随机外激励下齿轮非线性系统的全局分析  

Global Analysis for the Nonlinear Gear System with Stochastic External Excitation

作　　者：刘梦军[1] 沈允文[1] 董海军[1] 

机构地区：[1]西北工业大学机电工程学院,西安710072

出　　处：《中国机械工程》2004年第13期1182-1185,共4页China Mechanical Engineering

基　　金：国家自然科学基金资助项目 ( 5 0 0 75 0 70 )

摘　　要：结合随机激励下齿轮非线性系统的特点 ,研究了一种分析齿轮非线性随机系统的全局初值特性的方法。把系统所在的状态空间转化为胞空间 ,在胞空间内 ,用胞的中心点的初值特性来近似表示整个胞的初值特性。分析了系统的运动特性 ,通过MonteCarlo方法计算出胞与胞相互映射时的转移概率 ,获得了系统的转移概率矩阵 ,进而利用Markov链理论 ,对随机外激励下含间隙和时变刚度的单对齿轮非线性系统进行全局特性分析 。Considering the characteristics of a nonlinear gear system with stochastic excitation, a method for analyzing the system's global initial characteristics was described. The system's state space was turned into the cell space, in which the initial characteristics of a cell's central point were used to describe approximately the initial characteristics of all of the points in the cell. Then, the system's transition probability was calculated by using the numerical technology of Monte Carlo method and the transition probability matrix was obtained. The global characteristics were analyzed for a nonlinear gear system with backlash, time-varying mesh stiffness and stochastic external excitation. Based on the Markov chain, the system's final form of motion can be obtained. The analysis results were verified by using the numerical method.

关 键 词：齿轮系统 随机外激励 非线性动力学 全局分析 胞映射 

分 类 号：O322[理学—一般力学与力学基础]