Текст
BBK 34.636
083
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3a qepHOBbIMH 3y6b5lMH rrpOT5I}KKH rrepeMeHHoro pe3aHH5I pacrroJIa-
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Korna qepHOBbIe 3y6b5I B XOJI.51T H3 3arOTOBKH H HaqHHaIOT pa60TY
ItJHCTOBble 3y6b5l, T. e. OHH oOeCneQHBaJOT TIJIaBHOe YMeHbIIIeHMe CHJIbI
p e3 aJilUl L
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MeTpbI 3y6beB O){HOH rpyrrnbI O HHaKOBbI. BbIKPY)KKH .ll.eJIalOT IIa
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BbIKpY:>KKa JI.OJIMHa pacrrOJIaraTbC5I rrpoTHB pe)KYII.I.ero ceKTopa rrpo-
pe3Horo 3y6a rrOCJIe)J;HeH qepHOBOM rpynnM.
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pHC. 1.1, 8. CTpY)KeQHa5I KaHaBKa 3Toro npo H.15I, rrpHH5ITa5I y rrpo-
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crpY)KKa calMa BbIrra,naer H3 CTpY)KeQHOH KaHaBKH: -nJIHHa 3aJ.HeH
rrOBepXHOCTH b = (0,3 -;- 0,35) t, rJIyoHHa BrranHHbI (BbIcoTa 3y6a)
h= (Q,3+0,4)t; pa,lJ,Hyc crrHHKH 3y6a R= (0,65+0,7)t; paJI.HYc conp5I-
}KeHH5I rrepeJI.HeH rrOBepXHOCTH C ,llHOM Brra)J;HHbI , = (0,15 -;- 0,20) t.
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fOCT 20364-74 H rOCT 20365-74.
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nOp5I)I.Ke npH nO.lI.'beMe Ha Ka:>KLI.bI H: 3y6, B ,lI,pyroM - ,l!,Ba qHCTOBbIX
3y6a HMefOT OJU1HaKOB 1 bIH JI.HaMeTp, a BbIKPY}KKH HaHOC5IT TO TIbKO Ha
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TIepBblM QHCTOBOH. 3y6 OJI:>KeH HMeTb mar t J HaH60JIblllHM 113 1113.fOB
OCTa.lIbHbIX LfHCTOBbIX 3y6beB.
TIpH H3fOTOBJIeHHH npOT5I){{eK K 4HCTOB,bIM 3y6b5IM npeLI.D BJI5IIOT-
CH oco6eHHO B COKHe Tpe6oBaHHH. 3TO OODHCHHeTCH TOH pORbID, KO-
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8
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na qHCTOB X 3y6beB COCTOHT H3 BYX 3y6beB OAHHaKOBoro HaMeT-
pa. BbIKPY1KKH HaHOC51T Ha Ka)K!lOM 3y6e B rnaXMaTHOM ,IIOp51 JI K;
(npH TIlI.aTeJIbHOM BbInOJ1HeHHH 3y6beB .ll.OnYCKaeTC51 .lI.eJIaTb BTOpOH
3y6 rpynnbI I:fHCTOBbIX 3y6beB KpyrJIbIM - 6e3 BbIKPy*eK). XapaK-
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T04HOCTI1 o6pa6oTKH CJIe,llyeT cpe3aTb qHCTOBbIMH 3y6b5IMH OQeHb
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60JIbllIHe rrepe.ll.HHe yrJI1bI H BbICOKa5I TOqHOCTb .l(HaMeTpa lIHCTOBbIX
3y6beB. -A\ 'fI
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3aHH5I paBHOH CTOHKOCTH B Cpe,lI,HeM B 2 pa3a BbIllie no cpaBHeHHIO
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neHHO YMeHbWa5ICb B pa3Mepe, CTaHOB5ITC5I 'qHCTOBbIMM. TI03TOMY HX
marH, KaK If lIHCTOBbIX 3y6beB, .ll.eJIaIOT nepeMeHH1bIMH.
B p5I.ae KOHCTPYKUHH npOT5ILKeK KaJIH6pYlOIlI.He 3y6b5I MMeIOT UH-
JIHH,11,pHQeCKHe cpacKH C HYJIeBbIM 3a,L(HHM yrJIOM. lllHpMHa cpacoK
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33 Ta tJHBaIOT, a JIHllIb .l(OBO.ll.5IT no rrepe,llHeH nOBepXHOCTH, CHHM a5J
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npli Ka}K,[I.OH nOBTopHOH 3aTOQKe Bcex OCTaBlllHXC5I 3y6beB, a 'tIepe3
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3YObeB ,lI,OJI)KHO 61bITb orrpe,IJ.eJIeHHOe COOTHOllIeHHe, KOTopoe o6ecne-
tJHBaeT O.ll.HHaKOBYJO CTOHKOCTb qepHOBOH 11 QMCTOBOH lIaCTeH rrpo-
T5I./KKH (fOCT 20364-74 H rOCT 20365-74).
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9
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WYIO 3KOHOMRlO 6bICTpOpe)KYI..Ueli CTaJIH.
O.ll.H3 li3 oco6eHHocTeti IIpOT5IrHBaHluI - TO, qTO CTpY)KKa cpe-
3aeTC5I 3y6oM co BCeM: ,L(JIHHbI o6pa6aTbIBaeMOH rrOBepXHOCTH M ,aOJLIK-
Ha rrOJIHOCTbIO I10MeCTI1TbC5I B CTPYlKeqHOll KaHaBKe. TIpH o6pa60TKe
fMeTaJIJIOB, 06pa3YIOIJ..(HX CJIHBHYIO CTPY)KKY, HanpHMep CTaJIeR, CTPY:tK-
Ka 06pa3yeT 3aBHTOK nO,L(06HO CnHpaJIbHOH rrrpY:>KHHe. 4eM TOJI e
crpY*Ka, TeM 60JIbWe 3a30p 1 bI Me:>KJI.Y KaLKJ(bIMH COCe.ll.HHMH BHTKaMH
H TeM 66JIbiliHe pa3MepbI KaHaBOK Tpe6YIOTC5I )J.JI5I Toro, qTo6bl
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crpY)KKa, reM '60JIbIIIHM J(OJI)KeH 6bITb K03cpcpHUHeHT nOMeru;aeMOCTH.
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10
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r..ne B - .u.JIHHa peLKymeH KpOMKH 3y6a, IMM; D - HaMeTp 3y6a, MM.
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3aTpY HHeT Y.1I.aJIeHHe KOJIbI.l,a CTPY2KKH H3 CTpY)KeQHOH KaHaBKH.
DpHMeHHeMbIe B 3THX CJIYIIa5lX JI.JI5I OCBo6o)K,lI,eHHH npOT5I}KKH OT T3-
KOM CTPY}KKH CTaJIbHbIe KpI01JKH IIaCTO nOBpe)K)l.aIOT pe)KYll{He
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Y npOT5I}KeK, HMeIOlII.HX (no.u.'heM H3 Ka)K,QlbIH 3y5, pa3,neJIeHHe
CTPY)KKH no ee nepMMeTpy npOH3BO,lI,5IT C rrOMOIl1.bIO Y3KHX HerJIy6o-
KHX CTpYLKKopa3,lI,eJIHTeJIbHbIX KaHaBOK. KaHaBKH pacrrOJIaralOT Ha
Bcex IIepHOBbIX H IIHCTOBbIX 3y6b5fX B lllaXMaTHOM nOp51):{Ke TaK, IIJTO-
6bI KaHaBKH npe,QbIJI.ymero 3y6a nepeKpbIBaJIHCb CnJIOlllHbIMH yqaCT-
KaMH peLKYlII.eH KpOMKH nOCJIe,QYIOII.(ero. PaCCT05IHHe Me)K,QY KaH3B-
KaMH OJI.HOro 3y6a rrpOT.H)KKH 5-12 MM.
CTPY:>KKOpa3JI.eJIHTeJIbHa5I KaHaBKa OCTaBJI5IeT Hecpe3aHHbIM Y3-
KHH CJIOH MeTaJIJIa, 51BJI5IIOIII.HHC5I cBoeo6pa3H 1 bIM pe6pOM :>KeCTKOCTH,
Y KOToporo BbIcora HeCKOJIbKO OOJIbllle TOJII..U.HHbI CTQY)KKH. IlocJIe.ZJ.-
Hee OO'bHCH5IeTC5I TeM, I1J:TO CJIOH MeTaJIJIa, 06pa3YIOII.(HH peopo LKeCT-
12
KOCTIf B npouecce pe3aHHH, He MOllieT YBeJIH1.IHBaTbCH no IllHpHHe,
TaK K3K OH OrpaHHQeH C o6eHx CTOpOH 60KOBbIMH nOBepxHoCTHIMM
KaHaBKH. B CBH3H C 3THM pe6po )KeCTKOCTH YTOJIll.(aeTC5I 60JIbIlle,
'1eM OCTaJIbHbIe Y1.IaCTKM CTPY)KKH. 3aMepbI cTpY)KeK nOKa3aJIH, 1.ITO
BbICOT3 pe6pa LKeCTKOCTH YBeJIH1.IHBaeTCH 3a C1.IeT .u.ecpopMaUHH npH
CBepTbIBaHHH CTPY:>KKH.
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cpaBHeHHlO C OCTaJIbHbIMH yqaCTKaMH CTPYlliKH IToBbIllleHl1e MHKpO-
TBepLlocTH Ha 60KOBbIX nOBepxHocTHX pe6pa OTHOCHTeJIbHO MHKpO-
TBep.J.ocTH co6CTBeHHo CTPYLKKH )J.OXO,QHT ,QO 200 % H BlbIllle T1pH
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7bIBaHHIO CTPY)KKH B KOMnaKTHbIH: BliTOK. 3aTpY,QHeHHoe CBep'flbIBaHHe
CTPY}KKH C pe6pOM LKeCTKOCTH npHBO,QHT K YBeJIH1.IeHHIO LlHaMeTpa
ee BHTKa. 50JIbllIOH ra6apHTHbIH pa3Mep BHTKa, B CBOID OtIepeJJ.b,
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'THlliKH 60JIblIIOrO pa3Mepa, 1.IeM OCJIa6JIHeT TeJIO rrpOTH)KKH H YBeJIH-
IJHBaeT ee ,lI,JIHHY.
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npOTHrHBaHHH CTaJIH ,lI,OCTHraeT BOCbMH. YBeJIH1.IeHHe K03cpcpHI..(HeHTa
nOMemaeMOCTH BlbI3 1 bIBaeTCH Ta K)Ke CTpeMJIeHHeM KOHCTPYKTOPOB
06eCne1.IHTb Ha,ne)KHOe BbIrra,lI,eHHe ICTPYLKKH H3 KaHaBKH nOCJIe BbIXO-
..n.a 3y6a npOT5ILKKH H3 3arOTOBKM. 3TO 05'bHCHHerCH TeM, qTO npH Ha-
JIH1.IHH pe6pa }l{eCTKOCTH cpe3aHHaH CTpY)KKa C caMoro Ha1.IaJIa 06-
pa30BaHH5I BHTKa CBepTbIBaeTCH He C 3a30pOM Me)K)I.Y o6pa6aTbIBae-
MOM nOBepxHocTblO H nOBepxHocTblO CTpY)KeqHOii KaHaBKH, KaK 3TO
Tpe6yeTC5I, a rrJIOTHO npHMHMaHcb K nOCJIe,QHeH. TaKHe CTPY)KKli 1.Ia-
e Bcero 3acTpeBaIOT B cTpY)Ke1.IHbIX KaHaBKax, oco6eHHO eCJIH 3y6
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]{03cp<pHIJ:HeHTa nOMemaeMOCTH YBeJIH1.IJiBaIOT r JIy6HHY cTpYLKe1.IHbIX
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IJae «oCJIa6JIHeTC51» TeJIO npOTH)KKIf, 1JTO, KaK npaBHJIO, oco6eHHO
npH npOT51rHBaHHH OTBepcTHH He6oJIblliOrO ,lI,HaMeTpa, He)I.OrrycTHMo;
BO BTOpOM cJIY1.Iae Y,QJIMH5IeTC5I rrpOTH)KKa.
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Y npOTH}KeK nporpeCCHBHoro pe3aHHH pa3,lI,eJIeHHe CTPY)KKH npOH3-
BO HTC5I pa36HBKOH pe:>KymeH KpOMKH 3y6a no nepHMeTPY Ha pe-
}f{YIlI.He ceKTopbI; 3TH ceKTopbI 1.IaCTO HMeIOT 60JIbIllYlO ,QJIHHY (tIame
Bcero Ha nOCJIe,QHHX 3y6bHX pe}KYIJJ;HX KpOM OK CeKIl.HI1), H n03TOMY
nOHBn5leTC Heo6xo,QHMOCTb pa3,QeJIeHHH CTPYlliKH B rrpe,lI,eJIax caMO-
ro pe:>KYIII.ero ceKTopa. aTO ,QonOJIHHTeJIbHOe pa3,QeJIeHHe npOH3BO-
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JlHTeJIbHlbIX KaHaBOK, KaK H Ha rrpOTHLKKax, HMelOIJJ;HX nO"l);'beM Ha
13
Ka1K.rlbIH 3YO. n03TOMY OlLHOBpeMeHHO \C Y3KHMH KaHaBKalMH npOT5I)K-
KH npOrpeCCHBHOrO pe3aHH5I rrpHo6peTalOT Ii BCe CBOHCTBeHHbIe no-
CJIeJI.HHM OTpuu.aTeJIbHbIe KaqeCTBa.
CorrpOTHBJIeHHe CBepTblBaHHIO pe6pa *eCTKOCTH H OCTaJIbHOH: qa-
CTH CTPY}I{KH pa3JIHqHO, n03TOMY CTpYJKKa pa3pbIBaeTC5I, pe6p<>
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HeCKOJIHKO paCrrp5IMJI5IeTCH. 9ro npHBO,QHT K YBeJIHQeHHIO pa,rr,Hyca
BHTKa, InpHJIMnaHHlO MeTaJIJIa CTPY}KKH K rrOBepXHOCTH CTpY:tKe'4HOa
KaHaBKH H rrO£BneHHIO rJIy6oKOH: npO OJIbHOH apanHHW Ha npOTH-
HYTOA nOBepXHOCTH. 3Ta u.apanHHa rrOHBnHeTCB B MeCTe OT e eHHH
peopa )J{eCTKOCTH OT OCHOBHoro MeTaJlJIa CTPY)KKH, a rny6HHa ee
lIaCTO HaCTonbKO BeJIHKa, IITO ,rr,aLKe nOCJIe CH51TH5I Bcero npHnYCKa
ee He y aeTcH y anHTb, oco6eHHO npH o6pa6oTKe 3arOTOBOK H3 B5I3-
KHX CTaJIeH.
B KpyrJIbIX npOT5I)KKaX nepeMeHHoro pe3aHH5I pa3J\eJ1eHHe CTPY)l{..
KH rrpOJf3BO,QHTC5I BblrrOJIHeHHbllMH no JI.yre OKPYIKHOCTH llIHpOKHMH
BbIKPY)KK3'MH, HMeIO HMH 3aJI.HHH: yrOJI 'no BceMY npocpHJIIO. TIpH Ta-
KOM cnoc06e pa3JI.eJIeHHH CTPYLKKH npope3HibIe H 3aIIHrn:aIOIlI,He 3y6b5I
K8JKJl.OH ceK HM cpe3alOT CJIOH MeTaJIJIa o,nHHaIKOBOH lllHpHH1bI. lllH-
PHHY BbIKPYIKKH, onpe,Qe.;'15I1Olll.YIO JIHHY CTPY)KKH, paCCIIHTbIBaIOT
TaK, QTo6bI IlIHpHHa CTPY}I{KH 6bIJIa He 60JIee orrpeJI.eJIeHHOrO 3Ha-
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TbIBaHH5I ee 8 IBHTOK. IlpH TaKOM pa3.QeJIeHHH CTpY*Ka He HMee'F
pe6pa )KeCTKOCTH.. TOJIIlLHHa ee oJI.HHaKoBa no BceMY CeqeHHIO Ii
JIHllIb Y caMbIX IKpaeB MO)KeT HeCKOJIbKO YMeHbmaTbC.H. BJIarO,QapH
OTCYTCTBHIO peopa }l{eCTKOCTH oT,QeJIbHbIe BHTKH CTPY)KKH TeCHee
npH)KHMaIOTC5I .,aPyr K ,Qpyry, IMe)l{J(Y HHMH OCTaIOTCH OIIeHb MaJIbIe
3a30pbI. ,[{JI5I pa3Mew;eHHH HX B K3HaBKe rpe6yeTc5I ropa3,lI,o IMeHb-
lie MeCTa, lITO aeT B03MomHOCTb IIpHMeHHTb MaJIble K03cpcpHlI,HeHl1bl
rr 0 M eII.t a eM 0 CT H.
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He B BHTOK, Haxo,nHInHMC5I B O,lI.HOH rrIlTJOCKOCTH, a B BHTOK KOHycoo6-
pa3HOH cPOpMbI (pRC. 2.1). BepllIHHa TalKOH KOHycoo6pa3HoH CTPY)!{"
KH HarrpaBJIeHa BHYTPb lliJlHueBOro rr33a, T. e. B CTOpOHy OT ero 00-
KOBOR IIOBepXHOCTH. 3TO 3HaQHTeJIbHO oOJIerQaeT YCJIOBH5I pa60Tbl
yrOJIKa 3atIHIUalOInero 3y6a. BJIarOLlap51 3TOMY 3allH alOIll.HM: 3y6
JlerKO cpe3aeT C OOKOBOH nOBepxHocTM llIJIMua CTPY>KKY 3Hat:IHTeJIb"
HOM TOJIIII.HHbI. lIlepoxoBaTocTb OOKOBbIX nOBepxHoCTeii llIJIHI.LeBoro
na3a 3HaQHTeJlbHO YMeHbIlIaeTc5I ,rr,a}l{e rrpH YBeJIHqeHHbIX nO,Qaqax
Ha 3y6 npOTH)I{KII.
B rrpOJl.OJIbHOM CeQeHHH BHTOK CTPY)I{KH npe.1I.cTaBJI5IeT C060R CIlH-
paJIb. B 3aBHCHMOCTH OT CPH3HKO-MeXaHH1JeCKHX CBOHCTB CTaJIH, TOJI"
tnHHbI cpe3a H nepeAHero yrJIa 3y6a npOTH)KKH BH'DKH CTPY)l{KH 60-
JIee HJIH MeHee fIJIOTHO npHMbIKaIOT JI.pyr K .rlpyry HJIH, HaooopoT,
HMelOT 3HaqHTeJIbHbIe 3a30pbI Me:tKJ(Y coaoH. qeM TOHblIle cTpY:iKKa,
TeM fIJIOTHee 33KpYQHSaIOTC5I ee BHTKH H IMeHbllIe HX ,lI.HaMeTp. I10):l
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THBOIIOJIO>KHbIMH TOqKaMH HapY)KHOH nOBepXHOCTH BHTKa B CBOOO,Q-
HOM COCT05lHIIH, T. e. co BceMH 3a30paMM MelK,lI.Y OT,[(enbHbIMH qa-
14
Puc. 2.1.
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KOHycoo6pa3HblX BUT"
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MeHHoro pe3aHUSI
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HO IIOMemaTbC5I B CTPY}I{eqHbIe KaHaBKH npOTH)KKH, n03TOMY
rJIy6HHa I1X ,QOJI}I{Ha 6bITb paBHa "l]}laMeTpy BHTKa HJIM HeMHoro
tM:eHblIIe ero B MOMeHT BbIXO)l.a 3y6a npOTH)KKH H3 3arOTOBKH. LlHa-
MeTp BHTKa MOLKeT 6bITb 60JIbille rJIy6HHbI KaHaBKH TOJIbKO B TOM
CJIY4ae, eCJIH MeLK,QY OT,lI,eJIbHbIMH BlfTKaMH HMeeTC51 ,lI,OCTaTOIIHbIH:
3330p. B 3TOM CJIYIIae BHTOK CTPY}I{KH ynpyro CO)K\1eTCH, 3 rrpn BlbI"
xo..ae 3y6a npOT5I:>KKH JI3 3arOTOBKH pa30LKMeTCH H BbIrra.rr.eT H3 IKa..
HaBKH. 50JIbillOe BJIH5IHHe H3 pa3Mew;eHHe BHTK3 CTPY)KKH B CTPY"
eqHOH KaHaBKe H Y,QaneHHe ee oTTy.rr.a OKa3 BaeT opMa crrHHKH
3y6a.
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ee, 3aCTpeBaeT B CTpYLKeIIHOH: IKaHaBKe. B 3TOM CJIyqae HeH36e}l{HhI
IIOTepH BpeMeHH Ha OqHCTKY rrpOT5I:>KKM OT CTPY)l{KH. ECJIH )Ke cnHH"
Ka 3y6a BJbInOJIHeHa no ,rr,yre OKPY*HOCTM, K3K 3TO rrpe,lI,YCMOTpeHO
fOCT 20364-74 H fOCT 20365-74, TO CTpY:>KKa 6eCrrpen5ITCTBeHHO
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KH He TpeoyeTCH.
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HaBKP. OT cpOpMhI nOnepeqHOrO CeqeHHH CTPYLKKH 3aBHCHT K03cp H-
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TOJIIIJ.HHe fIO BceMY ceIIeHHIO ICTpY}I{Ka YKJIa,lI,bIBaeTCH B BHTOK MeHb-
mere JI:HaMeTpa, IIeM B Tex CJIyqa5IX, KOf,Qa llIHpHHa CTPY}I{KH He CO"
OTBeTcTByeT ,n;HaMeTpy npOT5I)KKH H Kor,n;a CTpY2KKa HMeeT MeCTHbIe
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nOMem:aeMocTH, cooTBeTcTBYIO HH: TOHKHM cTpYLKKa M: IIHCTOBhIX
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15
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nOJIyqaeMbIX rrpOT5I)KKaMH rrepBbIX ,lI,BYX BH.lI.OB.
B HaCTOHmee BpeM5I Ha Ka 0 pe33HHH MeTanJIOB He pacrronaraeT
,lJ.OCTOBepHbIMH TeOpeT QeCKHMH 3aBHCHMOCTHMH )(JI5I orrpe,lI.eJIeHH5I
eRJI pe3aHH5I npH npOT5IrHBaHHH. I<OHCTPYKTOPbl H 9KCITJIyaTalI.HOH-
HHKH npOTHLKHOfO HHCTpYMeHT3 IIOJIb3YIOTC5I 33BHCMMOCT5IMH, nOJIy-
qeHHbIMH B pe3YJIbTare 3KcnepHMeHTOB B Tex MJIH HHblX YCJIO-
BH51X.
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JI5IeTC51 cnopHbI'M. Do 'MHeHHIO HeKOToplbIX aBTopoB, TaKoro pO.1l.8 HC-
CJIe,lI.OBaHH5I ,L{OJI}I{HbI rrpOBO.1XHTbC51 nHllIb c rrOMOlll.blO 0.nHo3y6oro
HHCTpY'MeHra, T. e. pe3I(a, TaR KaK HeB03MOlKHO 06eCneQHTb TOIIHO
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HOCTb TOPU;OB 06pa3lI.a IK OCR OTBepCTH51, H3-3a qero 6Y.l1eT B03HHKaTb
CHJla, H3rH6aIOIIl.a51 rrpOT51)l{KY. Do HallleMY MHeHHIO, Hcc.TIe.rr.OBaHHe
CMJI, B03HHKalOmHX rrQM BHYTpeHHeM npOT5IfHBaHHH, ueJ1ecoo6pa3HO
npOBO,lI.HTb MHor03y6bIMH npOTH}KKaMH. DpM 3TOM nponecc He MO,lle-
16
JlHpyeTcH, KaK 3TO npOHCXO.ll.HT npH HCCJIe OBaHM5IX C O,l!H03y6bIMH
npOT5ILKKaMH, a Bocn..2oH3BOJI.HTC5I HenOCpeJI.CTBeHHO. C nOMOIllbIO
,aOBO KH 3a,aHHX InOBepXHOCTeH 3y6beB npOT51)KKH JIerKO BbI;I.ep*H-
BaeTC5I )].onYCK Ha lI.HaMeTp 3y6beB 0,005 IMM.
dKcnepHIMeHTaJIbHlbIe IJ.HJII1HJI.pHIIecKHe MHoro3y6bIe npOT5I)KKH 113
6bICTpOpe)KY HX CTaJIeR P 18 H P6M5 nO,QBepraJIHCb 3aKaJIKe H Tpex-
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3y6beB H TPH pa60QHX CeKl.(HH H3 rr51TH 3y6beB KaLK,rr,3H. 3y6b51 pa-
60IlHX ceKUlfH HIMeJIH llIar 19 MM. JlJI5I rrOJIYIleHH5I HaH60JIbillefI TOq-
HOCTH pe3YJIbTaTOB Bce n5ITb 3y6beB Ka)K.D.OH: pa60Qeii CeKIJ.HH HMevllI
O,lI.HHaKOBwA nO,lI. eM. aTO rr03BOn5IJIO MHorOKpaTHO H3Mep Tb CHJI
npH O,lI.HOH 11 TOM Me no aqe 13a O,QHH pa60QHH npoxo HHCTpYMeHTar
3a HHe nOBepXHOCTH 3y6beB OBO,QHJIHCb, AonYOK Ha HaMeTp 3y5beB
6bIJI 0,005 MM Ha Bcex 3y5bHX. IlOLl'beM Ha AHaMeTp 3y6beB KOMn-
JIeKTa npOT5I)KeK 6bIJI paBeH 0,02-0,7 M'M. 3y6bH npOT51lKeK He MiYle-
JIH CTpYlKKopa3AeJIHTeJIbHbIX KaHaBOK, TaK KaK pa3)].eJIeHHe CTPY)KKH
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TOBJIeHHOrO no,lJ, npOTHfHBaHHe. BJIHHHHe cnoco60B pa3,lI.eJIeHI151
CTPYMKH Ha CHJIbI pe33HH5I HCCJIe,QOBaJIOCb Ha Crrel1.HaJIbHO IIO;I,rO-
TOBJIeHHbIX pe3lI.ax. ,UJI51 HCCJIe,1J.OBaHH51 HCnOJIb30BaJIHCb OCTpbIe Ii 3a-
TynJIeHH'bIe npOT5I}I{KH. HapY)KHOe npOTHrHBaHHe npOBOII.HJlOCb pe3-
ll,OM C 'npHMOH pe}KymefI KpOMKOH: 11 npOT }KKaMH C KpHBOJIHHeHHbIMlI
KpOMKaMH.
P e3 y JI b T a T\bI :3 K C Il e pH M e H T a Jl bH bI X M CCJl e.n 0 B a H H fI CB H)]. eTeJI bCTBY lOT
o TOM, lITO TOJI HHa ,cpe3a 5IBJI5IeTC5I O,QHJitM H3 rJIaBHbIX <paKTopOB,
BJIH51IOIl1JIX Ha CHJIbI pe3aHHH npH 'npOT51rHBaHHIL
B pe3YJIbTaTe MaTeM8THQeCKOrO aHaJIH3a HaIllHX onbITHbIX .rr.aH-
HbIX nOJlYIIeHa 3aBHCHMOCTb y,neJIbHOH: CHJIbI pe3aHH5I qo (Hj'M/M) OT
TOJIll1.HHbI cpe3a npH npOT51rHBaHHH CTaJIH 45 CJIe,QYIO ero BH.rr.a:
qo== 18+ 1932a,
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pe,QHero yrJIa 15° npE OXJIa)KJI:eHHH CYJIbcpocppe30JIOM. 3HaIIeHH51 CH-
JIbJ qo ,lI.JI5I ,n:pyrHx nepe)J:HHx yrJIOB npMBe,rr,eHbI B Ta6JI. TI.20 rrpH-
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u
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pe3aHH51 rrpH npOT51rHBaHHH HX npaKTHqeCKH O HHaKOBa.
AHaJIOrHIlHbIe pe3ynbTaTbI nOJIyqeHbI H npH rrpOT5IrHBaHHH 3aro-
TOBOK H3 CTaJIeH: ,lI.pyrHx Ma pOKe
3aBHCHMOCTb OCeBOH CHJIbI pe3aHH5I OT TO,,1IJJ;HH l bI Cpe3a rrpH Ha-
PYlKHOM npOTHrHBaHHH aHaJIOrI1QHa 3aBHCI1MOCTM (2.1) npH BHYT-
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CH1tOCTH He 60JIee qeM Ha 5 %.
C YBeJIHqeHHeM TOJIInHHbI cpe3a YBeJIHtJHBaeTC5I TaK)Ke Y)teJIbH3H
17
2.1. Pe3YJlbTaTbi H3MepeHHH CRJI pe3aHRH
.IlaaMeTp
qo (H/MM) npH a, p.{M
l\1apKa COCTOSJHHe OTneqaTKa
CTa"lH no BPH- 0,03 0,05 0,07 0,1 0,15 0,2 0,3
HeJIJIIO, MM
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npOKaT
OT)K Hr 4,4-4,5 69 112 169 218 319 406 593
HopMaJIH 4,0-4,2 83 113 162 227 297 415 613
3alI.HH
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npOKaT
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3aUH5I
20r fOPHQHH) 5,0-5,1 81 119 174 211 308 416 611
npOKaT 416
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npOKaT 90 413
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3aaHSI
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TOB HapY2KHOfO rrpOT5IfHBaHM5I rrOKa3bIBaeT, QTO
qp=29,4+ 785a. (2.2)
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maeTC5I C YBeJIHqeHHeM CKOpOCTH pe3aHHH OT 1 J{O 2,5 M/MHH; IIPH
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npeHe6peIIb.
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npOT5IrHBaHHH BJIHHIOT: IlIHpHHa cpe3a, 3a,nHHH yroJI 3y6beB M M3HOC
rrpOTH)KKH, 1JHCJIO OJI.HoBpeMeHHo Y1JaCTBYlOrn:MX B pa60re 3y6beB,
CMa30qHO-OXJIa)KJI.alOm.a5I )KH,QKOCTb H cnoco6 pa3 eJIeHHH CTPY}KKH.
H3 nepeqHCneHHwx aKTopOB ABa IIOCJIe,nHHx OKa3WBalOT HaH60JIee
3aMeTHoe BJIM51HHe Ha CMJIY pe3aHM5I KaK npH BHYTpeHHeM, TaK H
npH HapY)KHOM IIpOT5IfHBaHHH. npH paCqeTe CRJI BJIH51HHe 3THX cpaK-
TOpOB YIIH'f1bIBaeTCH BBe.aeHHeM B paCqeTHYIO <POPMYJIY TIOrrpaBOqHbIX
K03cp cp HU HeHTOB.
JIR HCCJIe OBaHH BJIHHHHH H3Hoca Ha CHJIY pe3aHH5I H3Mep H
18
H3HOC fIO 3a,lI.HeH \IIOBepXHOCTH II pa):{HYC oKpyr JIeHH5I pe)l{y eH KpOM-
KH C nOMOInbID CBeTOBOrO -ce1J.eHH5L Pe3YJIbTaTbI OI1bITOB TIOKa3aJ1H
I.JTO npl1 HOpMaJIbHOiM H3Hoce no 3aJ(HeH nOBepXHOCTH 0,1 MM, COOT-
BeTcTBYIOIl(eM pa,QI1Ycy cKpyrJIeHH5I pe2KYLUeH: KpOMKH 0,02-0,03 MM
oceBa CH a npaKTHqeCKH He OTJIHqaeTCH OT CHRM npH npOTHrHB3HHH
OCTpOH npOT5ILKKOH. Ha pa,QHaJIbHYIO CHJIY H3Hoe 3y6beB npOTH}I{KH
BJIH5IeT B 60JIbilleH CTeneHH.
06InaH 3aBHCMMOCTb JI.JI5I onpe.n.eJIeHH5I oeeBoH CHJIbI pe3aHH51
.rr.eH:CTBYIOIAeii Ha rrpOT5I>KKe, HMeeT BH,lI.
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3JI.eCb qo - OCeBa5I CHJIa pe3aHH , rrpHxO,lI,HIIJ.aHC5I Ha 1 MM .uJIHHbI
pe*ym eH ,KpOMKH; lp - cYMMapHaH ,L(JIHHa peLKymHX KpOMOK 3yobeB,.
oJ{HoBpeMeHHo YlJaCTBylOmHx B pa6oTe; Kp - nOnpaBOQHbIH K03 cpH-
UHeHT Ha H3MeHeHHble YCJIOBHH o6pa6oTKH; Kp= KPMKpoKppKpl\J
r,Qe KPM - K03cpQJHIJ.HeHT, yqHT1bIBalOllI.HH rpyrrrry oopa6aTbIBaeMocTH
MaTepHaJIa II era COCT05lHHe; Kpo - K03 £pHlI.HeHT, yqHTbIBalOlll,HH
BIIJ1. CO)I(; Kp p - K03cpcpHIJ.HeHT, YIIHTbIBalOIIJ.HH: cnoco6 pa3,QeJIeHH5I
CTPYLKKH; KpR. - K03cpcpHIJ.J1eHT, YIIH'fIbIBalOIJJ;HH Tpe6yeMoe KaqeCTBO
o6paooTaHHoH IITOBepXHocTH.
Cpe,lI.HIOIO YCTaHoBHBlIlYIOC5I reMnepaTYPY B 30He pe3aHHH H3Y1.Ia-
JIH npH npOT5IrHBaHHH 3arOTOBOK H3 CTaJIH, IIyrYHa H J.1.PyrHx IMeTaJI-
JIOB. I1ccJIe.n.oBaHHH npOBo,lI.HJIHCb Ha ropH30HTaJIbHO-npOTH)KHbIX
CTaHKax. ,UJIH 3aKpenJIeHH5I 06pa3IJ.OB 6bIJIO cnpoeKTMpoBaHo H 113-
rOTOBJIeHO rrpHcrroco6JIeHHe, rr03BOJIHIOIIJ.ee pa60TaTb IKaK npOT.H)KKOH,.
TaK H pe3AoM. 06a HHCTp MeHTa H3rOTOBJI5IJIHCb H3 O Horo rrpYTKa
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repMHIIeCKOH o6pa6oTKe. TIpOT5I)KKa HMeJIa rpyrrrrbI 3y6beB C OJ{HHa-
KOBbIM nO,Q'beMOM H C MHHYCOBbIM OTKJIOHeHMeM Ha ,QHaMeTp 0,005 MM.
H3MepeHHe TeMrreparypw rrpOBO HJIOCb no MeTO y eCTeCTBeHHOH Tep-
MOnaplbI. PerHCTpau.H51 TepMo3LLC BeJIaCb Ha OCL(HJIJIOrpacpe MTIO-2
C rrOMOIlI,blO TpeXKaCKa,QHoro YCHJIHTeJI5I rrepel\1:eHHOrO TOKa. TI pH P a-
60re rrpOT5I}I{KH 6bIJI H30JIHpOBaH 06pa3el(, npH pa60Te pe3ua - pe-
3ell.. TOKOC'beMHHKH H3fOTOBJI5IJIH H3 Toro :>Ke npYTKa, 1.ITO H rrpOT5I-
rHBaeMble 06pa3U ' bI, H nO):{BepraJIH COBMeCTHO c nOCJIe,lI.HHMH TepMH-
qeCKOH: oopa60TKe. TapHpOBaHHe npOBO HJIOCb rrpH nOCTORHHOH TeM-
rrepaType XOJIO HOrO Crr35I, paBHoH 20° + 1°, KOTopaH no.,l1)I,ep)KHBaJIaCb
C nOMOIlI,bIO CHcreMbI rrOJLaqH CTPYH C}I{aTOrO B03 YXa.
113 1 MepeHHe TeMrrepaTypbI rrpH pa3HOH: TOJIlUHHe cpe3aeMoro CJIOH
H CKOpOCTH pe3aHH5I nOKa3aJIO, IITO C YBeJIHIIeHHeM TOJIlUHHbI cpe3a
H CKOpOCTM pe3aHHH TeMnepaTypa B03pacTaeT, J(OCTHraH 550 0 C npH
TOJIlll,HHe cpe3aeMoro CJI05I 0,4 MM H CKOpOCTH pe3aHHH 12,6 M/MHH.
CJIe,n:oBaTeJIbHO, j{JIH ooeCrreQeHH BbICOKOH: npoH3Bo)J,HTeJIbHOCTH rrpo-
THrHBaHH5I H MHHHMaJIbHOH ,QJIHHbI rrpOTH)KKH ee c.rre,QyeT H3rOTOBJIHTb
H3 ObICTpOpe}KYlUHx craJIe", H'MeIOI1J;I1X ,n:ocTaToIIHylO TeIIJIOCTOHKOCTb.
BJIHHHHe TOJIInHHbI cpe3a Ha YCTaHoBHBllIylOcH reMrreparypy B 30He
pe3aHHH npH pa3HbIx CKOpOCTRX pe3aHHH pa3JIH1.IHO, H qe 1 60JIbllIe
CKOpOCTb pe3aHH5I, TeM CHJIbHee 3TO BJIH5IHHe.
BJIH5IHMe CKOpOCTH pe3aHH5I Ha TeMnepaTYPY B 30He pe3aHHH He-
19
o,nHHa KOBO rrpH pa3JIIP-IH l bIX TOJIlUHHaX Cpe3a, If qeM 60JIblIIe TOJII..U.HH3
Cpe33, TeM CHJlbHee BJIHHHHe CKOpOCTH.
BJIH5IHHe p0,Qa OXJIa)K)].aIOlUeif LKH)].KOCTH Ha TeMIIepaTYPY pe3a-
HH5I npOBep5IJIH Ha ,QBYX llII1pOKO npHMeHHeMbIX rrpI1 rrpOTHrHBaHHH
1KHJI.KOCTHX - 5 % -HOM paCTBOpe MYJIbCOJIa 32 B BQ,Qe H CYJIbcpocppe-
30JIa. YcraHOBJIeHO, qTO npH TaKHX YCJIOBHHX npoBe,QeHHH 3KcnepH-
MeHTOB BJIH5IHHe HX Ha TeMrrepaTYPY pe3aHHH rrpaKTHqeOKH O,QHHa-
KOBO. TIpoBepKa 3cpcpeKTHBHOCTH OXJIa)K,QeHHH a3p030JIH rrOBepXHOCT-
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30HY pe3aHH5I a3p030JIH TeMrrepaTypa pe3aHHH CHH}I{aeTCH Ha 40 %
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HOCTb pe)KYllI.HX KpOMOK nOBbIwaeTCH, lITO, eCTeCTBeHHO, npHBOlI.I1T K
naJI.eHHIO nepHO,Qa CTOH:KOCTH npOTH)KKH. C YBelIH4eHHeM nepe,QHero
J{ 3a,lIHerO yr JIOB 3y6beB rrpOTH)KKH TeMnepaTypa B 30He pe3aHHH
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npOr5I)f{KH 3TH reOMeTpHQeCKHe rrapaMeTpbI era 3y6beB ITO B03MOlK-
HOCTH Heo6xo)].HMO YBeJII1qHBaTb.
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YCTaHOBJIeHO, qTO TeMneparypa B CTpY*Ke H HHCTpYMeHTe pac-
npe,n;eJIHeTCH OqeHb HepaBHOMepHO. B npMJIeraIOIllJ1X K rrepe,lI,HeH: no-
nepXHOCTH HHCTpYMeHra CJIOHX CTPY)KKH TeMlrrepaTypa ,QOCTHraeT
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npOTHrHBaHHH qaCTO JIHMHTHPylOI..UHM H3HOCOM 3YObeB npOTH}I{KH 51B-
JI5IeTC5I cKpyrJIeHHe pe)Ky eH: KpOMKH.
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ro H HHCTpYMeHTaJIbHOrO MaTepHaJIOB; 3JIeMeHTaMH pe)KHMa pe3a-
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(2.4 )
20
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21
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22
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23
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29
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30
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36
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37
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38
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39
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40
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co C'beMHbIMH XBOcToBHKaMH, :tKeCTKO COeJl.HHeHHbIMH C OCHOBHOH
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41
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42
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onpaBKH ):lHaMeTpoM 2,5 MM If npHrraHHo K onpaBKe. 06 3cpcpeKTHB"
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rr03BOJIHJIO 3aMeHHTb onepaUHIO XOHHHfOBaHH5I.
AJIH oopaooTKH CKB03HWX oTBepcTMH MaJlOrO HaMeTpa (JI.O 12--
20 MM) MorYT npHMeHHTbC5I MOHOJIHTHble TBepJI.OCIIJIaBHbIe MHoroma-
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CrrJI3BHbIMH OJIOKaMH.
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43
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44
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KHe KOHCTPYKI(HH npOTH)KeK C03){aHbI, B qaCTHOCTH, B CKE npOT5I>K-
HbIX CTaHKOB (r. MHHCK). C60pHa51 TBepJI.OCnJIaBH351 npOT5I:>KKa npH
oopaOOTKe ueHTpaJIbHOrO OTBepCTHH B KapTepe aMopTH3aTopa aBTO-
Mo6HJI5I OOecrreQHBaeT rronyqeHHe IIOJIH ,nonYCKa H7 H napaMeTp we-
pOXOBaTOCTH IIOBepXHOCTH Ra=0,63 MKM. npH HCIIOJIb30BaHHH ,lI.JIH
pe)Ky eH: qaCTH TBep,lI,OrO CnJIaB8 BKIOM CTOHKOCTh npOT5I:>KKH Me}£{-
ll.Y IIOBTOpHbIMH 3aTOtJKaMH COCTaBJ1HeT 5000-6000 M AJIHHbI rrpOTH-
HYTOH rroBepxHocTH. BHe.n.peHHe J(aHHbIX rrpOTH}I{eK II03BOJlHJIO 3aMe-
HHTb ){Be onepaUHH: qHCTOBOe paCTaqHBaHHe H XOHHHrOBaHHe. CToH-
KOCTh rrpOT5ILKeK B Cpe,lI.HeM B 400 pa3 rrpeBblmaeT CTOHKOCTb npoTH-
}KeK 113 6bICTpope}l{ymeH CTaJIH. C0311.aHHe KOHCTPYKQHH: TBeplI.OCnJIaB-
HbIX peJKyme-BbIrJI8>KHB8IOIUHX npOT5I:>KeK OTKpbIBaeT B03MO}J{HOCTH
J15I npOT5IrHBaHHH H8 nOBbIllleHHbIX CKOpOCT5IX pe33HH5I.
JI.ecpopMUPYIO ue U KOM6uHupOBaHHbte (c aecpopMupYIOt.l!UMU 3/te-
MeHTaMU) npOTJl/JICKU. ,[{e4JopMHpYIOIItHe IIpOT5I)KHble HHCTpYMeHTbI
OTJIliflI3IOTCH OT BblrJIaLKHBaIOrnHX 60JIblllHMH HaT5IraMH H3 Ka:>KJI.Oe
KOJIbLLO (,no 1 MM If oOJIee). n pH 3TOM TBep,l(OCIIJIaBHble .n.ecpOpMHPYIO-
lItHe 3J1eMeHTbI BbIIIOJIH5IIOTC.H QJJ:H03y6bIMH H pa3,L{eJIHIOTCH J1HCTaH-
II.HOHHbIMH BTYJlKaMH, lI.JIHHa KOTOpbIX 33BHCHT OT pa3MepOB o6pa6aTbI-
B3eMOH 3arOTOBKH. npH HeBNCOKHX TpeOOBaHH5IX K TOqHOCTH (10--
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= 2,5 MKM) ,lI.eTaJIH THna BTYJIOK H3rOTOBnHIOT H3 HeoopaooT8HHbIX
3arOTOBOK B BH,ne TPYO. npH 3TOM OTKnOHeHH5I reOMeTpHqeCKOH <pop-
MbI oTBepCTH5I HCXO,nHOH «qepHoii» Tpy6HOH 3arOTOBKH YMeHbwaIOTcH
B 10-20 pa3. HarrpHMep, np" Aeq,opMHpYlOIneM npOT5IfHBaHHH oTBep-
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MeHTOM oOeCneQHBaeTC5I napaMeTp lllepoxoBaTocTH nOBepXHOCTH
Ra 1,25 MKM (HCXO,lI,H35I 3arOTOBKa - rOp511.JeKaTaHaH Tpy6a).
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H BbICOKHX Tpe6oBaHH5IX K mepoxoBaTocTH (Ra = 0, 16-.;-1 ,25 MKM) ,lI,e-
Ta,TI H THIIa rHJIb3 co 3HaqHTeJIbHbIM OTHOIIIeHMeM ,lI,J1HHbI K ){HaMeTpy
oTBepCTH5I o6paoaTbIBalOTc5I Jle<popMHpyroInHMH IIpOT5I>KKaMH IIOCJIe
MeX3HHQeCKOA o6pa6oTKH oTBepcTHH. BOJIblllOH onWT 3<p eKTHBHoro
rrpHMeHeHH5I ,U.e4JopMHPYIOrnHx npOT5I}KeK HaKOIIJIeH B I1HcTHTYTe
cBepxTBep,U.bIx MaTepHaJIOB H CnJIaBOB (r. KHeB).
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'lame Bcero BbIIIOJIH5IIOTCH JJ:e<popMHpYIO e-pelKYIl.(HMH HJlH ,necpopMH
45
PYIOI.l'(e-pe:>Kyrne-BblrJIa)KHBaIOInHMH. ilepBbIH BHA npOT5I)KeK npHMe-
H5IeTCH npM CpaBHMTeJIbHO HeBbICOKHX Tpe6oBaHM5IX K KaqeCTBY npOT5I-
HYTOrO OTBepCTM5I; nOBepXHOCTb 3arOTOBKH - Heo6paOOTaHHa5l. ,Qe..
CPOpMHPYIOIll.Me 3JIeMeHTbI HCrrpaBJIHIOT OTKJIOHeHHH cpOpMbI OTBepCTHSi
HCXO,LlHOH 3arOTOBKM H CHM)KaIOT 6J1arOJlapH 3TOMY npHnYCK Ha o6pa-
60TKY. CYMMapHbIH HaTRr Ha .n.ecpOpMHpyroInYIO qaCTb j{OJIJKeH rrpe-
BbIlIIaTb OTKJIOHeHHe OT KpyrJlocTH OTBepCTMH HCXO.l1HOH 3arOTOBKH.
Pe)KYIll.aH qaCTb H3rOTOBJIHeTCH H3 HHCTpYMeHTaJ1bHOH CTa.TIH. K nepe)J,-
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C onpaBKOH pe3bOOH. Pe)KYI.l'(YIO lIaCTb npOT5I)I{KH H3rOTOBJ1HIOT IIe)
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BepCTMH 0 70t :24 MM B rOpHQeKaTaHoH Tpy6e (cTaJIb 45) cYMMapHbI1I
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OTBepCTMH 110CJle npOXO,lI,a JI.ecpopMHPYIOIneH \laCTH 0,2 MM). OOI.l'(HH
npHrrycK Ha pe}KYI.l'(YIO qaCTb (Ha CTOPOHY) 0,5 MM. War ecpopMM"
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CH )l.Jl5I HeoopaooTaHHblx oTBepcTMH. K TOtJHOCTM H KaqeCTBY rrpOT5I}K-
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BalOll1.a51 qaCTb oCYI.l'(ecTBJI5IeT nOBepxHocTHoe .n.ecpOpMHpoBaHHe, 1fT()
cIIoco6cTByeT rrOJIyqeHMIO TOqHOCTH 110 7-6-MY KBaJIMTeTY H napa-
MeTpa rnepoxoBaTocTM rrOBepXHOCTM Ra=O,8-;.-O,16 MKM. fIpM 3TOM
)I.OCTHraeTC5I ynpolIHeHMe rroBepxHocTHoro CJIOH, H B HeM C03,u.aIOTCS
C.IKHMaIO He HarrpR)KeHHH.
n pOTRJlCKU OAR o6pa6oTKU UlJlUl{eBbtx Of8epCTUU. I1pH u.eHTpHpo-
BaHMH WJlMueBbIX COe,l(MHeHHH: 110 BHYTpeHHeMY ,lI,MaMeTpy Heo(5xO,lI,MMO
06ecrrelIHTb MaJIOe OTKnOHeHMe COOCHOCTH no rOTOBJleHHOrO rro,l( npo-
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pemeHHH 3TOH: npOOJIeMbI 51BJI5IeTC5I C03J(aHMe KOHCTPYKUHH npOTH)KeK
C qepeJI.YIOIIJ.HMMCH KpyrJIblMM H lllJIHueBbIMM 3YOb5lMH. npHMepOM MO-
}KeT CJIY}I{HTb WJIHueBa5I rrp5lMOOOQHaH rrpOT5I>KKa BToporo paOoqer()
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pa3MepbI: BHYTpeHHMH JI.MaMeTp 84,45 MM, lllHpMHa UIJIMII.eBOro na3&
11,5 MM, HapY)KHbIH ,l(HaMeTp 92 MM. ITepBble BoceMb 3y6beB npOTH)K-
KM - llIJIHneBble. 3YObH C 9-ro no 40-H: qepe,u.YIOTc5I (KpyrJIbIe H llIJIM"
u;eBble). 3y6bH C 4I-ro no 44-ii--q,aCOQHbIe. KpyrJIbIe 3y6bH C 9-r()
lIO 39-H (HeQeTHbIe HOMepa) YCJIOBHO MO}l{HO pa3JleJlMTb Ha TPM lIaCTH:
OO,l{HpOlIHYIO, QHCTOBYIO M KaJIH6pYIOInYIO. Ha 06J(HPOtJHhIX H qHCTO-
BbIX KpyrJIbIX 3YObHX (c 9-ro no 29-ii) BbIIIOJIHHIOT CTpY1KKOpa3){eJIHoo
TeJIbHble KaHaBKM Ha paCCT05lHHH 2,5 MM OT OCH Bna HHhI B waXMaT-
HOM IIopHAKe.
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TH)KKa BToporo pa6otJero xO)J.a c qepe,lI,YIO HMHC5I IllJIHu.eBbIMH If
KpyrJlbIMH 3y6bHMM. TIpOT5I}KKOH OKOHQaTeJIbHO o6pa6aTbIBalOT OTBep-
46
CTHe c qHCnOM WJIHUCB 16, Mo,nyneM 3,5 MM, ,nHaMeTpoM Coe.ll.HHeHHH
62 MM (rrpocpHJIbHbIM yroJI HCXO,U.Horo KOHTypa 15°). nepBble .lI.Ba
3y6a - I11JIHIJ.eBbIe; Jl,aJIee Kpyr JIbIH, 3a TeM LlBa IIIJIHueBbIX, Kpyr.,TlbIH
H T. .lI.. KpyrJIhle 3YObH, KOTopbIe HMeIDT HOMepa, KpaTHbIe TpeM, MOIK"
HO TaK)Ke pa3.l1.eJIHTb Ha TPH BH.lI.a: 06LlHpOQHble, QIICTOBble H KaJIH6-
PYIOIlLHe.
DpH oopaooTKe IlIJIHu.eBbIX oTBepcTHH 3BOJIbBeHTHbIMH npOT5I)KKa..
MH HeOJIarOnpH5ITHbIe YCJIOBHH pe3aHH5I C03.l1.alOTCH npH paooTe IlIJIH..
neBbIX, ocooeHHo IllJIHueBbIX 06JI.HPOqHbIX 3yobeB. Cpe3aHHe CTPY)KKH
fI..oopa3Horo BHJI.a 3aTpY.lI.HHeT ee pa3MeIll.eHHe B cTpY>KeqHOH Bna-
)1.HHe, YBeJIHtIMBaeT lllepOXOBaTOCTb npOT5IHYTOH rroBepxHocTH. TI03TO-
MY B npOMbIlllJIeHHOCTH rrpHMeHHIOT npOT.H)KKH, Y KOTOpbIX Ha lIIJIHae-
BbIX 3BOJIbBeHTHbIX 3y6bHX npe.llYCMOTpeHO pa3LleJIeHHe cpe3aHH5I
-CTPY*KH 60KOBbIMH (npocpHJIbHbIMH) KpOMKaMH H .lI.HaMeTpaJIbHbIMH
KpOMKaMH, <POpMHPYIOIl\HMH nOBepXHOCTb Bna,lI.HH npOT5IrHBaeMoro
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IIIJIHII.eBa51 3BOJIbBeHTHa51 npOTH)KKa JI.Jl5I oopa60TKH oTBepcTHH
075 X H8X2,5 (fOCT 6033-80). n POT51)KKa COCTOHT 113 CJIe.n.YIDIllJIX
rpynn 3y6beB: <paCOQHble (c l-ro no 13-11), KpyrJIbIe (c 14-ro no
26-if), IIIJIHII.eBbIe npe.ll.BapHTeJIbHbIe C pa3.l1.eJIeHHeM CTpY)I{KH (c 27-ro
no 57-if), IDJIHlI.eBbIe qHCTOBbIe (c 58-ro no 74-ii), IIIJIH eBbIe Ka.nHo"
PYIO He (c 75-ro no 80-H). Y IIIJlHueBbIX npe.ll.BapHTeJlbHbIX 3y6beB
(c 27 -ro no 52-H) HenpepbIBHaH pe>Kyr.u.a51 KpoMKa O){HOrO lIIJIH eBOro
13bIcTyna pa3,U.eJIeHa Ha TPH yqaCTKa: .lI.Ba npocpHJlbHbIX yqaCTKa B BHJI.e
JJ..yr OKPY>KHOCTH H rrepR<pepHHHaH KpOMKa llIHpHHOH 2,92 MM, OTJ].e..
eHHaH OT npo H bHWX yqaCTKOB JI.BYMH KOpOTKHMH np5IMOOOQHWMR
cTopoHaMH. lllJIHu.eBbIe npe,U.BapHTeJIbHble 3y6b5I C 53-ro no 57-H CHao..
)KeHbI YCHKaMH, KOTopble pa3JleJI5IIOT nepHMeTp IlIJIHII.eBOH BITa,U.HHhI
..lI.JI5I OOJIerqeHHH paOOTbI IlIJIHueBbIX qHCTOBhIX H KaJIH6PYlOII..{HX 3y6beB.
,LLJI5I 06J1erQeHH5I paOOTbI nepHcpepHHHbIX KpOMOK npH lI1HpHHe 4 MM
}f oOJIee IlIJIHu.eBble npe,U.Ba pHTeJIbHbIe 3YObH BbII10JIHHIOTC5I ceKII.HOH..
HbIMH (c rpYIIITOBOH CXeMOH: pe3aHHH). I1pRMepoM MOJKeT CJIY*HTb
9BOJIbBeHTHaH IlIJIHII.eBaH npOT5I:tKKa BToporo paooqero XO)1.a ):(JIH 00"
pa60TKH IIIJIHII.eBOro oTBepcTHH 075XH8X3,5 (fOCT 6033-80),
npOTHJKKa HMeeT rpynrry IlIJIHIl.eBbIX 3y6beB (c I-ro ITO 21-H) OObyq..
Rora npO<pHJIH. 3TH 3y6bfl paClIIHp5lIOT lIIJIHueBbIe Bna.ll.HHbI, nOJIyqeH"
HbIe npOTH)KKOH: nepBoro paoot:Jero xO,lI.a. 3y6b51 C 22-ro no 49-n HMeIOT
lliJIHneBbIe BblcTynbI C onHcaHHbIM BblIIIe pa3,U.eJIeHHeM pe}KY HX KpO-
l\10K, 06paoaTbIBaIOIII.HX OOKOBOM npocpHJIb IlIJIH eBOro na3a H nOBepx-
1i0CTb Brra,n:HHbI IlIJIHu.eBoro OTBepCTH5I. ,LlJI5I 06JIerQeHH5I YCJIOBHH:
-cTPY)KKOo6pa30BaHH5I npH pa60Te pe)KymHx KpOMOK, <fJOPMHPYIOl.I.(HX
nOBepxHocTb BIIaJI.HH, 3TH KpOMKH CHaO:tKeHbI BbIKpY}I{KaMH, pacnOJIO-
JKeHHbIMH B lIIaXMaTHOM nOp5I,L(Ke. DpH 3TOM 3YObH C 22-ro no 43-ii
BbInOJIHeHbI B BH,lI.e LlBY3y6bIX ceKUHH. Ka:tK.lI.aH I1apa 3yobeB (o,n:Ha
-ceKUHH) HMeeT oAHHaKOBbIH .lI.HaMeTp, a nO,U.'beMbI BbIITOJIHeHbI Ha
ceKUHIO. JI.JI5I npoTHrHBaHHH lllJIHQeBbIX oTBepcTHH B TPYJI.HOo6pa6aTbI-
BaeMbIX MaTepHaJIaX npHMeH5IIOT C60pHble I1pOTH)l{KH C HaCa.ll.HbIMH
TBep.rr.oCnJIaBHbIMH pe)KYIUHMH 3y6b5IMH. TIpH 3TOM Bce pe)KYl.I.(He 6JIo-
KH BbIrrOJIHeHbI 0,lI,H03y6bIMH.
47
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3.
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H qHCTOBb1e 3YObjl, MM;
ao, aD, aq - WHpHHa BbIKPY)KeK COOTBeTCTBeHHO Ha qepHOBbIX, rre-
peXO,l\HbIX H 1fHCTOBbIX ay6bHx, MM;
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ceKTopa), MM;
b, b l - lIIHpHHa 3y6a (LlJlHHa aaJI.HeH nOBepXHOCTH) COOTBeT-
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PYIOIII-HX 3YObeB, MM;
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BaRHe, MM;
D - J{HaMeTp oTBepcTHH IIOCJIe npoTSlfHBaHHSI, MM;
D XB - ,l{H3MeTp nepe,l{HerO XBOCTOBHKa, MM;
Dn.u - ,lI,HaMeTp nepeJ1HeH HanpaBJIHIO eH, MM;
D 3 . a - ){IIaMeTp 3aJ(HeH HarrpaBJIHlOrueH, MM;
D 3 . XB - .DJIaMeTp aaJ(Hero XBOCTOBHKa, MM;
Don - AHaMeTp onaCHoro CeqeHHH pe>KymeH qaCTH npOTH}K..
KH, M M ;
io, in, i1:{ - qHCJIO rpynn COOTBeTCTBeHHO qepHOBbIX, rrepeXO)I.HbIX
If QHCTOBbIX 3YObeB;
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Kpll. - nOnpaBOQHbIH K03cp<pHlI.HeHT H3 CHJIY pe3aHI1H B 33BH-
CHMOCTH OT BH)I.a, COCTO HH H TBep,nocTH MaTepH8JIa;
Kpo - TO )Ke, B 3aBHCHMOCTH OT BH a OXJ18}K,neHHg;
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lOI l lq, lK - AJIHHa COOTBeTCTBeHHO qepHOBOii, nepexoJlHoii, qHCTO-
BOM H KaJIHOPYlOmeH qacTeii npOTH)I{KH, MM;
11 - AJIHHa qaCTH IIepe Hero XBOCTOBHKa, 3aXBaTblBaeMOH
naTpOHOM, MM;
1 2 - paCCTOHHHe OT TOpua pa6oQero naTpOHa 11.0 onopHOH
TIJIOCKOCTH, MM;
13 - TOJIlltHH3 orropHOH IIJIaHllIaiiobI, MM;
In.s - )J.JIHHa nepe)1.Heii HarrpaBJIHIOIneH, MM;
48
In.I( - .l1.JIHHa nepeXO,ltHOrO KOHyca, MM;
lCB - ,lI,JIHHa OT nepeLlHerO TOpua .aO MeCTa CBapKH, MM;
13.H - A.JIHHa 3aLlHeH: HanpaBJI51lOllI.eH qaCTI1, MM;
l3.B - .lI}IHHa 3a):{HerO XBOCTOBHKa, MM;
L- o6ll1.a51 )])IHHa npOT5L/KKI1, MM;
Ll - paCCTO}JHHe OT nepe,l{HerO TOPUa )10 nepBOrO 3y6a npo-
TH)KKH, MM;
L p - ,lI,JIHHa pe:tKYIUeH qaCTH npOT5IlKKM, MM;
Lmax - MaKCHMaJIbHbIH: X0.ll. IIITOKa CTaHKa, MM;
a - r JIaBHbrH 3a.ll.HHH yrOJI (ao - qepHOBbIX If nepeXO,lI,HbIX
aq - qIfCTOBbIX, al{ - KaJIH6PYIO HX 3YObeB), 0;
aB - 3a,lI,HI1M yroJl no BhIKpy:tKKe, 0;
"y - nepe,lI,HIfH yrOJI tJepHOBbIX H nepeXOlI.HbIX 3y6beB, 0;
1'1 - nepe)J.HHH yrOJI qHCTOBbIX 11 KaJlH6pYIOIll.I1X 3y6beB, 0;
N - qHCJIO BbIKpY}KeK;
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pe)l{y eH KpOMKH, H/MM;
p - OCeBa51 CHJIa pe3aHH5I, H;
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JIH6PYIOll\HX 3y6beB, MM;
RB - paLlHYC BbIKpYLKeK, MM;
RH - pa,LU-IYc IllJIHqJOBaJIbHOrO Kpyra )l.JIH BbIKPYLKKH, MM;
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H3 YCJIOBI1H paBHOH CTOHKOCTH (HapaOOTKM) qepHOBOH
... "
H qliCTOBOM 'IaCTeH npOTH}I{KM, MM;
SZO, SZIb SZTJ. - no.naqa Ha 3y6 Ha CTOPOHY (rrO.ll.a1Ja) COOTBeTCTBeHHO
u u u u
lJepHOBOH, nepeXO,lI.HOH Ii qHCTOBOIi qaCTeH npOTH1KKH,
MM;
t - mar qepHOBbIX If rrepeXOJlHbIX 3y6beB, MM;
t s , t 2 , t l - nepeMeHHbIe marH COOTBeTCTBeHHO QMCTOBbIX H K3-
JIM6pYIOmHX 3y6beB, MM;
h, hI - r.n:y6HHa cTpY./KeQHOH KaHaBKH COOTBeTCTBeHHO qepHO-
BbIX Ii nepeXo)I.HbIX, qliCTOBbIX Ii KaJlli6pYIOIII.MX ayab-
eB, MM;
ZOI ZIIJ zq, ZR - qliCJIO COOTBeTCTBeHHO lIepHoBbIX, rrepeXOJI.HhIX, qHCTO-
BbIX Ii KaJIli6pYIO I1X 3y6beB;
z - o6r.uee qHCJIO 3y6beB rrpOT5I1KKIi;
Zp - qHCJIO 3y6beB, oLlHoBpeMeHHo yqaCTBYIO liX B pa60Te;
Zc - qHCJIO 3y6beB B ceKUHM.
49
MeTOAHKa paC1JeTa npOTSI>KKH
HCXOAHble aHHble. ITpOT51rMBaeMaH 3arOTOBKa: MaTepHaJI; TBep..
}l.OCTb no BpHHeJIJIIO H B; COCTOHHHe (nOCJIe HOpMaJIH3a HH OT)KHra,
3aKaJIKH); no rOTOBKa nOBepXHOCTH no npOTHrHBaHHe (npOKaT,
JIHTbe, lIlTaMnOBKa HJIH I10CJIe MeXaHHQeCKOH: o6pa6oTKH); )J.HaMeTp
()TBepCTHH O o6pa6oTKH H nOCJIe oopa60TKH C nOJIeM onYCKa; I1apa-
MeTp IlIepOXOBaTOCTH nOBepXHOCTH; HaHoo.i'IbIlIaH ,lI.JIHHa npOTHrHBaHH5I
(HJIH npH HaJIHqHH HeCKOJIbKHX yqaCTKOB - JIHHa Ka:>K OrO YtJaCTKa
II T. ,a.).
2. CTaHoK: THrr; MO eJIb; THfOBa51 CHJIa; J(Hana30H CKopocTei'I; ,l(JIII-
Ha xo a lIlTOKa; THn naTpoHa; pa3MepbI OnOpHOH: nJIHTbI; COCTOHHHe
CTaHKa.
3. XapaKTep npoH3BoAcTBa (MaccoBoe, cepHHHoe, e)J.HHHtJHoe).
4. B03MOJKHOCTH HHcTpYMeHTaJlbHOrO uexa H 3aTOQHOrO OT,neJIe-
HHH: HaH60JlbIllee paCCT05lHHe Me2K,ay ueHTpaMH KpyrJlolllJlHcpoBaJlb-
Horo H 3aTOtIHOrO CTaHKOB, rJly6uHa BaHH HJlH waXT lI.Jf51 HarpeBa no.ll
3aKaJIKY H oTnycK.
nOpSiAOK paC1JeTa. PaCtIeT rrpOT5I}I{KH HatJHHalOT C YCTaHOBJIeHHB
rpynnbI oopaoaTbIBaeMocTH MaTepHaJIa 3arOTOBKH H rpyrrnbI KatJeCTBa,
K KOTOpOH OTHOCHTCH npoT5IHYTaH nOBepxHocTb, TaK KaK orrpe,aeJIeHHe
MHOfHX 3JIeMeHTOB rrpOTH:>KKH B JlaJIbHeHrneM 3aBHCHT OT 3THX <!JaK-
1'OpOB.
1. YCTaHOBJIeHMe rpynrrbI o6pa6aTbIBaeMocTH rrpoH3BoAHTCH C no..
MOIl{bIO TaOJ1. IT! rrpHJIO}KeHH5I no MapKe H TBepJI.OCTH MaTepHaJI8
3arOTOBKH. ECJIH B Ta6JIHlI.e HeT 3a,aaHHoH MapKH MaTepHaJIa, TO
rpynrry o6pa6aTbIBaeMOCTH Ha3HaqalOT ,aJI5I HaH60JIee 6JIH3KOH no Xli..
MHqeCKOMY COCTaBY H TBeplI.OCTII MapKH MaTepHaJIa, HMelOrne:HCH B
Ta6JIHll.e.
2. fpyrrny KatJeCTBa npOT5IHYTOH: rroBepxHocTH YCTaHaBJIHBalOT C
nOMOll.'(bIO Ta6JI. IT2 npHJIO)KeHHH no KBaJIHTeTY H napaMeTPY Illepo-
XOBaTOCTH nOBepxHocTH oTBepCTH5I, 3a aHHoro qepTe}l{OM Ha ,aeTaJ1b.
IlpH rrpoeKTHpoBaHHH KOM6HHHpOBaHHOH: rrpOT5I)KKH C TBepJI.o.
CITJIaBHWM 6JIOKOM B KaqeCTBe HCXOJ(HWX aHH X A H onpe,aeJleHH
rpynnbI KaqeCTBa o6paoOTaHHOH: rroBepxHocTH ,L{OJI}KeH rrpHHHMaTbcSI
110 Ta6JI. IT2 rrpHJIO)KeHH5I rrapaMeTp IIIepoxoBaTocTH IIoBepxHocTR
nOCJIe o6paooTKH pe)KyrnHMH 3YOb5lMH.
3. MaTepHaJI pe:>KYIII.eu qaCTH rrpOTSI}KKH BbI6HpalOT B 3aBHCHMOCTH
OT rpyrrrrw o6paoaTwBaeMocTH H THna npOH3BO,L{cTBa no Ta6JI. n3
np HJIO:>KeHH5I.
4. ITpOTHLKKH H3 6blcTpope}l{yrneH: CTaJIH )J.HaMeTpoM ,no 15 MM II
npOT5I>KKH H3 XBf Bcex pa3MepoB H3rOTOBJI5IIOT ue bHbIMH; HaMeT-
pOM 15-40 MM - cBapHbIMH; HaMeTpoM oOJ1ee 40 MM - cBapHbIMII
HJlM C60PHbIMH (XBOCTOBMK BMeCTe C rrepe,lJ,HeH rneHKoH, rrepeXO,L{HbIM
KOHYCOM H qaCTbIO rrepe.n.HeH HarrpaBJl5IIOrneii COe,L{HHHIOTC5I C paootJe:ti
qaCTblO npH nOMOll.'(H pe3bobI). CBapHBalOT XBOCTOBRK co CTep}KHeM
npOT5I)KKH no llleiiKe Ha paCCT05lHHH 15-25 MM OT HaqaJIa nepexo.ll-
Horo KOHyca.
50
MaTepHaJI XBOCTOBHKa - CTaJIb 45X HJIH 40X. THII XBOCTOBHKa
BbI6HpalOT B 3aBHCHMOCTH OT HMelOllI.erOCH Ha CTaHKe 11aTpOHa. ,[{JUI
CTaH,l(apTHbIX XBOCTOBHKOB pa3MepbI npHHHMalOT 110 rOCT 4044-70..
P a3MepbI CTaH,lI.apTHbIX XBOCTOBHKOB npHBeJI.eHbI B TaOJI. n4 npnJIo"
:/KeHH5I.
4T06bI XBOCTOBHK CBo6o,lI,HO npoxo,U.HJI qepe3 oTBepcTHe B 3aro-
TOBKe H B TO :>Ke BpeM5I ObIJI )J.OCTaTOqHO 11pOqHbIM, AH3MeTp ero BbI-
OHpaIOT no Ta6JI. IT4 11pHJIO)KeHH5I 6JIH)KaHlIIHM MeHbIllHM K ,lI,HaMeTpy
OTBepCTHH )J.O npOT5IrHBaHH5I. CHJIa, ,L{OnYCTHM a51 npOqHOCTbIO XBOCTO-
BHKa, paCCqHTbIBaeTCH no cpopMYJle
Pxo==Ia]pFolH (3.1)
r,lI,e [Ia]p - JI.011ycTHMoe Hanp5l>KeHHe IIPH paCTH)KeHHH, MIla; Fon-
llJ10II.l.a):lb OIIaCHoro CeQeHH5I XBOCTOBHKa, MM 2 .
ITJIOlII.a,lI,H on aCHbIX CeqeHHH CT aH,lI,a pTHbIX XBOCTOB HKOB rrp HBe,lI,eHbt
B rOCT 4044-70 ,L{JI5I XBOCTOBHKOB H3 6bICTpOpe)KymeH: CTaJIR
[a]p=400 MIla; ,lI,JI5I XBOCTOBHKOB H3 CTaJleH XBf H 40X a]p=
=300 Mna.
ECJIH Bb16paHHoMY ,lI.HaMeTpy XBOCTOBHKa cooTBeTcTByeT CMJIa IIpO-
T5IrHBaHH5I, ,lI,OnycTHMa51 no YCJIOBHIO ero npOqHOCTM H 3HalIMTeJIbHO'
06JIblllaH, qeM THrOBoe YCHJIHe, TO ,lI.MaMeTp XBOCTOBHKa MO}l{HO YMeHb-
IIIHTb. B 3TOM CJIyqae XBOCTOBHKY rrpMHHToro ,lI,H3MeTpa JI.OJl}l{Ha COOT-
BeTCTBOBaTb CHJIa, .n.onYCTHMaH rrpOqHOCTbIO ero onaCHoro CeqeHHH,
HeCKOJIbKO 66JIbIIlaH, qeM THrOBaH CHJIa CTaHKa.
5. Depe,lI,HHH: "y H 3a,lI.HHH a, yrJIbI BbI6HpalOT no TaOJI. Il5 IIpHJIO-
}l{eHHH. ITepeLlHHH: yrOJI BbIoHpaIOT B 3aBHCHMOCTH OT rPY11I1bI oopa-
oaTbIBaeMocTH Ii BH)J.a 3y6beB.
6. CKOpOCTb pe3aHHH BbIoMpalOT no Ta6JI. Il6 rrpHJlO)KeHHH B 33"
BMCIiMOCTIi OT THrra rrpOH3BO,l{CTBa, rpYIIIIbI K31JeCTBa H rPYIIIIbI oopa-
63TbIBaeMOCTH H IIpOBep>IJOT no xapaKTepHCTHKe CTaHKa. ECJIH Ha
CTaHKe He npeJI.YCMOTpeHa TpeoyeMa51 CKOpOCTb, TO 11pHHHMaIOT ,ltJIH
paCqeTa HMeIO yIOC5I CKOpOCTb.
7 TIpH onpe e eHHH nO aqH qepHOBWx 3y6beB no cpe HeH Hapa-
60TKe MeiK.l1.Y OTKa38MH Szc CHaQaJI8 YCTaHaBJIIiBaIOT HapaooTKY IJHC--
TOBOH qaCTH no Ta6JI. IT7-IT16 rrpHJIO)KeHH5I ,l(JI5I npHH5ITOM B TaOJI. TIfi.
npHJIO eHHH CKOpOCTH pe3aHH npH MaKCHMaJIbHOH rrOLlaqe qHCTOBWX
3yobeB 0,02 MM ITo.naqy qepHOBbIX 3y6beB BbI6HpaIOT H3 YCJIOBHH
paBHoH CTOH:KOCTH QepHOBOi1 H lIHCTOBOH qaCTeH rrpOT5I KM no TeM }l{e
npHJIOlKeHH5IM ,l{JIH TOH 1Ke CKOpOCTH pe3aH.H5I Ii rrpHHHMalOT JIeBee
)KHPHOH JIOMaHOH: JIHHHM B Ta6JI. TI7-TI16 npHJlOLKeHH5I. Hapa60TKa
lIepHoBbIX 3yobeB ,lJ,OJI)KHa 6bITb paBHa Hapa60TKe QHCTOBbIX 3y6beB
HJIH HeCKOJlbKO 60JIblIIe ee.
BbI6paHHbIe no.u.aQH qepHOBbIX 3yobeB H3 YCJIOBH5I paBHoH CTOH-
KOCTH rrpH npoTHfHBaHHH oTBepcTIiH I-H Ii 2-H rpynrr KaqeCTBa B 38-
rOTOBKax H3 B5I3KHX MHfKHX MeTaJIJIOB (I, II, III H X rpynrrbI oopa-
6aTbIBaeMocTH), a TaK)Ke H3 XPYI1KHX MeTaJIJIOB (VI, VII, VIII H IX
rpynnbI oopa6aTbIBaeMocTH) BO H36e)KaHHe BbIpbIBOB, pBaHHH 11 CKO-
\II
OB Ha IIPOTHHYTOH nOBepxHocTH cneAyeT OrpaHHqHBaTb B COOTBeTCT-
BRR C Ta6JI. n 17 npRJI01KeHHH.
51
nOrrpaBOQHble K03cpcpHLIJleHTbI Ha CpeAHlO1O HapaOOTKY Me>K.llY OT"
Ka3aMH 6epYT H3 TaOJI. n 18 npHJIO)KeHHH.
8. rJIy6HHY cTPY>KeQHOH KaHaBKH h, HeOOxOJJ;HMOH JIH pa3Meme..
HHH CTPY.>KKH npH nO 'beMe qepHOBbIX 3yobeB Szc, onpe,neJIHIOT IIO
<popMYJIaM:
u
.lI.JIH CJIHBHOH CTPYLKKH
Iz = 1, 1283Vl K lsSzc, (3.2)
AJISI CTPY}KKH HaAJIOMa
h==O,8917 V K IsSzc'
(3.3)
r,ne is - cYMMapHaH JIHHa npoTHrHBaeMblx yqaCTKOB, MM.
PeKOMeH,nYIOTCH CJIeJ{YIOInHe 3HaQeHHH K ,nJIH CTaJIeH BCeX rpynn
H aJIIOMHHH5I: X rpynnbI o6pa6aTbIBaeMOCTH K =3 ( onycKaeTcH K =
=2,5); VI, VII, VIII II IX rpynn oopaoaTbIBaeMocTH K =2,5 .(J1onyc-
KaeTCH K =2).
Do paCqeTHoMY 3HaQeHHIO h BbIoHpalOT H3 TaOJI. DIg IIpHJIO:>KeHHH
6JIH}KaHllIee OOJIblIIee 3HaqeHHe rJIyoIIHbI cTpYJKetIHOM KaHaBKH.
OCTaJIbHble pa3MepbI cTpy*eqHOH KaHaBKH (b , R, r) npHHIIMalOT H3
Toro lKe npHJIO}{{eHHH.
,QJIH 06eCneqeHHH ,nOCTaTOtIHOH 2KeCTKOCTH rrpOTH}KeK, IIMelOInHX
JI.HaMeTp CeQeHH5I no ,nHy CTPYlKeqHOM KaHaBKH MeHblIIe 40 MM, Reoo..
XO,lI.HMO, qTOObI rJIy6HHa cTpy}{{eQHOH KaHaBKH:
h A{ == (0,2 --;- 0,23) Do. (3.4)
MeHblIlee 3HaqeHHe K03<pcpHLtHeHTa B cpopMYJIe (3.4) BbI6HpalOT rrpH
Do 20 MM. ECJIH h m OOJlblIIe BbIopaHHoro TaOJIHtIHOrO h, TO Heooxo..
.QHMO, QTOObI Szo=rSzc. ECJIH hm<h, TO JLJIH pa3Me eHHH CTPY}KKII
nO,lI.aqa ,LI.OJI./KHa 6bITb Y IeHbweHa
u
J(JIH CJIHBHOH CTPYlKKH
2
h >K.T
Szo:::::=O,785 ;
Kls
(3.5)
JIH CTPYiKKH H8,nJIOM a
2
h)K.T
S zO ==:::. 1,267 ,
Kls
(3.6)
r,ne h m . T IIpHHHMalOT OJIHiKaMUIeH MeHblIIeH K h m no TaOJI. n 19 rrpH"
JIOJKeHH5I.
