ADAMS路面模型和輪胎UA模型中各全參數(shù)含義

實用文案實用文案標準文檔標準文檔2DRoadTypesTheavailableroadtypesare:?DRUMTiretestdrum(requiresazero-speed-capabletiremodel).FLAT-Flatroad.?PLANKSingleplankperpendicular,orinobliquedirectionrelativetox-axis,withorwithoutbeveledges.?POLY_LINE-Piece-wiselineardescriptionoftheroadprofile.Theprofilesfortheleftandrighttrackareindependent.?POT_HOLESinglepotholeofrectangularshape.?RAMPSingleramp,eitherrisingorfalling.?ROOFSingleroof-shaped,triangularobstacle.SINE-Sinewaveswithconstantwavelength.?SINE_SWEEPSinewaveswithdecreasingwavelengths.STOCHASTIC_UNEVEfSyntheticallygeneratedirregularroadprofilesthatmatch^measuredstochasticpropertiesoftypicalroads.Theprofilesforleftandrighttrackareindependent,ormayhaveacertaincorrelation.Examplesof2DRoadsSamplefilesforalltheroadtypesforAdams/CarareinthestandardAdams/Cardatabase:install_dir /shared_car_database.cdb/roads.tbl/SamplefilesforalltheroadtypesforAdams/Tirearein:install_dir /solver/atire/SamplefilesforalltheroadtypesforAdams/Chassisarein:install_dir /achassis/examples/rdf/Notethatyoumustselectaspecificcontactmethod,suchaspoint-followerorequivalentplane,todefinehowtheroadswillinteractwiththetires.Notallcombinationsofroad,tire,andcontactmethodsarepermitted.AllowablecombinationsareexplainedinTireModelshelpunderthedescriptionofthespecifictiremodel.2DRoadModelParametersThe[PARAMETERS]blockmustcontainthefollowingdata,someofwhichareindependentofthetypeofroad.Learnaboutparameters:IndependentofRoadTypeDrumFlatPlank>Polyline

PotholeRampRoof>Sine>SweepStochasticUnevenParametersIndependentofRoadTypeThefollowingparametersarerequiredregardlessoftheroadtype.[PARAMETERS]IndependentofRoadTypeTheparameter:Indicates:offsetAconstantshiftoftheroadheightvalues.Foraflatroadandoffset=0,theroadheightiszero.rotation_angle_xy_planeRotationangleofthexy-planeabouttheroadz-axis.InAdams/Car,vehiclesstartrunningalongthenegativex-axisbydefault.Italsomightbeconvenienttousepositivex-valuesinthe.rdf.Inthatcase,chooserotation_angle_xy_plane=180(deg).muRoadfrictioncorrectionfactor(notthefrictionvalueitself),tobemultipliedwiththerespectiverubberfrictionvaluesofthetiremodel.Defaultsetting:mu=1.0.ParametersforRoadTypeofDrumIfROAD_TYPE=drum,thendefinethefollowingparameters:[PARAMETERS]forRoadTypeofDrumTheparameter:Indicates:diameterDiameterofthetiretestdrum.Whenthediameteris<0,theroadmodelsimulatestheouterdrum.Withpositiverollingspeed,theinnerdrumwillrotateclockwiseandtheouterdrumcounter-clockwise.vRollingspeedofdrumsurface(besuretokeepvehicleatspeedzero,otherwise,thewheelsmoveawayfromthedrum).Drumcenterislocatedatx=0.number_cleatsNumberofextracleatsondrum(number_cleats=0allowed).cleat_heightHeightofextracleats.cleat_starting_angleDrumanglecoordinateoffirstcleat.

