Improved Mathematical Approach for Modeling Sport Differential Mechanism

Abstract

Improved mathematical and simulation modes of the active differential mechanism (DM) with controllable torque redistribution would better contribute to developing intelligent vehicle transmissions. The issue is caused by actualizing the precise steerability control using advanced automated transmissions, allowing torque vectoring for all-wheel-drive vehicles and ensuring an option for correcting the vehicle trajectory. This paper presents an alternative mathematical method for obtaining differential equations for modeling vehicle transmission components and its implementation for simulating the Audi sport DM. First, the steerability issues of sport DM technology are discussed, and the sport DM design is described in detail. Then, a mathematical approach is proposed that includes three types of equation systems: generalized dynamics equations, kinematic constraint equations, and gearing condition equations. The approach also considers the flexibility of the clutch’s frictional pack, friction torque, lockup condition, and piston dynamics. Finally, a Simulink model that reflects the DM operation and calculation procedures is developed. A series of simulations of the sport DM operation with forcible torque distribution is carried out. The results show that the proposed mathematical model is universal, efficient, and accurate.