9. War tIepHOBbIX 3y6beB to BbloHpalOT no TaOJI. I119 rrpHJIO}{{eHHH
B 3aBHCMMOCTH OT rrpHH5ITOH B rr. 8 rJIy6MHbI cTpy:tKetIHOH KaHaBKH
Ta6JI. n 19 rrpHJIO}{{eHfIH. nOCKOJIbKY o Hoii H TOM me rJIYOHHe CTPY--
}KeQHOH KaHaBKH cooTBeTcTByeT HeCKOJ1bKO 3HaqeHHH mara, TO JI.JlSl
rrepBoro BapHaHTa oepYT MeHblIlHH H3 HfIX. War Ii rrpocpHJIb rrepeXO,Ll--
HblX 3YObeB - TaKHe }Ke, KaK y qepHOBbIX.
n p H M e q a H H e. ECJlH pac4eT npoT nKKH rrpOH3BO.LlHTCH Ha 3BM, TO r JIYOHIIY
CTpYiKeQHblX KaHaSOK paCC4HTbIBaIOT He TO 1JbKO JIH HaHMeHblllero lllara 3yoa, HO
H .LlJHI OCTaJ1bHbIX B03MO)KHbIX ero 3Ha4eHHH.
52
qHC O O HOBpeMeHHO yqaCTByroIUHX B paOOTe 3YObeB HaXO HT no
(pOpMy e
Zp= Lmax + 1. (3.7)
to
ECJIH zp rro yqaeTCH Heu.eJIbIM lIHCJIOM, TO POOHYIO qaCTb He ytIH"
1'bIBaIOT.
ilpH IIpOT5IrHBaHHH rrpepbIBHCTbIX OTBepCTHM Zp IIO,[{CtIHTbIBaIOT
JlJIH Ka}K OrO yqaCTKa H oKpyrJIeHHbIe HX 3HaqeHHH CYMMHpyIOT:
Zp=== Zpl + Zp2+ Zp3 + ... (3.8)
MHHHMaJIbHO OIIycTHMoe zp=3. B HCKJIlOtIHTeJIbHblX CJIyqaHX (IIpH
OtIeHb KOpOTKOH: JIHHe rrpOT5IrHBaeMoro ytJacTKa) orrycKaeTcH
Zp == 2.
10. CHJIa pe3aHHH OrpaHHtIHBaeTCH THroBoH CHJIOH CTaHKa PCT HJIH
npOqHOCTblO IIpOTHmKH B onaCHblX CetIeHHHX no XBOCTOBHKY P XB H no
BnaJI.HHe rrepe rrepBbIM 3y60M P O.II. HaHMeHbIIIYIO H3 3TH X CHJI CJIe..
JI.yeT npHHHMaTb B KaqeCTBe MaKCHMaJIbHO onYCTHMOH CM.nbI pe3aHH5I:
p o.n == (0,8 -+- 0,9) Q,
(3.9)
r e Q - nacrropTHaH THfOBa5I CHJIa CTaHKa.
BeJIHQHHY P XB paCCqHTbIBaroT IIO cpopMYJIe (3.1), a P O.fl - 110 <pop..
MYJIe
P 0.11 === F o..n [a ]p,
(3.10)
rJI.e
F 0.[1 == 0,785 (Do - 2h)2.. (3.11 )
Ll H npOTH)KeK Ha ObICTpOpe)KYllI.eii CTaJIH HaMeTpOM o 15 MM
06bIQHO npHHHMaIOT [a]p==4007500 MIla; ,LLHaMeTpoM 60,nee 15 MM-
Ia}p==3507400 Mila; JI5I npOT5I)KeK H3 XBf (a]p==250 Mrla.
11. l.JHCJIO 3yobeB B rpynne Zc MO>KeT MeHHTbC5I OT 2 ,[{O 5; era
oopeJJ.eJIHIOT no cpopMYJIe
nDqoz pK pM.K poK PKK Pp
Zc==
Pmax
,
(3.12)
r e qo rrpHHHM810T no TaOJI. n20 npHJIO>KeHHH B saBHCHMOCTH OT SZC
Ii v; nOnpaBOqHbIe K03<pq H1 ll.HeHTbI KPM, Kpo, KPK, Kp p - no Ta6JI. [121
npHJ10>KeHHH.
ilorrpaBotJHbIH K03cpcpHIl.HeHT Kpo 3a alOT B aaBHCHMOCTH OT BH a
CO)l(, KOTOPYIO KOHCTPYKTOP HaSHaqaeT IIO TaOJI. n18 npHJIO>KeHHH.
ECJIH nO,[{CtJHTaHHoe IIO cpopMYJIe (3.12) Zc <2, TO aJIbHeHIIIHe
paCqeTbI Be YT JIH Zc = 2. ECJIH ZC - p06Hoe qHCJIO, OOJIbllIee JI.BYX,
TO ero oKpyrJIHIOT o OJ1J:1}{{aHIllerO 60JIbIIlerO qHCJIa ( O 3,4 HJIH 5).
ECJIH ZC >5, TO rrpH Zc == 5 onpe eJI5IIOT qo:
qo===
zcPrnax
nDz pK PMK poK PKK Pp
.
(3.13 )
53
113 Ta6JI. n20 npHJIOlKeHH5I 6epYT HOBOe 3HaqeHHe nOAa1.IH no tSJIH"
1KaiirneMY 3HaQeHHIO qo, MeHbIIleMY, qeM paCtIeTHoe.
fIpn paClIeTe H8 9Blv\ 3TY OnepallJllO He BbInOJIH5IIOT, a paCCtIHTbI-
BalOT HOBbIe BapHaHTbI npH nO,D.atIe, YMeHbUIeHHOH Ha 0,01 MM.
12. CHJIY npoTHfHBaHHH OIIpeLleJI5IIOT no <popMYJIe
'ItDqozpK PMK poK PKl\ Pp
p= . (3.14)
Zc
13. I10JIHbIH rrpHnycK Ha HaMeTp p8Cnpe eJIHIOT Me1KJ{Y qepHOBbI-
MH, rrepeXO,D.HbIMH H qHCTOBbIMH 3YObHMH.
IloJIHblH npHrrycK
A == Dmax - DOmin.
( 3.15)
IlpHrrycK H8 qepHOBhIe 3y6bH
Ao==A-(An+Aq), (3.16)
r e npHnycK Ha nepexo Hble 3y6b An oepeTCH H3 Ta6JI. n23 npHJlO-
:>KeHHH, Ha qHCTOBbIe 3y6b5I - A-q - H3 Ta6JI. 022 rrpHJIOLKeHH5I.
14. LIHCJIO rpynrr lIepHOBblX 3y6beB onpe.I(eJI5IIOT no cpopMYJIe
io= Ao . (3.17)
2S zo
ECJIH io nOJIYtIaeTCH ,apOOHbIM, era oKpyrJIHIOT .lI-O 6JIH)KaHillerG
MeHbllIero Il.eJIOfO tIaCJI8. IlpH 3TOM OCTaTOtIHYIO qaCTb rrpHrrycKa oIIpe-
.neJIHIOT no CPOPMY JIe
AOCT==Ao- 2S zo i o . (3.18)
B 3aBHCHMOCTH OT 3HaIIeHHH OCTaTOQHbIH rrpHnycK MOLKeT ObITb
OTHeceH K qepHOBOH, rrepexo HoH HJIM lIHCTOBOM lIaCTHM.
ECJIM nOJIOBHHa OCTaTOllHoro npHnycKa npeBblllIaeT nO):(1)eM 3y6beB
na CTOPOHY rrepBoH nepexo HoH rpynIIbI, TO ,QJIH cpe3aHH5I ero Ha3Ha-
q8IOT OJl.HY Jl.OnOJIHHTeJIbHYIO rpYIIrry qepHOBbIX 3YObeB. TIOJI.'beM 3y6beB
Ha rrepeXOJI.HOH qaCTH BbI6HpalOT H3 TaOJI. Il23 npHJIOLKeHHH.
ECJIH 1/2 A OCT MeHbllie nO DeMa Ha CTOPOHY nepBoH rrepexo HoH
rpyrrrrbI, HO He MeHee 0,02-0,03 MM, TO OCTaTOQHbIH npHIIYCK JI.06aB-
JI5IIOT K rrpHrrYCKY Ha nepeXO HYIO qaCTb. ECJIH Me 1/2 A OCT <0,02-:--
-:--0,03 MM, TO OCTaTOQHbIH npHnYCK CYMMHpyeTcH C npHnYCKOM Ha
tIHcTOBbIe 3y6b5I, qHCJIO KOTOpbIX COOTBeTCTBeHHO YBeJIHQHBaIOT. MHK-
pOHHaH QaCTb OCTaTOtIHOrO rrpl1rrYCKa CYM 1HpyeTcH C npMnYCKOM Ha
noc.ne HHe QHCTOBble 3y6b5I. TIoA'beMbI 3YObeB Ha 1.J:HCTOBOH qaCTH BbI-
6HpaIOT H3 Ta6J1. il22 npHJIO}KeHH51.
15. 4HCJIO tIepHOBbIX 3y6beB
Zo === lOZco,
(3.19 )
r.ll.e io - rrpHHHToe OKOHqaTeJIbHO qHCJIO rpynrr lIepHOBbIX 3yobeB rrOCJIe
pacrrpe e eHHH OCTaTOtIHOrO IIpHIIycKa.
"4HCJIO nepexo HbIX, tIHCTOBbIX H KaJIH5pYIO HX 3y6beB BbIoHpalOT
H3 TaOJI. I123 H TI22 npHJIO}KeHHH H KoppeKTHpylOT B 3aBHCHMOCTH OT
54
p aCnpeJLeJIeHHH OCTaTOtJHOrO npHrrYCKa. 06mee tlHCJIO BCeX 3YObeB
npOTH1KKH
z=zo+ZI1+Zq+ZK. (3.20)
16. ,[lJIJIHa pemymeM qaCTH npOT5I>KKH
Lp=lo+ln+lq+IK=io(zo+zn>.{- t\{+ tK' (3.21)
r e tq H tK - CYMMbI rrepeMeHHblx llIarOB COOTBeTCTBeHHO tllICTOBbIX
H KaJIH6pYIO HX 3y6beB.
IIlarH qHCTOBbIX H KaJIHopYIOInHX 3y6beB - nepeMeHHhIe, COCTO.R-
Ill.He H3 Tpex 3HaqeHHH. MeHbllIHH mar t l npHHHMalOT JI3 Ta6JI. il24
npUJIO)KeHH5I B 3aBHCHMOCTJI OT llIara tJepHoBhIX 3yobeB to. 3,LleCb >Ke
.,naHbI 3HaqeHH5I cpeAHero JI 60JIbllIerO rnara (t 2 II t 3 ).
I1epBbIH mar Ha qHCTOBO:H qaCTH (Me)l{ y nepBbIM H BTOpbIM qJICTO-
BbIMH 3y6b.HMH) HMeeT 60JIbllIee 3Ha1JeHHe - t 3 .
I1pOcpHJIb cTPY}KeqHOH KaHaBKH JI.JISI Bcex Tpex llIarOB Q,ltHHaKO-
BbIH (T. e. OLlHHaKOBbI h, b, r, R), BbI6HpalOT H3 Ta6JI. TI19 npJIJIo}l{e-
fiftH no MeHbllIeMY IUary t 1 H cpe HeH rJIyoHHe rrpocpHJI5I.
B Tex CJIyqaHX, KorLla nOJIY1JaeTC5I HemeJIaTeJIbHO MaJIaH IIIHpHHa
3y6a, CHH)KalOmaH rrOJIHhU1 nepHO CTOHKOCTH, ee CJIe yeT YBeJIHqIiTb
rrYTeM H3MeHeHHH npocpHJ1H cTpY)KeqHOH KaHaBKI1 B npe.lI.eJIax BblopaH-
Horo llIara fl. DpH 3TOM Heo6xo,aHMO npOBep5lTb nOMe aeMOCTb
('TPYJKKH B KaHaBKe npH no,aaqe Szq=O,02 MM.
Ha 3TOM paCtIeT nepBoro BapHaHTa 3aKaHtIHBaeTCH.
ilOCJIe,n.YIOInHe Ba pHaHTbI CqHTalOT AJIH YMeHbllIalOInIIXCH no aq
qepe3 0,01 MM .lI.O Szo=0,03 MM. I10pH OK paCqeTa nOCJIe,aYIOInHX Ba-
pHaHTOB TOT )Ke, qTO Ii JI.JI5I rrepsoro (c JI.OIIOJIHHTeJIbHbIM H Ba-
pHaHTaMH), Ha1.J:HHaeTCH C n. 8, KOHqaeTCH n. 16 (T. e. onpe.lI.eJIeHHeM
)I. lHHbI peLKyr.qeH qaCTH).
ITpH pyqHOM CqeTe OOWQHO orrO HHTe bHwe BapHaHTW nH Bcex
marOB B Ta6JI. n19 npHJI02KeHHH rrpocpH.neH npH npMHHToM r.nyoHHe
cTpy}{{e1JHOH KaHaBKH He npOC1JHTbIBaIOT, a OCHOBHbIe BapHaHTbI BBH Y
60.HbllIoro OO'beMa BbIqHCJIeHHH onpeJl.eJIHIOT CKaQKOo6pa3HhIM H3MeHe...
HHeM nOAa1.J:H nYTeM YBe HqeHHH 1JHCJIa OAHOBpeMeHHO paOOTaIDInHX
3y6beB Zp Ha e,aHHHIJ.Y JI.JIH Ka}K.lI.OrO nOCJIe YIDrnero BapJIaHTa, T. e.
Zp + 1, zp+2, zp+3 If T. ,l{., r,ae zp onpe,neJIeHO B II. 9. 3aTeM H3 cpop-
l\11Y"TJbI (3.7) HaXO HTCH mar to; no Ta6JI. 019 npHJIOmeHHH OrrpeLleJISI-
lOT rJIy6HHY npocpHJI5I, COOTBeTCTBYIOmYID 3TOMY rnary; no cpopMYJIaM
(3.5) HJIH (3.6) JI.JIH HaH,QeHHoH r JIYOHHbI paCCtIJITbIBaeTcH HOBoe
3HaqeHHe IIO)I.aqH. C n. 11 paCqeT HOBoro BapHaHTa npO.lI.OJI>KaIDT KaK
)1.JIH nepBoro BapHaHTa.
I1p e .lI. B apHTeJIbHOe orrpeJI.eneHHe rrO aqH no MeTOLlY paBHoH cToA-
KOCTH HCKJIlOqaeT Te BapHaHTbI, B KOTOpbIX MOrJIH ObI 6bITb CJIHlIIKOM
60JIbIIlHe nOjJ:aIJH, KOTopble CHH1KaIOT HapaOOTKY rrpOT.H2KKH. )KeJIa-
Te T1bHO, qTOOhI npOTH)KKrl HMeJla OTHOCHTeJIbHO He6oJIbWYlO JIHHY
L p , OOJIbllIYIO llIHPHHY 3y6a b, B03MO}{{HO MeHhWYIO no,aaqy qepHOBbIX
3y6beB Szo, HaHMeHbllIee tIRCJIO Bcex 3y6beB Zmln.
I10cne Bw60pa OITTHMaJIbHOrO BapHaHTa COCTaBJI eTCH TaonHua
,AHaMeTpOB 3y6beB H HaXO,1.!HTCSI Bce OCTaJIbHbIe napaMeTpbI npOTjJ)J{KH.
55
17 LLRaMeTp KaJIR6pYIOI.1LRX 3y6beB D H Ii ,lI.RaMeTp nOCv1Je,lI.HerO
QIfCTOBOro 3y6a MO)KHO npHHHMaTb paBHbIMH MaKCHMaJIbHoMY B rrpe-
.lleJIax JI.OnycKa ,lI.H3MeTpy OTBepCTHH DR = Dmax.
B OT,lI.eRbH X cny aHx DR YCTaHaBRHBaeTCH B pe3YRbTaTe OOMepa
eTaneH rroc e npOTHrHBaHHH (TOHKOCTeHHWe eTa H, eTaRH cno*-
HOH KOH<pHrypa HH, BbICOKOH H H OqeHb HH3KOH TBep OCTH H p.).
)10IIYCKH Ha H3rOTOBReHHe 3YObeB npOTH)KKH Cne.ayeT npMHHMaTb
no rOCT 9126-76.
18. ,.QJIH Ha3HaqeHHH qHCna BbIKPY)KeK H HX mHpHHbI Ha tJepHo-
BbIX 3YOb5IX BeCb nepHMeTp CTPY}KKH, cpe3aeMbIH OAHOM rpynIIoH, pa3-
AenHIOT Ha paBHbIe 1JaCTH Me)KJlY 3y6bHMH rpynnhI (CM. pHC. 3.1). Ha
Ka)KAbIH 3y6 rpyrrllbI rrpHxoAHTCSl qaCTb nepHMeTpa:
!tD
lz == (3.22)
Zc
CTpY)KKa, cpe3aeMaH Ka*JLbIM ay6oM, paBHoMepHo pacnpe,aeRHeT-
CH MeLK.lI.Y ero HeCKonbKHMH pe)KY HMH ceKTopaMH, paCIIOJIOmeHHhIMH
Ha paBHoM paCCTO HHH .apyr OT ,apyra no nepHMeTpy 3y6a H pa3 e-
JIeHHbIMH Me)K,lI,Y C060H BbIKpYLKKaMH.
4HCJIO pe}KYIU.Hx ceKTopOB, a 3HatJHT, H BbIKpY}KeK onpe.aeJI5I10T no
<popMYJIe
[z
E
r,L{e E - IlIHpHHa pe>Kyrnero ceKTopa, peKoMeH yeTcH B= (1,07
-;.-1,3)V D nH npOT5ILKeK C .lI.HaMeTpoM MeHee 100 MM H E= 10--7-
-;.-12 MM ,Z:(RH npOTH}KeK c HaMeTpoM 60JIbme 100 MM.
TIOJl.CTaBHB B CPOPMYJIY (3.23) 3HaQeHHSI lz H B, IIOJIyqHM:
Jl.nH npOTH)KeK HaMeTpoM MeHbIlle 100 MM
N = (2,4 + 3,1) Vi) ; (3.24)
N=
(3.23)
Zc
.a SI npOTH}I{eK H8MeTpOM oOJIee 100 MM
N = (0,25 + 0,3) D
Zc
(3.25 )
3HaqeHHH N oKpyrR5IIOT ,ao 6JIH>K8HlliHX 66JIbmHX qeTHbIX tIHCeJI.
IIlHpHHY BbIKPY}KKH OIIpe en5llOT no cpopMyne
ao= nD(zc - J) . (3.26)
Nz c
4HCJIO BbIKpY>KeK H IIIHPHHY tJepHoBbIX ayobeB MO}KHO orrpe,neJIHTb
c nOMO blO TaOJI. n25 npHJIO)KeHH5I.
Pa HYc BblKpY}KeK RB Ha3HaQaIOT B 3aBHCHMOCTH OT WHpHHbI BbI-
KPYJKKIi Ii AHaMeTpa rrpOT5I:>KKH; RB IIpHBe eHbI B Ta6JI. TI27 npHJIo.
)KeHH5I. TaM }Ke .aaHbI HaHoonbIlIHe ,L{OnycTHMbIe pa,L{HycbI IllRHcpOBaJIb-
Horo Kpyra. ,LLJIH o6eCrreQeHHH CBoOO,lI.HOrO npOXO>K)I.eHHH CTPY>KKR B
HHlKHeH qaCTH npocpHJIH BbIKPYlKKH Heo6xo HMO, QTo6bI C>3S zo .
56
19. qHCJIO BbIKpy*eK JI.JI51
nepexoAHwx H qHCTOBWX
3yobeB paCCQHTbIB3IOT (C OK'"
pyrJIeHHeM JI.O 6JIHlKaHmerO
qeTHOrO tIHCJIa) no <popMYJIe
N q = 1,45-.f D.
(3.27)
lIlHPHHY BhIKpYlKeK (MM)
Ha rrepeXO.lI.HbIX M IJHCTOB'bIX
3YOb5IX .lI.JIH 06eCneqeHH5I ne...
peKpbITHH BbIKpYlKeK pe)l(Y-
mHMM ceKTopaMH rrOCJIe.lI.YIO-
llI.HX 3YObeB npHHI1MaIOT Ha
2-3 IM MeHbille, IJeM Ha qep-
HOBbIX:
2
PRC. 3.1.
CxeMa paCIJeTa )l.JlHHhI OT nepe,IJ.HerO Topu:a
npOTH)KKH no nepBoro 3y6a:
1 - nepeJI.JHHA XBOCTOBHK; 2 - naTpOH; 3 - OTIOpHaH
nJIHTa; 4 - nepexo,nHag BTYJIKa; 5 - 3arOTOBKa
an == a o - (2 -;- 3). (3.28)
4HCJIO BbIKpYLKeK H UIl1pHHY HX MOLKHO npMHHMaTb no TaOJI. TI26
npHJIO>KeHH5I.
DpH rpynnoBoM nocTpoeHHH rrepeXO.lI.HbIX H qHCTOBbIX 3yobeB
(zc.q=2) .lI.HaMeTpbI HX (BHYTPH O.lI.HOH rpynnbl) O.lI.HHaKOBbI. BbIKPY>K-
KIf Ha nepeXO HbIX H QHCTOBbIX 3YObHX HaHOCHT Ha Ka>K.lI.OM 3yoe H
pacrrOJIaraIOT B waXMaTHOM IIopHJ(Ke OTHOCMTeJIbHO npe,[{bIJI.yrnero
3yoa. I1pH OqeHb TOIJHOM BblnOJIHeHHH JI.HaMeTpOB nepeXO,lI.HbIX H IJH-
CTOBbIX 3y6beB BTopble 3y6b5I B rpynne MO)KHO JI.eJIaTb KpyrJIbIMM (6e3
BbIKPY)KeK), KaK Ha tIepHOBbIX, HO oe3 3aHHIKeHHH no JI.HaMeTpy. Pa-
.lI.HYC BbIKpYIKeK Ha nepeXO,LLHhIX H IJI1CTOBbIX 3YOb5IX onpe.lI.eJI5IIOT no
TaOJI. TI27 rrpHJIOIKeHR5I.
20. ,[{HaMeTp rrepeJI.HeH HarrpaBJI5IIO eH rrpHHIIMalOT paBHbIM HaH-
MeHbilleMY AHaMeTpy oTBepcTHH o npoTHrHBaHH£ C noneM AonycKa
no e8. B Tex cJIYIJa5lx, KOr,LLa y oTBepCTH5I rro.lI. npoTHrHBaHHe eCTb
60JIbIIlHe OTKJIOHeHH5I OT I1.HJIHHJI.pHIJeCKOH cpOpMbI HJIH Kor.lI.a oTBep-
CTHe npeJI.BapHTenbHO He oopaOOTaHO nocne lliTaMnOBKH H OTRHBKH,
lIepe.lI.HIOIO HarrpaBJI£IOIII.YIO BbIIIOJIHHIOT C TpeMH IIIHpOKMMH JIbICKaMH,
pacrrOJIO)l{eHHbIMH noJI. yrRoM 120 0 .lI.pyr K JI.pyry, C TaKHM paCqeTOM,
IlTOObI IlIHpHHa OCTaBIIIHXCH IlJIJIHH,n:pHIJeCKHX nOBepxHocTeif 6bIJI8
paBHa 8-12 MM.
,rrJIHHY rrepe)];HeH HanpaBJIHIOIIJ;eH lrr.H BbIOHpaIOT B 3aBHCHMOCTH OT
OTHOllIeHHH RHHbI npOTHrMBaHHH K JI.HaMeTPY npOTH>KKH: npM liD R
> 1,5 lIT H==0,75l, npH ljD< 1,5 lrr.H=l.
21. ,LLJIHHa nepeXO.lI.HOro KOHyca BbIoHpaeTcH H3 TaOJI. D28 npHno"
LKeHHH.
22. PaccToHHHe OT nepeJI.HerO TOpu.a npOT5ILKKH o nepBoro 3yoa
onpeJI.eJI5IIOT no cpopMYJIe (pHC. 3.1)
L I == II + l2 +l.s +.l + 25. (3.29)
57
Pa3Mep l] npHHHMalOT B 3aBHCHMOCTH OT ,l1JIaMeTpa XBOCTOBHKa
Dxn, MM 12-20 22-28 32-50 55-70
iI, MM 115 150 160 205
,L{JI5I npOTH}KHbIX CTaHKOB 7E64, 7665, 7E66, 71566-1, 7623, 7633
7723 1 2 = 15 MM, 13=50 fvIM, a JI51 CTaHKOB 7555, 7E56, 7E57, 7733
1 2 ==25 MM, l3=40 MM.
23. ,L(HaMeTp 3a HeH HanpaBJIHIO eH D 3 . H npHHHMaIOT paBHbIM
HaHMeHbllieMY rrpeAe bHoMY AHaMeTpy npoT HYTOfO oTBepcTHH C no-
.HeM ,LLOrrycKa no f7, a B HeKoTophIX cJIYQa5Ix - no f9.
PeKoMeH yeMa51 JIHHa 3aJI.HeH HanpaBJIHIOIneH IIpJIBe eHa B
Ta6JI. n29 npHJIOLKeHHH.
T5I}KeJIbIe HJIH ,QJIIfHHbIe npOTH)KKH, a TaKLKe Bce rrpOT5IJKKM, pa6o-
TaIOmMe B aBTOMaTHtIeCKOM UMKJIe, H3rOTOBJIHIOT C 3a,[{HHMH XBOCTO-
BHKaMH, KOTopbIe MorYT 6bITb TaKHMH LKe, KaK rrepe,lI.HHe, HJIH MeHb-
llIHX pa3MepoB, TaK KaK OHM CJIY)KaT TOJIbKO )l.JI5I nO,LtQep}KKH npo-
TH)KKH.
PeKOMeHJl.aII.HH no ,LLJIHHe 3aJl.HHX XBOCTOBHKOB npHBe eHbI B
TaOJI. n30 npHJIOLKeHHH. 3a)l.HHe XBOCTOBHKH MorYT npHBapHBaTbCH
HJIH BBepTbIBaTbCH; HX H3rOTOBJI5IIOT H3 CTaJIeH 40X HJIH 45X.
24. 06I.I."(aH ,LLJII1Ha npOT5I)KKH paBHa CYMMe ,LLJlHH rrepe HeH: qaCTII
(OT nepeLlHero TOPUa o nepBoro 3y6a) Lt, pe)l{YIneH qaCTH L p , 3a -
Hei1 HarrpaBJIHIOInei1 1 a . H H 3aJI.HerO XBOCTOBHKa la.xB:
L == L 1 + Lp + 13.H+ l3.XB. (3.30)
06Ina51 .llJIHHa rrpOT5I}{{KH He OJI)KHa npeBbIllIaTh xo a IlITOKa npo-
TH)KHOrO CTaHKa, HaH6oJIbllIerO paCCT05lHH5I Me)K,LLY neHTpaMH Kpyr.no-
IlIJIH<pOBaJIbHOrO II 3aTOQHOrO CTaHKOB, r JIYOHHbI BaHH HJIH lll2.XT ,ZI,.H5I
HarpeBa rro)J. 3aKaJIKY H ornYCK. B npOTHBHOM CJIyqae HY)KHO CIIpoeK-
THpOBaTb KOMnJIeKT H3 ,lI.BYX npOTH)KeK.
npHMep paC1JeTa npOTSlJKKH
HcxOAHbIe ,Il.aHHbIe. 1. IIpoTHrHBaeMaH 3arOTOBKa: fa-
TepHaJI - CTaJIb 20XH3A; TBep ocTb IIPH npOTHrHBaHHH HB 207-241
3arOTOBKa - IIOCJIe oTIIycKa; OTBepCTHe IIO,L( rrpoTHrHBaHHe o6pa6oTa-
HO; HaMeTp oTBepCTH5I o npOT51rHBaHH5I (M f) d o ==63,6H12+o,19; ,LlHa-
Merp OTBepCTHH nOCJIe npOT5IrHBaHH5I (MM) D=65H7+ o ,030; napaMeTp
lllepoxoBaTOCTI1 nOBepxHocTH Ra= 1,25 MKM; .II.JIMHa rrpoTHfHBaHH5I
1=120- 1 M \1:.
2. CTaHoK: ropH30HTaJIhHO-rrpOT5I)KHOii, MO)leJIh 71356; T5IfOBa51
cY!JIa CTC!.Hi<a Q == 196 200 H; :tv13KCHMaJIbHaH .llJIHHa XO,LLa lUTOKa Lmax =
= 1600 MlVl; )I.Hana30H pa60QHX CKopocTei1 1,6-11,5 M/MHH; COCTOH.
HHe CTaHKa - y):{oBJIeTBOpHTeJIhHOe; npOTSI:>KKa 3aKpenJIHeTCH B 6bICT-
pOCMeHHOM aBTOMaTHqeCKOM rraTpoHe.
3. XapaKrep I1pOM3Bo):{cTBa - MaccoBbIH.
4. ,L{JIHHa rrpOT5I)l(KI1, ,rr.orrycTHMaH B03MO)KHOCTHMH HHcTpYMeH-
TaJIhHOrO aexa Ii 3aTOQHOrO OT.D.e,J1 eHII5I , He oOJIee 1500 MM.
58
nOpH,lI.OK paCqeTa. 1. YCTaHaBJIHBaeM rpynrry o6pa6aTbIBaeMocTH
c nOMOIll.blO Ta6JI. rI 1 npHJIOLKeHHH: CTaJIh 20XH3A C TBep ocTblO
HB 207-241 OTHOCHTCH KO II rpynne 06paoaThIBaeMocTH.
2. Y CTaHaB..TIHBaeM rpynny KaqeCTBa no Ta6JI. rI2 npHJIO>KeHH5I.
napaMeTpa rnepoxoBaTocTH nOBepxHocTH Ra= 1,25 MKM .lI.OCTH1Jb
TpY.lI.Hee, qeM KBaJIHTeTa oTBepCTH5I H7, n03ToMY rrpHHHMaeM 1-10
rpynny KatIeCTBa no rnepoxoBaTocTH.
3. MaTepHaJI paooIJetf tIaCTH npOTH}KKM IIpHHHMaeM B COOTBeTCT-
BHH C peKOMeH.lI.a HHMH Ta6JI. rI3 npHJIO.lKeHHH - ObIcTpopeLKYI.I."(aH
CTa.Hb P6AM5.
4. KOHCTPYKUHIO rrpOT5I)KKM npHHHMaeM c npHBapeHHbIM XBOCTO"
BHKOM, MaTepHaJI XBOCTOBHKa - CTaJIh 40X. Pa3MepbI - no rOCT
4044-70 (HJIH no TaOJI. 114 npHJIO}KeHHH). ,QHaMeTp nepe.lI.Hero XBOC-
TOBHKa D XB = 50 MM, F on = 1134,1 MM 2 . CHJIY, .lI.OrrYCTHMYIO XBOCTOBH-
KOM, paCCqHTbIBaeM no cpopMYJIe (3.1), npHHHB {,cr]p=300 MITa:
P XB == 1134,1.300=340 230 H.
5. rrepe HHe H 3a.lI.HHe yrJIbI BbloHpaeM no Ta6JI. n5 rrpHJIO)KeHHH.
nepe.lI.HHH yrOJI 1JepHOBbIX H nepexo,aHbIX 3y6beB l' = 15°, a tIHCTOBbIX
H KaJIH6pYlOInHX 3y6beB 1'1 = 18° 3a.lI.HHH yroJI 1JepHOBbIX II nepexo.lI.-
HbIX 3yoheB ao=3°, lIHCTOBbIX a't!=2°, KaJIHopYIOInHX aK=I°.
6. CKOpOCTb pe3aHH5I YCTaHaBJIHBaeM no Ta6JI. IT6 npHJIO)KeHHH:
v = 8 M/MHH. 3Ta CKOpOCTb CTaHKOM 06eCrre1JHBaeTc5I.
7. TIOJI.'beM qepHOBhIx 3yobeB Szc OIIpe,lI.eJIHeM H3 YCJIOBHH paBHoH
CTOHKOCTH qepHOBOH H qHCTOBOM tIaCTeH no TaOJI. ITS rrpHJIOLKeHH5I JI.JIH
II rpynnbI o6paoaTbIBaeMocTH. BHatIa.fIe ,lI.JIH CKOpOCTH pe3aHHH v =
= 8 M/MHH H nO aqH tIHCTOBhIX 3y6beB Sz't!= 0,02 MM YCTaHaBJIHBaeM
Hapa60TKY qHCTOBOH tIaCTH: T==56 M. rIo TOM )Ke CKOpOCTH pe3aHHH H
CTOHKOCTH 1JepHOBbIX 3y6beB T = 59 M HaXOJ1.HM nOJ1.'beM qepHOBbIX
3yobeB Szo=0,18 MM Ha 3y6 Ha CTOPOHY. ,[{JI5I II rpyrrnbI o6pa6aTbI-
BaeMOCTH II I-H rpynnbI KalIeCTBa npH CKOpOCTH pe3aHH5I v = 8 M/MHH
no Ta6JI. TIl7 npHJIO)K HH OrpaHHtIHBaeM nO 'beM 1JepHOBWx 3y6heB
o Szo=O,l MM. ITonpaBOtIHbIe K03<p<pHUHeHTbI Ha Hapa60TKY nplIHH-
MaeM IIO TaOJI. ITI8 rrpHJIO)KeHHH: KTB=0,7; KTp=l; KT3=1; /(TA=l;
KTo=l; KTM=l (Ha3HaqaeM CO>K-CYJIbcpocppe30JI faCT 122-54).
Hapa60TKa C rrOnpaBOlIHbIMH K03<p<pH HeHTaMH T M.H== T MKTBKrpKT3X
X K TM K TO = 56. 0,7. 1 · 1. 1. 1 · 1 = 39,2 MM.
8. r JIYOHHY cTpY)Ke1JHOH KaHaBKH h, Heo6xo.lI.HMOM .lI.JI5I pa3Me e-
HIIH CTPY}KKH npH rrO)l'beMe Szc = 0,1 MM, orrpe eJI5IeM IIO cpopMYJIe
(3 .2), npHHH B K03<P<PH HeHT rrOMeIll.aeMOCTH K = 3; h === I, 1283 / 3 x
y x .120.0,1 ===6,7698 MM.
B Ta6JI. IT 19 npHJIO}KeHHH OJIH}{{aHIlIaH 66JIhmaH rJIyoHHa CTPY-
}KeQHOM KaHaBKH h=7 MM. Ee H npHHH IaeM .lI.JI5I .lI.aJIbHeHllIero pac-
qeTa. IlpoBepKY Ha LKeCTKOCTb npOTH)KKH He ,LLeJIaeM, TaK KaK HaMeTp
no )1;HY CTpY)KetIHOH KaHaBKH paBeH D-2h =65-2. 7 =51. _MM, T. e.
oo.nbllIe 40 MM.
9. War qepHOBbIX 3yoheB rrpHHHMaeM Ii3 TaOJI. D19 npHJIO)KeHHH.
l'aK KaK fJIy6I1He h==7 MM cooTBeTcTBYIOT HeCKOJIhKO 3HaqeHHH rnara,
TO COrJIaCHO n. 9 MeTO.lI.HKH rrpHHHMaeM MeHbwHH t o = 16 M:M - npo..
59
cpHJIb N2 11. OCTaJIhHbIe 3J1eMeHTbI cTpY1KetIHOH: KaHaBKH: b o = 5 MM;
r=3,5 MM; R= 11 MM. 4HCJIO O HOBpeMeHHO yqaCTByIOlU-HX B pa60re
3y6beB onpe,neJI5IeM no cpopMYJIe (3.7), oT6paCbIBa5I POOHYIO qaCTb:
Zp= 120/16+ 1 =8.
10. MaKCHMaJIbHO OI1YCTHMYIO CHJIY pe33HHfl 6epeM MHHHMaJIbHOH
83 Tpex PCT, P XT , POll; P cT =0,8.20000.9,81=156960 H; P XB =
=340230 H (CM. fi. 4).
BeJIHQHHY Pon onpe eJI5IeM no cpopMYJIe (3.10), a nJIOmaAb onac..
Horo CeQeHH5I - no <popMYJIe (3.11): F orr =O,785 (63,6-2-7)2= 1931 MM 2 ;
Pon=1931.400=772400 H; Pmax===156960 H.
II. 4HCJIO 3yobeB B rpyrrne Zc onpe,aeJISleM no <popMYJIe (3.12),
r,l{e qo===212 MIla JlJI5I Szo==O,1 MM H 1'=15° H3 TaOJI. TI20 npHJIO)Ke-
HH5I; zp=8; KpM=I; Kpo=l; KpH=l; Kpp=l H3 Ta6JI. n21 npHJIO-
. _ 3, 14.65 .212 . 8 . I 1 1 I _ 2 2
meHH5I, Zc - 156960 - · ·
npHHHMael\l zc=3.
12. Onpe,QeJI5IeM paCqeTHYIO CHJIY npOT5IrHBaHH5I no <popMYJIe
.( 3.14) : P = 3 · 14 .65. 212 8 . 1 I I I = 115 384 H.
13. ilOJIHbIH rrpHnycK onpe,neJISIeM no cpopMYJIe (3.15) : A =
=65,03 63,6= 1,43 MM.
n pHnYCK Ha 1JepHOBbIX 3YObSiX Haxo,nHM no <popMYJIe (3.16), r,LI.e
A n =O,14 MM H3 Ta6JI. 1123 npHJlO}KeHHSI, A =0,14 MM 113 TaOJI. Il22
npHJIO)KeHHSI; Ao= 1,43-(0,14+0,14) = 1,15 MM.
14. lIHCJIO rpynn qepHOBhlx syobeB onpe,neJISIeM no CPOPMY JIe (3.17):
- 1,15 5 75 . 5
'0= =,; 10= ·
2.0 1
,
OCTaTOtIHYIO qaCTb rrpHnYCKa Haxo,nHM no cIJ o pMYJIe (3.18): A OCT =
=1,15-2.5.0,1=0,15 MM.
TaK KaK A OCT >S:rnl, TO A OCT OCTaBJI5IeM B qepHOBOH tI3CTH H YBe-
JlHqHBaeM qHCJIO rpynrr Ha eJlHHHU;Y; io= 6.
15. 4HCJIO qepHOBhIx 3yobeB onpe eJISIeM no cpopMYJIe (3.19):
zo=6.3= 18, QHCJIO nepexo HbIx 3yobeB zu=4 113 TaOJI. Il23 npHJIOllie-
HHSI 1JHCTOB-bIX 3YObeB Zq= 12 H qHCJIO KaJIHoPYJOInMX ZI\ = 7 H3 Ta6JI.
022 npHJIO}KeHHH.
06Ill.ee tIHCJ10 Bcex 3y6beB HaXO HM no cpopMYJIe (3.20): z= 18+
+4+ 12+ 7=41.
16. ,QJIHHY pe}KYIneH qaCTH npOTSI>KKH onpeJleJlHeM no 4>opMYJIe
t(3.21); rnarH 1JHCTOBbIX H KaJIH6pYIOInHX ayobeD - nepeMeHHbIe, npH-
HHMaeM H3 TaOJI. TI24 npHJIO>KeHHfl t1=11 MM, t 2 =12 MM, t 3 =13 MM.
Pa3MephI rrpocpHJISI hI b, r , R - O,l1HHaKOBbIe ,nJI5I Bcex Tpex 1II3rOB
HX 6epeM H3 Ta6JI. IT 19 rrpHJIO>KeHH5I no MeHbweMY wary. ,AJLH t 1 =
= 1 I: h=4 MM, r=2 MM, b =4,5 MM, R=6 MM, L p = 16 (18+4) +
+ (13+ 12+ 11 )4+ (13+ 12+ 11) 2+ 11 = 579 MM.
HOBbIe ABa BapHaHTa paCC1.J:HTbIBaeM )l..,TI5I Zp11=Zp+ 1 ==9 11 ZpIII=
=zp+2= 10.
113 <pOpl\tIYJIbI (3.7) HaXO.llHM IIJar 1JepHOBhIx ayobeB ,nJISI 060HX Ba-
pHaHToB: t 011 =120/(9-1) =15 MM; t O III=120/(lO-I) =13,3 MM.
60
3.1. Pe3YJlbTaTbi pactleTa BapHaHTOB npOT I)KKH
BapuaHT
HCKOMhlA napaMeTp III
I
zp 8 9 10
to, MM 16 15 13
ho, M M 7 6 5
bo, MM P 5J5_ ...
_0__
S zo, M M QJ Q;Q8 0,055
Zc 3 2 2
P, H 115 384 156960 126 542:
A, MM 1,43 1,43 1,43
A II, MM 0,14 0,14 0,04
A., MM 0,14 0,14 0,14
Ao, MM 1,15 1,15 1,25
A ocT , MM 0,15 0,03 0,04
io 6 7 11
20 18 14 22
z. _4- 4 .2.-
Zq 12 12+2= 14 12+2= 14
ZH 7 7 7
2 41 39 45
SZD Ha rpynnax: 0,02
nepBoH 0,04 0,04
BTOpOH 0,03 0,03
Sz., MM (QHCJ10 rpynn) 0,02 (2) 0,02 (2) 0,02 (3)
0,01 (2) 0,03 (1 ) 0,01 (2)
0,005 (2) 0,0 I (2) 0,005 (2)
0,005 (2)
t., MM 11,12,13 11,12,13 9, 10, 11
t H (ta. t,J, MM 11, 12; 13 11,12,13 9, 10, 11
h-q, MM 4 4 3,6
b q, M M 4 4 3,5
1 0 , MM 288 210 286
In, MM ( 64 60 26
k
I., MM 144 169 141
lx, MM 83 83 69
L p , MY _5..79 522 522
B TpeTbeM BapHaHTe 3HaIJeHHe llIara t OII1 oKpyrJI5IeM .lI.O 6.rIH:>KaH:-
wero MeHbllIerO 3HaQeHH5I, T. e. t01II== 13 MM. nO Ta6JI. DIg npHJIO}Ke-
HHH onpe eJI5IeM COOTBeTCTBYIOIUHe 3THM ll1araM rJIYOHHbI rrpocpHJISI
CTpYLKeIJHhIX KaHaBOK (H3 TaOJIHII.bI oepeM OOJIblIIee 3HatJeHHe rJIy6H-
HbI). ,[{JI5I t 01 I=15 MM h I I=6 MM, JIH tOil I = 13 MM h I II=5 MM. ITo
cJ>opMYJIe (3.5) HaXO HM npH K=3: SZOII=O,785 -6 2 / (3 -120) O,08 MM;
SZOI1I==O,78S.S 2 j(3.I20) ==0,055 MM. C TI. 11 paCqeT II HIlI sapHaHToR
npo OJI}KaeM KaK JI5I I BapHaHTa. Pe3YJIbTaTbI paCIJeTa CBe,aeHbI B
TaOJI. 3.1.
CpaBHHB OCHOBHbIe nOK83aTeJIH Lp, b, Szo H Z, BH,nHM, tITO onTH-
MaJIhHbIH BapHaHT - III, TaK KHK npOT5I)KKH rrpH HaHMeHbIIIeif )I.tlIHHe
HMelOT TaKYIO }{{e, KaK B BapHaHTe I, llIHPHHY 3y6a H MHHHMa"TIhHYIO
no,naqy. Onpe eJIeHHe OCTaJIbHbIX 3JIeMeHTOB KOHCTPYKUHH rrpOTH)KKH
npOH3BO,lI.HM TOJIbKO ,lIJI5I 3Toro BapHaHTa.
61
Q..)
\
6.
..r
tJ)
PHe. 3.2.
npOTsnKKa KpyrnaJl 0'65H7:
a - o6I1J,lni BH)1., 6 - nOnepeqHblfi npoQJHJIb tJepnOBbIX 3YObeB; 8 - rrOnepeqHblfi npoc1>HJIb nepe..
XOJ1.HbIX Ii tJHC'fOBblX sy6ben; e - nonepe'lHbIA npo4>HJIb KaJIH6pYIOIIJ.liX 3y6ben; iJ - npo.n.OJIbHblA
npO<pHJIb tJepHOBbIX H nepeXOJUlbIX 3y6beB; e - rrpO.II-OJIbHbl:R npo<pHJIb tJHCTOBbIX Ii KaJ1H6pylO-
41.{HX 3y6beB
17. ,UHaMeTp KaJIHOPYIOInHX 3YObeB D K =D max =65,03 MM.
18. l.JHCJ!O BbIKpYJKeK H HX WHPHHY Ha qepHOBbIX 3YObHX onpe.ne-
JI5IeM no Ta6J1. TI25 npHJIO:>KeHHH: N= 12, ao=8,5 MM.
19. l.JHCJIO BbIKpYJKeK Ha nepexoAHbIX Ii tIHCTOBbIX 3YObHX npHHH-
1YiaeM no Ta6J1. n16 npHJlOLKeHHH: NT{= 12, a n =a q =6,5 MM.
20. ,QHaMeTp H J{JlHHy nepeJ{Heii HanpaBJlHIOm.eii HaXO HM corJIac-
EO n. 20 MeTO,lI.HKH: D II . n =63,6 e8, In.H=0,75.120=90 MM, TaK KaK
120/65> 1,5.
21. LLJIHHY nepexO,Il.HOrO KOHyca BbI6HpaeM no TaOJI. 1128 npHJIO-
2KeHH5I: Irr.l<=20 MM.
22. PaCCTOHHHe OT nepe Hero TOpII.a rrpOTHLKKH ,Il.O nepBoro 3y6a
onpeAeJI5IeM no cpopMYJle (3.29): Ll = 160+25+40+ 120+25=370 MM.
23. ,QHaMeTp H JlHHY 3a,lJ.HeH HanpaBJI5IIOIlI.eH HaXO,lJ.HM COrJIaCHO
IT. 23 MeTO,lJ.HKH: D 3 . H =65f7 MM, l3.H=50 MM (CM. Ta6JI. TI29 npHJIO-
;}KeHH5I). TIpOTH}KKY BbInOJIHSIeM C 3a HHM XBOCTOBHKOM. ,UHaMeTp
3a,a.Hero XBOCTOBHKa npHHHMaeM no rOCT 4044-70 (TaOJI. 114 npH-
JlO)KeHHSI), MeHbIIIHM, qeM AHaMeTp nepe,nHero XBOCTOBHKa Da.xB =
=36 MM, ,L(JIMHY 3a,lIHero XBOCTOBHKa 6epeM no Ta6J1. TI30 npHJI01Ke-
HH5I: 13.xB = 125 MM.
24. 06rnyro JIHHY npOTH2KKH paCCIIHTbIBaeM 110 <popMYJIe (3.30):
L=370+522+50+125=1067 MM.
npHHHf\1aeM L= 1065 MM.
4epTem npOT51}KKM nOKa3aH Ha pHC. 3.2, ,ltHaMeTpbI 3yobeB - B
7a6JI. 3.2. MaTepHaJI: pa601IeH lIaCTH - CTaJ!b P6AM5, (fOCT
19265-73); XBOCTOBOH qaCTH-CTaJIb 40X (fOCT 4543-71); TBep-
62
3.2. AHaMeTpbl 3y6beB npOTH}KK"J
0- Pt
1-0 1-0
'0 Q) '0 C>::g
» :s
") ('I)
::s:: _ z; :s::
Q t::iC4
1 63,71 12 64,22
2 63,67 13 64,37
3 63,82 14 64,33
4 63,78 15 64,48
5 63,93 16 64,44
6 63,39 17 64,59
7 64,04 18 64,55
8 64,00 19 64,70
9 64, 15 20 64,66
10 64, 11 21 64,81
11 64,26 22 64,78
CI:3
'0
"'I')
0.. 0.
f- CI:3 1-0
C) '0 ::g
» :s
(f')
= .. t::1:Q
t:tC4
64,85 35 65,02
64,85 36
64,89 37 65,03
38
64,93 39
40
64,97 41
42 65,03
64,99 43
44
45
65,01
23
24
25
26
27
28
29
30
31
32
,.....-
33
34
n p H M e 11 a H Ii e. ,LLJI5I 3yobeB NQ 1 22 3a,LI.I-IHH yroJI a= 3°, ,lI.OnYCK Ha JJ.HaMeTp
-0,016 MM; ,lI.JUI 3y6beB NQ 23-30 a= 3°, ,lI.OnYCK Ha ,lI.HaMeTp -0,008 MM; ,LJ,JU'
sy6beB NQ 31-38 a=2°, ,LJ,OnycK Ha ,lI.MaMeTp -0,008 MM; )J.JI5I 3yobeB N2 39-45
a= 1°, ,lI.OnycK Ha ,lI.HaMeTp -0,008 MM.
,n:OCTb H RC a 63-66 pe)Ky eH qaCTH H 3a,l(HeH HanpaBJlHlOIneH,.
HRC a 61-66 - nepe,l(HeH HanpaBJIHlOlI.\eii, HRC';3 43-51 - XBOCTO-
BliKa. BbIKpY)KKH Ha 3y6bHX 23, 25, 27, 29, 31, 33, 35, 37 OTHOCH-
TeJlbHO 3y6beB 21, 24, 26, 28, 30, 32, 34, 36 H 38 paCilOJIaralOT B II1ax-
MaTHOM nopH Ke. HeYKa3aHHwe rrpe eJIbH e OTKJlOHeHHH pa3MepOB:
OXBaTbIBaeMblX no H14, OCTa,lIbHf-,;X + 1714/2. OCTaJIbHble TeXHHqeCKHe
Tpe60BaHHH no fOCT 9126-76.
npoeKTHpOBaHHe H paCqeT BblrJIa}KHBalOlI.(HX
SJleMeHTOB
IlOBblIIIeHHe KaqeCTBa HJIHH,apHqeCKHX nOBepxHocTeH
B HeMaJIOH CTeneHH 3aBHCHT OT pe3YJlbTaToB paCqeTa H rrpoeKTHpoBa-
HHH BblrJIaMHBalOIII.eM qaCTH KpyrJIbIX pe>Kyrne-Bblr.lIa}KHBarornHx rrpo-
T )KeK, a TaK>Ke TOJIbKO BbIrJla)KHBaIOInHX. TIO,l( TepMHHoM BhlrJlamH-
BaHlIe HMeeTCH B BH,lLY o6paooTKa C BeChMa He60JIbllIHMH HaTHraMII,.
npH KOTOpbIX IIJIaCTHqeCl{a£ ecpopMalI.H.H pacnpocTpaH£eTC5I Ha He-
3Ha4HTeuTJbHYlO TOJII.lJ):IHY CTeHKH 3arOTOBKlI - He 6o.J1ee 5 MM." TICA
HaTHrOM i B IIOHHMaIOT pa3HOCTb J(HaMeTpOB BbIrJIa>KHBaIOIUHX 3y6beB
H O'fBepCTH5I ,lLO Bblf JIa)KHBaHHH, ilOJl OTHOCHTeJIbHbIM HaTHrOM 'A - OT-
HOllIeHHe a6CO,TIlOTHOrO HaT5Ira i B K AHaMeTpy OTBepCTH5I. IlpH A>0,007
nJIaCTHqeCKOii ,lLecpopMaI..LHH lVIO)KeT nO)J.BepraTbCH 3HaQUTe,HbHaH qaCTb
II ,aa)Ke BCH TOJIIUHHa CTeHKH, 11 B 3TOM CJIyqae npOTHrHBaHHe CTaHO-
BHTCH ,lI,ecpopMHpYIO IIM. TIpHBO,lLHMhle peKOMeHLLalLHH no paCqeTY If
npoeKTHpOBaHHIO OTHOCHTCH TOJIbKO K BblrJIa}KHBaIOrnIIM II pe)Kyme-
63
b to
,rr
aJ
d)
O,1t e H
0)
PHC. 3.3.
BblfJla.>KHBafOlI(aH qaeTb npo-
TH)KKH:
a - cxeMbI BhIrnamHB3RHSI; 6 - KOB"
CTPYK HSI BbIrnamHBaTeJIeA; 8 - 3a"
MOK J],JISI KpenneHHSI BbIrna}KHBalO-
UJ,HX 3y6beB
BbIrJIamHBalOInHM rrpOTHjKKaM. CXeMa BbIrJIa)l{HBaHHH R KOHCTPYKlI.HSI
Bblr.n: a}I{HBaTeJIeH nOKa3aHbI Ha pHC. 3.3, a, 6.
BbIrJIa}I{HBaIOIll)fe 3y6bH B 3aBHCHMOCTH OT KOHcpHrypaUHH H Mare-
pHaJIa 3arOTOBOK n03BOJI5IIOT rrOBblCHTb reOMeTpHIIeCKYIO TOqHOCTb
orBepCTHH Ha 30-50 %, YMeHbllIHTb mepOXOBaTOCTb nOBepXHOCTH ]10
Ra == 0, 16+0,63 MKM, nOBblCHTb H3HOCOCTOHKOCTb .lleTaJIH.
TBep.n.OCnJIaBHble BblrJIa>KHBaIOInHe 3y6bH, OOJI3.n.a51 BhlCOKOH H3HO-
COCTOHKOCTblO, n03BOJI£IOT CY1[(eCTBeHHO YBeJIHtJHTb oomylO Hapa(5oT"
KY npOTH)KKH, TaK KaK HX HaJIHtJHe .naeT B03MO)J{HOCTb B onpe,lI.eJIeH-
HbIX IIpe eJIax KoppeKTHpOBaTb HaMeTp OTBepCTHH H, CJIe.nOBaTeJIbHO,
HCnOJIb30BaTb npOT5I)J{KH, Y)J{e He o6ecnetJHBalOIII.He Heo(5xO.llHMbIA
pa3Mep. CJIe,lI.yeT HMeTb B BH.LlY, qTO TOtIHOCTb OTBepCTRH nocne o6pa..
OOTKH BblrJIa/KHBaIOInHMfI 3y(5bHMH, paOOTaIOInHMH C MaJlbIMH HaTH"
raMH, HeCKOJIbKO B03paCTaeT (He 6oJIee, qeM Ha 50 0 /0), npH Cpe,lI.HHX
HaT5IraX - npaKTHtJeCKH He H3MeH5IeTCH, a npH 60JIbIIlHX - ,aame CHH-
aeTCH (B 30He TopnOB H npH 06paOOTKe 3arOTOBOK nepeMeHHOH
):(HaMeTpaJlbHOH 2KeCTKOCTH). BMeCTe C TeM YBeJIH1JeHHe HaTHr3 BeLleT
K 3Ha4HTeJIbHOMY YMeHbIIJeHHIO mepOXOBaTOCTH IIOBepXHOCTH. B CBH3H
C TeM, qro OCTaTOQH3H ,l(ecfJopManH£ OTBepCTHH nOCJIe BbIrJIaLKHBaHHg
3aBHCMT OT OqeHb MHorHX npnQHH, npaKTHqeCKH TPY HO paCCQHTaTb
pa3MepbI BbIrJIa)KHBalOIII.UX 3YObeB, KOTopbIe cpa3Y OOeCrreQHBaJIH Obi
3HaQHTeJIbHOe YMeHbllieHHe mepOXOBaTOCTH npH oopaOOTKe OTBepCTH
no 6-9-MY KBa.nHTeTaM. TIO.3TOMY paCCQHTaHHble no rrpRBeLleHHbIM
<popMy.naM pa3MepbI BbIrJla>KHBalOIII.HX 3y(5beB o6ecnetJHBaIOT nOJIyqe.'
HHe OTBepCTH5I C M8KCHM3J1bHO )lOnYCTHMbIMH pa3MepaMH. aTO n03BO-
JI5IeT B ,AaJIbHeHIlleM JIerKO o6ecnetJHBaTb TpeoyeMbIH pa3Mep OTBep-
CTHH nOCJIe He3Ha tIHTeJlbHOrO YMeHbweHH£ .nHaMeTpOB Bblr J1 a>KHBalO-
I1{HX 3y6beB C nOMOInblO .nOBO KH. BbIrJIa}KHBaIOInHe 3y6b£ B BH.n.e
OT,QeJIbHbIX KOJIeu HJIH 6JIOKa 38KpenJIHIOT H8 npOT5I)KKe pa3JIHQHbIMR
cnoco6aMH. Pe3b6oBoe 3aKperrJIeHHe 06blqHO npHMeHHIOT Ha npOTH)K...
Kax HaMeTpOM ,lI.O 20-25 MM. 3aMOK C BTYJlKOH, rrPY)KHHOH H ,QBYMH
64
3.3. OrpaHHlJeHHSI no CHH)KeHHIO napaMeTpa mepOXOBa TOCTH Bblr JI a)K H BaHHeM
KBaJIHTeT Ra', MKM, Ra'/Ra, 'LIHCJIO Bbl r JI3)iOiBa}()-
OTSCpCTHH He 60JIee He 60.aee ll.I.HX 3ytSbeB Z B
6 1,25 2-4 1-3
7-8 2,5 4-6 2-4
9-10 5 8-10 5
cyxapHMH OOJIee TeXHOJIOfHqeH, 06eCneLII1BaeT xopornee 6a3HpOBaHHe,
HO Ha npOT5I)KKaX MaJIOrO .l1.HaMeTpa H npII o6pa6oTKe 3arOTOBOK Ma..
JlOM .l1.JIHHbI npIIMeHeHHe ero OrpaHIIqeHO (CM. pHC. 3.3,8). TIpHMeHH-
eTCH II saMOK C ynopoM 6J10Ka HJIH KOJIeu. B cyxapH, KOTopble OXBaTbI-
BalOTCH 3aMbIKalOIIl.eH BTYJIKOH, Y.l1.ep)KHSaeMOH OT oceBoro CMemeHHH
CTonopHbIM KOJIbU.OM. SrOT 3aMOK MeHee TeXHOJIOrHqeH - Tpe6yeTcH
TOqHOe o6ecne eHIIe pa3MepOB Bcex ero .l1.eTaJIeH. 3aMKH C HeCKO b-
KHMH npYiKHHaMH, cyxap5IMH, C cpHKcaUHeH: 6JIaro.z:r.3pH CHJIaM TpeHHH
KOHUqeCKHX nOBepXHOCTefi CJIO)KHee B H3rOTOBJIeHHII H MeHee H3.l1.e:>K-
fibI no cpaBHeHHIO C 3aMKaMH YKa3aHHbIX Tpex THnos. OCHOBHble 3JIe..
MeHTbI BbIrJIa}KHBalOlI.\eH qaCTH npOTH}l{KH H 3arOTOBKH nOKa3aHbI Ha
pHC. 3.3.
MeTO.l1.HKa paClIeTa Bblf Jla>KHBalOw.eH lIaCTH
OT TOJIIl..{HHbI CTeHKH 3aBHC5IT :>KeCTKOCTb 3arOTOBKH,
r y6HHa pacnpocTpaHeHHH nJIaCTHqeCKOH: .l1.e OpMau.HH, KOHTaKTHoe
JJ.aBJIeHHe. )KecTKocTb CTeHKH o6pa6aTbIBaeMOH: 3arOTOBKH xapaKTepH-
3yeTcH OTHOllIeHHeM HapYlKHoro tlHaMeTpa DR K BHYTpeHHeMY D H B
60JIbllIOH CTeneHH BJIH5Ie r Ha Ha3HaqeHHe HaTHra H THrosyIO CHJ1Y.
B CJIyqae 3HaqHreJIbHOrO pa3JIHQHH TOJII.I.I.IIHbI BTYJIKII B paCtJeTax
HCIIOJIb3YIOT HaH6oJIbllIYIO )KeCTKOCTb IIPII HaH60JIbllIeM 3HaqeHHR Ha-
pYJKHOrO .l1.HaMeTpa 3arOTOBKH D H .
ITapaMerp llIepOXOBaTOCTH nOBepXHOCTII nOCJIe o6pa6oTKII pe:>KY-
lIteM qaCTblO npOT5I)KKH Ra' Ha3HaQaeTC5I B 33BHCHMocrH OT KSaJIII-
TeTa oTBepCTH5I, B03MO}KHOrO YMeHbllIeHH5I napaMeTpa rnepoxoBarocTH
o6pa6oraHHoM nosepxHocTH SbIr JI3)KHS3 JOIll,eH qaCTbfO npH B03MO:tKHO
MeHbllIeH: ,lJ.JIHHe Bceif npOTH}KKH (Ta6JI. 3.3).
4HCJIO BbIrJIa}KIIBaJOmHX 3y6beB ZB peKoMeH.l1.yeTcH npHHIIMaTb H3
Ta6JI. 3.3. lJeM 60JIbllle BbIf JIamHBaIOmHX 3y6beB, TeM BbIllie reOMeT'"
pHQeCK8H TOtJHOCTb o6pa6oTaHHbIx oTBepcTHH, 60JIbllIe ocesa51 CHJIa.
IlpHMeHeHHe 6JIOKOB C QHCJIOM 3y6beB 60JIee nHTII Heu.eJIecoo6pa3Ho
113"'3a YXY.l1.UleHHH o6pa6oTaHHOH: nosepXHOCTH BCJIe.l1.CTBHe tJpe3MepHO-
TO ynpOQHeHHH, B03MO}KHOCTH n05lBJIeHH5I HapOCTa, Y.l1.JIIIHeHH5I npo-
TH/KKH.
4HCJIO 3YObeB MO)KeT 6bITb onpe.u.eJIeHO no cpopMYJIe
Ra'
zA===O,5 + 1,05 (3.31)
Ra
C oKpyr .neHHeM .l1.0 l1.eJIoro MeHbllIero tJIICJIa.
3-338
65
3.4. CKOpOCTb BbIrJla1KHBaHHSI TBep)l.OCDnaBHhlMH SyfihHMH, M/MHH
YMeHbllIeHHe Ra
0«5pa6aThlBaeMbIA MaTepllaJI
B 2 pa3a
B 4 pa.:Sa
B 8 pa3
CTaJIb c as, Mila:
AD 650
CB. 660 .l{Q 800
CB. 800
qyrYH KOBKHH, }J{eJIe3HCTaSi JIaTYHb
tIyrYH cepbIH, Oe30JIOB HHa51 6poH3a
OJIOB5IHHaH 6poH3a, aJIIOMHHHeBbIe CDJIaBbI,
6a66HThI
24
16
10
22
36
70
17
11
7
16
25
50
12
8
5
11
18
35
BpeMeHHoe conpOTHBneHMe npM paCTH eHHH aB H MOAynb ynpy-
rOCTH E oopa6aTbIBaeMoro MaTepHaJIa B 3Ha1JHTeJIbHOH CTeneHH
BnH IDT Ha pa3Mepw B HaMeTpanbHOM HanpaBneHHH Bwrna*HBaID-
HX 3y6beB.
1.IacTb HCXO,l:{HWX ,naHHblx ,nnSI paCqeTa BbIrJ1aLKHBalO eif 'tlaCTH
npOT LKKH:
Ra - napaMeTp lllepOXOBaTOCTH nOBepXHOCTH rrocne npOTRrI1Ba
HH£; D - HOMHH8JIbHbIH ,QlIaMeTp OTBepCTHH; DB - BepXHHH npe enb-
HblH pa3Mep npOTHHYToro OTBepCTH£; Imax - HaH6oJIbllIa£ ,ltJIHHa OT-
BepCTH .n.eTaJIH; l)p - pa30HBKa HJIH yca,nKa OTBepCTHH nOCJIe oopa..
OOTKH pe}J{y eH 'tJaCTbID npOT£)KKH, H3BeCTHa 1I3 KOHCTPYKTOpCKO"
u
TeXHOJIOrHQeCKOlf ,lI.OKYMeHTanHH.
,[{nH oopa60TRH 3arOTOBOK H3 tJyrYHa, CTaJIH, oe30nOB5IHHCTOli
OpOH3bI, JIaTYHH npHMeHHIOT BblrJIaLKHBalO He 3YObH H3 TBep,lLbIX
CrrJIaBOB BK8, BK15, BI(6M, B1(10M, T5KIO, T5K12B, a 3arOTOBOK
H3 aJIIDMHHlIeBbIX CrrJlaBOB H OJIOB£HHCTbIX OpOH3 - 3y6bH li3 HHCTPY-
MeHTanbHbIX H 6bICTpOpe>KYInHX CTaJIeH P9KIO, P6M5, XBr, IlIX15,
YIOA, YI2A. C YBenHqeHHeM xapaKTepHCTHK MexaHHtJeCKHX CBOHCTS
MaTepHana 3arOTOBKH, TOJI HHbI ee CTeHOK Ii CTerreHII YMeHbIl1eHH5I
(H3MeHeHH ) napaMeTpOB mepOXOBaTOCTH 6epYT (Heo6xOAHMO B 6H-
paTb) 60nee npOtlHbIH MaTepHaJI BblrJIa)I{HBaTeneH.
CKOpOCTb BhlrJIa2KHBaHH5I Ha3HaQalOT no Ta6JI. 3.4 B 3aBHCHMOCTH
OT o6pa6aTwBaeMoro MaTepHana H H3MeHeHHH rrapaMeTpa mepoxo.
BarOCTH rrOBepxHocTH oTBepcTH£. CKOpOCTb pe)Ky e-BWrJIa2KHBalOmeH
u
npOT5.I)KKH qaIne Bcero Ol'paHHtJHBaeTc£ CKOpOCTblO pe:>Kyw.eH qaCTII
(CM. Ta6J1. D6 npHJIOLKeHHH).
,[ln5I rrpe,lI.OTBpa eHH5I HapocToB Ha BblrJla:>KHBalOw.HX 3YOb5IX B
p£)J.e CJIyqaeB Cne,lLyeT rrpHMeH£Tb oOJIee 3<pq>eKTHBHYro CO)K, qe!\.1
3TO peKoMeH yeTcj{ ,lI.nH pa60TbI pe)Kyrueii tJaCTH npOT£JKKH (CM..
TaOJI. fIl8 npHJIOmeHH5I). npH BbIfJIaJKHBaHHH 3afOTOBOK H3 II.BeTHbIX
CnJIaBOB H tJyrYHa rrplIMeHflIDT MaCJ1a HH ycTpHaJIbH e, a 3arOTOBOK
CTane:a - CYJlbcpo<ppe30n, ocepHeHHbIe H cpoccpaTHpoBaHHbIe MHHe-
paJIbHbIe Macna c IIpoTHBo3aJI.HpHbIMH npHCaJI.KaMH BblCOKoro ,lLaBcJ1e-
HHSI, KOMIIaYH,lLHpOBaHHble Macna. DpH oopaooTKe JIerHpOBaHHblX CTa-
neM B CYJIb4Jocppe30n ,lI.06aBJI IDT MenKo HcnepcHbIH IIOpOlliOK rpacpH-
66
Ta HJIH ,lI.MCYJIbcpH,lI.a MOJIHD,l{eHa ,lI.O 10%. npM3HaKoM, xapaKTepH3YlO"
IUHM He,lI.OCTaTOIIHO 3<pcPeKTHBHoe CMa3bIBaHHe, HBJI5IeTC5I HapOCT 06..
pa6aTbIBaeMoro MeTaJIJla Ha pa60IIeii qaCTH BbIrJIa}KHBaIOInHX 3yobeB.
TIpoAOJILKaTb pa60TY B 3TOM CJIytJae He.nonycTHMo H CJIe,lI.yeT npHMe-
HHTb DOJIee 3cpcpeKTHBHYlO CO)l(.
PaCCT05lHHe OT nOCJIe HerO KaJIH6pYlOInero 3y6a ,no nepBoro BbI-
r JI a)KHB a IOI1I.ero II (CM. P HC. 3,3, 8) JI.OJIlKHO 6blTb He MeHbllle HaROOJIb-
IDeM ,lLJIHHbI oTBepcTHH ,AeTaJIH ,l1JI£ Toro, tJTOObI npe oTBpaTHTb o6pa-
30BaHHe Ha oopaoaT BaeMoH nOBepxHocTH KO b eB X KaHaBOK (pH"
COK) H3-3a Bpe3aHH5I KaJIH6pYlOmHX 3y6beB B TOT MOMeHT, Kor,na
BCTynalOT B pa60TY BbIrJIa:>KHBaIOIIIJie 3YOb5l. OHM ,l1.0JI}KHbI BXO HTb B
u u
OTBepCTHe JIHilib nOCJIe Toro, KaK H3 3arOTOBKH BbIH,lI.eT nOCJIe,LI.HHH
KaJIH6PYlOIUHH 3y6 peLKyw.eH qaCTH npOTH:tKKH. OnaCHOCTb Bpe3aHH£
KaJIH6pYIOll(HX 3y6beB oco6eHHO BeJIHKa npH oopa60TKe 3arOTOBOK
60JIbillOH MaCCbI Ha ropH30HTaJIbHO-npOT.H}KHbIX CTaHKax, npH nJIOXOM
3aKpeIIJIeHHH H 6a3HpOBaHHH o6pa6aTbIBaeMOH 3arOTOBKH, np" OTKJIO-
HeHHH OT nepIIeH HKYJl£PHOCTH JII06oro TOPUa 3arOTOBKH 110 OTHome-
HHIO KOCH OTBepCTH5I. Y rrpOTH>KeK, paOOTalO HX Ha ropH30HTaJIbHO-
npOT£>KHbIX CTaHKax 6e3 no,a,lLep)KHBaIOIUero YCTpoiicTBa, MO>KeT npo-
H30HTH 06PbIB B HaHOOJIee CJIaOOM MeCTe. B 3TOM CJIyqae peKOMeH.lI.Y-
eTCH BblrJIa)KHBaIOIUHe 3YOb5I YCTaHaBJIHB8Tb KaK M01KHO 6JIH>Ke K
peLKYlII.HM, QT06bl 3arOTOBKa Bee BpeM5I 6bIJIa npHlKaTa CHJIaMH pe3a-
HH51, a 3aTeM BbIrJlalKHB8HHH H He MOfJIa CMeCTHTbCH.
nOpSl OK paCqeTa BblrJla}KHBalO eH qaCTH
1. 06 HH HaTHr in 3aBHCHT OT pa3Mepa o6pa6aTbIRa..
eMoro OTBepCTH5I, TOJIInHHbI CTeHKH 3arOTOBKH, MaTepHaJI3 3arOTOBKH,
napaMeTpa lllepOXOBaTOCTH nOBepXHOCTH OTBepCTHH ,lI.O BblfJIa}KHBaHHH,
yrrpyroH ecpopMaUHH BblrJIa)KHBaIOIII.HX 3y6beB H T. . CHaqa.na onpe-
.neJIHIOT K03£p<pHII.HeHT nO,l1.aTJIHBOCTH Ko, a 3aTeM K h K2, in:
Ko= (( H r + 1) I (( H r - 1)+ 1.
(3.32)
ECJIH mepOXOBaTOCTb nOBepXHOCTH 3a,lLaHa KaK Rz (no qepTe)KY
Ha ,lLeTaJIb HJlII noc.ne o6pa6oTKH pe}KymeH qaCTblO npOT5LiKKH), TO B
AaJIbHeHIlIHX paCqeTaX CJIe yeT rrpHHHMaTb, qTO Ra=Rz/4 HJ1H COOT"
BeTCTBeHHO Ra' == Rz' /4.
Kl = (3,1+0,28 : ) y Ko ; (3.33)
(( Ra' ) 0,3 )
K 2 = Ra -0,68 Ko;
(3.34 )
ia=KtRa' + K2 BDo,8/E;
A=iJD.
(3.35)
(3.36 )
67
3*
3.5. AHaMeTpbl BblfJla>KHBa!OlI.lHX 3y6beB, MM
nOpHJJ.KOBblA HOMep BhlfJIa>KHBalOlU,erO 3y()a
ZB
I-A
2-11
3-it
4-A
5-A
z.
Xi.;. ilK-
\1
1 dB - - - - i.
2 d B -O,5i B dB - - - 1,5i.
3 d B -O,65i B d B -O,25i B dB - - 2,1 i.
4 d B -O,7i B lt B -O,4i B d B -O,15i B dB -- 2,75i.
5 d B -O,8i B d B -O,55i B d B -o,3i B dB-O, 1 i B dB 3,25i.
n p II M e q 3 H H e: dB =d H +i B + p, r.u.e + p - npH pa36HBKe OTBepCTHH; -6 p -
"PH YC3)I.Ke OTBepCTH5I IIOCJIe o6pa6oTKH peLKyw..eH qaCTbIO npOT5DKKH.
2. ,I:LHaMeTp (MM) KaJIHopYIOIll}IX 3yobeB pe)Kym.eii qaCTH npOTSIJK-
KII C yqeTOM pa36HBKII (-cS p ) HJIH yca,lLKII (+6 p )
dK=DB-K1Ra' -0,02 + Ope (3.37)
Ilpe,lJ.BapHTeJIbHO B paCIJeTaX npIIHHMaIQT, '-ITO pa30HBK3 (yca.nKa)
tJ p OTBepCTH5I nOCJIe o6pa6oTKH pe}KymeH: qaCTblO npOT£)KKH OTCyTCTBY-
eT. ECJIH i B ID>O,007, d H (MM) MO)KHO npH6JIH)KeHHO onpeJJ.eJIHTb CJIe-
JlYIOIllJfM 06pa30M:
d K -::::::, DB - 0,3i B . (3.38)
B 3TOM CJIyqae npH A>O,007 paClIeTHble 3HaqeHH51 oceBbIX CHJI Bbl-
r JIa2KHBaHHH 3Ha 1JHTeJIbHO 60JIbllIe ,lLeH:CTBYIOmHX.
3. ,LLH3MeTpbI (MM) BblrJI3}KHB31OllI.HX 3y6beB orrpe,lLeJI5UOT JlH60 no
T36JI. 3.5, JIII60 no cpopMYJIaM
dB=d + op+ i B ;
dBj=dK+o p + 1,15i B j/zB'
r,ne dB - ,lJJI3MeTp nOCJIe.n;Hero 3y6a; j = 1, 2, 3, ..., (ZB- I).
PaCqeTHble 3HaqeHH5I peKOMeH,lLyeTC5I oKpyrJlSlTb JI.O 0,005 MM. ,lto-
rrYCK ,lI.HaMeTpOB 3y6beB paBeH -0,005 MM.
4. Pa60q3H Q3CTb BbIrJIa)KHBalOmHX 3y6beB MO>KeT BbInOJlHBThCSI
C ,lLBYM5I KOHHqeCKHMH nOBepxHocTHMH, pa3.n;eJIeHHbIMH II.HJIHH,lI.pHIJe-
CKOM JIeHTOlIKoH, JIH60 no .n.yre OKPY)KHOCTH (CM. pRC. 3.3, 6). KOHH-
qeCKHe nOBepxHocTH 3yobeB HMeIOT HeCKOJIbKO 60JIbllIYlO CKJIOHHOCTb
K HapocToo6pa30BaHHIO II 06HaJIeQHBaHHIO, qeM ccpepHQeCKHe, HO 60JIee
TeXHOJIOrH1JHbI B H3rOTOBJIeHHII. I1pH o6pa6oTKe 3arOTOBOK H3 qyrYHOB,.
I.I.BeTHbIX MeTaJIJIOB H CnJIaBOB IJ,eJIeC006pa3Ho npHMeHHTb KOHHqeCKHe
3YOb5I, npH o6pa6oTKe 3arOTOBOK II3 cTaJIeii - TopoH.n;aJIbHble (cH31JaJIa
MO}KHO II3rOTOBHTb 3y6bH KOHH1JeCKHe, 3aTeM cKpyrJIIITb HX BepllIHHbI)..
feoMeTpH4ecKHe napaMeTpbI (MM) 3y6beB MorYT 6bITb onpe,lI.eJIeHbl
c nOMO bIO Ta6JI. 3.6 HJIII no cpopMYJIaM
b === 0,07 DO,85;
(3.39)
( 3_ 40)
(3.41 )
68
3.6. reOMeTpHQeCKHe napaMeTphi BhlrJla}l(HBalOw,HX 3y6beB
TOPOHJ1.aJ1bHble 3y6bH KOHHqeCKHe 3y6L$I
D MM R t s b t B
a. 0
!riM MM
JJ.O 30
Cs. 30
(80-70) i B
(70-60) i B
(60-40) i B
(40-30) i B
5 + 1
5 + 1
0,05D
0,04D
(60-40) i B
(40-30) i B
n p H M e q a H H e. E6JIblllHe K03cpcpHu,HeHTbI npH i B CJIe,lI.yeT 6paTb npH oopa6oTKe
oTBepcTHH MeHblllero ,Ll.HaMerpa H npH MaJIhIX iB'
R== 110i B K 3 D -o,125;
f == 110i K D-O,3
B B 3 ,
rJ{e K 3 = 1,25750 A npH A O,007; K 3 ==O,85 npH A>O,007.
OO.llCQHTaHHble 3HaqeHH5I B HeKOTopbIX cJIyqa5lx IJ,eJIeCOOOpa3Ho OK-
KpyrJIHTb. ,L:LJIHHa (MM) OJIOKa (HJIH Haoopa KOJIeu)
(3.42)
(3.43)
LB==fBZBe (3.44)
Heooxo,nHMO, qTOObI y paOOqeH nOBepxHocTH 3yobeB Ra O,02-:-
-;-0,04 MKM, H no Mepe n05IBJIeHH5I CJIe,lLOB 11 pHCOK H3Hoca ayob5I CJIe-
JlyeT nOJIHpOBaTb. MaJIa51 llIepoxoBaTocTb 3yobeB B HeMaJIOH CTeneHH
CHMlKaeT Bep05ITHOCTb nOHBJIeHH5I HapocTa H nOBbIlliaer KaqeCTBO oopa-
6oTaHHoH nOBepxHocTH.
