Why homogenization should be the averaging method of choice in hydrodynamic lubrication

Abstract

For the computation of the hydrodynamic pressure distribution in fluid film lubrication problems, averaging techniques are frequently used for applications with rough or textured surfaces to reduce the computational cost. The present work shows the excellent suitability of homogenization for this purpose. For comparison, the most frequently applied averaging method is used: the average flow model by Patir and Cheng. The two models are briefly summarized to show the similarity of the formulations, resulting in the same implementation effort. By means of two textured applications, the superiority of the homogenization method is demonstrated and errors inherent in the average flow model are quantified. Homogenization provides averaged pressure distributions with a significantly higher accuracy and allows for efficiently restoring local information to resolve pressure peaks by computing a higher-order solution. The latter is an accurate approximation of the solution of the original Reynolds equation and can be obtained with negligible additional computational cost. Further important advantages of the homogenization method such as its extensibility to simultaneously account for roughness and textures are pointed out.