螺旋锥齿轮振动研磨的运动模型研究与分析

:20030325:(2003kycx012):(1966-),(),,E2mail:[e-mail]:100328728(2004)03202532031,1,2,2(1,710072;2,471003):,V/HTCA,,,:;;V/H;TCA:TH132.4:AStudyonKinematicsModelofVibrationLappingProcessforSpiralBevelGearsWEIBing2yang1,FANGZong2de1,ZHOUYan2wei2,DENGXiao2zhong2(1SchoolofMechanicalandElectronicEngineering,NorthwesternPolytechnicalUniversity,Xian710072;2HenanUniversityofScience&Technology,Luoyang471003)Abstract:Thevibrationlappingmethodforspiralbevelgearsisfirstpresented.Twocorrespondingmodelsaresetup,i.e.themathematicrelationmodelbetweenV/Hpositionandthetoothsurfacecontactpoints,andthekinematicsmodelforthevibrationlapping.Simulationanalysisareperformedfortoothsurfacecontactpath,contactpattern,lappingpathandvelocity.Itisprovedthatthemodelscancontrolpreciselythecontactpathandpatternonsurfaceunderlapping,thevibrationlappingefficiencyandqualityarebetterthanthetraditionallapping.Keywords:Spiralbevel;Vibrationlapping;V/Hadjustment,,,;,[1],,,,,[2],,,10.1m,,,,V/H,TCA(ToothContactAnalysis)[35],,1,,,,,,1[1],3VHJ(V/H),,(),VHJ3233Vol.23No.320043MECHANICALSCIENCEANDTECHNOLOGYMarch2004©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.1,[1],,,,,,;,,,VHJ3,,V/H2V/H2.1V/H2,y1z2,x,x=y1z2sin:2,C1C22x,V,O1O212(),HJy1z2r1r2C1C2Mr(1)r(2)M12O1O2(1)(2)122VHJ()2,Jz2+r(2)=Vx+Hy1+r(1)(1)n(1)f(u1,1,1)=n(2)f(u2,2,2)(2)n(2)fv(12)f=f(u1,1,1,u2,2,2,V,H,J)=0(3):u;;fSfVHJ,J,JH,J=-Htan1(4):1(1)(2),5,V/H,(3)(4)7,,[6,7](),V/H,:,V/H;,V/HV/H,3,V/H3(),O2,P,A,M(),,M3V/H(,),s1s2()M3O2X2Y2(X32,Y32),x2=X32y22+z22=Y32(5):(x2,y2,z2)r(2)(u2,2)(5)u2,2,(1)(4)(V,H,J)(1)(5)V/H2.2V/H25/32,36mm,9mm,102mm()V/H,(V,H,J)0,TCA,,4a,4s1=10mm,s2=0s1=-10mm,s2=0,(1)(5)(V,H,J)(V,H,J)=45223©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(-0.492,0.130,-0.114)(0.420,-0.157,0.138),TCA,4a10mm()V/HV[-0.492,0.42];H[0.130,-0.157];J[-0.114,0.138],s1=-5mm,s2=2.5mms1=5mm,s2=-2.5mm(V,H,J)(V,H,J)=(0.310,0.027,-0.024)(-0.340,-0.055,0.049),,TCA,5as1,s25a,(1)(5)(V,H,J),533.1,,v(21)=v(2)-v(1)=(21)r(2)+(1)O2O1(6):O2O1=Hy1-Vx-Jz2,(21)=(2)-(1),2=m211,2=|(2)|,1=|(1)|,m21m21=d2d1(1)(5),(6)6V/H(V,H,J)2.2,1=1v(21),4b,5b(),,(4b),V/H,,V/H,,(V,H,J)3,3.2(V,H,J)3EDT,6R=E+D+T(7):E=dV(t)dt;D=dH(t)dt;T=dJ(t)dtvs=v(21)+R(8)(4)J(t)=-H(t)tan1(9)T=-Dtan1(10),TDP,PER,6E=Dtancos1(11)V(t)H(t)H,H(t)=H0+Hmsin(2ft)(12):HmH,;H0,,VV(t)=V0+v0t+H(t)tancos1(13):V(t)V,,V0;V0/H0;v0V,(9)(12)(13)V/H(12)ff50Hz,,200Hz,fN1,n(r/s),f=2knN150f200(14):k=,-2,-1,0,1,2,3,V/H(9)(12)(13)(14)(259)5523:©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.=0.1=0.03,,GM(E,1,1)4,2d:GM(E,1,1),4(1)12AGO,;(2),,;(3),GM(1,1),GM(E,1,1),[][1]JS,.[M].:,1990[2].[M].:,1986[3]ChenCK,TienTL.Anewforecastingmethodfortimecontinuousmodelofdynamicsystem[J].AppliedMathematicsandCompu2tation,1996,80:225244[4]ChenCK,TienTL.Anewforecastingmethodfordiscretedynamicsystem[J].AppliedMathematicsandComputation,1997,86:6184[5]TsengFM,YuHC,TzengGH.Appliedhybridgreymodeltofore2castseasonaltimeseries[J].TechnologicalForecastingandSocialChange,2001,67:291302[6],.GM(1,1)[J].,2000,20(5):121124[7],.[J].,2001,23(3):277279[8].[J].,2000,10(5):4954(255)7,1=1,f=2nN1,7a,7b,(),,;,,,,,4,,V/HTCA,,,[][1].,[M].:,1983[2],.[M].:,1985[3]LitivinFL.LocalSynthesisandToothContactAnalysisofFace-MilledSpiralBevelGears[R].NASA,CR4342,1991[4]LitvinFL.GearGeometryandAppliedTheory[M].EnglewoodCliffes,NewJersey:PrenticeHall.Inc.,1994[5].(LTCA)[J].,1998,22(2):13[6].[D].:,2000[7],.[J].,1994,26(5):1141179523:©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.