOIDIIOT rrOq'fH rron-
HOCTblO aBTOMaTH3HpOBaTb rrpoI(ecc rrpOH3Bo,nCTBa, qTO BneqeT 3a C060H rrOBbIme-
HHe ypOBIDI rrpOH3Bo,nCTBa, y meHHe KOH1pOIDI KaqeCTBa H 60nee 6bIC1pyID peaK-
I(HIO Ha H3MeIDIIO HeCB 1pe60BaH:IDI. Bo- BTOpbIX, OHH 06eCrreqHBalOT 6bIC1pyID
rrpHcrroc06IDIeMOCTb rrpOH3Bo,nCTBeHHOH e,nHHHI(bI. TeXHonOrwIeCKasI nHH:IDI MO-
xeT 6bITb 6hIC1p0 rrepeKJIlOqeHa C o,nHoro rrpo a Ha ,npyrOH aHaJlOIWIHbIH rrpo-
, HarrpHMep C O,nHOH MO,l(enH aBTOM06H.IDI Ha ,np . K TOMY xe ecnH H3-3a
v
rronOMKH MexaHH3Ma OCTaHaBnHBaeTCB O,nHH 3neMeHT rrpOH3Bo,nCTBeHHOH e,nHHH-
I(bI, <pyHKQ:IDI 3Toro 3neMeHTa MoxeT 6bITb 6bIC1p0 3aMeHeHa.
nepeHaJlIDKHBaeMhIe rrpOH3Bo,nCTBeHHbIe e,nHHHI(bI Ha3bIBalOTCR rn6KHMH rrpo-
H3Bo,nCTBeHHbIMH CHCTeMaMH. fH6KasI rrpOH3Bo,nCTBeHHasI e,nHHHI(a Morna 6bI
BKJIlOqaTb B ce6B He60nbmoe KonWleCTBO P060TOB H CTaHKOB C qny, CBB3aHHbIX
Me C060H, qT06bI H3rOTannHBaTh HJIH qaCTWlHO H3rOTaBJIHBaTb orrpe,neJIeHHhIe
KOMrrOHeHTbI HJIH BhIrronIDITb c60pKy. JIOnrqeCKHM pa3BHTHeM TaKHX CHCTeM ,non-
)l{}f0 CTaTb 06'be,lUfHeHHe MHoxeCTBa rn6KHX e,nHHHI( B rronHOCTblO aBToMaTH3Hpo-
u
BaHHhIH I(ex HJIH 3aBO,n.
Cne,nyeT rroMHHTb, qTO P060T, XOTB H OqeHb cno)I{Hoe YC1pOHCTBO, He MoxeT
caM pemHTb Bce rrp06neMbI, KOTopbIe MOryT 6bITb pemeHhI qenOBeKOM-orrepaTO-
pOM. n03TOM)' OHH ,nOIDKHbI 6hITh CBB3aHhI Me C060H ,norronHHTenbHhIMH MeTO-
,naMH (HarrpHMep, qepe3 aBToMaTH3HpoBaHHoe yrrpanneHHe).
Tep «p060TOTeXHHKa» B HaCTO.sImee BpeWl HCrrOnb3YeTCB B ,nBYX 3HaqeHIDIX:
1. B caMOM C1]>orOM CMbICJIe cnOBa OH rro,npa3YMeBaeT ,naJIbHeHmee pa3BHTHe
aBTOMaTH3aI(HH Qepe3 y meHHe P060TOB B TOM BH)(e, B KOTOpOM OHH H3-
BeCTHbI B HaCTOB ee BpeWl.
2. B 60nee mHpOKOM CMhIcne OH BKJIlOqaeT B ce6B pa3BHTHe He TonbKO caMoro
p060Ta, HO TaIOKe H rrpoI(eccoB, CBB3aHHbIX C P060TOM (HarrpHMep, C ),
HJIH paccM01peHHe p060Ta KaK CTaHKa CO CrreI(HaJlbHbIMH CBOHCTBaMH B coe-
,nHHeHHH c,np MH CTaHKaMH (HarrpHMep, rH6KHe rrpoH3Bo,ncTBeHHbIe
gqeHKH HJIH CHCTeMbI).
