间隙对含摩擦和时变刚度的齿轮系统动力学响应的影响

主要研究在考虑摩擦和时变刚度时，轮齿间隙对齿轮系统动力学响应的影响。建立常间隙、时变间隙和随机间隙三种不同的间隙形式。利用数值仿真的方法得到系统的幅频响应曲线和时间历程曲线。分析发现：①在低速时，随着摩擦因数的增大，系统响应的方均值和平均分量增大；并经过三次跳跃之后系统进入混沌运动状态；②时变间隙幅值增大导致系统提前进入混沌状态，而且随着时变幅值的增大跳转频率逐渐减小；时变间隙频率较小时，间隙对系统的影响较小；当时变间隙的频率较大时，系统在 =0.2，0.3时出现明显的共振响应，系统的响应以高频率分量4、5和6为主；③考虑随机间隙时，随着 的增大，齿轮系统响应的平均分量波动比较大。

Effect of Backlash on Dynamics of Spur Gear Pair System with Friction and Time-varying Stiffness

The chief objective is to study the effect of backlash on nonlinear dynamic response of spur gear pair system with consideration of friction and time-varying stiffness. Three different kinds of backlash, i.e. constant backlash, time-varying backlash and stochastic backlash, are established. The dynamic responses are studied over a wide frequency range by using numerical integration, Runge-Kutta method, to check the nonlinear behavior and jump phenomena in the frequency response. The results indicate that：① At low speed, with the increase of friction coefficient, the root-mean-square value and mean value of system response increase, and the system enters into chaotic motion state after three times of jump. ② The increase of amplitude of time-varying backlash causes the system to early enter into chaotic state, and with the increase of time-varying amplitude, the jump frequency decreases gradually. When the frequency of time-varying backlash is small, the influence of backlash on the system is small. When the frequency of time-varying backlash is great, the system produces obvious resonance response at =0.2 and =0.3.The frequency responses are mainly 4, 5 and 6. ③ With consideration of stochastic backlash, the value of has less change, but has obvious fluctuation.