cleat_lengthLengthofcleat,measuredincircumferentialdirectionofdrum.cleat_bevel_edge_lengthLengthofbeveledgeofcleat,measuredincircumferentialdirectionofdrum.Beveledgehas45 °slope.acceleration_timeOptionaltimespanatthebeginningofthesimulation,duringwhichthedrumisacceleratedtoanominalrollingspeed.ParametersforRoadTypeofFlatIfROAD_TYPE=flat,thennofurtherparametersarerequired.ParametersforRoadTypeofPlankIfROAD_TYPE=plank,thendefinethefollowingparameters:[PARAMETERS]forRoadTypeofPlankTheparameter:Indicates:heightHeightofplank.startStartofplank(traveldistanee).lengthLengthofplank,measuredalongx-axis.bevel_edge_lengthLengthofbeveledge,measuredalongx-axis.Beveledgehas45°slope.Whenbevel_edge_length<0,roundedcornersinsteadofbeveledgesareused.Inthiscase,radiusofthecorneris|bevel_edge_length|.directionDirectionofplankrelativetoy-axis.Iftheplankisplacedcrosswise,direction=0.Iftheplankisalongthex-axis,direction=90.ParametersforRoadTypeofPolylineIfROAD_TYPE=poly_line,thenthe[PARAMETERS]blockmusthavea(XZ_DATA)subblock.Thesubblockconsistsofthreecolumnsofnumericaldata:Columnoneisasetofx-valuesinascendingorder.?Columnstwoandthreearesetsofrespectivez-valuesforleftandrighttrack.Thefollowingisanexampleofthefull[PARAMETERS]Bodyforaroadtypeofpolyline:$ PARAMETERS[PARAMETERS]OFFSET=0ROTATION_ANGLE_XY_PLANE=180$(XZ_DATA)0001000100502000-1000100-1001005004000-100100TheXZ_DATAsubblockcanbeextremelylarge.Inthiscase,onlytheportionthatisneededatthemomentisloaded.Tofacilitateefficientreloadingwhilesimulationisrunning,donotuseanycommentlinesinasubblockthatcontainsmorethan2000lines.ParametersforRoadTypeofPotholeIfROAD_TYPE=pot_hole,thentheparametersare:[PARAMETERS]DataforRoadTypeofPotholeTheparameter:Indicates:depthDepthofpothole.startStartofpothole(traveldistanee).lengthLengthofpothole.ParametersforRoadTypeofRampIfROAD_TYPE=ramp,thentheparametersare:[PARAMETERS]DataforRoadTypeofRampTheparameter:Indicates:heightHeightoframp.startStartoframp(traveldistanee).slopeSlopeoframp.1means45 °.ParametersforRoadTypeofRoofIfROAD_TYPE=roof,thentheparametersare:[PARAMETERS]DataforRoadTypeofRoofTheparameter:Indicates:heightHeightofroof(triangle-shapedobstacle).startStartofroof(traveldistanee).lengthLengthofroof,measuredalongx-axis.ParametersforRoadTypeofSineIfROAD_TYPE=sine,thentheparametersare:[PARAMETERS]DataforRoadTypeofSineTheparameter:Indicates:

amplitudeAmplitudeofsinewave( a).wave_length￡Wavelengthofsinewave( c).startStartofsinewaves(traveldistanee)( ss).Theroadheight,z,isgivenby:衛(wèi))=a?ParametersforRoadTypeofStochasticUnevenAstochasticunevenroadprofilebothforleftandrightwheelsisgenerated,withpropertiesveryclosetomeasuredroadprofiles.Inafirststep,discretewhitenoisesignalsareformedonthebasisofnearlyuniformlydistributedrandomnumbers.Twoofthesenumbersareassignedtoevery10mmoftravelpath.Thedistributionoftheserandomnumbersisapproximatedbysummingseveralequallydistributedrandomnumbers,takingadvantageofthe 'lawoflargenumbers'ofmathematicalstatistics.Next,thesevaluesareintegratedwithrespecttotraveldistanee,usingasimplefirstordertime-discreteintegrationfilter.Theindependentvariableofthatfilterisnottime,buttravelpath.Thatiswhythefiltercutofffrequencyiscontrolledbyapathconstantinsteadofatimeconstant.Thefilterprocessresultsintwoapproximaterealizationsofwhitevelocitynoise;thatis,twosignals,thederivativesofwhichareclosetowhitenoise.Signalswiththatpropertyareknownasroadprofileswithwaviness2.Severalinvestigationsinthepastshowedthatthewavinessderivedfrommeasuredroadspectraldensitiesrangesfromabout1.8to2.2..Thisis=0.0,andThelaststepistolinearlycombinethetworealizationsoftheabove2i(5).Thisis=0.0,andprocess: , ,resultingintheleftandrightprofiledonesuchthatthetwosignalsarecompletelyindependentifidenticalifIfROAD_TYPE=stochastic_uneven,thentheparametersare:[PARAMETERS]forRoadTypeofStochasticUnevenTheparameter:Indicates:intensityVariabletocontrolintensityofwhitevelocitynoise,whichapproximatesmeasuredspectraofroadprofilesfairlywell.path_constantVariabletocontrolhigh-passintegrationfilter.correlation_rlVariabletocontrolcorrelationbetweenleftandrighttrack:?f0,nocorrelation.