8.3.2. YnpsSneHJfe P060TOM
M C1pHaJlbHbIH P060T HMeeT MHoro 06 HX rrpH3HaKOB co CTaHKOM C q .
rrpHBe,neH:IDI B ,neHCTBHe MexaHWleCKOH p p060Ta HCrrOnb3yeTcB Ta xe TeXHOJIO-
r:IDl, qTO H ,lUUI yrrpaBneH:IDI CTaHKOM C qny. O,nHaKo rrpHMeHeH:IDI p060Ta, KaK
rrpaBHJIO, 60nee 06 He H 06bl'IHO BKJIlOqalOT 06pa60TKY ,neTaJIeH. P060TbI MOryr
6bITb 3arrporpaMMHpOBaHbI OT KOMrrblOTepa B pe)I{HMe peaJIbHOrO BpeMeHH HJIH
rrpe,nBapHTenbHO. AnbTepHaTHBHO, P060T MoxeT yrrpaBIDITbCB qepe3 nocne,nOBa-
TenbHOCTb ,l(BIDKeHHH C OT,naJIeHHOH KJIaBHa bI, coe,nHHeHHOH C P060TOM m6
626 r.lla8a 8. A8moMamU3upo8oHHoe ICOHcmpyup08aHue
Ka6eneM. HaKOHel(, P060T MoxeT yrrpaBIDITbcB Bpyq , qepe3 nocne,nOBaTenb-
u
HOCTb ,nBIDKeHHH, KaK B C ae oKpacKH pacnbmeHHeM, Kor,na onepaTop y,nep)J(HBa-
eT H HanpaBIDIeT nHcToneT-paCnblJIHTenb p060Ta. MHCTP HH COXpaIDIlOTCB B
3ne OHHOH naWlTH p060Ta. HeCM01pB Ha 3TH pa3HWI:IDI, eCTb onpe,neneHHbIe
06 He qepTbI Me po60TaMH H CTaHKaMH qny B TOM, qTO KacaeTCB TepMHHax
TeXHonornH CHJIOBOrO npHBo,na, CHCTeM C 06paTHOH CBR3blO, Hcnonb30BaH:IDI
u
yrrpaBneH:IDI KOMnblOTepOM H ,nIDKe HeKOTopbIX H3 H C1pHaJlbHbIX npHJIOXeHHH.
8.3.3. reOMeTpJffl PYKJf P060T8
P060T ,nOJDKeH 6bITb B COCTOBHHH ,nOCTaTb 3aroToBKH H HHC1pYMeHTbI. 3Toro
1pe6yeTcB COqeTaHHe p H no,nCHCTeMbI 3aIDICTh.sI, DJIIOC KHCTb, 06bl'IH0 Ha3bIBae-
MasI pa60qHM opraHOM. 30Ha 06c BaH:IDI p060Ta onpe,neIDIeTCB 06'beMOM npo-
C1paHCTBa, B KOTOpbIH PYKa p060Ta MOXeT ,nOCTaBHTb no,nCHCTeMY 3aIDICThB. bbmo
Hccne,noBaHo MHOXeCTBO reoMe1pWIecKHX KOH<pHrypal(HH H Ol(eHeHbI HX OTHocme-
nbHbIe KHHeMaTWIeCKHe B03MO)l{}fOCTH. K HaCToBIUeMY BpeMeHH H3rOTOBHTeJIH po-
60TOB Cnel(HaJlH3HpyIDTCB Ha cne IIUIX reoMe1pWlecKHX KOH<pHrypauIDIX:
1. )];eKapToBbI Koop,nHHaTbI: 1pH nHHeHHbIe OCH.
2. QHJIHH,npWIeCKHe Koop,nHHaTbI: ,nBe nHHeHHbIe OCH H o,nHa OCb nOBopOTa.
3. C<pepWlecKHe Koop,nHHaTbI: o,nHa nHHeHHasI OCb H ,nBe OCH nOBopoTa.
4. Bpa alO asIcB CHCTeMa Koop,nHHaT: 1pH nOBopOTHbIe OCH.
POOOThI, paOOTaIOIlUle B ,lJ.eKapTOBoi CHCTeMe KOOp aT
P060TbI, pa60TalO He B
u
,neKapTOBOH CHCTeMe KOOp,nH-
HaT, COCTOBT H3 1pex opToro-
u
HaJlbHhIX nHHeHHbIX CKonb-
'-' '-'
3.sImHX oceH, MexaHWIeCKOH
qaCTH MaHHrryIDITopa H HHTep-
nOIDITopa. AnropHTMbI yrrPaB-
neH:IDI aHaJlOfWIHbI TeM, KOTO-
pbIe HcnOnb3yIDTCB B cTaHKax
qny. n03TOMY pa3pemefile H
TOqHOCTb P TaIOKe 6y:
nOPMKa pa3pemeH:IDI CTaHKa.
