Modelling Effects due to Small-Scale Roughness in Tyre/Road Contact

The interaction process between a rolling automotive vehicle tyre and a road is influenced by the geometry of the interacting bodies on a wide range of length scales down to the micrometer length-scale. The smaller length-scales determines the details of pressure and strain distributions in the contact, that in turn affects rolling resistance, noise generation, wear, and grip. These small scales also determine, via the area of real contact, the non-linear contact stiffness and the adherence forces between the two surfaces. These two effects have been included in a tread block / road surface contact model, which is based on spatial discretisation of the contact geometry. The model is formulated in the time domain and the dynamic response is calculated convolving contact forces with pre-calculated impulse responses of the interacting objects. The effects due to roughness on length scales smaller than the dimensions of contact elements are included by non-linear relations between force and separation distance for each pair of contact elements. Comparison with results from a standard Lagrange contact formulation reveals the importance of including also the smaller length-scales