齿轮传动系统的非线性冲击动力学行为分析

Analysis of nonlinear impact dynamic behavior for a gear pair system with time-varying stiffness and friction

主要研究在考虑时变刚度和摩擦时,轮齿间隙及载荷参数对齿轮系统冲击动力学响应的影响,首次研究了齿轮传动非线性动力学的脱啮冲击、周期解的形成过程及对应的非光滑系统冲击中出现的切分岔行为。含时变参数系统的解析求解非常困难,根据间隙函数,将相平面划分为三个区域并构建了与之相对应的Poincare映射,结合谐波平衡法及序列二次规划方法求得了区域D+和D-内的解,利用数值仿真的方法分析了载荷参数、初始条件等因素对齿轮冲击响应的影响,本文研究表明:1)随着常量载荷f0的增大,脱齿运行的时间减小,且啮合冲击的速度也逐渐减小,齿轮的运动也相对平稳,同时出现切分岔的初始速度的绝对值迅速增大;2)随着载荷波动分量f1的增大,脱齿运行的时间减小,但是啮合冲击的速度也相应的有所增大,轮齿间冲击的冲击比较剧烈。

Nonlinear impact dynamic behavior of a gear pair system with time-varying stiffness and friction was studied. Firstly, the phase plane was divided into three different parts to construct Poincare mappings of a piecewise linear gear pair system. Then, the influences of load parameters and initial conditions on the impact responses of the gear pair system were analyzed with numerical method. The results showed that: 1) with increase in constant load f0, the interval of off-meshing and the impact velocity drop, the gears have steady movement; the initial velocity for grazing bifurcation appearing rises; 2) with increase in the load fluctuating component f1, impact velocity rises and the interval of off-meshing drop, the gears have unstable movement.