BIDKHasI oco6eHHOCTb pO-
60Ta, pa60TaIO ero B ,neKap-
u
TOBOH CHCTeMe Koop,nHHaT
3TO ero o,nHHaKOBoe H nOCTO-
BHHoe npOC1]>aHCTBeHHoe pa3-
pemeHHe, T. e. pa3pemeHHe
<pHKCHpOBaHO no BceM OCBM
,nBIDKeH:IDI H BO BceM pa60qeM
06'beMe p po60Ta. C ,np -
MH CHCTeMaMH Koop,nHHaT
,neno 06CTOHT He TaK.
...,
y
z
,
x
8.3. IIpoMblUUleHHble po6ombl 627
POOOTLI, paooTaIOIlUle B QllJllIII.npJl1lecKoi CHC-
TeMe KOOp,lUlHaT
P060TbI, pa60TalO He B IJ;HJIHH,npWleCKOH CH-
u
CTeMe Koop,nHHaT, COCTOBT H3 ropH30HTaJlbHOH
u u u
p , YCTaHOBneHHOH Ha BepTHKaJlbHOH CTOHKe,
KOTOpasI B CBOIO Oqepe,nb YCTaHOBJIeHa Ha Bpa a-
lO eMCB OCHOBaHHH. fOpH30HTaJIbHasI PYKa BbI-
,nBHraeTCB H BTBrHBaeTCB, KapeTKa ,nBIDKeTCB B
BepTHKaJlbHOM HanpaBneHHH BBepx H BHH3 no
u
CTOHKe, H 3TH ,nBa MO,l{yIDI Bpa aIOTCB KaK e,nHHasI
CHCTeMa Ha OCHOBaHHH. n03TOMY pa60qHH 06'beM
B ,naHHOM C ae KOnbl(eBOe npOC1paHCTBO l(H-
nHH,npa.
Pa3pemeHHe p060Ta, pa60TalO ero B l(HJIHH)(-
u
pHQeCKOH CHCTeMe Koop,nHHaT, He BBIDIeTCB no-
u
CTOBHHbIM H 3aBHCHT OT paCCTOBH:IDI Me CTOH-
u u
KOH H 3aIDICTbeM B,nonb ropH30HTaJIbHOH p .
EcnH B3BTb CTaH,napTHOe pa3pemeHHe l(H<PPOBoro
HHKpeMeHTHoro KpyroBoro ,naTqHKa nOnOXeH:IDI
Ha OCH Bpa eH:IDI H ,nJIHHY P , paB TonbKO 1 M, Tor,na p33pemeHHe npH BbI-
TR OH Ha non ,L{JIHHY PYKe 6y,neT COCTaBIDITb nOPMKa 3 MM. 3TO Ha ,nBa no-
pHJJ;Ka BenWlHHbI 60nbme, qeM cymecTByID ee B HacToB ee BpeWl pa3pemeHHe
CTaHKOB (0,01 MM). 3TO O,nHH H3 He,nOCTaTKOB P060TOB, pa60TalO HX B l(HJIHH,nPH-
qeCKOH CHCTeMe Koop,nHHaT, no cpaBHeHHIO C p060TaMH, pa60TalO HMH B ,neKap-
TOBOH CHCTeMe KOOp,nHHaT . Ronee BbICOKasI CKOpOCTb Ha KOHl(e p , KOTOpyro
06eCneqHBaeT nOBopOTHasI OCHOBa, ,neHcTBHTenbHo ,naeT HeKOTopoe npeH eCTBO
p060TaM C l(HJIHH,npWlecKOH reOMe1pHeH, o,nHaKO 3Ty CKOpOCTb qaCTO orpaHWIHBa-
eT MOMeHT HHepl(HH p .
OT P06OTOB, BKJIIOqalO HX B ce6B Bpa alO eeCB OCHOBaHHe, TPy,nHO no lITh
xopomHe ,nHHaMWleCKHe xapaKTepHCTHKH. MOMeHT HHepl(HH, nepe,nalO HHcB Ha
npHBO,n OCHOBaH:IDI, 3aBHCHT He TonbKO OT
Beca nepeHOCHMoro 06'beKTa, HO TaIOKe H OT
paCCTOBH:IDI Me BaJlOM OCHOBaHIDI H ne-
peMe aeMbIM 06'beKTOM. 3TO CqHTaeTCB o,n-
filM H3 rnaBHbIX He,nOCTaTKOB P06OTOB,
BKJIlOqalOIUHX B ce6B nOBopOTHbIe coe,nHHe-
H:IDI.
