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40KSMEJournal VolA No 1 pp 40 47 1990 ANALYTICALANDEXPERIMENTAL MOTION ANALYSIS OFFINGER FOLLOWER TYPE CAM VALVE SYSTEM WITH A HYDRAULICTAPPET Won Jin Kim Hyuck Soo Jeon and Youn Sik Park Received September11 1989 Inthis paper the motionofa finger follower type cam valve system with a hydraulic tappet was analytically and experimentally studied First the exact contact point between cam and follower for each corresponding cam angle was searchedbykinematic analysis Then a 6degree of freedomlumpe jspring damper mass model was constructed to simulate the valve motion analytically When constructing the model mostofthe parameters were experimentally determined Butseveral values which are difficult to derive experimentally such as damping coefficients were determined with engineering intuition Inorder toshowthe effectiveness of the analyticalmodel the predicted cam valve motion was directly compared with the measured valve and tappet motions Key Words Finger Follower Oscillati wRoller Follower Overhead Cam OHC Cam Valve System Jump Bounce NOMENCLATURE Ae Equivalent cross sectionalareaof oil chamber in tappet m2 C C 2 C 3 Equivalent damping coefficients of valve spring N m C e Damping coefficient of valve seat N s m c f CVf Cfe Equivalent damping coefficients ofcontact point N s m c p Equivalent damping coefficient of tappet N s m 0 Fundamental natural frequency of valve spring Hz Fo Initial compression force of valve spring N Fif Fvf Ffe Contact forcesateach contact point N FifO Fvfo Ffeo Initial contact forcesateach contact point N h Clearance between cylinder and plunger mm He Lengthofcompressed oil chamber mm If Follower moment of inertia kg m2 Ko Valve spring stiffness N m Ke Equivalent stiffness oftappetoil chamber N m K 1 K 2 K 3 Equivalent stiffness coefficients of valve spring N m K Stiffness oftappetsoft spring N m K f Kvf Kfe Equivalent stiffness coefficients of contact point N m L Plunger length mm L f Leverarmof forceF f mm Lvf Leverarmof forceFvf mm me Mass of oil insidetappetoil chamber kg Mf Follower mass kg Mt Equivalenttappetmass kg Mv Equivalent valve mass kg DnpartmentofMechanical Engineering Korea Advanced Insti tute of Science and Technology P O Box150Cheongruarlg Seoul 130 650 Koera m m2 Equivalent valve spring masses kg Rp Radiusoftappetplunger mm Re Radius of cam base circle mm Rab Distance fromcampivot to follower pivot mm R length of oscillating roller follower mm Rf Radius of roller in roller follower model mm Yf Follower displacement mm Y Tappetdisplacement j tm Ye Cam lift mm Yv Valve displacement mm Y Y 2 Displacements of equivalent valve spring masses mm 8f Angularrotationof follower radian j t Oil viscosity coefficient Pa s E Bulk modulus N m2 8 Angular rotation of cam radian 1 INTRODUCTION When designing a cam valvetrainofinternal combustion engine therearemany thingstobe considered suchasvalve lift area peakcamacceleration propercamevent angle rampvelocity etc As increasingtheoperation speed of internal combustion engine the dynamic effect of cam valve system becomes more important Recently some researches have been done focusing the dynamic effects on cam valve system Akiba etal 1981 constructed a 4 degree of freedom model to analyzeanOHV Overhead Valve type cam valve system and studiedthedynamic effects onthesystem motion Jeanand Park 1989 tried to analyze the same type of valve system with a lumped mass dynamic model and designed an optimalcamshape considering dynamiceff Pisano and Freudenstein 1982 developed a dynamic modelofa high speed valve system capable of predicting both normal system response as wellaspathological behavior associated with onsetof jumping bounce andspringsurge Previous researches in high speedcamsystem had been almost focused on systems with a constant rocker armratioand onthevalve ANALYTICALANDEXPERIMENTAL MOTIONANALYSISOF FINGER FOLLOWERTYPECAM VALVESYSTEMWITH 41 train separation phenomena Especially the analysis for cam system having a hydraulic tappet has not been thoroughly studied In this work an OHC cam valve train with a hydraulic tappet and a finger follower was analyzed analytically with lumped mass model and its reliability was verified experi mentally Thecam follower system usedinthis work is characterized with its complex dynamics of hydraulic tappet and the nonlinearity from varying rocker arm ratio The rocker arm ratio deviates as much as34percent from a baseline value of I 47as the contactpoirUbetweencamand