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Research Papers: Contact Mechanics

# Simulation of Fretting Wear in Half-Plane Geometries—Part II: Analysis of the Transient Wear Problem Using Quadratic Programming

[+] Author and Article Information
D. Nowell

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UKdavid.nowell@eng.ox.ac.uk

It should be noted that the results given in Ref. 4 are based on a remote applied displacement of $10 μm$. This leads to a slip displacement, which varies slightly during the course of their simulation (as well as from point to point within the contact). For the purposes of the comparison shown here, a single value of $Δ=7.5 μm$ has been used, which is close to the average value shown in Fig. 5 of Ref. 4.

J. Tribol 132(2), 021402 (Mar 11, 2010) (8 pages) doi:10.1115/1.4000733 History: Received July 18, 2008; Revised January 26, 2009; Published March 11, 2010; Online March 11, 2010

## Abstract

This paper presents an efficient numerical method based on quadratic programming, which may be used to analyze fretting contacts in the presence of wear. The approach provides an alternative to a full finite element analysis, and is much less computationally expensive. Results are presented for wear of a Hertzian contact under full sliding and under partial slip. These are compared with previously published finite element analyses of the same problem. Results are also obtained for the fully worn problem by allowing a large number of wear cycles to accumulate. The predicted traction distributions for this case compare well with the fully worn analytical solution presented in part one of this paper.

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## Figures

Figure 1

Contact with applied normal force P and applied tangential displacement δ

Figure 2

Two bodies in contact showing the coordinate set and initial gap function

Figure 3

Overlapping triangular elements for pressure (and shear traction)

Figure 4

Comparison of numerical solution with theoretical pressure distributions: (a) Hertzian contact of cylinders (M=22), (b) contact of rigid frictionless punch (M=47), and (c) contact of elastic wedge (M=49).

Figure 5

Evolution of peak pressure with wear cycles, fully sliding Hertzian contact plotted (a) against the wear block number for different values of λ and (b) against the normalized wear cycle number

Figure 6

Pressure distributions at various stages of wear for full sliding of an initially Hertzian contact, including comparison with finite element results of Ding (4) (M=99, λ=0.018)

Figure 7

Variation in the maximum contact pressure with contact size as wear proceeds, showing approach to uniform pressure asymptote

Figure 8

(a) Worn profiles during wear of a fully sliding contact at different numbers of wear cycles; (b) comparison of fully worn profile with that generating uniform pressure

Figure 9

Pressure distributions at various stages of wear for partial slip of an initially Hertzian contact, including comparison with finite element results of Ding (4) (Q/fP=0.83, M=63, and λ′=0.04)

Figure 10

Comparison of fully worn pressure distributions with analytical solution from part 1 (7) (M=63, λ′=0.02)

Figure 11

Comparison of fully worn shear traction distributions in the stick region (normalized with respect to fp(x)) with analytical solution from part 1 (7) (M=63, λ′=0.02)

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