A 3D Contact Model with Shoulder-to-Shoulder Paraboloidal Asperities for Rough Surfaces

To address the limitations of existing two-dimensional asperity shoulder-to-shoulder contact models and to investigate the normal and tangential contact mechanisms of rough surfaces, this study proposes a three-dimensional elastic contact model based on shoulder-to-shoulder paraboloidal asperities within the framework of Hertzian contact theory. The proposed model extends the conventional two-dimensional elastic shoulder-to-shoulder asperity contact model developed by Sepehri by explicitly incorporating the effects of principal surface curvatures, thereby enabling the accurate representation of three-dimensional contact conditions. Analytical relationships among contact load, elastic interference, contact area, and contact pressure are derived. The predictive performance of the proposed model is evaluated through systematic comparisons with Sepehri’s model and finite element analysis (FEA) results. The results demonstrate that the proposed model exhibits significantly improved agreement with the FEA predictions. The maximum relative errors for contact area, maximum contact pressure, and contact interference are 5.74%, 5.96%, and 2.77%, respectively. Furthermore, parametric studies examine the effects of relative offset r and pressing amount Δd on contact displacement, contact area, and maximum contact pressure. Furthermore, parametric studies are conducted to examine the effects of the relative offset r the pressing amount Δd on contact displacement, contact area, and maximum contact pressure. The results indicate that the contact area increases with both r and Δd, whereas the maximum contact pressure and contact displacement exhibit similar trends, increasing with Δd but decreasing with increasing r. These findings validate the accuracy and applicability of the proposed model under varying contact conditions, providing a reliable theoretical foundation for refining asperity contact models and supporting practical engineering contact analyses.