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40 KSME Journal, VolA, No.1, pp. 40-47,1990. ANALYTICAL AND EXPERIMENTAL MOTION ANALYSIS OF FINGER FOLLOWER TYPE CAM-VALVE SYSTEM WITH A HYDRAULIC TAPPET Won-Jin Kim-, Hyuck-Soo Jeon- and Youn-Sik Park- (Received September 11, 1989) In this paper, the motion of a 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 searched by kinematic analysis. Then a 6 degree of freedom lumpej springdampermass model was constructed to simulate the valve motion analytically. When constructing the model, most of the parameters were experimentally determined. But several values which are difficult to derive experimentally such as damping coefficients were determined with engineering intuition. In order to show the effectiveness of the analytical model, 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- A e : Equivalent cross-sectional area of oil chamber in tappet, m 2 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, C fe : Equivalent damping coefficients of contact point, Ns/m c,p: Equivalent damping coefficient of tappet: N-s/m /0: Fundamental natural frequency of valve spring, Hz F o : Initial compression force of valve spring, N F if F vf F fe : Contact forces at each contact point, N FifO, F vfo , Ffeo: Initial contact forces at each contact point, N h: Clearance between cylinder and plunger, mm He: Length of compressed oil chamber, mm If: Follower moment of inertia, kg-m 2 K o : Valve spring stiffness, N/m K e : Equivalent stiffness of tappet oil chamber, N/m K. 1 K. 2 K. 3 : Equivalent stiffness coefficients of valve spring, N/m K.: Stiffness of tappet soft spring, N/m K,f, Kvf, K fe : Equivalent stiffness coefficients of contact point, N/m L: Plunger length, mm Lf: Lever arm of force Ff mm L vf : Lever arm of force F vf , mm me: Mass of oil inside tappet oil chamber, kg M f : Follower mass, kg M t : Equivalent tappet mass, kg M v : Equivalent valve mass, kg Dnpartment of Mechanical Engineering, Korea Advanced Insti tute of Science and Technology, P.O.Box 150 Cheongruarlg, Seoul 130-650, Koera m m2: Equivalent valve spring masses, kg Rp : Radius of tappet plunger, mm R e : Radius of cam base circle, mm R ab : Distance from cam pivot to follower pivot, mm R, : length of oscillating roller follower, mm R f : Radius of roller in roller follower model, mm Y f : Follower displacement, mm Y,: Tappet displacement, j.tm Y e : Cam lift, mm Y v : Valve displacement, mm Y. Y. 2 : Displacements of equivalent valve spring masses, mm 8 f : Angular rotation of follower, radian j.t: Oil viscosity coefficient, Pa-s E: Bulk modulus, N/m 2 8: Angular rotation of cam, radian 1. INTRODUCTION When designing a cam-valve train of internal combustion engine, there are many things to be considered such as valve lift area, peak cam acceleration, proper cam event angle, ramp velocity, etc. As increasing the operation 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, et al.(1981) constructed a 4 degree of freedom model to analyze an OHV (Overhead Valve) type cam-valve system and studied the dynamic effects on the system motion. Jean and Park(1989)tried to analyze the same type of valve system with a lumped mass dynamic model and designed an optimal cam shape considering dynamiceff.Pisano and Freudenstein (1982) developed a dynamic model of a high speed valve system capable of predicting both normal system response as well as pathological behavior associated with onset of jumping, bounce, and spring surge. Previous researches in high-speed cam system had been almost focused on systems with a constant rocker-arm ratio and on the valve . ANALYTICAL AND EXPERIMENTAL MOTION ANALYSIS OF FINGER FOLLOWER TYPE CAM- VALVE SYSTEM WITH . 