An extended LuGre-brush tyre model for large camber angles and turning speeds

This paper presents a novel tyre model which combines the LuGre formulation with the exact brush theory recently developed by the authors, and which accounts for large camber angles and turning speeds. Closed-form solutions for the frictional state at the tyre-road interface are provided for the case of constant slip inputs, considering rectangular and elliptical contact patches. The steady-state tyre characteristics resulting from the proposed approach are compared to those obtained by employing the standard formulation of the LuGre-brush tyre models and the exact brush theory for large camber angles. Then, to cope with the general situation of time-varying slips and spins, two approximated lumped models are developed that describe the aggregate dynamics of the tyre forces and moment. In particular, it is found that the transient evolution of the tangential forces may be approximated by a system of two coupled ordinary differential equations (ODEs), whilst the dynamics of the self-aligning moment may be described by combining two systems of two coupled ODEs. Given its stability properties and ease of implementation, the lumped one may be effectively employed for vehicle state estimation and control purposes.

Automated summary

This paper presents a novel tyre model that combines LuGre formulation with an exact brush theory, taking into account large camber angles and turning speeds. Closed-form solutions for frictional state at the tyre-road interface are provided for constant slip inputs, considering rectangular and elliptical contact patches. The proposed approach is compared to standard LuGre-brush tyre models and exact brush theory for large camber angles. Two approximated lumped models are developed for the general situation of time-varying slips and spins. The paper concludes that the lumped model is stable and easy to implement, making it effective for vehicle state estimation and control purposes.