基于图胞映射方法的单自由度非线性齿轮系统全局特性分析  

Analysis of Global Character of Single Degree of Freedom Nonlinear Gear System Based on Digraph Cell Mapping Method

作　　者：唐进元[1] 熊兴波[1] 陈思雨[1] 

机构地区：[1]中南大学现代复杂装备设计与极端制造教育部重点实验室,长沙410083

出　　处：《机械工程学报》2011年第5期59-65,共7页Journal of Mechanical Engineering

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);中南大学研究生学位论文创新(2009ssxt055)资助项目

摘　　要：建立含时变刚度、齿侧间隙等非线性因素的单自由度非线性齿轮系统的数学模型,介绍以图论理论和广义胞映射理论为基础的图胞映射方法,并据此提出一种解非线性问题的图胞映射算法,运用提出的图胞映射算法对齿轮非线性系统进行全局分析,得到系统的吸引子、吸引域、不稳定解以及吸引域边界等全局特性。结果显示:当Ω=0.45,0.80,1.50时,系统分别具有1个、3个和2个稳定的吸引子,当Ω=1.50时,系统还具有一个不稳定的吸引子。最后利用系统的相图进行对比分析,分别取不同吸引域内的点为初始点,最终收敛于相应的稳定的吸引子,从而验证图胞映射算法的有效性和可信性。利用图胞映射算法的计算结果可实现在不良参数条件下,通过合理控制系统的初始条件获得良好的系统响应。The mathematical model of single degree of freedom gear system with time varying stiffness and clearances is set up.The digraph cell mapping method based on graph theory and generalized cell mapping theory is introduced,and accordingly a digraph cell mapping algorithm for solving nonlinear problems is put forward.The global character of nonlinear gear system is analyzed by using the digraph cell mapping algorithm,and a series of the attractors,the domain of attraction,unstable solutions,and the attractive basin boundaries of the gear system are obtained.The result shows： there are one,three or two stable attractors respectively in the system when is 0.45,0.80,or 1.50 and there is also an unstable attraction when is 1.50.Finally,comparative analysis is carried out by using the phase diagram of the system.Initial points are picked up from different domains of attraction and converge at corresponding stable attractors,thus verifying the effectiveness and credibility of the digraph cell mapping algorithm.Using the result of digraph cell mapping method,a good system response can be obtained by rationally controlling the initial conditions in case of bad parameters.

关 键 词：图胞映射 全局分析 齿轮系统 

分 类 号：TH113.1[机械工程—机械设计及理论]