渐开线花键连接的非线性动力学特性

Nonlinear dynamic characteristics of involute spline couplings

摘要:

为给花键连接磨损分析和寿命预估提供精确的数值基础,对渐开线花键的非线性动力学特性进行研究.利用集中质量模型建立具有齿侧间隙的花键连接四自由度非线性动力学方程,计算花键连接实际接触齿对数及综合时变啮合刚度,采用四阶Runge-Kutta法求解花键连接非线性动力学方程.计算结果表明:花键副啮合刚度随时间呈周期性变化,随扭矩呈分段线性分布;当系统转速为300 r／min时,系统呈简谐响应;转速为348 r／min时,系统呈两周期响应;转速为360 r／min时,系统呈5周期响应;转速为1 080 r／min时,系统进入混沌响应;花键副的动载系数也呈周期性变化,并随扭矩及齿侧间隙的的增大而增大．减小渐开线花键链接的齿侧间隙,有利于降低动态载荷,提高花键副工作的稳定性.

Abstract:

To provide accurate numerical basis for the forecast of lifetime and analysis of fretting wear of the spline couplings, the nonlinear dynamic characteristics of involute splines was studied. Four degrees of freedom nonlinear dynamic equations of the spline couplings using the lumped mass model was established, the number of actual meshing teeth and the time-varying mesh stiffness of the systems were calculated, and the nonlinear dynamic equations adopting the fourth order Runge-Kutta method was solved. The results show that: the time-varying mesh stiffness changes periodically with time and is a piecewise linear distribution with torque changing; when n=300 r／min, the system presents harmonic response; when n=348 r／min, the system presents double-cycle response; when n=360 r／min, the system presents 5-cycle response; and when n=1 080 r／min, the system gets into chaos response. The dynamic load coefficient of the spline couplings changes periodically and increases with torque and backlash. It is concluded that reducing the clearance of the spline couplings is beneficial to lowering the dynamic load and improving the stability of involute splines.