Abstract
In recent years, machine component design has been a major concern for researchers. Emphasis has been placed especially on the analysis of bearing systems in order to avoid detrimental contact. The shaft misalignment is one of the most problems that affects directly the operating conditions of these components. In this context, the present study proposes a reduced-order method "Proper Generalized Decomposition" (PGD) using the separation technique through the alternating direction strategy to solve the modified Reynolds equation, taking into account the presence of misalignment in the shafting system. The solution shows the representation of two types of misalignment geometry, especially axial and twisting. A comparison of the results between the proposed approach and the classical method, through several benchmark examples, made it possible to highlight that the new scheme is more efficient, converges quickly and provides accurate solutions, with a very low CPU time expenditure.
Highlights
Hydrodynamic bearings are important components of rotating machines, which are considered to be the best technological solution currently available in various industrial fields like thermal engines, turbomachines, alternators, compressors, etc
The Reynolds equation is an second-order partial differential equation, which is derived from the Navier–Stokes and continuity equations for incompressible flows [4], whose solution provides the pressure distribution in lubricating fluid
In this work the Proper Generalized Decomposition" (PGD) is used for the analysis of misaligned journal bearings with consideration of Swift-Steiber boundary conditions, in order to reduce the computational costs, Section2 describes the governing equations for misaligned hydrodynamic journal bearing, section3 details the application of the PGD on the Reynolds equation, section 4 presents a comparison between the results obtained by the PGD and other methods, section5 concludes the work
Summary
Hydrodynamic bearings are important components of rotating machines, which are considered to be the best technological solution currently available in various industrial fields like thermal engines, turbomachines , alternators, compressors, etc,. Group of method called reduced-order models(ROM) was proposed to resolve problems of fluid mechanics , the most popular of this method is an aposteriori methods named the proper orthogonal decomposition (POD) which was used in [12,13,14,15,16], this category of method often require some snapshots of the flow, which mat takes significant computation time. To circumvent this problem, apriori methods have been developed, which consist in building a reduced base without the "apriori" knowledge of the solution. In this work the PGD is used for the analysis of misaligned journal bearings with consideration of Swift-Steiber boundary conditions, in order to reduce the computational costs, Section describes the governing equations for misaligned hydrodynamic journal bearing, section details the application of the PGD on the Reynolds equation, section 4 presents a comparison between the results obtained by the PGD and other methods, section concludes the work
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