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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 Re increases with increasing inflation pressure and decreases with increasing load; the sensitivity of Re to the inflation pressure is greater than the sensitivity of Re 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. [ABSTRACT FROM AUTHOR]

A new analytical formula to describe the vertical stiffness of a rolling lobe spring has been established; the equation incorporates the rate of change of the effective area of the spring. Two rolling lobe air springs were studied by performing analytical calculations, and the results were verified by comparisons to finite element simulations and experimental data. The analytical formula can be used to qualitatively predict the vertical stiffness of a rolling lobe air spring. Precise prediction of the value of the vertical stiffness can be obtained using the formula in cases where the reservoir volume is not very large. The influence of geometric parameters on the vertical stiffness of a rolling lobe air spring has been studied using the proposed formula and a guideline for its design has been obtained by plotting a cause–effect chart. [ABSTRACT FROM AUTHOR]

It is well known that the tyre steering torque is highly dependent on the tyre rolling speed. In limited cases, i.e. parking manoeuvre, the steering torque approaches the maximum. With the increasing tyre speed, the steering torque decreased rapidly. Accurate modelling of the speed-dependent behaviour for the tyre steering torque is a key factor to calibrate the electric power steering (EPS) system and tune the handling performance of vehicles. However, no satisfactory theoretical model can be found in the existing literature to explain this phenomenon. This paper proposes a new theoretical framework to model this important tyre behaviour, which includes three key factors: (1) tyre three-dimensional transient rolling kinematics with turn-slip; (2) dynamical force and moment generation; and (3) the mixed Lagrange–Euler method for contact deformation solving. A nonlinear finite-element code has been developed to implement the proposed approach. It can be found that the main mechanism for the speed-dependent steering torque is due to turn-slip-related kinematics. This paper provides a theory to explain the complex mechanism of the tyre steering torque generation, which helps to understand the speed-dependent tyre steering torque, tyre road feeling and EPS calibration. [ABSTRACT FROM PUBLISHER]