外文文献.pdf

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 fingerfollower 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 freedomlumpejspringdampermass 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 camvalve motion was directly compared with the measured valve and tappet motions. Key Words:FingerFollower(OscillatiwRoller Follower), Overhead Cam(OHC), CamValve System, Jump, Bounce NOMENCLATURE- Ae:Equivalent cross-sectionalareaof oil chamber in tappet, m2 C.C.2C.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,Ns/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.1K.2K.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 Lf:Leverarmof forceFfmm 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 mm2: 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,Yfinger-follower translational and rotational motion,Y/and 8/, and two additional degree of freedomYS!andYS2which 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 thecompotsand the contact points of the cam-valve system wererueledwith equivalent mass, springs and dampers asshoinFig.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 Possons 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 Kl=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 KsandKsa),and 3 dampers(CshCszandC.a)with 2 degree of freedom(sandz).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 Cf 118.97 Mv 0.08544Kfc8.37x 10 Cfc 197.97 m,0.0092KVf4.33x 10CVf94.13 m20.0092K 1.31x10C634.77 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(OaI,Op1),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 cent