Improving-the-braking

Availableonlineat(2014)91–101⇑,P.SchalkElsDepartmentofMechanicalandAeronauticalEngineering,UniversityofPretoria,SouthAfricaReceived26May2014;receivedinrevisedform25September2014;accepted28September2014AbstractRapidadvanceshavebeenmadeinthefieldofvehicledynamicsintermsofimprovingtheride,handlingandsafetyusingactuatorsandcontrolsystems.Optimisingavehicle’sridecomfortorhandlinghasledtothedevelopmentofsemi-activesuspensionsystems.Anti-lockbrakingsystems(ABS)haveresultedinsignificantimprovementsinvehiclebrakingwhilstmaintainingdirectionalcontroloverthevehicle.Theseadvanceshaveimprovedvehicleandoccupantsafetyingeneral,butthereareoftensometrade-offs.Forexample,thestop-pingdistanceofavehiclefittedwithABSonanundulatingroadissignificantlyincreasedcomparedtobrakingwithoutABS.Thishassevereimplications,especiallyintheoff-roadvehicleindustry.Theeffectsofspringanddampercharacteristicsonthebrakingperfor-manceofasports-utility-vehicle(SUV)onhardroughterrainareinvestigated.Theapproachissimulationbased,usinganexperimen-tallyvalidatedfullvehiclemodeloftheSUV,builtinAdamsinco-simulationwithMATLABandSimulink.ThesimulationswereperformedonmeasuredroadprofilesofaBelgianpavingandparallelcorrugations(orawashboardroad).Theresultsindicatethatthesuspensionsystemhasasignificantimpactonthebrakingperformance,resultingindifferencesinstoppingdistancesofupto9m.Ó2014ISTVS.PublishedbyElsevierLtd.Allrightsreserved.Keywords:Off-roadvehicles;ABSsystems;Semi-activesuspension;Tyremodelling;Multi-bodydynamicsmodelling1.Introductionbetweenthetyreandtheroadsurfacewhilehysteresisisduetothedeformationofthetyreoveraroughroadsur-face[1].Theresultofthesephenomenaisthatthefrictioncoefficientbetweenthetyreandtheroadsurfacereliesonslipbetweenthetyreandtheroad.Thelongitudinalfric-tioncoefficientistypicallycharacterisedasafunctionoflongitudinalwheelslip.LongitudinalwheelsliponaflatroadisgivenbyEq.(1)[1].Examplesoftypicallongitudi-nalfrictioncoefficientsfordifferentverticalloadsareshowninFig.1.ThedatausedinFig.1isfromthePace-jka-modelusedinthisstudy(furtherdiscussioninSection2.4).Stoppingintheshortestpossibledistancewithoutlosingcontroloveravehicleisprobablythemostimportantactivesafetyrequirementofanyvehiclethatcanpreventaccidentsoratleastlessentheimpact.Significantadvanceshavebeenmadesincethedawnofbrakesonvehicles,mostnotablythedevelopmentofanti-lockbrakesystems(ABS).PriortodiscussinghowABSworks,itisimportanttounderstandthefrictiongenerationmechanismoftyres.Atyre’sfrictiongenerationmechanismisduetoadhesionandhysteresisbetweenthetyreandtheroadinthecontactpatch.Adhesionarisesduetotheintermolecularbonds%slip¼VÀxReffÂ100%ð1ÞV⇑Correspondingauthor.E-mailaddresses:[e-mail](H.A.Hamersma),[e-mail](P.SchalkEls).CurvessimilartothoseshowninFig.1maybeobtainedforthelateralfrictioncoefficient,usuallyasafunctionofÓ2014ISTVS.PublishedbyElsevierLtd.Allrightsreserved.92H.A.Hamersma,P.SchalkEls/JournalofTerramechanics56(2014)91–101NomenclatureofsymbolsfCoefficientoffriction[Dimensionless]TBraketorque[Nm]pariroReffBrakelinehydraulicpressure[Pa]Innerbrakepadradius[m]Outerbrakepadradius[m]Effectiverollingradius[m]VDhxVehiclespeed[m/s]Brakepadangle[rad]Wheelangularspeed[rad/s]side-slipangle.FromFig.1onemayconcludethatbrakingwithlongitudinalslipatapproximately15%resultsinmax-imumbrakeforceandtherebythehighestdecelerationandtheshortestpossiblebrakingdistancewillbeattained.However,whenthetyreisgeneratingmaximumlongitudi-nalforce(forexampleduringbraking)thetyrecannotgen-erateanylateralforce[1].Sincelateralforceisessentialtocontrollingthelateralstabilityofthevehicle,brakingatmaximumlongitudinalforcemayresultinanuncontrolla-bleorunstablevehicle.ThisledtothedevelopmentofABS.Whenthevehiclebrakesareinitiallyapplied,thetyredeflects,generatinglongitudinalslipthatresultsinacorre-spondinglongitudinalforceasdictatedbytherelationshipindicatedinFig.2.Ifthelongitudinalforceexceedstheavailablefrictionforce,thewheellocksupalmostinstantaneously.ABSsenseswhenwheellock-upoccursorisabouttooccurandreducesthehydraulicbrakepressureaccord-ingly.Thisnotonlypreventsthewheelfromlockingbutalsogeneratessomecapacityforthedevelopmentoflateralforcebetweenthetyresandtheroadthathelpstomaintaindirectionalcontrol[2].Oncethecontrolsystemdetectsthatthewheelisnotlockedandspinningfreely,thebrakepres-sureisgraduallyreapplied.Thisprocessisthenrepeateduntilthebrakeisreleasedbythedriverorthevehiclespeedreducesbelowasetvalue[2].ThisisthecyclingindicatedinFig.2.TheABScyclehasthreedistinctphases,namelyhold,reduceorincreasepressure.Initially,asthedriverappliespressuretothebrakepedal,thehydraulicpressurerisesandthewheelisbraked.Thewheelspeedthusdecreases,butABShasnocontroleffectatthisstage.Ifthewheelspeeddecreasestoorapidly,thecontrolsystemdetectsthatlockupisimminent.Atthis