The approached analytical decision of the flat contact problem into account wear of the thin elastic layer at the fixed area of contact.

Abstract

Dyachenko N.N., Manko N.I.-V. The approached analytical decision of the flat contact problem into account wear of the thin elastic layer at the fixed area of contact. The decision of a problem on linear wear process of a thin elastic strip is received at sliding on it of a stamp with the flat basis. I.G.Goryacheva [1] is offered a step-by-step method of digitization of time, where on each step the system of the integral equations is solved numerically. In the given work on each step to time the system of the integral equations is shown to one Fredholm operational equation of the second sort. The set to which belongs required decisions of such equation is found, and existence of the unique decision on this set is proved. On each time step the analytical decision in the form of the power series is found. Coefficients of this series can be found from infinite system of the linear algebraic equations. The ap-proached decision is found by a reduction method and a iteration method. The analysis of distribution of pressure and a thickness of a worn out strip in different time intervals is carried out: at a stage of the run-in and at a stage of the steady-state wear. The comparative analysis with the known decision from work [1] is carried out. Keywords: the flat contact problem, thin elastic strip, wear, iteration method, reduction method.