Frictional Energy Dissipation in a Contact of Elastic Bodies Subjected to Superimposed Normal and Tangential Oscillations

T Hanisch,Q Li,I Richter

doi:10.1134/s1029959920060119

Abstract

Frictional damping in elastic contact of a parabolic indenter subjected to a combination of oscillations in normal and tangential directions is numerically simulated. The dissipated energy first increases linearly with coefficient of friction, then decreases linearly, and finally reaches a constant value. These three regions correspond to the states of complete slip, partial slip and complete stick. All three asymptotical dependencies can be described analytically. The dissipated energy in a dimensionless form is function of the ratio of normal oscillation amplitude and mean indentation depth, the ratio of change in contact area and sticking area, and phase shift between normal and tangential oscillation. Master curves are suggested.

Highlights

In frictional contacts, energy is dissipated when two contacting bodies have a relative sliding movement
We numerically study the frictional damping due to a combination of vertical and tangential oscillation with constant coefficient of friction in contact under the Coulomb’s law of friction
The frictional contact of a parabolic indenter and an elastic half space, while the indenter is subjected to oscillations in normal and tangential directions, is numerically simulated using the method of dimensionality reduction

Summary

Introduction

Energy is dissipated when two contacting bodies have a relative sliding movement. That even in the case of infinitely large coefficient, energy dissipation still occurs if the body oscillates in both vertical and tangential directions, because the elastic energy stored at the boundary elements of contact is suddenly relaxed during the composed oscillating process [6]. We carry out simulations of contact due to a combination of normal and tangential oscillation using the method of dimensionality reduction [15,16,17] This is a very effective analytical and numerical tool exactly for this type of contact problems where only the total macroscopic force and displacement are of importance. Both these quantities are determined in the framework of method of dimensionality reduction exactly, provided Coulomb’s law of friction is assumed

Mathematical model

Theoretical analysis

Numerical results

Conclusion