PeKOMeH,lLyeMoe 3HaqeHHe yrJIOB 3aoopHoro H o6paTHoro KOHYCOB
a=5° + 1°
5. 4HCJIO O,lLHOBpeMeHHo paOOTalOllI.HX 3yobeB Zp.B 3aBHCHT OT )J.JIH-
Ubi o6pa6a TbIBaeMoro oTBepCTH5I Lmax, ,lLJIHHbI Bblf JIa)KHBalOIIlero OJIOKa
L B , IlIHpHHbI JIeHT01JKH b, BeJIHqHHbI HaT5Ira i B , yrJIa 3aoopHoro KOHyca a.
npH TOpOH,lLaJIbHOH H KOHHqeCKOH opMax paOOQHX nOBepxHocTeH
qHCJIO O,lLHOBpeMeHHo paOOTalOllI.HX 3yobeB onpe,lLeJI5IIOT no cpopMYJIe
(3.45) C oKpyrJIeHHeM ,lI.O 60JIbIllerO II.eJIoro Y.IHCJIa
zp.8==(lmax+ b + 5,7i B )!f B , (3.45)
r,ne 5,7i B =O,5i B ctga, a=5°
ECJIH nOCJIe onpe,lLeJIeHHH Zp.B no cpopMYJIe (3.45) OKa)KeTC5I, qTO
Zp.B>ZB, CJIe,lLyeT npHHHMaTb Zp.B ==ZB, TaK KaK Zp.B He MOLKeT ObITb
60JIbllIe ZB.
6. Onpe.l1.eJI5IIOT CYMMY HaT5IrOB BblrJIa)KHBaIOIUHX 3y6beB. ECJIH
npR BblrJIaLKHBaHHH Zp.B = ZB, a )I.HaMeTpbI BblrJIalli.HBalOllI.HX 3y6beB
COOTBeTCTBYIOT peKoMeHLlyeMbIM, CYMMY HaT5IfOB 0J10Ka oepYT H3
TaOJI. 3.5. B TOM cJIyqae, KOr,lLa He Bce BbIrJ1a:tKHBaIOIlI.He 3YObH O,lLHO-
BpeMeHHO yqaCTBYIOT B paOOTe H KOr,lLa ,lI.HaMeTpbI BbIrJIamHBalOmHX
aYObeB OTJIHqaIOTC5I or peKOMeH,lLyeMblx BCJIe,l(CTBHe oKpyrJIeHHH HX .il.O
69
"
neJIOfO qHCJIa HJIH H3-3a rrOfpellIHOCTeH rrpH H3rOTOBJIeHHH Onpe,ll.eJIHIOT
t!>aKTHIIeCKHe HaTHfH (MM) Ka>K,l{OrO 3y6a
iBj=d Bj - d K - Ope (3.46)
CYMMY HaT5IfOB B 3TOM CJIyqae orrpe,n:eJI5HOT )I}IH Zp.B C HaHOOJlb-
WHMH HaTHraMH.
7. OceBaH CHJIa (H)
P B =O,054DE ( lBJ-K1Ra'(zp,B-1» ) :: . (3.47)
ZB- Z p.B+ 1
BJIH£HHe BH,na CO)K H3 tJHCJIa peKoMeHAyeMbIx BbIllIe H CKOpOCTb
BbIrJla>KHBaHHH 0,5-30 M/MHH ,n:JI51 pa60TbI BbIfJIaLKHBalOInnX 3y6beB
Ha P B HeBeJIHKH, rr03TOMY nOrrpaBOQHble K03cpcpHIJ,HeHTbI Ha HHX He
BBe,lI.eHbI.
npHMep paCIJeTa BbIrJIa>KHBaIOIneH IJaCTH
HCXO)J.HbIe )J.aHHble. ,UeTaJlb - BTYJIKa. MaTepHaJI -
eTaJlb 45, Ha orrepanHH npoTHrHBaHH£ HB 217-241, <J'B=600 MTIa,
£==2,1.10 5 MI1a. ,QHaMeTp (MM) oTBepcTHH rrOCJIe rrpOT5IrHBaHHH
D=60H7<+0,03). HapY2KHbIH HaMeTp BTyJlKH D H =90 MM. ,L:LJIHHa npOTH-
rHBaHH£ l= 100-1,0 MM. Y IIOBepXHOCTH OTBepCTH5I Ra=0,63 MKM.
I1pHMeHHeM CTaHOK 7556 C T5IfOBOH CHJlOH 196 KH. ,LLHarra30H CKO-
pocTeH pa6oqero XO,lI.a rrOJI3YHa 1,6-11,5 M/MHH. HaHooJIblliHH XO,lt
nOJI3YHa 1600 MM. COCTOHHHe CTaHKa - xopornee. TIaTpoH ,lI.JIH 3aKpen-
JIeHH5I rrpOTH>KKH 6bICTpOCMeHHbIH 3BTOMaTHtJeCKHH, xapaKTep npOH3-
BOJI.CTB3 - MaCCOBbIH, IJ,HKJI pa60TbI CTaHKa - nOJIyaBToMaTHqeCKHH.
PaCCTOHHHe Me>K Y neHTpaMH KPYfJIOIlIJIH<pOBaJlbHOrO H 3aTOqHOfO
CTaHKOB 2200 MM. HaH6oJIbllIa£ AJIHH3 o6pa6oTKH B TepMHtJeCKOM OT"
.neJIeHHH 2000 MM.
,I:{JI5I nOJIYtJeHH£ oTBepCTH5I 7 -fO KBaJIHTeTa C Ra = 0,63 MKM IIPHHH-
u u
MaIOT KOHCTPYKIJ,IIIO npOT£)KKH nepeMeHHofo pe3aHHH paBHOH CTOHKO-
erH C BblrJIa}l{HBalO HM 6JIOKOM.
MaTepHaJI 6JIOKa BbI6HpaIOT B COOTBeTCTBHH c peKOMeHAaIJ,HHMH.
MaTepHaJI BblfJIa>KHBaIOIUHX 3y6beB - BK8. ITpHHHMaIOT ZB = 4 corJIac-
HO TaOJI. 3.3 (H3 peKOMeH,lI.yeMoro 1JHCJIa Zs BhI()paHo OOJIbIlIee 3HaqeHHe
.nJI5I o6eCneQeHH£ HaH60JIbllIeH reOMeTpHQeCKOH: TOqHOCTH oTBepcTH£
H HapaooTKH npoT£LKKH). B eOOTBeTCTBHH C Ta6JI. 3.3 KBaJIHTeT OT-
BepCTHSI nOCJIe npOT5IrHBaHH5I - 7, wepoxoBaTocTb nOBepxHocTH Ra' =
= 2,5 MKM, tlTO COOTBeTcTByeT 2-H rpyrrrre KaqeCTBa (CM. Ta6JI. TI2
npHJIO>KeHH5I) .
ITo Ta6JI. 3.4 H TI6 npHJIO}KeHHH y TaHaBJIHBaIOT COOTBeTCTBeHHO
CKOpOCTH BblrJIa2KHBaHH5I H pe3aHH5I. npHHHMaIOT MeHbllIYIO H3 HHX-
9 M!MHH. CTaHKoM TaKaH CKOpOCTb 06eCrreQHBaeTC5I.
HaH60JIee 2KeCTKHe Tpe60BaHHH K BbI60py CO)l( npe,lL'b5IBJI5IIOTCH
pa6oToH BblfJIa>KHBaIOmeH QaCTH rrpOT£2KKH. npHHHM310T CYJIbcpocppe-
30JI. 3TOT CMa30tJHbIH MaTepHaJI Y,lLOBJIeTBOp5IeT Ii pa60Te pe2KYIneii
QaCTH npoT£LKKH.
70
nOpg OK paCqeTa. 1. no cl>opMYJIaM (3.32) - (3.36) orrpe,lLeJIHIOT
06W.HH HaT5Ir (is) H OTHOCHTeJIbHbIH HaTHr (A), K03<p<P II II.MeHTbI Kat
Kl H K 2 :
( r+l ( : r+1
Ko + 1- + 1=3,6;
= ( H r - 1 - ( : y - 1
K 1 = ( 3,1+0,28 Ra' ) V Ko = ( 3,1+0,28 0,0025 ) V 3 ,6 =7,99;
Ra 0,00063
K = (( Ra' ) 0,3 _ 0 68 ) K = (( 0,0025 ) 0,3 _ 0 68 ) 3 6=3.
2 R a ' 0 0,00063 ' , ,
i =K 1 Ra' + K a DO,8 / E= 799.0 0025 + 3.600.60°,8 =0 247 MAl.
B 2 B " 210 000 ' ,
A=i / D= 0,247 =0,0041.
B 60
2. ,[(IIaMeTp KaJIH6PYIOIUHX 3y6beB pe:>KYIUeH tJaCTH npOT5I}KKH on..
pe eJl5IIOT no <popMYJIe (3.37). TIpHHHMalOT npe,nBapHTeJIbHO 6 p = 0;
dK=DB-KtRa' - 0,02- op=60,03-7,99.0,0025,- 0,02=59,99 MM
3. TIo cpopMYJIaM (3.39) H (3.40) onpe.n;eJI5IIOT ,lLHaMeTpbI BbIrJIa}KH-
BalOIUHX 3y6beB, lIO MOLKHO BOcnOJIb30BaTbC5I II Ta6JI. 3.5.
d B =d K +i D +o p =59,99+0,247=60,237 MM;
d Bl = d K + 1, 15i D . l/z. = 59,99 + 1, 15. 0,247. 1/4= 60,061 MM;
d B2 =59,99+ 1,15.0,247-2/4=60,132 MM;
d B3 = 59,99+ 1,15.0,247. 3/4=60,203 MM;
d B4 =d B =60,237 MM_
IlocJIe oKpyrJIeHH£ ,lI.HaMeTpbI 3y6beB HMelOT pa3MepbI: d Bl =
=60,060 MM; d B2 =60,130 MM; d B3 =60,205 MM; d B4 =60,240 MM.
4. no TaOJI. 3.6 HJIH nOCJIe onpe eJIeHH5I K3 HaXO,il.SlT no cpopMYJIaM
l(3.41)- (3.43) reoMeTpHtJecKHe napaMeTpbI 3y6beB:
K 3= 1,25- 50A= 1,25- 50.0,0041= 1,045.
TaK KaK o6pa6aTbIBaeMbui MaTepHaJI - CTaJIb, npocpMJIb 3y6beB BbI-
nOJIH5IIOT no pa,lLHYCY R, JIeHTOIIKa OTCYTCTByeT.
R= 110iJjK 3 D-o,125= 110.0,247 -1,045.60- 0 ,125= 17 MM;
b=0,07Do,S5=O,07-600,85=2,27 MM;
t B = 110i B K 3 D-o,3= 110.0,247.1,045.60- 0 ,3=8,3 MM.
ECJIH B35ITb 3arOTOBKY c pa3MepaMII: HapY>KHbIH ,D:HaMeTp
60,8+1,8 MM, BHYTpeHHHH 39,4- 1 ,2 MM, ,lLJIHHa 20+1,0 MM, TO B II.eJI5IX YMeHb-
71
weHHH CHHMaeMOrO rrpHnYCK3 C 3arOTOBOK 6JIOKOB Bblr JIa}l{HBaIOInHX
3y6beB liar ueJIeC006pa3HO YBeJII1QHTb o 10 MM. Tor,lI,a no (3.44)
L B =i B z B =10.4=40 MM.
5. 4HCJlO o,l1.HOBpeMeHHo pa60TalOlll.HX 3y6bes zp B = 4, TaK KaK
Jl.JlHHa 6JIOKa 3y6beB MeHblIIe JIHHbI o6pa6aTbIBaeMoro oTBepcTHH
(lmax=100 MM, L B =40 MM).
6. no cpopMYJIe (3.46) onpe,lI,eJISIIOT HaTHr Ka}K,lI,orO BbIrJIa}KHBaIO-
ero 3yoa iB)=dBJ-dR-6p; npM op=O lBI =60,060-59,99=0,07 MM,
i B 2=60,130-59,99=0,14MM, i B3 =60,205-59,99=O,215 MM, i 04 =
=60,24-59,99=0,25 MM, iBJ=O,07+0,14+0,215+0,25=0,675 MM.
OceBYIO CHJIY (H) npH BbIrJIa}l{HBaHHH HaXO,lI,HT no cpopl\1YJIe (3.47)
P a =0,054DE ( iaj-KIRa' (Zv,a- 1 ) ) ;
Za-zp.B+ 1
p 8=0,054 -60. 210000 (0,675 - 7,99.0,0025 (4 - 1» 1,045 == 121480 H
3,6
MeTO,l(HKa paCqeTa SJleMeHTOB KpenJleHHSI
BLlrJIa}l{HBalO HX 3yoLeo
PaCqeT 3neMeHTOB KpenJIeHHSI OCHOBaH Ha H3BeCTHWX
3aB11CHMOCT51X no paCqeTY rrpY)KI1H 11 .n.eTaJ1ei1 3aMKa (pHC. 3.3).
1. nOCa,lI,OQHbIH HaMeTp BblrJIa)KHBaIOIII.HX 3y6beB H BTYJIKH 3aM"
Ra BbI6HpaIOT B 3aBHCHMOCTH OT pa3MepoB 3arOTOBKH, HanpHMep, co..
fJIaCHO OCT 23.4.101--76. ECJIH 3aroroBKY ,lI,JIH BbIrJIa)KHBalOIll.HX
3y6beB eIll.e TOJIbKO npe,lI,CTOHT H3rOTOBHTb no qepTe}KaM pa3pa6oTQH-
Ka, d BH (MM) onpe,lI,eJI£IOT no cpopMYJIe
dnM Djl,55
(3.48)
H 3aTeM oKpyrJISIlOT ,lI,O 60JIbllIerO 3HaQeHHH,
MY H3 YCJIOBHH:
d BH KpaTeH
d BH KpaTeH
d BH KpaTeH
d eM KpaTeH
COOTBeTCTBYlOInerO O,lI,HO"
0,5, eCJIH d BH -< 7 MM;
1, eCJUI 7 < d BM -< 10 MM;
2, eCJIH 10 < d RH -< 40 MAl;
5, eCJIH d BH > 40 MM.
(3.49)
2. BbIopaB HaMeTp (MM) npOBOJIOKH 113 pH,lI,a d[T1 ===0,5; 0,56; 0,6;
0,7; 0,8; 0,9; 1; 1,1; 1,2; 1,4; 1,6; 1,8; 2; 2,2; 2,5; 2,8; 3; 3,5; 4; 4,5; 5;
5,5; 6; 7; 8; 10; 11; 12 MM, cpaBHHBaeM era C nO CqHTaHHbIM 3HaqeHH-
eM d rr :
d n ===0,05D.
( 3.50)
I1epBbIH 113 pH.l{a HaMeTpOB, Jl.rIH KOTOpOrO 6y.u.eT BbIrrOJIHeHO YC-
JIOBHe d rI1 <d rr , npHHHMaIOT JIH .u.aJIbHeHlllHX paCQeTOB.
72
3. Hapy:mHblH .lI.naMeTp npY}I{HHbI (MM) H3XOJI,5IT no cpopMYJIe
Dn 1,02dBH+2du (3.51)
H oKpyrJ1HIOT ero ,lJ.O OOJIblllerO 3HaqeHRH no cooTBeTcTBYlO1lI.HM p5Ij1aM
(3.49). ECJIH He BbII10JIHHeTCH YCJIOBHe
D+2d n +d BH > 2Drn (3.52)
Heooxo.aHMoe )J.JISI Toro, qTo6bI npY)KHHa He MOrJIa npH CMe:rneHHH B
CTOPOHY 3a,aeTb o6pa6aTbIBaeMYlO nOBepXHOCTb 3arOTOBKH, Dn oKpyr-
JISIIOT .ao 3Ha 1.JeH 11M B npe.abIAYlUeii cTpoKe pH,aa (CM. II. 1). ECJIH He
BbInOJIHSIeTC5I YC.J1oBHe (3.52) ,lJ.JlH nepBoM CTpOKH, TO CJIeJ1.yeT paccqu-
TbIBaTb 3aMOK 6e3 npY)I{HHbI.
4. KaK TOJIbKO YCJIOBHe (3.52) 6y.aeT BbInOJIHeHO, oIIpe.aeJI5IIOT
max (MDa), C, Kn, II1ar npY}I{HHbI B CBOOO.lI.HOM COCT05lHliH lCD (MM)
H 3a30p MeLKJlY cyxap5lMH h (MM):
tmax
1050
_5/-
JI dJ1
(3.53)
c
Dn - d n
d u
(3.54 )
K === 4C - 1
n 4C _ 4
+ 0,615
C
(3.55)
t CB =
(D n - d ll )2't'max
24976Kn d n
+d n ;
( 3.56 )
...3;-
h=O,6 V D;
(3.57)
t CB H h oKpyrJ1SIlOT C TOQHOCTblO .ao 0,5 .ao MeHbllIero 3RaqeHHH.
5. Onpe,ll.eJISIlOT II1HPHHY KaHaBKH nOJl cyxapH leI (MM), Xo.a npy-
)KHHbI npH 3anRpaHHH 3aMKa Ie II (MM), TOJ111IJIHY cyxapeM Ie (MM)
npH M = 3,2. 3Ha QeHHe K03cpcpHIl,HeHTa M onpe,neJIHeTC5l TeXHOJIOrHtJHO-
CTblO npope3KH KaHaBKH II1HpHHOH ICI (MM)
IcI =lVIDo,4,
lc.n = 0,68/ e1 ,
Ie = leI
C oKpyrJIeHHeM .ao MeHblliero IJ,eJIoro 3HaqeHHH.
6. Orrpe,aeJISIIOT QHCJIO pa60QHX BHTKOB npY)I{HHbI
(3.58)
(3.59)
(3.60)
n 0,5l min --lc.1I - d n
1, 2d rr.
(3.61 )
H oKpyrJIHIOT ero C TOqHOCTbIO .ao 0,25 )J.O MeHblliero IJ,e "10ro 3HaQe-
HH.H.
npHH.HTO n 3 B IJ,eJIHX YMeHbllIeHHH oceBbIX pa3MepoB 3aMK3. Ec-
JIM OKa>KeTCSI, lITO n< 1, TO MeHHeTC51 3HaqeHHe M Ha 2,4. CHoBa onpe-
73
.neJIHIOT IcI, Lc.n, le H n. ECJIH CHOBa OKa:>KeTCH, tITO n< 1, TO le H le.n on..
pe,neJI5IIOT H3 YCJlOBHH npOqHOCTH Ha cpe3 cyxapeH no cpopMYJIe
1 =l = Pa
c c.n (nd BH _ 2h) ['t]
If oKpyr JIHIDT .ao 60JIblllerO ueJ1oro 3Ha!leHH5I.
7. CHoBa onpe.aeJI5IlOT tIHCJIO BHTKOB n. ECJIH II B 3TOM cJIyqae OKa-
>KeTCH, IITO n< 1, TO CJIe.ayeT paCCqHTbIB3Tb 3aMOK 6e3 npY}l{HHbI. eTO
3HaqHT, IITO lmin HaCTOJIbKO MaJIO npH npHH5ITOM 3HaIIeHHH P B , !lTO pa3-
MeCTHTb npY)KHHY Me)K.lI.Y 6JIOKOM H 3a HeH HarrpaBJIHIOIneH HeB03-
MO)KHO.
8. nOCJIe onpe.aeJIeHH5I tIHCJIa BHTKOB n BbltIHCJIHIOT CHJIY C)I{aTH5I
P cm (H) npY)KHHbI o conpHKocHOBeHII5I BHTKOB:
981 0 d
P C>K == (t CB - d n ).
(Dn - d n )3
ECJIH OKa)KeTC5I, !lTO P cm <3,43D, TO ,lI.HaMeTp npOBOJlOKH npMHH-
MalOT no PSI.ay 3Ha!leHHH 60JIblIIHM H Il)1KJI CqeTa C n. 3 nOBTopHIOT ,lI.O
Tex nap, nOKa P cm He CTaHeT 60Jlee 3,43 D.
9. B TOM CJIyqae, eCJIH npH n=3 P cm >4,4D, YMeHbllIalOT war npy-
:tKHHbI B cBo6o HOM COCTO£HHH ,lI.O Tex nop, nOKa P cm He CHH3HTC5I .no
4,4 D. ECJIH n<3, TO 3TY OnepaIl,HlO He BblrrOJIHSIIOT.
1 o. Onpe eJIHB ,lI.JIHHY (MM) npY)KHHbI B CBo6o,lI.HOM lCB II pa60qeM
In COCTOHHHSIX, CHJIY C)KaTH£ ee (H) ,[LO pa6oQero COCTOSIHII5I II npH 3a-
KpbITHH 3aMKa (PI II P2) no cpopMYJIaM
lCD === tcBn + dn;
(3.62)
( 3.63)
In=d n (1,2 n+ l)+lcn;
9810d n 4 l l
P CB - n .
1 = (Dn - d n )3 n '
9810d LCD -iu + le.n
P2=
(Dn - d n )3 n
Ii oKpyrJIHB In AO OOJIbWerO Il,eJIoro 3HaQeHHSI, cpaBHHBalOT PI H P2 c
AonYCTHMbIMH 3HaqeHH5IMH. ECJIll HepaBeHCTBa
PI >D HJU1 P 2 >-3D
(3.64)
(3.65)
(3.66)
( 3.67)
(3.68)
He BbITIOJIH£IOTCH, TO PI H P2 YBeJIHqHBalOT nYTeM H3MeHeHM5I n, lCI, le.n,
Ie C yqeTOM n. 6, T. e.
a) npH M=3,2 H3MeH5IIOT M ,lI.O 2,4 H paCqeT nOBTopSIIOT, onpe.ne-
JIHH lCI, lc.n, Ic;
6) npH M = 2,4 Ie onpe,[LeJISIIOT no cpopMYJ1e (3.62) H paCqeT nOBTO-
p£IOT, onpeJJ.eJIHB n.
ECJIH YBeJIHQHTb CHJlY C}KaTH5I npY}KHHbI .ao paooqero COCTOHHH£ PI
H npH 3aKpbITHH 3aMKa P2 He y.aaeTC5f, CJIe,LLyeT C!vleHHTb 3aMOK.
11.. DpH BbIIIOJIHeHHH HepaBeHcTB (3.68) BblqHCJISIIOT pa3Mepbl cpa-
COK H pa.nHYCbI 3aKpyrJIeHHH f (MM), ,l1JIHHY npOBOJIOKH npY}KHHbI
74
Ln (MM), ,l(HaMeTpbl IIIeHKH 3aMKa H cyxapeii de (MM), HapY>KHbIH JIJla..
MeTp cyxapeH Ii BTYJIKtI Dc (MM), lIHCJIO rrOJIHbIX BHTKOB npY)KHHbI n}o,
JIHHY BTYJIKH laT (MM), JlJIHHY 3JIeMeHTOB KpenJIeHHH C BblrJIaLKHBaIO'"
I.qHMH 3YObHMll LH. (MM):
Ln= n (Dn- dn)(n+ 1,5);
f = O,02D;
d c =2( -;- - I) +
+21/ (/+ = )2+
(3.69)
(3.70)
d;H d ( " f h 'Po 1 )
4 - DB + -;-) - :rt CalK (3.7
Dc= 2d oH - dc; (3.72)
nl=n+ 1,5; (3.73)
lOT= O,4D + lcl -lc +lc.n; (3.74)
LK=ln+LB+loT-lcJ1+lc+lcl +2; (3.75)
f oKpyrJI5IIOT C TOtlHOCTblO ,no 0,1 ,no OOJIbllierO 3HatleHHSI, dc, Lrr H lBT
oKpyrJI.SIIOT ):(0 6J1M)KaHmerO IJ,eJ1oro IlHCJIa, L K - no YCJJOBH5IM (3.49).
12. TIocJIe OKOHLJ:aTeJIbHOrO Bbloopa Bcex napaMeTpoB 3aMKa onpe-
JI,eJIHlOT 3anac npOQHOCTH rneHKH ):(HaMeTpoM d c Ha pa3pbIB:
1td [a]p
m= .
6,8P B
K03cpcpHI1.HeHT 6,8 = 4. 1,7, r,ne 1,7 - K03cpcpHIJ,HeHT KOHll.eHTp aQHH
HanpSI:>KeHHH npH npHHHToM f. K03cpcpHUHeHT KOHII.eHTpaUHH HanpH)Ke-
HHH aa= 1,7 cooTBeTcTByeT HaH60JIbilleH TBep,.QocTH MaTepHaJ1a rneHKH
3aMKa (JlJISI P6AM5 H RC 3 62-66, ,nJIH 40X H RC 3 48-56 H T. )I..). TIpH
YMeHbIIIeHHH TBep,nocTH MaTepHaJIa rneHKH H YBeJIHqeHHH f K03cpcpHIl,H-
eHT a(J YMeHbllIaeTcH )LO e,nHHHII.bI.
,[{orrycTHMbIe HanpHlKeHH5I JIH orraCHoro CeqeHHH XBOCTOBHKa npo-
fR)KKH H 3JIeMeHTOB KpenJIeHHSI 3y6beB (cyxapH, BTYJIKa 3aMKa) MO)l{..
HO B3SITb H3 Ta6JI. 3.7.
(3.76 )
3.7. MexaHHlfeeKHe xapaKTepHeTHKH cTaJleA
J{onYCTHMhle 8anpSl}KeHHSI. Mna
[a]p ['t] [a]H
343 196 981
392 245 1079
441 294 1275
540 343 1471
245 245 1570
785 441 2354
490-589 343 1962
392-490 294 1668
Ma pKa
CT aJIH
TBep.ZI.OCTb HnH D", MM
45
40X
40X
50X
XBr
PI8
P6AM5
HRC a 40-44
HRC a 38-42
HRC a 45-50
HRC a 45-55
D 10
10<D 20
D>20
· D - .lI.HaMeTp rrpoT5DKKH.
75
fJIaBa
4.
PaClJeT npOTSI>KeK ,lI.JlSI o6pa6oTKH
npSlM0601JHbIX WJIH eBbIX OTBepCTHH
Y CJlOBHble 0603HaQeHHSI
d - BHYTpeHHHH: .l{HaMeTp IllJIHueBOro OTBepCTHH .lleT3J1H
(,nH3MeTp OKPYlKHOCTH BbIcTynOB), MM (pHC. 4.1);
b
d
PRe. 4.1.
nOnepeqHOe CeqeHHe npHMOoOttHOro WJlH eBOro OTsepCTHH
D - H3PY1KHhIH J1H3MeTp IlIJIHu.eBoro oTBepCTHH (llHaMeTp
OKPY1KHOCTH Bna,nHH), MM;
b - IIIHpHHa IlIJIHueBblx npHM060tIHbIX na30B, MM;
z - qHCJIO lllJItIu.eB;
c - pa3Mep cpaCKH B IlIJIHI1.eBhIX np5IMo60QHhIX na3ax, MM;
- yroJI HaKJIOHa <paCKH OTHOCHTeJIbHO OCM CHMMeTpHM na-
3a 0.
, ,
14h lR, lm - ,I(JIRHa COOTBeTCTBeHHO cpaCOIlHOH, KpyrJIOH: Ii WJIHu.eBOH
qaCTeU npOTHLKKH *, MM;
Z<t>, ZKJ Zm - !lHCJIO 3y6heB COOTBeTCTBeHHO cpaCOqHOH, KpyrJIOH H
IlIJIHQeBOI1 qaCTeH npoTstlKKH;
A<t>J A KJ Am - nOJIHhIe npHnYCKH COOTBeTCTBeHHO Ha <!>aCOqHYIO, Kpyr-
JIYlO H IlIJIHIJ,eBYlO qaCTH, MM;
D n . H - .aHaMeTp nepe.aHeiI HanpaBJI£IOllI.ei1, MM;
DB.<p - .aHaMerp no Bna.aHHaM cpaCOQHOH: llaCTH, MM;
DB m - .aHaMeTp no Bna.aHHaM llIJIIIueBOH: QaCTH, MM;
B , BK' Bm - ,D,JIHHa rJ1aBHbIX pe}KYIllJIX KpOMOK COOTBeTCTBeHHO Ha
cp a co Q H hI X, KP yr JI hI X H llIJI Hll. e B hI X 3 y6 h 51 X, M M ;
BI\, E4»J Em - IIIHpHHa peLKYIlI.erO ceKTopa npope3HbIx COOTBeTCTBeH-
HO KpyrJIbIX, cpaCOqHbIX II IlIJIHIJ,eShIX 3y6beB, MM;
* Y KOM6HHHpoBaHHoH IlIJIHu,eBOH npOTHJKKH TPH BRAa 3y6beB. <!>aCOllHbIe, KpyrJlhle
H lllJIHlI.eBbIe.
76
H A , H B - paCCT05IHHe OT OCM npOTSI}KKH )1.0 60KOBbIX KpOMOK CO-
OTBeTCTBeHHO nepBOrO H nOC eJlHerO aC04HWX 3y6beB.
MM;
«PI - BCnOMOraTeJIbHbIH yrOJI B IIJIaHe (yrO,}1 rrOJlHYTpeHHH), 0;
C - nO,A'beM 3a,I(HerO u.eHTpa npOT£)KKH OTHOCHTe bHO nepe.n-
Hero npH llIJIHcpOBaHHH 60KOBoro IIpOcpH SI aCOqHbIX
HJIH IIIJIHIl,eBbIX 3y6beB, MM;
DctJ - ,llHaMeTp nOc eJlHero cpaCOqHOrO 3y6a, MM;
13K - KoppHrHpOBaHHbIH yro npocpHJISI cpaC04HbIX 3y6beB
(yron HaK.nOHa 60KOBOH KpOMKH lllJJHueBOro BbIcTyna
<!>aCOtIHbIX 3y6beB OTHOCHTeJIbHO OCH CHMMeTpHH era), 0;
(0 - nOJIOBHHa yrJIa npocpllJI£ IIIJIMQeBoro BbIcryna OTBepCTHH
(yro HaKJIOHa np£M06oQHOrO 60KOBoro npocpHJI£ JIH60
$aCKH OTHOCHTeJIbHO OCH CHMMeTpHH llI Hl.I,eBOrO BbICTY"
) Q.
na , ,
6)K - IIOJIOBHHa yrJIa npacpH.JISI llI HIl,eBOH: BnaJlHHbI llIJIHll.eBblX
JIH60 <!>aCOQHbIX 3y6beB, 0;
6 - nOJIOBHHa yr oBoro llIara Me)I{,Z:LY ,Z:LBYM5I coce HHMH ll1J1H-
o
llaM H, .
0611.\ue cBeAeHHSI
Ha pHC. 4.2 npHBe.l{eHbI KOHCTPYKTHBHble 3JIeMeHTbl H
napaMeTphi paCqeTa IIIJIHQeBoH KOM6HHHpoBaHHoH npOT£}KKH nepe-
MeHHoro pe33HHH.
If
4
L
5
4
. I .. 4. H-'I4C L 1-1'1
11r
- I JJ--tllEt
r
B 8
0)
5-5
l
L p
r-r
a-6°
tC,,=6° \
-<::::.
.HI:. 4.2.
l(oM6HuIipOBaHHaH mJlHo,eBaH npOTH>KKa:
6 - pe m.aa: ..aCTh fiPOT)l KH. 6 - napaMeTpbI qepHOBblX H nepeXOAHhIX 3Y(SbeB; 8 - napa
.e1'pY '1BCTOa1.1I H IU1JlK6pYliOW,HX 3y6beB
77
IllJIHIl.eBble npOTH)I{KH nepeMeHHOrO pe3aHH5I HMeIDT TaKoe )Ke no-
CTpoeHHe 3y6beB, KaK H KpyrJIbIe, T.e. )l,Ba 3y6a 06'be)l.HHeHbI B O)l.HY
pe)KY YIO rpynny (ceKIl,HIO). ,LLHaMeTp BToporo 3y6a Ka)K,lI.OH rpynI1bl
Ha 0,02-0,04 MM MeHbllle ,AHaMeTpa npe,lI.bI,lI.YII.I.erO 3y6a. Ha Ka)K,lI.OM
nepBoM 3y6e rpyrrnbI llIJIHcpoBaJIbHbIM KpyroM CHHMalOT C 06eHx CTOpOH
cpacKH, BbInOJIHeHHbIe no ,lI.yre OKPYX(HOCTH. IlepBb!H 3y6 rpynnbI C cpac-
KaMH Ha3bIBalOT npope3HbIM, BTopoH, HMelO HH MeHbllIl1H ,lI.HaMeTp,-
3aQHmalOII.I.HM. CTPY)I{Ka, cpe3aeMaH nepBbIM IlIJIHIl.eBbIM 3y6oM, no
wHpHHe MeHbwe npope3aeMoro na3a, n03ToMY OHa He KacaeTCH ero
CTOpOH npM npO BH)KeHHH BHYTPH KaHaSKH H, 3HaqHT, He BJIHSIeT Ha
mepOXOBaTOCTb ee 60KOBbIX CTOpOH. CTpYMKa, cpe3aeM aH 3a T IHI..IJ;aJO-
IUHM 3y60M, CBepTbIBaeTCSI B BHTOK KOHyco06pa3HOH cpOpMbI. BepllIH-
Ha TaKOH KOHyco06pa3HOH CTPY}I{KH HanpaBJIeHa BHYTPb IlIJIHIJ,eBOro
na3a, T. e. B CTOPOHY OT ero 60KOBOH nOBepXHocTH. 3TO 3HaQHTeJIbHO
OOJIerQaeT YCJIOBHSI paOOTbI yrOJIKa 3atlHIII.alO erO 3y6a a)Ke npa
3HatlHTeJIbHbIX nO,1J.atlax Ha 3YO.
OO'be,lI.HHeHHe JlBYX 3y6beB IIIJIHli,eBOH npOTH}I{KH B pe}KYIII.YlO rpyn-
ny Jl.aJIO B03MO)KHOCTb 3HaQHTeJIbHO YBe.nHqMTb nO,lI.'beM Ha 3y6. TaK
KaK OCHOBHYlO HarpY3KY HeceT Ha ce6e npope3HOH 3y6 (a OH B ,lI.aHHOM
CJIYIIae pa60TaeT B oco6eHHO 6JIarOnpH.HTHbIX YCJ10BHHX 11 BMeCTO yrJ10a
npH BeplIIHHe, paBHbIx 90 0 , HMeeT 3HaQHTeJIbHO 60JIblllHe yrJIbI), T()
nOJ}.'beM Ha 3y6 BMeCTO 06hIQHbIX 0,05-0,06 MM MO)KeT ,lI.OCTHraTb 0,2-
0,3 MM. <PaCKH (BcnOMOraTeJIbHble pe)KY He KpOMKH) Ha npope3HbIX
3y6'bHX HMelOT 3a,Z:LHHH: yrOJI.
06'be.l{HHeHHe 3y6beB B rpynnbI ,lI.aeT B03MO)KHOCTh no.n:YQHTb O,Z:LHO-
rrpOXOJlHYlO lllJIHu.eBYIO npOTH)KKY H o6pa6aTbIBaTb eJO ll.HJIHH,lI.pHQe-
CI{YID QaCTb OTBepcTHSI. B Tex CJIYl.JaSIX, Kor)J.a He Y,Z:LaeTCH 3aKOHQIiTb
npOTHrHBaHHe lIIJIMIl,eBbIX na30B 3a O.l1.HH TeXHOJIOrHQeCKHI1 rrepexo,Z:L,
rrpHMeHHIOT rrpOTH}KKH BToporo TeXHOJIOrI1IIeCKOro rrepexoj.(a. npOTH}K-
Ka BToporo TeXHOJIOrHtleCKorO nepeXO.l{a HMeeT IlIJIHlI.eBYIO nepe,lI.HIOIO
HanpaBJI5IIOIII.YIO tlaCTb, a B pSI.l1.e CJIYQaeB ,Z:LOnOJIHHTeJIbHbIe I.I.HJIHH,lI.pH-
tIeCKHe nOSICKH, pacnOJIO)l{eHHbIe Me)K.l1.Y 3y6bHMH. D05ICKH HaI1paBJISI"
lOT npOT5ILKKY B OTBepCTHH. lllJIHcpYIOT rrOHCKH Ha TOM 2Ke onepalLH H ,.
tlTO Ii 3y6bH no 3a,Z:LHeH: I10BepXHocTIi, QeM H ,lI.OCTHraeTcSI HX COOCHOCTb.
KOHCTPYKTHBHbIe oc06eHHOCTH IllJIHlLeBOH npOT5I2KKH saBHCHT OT
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JIOLKeHHe HX OTHOCHTeJIbHO OCH, KOHILeHTpH1!HOCTb HapY)KHOrO H BHYT-
peHHero JI.HaMerpOB, OTCYTCTBHe 3ayceHlLeB Ha 60KOBbIX nOBepXHOCTSIX
lllJIHueBWX na30B H Ha BHYTpeHHeH: nOBepXHOCTH OTBepCTHSI) Y,Z:LaeTCH
nOJIytlHTb B TOM CJIYQae, eCJIH OJlHOBpeMeHHO npOTSIrHBaIOT llIJIHIl,eBbIe-
rra3bI H OTBepCTHe.
LITOObI 06eCneQHTb YKa3aHHble nOKa3aTeJIH KaQeCTBa, npOTH}KKY
KOHCTPYHpylOT CJIeJlYlOllI.HM 06pa30M. B HatlaJIe pe}KYIIJ,eH QaCTH pac-
nOJIaralOT cpaCOQHble, 3a HHMH Kpyr JIbIe, 3aTeM IIIJIHI.I.eBbIe 3YObSI
(cxeMa CI>Klll). DpH TaKOM pacnOJIO}KeHHH 3y6beB, eCJIH Ii o6pa3yeT-
CH 3ayceHeIl. OT KpyrJIbIX H lllJIHIl,eBbIX SYObeB, TO OH KOHTaKTHpyeT C
Hepa60tleH nOBepxHOCTblO - cpacKoii. Cl>aCKY HY2KHO CHHMaTb BO Bcex
CJIyqaHX, J1a1Ke TOr.l{a, Kor,Z:La .9TO He rrpe,lI.YCMOTpeHO QepTe2KOM. P a3Mep.-
78
<paCKH B 3TOM CJIyqae MO}KeT 6bITb He..
60.rIblIIHM (0,2-0,3 MM). ECJIH cpaCoq-
HbIe 3y6b5I HaXOJJ.£TCSI nepe.rr. KpyrJIbIMH
H UlJIHQeSbIMM, OHM COBeprnafOT ,.QorrOJI-
HHTeJIbHYIO pa60TY. Cl>aCOqHble 3y6bH
HCnOJIb3ylOTCH ,Z:LJIH npOTSIrHBaHHH BHYT-
peHHeH nOBepXHOCTH H BwnO HHIOT
<PYHKll.HH npope3HbIX 3y6beB ceKUHH
Kpyr JIOH qaCTI1. KpOMe Toro, cpe3aH Me-
Ta,TIJI )lJIH 06pa30BaHH£ cpaCKH (pHC.
4.3), OHH YMeHbllIalOT rrpHnycK Ha llIJIH-
ueBble 3YOb5I, a CJIe,Z:LOBaTeJIbHO, If qHC-
JIO WJIHn:eBlbIX 3yobeB. HeJIb3H pa3Me-
aTb cpaCOQHble 3y6b5I n03a H llIJIHueSbIX, TaK KaK npH 3TOM npo-
T5I)KKa YJI.JIMH5IeTC5I H o6pa3YlO MHC5I rrpH pa60Te cpaCOqHbIX 3y6beB
3ayceHell. 3aBepTwBaeTcH Ha oOKoBwe nOBepxHocTH na30B H Ha no-
BepxHocTb oTBepcTH£.
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10 Kpyr JIa51 qaCTb npOTSIJKKH 6Y,Z:LeT HMeTb cpaBHHTeJIbHO 60JIbillYlO
)I.JIHHy. B 3TOM CJIyqae B HaqaJIe pe)l{yr..u.ei% qaCTH npOT£)KKH nOMeIII.alOT
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KpyrJIbIX 3YObeB. BCJIe,nCTBHe nOBopOTa rra3bI, npope3aHHbIe cpaCOqHbIMH
3y6b5IMH, MorYT CMeCTHTbC5I OTHOCHTeJIbHO IlIJIHll.eBbIX 3y6beB. TIpH Ta-
ROM paCnOJIOLKeHHH 3YObeB 3ayceHeIl. OT cpaCOqHbIX 3y6beB OTKJIOH5IeTCH
B CTOPOHY BHYTpeHHeH nOBepXHOCTH OTBepCTH5I Hero npHXO,.QHTC5I cpe-
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(KpyrJIble 06.l{HpOqHble H nepexo,nHble, cpaCOqHble, KpyrJIbIe qHCTOBble H
KaJIH6pYIOIII.He, IIIJIHll.eBble).
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Ka nOBepXHOCTH BblcTynoB (HanpHMep, OTBepCTHe npOllIJIHcpOBaHO rroc-
JIe TepMHqeCKOH: oopa60TKH), TO npOT5I2KKa He HMeeT KpyrJIbIX 3YObeB
(cxeMa <Pill). <PaCOqHbIe 3y6bH pacnOJIaralOT B HaQaJIe pe2KYlll.eH: qaCTH
nepe)l. llIJIHll.eBbIM. ECJIH )l.OnYCK COOCHOCTH pacnOJIO}KeHHH IllJIHueBbIX
na30B H OTBepCTHH .u.eTaJIH M aJI, TO Me2K,Z:Ly Ka)l{.l{bIM TpeTbHM, nSITbIM Ii
)];eC£TbIM 3YOOM pa3Mem;aIOT HanpaBJI5IIO He rrOHCKH.
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nOnepeqHbIe CeqeHHSI pa3JIHqHbIX rpynn H ee 3yobeB. Pe}KYIII.a£ qaCTb
npOTSI}KKH COCTOHT H3 3y6beB Tpex rpynn: I - cpaCOqHbIX; I I - Kpyr-
JIbIX, I J I - IllJIHIJ,eBbIX. KpyrJIble H IIIJIHIl.eBble 3y6b£, B CBOIO Oqepe,D,b,
rro.apa3,Z:LeJI5IIOTC5I Ha qepHOBbIe, nepeXO)lHble, qHCTOBble H KaJIH6pylO"
He.
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npe)].Ha3HaQeHHble ,Z:LJIH CHHTH5I cpacoK Ha IIIJIHll.eBbIX BblcTynax, HHOr,Z:La
B ueJJHX pa3,.QeJIeHH£ CTPY)KKH 06'beJlHH£IOT B rpynnbI H3 J(BYX 3y6beB
pHC. 4.4, ). Dpope3HoH 3y6, nO,LL06HO IlIJIHl1.eBoMY, HMeeT HeCKOJIbKO
f
PUC. 4.3.
npHnyeK, CHHMaeMblH 3y6bH-
MH WJlHu,eBOH npOTH1KKH:
1 - lIIJIHu.eBbIMH; 2 - cPaC01.J:HbIMH;
a - KpyrJIblMH
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HSUI HanpaBnSlIOIII.aSl npoT5DKKH nepBoro TeXHO;IorHtJeCKoro nepexoJJ,a, 2 - nepe)J.HHH XBOCTOBHK;
3 - 3a.l1.HSISI HanpaBJHIIO aJl, 4 - 38.LI.HHH XBOCTOBHK, 6 - nepe.LI.HSlSl HanpaBJHIIOU aH npOTSI)KeK
BToporo If nOCJIe.LI.YIOIII.HX TeXHOJIOfHqeCKHX nepeXOJJ,OB; 8 - CeqeHHe nepeJ1, nocne)I.HHM ij.'Iaco'tJHbIM
3y6oM; z - rpynna 83 JJ,BYX cPaCOt{HbIX 3y6beB: 5 - npOpe3HOJ'! 3y6, 6 - 3atIHllJ,alOInHit 3}'6;
d - celfellHe nepe;I. rpynna\lH (H3 ;I.B\X 3y6beB) KpyrJIblX H llJJIHll.eBbIX 3y6bes H pacno."ome-
HHe BbIRpy*eK Ha HHX
60JIbllIIU1 ,lJ.HaMeTp, qeM 3a qHr..u.alOI.ll.HH, H cHa6)KeH BbIKpY)KKaMH, HMe-
lOIUHMH 3a,lJ.H11l1 yrOJI no BceMY npocpHJIlO.
Do KOHCTPYKll.HH KpyrJIaSI qaCTb lIlJIHlI.eBoH npOTSI)KKH OTJIHqaeTC5I
OT KpyrJIOH qaCTH Kpyr JIOM npOT5I)KKH TOJIbKO TeM, qTO Kpyr JIbIMH
3y6b£MH cpe3aeTcH CTpY)KKa He no BceMY nepHMeTpy OTBepCTHSI, a
JIHlllb Ha yqaCTKaX, He cpe3aHHhIX cpaCOQHbIMH 3y6bSIMH. B CBH3H C
3THM Y 3y6beB KpyrJIoi1 qaCTH npe,ll.YCMaTpHBalOT nO,lJ.'beM Ha Ka)KJlbIH
3y6 H.JIH HX 06'be,lJ.HHSIJOT B ceKIl,HH no JlBa 3y6a, pa3,Z:LeJISISI MeJK,Z:LY co-
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HHIO K nepe,lJ.HeMY. I1cKa}l{eHHe npocpHJI5I 3y6beB KoppeKTHpYIOT paCtleT-
HbIM I1YTeM.
MeTO HKa paClJeTa KOM6HHHpoBaHHbix npOT5I.>KeK
HCxO.ll.HbIe .lI.aHHble. 1. n pOTHrHBaeM aH 3arOTOBKa:
MaTepHa.H, TBepJI.OCTb no 5pHHeJIJIIO H B, COCTO£HHe (nocJIe HOpMaJIH3a-
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HHe, JlHaMeTp orBepCTHH ,lJ.0 npOTRrHBaHHH, BHYTpeHHHH ,lJ.HaMerp lllJIH-
ueB, HapY)KHbIH ,LLHaMeTp IIIJIHll.eB If KBaJIHTeT HapY)KHOH nOBepxHocTH
lllJIHI1.eB, IlIHpHHa IlIJIHIl,eB C ,lJ.OnYCKaMH, qHCJIO lllJIHll.eB, pa3Mep H yroJ1
<pacKH IIIJIHneBblX na30B (eCJlH qepre)KOM ,Z:leTaJIH lie 3a.l{aH, TO KOHCT-
80
PYKTOP Ha3HaqaeT ero caM), napaMeTp rnepOXOBaTOCTH nOBepXHOCTeH
HaH60JIbillaSI ,LI}IHHa npoTflfHBaHH.H.
2. CTaHoK: THn, Mo,aeJIb, T.HrOBaSI CHJIa, )I.Hana30H CKopocTefI, JIHHa
xo,aa llITOKa, THII naTpoHa, pa3MepbI onopHoll nJIHTbI, COCTOHHHe.
3. XapaKTep rrpOH3Bo,LI,cTBa.
4. B03MO./KHOCTH HHcTpYMeHTaJlbHoro ll.exa H 3a rOqHOrO OT.J.e.neHHH
HaH60JIblllee paccToHHHe Me2K,I1.y IJ,eHTpaMH KpyrJIOIllJIH<poBaJIbHOrO,
IllJIHueIllJIHcpoBaJIbHOrO H 3aTOQHOrO CTaHKOB, rJIy6HHa BaHH HJIH IllaXT
,l{JIH HarpeBa rro,a 3aKaJIKY H OTrrYCK.
nOpSl OK paClJeTa KOM6HHHpoBaHHblx npOTSI)I{eK
BHaqaJIe Ha3HaqalOT cxeMY pacnOJIO)KeHHH 3y6beB Ha
npOTH2KKe. HallJIyqlllHM BapHaHToM: cxeMbI pacnOJIO)KeHHSI 3y6beB Ha
npOT51:JKKe RBJI51eTC51 cxeMa <pKlll. ilocJIe paCqeTa ,aJIHHbI KpyrJIOH
qaCTH cxeM a pacno.TIO:JKeHH5I 3y6beB MO)KeT 6bITb H3MeHeHa Ha K <1> III
HJIM Koncl> KqI{lll, eCJIH OKa)KeTC5I, qTO II{ > 1,5 t.
3aTeM paCqeT IIIJIHll.eBOH: npOTSI)KKH He3aBHCHMO OT cxeMbI pacno-
O)KeHHH 3y6beB aHaJIOrH4eH paCqeTY npOTSI)KeK ,aJIH o6pa6oTKH QH-
JIMH,Z:LpHqeCKHX oTBepcTHH (rJr. 3, n. 1-11), rrOCJIe qero ero npOAOJI:JKa-
lOT CJIe,llYIOIII.HM o6pa30M.
1. Onpe,aeJIHlOT QHCJIO 3y6beB B ceKQHH Zc. 4HCJIO 3y6beB B ceKUHH
Ha cpacollHoH, KpyrJIOM H IllJIHll.eBOM qaCTHX IllJIHueBbIX npOTH)KeK MO-
)KeT 6bITb Heo,aHHaKOBbIM. LlJISI o6eCrreqeHHH Y nOBepxHocTH 60KOBbIX
CTOpOH na30B Ra 2,5 H YJIYQrneHHH YCJIOBHH: pe3aHHSI peKoMeH,ayeTcH
QHCJIO qepHOBbIX 3y6beB B CeKll.HH Ha lllJIHll.eBOH: qaCTH Zc 1lI 2. 4HCJIO
3y6beB B ceKIl,HH Ha cpaCOqHOH H Kpyr JIoif qaCTHX (eCJIH aHa nOMell.\aeT-
CH Me)K,LI.y <paCOqHOH H IllJIHIl,eBoI'i qaCTHMH) B Il,eJI51X YMeHbllleHH5I
,l{JIHHbI peKOMeH.l{yeTC5I rrpHHHMaTb paBHbIM e.l{HHHI1.e, eCJIH 3TO ,nonyc-
KaeTCH YCJIOBHHMH HOpMaJIbHOrO CTpy:tKKOo6pa30BaHHSI H CH v 10M npo-
THrHBaHHR.
LLJISI C03,aaHHSI HOpMaJIbHbIX YCJIOBHH 06pa30BaHHH BHTKa CTPY)I{KIf
,Z:LJIHHa pe)KymHX KpOMOK Bmax He ,aOJILKHa npeBbIIllaTb 3HaqeHHM, npn-
Be.l{eHHbIX B TaOJI. TI31 npHJIO)K HHSI. EC.THf Bmax nOJIyqaeTC5I 60JIbllle
TO Heo6xo)lHMO pa3,aeJIHTb CTPY)KKY BbIKpYMKaMH H Zc IIpHHHMaTb
paBHbIM ,lJ.BYM.
4MCJlO 3y6beB B rpynne Ha JIIOOOH: tlaCTH rrpOTR)KKH cxeM pacnO.J10-
}KeHH5I 3y6beB <l>KIlI, <l>lllK, .l{OnYCTHMoe MaKCMMaJIbHOH CM.i10H pe3a-
HHH,
BmaxzqozpK PMK poK PKK Pp
Pmax
( 4.1 )
z=
c
LLJISI cxeM K <P III H Korr<P KlJl\IlI QHCJIO 3y6beB B rpynne .1I)IH Kpyr-
JIOM qaCTH paCCqHTbIBalOT no cpopMYJIe (3.12).
J{JISI onpe)I.eJleHHH Zc Ha KpyrJIOH H cpacoqHoii qaCTHX npOT5!lliKlf
HY}I{HO B <POPMYJIY (4.1) IIO,aCT8BHTb BMeCTO Bmax cooTBeTcTBYIOllI.He
3HaqeHHH B1\ max H B4J max.
MaKCHMaJIbHYlO )lJIHHY pe)KYIII.Hx KpOMOK Ha cpaCOqHbIX 3y6bSIX
BcJJ max (MM) onpe)leJI51IOT npH6JIH)KeHHO no tPopMYJIaM:
81
B Ip max
B UL mIlK
c
b
c
o
PRe. 4.5.
HaH60JlbWaH AnHHa pe.y-
Il{HX KpOMOK (wHpHHa epe-
3a) Ha pa3J1UQHblX 3YObSIX
npHM06oQHOH WJlHl(eBoii npo-
TH1KKH
PHe. 4.6.
HexoAHblH npocIJHJlb yr JlOBOrO
nasa (nocne npoTHrHBaHHSI
4JaCOQHblMH SYObSIMH) e no-
CTpoeHHHMH AnSI onpeAeJle-
HUH AHaMeTpa OKPY1KHOCTH
DE, npoxoJl.SIlI{eA Qepe3 TOQ-
KY E BCTpeQU HCXOAHblX 60-
KOBblX npocfJHJleA H npSIMo-
OOQHOrO na3a
.nJlH cxeM cI> KIll H cI> IllK (p HC. 4.5)
B max=b+2c +(d - do> (4.2)
(HHLKe .naH TOIlHbIH paCtleT Bib max) ;
.nJIH cxeM K <1> III Ii Korr<p K lIK ill H ,lI.OrrOJIHHTeJIbHbIX cxeM III Ii <Pill
B max=b+2c. (4.3)
MaKCHMaJIbHYIO ,lI.JlHHY pelKYII(HX KpOMOK Ha KpyrJIbIX Sy6b5IX Ha-
XO 5IT TOJIbKO .nJIH cxeM cI> Kill H <t> llIK
n.d
B Kmax = -(b+2c). (4.4)
z
Y rrpOT5I}KeK co cxeMaMH K <DIll, Ko n<DKlI I\Ill H KIll KpyrJIYIO qaCTb
paCCqHTbIBalOT rro MeTO,lI.HKe paCqeTa KpyrJIbIX npOT5I}KeK.
JI.JIHHY peLKYII(HX KpOMOK lIIJIHJJ.eBbIX 3y6beB ,lI.JI5I rrpOTH>KeK Bcex
cxeM pacnOJIOjl{eHH5I 3y6beB npHHHMalOT paBHoH MaKCHMaJIbHOH WII-
pHHe na3a B npe eJIax ,lI.OnYCKa Bm = b max .
ECJIH Bcp max Ii BI\ max He rrpeBbIllialOT 3HaQeHHH, rrpHBe,lI.eHHbIX B
Ta6JI. 031 rrpHJIO}KeHH5I (T. e. ,lI.OrrYCKaeTC5I Zc = 1), a Zc, rrOJIyqeHHOe
B pe3YJIbTaTe paCqeTa ITO cpopMYJIe (4.1), OKa3bIBaeTC5I 60JIbllIHM e,lI.H-
HHI.I.bI, TO rrpHHHMalOT zc=2. ECJIH rro cpopMYJIe (4.1) zc>2, TO BapH-
aRT nponYCKaeTC5I H paCCqHTbIBaeTC5I HOBbIH C IIO,QaqeH: Szo=Szc-
-0,01 MM.
ECJIH zc 1, TO rrpHHHMalOT Zc = 1.
82
2. Pacnpe,lJ.eJI5IIOT npHnycK Me}K,lJ.Y pa3HbIMH qaCTHMH H 3y6bHMII
npOT5I}KeK. BeCb npHrrycK Ha npoTHrlIBaHHe pacnpe.u.eJIHlOT Me){(,lI.Y
OT,lJ.eJIbHhIMH qaCT5IMH npOT5I)KKH - acotJHoH, KpyrJIOH, llIJIHl1,eBoH.
Ha KpyrJIOH H llIJIHlI.eBOH qaCTHX HMeIOTC5I 1JepHOBble, nepeXO.LI.HbIe H
qHCTOBhIe 3y6b5I, Me>K.LI.Y KOTOpbIMH, B CBOIO Oqepe,lJ.b, pacnpe)I.eJIHIOT
,lI.OJIIO npHnYCKa, npHxO,lI.5III(yrocH Ha ,l(aHHYlO qaCTb. Ha aCOqHDH qac-
TH nepeXO,lI.HbIX, 1JHCTOBbIX 3y6heB HeT, n03ToMY BeCh npHnycK, npHxo-
,nH HHCH Ha Hee, cpe3alOT qepHOBbIMH 3y6h5IMH.
DpHnycK (MM) Ha cpaCOqHYIO qaCTh ,lJ.JIH cxeM <DKill H <DIllK orrpe-
,lI.eJI5IIOT no cpopMYJIe
Act»=D -domID. (4.5)
,QHaMeTp OKPY>KHOCTH (DE), npOXO,lJ.HlI(eH 1Jepe3 T01JKY E nepeceqe-
HH5I HCXO,lI.HbIX npO HJIeH aCKH H np5IM060tIHOrO na3a, - paCtJeTHhIH
,lJ.H3MeTp nOCJIe,lI.HerO aCOqHOrO 3y6a - HaxO,lI.5IT H3 nOCTpOeHH5I (pHC.
4.6). HCXO,lI.HbIMH ,lI.aHHbIMH ,lI.JI5I onpe,lJ.eJIeHH5I ,lI.HaMeTpa DE 5IBJI5IIOTC5I
CJIe,lJ.YIOl.I.\He napaMeTphI IlIJIHl1,eBOrO OTBepCTH5I: b, c, d, cp.
,aHaMeTp DE paCCqHTbIBaIOT B TaKDif rrOCJIe,lI.OBaTeJIhHOcTH:
. \ b + 2c .
SIn 1\= ,
d
( 4.6)
t \ - (b +2C)ctgA+2cctg
c g I\E-
b
b
(4.7)
sin AE
( 4.8)
D E =
"QJI51 rapaHTHpoBaHHoro rrOJIYQeHH5I cpaCKH BO Bna,lI.HHaX llIJIHueBOro
oTBepCTH5I TeOpeTHqeCKHH AHaMeTp (MM) nOCJIe,lI.HerO aCOqHOrO 3y6a
YBeJIHqHBalOT H3 HeCKOJIbKO ,QeC5ITbIX MHJIJIHMeTpa:
Dct»=== DE + 0,4.
( 4.9)
cI>OPMYJIhI (4.6)-(49) CnpaBe,lI.JIHBbI ,lI.JI5I Bcex YKa3aHHhIX BhlIIIe
cxeM p acnOJIO}KeHH5I 3y6beB Ha rrpOT5I)KKe.
npHnycK (MM) Ha <!>aCOqHble 3y6b5I ,lI.JI51 cxeM pacnOJIO)l{eHH5I 3y6beB
KcI>lI1 H cI>IIlK Ha npOT5I}Kl\e orrpe,lI.eJI51IOT no cpopMYJIaM:
,lI.JI5I cxeMhI K ct> III
Acp==D -d;
(4.10)
,lI.JI5I cxeMhI Ko n KlI HIll
A ===D.p- d +0,12;
( 4.11 )
,QJI5I rpyrrrrbI Ka qeCTBa llIJIHl1,eBOrO oTBepCTH51 no BHYTpeHHeMY ,lI.HaMeT-
PY (3-ii)
A ===A<p- 0,02.
TIpHrrycK (MM) Ha KpyrJIYIO qaCTh rrpOT5ILKeK Bcex cxeM
A K = d max - d Omln .
( 4.12)
( 4.13)
83
npHnYCK (MM) Ha lIepHOBbIe 3y6bH KpyrJIOH qaCTH
AKO==A'1(-(AK.n+AK.q), (4.14)
r.n;e AI\ II - npHrrycK Ha rrepeXo,lI.Hble KpyrJIbIe 3y6bH, npHHHMalOT no
"Ta6JI. 023 rrpHJIOLKeHHH; AI< 11 - npHnYCK Ha qHCTOBble KpyrJIhIe 3YObH,
npHHHMalOT no Ta6JI. TI22 npHJIO)KeHH5I.
npHnycK (MM) Ha lIIJIHll,eBYlO qaCTb ,lI.JI5I npoTHLKeK Bcex cxeM
Aw=Dmax- D wl' (4.15)
l",lJ.e D rn1 - ,1IJlaMeTp (MM) nepBoro IIlJIHl1,eBOrO 3y6a,
Dwl=DE+2Szo. (4.16)
nepBbIH IIIJIlIl(eaOH 3y6 B rpynny He 00 'be,lJ.H H 51 lOT, BhIKPYLKKH Ha
HeM He ,L{eJIaIOT. npH OTCYTCTBHIf <paCOQHbIX 3y6beB ,lJ.JI5I rrepBoro IlIJlH-
ueBoro 3y6a rrpe,lI.YCMaTpHBalOT rpynnoBoe nOCTpoeHHe (ABa 3y6a B
rpynrre), a ,lJ.HaMeTp ero onpe eJI5IIOT B 3aBHCHMOCTH OT cxeMhI pacno-
JIO}l{eHH5I 3y6beB.
1{JI5I cxeMbI Kill
D w1 = d +2S zo .
( 4.17)
l(JI5I cxeMbI lIlK
DWl = d Omln +2S zo .
( 4.18)
ITpHnYCK (MM) MeJK,lJ.Y qepHOBbIMH, nepeXQ,lI.HbIMH H qHCTOBblMH
WJIH eBbIM H 3YOb5IMH P acnpe,lJ.eJI5IIOT CJIe,lI.YIOl.I..\HM o6pa30M:
Awo=Aw-(Aw.I1+Aw.q), (4.19)
r.n.e Am II BbI6HpalOT no TaOJI. D23 npHJIO}KeHH5I; AlII 11 - no TaOJI. n22
up HJIO}KeHHH.
3. HaXO.lI.HT qHCJIO rpyrrrr qepHOBbIX 3y6beB i o , OCTaTOqHhIH rrpHnycK
A OCT H pacnpe eJI5IIOT ero. 4HCJIO rpynn tlepHOBbIX 3y6beB io (HJIH qHC-
JIO 3y6bes npH Zc = 1 ,lI.JIH cpaCOlJHbIX H KpyrJIhIx) Ha Bcex qaCT5IX npo-
'TH}KKH (cpaCOqHOH, KpyrJIOH H lIIJIHII,eBOH: npH Zc = 2) npe,lI.BapHTeJIbHO
OrrpeAeJI5IlOT no cpopMYJIe (3.17), nO,lI.CTaBHB B Hee cooTBeTcTBYIOIlI.He
3HaqeHH51 Ao H Szo, npHH5ITbIe JI5I npOCqHThIBaeMoH qaCTH npoTHLKKH.
HanpHMep, J1.JIH IlIJIHneBOH qaCTH QJopMYJIa (3.17) 0Y,l{eT HMeTh BH,l(
· Awo
l -
wo- '> s
zrna
!10JIYQeHHOe pot5Hoe qHCJIO rpyrrrr qepHOBbIX 3y6heB oKpyrJI5IIOT )(0
6JIH)KaHIIlerO MeHblllero u:eJIoro 3HalleHH5I. OCTaT01JHhIH npHTIycK, no-
JIyqeHHbIH npH 3TOM, onpe,lI.eJIHIOT no cpopMYJIe (3 18) H OTHOCHT B 3a-
BHCHMOCTM OT ero 3HaqeHH5I K lJepHOBhIM, TIepeXO HhIM HJIH qHCTOBhIM
3YOh5IM. ECJIH rrOJIOBMH3 OCT3TOtIHOro rrpHrrycK3 npeBbIIllaeT no,n'beM
3yobeB H3 CTOPOHY rrepBoH rrepeXO,lJ.HOH rpynn , TO ,lI.JIH cpe3aHHH ee
Ha3HaqaIOT O)l.HY J1.0rrOJIHHTeJIbHYIO rpyrrny qepHOBbIX 3YObeB. ECJIH
nOJIOBHHa OCTaT01JHOrO npHnYCKa A ocT MeHblIIe nO,lI.'beMa Ha CTOPOHY
nepBOH rrepeXO,lJ.HOH rpynnhI (KaK ,lJ.JIH KpyrJIbIX, TaK H ,lJ.JI5I IIIJIH eBbIX
3YObeB), HO He MeHhlIIe 0,02-0,03 MM, TO OCTaTOQHbIM npHnYCK )(0'"
84
OaBJI51IOT K npHnYCKY Ha nepeXO,L{HYIO lIaCTb. ECJIH me 1/2 AOCT
O,02 MM, TO OCTaTOQHbIH npHnYCK CYMMHpyeTcSI C npHnYCKOM Ha
QliCTOBble 3y6h5l, qHCJIO KOTOpbIX COOTBeTCTBeHHO YBeJIH1JHBaIOT. «MHK-
POHHYro» lIaCTh OCTaTOqHOrO npHnYCKa nepeHOCHT H3 nocReAHHe qHC-
TOBble 3YOb5I. 1.JTOOhI He YBeJIHQHB3Tb tlHCTOBYIO qaCTh, npHnYCK
AOCT O,04 MM MO)KHO pacnpe,lJ.eJIHTh Mem,lJ.Y nepeXO,lJ.HbIMH H qHCTO'"
BbIMH CeK H5IMH, YBeJIHQHB HX nO,lJ.'beM no 0,01 MM HJIH MeHee.
4. HaXO,lI;51T qHC TJO Bcex 3yoheB npOT5I}KKH z. Ooruee 1JHCJIO 3y6b-
eB .lI.RH npOT5I}I{eK Bcex cxeM onpe,lJ.eJIHIOT no CPOPMY JIe
Z===Z<tJ+ZK+ZW; (4.20)
JI,JI5I npOT5I)I{eK cxeMbI <I>IlI
z=z<p+zw. (4.21)
<1>aCOQHhIe 3YOb5I - TOJIhKO qepHOBbIe. 4HCJIa KpyrJIbIX ZI\ H illJlH-
ueBbIX Zm 3y6beB HBJI5IIOTC5I cYMMaMH qepHOBbIx, nepeXO,lJ.HbIX, qHCTO-
BbIX 11 K3JIH6PYIOlI(HX 3y6heB
ZK=ZKO+Ztc.n+ZK.q+Z .K; (4.22)
Zw = ZillQ + zw.n + Z1l1.1I + ZW.K. (4.23)
t.{HCJ1a Bcex 3y6beB Ha $aCOIlHOH qaCTH Ii qepHOBbIX 3y6beB H3
KpyrJIOH qaCTH onpe,lI.eJI51IOT TaK me, KaK H Ha KpyrJIblX npOT5IJKKax:
.3(p == i«J>zc. ; (4.24)
ZKO= iKoZ C . K ; (4.25)
H3 llIJlHueBOH QaCTH no cpopMYJIe
ZmO== iWOZC.Ul + 1;
Zwo=== iWOZC.Ul.
( 4.26)
( 4 .27)
,AJI5I cxeM Kill Ii llIK
4HCJIO qepHOBhIX 3y6heB KoppeKTHpYlOT B 3aBHCRMOCTH OT pa3Me-
eHH5I OCTaTOqHOrO npHnYCKa. 4HCJIO nepeXO,lI.HblX 3y6heB oepYT B
3aBHCHMOCTH OT rrpHnYCKa rrplIH5ITOrO H3 Ta6JI. n23 npHRO)l{eHHfl.
HCJIO QHCTOBhIX H KaJIHopYIOII(HX 3yobeB 6ePYT H3 raoJI. 022 npHJIo"
)f{eHH5I.
4HCJIO YKa3aHHhIx 3yobeB KoppeKTHpYIOT B 3aBHCHMOCTH OT pa3-
MemeHH5I OCTaTOqHOrO rrpHnycKa.
5. ITO.lI.'beMhI nepexoAHbIX 3yoheB KpyrJIOH Ii llIJIHu.enoH qaCTeH Ha..
.xO.lI.5IT H3 Ta6JI. 023 npHJIO)KeHH5I B 3aBHCHMOCTH OT npHH5ITOrO npH"
nYCK3. DO.lI.'beMbI 'IlHCTOBbIX 3y6heB KpyrJIOH H IllJIHll,eBOH 1.J:3CTen nplI"
HHMalOT H3 TaoR. I122 npHJIOlKeHH5I.
6. HaxO.ll.5IT ,lI.JIHHY pe}Ky eH qaCTH npOT5I)I{KH Lp (MM), mar II
npocpHJIb QHCTOBbIX 3yobeB. ,I:(JI5I rrpOT5I)I{eK cxeM <D KIlI H cI> WK.
Lp=l4»+lK+lw, (4.28)
l",L{e
IctJ = ioz«J>.
( 4.29)
85
,l{JIHHY KpyrJIOH II( Ii llIJIHl.{eBOH: 1m qaCTeH onpe,lJ.eJIHIOT KaK CYMMY
npOH3Be,lJ.eHHH COOTBeTCTBYIOl.I..\HX BeJIHqHH IllarOB H qHCeJI 3YObeB:
lK=to(zKO+ZK.n>+tq(ZK.q+ZK.K- 1); (4.30)
11U to (ZwO +Zw.n + l}+t q (Zw.q +ZW.K- 1). (4.31)
,QJI5I OIIpe eJIeHI1H L p B cxeMax KCPIIl H Ko.n<pK .l(lll HCnOJIb3YlOT
Te LKe cpOPMYJIhI C He60JIbllIHMH H3MeHeHHHMH. TaK, npH orrpe.n.eJIeHHH
,nJIHHbI cpacoqHOH lIaCTH OJILKHO yqHThIBaTbCH YBeJIHqeHHe ee Ha O,1HH
mar:
l«j>=to(zcp+ 1). (4.32)
,[(JIHHa lIIJIHQeBOH lIaCTH YMeHbllIHTC5I Ha O)1.HH llIaf
Iw=to(zwO+zw.n>+tq(zw..q+zw.K-l). (4.33)
JIHHY KpyrJIOH qaCTH nO CIIHTbIBaIOT no cpopMYJIe (4.30) oe3 H3-
MeHeHHH.
,QJIjJ onpe..QeJIeHH5I L p B cxeMe <Pill Heo6xo,LUfMO HaHTH JIHilih liP H
lm; lif> onpe,lI.eJIHIOT, KaK H JIH cxeMhI <pKlll, 1m HaXOJ(HT no cpopMYJIe
(4.33) .
Kor,lI.a Tpe6yeTcH, IITOOhI Ha BHYTpeHHHx nOBepxHocTHX lIIJIHueBhIX
BblcTynoB He OCTaBaJIOCh 3ayceHll.eB, HeH30eLKHQ 06pa3YlOIII.HXCH npa
pa60re cpaCOllHhIX 3y6beB, nOCJIe HHe paCIIOJIaralOT MeLK,lI.Y nepexo,lI.-
HhIMM H lIHCTOBhIMH KpyrJIblMH 3y6bHMH, pa60TalOII.\HMH no cxeMe
Ko n<I>KlI Rlil. OpH 3TOM ,lI.JIHHY cpaCOqHOH 11 IIIJIHueBOH qaCTeH TaKMX
npOTHLKeK lIO,lI.CqHThIBaIOT lIO cpopMYJIaM (4.32) H (4.31).
lllar qHCTOBbIX H KaJIHoPYIOIII.HX 3yoheB t lI = t R 6epYT H3 Ta6JI. TI24
npHJIOLKeHH5I H rrpHHHMalOT paBHbIM Cpe,lI.HeMY lIIary. ilpOcpHJIb 3y6bes,
T. e. h, b, R H r, BhI6HpalOT H3 TaOJI. ilI9 rrpMJIOLKeHHH no Illary f lI .
B Il,eJI5IX ooeCneQeHH5I BbIxo.n.a llIJIHcpoBaJIhHOrO Kpyra IIPH o6paooT-
Ke OOKOBbIX CTOpOH cpaCOqHOH M lIIJIHI.I.eBOH: qaCTeH Me}K y 3THMH qac-
THMH M lIpHMbIKalO HMH K HHM J(pyrMMH qaCTHMH npoTHLKKH HYMHO
lIpe,n:ycMaTpHBaTb .n.OCTaTOqHOe paCCTOHHHe (He MeHee 15-30 Mrvl). ,QJl5I
llIarOB to MeHee 15 MM K JIHHe pe)KYIII.eH qaCTH L p ,lI.06aBJIHIOT
[(15+30)-t ] MM (nocJIe cpaCOQHbIX 3y6beB) H [(15+30)-t llI ] MM
(IIOCJIe Kpyr JIbIX 3yobeB).
TIpn BbI60pe pa3JIHQHhIX qacTeiI npoTjJ}KKH H3 pa3Hblx BapHaHToB
paCqeTa HY2KHO CJIe.n.HTb 3a TeM, qTo6hI Illar 3yobeB Ha CThIKe ,lI.BYX qac-
TeM ObIJI He MeHbllle rnara, npHH5ITOrO ..QJI5I nOCJIe)l.YJOru:eH 1I3CTH.
7 CHJIY pe3aHHR npH npoTHrHBaHHH Ha Ka)K.n.oH qaCTH npOTHLKKH
paCC1JHTbIBaIOT no <popMYJIaM:
Ha cpaCOqHOH qaCTH
B maxzqozpKp
P cp -==
Z c.$
.
,
(4.34 )
Ha KpyrJIoH qaCTH ,l(JIH cxeM cI>KIll, <DlllK
BKmaxzqozpKp
P K =
ZC.K
.
,
( 4.35)
86
H3 KpyrJIOH qaCTH JI51 CXeM K<PIlI, KIll, Ko.n<1>Kq.}{Ill
'!tdqozpK p
P K = ;
ZC.K
( 4.36)
1i3 WJI HlleB OH: qaCTH
Pw=
BwmaxzqozpKp
,
( 4.37)
Zc.w
r e Kp - rrpOH3Be eHHe rIOnpaBOqHhIX K03<pCPHIl,HeHTOB H3 T30JI. n21
npH,,10}KeHH5I.
I1pHBe,l(eHHb H p3CqeT npOT51}KKH - nepBhIH B3PH3HT p3CqeT3. B03"
MO)KHbI M .n.pyrHe.
8. PaCCQHTbIBaIOT JI.pyrHe BapH3HTbI C MeHbWHMH rrO,lJ.aqaMH 3a CqeT
H3MeHeHH5I zp H3 e)IJIHHUY B 60JIhllIYlO CTOPOHY no cp3BHeHHIO C rrepBbIM
B3pH3HTOM. YqHThIB351, qTO 3TH p3CQeTbI TpY,lI.OeMKH, BPY1JHYIO P3CCQH-
1'bIB3IOT 2-4 B3pM3HT3. npMMep TaKoro p3CqeT3 nOK333H HH}Ke.
npH paCqeTaX rrpOT51)KKH Ha 3BM nO 'beM Ha 3y6 rrepBoro BapH3H-
1'a YMeHbllI310T ,lI.JI5I Ka}K,lJ.OrO cJIe,lI.YIOlI(ero Ba pHaHTa Ha 0,01 MM H no-
JIyqalOT ,L{O 100 H oOJIee BapHaHToB.
113 IIOJIyqeHHbIX BapHaHTOB BbI6HpalOT OnTHMaJIhHhlit OCHOBaHHeM
){JI5I BhIOOp3 MorYT CJIY)l{HTh CJIe.n.YIOII(He n3paMeTpbI: ,L{JIHHa pe}KYlI(eH
qaCTH rrpOT5lJKKH, Herrocpe.n.CTBeHHO BJ1H5HOIlI.aH H3 3KOHOMHIO 6hICTpope-
JKyrneH CT3JIH, rrO,lJ.3 Q3, OOeCrreQHB31OII(351 Tpe6yeMYlO IlIepOXOBa TOCTh
o6pa60TaHHOH nOBepXHOCTH; ,lJ.JIHH3 33,lI.Heii nOBepXHOCTH, onpe,aeJI51IO-
351 IIOJIHbIM nepHO,lI. CTOHKOCTH rrpOT5I}KKH, H qHCJIO 3y6heB, BJIH5IIOlI(ee
H3 Tpy oeMKoCTh H3rOTOBJIeHH5I rrpOT5I}KKH. I1cXO,lI.51 H3 KOHKpeTHbIX yc-
JIOBHH MO}KeT OhITb BbI6paHa C3Ma51 KOpOTK351 npOT5L/KK3, JIHOO rrpo..
TH}KK3 He C3M351 KOpOTK351, HO C MeHhIlIHM IIO,l('beMOM H3 3YO, ooecne-
HBaIOlI(HM MHHHM3JIbHYIO mepOXOB3TOCTh, JIHOO npOT5I)J{K3 C 3y6h51MH,
HMelOlI(HMH H3HOOJIhWYIO ,lJ.JIHHY 33 HeH nOBepXHOCTH 3YOheB, JIH60
npOT5I)KKa, HMelOlI(aH MHHHM3JIbHOe qHCJIO 3y6heB.
,L{onYCK3eTC5I p33,lI.eJIhHhIll BhI60p OllTHM3JIbHOrO B3pn3HT3 ,lJ.JI5I
K3}K,lJ.OM q3CTH rrpOT51)l{KH (cp3COQH0i1, KpyrJIOM H IlIJIHIl,eBoi1). ,[{JI5I 011-
THM3JIbHOrO B3PH3HT3 P3CCqHThIB31OT ,lI.H3MeTpbI 3y6heB, 1JnCJIO H IlIH-
PHHY BhIKpY}KeK, n3p3MeTphI OOKOBoro rrpocpHJI5I CP3COQHbIX H IlIJIHne-
BbIX 3YObeB, 3 TaKJKe Bce OCT3JIhHbIe 3JIeMeHThI KOHCTPYKIl,HH npo-
T5I}KKH.
