齿轮-轴承传动系统擦边碰撞的动力学特性分析

Dynamic characteristics analysis of grazing impact of gear-bearing transmission system

齿面间的擦边碰撞是齿轮-轴承传动系统中一种特殊碰撞形式,可能会导致系统的动力学特性发生改变。为深入探究擦边碰撞对齿轮系统动力学特性的影响,基于频闪映射、齿面和齿背碰撞面Poincaré映射得到系统周期及啮合力变化规律,揭示齿轮副啮入、啮出冲击特性。并利用分岔图、啮合力变化图、相图和最大Lyapunov指数图(the largest Lyapunov exponent,TLE)分析擦边碰撞对系统动力学特性的影响。研究表明,擦边碰撞会引起系统动力学行为发生复杂的变化,导致系统运动和冲击状态发生改变。当啮合力突变点处TLE小于零时,系统周期保持不变而啮合力发生突变,但相轨迹的拓扑结构未发生变化。当啮合力突变点处TLE近似为零时,系统运动发生分岔,系统周期数和啮合力均发生改变。该研究揭示了齿轮-轴承系统擦边碰撞引起的一些复杂动力学现象,为系统的安全运行、优化设计等方面提供参考。

Grazing impact between tooth surfaces is a special impact form in a gear-bearing transmission system,it may change dynamic characteristics of the system.Here,to deeply explore effects of grazing impact on dynamic characteristics of the system,based on stroboscopic mapping and Poincarémapping of tooth surface and tooth back impact surface,variation laws of the system’s period and meshing force were obtained to reveal meshing-in and meshing-out impact characteristics of gear pair.Bifurcation diagram,meshing force variation diagram,phase diagram and maximum Lyapunov exponent diagram were used to analyze effects of grazing impact on dynamic characteristics of the system.The study showed that grazing impact can cause complex changes of dynamic behavior of the system to result in changes of motion and impact state of the system;when TLE at mutation point of meshing force is less than zero,system period remains unchanged and meshing force changes suddenly,but topologic structure of phase trajectory does not change;when TLE at mutation point of meshing force is approximately zero,motion of the system bifurcates,both the number of periods and meshing force of the system change;this study can reveal some complex dynamic phenomena caused by grazing impact of gear-bearing systems,and provide a reference for their safe operation and optimal design.