Cylinder-Flat Contact Mechanics with Surface Roughness
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ORIGINAL PAPER
Cylinder‑Flat Contact Mechanics with Surface Roughness A. Tiwari1,2 · B. N. J. Persson1,2 Received: 10 September 2020 / Accepted: 20 November 2020 © The Author(s) 2020
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 𝛼 < 0.01 and Gaussian-like for 𝛼 > 10 , where the dimensionless parameter 𝛼 = hrms ∕𝛿 is the ratio between the root-mean-square roughness amplitude and the penetration for the smooth surfaces case (Hertz contact). Keywords Contact pressure · Surface roughness · Plastic deformation
1 Introduction 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 many of these applications, the surface roughness has a big influence on the nominal contact pressure profile. 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]. 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. In a classical study, Greenwood an Tripp [2] (see also Ref. [3]) studied the influence of surface roughness on the elastic contact of rough spheres. They used the Greenwood–Williamson [4] (GW) contact mechanics theory where the elastic coupling between the asperity contact regions is neglected. However, later studies have shown that this coupling is very important even for small nominal contact * B. N. J. Persson b.persson@fz‑juelich.de http://www.MultiscaleConsulting.com 1
PGI-1, FZ Jülich, Jülich, Germany
Multiscale Consulting, Wolfshovener str. 2, 52428 Jülich, Germany
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pressures, where the distance between the macroasperity contact regions may be large [5]. The reason is that there are smaller asperities (microasperities) on top of the big asperities, and since the contact pressure in the macroasperity contact region in general is very high, the microasperity contact regions are closely spaced and the elastic coupling between them cannot be neglected. In the present study, we will use the Persson contact mechanics theory which includes the elastic coupling between all asperity contact regions in an approximate but accurate way [6, 7]. We note that the GW model is approximately valid if roughness occurs on just one length scale [8]. Now, when the applied squeezing force is small, the average surface separation, which determines the influence of the surface roughness on the nominal contact pressure, depends mainly on the most long wavelength roughness component. Thus, for
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