saej266v001

SAETechnicalStandardsBoardRulesprovidethat:“ThisreportispublishedbySAEtoadvancethestateoftechnicalandengineeringsciences.Theuseofthisreportisentirelyvoluntary,anditsapplicabilityandsuitabilityforanyparticularuse,includinganypatentinfringementarisingtherefrom,isthesoleresponsibilityoftheuser.”SAEreviewseachtechnicalreportatleasteveryfiveyearsatwhichtimeitmaybereaffirmed,revised,orcancelled.SAEinvitesyourwrittencommentsandsuggestions.QUESTIONSREGARDINGTHISDOCUMENT:(724)772-8512FAX:(724)776-0243TOPLACEADOCUMENTORDER;(724)776-4970FAX:(724)776-0790SAEWEBADDRESShttp://www.sae.orgCopyright1996SocietyofAutomotiveEngineers,Inc.Allrightsreserved.PrintedinU.S.A.SURFACEVEHICLE400CommonwealthDrive,Warrendale,PA15096-0001RECOMMENDEDPRACTICESubmittedforrecognitionasanAmericanNationalStandardJ266ISSUEDJAN96Issued1996-01STEADY-STATEDIRECTIONALCONTROLTESTPROCEDURESFORPASSENGERCARSANDLIGHTTRUCKSForeword—ThisDocumenthasnotchangedotherthantoputitintothenewSAETechnicalStandardsBoardFormat.1.Scope—ThisSAERecommendedPracticeestablishesconsistenttestproceduresfordeterminationofsteady-statedirectionalcontrolpropertiesforpassengercarsandlighttruckswithsingleaxles.Thesepropertiesincludethegradientswithrespecttolateralaccelerationofsteeringwheelangle,understeer/oversteer,sideslip,rollangle,andsteeringwheeltorque;thegainswithrespecttosteeringwheelangleofyawvelocity,lateralacceleration,andsideslip;thecharacteristicspeedorcriticalspeed;andthetotal,steering,andtirecompliancesatthefrontandrearwheels.2.References2.1ApplicablePublications—Thefollowingpublicationsformapartofthisspecificationtotheextentspecifiedherein.Unlessotherwisespecified,thelatestissueofSAEpublicationsshallapply.2.1.1SAEPUBLICATIONS—AvailablefromSAE,400CommonwealthDrive,Warrendale,PA15096-0001.SAEJ670e—VehicleDynamicsTerminologySAEJ2181—Steady-StateCircularTestProcedureforTrucksandBusesSAEPaper670078—TheInfluenceofVehicleDesignParametersonCharacteristicSpeedandUndersteer,R.T.Bundorf2.1.2ISOPUBLICATIONS—AvailablefromANSI,11West42ndStreet,NewYork,NY10036-8002.ISO4138:1982(E)—Roadvehicles—SteadystatecirculartestprocedureISO7401:1988(E)—Roadvehicles—Lateraltransientresponsetestmethods2.2RelatedPublications—Thefollowingpublicationsareprovidedforinformationpurposesonlyandarenotarequiredpartofthisdocument.2.2.1SAEPUBLICATIONS—AvailablefromSAE,400CommonwealthDrive,Warrendale,PA15096-0001.SAEPaper760713—TheCorneringComplianceConceptforDescriptionofVehicleDirectionalControlProperties,R.T.BundorfandR.L.LeffertSAEJ266IssuedJAN96-2-SAEPaper741096—APrimeronNonlinear,Steady-StateVehicleTurningBehavior,R.W.Topping,October1974SAEPaper720473—ANewLaboratoryFacilityforMeasuringVehicleParametersAffectingUndersteerandBrakeSteer,A.L.NedleyandW.J.WilsonSAEPaper741104—UnderstandingTireIntermixThroughtheCorneringComplianceConcept,R.L.Leffert,P.M.Riede,andR.E.Rasmussen2.2.2ISOPUBLICATION—AvailablefromANSI,11West42ndStreet,NewYork,NY10036-8002.ISO8855-1991—Roadvehicles—Vehicledynamicsandroadholdingvocabulary3.Definitions—TheterminologyusedhereinfollowsthestandarddefinitionsasfoundinSAEJ670e.4.General4.1TestMethods—Fivetestmethodsaredescribed:Method1—ConstantradiustestMethod2—ConstantsteeringwheelangletestMethod3—Constantspeed/variableradiustestMethod4—Constantspeed/variablesteertestMethod5—Responsegain/speedtestThefirstfourmethodsyieldsubstantiallysimilardata,buttheydifferinrequirementsfortestingspace,driverskill,andinstrumentation.Methods1and3dependuponthepath-keepingabilityofthedrivertominimizeinstrumentationrequirements.Methods2and4usefixedsteeringwheelangleandmeasurepathradiuswithinertialinstruments.Method5utilizestheratiosofthevariousresponsestosteeringwheelangle.Method4isgenerallyrunat80to100km/h.Method5islimitedtothe0to0.4g"linearrange"ofvehicleoperation,butcanberunatconsiderablyhigherspeedsthantheothermethods.ThedataplotofMethod5alsodemonstratesmostclearlytheconceptsofcharacteristicspeedandcriticalspeed,asdefinedinSAEJ670e.4.2RelationshiptoOtherStandards—ThisdocumentisasupersetofInternationalStandardISO4138:1982(E)andacomplementtoInternationalStandardISO7401:1988(E).Method1isthesameastheproceduredescribedinISO4138.Method4issimilartothestep/rampsteerinputtestprotocoldescribedinparagraph5.4ofISO7401.Thetestproceduresdifferonlyintheamountofthrottleapplied,buttheproceduredescribedhereinisusedtoextractonlysteady-statevehiclecharacteristics,whereasISO7401extractsonlytransientresponsecharacteristics.SAEJ2181OCT91describesthetestofMethod1andMethod2adaptedforbusesandheavytrucks,includingarticulatedvehicles.4.3TheoreticalBasisfortheTestProcedures—Thepathcurvatureofanautomobileinsteadyturningatagivenspeed(thatis,inagivenstateofequilibrium,ortrim)isdeterminedbyspeed,steeringwheelangle,wheelbase,andtheelasticandkinematiccharacteristicsofthefrontandrearsteeringsystems,suspensions,andtires.Intheabsenceofelasticandkinematicsteereffects—forexample,atverylowspeeds—theAckermanturnradius(FigureA1inAppendixA)isdefinedgeometricallybywheelbaseandbyfrontwheelandrearwheelsteerangles.Atincreasingspeed,steadyturningresultsincentrifugalforce,whichproducesdeflectionsinsteering,suspension,andtiresystems.AsdescribedinSAEPaper670078,theseincludelateralforcedeflectionsteer,aligningtorquedeflectionsteer,rollsteer,tireslipanglesfromlateralforceandcamberforce,etc.Whenexpressedindegreespergoflateralaccelerationandlumpedtogether,these"corneringcompliances"producesteeranglesandtireslipanglesinfrontandrearwhichmodifytheAckermanturnradius.CorneringcompliancessubtractfromthefrontandrearAckermansteeranglesasshowninFigureA1.CorneringcompliancesgreaterinthefrontthanintherearincreasepathradiusfromtheAckermancondition,andproduceundersteer,whilecorneringcompliancesgreaterintherearthaninthefrontreducepathradius,SAEJ266IssuedJAN96-3-causingoversteer.Thedifferencebetweenthetotalfrontandrearcorneringcomplianceiscalledundersteer/oversteergradient,expressedindegreesperg.Likewise,thechangeinsteeringwheelanglerequiredtomaintainagivenradiuswithincreasinglateralaccelerationiscalledsteeringwheelanglegradient,thechangeinrollanglewithlateralaccelerationiscalledrollanglegradient,etc.Thetestproceduresdescribedhereinaredesignedtomeasurethesevariousvehicleresponsegradients.Thesensitivitiesofthevehicle'sresponsestosteerinputsarecalledyawrategain(degreespersecondperdegreeofsteeringwheelmovement),lateralaccelerationgain(g'sperdegreeofsteeringwheelmotion),sideslipgain,etc.Thesecanbecalculatedfromthevehiclespeed,steeringwheelangle,steeringratio,wheelbase,andundersteer/oversteergradient,ortheycanbeobtaineddirectlyfrommeasureddata.4.4EquivalenceofTestProcedures—Thenatureofanystablesteadystateisindependentofthemethodbywhichitisachieved.Therefore,toobtainadesiredsetofsteady-statetrimconditionsofspeed,steeringwheelangle,andturnradius,itispossibletoholdanyoneofthemconstant,varyasecond,andmeasurethethird.Thusonemayuseaconstantradiustest,inwhichspeedisvariedandsteerangleismeasured;aconstantsteerangletestinwhichspeedisvariedandradiusismeasured;aconstantspeedvariableradiustestinwhichradiusisvariedandsteerangleismeasured;oraconstantspeedvariablesteerangletestinwhichsteerisvariedandradiusismeasured.Allofthesetestmethodswillproduceequivalentresults,providedtheyspanthesamevariationofspeed-steer-radiussteady-stateconditions.Infact,onemayinprincipleobtainanequivalenttoanyofthetestsbycross-plottingaseriesofoneoftheothertests:forexample,onecouldtakepointsatconstantspeedfromaseriesofconstantradiustestsrunondifferentradii.Inpractice,resultsobtainedfromsignificantlydifferentcombinationsofspeed-steer-radiusmaydiffersomewhatduetodifferencesinroad-loadthrottle,aerodynamics,tireslip,andinclinationanglesatdifferentsteeringangles,etc.Somegradientsobtainedbydifferentmethodsfromagivenspeed-steer-radiustrimconditionmaydifferbecauseinsomemethodslateralaccelerationiscontrolledbychangingspeed,andinothermethodsbychangingsteerangle.Practicalconsiderationssuchastireheatingduringlongtestrunsandfailuretomaintaintruesteady-statealsotendtoaffecttestresults.4.5SteeringSystems—Understeer/oversteergradientsarestatedintermsofthedifferenceincorneringcompliancesbetweenthefrontandrearroadwheel"axles";however,corneringcompliancesincludedeflectionsofthesteeringsystemundersideloadsandaligningtorques.Inordertoincludesteeringsystemcompliances,understeer/oversteeraredeterminedfrommeasurementsatthesteeringwheel.Steeringwheelanglesarereferredtotheroadwheelsbytheoverallsteeringratio."Overallsteeringratio"isavariablewhichdescribesthegeometricrelationshipbetweensteeringwheelangleandaverageroadwheelangle,measuredunderconditionsofzeroaligningtorqueandsideforce(see7.1).Itdoesnotimplyasteeringsystemwithafixedratio:Inmanyvehiclesthesteeringsystemissignificantlynonlinear,duetosteeringarmgeometry,universaljointrelationships,oravariableratiosteeringgear.Ifthesteeringsystemissignificantlynonlinear,eachmeasuredsteeringwheelanglemustbeusedtogetherwithaplotofaverageroadwheelangleversushandwheelangletoobtainthecorrespondingroadwheelsteerangle.Steeranglegradientsareobtainedfromaplotofroadwheelsteerangleversuslateralacceleration.4.6VehicleswithFour-WheelSteer—Currentfour-wheelsteeringsystemscanbedividedintothreegeneraltypes:rearsteerhavingaprogrammedrelationshiptosteeringwheelangle;rearsteerprogrammedaccordingtolateralacceleration;andrear/frontsteerratioprogrammedaccordingtospeedorother,morecomplex,relationships.Thefirsttypecreatesacombinednet-effectfront-rearsteeringratio(FigureA1andFigureA2)whichisingeneralnonlinear,andwhichmaybetreatedasdiscussedin4.5.Thesecondtypecanbetreatedasonlyanadditionalsourceof(usuallynegative)rearwheelcompliancesteer.However,thethirdtypemustbeconsideredasaseparatecontrolinput.Forsteady-statetestingofthisthirdtypeofvehicle,itmaybenecessarytodisabletherearsteeringtomeasure"basic"responseparameters,thenbyadditionaltestingwithrearsteerenabled,determinetherear-steercontrolalgorithmandmeasureitseffectonsteady-stateresponseparameters.SAEJ266IssuedJAN96-4-5.Instrumentation5.1Description—Thevariablesselectedfortestpurposesshallbemonitoredusingappropriatetransducers,andthedatashallberecordedonamultichannelrecorderhavingatimebase.Thefrequencyresponseoftheentiremeasurementsystem,includingtransducers,datafilters,andrecorder,shallhaveamplitudeerrors(combinedattenuationandripple)lessthan±0.5%intherelevantfrequencyrangeof0to5Hz.Iftherecordingsysteminvolvessamplingratherthancontinuousrecordingofalldatachannels,pre-sampling,anti-aliasingfiltersarerequired.For0.5%dataaccuracy,theanti-aliasingfiltersmustensurethatanynoisecomponentsatfrequenciesgreaterthan1/2thesamplingfrequencyhaveamplitudeslessthan0.5%ofthesignalamplitude.Theorderandpassbandofthefilters,andthesamplingrate,shallbeselectedtogethertoprovidetherequiredperformance.Allpre-recordinganalogfiltersshallhavesufficientlysimilarphasecharacteristicstoensurethattimedelaydifferencesliewithintherequiredaccuracyfortimemeasurements.Additionalfilteringfordataevaluationandanalysisshallutilizephaseless(zerophaseshift)methodologies.Correspondingsamplesofalldatachannelswhicharetobecomparedinanalysisshallbetakensimultaneously,orseparatedintimebyadelaysufficientlyshorttomaintaintherequireddataaccuracy.(Notethatthemaximumrateofamplitudechangeofa5Hzsignalis3%permillisecond.)Thetypicaloperatingrangesandrecommendedmaximumerrorsofthetransducer/recordingsystemareshowninTable1.5.2TransducersandTheirInstallation—Transducersofvarioustypes,somecommerciallyavailableandsomespeciallyfabricated,areusedinmeasuringtheseveralvariables.Ifatransducerdoesnotdirectlymeasuretherequiredvariable,appropriatecorrectionsshallbemadetoitssignaltoobtaintherequiredvariablewithasufficientlevelofaccuracy.Becauseofthevarietyofinstrumentationpossibilities,thetypeofeachinstrumentusedshallberecorded;andwhereapplicable,itslocationonthevehicleshallbeenteredonthetestdatasheets.Typicalerrorsforvariousdirectmeasurementtransducersaregiveninfollowingparagraphs.Netpercentageerrorforavariablecomputedfromtheoutputsignalsofseveraltransducersisfoundbytakingthedifferentialofthecomputedvariableanddividingitbythecomputedvariable.TABLE1—VARIABLESVariableTypicalOperatingRangeRecommendedMaximumErroroftheCombinedTransducer/recorderSystemSteeringwheelangle±180deg±1.0degLateralacceleration±10m/s2±0.10m/s2±1.0g±0.01gYawvelocity±50deg/s±0.5deg/sForwardvelocity0to50m/s±0.5m/sLateralvelocity±10m/s±0.1m/sSideslipangle±15deg±0.5degVehiclerollangle±15deg±0.15degFrontwheelangle±10deg±0.2degRearwheelangle±10deg±0.2degSteeringwheeltorque±30Nm±0.3NmSAEJ266IssuedJAN96-5-5.2.1STEERINGWHEELANGLE5.2.1.1Steeringwheelangleismeasuredrelativetothesprungmass.Typicaltransducersaremultiturnpotentiometersordigitalshaftencoders,gearedtothebackofthesteeringwheelorattachedtoa"secondsteeringwheel."5.2.2FORWARDVELOCITY5.2.2.1Aforwardvelocitytransducershouldbeinstalledascloseaspossibletothemid-trackpositiononthevehicle.Ifnotlocatedatmid-track,itslocationmustberecordedanditssignalcorrectedasnecessaryindataprocessing.Typicaltransducersarefifthwheelswithaccuraciesto0.2km/h,and"contactless"velocitytransducersbaseduponopticalprincipleswithaccuracyof0.5km/h.