含随机间隙的齿轮非线性系统的全局分析  

A Global Analysis for Nonlinear Gear System with Stochastic Backlash

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,陕西西安710072

出　　处：《西北工业大学学报》2004年第4期482-486,共5页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金 (50 0 750 70 )资助

摘　　要：齿轮非线性系统的初值特性对其最终的运动状态有重要的影响。由于系统中的齿侧间隙的大小是随机分布的,因此在建立含随机间隙和时变啮合刚度的齿轮系统动力学模型的基础上,研究了分析系统非线性随机动力特性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后,用胞的中心点的初值特性来近似表示整个胞的初值特性。齿轮随机非线性系统的胞映射过程是一Markov过程,由映射得到的胞序列构成Markov链,采用Monte-Carlo方法计算出系统的转移概率矩阵。通过研究吸引胞之间的转移概率,得到系统的最终运动形式。最后用随机模拟的数值方法对计算结果进行了验证,证明了该方法的有效性。For a nonlinear gear system, the initial state of the motion has important effect on the final form of motion. If the initial state of the motion is different, then the final form of the motion may be different. And in fact, the backlash values between the gear teeth are not constant, but are stochastic. Up to the present, there has been no paper in the open literature giving detailed analysis of the effect of initial state on the final form of motion of a nonlinear stochastic gear system. In this paper, the nonlinear gear model with stochastic backlash and time-varying mesh stiffness is established. A method for analyzing the global initial character of this kind of system is put forward. The system's state space is turned into cell space, in which the initial character of a cell's central point is used to describe approximately the initial characters of all the points in the cell. Then, the transition probability of system is calculated by using the numerical technology of Monte-Carlo method and further the transition probability matrix is obtained after finishing the analysis of all the cells. Based on the Markov theory, the final motion of system can be got by studying only the transition probabilities between the attraction cells. We applied our method of detailed analysis to a specific nonlinear gear system, whose design parameters are all known. We found that results are different for two different situations: (1) the situation in which backlash is constant, as is commonly assumed to be; (2) the situation in which backlash varies stochastically. When the backlash is constant and in the range of 0.016 to 0.024 mm, the system′s final form of motion is decided by the initial state and may be period-1 or period-2. However, when the backlash changes stochastically in the range of 0.016～0.024 mm, the final results are quite unexpected; if the initial form of motion, which is decided by the initial state, is quasi-period-1, the final form, as may be expected, will not change; but if the initial form of motion

关 键 词：随机间隙 齿轮非线性 全局分析 胞空间 

分 类 号：TH113[机械工程—机械设计及理论]