A multiscale method for the Elastohydrodynamic Lubrication (EHL) of line contacts is derived based on the Heterogeneous Multiscale Methods. Periodicity applies to the topographical features and lubricant flow, data is homogenised over a range of variables at a micro-scale and coupled into a macro-scale model. This is achieved using flow factors as calculated from metamodels, which themselves evolve with the solution procedure. Results are given for an idealised topography and illustrate significant deviations from smooth surface assumptions as quantified by the flow factors. Improvements in the accuracy and efficiency with previous work and large fluctuations due to micro-EHL are also presented. Validation of the multiscale method with a deterministic topography is provided demonstrating good accuracy and efficiency.Keywords: EHL; micro-EHL; Surface Topography; Metamodelling.
INTRODUCTIONThe Elastohydrodynamic Lubrication (EHL) of line contacts generates high pressures which result in the bounding surfaces being separated by a thin lubricant film [1]. Surface topography can be of a similar scale to the film thickness and therefore has an effect on the performance of the tribological system [2]. For example Etsion et al. [3] showed that surface features can reduce the contacting friction of an EHL contact and Greenwood and Johnson [4] demonstrated that transverse waviness caused ripples in EHL pressure distributions. Reconciling the disparity in scales between surface topography and the contact region is a challenging computational problem for which many authors have sought solutions. Waviness in EHL has been modelled for example by Hooke [5] and Venner and Lubrecht [6] who investigated the amplitude reduction effect, but no such general method for describing the influence of surface topography in EHL as yet exists. The level of discretisation necessary to successfully solve fully deterministic problems, where both the contact region and surface topography are modelled simultaneously, has led to the development of homogenisation based models [7]. In such models information pertaining to the EHL of a topographical feature is characterised over a range of variables and subsequently coupled into a model for the EHL of the contact region. Periodicity in the lubricant flow and topographical features ensure that homogenisation of the solutions obtained at the smaller scale produces data which represents the behaviour of the larger scale [8,9]. Solutions to the EHL problem which are deterministic by nature also remain the subject of a significant amount of recent research [10][11][12][13][14][15][16][17].Patir and Cheng [18] first developed a two-scale model to include the effects of surface topography in hydrodynamic lubrication known as the flow factors method. In this approach the terms of the Reynolds equation, which describes the lubricant flow in the contact under smooth surface assumptions [19], were multiplied by flow factors which include the homogenised effects of surface topography. Sahlin, et al. [2...