Parallel iterative solution schemes for the analysis of air foil bearings

N. Wang*, S. H. Chang

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

9 Scopus citations


In an air foil bearing analysis the model is usually solved iteratively due in part to the nonlinearity of the modeling Reynolds equation and the compliance of the bearing surface. The solution procedure requires a multiple-level-deep nested iteration, which involves extended solution time and convergence difficulty. In this study, a simple air foil bearing model is used and the compressible-fluid Reynolds equation for modeling gas lubrication is linearized by Newton's method. The discretized equation is solved by one of the two parallel iterative methods, red-black or strip partition successive-over-relaxation (SOR) method. The parallel programming is conducted using OpenMP programming in an eight-core work-station. Then, a numerical damping scheme for the film-profile convergence is presented. Finally, a root-finding process is conducted to iteratively attain the eccentricity of the bearing for a given load. It is found that the numerical damping step is crucial, which allows the use of a larger relaxation factor to have a fast rate of convergence. Both the parallel SOR methods are easy to implement and the red-black SOR method exhibits better efficiency in the studied cases. This study presents a parallel computing scheme for analyzing air foil bearing of bump-type by today's shared-memory multicore platforms.

Original languageEnglish
Pages (from-to)413-422
Number of pages10
JournalJournal of Mechanics
Issue number3
StatePublished - 09 2012


  • Air foil bearing
  • Parallel computing
  • Relaxation method
  • Reynolds equation


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