Simulation of the Wear Process of a Thin Coating of an Elastic Semi-Plane by Stamps of the Canonical Form

• Date: 2022
• Main Authors: Максимук, Олександр, Сачук, Юрій, Лехіцький, Тарас
• Format: Article
• Language: Ukrainian
• Published: Кам'янець-Подільський національний університет імені Івана Огієнка 2022
• Online Access: http://mcm-math.kpnu.edu.ua/article/view/274620
• Journal Title: Mathematical and computer modelling. Series: Physical and mathematical sciences

In the article, using mathematical modeling methods, the contact interaction 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 based on the abrasive wear model, which is expressed through a linear relationship 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 Chebyshov po­lynomials has been developed, which reduces the problem to an infinite 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 constant at each time interval. When constructing graphs of contact pressure at different fixed moments 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 obtained numerical data to one coordinate system, taking into account the proportionality of the ratio of the current area of the contact at the corresponding 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 intervals of the friction pair's operation. The characteristics of wear of the coating for four canonical forms of stamps were studied and analyzed.