Article ID:100420579(2000)0420375205Multibody System Dynamics Analysis for V alve T rainsQ IN Wen2jie,　ZUO Zheng2xing(School of Vehicle and Trans portation Engineering,Beijing Institute of Technology,Beijing100081)Abstract:The theory of multibody system dynamics is used to simulate valve trains’kinematicsand dynamics characteristics,and the methods of establishing and analyzing the multibody sys2tem dynamics model for valve trains are discussed.Since most of the flexible bodies of a valvetrain are slender parts,the finite segment method is used to build their models.Other parts suchas cams,valve heads etc.,are built as rigid bodies.After applying the constraints,forces andmotions,the establishing of the whole system is accomplished,and the Lagrange’s multipliermethod can be used to obtain its dynamics constitutive equations.As an example,a valve trainπsmultibody system model of4100QB engine made by the Yunnan Internal Combustion EngineLimited2Liability Company is established,and the analysis results obtained show that its work2ing performance is generally good except that the air2pass ability and the lubrication effect of thecam and the tappet have to be improved.K ey w ords:valve train;multibody system;dynamicsC LC number:T K4 Document code:AValve trains are broadly used to control the induction and exhaust of four2stroke engines. They are usually designed as rigid systems,in which valves’movements are completely controlled by the cam’s profiles.In fact,a valve train is an elastic system and the valve’s motion will devi2 ate from the theoretical result derived from the kinematics analysis due to the effect of the inertia and the elastic vibration.Thus the separation in the mechanism will occur and this will make its working conditions worse[1].With the improvement of engine’s speed,these dynamics problems become more and more significant.Therefore,the valve train’s dynamics characteristics must be checked.Usually a valve train is considered as a single2mass or multi2mass vibration system in the dy2 namic analysis[2].But this method cannot reflect the parts’movement and deformation directly, and the model’s parameters must be derived from experiments or other analysis.This will in2 crease the difficulties of model establishment and influence the calculation’s explicitness.Multi2 body system dynamics is a new science which studies the mechanics properties of the system com2 posed of flexible bodies and rigid bodies during the large span spatial movements.According to such a structure2mechanism system as a valve train,using it can not only simulate the motions andR eceived d ate:2000206212Biography:QIN Wen2jie(1968-),female,lecturer,master.dynamics properties of the system,but also calculate the loads of each part,which can be provid2 ed for part’s structure analysis and design.1　V alve T rain’s Multibody System Model EstablishmentThe process of model establishment can be divided into two stages.The first is to build the single valve train’s model for the calculation of valve’s motion and optimization of cam’s profile. The second is to build the whole valve train’s model for the torsion dynamics analysis of the camshaft.However,the establishment of single valve train’s model is the basis for all these anal2 yses,and its method is discussed as follows.111　Establishing Parts’ModelsIf a part’s deformation is not taken into account,it is called a rigid body.If the deformation of a part must be calculated,it is called a flexible body.If just a part’s translation must be calcu2 lated and its rotation is ignored,it can be simplified as a point mass.It is relatively simple to es2 tablish the model of a rigid body or a point mass,so only the method of establishing the flexible body model is discussed here.During the establishment of a flexible body’s model,the finite element method is usually used as preprocessing to obtain mode shapes.By using the relative description method,a part’s motion can be divided into the global reference frame’s large displacement and rotation and its de2 formation motion which is definite with respect to the moving reference frame and can be approxi2 mated with a linear combination of mode shapes[3].Most of the flexible parts of a valve train are slender parts such as rods(tappets,radius rods and valve stems)and beams(camshafts and rocker shafts),so the finite segment method is a sim2 ple and effective way to establish models of this kind of part.The thought of this method is to di2 vide a rod or beam into several rigid segments which are linked with flexible connectors.For a uniform cross2section rod,since only the axial stiffness is concerned,a spring2damper can be added to the two ends of each segment and its stiffness value is[4]k=2A E/L,(1) where A is the uniform area of the rod’s cross section;E is the Y oung’s modulus of elasticity for the material;L is the length of the rod segment.For a uniform beam,the constitutive equation of the flexible connector on each end of the segment is[5]Q=-Kδ-Cδ・,(2) where Q,δ,δ・are the force,displacement and velocity vectors respectively in the local coordinate system;K and C are the stiffness and damper matrix.Both of them are symmetric.According to the theory of Timoshenko Beams,concerning the effect of cross2section rotation and shearing,K can be defined as[5]K =EA /L 00000012EI zL 3(1+P y )000-6EI z L 2(1+P y )0012EI yL 3(1+P z )06EI y L 2(1+P z )0000GI x L 00006EI yL 2(1+P