9. ,LLH3MeTpbI KaJIHopYIO HX (KpyrJIbIX D H 1< II IlIJIHI.I.eBbIX D R . m )
3y6beB rrpHHHMalOT paBHhIMH MaKCHMaJIbHOMY COOTBeTCTBeHHO BHyT-
peHHeMY H H3PY)I{HOMY ,lJ.HaMeTpy llIJIHneBOro OTBepCTH5I.
,QonycKH Ha HHX, 3 TaK}Ke Ha ,L{PyrHe 3y6h5I Ha3HallalOT ITO rOCT
7943-78. I1Hor,lI.a B 3aBHCllMOCTH OT KOHcpHrypauHH .n.eT3JIeH: ,lI.HaMeTp
Ka,TIH6pYIO HX 3yoheB H3MeH5IIOT nOCJIe HcnhITaHH5I HOBbIX rrpOT5I)KeK.
10. Haxo)].HT )J.HaMeTp Bna,IJ.HH <!JaCOqHbIX 3YObeB DB Ii lliJIlIII-e..
BbIX 3YObeB DB m. Ha npOT5ILKKaX co cxeMaMH cI>KIIl H cI>lllK DB.(f)
npUHHMaIOT paBHhIM do mln C IIOJIeM Jl.OnycKa rIO dI 1.
,QJI51 npOT5I}KeK co cxeMaMH I< <Dill H cpllI DB.(f) npHHHM310T paB-
HhIM d min .
81
,l{HaMeTp BIIa,lIJiH cpaCOtIHbIX 3y6heB co CXeMOH paCnOJIOLKeHH5I
Ko.n<l> Kq.l\lll npHHHMalOT paBHbIM .lI.HaMeTPY nOCJIe.rr.HerO nepeXO.lI.HorO
Kpyr .lIOrD 3y6a npe.rr.nocJIe.rr.Heii rpynnhI 3y6beB. nOJIe ,L{OrrYCKa Ha DB.ip
Ha3HaqaIOT no f9 HJIH no dll.
,LLHaMeTp Bna.lI.HH Ha 1ll.TIHueBOH qaCTH npOT5I)KeK Bcex npHHHThIX
cxeM, KpOMe <I>II1K, npMHHMalOT paBHbIM d min C nOJIeM JI.onYCKa no
f9 H dl1 B 3aBHCHMOCTli OT TeXHHqeCKHX Tpe60BaHHH Ha pacnOJIO)Ke-
HHe 1ll.HHI..I.eBbIX rra30B OTHOCHTeJIbHO OCM OTBepCTHH. TIpH MaJIhIX .lI.0-
nYCKax COOCHOCTH OT.lI.eJIbHhIX 3JIeMeHTOB lllJIHll,eBOrO OTBepCTHH MO}K-
HO npHMeHHTh nOJIe JI.OnYCKa rro e8. B 31 HX CJIyqa5IX 065I3aTeJIhHO CJIe-
JlyeT npllTynJI5ITh MeCTa nepeXO,L{OB nOBepXHOCTH Bna,L{HHhI K CTpYLKeq-
HOM KaHaBKe, HHaqe Ha BHYTpeHHefi IIOBepXHOCTH lIIJIHI..I.eBoro OTBepCTH5I
MorYT n05lBHThC5I 3a,llHphI.
,L:LJIH cxeMbI <f> IllK
DHoW =f,dOmin°
( 4.38)
11. OCYIll.eCTBJIHlOT paCqeT QHCJIa BbIKpY)l{eK N, IlIHpHHbI pe)KYIII.MX
ceKTopoB E, lllHpHHhI BbIKpYMeK a, pa.lI.Hyca Kpyra Rl\, paJI.Hyca BhIKPy-
MeK RB Ha npope3Hhlx 3y6b5lX Bcex qaCTeH npOT5I)KKH Bcex cxeM. Dpo-
pe3Hble qepHOBble H nepeXO.lI.Hble 3y6b5I lIIJIHl1,eBOH qaCTH Bcex BhInOJIH5I-
lOT C BbIKpY)KKaMH, TaK KaK Bcer.lI.a Ze.m = 2. BhIKPY)KKH Ha cpaCOqHbIX
3y6bHX HaHOC5ITC5I TOJIbKO Tor.rr.a, Kor,Ua qHCJIO 3y6beB B CeKII.HH ZC.Q.> ==2.
"4HC.TIO BbIKpy:tKeK Ha IIIJIHueBhIX npOT5I)KKaX paBHO qHCJIY Bna.rr. H:
N4J===N m =z. (4.39)
IT pH 3TOM Ha Ka)K.lI.OM 3y6e 06pa3yeTC5I no .lI.Be KpHBOJIHHefIHhIe cpaCKH.
3aqHIlI.alO He 3y6h5I <paCOK He HMeIOT.
IlIHPHHY (MM) pe:tKYInHX ceKTopOB rro TeXHOJIOrHqeCKHM C006pa)Ke-
HH5IM Ha npope3Hhlx cpacOlIHbIX H IllJIHueBhIx 3y6b5IX Ha3HaqaIOT o)tHHa-
KOBoil H onpe)l.eJI5IIOT no cpopMYJ1e
EctJ==EUl==b-2f, (4.40)
r.rr.e t -llIHpHHa cpacKH Ha Ill.HHl1,eBOM 3y6e, 6epYT H3 Ta6Jl. 032 npH-
JIO)KeHH5I.
YHcToBbIe IIIJIHueBble 3y6b5I npOT5IlKeK )1)151 IIIJIHI..I.eBoro OTBepCTHH
c I-M H.rIH 2-M rpynnoH KaqeCTBa no Hapy:tKHOMY .lI.HaMeTpy HMeIOT rpyn-
nOBoe nOCTpoeHHe (Zc.m.q = 2). Dpope3HhIe IIHCTOBble lliJIMI..I.eBhle 3y6h51
BhInO.llH5IIOT KaK qepHOBble H rrepeXO).I.Hble c cpacI<aM H C 06enx CTOpOH.
YHcToBbIe 3y6bH npOT5I)KeK, npe).I.Ha3HaQeHHhIe JI.JI5I rrpOT5IrHBaHH5I
IlIJIHueBbIX oTBepcTHH C 3-11 rpyrrnolI KaqeCTBa, BhInOJIH5IIOT c nO).I.'beMOM
Ha Ka/K,L{bIH 3y6 (zc.m.tl == 1), cpacoK OHH He HMeIOT. KaJIH6pYlOInHe 3y6h51
TaK}Ke He HMelOT cpaCOK. L{.H5I CJIYQa5I rK2<3 M Zc.m.-q= 1 qHCTOBhIe
lllJIHI..I.eBbIe 3y6b51 TaK:tKe HMeIOT nO.lI.'beM Ha Ka)K.lI.hIH 3y6 H cpaCOK He
HM eIOT.
IllHpHHa BhIKpY)l{eK Ha cpaCOqHhIX H IIIJIH eBbIX 3y6h5IX npH rrpHH5I-
TOM IIIHpHHe pe)l{yII(HX ceKTopOB 5IBJI5IeTC5I BeJIH41IHOH nepeMeHHoii
JI5I B qHCJIeHH5I pa).I.Hyca Kpyra 3TO He HMeeT 3HaqeHH5I, H rr03TOMY
IIIHPHHY .(MM) onpe,lI.eJI5IIOT npH6JIHLKeHHO no cpopMYJIe
88
nD
N
-Sw.
(4.41 )
a ==
ill
Pa,lJ.HYC Kpyra R K H pa,lI.HYc BbIKpY)KeK RB orrpe,lJ.eJI5IIOT no Ta6JI.
n27 npHJIOLKeHH5I.
4HCJIO 3y6heB B CeKIl,HH Ha KpyrJIOH qaCTH npOT5I)KeK cxeMbI <l>KllI
MO)KeT 6bITb paBHO O,lJ.HOMY HJIH ,lJ.BYM. ECJIH 3y6b5I HMelOT nO,lI.'beM Ha
Ka}K)].bIH 3y6 (ZC.K. == 1), TO KpyrJIbIe 3y6b5I BbIllOJIHHIOT 6e3 BbIKpYlKeK.
npH ,U.BYX 3y6b5IX B ceKURH Kpyr JIble npope3HbIe 3y6bH ,n:eJIalOT C BbI-
KpY)KKaMH, pacnOJIaralOlUJ'IMHCH CHMMeTpHqHO OTHOCHTeJIbHO cpaCOqHhlX
3y6heB. "4HCJIO BhIKpYLKeK Ha KpyrJIhIX qepHOBbIX Ii nepeXO,lI.HbIX 3y6bHX
j:lOJI)KHO 6hITb paBHO qHCJIY IIIJI!iueB, T. e. N R == z.
lllHpHHY (MM) pe}KyII(ero ceKTopa Ha npope3HOM 3y6e KpyrJIOH qac-
TH npOT5ILKKH nOCJIe CHHTHH BbIKPY}KKH D K npHHHMalOT paBHOH npHMep-
80 0,5BI\:
EK O,5BK.
( 4.42)
lIlHPHHY (MM) BhIKPY}KKH Ha npope3HhIx 3y6h5IX KpyrJIOH qaCTH
BbIqHCJIHIOT no cpopMYJIe
nD
a K == -E K .
N
( 4.43)
Pa,lJ.HYC Kpyra RR BhIKpYLKeK R B rrpH ,lJ.BY3y6oH ceKUMH BhI6HpalOT
H3 Ta6JI. 027 npHJIO)KeHH51.
4HcToBhIe H KaJIH6pYIOlll.He KpyrJIble 3y6h5I BhlnOJIHHIOT 6e3 BhIKPY-
)l{eK. Orrpe,lJ.eJIeHHe 3JIeMeHTOB BbIKpY}KeK H HX qHCJIa ,lI.JIH Kpyr JIOM qac-
TH npOTH)KKH cxeM K <I> ill H Ko.rr<l> Kq.RllI CB5I3aHO C MeCTOHaXO}K,lI.eHHeM
<!JaCOqHbIX 3y6heB. ,L:LJI5I cxeMhI K 1Il OHM paCnOJIOlKeHhI rrOCJIe KaJIH6-
PYIOl.I..\HX KpyrJIbIX 3y6heB; N, D, a H RB paCCqHThIBaIOT TaK }Ke, KaK H
.nJIH KpyrJIhIX npOTHllieK (CM. f.n. 3, n. 18 H 19).
JI51 cxeMhI Ko.nCPKlI.RlU cpaCOQHble 3y6b5I nOMern.31OT Me)KJlY Kpyr-
JIbIMH rrepeXO,lI.HhIMH H qHCTOBbIMH: 3JIeMeHTbI BbIKpYlKeK ,lI.JIH qepHOBhIX
I{ nepexO,lI.HhIX 3y6beB paCCqHTbIBalOT TaK }Ke, KaK If ,lI.JI5I KpyrJIbIX npo-
T5I}KeK, a qHCTOBbIe H KaJIH6pYlOI.IJ.He BbHI0JIHHIOT 6e3 BhIKpYlKeK.
12. ,LLHaMeTp H ,lI.JIHHY nepe,lI.Heii HanpaBJI5IIOIII.eH onpe,lI.eJI5IIOT TaK
JKe, KaK H ,lJ.JI5I KpyrJIbIX npOTH}KeK (CM. rJI. 3, rr. 22 MeTO,lI.HKH).
13. ,LLJIHHY nepeXO,lI.HOrO KOHyca Ln BbI6HpalOT H3 Ta6JI. il28 npHJIO-
JKeHH5I.
14. PaCCT05IHHe OT nepe,L{HerO TOpl1,a rrpOT5I)KKH ,lJ.O nepBoro 3y6a 00-
pe,lJ.e.H5IIOT B COOTBeTCTBHH C n. 22 MeTO,lI.I1KH (rJI.3)
KpyrJIhIX npOT5I}KeK. .: ......
15. HaxO,l(HT ,lI.HaMeTp H ,L{JIHHY 3a,L{HeH HanpaB- .::.......
JI5IIOII(eH.
,I:lMaMeTp 3a,lI.Hen HarrpaBJI5IIOII(en D 3 . H rrpHHHMa-
lOT paBHhIM ,L{HaMeTpy Bna,lI.HHhI lllJIHueB npOT5I}K-
KH: D 3 . H = D B . Ill . nOJIe ,lJ.OrrYCKa Ha D 3 . H TO )Ke, qTO
If Ha D B . Ill .
P u... PHe. 4.7.
eKOMeH,lI.yeMa5I ,lJ.JIHHa 3a,L{HeH HanpaBJI5I lO rneH BbloopKa Ha aopa-
npHBe.aeHa B Ta6JI. n29 npHJIO)KeHHH. 3HBHOM Kpyre
89
TH>KeJIbIe HJIH J(JIHHHhIe rrpOT5ILKKM, a TaK:iKe Bce npOT5I:iKKI1, pa6o-
TalO He B aBTOMaTHqeCKOM ll,MKJIe, M3rOTOBJI5IIOT C 3a HHMM XBOCTOBH..
KaMM, KOTopbIe MorYT 6bITh Tex ){{e pa3MepOB, 1ITO H nepe HHe, M.nH
MeHbIIIMX, TaK KaK OHM CJIY:iKa T TOJIhKO ,QJIfI nOJI..lI.epMKH rrpOT5I}KKH.
PeKOMeH aII.MH no .lI.JIHHe 3a.lI.HHX XBOCTOBHKOB npHBe.ll.eHhI B Ta6JI.
f130 npHJIO)KeHH51.
06I.I.(a5I .lI.J1MHa npOT5I}KKH paBHa CYMMe JIMH nepe.lI.HeH 1IaCTH (OT
(nepe,n:Hero Topn:a .lI.O rrepBoro 3y6a) L 1 , peLKymeH qaCTH L p , 3a,IlHea
HanpaBJI5IIOIII.eH 13.H M 3aAHero XBOCTOBMKa 13 XB:
L = Ll + Lp + 13eH + 13.xB.
( 4.44)
16. 06lI.\a51 Jl.JIHHa npOT51)l{KH He )J.OJI)l{Ha npeBhIlllaTb )J.J1HHbI, Jl.onyc-
THMOH iKeCTKOCThIO rrpOT51LKKM: L = (30-:-40) D, XO.ll.a lIITOKa npOT5I}KHO-
ro CTaHKa, HaMOOJIhIIIerO paCCT05lHH5I Me)K,n:y neHTpaMH KpyrJIOlllJIHcpO-
BaJIhHOrO M 3aT01lHOrO CTaHKOB, rJIy6HHbI BaHH HJIH IllaXT AJI5I HarpeBa
rro,a 3aKaJIKY H OTnYCK. B rrpOTMBHOM cJIyqae HY)I{HO cnpoeKTHpoB3Tb
.aBe rrpOT5ILKKH - nepBoro H BToporo TeXHOJIOrMqeCKMX nepeXO.lI.OB.
17. ECJIH npoT5ILKKY rrpHxO.ll.HTC5I ,n:eJIHTh Ha ,lJ.Be - nepBoro M BTOpO-
ro paoollero xo a, TO rrepe.rr.HIOIO HarrpaBJI5IIOIII.YIO BToporo pa6oqero
XOJI.a H3rOTOBJIRIOT co IIIJIMII.eBhIMH BhIcTyrraMH, pa3MepbI KOTOpbIX 6e-
PYTC5I no Ta6JI. I133 npMJIO}KeHH5I.
18. ,I::LJISI Toro lITOOhI llIJIHcpoBaJIbHhIH Kpyr npH IIIJ1H<poBKe oOKoBoro
npocpHJI5I cpaCOQHbIX M IIIJIMu.eBhIX 3y6heB He KaCaJ1C5I rrOBepXHOCTH Bna-
,QHH npOT5I)I(KH (3TO HarrpaBJl5I1OII(a51 rrOBepXHOCTh), Ha HeM .n.eJIaIOT BbI-
60PKY (pIiC. 4.7): h B ==C+O,5 MM.
MeTOAHKa paClIeTa npOTSI}KeK C KoppHrHpoBaHHblM
npocIJHJIeM 3y6beB
B n:eJI51x nOBblIIIeHH5I IIepHo a CTOHKOCTH IIIJIHIJ,eBbIX
rrpOT51)KeK HX 3y6b51 BhlnOJIH5IIOT CO BcnOMOraTeJIhHhIMH yrJIaMM B DJIa-
He (yr JIaMH rrOjI.HYTpeHH5I). ,LLJI5I 3Toro HX IIIJIMcpYIOT B HaKJIOHHOM rro-
Puc. 4.8.
nOJIOJKeHHe npOTSl1KKH npH IIIJ1H4JoBaHHH 6oKoBoro npocIJHJUI mnH eB c nOAHRTbiM
3a.a.HHM o.eHTpoM
90
JIOJKeHHH, nOJ.I.H51B 3a)1.HHH XBOCTO-
BHK IIO OTHOlIIeHHIO K nepe).J.HeMY
(pHC. 4.8). B pe3YJIbTaTe 3Toro
TIpOcpHJIb rrpHM060QHbIX H cpacoq-
HbIX 3y6beB B nOrrepeqHOM CeqeHHH
H3MeH5IeTC5I OTHOCHTeJIbHO npocpH-
JI5I IIIJIHI..I.eBOrO rra3a .ll.eTa,JIH. 9TOT
H3MeHeHHbIH rrpocpHJIb Ha3bIBalOT
KoppHrHpoBaHHlbIM.
3a,lJ.aBa5ICb BcnOMOraTeJIbHbIM
yrJIOM B nJIaHe <Ph paCCqHTbIBaIOT
nO DeM 3a HerO ueHTpa C H yrOJI
npOcpMJI5I Brra,lJ.HH lllJIHI..I.eBbIX
3y6beB npOT5I}KKH H IlIJIHcpOBaJIb-
HOrO Kpyra 2WK.
DOl('beMbI OCH rrpOT5I}KKH C UJ
(qepHOBbIX lIIJIHueBbIX 3YObeB) Ii
CcIJ (<paCOQHbIX 3y6beB) paCCqHTbI-
BaIOT ,l(JI5I COOTBeTCTBYIO HX yqaCT-
KOB rrpOT5I}KKH, Ha KOTOpbIX 3y6b5I
u v
HMeIOT rrOCT05IHHbIH nO,lJ.'beM H Illar, a BeplIIHHbI HX JIe}KaT Ha O,lJ.HOH
Boo6pa}KaeMOH KOHHqeCKOH rrOBepXHOCTH. TaKoH yqaCl0K, yqaCT-
BYIOll1. H fI B paCqeTe npocpHJI5I, 6y.aeM B ).J.aJIbHeHllleM Ha3bIBaTb pac-
qeTHbIM.
npOcpHJIb nepeXO).J.HbIX, qHCTOBbIX H KaJIH6pYIOIlI.HX IIIJIHI..I.eBbIX
3y6beB, He yqaCTBYlOmHX B paCqeTe, nOJlyqaeT He6oJIblllOe HCKa)KeHHe.
Ho TaK KaK B na3Y B MeCTe nepexo.n.a 60KOBoro rrpocpHJI5I B .n.HO Bna-
HHhI npeJ.I.YCMOTpeH pa.lI.HYC, a Ha BaJIY - cpaCKa, TO He6oJIbliiOH rrpH-
nYCK, KOTOpbIM cpe3aeTC51 nepeXO,lJ.HbIMH H qHCTOBbIMH 3y6b5IMH, npH-
XO.n.HTC5I Ha 3TOT Hepa60qHH yqaCTOK rra3a. CPaCOqHble 3y6b5I - TOJIbKO
qepHOBbIe, H B <pOpMHpOBaHHH rrpocpHJI5I cpaCKH yqaCTBYIOT Bce 3TH
3y6b5I.
P aClIeT rrpocpHJI5I IIlJIHneBbIX 3y6beB OTJIHtIaeTC5I OT paCqeTa npo-
<pHJI5I cpaCOqHbIX 3y6beB H npOH3BO!l.HTC5I pa3).J.eJIbHO.
PaClleT npo4JHJlSI llIJ1H eBbIX npSlMo6ollHbIX 3y6beB. PaCqeT IIpOcpH-
JI5I lllJIHI..I.eBhIX np5IMo6oQHbIX npOTH}KeK 3aKJIlOqaeTC5I B orrpe,lJ.eJIeHHH
nO,II.'beMa OCM npOT5IlKKH Ha paCqeTHOM yqaCTKe (nOCJle,1J.HerO 3y6a OT-
HOCHTeJIbHO nepBoro) G m , KoppHrHpOBaHHoro yrJIa rrpocpI1JI5I Brra).J.H-
HbI IIIJIHI..I.eBbIX 3y6beB H a6pa3HBHoro Kpyra 2(01\ H BeJIHtIHHbI rrO).J.'beMa
3aJ.I.HerO I..I.eHTpa C Ha ,lJ.JIHHe npOT5I}KKH L.
LCrI5I paCqeTa npocpHJI51 H3 Ta6JIHII.bI ,lJ.HaMeTpoB 3y6beB onpe,lI.eJI51-
lOT HOMepa nepBoro N A Ii nOCJle.n.Hero N E qepHOBbIX 3y6beB Ha pac-
qeTHOM yqaCTKe ,lI.JIHHOH lm', pa).J.HYCbI 3THX 3y6beB RA H RE. ,QpyrliMH
HCXO,L{HbIMH ,lJ.aHHbIMH ,lJ.JI5I paCqeTa 5IBJI5IIOTC5I HOMHHaJIbHbIH pa3Mep
IIlJ1HI..I.eBOrO na3a b, qHCJIO IIIJIHI..I.eB Z, Illar qepHOBbIX 3y6heB B orrTH-
MaJIbHOM BapHaHTe to H BcnOMOraTeJIbHbIH yrOJI B nJIaHe <PI, BeJIHQH-
HOM KOToporo 3a.n.aIOTCH B npe.n.eJIax 2-3 0
<POPMYJIbI )1.JIH paCqeTa BbIBO,ilHTC5I R3 lIocTpoeHHa pRC. 4.8
II 4.9.
Yf
---
x
PHC. 4.9.
nonepelfHoe CeqeHHe npHMOOOqHOrO
1UJlHneBOro na3a:
1 - HCXO)J.Hbltl npO<pHJIb na3a; 2 - KOp-
pHrHpoBaHH tl rrpO Hnb nocneAHero pac-
qeTHOrO 3y6a H a6pa3HBHoro Kpyra
91
B TaKOH noc e OBaTe bHOCTH:
sin A E = b .
DE '
rJ(e AA H /.wE - yrJIbI Me)J{ y OCblO CHMMeTpMH illJIHueBOro na3a eTa-
JlO H pa HycaMH, npOBe eHHbIMH K TOllKaM A H E H3 ueHTpa 0; 6 A H
6 E - yrJIbI, OnOJIH5IlOll\He O 8 yrJIbI AA If AE; hE - BbICOTa lllJIHUeBO-
ra BblcTyna ,LI.eTaJIH HJ1H pa3HOCTb opAHHaT TOqeK A H E, J1e:tKaIl\HX H3
OKPY2KHOCTHX paCqeTHbIX 3y6beB C .lI.HaMeTpaMH D A M DE B CHCTeMe
XOY.
B cpopMYJIe (4.52) BMeCTO L MO)Ker 6bITb 1000 MM MJIM Pyra5I yc-
TaHOBOllHa51 ,LI.JIHHa npOTH)KKH.
PaC'IeT npo4JHJIH (j)aCO'lHbIX 3y6beB. <l>acKH B illJIHII.eBbIX rra3ax OT-
BepCTH5I, 3aJl.aHHble qep-
Te)KOM HJIH rrpe,UycMoT-
peHHbIe H3 TeXHo orH-
qeCKHX co06pa)KeHMii,
o6pa3yroTcH npM npoTH-
rHBaHHH oTBepCTH5I 4>a-
COQHbIMH 3y6b5IMH, pac-
nOJIO)KeHHbIMM nepe,lt
KpyrJIbIMH MJIH lllJIHue-
BbIMH 3y6b5IMH. B OT-
JIMtIMe OT np5IMo6oq-
HbIX 3y6beB ,Zl,JI5I cpaco1.J-
HbIX 3a)J.alOT He BcnO:\10-
u
raTeJIbHbIH yrOJI Ha nJ1a-
He <PI, a KoppHrMpOBaH-
HbIH yrOJI npO<pHJI51 H
u
KOTOpbIH nOJIyqalOT noc-
JIe llIJIHcpOBaHHH c noJI.'b-
eMOM 3a,LI.HerO ueHTpa.
PaCqeT npocpH H rrpOH3Bo,aHTC5I
.... b
Sin AA =
DA
180
°A=
AA; 0E=
z
( DE
hE=REcos oE-R A cas 0A; R E = 2
180
w==B-
z
w K = (t) - <Pt;
C - hE (tg U) - tg U)K)
w-
tg O>K
l :::::: to (N E - N A);
c CwL
I '
1 ill
yt
to
I
!
""I(,
o
.l
Pac. 4.10.
WJlH4JoBaHHe 60KOBoro npocjJHJlH 4>aCOQHblX
sy6bes nepH4JepHeH WJlH4JoOaJlbHOrO Kpyra:
1 - HCXO,II.Hbta npO HJlb yrJIOBblX (<baCOtlHblX) na30B;
2 H 8 - 60KOBOA npoq)lfJIb DOCne,IJ.HerO H nepBoro 4>a.
C04HbIX 3y6beB (KoppHrHpOBaHHb!ii)
92
( 4.45)
180
-AE;
( 4.46)
z
; R A = D );
(4.47)
( 4.48)
( 4.49)
( 4.50)
(4.51 )
( 4.52)
nnH KOHTpO H npO HnH aCOqHWX 3y6heB Heo6xo HMa napa nenb-
HOCTb .ZI.BYX CTOpOH cpaCOqHbIX 3y6heB. ,Q H 3TOrO npH llIJIHcpOBaHHH
yro K O )KeH HMeTb Onpe eJIeHHOe 3HaqeHHe, ero npHHHMalOT no
Ta6JI. I134 npHJIO)KeHH5I. YrOJI <paCKH Ha eTaJIH cp He3aBHCHMO OT
3aJ{aHHoro qepTe>KOM nOCJIe npOT5IrHBaHH5I 6y eT COOTBeTCTBOBaTb
3HaqeHHHM, npHBe eHHbIM TaK)Ke B Ta6JI. 034 npHJlO)KeHHH.
ll1JIH OBaHHe cpacoIIHbIX 3y6beB C nO,lI,H5IThIM 3a,lI,HHM UeHTpOM MQ-
.>KeT BhlnOJIH5ITbCH ,ZI.BYM5I cnoco6aMH:
I) 06pa3YIO eH (nepHcpepHeH) nJIOCKOrO np5IMOrO Kpyra - 3a,n-
HHH ueHTp nO HHMaeTC5I B HanpaBJIeHHH CTpeJlKH B (pHC. 4.10);
2) npocpHJIbHbIM KpyroM - 3a,lI,HHll U.eHTp nO.lI-HHMaeTCH B HanpaB-
JIeHHH CTpeJIKH F (pHC. 4.11).
Cl>opMynbI J{JIH paCqeTa nO 'beMa OCH npOTH}KKH Ha paC1JeTHOM
yqaCTKe C cP H pa3MepbI H A H H B npH Ill HcpOBaHHH cpaC01JHbIX 3y6beB
nepHcpepHeH np5IMOrO Kpyra BbIBeJI.eHbI H3 nOCTpoeHHH pHC. 4.10 H 4.11.
OOC eJI.OBaTeJIhHOCTb pacIIeTa C cP npl1 llIJIHcpoBaHHH npo<pHJI5I nepH-
q>epHeH np5IMOrO Kpyra cJIeJJ.YlOma5I:
.) b + 2C
SIn 1\===
d
( 4.53)
d sin (A + cP)
sin PA ===
2RA
. d sin (A + cP)
SIn P E===
2RE
AA === P A - <fJ; AE=== P E - <p;
H A ===R A sin ( K+AA);
HB=R E sin ( K+AE);
Ccp=HA-H B ;
( 4.54 )
( 4.55)
( 4.56)
( 4.57)
( 4.58)
( 4.59)
( 4.60)
B<p max =2R A sin AA,
rJI.e PA If PE - BHellIHHe yrJIbI KocoyrOJIbHbIX TpeyrOJIbHHKOB COOTBeT-
BeHHO OAK HOEK (pHC. 4.11).
BeJIHqHHbI 1({>' H C onpeJJ.e 5IlOT no cpopMYJIaM (4.51) H (4.52), no,l{-
CTaBHB B HHX BMeCTO fill' BeJIHqHHY [cP'
OOA'beM OCH npOT5I)KKH Ha paCqeTHO f yqaCTKe CcI>' npH llIJIHcpOBa-
HHH npO HJIbHbIM KpyroM paCCllI1TbIBalOT no cpopMy e
C' = H A - H B .
cp sin W K
(4.61 )
cI>opMy a BI:,IBeJI.eHa H3 nOCTpOeHH5I pHC. 4.12. B cpopMYJIe (4.61)
yrOJI (OR BbI6HpaIOT no ra6JI. 034 npHJIO)KeHH5I B 3aBHCHMOCTH OT 1JHC-
JI3 Ill HII.eB z, pa3MephI H A H H B BbIQHCJI5IIOT no cpOPMY JlaM (4.57) 11
(4.58), Bcp max - IDO cpopMYJIe (4.60).
93
Pue. 4. t 1.
n OnepeqHOe CeqeHUe oTBepeTHSI e 4» a -
COIJHblMH na3aMH (1) H nepBblH (3) H
nOCJIe,ll.HU" (2) r!JaCOqHbIe 3y6bSl
I
1:/'
II-
()
PHe. 4. t 2.
CxeMa WJIHr!JoBaHHSI oOKoBoro npo4tHJlSI
lJJaeOqHhIX syobeo npo4JHJlbHblM WJJH4JO-
BaJIbHbIM KpyrOM:
1 - HCXO,nHhlA npO HJIb; 2 - KoppHrHpoBaHHhlA
npo4>HJlh nOCJIe,nuero aCOqROrO sy6a
npHMep paC1JeTa npSlMo6oqHOH npOTSI}I{KH
HCXO,Il.Hble Jl.aHHbIe. 1. npOT5IrHBaeMaH 3arOTOBKa: Ma-
TepHaJI - CTaJIb 40X; TBep,ZI.OCTb Ha onepaaHH npOT5IfnBaHH5I H B
229; COCTO.HHHe - nJCJIe OT)I{llra, OTBepcTHe nOJL npoTHrHlBaHHe no-
JIyqeHO 3eHKepOBaHHeM, ,ZI.HaMeTp ero JI.O rrpOT.HrHBaHH.H do =
=- 35, 1 H 11 (+0, 16), BHyTpeHHHH HaMeTp lIlJIHueB d = 36H7+ 0 ,025; Ha py2K-
HbIH JI.HaMeTp IlIJIHueB D=42HI2+o,25; IlIHpHHa IlIJIHueBbIX Bf1aJI.HH
b=7D9+o,076; qHCJIO IlIJIHueB z=8; pa3Mep cpacKH 0,5X45°, napaMeTp
wepoxoBaTocTIi nOBepxHOCTeH: Ra 2,5 MKM no d, Rz 20 MKM no
b, Rz::::;;20 MKM no D, ,llJIHHa npOT5IrHBaHHSI 1=80 MM.
2. CTaHoK: ropH30HTaJIbHO-npOT5.L}KHOM, MO,ZI.. 7B56; T5IrOBa.H CIIJIa
Q== 196 000 H; MaKCHMaJIbHa.H AJIHHa XO,lLa IIITOKa Lmax= 1600 MM,
J(Hana30H pa60QHX CKopocTeii 1,5-11,15 M/MHH, COCT05IHHe - Y OB-
JIeTBOpHTeJIbHoe.
3. npOH3BO CTBO - KpynHocepHHHoe.
4. ,[{JIHHa npOT.H2KKH, )I.OrrYCTHMaH B03M02KHOCT.HMII HHcTpYMeH-
TaJIbHOrO npoH3Bo cTBa II 3aTOlfHoro OT,lI.e,TIeHH.H, Lmax= 1500 MM.
nOpSlJI.OK paCqeTa. PaCqeT HaqHHaeM C YCTaHOBJIeHHSI cxeMbI pac..
nOJ10)KeHH5I 3y6betB H3 npOT.H)I{Ke, rpynnbI o6pa6aTbIBaeMOCTH H rpyn-
DbI KaIJ:eCTBa. llpHHHMaeM npeJJ.BapHTeJIbHO cxeMY paCIIOJIO)l{eHHH
ay6beB <pKlll. OKOHqaTeJIbHO cxeMa pa.cnOJIO}KeHHH 3y6beB 6YJI.eT yc-
TanOB.;rreHa nOCJIe paCqeTa JI.JIHHbI KpyrJIOM qaCTH. ECJIH lK> 1,51, TO
aCOqHble 3y6bSl CJIeAyeT pacnOJIO)J{I1Tb Me)KJI.Y nepeXO,ZI.HbIMH Ii QHC-
TOBbIMH Kpyr JIbIMH 3y6b.HMH, T. e. npHH.HTb cxeMy Ko.n<p Kq.l<lll.
1. fpYIIIIY oopa6aTbIBaeMocTH YCTaHaBJIHBaeM no Ta6JI. nI npHJIO-
LKeHH5I. CTaJIb 40X C HB 229 OTHOCHTCH K I-H rpYIIrre o6pa6aTbIBa-
eMOCTH (CT3JIb BH3KaH).
94
2. fpyrllrry KarIIeCTBa YCTaHaBJIHBaeM )l}I5I Ka)K,[{oH IIOBep HocTI1
IIIJlHII.eBOrO oTBepCTH51 OT,QeJIbHO lID Ta6JI. TI2 rrpHJIO)KeHH51. TaK KaK
l.(eHTpHpOBaHHe rrpOM3BOJI.HTC5I no BHYTpeHHeMY .J.HaMeTpy C d = 36H7
II napaMeTpOM rnepOXOBaTOCTH nOBepXHOCTH BhIcTynoB Ra 2,5 MKM,
TO rpyrrna KaqeCTBa nOBepXHOCTH BblcTynoB - 2-51, 60KOBbIX CTOpOH II
nOBepxHocTeH 'Bna,lI.HH - 3-51.
3. 3a MaTepnaJI pa60lJeH IIaCTH npOT5I)KKH (rrepeXOJI.HbIH KOHYC, ne-
peAH5I51 HalllpaBJI5IlOrna5I, pe:m:YIll.a51 IIaCTb, 3a,L(H5I5I HanpaBJl5IIOIlI.a51 11
3a)1.HHH XBOCTOBHK) npHHHMaeM 6bICTpOpeJKYIll.YlO CT3J!b P6AM5 no
Ta6JI. 03 InpHJI02KeHHH.
4. KOHCTPYKILHIO InpOT5I}KKI1 rrpHHHMaeM C rrpHBapeHHbIM XBOCTOBH"
KOM, MaTepIIaJI XBOCTOIBHKa - CTaJIb 40X. KOHcTPYKnHIO XBOCTOBHKa
II pa3MepbI npHHHMaeM no rOCT 4044-70 (MJIH no Ta6JI. n4 npHJIO-
>KeHH5I). ,[{HaMeTp nepe,ZI.HerO XBOCTOBMKa D XB = 32 MM, AHaMeTp 3a)L-
Hero XBOCTOBHKa D3 XB = 25 MM.
CHJIY, ,nonYCTHMYJO npOlJ:HOCTb1O nepe,L(HerO XBOCTOBHKa, paCCqH-
TbIBaeM no cpOPMY cJle (3.1), npHH5IB nJIOIll.a,LLb onaCHoro CelJeHHH F on =
=490,9 MM 2 no Ta6JI. TI4 npHJIO)l{eHHH H peKOMeH,lI.yeMoe H3np5I}KeHHe
npH paCTH}KeHMH [a]p=300 Mila;
PXB=SOO.490,9= 147270 H.
5. TIepe,lI.HHe 'M 3aJI.HHe yrJIbI 3y6beB npOT5I)KKH BbI6HpaeM no Ta6JI.
TIS npHJIO}KeHH51.
Ilepe,lI.HHH yrOJI lJ:epHOBbIX M rrepeXO,II.HbIX 3y6beB l' = 20°, IIHCTOBbIX
M KaJlH6pYIOIII.HX v= 20° 3a HHM yroJI qepHOBbIX H nepeXOJI.HbIX 3y6b-
eB uo= 3°, q}TCTOBbIX at! = 2°, KaJIH6pYIOIII.IlX aI\ = 1 0 LLonycKH H3 [Ie-
peAHHe H 3aJI.HHe yrJIbI no faCT 9126-76.
6. CKOpOCTb pe3aHI151 YCTaHaBJIHBaeM no Ta6JI. D6 npHJIO}KeHHH,
J(JIH KpyrJIOH lJ:aCTI1, KOTopaH HMeeT HaH6o lee BbICOKYIO rpynny KalJ:e..
CT1Ba (2-10), v=7 M/MHH. TaK KaK B Ta6JI. TII npHJIO)KeHH5I CTa.JIb 40X
OTMeqeHa 3Be3,lI.OqKOH (B5I3Ka5I), TO CHH}KaeM CKOpOCTb Ha 20 0/ 0 , T. e.
v = 7 · 0,8 = 5,6 M/MHH. 9ra CKOpOCTb BXOAHT B ,ZI.H3rra30H CKopocTeti
CTaHKa.
7. Onpe,lI.eJI5IeM nOAaqy qepHOBbIX 3y6beB no cpe HeH Hapa60TKe
Me>KJI.Y BYMH OTKa3aMM (no Ta6JI. IT7 npHJIO}l{eHH5I). CHalJ:aJIa YCTa-
HaBJIHBaeM Hapa60TKY iJnCTOBOH IIaCTH npH Sz. = 0,02 MM H v =
= 5,6 M/MHH: T = 83 M. ,.QJIH qepHOBbIX 3y6beB npM t' = 5,6 M/MHH If
T=89 M Szc=0,25 MM Ha 3y6 H3 CTOPOHY. Hapa60TKa C YIIeToM no..
npaBOQHbIX K03cpcpHUHeHToB, npHH5ITbIX no Ta6JI. IT 18 npHJIOmeHH5I,
COCTaBJI5Ier T M.H= 83 · 0,8. 1 1. 1 1 1 = 66,4 M.
,UJI51 Kpyr JIOH qaCTH, npe,II.Ha3HaqeHHOH )1.JI5I o6pa6oTKII nOBepxHo"
CTH 2-H rpynnbI KaqeCTBa, nO,ZI.a1JY qepHOBbIX 3y6beB OrpaHHqMBaeM
peKOMeH,lI.aII.l151MH Ta6JI. TI 17 npHJIOMeHH5I: ,lI.JIH v = 5,6 I/MMH H no..
lBepxHocTH 2-H rpynIIbI KaIIeCTBa Szc = 0,19 MM.
8. OnpeJI.eJI5IeM rJIy6HHY cTpy:tKeQHOH KaHaBKH no cpopMYJIe (3.2) t
npHH5IB npe,lI.BapHTeJIbHO K03cpcpHUHeHT nOMe aeMOCTH K = 3 COfJIaCHO
peKoMeH a HHM MeTO,QHKH.
JIH KpyrJIbIX 3y6beB
h= 1,1283 y 3.80.0,19=7,62 MM.
95
no Ta6JI. n 19 npI1JIO)l{eHI151 npHHlIMaeM OJIH}KaHlI1YlO 60JIbWYlO
I\rIy6HHY crpy*elJ:HOH KaHaBKH h= 8.
,lIJI5I cpaCOQHbIX 11 1Il.1IHueBbIX 3y6beB
h= 1, 1283y3 .80.0,25 =8,74 MM.
ITa Ta6JI. D19 npHJIOmeHHH npHHHMaeM h=9 MM. rJIY Y CTPY-
)KelJHOH K3HaBKH, ,II.OnYCTHMyIO )KeCTKOCThlO llPOT5I)KK r ,II.H:aMeTP ce-
GeHHH no ,LLHY CTpYLKellHOH K8HaBKH < 40 MM), OrIpe.a. JIHeM no cpop-
M}\,le (3.4).
AJI51 cpaCOqHbIX 11 KpyrJIbIX 3y6beB /1
h)l(=O,23.35,1 =8,073 MM, I
I
)I.Jl51 IlIJJIIll.eBbIX j'
h)K=O,23.36==8.,28 M
113 Ta6JI. n 19 npI1JIO)KeHH5I npHHHMaeM ,.6JIHLK3HIllYIO MeHbwyIO no
OTHOll1eHHIO K paCqeTHOH rJIy6HHY h= 8 Mi U}IH Bcex lJacTefi npOT5I}I{..
KH.
TaK KaK rJIy6HHa cTpYJKeqHOH K8HaBKH )l.JI.H cpaCOlJHbIX H lliJIMije-
BbIX 3y6beB npHH5ITa H3 yCJIOBHH )l{eCT!<OCTH rrpOT5I)KKH, TO )l.JIH p33Me-
UJ,eHHH CTPY)l{KM B cTpy*etIHOM KaH Ke YMeHblllaeM no..naqy no <pop-
MY.TJ e ( 3.5) :
82
Szo=O,785 I O,209 O,21 MM.
3.80(
BCJIe CTBHe oKpyrJIeHH5I nO;iaQI1 .no 60JIbWerO 3HaqeHH5I K03<pcpa-
1I.HeHT nOMeInae '10CTH YMeHb1ll3.eTC51 AO 2,99. ·
9. OIIpe,AeJIHeM mar 1JepHoBbIx 3y6beB to H tJHCJIQ o HoBpeMeHHo pa-
6oTaIOIllHx 3y6heB zp. War IIepHoBbIX 3y6beB npHH11MaeM rIO Ta6J1.
n I 9 npI1JIO}KeHH5I H3HMeHbIll11M H3 Bcex HMelO nXC51 Ii cooTBeTcTBYlO..
InHl\f JJ.8HHOH rJIy6HHe cTPY)I{eQHOH KaHaBKH h = 8 MM : to = 18 MM. Oc-
TaJIbHble 3JIeMeHTbI npocpHJI5I: b =6 MM; r=4 'MM; R= 12 MM.
4I1CJIO OAHOBpeMeHHO pa60ralOIlIJIX 3y6beB paCCQRTblBaeM rIO <pop-
MY.}Ie (3.7);
Zp=
80
18
+ 1 5.
10. OrrpeAeJlHeM MaKCHMaJlbHO onycTHMYIO CHlIY pe3aHHSI Pmax-
npHHHM3eM Pmax HaHMeHblUeH 113 Tpex CHJI: PCT' P XB 11 p o . n :
P cT =O,S.20000.9,81= 156960 H;
P XB ==== 147270 H (CM. n. 4).
BeJIl1QHHY Po.n orrpe)l.eJI5IeM no cpop IYJIe (3.9), npHH5IB [o]p=
=400 Nina:
po.n=O,785<35,1-2.8)2 400=114550 H.
CJIe).1.0B8TeJIbHO, rrpHHHMaeM Pmax=Po.rr= 114 550 H.
11. OnpeJI.eJIHeM lll1CJIO 3y6heB B rpyrrrre Zr no <POPMY JIe (4.1) AJlD
Ka}KAOH qaCTH npOT5I)I{KH pa3JJ.eJIbHO, IIO)J.'craBHB B <POPMYJIY (4.1)
96
BMeCTO Bmax 3HaqeHH5I B(fJ DlaX, B K max H Bm max. MaKCHMaJIbHYIO ,QJIH-
BY pe)KYIIJ;HX KpOMOK Ha cpaCOQHbIX 3y6b5lX onpeAeJI5IeM rrpHOJIH}KeHHO
no cpOPMY JIe (4.2):
Bq.max=7 +2.0,5+<36-35,1)=8,9 MM.
B Ta6J1. n31 npH 7JO}KeHH.H npH Bq, max 9 11 D=25-.;-50 MM ,nony-
CKaerC.H Zc = 1.
MaKC11MaJIbHYlO )J}IHHY pe}KYIIl.HX KpOMOK Ha KpyrcTIbIx 3y6bHX on..
peAeJI5IeM no cpOp IY JIe (4.4):
3, 14 . 36
B Kmax = -(7+2.0,5)=6,14 MM.
8
3HaqeHHe B1\ max MeHbllle 3HaQeHH5I, npH KOTOpO .lI.OnycKaeTcSI
pa60Ta 6e3 pa3,II.e.neHI15I CTPY)KKH; CJIe.rr.oBaTeJIbHO, npHHHMaeM Zc I( = 1.
MaKCHMaJIbHa.H ,lI.JIHHa pe)KYllI.Hx KpOIvIOK Ha illJIHueBbIX 3y6bHX
Bmrnax=b max =7,076 MM.
Y.J:eJIbHYIO CHJIy pe3aHH5I qo fB cpopMy.ne (4.1) onpe eJI.HeM 113 Ta6J1.
020 npHJlO)KeHHH: JJ.JI5I V=20° H Szo=0,21 MM qo=398 H/MM, JIH
Szo= 0, 19 MM qo = 362 H/MM; nOnpaBOtIHble K03cpcpHll.HeHTbI HaXO,l(HM
no Ta6JI. TI21 npI1JIOmeHH51: K p r>.l= 1; K pp == 1; K PK = 1,1 ,lI.JI5I cpaGOllHblX
H illJIHll.eBbIX 3y6beB, TaK KaK rpynna KaqeCTBa JI,JI51 HIIX 3-51; ,nJI5I Kpyr...
JIbIX npH 2-11 rpYIIrre KaqeCTBa K PR = 1. rIorrpaBOQHbIH: K03cpcpJ1QHeHT
I(ro= 1 ){JI5I COIK, npHH51ToH no Ta6JI. n18 npHJIO)KeHH.H (CYJIbcpocppe-
SOJI B),
8,9.8 398.6 1 I I I 1
Zc.<t> = 114550 = 1,63;
ZC.K =
6,13.8 362.6.1 I I 1
114550
= 0,93;
7 076.8.398.6.1 1 I 3
Z c.w = ' = 1 , .
114550
TIpHHHMaeM: zc.d:I = 2; ZC.R= 1; ZCIII == 2.
12. PacIIpe,il.eJI5IeM npHIIycK Me:iKAY pa3HbIIVIH tIaCT5IMH M 3y6b5lMH
npOT.H)l{KH. TIpnnycK Ha cpacolIHYlO qaCTb onpe,lI.eJI.HeM no cpopMYJle
(4.5), fAe D<fj HaXOJ(I1M no cpopMYJIe (4.9), a ,lI.HaMeTp OKPY)KHOCTH
DE, npOXO)l5ILQHH Qepe3 rOQKY nepeCeqeHH5I HCXO)lHbIX npocpHJIeH cpac-
KIf H np5IMo6oQHOrO IIa3a, no cpopMYJlaM (4.6) - (4.8):
sinA= 7,076+2.0,5 ==0224178- A=129545°.
36,025 ' , , ,
ctg "E=
(7,076 +2.0,5) ctg 12,9545° +2.0,5 ctg45°
7,076
AE= 11,0876°;
D E = 7,076 36t8 MM;
sin 11 ,0876°
DtP=.36,8+0,4==37,2 MM;
A4J=37,20 - 35, 1 == 2,1 MM.
=5,102904;
4-338
l¥1
npHUYCK H3 KpyrJIYIO qaCTb H3XOJI.HM no <popMYJIe (4.13)
A K ==36,025- 35, 1==0,925 MM.
IlpHnycK Ha IIepHOBbIe 3y6b5I A HO onpe eJ1.HeM no cpopMYJIe (4.14)
r,lI.e A H . n = 0,24 MM H3 Ta6JI. Il23 npHJIO)KeHH5I A1Ct} = 0, 12 MM H3 Ta6J1.
022 npHJIO)KeHH.H:
AI{O=== 0,925 - (0,24 + 0, 12)== 0,565.
ilpRIIYCK H3 1ll.1IHl(eBYJO qaCTb HaXO,lU1M no cpopMYJIe (4.15), a Ha-
MeTp IIepBoro llIJIHll.eBOro 3y6a Dill) - no cpopMYJIe (4.16):
DUll = 36,8 + 2. 0,21 === 37,22 MM;
Aw===42,25- 37,22==5,02 MM.
IlpHny,cK Ha IIepHOBbIe IlIJIHueBbIe 3y6b51 OIIpelI.eJI.HeM IIO <popMYJIe
(4.19), B KOTOpOH Ala n= 0,24 MM H3 Ta6JI. Il23 npHJIO)KeHH5I, Am. =
= 0,08 MM H3 Ta6JI. Il22 npHJlO)KeHH.H:
Awo=== 5,02 - (0,24 +0,08)===4,70 MM.
13. HaXO,II.HM I.J:HCJIO rpyrrII IIepHOBbIX 3y6beB io, OCT8TOIIHbIH IIPH-
nYCK A OCT H pacnpeJI.eJIeHIfe ero. 4HCJIO rpyrrn qepHOBbIx 3y6beB io on-
peJI.eJI5IeM no <popMYJIe (3.17), IIO,il.CTaBHB B Hee COO11BeTcTBYIO He
3HalJeHH5I Ao H Szo, npHH.HTbIe ,lI.JI5I "Ka)K,II.oi1 IIaCTH; OCT3TOIIHbIH npH-
nycK HaXOAHM no cpopMYJIe (3.18):
. A<tJ 2 , 1 - 5 .
ltP=== - ,
2S zcP 2.0,21
i KO == A Ko _ 0,565 === 1,49;
2S ZOK 2 . 0 t 19
A OCTeK ===0,565- 2.0,19.1=0,185 MM.
TaK KaK AOCT.K>2Snl (CM. Ta6JI. Il23 npHJIO)KeHH.H), TO JI.o6aBJI5IeM
O HH lJepHOBOi1 KpyrJIbIH 3y6 C nO,II.'beMOM 0, 18 [M, Tor)I.a i KO = 2; IIaCTb
OCT3TOIIHoro npHnycKa, paBHaH 0,005 MM, Cpe)KeTC5I nepBbIM qHCTO-
BbIM 3y6oM:
4 t 70 - 11 19.
2.0 21 "
,
A OCT . W === 4,70 - 2.0,21.11 === 0,08 MM.
TaK KaK AocT.m<2Sn1, TO OCTaTOIIHbIH npHnYCK 6YJI.eT cpe3aH ne-
peXO,lI.HbIMH 3y6b.HMH, lJHCJIO KOTOpbIX onpe,l{eJIeHO HH)Ke, a 1JUCJ10 qep-
HOBbIX rpynn i mo = 11.
14. 06 ee I.J:HCJIO 3y6beB onpeJI.eJI5IeM no cpopMYJIe (4.20), 1JHCJIO
4>acoIIHbIX - IIO cpopMYJIe (4.24), IIHCJIO KpyrJIbIX - no opMYJIe
(4.22) If 1JHCJIO 'lliJIHueBbIX -IllO cpopMYJIe (4.23):
. A ruO
lwo=
2S zwo
z<p=5.2== 10.
4HCJIO KpyrJIbIX qepHOBbIX 3y5heB paCClIHTbIBaeM no <popMyJle
(4.25):
ZKO= 2.1 === 2.
HCJIO KpyrJIbIX nepexoJI.HbIX 3y6heB ZH.rr== 2 H3 Ta6JI. D23 npHJIOJKe'"
HH5I, qlICJIO Kpyr JIbIX qH CTOBbIX 3y6hetB Zl\.'tJ == 4, l.J:HCJIO KaJIH6pYlOInHJ
ZH.K === 4 I13 Ta 6JI. D22 np HJIO)KeH.H5I:
zK===2+2+4+4=== 12.
LIHCI.TIO lllJIHueBbIX 3y6beB onpe,LI.eJl5IeM no CPOPMY JIe (4.26):
Zwo= 11.2+ 1 === 23.
4HCJIQ llIJIH eBbIX nepeXO)I.HbIX 3y6beB li3 Ta6JI. 023 npHJIOLKeHHSI
2m.n=4, cKoppeKTHpoBaHHoe QJ1CJIO nepexo)I.HbIX 3y6beB 3a cqer OCTa-
ToqHOrO npHnycKa ZIII,n == 6, qHCJIO lllllIHueBhIX qHCTOBbIX 3y6beB ZIII.ll = 2
(IIIpH ZC.III.ll = 1), qH.cJIO KaJIH6pYlOrnI1x 3y6beB Zm.l\ === 3:
zw==23+6+ 2+3==34;
z= 10+ 12 +34=56.
15. IT OJI.'beMbI nepeXOJI.HbIX 3y6beB Kpyr JIOH If IIIJIH eBOii qaCTeH
npHHHMaeM no Ta6JI. ll23 rrpHJIO)KeHH5I: ,lI.JIH KpyrJIbIX Snl == 0,08 MM,
Sn2 === 0,04 MM, ,ZI.JIH lllJIH eBbIX Srrl == 0,08 MM, Srr2, 3 == 0,04 MM.
llO,II,1>eMbI qHCTOBbIX 3y6beB Kpyr JIOH II IllJIH eBOH lJaCTeH npHHHMa-
eM no Ta6JI. n22 npHJIO)KeHH5I: ,lI.JIH KpyrJIbIX Szq=0,02 MM (JI.Ba 3y6a)
M SztJ=O,Ol MM (.II.Ba 3y6a) K nO.II.'beMY nepBoro tIHCTOBOro 3y6a npa-
6aBJIHeM 0,005 MM OT OCTaTOqHOrO npHnycKa, T. e. Sz 3=O,015 MM H
SZ\{4 = 0,01 MM; ,ZI.JI5I lIIJIHueBbIX SZq == 0,02 MM (JI.Ba 3y6a).
16. OnpeAe.TI5IeM JI.JlHHY pemyrnefi qaCTH npOTH)I{eK Lp, lllarH H rrpo-
.pHJIb qHCTOBbIX KpyrJIbIX H lllJIH eBbIX 3y6beB. BHaqaJIe HaXO,L:LHM ,lI.JIH-
HY cpacoqHoii qaCTH no <popMYJIe (4.29), KpyrJIOH lJa,CTH - no opMYJIe
(4.30), IIIJIH eBOH lJaCTH - IDO cpOPMY JIe (4.31):
l<p= 18-10== 180 MM.
JIJIH KpyrJIoti If IIIJIH eBOH qaCTeH HaXO,ll.HM lllar lJHCTOBbIX 3y6beB
no Ta6JI. D24 npH.nO)KeHHH (6epeM cpeJI.HH i1 lllar t 2 ). Wary to = 18 MM
cooTBeTcTByeT lllaf qHCTOBbIX 3y6beB tl\. =tR.ll1=t2= 14 MM. OCTaJIb"
HbIe 3JIeMeHTbI CTpY}KelJHOH KaHaBKH qI1CTOBhIX 3y6beB 6epeM H3 Ta6JI.
n19 npHJIO eHHH: h=6 MM; b=4,5 MM; R= 10 MM; r=3 IM;
lK= 18(2+2)+ 14(4+4-1)= 170 MM.
lw=== 18(23+6+ 1)+ 14{2+3-1)==596 MM;
L p = 180+ 170+596=946 MM.
17. CHJIY npoTHrHBaHH5I Ha KaM)I.ofi qaCTH npOT5I)KKH paCCQHTbIBa-
eM no cpopMYJIaM (4.34)-(4.36):
8,9.8.398.5.1,1
p = 2 =77928 H;
4*
99
4.1. Pe3YJlbTaTbI paCqeTa sapHaHTOB
BapHaHT
BapHaHT
J1CKOMhJA HCKOMhlA
oapaMeTp I II , IV napaMerp I (II III
IV
Zp 5 6 7 8 t 5 7 9 14
to, MM 18 16 14 12 h<o 2 () 3 5
-
ho, MM 8 7 6 5 lmo 11 15 21 32
b o , \1M 6 5 4,5 4 2cIJ 10 14 9 14
Szo, \1M 0,19 0,16 0,12 0,08 ZHO 2 2 3 5
0,21 Zmo 23 31 43 65
Zc <p, Zc K, Zc IJ1 2,1;2 2,1,2 1,1,2 1,1,2 ZH D 2 2 2 1
A4>, MM 2,1 2,1 2,1 2, I ZH II 4 4 4 4
A R , MM 0,925 0,925 0,925 0,92t ZH K 4 4 4 4
AI< II. MM 0,24 0,24 0,18 0,06 ZH 12 12 13 14
AI< , MM 0,12 0,12 0,12 0,12 Zm ]I 6 4 4 2
A Ro , M\f 0,565 0,565 0,625 0,745 Zm 2 2 2 2
Dmlt MM 37,22 37,12 37,04 36,96 Zm K 3 3 3 3
Am, MM 5,02 5,13 5,21 5,29 Zm 34 40 52 72
Am]l, MM 0,24 0,24 0,18 0,06 z 56 66 77 100
Am q, MM 0,08 0,08 0,08 0,08 14l1J MM 180 224 126 168
Amo. MM 4,70 4,81 4,95 5 15 tTJ., /R, M?vt 14 12 11 9
,
t4» up 5 6 8 13 hTJ., MM 5 4,5 4 3
tHO up 1 1 2 4 b q , MM 6 5 4,5 4,3
tmo up 11 15 20 32 [H, MM 170 148 147 144
A ocT 4J, MM ° 0,18 0, I 8 0,02 lw, M\I 596 624 688 852
A OCT H, \1M 0,185 0,245 0,145 0,105
A ocT m, MM 0,08 0,01 0,15 0,03
P K =
6 . 13 8 362 5 1
1
=88762 H;
Pw= 7.076 8 398 5 1,1 =61957 H.
2
18. PaCCqHTbIBaevt .lI.OnOJIHHTeJIbHble BapHaHTbI, YlBeJIHQHBa5I qHCJIO
O)l.HOBpeMeHHO pa60TalOIlI.HX 3)' 6beB Zp (3a CqeT YMeHbWeHH5I nO,QaQH
H3 0,01 MM): II BapHaHT zp=6, III BapHaHT zp=7, IV BapHaHT zp=8.
,aJI5I JI.OnOJIHHTeJIbHbIX BapIIaHTOB paCC4HTbIBaeM IllarH 4epHOBbIX
sy6beB Ii no cpopMYJIe 1 0 = 1 6epeM 6muKaHllIHe 66.1JbllIHe K HIIM
Zp-l
3HdqeHHH H3 Ta6,,1. TI21 npHJI02KeHH5I
I I BapHaHT
/0= 16 MM
I I I BapHaHT
t o = 14 M\1
IV BapHaHT
t o = 12 MM
HaHAeM r.ny6HHbI cTpY)Ke4HbIX KaHaBoK, cooTBeTcTBYJOI..I..I.He
III a raM, H3 Ta6"TJ. 021 npHJ10)KeHH5I h paBHo COOTBeTCTBeHHO
5 MM.
PaCClIHTaeM nO,J.aQH )J.JIH Ka)K)J.oro Bapl1aHTa no cpop\fYJIe
Szo paBHO COOTBeTCTBeHHO 0,16, 0,12,0,06 MM.
HaXOJI.HM, KaK 11 B I BapHaHTe, Bce Heo6xo,JJIMble napaMeTpbI
T.H)KeK; pe3Y JIbTaTbI paCqeTOB CBe eHbI B Ta6JI. 4.1.
]00
9THM
7, 6,.
(3.5) :
npo-
DpIfHIfMaeM JI.JIH Ka)K;I.OM lJaCTH npOTH)l{KH OIITI1MaJIbHbIH BapHaHT.
gJIH cpaCOqHOH If KpyrJIOH qaCTeH IIpIfHHMaeM III BapHaHT, ,lI.JI.H lllJIK-
aeBoH - II BapHaHT.
TaK KaK )LJIIIHa KpyrJIOH QaCTI1 11{= 147 MM, qTO 60JIee 1,51, TO 4ep--
HOBbIe IIepeXO)I.HbIe 3y6h5I BbIIIOJIH5IeM no rpyrrrroBoH cxeMe (ZC K = 2)
nepec4IfTbIBaeM If X tIHCJIO If rrOMellI,aeM rrepe,lI. cpaCOqHhIMH 3y6h.HMH
( cxeM a Ko ncl> KtJ Klll) :
zKo=3.2===6, zK.n=2.2=4.
.lIJIHHY KpyrJIOM qepHOBOH: 11 rrepexoJJ.HOH:, a TaK)I{e qHCTOBOH If Ka..
el1H6pYIOllI.eH 4acTeH paCCqHTbIBaeM c yqeTOM BbIXO)I.a llIJIHcpOlBa,,TIbHOra
Kpyra, IIP11 IlIJIHcpoBaH1111 6oKoBoro rrpocpHJIH cpaCOqHbIX 3y6beB:
lKo+IK.rr== 14(6+4)+2= 142 MM;
IK.4+IK.K=== 11 {4+4- 1)+5==82 MM.
06 ee QI1CJIO 3y6beB rrpOT5IMKH paBHO CYMMe lJepHOBbIX II nepe-
}.OJI.HbIX Kpyr JIbIX, cPaC04HbIX, 4HCTOBbIX If KaJI116pYIOIll.HX Kpyr JIblX H
llIJII1ueBbIX 3y6beB
Z= ZKOIII + ZK.nIII + Zcp.LU + ZK.tIlIl + ZK.KIII + ZillIl === 6 +4+ 9 +
+4+4 + 40=== 67.
AHaJlOrHqHO onpe;I.eJI5IeM )1.JIHHY pe)KYI.QeH QaCTIf:
L p = (I KO + [K.rr). I IT lcPI II + (lK.t.{ -t- l K.K). I I + IlliII === 142 + 126 +
+82+624==974 MM.
19. Pacc411TbIBaeM CHJIbI rrpOT5IfHB3HH.H Ha Ka)KJI.OM qaCTH npOT5I)K-
J{I1 no cpOPMY JIaM (4.34) - (4.37), IIPHH5IB Cpe,LI.HlOlO JI.JIHHY pe)Kym ea
KpOM KH Ha cpacoIIHbIX 3y6b5IX:
B<t>= 8,9+7 =7,95 MM;
2
P _ 7,95 8 23'2 7 1 11 28 H
cP- == 3 6 ;
1
P == 6, 13 8 232 7 I
K 1 === 79 64 1 H;
p == 7,076 8 304 6 I, I ===56789 H.
ill 2
20. ,a 11 a MeT p bI (M 1vl) K a JI}I 6 P Y 10 llI. 11 X 3 Y 6 be B :
D K . K == 36,025 - 0,007;
D m . K ===42,25-0,OI6 MM.
21 ,aJI.H cxeMbI Ko nel> K q hill COfJIaCHO peKOMeHAaUI1HM n. 10 MeTO-
,lI.HKIf npHHHMaeM ,LlHaMeTp Bna.z:U1H cpaCOQHbIX 3y6beB paBHbIM .LIJlaMeT-
py rrOCJle,II.Hero rrepeXO,ll.Horo 3y6a DB. = 35,86d 11 (= ,g l)' AHaMeTp
25 '
Sna,ll.HH illJIHl(eBbIX 3y6beB D H . w == 36f9 (=g:g87) M.
lor
22. qHCJIO BbIKpYiKeK Ha KpyrJIbIX tIepHOBbIX It nepeXO)l.HbIX 3y6b5lX
H HX IIll1plIHY onpe eJIHeM no Ta6JI. 025 rrpHJIO)l{eHHH: N K =8; a K =
7 MM; RB==30 MM; RI{ 25 MM 11 Ta6JI. rI27 npHJI02KeH11H. 1.IHcToBbIe
KpyrJIble 3y6bH BbInOJIHHIOTCH 6e3 BbIKpY2KeK.
tIHCJIO BbIKpY2KeK IIlJIHueBbIX 3y6beB N m = 8. llIHPIIHY pe2KYIUHx
;re3BIIH Ha npope3HbIx 3y6b5lX orrpeJleJIHeM no cpopMYJIe (4.40), npHHHB
npe)J.BapHTeJIbHO pa3Mep KpI1BOJIHHeHHOH cpacKH H3 Ta6JI. 032 npIIJIO-
meHI1H: frr= 1 MM; B m =7-2.1 =5 MM.
,QJIH onpe)J.eJIeHH5I pa)J.Hyca BbIKPY)KKH R B H pa)l.Hyca IIlJIHcpOBaJIb-
Horo Kpyra RI{ BblqHCJIHM IIll1pHHY BbIKpy2KeK IIIJIHueBbIX 3y6betB no
CPOPMY JIe (4.41):
a == 3,14.42 _ 5== 11,5 MM.
ill 8
TIo Ta6JI. TI27 rrpHJIO}l{eHHH )l.JIH alII = 11,5 MM H D == 42 MM; R B =
==36 MM 11 RI\=30 MM.
23. .lI.MaMeTp nepeJI.Hei-i HanpaB.TJHIOllJ,eii Dn.H = 35, le8 (=g: n) I MM,
JIHHa nepe,lI.Heii HarrpaBJIHIO eH lrrH=0,75.80=60 MM, TaK KaK D >
> 1,5.
24. J(JIHHY nepexO)I.HOrO KOHyca rrpHHHMaeM no Ta6JI. TI28 rrpHJIO-
}KeHHH: lrr==20 MM.
25. PaCCT05lHHe OT nepe,lI.Hero Topua rrpOT5I2KKH )1.0 rrepBoro 3y6a
orrpeJI.eJI5IeM B COOTBeTCTBHH IC rr. 4 MeTO IIKH
LI === 160+25+40+80+25=250 MM.
26. ,lJ.HaMeTp 3a,lI.HeH HanpaBJI5IIOrneH D .H === 36 /9 (=g:g ) MMt )I.JIH-
BY 3aJI.Heii HarrpaBJI5IIO eH np.HHHMaeM 'no Ta6JI. TI29 npIIJIO)KeHH5I:
1 3 . n == 35 MM. TIPOTH)KKY ,lI.eJIaeM 6e3 3a)l.Hero XBOCTOBHKa.
27. 06 yIO ,lI.JIHHY npOT5I)KKH orrpe,lI.eJI5IeM no CPOPMY JIe (4.44):
L=250+974+35= 1259 MM.
OKpyrJIHeM L ){O 1260 MM 3a ClJeT 3a,lI.Hero HanpaBJIeHII5I - 1 3 .'£1=
= 36 MM.
PaClleT KOppHfHpOBaHHOfO npo4JHJISI t!JaCOIIHbIX H WJIHu.eBbIX npSl-
Mo6ollHbiX 3y6beB. ,QJI5I paClleTa KoppHrHpOBaHHoro 60KOBoro npocpHJIH
lllJIHlJ.eBbIX rrp51Mo6oQUbIX 3y6beB 113 Ta6JlHll.bI ,lI.HaMeTpOB 3y6beB Ha-
3HaqaeM HOMepa rrepBoro N A = 29 H rrOCJIe,lI.Hero N E = 57 3y6beB Ha
paCqeTHOM yqaCTKe, pa,lI.IIycbI 3THX 3y6beB R A = 18.77 MM H R E =
=21,46 MM. ,[lJI5I paClleTa H'CnOJIb3yeM TaK}I{e lllHPHHY rra3a b = 7 MM,
lIlar qepHOBbIX 3y6ben t o = 16 MM. B'crrOMOraTeJIbHbIM yrJIOM B llJIaHe
3aJI.aeMC5I: CPI = 3°
TIO)I.'beM 3a,lI.Hero ueHTpa C Ha ,lI.JIHHe npOT5I}I{KII L 11 nOJIOBHHY yr-
JIa KoppHrHpoBaHHoro 6oKoBoro rrpocpHJI5I 3y6beB 11 IIIJIHcpoBaJIbHOrO
Kpyra ffil( paCClJIITbIBaeM no cpopMYJIaM (4.45) - (4.52) :
7
sin AA = ===0,372936; AA = 21,8968°;
1-8 , 77
102
7
sin AE= =0,326188; /\E= 19,0376°;
21 J 46
]80°
°A = 8 - 21,8968°==0,6032°;
180°
°E= 8 - 19,0376°=3,4624°;
hE=21,46-cos 3,4624° - 18,77 -cas 0,6032°= 2,651865;
0)= 180° = 22°30';
8
0)1(= 22°30' - 3°= 19°30';
C m = 2,651868 (tg 22°30' - tg 19°30') ==0 45 MM;
tg ]9°30' ,
l = 16(57 - 29)=448 MM;
C == 0,45.1260 _ I ' 26
-, MM.
448
,II)I5I paCqeTa nO 'beMa 3a)I.Hero ueHTpa C, pa3MepoB AJI5I KOHTp0J151
60KoBoro npocpHJI5I cpaCOqHbIX 3y6beB H A H H B Ha3HaqaeM HOMepa
nepBoro (NQ II) H nOCJIe)l.Hero (NQ 19) cpaCOqHbIX 3y6beB H
pa.rUIYCbI 3THX 3y6beB: R A = 17,64 MM If R E = 18,6 MM; yrOJI <p acoK <IJ
H KoppIfrHpoBaHHbIH yrOJI cpacoK R rrpHHHMaeM H3 Ta6JI. n34 npHJlO-
JKeHIf51 )l.JI5I lIHCJIa lllJIHl1.eB z= 8: p(jJ =47°, 13 R = 45°
pyrIIe ,naHHbIe, Heo6xo)I.I1MbIe ,aJIH paCqeTa, CJIe,nylOI..nHe: b =
=7 MM; c=O,5 MM; d=36 MM.
PaClIeT ,npoH3BoAHM Ino cpopMYJIaM (4.53) - (4.61) :
sin A= 7 +2.0,5 ==0 222222- A== 12 8396°-
36 ' , "
36. sin (12,8396° + 47°) 7
sin PA= =0,882267; PA=61,91 1°;
35,28
36. sin (12,8396° + 47°)
sin PE= =0,836731; PE=56,7965°;
37,2
AA = 61,9171° _47°= 14,9171°;
A E == 56, 7965° - 47° = 9, 7965°;
H A = 17,64-sin (36°+ 14,9171°)= 13,69 MM;
H B == 18,6-sin (36°+9,7965°)= 13,33 MM;
C === 13,69- 13,33=0,36 MM.
103
-'=::
LYIJ "\
0,01
72£0
t-
5/
/
S
G
A-A
tJ
7
r-r
at
"w)
/
Put. 4. t 3.
l(oM6HHHpoBaHHaSl npOTSl1KKa e npSlM0601.JHblMM 11IJlHlJ,aMH d - 8X 36H7 X 42H 12 X 7 D9:
a - 06I..U.HA BH.lI. 6 - nOnepeGHblA [fPOcPHJIb KpyrJIblX tIepHOBblX H nepeXOJ],HblX 3YObeB, 8 - no.
nepetIHblH: npo<pHJIb cPaCOlfHblX 3YObeB, Z - nOnepeGHbIH npO<pHJIb IlIJIHu.eBbIX 3y6beB; a - npo..
OJIbHblH: npocPHJlb qepHOBblX cPaCOqHbIX H Kpyr J1 IX 3y6beB, e - npOJ1.0JIbHbl rrpocPHJIb tlHCTOBbIX
KpyrJIblX H lllJIHu,eBbIX 3y6beB, - ceqeHHe 3y6a no BbIKpY>KKaM KpyrJIblX H UIJIHu,eBbIX 3y6bea
IIIJIHcpoBaHHe 60KOIBOfO npoqHiJI5I cpaCOl.JHbIX 3y6beB npOH3BO,lI.HM
npOq,HJIbHbIM IIIJIHQJOBaJIbHbIM KpyroM C ffiK==67°30' (H3 Ta6JI. n34
npH.nO)KeHH5I). CJIe,nOBaTeJIbHO,
C ' O,36MM
A\=
't' SIn 67'30°
== 0,39 MM;
l ==14(19-11)==112 MM;
C = 0,39 1260 _ 4 38 ·
-, MM,
112
B4>max=35,28. sin 14,9171°=9,08 MM;
Bcpmln=37,2.sin 9,7965°=6,33 MM.
KOppHflfpOBaHHbIH yrOJI npO\pHJI5I cpaCQQHbIX Brra,lI.MH Ha l1pOT5I}KKe
2W1\ == 135 0 (H3 Ta6JI. I134 npMJIO)KeHM5I).
4epTe2K l1POT5I)KKII npHBe)I.eH Ha pYlc. 4.13, ;I.rlaMeTpbI 3y6beB - B
Ta6JI. 4.2. ,LLJIH nepBoro 3y6a HI = 13,69 MM, ,nJI5I I10CJIe;r,Hero H 2 =
= 13,33 MM; npH lllJIHcpOBaHHII 60KOBbIX IlOBepXHocreH cpaCOQHbIX 3y6b-
eB c NQ 11 no NQ 19 3a)J.HliI1 XBOCTOBHK Heo6xo;U1MO nO,L{H5ITb B Hal1paB-
.JIeHHH CTpeJIKH E, nO)J.'beM paBeH 4,38 MM Ha )J.JIHHe 1260 MM. OpH
IlIJIHcpOBaHHH 60KOBbIX 110BepXHOCTeH llIJIHQeB C 3y6a NQ 29 no N2 57
104
4.2. )l.HaMeTpbl 3y6beB npoTsDKKH
0. P-
ro I- (OJ E- o.::
'\0 a; c.o u BH.rI. \0 a; u BHJI
;>. ::E a; >- a 3y6b€,B >- ::EQ) >- a
tf) I:: M C'Cj.!l t:: sy (Sbe8'
\O:= o ==: \0 0
t:::i t:::i
1 35,34
2 35,30
3 35,58
4 35,54
5 35,72
6 35,68
7 35,84
8 35,80
9 35,90 3° + 30'
10 35,86
11 35,28 -0,016
12 35,52
13 J6,76
14 36,00
15 36,24
16 36,48
17 36,72
18 36,96
19 37,20
20 35,94 2° + 3D'
21 35,98
22 36,005
23 36,025 -OJ0 07
24 36,025 1 0 + IS'
25 36,025
26 36,025
27 36,025
28 37,22
29 J 7 , 54
30 37,50
31 37,86 -0,016 3 0 + 3O'
32 37,82
33 38,18
34 38,14
\ 35
I 38,50
\ 36 38,46
37 38,82
4epHo r 38 38,78
B bJ e H 39 39,14
nepe- 40 39,10
\. 0 .ll. H bI e 41 39,46
upyr,Ible 42 39,42
43 39,78
44 39,74
45 40,10
46 40,06
47 40,42
48 40,38
acoq- 49 40,74
HbIe 50 40,70
51 41,06
52 41,02
53 41,38
54 41,34
55 41,70
56 41,66
57 41,92
58 41,88
lJHCTO-
BhIe H 59 42,09
KaJIaO- 60 42,05
pY IO ll1.He 61 42,17
KpyrJIbIe 62 42,13
63 42,21
64
IIIJIHue.. 65 42,25
BbIe qep-
HOBbIe 66 42,25
67 42,25
1 0 + 15 '
KaJlHo"
PYIOll.{He
-0,016 3° + 30' IlInHue-
BbIe qep."
HOBbie
nepe..
xo.nHble
2° + 3D'
l.JHCTO'-
Bble
-0,007
3a HHfi XBOCTOBHK c,ne.n.yeT llO)I.H5ITb B HallpaBJIeHHH CTpeJIKH F, no..!l'b
eM paBeH 1,26 MM Ha )I..JIHHe 1260 MM.
LLJIH qepHOBbIX 3y6heB: cpaCOqHbIX Ii KpyrJIbIX t= 14 MM n=fi MM,
b=4,5 MM, R=lO MM, r=3 MM; lllJII1u.eBbIX t=16 MM, h=7 MM, b:::&
=5 MM, R= 11 MM, r=3,5 MM.
LLJI5I qHCTOBbIX 3y6beB: KpyrJIbIX t q =11 MM, h 1 =4 MM, b 1 =4,5 MM.
R=6 MM, r=2 MM; llIJIHueBbIX t-q= 12 MM, hI =4,5 MM, b 1 =5 MM,. .R I
= 7 MM, r === 2,5 MM.
MaTepHaJI pa60qeti qaCTH - CTaJIb P6AM5; MaTepHaJI XBOCTOBO}i
qaCTH - CTaJ1b 40X; H RC a 62-66 pa604efi qaCTlf II 3aJI.HeH HanpaBJIH-3t
IOllI.eH; HRC a 61-66 nepe)I.HeH HallpaBJIHIOllI.eH; HRC a 42-46 nepeA
]05
Hero XBOCTOBHKa; )I.OnYCTH!\10e OTKJIOHeHHe OKpY>KHOrO wara illJIIU..{eB
H(1 60JIee 0,01 !vIM; HaKOrrJIeHHa51 nOrpelllHOCTb OKpY}KHOrO lllara He 60-
J1ee 0,015; OTKJJOHeHHe OT napa 1JJIeJ1bHOCTa 60KOIBbIX nOBepxHocTeM
3y6beB OTHOCI1TeJIbHO OCM QeHTpOB Ha .rr.JIHHe lllJIHILeBOH qaCTH He 60JIee
0,015 MM; OTKJIOHeHHe OT cHMMeTpl1QHOCTlI 3y6a OTHOCHTeJIbHO OCH
u.eHTpOB B nOnepeQHO'1 CeqeHI1H He 60JIee 0,01 MM.
