# Hydrodynamic lubrication of rough surfaces

Sammanfattning: Interacting surfaces are frequently found in mechanical systems and components. A lubricant is often added between the surfaces to separate them from mechanical contact in order to increase life and performance of the contacting surfaces. In this work various aspects of hydrodynamic lubrication are investigated theoretically. This is where interacting surfaces are completely separated by a fluid film which is often the desired operating condition of machine components when wear and friction is to be reduced. Different flow regimes can be identified within the scope of hydrodynamic lubrication. If the surfaces are separated by a thick fluid film the influence from surface asperities is small and the surfaces can be treated as smooth. If the rate of change in film thickness with respect to the spatial directions is significantly large and if the flow velocity or Reynolds number is large, the ordinary fluid mechanical approach treating viscous flow with Computational Fluid Dynamics (CFD) has to be used. CFD is used to investigate influence from the use of an artificial microscopic surface pattern on one of the two interacting surfaces. The influence from the pattern is isolated from any other pressure generating effects by keeping the interacting surfaces parallel. Results are shown for different shapes of the micro-pattern. If the Reynolds number decreases, the system enters a regime called Stokes flow where the inertia effects are neglected. The full CFD approach is compared with the Stokes for various physical and geometrical cases. If the change in film thickness is small in the spatial directions, the thin film approximation is applicable and the full momentum equations describing fluid flow together with the mass continuity equation can be reduced to the Reynolds equation. Depending on boundary conditions, low pressures can occur at location of expanding fluid gap leading to tensile stress applied to the lubricant. However, a real liquid lubricant can only resist small tensile stresses until it cavitates into a mixture of gas and liquid. This often happens close to atmospheric pressure due to contamination and dissolved air into the liquid and occurs at higher pressures than the actual vaporization. To avoid pressures reaching too low levels, a general cavitation algorithm applied to the Reynolds equation is presented that accommodates for an arbitrary density-pressure relation. It is now possible to model the compressibility of the lubricant in such a way that the density-pressure relation is realistic through out the contact. The algorithm preserves mass continuity which is of importance when inter-asperity cavitation of rough surfaces is considered. For small film thicknesses the surface roughness becomes important in the performance of the lubricated contact. Even the smoothest of real surfaces is rough at a microscopic level and will influence the contact condition. The Reynolds equation still applies since the heights of the surface asperities are small compared to the spatial elongation. Treatment of the roughness of a real surface in a deterministic fashion is however beyond the scope of today's computers. Therefore other approaches need to be employed in order to take the surface roughness into account. In this work a homogenization method is used where the governing equation of the flow condition is formulated with a two-scale expansion, the global geometry and the roughness. Solutions are achieved for the limit of the roughness wavelength approaching zero and the method renders a possibility to treat the two scales separately. A method to generate dimensionless flow factors compensating for the surface roughness is developed. The flow factors, once solved for a particular surface, can be used to compensate for the surface roughness in any smooth global problem for any film thickness.

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