Tyre–road contact using a particle–envelope surface model

Determination of the contact forces is the central problem in all aspects of road-tyre interaction: i.e. noise, energy loss and friction. A procedure to find the contact forces under a rolling tyre is presented in four stages. First, the contact stiffness of a uniform peak array from indentations in the rubber tread, and also tyre carcass deflection, is described by some new simplified expressions. Second, a routine divides a single surface profile into equal search intervals, in which the highest peaks are identified. These are used to obtain the parameters for the interval, i.e. the mean envelope and the mean interval. The process is repeated at geometrically decreasing search intervals until the level of the data resolution, thereby describing the profile by a set of envelopes. The ‘strip profile’ ultimately used to describe the surface, is obtained by selecting the highest points across the profiles of one stoneʹs width. The third stage is to combine the strip profile envelopes with the contact stiffness expressions, yielding the nonlinear stiffness–displacement, and force–displacement relationships for the chosen road–tyre combination. Finally the contact pressure distribution from a steady-state rolling tyre model is applied to the strip profile, via the force–displacement relationship, giving the local tyre displacements on the road texture. This displacement pattern is shown to be proportional to the time and space varying contact pressure, which then is incorporated into a wave equation for rolling contact.