A Brush-Model Based Semi-Empirical Tire-Model for Combined Slips

This paper presents a new method to derive the tire forces for simultaneous braking and cornering, by combining empirical models for pure braking and cornering using brush-model tire mechanics. The method is aimed at simulation of vehicle handling, and is of intermediate complexity such that it may be implemented and calibrated by the end user. The brush model states that the contact patch between the tire and the road is divided into an adhesion region where the rubber is gripping the road and a sliding region where the rubber slides on the road surface. The total force generated by the tire is then composed of components from these two regions. In the proposed method the adhesion and the sliding forces are extracted from an empirical pure-slip tire model and then scaled to account for the combined-slip condition. The combined-slip self-aligning torque is described likewise. The separation of the adhesive and sliding forces makes it possible to let the sliding force depend on the relative velocity between the tire and the road. This introduces a velocity dependence in the model, even though this is not explicitly present in the pure-slip model. The approach is quite different from most previous combined-slip models, in that it is based on a rather detailed mechanical model in combination with empirical pure-slip models. The model is computationally sound and efficient and does not rely on any additional parameters that depend on combined-slip data for calibration. It can be used in combination with virtually any empirical pure-slip model and in this work the Magic Formula is used in examples. Results show good correspondence with experimental data.