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Research Papers: Contact Mechanics

# On a Simplified Model for Numerical Simulation of Wear During Dry Rolling Contacts

[+] Author and Article Information
L. Chevalier1

Laboratoire MSME, Université Paris-Est, 5 Boulevard Descartes, Champs sur Marne, 77454 Marne la Vallée, Cedex 2, Franceluc.chevalier@univ-paris-est.fr

A. Eddhahak-Ouni

CRCHM, Université Paris, 12 Val de Marne, 8 rue du Général Sarrail, 94010 Créteil, Franceanissa.eddhahak-ouni@univ-paris12.fr

S. Cloupet

ISTIA–LASQUO, 62 Avenue Notre Dame du Lac, 49000 Angers, Francesylvain.cloupet@istia.univ-anger.fr

1

Corresponding author.

J. Tribol 131(1), 011402 (Dec 03, 2008) (15 pages) doi:10.1115/1.3002322 History: Received December 04, 2007; Revised September 18, 2008; Published December 03, 2008

## Abstract

We deal with rolling contact between quasi-identical bodies. As normal and tangential problems are uncoupled in that case, the simplified approach to determine contact area and normal loading distribution for rolling contact problems is presented in Sec. 2. In Sec. 3, the solution of the tangential problem is used to update the rolling profiles and enables to follow the wear evolution versus time. The method used to solve the normal problem is called semi-Hertzian approach with diffusion. It allows fast determination of the contact area for non-Hertzian cases. The method is based on the geometrical indentation of bodies in contact: The contact area is found with correct dimensions but affected by some irregularities coming from the curvature’s discontinuity that may arise during a wear process. Diffusion between independent stripes smoothes the contact area and the pressure distribution. The tangential problem is also solved on each stripe of the contact area using an extension of the simplified approach developed by Kalker and called FASTSIM . At the end, this approach gives the dissipated power distribution in the contact during rolling and this power is related to wear by Archard’s law. This enables the profiles of the bodies to be updated and the evolution of the geometry to be followed.

## Figures

Figure 1

Position of points M and M′

Figure 2

Position of the two solids in the Cartesian coordinate system

Figure 3

Definition of the geometrical characteristics of the indentation method

Figure 4

Stripe definition

Figure 5

Symmetric profile of the roller along y

Figure 6

Contact patch (a) and distribution of the normal load by unit of length (b). Comparison between semi-Hertzian method and analytical solution.

Figure 7

(a) Curvature B along y, (b) contact areas obtained by exact and semi-Hertzian methods, and (c) normal load by length obtained by exact and semi-Hertzian methods

Figure 8

(a) Curvature B along y before and after diffusion, (b) contact areas obtained by SHAD and CONTACT , and (c) normal load by length obtained by SHAD and CONTACT

Figure 9

Variation of C∗ with normal load (left) and with curvature A (right)

Figure 10

Profile of the roller in the plane (yOz)

Figure 11

(a) Curvature B along y before and after diffusion, (b) contact areas obtained by SHAD and CONTACT , and (c) normal load by length obtained by SHAD and CONTACT

Figure 12

Variation of C∗ with normal load

Figure 13

Roller’s profile in the plane (yOz)

Figure 14

(a) Curvature B along y before and after diffusion, (b) contact areas obtained by SHAD and CONTACT , and (c) normal load by length obtained by SHAD and CONTACT

Figure 15

Variation of C∗ with normal load

Figure 16

Definitions of yaw angle φy and spin angle φx

Figure 17

Test case (benchmark) of a non-Hertzian contact

Figure 18

Comparison between CONTACT and SHAD normal problem results

Figure 19

Comparison between CONTACT and SHAD tangential problem results. Shear force and slip velocity distributions.

Figure 20

Dissipated power per unit length Pl obtained with CONTACT and SHAD

Figure 21

Definition of Archard’s wear law

Figure 22

Half length of the contact stripe a(y) and contact area S

Figure 23

Incremental procedure to solve the wear problem

Figure 24

Test bench

Figure 25

Definition of the D parameter

Figure 26

Definition of the roller and the specimen initial profiles

Figure 27

Wear profile of specimen after several roller passages

Figure 28

Evolution of the maximum wear umax versus cycles

Figure 29

Specimen profile at the end of the simulation (left) and qualitative comparison with a picture of the wear profile (right)

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