齿侧间隙对齿轮系统动态特性的影响分析

Analysis of gear system dynamic characteristics with tooth backlash

为了研究齿侧间隙对齿轮系统动态特性的影响,建立同时考虑齿侧间隙、齿面摩擦和时变啮合刚度的齿轮非线性动力学系统模型,并采用Runge-Kutta法对系统进行求解,得到系统响应的分岔特性与参数平面内的动态特性.结果表明:齿轮系统分岔特性受齿侧间隙的影响较小;齿侧间隙影响极小阻尼下的系统运动形态,系统刚度随着齿侧间隙的增加而降低,阻尼和齿侧间隙的耦合效应强于刚度和齿侧间隙的耦合效应;选择间隙小、阻尼大且刚度波动系数小的齿轮系统有利于传动系统的稳态控制.

In order to study the effects of tooth backash on the dynamic characteristics of the gear system,a nonlinear dynamic gear system was established,in which the tooth backlash,surface friction,time-varying meshing stiffness and other factors were considered as well.The differential equations of the dynamic system solved by Runge-Kutta integration method and the bifurcation diagram of system response and the dynamic characteristics in plane were obtained.The results show that tooth backlash has fewer effects on bifurcation characteristics.The tooth backlash has a great influence on motion pattern of the system under minimal damping.The meshing stiffness of the gear system is reduced with the increase of tooth backlash.The coupling effect of damping and friction is stronger than the coupling effect of stiffness and friction.The selection of gear system with small clearance,large damping and small fluctuation coefficient of stiffness is beneficial to the steady control of transmission system.