Investigation of steady-state tyre force and moment generation under combined longitudinal and lateral slip conditions

The paper provides an insight into the contact mechanical behaviour of pneumatic tyres in a wide range of steady-state operating conditions. Tyre forces and self-aligning moment generation during steady-state manoeuvres are studied in some depth. For this purpose, two different versions of a dynamic model of a tyre are developed. The simplest version consists of a one-dimensional series of bristles distributed on the tyre periphery. The bristles incorporate anisotropic stiffness and damping in the lateral and longitudinal directions, while the distributed tread mass is also taken into account. The vertical pressure distribution along the contact patch is assumed to be parabolic and the length of the contact area is assumed to be known apriori. The friction forces developed on the contact patch follow a stick-slip friction law. The second version of the tyre model improves the potential of the simple model by introducing radial and tangential stiffness and damping, as well as a Kelvin element for rubber behaviour in the simulation of the impact on the leading edge of the contact area. The Kelvin model closely conforms to the semi-infinite incompressible nature of rubber. The tyre models show effective reproduction of measured longitudinal and lateral forces, as well as the self-aligning moment, under pure side-slip, pure longitudinal slip and combined slip situations. The generated curves show qualitative concordance with the results obtained experimentally, or by semi-empirical models such as the Pacejka’s Magic Formula. In addition, the tyre models seem to be capable of reproducing the generated contact pressure profiles and the shape of the observed variations in tyre forces between side-slipping, braking and traction diagrams. An investigation of these three situations reveals the different mechanisms that result in the different shapes of the diagrams. Finally, a study is carried out for tyre behaviour at very high speeds, which indicates deviations from the results of traditional investigations.