Abstract
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 alpha < 0.01 and Gaussian-like for alpha > 10, where the dimensionless parameter alpha = h_{rm rms}/delta is the ratio between the root-mean-square roughness amplitude and the penetration for the smooth surfaces case (Hertz contact).
Highlights
The pressure or stress acting in point contacts, e.g., when an elastic ball is squeezed against a nominal flat surface, or in line contacts, e.g., when an elastic cylinder is squeezed against a flat surface, has many important applications, such as the contact of a railway wheel and the rail or in O-ring seals
In a recent study for metallic seals, we found that the maximum of the nominal contact pressure was reduced by a factor of ≈ 3 when the surface roughness was taken into account in the analysis [1]
This has a huge influence on the fluid leakrate and led us to perform a more general study, which we report here, of the influence of the surface roughness on the pressure profile for line contacts
Summary
The pressure or stress acting in point contacts, e.g., when an elastic ball is squeezed against a nominal flat surface, or in line contacts, e.g., when an elastic cylinder is squeezed against a flat surface, has many important applications, such as the contact of a railway wheel and the rail (point contact) or in O-ring seals (line contact). In a recent study for metallic (steel) seals, we found that the maximum of the nominal contact pressure was reduced by a factor of ≈ 3 when the surface roughness was taken into account in the analysis [1]. For small applied force, the GW theory gives an approximately correct nominal pressure distribution if the asperities in the GW model are chosen as the long wavelength roughness part of the roughness spectrum. This approximation breaks down at high enough applied force and cannot describe the area of real contact for any applied force as it depends on the whole roughness spectrum. Numerical methods cannot be applied to real surfaces of macroscopic solids, which typically have roughness extending
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