Hertzian Contact

Abstract

If the contacting bodies are smooth, the gap function of Eq. (1.1 ) can be expanded as a power series in x and y, for points sufficiently near the origin. Furthermore, since the coordinate system in Fig. 1.2 satisfies the conditions g0(0,0)=0;∂g0∂x(0,0)=0;∂g0∂y(0,0)=0, the first non-zero terms in this series are the quadratic terms g0(x, y) = Ax2+ By2+ Cxy. The problem of Eq. (1.3 ) is influenced by the gap function only in the contact region A which is generally small in non-conformal contact, so the higher order terms in g0 can often be neglected even when the surfaces are not strictly quadratic. The elastic contact problem for a gap function defined by Eq. (3.2) was first solved by Hertz (1882) (Journal für die reine und angewandte Mathematik, 92: 156–171, 1882) and the resulting stress and displacement fields are generally referred to as Hertzian contact.