Abstract: Considering the time-varying meshing stiffness, damping, teeth errors and backlash of the gear pairs, the dynamic governing equations of a two-staged gear system with 5 degree of freedom are established. In the equations, in order to apply the A-operator method (AOM), the backlash of the Gear pair is expressed into multinomial, and the meshing stiffness, teeth errors of the gear pair, input and output torque fluctuation are expand into Fourier series. By adopting the thought of Adomian’s decomposition method, the A-operator method (AOM) is used to obtain the response of the gear system with approximate analytic form. According to the simulation results, AOM can overcome the filtering faults of harmonic balance method, and its results can contain all frequency components. There exist fundamental, double and combined frequency components in the response of the gear system. Therefore, AOM can be used to research the dynamic characteristics of the gear system conveniently and reliably.

Key words: A-operator method (AOM), Gear system, Multi-frequency response, Nonlinear