?f1,completecorrelation(thatis,lefttrack=righttrack).Canbeanyvaluebetween0and1.startStartofunevenness(traveldistanee).ParametersforRoadTypeofSweepIfROAD_TYPE=sine_sweep,thentheparametersare:[PARAMETERS]DataforRoadTypeofSineSweepTheparameter:Indicates:startStartofsweptsinewave(traveldistanee)( ).endEndofsweptsinewave(traveldistanee)( ).amplitude_at_startAmplitudeofsweptsinewaveatstarttraveldistanee( *).amplitude_at_endAmplitudeofsweptsinewaveatendtraveldistanee( 叫).wave_length_at_startWavelengthofsweptsinewaveastarttraveldistanee(%nwave_length_at_endWavelengthofsweptsinewaveatendtraveldistanee.Mustbelessthanorequaltowave_length_at_start( ).sweep_type?sweep_type=0:frequencyincreaseslinearlywithrespecttotraveldistanee.?sweep_type=1:wavelengthdecreasesbyaeonstantfactorpercycle.Dependingonthevalueofsweep_type,theroadheightisgivenbythefollowingfunetions,where:f七aM人=￡Linearsweep:(sweep_type=0)Thefrequencyincreaseslinearly?withrespecttotraveldistanee.Theroadheightvalue z(s)asfunetionoftraveldistanee sisalculatedasfollows:rt ,3「叫心7畀.（（占呦=帆十（D丿3?乜十“-昭丿3勺Notethefactor2inthedenominatorisnotanerror.Theactualfrequency(=derivativeofthesinefunetionargumentwithrespecttotravelpath,dividedby - ;thisisnotequaltothatfactorthatismultipliedby 丨? -1inthesinefunetion)isgivenbythefollowing:

Logarithmicsweep:(sweep_type=1)witheverycycle,thewave?lengthdecreasesbyaconstantfactor.Theroadheightvalueiscalculatedasfollows:sinwhere:.Theisthetravelpathwheretheoreticallyaninfinitelyhigh.Thefrequencywasreached,measuredrelativetosweepstartactualfrequencyisgivenby:UsingtheUA-TireModelLearnaboutusingtheUniversityofArizona(UA)tiremodel:?BackgroundInformation?TireModelParameters?ForceEvaluation?OperatingMode:USE_MODE?TireCarcassShape?PropertyFileFormatExampleBackgroundInformationforUA-TireTheUniversityofArizonatiremodelwasoriginallydevelopedbyDrs.P.E.NikraveshandG.Gim.Refereneedocumentation:G.Gim,VehicleDynamicSimulationwithaComprehensiveModelforPneumaticTires,PhDThesis,UniversityofArizona,1988.TheUA-Tiremodelalsoincludesrelaxationeffects,bothinthelongitudinalandlateraldirection.TheUA-Tiremodelcalculatestheforcesatthegroundcontactpointasafunctionofthetirekinematicstates,seeInputsandOutputoftheUA-TireModel.Adescriptionyoftheinputslongitudinalslipk,sideslipaandcamberangle canbefoundinpAboutTireKinematicandForceOutputs.Thetiredeflection anddeflectionvelocityaredeterminedusingeitherapointfollowerordurabilitycontactmodel.Formoreinformation,see RoadModelsinAdams/Tire.Adescriptionofoutputs,longitudinalforceFx,lateralforceFy,normalforceFz,rollingresistaneemomentMyandselfaligning

momentMzisgiveninAboutTireKinematicandForceOutputs.Therequiredtiremodelparametersaredescribedin TireModelParameters.InputsandOutputoftheUA-TireModelForcesatthecontactpatch(X

