行星齿轮传动非线性动力学模型与方程  

STUDY ON NONLINEAR DYNAMIC BEHAVIOR OF PLANETARY GEAR TRAIN DYNAMIC MODEL AND GOVERNING EQUATIONS

作　　者：孙涛[1] 沈允文[1] 孙智民[1] 刘继岩[2,3,4] 

机构地区：[1]西北工业大学机械系,西安710072 [2]天津职业技术师范学院行星齿轮传动 [3]非线性振动 [4]齿轮动力学

出　　处：《机械工程学报》2002年第3期6-10,共5页Journal of Mechanical Engineering

基　　金：国家自然科学基金重点资助项目(59835040)。

摘　　要：建立了２Ｋ－Ｈ型行星齿轮传动的弯扭耦合非线性动力学模型，模型中考虑了太阳轮的横向振动、齿轮啮合综合误差、齿轮副啮合间隙以及时变啮合刚度，获得了系统的运动微分方程。针对系统微分方程的半正定、变参数和非线性特点，采用以齿轮副相对啮合位移作为系统的广义坐标，将线性与非线性恢复力共存的方程组转换为统一形式的矩阵形式，并对方程进行量纲一化处理，方便地达到了将单自由度的非线性方程的解法推广到多自由度非线性微分方程组中。：A torsional-lateral nonlinear vibration model is established to predict the dynamic characteristics of planetary gear train．It includes the time-varying mesh stiffness，gear meshing errors and gear backlashes．The originally derived governing equations are very hard to solve for which are characterized by semi-definition，time-variation and backlash-type nonlinearity．A linear transformation method is presented to obtain a new generalized coordinates based on the relative meshing displacement. Then the original equations are transformed to identical dimensionless nonlinear differential equations in matrix form. The analytical solution for SOD differential equation can be improved to solve the MOD differential equations．

关 键 词：行星齿轮传动 非线性振动 齿轮动力学 非线性动力学模型 

分 类 号：TH132.425[机械工程—机械制造及自动化] TH113