8
y
z
y
POOOTLI, paOOTaIOID.He B ccI»epJl1lecKoii CH-
CTeMe Koop HaT
KHHeMaTWleCKasI KOH<pHrypal(:IDI p
p06OTa, pa60TalO ero B c<pepWIeCKOH CHCTe-
Me Koop,nHHaT, aHaJlOmqHa enH TaHKa.
3Ta PYKa COCTOHT H3 Bpa alO eHCB OCHOBbI,
mapHHpa, onpe,neIDIIO ero yron B03BbIme-
u
H:IDI, H TeneCKonWleCKOH p , KOTOpaH BbI-
,nBHraeTCB H BTBrHBaeTCB. BenWlHHa nOBOpo-
8
628 r.l1080 8. A8moMomU3upo8oHHoe ICOHcmpyupo80Hue
Ta 06bl'IHO H3MepBeTcB HHKpeMeHTHbIMH KPyrOBhIMH ,naTtlHKaMH nOnOXeH:IDI Ha
oc Bpa eHIDI. Pa60qasI 30Ha mHpoKasI c<pepWlecKasI 060nOqKa.
He,nocTaToK P060TOB, pa60TalO HX B c<pepWlecKoH CHCTeMe Koop,nHHaT, no
cpaBHeHHIO C HX aHaJlOraMH, pa60TalOIUHMH B ,neKapToBoH CHCTeMe Koop,nHHaT
u
HaJlWlHe ,nBYX oceH C HH3KHM pa3pemeHHeM, KOTopoe MeIDIeTCB B 3aBHCHMOCTH OT
,nJIHHbI P .
fnaBHoe npeHMymecTBo P060TOB, pa60TalO HX B c<pepWlecKoH CHCTeMe KO-
op,nHHaT, no cpaBHeHHIO C p060TaMH, pa60TalO HMH B ,neKapToBoH H UHJIHH,nPH-
qeCKOH cHcTeMax Koop,nHHaT, 60nbmWI MexaHWleCKasI rn6KocTb. OCb nOBOpo-
Ta B BepTHKaJlbHOH llJIOCKOCTH n03BOIDIeT ocymecTBIDITb y,n06HbIH ,nOC K YPOB-
HIO OCHOBaH:IDI HJIH ,naxe 60nee HH3KOMy ypOBHIO. KpoMe Toro, ,nBIDKeHHe OTHO-
CHTenbHO oceH Bpa eHIDI HaMHoro 6bIC1pee, qeM ,nBIDKeHHe B,nonb nHHeH
u
oceH.
POOOTY, paooTaIOIlUle BO BpalQaIOlQeicB CHCTeMe Koop HaT
P060T, pa60TalO HH BO Bpa alO eHcB CHCTeMe Koop,nHHaT (HJIH mapHHpHbIH
p060T), COCTOHT H3 1pex xeCTKHX 3BeHbeB, CBB3aHHbIX,nB mapHHpHbIMH Coe,lUl-
HeH:IDlMH, H YCTaHoBHeH Ha Bpa alO eHcB OCHOBe. 3TO OqeHb HanOMHHaeT qeno-
BeqeC p . Pa60qHH opraH aHaJlOIWIeH KHCTH, KOTOpWI npHKpellJIeHa K rrpe,n-
llJIeqblO qepe3 3aIDICTbe. JIOKTeBOe COqrreHeHHe coe,nHIDIeT npe,nllJIeqbe H llJIeqo, a
llJIeqeBOe COqneHeHHe coe,nHIDIeT llJIeqo C OCHOBaHHeM. MHor,na Bpam;arenbHOe
u
,nBIDKeHHe B ropH30HTaJlbHOH llJIOCKOCTH
TaIOKe 06eCneqHBaeTCB llJIeqeBbIM coe,nHHe-
HHeM.
TaK KaK Y p060Ta, pa60TalO ero BO Bpa-
'-'
alO eHCR CHCTeMe Koop,nHHaT, eCTb 1pH
BpamaTenbHbIe OCH, Y Hero OTHOCHTeJIbHO
HH3Koe p33pemeHHe, KOTopoe nOJIHOCThIO
3aBHCHT OT ,nJIHHhI P . Ero TOqHOCTb
TaIOKe caMasI HH3KasI, TaK KaK COqneHeHHasI
KOHC1p :IDI HaKaDJIHBaeT omH6KH mapHH-
pOB H MaKCHMaJlbHasI omH6Ka rrpHXO,lUfTCa
Ha KOHel( p . npeH eCTBO TaKOH
C1p hI H KOH<pHrypanHH 3aKJIIOqaeTCB B
TOM, qTO OHa MoxeT nepeMe aTbCB Ha BhI
COKHX CKOpOCT H HMeeT npeBOCXO
MexaHWlec rn6KOCTh, KOTOpasI c,nenaJIa
ee caMbIM norryIDIpHbIM P060TOM cpe.lUlero
pa3Mepa.
a
p
(J
3aDJIcThe
.
