Development of theoretical contact width formulas and a numerical model for curved rough surfaces

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.