A Novel Approach for Modeling Surface Effects in Hydrodynamic Lubrication

Abstract

Abstract:The common approach for the flow factor calculation is based on using the Reynolds equation to simulate the micro-level flow. However, for structured surfaces the fluid flow cannot be represented correctly, due to the assumptions made when deriving the Reynolds equation. In this work, a novel method using the Navier-Stokes equations for the calculation of the micro-level flow is presented and validated against results from Patir and Cheng. The three-dimensional lubrication gap was generated by a rough Gaussian random surface and a perfectly smooth moving counter surface, in order to be available for different numerical methods. The presented results illustrate similar trends for both the approaches. Additionally, the use of the Navier-Stokes equations allows for the observance of surface induced effects which cannot be resolved by the approach of Patir and Cheng. Furthermore, a numerical approach for a shear flow factor calculation with a rough moving surface is presented and validated against other simulation methods. While the validation is maintained with pressure-and temperature-independent density and viscosity, these effects will be taken into account for later research activities of textured surfaces.

Multi-Scale Surface Texturing in Tribology—Current Knowledge and Future Perspectives

“…Furthermore, the consideration of rough contact mechanics and micro-cavitation effects also significantly affect the accuracy of the flow factor coefficients. In many successful cases, deterministic simulations of representative bearing unit cells at different length scales have been carried out to estimate the flow factors, as reported in several publications involving surface textures [155,156], honing grooves [157,158] and general roughness patterns [159][160][161][162].…”

SPH Modelling of Hydrodynamic Lubrication along Rough Surfaces

“…In [2], it has also been demonstrated that it is possible to derive the set of reduced equations for the classical lubrication approximation governing incompressible and iso-viscous flows from the full Navier-Stokes equations specialized for flows in thin gaps and applying dimensional analysis considerations. is no longer valid to describe the flow through the rough gap" [18]. The authors highlighted the advantage of Navier-Stokes equations in providing greater detail of the fluid dynamics fields with respect to Reynolds models for fluid films, thus enabling to assess the effects of structured and textured surfaces under hydrodynamic lubrication.…”

“…This study highlights the importance of the texture geometry features in the formation of the fluid films and the reduction of the transient time to reach the lubrication regime, which minimizes the damage (stress concentrations over surface roughness peaks can lead to wear debris which deteriorate the bearing performance).Pusterhofer et al[18] presented a CFD-FVM model for modelling surface effects under hydrodynamic lubrication. On the use of Reynolds models for fluid films, they stated: "for structured surfaces the fluid flow cannot be represented correctly, due to the assumptions made when deriving the Reynolds equation" [18]. Their model was based on Navier-Stokes equations, was applied to a 3D rough lubrication gap at the micro-scale, and was coupled with a Reynolds-based model working at a coarser scale.…”

“…. hydrodynamic effects because of the microscopic surface structure are not taken into account" [18]. Furthermore, the authors reported that "when the surface profile shows strong height changes, which can cause velocity changes in height direction .…”

“…[18] presented a CFD-FVM model for modelling surface effects under hydrodynamic lubrication. On the use of Reynolds models for fluid films, they stated: "for structured surfaces the fluid flow cannot be represented correctly, due to the assumptions made when deriving the Reynolds equation" [18]. Their model was based on Navier-Stokes equations, was applied to a 3D rough lubrication gap at the micro-scale, and was coupled with a Reynolds-based model working at a coarser scale.…”