支承阻尼对多自由度齿轮系统非线性动力学的影响  

Effect of supporting damping on the nonlinear dynamics of multi-freedom gear systems

作　　者：向玲 高雪媛 张力佳 贾轶 

机构地区：[1]华北电力大学(保定)机械工程系,河北保定071003

出　　处：《振动与冲击》2017年第19期139-144,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(51475164);河北省自然科学基金(E2013502226)

摘　　要：基于周期扩大法的思想,在考虑齿轮副间的时变啮合刚度、齿侧间隙、齿面摩擦等非线性因素的基础上,建立了齿轮副的六自由度非线性动力学模型;采用数值积分方法求解系统响应,结合分岔图、poincaré截面图、FFT频谱及最大李雅普诺夫指数图(Largest Lyapunov Exponent,LLE),系统地分析了支承阻尼对齿轮系统的影响。结果发现:支承阻尼的提高对系统的混沌吸引子和吸引域有着明显影响,会使其逐渐减小,并使系统的混沌运动逐步退化稳定的周期运动,进而使系统的分岔特性变得更为复杂;随着支承阻尼的提高,系统在径向和扭转方向的1/2次谐振幅度有所降低;支承阻尼对轮齿的啮合的状态有着重要影响,在一定转速区可使系统发生双边冲击到单边冲击的变化。Based on the period-enlargement method, a six-degree-of freedom nonlinear dynamic model with rectangular-wave mesh stiffness, backlash, sliding friction and other nonlinear factors of a spur gear pair is established. The numerical integration method is applied to solve the response of the system. The bifurcation diagrams, Poincaré maps, FFT spectrum and the largest Lyapunov exponents are used to systematically analyze the effect of supporting damping on gear system. The results shows that the chaotic attractor and chaotic domain would decrease gradually and even degenerate to stable periodic motion as the supporting damping is improved, resulting in the complexity of the bifurcation characteristic of the gear system. Moreover, the resonance of the system at w/2（w is the exciting frequency） would be weakened. Finally, support damping have an important effect on the meshing state of gear system and could make the system exhibit a change from double-side impact motion to single-side impact motion.

关 键 词：齿轮副 非线性动力学 摩擦 间隙 支承阻尼 

分 类 号：TH113[机械工程—机械设计及理论]