A surface roughness parameter in Hertz contact

Abstract The influence of surface roughness on the accuracy with which the Hertz theory of elastic contact predicts the contact pressure and contact area between a sphere and a plane is examined theoretically and experimentally. Statistical theories of surface contact suggest that the influence of surface roughness is governed primarily by a single non-dimensional parameter α defined by α  σR a 0 2 where σ is the combined roughness of the two surfaces, R is the radius of the sphere and a 0 is the contact radius for smooth surfaces given by the Hertz theory. Experimental measurements of contact area correlate well with this parameter. Provided that the value of α is less than about 0.05, errors in the application of the Hertz theory due to roughness of the surfaces are not likely to exceed about 7%.