The rolling of a wheel with a reinforced tyre along a plane with slipping

Abstract

A previously proposed model [1] of a wheel with a reinforced tyre in which the side walls of the tyre are represented by reinforced membranes consisting of incompressible rubber, in accordance with the Mooney-Rivlin model [2] , is considered. When the tread is deformed, the exact non-linear conditions for the inextensibility of the reinforcing cords are taken into account, unlike the conditions in the linearized form used previously in [1] . A potential-energy functional of the deformed tyre as a function of the deformations of the centre line of the tread and the displacements of the wheel disc, which has six degrees of freedom, is obtained using a number of hypotheses. A complete system of equations is derived and the conditions imposed on the sudden jumps in the functions describing the deformation of the tread at the boundary points of the previously unknown area of contact of the tread with the plane when there is slipping is obtained using a model of dry friction. Two steady modes of motion of the locked wheel are investigated: rectilinear translational motion at a constant speed and spinning around an axis orthogonal to the rolling plane of the wheel with constant angular velocity.