正交面齿轮传动系统的非线性振动特性

Nonlinear dynamical characteristics of face gear transmission system

基于集中参数理论,考虑支撑的弹性变形、啮合齿轮副的时变啮合刚度激励和误差激励,建立正交面齿轮传动系统的多自由度弯曲-扭转-轴向移动耦合振动三维空间动力学模型;采用有限元方法计算点接触面齿轮传动系统的轮齿啮合刚度;借助动态相对传动误差,合并两轮转动自由度,将系统等效处理为5自由度非线性振动方程;采用自适应变步长Runge-Kutta数值积分方法,获得该系统的动态响应,并分析间隙对动载荷系数的影响。研究结果表明:随着啮合频率的变化,系统将出现单周期、2倍周期、拟周期和混沌响应;在周期响应状态下动载荷系数对间隙较敏感;间隙的改变对齿轮副的冲击状态没有影响,需通过调整支撑刚度等参数来实现单边冲击。

Based on the theory of the concentrated parameter,considering the elastic deformation of the bearings,the time-varying meshing stiffness and error,a three-dimensional dynamic model with multiple degrees of freedom for the face-gear transmission system was developed,including the flexional,torsional and axial motions.The mesh stiffness of face gear transmission system was calculated by FEM.By introduction dynamic relative transmission error,the nonlinear equations were simplified with 5 degrees of freedom.Using the Runge-Kutta numerical integral method of self-adaptive varied steps,the dynamic responses of the face gear transmission system was obtained.Moreover,the influence of clearance on dynamic load coefficient was analyzed.The results show that the single-period syntonic,double-period subharmonic,quasi-period and chaos response increase in the system when the excitation frequency changes.The clearance affects the dynamic load coefficient greatly but has no influence on the impact state of gear pair,that is to say,the single sided impact of gear pair is obtained by modification the stiffness of bearing and so on.