A differential mechanism is an essential component in the majority of automotive applications. Its vitality stems from the fact that it allows a wheel-drive vehicle to take a curve safely. On the other hand, it can ratchet up the vibration in the wheel-drive vehicle due to the excessive gear tooth deflection from applied torque. Some gear tooth modifications can increase or decrease the level of vibration in the mechanism. So far, very little attention has been paid to the effects of the uncertain geometric deviation of the tooth profile and uncertain crowning parameters on the dynamic performance of the mechanism. This study aims to investigate the impacts of these uncertain parameters on the gear systems’ dynamic performance. To this end, the nonlinear interval model of the differential mechanism is proposed. The mesh stiffness for straight bevel gear is modelled through the potential energy method and slice theory, while bearing stiffness elements are calculated at each time step. A refined computational algorithm is proposed to deal with any gear system with multiple interval variables. The scanning method is used as a reference method in this paper. The main outcomes of this study are that the crowning design can slightly reduce the vibration in the mechanism, and the profile errors can increase its vibration level excessively. Besides, the results derived from the refined algorithm show similarities to those determined by the scanning method, and the study shows that the refined algorithm can handle any gear system with uncertain static or time-varying parameters.
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