# Lubrication, contact mechanics and leakage between rough surfaces

Sammanfattning: Mechanical components with interacting surfaces are central in everyday life. Interactions between surfaces, such as the sliding, rolling and bouncing, on one another may be found everywhere. These surfaces are often required to withstand severe conditions resulting in wear, which may ultimately lead to failure. To reduce the risk of failure, a lubricant is often added between the surfaces that partly or completely separates the surfaces from direct mechanical contact. The physical conditions existing between two interacting surfaces are complex, with parameters such as colliding surface asperities, mechanical deformations, lubricant flow transport and chemical reactions. A combination of all these parameters will affect the output parameters of interest for the consumer, e.g., friction, wear rate and leakage a.k.a. energy efficiency, service life and environmental impact in other terminologies. To design components with improved performance, more knowledge of the tribological (interacting surfaces) interface is needed both from experimental and theoretical viewpoint. In this work, various aspects of the lubrication between surfaces were theoretically simulated, to gain a greater understanding of tribological interfaces and to develop tribological design tools. When the interacting surfaces are separated by a thick fluid film, the influence from surface asperities is small and the surfaces can be treated as if they were smooth. For this type of lubrication condition, Computational Fluid Dynamics (CFD) is used to investigate the influence from a surface pattern applied onto one of the two interacting surfaces. It is shown that parallel surfaces generate a pressure increase originating from fluid inertia between the surfaces as a result of introducing the micro-pattern. In some lubricant films low pressures may occur at region of an expanding gap between the interacting surfaces. A liquid lubricant can only resist small tensile stresses until it cavitates into a mixture of gas and liquid. Hence, a cavitation model is presented that accommodates for an arbitrary lubricant compressibility. It was found that the geometry and lubricant starvation at the inlet of the tribological interface, as well as the compressibility model, are significant factors for load carrying capacity of the lubricant when cavitation is considered. For thin lubricant films, surface roughness becomes important in the performance of the tribological interface. Direct numerical simulations of the interface with measured surface roughness requires too many degrees of freedoms to be accounted for in computations. Therefore, a homogenization method is used, where the gap between the surfaces in the tribological interface may be modeled by two scales; a global geometry scale and a local surface roughness scale, where the method enables the two scales to be treated separately. A method to generate dimensionless flow factors to compensate 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. It is shown that the cumulative distribution of heights of the surface roughness (bearing ratio) completely determines the lubricating conditions for two-dimensional roughness and that the effects of the roughness increase as the film thickness decreases. By further decreasing the film thickness, into the mixed lubrication regime, the surface asperities will start to collide and take over some of the load carried by the fluid. The surface roughness has a crucial influence on the performance in this regime. A model to simulate the linear elastic perfectly plastic deformation of rough surfaces is developed. The model is based on FFT to improve the computational efficiency. Thus, the model is suitable to accept periodic input, which is a demand for the homogenization method previously mentioned. To consider both the asperity collisions and the hydrodynamic effects, a mixed lubrication model is developed capable of using three-dimensional measured surface roughness as input. The model is based on computing flow factors that carry the effects of a specific surface roughness in all regimes from completely separated surfaces to dry contact and full asperity deformation. An efficient simulation procedure is described, from importing the roughness measurement data to the simulation of a complete application. Linear elastic perfectly plastic displacement is considered and a homogenization method for fluid transport is used. The mixed lubrication model is validated through experiments with good correlation. It is shown that real deterministic surface roughness measurements may be efficiently imported and used in the model. Also, any global geometry may be simulated in any regime once the rough surface flow factors have been calculated. An important property of a tribological interface, especially in seals, is the flow or leakage through the contact. In many applications, leakage is crucial in terms of environmental impact. By using the mixed lubrication model previously developed, leakage through a range of measured elastomer and seal surfaces is investigated (see cover figure). It is found that the mixed lubrication model permits an efficient analysis of the leakage, even though real measured surface roughness was used as input. Moreover, the valley roughness parameters are shown to be important in characterizing the leakage and the peak roughness parameters are important for the percolation threshold.

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