Formulas for Moderately Elliptical Hertzian Contacts

Abstract

For small ellipticities the Hertzian contact pressure and approach can be obtained to a good approximation by using the formulae for circular contact with an equivalent radius of curvature (AB) −1/2, where A and B are the principal relative curvatures. For higher ellipticities (AB(A + B)/2)−1/3 should be used to find the contact area and pressure; an equivalent radius for finding the approach is also given. The ellipticity of the contact can be estimated from the asymptotic equation (a/b) ≈ (B/A)2/3.