车辆工程ii－vibration of vehicle system课件

3VibrationofVehicleSystem Freedoms coordinateandvibrationmodesVibrationofvehiclewithonlysecondarysuspensionMethodofderivingdifferentialequationofvehiclesystemVibrationofvehiclewithwithprimaryandsecondarysuspensions Byzhoujinsong2004TongjiUniversity 3VibrationofVehicleSystem Freedoms coordinateandvibrationmodes Degrees offreedom 1bodywith5dofs 52bogieswith5dofs 104wheelsetswith2dofs 8Total 26 i e 52states 3VibrationofVehicleSystem Freedoms coordinateandvibrationmodes Bodyframe 6DOF Bogieframes 2 6DOF Wheelsets 4 6DOF bounceandrollmodesareconstrainedbyrail SuspensionsWheel railcreepforcesBodyFlexibilitiesOthercomponentsorsub systems 3VibrationofVehicleSystem Freedoms coordinateandvibrationmodes Body x z y pitch lateral 3VibrationofVehicleSystem Freedoms coordinateandvibrationmodes x z y bounce yaw Body 3VibrationofVehicleSystem Freedoms coordinateandvibrationmodes x z y forward Body roll 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionFreeVibration Topologyrelationsintheresearchedsystem includingconnectinginformation dimension CoordinatesdefinitionPhysicalproperties Whenbuildingsystemmotionequations especiallypayattentiontothefollowingmainpoints 3VibrationofVehicleSystem Plot makecleartheconnectionrelationsbetweeneachpartDefinecoordinatesMarkthephysicalproperties anddimensions accordingly stepsofderivingmotionequationsare TheMostImportantstepistheFirststep whichsimplifytherealsystemandisthebaseoftheoryanalysis VibrationofvehiclewithonlysecondarysuspensionFreeVibration 3VibrationofVehicleSystem UseNewton ssecondlaw yields VibrationofvehiclewithonlysecondarysuspensionFreeVibration 3VibrationofVehicleSystem Withviscousdamperinthesuspension onehas VibrationofvehiclewithonlysecondarysuspensionFreeVibration parameters Mc 36000kgJcy 2300000kg m 2Ksz 0 36e6N mCsz 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionFreeVibration 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionFreeVibrationNoviscousdamper stepinputresponse 0 08mStepinput f 0 8554T 1 1690 Csz 0 displacement 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionFreeVibrationNoviscousdamper stepinputresponse f 0 9632T 1 0382 displacementdisplacement 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionFreeVibrationNoviscousdamper stepinputresponse c o g Centerplate Responseofthispoint displacement 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionFreeVibrationviscousdamper stepinputresponse parameters Mc 36000kgJcy 2300000kg m 2Ksz 0 36e6N mCsz 0 08mStepinput 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionFreeVibrationviscousdamper stepinputresponse Czs 2500Zeta Zc 0 0258 Czs 2500Zeta Phic 0 0291 displacementdisplacement 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionFreeVibrationviscousdamper stepinputresponse Czs 2500N m s displacementdisplacement 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionFreeVibrationviscousdamper stepinputresponse Czs 10000N m sZeta zc 0 1034 Czs 10000N m sZeta zc 0 1164 displacementdisplacement 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionFreeVibrationWithviscousdamper stepinputresponse displacementdisplacement 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionFreeVibrationWithviscousdamper Thesystemstepinputresponseisasfollowing Czs 20000N m s Czs 0N m s accelerationacceleration 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionForcedVibration Where a amplitudew trackirritatingfrequency Lr trackwavelengthV speed 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionForcedVibration Trackcircularfrequency Timedelay Displacementatthecenteroffirsttruckcanbewrittenas Displacementatthecenterofsecondtruck 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionForcedVibration UseNewton ssecondlaw thedifferentialequationsofmotion Simplifyupperequations onehas So yields 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionForcedVibration Parameters Csz 0N m sZt sin t displacementacceleration 3VibrationofVehicleSystem VibrationofvehiclewithonlysecondarysuspensionForcedVibration Parameters Csz 10000N m sZt sin t displacementacceleration 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemMainmethodstoderivethemotionequationareNewton ssecondlawLagrange sequationHamiltons sprincipleInfluencecoefficientmethod Plot makecleartheconnectionrelationsbetweeneverypartDefinecoordinatesMarkthephysicalproperties anddimensions Beforeusethesemethods onestillhastodofollowingworkstodefinethesystem 3VibrationofVehicleSystem Methodsofderivingdifferentialequationsofvehiclesystem Body V 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethod Differentialmotionequationsusuallyarewritteninmatrixformasfollowing where M inertiamatrixofsystemC dampingmatrixK stiffnessmatrixF forcematrixAllmatricesaredefinedinthesamecoordinate globalcoordinate influencecoefficientmethoddirectlyderivestheMmatrix C Kmatrix canbeobtainedattheaidofcomputer Farewrittenmanuallylatter 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethodFirst derivetheKmatrixdefinecompressingispositive pullingisnegative Generalizedcooridnates