具有动态侧隙的齿轮传动系统动力响应分析

Dynamic Response Analysis of Gear Transmission System with Dynamic Backlash

综合考虑动态侧隙、时变啮合刚度、齿轮偏心和传动误差等非线性因素,建立齿轮-转子-轴承传动系统的非线性动力学模型。以分形理论为基础,引用尺寸一致性的Weierstrass-Mandelbrot函数模拟动态侧隙的变化趋势。利用4阶龙格-库塔法对系统的非线性动力学微分方程求解,探究动态侧隙对系统响应的影响。结果显示:综合对比定侧隙系统和动态侧隙系统,齿轮在扭转方向上振动幅值的波动较大,动态侧隙系统由准周期运动渐变为混沌运动,并且与动态侧隙曲线的复杂程度有关;齿轮在扭转方向相平面的轨迹随动态侧隙的标准差(standard deviation,简称STD)呈现出规律性变化;在系统振动响应频谱中,随着动态侧隙曲线的复杂程度的加剧,频率成分多样性增强,噪声频率的幅值逐渐增加,高倍频的幅值激增。

A nonlinear dynamic model of gear-rotor-bearing transmission system is developed with synthetically considering dynamic backlash,time-varying meshing stiffness,gear eccentricity and transmission error,using weierstrass-mandelbrot function with dimensional consistency to simulate the variation trend of dynamic backlash.The nonlinear dynamic differential equations are solved using the Runge-Kutta method,and the effect of dynamic backlash on system response is explored.The results show that the vibration amplitude of gear prominently fluctuates in torsion direction,and system kinestate is changed from quasiperiodic motion to chaotic motion with increasing complexity of dynamic backlash curve.The phase plane trajectories of gear in torsion direction present regular variation with the standard deviation value(STD)for short of the dynamic backlash.With increasing complexity of dynamic backlash curve,the diversity of frequency components and the amplitude of noise frequency clearly argument and the amplitude of high frequencies increases sharply.