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40KSMEJOURNAL,VOLA,NO1,PP4047,1990ANALYTICALANDEXPERIMENTALMOTIONANALYSISOFFINGERFOLLOWERTYPECAMVALVESYSTEMWITHAHYDRAULICTAPPETWONJINKIM,HYUCKSOOJEONANDYOUNSIKPARKRECEIVEDSEPTEMBER11,1989INTHISPAPER,THEMOTIONOFAFINGERFOLLOWERTYPECAMVALVESYSTEMWITHAHYDRAULICTAPPETWASANALYTICALLYANDEXPERIMENTALLYSTUDIEDFIRST,THEEXACTCONTACTPOINTBETWEENCAMANDFOLLOWERFOREACHCORRESPONDINGCAMANGLEWASSEARCHEDBYKINEMATICANALYSISTHENA6DEGREEOFFREEDOMLUMPEJSPRINGDAMPERMASSMODELWASCONSTRUCTEDTOSIMULATETHEVALVEMOTIONANALYTICALLYWHENCONSTRUCTINGTHEMODEL,MOSTOFTHEPARAMETERSWEREEXPERIMENTALLYDETERMINEDBUTSEVERALVALUESWHICHAREDIFFICULTTODERIVEEXPERIMENTALLYSUCHASDAMPINGCOEFFICIENTSWEREDETERMINEDWITHENGINEERINGINTUITIONINORDERTOSHOWTHEEFFECTIVENESSOFTHEANALYTICALMODEL,THEPREDICTEDCAMVALVEMOTIONWASDIRECTLYCOMPAREDWITHTHEMEASUREDVALVEANDTAPPETMOTIONSKEYWORDSFINGERFOLLOWEROSCILLATIWROLLERFOLLOWER,OVERHEADCAMOHC,CAMVALVESYSTEM,JUMP,BOUNCENOMENCLATUREAEEQUIVALENTCROSSSECTIONALAREAOFOILCHAMBERINTAPPET,M2CC2C3EQUIVALENTDAMPINGCOEFFICIENTSOFVALVESPRING,N/MCEDAMPINGCOEFFICIENTOFVALVESEAT,NS/MC,F,CVF,CFEEQUIVALENTDAMPINGCOEFFICIENTSOFCONTACTPOINT,NS/MC,PEQUIVALENTDAMPINGCOEFFICIENTOFTAPPETNS/M/0FUNDAMENTALNATURALFREQUENCYOFVALVESPRING,HZFOINITIALCOMPRESSIONFORCEOFVALVESPRING,NFIFFVFFFECONTACTFORCESATEACHCONTACTPOINT,NFIFO,FVFO,FFEOINITIALCONTACTFORCESATEACHCONTACTPOINT,NHCLEARANCEBETWEENCYLINDERANDPLUNGER,MMHELENGTHOFCOMPRESSEDOILCHAMBER,MMIFFOLLOWERMOMENTOFINERTIA,KGM2KOVALVESPRINGSTIFFNESS,N/MKEEQUIVALENTSTIFFNESSOFTAPPETOILCHAMBER,N/MK1K2K3EQUIVALENTSTIFFNESSCOEFFICIENTSOFVALVESPRING,N/MKSTIFFNESSOFTAPPETSOFTSPRING,N/MK,F,KVF,KFEEQUIVALENTSTIFFNESSCOEFFICIENTSOFCONTACTPOINT,N/MLPLUNGERLENGTH,MMLFLEVERARMOFFORCEFFMMLVFLEVERARMOFFORCEFVF,MMMEMASSOFOILINSIDETAPPETOILCHAMBER,KGMFFOLLOWERMASS,KGMTEQUIVALENTTAPPETMASS,KGMVEQUIVALENTVALVEMASS,KGDNPARTMENTOFMECHANICALENGINEERING,KOREAADVANCEDINSTITUTEOFSCIENCEANDTECHNOLOGY,POBOX150CHEONGRUARLG,SEOUL130650,KOERAMM2EQUIVALENTVALVESPRINGMASSES,KGRPRADIUSOFTAPPETPLUNGER,MMRERADIUSOFCAMBASECIRCLE,MMRABDISTANCEFROMCAMPIVOTTOFOLLOWERPIVOT,MMR,LENGTHOFOSCILLATINGROLLERFOLLOWER,MMRFRADIUSOFROLLERINROLLERFOLLOWERMODEL,MMYFFOLLOWERDISPLACEMENT,MMY,TAPPETDISPLACEMENT,JTMYECAMLIFT,MMYVVALVEDISPLACEMENT,MMYY2DISPLACEMENTSOFEQUIVALENTVALVESPRINGMASSES,MM8FANGULARROTATIONOFFOLLOWER,RADIANJTOILVISCOSITYCOEFFICIENT,PASEBULKMODULUS,N/M28ANGULARROTATIONOFCAM,RADIAN1INTRODUCTIONWHENDESIGNINGACAMVALVETRAINOFINTERNALCOMBUSTIONENGINE,THEREAREMANYTHINGSTOBECONSIDEREDSUCHASVALVELIFTAREA,PEAKCAMACCELERATION,PROPERCAMEVENTANGLE,RAMPVELOCITY,ETCASINCREASINGTHEOPERATIONSPEEDOFINTERNALCOMBUSTIONENGINE,THEDYNAMICEFFECTOFCAMVALVESYSTEMBECOMESMOREIMPORTANTRECENTLY,SOMERESEARCHESHAVEBEENDONEFOCUSINGTHEDYNAMICEFFECTSONCAMVALVESYSTEMAKIBA,ETAL1981CONSTRUCTEDA4DEGREEOFFREEDOMMODELTOANALYZEANOHVOVERHEADVALVETYPECAMVALVESYSTEMANDSTUDIEDTHEDYNAMICEFFECTSONTHESYSTEMMOTIONJEANANDPARK1989TRIEDTOANALYZETHESAMETYPEOFVALVESYSTEMWITHALUMPEDMASSDYNAMICMODELANDDESIGNEDANOPTIMALCAMSHAPECONSIDERINGDYNAMICEFFPISANOANDFREUDENSTEIN1982DEVELOPEDADYNAMICMODELOFAHIGHSPEEDVALVESYSTEMCAPABLEOFPREDICTINGBOTHNORMALSYSTEMRESPONSEASWELLASPATHOLOGICALBEHAVIORASSOCIATEDWITHONSETOFJUMPING,BOUNCE,ANDSPRINGSURGEPREVIOUSRESEARCHESINHIGHSPEEDCAMSYSTEMHADBEENALMOSTFOCUSEDONSYSTEMSWITHACONSTANTROCKERARMRATIOANDONTHEVALVEANALYTICALANDEXPERIMENTALMOTIONANALYSISOFFINGERFOLLOWERTYPECAMVALVESYSTEMWITH41TRAINSEPARATIONPHENOMENAESPECIALLY,THEANALYSISFORCAMSYSTEMHAVINGAHYDRAULICTAPPETHASNOTBEENTHOROUGHLYSTUDIEDINTHISWORK,ANOHCCAMVALVETRAINWITHAHYDRAULICTAPPETANDAFINGERFOLLOWER,WASANALYZEDANALYTICALLYWITHLUMPEDMASSMODELANDITSRELIABILITYWASVERIFIEDEXPERIMENTALLYTHECAMFOLLOWERSYSTEMUSEDINTHISWORKISCHARACTERIZEDWITHITSCOMPLEXDYNAMICSOFHYDRAULICTAPPETANDTHENONLINEARITYFROMVARYINGROCKERARMRATIOTHEROCKERARMRATIODEVIATESASMUCHAS34PERCENTFROMABASELINEVALUEOFI47ASTHECONTACTPOIRUBETWEENCAMANDFOLLOWERMOVESTHEPIVOTENDOFTHEOSCILLATINGFOLLOWERISSUPPORTEDNOTATAFIXEDPOINTBUTATAVERTICALLYMOVINGPIVOTMOUNTEDATTOPAHYDRAULICTAPPETTHEMAJORROLEOFTHEHYDRAULICTAPPETISTOREMOVETHEVALVELASHWHICHGIVESHARMFULIMPACTWITHINVALVETRAINBUTINHIGHOPERATINGSPEEDREGION,THEHYDRAULICTAPPETCANBEOPRATEDABNORMALLYANDCANMAKEANUNUSUALVALVETRAINMOTIONTHEREFORE,THECHARACTERISTICSOFTHEHYDRAULICTAPPETMUSTBECONSIDEREDINVALVETRAINDYNAMICMODELTHEPRIMARYRESEARCHFORASIMILARCAMSYSTEMWASDONEBYCHANANDPISANO1987THEYESTABLISHEDSIXDEGREESOFFREEDOMMODELCONSIDEREDTRANSLATIONALANDROTATIONALMOTIONOFOSCILLATIONGFOLLOWERANDVALVEBUTTHEYUSEDASIMPLESINGLEDEGREEOFFREEDOMMODELFORTHEHYDRAULICTAPPETTHEYFOCUSEDONLYONANALYTICALWORKANDDIDNOTATTEMPTTOVERIFYTHERESULTSEXPERIMENTALLY2VALVETRAINMODELINGTAPPETFIG10BII\PVALVEIISPRINGIF0IIVALVESEATSCHEMATICOFFINGERFOLLOWERVALVETRAINTHEACTUALOVERALLSHAPEOFANOHCTYPECAMVALVETRAINISSHOWNINFIGIINORDERTODESCRIBETHEVALVEMOTIONPRECISELY,THEVALVETRAINWASMODELEDWITH6DEGREEOFFREEDOMTHOSEAREVALVEOPENINGANDCLOSINGMOTION,YV,HYDRAULICTAPPETTRANSLATIONALMOTION,YFINGERFOLLOWERTRANSLATIONALANDROTATIONALMOTION,Y/AND8/,ANDTWOADDITIONALDEGR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