In this paper a multiscale method is presented that includes surface texture in a mixed lubrication journal bearing model. Recent publications have shown that the pressure generating effect of surface texture in bearings that operate in full film conditions may be the result of micro-cavitation and/or convective inertia. To include inertia effects, the Navier-Stokes equations have to be used instead of the Reynolds equation. It has been shown in earlier work  that the coupled 2D Reynolds and 3D structure deformation problem with partial contact resulting from the soft EHL journal bearing model is not easy to solve due to the strong nonlinear coupling, especially for soft surfaces. Therefore, replacing the 2D Reynolds equation by the 3D Navier-Stokes equations in this coupled problem will need an enormous amount of computing power that is not readily available nowadays. In this paper, the development of a micro-macro multiscale method is prescribed. The local (micro) flow effects for a single surface pocket are analysed using the Navier-Stokes equations and compared to the Reynolds solution for a similar smooth piece of surface. It is shown how flow factors can be derived and added to the macroscopic smooth flow problem, that is modelled by the 2D Reynolds equation. The flow factors are a function of the operating conditions such as the ratio between the film height and the pocket dimensions, the surface velocity and the pressure gradient over a surface texture unit cell. To account for an additional pressure build up in the texture cell due to inertia effects, a pressure gain is introduced at macroscopic level. The method also allows for micro-cavitation. Micro-cavitation occurs when the pressure variation due to surface texture is larger than the average pressure level at that particular bearing location. In contrast with the work of Patir and Cheng , where the micro-level is solved by the Reynolds equation, the Navier-Stokes equations are used at the micro-level. Depending on the texture geometry and film height, the Reynolds equation may become invalid. A second pocket-effect occurs when the pocket is located in the moving surface. In mixed lubrication, fluid can become trapped inside a pocket and squeezed out when the pocket is running into an area with higher contact load. To include this effect, an additional source term that represents the average fluid inflow due to the deformation of the surface around the pocket is added to the Reynolds equation at macro-level. The additional inflow is computed at micro-level by numerical solution of the surface deformation for a single pocket that is subject to a contact load. The pocket volume is a function of the contact pressure. It must be emphasized that before ready-to-use results can be presented, a large number of simulations to determine the flow factors and pressure gain as a function of the texture parameters and operating conditions have yet to be done. Before conclusions can be drawn, regarding the dominanant mechanism(s), the flow factors and pressure gain have to be added to the macro bearing model. In this paper, only a limited number of preliminary illustrative simulation results, calculating the flow factors for a single 2D texture geometry, are shown to give insight into the method.
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A Multiscale Method Modeling Surface Texture Effects
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de Kraker, A, van Ostayen, RAJ, Rixen, DJ, & van Beek, A. "A Multiscale Method Modeling Surface Texture Effects." Proceedings of the STLE/ASME 2006 International Joint Tribology Conference. Part A: Tribomaterials; Lubricants and Additives; Elastohydrodynamic Lubrication; Hydrodynamic Lubrication and Fluid Film Bearings; Rolling Element Bearings; Engine Tribology; Machine Components Tribology; Contact Mechanics. San Antonio, Texas, USA. October 23–25, 2006. pp. 485-497. ASME. https://doi.org/10.1115/IJTC2006-12256
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