Theoretical Formula for Calculation of Line-contact Elastic Contact Deformation

Based upon the theory on general smooth elastic contact, the finite length line contact problem was analyzed and the theoretical formula of elastic line contact deformation derived. It has been found that the analytical solution is consistent with the numerical one. As compared with the empiric formulae, the formula derived reveals the effect of material characteristics, load and radius of curvature on the elastic line contact deformation more accurately. Thus Hertz line contact theory could be improved by applying the derived formula, while the line contact problem in practice be calculated more conveniently.