follower moves The pivot end of the oscillating follower is supported notata fixed point butata vertically moving pivot mountedattop a hydraulic tappet Themajor role of the hydraulic tappet is to remove the valve lash which gives harmful impact within valve train But in high operating speed region the hydraulic tappet can be oprated abnormally and can make an unusual valve train motion Therefore the characteristics of the hydraulic tappet must be consideredin valve train dynamic model Theprimary research for a similar cam system was done by Chan and Pisano 1987 They established six degrees of freedom model considered translational and rotational motion of oscillationg follower and valve But they used a simple single degree of freedom model for the hydraulic tappet They focused only on analyti cal work and did not attempttoverify the results experimen tally 2 VALVETRAINMODELING TAPPET Fig 1 0 b Ii P VALVE I ISPRING If 0 II VALVE SEAT Schematicoffinger follower valve train Theactual overall shape of an OHC type cam valve train is shown in Fig I Inorder to describe the valve motion precisely the valve train was modeled with 6 degree of freedom Those are valve opening and closing motion Yv hydraulic tappet translational motion Y finger follower translational and rotational motion Y and 8 and two additional degree of freedomYS andYS2 which represent valve spring translational motion Thereason for taking valve spring motionsYS andYS2is to consider valve spring surge phenomenon Itis knownthatvalve spring surge affects greatly on valve motion especially when the operation speed is high Because camshaft can be consideredasrigid and fixed on its bearing its dynamic characteristics was neglect edinthe model All thecompo tsand the contact points of the cam valve system wereru eledwith equivalent mass springs and dampers assho inFig 2 Thedetails of modeling proce dureareexplainedasfollows 2 1ContactPointModeling As showninFig 1the finger follower type cam valve train CAM TAPPET I VALVE SEAT VALVE SPRING Cse Fig 2Usedmodel 42 Won inKim Hyuck SooJeonand Youn Sik Park Theequivalent mass Me offinger followerateach contact point can be obtained fromEq 2 asconsidering the follower moment of inertia If whereMfis the follower equivalent mass andIis the dis tance between follower mass center and each corresponding contact point Theequivalent mass of camshaftatcontact point is estimated to infinity as assumingthatit is rigid and has4 contact points between valvetraincomponents Those arebetween follower and tappet follwer and cam follower and valve and valve seat and valve Thecontactatvalve seat occurs periodicallyasdifferent with others which should maintain continuous contact Theequivalent valveseatstiff ness Kse anddamping Cse cofficients weretakenfrom the previously published literature Chan and Pisano 1987 On the other hand the equivalent damping and stiffness coeffi cientsatother contact points were predicted by Hertz con tacttheory utilizing shape factor modulus of elasticity and Posson s ratio AJ assuming the proper range of contact forces the corresponding contact stiffness was calculated by Hertz contact theory Thenthe equivalent stiffnessesateach contact point were determined by least squareerrorcurve fit from obtained contact stiffnesses Roark and Young 1976 It was assumedthatthe contact between tappet and follower is aninternal contact of two spheres between cam and follwer is a contact of two cylinders and between follower and valve is a contact of a cylinder on a plane Thedamping coefficientsateach contact point were assumedas0 06and the critical damping coefficient Ccr can be calculated using Eq I WhereM andMzarethe equiva lent masses of each contacting component it was assumed thatthe equivalent masses of each contacting component M andMz areconnected by a spring and a damper 3 2 m mz rKol flo 8 K l K a rKo K z 4Ko 2 3HydraulicTappetModeling Theleft side of Fig 3 shows the cross section shape of hydraulic tappet Oil enters through entrance and fills the central cavity of tappet plunger As the plunger moves down the check valve is closed and the oil flows from oil chamber through narrow clearance between plunger and cylinder and generates damping force In next step when the plunger moves upward due to the spring positioned inside of oil chamber the check valve is opened and oil is refilled in oil chamber Thehydraulic tappet was simplifiedasshown in the right side of Fig 3 and the equivalent stiffness of the tappet was estimated by