Application of topological optimisation methodology to infinitely wide slider bearings operating under compressible flow

Abstract

It has been over a century since the interest in inventing the optimal topology for bearings arose. A significant achievement was published by Lord Rayleigh, who found the step-bearing geometry which maximise the load-carrying capacity when the classical Reynolds equation is used to model thin film flow of an iso-viscous and incompressible fluid. Since then, new optimisation methods considering some variants of governing equations for finding the best possible bearings have surfaced, one of which will be presented in this paper. Here, two different formulations for compressible flow, i.e. ideal gas and constant bulk modulus compressibility, as well as the classical Reynolds formulation will be used in combination with the method of moving asymptotes for topological optimisation. All three of these problem formulations provide us with unique geometries, which either maximise the load-carrying capacity or minimise friction, for fluids with a wide variety of compressibility.

Application of topological optimisation methodology to finitely wide slider bearings operating under incompressible flow

“…The topology optimisation method globally convergent method of moving asymptotes (GCMMA) is available in COMSOL Multiphysics® 19 and was developed by Svanberg; 20,21 this method can be used in structural analysis and recently, Kalliorinne et al. 22 used it to optimise the bearing geometry of infinitely wide sliders for maximum LCC as well as minimum COF. Kalliorinne et al.…”

Application of topological optimisation methodology to hydrodynamic thrust bearings

“…In this section, the results of minimising the COT, obtained using the same mesh resolutions i.e. E ¼ 2 13 and E ¼ 2 17 , partitioned in the same way as the result in the previous section will be presented. Figure 5 depicts the bearing geometries that minimises the COT.…”

“…The algorithm is for example available in the finite element software COMSOL Multiphysics. 12 Recently, Kalliorinne et al, 13 managed to successfully implement a Reynolds' equation based model for bearing geometry optimisation in COMSOL Multiphysics, 12 and the algorithm was able to replicate results from Refs., 1,3 as well as optimising bearings under compressible flow with different optimisation objectives.…”

“…The bearing geometries that maximises LCC for two differently refined meshes, with contours levels. (a) E ¼ 213 and (b) E ¼ 2 17 .…”

“…The Couette-flow shear stresses corresponding to the bearing geometries that minimises COF for two differently refined meshes. (a) E = 213 and (b) E = 2 17 .…”