Evaluation of approximations used for the tread layer response and road surface roughness in numerical models of the tyre/road contact

The detailed behaviour at the interface between automotive tyres and roads is important in numerical contact models aiming at prediction of rolling resistance, traction, wear, excitation of vibrations, and noise generation. The detailed behaviour depends on the local dynamic response of the tread and the small-scale roughness of the road surface. For complete tyre-road interaction simulations predicting global vibrations, the tread layer has commonly been modelled using approximations such as a set of uncoupled linear springs or an elastic half-space. These computational efficient approximations have been introduced in an ad hoc manner and they have seldom been evaluated in detail. This paper evaluates these two simplified approaches by comparison to results from a detailed numerical model for a tread layer on a rigid backing that is pressed into a road surface. The detailed contact model is formulated in the time-domain and includes the effect of small-scale roughness by non-linear force-indentation functions between each pair of contact elements. The results show that the effect of the inertia in the tread layer is insignificant for typical contact conditions. The stiffness of the linear springs and the elastic half-space must be tuned to account for the actual coupling within the tread layer and the small-scale roughness of the road. The set of uncoupled linear springs can be tuned to closely follow the force-indentation relation of the detailed model. The elastic half-space can only be tuned for a specific indentation, force or contact stiffness, since its relation has a slightly different character. It is concluded that purely elastic models of the tread are relevant and that the set of uncoupled linear springs performs better than the elastic half-space. However, the tuning of the stiffness is not trivial without results from more elaborate models including the influence of local tread properties and small-scale surface roughness