Application of Multigrid for the Solution of Compressible Reynolds Equation of Gas Foil Bearings

The multigrid algorithm can reduce the iterative residuals quickly, but it is rarely used in research about gas foil bearings. This article adopts the Reynolds equation as the pressure governing equation of bump-type foil journal bearings to study the effect of different numerical methods on the exe...

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Published in:Tribology transactions Vol. 66; no. 3; pp. 431 - 442
Main Authors: Xu, Kefan, Zhang, Guanghui, Han, Jiazhen, Gong, Wenjie, Huang, Yanzhong, Guo, Yang
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 04.05.2023
Taylor & Francis Inc
Subjects:
Algorithms
Compressibility
Foil bearings
Gas foil journal bearing
Gas lubrication
iterative method
Iterative methods
Journal bearings
multigrid algorithm
Numerical methods
Parameters
Reynolds equation
ISSN:1040-2004, 1547-397X
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Abstract The multigrid algorithm can reduce the iterative residuals quickly, but it is rarely used in research about gas foil bearings. This article adopts the Reynolds equation as the pressure governing equation of bump-type foil journal bearings to study the effect of different numerical methods on the execution time of the algorithm program, including the direct method, the iterative method, and the multigrid algorithm. The results indicate that the algorithm performs best, based on the nonlinear discretization scheme and multigrid, and the execution time is generally reduced by 50% compared to the traditional direct method under the same operating parameters. For the case of a large eccentricity ratio, the execution time can even be reduced by up to 68%. The multigrid algorithm is greatly affected by the cycle type parameter and the level numbers of the grid. V-cycle and larger grid-level numbers are recommended on the premise of program convergence. In summary, the multigrid algorithm is an excellent numerical solution that can balance computational accuracy and efficiency when solving the gas lubrication problem of foil bearings.
AbstractList The multigrid algorithm can reduce the iterative residuals quickly, but it is rarely used in research about gas foil bearings. This article adopts the Reynolds equation as the pressure governing equation of bump-type foil journal bearings to study the effect of different numerical methods on the execution time of the algorithm program, including the direct method, the iterative method, and the multigrid algorithm. The results indicate that the algorithm performs best, based on the nonlinear discretization scheme and multigrid, and the execution time is generally reduced by 50% compared to the traditional direct method under the same operating parameters. For the case of a large eccentricity ratio, the execution time can even be reduced by up to 68%. The multigrid algorithm is greatly affected by the cycle type parameter and the level numbers of the grid. V-cycle and larger grid-level numbers are recommended on the premise of program convergence. In summary, the multigrid algorithm is an excellent numerical solution that can balance computational accuracy and efficiency when solving the gas lubrication problem of foil bearings.
Author Gong, Wenjie
Zhang, Guanghui
Huang, Yanzhong
Guo, Yang
Xu, Kefan
Han, Jiazhen
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  organization: School of Energy Science and Engineering, Harbin Institute of Technology
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Snippet The multigrid algorithm can reduce the iterative residuals quickly, but it is rarely used in research about gas foil bearings. This article adopts the Reynolds...
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SubjectTerms Algorithms
Compressibility
Foil bearings
Gas foil journal bearing
Gas lubrication
iterative method
Iterative methods
Journal bearings
multigrid algorithm
Numerical methods
Parameters
Reynolds equation
Title Application of Multigrid for the Solution of Compressible Reynolds Equation of Gas Foil Bearings
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