assumingthatthe fluid is totaly compres sive and there is no flow through diametral clearance The Thespringrateand fundamental natural frequency of used valve springare35KN1mand 504 46Hz respectively The damping is assumed as4 proportional viscous damping fixed on its bearing Theequivalent masses of tappet and valveatother contact points areM andMv 2 2ValveSpringModeling In order to consider valve spring surge effect the valve spring was modeled with 2masses m andmz 3springs KSh Ks andKsa and 3 dampers CshCszandC a with 2 degree of freedom s and z Several assumptions were made in the valve spring modeling Those are i symmetricity K KsaandC Csa ii equivalency ofstaticstiff ness and fundamental natural frequency between model and fundamental natural frequency between model and actual system iii proper damping assumption As consideringthatvalve spring is in clamped clamped boundary conditon the secondary natural frequency of valve spring becomes twice of the fundamental spring natural frequency All the above assumptions give 1 2 C 2 KM Mz crM M OIL ENTRANCE hJ 0 Mf0 05981K 5 92x 10 1 1280 0 h 1 1527X10 Kif 5 52X10 C f 118 97 Mv 0 08544Kfc8 37x 10 Cfc 197 97 m 0 0092KVf4 33x 10 CVf94 13 m20 0092K 1 31x10 C 634 77 K K 9 33xlO Cu C a 2 35 5 K 2 1 40 x 10 C 23 534 relationship is 4 was carefully calculated considering its geometrical shape All the used mass stiffness and damping values were sum marizedinTable2 whereaandpcan be determined by comparing model simulation result with experimentally measured record 2 4Mass and MomentofInertia Modeling Valve tappet plunger and follower mass Mv Mt andMf were directly measured Thefollower moment of inertia If whereEis bulk modulus Heis the length of compressed oil chamber andAeis plunger area Onthe other hand the equivalent damping coefficient was estimated by assumingthatthe oil is totally incompressive It was assumedthatthe excessive oil due to plunger motion flows completely through the diametral clearance Then the equivalent damping value can be predicted from the theory of fluid mechanics Itis knownthatthe damping coefficient changes with the direction of plunger motion Those are 7 X Rc S cosO sinO Y Rc S sinO cosO 3 1Kinematical Analysis When searching the point where cam and follower con tacts the tappet was considered fixed point It was foundthat the influence of tappet motion upon contact point is negli gible Thetappet motion which isatmostO I mm is enough small and can be considered negligible and differs in order of magnitude with cam lift When the camdatais given with desired cam lift S the actualcamshape X Y contacting with a flat follower can be obtained fromEq 7 Thebaseline rocker arm ratio is1 47and the fluctuating range of rocker armratio varies from1 15to1 97during the cycle Thefinger follower type ORC cam valve system is char acterized with varying rocker arm ratio with cam shaft rotations So the kinematical analysis to search theexact contact points between cam and follower is inevitable before doing dynamic analysis 3 ANALYSIS whereRcis cam base circle 0is cam angle Sis flat follower displacement andXandYspecify cam shape Theincre ment ofSabout0can be calculated with cubic spline inter polation Shoup 1979 When the cam shape X Y is given the contact point between cam and follower can be found by kinematical analysis Fig 4 shows the idea how to find the contact point Theprocedures are first rotatethe follower around a fixed cam then find out the locus of follower center CC Next search the contact point for each follower rotatingangle Oc using the principlethatthe contact point is 6 whereJ1 is oil viscous coefficient Lis plunger length Rpis plunger radius andhis clearance between cylinder and plunger All tappet dimensions and propertiesaregiven in Table1 Equations 4 5 derived above are two extreme cases one is assumed totally compressive and the other is totally incom pressive Butinactual situation the dragforce Fd dueto plunger motion will be placed somewhere in the middle of the two values Kreuter and Mass 1987 As introducing two coefficientsaandP O a I O p 1 the drag forcecanbe modeledasEq 6 44 Won JinKim Hyuck Soo JeanandYoun Sik Park the point where the line connectingcamcenter A and the follower center any point in locusCC crosses with the tangent lineatthe correspondingcamangle Thenthe con tactpoint locuscanbe determined byrotatingthe searched contactpointtothebackwardas much asthecorresponding camangle 8e Thekinematic dimensions of Fig 4aregiven inTable3 Theinstantaneous rocker