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Elastic contact stiffness and contact resistance for the Weierstrass profile

Elastic contact stiffness and contact resistance for the Weierstrass profile
Elastic contact stiffness and contact resistance for the Weierstrass profile
The Weierstrass series comprises a system of superposed self-affine sine waves that can be used to define a simple idealization of a two-dimensional fractal rough surface profile. The load–compliance relation for the contact of this profile with a rigid plane is here estimated using Westergaard's solution for the contact of a single sine wave with a plane and various approximations concerning the interaction of the different terms in the series. These approximations are compared with a numerical solution for the contact of the profile defined by the first few terms of the series. Once the load–compliance relation is established, the electrical contact resistance can be determined, using an analogy between the conduction and incremental elastic contact problems. The results show that these simple estimates give quite good predictions of the relations between load, compliance and contact resistance. They also confirm that these relations are largely determined by the coarse scale features of the surface profile, in contrast to the predictions of classical asperity model theories.
contact resistance, contact stiffness, Weierstrass profile, fractal surfaces, multiscale models
0022-5096
1247-1265
Ciavarella, M.
d5aa6350-b3d4-4a78-a670-9d78242f58c5
Murolo, G.
b145c47d-7433-4261-9d9c-7c74c901a7ab
Demelio, G.
cb38aabe-9837-4ab2-aa87-60028fd7b82c
Barber, J.R.
af9edfeb-4ab0-4c9a-9974-12f1e993e10b
Ciavarella, M.
d5aa6350-b3d4-4a78-a670-9d78242f58c5
Murolo, G.
b145c47d-7433-4261-9d9c-7c74c901a7ab
Demelio, G.
cb38aabe-9837-4ab2-aa87-60028fd7b82c
Barber, J.R.
af9edfeb-4ab0-4c9a-9974-12f1e993e10b

Ciavarella, M., Murolo, G., Demelio, G. and Barber, J.R. (2004) Elastic contact stiffness and contact resistance for the Weierstrass profile. Journal of the Mechanics and Physics of Solids, 52 (6), 1247-1265. (doi:10.1016/j.jmps.2003.12.002).

Record type: Article

Abstract

The Weierstrass series comprises a system of superposed self-affine sine waves that can be used to define a simple idealization of a two-dimensional fractal rough surface profile. The load–compliance relation for the contact of this profile with a rigid plane is here estimated using Westergaard's solution for the contact of a single sine wave with a plane and various approximations concerning the interaction of the different terms in the series. These approximations are compared with a numerical solution for the contact of the profile defined by the first few terms of the series. Once the load–compliance relation is established, the electrical contact resistance can be determined, using an analogy between the conduction and incremental elastic contact problems. The results show that these simple estimates give quite good predictions of the relations between load, compliance and contact resistance. They also confirm that these relations are largely determined by the coarse scale features of the surface profile, in contrast to the predictions of classical asperity model theories.

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More information

Published date: 2004
Keywords: contact resistance, contact stiffness, Weierstrass profile, fractal surfaces, multiscale models

Identifiers

Local EPrints ID: 23244
URI: http://eprints.soton.ac.uk/id/eprint/23244
ISSN: 0022-5096
PURE UUID: 6bd94d41-1186-49f8-b416-747bfcb1eb93

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Date deposited: 23 Mar 2006
Last modified: 15 Mar 2024 06:45

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Contributors

Author: M. Ciavarella
Author: G. Murolo
Author: G. Demelio
Author: J.R. Barber

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