Dynamic modelling of differential bevel gear system in the presence of a defect.

• A linear time-varying model of a differential bevel gear set is proposed. • A 3D lumped parameter model of a differential bevel gear set is developed. • Free and forced vibration response of the differential bevel gear set is scrutinized. • The effects of the differential pinion position error are determined. A differential bevel gear set has a pivotal role in automotive applications. Unlike spur or helical planetary gear set, up to now, far too little attention has been paid to propose an adequate analytical model to analyze the dynamic behavior of the differential due to its complexities. One of the complexities is the fact that the differential pinion possesses simultaneous angular velocities about non-collinear axes. The aim of this paper is to investigate the dynamic response of the differential system whose bearings are deemed to be flexible and gear mesh stiffnesses are computed through potential energy. The analytical model of the differential bevel gear has been developed by means of Newton-Euler formulation and utilized it to scrutinize differential's natural frequencies and vibration modes. The sweep frequency analysis has been used to represent the dynamic response of the system. After that, we have incorporated the position error of the differential pinion into the differential model, and the obtained results have been compared with a healthy one. This work may be considered as an important threshold to get full dynamic details of the differential bevel gear set, and to offer insights for enhancing the differential design. [ABSTRACT FROM AUTHOR]