1394A-semi-physical-tire-model-for-a-vehicle-dynam

FullTerms&Conditionsofaccessandusecanbefoundat=nvsd20Downloadby:[UniversityofArizona]Date:22March2017,At:14:53VehicleSystemDynamicsISSN:0042-3114(Print)1744-5159(Online)Journalhomepage::G.Gim,Y.Choi&S.Kim(2007)Asemi-physicaltiremodelforavehicledynamicsanalysisofhandlingandbraking,VehicleSystemDynamics,45:S1,169-190,DOI:10.1080/00423110701723799Tolinktothisarticle::11Mar2008.SubmityourarticletothisjournalArticleviews:289ViewrelatedarticlesCitingarticles:4ViewcitingarticlesVehicleSystemDynamicsVol.45,Supplement,2007,169–190Asemi-physicaltiremodelforavehicledynamicsanalysisofhandlingandbrakingG.GIM*,Y.CHOIandS.KIMR&Dcenter,HankookTireCo.Ltd,23-1Jang-Dong,Yuseong-Gu,Daejeon,305-725,RepublicofKoreaForasemi-physicalmodel,thispaperfirstpresentsitsbasicconcept,transientsteereffectanddrivingconditions.Themodelexperimentallyformulatesverticalforceasafunctionoftiredeflection,camberangleandlateralforce.Inordertodescribelongitudinalandlateralforcesasfunctionsoftirecharacter-isticparameterssuchasstiffnessandfriction,thebasicformulationsoftheUAtiremodelarere-used.Forself-aligningandoverturningmoments,theapplicationpointsofthreeforcesarefirstexperi-mentallyformulated,andthenthemomentsareexpressedasfunctionsofthethreeforcesandtheirapplicationpoints.Allcharacteristicparametersareexperimentallydeterminedasfunctionsofload,camberangle,slipangle,slipanglesweeprateand/orslipratioforcorneringand/ordriving/braking.Forthepurposeofvalidation,themodelisimplementedintoADAMSandthenitssimulationresultsarecomparedwithmeasurementdataforvarioustestconditions.Keywords:Tiremodel;Tirecharacteristicparameters;Transientsteer;Timedelay;Stressrelaxation;Heatgeneration;Loadedradius;Verticalstiffness1.IntroductionNowadaysthevariousvirtualtestsofavehicleareincreasinglyondemandtoreducedevel-opmentcycletime.Forthepurposeofpredictingrealisticandaccuratevehicleresponsethroughthevirtualtest,atiremodelpreciselyrepresentingrealtirepropertyalreadybecameaninevitablechoice.Tiremodelsrepresentedwithonlytireforcesandmomentsgeneratedbetweenatireandroadsurfaceisnotenoughtoexpressadriver’ssubjectivefeelingontiremotionduringcornering.Duringpracticalhandlingmanoeuvresofavehicle,eachtireingeneralyieldsdifferenttransientresponsedependingoncorneringconditions.Sinceitstransientcharacterizationisquitecomplicatedandalsoitsmeasurementrequiressophisticatedtestdevices,mostofanalyticalstudiesontiremodellingforvehicledynamicsanalysishavebeenbasedon*Correspondingauthor.Email:[e-mail]ISSN0042-3114print/ISSN1744-5159online©2007Taylor&Francis[1–3].Evenvariousnumericalstudieshavealsobeenfocusedonthesecharacteristics[4,5].Loebetal.[6]derivedrelaxationlengthasthetransientresponseofasteeredtire.Intheirstudy,therelaxationlengthwasexpressedasafunctionoflateralandcorneringstiffness.Leeetal.[7]formulatedtheequationsofmotionforthelongitudinalandlateraldisplacementsofthecontactpatchwhichhasalumpedmass.Theytriedtoextracteffectivemass,dampingcoefficientandstiffnessrelatedtothelateraldisplacement.Pacejkaetal.[8]improvedtheirmagicformulawithtransientproperties.Gimetal.[9–11]developedananalyticalmodelforvehicledynamicssimulationswhichprovidesreasonablevaluesoflongitudinalforce,lateralforceandself-aligningmomentwiththerequirementoftheminimuminputdata.Afterwards,theauthorsperformedanotherana-lyticalstudytoovercometheshortcomingofthepreviousapproach[12,13].Forthepurposeofdescribingthecomplicatednonlinearitycharacteristicsofamoderntire,severalimprovedapproachesoftiremodelswithnewconceptualparametersarestillbeingdevelopedandenhanced[14–17].ThegroupofTMPTconsistsoftiremanufactures,tiremodelproviders,MBSprogramprovidersandmembersfromindustryanduniversity.Theyconsideredallessentialaspectsofhowtoestablishtiremodelsandtoapplytheminvehicledynamicssimulations[18].ThemainpurposeofTMPTis‘validationtests’forvariouscomparisonswithmeasurementsand‘capabilitytests’toshowtheperformanceofeachtiremodelinsimulatedbutnotmeasuredconditionsinvariousMBSenvironments.TheotherpurposeofTMPTistoprovideasourceofinformationforselectingapropertiremodelforanindividualsimulationtaskusingacertainMBSsoftware.Inordertosatisfytherequirementsforapracticaltiremodel,asemi-physicalmodelpresentedherefirstincludesthetime-delayeffectoftransientsteeringapplicationcausedduetotirevisco-elasticpropertyexistingbetweenwheelcentreandcontactpatch.Slipanglegeneratedatthecontactpatchisformulatedasafunctionofslipangleinducedatthewheelcentrewithasecond-orfirst-orderdifferentialequation.Transientcharacteristicparametersareempiricallyformulatedasfunctionsofslipanglesweeprate.Verticalforceisexperimentallyformulatedasafunctionoftiredeflection,camberangleandlateralforce.Inordertodes