外文翻译--分析和实验输出式凸轮阀系统的液压挺杆 英文版

40 KSME Journal, VolA, No.1, pp. 40-47,1990.ANALYTICAL AND EXPERIMENTAL MOTION ANALYSISOF FINGER FOLLOWER TYPE CAM-VALVE SYSTEMWITH A HYDRAULIC TAPPETWon-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 experimentallystudied. First, the exact contact point between cam and follower for each corresponding cam angle was searched by kinematicanalysis. 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 toderive experimentally such as damping coefficients were determined with engineering intuition. In order to show the effectivenessof 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, BounceNOMENCLATURE-Ae: Equivalent cross-sectional area of oil chamber in tappet,m2C. C.2 C.3: Equivalent damping coefficients of valvespring, N/mC.e: Damping coefficient of valve seat, N-s /mc,f, CVf, Cfe: Equivalent damping coefficients of contactpoint, Ns/mc,p: Equivalent damping coefficient of tappet: N-s/m/0: Fundamental natural frequency of valve spring, HzFo: Initial compression force of valve spring, NFif Fvf Ffe: Contact forces at each contact point, NFifO, Fvfo, Ffeo: Initial contact forces at each contact point,Nh: Clearance between cylinder and plunger, mmHe: Length of compressed oil chamber, mmIf: Follower moment of inertia, kg-m2Ko: Valve spring stiffness, N/mKe: Equivalent stiffness of tappet oil chamber, N/mK.1 K.2 K.3: Equivalent stiffness coefficients of valvespring, N/mK.: Stiffness of tappet soft spring, N/mK,f, Kvf, Kfe: Equivalent stiffness coefficients of contactpoint, N/mL: Plunger length, mmLf: Lever arm of force Ff mmLvf: Lever arm of force Fvf, mmme: Mass of oil inside tappet oil chamber, kgMf: Follower mass, kgMt: Equivalent tappet mass, kgMv: Equivalent valve mass, kgDnpartment of Mechanical Engineering, Korea Advanced Institute of Science and Technology, P.O.Box 150 Cheongruarlg,Seoul 130-650, Koeram m2: Equivalent valve spring masses, kgRp : Radius of tappet plunger, mmRe: Radius of cam base circle, mmRab: Distance from cam pivot to follower pivot, mmR, : length of oscillating roller follower, mmRf: Radius of roller in roller follower model, mmYf: Follower displacement, mmY,: Tappet displacement, j.tmYe: Cam lift, mmYv: Valve displacement, mmY. Y.2: Displacements of equivalent valve spring masses,mm8f: Angular rotation of follower, radianj.t: Oil viscosity coefficient, Pa-sE: Bulk modulus, N/m28: Angular rotation of cam, radian1. INTRODUCTIONWhen designing a cam-valve train of internal combustionengine, there are many things to be considered such as valvelift area, peak cam acceleration, proper cam event angle,ramp velocity, etc. As increasing the operation speed ofinternal combustion engine, the dynamic effect of cam-valvesystem becomes more important. Recently, some researcheshave been done focusing the dynamic effects on cam-valvesystem. Akiba, et al.(1981) constructed a 4 degree of freedommodel to analyze an OHV (Overhead Valve) type cam-valvesystem and studied the dynamic effects on the system motion.Jean and Park(1989)tried to analyze the same type of valvesystem with a lumped mass dynamic model and designed anoptimal cam shape considering dynamiceff.Pisano andFreudenstein (1982) developed a dynamic model of a highspeed valve system capable of predicting both normal systemresponse as well as pathological behavior associated withonset of jumping, bounce, and spring surge. Previousresearches in high-speed cam system had been almost focusedon systems with a constant rocker-arm ratio and on the valve.ANALYTICAL AND EXPERIMENTAL MOTION ANALYSIS OF FINGER FOLLOWER TYPE CAM- VALVE SYSTEM WITH . 41train separation phenomena. Especially, the analysis for camsystem having a hydraulic tappet has not been thoroughlystudied.In this work, an OHC cam-valve train with a hydraulictappet and a finger follower, was analyzed analytically withlumped mass model and its reliability was verified experi mentally. The cam-follower system used in this work ischaracterized with its complex dynamics of hydraulic tappetand the nonlinearity from varying rocker-arm ratio. Therocker-arm ratio deviates as much as 34 percent from abaseline value of I.47as the contact poirU between cam andfollower moves. The pivot end of the oscillating follower issupported not at a fixed point but at a vertically moving pivotmounted at top a hydraulic tappet. The major role of thehydraulic tappet is to remove the valve lash which givesharmful impact within valve train. But in high operatingspeed region, the hydraulic tappet can be oprated abnormallyand can make an unusual valve train motion. Therefore, thecharacteristics of the hydraulic tappet must be considered invalve train dynamic model. The primary research for asimilar cam system was done by Chan and Pisano (1987).They established six degrees of freedom model consideredtranslational and rotational motion of oscillationg followerand valve. But they used a simple single degree of freedommodel for the hydraulic tappet. They focused only on analyti cal work and did not attempt to verify the results experimen tally2. VALVE TRAIN MODELINGTAPPETFig. 