非光滑平面运动刚体动力学建模与数值计算方法

Modeling and simulation for non-smooth dynamics of planar-motion rigid-body

基于接触力学理论和线性互补问题的算法,给出了一种含接触、碰撞以及Coulomb干摩擦的平面运动刚体动力学的建模与数值计算方法。文中的摩擦力模型采用Coulomb干摩擦模型;考虑刚体模型在接触点的局部变形,用局部变形量与变形速度的非线性函数表示物体间的法向接触力;应用牛顿欧拉方法建立系统的动力学方程。为计算非光滑动力学方程,建立了摩擦定律的互补条件和互补关系式,并利用事件驱动法,将接触点黏滞与滑移运动状态切换的判断以及静摩擦力的计算转化成线性互补问题的求解。最后通过数值算例分析含摩擦与碰撞平面运动刚体的动力学特性,并验证了该算法的有效性。

A modeling and numerical method for the dynamics of a planar motion rigid- body with contact,impact and Coulomb＇s dry friction is presented based on the theory of contact mechanics and the arithmetic of linear complementarity problem（ LCP）. The friction law adopts Coulomb＇s dry friction model. The local deformations in contact bodies are taken into account although bodies are assumed to be rigid. The normal contact forces are expressed as nonlinear functions of penetration depth and its speed. The dynamical equatuons of the rigid- body are obtained by using Newton- Euler nethod. The complementarity conditions and formulations about the friction law are given in order to compute the non- smooth dynamical equatiions. Based on the event- driven scheme,the problems of detecting stick- slip state transitions and solving the static frictional forces are formulated and solved as a linear complementarity problem. Finally,the numerical example of a planar- motion rigid- body is given to analyze its dynamical behaviour affected by impact and dry friction as well as shown that the proposed method is effective.