Effects of interval friction coefficients on the differential mechanism dynamics

Abstract

The presence of a differential mechanism is fundamental in most automotive applications. Its importance stems from allowing a vehicle to take a curve. The differential should be well-lubricated to ensure its smooth operation and mitigate its vibration level. With lubrication conditions deteriorating over time, the sliding friction coefficient becomes difficult to predict its accurate value. Thus, scrutinizing the dynamic performance of the mechanism with deterministic sliding friction can be misleading. This paper aims to investigate the dynamic performance of the automotive differential with the presence of interval sliding friction. To this end, a 3D dimensional model of automotive differential with time-varying mesh stiffness (TVMS) and bearing flexibility is proposed. The influence of sliding friction on TVMS for straight bevel gear is revealed. The Newton-Euler formulation is used to derive the dynamic equations governing the motions of the automotive differential with friction. The Chebyshev inclusion function and the least square method are used to deal with the interval mathematical formulation of the model. The scanning method is used as a reference method in this paper. There are quite similarities between the results derived by the scanning method and that of the interval process method. The reliability analysis of the differential is conducted. The outcome of this research shows that any variation of the sliding friction can alter the dynamic performance of the differential significantly. The differential is more sensitive to the friction coefficient between the ring gear and the drive pinion and between the left-side gear and two planets. The findings should make an important contribution to the analysis of the differential mechanism.