Modeling of Finite-Length Line Contact Problem with Consideration of Two Free-End Surfaces

Finite-length line contact conditions, existing in applications such as gears or roller bearings, lead to subsurface stress distribution influenced by the free boundaries. This paper presents a semi-analytical method (SAM) for the finite-length line contact problem, based on the overlapping concept and matrix formation, to consider the effect of two free-end surfaces. In order to obtain two free surfaces, three half-spaces with mirrored loads to be solved are overlapped to cancel out the stresses at expected surfaces. The error introduced by this method is analyzed and proven to be negligible. The conjugate gradient method (CGM) is used to solve the pressure distribution, and the fast Fourier transform (FFT) is used to speed up the elastic deformation and stress-related calculation. The model is verified by finite element method (FEM) and shows a high conformity and efficiency. Besides, the line contact situations are discussed to explore the effect of free surfaces.