PpTiremodelparameters

(storedintirepropertyfile)^『Fz^ywzDefinitionofTireSlipQuantitiesSlipQuantitiesatCombinedCorneringandBraking/TractionForcesatthecontactpatch(X

PpTiremodelparameters

(storedintirepropertyfile)^『Fz^ywzDefinitionofTireSlipQuantitiesSlipQuantitiesatCombinedCorneringandBraking/TractionVrTheIongitudinalslipvelocityVsxintheSAE-axissystemisdefinedusingtheIongitudinalspeedVx,thewheelrotationalvelocity 」,andtheeffectiverollingradiusRe:匕工=匕-。陷Thelateralslipvelocityisequaltothelateralspeedinthecontactpointwithrespecttotheroadplane:Thepracticalslipquantities '(longitudinalslip)and (slipangle)arecalculatedwiththeseslipvelocitiesinthecontactpoint:K-andtnnft=:―-WhentheUATireisusedfortheforcecalculationtheslipquantitiesduringpositiveVsx(driving)aredefinedas:K= andtanot=TherollingspeedVrisdeterminedusingtheeffectiverollingradiusRe:Notethatforrealistictireforcestheslipangle 「islimitedto45degreesandthevlongitudinalslipSs(= ■)inbetween-1(lockedwheel)and1.Laggedlongitudinalandlateralslipquantities(transienttirebehavior)Ingeneral,thetirerotationalspeedandlateralslipwillchangecontinuouslybecauseofthechanginginteractionforcesinbetweenthetireandtheroad.Oftenthetiredynamicresponsewillhaveanimportantroleontheoverallvehicleresponse.Formodelingthisso-calledtransienttirebehavior,afirst-ordersystemisusedbothfor|Cthelongitudinalslip asthesideslipangle,.Consideringthetirebeltasastretchedstring,whichissupportedtotherimwithlateralspring,thelateraldeflectionofthebeltcanbeestimated(seealsoreferenee[1]).Thefigurebelowshowsatop-viewofthestringmodel.StretchedStringModelforTransientTireBehaviorWhenrolling,thefirstpointhavingcontactwiththeroadadherestotheroad(noslidingassumed).Therefore,alateraldeflectionofthestringwillarisethatdependsontheslipanglesizeandthehistoryofthelateraldeflectionofpreviouspointshavingcontactwiththeroad.Forcalculatingthelateraldeflectionv1ofthestringinthefirstpointofcontactwiththeroad,thefollowingdifferentialequationisvalidduringbrakingslip:1則v,一—十——=tanta)+aQ

withtherelaxationlength ■inthelateraldirection.Theturnslip ，?canbeneglectedatradiilargerthan10m.Thisdifferentialequationcannotbeusedatzerospeed,butwhenmultiplyingwithVx,theequationcanbetransformedto:爲少十I小"出Whenthetireisrolling,thelateraldeflectiondependsonthelateralslipspeed;atstandstill,thedeflectiondependsontherelaxationlength,whichisameasureforthelateralstiffnessofthetire.Therefore,withthisapproach,thetireisrespondingtoaslipspeedwhenrollingandbehavinglikeaspringatstandstill.WhentheUATireisusedfortheforcecalculations,atpositiveVsx(traction)theVxshouldbereplacedbyVrinthesedifferentialequations.Asimilarapproachyieldsthefollowingforthedeflectionofthestringinlongitudinaldirection:乞石十出H=-為乙Nowthepracticalslipquantities, -'and' ',aredefinedbasedonthetiredeformation:kct aoiThesepracticalslipquantities and'areusedinsteadoftheusual 一anddefinitionsforsteady-statetirebehavior.kVlow_xandkVlow_yarethedampingratesatlowspeedappliedbelowtheLOW_SPEED_THRESHOLDspeed.FortheLOW_SPEED_DAMPINGparameterinthetirepropertyfileyields:kVlowx=100 ?kVlowy=LOWSPEEDDAMPINGNote:Ifthetirepropertyfile'sREL_LEN_LONorREL_LEN_LAT=0,thensteady-statetirebehavioriscalculatedastireresponseonchangeoftheslipandtirebehavioriscalculatedastireresponseonchangeoftheslipandTireModelParametersDefinitionofTireParametersSymbol:Nameintirepropertyfile:Units*:Description:r1UNLOADED_RADIUSLTireunloadedradiuskzVERTICALSTIFFNESSF/LVerticalstiffnessczVERTICAL_DAMPINGFT/LVerticaldampingCrROLLING_RESISTANCELRollingresistaneeparameterCsCSLIPFLongitudinalslipstiffness,

