A model for steady-state tire contact pressure distribution

Tire modelling has received much attention because of its practical importance in vehicle dynamics simulation. When a vehicle is steered at low speeds or at a standstill, the tire-road contact cannot simply be treated as a point contact because the tire treads behave very differently at different parts of the contact patch, and this distributed behaviour is dominant in this situation. To simulate the local tread behaviour, it is essential to determine the normal contact pressure as it is a key factor for the friction force. Among the different approaches to model the contact pressure distribution, light-weight empirical models are very interesting in various applications by having the advantages of easy implementation and efficient evaluation. However, the published models we found do not provide satisfactory results in simulating the contact pressure distribution under changing wheel load and camber angle, which typically occurs during a parking maneuver. In this paper, we propose an empirical model for the steady-state tire contact pressure distribution on a flat and rigid surface. The geometry of the contact patch and the pressure distribution on it are described by a combination of different mathematical functions, such as superellipses and polynomials. The dependence on operating conditions, i.e. inflation pressure, wheel load and camber angle, is given by a regression model using artificial neural networks. Validations were carried out by comparing the predicted contact pressure distributions of the proposed model with the measured ones. The results show a high prediction accuracy of the proposed model, particularly in those aspects that are relevant to the tire force and torque during steering at low or zero wheel rolling speed, such as the point of action of the net vertical force and the friction torque when rotating around a vertical axis.