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40KSMEJournal,VolA,No.1,pp.4047,1990.ANALYTICALANDEXPERIMENTALMOTIONANALYSISOFFINGERFOLLOWERTYPECAMVALVESYSTEMWITHAHYDRAULICTAPPETWonJinKim,HyuckSooJeonandYounSikParkReceivedSeptember11,1989Inthispaper,themotionofafingerfollowertypecamvalvesystemwithahydraulictappetwasanalyticallyandexperimentallystudied.First,theexactcontactpointbetweencamandfollowerforeachcorrespondingcamanglewassearchedbykinematicanalysis.Thena6degreeoffreedomlumpe0Mf0.05981K5.92x101.1280,0h1.1527X10Kif5.52X10Cf118.97Mv0.08544Kfc8.37x10Cfc197.97m,0.0092KVf4.33x10CVf94.13m20.0092K1.31x10C634.77K...K..9.33xlOCu.C.a2.355K.21.40x10C.23.534relationshipis4wascarefullycalculatedconsideringitsgeometricalshape.Alltheusedmass.stiffnessanddampingvaluesweresummarizedinTable2.whereaandpcanbedeterminedbycomparingmodelsimulationresultwithexperimentallymeasuredrecord.2.4MassandMomentofInertiaModelingValve,tappetplunger,andfollowermassMv,Mt,andMfweredirectlymeasured.ThefollowermomentofinertiaIfwhereEisbulkmodulus,Heisthelengthofcompressedoilchamber,andAeisplungerarea.Ontheotherhand.theequivalentdampingcoefficientwasestimatedbyassumingthattheoilistotallyincompressive.Itwasassumedthattheexcessiveoilduetoplungermotionflowscompletelythroughthediametralclearance.Thentheequivalentdampingvaluecanbepredictedfromthetheoryoffluidmechanics.Itisknownthatthedampingcoefficientchangeswiththedirectionofplungermotion.Thoseare7XRcScosOsinOYRcSsinOcosO3.1KinematicalAnalysisWhensearchingthepointwherecamandfollowercontacts,thetappetwasconsideredfixedpoint.Itwasfoundthattheinfluenceoftappetmotionuponcontactpointisnegligible.Thetappetmotion,whichisatmostO.Imm.isenoughsmallandcanbeconsiderednegligibleanddiffersinorderofmagnitudewithcamlift.WhenthecamdataisgivenwithdesiredcamliftS,theactualcamshapeX,.Y,contactingwithaflatfollower,canbeobtainedfromEq.7Thebaselinerockerarmratiois1.47andthefluctuatingrangeofrockerarmratiovariesfrom1.15to1.97duringthecycle.ThefingerfollowertypeORCcamvalvesystemischaracterizedwithvaryingrockerarmratiowithcamshaftrotations.Sothekinematicalanalysistosearchtheexactcontactpointsbetweencamandfollowerisinevitablebeforedoingdynamicanalysis.3.ANALYSISwhereRciscambasecircle.0iscamangle,Sisflatfollowerdisplacement,andXandYspecifycamshape.TheincrementofSabout0canbecalculatedwithcubicsplineinterpolationShoup.1979.WhenthecamshapeX.Yisgiven,thecontactpointbetweencamandfollowercanbefoundbykinematicalanalysis.Fig.4showstheideahowtofindthecontactpoint.Theproceduresare.first,rotatethefolloweraroundafixedcam.thenfindoutthelocusoffollowercenterCCNext.searchthecontactpointforeachfollowerrotatingangleOcusingtheprinciplethatthecontactpointis6whereJ1.isoilviscouscoefficient,Lisplungerlength,Rpisplungerradius,andhisclearancebetweencylinderandplunger.AlltappetdimensionsandpropertiesaregiveninTable1.Equations4,5derivedabovearetwoextremecases.oneisassumedtotallycompressiveandtheotheristotallyincompressive.Butinactualsituation,thedragforceFdduetoplungermotionwillbeplacedsomewhereinthemiddleofthetwovaluesKreuterandMass.1987.AsintroducingtwocoefficientsaandPOaI,Op1,thedragforcecanbemodeledasEq.6.
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