In this paper, we theoretically investigate the nonlinear dynamic characteristics of gear pair system under combined internal and external periodic excitations. The dynamic model of a viscously damped gear pair model with periodic time-varying stiffness, backlash, static transmission error and external periodic excitation is established. The incremental harmonic balance method (IHBM) is applied to analyze the frequency response characteristics as well as the effects of the periodic time-varying stiffness, excitation force amplitude and viscous damping ratio on the dynamic characteristics. Results show that, under combined internal and external periodic excitations, the multi-valued properties and jump phenomena occur not only in primary resonance frequency but also in super harmonic frequency, the excitation force amplitude has less influence on the nonlinear dynamic characteristics and the increase of the excitation force amplitude could no longer control the nonlinear vibration of gear system, which are different from the dynamic characteristics under internal periodic excitations.

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