40KSMEJournal,VolA,No.1,pp.40-47,1990.ANALYTICALANDEXPERIMENTALMOTIONANALYSISOFFINGERFOLLOWERTYPECAM-VALVESYSTEMWITHAHYDRAULICTAPPETWon-JinKim-,Hyuck-SooJeon-andYoun-SikPark-(ReceivedSeptember11,1989)Inthispaper,themotionofafingerfollowertypecamvalvesystemwithahydraulictappetwasanalyticallyandexperimentallystudied.First,theexactcontactpointbetweencamandfollowerforeachcorrespondingcamanglewassearchedbykinematicanalysis.Thena6degreeoffreedomlumpejspringdampermassmodelwasconstructedtosimulatethevalvemotionanalytically.Whenconstructingthemodel,mostoftheparameterswereexperimentallydetermined.Butseveralvalueswhicharedifficulttoderiveexperimentallysuchasdampingcoefficientsweredeterminedwithengineeringintuition.Inordertoshowtheeffectivenessoftheanalyticalmodel,thepredictedcamvalvemotionwasdirectlycomparedwiththemeasuredvalveandtappetmotions.KeyWords:FingerFollower(OscillatiwRollerFollower),OverheadCam(OHC),CamValveSystem,Jump,BounceNOMENCLATURE-Ae:Equivalentcross-sectionalareaofoilchamberintappet,m2C.C.2C.3:Equivalentdampingcoefficientsofvalvespring,N/mC.e:Dampingcoefficientofvalveseat,N-s/mc,f,CVf,Cfe:Equivalentdampingcoefficientsofcontactpoint,Ns/mc,p:Equivalentdampingcoefficientoftappet:N-s/m/0:Fundamentalnaturalfrequencyofvalvespring,HzFo:Initialcompressionforceofvalvespring,NFifFvfFfe:Contactforcesateachcontactpoint,NFifO,Fvfo,Ffeo:Initialcontactforcesateachcontactpoint,Nh:Clearancebetweencylinderandplunger,mmHe:Lengthofcompressedoilchamber,mmIf:Followermomentofinertia,kg-m2Ko:Valvespringstiffness,N/mKe:Equivalentstiffnessoftappetoilchamber,N/mK.1K.2K.3:Equivalentstiffnesscoefficientsofvalvespring,N/mK.:Stiffnessoftappetsoftspring,N/mK,f,Kvf,Kfe:Equivalentstiffnesscoefficientsofcontactpoint,N/mL:Plungerlength,mmLf:LeverarmofforceFfmmLvf:LeverarmofforceFvf,mmme:Massofoilinsidetappetoilchamber,kgMf:Followermass,kgMt:Equivalenttappetmass,kgMv:Equivalentvalvemass,kgDnpartmentofMechanicalEngineering,KoreaAdvancedInstituteofScienceandTechnology,P.O.Box150Cheongruarlg,Seoul130-650,Koeramm2:Equivalentvalvespringmasses,kgRp:Radiusoftappetplunger,mmRe:Radiusofcambasecircle,mmRab:Distancefromcampivottofollowerpivot,mmR,:lengthofoscillatingrollerfollower,mmRf:Radiusofrollerinrollerfollowermodel,mmYf:Followerdisplacement,mmY,:Tappetdisplacement,j.tmYe:Camlift,mmYv:Valvedisplacement,mmY.Y.2:Displacementsofequivalentvalvespringmasses,mm8f:Angularrotationoffollower,radianj.t:Oilviscositycoefficient,Pa-sE:Bulkmodulus,N/m28:Angularrotationofcam,radian1.INTRODUCTIONWhendesigningacam-valvetrainofinternalcombustionengine,therearemanythingstobeconsideredsuchasvalveliftarea,peakcamacceleration,propercameventangle,rampvelocity,etc.Asincreasingtheoperationspeedofinternalcombustionengine,thedynamiceffectofcam-valvesystembecomesmoreimportant.Recently,someresearcheshavebeendonefocusingthedynamiceffectsoncam-valvesystem.Akiba,etal.(1981)constructeda4degreeoffreedommodeltoanalyzeanOHV(OverheadValve)typecam-valvesystemandstudiedthedynamiceffectsonthesystemmotion.JeanandPark(1989)triedtoanalyzethesametypeofvalvesystemwithalumpedmassdynamicmodelanddesignedanoptimalcamshapeconsideringdynamiceff.PisanoandFreudenstein(1982)developedadynamicmodelofahighspeedvalvesystemcapableofpredictingbothnormalsystemresponseaswellaspathologicalbehaviorassociatedwithonsetofjumping,bounce,andspringsurge.Previousresearchesinhigh-speedcamsystemhadbeenalmostfocusedonsystemswithaconstantrocker-armratioandonthevalve.ANALYTICALANDEXPERIMENTALMOTIONANALYSISOFFINGERFOLLOWERTYPECAM-VALVESYSTEMWITH.41trainseparationphenomena.Especially,theanalysisforcamsystemhavingahydraulictappethasnotbeenthoroughlystudied.Inthiswork,anOHCcam-valvetrainwithahydraulictappetandafingerfollower,wasanalyzedanalyticallywithlumpedmassmodelanditsreliabilitywasverifiedexperimentally.Thecam-followersystemusedinthisworkischaracterizedwithitscomplexdynamicsofhydraulictappetandthenonlinearityfromvaryingrocker-armratio.Therocker-armratiodeviatesasmuchas34percentfromabaselinevalueofI.47asthecontactpoirUbetweencamandfollowermoves.Thepivotendoftheoscillatingfollowerissupportednotatafixedpointbutataverticallymovingpivotmountedattopahydraulictappet.Themajorroleofthehydraulictappetistoremovethevalvelashwhichgivesharmfulimpactwithinvalvetrain.Butinhighoperatingspeedregion,thehydraulictappetcanbeopratedabnormallyandcanmakeanunusualvalvetrainmotion.Therefore,thecharacteristicsofthehydraulictappetmustbeconsideredinvalvetraindynamicmodel.TheprimaryresearchforasimilarcamsystemwasdonebyChanandPisano(1987).Theyestablishedsixdegreesoffreedommodelconsideredtranslationalandrotationalmotionofoscillationgfollowerandvalve.Buttheyusedasimplesingledegreeoffreedommodelforthehydraulictappet.Theyfocusedonlyonanalyticalworkanddidnotattempttoverifytheresultsexperimentally2.VALVETRAINMODELINGTAPPETFig.1:0:bIiP:VALVEI()ISPRINGIf0:IIVALVESEATSchematicoffingerfollowervalvetrainTheactualoverallshapeofanOHCtypecam-valvetrainisshowninFig.I.Inordertodescribethevalvemotionprecisely,thevalvetrainwasmodeledwith6degreeoffreedom.Thosearevalveopeningandclosingmotion,Yv,hydraulictappettranslationalmotion,Yfinger-followertranslationalandrotationalmotion,Y/and8/,andtwoadditionaldegreeoffreedomYS!andYS2whichrepresentvalvespringtranslationalmotion.ThereasonfortakingvalvespringmotionsYS!andYS2istoconsidervalvespringsurgephenomenon.Itisknownthatvalvespringsurgeaffectsgreatlyonvalvemotionespeciallywhentheoperationspeedishigh.Becausecamshaftcanbeconsideredasrigidandfixedonitsbearing,itsdynamiccharacteristicswasneglectedinthemodel.Allthecompotsandthecontactpointsofthecam-valvesystemwererueledwithequivalentmass,springsanddampersasshoinFig.2.Thedetailsofmodelingprocedureareexplainedasfollows.2.1ContactPointModelingAsshowninFig.1thefinger-followertypecam-valvetrainCAMTAPPETIVALVESEATVALVESPRING.CseFig.2Usedmodel42Won-inKim,Hyuck-SooJeonandYoun-SikParkTheequivalentmass(Me)offingerfollowerateachcontactpointcanbeobtainedfromEq.(2)asconsideringthefollowermomentofinertia(If).whereMfisthefollowerequivalentmassandIisthedistancebetweenfollowermasscenterandeachcorrespondingcontactpoint.Theequivalentmassofcamshaftatcontactpointisestimatedtoinfinityasassumingthatitisrigidandhas4contactpointsbetweenvalvetraincomponents.Thosearebetweenfollowerandtappet,follwerandcam,followerandvalve,andvalveseatandvalve.Thecontactatvalveseatoccursperiodicallyasdifferentwithotherswhichshouldmaintaincontinuouscontact.Theequivalentvalveseatstiffness(Kse)anddamping(Cse)cofficientsweretakenfromthepreviouslypublishedliterature(ChanandPisano,1987).Ontheotherhand,theequivalentdampingandstiffnesscoefficientsatothercontactpointswerepredictedbyHertzcontacttheoryutilizingshapefactor,modulusofelasticity,andPossonsratio.AJ；assumingtheproperrangeofcontactforces,thecorrespondingcontactstiffnesswascalculatedbyHertzcontacttheory.Thentheequivalentstiffnessesateachcontactpointweredeterminedbyleastsquareerrorcurvefitfromobtainedcontactstiffnesses(RoarkandYoung,1976).Itwasassumedthatthecontactbetweentappetandfollowerisaninternalcontactoftwospheres,betweencamandfollwerisacontactoftwocylinders,andbetweenfollowerandvalveisacontactofacylinderonaplane.Thedampingcoefficientsateachcontactpointwereassumedas0.06andthecriticaldampingcoefficient(Ccr)canbecalculatedusingEq.