On Asperity Distributions of Metallic Surfaces

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Abstract
A distribution of surface asperities is proposed for the case in which both mating surfaces are rough and asperities are in the form of right circular cones. The assumption of this particular asperity form is suggested by roughness measurements of ground steel, brass, and aluminum which yielded similar results for stylus traversing parallel, 45°, and perpendicular to lay. Considering the mating cones perfectly plastic and distributed in the proposed manner, bulk deformation‐load is related to compliance. The essential finding is that the load‐compliance characteristics for mating surfaces having comparable roughness have slopes much steeper than those predictable by previous theories, all of which involve the assumption that one of the surfaces is smooth and rigid. A simple experiment is described in which load and compliance are measured. Results seem to support the plausibility of the proposed theory. Moreover, this plausibility shows promise of the calculation of other bulk‐quantities such as frictional resistance.

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