On optimal contact shapes generated by wear

The optimal shape design of contacting surfaces has usually been aimed at controlling the contact pressure distribution. However, a much wider class of contact optimization problems can be formulated by maximizing contact force or displacement, torsional moment, or minimizing the friction dissipation. The special classes of optimization problems are considered, namely, minimization of generalized wear volume rate, minimization of generalized friction dissipation power and minimization of the generalized wear dissipation power depending on both normal pressure and slip velocity. The specific wear rule was assumed and the optimality conditions are derived. They generate optimal contact pressure distribution and the corresponding optimal wear rate. The optimization problems are reduced to non-linear programming problems and for their solution a special iteration process is used. The wear process is analysed in two specific cases. First, when the relative sliding velocity between bodies is constant and the second case, when one of bodies rotates with respect to another body. For rotational motion the problem of minimization of friction dissipation power is considered by applying the technique of control of contact pressure distribution and minimization of the generalized friction dissipation power with a new control parameter q. It is demonstrated that the wear dissipation power at the contact surface is minimal in the steady state of wear process and in many cases corresponds to the uniform wear rate. The illustrative examples for rotating bodies demonstrate the evolution of wear process toward a steady state. The minimization of the generalized wear volume rate and of generalized friction dissipation power does not induce the steady state of wear process in the rotation motion. The identification procedure is proposed to specify the wear parameters