Pressure Distribution between Closely Contacting Surfaces

The pressure distribution, contact arc extent, and deflection are determined for the elastic contact of a long roller and a cylindrical hole in an infinite body. It is shown that these variables depend on the degree of conformity of the two bodies and that Hertz's theory should not be used when the arc dimensions are of the same order as the radii of curvature, as its assumptions are violated. When the hole circumference available is reduced, pressure discontinuities can occur where the arc terminates. The results of the analysis have application in the design of some engineering components, such as complete and partial arc bearings and Novikov gears, where a knowledge of the magnitude and distribution of the contact stress is important.