多间隙高重合度齿轮传动系统动力学分岔与稳定性分析

Analysis of Dynamic Bifurcation and Stability of Gear System with Multiple Clearances and High Contact Ratio

建立了多间隙、时变啮合刚度的高重合度直齿圆柱齿轮传动系统的动力学模型,基于功能原理建立了模型的能量方程,采用有限元法计算了高重合度齿轮的啮合刚度,采用Runge-Kutta法获得了高重合度齿轮传动系统的动力学分岔和跳跃特性.结果表明:在间隙等因素影响下,高重合度齿轮传动系统具有丰富的分岔特性,随着转速的增大,出现了单周期、多周期和混沌等运动状态,系统通过激变途径在混沌运动和周期运动间跳跃;在混沌区域,系统有严重的跳跃现象;齿侧间隙对系统影响较大,较小间隙参数(<3.85×10-5m)下齿轮传动系统做周期运动,较大间隙参数下齿轮系统以混沌运动为主;小阻尼参数下,齿轮传动系统处于混沌和周期运动的激变区域,在较高阻尼参数下齿轮传动系统经多次倒分岔进入稳定的单周期运动;从动齿轮的支撑间隙对系统的运动状态影响较大,主动齿轮的支撑间隙则影响较小.

In this paper, a dynamic model of straight spur gear system with high contact ratio （HCR）, multiple clearances and time-varying meshing stiffness was established, the energy equations of the model were established based on the principle of work and power, the meshing stiffness of the gear system was calculated by means of finite element method, and the dynamic bifurcation and jump characteristics of the system were investigated Runge-Kutta method. The results show that （1） there are abundant dynamic bifurcation characteristics by using the in the HCR gear system influenced by multiple clearances; （2） with the increase of rotation speed, single-period, multi-period and chaotic motions appear in the system, and the motion state jumps from chaos to period motion in a crisis ma- nner; （3） there is an obvious jump in the chaotic area; （4） the backlash greatly affects the system; for instance, the motion state is periodic when the backlash is less than 3.85 ~ 10-5 m and is chaotic in most areas when the backlash is larger than 3.85 x 10-s m; （5） the motion state of the gear system is in the crisis area of chaotic and periodic motions at low damping ratios and may get into single-period stable state via the channels of reversing bifur- cation at high damping ratios ; and （6） the driven clearance greatly affects the motion state of the system, while the driving clearance only has little influence on the motion state.