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. The cam-follower system used in this 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 as 34 percent from a baseline value of I.47as the contact poirU between cam and follower moves. The pivot end of the oscillating follower is supported not at a fixed point but at a vertically moving pivot mounted at top a hydraulic tappet. The major 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 considered in valve train dynamic model. The primary 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 attempt to verify the results experimen tally 2. VALVE TRAIN MODELING TAPPET Fig. 1 :0: b Ii P: VALVE I()I SPRING I f 0: I I VALVE SEAT Schematic of finger follower valve train The actual overall shape of an OHC type cam-valve train is shown in Fig.I. In order 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 freedom Y S ! and YS2 which represent valve spring translational motion. The reason for taking valve spring motions Y S ! and Y S2 is to consider valve spring surge phenomenon. It is known that valve spring surge affects greatly on valve motion especially when the operation speed is high. Because camshaft can be considered as rigid and fixed on its bearing, its dynamic characteristics was neglect ed in the model. All thecompotsand the contact points of the cam-valve system wererueledwith equivalent mass, springs and dampers asshoin Fig. 2. The details of modeling proce dure are explained as follows. 2.1 Contact Point Modeling As shown in Fig. 1 the finger-follower type cam-valve train CAM TAPPET I VALVE SEAT VALVE SPRING . Cse Fig. 2 Used model 42 Won-in Kim, Hyuck-Soo Jeon and Youn-Sik Park The equivalent mass (Me)of finger follower at each contact point can be obtained from Eq. (2) as considering the follower moment of inertia(If). where M f is the follower equivalent mass and I is the dis tance between follower mass center and each corresponding contact point. The equivalent mass of camshaft at contact point is estimated to infinity as assuming that it is rigid and has 4 contact points between valve train components. Those are between follower and tappet, follwer and cam, follower and valve, and valve seat and valve. The contact at valve seat occurs periodically as different with others which should maintain continuous contact. The equivalent valve seat stiff ness (Kse)and damping (Cse)cofficients were taken from the previously published literature (Chan and Pisano, 1987). On the other hand, the equivalent damping and stiffness coeffi cients at other contact points were predicted by Hertz con tact theory 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. Then the equivalent stiffnesses at each contact point were determined by least square error curve fit from obtained contact stiffnesses (Roark and Young, 1976). It was assumed that the contact between tappet and follower is an internal 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. The damping coefficients at each contact point were assumed as 0.06 and the critical damping coefficient (Ccr) can be calculated using Eq.(I). Where M, and M z are the equiva lent masses of each contacting component. it was assumed that the equivalent masses of each contacting component(M, and M z ) are connected by a spring and a damper. (3) 2 m, = mz=:rKol (flo) 8 Kl=K.a=:rKo, K.z=4Ko 2.3 Hydraulic Tappet Modeling The left 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. The hydraulic tappet was simplified as shown in the right side of Fig.3 and the equivalent stiffness of the tappet was estimated by assuming that the fluid is totaly compres sive and there is no flow through diametral clearance. The The spring rate and fundamental natural frequency of used valve spring are 35 KN1m and 504.46Hz, respectively. The damping is assumed as 4% proportional viscous damping. fixed on its bearing. The equivalent masses of tappet and valve at other contact points are M, and Mv. 2.2 Valve Spring Modeling In order to consider valve spring surge effect, the valve spring was modeled with 2 masses (m, and mz), 3 springs (KSh K s and Ksa), and 3 dampers(Cs h C sz and C.a) with 2 degree of freedom (s and z). Several assumptions were made in the valve spring modeling. Those are; ( i ) symmetricity (K.,=K sa and C., = C sa ), ( ii) equivalency of static stiff ness and fundamental natural frequency between model and fundamental natural frequency between model and actual system, (iii) proper damping assumption. As considering that valve 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,M z cr M,+M. OIL ENTRANCE -hJ.-0) M f 0.05981 K: 5.92 x 10; 1.128 0,0) h 1.1527 X 10- Kif 5.52 X 10 Cf 118.97 M v 0.08544 K fc 8.37 x 10 Cfc 197.97 m, 0.0092 K Vf 4.33 x 10 CVf 94.13 m 2 0.0092 K 1.31 x 10 C 634.77 K . K . 