对称型内平动齿轮系统的非线性动力学分析

摘要

基于拉格朗日方程,建立了含有两个呈对称布置的平动齿轮的内平动齿轮传动机构的动力学模型,通过啮合相对位移函数分析及无量纲化处理,得到系统的无量纲6自由度运动微分方程.通过对系统可能存在的不对称因素(平动齿轮支撑轴承不对称、啮合间隙不对称以及平动齿轮受载不对称)对系统动力学特性的影响进行分析,表明三种不对称因素均会引起系统的分岔,且混沌区域随非对称因素的不同表现出不同的分布规律,并且使得周期解呈现出不同的特性.%Based on Lagrange equations, the dynamic model of an internal parallel moving gear transmission mechanism with two parallel moving gears distributed symmetrically was established. Through the analysis of relative displacement meshing function and dimensionless disposing, a 6 degrees of freedom dimensionless differential equation of the system was obtained. And through the analysis of the impacts on system's dynamical characters caused by asymmetrical factors, such as asymmetry of axial bearings disposal, asymmetry of meshing clearances or asymmetry of loads on two parallel moving gears, it is indicated that all these three types of asymmetrical factors will result in bifurcation of the system. Besides, different asymmetrical factors will lead to different distribution of the chaos area and different characteristics of periodic solutions.