In this study, a non-linear time-varying dynamic model of a spur gear pair system is used to investigate the dynamic behavior of the system by means of multiple scale approach. Both time-varying stiffness, transmission error and tooth backlash clearance of the system are taken into account in the model. The mesh stiffness fluctuation is developed as high order Fourier series and tooth backlash clearance is fitted by high order polynomial function. The frequency factors of the system are investigated and the frequency-response equations at the case of internal and external excitation, parametric excitation and combined excitation are obtained. The peak value of the amplitude of the primary resonance, super and sub harmonic resonance and combination harmonic under internal, external and parametric excitation are researched. The approaches of vibration reduction are investigated. Finally an example is investigated using the presented process and the results indicate the sensitivity and correctness of the presented analysis approaches.

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