Mathematical modelling of thermoelastic behavior of a coating taking into account frictional heating and wear

Abstract

This work describes application of the integral transform method to solution of a quasi-static contact problem of the coating wear-out. Frictional heating and wear of the coating occurs during the sliding of a rigid body over its surface. The problem is considered in the framework of the coupled thermoelasticity theory. The solution of the problem is constructed in the form of contour quadratures of the inverse Laplace transformation. After the calculation of the quadratures the solution of the problem is constructed in the form of series over the poles of the integrands. Investigation of the poles of integrands is performed in dependence on four dimensionless parameters of the problem. The solutions obtained are studied in detail with respect to the dimensionless and dimensional parameters of the problem. Numerical examples of the obtained solutions for contact stresses, displacements, temperature and wear of the coating are presented.Keywords: coating, friction, wear, frictional heating, thermoelasticity, Laplace transform, contour integral Introduction. The study of thermoelasticity problems, taking into account the interaction of deformation and temperature fields, began with [1][2][3]. This line of research was called the coupled thermoelasticity. Generalization and solution of particular problems of the new direction of research was continued in [3][4][5]. In subsequent years, both analytical, starting with [4,5], and numerical methods [6] were developed to solve problems of coupled thermoelasticity. In the latter paper the authors were one of the first who developed a scheme of application of the finite element method and gave its implementation for solving the coupled problems of thermoelasticity. Analysis shows that in the overwhelming majority of studies in the solution of coupled thermoelasticity problems the finite element models of a fairly general purpose were developed, for example [7][8][9][10][11].The analytical methods for solving this class of problems did not become as widespread as the numerical ones. The results obtained with their help were summarized in [12]. Beginning with papers [13][14][15][16][17][18], scientists consider uncoupled problems of thermoelasticity about the sliding contact of a rigid body with an elastic coating, taking into account friction, heating of the coating from friction, and abrasive wear. Because of the large number of parameters of the problem, the onedimensional and quasi-static problems were considered. In [15][16][17][18], for their solution the integral Laplace transform with a solution in the form of functional series along the poles of the integrands of the contour quadratures of the inverse Laplace transform were used. The solution method allows