含摩擦滑移铰平面多刚体系统动力学的数值算法

基于LuGre摩擦模型和线性互补问题(LCP)的数值算法,给出了具有双边约束含摩擦滑移铰平面多体系统动力学的数值算法.首先,根据滑移铰的特点,当间隙充分小时,将其视为双边约束,给出了滑移铰中滑道作用于滑块上的法向接触力的互补关系;LuGre摩擦模型能有效地描述机械系统中的黏滞与滑移运动,将该模型用于描述滑块与滑道间的摩擦力.其次,结合Baumgarte约束稳定化方法,应用第一类Lagrange方程,建立了该多体系统的动力学方程,给出了Lagrange乘子与滑移铰中作用于滑块上的法向接触力的关系式.然后,将滑块与滑道间多种接触状态的判断以及作用于滑块上的法向接触力的计算转换为线性互补问题的求解,并用常微分方程的数值算法求解该多体系统的动力学方程.最后,通过数值仿真算例揭示了滑移铰中滑块的黏滞与滑移现象,以及滑块在滑道内的多种接触状态;另外,在文中分别采用Coulomb干摩擦模型和LuGre摩擦模型,对算例中的某些工况进行了数值仿真,并且分别用本文方法得到的数值仿真结果与已有方法得到的数值仿真结果对比,表明了本文给出的方法的有效性. 

A NUMERICAL METHOD FOR DYNAMICS OF PLANAR MULTI- RIGID-BODY SYSTEM WITH FRICTIONAL TRANSLATIONAL JOINTS BASED ON LUGRE FRICTION MODEL

A numerical method for the dynamics of the planar multi-rigid-body system with frictional translational joints is presented in this paper. The multibody system consists of the several rigid bodies which are linked with ideal revolute joints and imperfect translational joints. The frictional forces on the slider in the imperfect translational joint are modeled by the LuGre friction law which can effectively describe stick-slip motion in the mechanical system. The sizes of the clearances and the impacts between the guide and the slider in the translational joints can be neglected when the clearance sizes are very small, so the geometric constraints of the translational joints are treated as bilateral constraints. In this work, firstly, the complementarity conditions and formulations about the normal forces on the slider in the translational joint are given. Secondly, the dynamical equations of the multibody system are obtained by the Lagrange's equations of the first kind and the Baumgarte stabilization method for the constrained multibody systems in order to reduce the constraint drift in the numerical simulation of the multibody systems. Thirdly, the problems of determining contact situations of the slider in the translational joint and solving normal forces on the slider in all contact situations are formulated and solved as a linear complementarity problem (LCP). Finally, two numerical examples of the planar multi-rigid-body system with a frictional translational joint are given to illustrate their dynamical behaviors such as stick-slip motion and several contact situations of the slider in the translational joint. The LuGre friction model and the Coulomb friction model are used in two numerical examples to compare the dynamical behaviors of two mechanical systems. The numerical results obtained by our method are compared with that obtained by other method. The numerical results of the examples show the availability of the method presented in this paper.