PaCqeT KOMnJleKTa WJlHu,eBbIX npOTSI}I{eK
B HeKOTopbIX CJIyqa51X 3a OAHH TeXHOJIOrHqeCKHH ne-
peXOA npOT rHBaHHH He Y)I.aeTCH nonyqHTb OKOHqaTe bHwe OPMY H
pa3MephI lliJIHueBOro oTBepcTHH. Tor Aa HCnOJIb3YlOT KOMn.TIeKT 1ll,lIHue-
bbl},. npOTHJKeK, COCT051lll.HH 113 npOT5I}KeK nepBoro H BToporo (HHOr,lI.a
tpeTbero) TeXHOJIOrH4eCKHX rrepeXO,II,OB. TaKHe CJlyqaH BCTpeTI3IOTC5I
'1'Of,aa, KorAa paCl1eTH85I ,ll.JIHHa npOT5I2KKH OKa3bIBaerC5I 60JIbille MaK-
CHMaJIbHOrO xO)J.a lllTOKa npOT5IlKHOrO CTaHKa HJIII npeBbIlliaeT 3Haqe-
HHe, ,nonYCTHMoe TeXHOJIOrHQeCKHMH B03MOJKHOCTHMH HHcrpYMeHTau1b-
Horo I.Lexa.. 3TO npHxoAHTCH ,lI.eJIaTh 11 B Tex CJIyqa5IX, Kor,LI.a COOTHOllIe-
U u
tIMe MeiKLlY p3CQeTHOli ,nJIHHOH H ,lI.HaMeTpOM rrpOT5I)KKH OKa3bIBaeTC5I
HaCTOJIbKO 60J1bllIHM, liTO CHHLKaeT 2KeCTKOCTb npOT5I}I{KH. H3rOTOBJIeHHe
h .9KCllJIyaTaUH5I rrpOT5I}I{eK, HMelO!4HX OTHOllIeHHe L/ D> 40, conpo..
BO:>K,naIOT QaCTbIMH HenOJIa,lI.KaMM. TI03TOMY, eCJIH Lj D > 40, TO O,lI.HY
npOTH)I{KY 3aMeHHlOT AfBYMH - nepBoro If BToporo TeXHOJIOrHqeCKHX
nepeXOAOB.
J1Hor,na npHMeHeHHe KOMnJIeKTHbIX npOT5L1KeK 06YCJIOBJII1BaeTC5I
TeXHOJIOrHQeCKHM npOl1.eCCOM H3rOTOBJIeHH5I ,AeraJ1eif, He3aBHCMMO OT
Toro, qTO BeCb l1pHnYCK MO)l{eT 6hITh cpe33H O,lI.HOH npOTH}I{KOH. TaK,
UInHueBoe OTBepCTHe qaCTO CJIY)KHT TeXHOnOrHqeCKOH 6a30H )I.n 06-
pa60TKH PyrHx 110BepXHocTeii. TIpI1 3TOM IIlJIHUbI MorYT nOBpe)I{, aTh-
CH BO BpeM5I YCTaHOBKI1 3arOTOBKH Ha orrpaBKY H .cH5ITH5I C Hee HJIH
H3-3a 60JIbllIHX CHJI, B03HHK31OllI.HX npH o6pa60TKe. STO BhI3bIBaeT He-
06XO)IJfMOCTb BbII10JIH5ITb OKOHQareJ1bHYlO o6pa60TKY llIJIlfI.LeBOro or-
BepCTH5I npOT5ILKKOH BToporo TeXHOJIOrHQeCKOrO TIepexo)I.a. ECJIM Tex..
HOnOfIlqeCKHM npouecc npe.rr.ycMaTpHBaeT npoT rHBaHHe 3arOTOBOK o
II nOCJIe TepMHQeCKOM 06pa6oTKI1, TO TaK}I{e l1pHMeH5IlOT KOMIIJleKTHbIe
npOTHLKKH.
Ha pHC. 4.14 l1pHB€)J.eHbI l1pHMeHHlOI.l.{HeCH Ha 3aBO)J.ax cxeMbI pac..
npe,neJleHH5I npHl1ycKa MelKLlY npOT5I)KKaMH o,nHoro KOMTIJIeKTa, npe)].-
I 2 f 2 1 2 2.
,.BiL/ /. /:
..
G)
PRe. 4.14.
Pacnpe.ll.eJIeHHe npHnycKa Me1K.lI.Y npOTSl1KKaMH OAHoro KOMnJleKTa:
, - npHnYCK, cpe3aeMbIfi npOTSI>KKoit nepBoro 1'eXHOJlOfHQeCKoro nepexo,ZJ.a; 2 - npunYCK, cpe-e
aaeMbiA npOTsnKKoA BTOpOfO TCJ\.HOJlOI H'leCKOrO nepexo)J.a
'06
Ha3HaQeHHOrO .7l.JI}I o6pa6oTKU rrp5IMo6oQHbIX lll.nHl.{eB. TIpH npOT5IfHBa-
HHH rpy6bIx IllJIHUeB, Y KOTOpbIX nOJIe J(onYCKa Ha llIHPHHY lllJIHueBOro
na3a npeBbIlllaeT 45 MKM H HMeeTC5I .lI.OCTaTOQHO 60JIhlllOH .lI.OnYCK
npHMO.lIHHeHHOcTH 60KOBbTX CTOpOH na33 ITO BbICOTe, npHMeHRIOT cxe-
MY, nOKa3aHHYIO Ha pHC. 4.14, a. 06pa60rKY 60JIee TOIIHbIX lllJIHueBbIX
oTBepcTHM no 3roM cxeMe He np0I13Bo,nHT, nOTOMY qTO norpeIllHOCTH,
HeH36elKHbIe rrpH 113rOTOBJIeHHH npOT5IlKeK pa3HbIX reXHOJIOrHtIeCKHX
nepeXOJI.OB (OTKJIOHeHHe OT paIBHOMepHOCTI1 paCnOJIOMeHHH lllJIHII.eB
no OKPY}I{HOCTI1, OTKJIOHeHHe OT napaJIJIeJIbHOCTH HX no OTHOlIleHHIO K
OCH rrpOTH2KKH 11 OTKJIOHeHHe or CHMMeTpHqHOCT i pacnOJIO)KeHH5I 3Y-
6beB OTHOCHTeJIbHO OCll), 60JIblIIeH qaCTblO CYMMHpyIOTCH. 113-3a .9TOrO
Ha 60KOBbIX nOBepXHOCT5IX na30B 06pa3YlOTCH YCTynhI, MeCTHbIe YllIH-
peHH5I na30B, a HHor,na H 33,nHphI. O,nHaKo npH pacnpe,neJIeHHH npH-
nYCKa no 3TOH cxeMe npOT5IlKKH nepBoro H BToporo TeXHO OrHqeCKHX
rrepeXO,L{OB rrOJIyqaIOTCH cpaBHHTeJIbHO KOpOTKHMM, H HX Y 06HO illJIH-
cpOBaTb no 60KOBbIM nOBepXHOCTHM IlIJII1u.eBbIX 3y6beB, nO)I.HHMa51 3a,n-
HHH XBOCTOBHK. STY cxeMY WHpOKO npHMeH5IIOT npH 06pa60TKe HeTOq-
HbIX llI.lIHueB. lllHpHHY llIJIHueBblx 3y6beB ,npOT5LIKKH Brn neplBoro rex-
HOJIOrWqeCKOrO rrepexo,na rrpHHI1MalOT paBHO bma B npe)I.eJIax Aorry-
CKa. B II.eJIHX YMeHblUeHI1H pa36HBI<H lllJIHueBOro OTBepcTHH Y npOTH}I{-
KI1 BToporo H Ka}l{)I.Oro H3 nOCJIeJI.ylO Hx reXHOJIOrHqeCKlfX nepexo,nOB
B rp Ha3HaqalOT Ha 0,005-0,01 MM MeHbll1e Bm npe,nbI,nYllI. ero .
Pacnpe,.QeJIeHHe rrpHnycKa no C1.eMe, npHBe,lI.eHHOH Ha pIlC. 14, 6,
npHMeH5IIOT npH npOTHrl1BaHHJI T04HbIX lllJIIIueB. B 3TOM CJIyqae lllH-
prIIIY lIlJIl1ueBhIX 3y6beB npOr5IlKKH nepBoro reXHOJ£OrHqeCKOrO nepe-
xo a Ha3HaqalOT Ha 0.6-0,8 MM MeHbllle OKOHqaTeJIbHOH lllHpHHbI
lIlJIHueBOro na3a ,lI.eTa.TII1. B CBH3H C 3THM cpopMYJIa (4.9) ,nJIH onpe,ne-
JIeHHH ,lI.HaMeTpa (MM) nOCJIe,lI.HerO aCOqHOrO 3y6a npl106peTaer BH
Dq.==2RE+O,4-2ilB, (4.62)
f,ne B - npHnycK no,n npOTH}I{KY BToporo TeXHO.JIOrHqeCKOrO nepexo-
.na Ha O,nHY CTOPOHY IlIJIHlI,eBOrO na3a.
I1poTH}I{Ka BToporo TeXHOJIOrHqeCKOrO nepexo,na HMeeT ,nBe rpyII-
nbI IlIJIHILeBbIX 3y6beB. lllHpHHa (MM) Bcex lliJIHueBbIX 3y6beB O.lI.HHa..
KOBa 11 onpe)J.eJI5IeTC5I no <POPMY JIe
2
Baq==hmln+ -118. (4.63)
3
3y6bH nepBoH rpynnbI, paCnOJIOlKeHHbIe cnepeAH, pa6oTaIOT Ha
yqaCTKe F (CM. pHC. 4.14, 6). 3TH 3y6b51 paCllll1p5IIOT na3,.Q0 OKOHqa-
TeJIbHOrO pa3Mepa. TaK KaK lIlHpl1Ha cpe3aeMhIX HMH CTpY}KeK C Ka}K-
.lI.OH CTOpOHhI rra3a HeBeJIHKa ( B = 0,3-:-0,4 MM), TO OHM HMeIOT no,n'b-
eM Ha Ka}K,.QbIH 3y6. DOA'beM Ha 3THX 3y6b5IX orpaHHIIHBaeTC5I rJIaB-
HbIM 06pa30M llIapOXOBaTOCTbIO nOBepXHOCTH 60KOBbIX CTOpOH H npaK-
THqeCKH He npeBbIllIaeT 0,5 MM Ha 3y6 Ha CTOPOHY. LLHaMeTp (MM)
nepBoro 3y6a 3TOH rpynnbI onpe;r.eJI5IlOT no cpopMY.lIe
DWl==DE+O,I. (4.64)
B CB5I3lf C TeM, liTO 3y6hH .9TOH rpynI1bI He paCCqHTaHhI Ha cpe3a-
HHe CTpYLKeK nOJIHOM llIHpHHbI, T. e. no BceH 111l1pHHe na3a, ,nl1aMeTp
nOCJIe HerO H3 HHX OJI}KeH 6blTb Ha 0,2-0,4 MM MeHbllle HaMeTpa
107
IllJII1UetBbIX KaJIH6pYlOllI.HX 3y6beB npOT5I}KKH rrepBOrO TeXHOJIOrIIqeCKO..
ro nepexo.rr.a.
BrOpaH rpynna 3y6beB o6pa6aTWBaeT na3 O nO HOH ero BWCOTW.
3TH 3y6b5I BbInOJIH5IlOT ceKIJJIOHHbIMH, 11 nO;I.'beM Ha HHX Ha3HaqalOT
TaKOH }Ke, KaK II )J)I5I O,lI.HOnepexOJI.HbIX npOTH2KeK.
npOcpI1 b ill Hu:eBbIX 3y6beB npOTJIMeK nepBoro TeXHOJIOraqeCKOrO
nepeXO,lI.a H3 KOMrr eKTa, KaK II O)1.HonepeXO;(HbIX npOT5IiKeK, lllJIHCPY'"
101', nO)I.HMMaH 3a HHH XBOCTOBHK. I1pOcpl1JIb 3y6beB npOTHMeK BTOpO-
fO TeXHO OrHqeCKOrO rrepexOAa H3-3a pa3 HqHH rrOA'beMOB Ha pa3HWX
rpynnax 3y6beB )I.OnYCKaeTC5I illJIHcpOBaTb, OCTaB H5I JIeHTOqKI1 Ha 60-
KOBbIX ICTopoHax.
Paonpe eJIeHHe npHnycKa no cxeM3I\'I, nOKa3a.HHbIM Ha pl1c.
4.14, 8, 2, npIIMeHHlOT B Tex CJIYIfaHX, KorJ(a Tpe6yeTC5I nOJIY411Tb BbI...
COKOKaqeCTtBeHHbIe IllJIHUbI. TaKoe pacnpe)I.e eHHe npHnYCKa HaH60JIee
qaCTO BCTpeqaeTCH npH npOTHrl1B3HHH 3arOTOBOK, nO BeprlliHXCH Tep-
IHqeCKOH o6pa6oTKe, B pe3YJlbTaTe KOTOpOH npelI.BapHTeJIhHO npOT5I-
HYTbIe lllJIHUbI ,QecpopMHpOBaJII1Cb II HX Heo6xo,QiIMO HcnpaBH rb. Ha
.cxeMe pHC. 4.14, 6 nOKa3aHO pacnpe,lI.eJIeHHe npHnYCKa Me)K.rr.y npOTH}K-
KaMII nepBoro H BToporo TeXHOJIOrHQeCKHX nepeXO OB ,lI.JIH o6pa6oTKH
IIIJIHu:eBoro OTBepCTH5I C nOCaJl.KOH no BHyrpeHHeMY ):(HaMeTpy, Ha cxe-
Me pHC. 4.14, c - C nOCa,lI.KOH no HapYLKHoMY )1)faMerpy.
f1 pIInycK Ha 60KOBble CTOpOHbI lllJIl1ueBOrO na3a, npeJ(Ha3Ha y:aeMbIH
).1)151 npOTH)KKH BToporo TeXHO OrtIT.}eCKoro nepexo,n,a, ,lI.aerC51 60JIbIlle,
qeM no cxeMe pHC. 4.14, 6. I1pl1nycK !J.B qaCTO YCTaHaBJIHBalOr no pe..
3Y JIbT3TaM 3aMe f)8 )1.ecpopMaU:IIH )J.eTaJII1. ITa )1.aHHbIM 3aBO,l{OB, 118 =
== O} '3 -:- 0,7 MM. 3a.LlaHHOe pacnOJIO}KeHHe OCH OTBepCTH5I OTHOCHTeJIbHO
.D.PYT'IIX nOBepXHOCTeH 06eCneQ11B3IOT CJIe,l1YlOllI.HM 06pa30M. IlocJIe
TepMI1QeCKOH o6pa6oTKH HCrrpaBJI5IIOT paCnOJIOiKeHHe OCH OTBepCTHH
OTHOCHTeJIbHO 6a30BbIX nOBepxHocTei1 (HarrpHMep, nOBepXHocreii 3y6b..
eB rneCTepeH) lIlJIHcpOBaHHeM H.11M paCTOqKOH BHyrpeHHei1 nOBepXHO"
CTII WJIHQeB B OKOHQaTeJIbHbIH pa3Mep. rro,rlyq -IHa51 nOBepXHOCTb B
J{aJIbHeHll1eM HBJIHeTCH 6a301BOH H HanpaBJIeHHH npOT51}KKH BToporo
ieXHOJIOrl1QeCKOrO nepexo,J,a np 11 KaJl116pOBKe lllJIllueBbIX na30B. CYllI. e ..
cTByeT HeCKonbKO BapHaHTOB KOHCTPYKUHH HanpaBJIHIDIu:IIX 3JIeMeHTOB
KaJIII6pYIOIu:HX npOT5IiKeK. HaHMeHbwee OTK.lIOHeHI1e OT COOCHOCTl1 pac...
IIOJIOlKeHHH lll Hu:eBbIX n330B 11 OTBepCTHH 06eCrreQHBaIOT HJIHH)J.pH-
QeCKl1e HanpaBJIHIOIlI.He nOJICKH, ,lI.11aMeTp KOTOpbIX llMeeT AonYCK nO
nOC8,lI.Ke 6g. 3TH nOHCKH B 3aBHCHMOCTH or ,n HHbI npOT5IrHBaHH5I pac-
nOJIaralOTCH I160 Me)K,ny Ka)K bIMH ;I.BYM5I coce HHMH 3y6b5IMH, JIH60
Qepe3 HeCKO.JlbKO 3y6beB.
TIpOTHiKKH nepBoro H IBToporo TeXHO OrHlJeCKHX llepeXOJl.OB, pa6o-
TaIOllI.He no C'xeMaM pIIC. 4.14, B H c, lll.lIH<pYlOT no npocpHJIlO lIlJIHu.eB,
nO,LlHHMaH 3aLlHHH XBOCTOBHK Y npoTHlKKH BToporo TeXHO..TJOrHQeCKOrO
nepexo,Lla, pa60Ta IO me}i no cxeMe pIfC. 4.14, 2; npHrrYCK Ha ) qaCTKe K
"cpe3aeTCH C YMeHblIleHHbIMH nO;LaQ3MH, 3HaqeHHH KOTOpbIX (11 cxeMa
nOCTpoeHHH 3y6beB) onpe;LeJIHlOT TaK )Ke, KaK H rI.JIH OJ,HOI1epeXO;:J.HbIX
,IIpOT5IlKeK. .QHaMeTpbI nOCJIe,nHero <paCOlJHOrO 3y6a npOTHlKKH nepBoro
'TeXHOJIOrHQeCKorO nepexO,lI.a H nepBoro llIJ1Hll,eBOrO 3y6a BToporo TeXHO'"
JIOrHlJeCKOrO nepexo,na orrpe,lI.eJIHIDT no cpopMYJIaM (4.62) H (4.64).
108
rJlaBS
5.
PaClJeT npOTSI>KeK ,lI.JlSI o6pa6oTKH
u
lllJlHQeBblX OTBepCTHH
C 9BOJlbBeHTHblM npo4JUJleM
YCJlOBHbIe 0003HaIJeHHH
m - MOJI.YJIb-;
a - npOcpHJIbHbIH yrOJI HCXO.lI.HOrO KOHrypa (yroJl .lI.aBJleHH5I no
)I.eraJIbHOii OKPYLKHOCTH);
e - HOMHHaJIbHaH )I.eJIHTeJIbHa5I OKpY}KHaH lllHpHHa Bna.lI.HHbI
BTYJIKH;
M i - pa3Mep l\le)KAY pOJIHKaMH;
DM - ,lI.HaMeTp H3MepHTeJIbHOro pOJIHKa;
W - ,lI.JIHHa 06w.eH HOpMaJIH;
Zw - QI1CJIO Bna)J.HH Ha JI.JIHHe o6r.uei1 HOpMaJIH;
f - pa3Mep cpaCKH B 3BOJIbBeHTHbIX na3ax;
d - ,lI.HaMeTp )J.eJII1TeJIbHOH OKPY)KHOCTH;
dB - )J.I1aMeTp OCHOBHOH OKPY)KHOCTH;
Da - )J.HaMeTp OKPY}I{HOCTII BeplllHH 3y6beB BTYJIKH;
D f - ,lJJlaMeTp OKPYlKHOCTH Brra)I.HH BrYJIKH;
Sp - paCqeTHa51 )J.eJIHTeJIbHaH OKpYLKHaH lllHpHHa 3y6a rrpo-
T5IlKKI1 ;
eo -- Ha qaJIbHbIH yrOJI 3BOJIbBeHTbI;
_ nOCT05lHHbrii rrapaMerp J1.aHHOH 3BOJIbBeHTbI (yrOJI, )J.OIIOJI-
HHIOr.uHH yroJI 8 0 .lI.O 90°) ;
ai - yroJI )J.aBJIeHH5I HCXO)I.HOH .9BOJIbBeHThI B i-H TOqKe;
t i I'- yroJI Me)K,lI.Y KaCaTeJlbHOH: K IiCXO)J.HOH 3BOJIbBeHTe B i-H
TOqKe Ii OChlO ox.
061l1.He CBe)l.eHHSI
B HaCT05IlUee BpeM5I B MalllHHocTpOeHHI1 llIHpOKO IIPH-
MeHHIOT llIJIHII.eBble coe)J.HHeHII51 C .9BOJIbBeHTHoH cpOpMOH: IlIJIHueB,
o6eCrrelJHlBalOIII.He 60JIblIlHe KPYTHlUHe MOMeHTbI no cpaBHeHHIO C IIPH"
Mo6otIHbIMH. Pa3MepbI 3BOJIbBeHTHhIX lllJIHu.eBb1X COe)I.IIHeHHH rrpe.1{Y"
cMoTpeHbI fOCT 6033-80.
3BOJIbBeHTHble llIJIHlLeBble oTBepCTH5I o6pa6arbIBaIOT npeI1MYIII.ecT-
BeI-iHO MeTO)J.OM npOT5IfHBaHH51. TIpH 3TOM rrpOT5IJKKH )I.OJliKHbI o6ec,rre-
HBarb BWCOKoe KaqeCTBO H TOqHOCTb 06pa6oraHHoH nOBepxHocTH H B
TO LKe BpeMH ,.QOJI}I{Ha 6bITb 06eCneQeHa BbICOKa51 CTOHKOCTb HX 3y6beB.
3TO )I.ocTHraeTcH lllJIrHpOBaHHeM 60KOBoro npocpHJI5I IllJIHu:eBbIx 3y6beB
npOr5I)KKH C nO,lI.'beMOM 3a,ElHero u:eHTpa rro OTHoweHIIIO K rrepe,LlHeMY,
B pe3YJIbTaTe qero Ha 60KOBWX TIOBepXHocTHX lliflHu.eB o6pa3yeTcH
BcnOMOrareJIbHbIH yrOJI B nJIaHe CPl (yrOJI nO)J.HYTpeHI151). YrJIbI rro -
109
fJ- 8
(-r
IX
..c:::
0)
PIIC. 5.1.
KOMOHHHpoBaHHaH 3BOJIbBeHTHaH npOTSI]KKa:
a - 06 H}t BHJJ.; 6 - rpynna H3 JI.BYX <!>aC01JBbIX sy6heB: 8 - rpynna H3 JJ.BYX lIIJIHU.eBbIX aY()heB;
e, a - npO;:I.OJIbHOe cetJeHHe qepHOBblX H tJHCTOBbiX 3y6beB
HYTpeHH5I <PI = 1+3°. TIpOcpHJIH 3BOJIbBeHTHbIX lIlJIHII.eBbIX rra30B 'lI
3y6beB rrpOT5ILKKH IIPH 3TOM 6Y YT pa3JIHQaTbc5I. TaK KaK np04>HJIb
.9BOJIbBeHTHbIX llIJIHlI,eBbIX na30B 3a aH, TO KoppeKTHpYlOT npocpHJIb
npOT5I2KKH.
9BOJIbBeHTHbIe npOT5I}I{KH, KOTopbIe HMeIOT rrOCT05lHHbIH rrO 'BeM II
llIar OT 3y6a K 3y6y (HJIH rrOCT05IHHOe OTHOllIeHHe nO aqH K mary),.
Ha3bItBaIDT O,1I.HOKOHYCHbIMH H.JIH JIHHeHHbIMH. BeplllIIHbI 3BOJIbBeHTHbIX
3YObeB TaKHX rrpOT5I}KeK (Ha paCqeTHOH QaCTH) JIe}l{aT Ha OJI.HOM BO-
05pa)KaeMOM KOHyce. BOJIhBeHTHbIe npOT5I)KKH, Y KOTOpbIX BeplIlHHbI
paCqeTHbIX 3y6beB JIeLKaT Ha HeCKOJIbKHX Boo6pa)KaeMbIX KOHycax, Ha-
3bIBalOT MHorOKOHYCHbIMII. OrHomeHHe llO,lI.aQI1 K IIlary Y TaKHX rrpo-
Tfl}KeK rrOCTORHHO TOJIbKO B rrpe eJIax O Horo KOHHqeCKOro yqaCTKa.
KOppHfHpOBaHHbIH rrpocpHJIb 3y6heB rrpOT5ILKKH rrpe CTaBJI5IeT co-
OOH TeOpeTHqeCKHH rrpocpHJIb 3y6beB (T. e. TaKOH rrpocpHJIb, rrpH KOTO-
pO 1 BepII1HHbI 3y6be.a npOT5ILKKH B rrpou:ecce rrpOT5IrHBaHH5I nonaAalOT
TOqHO Ha 3a aHHbIH: .9BOJIbBeHTHbIH rrpocpIIJIb )I.eTaJIH), aIIrrpOKCHMHpO-
BaHHbIM .rr.yraMH OKPYlKHOCTH HJIH .9BOJIbBeHTbI.
Ha pHC. 5.1 rrOKa3aHa KOM6HHHpOBaHHa5I 3BOJIbBeHTHa51 IIpOT5I}I{Ka,
Oopa6aTbIBaIO aH ll.HJIHH.D.pHqecKYIO rrOBepXHOCTb rro BHyTpeHHeMY
,Lu1aMeTpy H II1JIHIl.eBble rra3bI, a TaK)Ke nOnepeQHble CeQeHH5I pa3JIHQ-
HbJX BHlI.OB 3y6beB. DpOT5I)KKa COCTOHT H3 Inepe,lI.HerO XBOCTOBHKa 1,
llIeHKII 2, nepexo Horo KOHyca 3, rrepe HeH HanpaBJIHlOm;eH 4, pe)KY-
eH qa.CTH 5, 3a HeH HarrpaBJI5IlOm;eii 6, 3a Hero XBOCTOBIIKa 7
Pe)Ky a51 lJaCTb rrpOT5ILKKH COCTOHT H3 3y6beB Tpex BHl(OB: <pacolJ:-
HbIX I, KpyrJIbIX 11 H llIJIHU:efBbIX Ill. KpyrJIbIe H lIlJIHII-eBhIe 3y6bH, B
110
CBOIO 04epe,lI.b, nO pa3,lI.eJI5IIOTC51 Ha qepHOBhIe, nepeXO,l1.HbIe, lJHCTOBble
II KaJIH6pYIOIlI.He. <l>aCOQHbIC 3y6b5I TOJIbKO qepHOBbIe. I1HorJI.a JI.JI5I pa3-
)I,eJIeHI15I CTPY}I{KH HX 06'beJI.HH5IIOT B rpynIIbI 113 JI.BYX 3y6beB. ECJIH
KpyrJIble 3y6bH paCnOJlaraIOrCH Me)l{,QY cpaCOlJHbIMH II 3BOJIbBeHTHbIMII,
TO OHI! lIMelOT nOJI.'beM Ha KalK,lI.bIH 3y6. ECJIH 3y6b51 paCnOJIO}KeHbI Icrne-
pe,1I.H, TO HX rpynnHpYlOT no )I.Ba: nepBble - npope3Hble C BbIKpYJKKa-
MH, BTopble - Kpyr JIble 3a qHIlI.alOIlI.He.
MeTOAHKa pacIJera WJIHl(eBbIX npOTSI>KeK
C 3BOJIbBeHTHbiM npo<tJHJIeM
MeTO)I.HKa paCqeTa lUJIH eBbIX npOT5I)KeK C 3BOJIbBeHT-
HblM npocpHJIeM B OCHOBHOM aHaJIOrnQHa MeTO)l.HKe paCQera np5IMo6olJ:-
lIbIX llIJIHII.eBbIX npOTH}KeK.
B ){aHHOH MeTO):(HKe rrpHBe,lI.eHbI paCqeTbI rra paMeTpOB .3BOJIbBeHT-
HbIX npOT5I2KeK (rJI. 4, II. 1-18 paCqeTa npHM060QHbIX npOr5l}l{eK).
3,Qech paccMorpeHbI OJI.HOKOHycHble 3BOJIbBeHTHbIe rrpOT5I)KKH, y
KOTOpbIX OTHOlIleHHe rrO,lI.a4II Ha 3y6 K lllary Ha paCqeTHOM yqaCTKe-
BeJIlfqI1Ha rrOCT051HHaH, 60KOBOH npocpHJIb 3BOJIbBeHTHblX H <paCOqHbIX
3y6beB KoppHrHpoBaHHbIH.
HCxoAHble AaHHbie AJISI paCIJeTa 3BOJIbBeHTHoH npOTSI}KKH, OTJIHq..
HbIe OT I1CXO,lI.HbIX .rr.aHHbIX IIp5lI\to6oQHOH npOT5IJKKH, CJIeJI.yIOI1.(He: MO-
.my JIb (m), ,LlHaMeTp ,lI.eJIHreJIbHOM OKPY)KHOCTH (d), npocplfJIbHbIH yroJI
(a ), ,lI.HaMerp OKPY)KHOCTH 3y6beB BTY JIKH (D a) H ,lI.HaMeTp OKPYJKHO"
rCTII Brra,lI.HH BTYJIKH (Df) C ,lI.OnYCKaMH, pa3Mep cpaCKH (IX 45°), HOMH"
HaJIbHa5I ,QeJIHTeJIbH85I OKPy)KH8.H ll1HPHH8 BrrajI.HHbI BTYJIKH C jI.OIIYC"
KaMH (e) (pHC. 5.2). ,aeJII1TeJIbHa5I llIHplfHa Brra,lI.I1HbI, KpOMe pa3Mepa
e, MO)Ker 6blTb 3a,lI.aHa erue ,nBYM5l cnoco6aMH: 1) 3a,QaeTCH pa3Mep
MeJK)I.Y pOJIHKaMH (A'li) C ,QonycKaMH H ,lI.HaMeTp pOJIHKa (D ) (plfC.
5.3); 2) 3aJI.aeTC5I ,QJIHHa o6lII.efI HOpMaJIH W C ,lI.OrrycKaMH 11 IqHCJIO
Bna,lI.HH Ha ,nJIIIHe 06IlI.eH HOpMaJII1 (ZlV) (pHC. 5.4). OCTaJIbHble HC-
XO,lI.Hble )I.aHHble - q lCJIO llIJIHueB (z), ,lI.aaMerp ,QO npoTHrHBaHllH
(do), .lI.JIHHa npOT5IrHBaeMoH nOBepx-
HOCTH (l), napaMeTp mepOXOBaTOCTH
u
nOBepXHOCTerr BIIa,nHHbI, xapaKTepH-
CTHKa CTaHKa, xapaKTep rrpOH3Bo,nCT-
B8, M8KCHM3JIbH85I ,l(JIHHa npOT5tlKKH
B CBH3H C B03MOLKHOCTHMH HHCTPY-
MeHTa bHoro rrpOH3BO CTBa H 3aTOq..
Horo OT)I;eJIeHH5I - 3aJI;aIOTC5I no aHa-
.JIOfHH c rrp5IMo6oQHbIMH IlIJIHueBbIMH
npOT5IIKKaM Ii.
IT 0 P 5I ,n 0 K pac q eTa.. P a Cq eT
3BOJIbBeHTHbIX rrpOTH)I{eK rrpOH3Bo,nHT-
CSI no MeTO)I.HKe paClJeTa rrp5lMOOOq-
HhlX IllJIHUeBbIX npOT5I)KeK C HeROTO-
phlMH H3MeHeHH5IMH, CB5I3aHHbIMH C
KpHBOJIHHeHHOCTblO 60KOBoro npocpH-
U U
JI5I H HerrOCT05IHHOH IlIHpHHOH na3a
lliJIHueBOro OTBepCTHH.
PHC.. 5.2.
Hexo)].Hble napaMeTpY WJlHl(eoo..
ro oTsepeTHH C 9BOJlhSeHTHblMH
naaaMH
111
\ \
7fr
PHC. 5.3.
HCxoJl.Hbie napaMeTpbl Af 1 Ii d",
H paC eTa Sp (nepB A cnoc06
sa)l.aHHH e)
w
PUC. 5.4.
J.1cXO)J.Hble napaMeTpbl W H Z w ,lJ,JlH
paC\JeTa Sp (BTOpOH cnoc06 3a)l.aHHR e)
BHaqaJIe paC4er 3BOJIblBeHTHbIX npOT5I)KeK, K8K H npHM06oQHbIX,
nOJIHOCTbIO COoTBeTcTByeT paClJeTY Kpyr JIbIX rrpOTH1KeK (r JI. 3, fI. 1-11
pac'-leTa). ,I:laJIee pac"lleT npOH3Bo;1,HTC51 no IvleTO,lJ.HKe paCqeTa np51Mo"
60lJHbJX npOTH)KeK (rJI. 4, II. 1-18 paClJeTa) C Heo6xoP-HMbIMH H3Me-
HeHH5IMH H ;:I.OnOJIHeHH HMH, KOTopble rrpl1Bo,J5ITC5I B ;taHHoH MeTO HKe.
H 3.iHefleHUfl K n.l. 1. ECJIH AJI51 npHl\tl06olJ.HbIX lllJII1QeBbIX npoTHIKeK
J1.JI5I JIYlIlllHX YCJlOBHH pe3aHHH QHCJIO 3y6beB B CeKI.IJiH npHH>ITO Zc = 2,
TO ,.RJ151 3B0J1bBeHTHbIX npOT51mel{ MO:tKeT 6bITb Zc = 2 npH MHHHMaJIbHOa
J{JIHHe pelKYI.I..I.Hx KpOMOK Bm mln 3 MM, a TaK)I{e Zc = 1 npH Bill ffiln<
< 3 MM (TaK KaK ,lI.eJIeHI1e BbIKpy)KK8MH )I,.JIHHbI pe)KYIlI.eH KpOMKH He..
B03MO}KHO H3-3a MaJIOH WIIpHHbI 3y6a).
2. ECJIH llJJIHueBOe OTBepCTIIe C 3BOJIbBeHTHbIMH BfIa,J,I1HaMH npe,n-
eaplITeJIbHO npOT5IHYTO npOTH)KKOH H8 HenOJIHYIO 1I1HPHHY Brra,J.l1HbI, a
c npHnycKoM Ha BTOpoA TeXHOJIorHqeCKH rrepexo (UpH 3TOM npo-
TH)KKa nepBoro TeXHOJlOrHlJeCKOrO nepexoJ:(a MOlKeT HMeTb He 3BOJIb-
Be lIT H bI fi rr p 0 cp H" 1 b a, H a n p 11 M e p, T pan e ll. e 11,]. a J1 b H bI Ii), TO ,J..J15I n p OT 51 JK KH
BToporo TeXHO.noryflleCKOro nepeXO:.La He38BHCHMO OT Bill mln CJIeJI.yeT
BCer.lI.a npHHHMaTb Zc = 1.
3. DpH orrpe,J,eJIeHHH lJHC 1Ja 3y6beB B rpyrrne Zc B 3aBlfCHMOCTH OT
'MaKCHM8JIbHO ,J.onycTHMoH Cll,, bI pe3aHH5I Pmax no <popMy.ne (4.1) B
Hee BMeCTO B 1nax nO;:I.CTaBJ15IIOT 3HaqeHH5i MaKCHMaJlbHbIX ;I,J1HH pe)KY-
InHX KPOMOI<: cpaco4HbIX BfP max, Kpyr JIbIX B}{ max 11 3BOJIbBeHTHbIX
Bm max 3y6bes. BeJIHqIiHbI BdJ ma:K 11 Bl\ max, K8K Ii ,IlJI5I np5IMo6oQHbIX
sy6beB, onpe eIJ1 lOT IIpH6J1H)KeHHO no CPopMYtJ1aM (4.2), (4.3) H (4.4).
,QJI5I lIIJIHueBbIX 3BO,,1hlBeHTHbIX 3y6beB, B OT.lIHqHe OT IIP M06oqHbIX,
Bm max paCClJHTbIBalOT B 3aBHCHMOCTH OT paCqeTHOH TOJIlll)1HbI 3BOJIb-
BeHTHoro 3y6a Sp no cpopMy.ne
BWi=D,( Sp +inva,-inva i ) , (5.1)
\ d
r,ne Dz - H8MeTp OKPYlKHOCTH, npoxo.lI.51 eii lJepe3 i-lO TOqKY; a£-
yroJI J1.aBJIeHM5I B i-If T04Ke 3BO.,lbBeHTbl.
112
OpH onpe eneHHH MaKCHManbHOH
,nJIHHbI peMYIll,HX KpOMOK (Brn max)
3BOnbSeHTHbIX 3y6bes npOT5IlliKH B <pop..
MYJ1bI (5.1) H (5.2) BMeCTO Dt CJIe.lI.yeT
nO,l1.CTaB..1HTb D Q, a npR onpe)J,eJIeHHH
MaKCHMaJIbHOll .lI.nHHbI (Brn mad - Df
(pHc.5.5).
B <POPMYJIY (5.1) BXO,llHT paCQeTHa5I
.n.eJIHTeJIbHa5I OKpYlKHa5I lllHpHHa 3Y-
6a Sp. DepsoHaqaJIbHO peKOMeH.lI.yeTC5I
rrpHHHMaTb ee paBHOM MaKCHMaJIbHOMY
3HaqeHHIO .lI.eJIHTenbHOH OKPY2KHOH IllH-
pUHe sna HHbI OTsepCTHH B npe,LleJIax onYCKa (Sp==emaA)' eCJIH
HeT onbITHbIX .lI.aHHbIX 0 pa36HBKe HJ1H yca.lI.Ke IllJIHueSOro OTsepCTHH
nocne rrpOT5IrHSaHH5I. 3HaqeHHe Sp YTOqHHIOT rroc.ne HCTIbITaHHH
OTIbITHbIX rrpOT5I)I{eK. ECJIH eCTb TaKlIe AaHHbIe, TO 3HaqeHHe Sp MO}K-
HO TIpHHHMaTb cpa3Y C Y4eTOM pa36HBKH HnH yca,LI.KH. npH rrpe.lI. no -
JIaraeMofi pa36HsKe IllnHuesoro oTBepCTHH peKoMeH yeTcH sW4HTaTb
OT Sp O)J.HY TpeTbIO HJ1H OAHY qeTSepTYiO QaCTb AonYCKa Ha ,il.eJ1HTeJlb-
HYIO OKPY)I{HYIO WHPHHY Bna.lI.HH sTynKH, a rrpH rrpe.lI.rro.TIaraeMOH
yca.lI.Ke CTO"lbKO }Ke npH6aBJIHTb.
ECc/TJ}l B HCXO,J.HbIX ,J,aHHbIX 3a)1.aH He pa3 1ep P, a pa3\Iep Me)K)].Y
ponHKaMH M l C ,LlonYCKaMH H .lI.HaMelp pOJIHKa D (C.M. pHC. 5.3), TO
Sp pac.CqHTbIBaIOT no cpopMy.ne
YrOJ1 ,nasneHHH B i-H TOqKe HaXO,lI.5IT
no opMYJIe
a == arccos
l
dB
D 1
( 5.2)
r,J,c
d B == mz cos a 1 . (5.3)
PHC. 5.5.
HaH60JlblllaSi )J.JlHHa pe>Kyw. Hx
KpOMOK (lllHpHHa cpe3a) Ha pa3-
JlHIIHblX 3y6bSlX H npHnycKH, eHH-
MaeMble 3y6bHMH:
1 - 3BOJIbBeHTHbIMH; - c\1aCOQHbIMH;
3 - KpyrJ1blMH
Sp=d( \{ -invat+inva p ).
r)l.e ap - yrOJI .lI.aB.lIeHH5I B TOqKe KOHTaKT3 pO,,1I1Ka C l1CXO HbIM npo-
<p HJIeM .
,IlnH qeTHOrO qnCJIa rnnHuetB
a p == arccos
dB
M imax + D\f.
LLn5I HeqeTHOrO qHcna lllJIHueB
dB CDS
a p = arccos
(5.4 )
(5.5)
90°
z
(5.6 )
M i max + D\f,
r,LlC .iW i max - MaKCHM3JIbHbIH B npe)l.enax orrycKa pa3Mep Me}K.lI.Y po-
JIIIKaMH.
113
r.lI.e W max - MaKCHMaJIbHaH 8
npe.lI.eJIaX ,LlOnYCKa .lI.JIHHa 06-
eH HOpMaJIH.
H3MeHeHuH K n. 2. Pacnpe-
,neJI5IIOT npHnycK MeiK,ny pa3HbI-
MH QaCT5IMH H 3y6bHMH no MeTO-
AliKe lllJIHI.I.eBblx npHM060QHbIX
npOT5I)KeK, HCKJIIOqaH npHnYCK
Ha rrOCJIe.lI.HeM cpaCOQHOM 3y6e
DE- 06bIQHO cpaCKY 3a.lI.aK>T pa3-
MepOM f H yrJIOM cp (pHC. 5.6).
ECJIH cpacKa Ha qepTeJKe ,lI.eTa-
JIH He 3a.lI.aeTC5I, TO H3 TeXHOJIO-
rHlJeCKHX coo6palKeHHH ee Mom-
BO npHH5ITb paBHOH 0,1 m. YroJI cpacKH cp He3aSHCHMO OT Toro, Ka-
KHM OH 3a,QaH Ha qepTeJKe ,neTaJIH, npHHHMaIOT no Ta6JI. TI34 I1PH-
JIO>KeHHH (45 HJIH 47° B 3aSHCHMOCTH OT qHCJIa IllJIHIl.eB z).
PaCqeTHbIH ,QHaMeTp nOCJIe,QHero cpaCOqHOrO 3y6a DE onpe,neJI5IK>T
no opMYJIe
y
Xc
A
Pue. 5.6.
HCXO)l.Hb1H npo4>HJ1b 9B0J1bBeHTHoro na3a
c 4JaeKaMH, 3a,ll.aHHblMH yrJloM B(IJ H pa3-
MepoM f AJ1S1 TOQHOrO onpeAeJleHHH pac-
qeTHOrO AHaMeTpa DE 4>aCOlJHblX 3y6beB
ECJ1H 3a.lI.aHbI ,nJIHHa o6III.eii
HOpMaJIli W C .lI.OnycKaMH H qHC-
JIO cxsaT1bIsaeMbIX Brra.lI.HH Zw
(CM. pHC. 5.4), TO Sp paCCqHTbI-
BalOT no cpopMYJIe
S = W max - JIm (zw - I) cos a!(
p
cos a JI.
- dinva J , (5.7)
DE=d. -Vl+( -tE)2
3 ecb
( 5.8)
3t
= --8o,
2
r e
(5.9)
(j Jt Sp .
Va = - - - - lnv all;
z d
inv a)t=tg a lt - all;
(5.10)
(5.11 )
tf - yrOJI pa3ffiepHYTocTH 3BOJlbBeHTht B TOlIKe E.
B o6 eM CJIyqae rrepeMeHHbIH rrapaMerp 3BOJIbBeHThI C TeKYll(eH
TOqKOH i
ti= -tgai'
r,Qe at HaXO)l.HT no cpopMYJIe (5.2).
114
( 5.12)
CHCTeMa ypaBHeHHH 3BORbBeHTM OCHOBHOH OKPY)KHOCTH
TOQKI1 HMeeT Bll;:I.
d:
TeKyrueB
xi=R o Ieos ti-( -tl) sin tiI;
Y I = R 0 [ sin t I + ( - t I) cos t i ], ( 5.13'
r e Ro - paLLHYC OCHOBHOH OKPY)KHOCTH, R o =O,5d B .
1'OIfKa E rnpHHa)I.JIeJKHT .3BORbBeHTe H cpacKe (npHMoH). ITOJIO)Ke..
HHe ee onpe eJ15IIOT pelIII1B COBMeCTHO CI1CTeMbI ypaBHeHHH .3BOJ1bBeH....
TbI B TOqKe E H np5IMOH (cpacKH):
x E =O,5d B leos tE-( -tE) sin tEl;
YE=O,5d B [sin tE+( - tE) cos tEl; (5.14)
Y E - Yc= (x E - xc) ctgw.
B pe3YJIbTaTe rrOJ1YQaeTCH TpaHCI.I.eH eHTHoe ypaBHeHHe, 113 KOTO-
poro orrpe eJIHI{)T napaMeTp t E (6JIHiKaHIl1HH CJIeBa K KopeHb):
x cos w - y sin (a)
eos(w+tE)+(tE- )sin(w+tE)= c c , (5.15)
O,5d B
r,ne
180 0
z
+ 4»;
( 5.16)
w==
Xc, Yc - Koop.n.HHaTbI TOqKH C.
TOqKa C .SIBJ151eTC.SI T04KOH nepeCeQeHH5I )J.BYX OKPYLKHocTeH: rrep-
180H C Il.eHTpOM B TOqKe 0 H pa HYCOM R A = O,5D A 11 BTOpOH - C Il.eHT-
pOl\1 B TOqKe A 11 Ipa,LlHycoM j.
113 COBMeCTHOro perueHH5I ypaBHeHHH 3THX OKPY)KHOCTeH onpe,l(eJI5I-
lOTC5I KOOp;:I.HHaTbI T04KH C (xc, Yc).
CHCTeMa YKa3aHHbIX ypaBHeHHH CJ1e YIO a5I:
x +Yc=R ; (5.17)
(x c - XA)2+(yc- YA)2= /2,
r.n.e XA, YA - Koop,QHHaTbI TOqKH A .3BOJ1bBeHTbI, IJepe3 KOTOpylO rrpo-
XOJlHT OKPY2KHOCTb C pa,nHycoM R A == O, 5D a.
PeIlIHB cHcTeMy ypaBHeHHH (5.17) 11 C eJIaB p.SI):( npeo6pa30BaHHH,
nOJIYQMM
X (l+ : )-2C : xc-R +C2=O.
npHH.SIB B ypaBHeHHH (5.18)
(5.18 )
x
1+
y
_ A .
- ,
( 5.19)
2C XA
YA
_ B .
- ,
(5.20)
115
X +Y -f2+R ;
2YA
c 2 -Rl=D,
nOJIytIHM KBa paTHOe ypaBHeHI1e B 06 eM BHAe
Ax -Bxc+D=O
c=
(5.21 )
(5.22)
(5.23)
tJ
H peIIIHM era OTHOCHTeJ1bHO Xc, B3.SIB TOJIbKO MeHbllIHH KopeHb:
1/ R 2 2
yc= A-XC.
nOCJIe 3Toro HaXO,QHM op,nHHaTY Yo (6epeM TOJ1bKO
HbIii KopeHb):
Yc= V R -xt. (5.25)
Koop HHaThI TOqKH A onpe,QeJ1.SIIOT no opMYJ1aM (5.2), (5.9),
(5.10), (5.12), (5.13). B cpOPMYJIY (5,2) BMeCTO D i no,nCTaBJI5IIOT Da.
TaK KaK ypaBHeHHe (5.15) TpaHCI1.eHAeHTHoe, TO 3TOT crroco6 onpe..
eJ1eHHH pac eTHoro ,QHaMeTpa rrOCJIe HerO aCOqHOrO 3y6a onycTHM
TOJ1bKO npH pactJeTe Ha 3Blvl.
,[lJIH pyqHOro qeTa MOJKHO C ;:I.OCTaTOqHOH CTeneHblO TOqHOCTH Hau-
TH paCqeTHbIH HaMeTp nOCJIe Hero cpaCOqHOrO 3y6a DE rrpH6JIH}KeHHO.
TIpH6J1HJKeHHbIH MeTO}1. OCHOBaH H3 ,QonYIl(eHHH paBeHCTBa paLU'IY-
COB KPHBH3Hbl B TOqKaX A H E 3BOJlbBeHTbI B CB5I3H C MaJIbIM pa3Me-
pO t cpacKH (pHC. 5.7).
TOQKa E HBJ15IeTCH TOqKOH nepeCeqeHHH HCXO HbIX npocpHJ1eH cpac-
KH H BITaAMHW npH TOqHOM MeTo e onpe eReHH5I HaMeTpa nOCJIe He-
ro cpaCOqHOrO 3y6a DE.
,[(JIH rrpH6JIH)KeHHOrO onpe-
,neJ1eHHH ,nHaMeTpa rrOCJIe HerO
<paCOqHOrO 3y6a HaH eM pa,nHYC
KpHBH3HbI .3BO.TIbBeHTbI B TOq-
Ke A H npHMeM ero 3a pa HYC
3aMeH5IIOIUeH oKpymHocTH yqa-
CTKa 3BOJIbBeHTbI Me)K Y TOQKa-
MH A II E. B TOlJKe E pa,LLHYC
KpHBH3HbI 3BOJIbBeHTbI 6y eT
OTJIHqaTbCH OT paAHyca 3aMeHH-
IOrneti OKpY)KHOCTH PA Ha b, a
TOlJKa BCTpeqH HCXO HbIX rrpo-
<pHJIeH 6y,aeT He E, a E'.
0603HaQHM Qepe3 RE' pa..
,QHYC OKPY}I{HOCTH rrOCJIe,LlHerO
cpaCOlJHOrO 3y6a, npOXO HI..U.eM
Qepe3 TOqKY £1 H HaH eM ero
rrpH6JIH)KeHH 1 bIl\1 l\1eTO OM. Pa3"
HHua Me}J{ Y RE', HaH eHHbIM
y
a
.1
A'
PHe 5.7.
HCXO)l.HblH npo(jJHJlb WJlHQeoorO SBOJ1bBeHT-
Horo na3a C (jJacKaMH, aanaHHblMH yr JlOM
f3 H pa3MepoM f, 1I.JlH npH6J1H1KeHHOrO
MeTO.ll.a onpeJl.eJ1eHHSI paCqeTHOrO .lI.HaMeT-
pa DE nOCJJe,ll.Hero c1JaCOQHOrO ay6a
116
(5.24 )
n0J10LKHTeJ1b-
rrpH6JIlfllieHHbIM MeTO.lI.OM, H RE' HaHJJ.eHHbIM TOIJHbIM MeTOAoM, 6Y,lI.eT
nOrpeIllHOCTblO Orrpe.lI.eJIeHli5I RE' rrpH6.TIH}KeHHbIM MeTO.lI.OM.
180 0
Ha pHC. 5 7 CA = f, 00= + <t>. Pa,J,I1Yc KpHBH3HbI 3B0J1bBeHTbI
z
B TOlJKe A orrpe;I.eJI5IeM no cpopMYJIe
PA=Ro(r-tA). (5.26)
HaXO.lI.HM a, b - KOopJI.I1HaTbI u.eHTpa 3a 1eH5I1OIlI.eH OKPY)KHOCTH B
TOIJKe E' C KOOp.lI.H HaT al\111 XE' 11 YE':
(X - a);.l+ (y - b)2= R ( - t A)2, (5.27)
r,LLe a 11 b orrpe.lI.eJIHeM H3 ypaBHeHHH
a=xA +RO( -tA) sin fA;
b=YA -RO(p-t A ) cos tA.
( 5.28)
YpaBHeHHe cpaCKH 3arrHIlIeM B BH.lI.e
y - Yc=(X - xc> ctg 0),
( 5.29)
r)J.e Xc Ii Yc - KOOp.LUIHaTbI TOqKH C (HaqaJIa <paCKH).
KoopJ{HHaTbI Xc Ii Yc orrpe,QeJIHM no cpopMYJIaM (5.19) - (5.25).
113 COBMeCTHoro peIlleHH5I ypaBHeHHH (5.27) H (5.29) rroJ1YQliM
ypaBHeHHe
(X )2 (1 + ctg 2 oo)- 2x (.x c ctg 2 ill +a - Yc ctg ill + b ctg ill) +
+ [a 2 + x ctg 2 (1) + y + b 2 - 2x c Yc ctg ill + 2bxc ctg ill-
- 2byc- R (2- t.4)2] === o. (5.30)
0603HaLIHM K03cpcpHIl.HeHTbI rrpH HeH3BeCTHblX lJJIeHaX ypaBHeHH5I Ii
nOCT05lHHbIH qJ1eH ypaBHeHH.SI:
1 +ctg 2 (1)== At;
2 (a + Xc ctg 2 (I) - Yc ctg 0) + b ctg (1)= HI;
a 2 +X ctg2 (J) + y + b 2 - 2x;cYc ctg 0) + 2b.r c ctg.w - 2byc-
- R6 (3 - f A )2== C10
nO,LLCTaBHIB HX B ypaBHeHHe (5.30), IIOJ1YQHM KBa,QpaTHoe ypaBHe-
IHfe 8 06llI.eM BH e
(5.31 )
( 5.32)
( 5.33)
Al (X )2_ BIX +C 1 =0.
113 Hero, B351B TOJ1bKO MeHbIIIHH KopeHb, Ha H,QeM a6CUHCCY
B 1 - V B; - 4A 1 C d
x' ==
E 2Al '
a, CJ1e.noBaTeJIbHO, H op,QMHaTY
Y ==(X - Xc> ctg 0) + Yc.
(5.34)
( 5.35)
(5.36)
117
Pa,lU-fYc HCKOMOH OKPY)KHOCTM, npOXO,lIJIlIl.eH IJepe3 TOIIKY £1, OrrpeAe-
JISleM no cpopMYJIe
R = V (X )2 +(y )2
( 5.37)
(B3HB TOJIbKO nOJIO}KHTeJIbHbIH KopeHb).
KaK rrOKa3aJIM npOBepOIJHbIe paClJeTbI pa,lIJlyca RE no TOqHOMY Me-
TO y H RE' no npH6JIH)KeHHOMY, pa3HocTb HX COCTaBJIHeT MeHee 1 MKM,
llTO BnOJlHe npHeMJIeMO H rOBopHT 0 OCTaTOlJHO:H TOqHOCTH rrpH6JIHmeH-
Horo MeTo a.
K HaH eHHoMY JII06bIM M3 npHBe eHHblx MeTO OB 3HaQeHHIO paJJ.HY-
ca nOCJIe,il.Hero $aCOqHOrO 3yoa (RE HJIH REI) npH6aBJ15IeM no 0,2 MM
(HJIH 0,4 MM Ha HaMeTp) H rrOJIyqaeM HaMeTp rrOCJIe HerO <paCOqHOrO
3y6a:
D<I>=2(R E +O,2). (5.38)
nYHKTbI 3-17 paCqeTa llIJIHll.eBbIX npHM060IIHbIX rrpOT5I)KeK npHHM-
MalOT JIH paCqeTa .3BOJIbBeHTHbIX rrpOT5I)KeK C HeKoTopbIMH H3MeHeHHH-
MH, 3aMeqaHH5IMH HJIH Jl.orrOJIHeHH5IMH. K TaKHM nYHKTaM OTHOCHTC5J
II. 3, 9,10,11,17 II 18.
3aMettaflue 1(, n. 3. ECJIH JIH .3BOJIbBeHTHbIX npOT5I)KeK lJHCJIO 3y6beB
B rpynrre Zc ill = 1, TO rro cpopMYJIe (3.17) IIOJIYlJaeTC5I He 1IHCJIO rpynn
qepHOBbIX 3y6beB, a qHCJIO qepHOBbIX IllJIHll.eBbIX 3y6beB Zma.
3aMettaHue 1(, n. 9. ,I:LonycKH Ha ,lI.HaMeTpbI 3y6beB .3BOJIbBeHTHbIX
rrpOT5I)KeK Ha3HaQalOT no rOCT 6767-79.
3aMettaflUe 1(, n. 10. ITYHKT 10 rrpHeMJIeM nOJIHOCTblO ,QJI5I 3BOJIbBeHT-
HbIX rrpOT5I}KeK TOJIbKO B TOM CJIYlJae, eCJIH ,LlHO Brra,LlHHbI (D F) lllJIHcpY-
eTCH pa3)J.eJ1bHO c 60KOBbIM rrpocpHJIeM 3y6beB, T. e. IIIMpHHa BIIa)].MH
lliJIHueBbIX 3y6beB rrpOT5I}KKH y Ha 60JIee 3 MM (MO)KHO ,LleJIaTb YCHKH
Y IllJIMcpoBaJIbHOrO Kpyra). ECJIH x<e IllHpHHa ,LlHa Brra,lI.HHbI MeHbIlle
3 MM, TO OHO IIIJ1H<pyeTC5I BMeCTe c 60KOBbIM npO<pHJIeM, H B .3TOM CJ1Y"
1Jae ,lI.HaMeTp ,lI.Ha Bna,LlHHbI D F 6YJ{eT H3MeH5ITbCH no ,nJIHHe npOT5I}KKHp
Ha rrepBOM paCtJeTHOM 3y6e DF=D B . m . Ha rrOCJIe,lI.HeM paCqeTHOM 3y6e
OR 6y eT D F ' = D F -2C Uh r e G rn - rrO 'beM OCM rrpOTH>KKH Ha paCqeT-
HOM YQaCTKe.
3aMetJ,afllle 1(, n. 11. DYHKT 11 rrpHHHMaeTcH TOJIbKO ,LlJI5I paCqeTa BbI-
KpY}KeK Ha KpyrJIbIX H <paCOlJHbIX 3y6bHX.
BbIKPY)KKM Ha lllJIHueBbIX 3BOJIbBeHTHbIX 3y6bHX HaHOC5ITC5I TOJIb-
KO B TOM CJIYlJae, eCJI H lJHCJIO 3y6beB 8 CeKll.HH Zc m = 2. ECJIH Zc III = 1,
TO 3y6b5I pa60TalOT 6e3 pa3,LLeJIeHH5I CTPY}KKH.
ECJIH 3y6 IIIJIHu.eBOH npOTH}KKH HeBbICOKHH (HcrrOJIb3yeTC5I TOJIbKO
qaCTb npocpHJIH), TO MO)KHO rrpHHHMaTb IIIHPHHY pe)Ky ero ceKTopa
EIll no cpopMYJIe
Ern 0,25 (B wm1n +Bwmax).
( 5.39)
ECJ1H 3y6 3B0J1bBeHTHoH npOTH}KKH HMeeT nOJIHbIH rrpocpHJIb, TO
II1HPHHY pe)Ky ero ceKTopa npHMepHO ,lI,O cepe,lI.HHbI 3y6a HymHo 6paTb
E m1 , a OT Cepe,lI.HHbI 3y6a O ,lI,MaMeTpa nOCJIe,lI.HerO pe}l{YIl\ero 3ytSa
B m2 :
118
Ernt::::::; 0,25 (B wmax +B w . cp );
E w2 -::::::; 0,25 (B w.cp + Bill mln),
f')J.e Bm cp - TOJIII.I.HHa 3y6a no OKPY)KHOCTH cpe Hero HaMeTpa Me}K-
Jl.y nepBbIM H nOCJIe HHM 3y6oM paC1.J:eTHOrO YlJaCTKa.
BeJIHlJHHY Bill cp onpe e.TIHeM no cpopMYJ1aM (5.1), (5.2), KY,Qa
BMeCTO D i nOJI,CTaBJ1HeM D cp :
D cp ===O,5 (DIp + Drr.p)t
r,Qe DIp, Drr p - ,lI,HaMeTpbI rrepBoro H nOCJIe,lI,HerO IllJIHI..I.eBbIX 3y6beB
fla paclIeTHoM Y'llaCTKe.
3aMettaflUe 1(, n. 17 Pa3MepbI lllJIHueBbIX BbIcTynoB nepe.n.HeH: Ha-
npaBJIHIOIlI.ell npOT5[}KeK rrepBoro H nOCJIe.n.YIOIll.HX nepeXo,LLOB paCClJH-
TbIBalOT TaK }Ke, KaK H 60KOBOH npocpHJIb peiKYIll.HX 3y6beB (no TeM
JKe cpopMYJIaM - CM. paClJeT 60KOBoro npocpHJIH). ITpH .3TOM TOJIllI.HHY
lllJ1Hlla no .n.yre .n.eJIHTeJIbHOH OKPY}I{HOCTH rrepe HeH HanpaBJIHIOIll.eii
Sp rr H 6epYT paBHOH MHHHMaJIbHO:H .n.eJIHTeJIbHOH OKPYMHOH lllHpHHe
Brra,LLHHbI OTBepCTHH nOCJIe o6pa6oTKH npOT5I)KKOH nepBoro TeXHOJIOrH-
tIeCKOrO nepeXO,lI,a (HJIH npe bI.n.YIll.ero). ECJIH <popMa pe}KYIll.HX 3y6b-
€B npOT.H)KKH nepBoro TeXHOJIOfHqeCKOrO rrepexotz;a (UJIM npe,QbI,lI.Yil1.e-
TO) 6bIJ1a He 3B0J1bBeHTHaH (HarrpHMep, Tpanell.eH.n.aJIbHaH), TO <popMa
3y6beB nepe,lI.Heii HanpaBJIHlOIll.eH ,lJ.OJ1)1{Ha HM COOTBeTCTBOBaTb, H ee
paCCQMTbIBaIOT no COOTBeTCTBYlOil1.HM <popMe 3y6a <popMYJIaM.
,LLHaMeTp Drr H nepe,lJ.HerO HanpaBJ1eHHH npHHHMalOT TaK :/Ke, KaK If
j:{JIH npHM060lJHbIX npOTH)KeK, - no Ta6J1. IT33 npMJ10}KeHHH.
3aMettaflUe 1(, n. 18. ECJIH )l.HO Brra;::UfHbI IIlJ1HcpyeTC5I BMeCTe C 60KO-
BbIM rrpocpHJIeM, TO BbI60pKa B a6p a3HBHOTvI Kpyre He ,lJ.eJIaeTCH.
PaClIeT KOppHfHpooaHHoro npo4>HJlSI cpaCOlJHbIX 3y6beo. ,[LJIH C03-
)laHHH BcrrOMOraTeJIbHbIX yrJIOB B IIJIaHe CPl Ha <paCOQHbIX 3y6bHX MX
QOKOBO:H npocpHJ1b lIlJIM<PYIOT, nO)].HHMaH 3a.n.HHH lI.eHTp. PaClIeT KOPPM-
rHpOBaHHoro 60KOBoro npocpHJIH 3aKJ1IOlJaeTCH B onpe.lI.eJIeHHH .lI.HaMeT-
pa IIOCJIe,rr,Hero cpaCOQHOrO 3y6a D(f) (LITO Y)Ke 6bIJIO c.n.eJ1aHO B II. 2 npH
pacnpe,lJ.eJ1eHI1M npHrrycKoB Ha pa3HbIx BH,lJ.ax 3y6beB npOTH}KKH), no.n.'b-
eM a OCH npOTH}KKM Ha paCqeTHOM yqaCTKe Ccf,J H KOHTpOJ1bHbIX pa3Me..
pOB - paCCTOHHHH OT OCM npOTH)KKH O 60KOBbIX CTOpOH nepBoro
{H A) H no CJI e,lJ. Hero (H B) <p a COLI H bI X 3 Y 6 b e B ( P H c. 5.8).
YroJI HaKJ10Ha cpacKH ef> (He3aBI1CHMO OT Toro, KaKHM OH 3a.n.aH qep..
Te}KOM .n.eTaJIH), KoppHrHpoBaHHbIH yrOJI rrpo<pHJ1H cpaCOQHbIX 3y6beB
f3lh yroJI rrpocpHJ15I BIIa,lI,HH cpaCOQHbIX 3y6beB H aopa3HBHoro Kpyra
2001\, a TaK}Ke yrOJI IIo,lJ.HYTpeHHH Cj)l 6epYTCH 113 Ta6JI. 034 npHJ10)Ke-
HH5I B 3aBHCHMOCTH OT lJHCJIa lllJ1Hu.eB z.
KOHTpOJ1bHbIe pa3MepbI H A H H B onpe eJIHIOT H3 np5lMoyrOJIbHbIX
TpeyrOJIbHHKOB FOD H OBE (CM. pHC. 5.8) no cpopMYJ1aM
H A = R l sin ( K + AD);
HB===.R sin ( K+AE)'
r,lle R l II Ref> - pa,aHycbI COOTBeTCTBeHHO nepBoro H IIOCJIe)].Hero cpa-
COQHbIX 3yobeB Ha paC1.J:eTHOM yqaCTKe; 'An H /.wE - CM. B rJI. 4 paClJeT
119
( 5.40)'
(5.41 )
( 5.42)
y
Puc. 5.8.
CxeMa onpe.u.eJleHHR napaMeTpOB WJlH4>oBa-
HUH 60KOBoro npo4J1tJUI aeOIJHbIX 3YObeB
H A, H B, C <p, C' <p
y
o
,(
Puc. 5.9.
CxeMa onpe,lJ.eJleHIUI yrJloB Ai H ,lJ.JlHHLI
pe)l{Y Hx KpOMOK B$i U Bit» ma-x
aCOqHblX 3y6beB
npocpHJIH IllJIHueSbIX np5IMo6olJHbIX npOTH)KeK (TaM An cooTBercTBY-
eT AA).
YrJ1bI An H J"E onpeJle 15IIOT no cpopMYJIe
180 0 . Yc sin (J) - Xc cas (I)
)'i== -<.0+ arc SIn ,
z R i
( 5.43)
I<Y,Lla BMeCTO Ri CJ1eftyeT nO.lI.CTaBJ15ITb .lI.JI5I IIo.nyqeHHH yrJIa An pa.lI.HYC
R l, a ,lI.J15I rroJlyqeHHH yr"rra AE - pa)l.HYC Rep. 3HaqeHHe yrJIa (1) onpe-
,aeJI5IIOT no cpopMYJIe (5.16).
<DopMYJIa (5.43) nOJIyqeHa 113 nOCTpOeHH5I pHC. 5.9. TIOJI.'beM OCM
npOT5IMKH Ha paCqeTHOM Y4aCTKe C£P npH lllv1JHcpoBaHHH 60KOBoro npo..
cpHJl5I cpaCOqHbIX 3y6beB nepHcpepneH m.HHcP0SaJIbHOrO Kpyra TITI pa-
BeH pa3HOCTH H A If H B:
C<lJ=HA-HBO
TIpH lllJ1H<pOBaHHH npocpUti1bHbIM KpyroM nO.lI.'beM
paCqeTHOM yqaCTKe Ccb' orrpe,lJ.e.HFeM no cpopMYJ1e
HA-HB
( I80C> )
sin z + p"
C'-
4>-
(5.44 )
OCM npOTH}KKH Ha
( 5.45)
TIO.lI.'beM 3a,lJ.Hero ueHTpa Ha ,LlJIHHe npOT5I)I(KH (HJIH Ha YCTaHOBOq-
HOM .lI.J1HHe L YCTJ HJIH Ha ,LI)IHHe 1000 MM) HaXO,LlHM no QJopMYJle (4.52),
KY.lI.a BMeCTO C IlI nO,LlCTaSJ1HeM C(f) HJIH C i," BMeCTO 1m' -l£P' [CM. <pop-
MYJ1Y (4.51)], a SMeCTO L-L YCT HJIH 1000 MM.
120
MaKCHMaJIbHYIO .lI.JIHHY peLKYIII.HX KpOMOK Rm max - TOqHYIO [paHee
lJ.JIH HaXO>KJI.eHHH qHCJIa 3y6beB B CeKUHH Zc.m BblqHCJIHJIH npH6JIHllieH-
HO no cpopMYJ1aM (4.2), (4.3)] onpe.lI.eJI5IeM no opMy.JIe
. ( ]800 . YcSinOO-XCCoS(I) )
BctJmax=2R 1 SIn - (0 + arCSIn . (5.46)
z R l
PaCqeT KoppIlrHpoBaHHoro 6oKoBoro npocpHJIH .3BOJIbBeHTHbIX llIJIH-
ueBbIX 3yobeB C 3aMeHoH TeOpeTHQeCKOrO rrpO HJ1H ,LlyroH OKPY)l{HOCTH
rrpHBeJ1.eH B npHMepe paClJeTa .3BOJIbBeHTHoH npOTH:>KKH.
npHMep paClJeTa lUJIHl(eBOH 3BOJIbBeHTHoH npOTS1>KKH
HCXO)l,Hble ,lI,aHHble. 1. 3aroToBKa: MaTepHaJI - CTBJIb
20XH3A, H B 207-255; 3arOTOBKa - npoKaT, oTBepcTHe no BHYTpeH-
HeMY .l1.H8MeTpy o6pa6oTaHo OKOHtJaTeJIbHO, do ==Da == 1 OOH 10+ 0 . 14 MM;
HapY)KHbIH ,lI.HaMeTp IllJ1HueBOro orBepCTHH Dj== 110H8+ 0 ,054 MM; MO-
,nYJIb m==5 MM; tJHCJIO IllJJHl(eB z==20; rrpocpH.nbHbIH yrOJI HCXO)J.Horo
KOHTypa aA=20o; napaMeTp lllepOXOBaTOCTH 60KOBbIX rrOBepXHOCTeH
rra3a H rrOBepxHocTei1 BTIa,LlMH Rz= 20 MKM; D,JIHHa npOT5IrHBaHH5I 1 =
+ o. 100
=36 MM; .lI.eJIMTeJIbHaH OKpY)KHaH lIIHpHHa Brra,lJ.HHbI e==9,676+0,037 MM
(cTeneHb TOIJHOCTH 9H).
2. CTaHoK: THTI - BepTHKa.TIbHO-npOTH)KHOii, MO,lI,. 71356; THrOBaH
CHJIa 20 KH; .lI.HanB30H CKopocTeii v == 1,5+11,5 M/MHH; ,lI}lHHa xO,LLa
lIITOKa Lmax= 1600 MM; rraTpOH - 6blcTpocMeHHbIH aBTOMaTl-iIleCKHH;
COCTOHHHe - y,LlOBJIeTBOpHTeJIbHoe.
3. XapaKTep npoH3Bo.n.cTBa - MaccoBbIH.
4. B03MO)KHOCTH HHcTpYMeHTaJIbHOrO uexa H 3aTOQHCrO OT,lJ.eJIeHHH:
HaH6o.HbIIlHe paCCT05IHH5I MefK,lI,Y ueHTpaMH CTaHKOB KpyrJIOWJlHcpO-
BaJ1bHOrO IIIJIHll.elIlJIHcpoBaJIbHOrO, 3arOLJHOrO 1500 MM, rJIy6HHa BaHH
,aJI5I HarpeBa nOA 3aKaJIKY Ii oTnycK 1600 MM.
PaClJeT npOTSI}I{KH. 1. fpynrra o6pa6aTbIBaeMocTII (Ta6JI. TI 1 I1pl1-
JIO}KeHHH) - 11.
2. rpynrra KaQeC1Ba (Ta6J1. TI2 rrpHJIOiKeHHH): no 60KOBbIM nOBepx-
HOCTf.IM fK I = 2; ITO rrOBepXHOCT5IM Brra.lI.HH fK.2 == 2.
3. Onpe.lI.eJI5IeM MapI<y MaTepHaJIa pe}Kyrn.eH GaCTH npOT }KKIi
(Ta6JI. Il3 npHJIO)KeHH5I): rrpHH5ITa OCHOBHa5I MapKa 6bICTpOpe)KYlll.eH
CTaJIH P6AM5 no fOCT 19265-73.
4. BbI6HpaeM crroco6 coe.lI.HHeHHH pa60Qeti GaCTH C XBOCTODHI{OM:
npHHHMaeM C pe3b6oBbIM BBepTblweM, TaK KaK JJ.HaMeTp npOT5!)KKH
60JIbIIle 40 MM. Pa3MepbI pe3b6oBoro KOHua XBOCTOBI1KOB npHBeJI.eHbI
B Ta6JI. TI4 npHJ10)KeHH5I. MaTepHaJI XBOCTOBHKOB CTaJIb 40X no
rOCT 4543-71. Pa3Mep oTBepCTH5I B rraTpoHe CTaHKa D BX ==50 MM.
no rOCT 4044-74 BbI6HpaeM XBOCTOBHK JI.HaMeTpOM 50 MM, Y KOTO-
poro ,lI,I1aMeTp lIleHKH Dl == 38 MM, H rrJIOIlI.a,lI,bIO onaCHoro ce4eHHH
F on == 1134,1 MM 2 . CHJIa, ,lI,OrrYCTHMa5I np04HOCTblO XBOCTOBHKa,
p x 8 === 30. 1134, 1 · 9,8 1 = 333 766 H.
5. BbI6HpaeM rrepe.lI.HHH y II 3a.lI.HHH a yrJ1bI. COrJIaCHO Ta6 rr. TIS
npHJIO)KeHH5I rrepe,LlHHe yrJIbI J1.JI5I llepHOBbIX H nepeXO,lI.HbIX 3y6beB 15°,
121
J{JIH tIHCTOBbIX II KaJIHOPYIOmHX - 180; 3a,lI.HHe yr JIbI .lI.JI5I qepHOBbIX H
rrepexo)I-HbIX 3y6beB - 3°, tIHCTOBbIX - 2°, KaJIH6pYIOIIJ.HX - 1 0
6. BbI6HpaeM CKOpOCTb pe3aHH5I. no Ta6"TI. f16 npMJlO)KeHH5I MaKCH"
MaJIbHO .lI.OnYCTHMaH CKOpOCTb pe3aHHH 6 M!MHH. COrJIaCHO npHMeqa-
HHIO n. 2 K Ta6JI. n6 npHJIO)KeHHH YMeHbllIaeM CKOpOCTb pe38HH5I Ha
25 % :
1'=6- 1,5===4,5 M/MHH.
TaKa5I CKOpOCTb MO)KeT 6bITb 06eCneQeHa Ha CTaHKe.
7. Onpe.rr.eJI5IeM no.rr.aqy qepHOBbIX 3y6beB Szc no cpeJI.Heii Hapa6oT-
Ke MeIK.lI.Y BYMH OTKa3aMH no Ta6JI. 08 npHJIOJKeHHH. CHaqaJIa YCTa-
HaBJIHBaeT HapaooTKY tIHCTOBOH qaCTH SZlI=O,02 MM H v=4,5 M/MHH,.
T 77 M. ,LLJI5I qepHOBbIX 3yoheB 3TOH Hapa60TKe np" TOH :tKe CKOpOCTR
COOTBeTcTByeT no.n.aqa SZC = 0,2 MM. Ha pa60TKa c yqerOM nOnpaBOqHbIX
KO.9<pcfJHUHeHTOB (KTB=O,8; KTP l; KT3=1; KTM=l; K T J1.=I; KTo=l
CO)K - CYJIbcpocppe30JI, KTiI> =:: 1,2), npHH51TbIX no Ta6JI. fI8 npHJIO}l{e...
HH5I, COCTaBHT
T = 77.0 8. 1.1.1-1. 1. 1 2= 74 M
M .H' ,.
B COOTBeTCTBHH C TaOJI. n17 rrpHJIO)KeHHH rrOllaqa Ha tIepHOBbIX
3y6b5lX ,lI.OJLIKHa 6bITb He 60JIee 0,15 MM. npHHHMaeM Szc = 0, 14 MM.
8. r JIYOHHY cTPYMeqHOH !<aHaBKH h Haxo,aHM no <popMYJIe (3.2),
npHHHB K03<P<PHI..I.HeHT nOMelll.a eMOCTH K = 3;
h= 1, 1283V3-36.0, 14=4,005 MM.
TIpHHHMaeM h=4 MM. Do Ta6JI. n19 npHJIO:>KeHHH 3TOH r.ny6HHe co.
OTBeTcTByeT npocpRJIb N2 7. IlpoBepKY h no YCJIOBHlO )KeCTKOCTH He
npOH3BO,ll.HM.
9. OnpeJI.eJI5IeM IIIar tIepHOBbIX 3y6beB to H qHCJIO O,lI.HOBpeMeHHO pa-
OOTaIOIll.Hx 3y6beB zp. War qepHOBbIX 3y6beB no Ta6Jl. fI19 npHJIO>Ke-
HHH )I-JIH npocpHJIH NQ 7 paBeH 10 MM. 4HCJIO o,lI.HoBpeMeHHo pa60TaIO-
InHX 3y6beB onpeLLeJI5IeM no cpopMYJIe (3.7):
36
z = - + 1 =4,6.
p 10
OKpyrJIHB, IIOJIyqHM Zp = 4.
10. HaXO,lI.HM MaKCHMaJIbHO ,lI.OnYCTHMYIO CHJIY pe3aHH5I. CUJIa pe-
saHHH, OrpaHHQeHHaH T5IrOBOH CRJIOR CTaHKa,
PCT=O,8Q=O,8.20000-9,81==156960 H.
CHJIa pe3aHHH, OrpaHHqeHHaH npOqHOCTblO XBOCTOBHKa,
P xB ==333 766 H_
CHJIY pe3aHHH Pan He paCCtIHTbIBaeM, TaK KaK Do>40 MM.
MaKCHMaJIbHO ,lI.OnYCTHMOH CHJIOH pe3aHHH CQHTaeM MHHHMaJIbHYIO
1i3 ABYX paCCtJ:HTaHHb1X CHJI:
Pmax=' 156900 H.
122
11. Orrpe.neJIHeM qllCJIO 3y6beB B CeKII.HH. B npHBe,lLeHHOM rrpllMepe
J1Ha.MeTp ,lI.eJIHTeJIhHOH OKPY)KI-lOCTH paBeH ,lI.HaMeTpy OKPY)KHOCTM Bhl-
cTynoB. IT03TOMY MaKCHM8JIhHa5I TOJIllI.HHa illJIHlI.a
BUlmax=e max =9,776 MM.
Y,lI.eJIbHYIO CHJIY pe3aHH5I qo no TOJI HHe cpe3a 0,15 onpe,lI.eJI5IeM no
Ta6JI. TI20 npHJIO)l{eHH5I: qo=288 H/MM.
nOnpaBOqHhle K03cpcpI:l1I.HeIlTbI Ha YAeJIbHYIO CHJIY pe3aHHH ,lLJIH H3-
MeHeHHbIX YCJIOBHH rrpHHHMaeM no Ta6JI. IT21 npH"TIO)KeHHH: K PM = 1,0;
Kpo= 1,0; K pp = 1,0; K PH = 1,0.
Tpe6yeMoe lIHCtl1JO 3y6beB B ceK1I.HH HaXO,lI.HM no cpopMYJIe (4.1):
9,77 6 . 20 . 2 88.4.1
Z - == 1 , 44.
c- 156900
IlpHHHMaeM zc=2.