K=OCALPHAF/ACorn(遲Oueringsior=0tiffness,CCGAMMAF/ACamberstiffness,y=0UMINUMIN-Minimumfrictioncoefficient(Sg=1)UMAXUMAX-Maximumfrictioncoefficient(Ssg=0)°xREL_LEN_LONLRelaxationlengthinlongitudinaldirection°yREL_LEN_LATLRelaxationlengthinlateraldirection*L=length,F=force,A=angle,T=timeForceEvaluationinUA-TireNormalForce?SlipRatios?FrictionCoefficientNormalForceThenormalforceFziscalculatedassumingalinearspring(stiffness:kz)anddamper(dampingconstantcz),sothenextequationholds:Ifthetirelosescontactwiththeroad,thetiredeflection anddeflectionvelocitybecomezerosotheresultingnormalforceFzwillalsobezero.ForverysmallpositivetiredeflectionsthevalueofthedampingconstantisreducedandcareistakentoensurethatthenormalforceFzwillnotbecomenegative.Insteadofthelinearverticaltirestiffness cz,alsoanarbitrarytiredeflection-loadcurvecanbedefinedinthetirepropertyfileinthesection[DEFLECTION_LOAD_CURVE],seealsothePropertyFileFormatExample.Ifasectioncalled[DEFLECTION_LOAD_CURVE]exists,theloaddeflectiondatapointswithacubicsplineforinter-andextrapolationareusedforthecalculationoftheverticalforceofthetire.NotethatyoumustspecifyVERTICAL_STIFFNESSinthetirepropertyfilebutitdoesnotplayanyrole.SlipRatiosForthecalculationoftheslipforcesandmomentsanumberofslipratioswillbeintroduced:

LongitudinalSlipRatio:SsTheabsolutevalueoflongitudinalslipratio,Ss,isdefinedas:Q二|k|Wherekislimitedtobewithintherange-1to1.LateralSlipRatios:Sa,Sg,SagctThelateralslipratioduetoslipangle,S ,isdefinedas:itanctjduringbraking(1—S5)|tma|LongitudinalSlipRatio:SsTheabsolutevalueoflongitudinalslipratio,Ss,isdefinedas:Q二|k|Wherekislimitedtobewithintherange-1to1.LateralSlipRatios:Sa,Sg,SagctThelateralslipratioduetoslipangle,S ,isdefinedas:itanctjduringbraking(1—S5)|tma|duringfructionThelateralslipratioduetoinclinationangle,SSy-燭口了|,isdefinedas:Acombinedlateralslipratioduetoslipandinclinationangles,S"f,isdefinedas:duringbrakingduringtractionwhereisthelengthofthecontactpatch.=min(IQS*a-y)ComprehensiveSlipRatio: SsagAcomprehensiveslipratioduetolongitudinalslip,slipangle,andinclinationanglemaybedefinedas:九丫= 叭FrictionCoefficientTheresultantfrictioncoefficientbetweenthetiretreadbaseandtheterrainsurfaceOtyisdeterminedasafunctionoftheresultantslipratio(Ss )andfrictionparameters(UMAXandUMIN).Thefrictionparametersareexperimentallyobtaineddatarepresentingthekinematicpropertybetweenthesurfacesoftiretreadandtheterrain.AlinearrelationshipbetweenSs 'and1,thecorrespondingroad-tirefrictioncoefficient,isassumed.Thefigurebelowdepictsthisrelationship.LinearTire-TerrainFrictionModel