9.33xlO Cu. C.a 2.35!5 K.2 1.40 x 10 C.2 3.534 relationship is (4) was carefully calculated considering its geometrical shape. All the used mass. stiffness and damping values were sum marized in Table 2. where a and p can be determined by comparing model simulation result with experimentally measured record. 2.4 Mass and Moment of Inertia Modeling Valve, tappet plunger, and follower mass (M v , M t , and M f ) were directly measured. The follower moment of inertia (If) where E is bulk modulus, He is the length of compressed oil chamber, and Ae is plunger area. On the other hand. the equivalent damping coefficient was estimated by assuming that the oil is totally incompressive. It was assumed that the 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. It is known that the damping coefficient changes with the direction of plunger motion. Those are (7) X= (Rc+S)cosO-sinO Y= (Rc+S)sinO+cosO 3.1 Kinematical Analysis When searching the point where cam and follower con tacts, the tappet was considered fixed point. It was found that the influence of tappet motion upon contact point is negli gible. The tappet motion, which is at most O.I(mm). is enough small and can be considered negligible and differs in order of magnitude with cam lift. When the cam data is given with desired cam lift (S), the actual cam shape (X, .Y), contacting with a flat follower, can be obtained from Eq.(7) The baseline rocker-arm ratio is 1.47 and the fluctuating range of rocker arm ratio varies from 1.15 to 1.97 during the cycle. The finger-follower type ORC cam-valve system is char acterized with varying rocker-arm ratio with cam shaft rotations. So the kinematical analysis to search the exact contact points between cam and follower is inevitable before doing dynamic analysis. 3. ANALYSIS where Rc is cam base circle. 0 is cam angle, S is flat follower displacement, and X and Y specify cam shape. The incre ment of S about 0 can 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. The procedures are. first, rotate the follower around a fixed cam. then find out the locus of follower center(CC) Next. search the contact point for each follower rotating angle(Oc) using the principle that the contact point is (6) where J1. is oil viscous coefficient, L is plunger length, Rp is plunger radius, and h is clearance between cylinder and plunger. All tappet dimensions and properties are given in Table 1. Equations (4, 5) derived above are two extreme cases. one is assumed totally compressive and the other is totally incom pressive. But in actual situation, the drag force(Fd) due to plunger motion will be placed somewhere in the middle of the two values (Kreuter and Mass. 1987). As introducing two coefficients a and P(O a I,Op 1), the drag force can be modeled as Eq.(6). 44 Won-Jin Kim, Hyuck-Soo Jean and Youn-Sik Park the point where the line connecting cam center (A) and the follower center (any point in locus CC) crosses with the tangent line at the corresponding cam angle. Then the con tact point locus can be determined by rotating the searched contact point to the backward as much as the corresponding cam angle(8e). The kinematic dimensions of Fig. 4 are given in Table 3. The instantaneous rocker-arm ratio is calculated by dividing the total length of the finger-follower with the horizontal distance between the pivot point and cam and follower contact point for each corresponding cam angle. The obtained contact- point locus and the corresponding fluctuat ing rocker-arm ratio for this study are shown in Fig. 5 (a), (b). 3.2 Dynamical Analysis When the cam shape, operation speed and follower shape are given, the equations of motion can be easily constructed. During the calculation of contact point, all dimensions of L fc (distance between tappet and follower mass center), LoAdis tance between cam contact point and follower mass center), and L Of (distance between valve and follower mass center can be obtained. Here, L u and LVf given in Table 3 are constant. Lfc is calculated with instantaneous contact point. The effect of the fluctuating rocker-arm ratio on the valve train dynamics is represented by varying L fc . Then the equations of motion can be constructed as FOLLOWER M,Y,=F u - K,pY,-C,pY, M f Y f = Ffc - Ff - FOf fij, = FfLf+FfcLfc - FofLof ml YSI = KSI (Yo- YSI) + CSI (Yo- YSI) - K sz (Y SI - Y sz ) - Csz (YSI - Y sz ) mz Ysz = K sz ( YSI - Yd + Csz ( YSI - Ysz) (8) - KSI Ysz - CSI Ysz moYo=Fo f - KseY o - CseYo- K SI (Yo- YSI ) - C SI (Y o - YSI) if Yo Fo/ Kse where F o is the precompressed force of valve spring (in this study, F o =275N) The contact forces Ff F fc , and F Of can be determined as Eq.