行星传动系统的固有特性及模态跃迁研究

X1,1,1,1,2,1(1.,300072;2.,050003):2K2H,:,,,:;;;:TH132.425;TH113:A:100424523(2005)0420412206,,,,,,,[1,2][3],[4]2,:10,2,,[5],,[68],,,,11N2K2H,kjuj(j=c,r,s);Wnn(n=1,2,,N,);uj(j=c,r,s,1,2,,N);krn,ksnn1U=[uc,ur,us,u1,u2,,uN]T,,184200512JournalofVibrationEngineeringVol.18No.4Dec.2005X:2004208208;:2005204211:(50205019);(20040056018)©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=0(1)MKm[9]Xi,i=[Uc,Ur,Us,U1,U2,,UN]T(Km-X2iM)i=0(2)2,,(krnksn),1,(2)(2)(2),,2:1ökg4.901.500.285.81ö(Nm-1)0.001.01090.00ö()24.6ö(Nm-1)51082(Hz)2088.001671.43,6472.35,13742.1922,,2(a),2(b),2.1,:N-1;,:uj=0,j=c,r,s;,:Ui=BUj,i=1,2,,N,ij,j1jN:i=[0,0,0,B1U1,B2U1,,BNU1]T,(2),Xi=(ksn+krn)ömp,i=3,4,,N+1(3),mp,2.2,,:;,:Ui=U1,i=1,2,,Ni=[Uc,Ur,Us,U1,U1,,U1N]T,(2),Ki=X2i(4),,,(kcu,kru,ksu)=(,0,0)(0,,0)(0,0,),(2)Ki(+1K2i++2Ki++3)=0(5)+1=mrmsmpmcmsmpmcmrmp+2=-[Nksnmrmp+Nkrnmsmp+(ksn+krn)mrms]-[Nksnmcmp+(ksn+krn)mcms+N(ksn+krn)msmpcos2A]-[Nkrnmcmp+(ksn+krn)mcmr+N(ksn+krn)msmpcos2A]+3=Nksnkrn(Nmp+ms+mr)Nksnkrn(Nmpcos2A+mc+4mscos2A)Nksnkrn(Nmpcos2A+mc+4mrcos2A)mc,mr,msmp(5)3144,:©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=0X2,N+2=[(-+2+22-4+1+3)ö(2+1)]1ö2(6),,(3)(6)Xi=0(ksn+krn)ömp[(-+2+22-4+1+3)ö(2+1)]1ö2i=1i=3,4,,N+1i=2,N+2[3],,,,[3]+2+32.3,(1)(6),$1=+22-4+1+3,$1,:krn=mr(Nmp+ms)2ms(N2m2p+Nmrmp+Nmsmp-mrms)ksn(7),$1,,,,(2)(3)(6)krn=NmpN2m2p-4mrms2msksn(8),$2=N2m2p-4mrms0=00(9)3(),;,[10],(2)p(p)(5Ki5p=Ti(5K5p-Ki5M5p)i(10)Ti5K5pi=Ni=1(Dijn)2,p=krn,j=rp=ksn,j=s,n=1,2,,N0,p=mc,mr,ms,m1,,mN(11)Ti5M5pi=U2n,p=mc,mr,ms,m1,,mN,n=1,2,,N0,p=krn,ksn(12)j=r,Dirn=Uir-UiccosAr-Uin;j=s,Disn=Uis-UiccosAs+Uin(10)(12)(p5Ki5p=Ni=1(Dijn)2,p=krn,j=rp=ksn,j=s-KiU2j,p=mc,mr,ms,m1,,mN,j=c,r,s,1,,N(13)iTi=12õTiMõi=12KiUTiMUi=12KiNj=c,r,s,1,,NU2jmj(14)(12),(13)(14)Ti=-12Nj=c,r,s,1,,Nmj5Ki5mj,Ti=-12Nj=c,r,s,1,,NIj5Ki5Ij,mjIjCp5Ti5mj=-125Ki5mj,p=mj5Ti5Ij=-125Ki5Ij,p=IjiUi=Uirn+Uisn+Uihu(15)Uirn,UisnUihuUirn=12Nn=1krn(Dirn)2(16)41418©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=12Nn=1ksn(Disn)2(17)Uihu=12khuU2h,h=c,r,s(18)(10),(11),(13),(15)(18)Ui=krn25Ki5krn+ksn25Ki5ksn-12Kih=c,r,skhu5Ki5mh(19)(16)(18)krn,ksnkhu:X15Uirn5krn=125Ki5krn,X25Uisn5ksn=125Ki5ksnX35Uihu5khu=-12Ki5Ki5mh=-12Kir2h5Ki5Ih,h=c,r,s4,1,353455144,:©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(7)(9),,,ksn=2.512109Nöm(3(a)A):ksn=4.309107Nömksn=3.1081010Nöm(3(a)),,Js=1.521kg(3(b)B),Js=15.930kg(3(b))4(a)(b)X3,4(X3,4);X2,X5(X2,X5),,X2X5,5X3,4,X2,X54,,3,,,,5(1):,;,,(2),;,,(3),(6),,(7),,:[1],,.[J].,2001,16(2):163166.[2],,,.[J].,2001,37(12):1115.[3]KahramanA.Naturalmodesofplanetarygeartrains[J].JournalofSoundAndVibration,1994,173(1):125130.[4]KahramanA.Loadsharingcharacteristicsofplane2tarytransmissions[J].MechanismsandMachineTheory,1994,29:11511165.[5],.[J].,2001(4):4043.[6]PierreC.Modelocalizationandeigenvaluelociveer2ingphenomenaindisorderedstructures[J].JournalofSoundandVibration,1988,126(3):485502.[7]LinJ,ParkerRG.Sensitivityofplanetarygearnatu2ralfrequenciesandvibrationmodestomodelparame2ters[J].JournalofSoundandVibration,1999,228(1):109128.[8]PerkinsNC,CDMoteJr.Commentsoncurveveer2ingineigenvalueproblems[J].JournalofSoundandVibration,1986,106(3):451463.[9].[D].:,2005.[10].[J].,1997,16(1):7074.61418©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(1.SchoolofMechanicalEngineering,TianjinUniversity,Tianjin300072,China;2.ShijiazhuangMechanicalEngineeringCollege,Shijiazhuang050003,China)Abstract:Asimplifiedpurelytorsionalconcentratedparametermodelofasinglestage2K2Hspurplanetarygeartransmission(PGT)isdeveloped.Basedonthismodel,naturalfrequenciesandvibrationmodes,whichareclassifiedintotwogroups:planetmodesandrotationalmodes,areinvestigated.Theuniquecharacteristicsofeachtypeofmodesareanalyticallyinvesti2gatedindetail.Thereduced2ordereigenvalueproblemofeachtypeofmodesisstudiedandaclosedformexpressionfornatu2ralmodesofthePGThasbeenderived.Accordingtotheclosedformexpressionsfornaturalmodes,thenaturalfrequencysensitivitiestosystemparametersarerigorouslyinvestigated.Parametersunderconsiderationincludesupportandmeshstiff2ness,componentmass,andmomentsofinertia.Thephenomenonoflociveeringisanalyzed.Withthemodalstrainenergymethod,theinfluenceoflociveeringondynamiccharacteristicisstudiedandalociveeringcriterionisderived.Theconclu2sionsareverifiedbysimulationresult.Keywords:planetarygeartransmissions;freevibration;sensitivityanalysis;lociveering:(1974-),,:[phone];E2mail:[e-mail]7144,:©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.