Nonlinear modelling of transient tyre dynamics

Abstract

In this paper, a modern and refined formulation of the nonlinear full contact patch tyre model is developed and analysed. In particular, the representation introduced in the present work, formulated in terms of hyperbolic partial differential equations (PDEs) with boundary terms, considers explicitly the closed-loop dynamics between the tread particles travelling inside the contact patch and the compliance of the tyre carcass. A linearised version of the model—renamed linearised full contact patch—is also derived. In particular, the solution to governing PDEs of the linearised formulation is provided in closed form, and its regularity is discussed within different functional settings. A rigorous stability analysis of the linearised full contact patch model is also performed, revealing that the latter is exponentially stable owing to the assumption of a diagonal stiffness matrix for the tyre carcass. Finally, the transient behaviour predicted by the linearised version of the model is validated against the full nonlinear formulation for different operating conditions of the tyre, providing important indications about its domain of applicability.