行星齿轮系统弯扭耦合振动的增量谐波平衡法

针对行星齿轮传动机构弯扭耦合振动方程是半正定方程而无法直接采用增量谐波平衡法进行求解的问题，引入微小相对位移量来描述行星齿轮系统中各个部件之间的相对运动.采用运动转移矩阵将半正定方程转化为正定方程，同时考虑齿轮啮合刚度时变的非线性特性，采用增量谐波平衡法分析了行星齿轮系统非线性动力学响应.通过与数值求解方法Newmark-β法相对比，计算结果一致，验证了本文方法的正确性及高效性.

Incremental Harmonic Balance Method for Coupled Bending and Torsional Vibration in Planetary Gear System

Incremental harmonic balance (IHB) method could not solve the coupled bending and torsional vibration equation of positive semi definite in planetary gear transmission mechanism directly， and micro relative displacement was applied to describe relative motion between the parts in the planetary gear system. The motion transfer matrix was used to transform positive semi definite equation into positive definite equation. Meanwhile， considering the time varying nonlinear characteristics of gear mesh stiffness， the IHB method was used to analyze the nonlinear dynamics response in the planetary gear system. The correctness and efficiency of the proposed method were verified by comparison with Newmark β method.