ANSYS转子动力学分析

ANSYSANSYS•••••yybearingxzδδshaftrotorshaftbearingωCoriolis•–gyroscopic•–CoriolisCoriolisCoriolisCoriolis••,:globalCartesian(OXYZ)(O'X'Y'Z')yY’yYPP’r’X’Z’StationaryFrameRotatingFrameRroxZStationaryFrameRzDynamicequationinrotatingreferenceframe⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=−+++F}r]){uspin[KK(}ru]){cor[CC(}ru{M&&&Coriolisforce}u]{corioC[}c{fr&=∫ΦωΦρ=,T2]corC[dvCoriolismatrix⎥⎥⎥⎤⎢⎢⎢⎡ω−ωωω−=ω00xzyz⎥⎥⎦⎢⎢⎣ωω−0xyDynamicequationinstationaryreferenceframe⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=+++F{u}K}u]){gyr[CC(}u{M&&&⎭⎩⎥⎦⎢⎣⎥⎦⎢⎣⎥⎦⎢⎣gyGyroscopicmoment}u]{gyroC[}g{f&=••••••––––•––––CFD–CFD••••••(oilfilmbearings)(oilfilmbearings)••••••StationaryFrameRotatingFrame•••()•••()••Campbell••••MODAL,HARMONICandSTATIC,MODAL,HARMONIC,TRANSIENTTRANSIENTStationaryFrameRotatingFrameMASS21SHELL181BEAM4,PIPE16,MASS21,SOLID45,SOLID95,SOLID185,SOLID186,MASS21,SHELL181,PLANE182,PLANE183,SOLID185,SOLID186,SOLID187BEAM188,,,BEAM188,BEAM189.SOLID187,BEAM188,BEAM189,SOLSH190,SHELL281.PLANE223,SOLID226SOLID227SOLID226,SOLID227Modal,Transient,HarmonicStatic,Modal,Transient,HarmonicHarmonic•Omegacommand–(OMEGA,CMOMEGA)g•Corioliscommand–(CORIOLIS)•Campbelldiagram-(PLCAMPBPRCAMPBCAMPB)•Campbelldiagram-(PLCAMPB,PRCAMPB,CAMPB)•Backward/forwardwhirl&instabilityMlil•Multi-spoolrotors•Whirlorbitplots–(PLORB,PRORB)•Bearingelement–(COMBIN214)•Unbalanceresponse(SYNCHRO)Unbalanceresponse(SYNCHRO)OMEGA/CMOMGACommandOMEGA/CMOMGACommand•OMEGA:•Static•Harmonic-Fullormodesuperposition•Transient-Fullormodesuperposition•CMOMEGA:•OMEGAX,OMEGAY,andOMEGAZ–CMOMEGAs:•Static•Harmonic-Full•Transient-FullCoriolisCommandCoriolisCommand•OMEGAorCMOMEGACORIOLISCoriolis••Coriolis–Static-–Modal––Harmonic-FullorQRDAMP-–Transient-FullormodeQRDAMP-•CORIOLIS,Option,--,--,RefFrame–Option(Activate/Deactivate)–RefFrame(Rotating/Stationary)CampbellDiagramCampbellDiagrampgpg•ω,Campbell•:PLCAMP,PRCAMP,CAMPB–PLCAMP:Campbelldiagram–PRCAMP:PRCAMP:–CAMPB:CampbellCampbellCampbellppCampbellDiagramCampbellDiagram……ωywhirlmotionxEllipticalhirlorbitAsfrequenciessplitwithincreasingspinEllipticalwhirlorbitAsfrequenciessplitwithincreasingspinvelocity,ANSYSidentifies:•forward(FW)andbackward(BW)whirl•stable/unstableoperation•criticalspeeds(PRCAMP)••:A&BФ•PLORB()()•PRORB(print)andPLORB(plot)Zrotationaxis:xABФYФWhirlOrbitPlotsWhirlOrbitPlotsWhirlOrbitPlotsWhirlOrbitPlotsWhirlOrbitPlotsWhirlOrbitPlotsWhirlOrbitPlotsWhirlOrbitPlotsPrintorbit:PRORBPlotorbit:PLORBPRINTORBITSFROMNODALSOLUTION*****ANSYSVERIFICATIONRUNONLY*****DONOTUSERESULTSFORPRODUCTIONLOADSTEP=1SUBSTEP=4LOADSTEP1SUBSTEP4RFRQ=0.0000IFRQ=2.5606LOADCASE=0SHAPEATT=0,ORBITNODEUXUYUZABPSI10.00000.00000.00000.00000.00000.000020.00000.00000.00000.00000.00000.000020.00000.00000.00000.00000.00000.000030.00000.3823-0.7192E-120.38230.38230.000040.00000.7071-0.1132E-110.70710.70710.000050.00000.9230-0.1059E-110.92300.92300.0000orbitcharacteristics(COMBIN214)(COMBIN214)()()dhl–2Dspring/damperwithcross-couplingterms––⎬⎫⎨⎧=⎬⎫⎨⎧⎥⎤⎢⎡+⎬⎫⎨⎧⎥⎤⎢⎡xxfxyfxxxfxyfxxFuKKuCC&⎭⎬⎩⎨=⎭⎬⎩⎨⎥⎦⎢⎣+⎭⎬⎩⎨⎥⎦⎢⎣yyfyyfyxyfyyfyxFuKKuCC&()()()ω=ffCC()ω=ffKK(COMBIN214)(COMBIN214)()()!Exampleoftableparametersinputomega1=0.KYY1=1.e+4KZZ1=1e+7KZZ1=1.e+7omega2=250.KYY2=1.e+5KZZ2=1.e+7omega3=500Tabularinputforomega3=500.KYY3=1.e+6KZZ3=1.e+7/comTabulardatadefinitionREALconstantkk()/com,Tabulardatadefinition*DIM,KYY,table,3,1,1,omegsKYY(1,0)=omega1,omega2,omega3KYY(1,1)=KYY1,KYY2,KYY3*DIMKZZtbl311k=k(ω)c=c(ω)*DIM,KZZ,table,3,1,1,omegsKZZ(1,0)=omega1,omega2,omega3KZZ(1,1)=KZZ1,KZZ2,KZZ3et,3,214k32lkeyopt,3,2,1!YZplaner,1,%KYY%,%KZZ%ω•(ω)•(2*ω)(2ω)•,,,(s*ω)•(0.5*ω)••SYNCHRO•(F=Ω2*Unb)……LoadvectorLoadvector[][][]⎬⎫⎨⎧⎬⎫⎨⎧⎬⎫⎨⎧⎬⎫⎨⎧yyyyFuuuKCM&&&[][][]⎭⎬⎫⎩⎨⎧=⎭⎬⎫⎩⎨⎧⎭⎬⎫⎩⎨⎧+⎭⎬⎫⎩⎨⎧zyzyzyzyFuuuKCM&&&SpinωaboutX-axisLoadvectorSynchronous(s=1):UnbalanceforceFy=F0ω2cos(ωt+α)Synchronous(s1):UnbalanceforceF0=m*r(mass*distancetoaxis)FyF0ωcos(ωtα)Fz=F0ω2sin(ωt+α)AhElfFFy=F1cos(sωt+α)Asynchronous:ExternalforceF1y1()Fz=F1sin(sωt+α)αisthephaseangleoftheforce(usedforseveralforceswithdifferentdirections)αisthephaseangleoftheforce(usedforseveralforceswithdifferentdirections)sistheratioofthefrequencyofexcitationandthefrequencyofthespin:tjeFcosFFωωttjjbbyeFcosFFω==t()2/-tcosFsinFFbbzπωω==t!Exampleofinputfile/7tjbzejFFω−==zF202bFmrFω=ω=z/prep7…F0=m*rmtωrF,node,fy,F0F,node,fz,,-F0yFytωr•••••UnbalanceresponseofatwinspoolrotorTwinspoolrotormodel-2spools(BEAM188)-4bearings(COMBI214)-4disks(MASS21)Disksarenotvisible(MASS21)Unbalanceresponseofatwinspoolrotorf0=70e-6!unbalanceF7FYf0/SOLUCampbellplotofinnerspoolplcamp,,1.0,rpm,,innSpoolF,7,FY,f0F,7,FZ,,-f0finiantype,harmicsynchro,,innSpoolUnbalanceresponseofatwinspoolrotorOrbitPlotsTransientorbitalmotion–rotorinstabilityunsymmetricunsymmetricbearingsModalanalysisstableat30,000rpm(3141.6rad/s)unstableat60,000rpm(6283.2rad/sec)negativerealpartpositiverealparteigenfreqs.fromQRDAMPeigensolverTransientorbitalmotion–rotorinstabilityunsymmetricTransientybearingsstableat30000rpmunstableat60000Transientdynamicanalysisstableat30,000rpm(3141.6rad/sec)unstableat60,000rpm(62