z )0(4+P z )EI y L (1+P z )00-6EI zL 2(1+P y )000(4+P y )EI zL (1+P y ),where A is the uniform area of the beam ’s cross section ;L is the length of the beam segment ;P y =12EIz A y /(GA L 2);P z =12EI y A z /(GAL 2);G is the shear modulus.A y is the shear arearatio for shear deflection in the y direction.A zis the shear area ratio for shear deflection in the z direction.112　Applying Constraints ,Forces and MotionsThere are revolute joints ,translational joints ,fixed joints ,point 2to 2curve contacts and curve 2to 2curve contacts in a valve train.The revolute joints and translational joints can either be simply idealized joints or be joints with friction.The main forces in a valve train are the valve s pring force and gas pressure applied to the valve head.The gas pressure is usually ignored because its small effect on the mechanism.The valve spring can be defined as the linear spring 2damper ,non 2linear spring 2damper or multi 2mass spring.The motion is just the rotation of the camshaft.2　Constitutive Equations of Multibody System DynamicsUsing the Lagrange ’s equation ,the dynamics equation of each part can be described in the form of the blocking matrix as [3]M rrM r θM rf M rθM θθM θf M rf M θf R ff ¨r θ・q f +00000000K ff r θq f =Q r Q θQ f +Q vr Q v θQ vf ,(3)where M is the part ’s mass matrix ;r and ¨r are the location vector and acceleration of the moving reference frame respectively ;θis the Euler angles which describe the orientation of the moving reference frame ;and θ・is its derivative with respect to the time ;q f is the generalized coordinates to describe the deformation of the moving reference frame ;Q is the generalized force vector with respect to the active forces ;Q v is the generalized force vector relative to the second power of the velocity.The subscripts r ,θand f represent the translation ,rotation and deformation res pective 2ly.Apparently ,if a part ’s deformation is not taken into account ,i.e.q f =0, q f =0,¨q f =0,the dynamics equations for rigid bodies are obtained.QIN Wen 2jie et al./M ultibody System Dynamics A nalysis f or V alve T rainsAssembling the parts together by applying the constraint functions and using the Lagrange πs multiplier method ,the system πs dynamics constitutive equations and constraint functions are ob 2tained as [3]M ¨q +Kq +C T q λ=Q F +Q v ,　C (q ,t )=0.(4)In Eq.(4),the mass matrix M =diag [M 1,M 2,…,M n ];the stiffness matrix K =diag[K 1,K 2,…,K n ];the constraint ’s Jacobian matrix C T q =[C T 1,C T 2,…,C T m ]T ;the generalizedforces Q F =[Q F1,Q F2,…,Q F n ]T ,Q v =[Q v1,Q v2,…,Q v n ]T ;the generalized coordinate vectors q =[q T 1,q T 2,…,q T n ]T ;the Lagrange ’s multipliers λ=[λ1,λ2,…,λm ]Tin which n is the num 2ber of parts ,m is the number of constraints and t is the time.3　ExampleIn order to verify the design of the valve train of 4100QB engine made by Yunnan Internal Combustion Engine Limited 2Liability Company ,the single valve train ’s multibody system model is established using the mechanical system simulation software ADAMS as Fig.1,and the follow 2ing are some of theresults.Fig.1　The valve train ’s multibody system modelThe valve ’s displacement ,velocity and acceleration results under the camshaft ’s lowand Fig.2　The valve ’s displacement ,velocity and acceleration curveshigh rotation speed are shown in Fig.2.The contact forces and stresses of the cam 2tappet and the rocker 2valve under the engine ’s rated rotational speed are shown as Fig.3and Fig.4.Journal of Beijing Institute of Technology ,2000,Vol.9,No .4Fig.3　The cam 2tappet contact force and stress curves Fig.4　The rocker 2valve contact force and stress curvesThe figures show that there is no separation occurring in the mechanism ,and the velocity with which the valve drops to the seat and the contact stresses are less than the permissible val 2ues.These results indicate that the working performance of this valve train is generally good.From the valve ’s motion results ,the ample factor of the valve lift and the lubrication charac 2teristics coefficient of the cam and tappet can be calculated.The ample factor is equal to 01502and the derivative of the lubrication characteristics coefficient with res pect to the cam rotation an 2gle at the zero point is less than 3mm/(°).These results show that the air 2pass ability and the lu 2brication effect are not very good ,so it is essential to optimize the cam ’s profile.R eferences :[1]　Xu Wu.Modern design of vehicle engines (in Chinese )[M ].Beijing :People ’s CommunicationsPublishing House ,1995.[2]　Li Huizhen ,Yuan Zhaochen ,Le Yunbing ,et al.Development of valve cam design[J ].ChineseInternal Combustion Engine Engineering (in Chinese ),1989,10(1):32-37.[3]　Lu Y oufang.Dynamics of flexible multibody systems (in Chinese )[M ].Beijing :Higher Educa 2tion Publishing House ,1996.[4]　Huston R L ,Liu Y ouwu.Dynamics of multibody system (in Chinese )[M ].Tianjing :TianjingUniversity Press ,1987.[5]　Oden J T ,Ripperger E A.Mechanics of elastic structure[M ].New Y ork :Mc Graw 2Hill ,1981.配气机构的多体系统动力学分析覃文洁,　左正兴(北京理工大学车辆与交通工程学院,北京　100081)摘　要:运用多体系统动力学的原理来模拟配气机构的运动学和动力学特性,讨论了配气机构多体系统动力学建模和分析的方法.由于配气机构中的柔体多是细长零件,可采用有限段的方法建立其模型,其它零件如凸轮、气门头等视为刚体,再施加上约束、力和运动激励之后即完成了整个系统模型的建立.其动力学方程可采用拉格朗日乘子法建立.作为一个应用实例,对云南内燃机股份有限公司生产的4100QB 发动机的配气机构进行了建模分析,结果表明该机构的运行情况良好,但气门的通过能力以及凸轮2挺柱副的润滑效果有待进一步提高.关键词:配气机构;多体系统;动力学QIN Wen 2jie et al./M ultibody System Dynamics A nalysis f or V alve T rains。