(I).WhereM,andMzaretheequivalentmassesofeachcontactingcomponent.itwasassumedthattheequivalentmassesofeachcontactingcomponent(M,andMz)areconnectedbyaspringandadamper.(3)2m,=mz=:rKol(flo)8Kl=K.a=:rKo,K.z=4Ko2.3HydraulicTappetModelingTheleftsideofFig.3showsthecrosssectionshapeofhydraulictappet.Oilentersthroughentranceandfillsthecentralcavityoftappetplunger.Astheplungermovesdown,thecheckvalveisclosedandtheoilflowsfromoilchamberthroughnarrowclearancebetweenplungerandcylinderandgeneratesdampingforce.Innextstep,whentheplungermovesupwardduetothespringpositionedinsideofoilchamber,thecheckvalveisopenedandoilisrefilledinoilchamber.ThehydraulictappetwassimplifiedasshownintherightsideofFig.3andtheequivalentstiffnessofthetappetwasestimatedbyassumingthatthefluidistotalycompressiveandthereisnoflowthroughdiametralclearance.TheThespringrateandfundamentalnaturalfrequencyofusedvalvespringare35KN1mand504.46Hz,respectively.Thedampingisassumedas4%proportionalviscousdamping.fixedonitsbearing.TheequivalentmassesoftappetandvalveatothercontactpointsareM,andMv.2.2ValveSpringModelingInordertoconsidervalvespringsurgeeffect,thevalvespringwasmodeledwith2masses(m,andmz),3springs(KShKsandKsa),and3dampers(CshCszandC.a)with2degreeoffreedom(sandz).Severalassumptionsweremadeinthevalvespringmodeling.Thoseare；(i)symmetricity(K.,=KsaandC.,=Csa),(ii)equivalencyofstaticstiffnessandfundamentalnaturalfrequencybetweenmodelandfundamentalnaturalfrequencybetweenmodelandactualsystem,(iii)properdampingassumption.Asconsideringthatvalvespringisinclamped-clampedboundaryconditon,thesecondarynaturalfrequencyofvalvespringbecomestwiceofthefundamentalspringnaturalfrequency.Alltheaboveassumptionsgive(1)(2)C=2/KM,MzcrM,+M.OILENTRANCE-hJ.-0)Mf0.05981K:5.92x10；1.1280,0)h1.1527X10-Kif5.52X10Cf118.97Mv0.08544Kfc8.37x10Cfc197.97m,0.0092KVf4.33x10CVf94.13m20.0092K1.31x10C634.77K.K.9.33xlOCu.C.a2.35!5K.21.40x10C.23.534relationshipis(4)wascarefullycalculatedconsideringitsgeometricalshape.Alltheusedmass.stiffnessanddampingvaluesweresummarizedinTable2.whereaandpcanbedeterminedbycomparingmodelsimulationresultwithexperimentallymeasuredrecord.2.4MassandMomentofInertiaModelingValve,tappetplunger,andfollowermass(Mv,Mt,andMf)weredirectlymeasured.Thefollowermomentofinertia(If)whereEisbulkmodulus,Heisthelengthofcompressedoilchamber,andAeisplungerarea.Ontheotherhand.theequivalentdampingcoefficientwasestimatedbyassumingthattheoilistotallyincompressive.Itwasassumedthattheexcessiveoilduetoplungermotionflowscompletelythroughthediametralclearance.Thentheequivalentdampingvaluecanbepredictedfromthetheoryoffluidmechanics.Itisknownthatthedampingcoefficientchangeswiththedirectionofplungermotion.Thoseare(7)X=(Rc+S)cosO-sinOY=(Rc+S)sinO+cosO3.1KinematicalAnalysisWhensearchingthepointwherecamandfollowercontacts,thetappetwasconsideredfixedpoint.Itwasfoundthattheinfluenceoftappetmotionuponcontactpointisnegligible.Thetappetmotion,whichisatmostO.I(mm).isenoughsmallandcanbeconsiderednegligibleanddiffersinorderofmagnitudewithcamlift.Whenthecamdataisgivenwithdesiredcamlift(S),theactualcamshape(X,.Y),contactingwithaflatfollower,canbeobtainedfromEq.(7)Thebaselinerocker-armratiois1.47andthefluctuatingrangeofrockerarmratiovariesfrom1.15to1.97duringthecycle.Thefinger-followertypeORCca