12. Pacrrpe,lI.eJIHeM npHnycJ{ Me)K,lI.Y pe3HhIMH 3y6bHMH IIIJIHII.eBOH
qaCTII npOTH}I{KIf. DOJIHhII1 npanYCK Ha lllJIHu.eBble 3y6b5I
Aw= 110,054- 100= 10,054 MM.
TIpHnYCK Ha tJ:HCTOBhle 3y6b H onpe,lI.eJI5IeM no Ta6JI. D22 npHJIOLKe..
HII5I: A ur . q =0,08 MM. npHnYCK Ha nepeXO,lI.HbIe 3y6h5I onpe,lI.eJI5IeM no
Ta6JI. n23 rrpHJIO)KeHH5I: Aur.rr ==0,18 MM; zn=4: ,lI.Ba 3y6a C nO,lLatJ:eii
0,06 MM 11 ,lI.Ba - C 0,03 MM.
npHnYCK Ha qepHOBhIe 3y6b 5I npOT5I}KKH
Awo== 10,054- (0,18+0,08)==9,794 MM.
13. Onpe,neJIHeM qHCJ10 rpyrrrr qepHOBhIX 3y6beB io, OCTaTOQHbIH
npHnycK A OCT H pacnpe eJI5IeM ero:
io= Amo = 9,794 =34,978.
2S zc 2.0,14
DpHHHMaeM io=34. TOf,lI.a QCTaTOqHhIH npHnycK
AOCT=Awo- 2S zc i o = 9,794- 2.0,14.34=0,274 MM.
Ha OCHOBaHHH peKOMe H ,lLaI1.HH MeTO,[(HKH Ao6aBJI5IeM STOT npHnYCK
Ha nOC.JIe,lI.HHH qepHOBOH 3y6. B CB5I3H C 3THM KoppeKTHpyeM io: io = 35.
14. l.JHCJIO Bcex 3y6heB npOT5I)KKH
Zw === zm o + zw.rr + zw.q + ZW.K'
r,Lle Zru a = 4; Zili. tr = 3; ZIlI.H = 4;
zw=2. 35+4+3+4=81.
15. nOA'beMhI rrepeXO,lI.HbI)C 3y6beB: Sill = 0,06 MM; Srr2 = 0,03 MM.
nO,Ll'beMhI qHCTOBbIX 3y6beB SztJI =0,02 MM; SztJ2=O,OI MM; SzQ3=
=0,01 MM.
16. HaxoAHM ,nJIHHY p e)KyI-lI.ei1 qaCTH rrpOT5I)KKH L p , mar II pa3Me-
phI CTpY)KeqHOH KaHaBKH LlHCTOBhIX H KaJIH6pylO HX 3y6beB:
Lp=lw=t (z wO + Zw.n) + t q (Zw.q +ZW.K- 1),
123
r,ne t-q - mar tIHCTOBbIX 3y6beB (Ta6JI. TI24 npnJIO)KeHHH), t q = 7 MM;
L p =10(70+4)+7(3+4-1)=782 MM.
17. Onpe,lJ,eJI5IeM CHJIY pe3aHH5I Ha IIIJIHQeBOH qaCTH (CM. TI. 11). IlpH
npHH5ITOM QHCJIe 3y6beB B CeK1I.HH Zc = 2
P w = 9,776.20.288.4.1 ,0 112620 H.
2
18. ,[{onOJIHHTeJIbHbIe BapM3HTbI He paCCqHTblBaeM.
19. HaxoJ(HM ,lI.HaMeTp KaJIH6pYIOIllJIX lllJIHueBblX D!crn 3yobeB. ,[(0-
nycK Ha .lI.HaMeTpbl 3y6beB Ha3HaqaeM no rOCT 6767-79:
D K . UJ ==- 110,054 --7- 0,025 MM.
20. ,[{MaMerp no Bna,AHHal\1 lllJIHll.eB
DB.W= lOOd9 (= : ) MM.
21. PaCCtIHTbIBaeM qHCJIO, IIIHPHHY H pa.lI.HYC BbIl{pY2KeK. qHCJIO Bbl-
Kpy*eK N npllHHMaeM paBHbIM qHCJIY lllJIM1I.eB, T. e. N == z. MHHHM3JIb-
HYIO IIIHPHHY llIJIHQa onpe.lI.eJI5IeM no cpopMy.ne
Bwm!n=Dfmax( p +inva, -inva}
r,lle
Djmax===' 110,054 MM;
d=nzz===5.20= 100 MM;
Sp=e max =9,776 MM; inva'l=0,014904;
d COg an 100.0,939693
a 1 = arccos == arCcos -
DIll 110,054
== arccos 0,853847; a i =31,36739°;
in v a i === 0,062157 ;
B .'== 110 054 ( 9,776 + 0 , 014904 - 0 , 062.157 ) === 5 , 5585 5 , 6 MM.
w m 1 n , 100
HaXO,lI.HM IlIHPHHY pemYllJ,ero ceKTopa:
EUI =::::; 0,5 Bmml n +2 Bwmax = 0,5 5,6 + ' 776 = 3,844 MM.
TIpHHHMaeM Ern=4 MM. BbIKPY)f{KH Ha qHCTOBbIX H KaJIH6PYIOillHX
3y6bHX He ,lJ,eJIaeM.
lllHpHHY BbIKPY}KKH am onpe.n.e,H5IeM no cpopMY.Jle (4.41) ,[1,,,151 nepBO-
ro 3y6a:
== Jt 100 , 18 _ 4 - 11 75
a w - , MM.
20
no Ta6JI. 027 npHJIOlKeHHH paAHYC Kpyra Rh 30 l\1M Ii paJI,HYC Bbl-
KPY./KKH RB 36 MM.
124
II] 1
125
2cY6
(I O.KJi) J1-1] 51#'
12o()
a)
4 IljJol!t1.JlltJd
Ifz IJ JtZ 1It401Ot4'LI .J10
iY 31° ¥'
RzJ,£ --p 2)
d"'
0)
d)
I
c)
PHe. 5.10.
npOTsDKKa mJlHneSaH 9S0JlbSeHTHaH (100 X "8 X 5):
a - 06InUH BH)1; 1 - nepe)J.HHA XBOCTOBHK; 2 - pe)KYInaR qaCTb c nepe.aHefi H 3a.!lHeH HanpaB-
.nHlOW.HMH 3 - 3a.II.HHfi XBOCTOBHK, 6 - npo.nOJ1bHbtA npo<pHJ1b 3y6beB C Ng 1 no M 74, V-ISo;
B - npo.noJlhHhIA npo<l>HJIb ay6hea c Ni 75 no .M 81, 'V= 18°; 2 - npo<l>Hnb CeKII.HH pe>KYID.HX
syoheB; d - cxeMa KOHTponH pa3MepoB npo<pHJUI syt5a; e - cxeM8 llIJIHcI>oBaHHH BbIKpy*eK Jtn.
pa3.neJIeHHSI CTPY}I{KH Ha He 1 1eTHbIX HOMepax 3y6beB C Nq 1 no Ng 73
22. Onpe.IleJIHeM .IlHaMeTp H .lI.JIHHY nepe,AHeH HanpaBJI5HOilleH. ,.QHa-
u u
Merp nepeJI.HeH HanpaBJI5HOIIl.el1 npHHHMaeM paBHbIM HaHMeHbIlleMY
npe,lI.eJIbHOMY ,lI.HaMerpy OTBepCrH5I ,lI.0 npOT5IfHBaHH5I:
Dn.H= D Omin e8= 100=g: MM.
JIHHY nepe.IlHero HanpaBJIeHH5I KaK ,lI.JIH BBepTHOrO XBOCTOBHKa
(Ta6JI. D4 npHJIO:>KeHH5I) npHHHMaeM Ln.H=65 MM.
23. ,[LJIHHY nepeXO,lI.HOrO KOHyca Ha3HaqaeM no Ta6JI. [128 npHJIO-
LKeHHH: In ==30 MM.
24. PaCCT05IHHe OT nepe,lI.HerO TOpl.I,a ,lI.0 nepBoro 3y6a npOT5IIKKK
L 1 = 160+ 15+50+36+25=286 MM.
25. HaXO.lU1M ,lI.MaMeTp D 3 . H H .lI.JIHHY 3aAHeii HanpaBJI51IOIII.eH l3.He-
LLHaMeTp D a . H npHHHMaeM paBHbIM ,lI.HaMeTpy Bna,LlHH lllJIHUeB npOT5I}K-
KH, T. e. D 3 . H =D B . I1l ; D 3 . H = 100f9 (=g: ) MM.
00 Ta6JI. 029 npHJIO:>KeHH5I .lI.JIHHa 3a,lI.HeH HanpaBJI5IlOIIleH L3 H =
= 70 MM.
,LLJIH pa60TbI B aSTOMaTHqeCKOM UHK.Tle npOTHLKKY cHa6lKaeM 3a.ll.-
HHM BBepTHbIM XBOCTOBHKOM. ,IT,HaMeTp XBOCTOBMKa 40 M { no fOCT
4044-70. Pa3MepbI pe3b60Boro KOHu.a TaKHe lKe, KaK H Ha nepe,lI.HeM
XBOCTOBI1Ke. ,LLJIHHa 3a,lI.HerO XBocrOBHKa 125 MM (Ta6JI. 030 npHJIO-
JKeHH5I) .
125
.5.1. Pa3Mepb1 no poJlHKaM
,lI.HaMeTp
pOJIHKa, d
K
Pa3Mep (MM) no ABYM pOJlHKaM M
npH N 3y6a
19
'87
55
69
MM
8 6,6 113,932 113,824 113,776 113,632
10 - - 120,025 119,917 119,833
12 - - 125,715 125,631
26. 06rna5I .lI.JIHHa npOT5ILKKH L=286+ 782+ 70+ 125= 1263 MM.
OKpyrJIHeM .nO 1260 MM, YMeHbllIa5I AJIHHY 33,LlHeH HanpaBJI5IIOlIl.eH.
4epTe)l{ paCCqIfTaHHOH npOT5ILKKH nOKa3aH Ha pIfC. 5.10, pa3MepbI
3y6beB no pOJIHKaM ,aaHbI B Ta6JI. 5.1, HOMepa H ,LlHaMeTpbI 3y6beB-
13 Ta6JI. 5.2.
OpH llIJIHcpOB3HIfH npocpHJI5I lUJIHQeBbIX 3y6beB N2 1-81 3a,LlHHH
XBOCTOBHK npOT5I)KKH nO,lI.H5ITb; BeJIHtIHHa nO,lI.'beMa paBHa 0,25 MM Ha
JIHHe 840 MM.
MaTepHaJI npOT5I)I{KH - CTaJIb P6AM5, MaTepHaJI XBOCTOBHKOB-
.CTaJIb 45X; y pe)l{yrneH lIaCTH H 33,lI.HeH HanpaBJI5IIOIII.eH H RC 3 62-66,
y rrepe,LlHeH HarrpaBJIHlOrneH HRC;, 60-65, y XBOCTOBHKOB HRC 3
42-56.
OCTaJIbHbIe TeXHHlIeCKHe Tpe6oBaHH5I - no rOCT 6767-79.
5.2. AHaMeTpbl ayobeB npOTH1KKH
-); _::It _:S ....:s ::cs -
en ::!1 = ::s ::s p,.::S ::s
C1) Q) Q) Q) C1)
..a I-< . ..a I-< .. ..Q I-< . .Q I-< .. ..Q I-< .. ..a ..
Q) Q) '\0 Q) \0 a.> = '" Q) '"
::;:Q) ::!1Q) ::e Q) :>.. :s ::SQ)
C'j.Q C'j.Q (I') C'j.Q (I') (1j.Q (I') C'j.Q (I') ro..c:l
:s::\O ::\0 :s:\C :s:\C :s:'\O :=\0
I:::{ q q
1 100,28 15 102,24 29 104,20 43 106,16 56 104,80 69 1 09,79
2 100,24 16 102,20 30 104,16 44 106,12 57 108,12 70 109,75
3 100,56 17 102,52 31 104,48 45 106,44 58 108,08 71 1 09,91
4 100,52 18 102,48 32 104,44 46 106,40 59 108,4d, 72 109,88
5 100,84 19 102,80 33 104,76 47 106,72 60 108,36 73 109,97
6 100,80 20 102,76 34 104,72 48 1 06,68 61 108,68 74 109,94
7 101,12 21 103,08 35 105,04 49 107,00 62 108,64 75 110,01
8 101,08 22 103,04 36 105,00 50 106,96 63 108,96 76 110,034
'9 101,40 23 103,36 37 105,32 51 107,28 64 109,92 77 110,054
10 101,36 24 103,32 38 1 05,28 52 107,24 65 109,24 78 110,054
11 10 I ,68 25 103,64 39 105,60 53 107,56 66 109,20 79 I 10,054
12 101,64 26 103,60 40 105,56 54 107,52 67 109,52 80 110,054
13 101,96 27 103,92 41 105,88 55 107,84 68 109,48 81 110,054
14 101,92 28 103,88 42 105,84
n p H M e q a H H e. ,LLJI5I 3yobeB NQ 1-74 npe.rr.eJIbHbIe OTKJIOHeHHH ,lJ.HaMeTpoB
-0,02 MM, 3a)l.HHH yroJI a = 3°:r 30'; )1..,'151 3YObeB N2 75-81 npe)l.eJIbHbIe OTKJIOHeHHH
)l.HaMeTpOB -0,001 MM, ,lI.JIH 3yobeB N2 75-77 a=2° + 30', )l.JISi ayobeB N2 78-81
..a= 1 0 + 15'
i26
PaCqeT KOppUrHpOBaHHOrO npocIJHnH
3BOnbBeHTHOH npOTRJKKH
Ba)KHeHllIHM 3JIeMeHTOM llIJIHueBOH npOTH)KKM 5IBJIHeT-
C5i ee pe)KYIII.aH qaCTb, nOCKOJIbKY reOMeTpHqeCKHe norpellIHOCTH npo-
<p HJIH pe)KYIII.HX 3y6heB nOJIHOCTblO OTpa)KaIOTCH Ha npocpHJIe H3,ILeJIHH.
B03HHKHOBeHHe reOMeTpHqeCKHX norpellIHOCTeH npocpHJI5i 3y6beB rrpo-
T5i:tKKH HenocpeJ(CTBeHHO CB5i3aHO C TeXHOJIOrHeH ee H3rOTOBJIeHHH.
HaHooJIee npocrOH cnoco6 H3rOTOBJIeHH5i npOT5i)KKH ,[lJI5I o6pa60TKR
BHYTpeHHHX 3y6beB 3aKJIIOqaeTC5i B CJ1e.IlYIOIII.eM. I1pO,lI.OJIbHYIO KaHaB-
KY IlIJIHCPYIOT KpyroM, npocpHJIh KOToporo COBna,lI.aeT C npocpHJIeM IlIJIH-
LLeB H3rOTOBJI5IeMOH ,lI.eraJIH. I1ocTynaTeJIbHOe ,lI.BH)KeHlIe npOTH}KKH
npOHCXO.lI.HT napaJIJIeJIbHO ee OCH. CJIe,lI.OBaTeJIbHO, 06pa3YIOIII.He 60KO--
BbIX nosepXHOCTeH 3y6beB npH pa60Te npOT5i}KKH OKa3bIBalOTCH na..
paJIJIeJIbHbIMH ee OCH. B pe3YJIbTaTe npocpHJIb Ka)K,[lOrO 3y6a COBna,Lla-
€T C npocpHJIeM na3a B ,lI.eTaJIH, n03TOMY nJIOIII.a.Ilb KOHTaKTa nOBepXHO-
CTeH 3y6a H npOT5IrHBaeMoro na3a OLJeHb BeJIHKa, H3-3a 3Toro CHJIa A
rrpOT5IrHBaHHH TaK)Ke OqeHb BeJIHKa.
TIPH TaKOM cnoco6e H3rOTOBJIeHHH npOT5i)KKH 3a,lI.HHe yrJIbI Ha 60.....
KOBOM pe)KyIII.eM JIe3BHH HMeIOT HYJIeBble 3HaqeHHH, QTO pe3KO YXYll.-
waeT KatJ:eCTBO oGpa6oTaHHoH nOBepXHOCTH H CHH)KaeT CTOH:KOCTb 3y6b--
eB npOTHlliKH. I1HorAa qaCTh 60KOBOH nOBepXHOCTH 3y6a C HYJIeBbIM
3a,lI.HHM yrJIOM cpe3alOT, OCTaBJIH5i JIeHTOQKY llIHpHHOH: 0,5-2 MM B 3a-
BHCHMOCTH OT pa3Mepa npOT5i)l{KH. Ho 3TO JIHllib B HeKoTopoH Mepe
CHH)KaeT CHJIY npOTHrHBaHH5i.
,QJI5I Toro QTo6bI o6eCneQHTb 3a)l.HHH: yrOJI H TeM caMbIM YJIyqIIIHTh-
YCJIOBH5I pa60TbI 3y6beB npOTH)KKH npH IIIJIlfcpoBaHHH, 3a,LlHHH QeHTp
rrpOT5IlKKH nO,lI.HHMaIOT Ha HeKOTOpylO Bblcory, 3aBHC5iIII.YIO OT .IlJIHHbl
n pOT 51 }K K H, ,lI.JI H H hI e e p e)K y III. e H LJ aCT H, ,lI. 0 IT Y C K a III H pH H bI B n a,lI. H H bI .lI. e &""
TaJIH H T. .II.. B pe3YJIbTaTe IIIJIHcpOBaHHH npO,lI.OJIbHa5I KaHaBKa OKa3bI-
BaeTCH HaKJIOHeHHOH: KOCH npOTHIKKH no,lI. HeKOTopbIM yrJIOM. npH npo-
,lI.BH)KeHHH IllJIHcpOBaJIbHOrO Kpyra B.II.OJIb npOTH)KKH OT ee HaQaJIa K
KOHU.Y IIIHpHHa KaHaBKH Ha O.II.HOM H TOM Me Y,lI.aJIeHHH OT OCH npOT5I}K-
KH 6Y,lI.eT HenpepbIBHO YBeJIHqHBaTbCH, T. e. Ka}K,lI.bIH: 3y6 OT Ha qaJIa K
KOHll.Y 6Y,lI.eT nOCTeneHHO CY)KHBaTbC5i, CJIe,lI.OBaTeJIbHO, y Hero B03HHKa-
eT, XOT5I If BeCbMa He3HaQHTeJIbHbIH, nOJIO}KHTeJIbHbIH 3a)l.HHH yrOJIr
KpoMe TOrO, Ka)K,lI.bIH nOCJIe,lI.YIOIII.HH 3y6, CQHTa5I OT HaLJaJIa, 6Y,lI.eT Y)Ke
rrpe,lI.bI.IlYIII.erO (Ha O,lI.HOM If TOM )Ke paCCT05iHHH OT OCM npOTHlliKH), no..
3TOMY 60KOBaH nOBepXHOCTb JII06oro 3y6a npOT5I)KKH He 6Y,lI.eT KOHTaK-
THpOBaTb C TOM LJaCTblO nOBepxHocTH o6pa6aTbIBaeMoro oTBepCTH5I, KO-
TopaH ObIJIa nOJIYQeHa C nOMOIII.blO npe.IlIllecTBYIOIII.HX 3y6beB, T. e. nOH-
B HTC' 51 yroJI nO,lI.HYTp eH HH.
TaKHM 06pa30M, YCJIOBHH pa60TbI 3y6beB pe3Ko YJIYQrnaTC5I, O,lI.HaK()
rrpocpHJII1 na3a o6pa6aTbIBaeMoro oTBepCTH5i H IIIJIHcpOBaJIbHOrO Kpyra
6Y,lI.YT pa3JIHLJaTbC5i. BBHJI.Y Toro, qTO npocpHJIb oTBepcTHH 3a,lI.aH, Heo6-
XO,lI.HMO cKoppeKTHpoBaTb npocpHJIb lllJIHcpOBaJIhHOrO Kpyra, KOTopbIa
06bJI!HO H3 TeXHOJIOrHQeCKI1X coOOpa)KeHHH: BbInOJIH5ilOT JIH60 no .lI.yre
OKPY)KHOCTH, JIH60 no ,lI.yre 3BOJIbBeHTbI. fIpH 3TOM HeH36e}KHO HCKalKa..
eTCH npocpHJIb na3a npOTHHYTOH ,[leTaJIH.
12'1
4
J
l
HC. 5.11.
CxeMa o6pa30BaHHH npo HnH Bna-
AHHbI IIIJlHu.eBoro 3BOJlbBeHTHoro
OTBepeTHSI 3y6bHMH npOTSDKKH, npo"
WJlH(jJoBaHHoH c nO)l."beMOM 3a)l.HerO
XBoeTOBHKa:
1 - npO$HJlb nepaoro 3y6a; 2 - npo.
<PHJlb 3y6a, HaXOJ],Slw.erocSl B cpeJI.HeA
tlaCTB npoT1nKKH; 3 - npo<pHJIb nOCJIeA-
Hero 3y6a. 4 - npo<PHJIb Bna.lI.HHbI
1
KOppeKIl.HOHHbIH paCqeT rrpOcpHJI5I 3y6beB 3BOJIbBeHTHOH lIIJIHlI.eBOll
npoT5tIKKH 3aKJIIOQaeTC5I B CJIe,lI.ylOIII.eM.
,L{J15I nO.nYLJeHH5I 60JIblIIHX npOcpHJIbHbIX yrJIOB, 5IBJI5IIOIII.HXC5I yrJIaMII
60KOBOrO nO,.1,HYTpeHH5I Ha np5IM060qHbIX W.HHueBbIX rrpOT5I)KKaX, .n.OCTa..
iOQHbIX ,lI.JI5I YCTpaHeHH5I TpeHH5I 60KOBbIX nOBepXHOCTeH 3y6beB, H3 3a..
BOJI,e npI1MeH5HOT 3a,lI.HHe XBOCTOBHKI1 C 60JIbIIIHM nOJI.'beMOM: OKOJIO
0,3 MM Ha 1000 MM JI,JIHHbI npOT5I)KKH.
Ha6J1IOJI.eHH5I 3a pa60TOH npOT5I)KeK B npOH3BOAcTBeHHbIX YCJIOBH5IX
nOKa33tJ1H, Q10 npow.nHcpOBaHHble C T3KHM nO,l1.'beMOM rrpOT5IJKKH o6J1a..
AalOT CTOHKOCTblO, B 2-3 pa3a npeBbIIllalOlUeH CTOHKOCTh 06bIQHbIX
npOT5L/KeK.
Ha pHC. 5. I I nOKa3aHbI 60KOBOH 3BOJIhBeHTHbIH npoqH1JIb Bna,lI.HHhI
MHOrOIIIJIHll.eBOrO OTBepCTH51 H npO HJ1I1 OT.IleJIbHbIX 3y6beB npOT51}KKH,
paCrrOJIO)KeHHbIX B pa3HbIX MeCTax ee. TIpH lllJIHcpOBaHHH npOT5I)KKlf
nO.lI.HHMaJIH 3a,lI.HHH XBOCTOBHK. npOcpflJIh BnallHHbI lleTaJIH 06pa3yeTC5I
cpaBHHTeJIbHO MaJIbIMH YQ3CTKaMH npocpHJI5I 3y6beB npOT5I)KKH, pacno..
JIO:lKeHHbIMH y BepWHHbI. ,D.JIHHa 3THX YLJ3CTKOB paBH3 nO,lI.a4e Ha 3y6 Sz
(WTpMXOBOii JIHHHeH IIOKa3aHa BeplllHHa 3y6a, CJIe,lI.yKHIl,erO 3a 3y60M
1). DOJIhlIIOe qHC.TlO 3y6beB, o6pa6aTbIB31Oll1,HX Bna)].HHY, 06ecne4HBaeT
xopOlllHe KatIeCTBa OOKOBOH nOBepXHOCTH lllJIHIJ,eB Ii reOMeTpHqeCKHe
napaMeTpbI rrpocpHJIH.
fIpM TaKOM crroco6e H3rOTOBJIeHH5I npOT5IlKKH npocpHJIb Brra.lI.HHbI
IlIJIHua ,LleTaJIH orH6aeT TOtIKH, JIe:tK3lll.He Ha BepWHHe Kam,lI.OrO 3y6a.
Ho eCJIH lIIlIHcpOBaTb 60KOBOH npocpHJIb 3y6beB npOT5IJKKH KpyroM C
TeM me 3BOJIhBeHTHbIM rrpocpHJIeM, qTO II Y ,lI.eTaJIH, TO rrpocpHJIb 3y6beB
npOT5IlKKH H, CJIe,lI.OBa TeJIbHO, Bna,lI.HHa 3BOJIbBeHTHoro m.TI Hua ,LleTaJIH
6YJJ.YT HCK3lKeHbI.
lJT06bI nOJIyqHTb npaBHJIbHblt'I npOcPHJIb H Tpe6yeMbIe pa3MepbI Bna..
J(HHbI lIIJILILLa .LleTaJIM, KoppeKTHpYIOT npocpHJIb a6pa3HBHoro Kpyra, c
nOMOIII.blO KOToporo IlIJIHCPYIOT npOT5I:tKKY. [JOJIyqeHHbIH npocpHJlb ¥pyra
51B.TI5IeTC5I B TO Me BpeMH If 60KOBbIM npocpHJIeM Bcex pe*Ylll.HX 3y6beB
npOT5I)KKH. DOp5I,lI.OK KOppeKUHH CJIe,lI.ylOIII.Hit CHaLJaJIa HaxO,lI.51T KOOP"
,lI.HHaTbI Tpex TOqeK 3BOJIbBeHTbI - ,lI.BYX Kp3HHHX H O,lI.HOH npOMe*YTOLJ-
HOM. 3aTeM, npHH5IB onpe.n.eJIeHHOe 3HalleHHe nO)],'beMa 3aAHero XBOCTO-
BHKa, HaXO,lI.5IT HX HOBbIe Koop,lI.HHaTbI. Tenepb KOOp,lI.HHaTbI 3THX TOqeK
6Y,lI.YT rrpHHa,lI.JIe}KaTb YlKe He O,lI.HOMY H TOMY :tKe, a pa3HbIM 3y6b5IM,
HaXO,lIQll1,HMC5I Ha HeKOTopOM paCCT05IHHH OT rrOCJIe,II.HerO pelliyruero 3Y-
6a, rrpMHHMaeMoro 3a 6a30BbIH. 3TO paCCTOHHHe 33BI1CHT OT OTHOllleHH5I
npHH5ITOrO 3H3 qeHH5I no.n.'beM a 3a,lI.Hero XBOCTOBHKa KO BcefI ,lI..TIHHe npo-
T5I)KKH. KaJIH6pYIOIII.He 3y6b51 B paCqeT He npHHHMaIOT; OHM HMelOT 0.Il1I-
128
y t t Y f
Xo
XL
x'
o
. "....
::).;
X,
o
X
P IiC. 5.12.
npo<lH1J1b Bna,lJ,HH ("JIM llIJ1H4>oBaJlbHOrO Kpyra), OTKoppeKTHpOBaHHblH C YlJeTOM
nO,L\'beMa 3aJl.HerO XBOCTOBI1Ka (I), 11 3B0J1bSeH rHbl" npotPMJlb (/1)
HaKOBbIH HaPY)KHbIH: ,lI.HaMeTp. 9TO He CK83bIBaeTC5I Ha pa60re npor5I}K-
KH, nOToMY lJTO 3TH: 3y6b5I KaJIHopYIOT OTBepCTHe JIHlIlb no HapYlliHOMY
J(HaMeTpy H He YlIaCTBYIOT B cpOpMHpOBaHHH npocpHJI5I. 00 nOCJIe)J.HeMY
KaJ1H6PYIOIll.eMY 3y6y paClIeT BeCTH HeJIb3.H, T3K KaK npH TaKOM pacqe-
Te pa3MepbI 60KOBbIX npocpHJIeH Bcex pe>KY HX 3y6beB OKa3bIBalOTCH
3aHH)KeHHbIMH. 4HCTOBble 3y6b5I, KaK H np H paCLJeTe np5IMOOOtIHbIX IllJIH-
HeBbIX npOT51)KeK, He npHHHMalOT BO BHI1M aHHe.
,LlJIH paCqeTa KpaHHHe T01JKH 3BOJIbBeHTHoro npocpHJI5I BbI6HpalOT
C,,1e.lI.yIO HM oopa30M. DepsylO T01.IKY Bcer,Ll.a 6epYT Ha .lI.HaMeTpe BbI-
cTynoB AeTaJIH D([ IiJII1 HeMHoro BbI llIe ero. OO,;10)KeHHe BTOpOH Kpa H-
HeR T01.IKH 3aBHCI1T OT aeHTpHpOSaHH5I lll"lHll.eBOrO COe.lU1HeHH5I. TIpH
u.eHTpHpoBaHHH no 3BOJIbBeHTHbIM npocpH.JIHM llIJIHu.eB (ueHTpMpOBaHHe
no e no fOCT 6033-80) HJIH no ,L{HaMeTpy BbIcTynoB Da ,LlHaMeTp OK-
pY.lKHOCrH, Ha KOTOpOI1 ,LlOJI)KHa HaXO,LlHTbC5I BrOpa5I KpaHH5I5I TOQKa,
npHMepHo paBeH l1.nH HeMHoro 60JIbllIe HapY*Horo ,LlMaMerpa BaJIa, co-
np5IraeMOro C npOT5IrHBaeMbIM oTBepcTHeM. 3ror ,LlHaMeTp, KaK npaBH-
JIO, HeCKOJIbKO MeHbUle J(HaMerpa nOCJIe,LlHerO pe}Ky ero 3y6a npOT5I}K-
KH. TIpH lI.eHrpHpoBaHHH no HapY)KHoMY ,LlHaMerpy D f IIIJIHu.eBoro OT-
BepcTHH BTOpa5I KpallH5I5I TOllKa JIe)KHT Ha OKPY)KHOCTH, .lI.HaMerp
KOTOpOH cOBnaAaeT C ,LlHaMerpoM nOCJIe,LlHerO qepHOROro 3y6a.
npH ceK1I.HOHHOM nocTpoeHHH npOT5I)I{eK paCqeT MO)l{HO BeCTH no
JIIOOOMY H3 3yobeB ceKll.HH (BbIKpymKH Ha npope3HoM 3y6e HaHOC5IT
nocJle llIJIHcpoBaHH5I npo(IJl1.1I5I). Pa3Mep no pOJIHKaM 3a,LlalOT ,LlJI5I JIIO-
6bIX 3y6beB. Bee paCqeTbI npoH3Bo)J.5IT C TOtIHOCTblO,lI.O 0,000001 MM
AJIH JIHHeHHbIx pa3MepoB H ,Ll0 l' - .lI.JIH YLrIOBbIX. ,LLJI5I paccMaTpHBae-
Moro npHMepa npHHMMaeM npeBbIllleHl1e 33,LlHerO LLeHTpa HaA rrepe,LlHHM
0,3 MM Ha 1000 MM ,Ll.r1HHbI.
5-338
129
J{JI5I paCQeT8 npOcpHJI5I BbIOHpaeM ,lI.HaMerpbl OKpY)KHOCTeH, Ha KO-
TOpbIX HaXO,lI.5ITC5I HCXO,IT.Hble T01lKH. Ha p HC. 5.12 np HBe,lI.eHbI Heo6xo-
,lJ.HMble .lI-JIH paCqeTa nOJIO)KeHH5I npocpHJIH OOKOBbIX nOBepxHocTeH
3yobeB npOT5I}KeK B np5IMoyrOJIbHOH CHCTeMe KOOp,lI.HHaT OCb H36paH-
nOH CHCTeMbI 5ISJ1HerCfl OCbIO cHMMerpHH Bna,lI.HHbI MeiKAy 3YOb5lM H
npOT5I)KKH TaKoe pacrrOJIO)KeHHe oceff cooTBeTcTByeT nOJIO)KeHHlO npo-
<pHJIH IIIJIHcpoBaJIbHOrO Kpyra npH llIJIHcpoBaHHH 3y6beB. I1CXO,lI.HbIH npo-
<pHJIb - 3BOJIbBeHTHbIM npoqH-IJIb lll.rIHll.eS rOToBoH ,lI.eTaJIH. Bo H36e)Ka-
HHe 3aTeMHeHHH qepTe)Ka Ha HeM He HaHeceHbI pa,[lHYCbI OKPY)f{HOCTeH
Bb1CTynoB H Brra,n.HH. C TOH )Ke u.e.J1blO Ha 1.IepTeJKe He HaHeceHbl OKPYJK-
HOCTH H36HpaeMbIX TOlleK.
npHHHMaeM )].JI5I paCqeTa ,[lHaMeTpbI Tpex T01leK: nepBOH KpafIHeH
TOtIKH Dl = 100,28 MM (cooTBeTcTByeT HapYJKHoMY AHaMeTpy nepBoro
3y6a), BTOpOH TOllKH D 2 = 105,04 MM (cooTBeTcTByeT HapY)KHoMY,lI.Ha-
MeTpy TpHAll.aTb n5lTOrO 3y6a) 11 TpeTbefI KpaHHeH TOqKH D 3 = 109,79 MM
(cooTBeTcTByeT Ha PY)J{HOMY ,lI.HaMeTpy IlleTb)I.eCHT ,lI.eBHTOro 3yoa).
Ha qHCTOBbIX 3y6b5IX nO,ll.'beM MeHbllle, qeM Ha qepHOBbIX, lIT06hI
1I36e)KaTb HeKoToporo HCKa)l(eHH5I npoqH1,,15I H3 HHX, npOTH)KKY HYJI{HO
6bIJIO 6bI Ill.ilucposaTb B ,lI.se YCTaHoBKH C pa3HbIMH nO.A'beMaMH 3a He-
ra XBOCTOBHKa. Ho Y'lacToK npoq>HJ15I, o6pa3yeMbIH 'lHCTOBbIMH 3y6b51-
MH, OqeHb Ma"T{ - paseH 0,06 MM 11, KpoMe Toro, 5IBJIHeTC5I HepaOOqHM
(y co II pH r a e M 0 ti .A eTa JI H - B a JI a - 3,lI. ec b p a,[l H Y C 11 JI H cp a C K a ). no-
3TOMY HCK3)KeHHeM npocpHJ15I Ha 3TOM yqaCTKe MO)KHO npeHeOpetIb H
npOT5I)l{KY MO)KHO IllJIHcpOBaTb B O,llHY YCTaHOBKY.
HaXO)l.HM KOOp.lIJIHaTbI BbI6paHHbIX TOqeK B CHCTeMe XOY ,11J1S1
3Toro HaHeceM TOtIKY i, JIe)KallI.YIO Ha OKPY)KHOCTH pa Hyca R h C Te-
KYlI.\HMH Koop,Z\HHaTaMH XL H Y1:
Xl = Rl sin (6 0 + 6,);
!J l = R 1 cos (6 0 + B I).
3)1.ecb 8 0 - yroJI Mem.AY OCblO 0 Y H pa,lI.HycoM-BeKTopoM HaqaJIbHOH
TOtiKH 3BOJIbSeHTbI 0; yroJI 8 0 (pa,nJ onpe eJI5IIOT IIO cpopMYJIe
( 5.47)
a :rt Sp . .
Uo = - - - - I n V a. l'
Z d
8 1 - nOJI5IpHbIH yrOJI 3BO.TIbBeHTbI B TOqKe i 0; yrOJI e (pa,n) Haxo,n5lT
no cpopMYJIe
B,==tg a l - al=inv ai'
. dB
r,ne a -- yrOJI AaB.neHHH B TOqKe t, COS (J.I= - ;
D,
60+8,=57,29578 ( : - s; _ inv a\ - fnv a, );
6 - 3,141593 9,776 _ 0,014903= 0,044416 paJ{.
0- 20 100
(5.48)
130
,aJIH BCeX TpeX TOtteK
cosa 1 = 93,9693 =0,937069; Ql=204349E)o; iUVU1=O,015934;
100,28 '
cas a'l= 93,9693 = 0,894605; a 2 = 26 S4227°; inv a 2 = O,0362S3;
105,04 t
eos a1= 93,9691 =O,8Sr5900; a 3 =31 14066°; invaa=O,060700;
109,79 t
00 +61 = 57,29578 (0,044416 +0,0 15934)=3,4578°;
00 + 6 2 = 57,29578 (0,044416 + 0,036 253 )=4,621993°;
60+ 6 3 =57,29578 (0,044416 +0,067 00 )= 6,022703°;
X I := Rl sin (eo + 9 1 )-= 50,14 sin 3,4578°= 3,024094 MM;
Yl =R 1 cas (8 0 +e 1 )==50, 14 cos 3,4578°=50,048745 MM;
X 2 =R. 2 sin (9 0 +6 2 )=52,52 sin 4,621993°=4,232114 MM .
Y'J,= R7, cos (8 0 +8 2 }=&2,52 cos 4,621993°=52,349204 MM;
x3=R 3 5in (°0+68)=54,895 sin 6,02270::i°=5,759693 MM;
Ya= Rs cos (6 0 +6 3 )=54,895 cos 6,0227 03 ° =54,591979 MM.
ECJIH 6bI npOTH)KKa 6bIJ1a fIpOlliJIHcpOBaH3 06bltlHbIM cnoco60M, T. e.
6e3 nO,lUf5ITHH 3a,llHerO XBOCTOBHKa, npoqHiJIb Bcex 3y6bes ee 6blJI 6bI
O,LIJfHaKOBbIM If TOqHO COOTBeTCTBOBaJI npocpHJIIO llIJIHueB .lI.eTaJ1H-
3BOJIbBeHTe. TOJIIl..(HHa Bcex 3YObeB, H3MepeHfl aH B O)1.HOM CeqeHHH, 6bl-
Jla 6bI TaK)Ke OAHHaKOBOH.
Y npOTH}I{eK, npOlllJIHcpOS8HHbiX C JIO.llH5ITbIM XBOCTOSHKOM, npo-
<p HJIb OOKOBbIX rrOBepXHOCTeH O.lI.HHaKOB, a -rOJIllI.HHa 3y6beB, H3MepeH-
Ha51 B O,lJ.HOM Ce'leHHH, pa3JIHqHt1.
Ha pHC. 5.13 npeAcTaB.neHbI
3BOJIbSeHTa npoQ>HJIH llIJIHueB ,lJ.e-
TanH - reOMeTpHtleCKOe feCTO Hep-
lliHH Beex pe){(yIlI,HX 3y6beB npo-
THlKKH nOCJIe IIIJ1HcposaHH5I Ii npH
ropH30HTaJIbHOM nO OX{eHHH ce
OCH (KpHBaH 11), a TaKme orH6alO-
ma5I BeplllHH Bcex pe}l{ymHx
3y6beB npOT5I)KKH B npouecce lllJIH"
cpoBaHH51 npH nOAH51TOM 3a.lJ.He'1
XBOCTOBHKe - npocpHJIb Bcex 3y6b-
eB npOT5I)KKH H a6pa3HBHoro KPY-
ra (KpHBa51 Ill). TIocJle Toro KaK
rrpOTH/KKa npOI1l.lIH oBaHa M OCb
ee B03BpaTHJIaCb B ropH30HTa,TIb-
Hoe rrOJIO}f{emle, rrpo4>HJIh nOCJIe.II.- :: : : a npocIJHJlSI WJlHl\es .u.e-
Hero 3yoa 3aHHM aeT nO"TIOmeHHe raJiH H f1PO$HJlb 3y6beB npOTJUKKH
5.
j"
XJ
Xz
1..,
131
KpIIBOH I. T01.IKa l' npMHaJI..J1e)KHT Brra,lJ,HHe 3Toro 3y6a. npH no,nHH-
THH 3a.n.Hero XBOCTOBHKa TOqKa 1 nepBoro 3yoa Ii TOt.[Ka 0 1 , COOT-
BeTCTBYJOlI{aH II.eHTpy OKPY}KHOCTH 3TOrO 3y6a, Ha BepllIHHe KOTOpO-
ra HaXO,lU1TC5I TOQKa I, OCT3HYTC5I Ha MeCTe. TOqKa 3 nOCJJe,nHero
3y6a IIoJlyttaeT Hall60Jlbillee CMemeIlHe, paBHoe C'3' T. e. IIepeXO.lI.HT
B nOJIOlKeItHe 3" TaKoe me CMeIIJ.eHHe IIOJIyqaeT QeHTp OKPY)KHOCTH
BepillHH nOCJIe,nHero 3y6a - TOIIKa 0 3 .
DpH B03BpalIleHHH OCll npOTH)I{KH rrOCJIe lIlJ1HcpOBaHHH B ropH30H-
ravTJbHOe IIOJIOJKeHHe TOqKa 1 nepBoro 3y6a OCTaeTC51 Ha Mecre) a TOq
Ka 1 IIOCJIe)I.HerO 3y6a onycKaeTc5I Ha C 3 B TOqKY l' TO"llKa 3/1 B03Bpa-
IIJ.aeTCH B HCXO,QHoe rrOJIOlKeHHe, T. e. B TOqKY 3. Ha pHC. 5.12 npHBe)I.e-
Ha 3Ta )Ke KpMBaH I, cooTBeTcTBYIO aH ropH30HTaJIbHoMY nOJIO)KeHHIO
OCll npOTH)KKII.
3a IICKJII01.IeHIIeM TOtIKM 3 (CM. pHC. 5.13) Bce TOQKH npocpHJI5I no-
CJIe,L\Hero 3yoa onycKalOTC5I HH)Ke H oopa3YIOT KPHBYlO I, no KoropoI1 H
Jl-OJI)I{eH npocpUJIllpOBaTbC5I aopa3llBHbIH Kpyr. TaK KaK nOCJIe)J.HHH 3y6
IIMeeT IIOJIHbIH npo4JHJIb, TO HMeHHO ero BbICOTa onpe,lI.e.nHeT pa601l11l1
yqaCTOK npO<pHJIH Kpyra. KpUBYIO I, oopa30BaHHYIO onYCTHBIllHMHCH
TOqKaMH npocpHJIH IIOCJIe.n.Hero 3yoa, II CJIe.n.yer ,lI.JI5I YIIpo eHHH 3anpaB-
u
KH H KOHTpOJI5I Kpyra 3aMeHHTb ,lI,yroH OKPYlKHOCTH.
OTKJIOHeHHe .ayrII OKPY)KHOCTH OT KpliBOH IIpOcpHJI5I nOCJIe,QlIero 3Y
6a npOBepHIOT B )J.BYX JI.OIIOJIHIITeJIbHbIX npOMeJKYTOqHbIX TOqKaX, MMe-
IOmHX KOOp,ll.HHaTbI, OTJIHqHbIe OT Tex, no KOTOpbIM ObIJIa rrOCTpoeHa
OKPY)KHOCTb. B CJIY1.Iae nOJIyqeHHH OTKJIOHeHl1fI 6o.nbllie 0,006 l\1M
nO.lI.bICKHBaIOT ,apyrylO OKPY>KHOCTb HJIH npocpH.Hb pa36llBalOT Ha ,lI.Ba
ytJaCTKa II HaXO)J;51T )J;Be 3aMeHHIOIUHe OKPYlKHOCTH.
AJIH onpe,lleJJeHHH CMemeHIIfI KaiK,QoH H3 B3f1TbIX TOqeK rrp e,llB a pH
TeJIbHO onpe,lI.eJI5IeM CMel1I.eHIIe (MM), npHXO,ll5lI.IJ.eeCH Ha Kam,lI,bIM 3y6
6.C== Ay !!L = Ay t ( 5 49 )
1000 ZO 1000 Ot .
rJl.e y - IIO,ll eM 3a.lI.HerO XBOCTOBHK3 (uelITpa 3a,aHeH oaOKM) Ha
1000 MM .n.JIHHbI npOTH)I{KH, MM.
o 3 760
BHarneMc.lIyqaenpHH5IToL\y=O,3MM f n03TOMY AC= to o 76
=0,003 MM.
CMerueHIIe op)J;HHaTbI JIIo6oro 3y6a onpe.ne.HHel\I no cpopMYJIe
C i = f1C (Zi - 1). (5.50)
,lLJI5I pacqera lIO cxeMe, npHBelteHHOH Ha pHC. 5.11, 38 6a30BbIII
rrpHHHT pe}l{ymIIH 3y6 N2 69 C .nl1aMeTpOM D 3 = 109,95 MM; Bee OTCqe-
TbI qHC.na 3y6beB Be.n.eM Tenepb He OT nepBoro 3y6a npOT5I)KKH, a OT
3y6a N2 69.
B COOTBeTCTBHH C 3THM ,QJI5I TOlleK 1, 2 Ii 3 (pHC. 5.12)
C 1 =C 3 =O,003(69 - 1)=0,204 MM;
C 2 =O,003(69-35)=O,102 MM;
C a = 0,003.<69 - 69)= O.
132
HOBbIe 0pJI.HHaTbI TOqeK CJIeJI.YIOllI.He:
JIlo6oti TOtIKH y; === Y i - C i ;
TOQKH I'Y ===Yl - C 1 ==49,844745 MM;
TOIJKH 2' Y;=== Y2 - C 2 == 52,247204 MM;
TOIJI{H 3'Y ==Y3-C3==54,591979 MM.
,lI.JIH yrrpomeHHfI paCqeTOB rrepeHOCHM Ha qaJIO KOOpJI.HHaT B TOq...
KY I' (CM. pRC. 5.13) H nOJIyqaeM HOBYIO cHcTeMY KoopJJ.HHaT.
HaXOJI.HM KOOpJI.HHaTbI TOlleK B 3TOH CHCTeMe:
(5.51 )
6 .., , ",
JIlG Oll TOQKI1 xL==Xi-X 1 ; Yi=YL- Y l;
TOIJKH I' x === 0; Y == 0;
TOtIKI1 2' x;==x 2 -x 1 ==4,32114-3,024094=== 1,20802 MM;
Y;== Y - Y == 52,247204 - 49,844745= 2,402459 MM;
TOtIKH 3 x ==X 3 - Xl == 5,759693 - 3,024094=== 2,735599 MM;
Y == Y - Y == 54,591979 - 49,844745==4,747234 MM.
4epe3 3TH TOQKH npOBOJJ.HM OKPY)KHOCTb, onpeJJ.eJ1HB KOOp,lI.MH3TbJ
ee Il,eHTpa Xo, Yo H pa.n.HYC 'I. 3Ta OKPY)KHOCTb rrpoxo.n.HT lIepe3 Halla-
JIO HOBOH CHCTeMbI KOop.n.HHar l' KOOp.lI.HHaTbI lLeHTpa OKPY*HOCTH 1-1
paAHYc HaxOLLHM no cpopMYJIaM
Yo= x; [(x )2 + (Y, )2 - x [ X )2 + (y;)2] ; (5.52)
2 (Y3 x 2 - Y2x3)
Xo=
, n "
(x 2 )2 + (Y2)2 - 2Y2YO
( 5.53)
,
2x 2
Tl == V x3+Y6.
(5.54 )
DOACTaBHB COOTBeTCTBYIOIl1.He 3HaQeHH5I, nOJIYQI1M Yo ==
=-9 1 841642 MM; xo=22,565604 MM; rl =24,618374 MM.
4T06bI rrpOBepHTb, HaCKo.nbKO TOqHO 3aMeHfleT JI.yra 3TOH OKPY*HO-
CTI1 KPHBYIO I, HY}KHO onpeJJ.eJ1HTb ee OTKJIOHeHHH OT OKPY)KHOCTH B
.lI.BYX TOqKaX npocpHJIH, KOTopbIe He yqRTbIBaJIH npH paCqeTe na p aMeT'"
pOB OKPYMHOCTH. I1CXOJJ.HbIMH TOqKaMH Oy.n.YT TOllKH 4 H 5 3B0J1bBeHTbI..
,LLHaMeTpbI OKPY:>KHOcTeI1, Ha KOTOpbIX paCn0J10)KeHbI TOqKH, cJle.n.yIO....
Ill.He: D 4 = 102,52 MM (3y6 Ng 17) If D 3 = 107,56 MM (3y6 N 53). 11"
KOOp,LI.HHaTbI Ii rrpOMe)KYTOqHbIe rrapaMeTpbI HaXO.lI.HM TaK )Ke, KaK It
.lI.JIH .n.p yrlix TOlleK:
cos a4===O,916595; a4==23,56676°; inva4==0,02488;
5*-338
133
cosa 5 =O,873645; a,=29,11494°; inva 5 ==O,048782;
00 + 04 == 3,970368 0 ; 00 + 05== 5,339852 0 ;
x 4 ==R 4 sin (00+04)=3,549242 MM;
Y4==R4cos(eo+e4) 51,136976 MM;
XS==R5 sin (6 0 +e 5 )=5,004928 MM;
Y5==R 5 cos(e O +e.J==53,546594 MM;
C 4 =O,156; C 5 =O,048; y ===50,980976 MM;
y = 53,498594 MM; x =O,525148 MM; y = 1,136231 MM;
x === 1,980834 MM; Y;=3,653349 MM.
BbIQHCJI5IeM paCCTORHHH 3THX TOqeK O ueHTpa 3aMeHHIOIUeii OK-
PY}KHOCTH ITO <popMYJIaM
Pi= V (x; - XO)2+(y; - YO)2; (5.55)
P4= (0,525148 - 22,565604)2+<1,136231 + 9,841642)2=
== 24,623066 MM;
Ps= V< 1,980834 - 22,565604)2 + (3,653849 + 9,841642)2=
== 24,614244 MM.
OTIpe eJ1HeM HCKOMbIe OTKJ10HeHHR, KOTopbIe ITpe.n.CTaBJIHIOT co6oii
pa3HOCTb Me)l{.lI.Y P4 H Ps H pa,l1.HYCOM 'I 3aMeH5IIOIII.eH OKPY*HOCTH:
L\p4==P4- r l == +0,004692 MM; P5===P5-rl ==-0,00413 MM. ,LLJ1R J11000H
T01JKH
APi= Pi - rt. (5.56)
BeJIH1JHHbI OTKJIOHeHHH y.n.oBJleTBOpHTeJ1bHbIe, n03TOMY 3aMeHY HC-
KOMoro rrpocpHJ17I yroH 3HHO:H OKPY)KHOCTH CQHTaeM npHeMJ1eMofi.
HaXO)(HM KOOp)(HHaThI Il,eHTpa 33MeHHIOIII.eH OKPY)KHOCTII B CHCTeMe
XOy
x = XO+Xl === 25,589698 MM; Y = y + yo===40,003103 MM.
PaC1JeT pa3MepOB no pOJlHKaM npH KOppeKD-HH
npo(jJHJlst no ,lI.yre OKPY*HOCTH
DOKOBOH npocpH.ilb 3YObeB npOTH)KKH KOHTpOJ1HPYIOT
pa3MepOM ITO pOJIHKaM. KOHTponb rrpOH3BO T BYM HJ1H TpeMH po-
JIHKaMH pa3HbIX HaMeTpOB, KOTopbIe KacaIOTCH TOqeK npocpHJ1H Bila..
HHbI MeLK)J.Y ,aBYMH coce}J.HHMH 3y6bHMH Ha pa3HOH BbICOTe. 3TH TOQ-
KH JIeLKaT ITpHMepHO Ha BbICOTe, paBHOH O,ll.HOH TpeTH, rr0J10BHHe H )J.BYM
TpeT5IM BbICOTbI rrpocpHJI . Pa3MepbI ITO pOJIHKaM paCCQHTbIBalOT J1H
134
Y f t r'Xi
I
r x,
.-...)
A
Oc "-....a
x, Xo
....
x
0 X
a) 0)
PHC. 5.14.
CxeMa paeqeTa pa3Mepa no ponHKaM (a) H npooepKH KacaHHH ponHKOM )l.Ha Bna-
)J.HHbl (6)
ITOCJIe.LI.HerO 1JepHOBOrO 3y6a HJIH 3y6a, npHHHTOrO 3a 6a30BbIH. TIpo..
'<pH:JIb Bna,lUiHbI Ha pyrH:X 3y6b5lX KOHTpOJIHPYIOT C ITOMOl1I.blO Tex )Ke
pOJIHKOB. ITpH: 3TOM pa3Mep no pOJ1HKaM H:3MeHHeTC5I Ha Y.LI.BOeHHOe
3HaqeHHe CMellQeHHH JIH aHHoro 3y6a OTHOCHTeJIbHO 6a30Boro.
Ha pHC. 5.14 npe)J.cTaBJIeH npocpHJIb Bna)J.HHbI Me)K Y CMe.lKHbIMIi
lIIJIHIl,aMH: 6a30Boro 3y6a npoTHlliKH. "4To6bI He eJIaTb OITOJIHHTeJIb"
HbIX paCqeTOB, .lI.JI5I KOHTpOJIH npocpH:JIH HCnOJIb3YlOT Koop)J.HHaTbI TOqeK
2, 4 H 5 (c M. P 11 c. 5.12), H a H.LI. e H H bI e p a H b III e.
,U..TIH paclIeTa HY)KHO 3HaTb a6CIl.HCCbI B CHCTeMe KOOp.LI.HHaT XOY:
x4=3,549242 MM; x2=4,232114 MM; xs=4,950267 MM.
Pa3MepbI (MM) pOJIHKOB paCCqHTbIBaIOT ITO i}JopMYJIe
r .==::
pt
rlXI
( 5.57)
,
Xo - Xi
B .n.aJIbHefuneM BblqHCJIeHHble p a)J.HYC H HaMeTp pOJIHKOB 0003Ha..
<1IaeM rp Ii d p , a npHHHMaeMble pa3MepbI CTaH apTHbIX pOJIHKOB - R p
}I D p .
LlJIH TOqeK 4, 2 H 5:
r p4 ==::3,964372 MM; d p4 === 7,92 MM;
r p2 =4,878256 MM; d p2 =9,7565 MM;
rps=5,985648 MM; d ps = 11,9713 MM.
,[{JIJI H3MepeHHH npHHHMaeM CTaH)J.apTHble pOJIMKH C pa3MepaMH,
6JIH3KHMH K HaH.lI.eHHbIM, T. e. Dp4=8 MM; D p2 = 10 MM; D ps = 12 MM.
Pa3Mep (MM) no pOJIHKaM Ha nOCJIe.LI.HeM 1JepHOBOM 3y6e (B paCCMa..
TpHBaeMOM npHMepe - ITpe ITOCJIe.lI.HeM) onpe eJI.HeM no cpopMYJIaM:
5** 135
,l{JI5I qeTHorO QHCJIa 3YObeB npOTH)KKH (no OKPY:iKHOCTH)
M 1 === 2y + 2lz + D pL ;
,QJI5I HeqeTHOrO QHCJ1a 3YObeB
M z = 2 (y +ll) cos
( 5.58)
90° + D
p'
z
( 5.59)
r,ae M l - pa3Mep no pOJIHKaM )(JIH J11000H TOLJKH aHHoro 3yoa; [.1,-
paCCT051HHe no BepTHKa.JIH Me)K.lI.Y ueHTpaMH 3aMeH51101UeH OKPYJKHO-
CTH OC If pOJIHKa Cpo
113 TpeyrOJ1bHHKa OcAC p HaXOAHM
li= /(rl+Rpt)2_(X )2. (5.60)
,I1JI5I TOqeK 4, 2 Ii 5:
1 4 = 12,813222 MM; 1 2 = 14,913598 MM, 1 5 = 16,845148 MM.
HaXO.l1.HM pa3MephI no pOJlHKaM ,!I.JlH TOlleK 4, 2 H 5 Ha npe,!I.nOC"rreA-
HeM qepHOBOM 3yoe NQ 69, rrpHHHToM 3a oa30BhIH:
M 4 = 113,632 MM; M 2 = 119,833 MM; Ms= 125,631 \1M.
flP04JHJ1b Brra)J.HHbI CJ1e.n.yeT npoBepHTb H Ha .lI.pyrHx 3YObHX. Dpo-
BepKa .lJ.OJI)KHa BbITIOJlH51TbC5I B ,il.Byx-qeTblpex pa3Hblx MeCTax no .l1.JlH"
He npOTH:tKKH. TIpH 3TOM He"TJb35I .LI.OnYCKaTb, QTOObI pO"T(HK KaCaJ1CH
BeplllHH 3y6beB. TOQKH KaCaHH51 ero C npocpHJIeM ,!I.OJ1)}{HbI HaXOJI,lITbC51
npW6JIH3HTeJIbHO Ha 0,1-0,3 MM HIf){{e BeplllHH.
,IlJIH npoBepKH npocpHJl5I B6JIH3H T04KH 4 (CM. pHC. 5.12), HaX0,l151-
IneiicH Ha HapYLKHoM .lI.HaMeTpe 3yoa NQ 17, HCn0J1b3yeM 3y6 N2 21, Ha-
pymHbIH .n.HaMeTp KOToporo oo.Hbllle Ha 0,56 MM. ,IJ,Jl5I npOBepKH npocpH"
JIH B6J1H3H TOqKH 2 HCn0J1b3yeM 3y6 NQ 39. Ha 3yoe N2 39 npocpHJIb
6y.n.eT npoBepeH B ,llBYX TOqKaX, npHMepHo cooTBeTcTBylGIllHX TOllKaM
2 H 4 paCqeTHOrO rrpo<pHJ1H. npOcpHJ1b 3y6a N2 55 rrpOBep51eM B Tpex
T01JK3X, npHMepHo COOTBeTCTBYIO HX TOQKaM 2, 4 II 5.
HaH.LI.eM pa3MepbI no pOJ1HKaM Ha YKa3aHHblx 3y6b5IX C Y4eTOM HX
CMellJ.eHHR
Mz===M l + C l , (5.61)
r,ae M z - pa3Mep no pOJIHKaM H3 KOHTpOJIHpyeMoM 3y6e npOT5I)l{KH.
3HaKoM «+» B cpopMYJ1e (5.61) rrOJIb3YIOTC5I B Tex c.nYQa5lX, Kor)J.a
pOJIHK rrepeJJ.BHraeTCH B.LI.OJ1b npOTH}KKH B CTOPOHY nepe,LlHerO XBOCTOBH-
Ka OT 6a30Boro 3yoa; 3HaKOM «-» - Kor)J.a pOJIHK ,LI.BH)f(eTCR Ha qHCTO-
BbIe HJIH: KaJ1H6pYlOIlU1e 3y6b5I.
,L{JI5I 3y6a N2 21 B TOllKe, cooTBeTcTBYJOIlI.eH TOLJKe 4,
M 4 - 21 == M4 + 2C 21 == 113,632 + 2.0,003 (69- 21) 113,920 MM.
,aJI5I 3y6a N2 39
M 4 - 39 = M4 + 2C 39 = 113,632 + 2.0,003 (69- 39)=== 113,812
M 2 - 39 ==M 2 + 2C 39 = 119,833 + 2 .0,003 (69- 39)=== 120,013 MM.
)lJI5I 3y6a NQ 55
M4-55=M4+2Css= 113,632+2.0,003(69- 55)=== 113,716 MM;
136
M2-ss=M2+2CS5=== 119,833+0,084= 119,917 MM;
Ms-ss=Ms+ 2C ss === 125,631 +0,084= 125,715 MM.
HeOOXO.LI.HMO rrpOBepIfTb, He KacaeTCH JIH pOJIHK HaHMeHbIIIero )I.Ha--
MeTpa ,LI.Ha Bna)J.HHbI. TIpoBepollHbIH paCqeT npOH3BO.LI.HT no cpopMYJIe
ML-2Dp>DB.W. (5.62)
,IJJIH 3y6a Ng 21 npH pOJIHKe H3IfMeHblllero .lI.H3MeTpa (D p4 = 8 MM)
113,920-16=97,920 MM, D Blll = 100 MM, CJle.n.OBaTeJlbHO, pOJIEK 6y.n.eT
K a C 3 T bC H .LI. H 3 B I1 3.lI. 11 H bI. Ll J15I If 3 M e p e H If 51 3 T If M P OJI H K 0 M H Y)I{ HOC 0 lllJI Ii -
cpOBaTb l.JaCTb ero nOBepXHOCTH (CM. pHC. 5.14) Ha fJIy6HHY
K == (DB.ill - 2C z ) - (M z - 2D p )
+0,
2
( 5.63)
f,lI.e 6 - rap 3HTHHHbIH 3a30p MeLK,LI.Y pOJIHKOM If .LI.HOM Bna.LI.HHbI, npHHll-
M310T 6==0,1+0,3 MM.
flO.LI.CTaBHB paClIeTHble ,LI.aHHble, nOJIYl.JIfM
K == 99,88 - 2 0,003 (21 - 1) - 97 , 920
+ 0,2=== 1,12 MM.
2
Pa3Mep pOJIHKa OT OOp33YIO eH )J.O JIbICKH K1=8-1,12==6,88
6,9MM.
Ha qepTe)Ke npOTH)KKH YK33bIBalOT nO)J.'heM 3a)J.Hero LLeHTpa Ha ,lI.JIH-
He OT TOqKH nepeXO,Ll,a rrepe.n.Hero H a np aBJIeH H51 BO Bna.n.HHY nepe,Ll, nep-
BbIM 3YOOM .LI.O TOPUa 3a.LI.HerO HanpaBJIeHHH. 3TO paCCTOHHHe
Ly==L - L 1 + (t - b) -la.xB == 1260- 286 + (10 - 3)- 125== 856 MM,
oKpyrJIHeM: Ly== 860 MM.
flO.LI.neM 33)I.HerO XBOCTOBHKa C onpe.LI.eJIHIOT no cpopMYJIe
C= t1y L == 0,3 860 0 26 MM.
1000 y 1000 '
AnnpOKCHMaLtHSI TeOpeTHlJeCKOH KpHBOH
KOppHfHpoBaHHoH 3BOJIbBeHTHoH no ABYM TOIIKaM
PaccMOTpHM crrocoo anrrpOKCIfM3Il.HH TeOpeTHqeCKOH
KpHBOH 3BOJIbBeHTHoH, npOXO)I.fI ei1 l.Jepe3 )J.Be TOl.JKH TaK, liTO B 3THX
TOl.JKaX HJIH HX OKpeCTHOCTH ooe KpHBble HMelOT oO He KaCaTeJIbHble.
npH paclIeTe nO b3yeMcH ypaBHeHHeM TeOpeTHqeCKOH KpHBOH
- K (V x 2 + y2_ RE)==-YT - f (X).
(5.64 )
3 eCb
K - tg .
- ,
tg A
t "' R L - R L -l
g A===
(5.65 )
(5.66)
Zt - Zt-l
137
'I' - yrOJI HaKJIOHa OT npOTH)}{KH K
rOpH30HTaJIH rrpH IlIJIHcpOBaHHH 00-
KOBOrO rrpOcpHJIH 3y6beB; A - rro-
JIOBHHa yrJIa MeJKJl.Y o6pa3YIOIQH-
MH: KOHyca, rrpOXO,lIJ1rnerO no Bep-
IlIHHaM qepHOBbIX 3y6beB rrpOTH}K-
KH; Ri H Rt-l - pa HYCbI COOTBeT-
CTBeHHO i-ro H (i - 1) -ro 3y6ben;
Zt H Zt-1 - annJ1HKaTbI COOTBeT-
CTBeHHO i-ro If (i-I) -ro 3yobeB.
Ha pIlC. 5.15 nOKa3aHbI T04KH
AT H E T TeOpeTHqeCKOA KpHBOA
DpOBeJJ.eM tlepe3 HHX 3BOJIbBeHTY
TaK, qTOObI yrJI1bI HaKJIOHa Kaca-
TeJ1bHbIX 06eHX KpHBbIX COBrra.lI.a-
JIlL [(eHTp OCHOBHOH OKPYlKHOCTH
a II rr P 0 K C HM H P Y 10 Ill. e H .3 B OJ1 b B e HTbI
MO}KeT Jle}KaTb JII1Illb Ha 6HcceK-
TpHcax yrJIOB ArKET' SKT, ATKS,
ETKT, 06pa30BaHHbIX rrepeCeqeHHeM HOpMaJ1eH C KpHBbIMH B TOllKax
AT, E T . 9TO CJIe,LlyeT H3 OCHOBHoro CBOHCTBa 9BOJIbBeHTbI, y KOTOpOH
pa HYCbI OCHOBHOH OKpy:tKHOCTH aJ1)KHbI ObITb rreprreH)(HKYJIHpHbI
HOpMaJIHM ATT H E...S, a paCCTOHHHH OT u.eHTpa J!O 3THX HOpMaJIeH
AOJIR<HbI ObITb paBHbI (OIF=OIB=Ro); TaKHMH CBOHCTBaMH o6JIa-
)],aIOT TOqKM, JIe2Ka He Ha 6HcceKTpncax.
I1HTepec npe CTaBJIHIOT TOJIbKO TOQKH:, JIe:tKaml1e Ha OHcceKTpHce
yrJIa ATKS, rrOTOMY qTO OCHOBHble OKPY)KHOCTH, u.eHTpbI KOTOpbIX JIe-
)KaT Ha OHcceKTpHce yrJIa A T KE T1 HMelOT MaJIble ,QHaMeTpbI (U3-3a
HeOOJIbIIIOrO 3HaqeHHH 3Toro yrJIa), H JIH nOJ1YQeHHH 3B0J1bBeHTbI
npoXOJJ.5ImeH qepe3 TOtIKH AT H E T , MexaHH3MY npaBKH Kpyra HY)l(HO
ObIJIO ObI C,lI.eJ1aTb MHoro BHTKOB. ,llJI5I ynpo eHHH npHcrroco6JIeHIf51
)];JIH rrpaBKH Kpyra HeOOXO,lI.HMO, qTo6bI anrrpOKcHMaU,H5I npOH3Bo,nH-
JIaCb rrepBbIM BHTKOM 3B0J1bBeHTbI. 3TOMY TpeOOBaHHIO MorYT OTBeqaTb
u
JIHlIIb orrpe eJ1eHHbIe 3BOJIbBeHTbI, LLeHTpaMH OCHOBHbIX OKPY)KHOCTeH
KOTOpbIX CJIYJKaT ,lI.HCKpeTHble TOqKH, JIe}KaInHe Ha 6HcceKTpHce OlK
yrJIa ATKS.
HOBbIe rrapaMeTpbI R o, .i, Y H .3BOJIbBeHT, rrpOXO.lI.Hlll.HX Qepe3 TOQ-
KH E T HAT, y.u.OBJIeTBOp5IIOT ypaBHeHHHM BH)(a
y
, 0
PRe. 5. t 5.
nOCTpoeHHe )l.JISI onpe.n.eJleHHSI napa-
MeTpoB 3aMeHs1IOw.eH SBOJlhOeHTbI no
lJ.0YM ee TOI(KaM " Kaca TeJlhHbIM B HHX
X ai = Ro cos 1:{ - R o ( - 't/) sin Tl+ x ;
Y a1= R o sin t'i + R o ( - t'l) cas 1: 1 + y ,
rJI.e i = A HJIH E, a HH eKCOM a OTMeqeHbI KOOpJI.HHaTbI arrrrpoKcHMHPY-
IOInHX 3BOJIbBeHT.
KpoMe YKa3aHHbIX QeTbIpex rrapaMeTpoB OCHOBHOH OKPY2KHOCTH
9BOJIbBeHTbI, ypaBHeHH5I (5.67) cO,lI.ep}KaT Ba HeH3BeCTHbIX 3HaQeHHH
't'A II "t'E rrepeMeHHoH 't', COOTBeTcTBYlOrnHX TOllKaM AT 11 E T . IT03TOMY
,QJIH orrpe eJIeHHH weCTH HeH:3BeCTHbIX Heo6xo HMO HMeTb elUe .ZI.Ba
138
( 5.67)
ypaBHeHHfI, KOTOpble MO)KHO nOJIY-
qHTb H3 YCJIOBH5I, liTO annpOKCHMH-
PYIOIIl.3H 3BOJIbBeHTa KacaeTCH Teope-
THlJeCKOH KpHBOH B TOqKaX AT H E T .
TIpH 3TOM MOR<HO O)KH)].aTb n01.ITH
nOJIHOrO COBna)J.eHH5I 3BOJlbBeHTbI J1
TeopeTH4eCKOH KpHBOH n01.ITH Ha
BceM ee yqaCTKe ATE T (HMeeTC5I B
BH.lI.Y, liTO TeOpeTHlJeCKaH KpHBa51 Ma-
JIO OTJ1HqaeTC51 OT 3BOJIbBeHTbI).
B KaqeCTBe ,l(orrOJIHeHHH K CHCTe-
Me ypaBHeHH5! (5.67) MO}KeT ObITb
HcnO b30BaHO ypaBHeHHe, KOTopoe B
OOIIl.eM BH.l1.e 3anHCbIBaeTCH KaK
+ KRo
tg -r i== tg t i
cas tlR i
( 5.68)
y
I
x
Of
PHe. 5.16.
n oeTpoeHHe .I\JUI onpe,ll.eJleHHSI
napaMeTpoB 3aMeHSlIOw.eH SBOJlb-
BeHTbl npH paenOJlO)KeHHH u.eHT-
pa ee oeHoBHoH OKPY1KHOCTH Ha
OCH or
LLeHTp OKPY}KHOCTH arrrrpOKCHMH-
PYlOllI.efl 3B0J1bBeHTbI Jl.OJI)KeH Haxo-
,AHTbCH Ha OCH CHMMeTpHH npocpHJI51 npOTH)KKH. B 3THX ueJIHX HY:tKHO
CMemaTb UeHTp OCHOBHOH OKPYMHOCTH no OHcceKTpHce 01K (pHC. 5.15
Ii 5.16) )].0 Tex nop, rrOKa OH He nona,lI.eT Ha OCb opAHHaT. AnnpOKCH-
MHpYlOIll.aH 3BOJIbBeHTa rrpH 3TOM MomeT CMeCTHTbC5I TaK, liTO He
rrpOH)J.eT Henocpe)J.CTseHHO Qepe3 T01.IKH AT H E rJ a OKa)KeTCH B OK-
peCTHOCTflX 3THX TOlleK. O)l.HaKO yrJIbI HaKJIOHa KaCaTeJIbHbIX B COOT-
BeTCTBYIOIIl.HX TOllKax OCTaHYTCH O)J.HHaKOBbIMH, TaK KaK lI,eHTp
OCHOBHOH OKPY}KHOCTH 6Y.lI.eT OCTaBaTbCH Ha 6HcceKTpHce, a H3Me-
HHTCH (YBeJIHlIHTCH) JIHIllb pa.lI.HYC OKPY)KHOCTH. TaKoe pellleHHe
5IBJI5IeTCR npH6JIHlKeHHbIM, HO, KaK nOKa3bIBaIOT paCqeTbI, TOLJHOCTb
arrnpoKcHMaU,HH BWCOKa H BnOJIHe YJl.OBJIeTBOp5IeT npaKTH4eCKHM Tpe-
60BaHHHM.
P aCqeT BbIITOJIH5IIOT CJIe.aYIOI.I.I.HM 06pa30M: orrpe.n.eJIfilOT KOOP.LI.HHa-
TbI TOlleK AT (XTA, YTA) H E T (XTE, YTE) TeOpeTHqeCKOH KPHBOif, 3aTeM
HaXO.lI.HT yrJIbI LA H 'IE rro cpopMYJIe (5.68) H onpe.l1.eJl5!IOT napaMeTpbI
R o, y H (3 arrnpoKcHMHPYIOIII.eH 3BOJIbBeHTbI, rrpoxo)J.HIIl.eH B oKpecTHo-
CTH TOqeK AT H E T TaK, liTO yrJIbI HaKJIOHa KaCaTeJIbHbIX o6eHx KPH-
BbIX B 3THX TOqKaX COOTBeTCTBeHHO paBHbI. Ha plfC. 5.15 If 5.16 K -
TOllKa nepecelleHM HopMa eH C TeopeTHlIecKoH KpHBOH B ToqKaX AT
H ETo Ee KOOp.lI.HHaTbI XK H YK HaXOJl.HT B pe3YJIbTaTe COBMeCTHoro pe-
meHHR ypaBHeHHH HopMa eH. TOqKY nepeCeqeHHH 6HcceKTpHCW
01K C OCblO op HHaT HaXO,lI.5IT npH x=x=O H npHHHMalOT 3a lI.eHTp
OCHOBHOH OKPY)KHOCTH annpOKCHMHPYlOmeH 3B0J1bBeHTbI. BeJIHlIHH bI
01K H Ro HaXO)J.f1T H3 TpeyrOJIbHHKOB D 1 KF H D 1 KB. DapaMeTp
onpe e,n5IlOT HCXO)J.51 H3 Toro, IITO annpOKCHMHpYIOIll.aH 3B0J1bSeHTa
.lI.OJI)KHa npOHTH 'Iepe3 O.LI.HY H3 TOlleK TeopeTHlIeCKOH KpHBOH. B 3TOM
CJIyqae JIH onpeJl.eJIeHH MO)KHO BOCnOJIb30BaThC ypaBHeHHHMH
THna (5.67).
139
TIorpellIHOCTH annpOKCHMaUHH H3MepHlOT OT HeKOTOpbIX rrpOMe)KY..
TOlJHhIX T01.IeK A, C, E TeOpeTHqeCKOH KpIfBOH no HOpMaJ1H K KoppHrH-
pOBaHHoH 3BOJI bBeHTe H BbIqHCJIH IOT no cpopMYJIe
( V 2 - -2 V 2 --2
X lT +(Yir-y)2-R o t XlT+(Yir-y)2-Ro
i==: R o _ - arc g
RO Ro
X T + 6 ) .-
-arctg _ , t-A, C, E.
Yi -y
npHMep paCqeTa KOppUfHpOBaHHoro npoQJHJlSI. I1CXO.l1.Hble .lI.aHHbIe
npOTHrHBaeMoro OTBepCTH5I: aA=300; d=70 MM; Ro=30,310875 MM;
Jt Sp .
z==14; m=5 MM; Sp=7,944 M; B o == Z -7 -lnva l .
( 5.69)
TIoCJ1e nO,LI.CTaHOBKH COOTBeTcTBylOllI.HX 3HalJeHHH nOJIY4HM: 80=
== 0,057163 pa,LI. = 3° 16'31 / '
TIapaMeTpbI npOTH}KKH: Sz=0,12 MM; t o = 18 MM; L= 1400 MM;
l == 765 MM (,LI.JIHHa pe)Ky eH lJaCTH). TIp HHHM aeM Ha npocpHJIe nHTb
T01.IeK A, B, C, D, E, orrpe.l1.eJ15IeMbIX COOTBeTCTBeHHO pa)J.HycaMH RA =
=32,5 MM; RB==33,7 MM; Rc=35,02 MM; RD=36,22 MM H RE=
= 37,42 MM, KOTopble cooTBeTcTBYlOT 3YOb5IM NQ 1, 11, 22, 32 If 42.
l'o1.IKH B 11 D CJIY)KaT ,il,J1f1 onpe)J.eJ1eHHH HCKOMbIX napaMeTpoB annpoKOo
CHMHPYIO eH 3BOJIbBeHTbI, TOqKH A, C If E - )J.JIH pac4e Ta norpeIIIHo-
creH. TI03TOMY B Bblpa:tKeHH5IX .lI.J1f1 XK, YK, Y ED, R OBD H B BeJ1HqHHbI,
BXO.LI.5I He B paClJeT, BbI)J.eJIeHbI HH,LI.eKCaMH B H D. BcnOMOraTeJIbHbIH
yrOJI B nJIaHe Ha nepBOM 3y6e B TOlJKe A npHHHT paBHbIM CPlA =0°56'58".
TIpe,llBap HTeJIbHO nO.lI.CqHTbIBa lOT 3HaqeHHH ai .l1.JIH Bcex nHTH TOlleK
Jf3 BbIpalKeHHH cos a7 =: Ro/ Ri, r)J.e BMeCTO Rt nOCJIe,LI.OBaTeJIbHO rrO.lI.CTaB-
JI5IeM R A , RBI Rc, Rn If R F :. TIop5I.LI.OK paC1.IeTa KoppHrHpoBaHHoro npo..
4JHJI5I 3YObeB npOT5I)I(KH npe,LI.CTaBJIeH B Ta6J1. 5.3.
PaClfeT pa3MepOB no pOJIHKaM npH KoppeK"-HH
npocpHJISI no ,lI.yre 3BOJIbBeHTbi
TIpH 3aMeHe TeOpeTHlJeCKOrO rrpocpHJ1H 3yobeB npo..
T5I)KKH )(yroH 3B0J1bBeHTbI, KaK If npH 3aMeHe ero JI.yroH OKPYJKHOCTH,
CHa qaJIa onpe,LI.eJI5IIOT ,LI.HaMeTpbI pac4eTHblx pOJ1 HKOB, a 3aTeM BMeCTO
HIiX nO.lI.OHpaIOT CTaH.lI.apTHbIe H3 Haoopa pOJIHKOB TpHJI.uaTIf Tpex .lI.Ha-
MeTpoB.
PaccToHHHe OT HalJaJ1a Koop)J.HHaT AO npe,LI.TIOJIaraeMblx TOqeK KOH"
TaKTa pac4eTHblx pOJ1HKOB d qo C npocpHJIeM nepBoro 3BOJIbBeHTHoro
3y6a HaXO.l1.HT no cpopMYJIe
1
Rlqo==-Rl+ -(DN-D1)(q-l), (5.70)
4
T,lJ.e q = 1, 2, 3; Dl H D N - .l1.IiaMeTpbI COOTBeTCTBeHHO rrepBoro Ii IIO-
CJ1e,LI.HerO .3YObeB.
