Abstract: 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.

Key words: Gear dynamics, Harmonic balance method, Nonlinear vibration, Planetary gear train