A Simple Semi-Analytic Contact Mechanical Model for Tangential and Torsional Fretting Wear of Axisymmetric Contacts

Emanuel Willert

doi:10.3390/sym13091582

Abstract

Fretting wear of axisymmetric contacts is considered within the framework of the Hertz–Mindlin approximation and the Archard law for the linear wear. If the characteristic time scale for the wear is much larger than the duration of a single fretting oscillation, the profile change due to wear during one fretting cycle can be neglected for the contact problem as a zero-order approximation. This allows to give an exact contact solution during each fretting cycle, depending on the current worn profile, and thus for the explicit statement of an ordinary integro-differential equation system for the time-evolution of the fretting profile, which can be easily solved numerically. The proposed method gives the same results as a known, contact mechanically more rigorous simulation procedure that also operates within the framework of the Hertz–Mindlin approximation, but works significantly faster than the latter one. Tangential and torsional fretting wear are considered in detail. A comparison of the numerical prediction for the evolution of the worn profile in partial slip torsional fretting of a rubber ball on abrasive paper shows good agreement with experimental results from the literature.

Highlights

Many tribological contacts in technical or biological systems are subject to oscillations because they are part of a periodically operating machine or a periodically changing environment
The model for tangential fretting wear is detailed and its predictions are compared to a contact mechanically more rigorous numerical model in Sections 3.1 and 3.2
The Cattaneo–Mindlin loading only corresponds to the first loading of the fretting contact

Summary

Introduction

Many tribological contacts in technical or biological systems are subject to oscillations because they are part of a periodically operating machine or a periodically changing environment. The theoretical solution procedure for a given fretting problem should consist of at least three components: a contact mechanical solution (depending on the material model, the frictional regime, and so on) as the basis for the determination of local stresses and displacements [6,7], a wear routine [8,9,10], as well as a crack initiation and propagation routine [11,12,13]. Semi-analytic (contact mechanical) approaches—which already have various applications in tribology [15]—can be a good “trade-off” between effort and prediction quality [16]

Methods

Results

Discussion

Conclusion