Cylinder-flat contact mechanics with surface roughness

We study the nominal (ensemble averaged) contact pressure $p(x)$ acting on a cylinder squeezed in contact with an elastic half-space with random surface roughness. The contact pressure is Hertzian-like for $α< 0.01$ and Gaussian-like for $α> 10$, where the dimensionless parameter $α= h_{\rm rms}/δ$ is the ratio between the root-mean-square roughness amplitude and the penetration for the smooth surfaces case (Hertz contact).

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