弧齿锥齿轮传动系统的非线性振动特性研究

基于集中参数法建立了弧齿锥齿轮的多自由度弯-扭-轴-摆耦合振动三维空间十二自由度动力学模型。模型中考虑了传动轴和轴承的弹性变形以及齿轮的啮合刚度激励、误差激励和啮合冲击激励。在忽略扭摆振动的基础上，系统等效处理为八自由度模型，通过引入状态变量并用五阶变步长自适应Runge—Kutta数值积分方法直接求解该多自由度模型，得到系统的动态响应。随激励频率60h的改变，系统将出现单周期简谐、多周期次谐、拟周期和混沌响应，且发现各周期响应的过渡是通过拟周期的分叉实现的。

Study on Nonlinear Vibration Characteristics of Spiral Bevel Transmission System

Based on the theory of the concentrated parameter, a three-dimensional dynamic model with 12 degrees of freedom for the spiral bevel gear transmission system was developed, where the flexional, torsional, axial and rotational motion were considered. The elastic deformation of the transmission shaft and the bearing, the drive of the mesh stiffness, error and mesh impacts were considered in the model. On the foundation of neglecting the rotational vibration, the transmission system was dealt with a model with 8 degrees of freedom and analyzed using the 5-steps Runge-Kutta numerical integral method of self-adaptive varied steps by introducing state variable. The dynamic response was received and the dynamic behavior of the transmission system was analyzed. When changing the excitation frequency wh, the single-period syntonic, multi-period subhamonic, quasi-period and chaos response will appear, and the transient of the every period response are given by the bifurcate of the quasi- period.