共线三球链问题的碰撞动力学研究

STUDY ON COLLINEAR COLLISION DYNAMICS OF THE THREE-BALL CHAIN

共线三球链的碰撞动力学问题能够展示多刚体系统碰撞问题的困难之一:非唯一解的问题.本文建立了三球链碰撞的Hertz接触模型,研究对其求解的数值算法,并用有限元模型(FEM)对其进行验证,研究表明:同线性模型比较,采用Hertz接触力模拟小球之间的接触力更接近有限元计算结果;在Hertz接触模型基础上,分析碰撞过程中接触力的变化过程;研究刚度比和质量比对于碰撞结束后各个小球运动状态的影响,并研究了两种刚体模型下碰撞次序假设成立的条件.

One of the difficulties of the problem of collisions of multi-body system is non-unique solution. To overcome this problem the three-ball chain collision was modeled by Hertz contact and a numerical algorithm is proposed to solve the contact model. The finite element model was used to verified it. Based on the Hertz model, the change of the contact forces is analyzed during the collision process. The effect of the stiffness ratio and mass ratio on the state of motion of each ball after the collision, and the established condition of two girid body models collision orders were studied. Research shows compared with linear model, the contact forces between three balls by Hertz model are closer to the finite element results.