Abstract
A two-scale method for modelling the Elastohydrodynamic Lubrication (EHL) of tilted-pad bearings is derived and a range of solutions are presented. The method is developed from previous publications and is based on the Heterogeneous Multiscale Methods (HMM). It facilitates, by means of homogenization, incorporating the effects of surface topography in the analysis of tilted-pad bearings. New to this article is the investigation of three-dimensional bearings, including the effects of both ideal and real surface topographies, micro-cavitation, and the metamodeling procedure used in coupling the problem scales. Solutions for smooth bearing surfaces, and under pure hydrodynamic operating conditions, obtained with the present two-scale EHL model, demonstrate equivalence to those obtained from well-established homogenization methods. Solutions obtained for elastohydrodynamic operating conditions, show a dependency of the solution to the pad thickness and load capacity of the bearing. More precisely, the response for the real surface topography was found to be stiffer in comparison to the ideal. Micro-scale results demonstrate periodicity of the flow and surface topography and this is consistent with the requirements of the HMM. The means of selecting micro-scale simulations based on intermediate macro-scale solutions, in the metamodeling approach, was developed for larger dimensionality and subsequent calibration. An analysis of the present metamodeling approach indicates improved performance in comparison to previous studies.
Highlights
Tilted-pad bearings are found in lubricated rotating devices as they provide separation under heavy loads while keeping the power losses at a minimum [1]
Results are presented for the two-scale model to demonstrate the following: (i) verification of the two-scale method in comparison to well-established homogenization methods under hydrodynamic conditions; (ii) verification of the choice of macro-scale elastohydrodynamic lubrication (EHL) model comparing the pad and collar to the pad alone; (iii) macro-scale solutions with topography generated by the two-scale method; (iv) examples of micro-scale solutions corresponding to the macro-scale results; and (v) examples of the metamodel performance and verification for coupling the problem scales
The two-scale method for tilted-pad bearings derived in this paper facilitates the homogenized effects of surface topography at the micro-scale to be modeled at the macro-scale
Summary
Tilted-pad bearings are found in lubricated rotating devices as they provide separation under heavy loads while keeping the power losses at a minimum [1]. Titled-pad bearings typically have a facing comprised of a compliant material, e.g., Babbitt and polytetrafluoroethylene (PTFE). This means that they operate under elastohydrodynamic lubrication (EHL) conditions where the pressure that is generated in the lubricant deforms the facing and sometimes the backing, and significant fluid-structure interaction (FSI) occurs. The modelling approach including elastohydrodynamically generated FSI, is well-established in the literature under the assumption of perfectly smooth surfaces [2,3,4] For this purpose, it is conventional to use the Reynolds equation to model the hydrodynamic pressure generation, and to use infinitesimal strain theory to describe the deformation caused by the lubricant pressure.
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