stiffnesselements 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethod Itscoefficientmatrixis 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethod stiffnessmatrixis 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethodthen Cmatrixalsodefinecompressingispositive pullingisnegative Generalizedcooridnates dampingelements 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethodinertiamatrix inertiaelements Generalizedcooridnates 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethod so inertiamatrixis so thefreevibrationmotioneq is 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethod whenthereexiststrackirregularity 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethod whenthereexiststrackirregularity Trackinput 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethod so wecanseethismethodhasverygoodflexibility whenmored o fsandelementsaretobetakenintoconsideration justaugmenttheAmatrix thecomplexityincreasesonlylinearly so thevibrationmotioneq Withtrackirregularityinputisthesameformas note wherethevariablevectoris 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethod so motionequationsshouldbewrittenas but thelastfourwheelsetmotionequationsshouldbedeleted becausetheyareconstrained andequaltotrackinputaccordingtoassumption where 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemInfluencecoefficientmethod astotheFmatrix discomposetheforcesactedonvehiclepartsintogeneralizedforces definetheirsignsaccordingtothegeneralizedcoordinates thenFmatrixformed asaexample seethefigureatrightside FeccentricfromcenterlineofcarbodysothematrixFis f l so theforcedvibrationdifferentialeq is 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemLagrange sequation Body V 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemLagrange sequation Asasimpleexample derivethemotioneq Offollowingsystem 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemLagrange sequation Kineticenergy Potentialenergy Dissipationfunction 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemLagrange sequation Kineticenergy potentialenergy 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemLagrange sequation Dissipationfunction so Usethesamemethod wehave 3VibrationofVehicleSystem MethodsofderivingdifferentialequationsofvehiclesystemHamilton sprinciple AnotheralternateapproachforderivingthedifferentialequationsofmotionfromscalarenergyquantitiesisHamilton sprinciple OneofthemostapplicablevariationaltechniqueisHamilton sprinciple whichstatesthat WhereTisthesystemkineticenergy Visthesystempotentialenergy andisthevirtualworkofnonconservativeforces 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Body V 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Asanalternativemethod thetraditionalNewton ssecondlaw sareusedtoderivethemotionequationsasthetextbookdemonstrates themotionequationsare Simplifyas 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Where 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Considerthecarbodyandtruckmotionequations theyarecoupled soareanalyzedtogether Body Zt Mc Mt 4Ksz 8Kpz where Zc 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Theirsolutionsareassumedas Body Zt Mc Mt 4Ksz 8Kpz A B amplitudeofcarbodyandtruck psystemnaturalfrequency alphi phaseangle Substitutethesolutionintomotionequations yields Zc Characteristicfunctions SamewiththeSDOFsystem onehas 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Twod o fs therearetwonaturalfrequencies Solvethecharacteristicfunctions theloweroneis Body Zt Mc Mt 4Ksz 8Kpz Zc Theotheroneis 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Solutionare Body Zt Mc Mt 4Ksz 8Kpz Zc Modeshape Lowfrequency Highfrequency Atlowfrequency 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Body Zt Mc Mt 4Ksz 8Kpz Zc 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Body Zt Mc Mt 4Ksz 8Kpz Zc Asanexample aVehicleparameters Mc 36000kgMt 2100kgKsz 260000N mKpz 300000N m Whenzt1 0 0 02 zt2 0 0 02 zc 0 02 3 0670 thesimulationresultinmatlab simulinkisasfollowing fst1 0 1641m fst2 0 3392fst fst1 3 0670 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Carbodyverticaldisplacement Truckframeverticaldisplacement 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Truckframeverticalacceleration 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping V 0 08mStepinput Theresponseisasfollowing 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Carbodyverticaldisplacement Carbodypitchangleresponse 3VibrationofVehicleSystem VibrationofvehiclewithwithprimaryandsecondarysuspensionsAnalysisoffreevibration withoutviscousdamping Truckframeverticaldisplacement Truckframepitchangleresponse IncludingthreefrequenciesinthewaveWhy 3VibrationofVehicleSystem Multi DegreeofFreedomSystem Inthecaseofundampedfreevibrationofmulti degreeoffreedomsystems Assumeasolutionintheform Substitutetheupperformintothefirstequation leadto Whichleadsto Ascomparing standardeigenvalueproblemistheformasfollowing 3VibrationofVehicleSystem Multi DegreeofFreedomSystem Thisequationhasanontrivialsolutionifandonlyifthecoefficientmatrixissin