In this study, theoretical analysis is performed in order to investigate the nonlinear vibration response of the two-stage spur and straight bevel gears transmitting system. The system dynamic model of the transmitting system is considered in detail. The tooth contact analysis results are obtained through calculation and the dynamic model with time-varying stiffness, and backlash for both gear pair is built. The natural frequencies, mode shapes, and critical speed for the transmitting system with gyroscopic effects are calculated. The results show that the whirling motion due to the second shaft may be the main factor of vibration for the transmitting system and the lateral–torsional–axial vibration dominate the overall system vibration. Many critical characteristics cannot be represented in the transmission error, especially when the rocking and other freedoms are considered in the gear transmitting system. The rocking motion will be excited due to the coupled effect of bevel gear pair, which may be also the reason for the catastrophic damage of the thin web spur gear.
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