齿轮系统周期运动稳定性研究

Research on Stability of Periodic Motion of Gear Systems

针对含间隙的强非线性齿轮系统动力学模型,用数值方法研究了当系统参数和初始条件变化时周期运动的稳定性。基于Floquet分岔理论将预测-校正算法用于讨论参数变化时周期解的稳定性,得到精确的分岔点参数值;通过胞映射法求得周期吸引子的吸引域,引入稳定性品质因子用以定量分析初始条件变化时周期运动的稳定性。该研究结果可为非线性动力学行为的分析和齿轮系统的设计提供参考。

For the dynamic model of strongly nonlinear gear systems with backlash, the stability of periodic motion was studied by numerical methods when the system parameters and the initial conditions were changed. Based on the Floquet bifurcation theory, the predict-correct method was used to discuss the stability of periodic solutions with changing the parameters, and the parameter values of bifurcation points were obtained accurately. The attraction domains of periodic attractors are obtained by using the cell mapping method, and the stability factor is introduced to quantificationally analyze the stability of periodic motion with changing the initial conditions. According to the research results, the parameters and the initial conditions can be properly selected, and the foundation will be laid for analysis of nonlinear dynamic behavior and design of the gear systems.