armratiois calculated by dividingthetotallength of the finger follower with the horizontal distance betweenthepivot point and cam and followercontactpoint for each corresponding cam angle The obtained contact point locus and the corresponding fluctuat ing rocker armratiofor this studyareshown in Fig 5 a b 3 2Dynamical Analysis Whenthecamshape operation speed and follower shape aregiven the equationsofmotioncanbe easily constructed Duringthecalculation of contact point all dimensions ofLfc distance betweentappetand follower mass center LoAdis tance betweencamcontactpoint and follower mass center andLOf distance between valve and follower mass centercan be obtained Here LuandLVfgiven inTable3are constant Lfcis calculated with instantaneouscontactpoint Theeffect of the fluctuating rocker armratioon the valvetrain dynamics is represented by varyingLfc Thenthe equations of motioncanbe constructed as FOLLOWER M Y Fu K pY C pY MfYf Ffc F f FOf fij F fL f FfcLfc FofLof mlYSI KSI Y o YSI CSI Yo YSI Ksz YSI Ysz Csz YSI Ysz mzYsz Ksz YSI Yd Csz YSI Ysz 8 KSIYsz CSIYsz moYo Fof KseYo CseYo KSI Y o Y SI CSI Yo YSI if Yo Fo Kse whereFois the precompressed force of valve spring in this study Fo 275 N Thecontact forcesF f Ffc andFOfcanbe determinedas Eq 9 10 34 00 14 22 22 53 unit mm 36 40 31 67 13 00 Table 3Kinematic dimensions Betweentappetand follower Yf Y Lf sin8f F fo K f Between cam and follower Ye Yf Lfesin8f Ffeo Kfe Between valve and follower Yf Yo Lofsin8f 12 8 4048 x coord mml a 2 5 0 2 0 L E L 1 5 flI I L 1 0 0 5 1001 100 cam angle deg 1 b Fig 5Contact point locus and fluctuating rocker arm ratio ANALYTICALANDEXPERIMENTAL MOTION ANALYSISOFFINGER FOLLOWER TYPE CAM VALVESYSTEMWITH 45 Im expo 100 l 70 i 1 1 40 u i 10 0 20 30 70110 ca angIe deg a 150 190 1 expo 100 l 70 i e40 0 2 10 0 20 30 Fig 7 120 i OIl OIl 90 I 0 0 SO C lI 0 Cl 8 30 CI k l 0 90014002000260Q3200 ell shllftspeed rpm Fig 8Maximum tappet leakage down versus camshaft speed 70110150190 call1 ang e l Ie9 b a Camshaft speed900rpm b Camshaft speed1600rpm Tappet leakagedown 9 10 11 we can concludethatthe 6 degree of freedom lumped mass model used in this work is quite reliable to predict valve motion even in high operating speed Figure12shows a sample of contact forcesatall contact points when the operation speed is2450rpm Itcan be observedthatthe contact forcesatthe first peak position are reduced andatthe second peak position are accentuated as compared with the value of constant rocker arm ratiocam system duetofluctuationg rocker arm ratio As examining the contact force record we can easily predict the most possibleareaand correspondingcamangle where unwanted valvetrainseparationcanbe occurred Theexperimentally verified model can be expanded not only to predict the maximum operation speed but also to Fig 6Experimental apparatus 5 RUSULT AND DISCUSSION 4 EXPERIMENT Figure 7 compares the measured and simulated tappet leakage downatcamshaft speed900and1600rpm Figure 8 shows the measured maximum tappet leakage down Itis knownthathydraulic tappet is stiffened as the speed of camshaft is increased Themaximum compression of the hydraulic tappet was about100 lmat800rpm and approa ched a limit of about60 lmasthe camshaft speed goes beyond 3000rpm asshown in Fig 8 As explained before the measured tappet motion was used to determine the weighting paramentersaand 3 which determine the plungerdrag force by least square curve fit between the measurement and the analysis record Itwas foundthatthe weighting parame ter varies with operation speed For example aand 3where 0 0071and0 28when camshaft is driven by900rpm but the values were changed to0 0094and0 30when the running speed was raised to 1600rpm Figures9 10 11show the measured and simulated valve displacementsandvelocities Thevalvevelocitywas obtained by differentiating the measured valve displacement record Figure 9 compares the measured and analyzed valve motion when the camshaft was drivenat600rpm Itcan be saidthatthe model can simulate not only the peak valve displacement but also thecamevent angle quite precisely Figure10 11show the analysis and measurement when the camshaft speedsare1600rpm 2450rpm As glancingatFigs Inordertoprove the effectiveness of the model simulation experimental work was done and compared each other Figure6 shows the experimental apparatus While the OHC type cam valve train was driven by a 100 kW DC motor valve displacement and hydraulic tappet motion were measured simultaneously Thevalve displacement was