含非线性摩擦系数的单自由度颤振系统全局动力学行为数值研究  

Study of friction chatter of mechanical system based on cell mapping algorithm

作　　者：唐进元[1] 熊兴波[1] 陈思雨[1] 

机构地区：[1]现代复杂装备设计与极端制造教育部重点实验室(中南大学),中南大学机电工程学院,长沙410083

出　　处：《计算力学学报》2011年第3期417-422,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(50875263);国家重点基础研究发展计划(973计划)(2005CB724100)资助项目

摘　　要：摩擦系数模型取更具普适性的Stribeck非线性模型,基于事件驱动理论,利用C与Matlab联合仿真的方法开发了干摩擦颤振问题的快速求解程序。给出改进的胞映射算法,对含非线性摩擦的单自由度摩擦颤振系统的演化过程及其全局性态进行数值分析和研究,得到系统在任意的初始状态下的响应特性、系统收敛域的数值计算分析结果。分析结果表明:在激励速度vb不断减小的过程中,系统的稳定解由稳定的平衡点转变为稳定的极限环,并依次出现颤振、粘滑等非线性动力学现象;在整个相平面内,系统的收敛特性不发生改变,总是收敛于同一稳定的奇点或同一极限环。Based on event-driven theory,a rapid solving program for friction chatter is developed by jointly using the programming languages of C and Matlab after introducing the nonlinear Stribeck friction model.Numerical analysis is conducted to study the evolutionary process and global behavior of single-DOF friction chatter that involves nonlinear friction coefficient by using a revised cell mapping algorithm.Thus the response characteristics under arbitrary initial state and the result of numerical analysis in the domain of convergence are obtained.The result shows that the stable solution transforms to limit cycle from equilibrium point while the phenomenon of chatter and stick-slip vibration appearing in sequence with the decrease of excitation speed,and that the system invariably converges to the same stable singular point or the same limit cycle in the full phase plane.

关 键 词：摩擦颤振 胞映射 非线性 全局性态 

分 类 号：O322[理学—一般力学与力学基础]