SUMMARYThe 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.

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The transient wear process at contact frictional interface of two elastic bodies in relative steady motion induces evolution of shape of the interface. A steady wear state may be reached with uniform wear rate and fixed contact surface shape. In this paper, the optimal contact shape is studied by formulating several classes of shape optimization problems, namely minimization of generalized wear volume rate, friction dissipation power and wear dissipation rate occurring in two bodies. The wear rule was assumed as a nonlinear dependence of wear rate on friction traction and relative sliding velocity, similar to the Archard rule. The wear parameters of two bodies may be different. It was demonstrated that different optimal contact shapes are generated depending on objective functional and wear parameters. When the uniform wear rate is generated at contact sliding surfaces, the steady state is reached. It was shown that in the steady state the wear parameters of two bodies cannot be independent of each other. The solution of nonlinear programming problem was provided by the iterative numerical procedure. It was assumed that the relative sliding velocity between contacting bodies results from translation and rotation of two bodies. In general, both regular and singular regimes of wear rate and pressure distribution may occur. The illustrative examples of drum brake, translating punch and rotating annular punch (disc brake) provide the distribution of contact pressure and wear rate for regular and singular cases associated with the optimality conditions. It is shown that minimization of the generalized wear dissipation rate provides solutions assuring existence of steady wear states.

The rubber bumpers built into the air-spring structures of buses perform a number of critical tasks. Consequently, designing their shape requires considerable effort. This paper presents a novel solution for determining the required characteristics of axi-symmetric rubber parts, which can efficiently be used in practice.The procedure is based on the finite element method (FEM) and the support vector regression fSVRj model. A finite element code developed by the authors and based on a three-field functional is used for the rapid and appropriately accurate calculation of the characteristics of rubber bumpers. A rubber shape is evaluated via the work difference and the area between the desired and the actual load-displacement curves. The objective of shape optimization is to find the geometry where the work difference is under a specified limit. The tool of optimization is the SVR method, which provides the regression function for the work difference. The minimization process of the work-difference function leads to the optimum design parameters. The efficiency of the method is verified by numerical examples.

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