Development and analysis of the two-regime transient tyre model for combined slip

This paper refines the two-regime transient theory developed by Romano et al. [Romano L, Bruzelius F, Jacobson B. Unsteady-state brush theory. Vehicle Syst Dyn. 2020;59:11-29. DOI: 10.1080/00423114.2020.1774625.] to include the effect of combined slip. A nonlinear system is derived that describes the non-steady generation of tyre forces and considers the coupling between the longitudinal and lateral characteristics. The proposed formulation accounts for both the carcass and the bristle dynamics, and represents a generalisation of the single contact point models. A formal analysis is conducted to investigate the effect of the tyre carcass anisotropy on the properties of the system. It is concluded that a fundamental role is played by the ratio between the longitudinal and lateral relaxation lengths. In particular, it is demonstrated that the maximum slip that guarantees (partial) adhesion conditions does not coincide with the stationary value and decreases considerably for highly anisotropic tyres. The dissipative nature of the model is also analysed using elementary tools borrowed from the classic theory for nonlinear systems. A comparison is performed against the single contact point models, showing a good agreement especially towards the full-nonlinear one. Furthermore, compared to the single contact point models, the two-regime appears to be able to better replicate the exact dynamics of the tyre forces predicted by the complete brush theory. Finally, the transient model is partially validated against experimental results.