(9). (10) 34.00 14.22 22.53 unit:mm 36.40 31.67 13.00 Table 3 Kinematic dimensions Between tappet and follower: Y f - Y,-Lf ,sin8f -Ffo/Kf Between cam and follower: Y e - Y f - L fe sin8 f - Ffeo/K fe Between valve and follower: Y f - Yo+ L of sin8 f - 12 -8 -4 0 4 8 x-coord. (mml (a) 2.5 0 . 2.0 ., L. E L. 1.5 flI I L. 1.0 0.5 1001100 cam-angle(deg.1 (b) Fig. 5 Contact point locus and fluctuating rocker arm ratio ANALYTICAL AND EXPERIMENTAL MOTION ANALYSIS OF FINGER FOLLOWER TYPE CAM-VALVE SYSTEM WITH 45 .Im. expo 100 l: 70 , i 1:1 40 - u .! i- 10 0 -20 30 70 110 ca.-angIe (deg. ) (a) 150 190 . -, , , , , .1. expo 100 l: 70 i e 40 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 0 900 1400 2000 260Q 3200 ell_shllft speed (rpm) Fig.8 Maximum tappet leakage down versus camshaft speed 70 110 150 190 call1-ang) e(l:Ie9) (b) (a) Camshaft speed 900 rpm (b) Camshaft speed 1600 rpm Tappet leakage down 9, 10,11, we can conclude that the 6 degree of freedom lumped mass model used in this work is quite reliable to predict valve motion even in high operating speed. Figure 12 shows a sample of contact forces at all contact points when the operation speed is 2450 rpm. It can be observed that the contact forces at the first peak position are reduced and at the second peak position are accentuated as compared with the value of constant rocker-arm ratio cam system due to fluctuationg rocker-arm ratio. As examining the contact force record, we can easily predict the most possible area and corresponding cam angle where unwanted valve train separation can be occurred. The experimentally verified model can be expanded not only to predict the maximum operation speed but also to Fig.6 Experimental apparatus 5. RUSULT AND DISCUSSION 4. EXPERIMENT Figure 7 compares the measured and simulated tappet leakage down at camshaft speed 900 and 1600 rpm. Figure 8 shows the measured maximum tappet leakage down. It is known that hydraulic tappet is stiffened as the speed of camshaft is increased. The maximum compression of the hydraulic tappet was about 100 /lm at 800 rpm and approa ched a limit of about 60/lm as the camshaft speed goes beyond 3000 rpm, as shown in Fig. 8. As explained before, the measured tappet motion was used to determine the weighting paramenters a and 3, which determine the plunger drag force, by least square curve fit between the measurement and the analysis record. It was found that the weighting parame ter varies with operation speed. For example, a and 3 where 0.0071 and 0.28 when camshaft is driven by 900 rpm, but the values were changed to 0.0094 and 0.30 when the running speed was raised to 1600rpm. Figures 9, 10, 11 show the measured and simulated valve displacements and velocities. The valve velocity was obtained by differentiating the measured valve displacement record. Figure 9 compares the measured and analyzed valve motion when the camshaft was driven at 600rpm. It can be said that the model can simulate not only the peak valve displacement but also the cam event angle quite precisely. Figure 10, 11 show the analysis and measurement when the camshaft speeds are 1600 rpm 2450rpm. As glancing at Figs. In order to prove the effectiveness of the model simulation, experimental work was done and compared each other. Figure 6. shows the experimental apparatus. While the OHC type cam-valve train was driven by a 100kW DC motor, valve displacement and hydraulic tappet motion were measured simultaneously. The valve displacement was mea sured with an opt-follow(noncontact type optical dis placement measurement device), and the tappet motion was measured with a gap sensor. An encoder was placed at the one end of camshaft in order to average the measured signal. Special care was taken to eliminate problems caused by circulating engine oil. All the measurement were done as varying the camshaft running speed from 600 to 2450rpm. Won-jin Kim, Hyuck-Soo jeon and Youn-Sik Park 180 180 - 81 ._- expo - 81 -expo 45 90 135 cam-ang 1e (deg. ) 10.(; ,.-, E 7.5 ., C QJ E 5.0 QJ U l Q. 2.5tl U 0.0 0 600 u 300 QJ en - E B 0 - ., u 0 -300 QJ -600 0 45 90 135 cam-ang I e(deg. ) Fig. 11 Valve displace