Slip—?Slip—?Thiscanbeanalyticallydescribedas:m=UMAX-(UMAX-UMIN)*SsagThefrictioncircleconceptallowsfordifferentvaluesoflongitudinalandlateralfrictioncoefficients( xand1y)butlimitsthemaximumvalueforbothcoefficientsto.Seethefigurebelow.FrictionCircleConceptTherelationshipthatdefinesthefrictioncirclefollows:or：'or：'-；andwhere:cosp=―—arid疵口［5=—2cry ^saySlipForcesandMomentsTocomputelongitudinalforce,lateralforce,andself-aligningtorqueintheSAEcoordinatesystem,youmustperformatesttodeterminethepreciseoperatingconditions.Theconditionsofinterestare:Case1:0?Case2:?0andC'SCSCase3:0andC'SCS?ForcesandmomentsatthecontactpointThelateralforceFhcanbedecomposedintotwocomponents:FhaandFhg.Thetwo0.c,componentsareinthesamedirectionifa ?0.c,Case1.ag<0Beforecomputingthelongitudinalforce,thelateralforce,andtheself-aligningtorque,someslipparametersandamodifiedlateralfrictioncoefficientshouldbedetermined.IfaslipratioduetothecriticalinclinationangleisdenotedbySthenitcanbeevaluatedas:IfSscrepresentsaslipratioduetothecritical(longitudinal)slipratio,thenitcanbeevaluatedas:￡=3卩才IfaslipratioduetothecriticalslipangleisdenotedbySdeterminedas:'■c,thenitcanbeIfaslipratioduetothecriticalslipangleisdenotedbySdeterminedas:whenSs Ssc.Thetermcriticalstandsforthemaximumvaluewhichallowsanelasticdeformationofatireduringpureslipduetopureslipratio,slipangle,orinclinationangle.Wheneveranyslipratiobecomesgreaterthanitscorrespondingcriticalvalue,anelasticdeformationnolongerexists,butinsteadcompleteslidingstaterepresentsthecontactconditionbetweenthetiretreadbaseandtheterrainsurface.AnondimensionalslipratioSnisdeterminedas:

巧=（沖化卩一（3<7廬丿‘6=-[(C;Ss)2+(Ca5a)-]Anondimensionalcontactpatchlengthisdeterminedas:isevaluatedas:AmodifiedlateralfrictioncoefficientwhereG=1_名isevaluatedas:Amodifiedlateralfrictioncoefficientwhereistheavailablefrictionasdeterminedbythefrictioncircle.Todeterminethelongitudinalforce,thelateralforce,andtheself-aligningtorque,considertwosubcasesseparately.Thefirstcaseisfortheelasticdeformationstate,whiletheotherisforthecompleteslidingstatewithoutanyelasticdeformationofatire.Thesetwosubcasesaredistinguishedbyslipratioscausedbythecriticalvaluesoftheslipratio,theslipangle,andtheinclinationangle.Specifically,ifallofslipratiosaresmallerthanthoseoftheircorrespondingcriticalvalues,thenthereexistsanelasticdeformationstate,otherwisethereexistsonlycompleteslidingstatebetweenthetiretreadbaseandtheterrainsurface.Y<y < Ct<(X(i)ElasticDeformationState: S，Sc,Ss Ssc,andS ScIntheelasticdeformationstate,thelongitudinalforceF ,thelateralforceFandthreecomponentsoftheself-aligningtorquearewrittenasfunctionsoftheelasticstiffnessandtheslipratioaswellasthenormalforceandthefrictioncoefficients,suchas:化=十宀行（1-嗎十2身）G 求十叩氏（1-3時+2￡）十寧where:?r=■■■.-■--where:?r=■■■.-■--stheoffsetbetweenthewheelplanecenterandthetiretreadbase.F—P/4base.F—P/4issettozeroifitisnegative.thelengthofthecontactpatch.MZistheportionoftheself-aligningtorquegeneratedbytheslipangleMzs'■andMzsareothercomponentsoftheself-aligningtorqueproducedbythelongitudinalforce,whichhasanoffsetbetweenthewheelcenterplaneandthetiretreadbase,duetotheslipangleandtheinclinationangle,respectively.Thetreadbase,duetotheslipangleandtheinclinationangle,respectively.TheCt Ct Vself-aligningtorqueMzisdeterminedascombinationsofMz ,MzsandMzs(ii)CompleteSlidingState: S-Sc,Ss-Ssc,andS' -ScInthecompleteslidingstate,thelongitudinalforce,thelateralforce,andthreecomponentsoftheself-aligningtorquearedeterminedasfunctionsofthenormalforceandthefrictioncoefficientswithoutanyelasticstiffnessandslipratioas:Case2:「 0andS「 CSAsinCase1,aslipratioduetothecriticalvalueoftheslipratiocanbeobtainedas:%=刃hyAslipratioduetothecriticalvalueoftheslipanglecanbefoundas:whenSsSsc.ThenondimensionalslipratioSn,isdeterminedas:5 — where:6=(旳尸丿；一([匚廬丫戶比=心匸4巧=-[(C;S5)2+(CaSa)^]ThenondimensionalcontactpatchlengthInisfoundfromtheequationIn=1-Sn,andthemodifiedlateralfrictioncoefficient isexpressedas:Forthelongitudinalforce,thelateralforceandtheself-aligningtorquetwosubcasesshouldalsobeconsideredseparately.AslipratioduetothecriticalvalueoftheinclinationangleisnotneededheresincetherequiredconditionforCase2,C'?S'CS,replacesthecriticalconditionoftheinclinationangle.(i)ElasticDeformationState: Ss SscandS' SacIntheelasticdeformationstate:6=CQ疋7兀(1-鳩十駕)g=3?+叩必1一埒十訓)十寧T%=?%(一知凱)+胡"■"聞處。 3ii11戸M十討KS上十簽二(1_1吒十1毎_6?%丫=同隆> ct>(ii)CompleteSlidingState: Ss SscandS Sac化=出匚S=叭食%=0%=%M幀=

