Wear problem for tube with thin nonuniform inner coating and rigid insert with complex profile

Abstract

The article describes the formulation of the problem of wear of an elastic pipe with a nonuniform internal coating by a rigid insert, the diameter of which is variable. For this problem, a mathematical model is built, which is a mixed integral equation. The resulting integral equation contains functions related to the variable properties of the coating and the shape of the insert. When constructing an analytical solution, a special approach was used, since standard methods do not allow taking into account the presence of rapidly changing functions in the equation, which can describe the shapes and properties of materials. In the resulting solution, the functions describing the variable properties of the coating and the profile of the insertion are separated by separate terms. This allows you to always get accurate results.