Thesteady-statefifthwheelsignalisveryclosetopathvelocity,whileopticaltransducersmeasurethecomponentofpathvelocityinthexdirection(pathvelocitymultipliedbythecosineofthesideslipangle).5.2.3SIDESLIP5.2.3.1Sideslipvelocityatagivenpointcanbemeasureddirectlybymeansofabipolarvelocitytransducerbaseduponopticalprinciples,installedaccordingtothemanufacturer'sspecifications.Thetransducerlocationmustberecorded.Sideslipvelocityatanyotherpointcanbeobtainedbyinterpolationbetweentwovelocitytransducers;orbyextrapolationfromthesideslipvelocityatthepointofmeasurementbyaddingtheproductofyawvelocitytimesthedistancetothedesiredpoint.Sideslipangleiscomputedastheanglewhosetangentissideslipvelocitydividedbyforwardvelocity.Commerciallyavailablebipolarvelocitytransducershavefullscalerangeof±10m/sand±1%fullscalesteady-stateaccuracy.5.2.3.2Sideslipanglecanbemeasureddirectlybyacasteredtrolley,attachedtothevehiclethroughgimbalsandloadingspringstokeepthecasteraxisvertical.Thesideslipanglemeasuredisthatwhichexistsatthecasteraxis.Thesideslipangleatanyotherpointonthelongitudinalaxisofthevehiclecanbecomputedbyinterpolationbetweentwotrolleys,orfromthesideslipangleatthepointofmeasurementandtheyawvelocityasin5.2.3.1.Thevehiclesideslipangleisdefinedasthatobtainedforthecenterofgravitylocation.Steady-statesidesliptrolleyaccuraciesof0.25degreesarepossible.5.2.3.3Vehiclesideslipvelocitycanalsobecomputedbyintegrationofalateralaccelerationsignal(correctedforposition,rollangle,andsurfaceinclinationerrors)minustheproductofspeedandyawrate.Sideslipangleisthencomputedasin5.2.3.1.Thismethodissuitableonlyforshort-termtests,becausethenetaccelerationerrorincludingzerooffsetsisintegrated.5.2.4YAWVELOCITY5.2.4.1Yawvelocityismeasureddirectlybyanangularratetransducer,installedasspecifiedbythemanufacturer.Thetraditionalangularratesensorsarerategyroscopes:typicalgoodperformancehaslinearityof0.2to0.5%full-scaleto1/2fullscaleand1to2%tofullscale;cross-axissensitivityof0.04%;thresholdsof0.05%fullscale;andhysteresis0.15%fullscale.Sensorsbasedonvibratingstring,hotwiregasflow,laser,orotherprinciplesarealsocommerciallyavailable,withlinearity±1%fullscale,threshold0.01degree/s,andnohysteresis.Angularratetransducersarefixedinthevehicle:thereforeinsteady-stateturningtheymeasureearth-planeyawvelocitymultipliedbythecosineofthevehiclerollangle.5.2.4.2Whensidesliptransducersareinstalledatbothfrontandrear,yawvelocityintheearthplanemaybecomputedfromthedifferenceinfront-rearsideslipvelocity,dividedbythelongitudinaldistancebetweenthem.SAEJ266IssuedJAN96-6-5.2.5LATERALACCELERATION5.2.5.1Lateralaccelerationcanbemeasuredbyanaccelerometerhavingsufficientaccuracyoverasufficientbandwidthwhichincludessteady-state,andinstalledinoneofthefollowingways.a.Mountedonthesprungmassandalignedwithitssensitiveaxisalignedwiththevehicley-axis.Ifitisnotlocatedatthewholevehiclecenterofgravity,itsoutputwillhaveanerrorduetoyawaccelerations,andifitisnotontherollaxis,anerrorwillbecausedbyrollacceleration.Eventhoughtheseerrorsshouldnotexistundersteady-stateconditions,theaccelerometerlocationshouldberecorded.Theposition-correctedsignalwillmeasure"sideacceleration,"whichinturnmustbecorrectedforthecomponentofgravityduebothtothesineofthevehiclerollangleplusthatoftracksurfaceinclination.b.Mountedonaplatformstabilizedbyagyroscopesystem.Positioncorrectionconsiderationsareasin5.2.5.1(a).Considerationmustbegiventogyroerectionanddrifterrors,asdescribedin5.2.6.1.c.Mountedonareferencetrolleysuchasmaybeusedtomeasurevehiclerollangleandsideslipangle.Correctionsmustbemadebothforpositionrelativetothecenterofgravityandforanytracksurfaceinclination.Themeasurementmaybelateralorcentripetalacceleration,dependingonaccelerometerlocationrelativetothetrolleyyawpivot.Theaccelerometerusedmusthavesufficientamplituderangetoavoidsignalsaturationduetosmallamplitude-highfrequencyvibration,whichafterfilteringmaycauseundetectableerrors.Highquality"servo"accelerometershavelinearitiesof±0.05to±0.1%fullscale,with0.02%hysteresisand0.001%resolution.Accelerometersbaseduponmeasurementofbeamorspringdeflectiontypicallyhavelinearitiesof±1%offullscale.Measurementerrorscanbedominatedbyinstallationconditions:forexample,a0.6degreeerrorinrollanglecompensationwillcausea0.01gaccelerationmeasurementerror.5.2.5.2Steady-statecentripetalaccelerationmaybeobtainedastheproductofpathvelocityandyawvelocity.Steady-statecentripetalaccelerationdiffersfromlateralaccelerationbythecosineofthevehiclesideslipangle.Thiscorrectionfactormaybeappliedindataprocessing,orforsufficientlysmallsideslipangles(e.g.,cosine8degreesis0.99)thedifferencemaybeignored.5.2.5.3Whentravelingonaknownconstantradius,centripetalaccelerationmaybeobtainedfrompathvelocitysquareddividedbythecircleradius,orfromyawvelocitysquaredmultipliedbythepathradius.5.2.6ROLLANGLE5.2.6.1Rollanglewithrespecttothegravityverticalcanbemeasuredbyatwo-axisgyroscope,eitheracase-referencedfreegyroorgravity-referencedverticalgyro.Thefreegyroelementiscaged,orlockedtoitscasewhennotmeasuring.Whenuncaged,itremainsfixedininertialspace,enablingmeasurementofangularvehiclemotion.Afreegyromaybeusedtomeasurerollandyaw,orrollandpitchmotion.Averticalgyrois"erected"toagravityverticalbypendulousswitcheswhichwhenactivatedcontrolslow-actingtorquermotors.Neithertypecanmaintaintherequiredmeasurementaccuracyforlongperiodsofsteadyturning.Freegyrosandverticalgyroswithdeactivatederectionsystemstendto"drift"atarateusuallyspecifiedbythemanufacturerat0.5to1degreeperminutemaximum;andverticalgyroswithactivatederectionsystemsseekan"apparentvertical"whichisthesumofthegravityandlateralaccelerationvectors,atarateof2to5degreesperminute.Intheabsenceoflateralacceleration,verticalgyroerectionaccuracyistypicallyspecifiedat±0.15to±1degree.SAEJ266IssuedJAN96-7-5.2.6.2Rollanglewithrespecttotheroadsurfacecanbemeasuredby:a.Angularmeasurementtransducerinstalledintherollgimbalofasidesliptrolley.b.Measurementofchangesintheverticaldistancetothegroundfromreferencepointsoneithersideofthevehicle,byultrasonicoropticaltransducers.c.Measurementofwheeljounceandreboundmotionwithrespecttothesprungmass,takingintoaccountsuspensionlinkagefactors.(Thismethodwillnotaccountfortiredeflections.)Ineachofthesemethodsitispracticaltoattainthespecifiedaccuracy,withnorestrictionontestrunduration.5.2.6.3Changeinrollanglefromatestinitialconditioncanbemeasuredbyintegrationofthesignalfromarollrategyro.Thismethodissuitableonlyforshort-termtests,sincetheentiresignalincludinganyzerooffsetswillbeintegrated.5.2.7STEERINGWHEELTORQUE5.2.7.1Steeringwheeltorque