Flat Central Pressure in Elliptic Elastic Contacts Between High Order Surfaces

High order surfaces are often used in electrical contacts and micro-contacts aiming to generate a nearly uniform current density over most of contact area. In the case of homogeneous surface micro-topography, this aim is achieved if geometrical shape of the contact yields a nearly uniform central pressure bounded by a monotonous decrease to zero in contour points. This problem was recently solved by these authors for circular contacts and now it is natural to extend this procedure for the case of elliptical contacts. Recent results are used to this end, derived for elliptical elastic contacts between high order surfaces. As homogeneous high order surfaces lead to a highly non-uniform pressure distribution, central pressure is flattened by making the first derivatives of pressure vanish in contact centre. Then, the contacts between fourth, sixth and eight order surfaces are analyzed and general or recurrence relations for pressure distribution and contact parameters are proposed.