140
5.3. nOpHAOK paCtleTa KOppHfHpoBaHHoro npocltHJUI 3yobeo npoTsnKKH
PaCQeTH3H OP Y 3
Oap3MeTp
j(
;3 - - Ao
2
B = 86° 43'29"
;3 - tg' alP
t A = 64 °33'33"
t B = 58°52'59"
t c = 53°34' 09"
t v =49°14'42"
t E =45° 14'46"
i =- A, B, C, D, E
X rt == Ro [.:cs t t - (2 - t L) SIn t l]'
i == A, B, C, D, E
XT A = 2,431869
XTB =3,054607
x T c=3,887818
XT D = 4,7681 07
XTE =5,758106
K==
RA
Ro (ctg CflA cas t A - SIn t A)
K = 0,04285775
CL=k(RE-R L )
C A =0,21086026
C B = 0, 15943092
C c = 0, 1 0285836
C D =0,051429331
CE=O,OOOOOOO
i=A, 8, C, D, E
Y rl == R.o [sin t[ + ( - ti) cas t 1 - Cd
i = A, B, C, D, E
YT A = 32, 198027
YTB = 33,401847
YT C = 34,700665
YT D = 35,853355
YTE =36,974323
kRO
tg TJ = tg t i + , i = A, B, C, D, E
cos t jRj
't' A = 65°30'31"
't B = 59°59' 16"
't c = 54 ° 4 7'41 "
'tD = 50°33'03"
'tE =46°36'45"
IY r B - Y r D + x r Bet g 't B - X r D C tg 't D
XK=
ctg 'tB - ctg 'tD
XK= 18,801694
YK==- -ctg'tD(XK-XrD)+Y-rD
y K =24,305813
- 'tB + 'tD
WBD= -xKtg 2 +'YA
YBD=-2,8162168
141
n pOaO/lJICeHUe Ta6A. 5.3
PaC eTHag opMyna
fiapaMeTp
- cos 0,5 ('CB - 'tD)
ROBD = xKBD Cos 0,5 ('tB + '"CD)
R o = 32,889790
B =:::
Y'rn -- y - Ro sin 'tn
1<0 cos 't D
+ 'tD
B =86°56'19"
- 3't -
eO == - -
2
eo =3°3 f 41 ff
(V 2 --2
III = Ro XiT + (Y 't - y)2 - Ro
Ro
V 2 --2
XiT + (Yir - y)2 - Ro
-- arctg _
Ro
6A =0,0007334
«5 c = 0,0002927
6E = 0,000092
- arctg
Xi'r
+ 6), i == A, C, E
-
Yi -- Y
LkS z
c==
to
c = 0,40
<I>OPMYJIbI )1)151 onpeJ1.eJIeHH5I AHaMeTpOB paCqeTHbIX pOJIHKOB BbIBO-
J(51T CJIeJ1.YIO HM 06pa30M. CHaqaJIa C J1.0CTaTOqHOH CTeneHblO TOlIHO"
CTH paCCtIHTbIBalOT yrJIbI (pHC. 5.17):
V -2
(R qo - b 1 )2 - Ro
R o
a qo =
(5.71)
AaJIee onpeJ1.eJIHIOT d qo
d q - - _
a == tg (eo + a qo ) - (eo + cr qo ) + eo;
2Ro
- - -
tg (eo + a qo ) - (Bo + a qo )== inv (eo + qo)'
OTKYJ1.a
dqo=2 R o[inv(80+aqo)+BoI. (5.72)
113 Ha60pa CTaHAapTHbIX pOJIHKOB BbI6HpalOT Haw60JIee 6JIH3KHe
no l{HaMeTpy K paClIeTHbIM pOJIHKaM. CJIe,llyeT, O.QHaKO, HMeTb B BHJ1.Y,
QTO MHHHMaJIbHbIH J1.HaMeTp CTaH,llapTHoro pOJIHKa, npHrOJ1.Horo ,lI.JIH
H3MepeHI1H 3aMeH5IlOmeH 3BOJIbBeHTbI, d qmln He MOlKeT 6bITb MeHbllle
MHHHMaJ1bHOrO )1.HaMeTpa paCqeTHOrO pO.J1HK8 d q . KacalO erOCH
OmIQ'
3BOJIbBeHTbl B TOQKe ee CXOJ1.a C OCHOBHOH OKPYJKHOCTH (pHC. 5.18):
d q . = 2 J('0 tg a o . (5.73)
OmiD
142
y
PUC. 5.17.
nOeTpOeHHe )l.JUI onpeAe"
JleHHSI yr Jla (JqQ
y
y
A
A'
PHe. 5.18.
nOCTpOeHHe ,lI.JlSI onpe,ll.e"
JleHHSI MHHHMaJIbHOrO ,lI.Ha-
MeTpa paClfeTHoro pOJlHKa
d qO m 1 n
PHe. 5.19.
n OCTpoeHHe )l.JUI onpeAe-
JleHHH paeeTOHHHH OT OCD
npOTH1KKH
IToCJIe BbI60pa CTaH}I.apTHbIX pOJIHKOB d q orrpe1LeJIHlOT yrJIbI (J'q,
COOTBeTCTBYlO He 3THM pOJIHKaM, C nOMO blO ypaBHeHHH
_ - d q
Inv (B o + Oq)=== 2Ro - Bo-
(5.74 )
PaCCT05IHIle OT OCH rrpOT5I)KKH ,lI.O ueHTpa pOJIHKa d q B CeqeHHH
nepBoro 3BOJIbBeHTHoro 3y6a (pIlC. 5.19) HaXOJI.HT no cpopMYJIe
Ro
Tlq= + b 1 . (5.75)
cas (eo + Oq)
To )Ke paCCT05IHHe B CeqeHHH i-ro 3y6a
Tiq=Tlq-Zitg .
3Ha5I T 1q , MO:tKHO paCCqHTaTb cooTBeTcTBYlO He pa3MepbI rro pOJIHKaM.
Pa3Mep M 1q B CeqeHHR nepBoro 3y6a no pOJIRKaM orrpeAeJIHIOT no
cpopMYJIaM:
npH qeTHOM qHCJIe IlIJIHIJ.eB Z (pHC. 5.20)
( 5.76)
M 1q === 2T 1q + d q ;
np H HeqeTHOM Z (p HC. 5.21)
11:
./VI 1q = 2T 1q cos + d q .
2z
TOT )l{e pa3Mep B CeqeHHH i-ro 3y6a HaxOJI.HT no cpopMYJIaM:
PPH qeTHOM Z
npH HeqeTHOM n
(5.77)
Miq=Mlq-2zitg ;
(5.78})
11:
Miq=M 1q - 2z i tg cas -.
2z
(5.79)
143
'
PHC. 5.20.
CxeMa onpeAeneHH9 pa3Mepa no ponH-
RaM B celfeHHH nepBoro 3y6a npH lfeT-
HOM I.[HCne UlJl" eB
A'
PHe. 5.21.
CxeMa onpeAeneHHH pa3Mepa no ponH-
KaM B eelfeHHH nepBoro 3y6a npH He-
l.[eTHOM ItHCJle UlnH. eB
KaK YlKe OTMeqaJIOCb, )1.JIH npOBepKH npoqH1lIH 3y6beB npOTHfKKH
B O)1.HOM CeIJeHHM 3a,1J.aIOTCH pa3MepbI no pOJIHKaM pa3HbIx (06bIIJHO
jpex) .lLHaMeTpOB. ,Qnana30H pa3MepoB H3MepHTeJIbHbIX pO.T1HKOB ]J.OJI-
LKeH 6bITb no B03MOlKHOCTH MaKCHMaJIbHbIM, TaK KaK B 3TOM CJIY4ae
KOHTpOJIHpyeTcH 66JIbllIHH Y4aCTOK npoqH1JIH 3y6beB Ii, CJIeJ1..oBaTeJIbHO,
06eCneQHBaeTCH 60JIee TOQHaH npoBepKa npocpHJI5I.
Tpe6oBaHHSI, npe,ll,'bSlBJ1S1eMble K CTaH,L(apTHbIM
pOJIHKaM
npM H3MepeHHH pOJIHKOM J1.HaMeTpoM d q Tpe6yeMoro
pa3Mepa 3y6a C HOMepOM i He06xo,lJ.HMO npeJK,lJ.e Bcero, 4T06bI T04Ka
KOHTaKTa pOJIHKa C npocpH.rreM 3y6a npHxo)J.HtlTJaCb Ha Y4acToK pea,rlbHO
cy eCTBYIOr.u.ero rrpocpHJI.H. 3TO YCJIOBHe 6Y,lJ.eT BblnOJIHeHO, eCJIH pac-
'CT05IHHe Rl q OT HaqaJIa Koop,U.HHaT ,1J.0 TOQKH KOHTaKTa pOJ1I1Ka ,LI.IiaMeT-
pOM d q C npocpHJIeM i-ro 3y6a 6YlleT MeHbllle, IJeM pa)1.HYc 3y6a. Koop-
,QHHaTbI TOIJeK KOHTaKTa pOJIHKOB ,1J.HaMeTpOM d q C npocpH.nel\1 nepBoro
3BOJIbBeHTHoro 3y6a H HX pa,1J.HYC onpe,lJ.eJI5IIDT no cpopMy aM
(pRC. 5.22).
x1q= R o [cos t q - (2 -'t'q) sin tql;
Yl q = R o [sin Tq + ( -1'q) COS Tq I + b 1 ;
Rlq=VX q+yL. (5.81)
A6cI..LHCCa TOIJKII KaCaHH5I pOJIHKa C npocpHJIeM i-ra 3y6a TaKa.H )Ke,
'KaK H a6CI.LHCCa TOtJKH KaCaHH5I pOJIHKa C npocpHJIeM nepBoro 3y6a, a
op HHaTa YMeHbllIaeTC5I Ha Be JI1l4HHY Zl tg 'l'; CJIe )].oBaTeJIbHo)
Riq= V X q+(Ylq-Zitg )2.
144
( 5.80)
( 5.82)
yt
.l
--....
x
PHC. 5.22.
nOCTpoeHHe AnH onpeneneHHH KOopnH
HaT TOlfeK KOHTaKTa ponHKa AHaMeT-
pOM d q e npo<l>nneM nepBoro 9BOJIb-
BeHTHoro 3y6a
PHe. 5.23.
CxeMa KOHTaKTHpoBaHHH pOJlHKa e npo-
nneM 3y6a HH1Ke ero BepwHHbI
He06xo,lI,HMO, lIT06bI TOQKa KOHTaKTa ObIJIa He Ha BepllIHHe 3yoa, a
Ha HeKOTopOM paCCT05IHHH 81 (pHC. 5.23), T. e. )1.0JILKHO ObITh
R1Q<Ri-cl, (5.83)
r,lJ,e 81=0,1-;-.0,3 MM.
POJIHK, KOHTpOJIHPYIO HH npocpHJIb i-ro 3yoa, TaKLKe He ,lI,OJI)KeH
KaCaTbC5I ,lI,Ha BIIa,lJ,HHbI MeiK,lI,Y 3YObHMH IIpOTH)KKH, ,lJ,PyrHMH CJIOBaMH,
paCCT05IHHe OT HaqaJIa KOOp,lI,I:IHaT,lJ,O )1.Ha BIIa,lJ,HHhI RL 0 ,lJ,OJI)KHO OhITh
MeHblIIe, qeM paCCTOHHHe OT HaqaJIa KOOp.aHH3T .ao KpaHHeit HH}{(HeH
TOQKlf H3Mep5IIOI.I.I.ero pOJIHKa, T. e.
RiO < T 1q -
d q
2
t
( 5.84)
r,lI,e
Tiq=
cas (fio + a q )
CYI.I.I.eCTBYIOT ,lI,Ba BapHaHTa oopa6oTKH IJPOT5I)I(KH. B rrepBOM BapH-
8HTe ,lI,HO KaHaBKH B IIpOI..I.ecCe oopaooTKH OOKOBOH IIOBepxHOCTH 3y6h-
€B He IlIJIHCPYIOT. TorLl.a RL 0 He 3aBMCHT OT HOMepa 3yoa, rr03TOMY rrpo-
BepKY YCJIOBHH (5.84) HY)KHO npOH3BOLl.HTb TOJIbKO ,lI,JIH IIOCJIe,lI,HerO 3Y-
6a. Bo BTOpOM BapHaHTe ,LI.HO KaHaBKH lllJIHcpYIOT O.lI.HoBpeMeHHo C
60KOBOH IIoBepxHocTbIO 3y6beB. Tor,lI,a pa3Mep RL 0 OT 3yoa K 3y6y Me-
H5IeTC5I Ha TY me BeJIH4HHY, qTO H Tt, II03TOMY YCJIOBHe (5.84) MO)l(HO
npOSep5ITb TaKlKe Ha IIOCJIe,lI,HeM 3y6e.
ECJIH YCJIOBHe (5.84) He BbIIJOJIH5IeTCH, pOJIHK MO)KHO HCnOJIb30BaTb,
npetI,Ba pHTeJlbHO COlllJIHcpOBaB Ha ero rrOBepXHOCTH JIbICKY TaK, qTOObI
OH IIOCJ1e 3Toro He KaCaJIC5I )1.Ha Brra,1J.HHbI Me)l(,lI,Y 3y6b5IMH. P aCCTOH-
HHe OT BepXHeH T04KH pOJIHKa ,lI,0 JIbICKH
H =O,5M iQ - Rto- c2'
R o
+ b l .
(5.85)
(5.86 )
145
yt
....
x
PUC. 5.24.
CxeMa KOHTaKTuposaHUH
pOJlHKa e ,lI.HOM Bna,lJ.HHbI
MelK,lI.Y aYObHMH npOTJI]K-
xu
r,ae 82=0,1-;.-0,3 MM - 3aLl.aHHhIH 3a30p Me
JKJI.Y HOM Brra.ll.HHbI H JIbICKOH.
POJIHK C JIbICKOH MO:>KeT OKa3aTbCH He-
rrpHrO)1.HbIM JJ.JI5I H3MepeHHH, eCJIH OKaJKeT-
C5I COIIIJ1HcpOBaHHOH Ta ero qaCTb, KOTopaH
)1.0JI:>KHa KaCaThC5I OOKOBOH rroBepXHOCTH:
3yoa, T. e. OH B .lI.eHCTBHTeJIbHOCTH 6y eT
KOHTaKTHpoBaTb C OOKOBOH rroBepxHocTbID
CBOHMH OCTpbIMH KpoMKaMH. l.JTo6bI 3Toro
He npOH30111JIO, )1.0JI}KHO BbIIIOJIHHTbCH CJIe-
.nYlOInee YCJIOBHe (pHC. 5.24):
H-(1+sin ,\,q) d; >1>3' (587)
r.ll.e 83=0,2+0,5 MM.
ECJIH YCJIOBHe (5.87) He BhlnOJIHHeTCH,
CJIeJI.yeT HCIIOJIb30BaTb pOJIHK 60JIblIIOrO
,lI.H:aMeTp a.
fJIaBa
6.
OnTHMH3a HH napaMeTpOB
KOHCTPYK HH npOTQ)KKH
H pe}KHMa pe3aHHSI
BaJKHeHIlIHMH KOHCTPYKTHBHbIMH: rrapaMeTpaMH npo..
T JKKH 51BJIHIOTC nO)I.'beMbI Ha qepHOBbIX, rrepeXO)1.HbIX H lIHCTOBbIX
3y6bHX. OT BbI60pa 3THX napaMeTpOB 3aBHCHT )1.JIHHa pe}Ky eH lIaCTH:
.II CTOHKOCTb rrpOTH}KKH, a TaK}Ke KaqeCTBO )1.eTaJIeH II TeXHHKO-3KOHO-
MHqeCKHe rrOKa3aTeJIH OrrepaI.I,HH. B TO )Ke BpeM rrO)1.'beMbI Ha qepHO-
BbIX II qHCTOBbIX 3y6b5IX rrpOTH}l{KH 51BJIHIOTC5I rrapaMeTpaMH pe)KHMa
D6pa6oTKH H rrpH orrTHMH3a HH rrpo ecca He MorYT Ha3HaqaTbCH He-
3aBHCHMO OT )1.pyrHx pe)KHMHbIX rrapaMeTpOB, TaKHX, KaK CKOpOCTH pe..
3aHHH qepHOBbIMH H qHCTOBhIMH 3y6hHMH. TI03TOMY paCqeT rrpOTH)KKH:
HeOOXOLl.HMO COBMeII.I.aTb C paCqeTOM pe:>KHMa pe3aHHH. TaKa5I MeTO.ll.H"
Ka 3aJIO:>KeHa B HopMaTHBax rro pelKHMaM pe3aHHH, O)1.HaKO HopMaTHBbI
He MorYT CO)1.epLKaTh .lI.aHHbIX, rr03BOJIHIOII.I.HX Ha3HaqaTh orrTHM aJIhHbIe
-cOlleTaHMH no.n.atl Ii CKopOCTeii pe3aHHH B KOHKpeTHbIX npOH3BO)1.CT-
BeHHbIX YCJIOBHHX.
TIpoTH}l{Ka - HHCTpYMeHT .lI.OCTaTOqHO CJIO}l{HhIH II .lI.OpOrOH, JI.JI5I ee
H3rOTOBJIeHHH Tpe6yeTcH 60JIblliOH paCXOJI. )1.e HUHTHhIX HHCTpYMeH-
TaJIbHbIX CTaJIeH H TBep)1.bIX CrrJIaBOB. TI03TOMY BorrpOChI orrTHMH3aIlJIH:
KOHCTPYKTHBHhIX napaMeTpOB npOTH)KeK H pelKHMa rrpOT5IrHBaHHH HB-
JIHIOTCH aKTyaJIbHhIMH, oco6eHHO rrpH o6pa6oTKe 3arOTOBOK H3 TPYLI.-
Hoo6pa6aTbIBaeMhIX MaTepllaJIOB, npll npHMeHeHHR YHHKaJIbHbIX (no
ra6apHTaM H CJIO:>KHOCTH) rrpOT5I)KeK, rrpH MaCCOBOM xapaKTepe rrpo-
H3BOJI.CTBa. B YKa3aHHbIx CJIyqaHX 3KOHOMHqeCKHH 3cpcpeKT, nOJIyqa..
eMbIH OT 3KcrrepHMeHTaJIbHO-paCqeTHbIX pa60T rro onTHMH3aUHH pe:>KHM-
HbIX rrapaMeTpOB, 6bIBaeT oco6eHHO 3HaqHTeJIbHbIM H BrrOJIHe orrpaB-
.nhIBaeT Ll.OrrOJIHHTeJIbHbIe 3aTpaTbI Ha HX rrpOBe)J.eHHe.
TexHH4eCKHH rrporpecc B MalllHHOCTpoeHHH COrrpOBO)K)J.aeTC5I He-
npepbIBHhIM COBeprneHCTBOBaHHeM KOHCTPYK HOHHbIX H HHCTpYMeHTaJIb-
HhIX MaTepHaJIOB, rrOHBJIeHHeM HOBhIX KOHCTPYKUHH rrpOTH:>KeK H rrpo-
TH)KHbIX CTaHKOB C paClllHpeHHbIMH )1.Harra30HaMH CKopOCTeH rrpOT5IfH-
BaHHH B 3THX YCJIOBHHX pa3pa6oTKa MeTO)J.HKH onTHMH3a HH pe)l{HM-
HhIX napaMeTpOB npH BHYTpeHHeM rrpOT5IrHBaHHH 5IBJIHeTC5I HerrpeMeH-
HhIM YCJIOBHeM nOBbIrneHHH TeXHHKO-3KOHOM HqeCKOH 3cp<peKTHBHOCTH:
TeXHOJIOrHqeCKHX rrpoueCCOB
TIpH onTHMH3a HH pe:>KHMHbIX napaMeTpOB MO:>KHO yqHTbIBaTb TOJIb-
KO TY qaCTb rrpHBeLl.eHHbIX 3aTpaT Ha rrpOBe)].eHHe Onepau.HH npOT5IrHBa-
HHH, KOTOpa5I H3MeH5IeTC5I rrpH H3MeHeHHH YKa3aHHbIX rrapaMeTpOB 9Ta
qaCTb 3aTpaT, OTHeceHHaH K OLl.HOH 3arOTOBKe, MO:>KeT 6bITb HaHLl.eHa Ha
OCHOBe COOTHorneHHH
141
C 1 = (-r p + : )E +
J1
,
(6.1 )
n 3
r.lle Tp - BpeM5I pa6ollero XO,LI.a, MHH; LC'I - BpeMH npOCT051 CTaHKa,
CBjI3aHHoro C 3aMeHoM npOT5IfKKH npH ee 3aTynJleHHa MMH E - npH-
Be.lleHHbIe 3aTpaTbI H a 3KCTIJIyaTaUJ1IO CTaHKa (6e3 YlIeTa 3aTpaT Ha
pe}KYllU'1l1 HHcTPYMeHT) 11 3apa6oTHYlO llJlaTY pa6oqero, KonjMHH; H -
npMBeJI.eHHbIe 3aTpaTbI, 06YCJIOBJleHHbIe 3KCTIJIyaTauHeH npOTH)KKH 33
O.lI.HH rrepHO,LI. ee CTOHKOCTH (OTpe30K BpeMeHH Me:>KJ],Y OTKa3aMM), BKJllO-
qa5I 3aTpaTbI Ha nOBTopHYIO 3aTOQKY, Kon. fl3 - qHCJIO 3arOTOBOK, 06-
pa60TaHHbIx 3a nepHo,LI. CTOHKOCTH.
MeTOJI.llKa paclIeTa rrOKa3aTeJIeH E H H H Heo6xoaHMble QMCJ10BbIe
)laHHble npHBe eHbI B paooTe [8].
BpeM5I pa6ollero xOJI.a Ha npOT5IlKHbIX CTaHKax, HM eIOIII.HX YCTpoii-
CTBO JI.JI5I nepeKJIIOQeHH5I CKOpOCTM pe3aHMH nepe,lI. npOXO)K)1.eHMeM lIH-
CTOBOH qaCTH npOT.H)f{KM,
lo + l + /1.1. K -+- [3. H + 13. x + 1 11.. II
IOOOvo 1000u q
't'==
p
,!J 1
(6.2)
r,lI.e La - ,lI,JIHHa QepHOBOH qaCTH npOT5ImKH, BKJIIQqaH TIepexo,llHbIe
3YOb5J, MM; Vo- CKOpOCTb pe3aHHH TIPH 06pa6oTKe qepHOBbIMH 3y6b-
jIMH, M/MHH; 1- ,1J.JIHHa npOTHrHBaHH5I, M f; 1 Q . H - JI.JIH Ea lIHCTOBOH H
KaJIH6PYJOIIJ,eH qaCTeH npOT5I/KKH, MM; 13.H' la.x, l;I..IT - .lI.JIHH a COOTBeTCT-
BeHHO 3a,lJ,HeH HarrpaBJI5IIOIUeH, 3aL1.Hero XBOCTOBHKa H ,Z1.0fIOJIHHTeJIbHO-
ro nepe6era, MM; VtI - CKOpOCTb pe3aHH.H npM o6pa6oTKe IJHCTOBbIMH
}J KaJ1HopYlOlll.HMM 3y6b5IMH, M/MHH.
4HCJIO 3arOTOBOK, o6paooTaHHblx 3a nepHoJ{ CTOHKOCTM rrpOT5I:>KKH
I 000 T
1
n
3
(6.3)
r)1.e T - CTOHKOCTb (cpe,lI.HHH Hapa60TKa Me)i<:)I.Y OTKa3a MH) npOT51:>KKH,
BblpaiKeHHaH B MeTpax 06pa6oTaHHOH rrOBepXHOCTH.
OOJI.CTaBHB 3aBHCHMOCTM (6.2) H (6.3) B (6.1), rrOJIYlIHM
C1=O,OOlE [ : + : + f-(-ro + i: ) ]. (6.4)
rJ],e L 11 == 1+1"tJ.H+L 3 . H +1 3 . x +1JJ:.rr.
B 3aBHCHMOCTH OT KOHCTPYKllJIH npOT5I:>KKH H CTPyKT"""'YPbI ll.HI{JI3 06-
paooTKH ABa nOCJIeJI.HHX C.TraraeMbIX B 3TOH CYMMe Mc::::>rYT He yqHTbI-
B a TbC5I.
CooTHorneHHe (6.4) Ha3bIBalOT u.eJIeBOH CPYHKll.Hefi.. flpH OITTHMH-
3aI1.HH npOT5IrHBaHH5I HeOOxO,lJ,HMO HaHTH TaKYIO cOBoK nHocTb KOHCT-
PYKTHBHbIX H pelliHMHbIX napaMeTpoB, KOTopaH He npO'"I'HBOpellHJIa 6bI
HM OJI.HOMY H3 HaJIOLKeHHbIX OrpaHHIJeHHH 11 06ecnellllBC3.na MHHHMaJIb-
Hoe 3HaqeHHe l1,eJIeBOH CPYHKUHH.
TIpaBaH QaCTb BbIpallieHHH (6.4) - BeCbMa CJIO)KHa CPYHKUH5I pe-
)KHMHbIX M CBH3aHHbIX C HHMH KOHCTPYKTHBHbIX napaM TpoB rrpOT5IiK-
KH, riapaMeTpoB, xapaKTepH3YIOIll.HX 3arOTOBKY II YCJIOB HH o6paooTKH.
.[{ei1cTBHTeJIbHO, )1.JIHHa llepHoBoH GaCTH 10 3aBHCHT OT :rJpHnycKa no,lJ.
148
npOT51rHBaHHe, cnoco6a ero pacnpeJJ.eJIeHH5I Me)KJJ.Y 4epHOBbIMH, rrepe-
x O,lI. H bI M H Ii 1..I 11 C T 0 B bI M I1 3 Y 6 b 51 M H, no JJ. a Y H Hay e pH 0 B bI X ( So) 11 n e p e -
XO,LI,HbIX (Sn) 3y6b51X 0 TaKI1X KOHCTPYKTHBHbIX na paMeTpOB, KaK war
yep HOBbIX 3y6beB (to), 1..II1CJ10 3y6beB B ceKUHH (zc) H O,lJ,HOB peMeHHO
YlIaCTBYIOI.lJ,HX B pa60Te (Zp), 3HayeHH5I KOTOpbIX 3aBHC5IT OT SO, [ II
M aKC HM aJIbHO JJ.onycTH MOH CHJlbI npOT5IrHBaHH5I (P max) LL.n HHa lIHCTO-
BOH qaCTM ['I.I< 3aBHCHT OT pacnpetI,eJIeHH5I nO,lJ,allH Ha 4HCTOBbIX 3y6b-
HX, HX lIHCJIa, a Ta K)Ke OT CBH3aHHbIX C MaKCHM a.nbHbIM 3Ha4eHHeM IIO-
,l!aQ}1 Sq KOHCTPYKTHBI-IbIX na p3 MeTpOB, TaKHx, Ka K war t'4.' lIHCJIO Ka-
JIH6p YlOlIl,HX 3y6bes H 1'. ,lJ,.
CTOHKOCTb - CJlO/KI-IaH CPYHKLLI1H Bcex pe)KHM HbIX na paMeTpoB VOt
Vq, So, S-q, CB5I3aHHbIX C HHMH KOHCTPYKTMBHbIX IIa pa MeTpOB npOTHlKKR
H reOMeTpHlIecKHX nap8MeTpOB ee 3aTOllK . BeJIHlIHHa H npH npOTHrH-
BaHHH (B OTJIHqHe OT ,lI.pyrHx BH,lJ,OB o6pa60TKH) TaKMe 3aBHCHT OT
OllTHMH3HpyeMbIx napa.MeTpOB, B qaCTHOCTH OT So, S-q, a TaKme CBH-
3aHHbIX C HHM H la, L q II T. ,lJ..
YKa33HHbIe 06CT05rreJIbCTBa BeCbMa 3aTpYJ1.H5IIOT npeJ1.CTaBJIeHHe
UeJIeBOH CPYHKUHH (6.4) B BH,lJ,e aHaJIHTHlIeCI<11 3aJ1.aHHOii CPYHKUHH qe-
Thlpex aprYMeHToB (vo, V q , So, S-q) H nOHCK ee MHHHMYMa H3BeCTHbIMH
MeTO)1.aMH c yqeTOM MI-lOrOQHCJleHHbIX orpaHH4eHHH, paccMoTpeHHblx B
IIpe,lI.bI,lI.YIIJ.HX p a3J1.eJI aX.
BecbM a meCTKHe orpaHHlleHH5I CI3H3aHbI C He06xoJJ.HMOCTbIO nOJIY-
qeHH5I Tpe6yeMblx T01..IBOCTH H napaMeTpa wepoxoBaTocTH o6pa60TaH-
HOH nOBepxHocTH H cyMMapHoH pa3MepHoH CTOHKOCTH npOTH)KKH (.ILO-
nycTHMoro qHCJIa ee rrOBTopHbIX 3aTOlleK) 3TH orpaHHlleHHH npaKTH-
lIeCKH 0,LLH03HallHo onpeJ1.eJI5IIOT napaMeTpbI qHCTOBOH llaCTH rrpOT5L/K-
K Ii - q H CJI 0 1I H C TO B bI X, K a JI H 6 p y IO IIJ. H X (Ii B bI r JI a )K H B a IO III. H x) 3 Y t5 b e B,
3aKOHOMepHOCTb H3MeJ-leHHH HX pa3MepOB, war H T. II. TI03TOMY reo-
MeTpHqeCKHe napaMeTpbI qHCTOBOH qaCTH MO)KHO Ha3HaqaTb HCXO.il.5I 113
Tpe6yeMoro KaqeCTBa o6pa6oTKH Ha OCHOBe peKOMeHJ(aUHH, H3JIO:>KeH-
HbIX B npeJ1.bI,LlYIIJ.HX p83J1.eJIax. 3TO n03BOJIHeT HCKJIIOllHTb H3 qHCJT3
onTHMH3HpyeMbIx rrapa-MeTpOB pelliHMa MaKCHMaJIbHYIO nOjI,allY H3
1..I HCTOBbIX 3y6bHX S-q (If IIOHCK OI1THM aJIbHOrO 3aKOHa nOCTeneHHoro ee
YMeHbllIeHH5I) .
HaJIHqHe B COBpeMeHHWX CTaHKax YCTPOHCTB ,lJ,JIH rrepeKJIIDqeHHH
CKOpOCTH nepe BXO,lJ,OM B 3arOTOBKY lIHCTOB X 3y6beB I103BOJI eT Ha-
3HaqaTb CKOpOCTH pe33 HH5I J1.JIH qepHOBOH H llHCTOBOH qaCTeH: rrpOT5I)K-
KH aBTOHOMHO. O,LLHaKO napaMeTpbI pelKHMa pe3aHH5I J1.JI5I 1..IepHOBOH H
1..IHCTOBOH qaCTeH J1.0JI)I(HbI 6bITb CBH3aHbI YCJIOBHeM paBHOH CTOHKOCTH.
3T 0 Y c.n 0 B He, 060 C HOB a H Hoe p a H ee, rr p eJJ, Y CM a TP 11 B a eT p a 3Jl Hq H bI e
KpHTepHH 3aTyrrJIeHH51 ,LlJI5I llepHOBbIX H qHCTOBbIX 3y6beB B COOTBeTCT-
BHH C HX CPYHKUHOHaJIb HbIM Ha3HaqeHHeM. EC.11H J(JI51 lIHCTOBbIX 3y6heB
KpHTHqeCKOe 3aTynneHHe orrpeJJ.eJIHeTC5I TeXHOJIOrHQeCKHMH orpaHHlle-
HHlIMH, HanpHMep, yXy)llI1eHHeM Ka1..IeCTBa o6pa6oTaHHOH rrosepXHOCTH,
TO J1.JI5I qepHOBWX 3y6beB TaKHM KpHTepHeM HBJI5IeTCH onpe eneHHaH
CTeneHb IIOTepH pemyll1eH crroc06HOCTH, npn KOTOpOH pe3KO B03paCTa-
IOT oceBaH CHJIa, ypOBe Hb BH6p a UHH, HarpeB npOT5I)KKH, 3aTpY,L{HHeTC5I
OT1J,eJIeHHe cTpymKH H T. ,lJ,. npe:>K,lJ,eBpeMeHHaH nOTepH pe)KymeH cno-
C06HOCTH llepHOBhIMH 3y6b5IMH rrpI1BOJ(HT K 60JIee HHTeHCHBHOMY H3Ha-
149
IIIHBaHliIO qHCTOBbIX 3y6beB. TI03TOMY qepHOBbIe 3y6bH, H3HalIIHBaHCb
60JIee HHTeHCHBHO, HO HMeH H 60JIblllHM .lI.OnYCTHMbIH H3HOC, )I.OJIlKHbI
pa60TaTb npH TaKHX napaMeTpaX pelliHMa (So, Vo), KOTOpbIe o6ecne-
tIHBalOT HX CTOHKOCTb, He MeHbIllYIO, qeM Y qHCTOBbIX.
CJIe.n.yeT OTMeTHTb, qTO ,lI.JI5I CYllI.eCTBeHHoro ynpOllI.eHHH paCqeTOB
YCJIOBHe paBHOH CTOHKOCTH B )1.aJIbHeHllIeM BbIpaJKaeTC5I paBeHCTBOM
To= T . O.n.HaKO rrpM npaBHJIbHOM Ha3HaqeHHH npHnYCKa no)]. rrpOTHrH-
BaHHe qepHOBaH qaCTb npOT5L/KKH 6y.n.eT HMeTb HeKOTopbIH 3arrac CTOH-
KOCTH. 3TO 06'bHCHHeTCH TeM, qTO rrpH paCqeTHOM Ha3HaqeHHH rrpHrrYCKa
""tJHCJ10 qepHOBbIX 3y6beB rrpOTH)KKH 6YJI.eT orrpe)1.eJIHTbCH B OCHOBHOM
.lI.OrrYCKOM pa3Mepa OTBepCTHH nepe rrpOTHrHBaHHeM. 3HaqHTeJIbHOe
qHCJIO rrepBbIX qepHOBbIX 3y6beB 6YJI.eT pa60TaTb OTHOCHTeJIbHO pe)1.KO.
Y CJIOBHe paBHOH CTOHKOCTH To (vo, So) = T 1{ (v q ) rr03BOJIHeT rrpe.ll.-
CTaBHTb CTOHKOCTb rrpOTH}KKH T B ll.eJIeBOH: <PYHKIJ.HH (6.4) JII060H H3
YKa3aHHhIx <PYHKIJ.HH, T. e. BbIpa3MTb qepe3 rrapaMeTpbI TOJIbKO qepHO-
BOH HJIH qHCTOBOH qaCTeH rrpoTHlKKH. OJI.HaKO )].JIH pellleHHH 3aJI.aqH on..
THMM3all.HH pe)KHMHbIX rrapaMeTpoB Heo6xo,lI.HMO HaHTH 06e aHaJIHTH-
tIeCKHe 3aBHCHMOCTH: To (vo, So) R T q (v q ) .
AHaJIHTHqeCKHe 3aBHCHMOCTH T (v) 06blqHO HaXO,lJ,5IT rrYTeM Mare..
MaTHqeCKOH o6pa60TKR pe3YJIbTaTOB 3KcrrepHMeHTa, no ,lI.aHHbIM HOp-
M aTHBOB HJIH Ha OCHOBe pe3YJIbTaTOB rrpe.ll.bI)J.y HX HCCJIeJI.OBaHHH TIep-
BbIH crroc06 JI.aeT, KaK rrpaBHJIO, HaH60JIee )1.0CToBepHbIe pe3YJIbTaTbI H
HaH60.lIblllHH 3cpcpeKT npH paCqeTHOH: orrTHMH3al1,HH pe)KHMa, OJI.HaKO
npOBe,lJ,eHHe 3KcrrepHMeHToB CBH3aHO C 3aTpaTaMH BpeMeHH H CpeJI.CTB,
KpoMe 3Toro, npR rrpoTHrHBaHHH OHO 3aTpY)1.HeHo JI.BYMH 06CTOHTeJIb-
CTBaMH: Bo-nepBbIx, rrpOT5I}KKa e e He crrpoeKTHpOBaHa, TaK KaK rro..a.a-
qa So Ha qepHOBbIX 3y6bHX 5IBJIHeTC5I OTITHMH3HpyeMbIM rrapaMeTpOM;
BO- BTOpbIX, HYlliHO rrOJIyqHTb ,lJ,Be 3aBHCHMOCTH: To (vo, So) H T q (Vq) .
nOCJIe,lJ,HHH 3aBHCHMOCTb MO)KeT 6bITb rrOJIyqeHa nYTeM H3rOTOBJIeHHH
3KcrrepHMeHTaJIbHOH rrpOTH)KKH, CO)1.eplKa eH TOJIbKO qHCTOBYIO qaCTb,
Ii rrapTHH 06pa3l1,OB C TOqHO BbIrrO.IIHeHHbIM oTBepcTHeM, 06eCrreqHBa-
IO HM Ha3HaqeHHYlO rro,lJ,aqy Ha nepBoM qHCTOBOM 3y6e. OOJIyqeHHe 3a-
BHCHMOCTH To (vo, So) rrpH YCJIOBH5IX, ,lJ,OCTaTOqHO 6JIH3KHX K rrpOH3BoJI.-
CTBeHHbIM, B03MOlKHO rrpH H3rOTOBJIeHHH C60PHbIX rrpOT5I)KeK co CMeH-
HbIMH 6JlOKaMH 3y6beB. Kor,lJ,a llCnOJIb30BaHHe TaKHX npOT5I)KeK
3aTpy JI.HeHO, rrpHxO,lJ,HTCH OrpaHHqHTbCH 3KcrrepHMeHTaJIbHbIM 01Ipe,LI.e-
JIeHHeM TOJIbKO 3aBHCHMOCTH To(vo) C npHMeHeHHeM JIH60 CTaH,lJ,aplHbIx
npOT5IllieK, JIH60 rrpOTH)KeK, rrapaMeTpbI qepHOBOH qaCTH KOTOpbIX
(So, to H T. ,lJ,.) paCCqHTaHbI rro MeTO)J.HKe, H3JIO)KeHHOH B rrpeJ],bI)J.YIII.HX
pa3JI.eJIaX, H o6eCrreqHBaIOT MHHHMaJIbHYJO JI.JIHHY pe)Ky eH qaCTH rrpo-
TH)KKH. HHiKe 6YJI.eT rrOKa3aHO, qTO orrTHMaJIbHa5I rrO,llaqa Ha qepHO-
BbIX 3y6bHX So*, o6eCrreqHBalO a5I MHHHMYM ll.eJIeBOH CPYHKll.HH (6.4),
06bIqHO 6JIH3Ka K TOMY 3HaqeHHIO rrOJI.aqH So i, rrpH KOTOpOM o6ecne-
qHBaeTC5I MHHHMYM 10.
3TO n03BOJIHeT paCCqHTaTb (c JI.OrrycTHMoH rrorpelliHocTbIO) HHCT-
pYMeHTaJIbHbIe 3aTpaTbI H H CqMTaTb BeJIHqHHY H 3a,L{aHHbIM rrapaMeT-
pOM ue.neBOH ctJYHKI1.HH (6 4) HapHJI.Y C rrapaMeTpoM E. B rrpoTHBHOM
cJIyqae Heo6xoJI.HMO 6bIJIO 6bI HaHTH 3aBHCHMOCTb H (So), qTO eIlLe 60-
JIee 3aTpY)1.HHJIO 6bI <pOpMHpoBaHHe H aHaJIH3 ueJIeBOH CPYHKll.HH.
150
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l3HCHT OT COCT05IHH5I ee qHCTOBOH 1.IaCTH, oco6oe BHHMaHHe c.neJI.yeT YLl.e-
JIHTb rrOJIyqeHHlO 3aBHCHMOCTH T q (V-q) .
f1pH oopa60TKe CTaJIeH 3aBHCHMOCTb T'1 (V'1)' KaK npaBHJIO, He MO-
HOTOHHa5I, OHa HMeeT 3KCTpeMYM npH V'1==20-;-25 M/MHH. CJIeJI.yeT
yqHThIBaTh, qTO T'1 BbIpa)KaeTC5I He B MHHYTax, a B MeT pax o6pa6oTaH-
HOH nOBepXHOCTH. XapaKTepHbIH BHLI. YKa3aHHOH 3aBHCHMOCTH nOKa-
3aH Ha pHC. 6.1 (KpHBa5I 1). Ha 3TOM )Ke pHcYHKe HaHeceH xapaKTep-
HbIM rpacpHK 3aBHCHMOCTH rrapaMeTpa ruepoxoBaTocTH OT CKOpOCTM
pe3aHH51 lIHCTOBOH lIaCTblO paccMaTpHBaeMoH rrpOT5I)KKM (KpHBa51 2).
3Ta 3aBHCHMOCTb TaKlKe HMeeT 3KCTpeMaJIbHbIH: xapaKTep. flpOBeLl.51
npHMYIO Ra==Ra max (r,lle Ramax - MaKCHMaJIbHO J1.onycTHMoe 3HaqeHMe
napaMeTpa rnepoxoBaTocTH), rrOJIyqHM 3arrpeII.I.eHHYIO 3THM OrpaHHIJe-
HHeM OOJIaCTb V3-V5. BTopoe OrpaHHQeHHe - rro MHHHMaJIbHOH CKOpO-
CTH (VI) 06YCJIOBJIeHO Tpe6yeMoH rrpOH3BO,lI.HTeJIbHOCTblO o6pa6oTKH.
OOJIaCTblO, «3anpeIII.eHHofI» 3THM OrpaHMqeHHeM, 6Y,1J.eT Ta, rJI.e V-q<Vl.
TpeTbe OrpaHHQeHHe - no ,llonYCTHMOMY pacxoJJ.Y HHCTpYMeHTa-
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CJTO)KHOCTblO (H TpYLl.OeMKOCTbIO) H3rOTOBJIeHH51 npOT5LlKKH. f1poBeJI.51
np5IMYIO T-q==. T mIn, rrOJIYlIHM TOIJKH V2, V4, V6. B 3TOM CJIyqae J1.0nYCTH-
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VI-V2 M Vs-Va. Ha OCHOBaHHH nacrropTHbIX Ll.aHHhIX CTaHKa OrpaHHlJHM
MaKCHMaJIbHYIO CKOpOCTb npOTHrHsaHHH. ECJIH CTaHOK He rrpe,1J.Ha3Ha-
lIeH JI.JI5I CKOpOCTHoro rrpOT5IfHBaHH5I (orpaHHlIeHHe VCT 1), TO ,1J.OrrYCTH-
MOM 6YJI.eT 06JIaCTb VI-V2. ECJIH me CTaHOK HMeeT lllHpOKHH JI.Hana30H
CKopOCTeH (orpaHHlIeHHe V(,T 2), TO Ll.OnYCTHMa5I 06JIaCTb V'1 6Y.lI.eT Co-
CT05ITb M3 V1-V2 H VS-V6. B 3aBHCHMOCTH OT KOHKpeTHbIX YCJIOBHH
o6pa6oTKH n0J10)KeHHe T01.leK Ha OCM V-q, COOTBeTCTBYIOIIJ,HX paCCM3TpH-
BaeMhIM orpaHHlIeHH5IM, MO)KeT 6bITb H HHbIM, HO 3TO He HMeeT npHH-
II.HnHaJIbHOrO 3HaqeHHH, TaK KaK BcerJI.a MorYT ObITb BbIJI.e.TJeHbI aKTHB-
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OTJIHQaeTC5I OT xapaKTepa 3aBMCMMOCTM T q (V q ), O.l1.H3KO ,llJ151 OIITHMM-
3alI.HH pelKHMH bIX na paMeTpOB npOT5I}KKH .lI.OJI:/KHa 6bITb H3BeCTHa 3a..
BHCHMOCTb To (Vo, So), KOTOpa5I Ha pHC. 6.1 MO)KeT 6bITb rrpe,ll.CTaBJIeHa
ceMeHcTBoM KpHBbIX To (vo), rrocTpoeHHbIx ,l1JIH pa3JIHqHbIX nO,ll.aq. Ha
pHC. 6.1 rrpe,ll.c-raBJIeHO Bcero ,LI,Be TaKHX KpHBbIX - 3 H 4, KOTopbIe pac-
IIO.JIOllieHhI BbI1Jle H HH.lKe KpHBOH 1. XapaKTep H3MeHeHHH CTOHKOCTIf
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pOB So, V o TaK}J{e HeOlI.HoCB5I3Ha. C.JIe.llyeT OTMeTHTb, QTO rpaHHUbI 3TOH
06.JIaCTH <!JOPM ffPYIOTC5I If ,ll.pyrHMH OrpaHHQeHH5IMM, B qaCTHOCTH pac-
cMoTpeHHbIMH J3 npe,ll.bIJ1.yr.u.HX pa3,l1eJIaX OrpaHlJIleHH51MH Ha nO.llaqy So.
OrpaHHQeHI1e no napaMeTpy rnepoxoBaTocTH 3.ll.eCb MeHee 1KeCTKOe H,
KaK rrpaBH.J10, I-le BJIH51eT Ha cpOpMMpoB3HHe rpaHHU 1I.OnycTHMoH 06JIa-
CTli vo-So. 3TO 06'b5ICH5IeTC5I TeM, qTO qepHOBble 3y6bH He CPOpMHPYIOT
OKOHQaTeJIbHhIi1 rrpO H,,1b 06pa6oTaHHOH rrOBepXHOCTH H ,ll.OJIlKHbI o6ec-
neqHBaTb TOJIb1<O OTCYTCTBHe TaKHX Ae<!JeKTOB, KOTopble He MorYT 6bITh
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rueCTBOBaHH5I I1eJIeBOM CPYHKll.HH (6.4) B KOOp,ll.HHaTaX vq-vo-So He-
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Vo-V q . B qacTBOM CJIYQae, rrpH HCrrOJIb30BaHHH CTaHKa C Y3KHM .llHana-
30HOM CKOpOCTeH ()J.o 15 M/MMH), 06"TJaCTb cyl.IJ,eCTBQBaHHH ueJ1eBOM
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pHC 6.2. TIpH fICn0J1b30BaHHH CTaHKa C lllHpOKHM ,lI,Harra10HOM CKOpO
cTeH MHHHMYM ue.neBoH <PYHKll.HH MO)J(eT JIe)KaTb B JII060H 113 QeTbIpex
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T q (v q ) H To (vo, So), KaK npaBHJIO, TaKOB, liTO HCKJIIOqaeT H aXO)I{.lleHHe
MHHHMYMa ll.eJ1eBOH cfJYHKI1.HH B 06JIaCT51X 3 H 4. ,UeHcTBHTeJIbHO, MIf-
HHMYM ueJIeBoi1 YHKl.LHH (6.4) 6Y,ll.eT HaXOJI.HTbC5I B 06JIaCTH 4 TOJ1h-
KO B TOM c.nYQa e , eCJIH xapaKTep 3aBHCHMOCTH CYMMbI ee llSYX nOCJIe.ll-
HIfX C.JIaraeMbI", 0603HaQeHHOH C q , OT T 4, Ta J{OB, KaK rrOKa3aHO Ha
pMC. 6.3, T. e. rJT06aJIbHbIlf MHHHMYM Cr.I COOTBeTcTByeT T q*« T A. CJJe-
152
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HeO,lI.H03HatIHOCTblO <PYHKll.lll1 T q (V q ) - CM. pl1C. 6.1.
BTOpbIM YCJIOBHeM HaXOIK..QeHH5I MHHHMYMa l.I.eJIeBOH: CPYHKl.I.HH BOO.
J1aCTH 4 5lBJl5IeTCH B03MO)KHOCTb no.n..n.ep}KMBaTb .il.OCTaT01.IHO BblCOKRe
3HaqeHMH va (rrpH cooTBeTcTBYIOIll.eM CHH)KeHHH So) npH BblnO.J1HeHHH
paBeHcTBa T 0== T -q. B03MOLKHOCTb BblnOJ1HeHH5I ,LI.BYX YKa3aHHblx YCJIO-
BMH MaJIOBep05lTHa. ECJIH He BbInOJIH5IeTCH nepBoe YCJIOBHe, T. e. rJIO-
6adlbHbIH MHHHMYM C-q JIemHT rrpaBee T A (CM. nYHKTHpHYIO KPHBYIO Ha
pHC. 6.3), TO MHHHMYM UeJIeBOH <PYHKIl.HH nepeMeI.I.J.aeTCH B oo.naCTb 2;
eC.nH He BblnOJ1HHeTCH BTopoe YCJIOBHe - B OOJIaCTb 1.
MHHHMYM 1l.eJIeBOH CPYHKl.I.HH (6.4) MOLKeT HaXO,lI.HTbCH B OOJIaCTH 3
(CM. pRC. 6.2) rrpR O,lI.HOBpeMeHHoM BblrrOJIHeHHH TaK)Ke ,lI.BYX YCJIOBHH:
Bo-nepBblx, HeOOXO,lI.HMO, qTo6hI r.rlo6aJIbHbIH MHHHMYM C q JIeLK:3JI rrpa-
Bee T A (pl1c. 6.3), LITO 06blQHO MMeeT MeCTO BO-BTOpbIX, ,lI.JIH BbIITOJIHe-
HH5I YCJIOBHH paBHOH: CTOMKOCTH (To== T q) HeOOXO..QHMO 3HaqHTeJIbHO
CHH)KaTb Vo, nOCKOJIbKY ,U.eJlaTb 3TO 3a CqeT nO,lI.aqH HepalI.I10HaJIbHO C
n03H1l.HH: MHHHMH3a1l.HH l.I.eJIeBOH <PYHKlJ,HH (6.4). 3TOT CJIyqaH COOTBeT-
cTByeT TOLIKaM K H L Ha pHC. 6.1. BepoflTHoCTb ero TaKLKe MaJ1a, TaK
KaK Ha rrpaKTHKe npH Vo== V q 06bIQHO HMeeTC5I 3anac rro CTOHKOCTH
qepHOBO qaCTH npM swoope nO,lI.aQH SO H3 YCJIOBHH MHHHMH3alI.HH
)I. JI H H hI rr pOT 51 )K K H .
Cepe,lI.HHOa HHTepBaJIa, Ha KOTOpOM Heo6xo,lI.MMO HaHTH 3aSHCH-
MOCTb To (So), CJIe yeT rrpI1H5ITb nO,lI,aqy SOL, npH KOTOpOH ..QJIHHa qep-
HoaoH qaCTH Lo MHHHMaJIbHa. 3TO 3HaqeHHe rro,lI.aqH MOlKHO HaXO,lI.HTb
Ha OCHOBe paCLJeTOB, MeTO,lJ,HKa KOTOpbIX H3JIO)KeHa B npe..QbI..QYIllJIX pa3-
.aeJIax. Pe3YJIhTaTbI 3THX paCqerOB ..QOJI}KHbI ObITb HCrrOJIb30BaHbI H .lI}IH
HaxOlli,lI.eHHH aHa.IIMTH4ecKOH 33BHCHMOCTH La (So), HeOOXO,lI.HMOH ..QJIH
paCLJeTHOii onTMMH3aLlHlf pe)KHMHbIX rrapaMeTpOB.
B npocTeHweM CJIYLJae, Kor a paCLJeTHble 3HaqeHH5I qHCJIa qepHO-
BbIX (zo) H nepeAOAHhIX (Zn) 3yobes, qHC.na 3y6beB B ceKlLHH (zc) H
QHCJIa O,lI,HOBpeMeHHO paooTalO Hx 3y6beB (zp) nOJIYIIalOTCH l.I.eJIbIMM,
paClJeTHOe 3HaLJeHHe lllara qepHOBbIX H nepeXO,lI.HbIX 3yobeB (to) COOT-
BeTcTByeT CTaH,lI.apTHoMY (HJIH He oKpyrJIHeTC5I,lJ,O Hero), a MaKCHMaJIb-
HaH CHJIa (P ma "'\.) OrpaHHqeHa B03MO)KHOCTHMH CTaHKa, 3aBHCUMOCTb
La (So) HaXO..Q5IT H3 OCHOBe CJIe..QYIOIll.MX COOTHOllleHHH:
'0 === (Zo + zn) fa; Zo + ZII === Aozc/(SoKII); Zc == K p:TDzp (a + bS o )/ P rnax ;
( 6.5)
ZI->=[t- 1 + 1; to ===2,6611; h== V4n- 1 KIS o ,
A ( u u
B KOTOpbIX 0 - npHnYCK, cpe3aeMbIH qepHOBOH qaCTbIQ npOT.R)KKM;
KIT. - rrOnpaBOLJHbIH K03cpcp H ll.HeHT, yqHTbIBalO HH YMeHbll1eHHe nO..Qa-
1.IH Ha nepeXO,lJ,HhIX 3y6b5lX; D - ..QHaMeTp rrpOT5IrHBaHHH; K p - norrpa-
BOqHhIH K03cpcpHlI.HeHT, yqHTbIBalOIll.HfI YCJIOBH5I o6pa6oTKH; a + bS o -
9MITHpHLJeCKaH 3aBHCHMOCTb Y,lI.eJIbHOH CMJIW pe3aHHH (npHxo..QHllI.eHcH
Ha I MM pe)f{YIll.eti KpOMKH) OT rrO 3qH; h - r.lIy6HHa cTpYLKe1JHOH Ka-
HaBKH; K - K03cpcpHQHeHT nOMern:aeMOCTM CTPY)KKH.
153
B pe3YJIbTaTe COBMeCTHOrO pemeJ-lHH npHBe eHHbIX BhIIlle ypaBHe-
HHH nOJIYQaeTC5I 3aBHCHMOCTb
1 0 = AoKpnD ( + b ) ( 1+3V K1So ) . (6.6)
KnPmax So
3Ta 3aBHCHMOCTb MMeeT 3KCTpeMaJ1bHbIH: xapaKTep, H H3 Hee MO)KeT
6bITb HaH:,lI.eHO So l, o6eCrretIHBalOIll.ee MHHHMaJIbHYIO ,lI.JIHHY io. O,lJ,HaKO
BBH,lI.Y Toro, qTO npH peaJIbHOM pacqeTe npOT5I)KKH He06xo HMO oKpyr-
JI5ITb BeJIHqHHbI Zo, Zrr, Zp, Zc, fo, nepepacrrpe eJI51Th OCTaTOlJHbIH: npHnycK
Me)K Y qepHOBbIMM, rrepexo HbIMH H QHCTOBbIMH 3y6b5IMH, BBOJJ.HTb or-
u .., u
paHI14eHH5I no CYMMapHoH .pa3MepHoff CTOHKOCTH npOT5I)f{KH, paCqeT-
HaH 3aBHCHMOCTh 10 (So) npe,LLcTaBJI5Ie T co60H: Ta6JIHlJHO 3a.n.aHHYIO
CPYHKUHIO. O,lI.HaKO ee 3KCTpeMaJIhHbIJ1 xapaKTep COXpaH5IeTC5I. PaCqeT-
HYIO 3aBHCHMOCTh 10 (So), 3a aHHYIO 'f a 6JIHQHO, 6Y,lI.eM annpoKcHMHpO-
BaTb ,lJ,OCTaTOlJHO npocToH cpYHKUHeH::
1 - S -b e cSo
a-a 0 -
(6.7)
MHHHMYM 3TOH cpYHKIl.HH OCTHraeTC5I npM So==Soz=b/c.
fl pHBe,lI.eHHbIe BbIIlle co06pa)KeHH5I n03BOJI5IIOT Ha OCHOBe Il.eJIeBOH
cpYHKIJ,HH (6.4) CJIe YlO1.UHM oopa30M CcpOPMYJII1pOBaTb 3a aqy orrTH-
MH3au.HH pe)KHMHbIX napaMeTpoB npfJ rrpOT5IrHBaHHH. B 3a aHHoH 06-
JIaCTH Heo6xo.n.HMO HaHTI1 cOBoKynHocTb pe)KHMHbIX napaMeTpOB (va",
So", v-q*), o6eCneqHBalOmHX MHHHMaJIbHOe 3HaqeHHe cpYHKUHH
as-lJe cSo L 1 ('r CM + 11 IE)
C (Va, So, V lJ )= 0 + --!!. + (6.8)
Vo V q T lJ (vlJ)
npM CJIe,lI.YIO Hx OnOJIHHTeJIbHbIX yCJ10BH5IX:
T II (v 4 )== To ('Va, So);
V q == Vo-
(6.9)
(6.10)
fIepBoe YCJIOBHe - paBHa5I CTOHKOCTb qHCTOBoH H qepHOBOH qaCTeH
npOT5I)KKH. BTopoe YCJIOBHe CnpaBe,lI.J1HBO TOJIbKO npH paCqeTe pe)KHM-
u
HbIX napaMeTpoB CTaHKOB, He HMelOIUHX YCTpOHCTBa JI5I nepeKJIIOQe-
HH5I CKOpOCTH BO BpeMJI pa6olJero XO,Lla.
06.JIaCTb 3a,lI.aHM5I cpYHKU. HH (6.8) B oo eM C.JIYQae 5IB.JI5IeTC5I HeO,lI.-
HOCB5I3HOH; OHa COCTOHT H3 BYX O,LIJIOCB5I3HbIX 3aMKHYTbIX 06JIaCTeH:,
rpaHHUbI KOTOphIX onpe e.JI5IIOTCJI BYM5I 3aMKHYTbIMH HHTepBaJIaMH
onYCTHMbIX CKopOCTeH rrpOT5IrHBaHH5I (CM. pHC. 6.2). 3a aqy 6YlI.eM
peIllaTb JI5I Kalli,lI.OM 3aMKHYToH OOJI8CTH OT,lI.e.JIbHO, a 3aTeM, cpasHH-
Ba5I pe3YJIbTaThI, 6Y,lI.eM rrpHHHMaTb TY cOBoKynHocTb pelliHMHbIX napa-
MeTpoB, KOTOpa5I o6eCneQHBaeT HaHMeHbIllee H3 BYX nOJIyqeHHbIX
3HaqeHHH ueJIeBOH: <PYHKUHH. ,QJI5I nOHCKa OnTHMaJIbHOrO COqeTaHH5I
pe)KHMHbIX napaMeTpoB B Ka)K.n;OM oOJlaCTH 6YJJ.eM peIIIaTb 3aJJ.aqy Ha-
XO)K,lJ.eHH5I YC.JIOBHOrO MHHHMYMa CPYHJ{UHH (6.8) npH OnOJIHHTeJIbHbIX
YCJIOBH5IX no BYM BapHaHTaM: a) yLJHTbISa5I TOJIbKO YC.JIOBHe (6.9);
6) YQHTbIBa5I YCJIOBM5I (6.9) H (6.10). ,QJI5I nepBoH OOJIaCTH (COOTBeT-
]54
CTBYIOlII.eH ,lI.JI5I CKOpOCTH V q HHTepBaJIY VI-V 2 Ha pRC. 6.1) npHMeM an-
np OKC I1MaUHIO CTOHKOCTHbIX 3aBHCHMOCTeH CTeneHHbIMH CPYHKll.H5IMH:
T===
q
B4
vfl.
l[
(6.11 )
Bo
v s
LlJI5I BTOpOH o6JI aCTH (vs Vq V6) CTOMKocTHbIe 3aBHCHMOCTM 6y..
Jl.eM annpoKcHMHpoBaTb npoH3Be eHH5IMH CTeneHHbIX H I10Ka3aTeJIbHbIX
CPYHK HH [6]:
Tq===at.{v qe-ct.{Vq; (6.13)
To==aovgoe-covoSok (6.14)
To==-
( 6.12)'
PaCCMOTpHM perneHHe nOCTaBJIeHHOH 3a,lI.aqll. HaqHeM C perneHH5I
rrpH YCJlOBH5IX (6.9), (6.11) t (6.12). 113 3THX YCJIOBHH CJIeJI.yeT, tITO
1 n Y
- - --
v - ( B I B ) x V x S x
0- 0 q q 0
(6.15)
B 3TOM CJIyqae CPYHKUJ{H (6.8) npHHHMaeT BH}].
y
--b
as o x eCs 0 L 1 J1 E)
c== + 4 + ('(CM + !
.2... .!!.... v l( B q
n
Vq.
(6.16)
(Bol B 4 ) x v q X
Hati,lI.51 BhIpa)KeHRe qaCTHbIX npOH3BO.lI.HbIX ac H C II npH-
as o c1V q
paBH5IB HX HYJIIO, nOJIyqHM ,lI.Ba ypaBHeHHH JI.JI5I onpe eJIeHHH onTH-
MaJIhHbIX 3HaqeHHH So* M V q *. 113 nepBoro HaXO.ll.HM
S*= 3- - y (6.17)
o e ex
CpaBHeHHe BblpalKeHHH So l==::; ble H (6.17) IIoKa3bIBaeT, lITO So z-
-So*=:::::yj (ex) 3TO Ta norrpaBKa, KOTOPYlO CJIelI.yeT yqeCTb rrpH pacqe-
Te napaMeTpOB npOT5IJKKH, B TOM QHCJ1e npH onpe.n;eJIeHHH HHCTpYMeH-
TaJIhHbIX 3aTpaT H. CJIe,lI.yeT OTMeTHTb, QTO TaKOH pe3YJIbTaT paCQeTa
So* nO 1yqaeTCH JIHlllb B Tex CJIYQa5IX, KOr,lI.a MO)KHO HCnOJIb30BaTh BeCb-
Ma rrpOCTbIe annpOKCHMaIJJiH (6.11), (6.12). Ho .rr.aMe B 3TOM CJIyqae
,nJlH onpe,L(eJIeHH5I v q * npllxO,lI.HTC5I pemaTb ypaBHeHHe C JJ.pOOHhIMH no-
Ka3areJIHMH CTerreHH
D n+l A I-n/x_ L
qV q - Vii - 4'
(6.18 )
B KOTOPOM
D===
"I.
q (-C CM + ); A=
y
--b
anS X e CSo
o
(6.10)
1
x (Bol BtJ)X
155
a So onpe.n.eJI5IeTC5I BbIpa)l{eHHeM (6.17).
ECJ1H He Y4IfTbIBaTb BTopoe c.narae1\10e B JI€BOH qaCTH BbIpa}KeHHft
(6.18) BBH)].Y MaJIOCTH nOKa3aTeJIH CTerreHH (i-nix), 10
v* --- [ L4 B4 I - ] n:l (6.20)
q -- I n (T C \f + If E)
ECJIIf CTOHKOCTb npOT5LIKKH 1I3MepHTb He B MeTpax, a B MHHYTax
(T q . M = :: =B)v +t ). TO Ha OCHOBaHHH Bblpall<eHHH (611) H (620)
MO)l{HO HaHTH
" I ( H
T".,, -z:n Tc\t+ T)' (6.21)
Bblpa)KeHHe (6.21) OT JIHQaeTC5I OT TpaJJ.Hll.HOHHoro BbIpa)KeHHH
«3KoHOMHQeCKoM» CTOHKOCTH COMHO)KHTeJIeM l/Lq. 3ro, B qaCTHOCTH,
CBH)J.eTeJIbCTByeT a TOM, liTO «3KOHOMlflleCKaH» CTOHKOCTb npOTH)KKH
3aBHCHT He TOJIbKO OT LCl'vh H, £, n, HO If OT .lI.JIlfHbI npOT5IfHB3HH5I l
)laMe B TOM CJ1YQae, eCJ1H n, BUd L q npH H3MeHeH11H I He H3M eH)"]!DTC5I.
B ypaBHeHHH (6.18) nOKa3aTeJ1b CTeneHH BO BTOpOM cnaraeMOM
1- n / x> 0, T a K K a [{ B B bI P a)K eH 1151 x (6 11), ( 6 .12) 0 () bI II H 0 n < x . no..
CKOJIbKY no YCJIOBMHM 33,lJ,a4H A> 0, YlleT BToporo CJIarae oro AaeT
1
v*> [ 84 J ] n+l (6.22)
II I n (LCM + I1/E)
npaBa51 qaCTb nOCJIe.LlHerO BblpaMeHH5I cooTseTcTByeT OllTHMaJIb-
HOM CKOpOCTlf pe3aHH5I GnCTOBOH lIaCTbIO npoTH)J{KH 6e3 yqeTa YCJIOBI151
paBHoH CTOHKOCTH (6.9). 3HaqeHHe npaBofl lIaCTH MomeT 6bITb nOJIY-
qeHO npH Ml1HHMH3aUJIR lI.eJIeBoii CPYHKlI.l1H (6.8) 6e3 YlIeTa nepBoro
CJIaraeMOro B npaBoH qaCTH. KaK c.TIe,il.yeT H3 Bblpa)KeHlfH (6.22), JJ.JIH
o6eCrreqeHHfl YC OBH5I paBHoH CTOHKOCTH He06xo HMO HeCKO bKO YBe-
JIHlIHTb CKOpOCTb V q (H YMeHblllHTh CTOHKOCTb T q) .lI.JI5I .lI.OCTH)KeHHH
OnTH\1aJIbHOro KOMrrpoMHcc3 Me)K,LI.Y CTOHKOCT5Il\.fH T 1.J H To.
llocJIe HaXO)K)J.eHH5I 5 0 * H V q * 113 ypaBHeHHII (6.17) H (6.18) rro.lI.-
craBHM HX 3HaqeHH5I B ypaBHeHHe (6.15) H Hali,lI.eM Vo*
PaccMoTpHM BapHaHT, B KOTOpOM YQHTb1BalOTC5I 06a AOrrOJIHHTeJIb-
HbIX YC.,lOBH5I- (6.9) H (6.10) CTOHKocTHbIe 3aSHCHMOCTH no-npelK-
HeMY npIfHHMaeM B BH)].e CTerreHHbIX CPYHKUJfH (6.11) H (6.12). 113 OT"
HOllleHHH (6.9) - (6 12) cITIeJJ.yeT, qTO
1 Y
- -
VO (B4/Bo)n-x Son- x (6.23)
HCnOJIb3Y51 COOTHOllleHM51 (6.8), (6.10), (6.11), (6.23), MO)KHO HaH-
TH CPYHKUHIO C (So), MHHHMYM KOTOpOH, OTbICKHBaeMhIH Tpa.lI.HlI,HOHHbI-
MH MeTO,lI.aMH, Ii 6Y.ll.eT COOTBeTCTBOBaTb OrrTHMaJIbHOMY 3HalleHHIO 5 0 *.
nO,lI.CTaBHB 3TO 3HaQeHUe B npaBYlO qaCTb Bblpa}KeHH5I (6.23), HaH:JJ.eM
OnTHMaJIhHYlO CKOpOCTb pe33HIfH Vo*=V q * OJJ.HaKO CPY HK UH5I C(So)
u dC 0
fJOJIYQaeTC5I )I.OCTaTOllHO C.TIO)KHOH, KOpHH ypaBHeHHH dSo = MOMHO
156
HaRTH TOJlbKO qHCJIeHHbIMH MeTO.lI.aMH.
HCnOJIb30BaHHe JJ.pyroro MeTO,l1a OTbICKa-
lid
HHH YCJIOBHOrO MHHHMYMa YHKUHH
(6,8) rrpH YCJIOBM5IX (6.9) H (6.10)-
c nOMOInblO Heorrpe)J.eJIeHHibIX MHO)KHTe-
JIeM J1arpaHLKa - npHBO.ll.HT K TeM )Ke YoH
CJIO)KHOCTHM. OTCYTcTBHe aHaJlHTHqeCKO-
Jj
ro BblpalKeHH5I )J.JI5I 5 0 *, nOllo6Horo, Ha-
npHMep, BbIpa2KeHHIO (6.17), .n.eJIaeT
06a YI10M5IHYThIX MeTO,lJ,a MaJIOnpHroJJ.-
HhIMH .lI.JIH HH:tKeHepHOro aHaJIH3a 3aBM:..
CHMOCTH 3HaqeHHlf So'( If Vo:': OT YCJIO-
BHM npOBe.lI.eHH5I OrrepaIJ,HH. DOCKOJIbKY
06a MeTo a npeAI10JIaraIDT HCnOJIb30Ba-
HHe IIHCJIeHHbIX MeTO.lI.OB perneHH51 ypaB-
HeHHH, TO OHM B .lI.aHHOM CJIyqae HHqeM He JIyqrne rrpHMoro IIHCJIeH-
Horo MeT01I.a OTbICKaHH51 MHHHMYMa CPYHKUHH C (So). ECJIH :tKe Ka-
KHM-JIH60 KOCBeHHbI1\1 MeTOJJ.OM HaHTH xopOlllee HaIIaJIbHOe I1pH6JIH-
)KeHHe SOH, TO npHMOH MeTO,l( rrOHCKa MHHHMYMa <PYHKIJ,HH C (So)
5.IBJ151eTC5I npe)1.TIOQTHTeJlbHbIM. PeQb HAeT 0 KOHKpeTHOH CPYHKUHR, 0
KOTOpOH H3BeCTHO, qTO B paCCMaTpMBaeMOH 06JIaCTH OHa HMeeT O,lI,HH
3KCTpeMYM, II 3TOT 3KCTpeMYM HBJI5IeTC51 MHHHMYMOM.
O.n.HH H3 MeTOJJ.OB HaXO:>K.n.eHH51 HaqaJIbHoro npHOJIHLKeHHH So n CO-
CTOHT B CJIe.n.YIOI.II.eM. C yqeTOM YCJIOBHH (6.9) H (6.10) pa306beM npa-
BYIO qaCTb CPYHKlI,HH (6.8) Ha )1.Ba CJIaraeMblX
aSohecSo
Co ===
Va
ml.l7
So
JO mal
J OH Sot.
PHC. 6.4.
noeTpoeHHe )J.JlA HaXO>K.n.e-
MHS! OnTHMaJlbHOrO peilufMa
npH YCJlOBHSlX (6.9)-(6.12)
(6.24)
C4== + l(1"cM+H/E) . (625)
Vo To (vo, So)
113 YCJlOBl1H (6.9) H (6.10) npl1 I1CI10JIb30BaHlfH 3aBHcHMocTeH
(6.11) H (6.12) BbITeKaeT ypaBHeHHe JIHHHH CB5I3H, Ha KOTOpOH OTbIC-
KHBaeM YCJIOBHbIl1 MHHHMYM <PYHKLtHH (6.8). 3TO ypaBHeHHe rrOJIyqeHO
HaMI1 paHee [(6.23)]. Ha pRC. 6.4 ypaBHeHRIO (6.23) cooTBeTcTByeT
rHnep60JIa 1. Ha 3TOM me pHCYHKe HaHeceHbI JIHHHH paBHoro ypOBH5I
<PYHKUMH (6.24). Bce 3TH JIHHHH IIMelOT MHHHMYM npH 5 0 =5 0 l= blc.
TOQKe K, B KOTOpOH JIHHR5I CBH3H 1 KacaeTCH O,lI.HOH H3 JIHHHH paB-
Horo YPOBH5I Co=const, COOTBeTcTByeT YCJIOBHbIH MHHHMYM YHKUHH
( 6.24) II pH C B 513 51 X ( 6.9) H ( 6.1 0) 3 a.lI. a II a co C TO HT B TOM, q T 06 bI H a II -
TH Ha JIHHHH 1 TOqKY, cooTBeTcTBYIOIII.YIO YCJIOBHOMY MHHHMYMY He
<PYHKUHH (6.24), a CPYHKIJ,HR (6.8). n03TOMY TOqKa K HBJIHeTC5I Ha-
qaJIbHbIM rrpH6JIH)KeHHeM. KOOP.lI.HHaTbI 3TOH TOqKH (So H, Va H)
HaXOJ,5IT H3 YCJIOBH51 paBeHCTBa yrJIOBbIX K03cpcpMll.HeHTOB KacaTe.rIb-
HbIX K .nHHHH CBH3H 1 H JIHHHH paBHoro ypOBH5I. 113 ypaBHeHH5I (6 24)
npH Co=const HaXO.lI.HM
dvo = 3:.- Sob-l e cso (cS o - b).
dS o Co
(6.26)
157
113 ypaBHeHH5I (6.23) onpe,neJI5IeM
duo ( Bq ) y -..!!.- -1
d So = Bo n-x n _ X S -x
( 6.27)
npHpaBH5IB npaBble I.JaCTH ypaBHeHHH (6.26) H (6.27), fIOJIYtIHM
TpaHClI.eH,lI.eHTHOe ypaBHeHHe, H3 KOToporo MO)KHO HaHTH SO H, a 3aTeM
va H H3 ypaBHeHH5I (6.23) He pellla5I TpaHcaeH)I.eHTHOro ypaBHeHH5I
MO)KHO Oll,eHHTb SO H' KaK 6bIJIO orrpeJJ.eJIeHO paHee, n < x, n03ToMY
npaBa5I tIaCTb ypaBHeHH5I (6.27) OTpHuaTeJIbHa, I.JTO BnO.TIHe COOTBeTCT-
ByeT yrJIOBoMY K03cpcpHUHeHTY JI1060H: KaCaTeJIbHOH K rHrrep60JIe 1 Ha
pRC. 6.4. TaK KaK npaBaH qaCTb ypaBHeHHH (6.26) OTpHu,aTeJlbHa, TO
SO H< ble, qTO TaK)Ke HaXO,lI.HTC5I B rrOJIHOM COOTBeTCTBMH C reOMeTpn-
tIeCKOH: HHTepnpeTalI.HeH: ypaBHeHH5I (6.26). ,UeHcTBHTeJIbHO, OTpHua-
TeJIbHbIH: yr JIOBOH: K03cpcpHIJ,HeHT KaCaTeJIbHhIX HMelOT TOJIbKO JIeBbIe
BeTBH KpHBbIX Co=const. npoBe eHHaH Oll,eHKa n03BOJIH.na onpe)(e-
JIHTb, liTO TOtIKa K HaqaJIbHOrO npn6JIH)KeHH5I JIelKHT .TIeBee TOqKH N,
COOTBeTCTBYIO eH no.n.aqe So l=== ble.
Onpe,lI.eJIHM, B KaKOM HarrpaSJIeHHH CJIeJJ.yeT ,lI.BHraTbCH B)J.OJIb JIH-
HHH CB5I3H 1 OT HatIaJIbHOH TOI.JKII K ,lI.JI5I .n.OCTIf)KeHH5I YCJlOBHoro MH-
HHMYMa <PYHKII.RH (6.8). OqeBM.lI.HO, qTO nplI ,LlBH)KeHHH BnpaBo, T. e.
npH YBeJIHqeHHH So H YMeHbIIIeHHH Vo BTopoe CJIaraeMOe ueJIeBOH
<PYHKUMH (6.8), 3aBHCHIll.ee TOJIbKO OT V q = Vo 6Y,lI.eT YBeJIHlIHBaThC5I.
,UBHfKeHHe B JII060M HanpaBJIeHHH, B TOI\1 tIHCJIe BrrpaBo, YBeJIHtIHBaeT
3HaqeHHe nepBoro CJIaraeMOro, TaK KaK TOtIKa K - TOqKa YCJIOBHOrO
MHHHMYMa 31'OrO CJIaraeMoro. O.n.HaKo .n.BH)KeHHe BnpaBo MO)KeT aKa..
3aTbC5I rrpaBHJIbHbIM, eCJIH CTOHKOCTb T (V q ) = To (vo, So) 6YJJ.er npH
3TOM YBeJIHqHBaTbC5I, YMeHbllla5I TeM caMbIM nOCJIe,lI.Hee CJIaraeMoe.
Orrpe.n.eJIJIM, KaK H3MeH5IeTCH CTOMKOCTb rrpOT51)KKH B,lI.OJIh JIHHMH
CB5I3H (6.23). ,I:LJIH 3Toro nOJ].CTaBHM 3aBMCHMOCTb (6.23) B BbIpa)KeHlIe
(6.12) H nOCJIe npeoopa30BaHH5I rrOJIyqHM
.x nY
-
T 0=== T q==Bo {Bq/Bo} x-n So x-n .
(6.28 }
nOCKOJIbKY Bee BeJIH4HHbI B nOKa3aTeJIe CTeneHH npH So B nOCJIe.n.-
HeM BbIpalKeHHH nOJIO)KHTeJIbHbI, a x>n, TO rrpM YBeJIHtIeHlfH SO (H CO-
OTBeTCTBYIOIll.eM JIHHHH 1 YMeHbIlleHHH vo) CTOHKOCTh YBeJIHGHBaeTC5I.
npH 3TOM, KaK npaBHJlO, nOKa3aTeJlb CTerreHM ny > 1.
x-n
TaKHM o6pa30M, rrpH JJ.BM)KeHHH B)J.OJIb JIHHHH CB5I3H OT T04KH K B
CTOPOHY YBeJIH4eHH5I So BeJIHtIHHa To== T-q YBeJIHqHBaeTCH, YMeHbllla5I
nOCJIe,lI,Hee c.naraeMoe B npaBoH qaCTH CPYHKlI.HH (6.8) OJJ.H3KO npH
3TOM YBeJIntIHBaIOTC5I )(Ba nepBblx CJIarael\r1blX. rI03TOMY YCJIOBHhIH
MHHHMYM ueJIeBOH CPYHKUHH (6.8) MO:IKeT Jle1KaTb KaK JIeBee, TaK H
rrpaBee TOtIKH K Ha pIfC. 6.4. Ho npH npOT5IrHBaHHH Y,lI.eJIbHbIH Bec rro-
CJIe)1.HerO CJIaraeMoro B ueJIeBOH: CPYHKUHH (6.8), KaK rrpaBHJIO, HaH-
60JIblllHH. Ilo3ToMY B 60JIblllHHCTBe CJIyqaeB YCJlOBHbIH MHHHMYM Il.e-
,TIeBOH CPYHKUHH (6.8) JIe)KHT Ha JIHHHH CBH3H 1 npaBee TOllKH K. IlpH
3TOM He HCKJIlOqeHbI CJ1yqaH, KOr,lI.a TOqKa YCJIOBHOrO MHHHMYMa JIeIKHT
158
npaBee If TOtIKH N, COOTBeTCTBYIO:r.QeH So==blc. 3TO MOR<eT HMeTb MeC-
TO npH 60JIbIIIeM OTHOIIleHHH qHC.JIHTeJIH rrOC.JIe HerO CJIaraeMOro B npa..
