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 were derived, and a numerical contact model was developed based on an iterative scheme for the elastic deformation of the macroscopic surface profile and the asperity deformation. Both the theoretical formulas and the numerical model are 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 the dimensionless roughness parameter increases, or as the dimensionless load parameter decreases, while the effect of the load exponent is relatively small. The ratio of the contact semi-width to the Hertzian semi-width is mainly determined by a dimensionless contact parameter involving the root-mean-square roughness, the equivalent radius and the Hertzian semi-width or radius. When applied to fractal regular surfaces, the present theory 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.