多体系统摩擦接触问题的DAE-LCP方法  

DAE-LCP MIXED METHOD FOR MULTIBODY SYSTEM DYNAMICS WITH FRICTIONAL CONTACTS

作　　者：富立[1,2] 岳凤桐[3] 

机构地区：[1]河北联合大学理学院,唐山063009 [2]北京航空航天大学动力学与控制系,北京100191 [3]河北科技大学唐山分院,唐山063000

出　　处：《力学学报》2011年第2期400-407,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(10672007)~~

摘　　要：当多体系统的约束全部是摩擦接触时,其动力学问题可归结为一个常微分方程(ordinary differentialequation,ODE)与线性互补问题(linear complementarity problem,LCP)的混合动力学问题.如果除了摩擦接触之外还增加了光滑的双边约束,则需要将ODE-LCP混合动力学模型推广为微分代数方程(differentialalgebra equation,DAE)与LCP的混合动力学模型.该文采用DAE与LCP混合动力学方法求解不考虑碰撞但同时含有持续摩擦接触及光滑等式约束的多体系统动力学问题.在建立系统动力学模型时,首先将含摩擦的约束从系统中移去得到基本动力学系统.由于基本系统中带有等式约束,所以基本系统的动力学方程为一组DAE.结合基本系统的DAE与约束的互补条件便可以得到DAE-LCP混合动力学模型.数值计算采用基于DAE与LCF的步进(time-stepping)算法,将系统动力学方程及其约束离散化并转化为一个混合LCP进行求解.该算法无需进行滞-滑状态检测,避免了事件检测导致的繁复计算.利用所提方法对典型机构的非光滑非线性特征进行了数值分析,验证了该文方法的正确有效性.Presently,dynamics of nonsmooth multibody systems is a hot research topic.The usual approach in treating such systems is to derive basic system from the original system by removing the nonsmooth constraints firstly.The Lagrange equations of the second kind of basic system combine with the complementarity condition of the nonsmooth constraints to set up at each discrete moment in time a Linear Complementarity Problem （LCP）. This article focuses on the problem of dynamic modeling and numerical simulating of multibody systems with friction contacts.By neglecting the clearance and the effect of impact between rigid bodies and constraints, the state variables in the differential equations are continuous.Due to the set-value mapping characteristic of dry friction forces,the differential equations of motion have discontinuous right-hand vector fields,therefore to allow our system to be classified as a Filippov system.In addition to the friction constraints,our model also incorporates frictionless bilateral ones.If the simulation has only friction constraints,then the problem is an ODE-LCP model.Combining friction contacts with frictionless bilateral constaints,the ODE-LCP model has to be extended to DAE-LCP（DAE,Differential Algebra Equation） mixed model.In order to obtain the model, the basic system is derived from the original system by removing the friction constraints firstly.Because the equality constraints are retained in the basic system,the dynamic model of basic system is a set of DAE.With the aid of constraint Jacobian matrix,the normal contact forces and tangential friction forces of nonsmooth constraints,which obey the complementarity contact laws,are added to the DAE of the basic system to obtain the DAE-LCP mixed model. Approaches used in the past for simulating rigid multibody dynamics with friction contacts include piece-wise DAE approaches,acceleration-force LCP approaches,and velocity-impulse LCP-based time-stepping methods. Recognizing that the nature of the frictional constraint can induce sic

关 键 词：多体系统 摩擦 微分代数方程 线性互补问题 步进算法 

分 类 号：O313.7[理学—一般力学与力学基础]