Case3:「 0andS csSimilartoCases1and2,slipratiosduetothecriticalvaluesoftheinclinationangleandtheslipratioareobtainedas:3卩行十3卩行十OS乞=右J（沖行）2-（0?-乂吞）ThenondimensionalslipratioSn,isexpressedas:where:=（3pF.r-{3CySy）2比=R廠-［（c5s5）2+（casa）^jFortheIongitudinalforce,thelateralforce,andtheself-aligningtorque,twosubcasesshouldalsobeconsideredsimilartoCases1and2.AslipratioduetothecriticalvalueoftheslipangleisnotneededheresincetherequiredconditionforCase3,C'S' CS,replacesthecriticalconditionoftheslipangle.（i）ElasticDeformationState: S ScandSs Sscn clIntheelasticdeformationstate,F andMz?canbewritten:心=兀（1-舛十洞）J=GAW+叩化（1一埒十2/3）十寧丫。 3uiiF?M十拿十隹』（1-1陀十1暫-60耐6=同?。╥i）CompleteSlidingState:Inthecompleteslidingstate,Fusing:（ii）CompleteSlidingState:Inthecompleteslidingstate,Fusing:S ScandSs Ssc5nctct yf,F,Mz,Mzs,andMzscanbedeterminedbyJ=同化respectively.TheIongitudinalforceF ",thelateralforceF ,andthreecomponentsCt Ct voftheself-aligningtorques,Mz ,Mzs?,andMzs,alwayshavepositivevalues,buttheycanbetransformedtohavepositiveornegativevaluesdependingontheslipratios,theslipangle ',andtheinclinationangle intheSAEcoordinatesystem.TireForcesandMomentsintheSAECoordinateSystemForthegeneralformulationsofthelongitudinalforceFx,lateralforceFy,andself-aligningtorqueMz,intheSAEcoordinatesystem,thethreepossiblecombinationsoftheslipratio,theslipangle,andtheinclinationanglearealsoconsidered.LongitudinalForce:E.Fx=sin(k)F,forallcasesLateralForce:ctnFy=-sin( )F,forcases1and2Fy=sin( )F,forcase3Self-aligningTorque:嚨=sin()Mz-sin()[-sin( )Mzs+sin( )Mzs]RollingResistaneeMoment:My=-CrFz,foraforwardrollingtire.My=CrFz,forabackwardrollingtire.OperatingMode:USE_MODEYoucanchangethebehaviorofthetiremodelthroughtheswitchUSE_MODEinthe[MODEL]sectionofthetirepropertyfile.?USE_MODE=0:Steady-stateforcesandmoments?Thetireforcesandmomentsreactinstantaneouslytochangesinthetirekinematicstates.?USE_MODE=1:TransienttirebehaviorThetirewillhavealaggedresponsebecauseoftheso-calledrelaxationlengthin?bothlongitudinalandlateraldirection.See LaggedLongitudinalandLate