Імітаційне моделювання процесу зношування тонкого покриття пружної півплощини штампами канонічної форми

Abstract

In the article, using mathematical modeling methods, the contact inter-action of rigid bodies (stamps) of canonical form with an elastic half-plane protected by a Winkler coating is investigated, taking into account the wear of the intermediate layer.Under the conditions of a flat problem of the theory of elasticity basedon the abrasive wear model, which is expressed through a linear relation-ship between the intensity of wear and the work of friction forces, the main integro-differential equation of the problem for determining the contact pressure between the stamp and the coating is constructed.A technique for solving an integro-differential equation using Cheby-shov polynomials has been developed, which reduces the problem to an in-finite system of linear algebraic equations. A time-stepping algorithm was proposed for solving the equation. According to the algorithm, the working time of the friction pair with wear is divided into small time segments and the assumption is made that the contact area and contact pressure are con-stant at each time interval.When constructing graphs of contact pressure at different fixed mo-ments of time for the variable area of wear (contact), which, according to the assumption, is constant at each fixed step of the breakdown of the time of operation of the friction pair, an algorithm was used to reduce the ob-tained numerical data to one coordinate system, taking into account the proportionality of the ratio of the current area of the contact at the corre-sponding moment of time to the initial contact area at the moment of time equal to zero (problem without wear).The selection and analysis of contact pairs with various physical and mechanical parameters that would satisfy the selected mathematical model were carried out. For the dimensionless quantities described in the work, reverse calculations were carried out with the transition to dimensional quantities.For two different pairs of materials, based on the given force applied to the stamp, the corresponding initial contact area and the wear area were numerically calculated by the semi-inverse method at the given time inter-vals of the friction pair's operation. The characteristics of wear of the coat-ing for four canonical forms of stamps were studied and analyzed