A theoretical model for the tread slip and the effective rolling radius of the tyres in free rolling

A rigid–elastic coupling theory for the rolling kinematics of tyres, by which the tread slip, the effective rolling radius and the ply steering of the tyres can be analysed, was formulated. The theory demonstrates that, during free-rolling motion, the coupling between the rotational velocity Ω along the wheel axis and the circumferential displacement gradient generates the longitudinal tread slip, and the coupling between the rotational velocity Ω along the wheel axis and the lateral displacement gradient generates the lateral tread slip and the ply steering. Revisiting the tread slip phenomenon using the newly proposed method numerically proves the kinematic mechanism of the rolling friction. It can be found that the effective rolling radius R_e increases with increasing inflation pressure and decreases with increasing load; the sensitivity of R_e to the inflation pressure is greater than the sensitivity of R_e to the load. The good agreement between the theoretical predictions and the test results for the effective rolling radius of the radial tyres of a car is found. The coupling of the displacement gradient and the rigid rolling kinematics causes non-symmetry of the lateral tread slip which, in turn, leads to the ply steering and the residual aligning moment; these depend on the belt and tread design. The proposed theory and approach provide a quick and powerful tool for analysing the tread slip, the effective rolling radius and the ply steering of the tyres under free rolling.