1:0:bIiP: VALVEI()I SPRINGI f0:I IVALVESEATSchematic of finger follower valve trainThe actual overall shape of an OHC type cam-valve trainis shown in Fig.I. In order to describe the valve motionprecisely, the valve train was modeled with 6 degree offreedom. Those are valve opening and closing motion, Yv,hydraulic tappet translational motion, Y finger-followertranslational and rotational motion, Y/ and 8/, and twoadditional degree of freedom YS! and YS2 which representvalve spring translational motion. The reason for takingvalve spring motions YS! and YS2is to consider valve springsurge phenomenon. It is known that valve spring surge affectsgreatly on valve motion especially when the operation speedis high. Because camshaft can be considered as rigid andfixed on its bearing, its dynamic characteristics was neglect ed in the model.All thecompotsand the contact points of the cam-valvesystem wererueledwith equivalent mass, springs anddampers asshoin Fig. 2. The details of modeling proce dure are explained as follows.2.1 Contact Point ModelingAs shown in Fig. 1 the finger-follower type cam-valve trainCAMTAPPETIVALVESEATVALVESPRING. CseFig. 2 Used model42Won-in Kim, Hyuck-Soo Jeon and Youn-Sik ParkThe equivalent mass (Me)of finger follower at each contactpoint can be obtained from Eq. (2) as considering the followermoment of inertia(If).where Mfis the follower equivalent mass and I is the dis tance between follower mass center and each correspondingcontact point. The equivalent mass of camshaft at contactpoint is estimated to infinity as assuming that it is rigid andhas 4 contact points between valve train components. Thoseare between follower and tappet, follwer and cam, followerand valve, and valve seat and valve. The contact at valve seatoccurs periodically as different with others which shouldmaintain continuous contact. The equivalent valve seat stiff ness (Kse)and damping (Cse)cofficients were taken from thepreviously published literature (Chan and Pisano, 1987). Onthe 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, andPossons ratio. AJ； assuming the proper range of contactforces, the corresponding contact stiffness was calculated byHertz contact theory. Then the equivalent stiffnesses at eachcontact point were determined by least square error curve fitfrom obtained contact stiffnesses (Roark and Young, 1976). Itwas assumed that the contact between tappet and follower isan internal contact of two spheres, between cam and follweris a contact of two cylinders, and between follower and valveis a contact of a cylinder on a plane.The damping coefficients at each contact point wereassumed as 0.06 and the critical damping coefficient (Ccr) canbe calculated using Eq.(I). Where M, and Mzare the equiva lent masses of each contacting component. it was assumedthat the equivalent masses of each contacting component(M,and Mz) are connected by a spring and a damper.(3)2m, = mz=:rKol (flo)8Kl=K.a=:rKo, K.z=4Ko2.3 Hydraulic Tappet ModelingThe left side of Fig. 3 shows the cross section shape ofhydraulic tappet. Oil enters through entrance and fills thecentral cavity of tappet plunger. As the plunger moves down,the check valve is closed and the oil flows from oil chamberthrough narrow clearance between plunger and cylinder andgenerates damping force. In next step, when the plungermoves upward due to the spring positioned inside of oilchamber, the check valve is opened and oil is refilled in oilchamber. The hydraulic tappet was simplified as shown in theright side of Fig.3 and the equivalent stiffness of the tappetwas estimated by assuming that the fluid is totaly compres sive and there is no flow through diametral clearance. TheThe spring rate and fundamental natural frequency of usedvalve spring are 35 KN1m and 504.46Hz, respectively. Thedamping is assumed as 4% proportional viscous damping.fixed on its bearing. The equivalent masses of tappet andvalve at other contact points are M, and Mv.2.2 Valve Spring ModelingIn order to consider valve spring surge effect, the valvespring was modeled with 2 masses (m, and mz), 3 springs (KShKs and Ksa), and 3 dampers(CshCszand C.a) with 2 degreeof freedom (s and z). Several assumptions were made inthe valve spring modeling. Those are； ( i ) symmetricity(K.,=Ksaand C., = Csa), ( ii) equivalency of static stiff ness and fundamental natural frequency between model andfundamental natural frequency between model and actualsystem, (iii) proper damping assumption.As considering that valve spring is in clamped-clampedboundary conditon, the secondary natural frequency of valvespring becomes twice of the fundamental spring naturalfrequency. All the above assumptions give(1)(2)C=2/ KM,Mzcr M,+M.OILENTRANCE -hJ.