A Solution for the Contact Problem of Free Rolling on a Rigid Foundation of a Cylindrical Body with a Deformable Rim

The contact problem of free rolling on a rigid foundation of a cylindrical body consisting of a non-deformable central part and an elastic rim is considered. A technique for an analytical solution is developed on the basis of a second-order asymptotic approximation. The contact interaction of the composite body with a non-deformable foundation under the action of a vertical force is investigated as a calculation example assuming a small rolling resistance moment. The calculated distributions of normal and tangential contact stresses, the distribution of the stress tensor intensity in the rim near the contact area, and the “force–displacement” dependence are obtained. These data are compared with the estimates obtained by the authors on the basis of finite element modeling and the results of using an alternative version of the asymptotic approximation. A conclusion is made about the advantages of the developed technique in comparison with the known asymptotic approach in terms of the accuracy of calculating the contact parameters and the simplicity of the applied mathematical apparatus. It is shown that the maximum of the stress tensor intensity is localized on the line of action of the vertical force (axis of symmetry) for a deformable rim material with Poisson’s ratio ν less than 0.4 and on the inner surface of the rim near the boundary of the adhesion and slip zones for ν > 0.4. The data derived are used to analyze the loading of roller interfaces of mining equipment.