THE PROBLEM OF WEARING A WINKLEER-TYPE FOUNDATION WITH A RECTANGULAR PLAN PUNCH ACCORDING TO THE POWER LAW OF WEAR

Wear characterizes the process of removing material from the surface of contacting bodies. It is known that the dependence of the wear rate on the contact pressure is expressed by a linear or power law.The contact problem of wear of the foundation of the Winkler type due to the movement of a stamp rectangular in plan on it at the stage of steady wear is considered. The formulation of such a problem is described in the literature, where formulas for its analytical solution in the case of a linear wear law are also found.The work is devoted to the study of methods of solving the problem according to the power law of wear. The problem is modeled by a differential or equivalent integral solving equation and a force equilibrium condition.In the case of a plane punch, the nonlinear differential equation has an analytical solution. For a punch with a non-plane sole, approaches to using the numerical method of finite differences based on left or right difference relations are outlined. The iterative method and the power series method are used to solve the integral equation. As a result of the application of all the mentioned methods, functions are obtained that depend on the unknown parameter, which is from the equilibrium condition using the method of half-division.A comparative analysis of the results obtained by different approaches was carried out. Numerical results were obtained for rectangular punches with non-plane soles defined by certain polynomial or trigonometric functions.The influence of the law of wear, physical and geometric parameters on wear contact characteristics was revealed.