Rubber Friction Law Identification from Tyre Force Measurements Using a Stochastic Brush Model

It is often necessary to obtain complete friction maps for use with physical tyre models or simply for comparing friction envelopes on different surfaces. Exhaustive and controlled friction testing in the relevant environment is usually too costly, time-consuming and even prohibited (e.g. in motorsport due to regulations), so tyre forces must be inferred from full vehicle testing. Given measured tyre forces from a tyre test rig or vehicle based wheel force transducers, we present a method, based on an inverse brush model combined with Monte Carlo uncertainty propagation, to extract the friction at a given operating point. The method allows quantification of the uncertainty in friction estimation and it is shown that this uncertainty is higher at low slips, where structural parameters of the tyre dominate force generation. We also explore how brush model structural parameters impact the model and we demonstrate that uncertainty in the normal pressure distribution does not significantly affect the friction estimations. A simple friction mapping method is introduced utilising an empirical frictional heating term which is used to accurately predict tyre forces in new conditions.