-0)Mf0.05981K:5.92 x 10； 1.128 0,0)h1.1527 X 10-Kif5.52 X 10Cf118.97M v 0.08544 K fc 8.37 x 10 Cfc 197.97m, 0.0092 KVf4.33 x 10 CVf 94.13m20.0092 K 1.31 x 10C 634.77K . K .9.33xlOCu. C.a2.35!5K.21.40 x 10C.2 3.534relationship 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 modelsimulation result with experimentally measured record.2.4 Mass and Moment of Inertia ModelingValve, tappet plunger, and follower mass (Mv, Mt, and Mf)were directly measured. The follower moment of inertia (If)where E is bulk modulus, He is the length of compressed oilchamber, and Ae is plunger area.On the other hand. the equivalent damping coefficient wasestimated by assuming that the oil is totally incompressive. Itwas assumed that the excessive oil due to plunger motionflows completely through the diametral clearance. Then theequivalent damping value can be predicted from the theory offluid mechanics. It is known that the damping coefficientchanges with the direction of plunger motion. Those are(7)X= (Rc+S)cosO-sinOY= (Rc+S)sinO+cosO3.1 Kinematical AnalysisWhen searching the point where cam and follower con tacts, the tappet was considered fixed point. It was found thatthe influence of tappet motion upon contact point is negli gible. The tappet motion, which is at most O.I(mm). is enoughsmall and can be considered negligible and differs in order ofmagnitude with cam lift. When the cam data is given withdesired cam lift (S), the actual cam shape (X, .Y), contactingwith a flat follower, can be obtained from Eq.(7) The baselinerocker-arm ratio is 1.47 and the fluctuating range of rockerarm 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 shaftrotations. So the kinematical analysis to search the exactcontact points between cam and follower is inevitable beforedoing dynamic analysis.3. ANALYSISwhere Rc is cam base circle. 0 is cam angle, S is flat followerdisplacement, and X and Y specify cam shape. The increment of S about 0 can be calculated with cubic spline interpolation (Shoup. 1979). When the cam shape (X. Y)is given,the contact point between cam and follower can be found bykinematical analysis. Fig. 4 shows the idea how to find thecontact point. The procedures are. first, rotate the followeraround a fixed cam. then find out the locus of followercenter(CC) Next. search the contact point for each followerrotating angle(Oc) using the principle that the contact point is(6)where J1. is oil viscous coefficient, L is plunger length, Rp isplunger radius, and h is clearance between cylinder andplunger. All tappet dimensions and properties are given inTable 1.Equations (4, 5) derived above are two extreme cases. oneis assumed totally compressive and the other is totally incompressive. But in actual situation, the drag force(Fd) due toplunger motion will be placed somewhere in the middle of thetwo values (Kreuter and Mass. 1987). As introducing twocoefficients a and P(O a I,Op 1), the drag force can bemodeled as Eq.(6).44Won-Jin Kim, Hyuck-Soo Jean and Youn-Sik Parkthe point where the line connecting cam center (A) and thefollower center (any point in locus CC) crosses with thetangent line at the corresponding cam angle. Then the contact point locus can be determined by rotating the searchedcontact point to the backward as much as the correspondingcam angle(8e). The kinematic dimensions of Fig. 4 are givenin Table 3. The instantaneous rocker-arm ratio is calculatedby dividing the total length of the finger-follower with thehorizontal distance between the pivot point and cam andfollower contact point for each corresponding cam angle. Theobtained contact- point locus and the corresponding fluctuat ing rocker-arm ratio for this study are shown in Fig. 5 (a), (b).3.2 Dynamical AnalysisWhen the cam shape, operation speed and follower shapeare given, the equations of motion can be easily constructed.During the calculation of contact point, all dimensions of Lfc(distance between tappet and follower mass center), LoAdis tance between cam contact point and follower mass center),and LOf(distance between valve and follower mass center canbe obtained. Here, Luand LVf given in Table 3 are constant.Lfc is calculated with instantaneous contact point. The effectof the fluctuating rocker-arm ratio on the valve traindynamics is represented by varying Lfc. Then the equationsof motion can be constructed asFOLLOWERM,Y,=Fu- K,pY,-C,pY,MfYf= Ffc - Ff - FOffij, = FfLf+FfcLfc - FofLofml YSI = KSI (Yo- YSI) + CSI (Yo- YSI)- Ksz(YSI- Ysz) - Csz (YSI - Ysz)mz Ysz = Ksz( YSI - Yd + Csz ( YSI - Ysz) (8)- KSI Ysz - CSI YszmoYo=Fof- KseYo- CseYo- K SI (Yo- YSI )- CSI(Yo- YSI) if Yo Fo/ Ksewhere Fois the precompressed force of valve spring (in thisstudy, Fo=275N)The contact forces Ff Ffc, and FOfcan be determined asEq.