Comparison of models for the contact of rough surfaces

Numerical comparisons of the Greenwood-Williamson (GW) elastic microcontact model with two more general isotropic and anisotropic models suggest that the GW model gives good order-of-magnitude estimates of the number of contacts, real contact area fraction and nominal pressure that result at a given separation of a rough and a smooth flat plane. In effecting the comparisons, the three parameters of the GW model are related to the three spectral moments m0, m2 and m4 of an isotropic or equivalently isotropic surface. It is shown that the real contact area at a given mean plane separation depends only on the bandwidth parameter α = m0m4m22, while the elastically supported load depends on both α and m2. On the basis of the comparisons it is suggested that the GW model be adopted by metrologists to relate measured microgeometry to physically more understandable quantities such as contact density, load, real area and plastic contact density. Accordingly, this paper includes an expository presentation of the GW model complete with tables and a detailed numerical example of their use.