干摩擦对行星齿轮传动系统分岔特性的影响分析

为研究齿面摩擦对行星齿轮系统分岔特性的影响,考虑摩擦、时变啮合刚度、齿隙和综合误差等非线性因素,建立行星齿轮系统扭转振动模型,采用Runge-Kutta数值解法求解,结合非线性分析方法分析系统的分岔行为和齿面摩擦对系统分岔特性的影响。数值仿真得出:行星齿轮系统表现出Hopf分岔、跳跃激变、倍化分岔和逆倍化分岔行为。齿面摩擦对系统在低频区域的分岔行为影响小,系统分岔行为基本没有改变,齿面摩擦对系统在高频区域的分岔行为影响大,系统分岔行为变得模糊,提前进入混沌运动;随着摩擦系数的增加,系统随激励频率变化的周期运动受到抑制趋势更加明显,系统混沌运动区间增加。

Analysis of the Influence of Friction on Bifurcation Characteristics of Planetary Gear Transmission System

In order to study the influence of tooth surface friction on the bifurcation characteristics of planetary gear system, the torsional vibration model of planetary gear system is established by considering the nonlinear factors such as friction, time-varying meshing stiffness, backlash and comprehensive error. Runge-Kutta numerical method is used to solve the problem, and the bifurcation behavior of the system and the influence of tooth surface friction on the bifurcation characteristics of the system are analyzed by combining the nonlinear analysis method. The numerical simulation shows that the planetary gear system shows Hopf bifurcation, jump shock, doubling bifurcation and inverse doubling bifurcation. The influence of tooth surface friction on the bifurcation behavior of the system in the low frequency region is small, and the bifurcation behavior of the system is basically unchanged. The influence of tooth surface friction on the bifurcation behavior of the system in the high frequency region is large, and the bifurcation behavior of the system becomes fuzzy, and enters the chaotic motion in advance. With the increase of friction coefficient, the periodic motion of the system with the change of excitation frequency is restrained more obviously, and the chaos degree of the system is also increased obviously.