行星齿轮传动非线性动力学方程求解与动态特性分析

STUDY ON NONLINEAR DYNAMIC BEHAVIOR OF PLANETARY GEAR TRAIN SOLUTION AND DYNAMIC BEHAVIOR ANALYSIS

发展了单自由度解析谐波平衡法的应用。对行星齿轮传动系统的多自由度非线性动力学微分方程组，在考虑刚度波动的情况下，推导了行星齿轮系统微分方程组的解析谐波平衡法的计算公式，并采用Ｂｒｏｙｄｅｎ迭代方法求解非线性代数方程组。给出一个算例，用上述方法进行求解，得到了行星齿轮传动的非线性频响特性，与相应的线性系统进行了比较。并研究了时变啮合刚度、误差和齿侧间隙对系统非线性动力学行为的影响。

：The SDOF analytical harmonic balance method is developed. Based on the previously published work and considering the time-variant gear meshing stiffness, the calculating formulations of nonlinear dynamic equations of planetary gear train are presented. The relevant nonlinear algebraic equations are solved by using Broyden algorithm. At last, a calculating example is given. The nonlinear frequency response characteristics of 2K-H planetary gear train with backlash are obtained by employing this method and are compared with corresponding linear system. In comparison with numerical results using 5-order Runge-Kutta integration, the calculating results of MDOF analytical Harmonic Balance Method show a good agreement. It proves that the method proposed in this paper is reasonable and practicable.