Development of Theoretical Contact Width Formulas and a Numerical Model for Curved Rough Surfaces

[+] Author and Article Information
Shao Wang

School of Mechanical and Aerospace Engineering,  Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singaporemswang@ntu.edu.sg

J. Tribol 129(4), 735-742 (Apr 28, 2007) (8 pages) doi:10.1115/1.2768072 History: Received February 24, 2004; Revised April 28, 2007

The apparent contact area of curved rough surfaces can be larger than that predicted by the Hertz theory due to asperity interaction outside the Hertzian region. In the present study, simple theoretical formulas for the contact semi-width and radius for Gaussian and truncated Gaussian height distributions were derived, and a numerical contact model was developed based on a general power-law relationship between the local apparent pressure and real-to-apparent contact ratio. Numerical results of the contact semi-width agree well with the prediction of the formula. The apparent contact region becomes increasingly larger than the Hertzian region as a dimensionless roughness parameter increases or as a dimensionless load parameter decreases. The ratio of the contact semi-width to the Hertzian semi-width and the apparent pressure distribution are completely determined by a dimensionless contact parameter and the dimensionless roughness parameter, which are both independent of the instrument resolution, thus providing a long awaited solution to the problem of instrument dependency in a traditional theory. An application to fractal-regular surfaces indicates that the influence of the fractal dimension on the contact behavior is due to its effects on both the area-load coefficient and the load exponent.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Contact of curved rough surfaces simplified as a rigid equivalent indenter with a Hertzian shape interacting with a rigid plane through surface asperities modeled as springs

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Figure 2

Contour plot of the normalized contact semi-width, b∕a, in the plane of the dimensionless load parameter W, and the dimensionless roughness parameter Q for nominal line contacts

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Figure 3

Apparent pressure distributions and deformed surface profiles for different values of the dimensionless load parameter W for nominal line contacts (Q=1×10−5, β=1)

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Figure 4

Theoretical prediction (curves) and numerical results (data points) of the normalized contact semi-width, b∕a, versus the dimensionless load parameter W for different values of the dimensionless roughness parameter Q for nominal line contacts (β=1)

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Figure 5

Normalized contact semi-width, b∕a, predicted by the present indenter model for a truncated Gaussian surface compared to the results based on a first-order asymptotic model [19]



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