Generalised model of wear in contact problems: the case of oscillatory load

TL;DR

This paper develops a fractional integral-based wear model for contact problems under oscillatory loads, analyzing the stationary state and validating results through numerical simulations.

Contribution

It introduces a novel fractional integral wear model incorporating relaxation effects for oscillatory contact problems.

Findings

Identification of a time-dependent stationary state.

Quantification of convergence to the stationary state.

Numerical simulations demonstrating model behavior and parameter effects.

Abstract

In this short paper, we consider a sliding punch problem under recently proposed model of wear which is based on the Riemann-Liouville fractional integral relation between pressure and worn volume, and incorporates another additional effect pertinent to relaxation. A particular case of oscillatory (time-harmonic) load is studied. The time-dependent stationary state is identified in terms of eigenfunctions of an auxiliary integral operator. Convergence to this stationary state is quantified. Moreover, numerical simulations have been conducted in order to illustrate the obtained results and study qualitative dependence on two main model parameters.