刚度变化下直升机行星齿轮-转子系统非线性动力学

Nonlinear Dynamics of Helicopter Planetary Gear-rotor System Caused by Stiffness Variation

建立了行星齿轮-转子系统的非线性动力学模型,系统模型将内啮合刚度嵌入齿圈刚度进行建模,考虑了转子扭转效应、齿侧间隙、时变啮合刚度和综合传动误差等因素。采用分岔图、最大李雅普诺夫指数(LLE)、庞加莱截面图和相图来分析响应特征。研究齿轮与转子间扭转振动位移响应,分析了旋翼轴与传动轴扭转刚度比变化影响规律。研究发现,系统具有非线性动力学特性,通过准周期分岔和倍周期分岔进入混沌运动,获得了系统避免失稳的刚度比阈值区间。研究为直升机主减速器行星齿轮-转子系统的动力学设计和扭转振动控制提供了参考。

A nonlinear dynamics model of the planetary gears-rotor system is established with a devel-oped internal mesh stiffness embedded with ring gear stiffness.The torsional effect of rotor and pivotal parame-ters from gears including gear backlash,time-varying mesh stiffness and comprehensive transmission error areincorporated.Responses characteristic are analyzed with bifurcation diagrams,the largest Lyapunov exponents(LLE),Poincarémaps and phase diagrams.The torsional vibration displacement response between gear and ro-tor is studied,and the influence law of torsional stiffness ratio between rotor shaft and drive shaft is analyzed.Itis found that the system exhibits nonlinear characteristic,enters into chaotic motion through quasi-periodic bi-furcation and period-doubling bifurcation,threshold values for stiffness ratios to avoid bifurcation and chaos areobtained.The research provides a reference of undesirable torsional behaviors in dynamic designing and vibra-tion controlling for planetary gears-rotor systems in helicopter main reducer transmission.