Axi-symmetrical contact problem during braking with frictional heating and wear

The problem of transient contact with frictional heating and wear for two non-uniform sliding half-spaces is considered. One of the two half-spaces is assumed to be slightly curved to give a Hertzian initial pressure distribution; the other is a rigid non-conductor. On the assumption that the contact pressure distribution could be described by the Hertz formulas during whole the process of interaction, the problem is formulated in terms of one integral equation of the Volterra type an unknown radius of the contact area. A numerical solution of this equation is obtained using a piecewise-constant representation of unknown function. The influence of operating parameters on the contact temperature and the radius of the contact area is studied.