BOM qaCTH l.I.eJIeBOH CPYHKl.I.HH (6.8) K cYMMe lJHC.JIHTe.JIeW )J.BYX rrepBblX
CJIaraeMbIX:
p.= L"L + Lo ('t'CM + : ). (6.29)
B pe3Y JIbTaTe aHaJIH3a II.eJIeBofl <PYHKII.MH (6.8) npH annpOKCHMa-
H5IX (6.11), (6.12) MO}KHO C eJIaTb CJIe YIOrn:He BbIBO,lJ,bI. ECJIH CKO-
pOCTb pe3aHHH Vo MO}KeT Ha3HaQaTbCH He3aBHCHMO OT Vq, TO onTH-
Ma.JIbHaH rrO,lJ,aqa orrpe eJIHeTCH BbIpa1KeHHeM (6.17) H He 3aBHCHT OT
TeXHHKO-3KOHOMHtIeCKHX nOKa3aTeJIeH onepaUHH (I, L q , 'tc r, H, E).
OHa onpe eJI5IeTCH TOJIbKO napaMeTpaMH annpOKCHMHPYIO HX <PYHK-
I1.HH 10 (So), To (va, So) H Bcer a MeHbllle SOl. TeXHHKO-3KOHOMHqeCKHe
nOKa3aTeJIH onpe e.JI5IIOT OnTHMaJIbHble CKOpOCTH pe3aHHH V q * H Vo*
[CM. (6.20) H (6.15)].
IlpH HaJIR4HH LKe )1.0rrOJIHHTeJIbHOM CB5I3H (6.10), T. e. rrpH npoTHrH-
BaHHH C nOCT05lHHOH CKOpOCThlO pe3aHH5I, vo* H 5 0 * 3aBHC5IT OT TeXHH-
KO-3KOHOMHQeCKHX nOKa3aTeJIeM orrepaQHH. TIpH 3TOM So* 06bIQHO
MeHbllle So [, HO B pe KHX CJIYQa5IX MO)KeT H npeBocxo.n.HTb 3TO 3HatIe-
HHe. AnrrpoKcMMHpYIO a5I <PYHKl.I.H5I La (So), BOllle,l1111a5I B ue.JIeBYIO <PYHK..
UHIO (6.8), nOCTpoeHa Ha OCHOBe paCqeTHbIX aHHbIX, YtIHTbIBalOIll.HX
Bce OrpaHHtIeHH5I Ha rro,lI.aqy. O HaKo OHa cnpaBe JIHBa B OrpaHHtIeH-
HOM )J.Hana30He So min-So max (CM. pHC. 6.4).
ECJIH rrpH .n;BH}KeHHH B,lJ,O.JIh JIHHHH CB5I3H 1 6y.n;eT HapyrneHo KaKoe-
JlH60 H3 3THX OrpaHHtIeHHH, CJIe,lI.yeT YTOlJHHTb 3aBHCHMOCTb 10 (So), npo-
Be,1I,51 ,lI.OrrOJIHHTeJIbHble paCqeTbI J].JlHHbI qepHOBOH 1.IaCTH npH no.n.aqax,
cooTBeTcTBYIOIl1.HX TOMY OrpaHHlJeHHIO, I\OTOpOro MbI ,lI.OCTHrJIH, H no..
BTOpHTb onTHMH3aQHOHHbIe paCqeTbI rro rrpHBe.n.eHHoH BbIllie MeTO HKe.
CJIe,lJ,yeT OTMeTHTb, qTO YKa3aHHbIe C.JIYQaH BeCbMa pe.lI.KH, TaK KaK on..
THMaJ1bHaH rro.n.aqa, KaK npaBHJIO, JIe:IKHT )J.OCTaTOlJHO 6JIH3KO K So [. O -
lIaKO, YI.JHTbIBaH rrpe,lI.bI y He pe3Y.JIbTaTbI, Cepe,lJ,HHY HHTepBaJIa onpe-
)J,eJIeHHH <PYHKlI,HH La (So) CJIe,l1yeT C,llBHHYTb HeCKOJIbKO JIeBee rro OTHO"
lIleHHlO K TOMY 3HaQeHHlO rro.n;atIH (So z), npH KOTOpOM .n;JIHHa tIepHOBOH
.qaCTH npOT5I)KKH MHHHMa.JIbHa.
B COOTBeTCTBHH C pHC. 6.1 CJIe,lI.yeT BBeCTH OrpaHHtIeHHH II Ha CKO"
pacTb pe3aHH5I. Ha paccMaTpHBaeMoM HHTepBaJIe 3TH OrpaHHlJeHH5I
VI H V2. BBe.n;eM 3TH OrpaHHlJeHH5I If Ha pHC. 6.4. ECJIH rrpH .n.BH}I{eHHI1
B.n;OJIb .JIHHHH CB5I3H 1 MbI .n;OCTHraeM KaKOrO-JIH60 H3 YKa3aHHbIx or-
paHH4eHHH, TO H3 3Toro C.JIe.n;yeT, qTO CBoero HaHMeHblllero 3HalJeHHH
lI,eJIeBaH CPYHKUH5I (6.8) rrpH CBH3HX (6.9) H (6.10) )].OCTHraeT Ha co-
rOTBeTcTBYIOIll.eH rpaHHue.
HaH.n;eM YCJlOBHbIH MHHHMYM CPYHKll,HH (6.8) npH YC.JIOBH5IX (6.9)
'II (6.1 0) BO BTOpOH 3aMKHYToH 06JIaCTH ee onpe.n;eJIeHH5I, rAe npHH5ITbI
,anrrpoKcHMaUHH (6.13), (6.14). IlpHpaBHHBaH npaBbIe tIaCTH 3THX Bbl-
'pa}KeHHH R Y1.IHTbIBaH YCJIOBHe (6.10), nOJIyqHM ypaBHeHHe JIHHHH
tCB5I3H
lJo-b
tJ
Sa=(ao/a 4 ) K Vo K
1
c -co
q Vo
e K
(6.30)
159
V o
111{
c"
b .)0 So /; So
c c
a) 0) !)
va
So
PHC. 6.5.
noeTpoeHHe )l.JUI HaXOJK)J.eHHSI onTH-
MaJ1bHOrO pe)KHMa npH YCJlOBHSlX (6.9),
(6.10), (6.13), (6.14)
?)
B 3aBHCHMOCTH aT 3HaKOB H COOTHOllleHHH nOKa3aTeJ1eH CTeneHH
ypaBHeHHe (6.30) MO)i{eT onHCbIsaTb KpHBbIe 5 0 == f (vo), I1MelOlll.He
BH,l{ fHnep60JIbI (pnc. 6.5, a), napa60JIbI (pHC. 6.5, 6) HJIH HMeIOlilHe
3KCTpeMaJIbHbIH BH,l{ C TOqKOH MHHHMYMa (pRC. 6.5, B) HJIn MaKCHMYMa
(6.5, 2). B ,l{BYX rrOCJIe,llHHX CJIyqaHX 3KCTpeMYMa JIHHHH CB5I3H ,lJ,OCTM-
by - bo 0 .,
raeT npH Vo= npe,l{eJIHM, KaK H3MeH5IeTC5I CTOMKOCTb B,LI.OJIb
C q - CO
JIHHHH CB513H. COBMecTHoe pellleHHe ypasHeHHH (6.14) H (6.30) ,lI.aeT
b -c v
T 0 == a 4 v 0 yell o.
(6.31 )
CpaBHHSa51 BbIpa)KeHHH (6.31) H (6.13), BH.lI.HM, liTO YCL10BH5I To==
== T q 11 Vo= V q BbIHY)K,il.alOT TaKHM o6pa30M Bb16HpaTb nOllaqy So B
3aBHCHMOCTH OT Vo [cOrJIaCHO ypaBHeHHIO (6.30)], liTO CTOHKOCTb lIep-
HOBOH qaCTH npOT5I)KKH H3MeHHeTC5I B 3aBHCHMOCTH OT CKOpOCTH npo-
T5IrHBaHH5I vo== v q TOqHO TaK )Ke, KaK CTOHKOCTb qHCTOBOH lIaCTH.
M u b q
aKcHMYM CTOHKOCTH HMeeT MeCTO npH V OJf 1) === v Y . lI ;t == C JTa
q
T04Ka (TOQKa A Ha pHC. 6.1 H.rIH TOllKa Ail HJIH M 2 Ha pHC. 6.5, a) CQ-
OTBeTcTByeT MHHHMYMY nOCJIe,lJ.HerO C.rIaraeMoro ueJIeBOH CPYHKI..LHlf
(6.8) H MaKCHMaJIbHoMY qHCJIY 3arOTOBOK, o6pa6oTaHHbix 3a nepHoA
CTOMKOCTH. rrpOTHIKKH. EC\lTIH TOllKa M 1 MaKCHMYMa CToliKOCTH \/1eIKHT
HH)I{e TOllKH K KacaHHH JIHHHH CB5I3H C OAHOll H3 .lIHHHH paSHoro ypos-
HH nepBoro CJIaraeMOro ae.rreBOI1 CPYHKlIJIH (6.8), TO MO)KHO YTBep)K-
.n.aTb, 4TO TOllKa YCJIOBHOrO MHHHMYMa CPYHKll.HH (6.8) JIe)l{HT Me*.lI.Y
HHMH. ,[{eHcTBHTeJIbHO, npH )1.BIIlKeHHH OT TO'-lKH HaqaJIbHOro npH6JlH-
160
:>KeHHH M 1 BBepX MbI npHOJIH)KaeMCH K TOqKe K YCJIOBHOrO MHHHMYM3
nepBOrO CJlaraeMOro ueJIeBOH CPYHKI.IJ1lf (6.8) If YMeHbIlIaeM BTopoe ee
CJIaraeMOe (rrpH 3TOM rrOCJIe,lJ,Hee CJIaraeMOe yseJIHLJHBaeTC5I)
ECJIH :tKe TOqKa M 2 YCJIOBHOrO MHHHMYMa rrOCJIe,lJ,HerO CJIaraeMOro
JIe)KHT BbIllIe TOqKlf K, TO B03MO}l{eH CJIYlJaH:, rrpH KOTOpOM ueJIeco06-
pa3HO ,lI.BH)KeHHe He K TOLJKe K a B npOTHBOnOJIO)KHYIO CTOPOHY. O,lI.Ha-
KG TaKOH CJIyqaH MO}l{eT BCTpeTHTbCH BeCbM a pe,lI.KO, TaK KaK BJlH5IHMe
BToporo CJIaraeMOro Ha 3HaI.JeHHe <PYHKUHH (6.8), KaK rrpaBHJIO, Ha-
MHoro MeHbIlIe BJI HHHH5I rrepBoro H nOCJIe)J.Hero CJIaraeMbIX. D03TOMY B
60JIblllHHCTBe CJIyqaeB CPYHKUH5I (6.8) 6Y,lI.eT y6bIBaTb npH ,LlBH)KeHHH
OT TOLJKH M 2 K TOLJKe K, HecMoTpH Ha YBeJIHIIeHlfe ,lI.syx ee nOC.TIe,lJ,HHX
CJIaraeMbIX, H YCJIOBHbIl1 MHHHMYM CPYHKUHH (6.8) COOTBeTcTByeT He-
KOTOpOH TOqKe, JIe)KaIll.eH Me}l{,lJ,Y TOllKaMH M 2 H K.
PaccMoTpHM cJIyqaif, Kor.n.a 06a nOKa3aTeJIH CTerreHH B ypaBHeHHH
JIHHHH CB513H (6.30) rrOJIO)KHTeJIhHbI (pHC. 6.5, 6) 3JJ.ecb JIHHH5I CB5I3H
HMeeT rrOJIO)KHTeJIbHbIH yr JIOBOH K03cpcpHUHeHT KaCaTeJIbHOH H B 3aBH-
HMOCTH OT COOTHOIlIeHH5I nOKa3aTeJIeH CTerreHH MO}l{eT 6bITb BbIrrYKJIoi1,
BorHYToi1 HJIH HMeTb TOIIKY rreperH6a (rrOCJIe,lJ,HHH CJIYI.JaH Ha pHC.
6.5, 6 He nOKa3aH). T aK me KaK H B rrpe,lI.bI)J.YIl.I,eM CJIYLJ ae, TOlJI<a M
MaKCHMYMa CTOHKOCTH Ha JIHHHH CBH3H MO)KeT pacnOJIaraTbCH KaK
HH)Ke, TaK H BbIllle TOlJKH K YCJIOBHOrO 3KCTpeMYMa rrepBoro CJIara-
eMoro. B nepBOM C.TIYlJae (TOLJKa M 1 H.lIH M 2 ) HarrpaBJIeHHe )J.BH}I{eHHH
OT HaLJaJIbHOH TOqKH Ol1pe)J.e.lIHeTCH 0)J.H03HaI.JHO - B CTOPOHY YBeJIHI.Je-
HHH CKOpOCTH, T. e. K TOLJKe K 1 (HJIH K 2 ). Bo BTOpOM CJIYI.Jae (TOI.JKH
M3 H.JIH M 4 ) COrJIaCHO npe)J.bI,lJ,YIlI,HM paccY}I{)J.eHHHM B 60J1blIlHHCTBe
C.lIYlJaeB Heo6xo,lI.HMO TaK)I{e )J.BlfraTbCH K TOqKe KI (HJIH K 2 )
B cJIYtIa5Ix, KOr,lJ,a rrOKa3aTeJIH CTeneHH B ypaBHeHHH (6.30) HMelOT
pa3JIHI.JHbIe 3HaKH (pHC. 6.5, 8, 2), JIHHH5I CBH3H SO (Vo) HMeeT 3KCTpe-
b - ho
MYM npH V o === t.{ .
C 4 - Co
HarrOMHHM, liTO MaKCHMYM CTOHKOCTlf Ha JIHHHH CB5I3H HMeeT MeCTO
rrpH V or1JI === . OH COOTBeTcTByeT O)J.HOH H3 TOqeK M z Ha pHC. 6.5, 8, 2.
C q
TOLIKH M, MOrYT HMeTb JII060e paCrr0J10)KeHHe OTHOCHTe,,1bHO TOlJeK 3KC-
TpeMYMOB JIHHHH: CO==const H JIHHlfH CBH3H. KaK H B rrpe)J.bI,lI.YllI.HX CJ1Y-
lJa51X, TOQKa YCJIOBHOrO 3KCTpeMYMa CPYHKQHH (6.8) B rrO)J.aBJI5IIOIl.I,eM
60JIbllIHHCTBe CJIYLJaeB JIe}l{HT Melli,lI.Y TOIIKaMH M z H Kz. ,LlJI5I TOlJeK M 1
H M 2 Ha pHC. 6.5, 8, 2 3TO YTBep}l{)J.eHHe CrrpaBe)J.JIHBO BO BCeX C.lIYlJaHX.
OTMeTHl\I, liTO BapHaHTbI, H306pa)KeHHble Ha pHC. 6.5, 8, 2, He OTJIH-
lJalOTC5I OT BapHaHTOB Ha pHC. 6.5, a, 6, Tor)J.a, Kor,lJ,a 3KcTpeMYMa .lIH-
b -b o 0
HH5I CBH3H )J.OCTHraeT rrpH V o === t.{ < , nOCKOJIbKY npaKTHtIeCKOe
C q - Co
3HalJeHHe (vo>O) HMelOT TOJIbKO BepxHHe BeTBH KpHBbIX (6.30), co-
.Llep)KalllHe TOllKH M 2 , M4'
YCJ10BHbIH 3KcTpeMYM CPYHKUHH (6.8) npH YCJ10BH5IX (6.9) H (6.10)
B HeKoTopbIX CJIyqa5lX (HaLJa.lIbHa51 TOqKa M 2 Ha pHC. 6.5, a H HalJaJIb-
HbIe TOqKR M3 H M4 Ha pHC. 6.5, 6) 8, 2) COOTBeTcTByer V q === Vo < Va IIJI ===
= V q DJI, T. e. .lIe)KHT JIeBee TOqKH A Ha pHC. 6.1, I.JTO HBJIHeTC5:l cYIll.eCT-
BeHHbIM OTJIHI.JHeM OnTHMI13al.I.HH npOT5IrHBaHHH 110 cpaBHeHHIO C orrTH-
161
v*
IJ
1'0 H
b g
..co
"'H
MH3alI.HeH ApyrHx BHJl.OB 06pa6oTKH. 3TO
BnReTCR O HOH H3 rrpHqHH Bw60pa an-
npOKCHMHPYIOLUHX CPYHKUHH (6.13),
(6.14), OTIHCbIBaIOIIJ)1X 3KCTpeMaJIbHOe
(rrpH cooTBeTcTBYIO eM no 6ope rrOKa-
3aTeJIeM cTeneHH) H3MeHeHHe CTOHKOCTH
B 3aBHCHIYIOCTH OT CKOpOCTH rrpOT5IrH-
BaHH5I.
P accMoTpHM MeTo,L(HKY HaXO)KJl.eHHH
ycnoBHoro MHHHMYMa ueneBoH CPYHKUHH
(6.8) npH arrnpoKCHMaUH5IX (6.13),
.5 11 (6.14) H HaJIHqHH TOJIbKO O,L(HOH CBH3H
(6.9), T. e. npH o6pa6oTKe Ha CTaHKe,
HMelO eM IIIHpOKHH ,L(Hana30H CKOpO-
cTeI1 H YCTPOHCTBO Jl.nR nepeKJIIOQeHH5I
CKOpOCTH BO BpeMR pa6oqero xo a.
Ha OCHOBe ypaBHeHHH (6.9) H (6.14)
u u
YCJIOBHe paBHOM CTOHKOCTH
1 b o Covo
So= ( ;: )K V oK e-K
JON s;1L
c
"8
PHe. 6.6.
noeTpoeHHe ,lI.JUI HaX01K,lI.eHHSI
OnTHMaJIbHOrO pe1KHMa npH YCJlO-
BHSlX (6.9), (6.13), (6.14)
.3anHllieM
( 6.32)
<PYHKUH5I So (Va), onpe,L(eJIHeMa5I ypasHeHHeM (6.32), HMeeT MaKCH-
MYM npH vo=bo/C o , nOJIO)I{eHHe KOToporo He 3aBHCHT OT T-q. nOBepx-
HOCTb (a He nHHH5I, KaK B npeJl.bIAY1lI.eM cnyqae) CB5I3H Ha IlJIOCKOCTH
So-va H306pa)KaeTC5I ceMeHCTBOM KpHBbIX, rrOCTpoeHHbIX no ypasHe-
HHIO (6.32) rrpH KOHKpeTHbIx 3HaqeHH5IX T"lIe 3TH KpHSbIe nOKa3aHbI Ha
pHC. 6.6.
ITOCKOJIbKY Ka)KJl.OMY 3HaQeHHIO V-q cooTseTcTByeT CBoe 3HaQeHHe T 'll,
TO YKa3aHHoe ceMeHCTBO KpHBbIX MO)KHO paCCMaTpHBaTb KaK JIHHHH
paSHoro ypOBH5I ce,lI.JI006pa3HOH rrosepXHOCTH CB5I3H F (Va, So, V't{).
3aBl1CHMOCTb T 'll (V q ) COfJIaCHO BbIpaJKeHHlO (6.13) HMeeT MaKCHMYM
npH V 'll === bq/C q , TI03TOMY KpaHHH5I neBa5I KpHSa5I Ha pHC 6.6 COOTBeT-
cTByeT vq=bq/C q H Tq=Tqmax. OJl.Ha H3 KpHSbIX, pacnOJIO:>KeHHbIX npa-
Bee, COOTBeTcTByeT TaKOR CTOHKOCTH T'tJ* == T 0*, npH KOTOpOH CPY HK lI. H5I
(6.8) HMeeT YCJIOBHbIH MMHHMYM.
OTbIcKHBaTb 3TO 3HaqeHHe CTOHKOCTH If COOTBeTCTBYI01lI.He eMY 3Ha-
tJeHH5I vo*, So*, V 'll * rrpHxo.rr.HTC5I TaK )Ke, KaK H B rrpejJ.bIJl.Y1lI.HX CJIyqa5IX,
'tIHCJIeHHbIM H MeTO,L(aMH. HaqanbHOe rrpH6JIH)KeHHe K TOQKe onTHMYMa
(vo*, 5 0 *, v q *) 6YJl.eM HaXOjJ.HTb Ha OCHOBe CJIe.rr.YIOIll.HX paccYM,L(eHHH.
Jln5I paccMaTpHBaeMbIx ycnoBHH CCPOPMYJIHPyeM BcnOMOraTeJIbHYlO lI.e-
JIesyIO CPYHKQHIO
C _ + l (-r CM + HIE)
q- ,
V q T q (v q )
( 6.33)
B KOTOpOH <PYHKII.H5I Tl.{(v q ) onpe.rr.eJIeHa ypaBHeHHeM (6.13). Haxo,L(HM
npoH3Bo,lI.HYIO dCq/dv'tJ, rrpHpaBHHBaeM ee HYJIlO H nOCJIe rrpeo6pa30Ba-
HHH nonYQaeM TpaHCu.eH,lJ.eHTHoe ypaBHeHHe
162
eClJV4.V I-blJ ( c V _ b ) == LlJ
4. lJq lJ 1
"'eM + HIE
H3 KOTOpOrO MO)KHO HaHTH V q H. YpaBHeHHe (6.34) crrpaBe,LI.J1HBO np""
V q > b-qjC q , nOCKOJIbKY Bce OCTaJIbHbIe COMHO)KHTeJIH B ero rrpaBoH H JIe-
BOH lIaCT5IX nOJIO)KHTeJIbHbI no CMbICJIY pernaeMoH 3a,LlaQH. 3TO CBHJl.e-
TeJIbCTByeT 0 TO l, qTO M aKcHMYM BcrroMOraTeJIbHOH CPYHKllHH (6 33) co-
oTBeTcTByeT TOqKe V-q H, pacnOJIO)KeHHOH npaBee TOllKH A Ha pHC. 6.1,.
T. e. cooTBeTcTByeT TqH<T-qmax.
Onpe,LleJIHM, B KaKOM HanpaBJIeHHH CJIe,LlyeT H3MeH5ITb CTOHKOCTb
T"lJ. H, 3HalleHHe KOTOpOH npH H3BeCTHOM V q H MO)KHO HaHTH KaK H3 ypaB-
HeHH5I (6.13), TaK H H3 ypaBHeHM5I (6.34):
alJ
(6.3 4 r
1
T lJ.H = L (T: CM + J1 / E) v q . H (C q v q . H - blJ)'
II
(6.35)
J1I06oe H3MeHeHHe T tJ H BbI3bIBaeT B03pacTaHHe ,LlBYX nOCJ1eJl.HHX
CJIaraeMbIX B ueJIeBOH CPYHKlI.HH (6.8), rrOCKOJIbKY T q H cooTBeTcTByeT
MHHHMYMY <PYHKlI.HH (6.33). OJl.HaKO YBeJlHqeHHe T q H rrpHBoLLHT co-
rJIaCHO pHC. 6.6 K TOMY, qTO JIHHHH paBHoro ypOBH5I nOBepxHocTH CB5I.
3H H nOBepXHOCTH C 0, cooTBeTcTBYIO eH nepBOMY CJIaraeMOMY B rrpa-
BOH l.J3CTH CPYHKlLHH (6.8), KaCaIOTC5I npH MeHblIJeM 3H3QeHHH Va, a
CJIe)J.OB3TeJ1bHO, rrpM 60JIblileM 3H3qeHHH Co. YMeHbllIeHHe )Ke T q H rrpH-
RO.LI.HT K K3C3HHIO JIHHHH p3BHoro ypOBH5I npH MeHbilieM 3H3l.JeHHH Co.
CJIe)J.oBaTeJIbHO, ueJIeC006p33HO YMeHb1lI3Tb Tt.{ H, T. e. YBeJIHQHBaTb
VlJ H, eIll.e 60JIbllIe OT)J.3JI5I5ICb OT V q nJi= bt.{/Ct.{. TIpH 3TOM LLOJI)KHO co-
6JIIOJl.a TbC5I YCJIOBHe T q = To. IT03TOMY To AOJILKHO TaK)Ke YMeHbIlI3Tb-
C5I, npHlIeM 3a CqeT YBeJIHlIeHH5I va, TaK K3K K3caHHe Kpl1BbIX Ha
pHC. 6.6 paccM3TpHBaeTC5I B TOlIK3X, rJl.e vo>bo/C o , lITO cooTBeTcTByer
YlIaCTKaM KpHBbIX 3 H 4 H3 pHC. 6.1, paCnOJIOLKeHHbIx npaBee 3KcTpe-
MYMa.
I1ocTerreHHo YMeHbIlI35I T lJH , MO}KHO HaHTH TaKHe TlJ*=T o *, rrpH
KOTOpbIX CPYHKlI.H5I (6.8) HMeeT MHHHMYM.
OrrTHMaJIbHoMY 3HaqeHHlO T 0* MOlKeT COOTBeTCTBOBaTb 6eCKOHetlHo,
60JIblIlOe lIHCJIO COqeTaHHH (va, So), T. e. TOqeK H3 KpHBOH T o *=
= Tq*===const. TOJIbKO O Ha H3 HHX COOTBeTcTByeT YCJIOBHOMY MHHH-
MYMY lI.eJIeBofI CPYHKlI.HH (6.8). 3TO 6YLLeT TOlIKa, B KOTOpOH npH 3a-
3HHOH CTOHKOCTH ee nepBoe CJIaraeMOe HMeeT MHHHMaJIbHO B03MO)l{-
Hoe 3HaqeHHe. H3 pHC. 6.6 T3KHMH TOllKaMH 5IBJI5IIOTC5I TOqKH K3CaHH5I
BepXHHX BeTBeH JIHHHH nOCT05IHHOrO ypOBH5I nOBepXHOCTH CB5I3H II
JIHHHH Co === const. reOMeTpHl.JeCKHM MeCTOM TaKHX TOqeK 5IBJI5IeTC5I
KPHB35I 1, BLLOJIb KOTOpOH yrJIOBbIe K03cpcpHlI.HeHTbI KaC3TeJIbHbIX K
YK333HHbIM KpHBbIM paBHoro ypOBH5I OLLHHaKOBbI.
Yr.noBoH K03cpcpHlLHeHT K3C3TeJIbHbIX K JIeBbIM BeTB5IM KpHBbIX
Co=const orrpeJl.eJI5IeTC5I Bblpa)KeHHeM (6.26), a yrJIOBOH K03cpcpH-
lI.HeHT KaC3TeJIbHbIX K BepxHHM BeTB5IM JIHHHH p3BHoro ypOBH5I nOBepx-
HOCTH CBH3M (6.32) - BbIpaLKeHHeM
dvo
dSo
Kvo
So (bo - Cava)
(6.36)
163'
ITpHpaBH5IB rrpaBble qaCTH BbIpa)KeHHH (6.26) H (6.36), nOJIYQHM
ypaBHeHHe KpHBOH 1 Ha pHC. 6.6
vo== boCS o - (bbo + K) (6.37)
Cocso - Cob
YpaBHeHHe (6.37) - 3TO ypaBHeHHe rHnep60.TlbI C aCHMnTOTaMH
So=bjC, vo=bo/C o . Ha 3THX np5IMbIX JIeMaT 3KcTpeMYMbI paccMaT-
pHBaeMblx JIHHHH paBHofo ypOBH5I. YpaBHeHHe (6.37) n03BOJI5IeT II36e..
LKaTb TpY,lI.OeMKHX BbIqIICJIeHHH npH YTOl.JHeHHH 3HaqeHHH Vo, So, V q no
CJIeAYlOlil.HM npH4HH3M. 00 Hai1AeHHo y H3 yp3BHeHU51 (6 34) 3Haqe-
H H 10 V t. H H a x O.Ll H M T I.{ H. LL a JI e e H a x O,lI. H M K 0 0 p,lJ. H HaT bI SOH, V 0 II H 3 q a JI b.
HOM T04KH K Ha KpHBOM 1. ,LLJI5I 3Toro COBMeCTHO pernaeM ypaBHeHH5I
(6.37) H (6.32) npH Tq=T:.a.
TIo Be.nl1qHHaM T t.{ H= T OH, V tI H, VO H , Son HaXO,lIJIM HaqaJIbHOe 3Haqe-
HHe C H lJ.eJIeBOM <PYHKUHR (6.8). ,lJaJIee YBeJIHQHBaeM Ha OLlHH lllar
3HaqeHHe Vt.{H, T. e. npHHHMaeM Vl.{l=VqH+ Vq. 113 ypaBHeHHH (6.13),
(6 32), (6.37), (6.8) HaXO,lI.HM HOBbIe 3H8 qeHH5I T 41, Vo 1, SOL, C 1. ECJIH
C 1 < C Ih TO YBeJIHqHBael'vl VI.{ eme Ha OLlHH war, HaXO.ll.HM T t.{2, V02, S 02,
C 2 , cpaBHHBaeM C 2 H C 1 II rrOBTOp5IeM 3TY np0lI.e,L(YPY ,L(O OCTHlKeHH5I
MHHHMYMa C. YpaBHeHHe (6.37), YCTaHaBJIHBa1OI.I.Lee CB5I3b MeMJI.Y Vo
11 So, cooTBeTcTBYIOII.LHMH YCJIOBHOMY MHHHMYMY ueJIeBOH CPYHKlI.HH
(6.8), n03BOJI5IeT HaHTH VOL H SOL' HCnOJIb3y5I TOJIbKO ypaBHeHH5I (6.37)
H (6 32), a He HCn0J1b3Y5I ypaBHeHMe (6.32) Kalli,llblH pa3 COBMeCTHO C
ypaBHeHHeM (6 8) .LlJI5I rrOHCKa YCJIOBHOrO MHHHMYMa 3TOH CPYHKI..I.HH,
QTO OOJIee CJIOMHO.
TaKHI'vI o6pa30M, .lI.OKa3aHO (CM. pHC. 6.6), qTO npH annpoKcHMa-
!.LH5IX (6.13), (6.14) yc.rroBHbIH MHHHMYM ueJIeBOH <PYHKUHH (6,8) rrpII
HaJIHqI-H1 CB5I3R (6.9) If MeeT MeCTO npl1 So*<Sor==::::.blc; vo*>vo DJ1 =
=bo/co; V 4 k >V q nJI=b q /Ct.{, QTO cooTBeTcTByeT YCJIOBH5IM cymecTBoBa-
HHll YCJIOBHOfO MHHHMYMa lI.eJIeBOH CPYHKlI.HH, onpe,L(eJIeHHbIM npH an-
npoKCHMaUH5IX (6.11) H (6.12).
flpOBe,lI.eHHbIH aHaJIH3 n03BOJI5IeT C,LI.eJIaTb CJIe,lI.ylOllI.l1e 06ll1.He BbI-
BOAW. ECJIH B npo ecce npOT5IfHBaHH5I rrpOHCXO.LlHT nepeKJI qeHHe
CKOpOCTH pe3aHHH, TO onTHM aJIbHOe 3Ha qeHHe nO,LI.a qH Ha qepHOBbIX
3y6b5IX MeHbll1e TOfO 3HaqeHH5I no,nallH SOL, npH KOTOpOM ,lI.vlHHa qep-
HOBOH qaCTH npOT5I)KKH MHHHMaJIbHa.
ECJIH Me nepeKJIIOqeHHe CKOpOCTH He npOH3BO,lI.HTC5I, TO OnTHMaJIb-
Hoe 3HaqeHHe nO)1.aQH So MOMeT 6bITb KaK MeHbille, TaK If 60JIbllIe SOL
H 3aBHCHT aT TeXHHKO-3KOHOMHQeCKHX nOKa3aTeJIeH onepalI.HH.
3TH BbIBO,lI.bI CnpaBe,lI.JIIIBbI npM JIIO()OM BH)I.e CTOHKOCTHbIX 3aBHCH-
MocTeH (6.11), (6.12) HJ1H (6.13), (6.14).
TIpHMeHHTeJIbHO K 3aBHCHMOCT5IM (6.13) II (6.14), IIMeIOII.LMM TOll.
KH M3KCHMYMa npII V =Vl( fIJI=bl(/Cu.; Vo=VonJI=bo/C o , MO)KHO C,lI.e"
JIaTb BbIBO.Ll 0 TOM, liTO npH nepeKJI1Ol.JeHHH CKOpOCTH npOT5IrHBaHHH
OnTHMaJIbHble CKOpOCTII Vo*>Vo fIn ; Vq*>Vt.{ I1JI. ECJIH Me CKOpOCTb npo"
T5IfHB8HH5I nOCT05IHHa, TO ee OnTHMaJIbHOe 3HaqeHHe MOMer 6bITb KaK
60JIbille, TaK H MeHbIlle Vq nJI.
CJIe,L(yeT OTMerIITb, qTO JI.aLKe B TOM CJIyqae, KOr,lI.a 3HaqeHH5I OnTH-
Ma.nbHbIX CKOpOCTeH VO'" II Vl( - n0J1Y4alOTC51 AOCTaTOQHO 6J1H3KHMH, lI,eJIe-
164
coo6pa3HO HCn0J1b30BBTb Cr8HOK, HMeIOIUHH YCTPOHCTBO J{JI51 nepeKJIlO-
qeHH5I CKOpOCTH, TaK K8K ero CTQHMOCTb OT BBe.n.eHHSI TaKoro YCTpoA-
CTB8 nOBblCHTCR aeCbMa He3HalJ:HTeJIbHO {BeJIHtlrrHa Ii B u.eJIeBbIX 4>yllK-
nH5IX (6.5) H (5.8) npH 3TOM npaKTHqeCKH He H3MeHHTCH], a BblHrpbl W
B 3aTpST8X H8 o(5pa OTKY MO}KeT 6blTb cymecTBeHHffM.
nOCJIe paCqeTa OnTHMaJIbHbIX 3HaqeHHH peMHMHbIX napaMeTpOB
.lI.JHI OOJIaCTeH 1 H 2 [CM. pHC. (6 2) J Heo6xo HMO cpaBHHTb lI.eJIeBble
4JYHKlI.HH (6.8) TIPH ,lI.BYX HaH.lI.eHHbIX OnTHMaJIbHbIX COlleT8HHHX napa-
MeTpoB II BbI6paTb TY H3 HliX, KOTOpa5I 06eCnel.JHBaeT MeHblIlHe npHae-
eHHble 3aTpaTbl.
ECJIH me npOT5I}KHOH CTaHOK HMeeT Y3KHH .n.Hana30H cKopocr eH
npOT5IrHBaHH5I HnH BO BceM ero Hana30He cTofiKocTHwe 3aBHCHMOCTH
MorYT 6bITb annpOKcHMHpoBaHbI Bcero BYM5I CPYHKUH5IMH - Tt.{ (vt.{),
To(vo, So), HarrpHMep, BHJl.a (6.11), (6.12)) TO TaKoro cpaBIleHH5I He
nOTpe6yeTCR.
nOCJIe orrpeJl.eJIeHH5I OrrTHMaJIbHOro COQeTaHH5I napaMeTpOB pefK H -
M3 pe3aHH5I HeOOXO)J.HMO paCCqHTaTh Tpe6yeMoe lIHCJIO npOT5I)I{HbIX
CTaHKOB B rrOTOtIHOH JIIIHHH (Ha yqaCTKe). BCJIel1.CTBHe BbICOKOH npO-
H3BO)I.HTeJIbHOCTH OnepaIl.HH rrpOT5IrHBaHH5I paClJ:e1 Hoe qHC,JIO CTaHKOB,
KaK rrpaBHJIO, MeHbllIe e,lI.HHHlI.bI. ECTeCTBeHHO, qTO cpaKTHqeCKH nPH-
HHToe qIICJIO CTaHKOB 6Y,L(eT paBHO e HHHIl.e.
ECJIH no opraHH3aLI.HOHHbIM HJIH HHbIM rrpHqHHaM He YJl.aeTCH nOJI-
HOCTblO 3arpY3HTb npOT5I)KHOH CT3HOK .n.a)Ke 06pa6oTKOH 3arOTOBOK co
u
CMe)KHbIX JIHHHH HJIII YllaCTKOB, TO paCClIHTaHHbIe no npHBe.u.eHHbIM
BbIllIe MeTO)J.HKaM OnTHMaJIbHbIe CKOpOCTII npOT51rHBaHH5I Vo* If V'I*
He06xo HMO CHH:>KaTb ,LI.JI5I OOJIee paI.JJIOHaJIbHOrO HCn0J1b30BaHH5I npo-
TH)KeK. Dpe)I.eJ1bHOH HBJTHeTC5I CKOpOCTb, COOTBeTcTBylO a5I MaI<CH-
MaJIbHOH nJIO a.LI.H, o6pa6oTaHHOH 33 nepHO,lI. CTOHKOCTH npOT5I)i{KH.
DOCKOJIbKY CTOHKOCTb rrpOTR)l{KH BbIpa)KaJIaCb B Merpax, TO 3TOH CKO-
pOCTH COOTBeTcTByeT HaHBbICllIaH TOlIKa Ha KpHBOH Tt.{ (Vt.{), H306pa-
LKeHHOH Ha pRC. 6.1. 3Ta TOqKa MOlKeT JIeLKaTb KaK Ha nepBOM HH'fep-
BaJIe VI-V2, TaR II Ha BTOpOM - COOTBeTCTBOBaTb TOqKe A MaKCMMY-
M3 KpHBOH T q (v q ). 3TH }Ke TOlIKH MbI nOJIyqHM H B TOM CJIyqae, eCJIH
B u.eJIeBoA <t>YHKlI.HH (68) npHMeM £=0, T. e. 3a KpHTepHH 3<pcpeK'f H B"
HOCTH I1pMMeM MHHHMaJIbHbIe 3aTpaTbI Ha pe}KYUI.HH HHcTpYMeHT, fIpH-
XO,lI.H HeCH Ha O,ll,HY Jl.er8JIb. I13M:eHHH COCT8B rroKaS8TeJIel1 E H H B
ueJIeBOH: <PYHKLLHH (6.8), MO}KHO nepexo HTb K LlpyrHM KpHTepHHM-
ce6ecToHMoCTH o6pa6oTKH) HapoJI.HOX035IHCTBeHHbIM 3aTpaTaM, I1PH"
6bIJ1H Ha OI1epaIJ.HH, npOH3BO,L(HTeJIbHOCTH orrepaUHH H T. n. r[Il].
nOCJIeAHeMY KpHTepHIO COOTBeTcTByeT H =0, T. e. 3aTpaTaMJ{ Ha
HHcTpYMeHT npeHe6peralOT, yqHTbIBaH TOJIbKO npocToH CTaHKa npH ero
3aMeHe 'tCM=F=O. O)1.HaKO 3TOT Kpl1TepHH npH paClJ:eTe pe)KHMa npOTH-
rHB8HHH) KaK npaBHJIO, He HCIIOJIb3yerCfl.
npHMep. MCXO.ll.Hble .ltaHHbIe. MarepHaJI 06paoaThIBaeMOH 3arOTOBKH - CTaJlfJ 45,
TBepAocTb H B 290, )l.HaMeTp OTBepCTHS1 .lI.O o6pa6oTKH 28,9+ 0 ,1 MM, nocJle o6p86oT-
KH - 30+0,021 MM, .lI.JIHH8 npOTHrHBaeMoft nosepxHocTH 80 MM, Tpe6yeMbIH napa.MeTP
rnepoKoSaTOCTI1 Ra=2,5 MKM, MBKCHMaJIbH3H CKOpOCTb pa6oQero XQ,lt3 cr8HK8
40 M/MHH, \'laKCHMaJlbHaSl CHJIa 50 KH OrpalHPleIIHH Ha CKOpOCTb pe3aHHH: no npo-
H3Bo)tHTeJlbHOCTB onepa BB - v'i 5 I4/MBH; no KaqeCTsy o(5pa6oTKH 24 v.
165
6.1. PeJKHMbI peaaHHR
JL
4epHOBaSl lfaCTb npOT I>KKH t.JHCTOBaSi qaCTb npOTJI>KKR
CKOpOCTb
pe3RHHH, la, MM To, M Vo, M II\[ II SO. MM L"I' MM T'I' M v"I' Sq, MM
M/MHH MjMMR
,[(0 15 256,00 45,947 13,152 0,050 34 1,5 45,947 8,0 0020
o 15,5 259,88 45,982 15,378 0,034 341,5 45,982 7,989 o 020
Ca. 24 246,77 56,627 39,969 0,041 341,5 56.632 26,001 0,020
4t.\
15,5 M!MHH. TIpoT5DKKa - KpyrJIaH, nepeMeHHoro pe3aHMH, MarepHa.n pe}l{ymeA
qaCTH - P6M5. TeXHHKO 3KOHOMHqeCKHe nOKa3aTeJUI onepaUlHI: E = 8,5 Kon/MHH;
H=490 Kon; 1'cM=2,35 MHH.
no onHcaHHOH B fJI. 3 MeTO,LlHKe Ha 38M 6h1JIO npOCtIHTaHO 79 BapHaHToB npo..
TH}KKH npH H3MeHeHHH nO.lJ.atIH Ha tJepHoBbIX 3y6b X OT 0,02 .lJ.O 0,1 MM (qepea
0,005 MM). HaHMeHbllIaH ..1JIHHa peMywei% qaCTH - np" 8 0 =0,0.5 MM, np" 3TOM
10=256 MM; ITJ 1<=96,5 MM; L'I=341,5 MM; t o =8 MM; t TJ =6,5-;.-5,5 MM; QHCJlO 3y6beB:
tJepHoBbIX - 30, nepeXO.lJ.HbIX - 2, IJHCTOBbIX - 10, KaJIH6PYIOllI.HX - 6.
B pe3YJIbTaTe anrrpoKcHMauHH Ha 3TO" me 3BM 3aBHCHMOCTH Lo (So) B ,lJ,Hana-
30He 0,02-0,055 MM ypaBHeHIIeM (6.7) MeTO,lI.OM HaHMeHbU1HX KB3.llpaToB no.nY'IeHo
ypaBHeHHe
10:= 0, 1848S6,7443e'i9, 6537S o .
COrJlaCHO HopMaTHBaM [16] a3BHCHMOCTH (6.11) H (6.12) npH v 15 M/MHH
HMelOT COOTBerCTBeHHO BH,lI.
T 'I = 141 ,23v;;o,S4: To = 115v o O,67 8 0 °,27
3aBHcHMoCTH (6.13) H (6.14) np" 23 v 40 M/MHH HMelOT COOTBeTCTBeHHO BH.ll
T q = O,54.10-4v ,25e-O,25vlJ:
To = 0,11 IO-3vg I5 e-O,2'V o 5 0 °,27.
Pe3YJIbTaTbI paCQeT3 no onHc3HHoMY BblllIe anropHTMY rrpHBe.neHbI B T30.11. 6.1
H 6.2.
B rrepBOH: crpoKe Ta6JIHlt npHBe.lleHbl pe3Y JIbTaTbI paclfeToB, npOBe,lleHHbIX no
HopMaTHBaM.
KaK CJIe.lJ.yeT H3 npHBe.lleHHblx ,l{aHHblX, B paccM3TpHBaeMoM CJlyqae HopMaTHB-
Hble napaMeTpbI pe)l{HMa B HH3KOCKOpOCTH0\1 .n:Hana30He BeCbMa 6J1H3KH K OllTH-
MaJlbHHM. O.lJ.HaKo npH HaJIHqHH CT3HKa .nJlH CKOpOCTHoro npoTRrHBaHHfl CJIe yeT
npHH}1Tb napaMeTpbI pe)KHMa H JTo.lI.aqy, YKa3aHHble B TpeTbeH cTpoKe TaOJ1. 6.1. IlpH
ro.n:oBoH nporpaMMe 100 THC. .n:eTaJleH 3KOH0\1HtJeCKHH: s<pcpeKT COCTaBHT 509 pye>.
TIpH )J,onycTHMO\1 QHCJIe nOBTopHbIX 3aTOqeK npoTsnKKH. paBHoM 12, paCXo.lJ.yeTc
6.2. TeXHHKO-3KOHOMHQeCK"e nOH'a3aTeJlH Onepau.HH
CJIa ra eMbIe I.Le.nenoA
CKOpOCTb 3HaqeHHe cPYHKII.HH (6.8) ,lJHCJIO o6pa- nepeMeRHaSl
pe3aHHSI, neneBoA 60TaHHblx tIaCTb 3aTpar
M/KItH YHKnHH (6 8' 3arOTOBOK n 3 (6.4), !ton.
1 2 3
,lIo 15 166,62 19,465 42,688 104,467 574,34 1,416
,lI.0 15,5 164,030 16,900 42,747 104,384 574,77 1 394
Ca. 24 104,062 6,174 13.134 84,755 707,89 0,885
166
npHMepHO Ha TPH npOT5Df\KH B rO,l{ MeHbme, qTO )I.aCT CymecTBeHHYIO 9KOHOMHIO
ObICTpOpe}KYlll.eii CTaJlH.
npHBe,l{eHHaH MeTO,lJJIKa 001 HMH3aI..I,HH napaMeTpOB npOTSDKKH H pe)KHMa pe3a-
HHH paCCqHTaHa na npUMeHeHHe MHKpo3BM C OrpaHHtIeHHbIM 06'beMOM naMHTH H
nporp aMMHpyeM:bIX MHKpOKaJIbKY JlHTOpOB. HMeHHO 3THM 06'bHCHHeTCH npHHHTOe
paHee .llOnYllI.eHH.e 0 IIe3aBHCHMOCTJ.l napaMeTpa H OT SO, a TaK>Ke HCrrOJIb30BaHHe
rrpH paClfeTa:\ He HCXO.lI.HOH: Ta6JIHQHO 3attasaeMOH CPYHKL(HH 10 (So), nOJIyqaeMOH: B
pe3YJ1bTaTe paCqeTa npo U1JKKH, a annpOKCHMHpYlOIl{eH - (6.7).
YKa3aHHoe )].onYIll.eHHe H norpelliHocTM annpOKCHMau.HH B pH,lte CJ1YQaeB npH-
BO)]. T K 3HaQHTenbHWM norpewHocTHM npH onpe4eneHHH onTHManbHoro 3HaqeHHH So
(KaK npaBHJIO - 3aHH)KeHHe). n03TOMY npe)].nOQTHTeJIbHee HCnOJIb30BaTb 9BM.
B 3TOM cJrY'-lae nporpaMM8 OnTH\fH3ar(HH napaMeTpoB npoTHLKKH H peIKHM8 pe38HHR
MO)l(eT COCTaBJIHTbCH KaK )].onOJIHeHHC K nporpaMMe paCqeTa npOTHJKKH. 3a)I.aBaH
;:I.OCTaTOllHO MaJIbli1 HHTepBaJI H3\1eHeHHH nO)I.all.H So, HanpHMep, IllHpnHOH 0,005 MM,
B pe3YJIbTaTe paClleTa npOT5DKKH nOJIyQae:VI MaCCHB So-lo-l'rf..1<' KOTOpbIH Heo6xo-
JJ.HMO COKpaTHTb, OCTaBHB B HeM TOJIbKO Te npOTH)KKH, KOTopble npH 3a;:I.aHHOM So
HMelOT MHHHMaJIbllYlO Jl....IHHY pe*YIJ.J. H qaCTH Lo = 10 + 14 K. 3aTeM CJIe.lI.yeT onpe,ll,e-
J1HTb napaMeTp H .lI.J1H Ka)K)I.orO BapHaHTa npOTHiKKH, HanpHMep, no 3aBHCHMOCTH
H 1 =H o (l+K(Lp -Lpo)), r..u.e Ho-napaMeTp H, COOTHeTCTBYIOIlI.liH MHHliM8JIbHOMY
Lp=Lpo; K - 3MilHpH1JeCKHI1 K03cpcpH HeHT.
,lLanee Ha OCHOI3e ypaBHeHHH (6.18) HJlH (6.34) no H3JIOmeHHo}\ MeTO.ll.HKe Ha-
XO,lUiM ,11.JIH Ka)K OrO 3HaqeHHH Su (BapHaHT3 rrpOT.f.DKKH) OIITHMaJIbHbIe 3HaqeHH Vq
H Vo, a TaK)Ke 3Ha4eHHe u.eJleBoi% YHKII.HH (6.4). B apHaHT, HMelOllI.HH: MHHHMaJIbHOe
3HaqeHHe u.eJIeBOH q)YHKll.HH, H 6YJJ.eT OilTHManbHbIM. TaKaH AHcKpeTHaH OilTHMH3a-
UHH 6Y.ll.eT )].aBaTb GOJIee TOqH C pe3YJIbTaTW, TaK KaK npM 3TOM HCKnro4alOTcH no-
rpeIllHocTH BCJIe.llCTBHe annpOKCHMaII.HH CPYHKlI.HH La (So) Yl.JHTbIBaeTcH 3aBMCHMOCTb
JJ (So), H paCqeT Be eTCH cpa3Y JHI Tex ,l1,HcKpeTHblx 3HaqeHHH So, KOTopble Moryr
6bITb 3aJIOmeHbJ B KOHCTPYKI..I,IUO npoT5DKKH 6e3 )].onOJIHHTeJlbHOrO oKpyrJIeHHH.
fJIaBa
7
TeXHo orHR H3rOTOOneHHD
npOTJlJKeK
f1 pOT }KKH 5IBJI5IIOTC5I CJIO./KHbIM pe}KY HM HHCTpYMeH-
TOM, H3rOTOBJI5IeMbIM C BbICOKOH TOlIHOCTbIO. Hx H3rOTOBJI5IIOT KaK Ita
cneu.HaJIH3IIpOBaHHbIX HHCTpYMeHTaJIbHblX 3aBO,lI.ax, TaK II B HHCTPY-
MeHTaJIbHbIX u.exax M allIHHOCTpOHTeJIbHbIX 3aBo.rr.OB. B 3aBHCHMOCTH
OT xapaKTepa npOH3BOACTBa BbI6HpaeTC5I 060pYAosaHHe A 5I fiX H3fO-
TOBJIeHlf5I; B HHCTpYMeHTaJIhHbIX u.exax, KaK npaBH.no, npHMeH5IeTC5I
YHHBepCaJIbHOe 060pY)I.OBaHue, IIa cneQHaJIH3HpOBaHHbIX npe)J.IIpH5I-
Tli5IX Ha P5I)1,Y C YHHsepCaJIbHbIMH CTaHKaMH npHMeH5IIOT cnell.HaJIbHbIe
CTaHKH If craHKH C lIHC.J10BbIM nporpaMMHbIM ynpaBJIeHHeM.
CxeMbI TeXHOJIOfHIJeCKOrO npouecca
THfIOBOH TeXHOJIOfHqeCKHH npou.ecc H3rOTOBJIeHH5I npOT5I)KeK BK.,IIO-
tJaeT B ce05I C.J1e,lI.YIO He onepaUHH:
1) oTpe3KY 3arOTOBOK pe:tKYIII.eH qaCTH;
2) oTpe3KY 3arOTOBOK XBOCTOBOH qaCTH;
3) npOTOQKY llIeHKH nOA cBapKY Ha 3arOTOBKe pe)l{y ei1: TIaCTH;
4) raJITOBKY 3arOTOBOK XBOCTOBOH qaCTH;
5) CBapKY;
6) OT}I{IIr;
7) npOTOIIKY CBapOqHOrO llIBa;
8) IIo.rr.pe3KY TOpI.(OB;
9) I.(eHTpoBKY 3arOTOBKH C ,nBYX CTOpOH;
10) npaBKY;
11) rrpeABapHTeJIbHYIO TOKapHYIO o6pa6oTKY;
12) no,npe3KY TOpI.(OB, 3eHKOBKY ll,eHTpOBbIX oTBepcTHH, paCTOQKY
u
ropu.oBoH BbITOqKH C ,l!BYX CTOpOH;
13) qHCTOBYIO TOKapHYIO o6pa6oTKY;
14) npOTOqKY npo<pHJIH 3y6beB;
15) npaBKY;
16) <ppe3epoBaHHe rrpocpH.lI5I Y UlJI Hu.eBbIX Bcex THnOB Ff rpaHHblx
npoTHlKeK;
17) <ppe3epoBaHHe BbIKpY>KeK;
18) MapKHpoBKY;
19) npaBKY;
20) TepMHtlecKYIO o6palSoTKY;
21) 3aqHCTKY U.eHTpOBbIX oTBep THA C J1BYX CTOpOH;
22) IlIJIH<fJoBaHHe nepeJlHHx nOBepxHocTeH Ii Cf1HHOK 3y6beB;
23) rrpaBKY;
168
24) llIJIHctJoBaHHe no IIaMeTpy nepe,Z1HeH HanpaBJlHIO eA, XBOCTO-
BHKa, llIeHKH, 3aJl.HeH HanpaBJIHIO eH;
25) lllJIH<poBaHHe no HaMeTpy KaJIII6pYIOIII-HX 3y6beB;
26) llIJIHcpoBaHHe no KOHYCY pe)KYll{HX 3y6beB;
27) llIJIHcpoBaHHe 3a HeH nOBepxHocTH Y pe}KYInHx H KaJIHopylO"
HX 3y(5bes;
28) llIJIHctJosaHHe npocpHJIH Y llIJIHlI.eBbIX (Bcex THnoB) H rpaHHblI
npOT5tlKeK;
29) lllJIHctJoBaHHe 3a,aHeH rroBepxHocTH no rpaHHM;
30) lllJI H cpo B 3 H H e B bI K P Y }KeK;
31) .l1.0BOLlKY nepe,aHeH nOBepXHOCTH 3y(5beB;
32) ,aOBOJI.KY 3a HeH nOBepXHOCTH 3y6beB;
33) MapKI1pOBKY;
34) KOHCepBalI.HlO H yrraKoBKY.
TIpOT5IJKKH H3rOTOBJIHIOT H3 6bICTpOpe)KY Hx CTaJIeH P6AM5,
P6M5K5, P9M4K8 II JI.p. (faCT 19265-73) HJIH CTaJIH XBf
(fOCT 5950-73). ,QJI5I 3KOHOMHH 6blcTpopemYIlI.eH CTaJII1 npOT5I>KKH
113 3TOH CTaJIH )J.I1aMeTpOM 18 MM H 60JIee BbITIOJIH5IlOT CBapHbIMH IIJIH
C l\feXaHHlJeCKI1M KpenJIeHI1eM XBOCTOBI1Ka. XSOCTOBHK CBapHbIX rrpOT5I"
)KeK H3rOTOBJI5IlOT I13 CT3JIH 40X no fOCT 4543-71 * DPOT5I)KKH H3
6bICTpOpe)Ky eH CTaJIH LlHaMeTpOM 50 MM II 60JIee orrYCKaeTC5I H3ro...
TOBJIHTb lleJIbHbIMH. B M aCCOBOM np0I13Bo,acTBe, r)I.e 60JIee BbICOKHe
Tpe6oBaHII5I K pe)Ky eMY HHcTpYMeHTY, onYCKaeTC5I H3rOTOBJI5ITb
llpOT5I./KKH lI.eJIbHbIM Ii H3 6bICTpOpe)Ky eH CTaJIH, He3aBHCHMO OT pa3-
Mepa.
06pa6oTKa 3arOTOBOK
B KaqeCTBe 3arOTOSOK npOT5I)KeK 06bIQHO HCrrOJIb3Y-
lOT npOKaT Kpyr JIoro CeQeHI15I. OTpe3KY np0I13Bo,a5IT Ha cppe3epHO-OT'"
pe3HbIX, a6pa3HBHO-OTpe3HbIX CTaHKax, py6KOH B lIlTaMnax IIJIII H8
npeCC-HOMHI1UaX I1 ,aPyrHMH MeTOJl.aMI1. HaH60JIbIllee pacnpOCTpaHe-
HHe TIOJIYlJHJIH cppe3epHO.OTpe3HbIe CTaHKH (8f662 H ,lLp.). B KalJeCTBe
I1HCTpYMeHTa H3 3THX CTaHKax npHMeH5IIOT TIHJIbI HCKOBble cerMeHT-
HbIe Jl.HaMeTpoM 250-2000 MM. ITHJIbI MeHblllero .ZI.HaMeTpa 06JIa aIOT
60JIhllIefi :>KeCTKOCTblO I1 n03BOJI5IlOT pa60raTb C 60JIblIlHMI1 CKOPOCTH-
MH pe3aHH5I I1 no,aalJaMH, HO OHH npHMeHHMbI ,llJI5I pe3KH rrpYTKOB cpaB-
HHTeJIbHO He6oJIbliiOrO ,lLI1aMeTpa. ,L:lJI5I pe3KH KpynHbIx llITaHr HJIH na-
KerOB npYTKOB rrpHMeHBIOT nHJIbI 60JIbiliOrO Jl.HaMeTpa. Han60JIbmee
npHMeHeHHe Halll.III1 nHJIbI ,aHaMeTpoM 710 MM, IllHpHHOH 6,5 MM. <I>pe-
3epHO-OTpe3HbIe CTaHKH HMeIOT MeXaHI13MbI aBTUMaTHlJeCKOH 3arOTOB-
KH Ha 3a,aaHHoe paCCT05IHHe, O,aMH pa601.IHH MO)KeT 06CJIYMHBaTb ,ltO
fi5ITII CTa HKOB.
BOJIee BbICOKOH npOH3Bo,aHTeJIbHOCTblO 06JIa,aaIOT a6pa3I1BHO.OTpe3-
HbIe CTaHKH. Ha 3TI1X CTaHKax (MO,a. M<P-332) pa3pe3alOT npYTKH
.l\HaMeTpOM ,ao 80 MM llIJII1cpoBaJIbHbIMH KpyraMH HaMeTpoM 400 MM,
BbICOTOH 4 MM Ha BYJIKaHI1TOBOH I1J1H 6aKeJJHToBOH CB5I3Ke. He,aocTaT-
KOM MeTo,aa 5IBJI5IeTC5I 60JIblilOH pacxo,a OTHOCHTeJIbHO e HUHTH@X H
Jl.OpOrHX lllJIHcpoBaJIbHbIX KpyrOB.
6--338 169
7. t. 06U(He npHnycKH no ):tHaMeTpy npoTHlKeK H3 rOpH'leKaTaHoH eTaJlH, MM
06w.sSI JlJlHHa npOTsnKKH. MM
HaH60JIbllIHft
JlHaMeTp npo- c . 1200
TsnKKH. MM .no 300 300-600 600-900 900-1200
L{o 30
30-50
50-80
80-120
120-145
4,0
5,0
6,0
6,5
7,0
4,5
5,0
6,0
7,0
8,0
4,5
5,5
6,5
7,0
9,Q
5,0
6,0
7,0
7,5
10,0
7,0
7,5
8,0
12,0
Py6Ka 5IBJI5IeTC5I HaH60JIee npOH3BO)J.IITeJIbHbIM II oe30TXO)I.HbIM npo..
ueccOM. O,lI.HaKO npH py5Ke 6bICTpOpe:tKYlI.(eH CTaJIH B XOJIO,flHOM CO..
CT05IHHH qaCTO 06pa3YIOTCH Tpe HHbI. Bo H36e)KaHHe 06pa30BaHHH
TpellI.HH 6bICTpOpeJKYIUYlO CTaJIb py6HT C IIOAorpeBOM ):(0 500-600°C,
liTO YCJIO)KH5IeT TeXHOJIOrHqeCKHH npou.ecc.
TIpHrrYCKH no ,l(HaMeTpy Ha nOJIHYIO o6pa6oTKY rrpOTR)KeK npHBe..
,l( e H bI B T a 6 JI. 7. 1 .
PaCCQHTaHHbIe pa3MepbI 3arOTOBOK oKpyrJI5IlOTC5I ,lI.O 6JIH}KaHllIHX
60JIbllIHX pa3MepoB npoKaTa. ITpHIIYCK no ,lI.JIHHe Ha o6pa6oTKY aeJIb-
HbIX npOT5.DKeK He OCTaBJI5IeTC5I. 3arOTOBKH OTpe3alOT ,l(JIHHOi1, paBHOH
MaKCHMaJIbHOH ,l(JIHHe npOT5I)KeK C ,l(OnycKoM -2 MM.
ITpeJI.eJIbHbIe OTKJIOHeHH5I o6III.eti ,l(JIIIHbI npOT5IJKeK nOCJIe OKOHlJa-
TeJIbHOlf o6pa6oTKH YCTaHOBJIeHbI + 3 MM )l,JI5I npOT5.[)KeK .ll.JIHHOM )1.0
1000 MM II + 4 MM - AJIH npOT5IMeK ,l(JIIIHOH 60JIee 1000 MM.
ITpHnYCKH no AHaMeTpy Ha nOJIHYIO o6pa6oTKY XBOCTOBOA qaCTll
CBapHbIX npOT5I)KeK npHBeLLeHbI B Ta6JI. 7.2.
TIpHrrycKH no ,lJ.JIHHe peJKYIII.eH: H XBOCTOBOH qaCTeH cBapHblx npo-
T5I)KeK npHBeAeHbI B TaOJI. 7.3.
Ha 3arOTOBKe pe)Ky eH lJaCTH npOTaqHBalOT llIeHKY ,l(HaMeTpoM d p
paBHbIM ,L{HaMeTpy 3arOTOBKH XBOCTOBOH qaCTH. ,L(JIHHa rneHKH t/ 3aBH-
CIIT OT OTHOllIeHII5I ,lI.HaMeTpoB 3arOTOBOK pe}Ky eH (D) H XBOCTOBOH
.(d) tJacTeA (Ta6JI.7.3).
,L{JI5I YJIYIJ:rneHII5I KOHTaKTa rrpH cBapKe 3arOTOBKII pe:iKYIUeti qaCTH
06TalJHBaIOT no HapY}I{HoMy LLHaMeTpy Ha ,lI.JIHHe, paBHOM ,lI.JIHHe 3a-
)KHMa CBapOlJHOrO annapaTa; 3arOTOBKH XBOCTOBOH qaCTH ,l(JI5I 3TOH iRe
neJIH nO)J.BepralOT o6pa6oTKe B raJITOBOqHOM 6apaoaHe.
7.2. 06rn;He npHoycKH no HaMeTPY XBOCTOBOH tJaCTH cBapHblx npOTH1KeK, MM
06w.aSl .lI.JIHHa npOTSDKKH, MM
,Z:\HaMeTp
XBOCTOBHK8,
, MM Jl. 0 300 300-600 600-900 900-1200 Ca, 1200
,1],0 30 4,0 4,5 5,5 6,0
30-50 5,5 5,5 6,5 7,0 8,0
50-80 6,5 6,5 7,5 8,0 8,5
80-120 7,0 7,5 8,0 8,5 9,0
170
7.3. 06ll\He npHnyeKH no ,lI.JlHHe npOTH1KeK npH CTblKOBOH cBapKe
11 HaHMeHbllIHe ,lI.JlHHhI meAxH
.
I
"'t:j
t
Oc5 HA npHnYCK (MM)
no .lI.JIHHe t.{ aCTH
HaHMeHbllJaSl J],JlHHa 1, MM
I .llHaMeTp
3arOTOBKH
D.MM
pa60QeA
OCBOCTOBOft:
a
-;[<1,2
a
d
=-1,2+1,5
,.
..11 _ ,
Jlo 30 6 4 9 12
30-40 7 5 11 14
40-50 8 6 12 15
50-60 9 7 13 17
60-70 13 10 16 19
70-80 14 11 17,5 21,5
80-95 15 12 18,5 23,5
CBapKY 3arOTOBOK BbInOJIH5IIOT Ha CBapOIJ:HbIX annapaTax. ,I::LJIH
CBapKH 3arOTOBOK ,l\HaMeTpoM 20-60 MM fTpHMeH5IIOT 3JIeKTpOCBapOQ"
Hble no.nyaBToMaTbI CA-2. fIpH cBapKe 3arOTOBKH CJIe,L(yeT 3aJKHMaTb
TaK, IIT06bI HX oceBble JIHHHH H cBapHBaeMbIe TOpIJ.bI COBna,LlaJIH. MaK-
CHMaJIbHOe CMemeHHe 3arOTOBOK He OJI}KHO npeBbIlIlaTb 0,5-0,6 MM.
3arOTOBKH rrOCJIe CBapKH nOMe alOT B neqb (COOpHHK) C TeMnepa-
TYPOH 600--700°C. TIoCJIe BwpaBHHBaHHH TeMnepaTYpw 3arOTOBOK HX
OT}KHraIOT B 3JIeKTpOneQH.
B pe3YJIbTaTe OT)I{Hra JIHKBH HPYIOTC5I BHYTpeHHHe Hanp5I)I{eHH5I,
nOJIYQaeTC5I 60JIee OJIarOnpH5ITHa5I CTpYKTypa JI5I nOCJIe,L(YIOlIJ.eH Tep-
MHIJ:eCKOH o6pa6oTKH H CHH}KaeTC5I TBep OCTb, BCJIe,lI.CTBHe LJero YJIyq-
WaeTC5I 06paoaTbIBaeMOCTb 3arOTOBOK pe3aHHeM.
Pe:>KHM H30TepMHQeCKOrO OT:>KHra 3arOTOBOK H3 CTaJIH P6M5 CJIe-
.nYIO HH: rrOADeM TeMnepaTypbI JI.O 860°C co CKOpOCTblO He OOJIee
IOO°CjLJ (7-10 Q); BbI)1.ep)KKa rrpH TeMnepaType 860°C B TeqeHHe
5-7 Q; CHH:>KeHHe TeMnepaTypbI o 750°C PMeCTe C neqhIO; BbI,L(ep}KKa
npH TeMnepaType 750°C B TeqeHHe 6-7 Q; OXJIa)K eHHe 3arOTOBOK O
TeMnepaTypbI llexa Ha B03 yxe.
Pe}KHM H30TepMHqeCKOrO OT)KHra 3arOTOBOK H3 CTaJIH XBr CJIe-
.n.YlOmHH: nO 'beM TeMnepaTypbI)1.0 700°C co CKOpOCTblO He 60JIee
IOO°C/q (6-8 q); Bbl ep)KKa npH TeMrrepaType 700°C B TeqeHHe 3 q;
nO,lI.'beM TeMnepaTypbI O 790°C, BbI)J.eplliKa npH TeMIIepaType 790°C B
TeQeHHe 6 11; CHH}KeHHe TeMnepaTypbI o 70QoC BMecre C rreqblO; Bbl-
.ztep)KKa npH TeMnepaType 700°C B TeQeHHe 10 Q; OXJIalli,lI.eHHe BMeCTe
c neLJbIO o TeMIIepaTypbI 450°C; OXJIa)K.n.eHHe 3arOTOBOK o TeMnepa"
TYPbI uexa Ha B03.n.yxe.
6"'1'
171
Y OTO}J{}J{eHHbIX 3arOTOBOK H-2 TOKapHOM CTaHKe CHHMalOT 06JIOH H
aarOTOBKH IIepe,aalOT ,aJ15I nO,ape3aHH5I TOpU.OB H ueHTpOBKH.
ITO,ape3aHHe TOpUO B H ueHTpOBKY ueJIeC006pa3HO npOH3BO,aHTb H8
tPpe3epHO-neHTpOBaJIbHblX CTaHKaX (HaDpHMep, MP-75). Ha 3THX
CTaHKaX ,aBYM5I cppe33MH O HOBpeMeHHO <ppe3epYlOT 06a Topu.a, 3 3a-
TeM C ,aBYX CTOpOH npOH3BO 5IT u.eHTpOBKY KOM6HHHpOBaHHWMH eHT-
POBOqHbIMH CBepJIaMH THDa A (faCT 14952-75). 06pa60TKa H3
pe3epHO-u.eHTpOBaJ1hHWX CTaHKax o6eCneQHBaeT o,aHHaKoBYIO .aJIHHY
Bcex npOT5IMeK B napTHH II O,lJ.HH3KOBYIO rJIy6HHY ueHTpoBbIX oTBep-
CTHH, IlTO oc06eHHo BaMHO ,lJ.JI5I nOCJIe.aYlOmeH 06 p a 60TKH H a TOKa p-
HhIX CTaHKax C Qf1Y.
DpH OTCYTCTBHH cppe3epHo-ueHTpOBaJIbHbIX CTaHKOB rro,ape3aHHe
TOPUOB MOMeT 6hITb BhIIIOJIHeHO Ha TOKapHbIx HJIH ropH30HTaJIbHo-cppe-
3epHbIx CT3HKax. Y Il.eJIbHhIX npOT5IMeK 3Ta onep3UH5I HHor,aa Bo06me
He npeLlYCMaTpHBaeTC5I. UeHTpOBKa TaK}Ke M02KeT ocyIlI.eCTBJ15ITbCH H3
YHHBepCaJIbHbIX CBepJIHJIhHhIX CTaHKax HJIH cneUHa.HbHbIX ueHTpOBaJIb-
HbIX. KpynHhle npOT5I)KKH (D>75 MM) 60JIee Y,lJ.06HO o6pa6aTbIBaTb
Ha ropH30HTaJIhHO-ueHTpOBaJIhHbIX CTaHKax.
DocJIe Il.eHTpOBKH 3arOTOBKH no,aBepraIOT npaBKe, KOTOpa51 BbInOJI-
HReTC5I H3 BHHTOBbIX HJIH rH,apaBJIHqeCKHX npeccax.
TOKapHaSl o6pa6oTKa
TIpH TOKapHOH npe,asapHTeJIhHOH o6pa60TKe 3arOTOBKH
06Ta4HBaIDT no Il.H HH.apH4eCKHM cTyneHHM. CTyneHH .ae alOT npH
pa3HHue ,lJ.HaMeTpOB He MeHee 2 MM. ITpH OTHOllleHHH ,lJ.JIHHbI 3arOTOs"
KH K LlHaMeTpy CBbIllie 12 o6pa6oTKa npOH3BOJI.HTC5I C npHMeHeHHeM
JIlOHeTa. B 3TOM cJIyqae BHaqaJIe npoTaIlHBalOT MeCTO no,a JIlOHeT (Ha
nepe,aHeH HanpaBJI5IIOIlI.eii IlacTH).
7.4. CYMMapHble npHnycKH (MM) Ha 'IHeToBYIO o6pa6oTKY npOTR1KeK
no HaPYJKHoMY ,IJ.HaMeTPY
t:J
ll.lHHa npOTiDK}{H, \1\1
.llHaMeTp
OpOTSIJKKH,
MM )].0 300 300-600 600- 900 900-1200 CB. 1200
I
,[{o 30 2,4-0,3 2, -0,3 2,9-0,3 3,3-0,4 --
30-50 2,4-0,3 2,7-0,4 3,0-0,4 3,4-0,4 3,7-0,4
50-80 2,6-0,4 3,0-0,4 3,2-0,1 3,6-0,4 3,9-0,4
80-120 - 3,3-0,5 3,9-0,5 4,3-0,5
CB. 120 - 4,0-0,5 4,5-0,5
172
t 2
2
\.
\ 60
I
PHC. 7.1.
3aroToBKa npCTS1:>KKU:
1 - CHHMaeMbIA npHnycK; 2 - npo4>HJIb npoTsDKKH nepe.n o6pa-
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Puc. 7.2.
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B Ta6JI. 7.4.
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nax. Pa3Mepbl ueHTpoBbIX oTBepcTHH l2, d a H La npHHHMalOT B COOTBeT-
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JIHM6y nOnepe1:lHOrO XO,lJ.a CTaHKa h T = h+a3, r,LLe h - rJIy6HHa 3y6a
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pHHa llIJIHIla nepe)J.Hero HanpaBJleHHH.
n34. YrJlbl npolj>HJlH Bna)J.HH l}>aCO'lHblX 3y6beB B 3aBHCHMOCTH
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4 2 47 45° 2° 90° 180 0
6 2 40 30° 10° 60° 120°
8 3 47 45° 2° 67°30' 135 0
10 3 45 36° 9° 54° 108 0
11 3 45 32°43'38" 12° 16'22" 49°5'27" 98°10'54"
12 4 47 45° 2 0 60° 120 0
14 4 45 38°34'17" 6°25' 43" 51 °25' 43" 102°51'26"
16 5 47 45° 2° 56° 15' 112:;;30'
18 5 45 40° 5° 50° 100 0
20 6 41 45° 2° 54 0 108 0
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K Z K
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22 6 45 40°54'33" 4 °5'27" 49°5'28" 98° 10'56"
24 7 47 45° 2° 52°30' 105°
26 7 45 41 °32'18" 3°27' 42" 48°27' 41" '96°55'22"
28 8 47 45° 2° 51 °25'43" 1 02°51'26"
30 8 45 42° 3° 48° 96-
32 9 47 45° 2° 50°37'30" 101 ° 15'
34 9 45 42°21'11" 2°38' 49" 47°38'50" 95°17' 40"
36 10 47 45° 2° 50° 100°
38 10 45 42°37'54" 2°22'6" 47°22'7" 94°44'14"
40 11 47 45° 2° 49°30' 99°
42 11 45 42°5 1"54// 2°8"6" 4 7°9"3" 94° 18"6'"
44 12 47 45° 2° 49°5'27" 98° 1 0'54"
46 12 45 43°2'36" 1 °57'24" 46°57'28" 93°54' 46"
48 13 47 45° 2° 48° 45' 97°30'
50 13 45 43°12' 1°48' 46° 48' 93°36'
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3 0,511 14 1,591 25 3,287 36 5,493 47 12,423
4 0,572 15 1,732 26 3,3 10 37 6,212 48 13, 133
5 0,724 16 7,833 27 3,468 38 6,585 49 16,565
6 0,796 17 2,020 28 3,580 39 7,000* 50 17,362
7 0,866 18 2,071 29 3,665 40 7,500* 51 20,706
8 1,008 19 2,217 30 4,091 41 8,282 52 21,863
9 1,047 20 2,311 31 4,141 42 8,767 53 24,287
10 1,157 21 2,595 32 4,211 43 9,500* 54 26,231
11 1 ,302 22 2,886 33 4,400 44 10,353
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1. ACTa$bcB B. A. PaC'IeT .LI.HHaMHlleCKOii npO'lHOCTH pe}Kym.ero HHcTpYMeHTa. M
MaIllHHocTpoeHHe, 1979. 168 c.
2. rpaHoBcKHH f. H. Oopa6oTKa pe3YJlbTaToB 9KcnepHMeHTaJIbHbIX HCCJle.n.oBaHHH
peaaHHH MeTaJIJIOB. M.: MallHIHocTpoeHHe, 1982. 112 c.
3. )l(HraJiKO H. H. CKOpocTHoe npoTHrHBaHHe. MHHCK: BhIweAmaH WKOJJ8, 1982.
152 c.
4. J1allJHeS c. H., IOnHKoB M. H. PaCqeT H KOHCTpYHpoBaHHe MeTaJIJIOpe>KYllI.HX
HHCTpYMeHTOB C npHMeHeHHeM 3BM. M.: MaIllHHocTpoeHHe, 1975. 390 c.
5. MaMeT c. n. KpaTKHH CnpaBOqHHK KOHcrpYKTopa-craHKocTpOHTeJIH. M.: Ma-
WHHOCTpoeHHe, 1965. 688 c.
6. 06m.eMawHHoeTpOHTeJlbHble HopMaTHBbl pemHMoB pe3aHHH, H3Hoca H pacxo,ll.a
lllJIHueBblX npOTsnKeK. M.: HHI1Maw, 1981. 48 c.
7. 06m.eMawHHoeTpOHTeJlbHhle HopMaTHBbl pe>KHMOB peaaHHH, H3Hoca H pacxo.lJ,a
KpyrJIbIX npOTH:lKeK. M.: HHHMalll, 1982. 48 c.
8. PaclfeTLI 3KOHOMHlIeCKOH 3QJcl>eKTHBHoCTH HOBOR TeXHHKH. JI.: MallIHHocTpoe-
BHe, 1975. 432 c.
9. CeMeH'IeHKO H. H., MaTroIDHH B. M., CaxapoB r. H. npoeKTHpoBaHHe MeTaJI-
nOpeJKYI.qHx HHcTpYMeHToB. M.: MawrH3, 1962. 952 c.
1 o. CHHH blH B. H. MeTo,lJ.bl KoppHrHpoBaHHfl pa60 1 ufx npo<pHJIeH MeTaJIJIopelliY-
WHX HHcTpYMeHToB C HCnOJIb30BaHHeM 3BM. MHHcK: HaYKa H TeXHHKa, 1969. 132 c.
11. TBepcKoA M. M. ABTOMaTHqeCKOe ynpaBJIeHHe pe)KHMaMH o6pa6oTKH ,n.eT a-
neB Ha CT3HKax. M.: MaillHHocTpoeHHe, 1982. 208 c.
12. ll(erOJleB B. A. KOHCTPYHpoBaHHe npoTHx<eK. M.: MarnrH3) 1960. 351 c.
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