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ProcediaEngineering150(2016)128012861877-70582016TheAuthors.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(/licenses/by-nc-nd/4.0/).Peer-reviewunderresponsibilityoftheorganizingcommitteeofICIE2016doi:10.1016/eng.2016.07.288ScienceDirectAInternationalConferenceonIndustrialEngineering,ICIE2016SuspensionKinematicsStudyoftheFormulaSAESportsCarS.Chepkasov,G.Markin,A.Akulova*UralFederalUniversity,19Mirastreet,Yekaterinburg,620002,RussiaAbstractInthisarticlethedesignofthesuspensionofasportscarwiththeclass“FORMULASAE”isconsidered.Asuspensiondoublewishboneistakenasthebasis.Themainrequirementstothecharacteristicsofthesuspensionofthecarofthisclassareformulated.Calculatedsuspensionschemeisadduced.Themathematicalmodelfordeterminingthepositionofthesuspensiondependingontheangleoftheupperarmhasbeendrawnup.TheanalysisandthechoiceofthegeometricparametersofthesuspensionofasportscarwiththeclassFORMULASAEwerecarriedout.2016TheAuthors.PublishedbyElsevierLtd.Peer-reviewunderresponsibilityoftheorganizingcommitteeofICIE2016.Keywords:Racingcar;suspension;formulaSAE;drivability.1.IntroductionInourdaysthemostpopularautomotiveeventsintheworldareracingFormula-1.Thecarsthatarebuilttoparticipateinthesecompetitions,inadditiontotraction-speedcharacteristicshavethehighestlevelsofcontrollabilityisnecessarytoensuremaximumspeedcorneringandsafetypilotwhendrivingatextremespeeds.Theneedtoovercomethecurvedsectionsofthetrackathighspeedrequiresengineerstosolveadditionaltasksassociatedwithperformancehandling,stabilityandsafety.Whenthevehicleturns,thereareforcescausingthedemolitionandrollofthecar,inordertominimizethenegativeconsequencesofwhichneedtobetakenintoaccountparameterssuchasthecharacteristicsofthetire,thekinematicsofthesuspensionandsteeringanddampingcharacteristicsofthesuspension.Asaconsequence,theresultonthecompetitionofacardependsonthekinematicsofitssuspension.*Correspondingauthor.Tel.:+79502027731.E-mailaddress:79502027731ya.ru2016TheAuthors.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(/licenses/by-nc-nd/4.0/).Peer-reviewunderresponsibilityoftheorganizingcommitteeofICIE20161281S.Chepkasovetal./ProcediaEngineering150(2016)12801286WhendesigningthesportscarclassFORMULASAEauthorsfacedwiththeneedtooptimizethegeometricparametersofdoublewishbones,foritwasdevelopedamathematicalmodelofit,performedtheanalysisandselectionoftheoptimumgeometricalcharacteristics.2.ThekinematicsofthesuspensionofasportscarSuspensionofasportscarshouldprovidetheproperkinematicsofthewheelsofthecarandhaveaminimumweightoftheunsprungparts.Almostalloftheracingandsportscarsequippedwithsuspensiondoublewishboneinconnectionwiththeiroptimalkinematicparameters.Thelargesizeisadisadvantagewheninstallingthesuspensionofthistypeofcarsintendedfordailyuse,however,whenitisusedoncarsformulatypeitbecomesanadvantage,sinceitwouldchangethetrackwidthofthecarandresistrollover,regardlessofthesizeandstructureoftheload-bearingframework.Whenchangingtherelativepositionofdoublewishbonessuspensionlevers,changestheheightofthetransverseandlongitudinaltiltofthecar,sothatitisconsideredthatthistypeofsuspensionisabletoprovidetheperfectkinematicratio.Ontheotherhand,thechangeindistancebetweenthewishbonesaffectsthechangeofforcesactingontheguidedevicesandhinges.Accordingtotherules1hasbeentaskedtoselectthegeometricparametersofdoublewishbonescar(Fig.1).Fig.1DiagramofasportscarclassFORMULASAEItisbelievedthatthesuspensiondesignissuesareamongthemostinterestingfortheautomotiveengineers,becausetheyneedcreativesolutionsandagoodknowledgeofengineeringsciences.GreatcontributiontothestudyoftheissuessuspensionkinematicsintroducedProfessorJ.Reimpel,inhisbooksmorefullyreflectthevariousaspectsofthedesignofthechassisofthecar,aswellasdataforvariousvehiclesandformulatedkeyrecommendationstothekinematicdependences2,3.AmongdomesticauthorsdistinguishI.N.UspenskyandA.A.Melnikova4,whichsetsouttheissuesofselectionandcalculationofelastic-dampingelements,maderecommendationstothechoiceofthecharacteristicsofthesuspension,dependingonroadconditions.Thesource5providesageneralalgorithmforselectingparametersofthesuspension,formulatedthebasicloadmodes.Also,inthepreparationofthemathematicalmodelusedrecommendationsandsomeoftheapproachessetoutin6.RequirementsforthesuspensionofasportscarclassFORMULASAE:xKamberangleshouldvarywiththeanglethecross-rollthecar.Sothatwhenthevehicleturns,thesuspensionprovidesaconstantcontactpatch.Thisisnecessarytoallowthetransmissionoflargelateralforcesandmoreuniformtirewear1282S.Chepkasovetal./ProcediaEngineering150(2016)12801286xTrackchangeduringthecourseofthesuspensionshouldbesmallandbeintherange5-10mmtomaximizecontactwiththeroadwheelsxThelengthofthepintleshouldbethemaximumpossibleunderthetermsofthelayouttoreducereactionsinjointsoflevers3.MathematicalmodelInourcase,forconstructivereasons(forthepurposeofrationalplacingontheframe),thesuspensiontransmitsverticalforcesontheelasticmemberthroughthethrustandrockerarm,itselfresilientmemberislocatedatthebottomoftheframe.Inaddition,thefollowingassumptions:suspensioncomponents(exceptsprings)areconsideredtobeabsolutelyrigid.Thismathematicalmodelisnottakenintoaccountthekinematicsofthepusher,inviewofcomplexityofaconclusionofformulasthisquestionisleftforfutureresearch.Fig.2.Estimatedschemeoffrontsuspensionkinematics.Attheinitialstage,takentheoriginaldimensionsofthesuspension.Theinitialdataareconsideredcoordinatesmountingarmtotheframe,thelengthsofthearmsandpintles,thelengthofdiskoffset,thecamberangleintheinitialpositionandtheangleofinclinationofthetransversepintle(Fig.2).ThefollowingsymbolsareusedinFig.2:Zu,yuhorizontalandverticalcoordinatesoftheupperarmjointrespectively;zl,ylhorizontalandverticalcoordinatesofthelowerarmjointrespectively;zpin.u,ypin.uhorizontalandverticalcoordinatesofthehingepintleoftheupperarm,respectively;zpin.l,ypin.lhorizontalandverticalcoordinatesofthehingepinofthelowerarm,respectively;zh,yhhorizontalandverticalcoordinatesofthepointO,respectively;zk.c.,yc.c.respectivelyhorizontalandverticalcoordinateofthecenterofthecontactwheel;lpthelengthofthepintle;lofthelengthofthewheeloffset;lulengthoftheupperarm;llthelengthofthelowerarm;theinclinationangleoftheupperarm;theangleofinclinationofthelowerarm;ltheangleofinclinationoftherod;.angleofinclinationoftheaxisofpintletothevertical.1283S.Chepkasovetal./ProcediaEngineering150(2016)12801286FortheabovecalculationschemewasmadeamathematicalmodelinMathcadusingthemethodsoftheoreticalmechanicsandthetheoryofmachinesandmechanisms.TocheckthecalculationswasbuiltkinematicsinSolidWorkstiedtoMicrosoftExcel.Theproposedmathematicalmodelhasonedegreeoffreedom.Asamodifiableparameterselectedangleoftheupperarmtothehorizontal.Thehorizontalcoordinateoftheupperendoftheleverzpin.ucalculatedbytheformula:.cospinuuuzlzE(1)Theverticalcoordinateoftheupperendofthelevermpin.ucalculatedbytheformula:.sinpinuuuylyE(2)Theverticalcoordinateattheendofthelowerarmypin.lhasrathercomplicatedtrigonometricdependenceontheparameters,soforthesakeofsimplicity,additionalvariablesareintroduced(Formula4-10):.2pinldDye(3).22pinupinuaacdzybb(4)24Ddeh(5)21aeb(6).pinulayy(7).pinulbzz(8)222222.2lpllpinupinullzyzyc(9)2222.2ppinupinupinucchlzzybb(10)Thehorizontalcoordinateofthelowerendoftheleverzpin.lcalculatedbytheformula:.pinlpinlcayzb(11)Theangleofinclinationofthelowerarmcalculatedbytheformula:1284S.Chepkasovetal./ProcediaEngineering150(2016)12801286.arccospinlllzzlJ(12)Theangleofinclinationoftheaxisofpintletothevertical.calculatedbytheformula:.arcsinpinlpinulzzlD(13)Thecamberangle&calculatedbytheformula:00()ZZDD(14)TheverticalcoordinateofthepointOyh:0.cos2lpinllyyD(15)ThehorizontalcoordinateofthepointOzh:0.0sincos()2lpinuflzzlDD(16)Verticalcoordinateofthecenterofthecontactyc.c:.0coskkKLyyRZ(17)Thehorizontalcoordinateofthecenterofthecontactzc.c:.0sinkkKLzzRZ(18)whereRklstaticwheelradius.Track:.2ccBz(19)Changingtracks:0BBB(20)Consequently,toobtainamathematicalmodel,itispossibletoplotchangesincamberandtrack,dependingontheprogressofthesuspension,settingitsgeometricparameters.4.TheselectionofgeometricparametersofthesuspensionofasportscarclassFORMULASAEThenextstepistheselectionofthegeometricalparametersofthesuspensionoftheprojectedcar.Onthebasisoftherulesandconditionsofthelayout,theauthorsestablishedthefollowinglimits:xSuspensiontravelis60mm(30rebound,compression30)1285S.Chepkasovetal./ProcediaEngineering150(2016)12801286xCoordinatesthesupportofthelowerarmtotheframedefinedbytheconditionofthecarlayout,soforfurthercalculationsarepermanentxThelengthofthepintleisselectedtakingintoaccounttherequirementssetforthandsodonotchangexInitialcamber-31Accordingly,therequiredcharacteristicscanbeobtainedbychangingthemountingpointsoftheupperarmtotheframe,achangeofthelengthsoflevers,varyingtheangleofinclinationofthekingpin,tiltlevers.Inthispaper,asanexample,considertheeffectofthelocationofthesupportoftheupperarmandtheangleofinclinationonthecamberanglecharacteristicsandtrackchangesdependingonthesuspensiontravel.Geometricalparametersofsuspensionhavebeencalculatedforthethreevariantsofthepositionoftheupperarmbyusingformulas(1-20),theresultsisshowninTable1andthegraphs(Figure3).Table1.Resultsofcalculation.Z(mm)Y(mm)0()Suspensiontravel(mm)-30-20-1001020302703107,2B(mm)1341134413461349135113521353B(mm)-8-5,2-2,6023,24&()0,0470,161-0,16-0,52-0,92-1,33-1,732683313,8B(mm)1344134613471349135013501351B(mm)-5-3,1-1,5011,62&()0-0,16-0,34-0,52-0,75-0,97-1,232673540B(mm)1346134713481349134913491349B(mm)-3-2-10000&()-0,49-0,5-0,52-0,52-0,57-0,63-0,71Infigure3areshownthreecurves,whichillustrateinterrelationoftheinclinationoftheupperarmandcharacteristicsofstudysuspensionduringsuspensiontravelthatallowsgraphicallycompareparametersofseveraloptionsofsuspensionkinematic.Fromthesegraphsitcanbeconcludedthatathirdoption(=0)oftheinstallationoftheupperarmismorefullysatisfytherequirementssetforthinthisarticle,sincethetrackremainsconstantduringcompressionmotionanditschangeduringreboundisatapermittedrange.Thecamberanglethusisnegativeandalmostunchanged.Itsnecessarytonotethatresults,whichwerereceived,arevalidonlyforinitialconditionsdescribedaboveinthisarticle.5.ConclusionInconclusion,theauthorswouldliketonotethattheresultingmathematicalmodelisuniversalandallowsdefiningthekinematicsofanydoublewishbonessuspensionandcanbeappliednotonlyforsportscarsFormulaSAE.Thenextstepisthecompletionofthemodelandwritingacomputerprogram,whichwouldallowplottingthechangesofcamberandtrackcurvesfromgeometricalparameters,aswellasassessingthei