北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (11): 2023-2028.doi: 10.13700/j.bh.1001-5965.2014.0765

• 论文 • 上一篇    下一篇

含非对称摩擦平面运动刚体动力学LCP方法

王晓军1,2, 王琪2   

  1. 1. 常州工学院机电学院, 常州 213002;
    2. 北京航空航天大学航空科学与工程学院, 北京 100191
  • 收稿日期:2014-12-05 修回日期:2015-01-12 出版日期:2015-11-20 发布日期:2015-12-01
  • 通讯作者: 王琪(1959-),男,北京人,教授,bhwangqi@sina.com,主要研究方向为多体系统动力学. E-mail:hwangqi@sina.com
  • 作者简介:王晓军(1970-),女,安徽合肥人,副教授,wangxiaojunpz@163.com
  • 基金资助:
    国家自然科学基金(11372018)

An LCP method for dynamics of planar-motion rigid-body with non-symmetric friction

WANG Xiaojun1,2, WANG Qi2   

  1. 1. Department of Electron and Machine, Changzhou Institute of Technology, Changzhou 213002;
    2. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2014-12-05 Revised:2015-01-12 Online:2015-11-20 Published:2015-12-01

摘要: 基于接触力学理论和线性互补问题(LCP)的算法,给出了一种含接触、碰撞以及对称和非对称Coulomb干摩擦的平面运动刚体动力学的建模与数值计算方法.将研究对象视为刚体,考虑物体接触点的局部变形,将物体间的法向接触力表示成嵌入量与嵌入速度的非线性函数;物体间的摩擦定律采用对称或非对称Coulomb干摩擦模型.首先,为了用数值方法确定粘滞与滑移(stick-slip)运动状态的切换,本文利用摩擦余量、接触点的正向和负向相对加速度等概念,给出了该摩擦定律的互补条件和互补关系式.然后,利用事件驱动法,将由于摩擦引起的stick-slip运动状态切换的判断及粘滞(stick)状态下接触点静摩擦力的计算问题转化成线性互补问题的求解.最后,通过数值算例分析了含对称与非对称Coulomb干摩擦平面运动刚体的动力学特性,并说明了该算法的有效性.

关键词: 非对称, Coulomb干摩擦, 接触力, 线性互补问题(LCP), 非光滑

Abstract: A modeling and numerical calculation method for the dynamics of the rigid-body in planar motion with contact, impact, symmetric and non-symmetric Coulomb's dry friction was presented based on the theory of contact mechanics and the arithmetic of linear complementarity problem (LCP). The local deformations in contact bodies were taken into account although bodies were assumed to be rigid. The normal contact forces were expressed as nonlinear functions of penetration depth and its speed. The friction law adopted symmetric or non-symmetric Coulomb's dry friction model. Firstly, by using the friction saturation, the positive and negative parts of the relative acceleration of contact points, the complementarity conditions and formulations about the friction law were given in order to determine state transitions of stick-slip in numerical method. Then, based on the event-driven scheme, the problems of detecting stick-slip state transitions and solving frictional forces in stick situation were formulated and solved as a linear complementarity problem. Finally, the numerical example of a planar-motion rigid-body was given to analyze its dynamical behaviour affected by symmetric or non-symmetric Coulomb's dry friction and shown that the proposed method was effective.

Key words: non-symmetry, Coulomb's dry friction, contact forces, linear complementarity problem (LCP), non-smooth

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