(9).(10)34.0014.2222.53unit:mm36.4031.6713.00Table 3 Kinematic dimensionsBetween tappet and follower:Yf- Y,-Lf ,sin8f -Ffo/KfBetween cam and follower:Ye- Yf- Lfesin8f - Ffeo/KfeBetween valve and follower:Yf- Yo+ L of sin8f-12-8 -4 0 4 8x-coord. (mml(a)2.50. 2.0.,L.EL.1.5flIIL.1.00.51001100cam-angle(deg.1(b)Fig. 5 Contact point locus and fluctuating rocker arm ratioANALYTICAL AND EXPERIMENTAL MOTION ANALYSIS OF FINGER FOLLOWER TYPE CAM-VALVE SYSTEM WITH 45.Im.expo100l:70,i1:140-u.!i-100-2030 70110ca.-angIe (deg. )(a)150190. -,.1.expo100l:70ie 400.!2-100-2030Fig. 7120i:OIl.,OIl90I0-0SOClI:0Cl8,30CI.k:l0900 1400 2000 260Q 3200ell_shllft speed (rpm)Fig.8 Maximum tappet leakage down versus camshaft speed70 110 150 190call1-ang) e(l:Ie9)(b)(a) Camshaft speed 900 rpm(b) Camshaft speed 1600 rpmTappet leakage down9, 10,11, we can conclude that the 6 degree of freedom lumpedmass model used in this work is quite reliable to predict valvemotion even in high operating speed.Figure 12 shows a sample of contact forces at all contactpoints when the operation speed is 2450 rpm. It can beobserved that the contact forces at the first peak position arereduced and at the second peak position are accentuated ascompared with the value of constant rocker-arm ratio camsystem due to fluctuationg rocker-arm ratio. As examiningthe contact force record, we can easily predict the mostpossible area and corresponding cam angle where unwantedvalve train separation can be occurred.The experimentally verified model can be expanded notonly to predict the maximum operation speed but also toFig.6 Experimental apparatus5. RUSULT AND DISCUSSION4. EXPERIMENTFigure 7 compares the measured and simulated tappetleakage down at camshaft speed 900 and 1600 rpm. Figure 8shows the measured maximum tappet leakage down. It isknown that hydraulic tappet is stiffened as the speed ofcamshaft is increased. The maximum compression of thehydraulic tappet was about 100 /lm at 800 rpm and approa ched a limit of about 60/lm as the camshaft speed goes beyond3000 rpm, as shown in Fig. 8. As explained before, themeasured tappet motion was used to determine the weightingparamenters a and 3, which determine the plunger dragforce, by least square curve fit between the measurement andthe analysis record. It was found that the weighting parame ter varies with operation speed. For example, a and 3 where0.0071 and 0.28 when camshaft is driven by 900 rpm, but thevalues were changed to 0.0094 and 0.30 when the runningspeed was raised to 1600rpm.Figures 9, 10, 11 show the measured and simulated valvedisplacements and velocities. The valve velocity wasobtained by differentiating the measured valve displacementrecord.Figure 9 compares the measured and analyzed valvemotion when the camshaft was driven at 600rpm. It can besaid that the model can simulate not only the peak valvedisplacement but also the cam event angle quite precisely.Figure 10, 11 show the analysis and measurement when thecamshaft 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 theOHC type cam-valve train was driven by a 100kW DCmotor, valve displacement and hydraulic tappet motion weremeasured simultaneously. The valve displacement was mea sured with an opt-follow(noncontact type optical dis placement measurement device), and the tappet motion wasmeasured with a gap sensor. An encoder was placed at theone end of camshaft in order to average the measured signal.Special care was taken to eliminate problems caused bycirculating engine oil. All the measurement were done asvarying the camshaft running speed from 600 to 2450rpm.Won-jin Kim, Hyuck-Soo jeon and Youn-Sik Park180180- 81 ._- expo- 81 -expo45 90 135cam-ang 1e (deg. )10.(； ,.-,E7.5.,CQJE5.0QJUlQ.2.5tlU0.00600u300QJen-EB0-.,u0-300QJ-6000 45 90 135cam-ang I e(deg. )Fig. 11 Valve displacement and velocity (camshaft speed 2450rpm)180180-si.-expo45 90 135call1-angleldeg. )45 90 135cam-angleldeg.)4610.0E7.5.,CQJE5.0QJUlQ.2.5tlU0.00200U100QJtl-EU-0.,u0-100aJ-2000Fig. 9 Valve displacement and velocity(camshaft speed 600 rpm)400 .-.,45 90 135 180cam-ang 1eIdeg. )(h)45 90 135 180cam-angleldeg. )(a)16001200B 800400oo16001200800 f400o _.L-J:O:C:=.:；.；-.L-.-o18045 90 135cam-ang