Application of equivalent load method in finite-length elastic space with the consideration of two free-end surfaces

Non-conforming contact pairs, such as gears, roller bearings and rail-wheel systems, have free-end surfaces, and the classical Hertz theory generally is based on the assumption of half space, which neglects the influences of free-end surfaces. In this paper, the equivalent load method is presented to investigate the effect of free-end surfaces of finite-length elastic space on internal stresses and von-Mises stress. This method can effectively solve the free-edge problems and multi-direction stresses problem. The results obtained by the presented method are evaluated and validated by the results from quarter space model and finite element method. The distinctions among the half space model, the quarter space model and the finite-length space model are discussed. It can be found that when the edge distance is larger than 2a, the half space model can be approximately applied. And when the distances between two free end surfaces is less than 4a, the effect of two free end surfaces should be considered simultaneously. •Equivalent load method was applied to solve finite-length elastic space problem.•The effect of the free-end surfaces on internal stresses and von-Mises was discussed.•Two free-end surfaces interact when the distance is less than four times the Hertzian contact half width.