Effect of Wear on the Partial Closure of a Variable Width Slit in a Hub of a Friction Pair

The design of moving joints requires taking into account that some units of friction pairs (hub) can be weakened by a crack (slit). In this paper, a mathematical model of contact interaction and wear for a hub–plunger friction pair to calculate the optimal function of displacements of points of the external contour of a hub weakened by a slit (crack) is presented. The function of displacements of points is considered optimal, if the slit faces are closed, i.e., the slit remains stationary. A plane problem of fracture mechanics for a hub of a friction pair during operation is considered. It is assumed that there is a rectilinear variable width slit in the hub near the friction surface, which is comparable to elastic deformations. A criterion and method for solving the inverse problem of fracture mechanics for determining the function of displacements of points of the external contour of a friction pair hub with consideration for the temperature gradient in the hub are given. The obtained equations make it possible to determine the stress intensity coefficients in order to predict the slit growth and to establish the limit level of defectiveness and the maximum values of working loads for the given function of displacements of points of the external contour of the hub. The found function of displacements of points of the hub’s external contour provides an increase in the load-carrying capacity of the friction pair hub. The solution of the inverse problem on determining the function of displacements of points of the hub external contour makes it possible to choose optimal geometric parameters of the friction pair elements at the design stage.