Pa60tIHil OpraH CBB3aH C 6a30BbIM 6nOKOM p060Ta qepe3 3aIDICThe. 3aruICTLe
BKJIlOqaeT B ce6B 1pH nOBopOTHbIe OCH, 0603HaqaeMbIe KaK «KpeH», «TaHraJK» II
«pbICKaHDe». KpeH 3TO nOBopOT B DJIOCKOCTH, nepneH,n IDIpHOH KO P ;
TaHrIDK (HJIH H3rn6) nOBOpOT B BepTHKaJIbHOH llJIOCKOCTH, a pbICKaH:be nOBopoT
OTHOCHTenbHO p B ropH30HTaJlbHOH llJIOCKOCTH. O,nHaKO cym;eCTByIDT IIpHJIoxe-
H:IDI, B KOTOpbIX 1pe6yrorCB TonbKO ,nBe OCH Bpa eHIDI B 3aIDICTbe.
8.3. IIpoMblUUleHHble po6ombl 629
r ApaBn eCK /3neKTp -
eCK 6nOK n TaH
, I
PYKa
t-
"'
1l0KTeBOe CO'-lneHeH e
nne'-leBOe
CO'-lneHeHHe
«PblCKaHbe»
(nOBopOT BO-
Kpyr BepT -
K811bHO Oc )
3anRCTbe
nOBOpOT
PYK
1
5nOK ynpaBneH R
P060TOM
«KpeH» (nOBopOT
BOKpyr rop 30H-
"
T811bHOH oc B
"
nOnepe'-lHOH
nnOCKOCT )
1 «TaHrIDK» (rroBopoT BOKpyr rOpH30HTaJlbHOH OCH B rrpO,nOnbHOH llJIOCKOCTH)
QTo6bI }'MeHLmHTb Bec 3aIDICTbB, rrpHBO,n 3aIDICTbB HHor,na pacrronaraIOT B OCHO-
Be po6OTa, H ,nBIDKeHHe rrepe,naeTCB XeCTKHMH 3BeHbBMH HJIH IJ;eIDIMH. YMeHbmeHHe
Beca 3aIDICThB YBenWlHBaeT MaKCHMaJlb ,nO rryCT H HarpY3Ky H }'MeHbmaeT MO-
MeHT HHepIJ;HH, tfrO B CBOIO Oqepe,nb y maeT ,nHHaMINeCKHe xapaKTepHCTHKH p
po60Ta. B03MO)I{HbIe ,nBIDKeHIDI 3aIDICTbB rrOKa3aHbI Ha pHcyHKe po60Ta.
PO.lVKep JI. TRMHHrC
CpaBOQHHK HlDKeHepa-MeXaHlIKa
TIepeBO.n; B.B. BOJIbmaKOB
KOMnblOTepHaH BepCTKa B.IO. K03HOB
KOppeKTOp O.q. KOXaHOBCKaR
)];H3aHH KHIDKHbIX CepHH C.IO. BHpHqeB
)];H3aHH Ii .A. KYKOJIeBa
BhInycKalOm;HH pe.n;aKTOp A.IO. <l>HnaToBa
OTBeTCTBeHHhIH 3a BbInYCK C.B.3HHIOK
<l>opMaT 70xl00/16. TIeqaTb O<pCeTHWI.
fapHHTYpa HblOTOH
nell.n. 39,5. THpax 1500 3K3. 3aK. NQ 3255.
BYMara o<pceT N21, DJIOTHOCTb 65 r 1M 2 .
li3.n;aTeJIbCTBO « TeXHoc<pepa»
MOCKBa, YJI. KpaCHOnpOJIeTapCKaR, .n;.16, CTp.2
)];Han03HTHBbI H3rOTOBJIeHbI 000 «EBpOnonHrpa
HK»
OrneqaTaHO C rOTOBhIX J(Han03HTHBOB
.I
· B 000 TI <I> «TIo a<p- »
160001, I: BOJIor.n;a, yn. qeJIlOCKHHueB, .n;. 3.
TeJI.: (8172) 72-55-31, 72-61-75
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