An adaption of the Archard equation for electrical contacts with thin coatings

•A mathematical description of the available wear volume of frequently used hemispherical and U-type geometries is given.•The ploughing of surfaces with consideration of a linear progressive hardness is discussed.•A two stage model based on the Archard equation with consideration of the contact geometry and a linear progressive hardness is derived.

For the wear resistance of sliding contacts geometry, contact force and coating system are strong factors of influence. In this paper a mathematical description of the available wear volume of frequently used hemispherical and U-type geometries is given. Smooth surface layers are worn abrasively and adhesively. In the first stage the flat geometry becomes ploughed, in the second stage adhesive wear dominates. The hardness of the surface depends on the substrate, underlayer and finish layer. A wear model based on a flat distribution of the Archard work density with consideration of the abrasive wear and the depth depending hardness for hemispherical and U-type geometries is derived. With theoretical and experimental methods an optimization of the Archard equation is discussed.