A contribution to the calculation of the contact stress distribution between two elastic bodies of revolution with non-elliptical contact area

A numerical method is presented for calculating the contact area and the normal stress distribution between two elastic bodies of revolution with parallel axes. For the discretization of the Fredhom integral equation the contact area is divided into strips perpendicular to the axes of revolution. The stress distribution in each strip is assumed to be semi-elliptical in the strip direction and constant in the other direction. The contact area is calculated iteratively by satisfying the contact condition and the stress condition. In addition for a given total normal force an additional iteration is required to improve the value obtained for the rigid-body approach. The contact area and the stress distribution between two ellipsoids are compared with Hertzian solutions. To investigate the non-Hertzian contact problem a number of cases of wheel-rail contact are considered.