Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-13T06:09:06.052Z Has data issue: false hasContentIssue false
  • English
  • Français

Parallel Iterative Solution Schemes for the Analysis of Air Foil Bearings

Published online by Cambridge University Press:  09 August 2012

N. Wang  and
S.-H. Chang
N. Wang*
Affiliation:
Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan 33302, R.O.C.
S.-H. Chang
Affiliation:
Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan 33302, R.O.C.
*
*Corresponding author (nenzi@mail.cgu.edu.tw)
Get access

Abstract

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.

Keywords

Air foil bearingReynolds equationRelaxation methodParallel computing
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 3 , September 2012 , pp. 413 - 422
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. DellaCorte, C., Radil, K. C., Bruckner, R. J. and Howard, S. A., “Design, Fabrication, and Performance of Open Source Generation I and II Compliant Hydrodynamic Gas Foil Bearings,” Tribology Transactions, 51, pp. 254–264 (2008).Google Scholar
2. Jahanmir, S., Heshmat, H. and Heshmat, C., “Assessment of Tribological Coatings for Foil Bearing Applications,” Tribology Transactions, 52, pp. 231–242 (2009).CrossRefGoogle Scholar
3. Jahanmir, S., Heshmat, H. and Heshmat, C., “Evaluation of DLC Coatings for High-Temperature Foil Bearing Applications,” Journal of Tribology – Transactions of the ASME, 131, pp. 011301.1–011301.11 (2009).CrossRefGoogle Scholar
4. Feng, K. and Kaneko, S., “Thermohydrodynamic Study of Multiwound Foil Bearing Using Lobatto Point Quadrature,” Journal of Tribology – Transactions of the ASME, 131, pp. 0212702.1–0212702.9 (2009).Google Scholar
5. Lee, D. and Kim, D., “Thermohydrodynamic Analyses of Bump Air Foil Bearings With Detailed Thermal Model of Foil Structures and Rotor,” Journal of Tribology – Transactions of the ASME, 132, pp. 0212704.1–0212704.12 (2010).CrossRefGoogle Scholar
6. Lee, D. and Kim, D., “Three-Dimensional Thermohydrodynamic Analyses of Rayleigh Step Air Foil Thrust Bearing with Radially Arranged Bump Foils,” Tribology Transactions, 54, pp. 432–448 (2011).CrossRefGoogle Scholar
7. Song, J. H. and Kim, D., “Foil Gas Bearing with Compression Springs: Analyses and Experiments,” Journal of Tribology – Transactions of the ASME, 129, pp. 628–639 (2007).Google Scholar
8. Kim, T. H. and San Andres, L., “Thermohydrodynamic Model Predictions and Performance Measurements of Bump-Type Foil Bearing for Oil-Free Turboshaft Engines in Rotorcraft Propulsion Systems,” Journal of Tribology – Transactions of the ASME, 132, pp. 011701.1–011701.11 (2010).CrossRefGoogle Scholar
9. Lee, D., Kim, D. and Sadashiva, R. P., “Transient Thermal Behavior of Preloaded Three-Pad Foil Bearings: Modeling and Experiments,” Journal of Tribology – Transactions of the ASME, 133, pp. 021703.1–021703.11 (2011).CrossRefGoogle Scholar
10. Howard, S. A., DellaCorte, C., Valco, M. J., Prahl, J. M. and Heshmat, H., “Dynamic Stiffness and Damping Characteristics of a High Temperature Air Foil Journal Bearing,” Tribology Transactions, 44, pp. 657–667 (2001).Google Scholar
11. Radil, K., DellaCorte, C. and Zeszotek, M., “Thermal Management Techniques for Oil-Free Turbomachinery Systems,” Tribology Transactions, 50, pp. 319–327 (2007).Google Scholar
12. Heshmat, H., Walowit, J. A. and Pinkus, O., “Analysis of Gas-Lubricated Foil Journal Bearings,” Journal of Lubrication and Technology, 105, pp. 647–655 (1983).Google Scholar
13. San Andres, L. and Kim, T. H., “Analysis of Gas Foil Bearings Integrating FE Top Foil Models,” Tribology International, 42, pp. 111–120 (2009).Google Scholar
14. Salehi, M. and Heshmat, H., “On the Fluid Flow and Thermal Analysis of a Compliant Surface Foil Bearing and Seal,” Tribology Transactions, 43, pp. 318–324 (2000).CrossRefGoogle Scholar
15. Lee, N. S., Choi, D. H., Lee, Y. B., Kim, T. H. and Kim, C. H., “The Influence of the Slip Flow on Steady-State Load Capacity, Stiffness and Damping Coefficients of Elastically Supported Gas Foil Bearings,” Tribology Transactions, 45, pp. 478–484 (2002).Google Scholar
16. Peng, Z.-C. and Khonsari, M. M., “Hydrodynamic Analysis of Compliant Foil Bearings with Compressible Air Flow,” Journal of Tribology – Transactions of the ASME, 126, pp. 542–546 (2004).CrossRefGoogle Scholar
17. Peng, Z.-C. and Khonsari, M. M., “A Thermohydrodynamic Analysis of Foil Journal Bearings,” Journal of Tribology – Transactions of the ASME, 128, pp. 534–541 (2006).CrossRefGoogle Scholar
18. Park, D.-J., Kim, C.-H., Jang, G.-H. and Lee, Y.-B., “Theoretical Considerations of Static and Dynamic Characteristics of Air Foil Thrust Bearing with Tilt and Slip Flow,” Tribology International, 41, pp. 282–295 (2008).CrossRefGoogle Scholar
19. Iordanoff, I., Bou-Said, B., Mezianne, A. and Berthier, Y., “Effect of Internal Friction in the Dynamic Behavior of Aerodynamic Foil Bearings,” Tribology International, 41, pp. 387–395 (2008).CrossRefGoogle Scholar
20. Wang, N. and Chang, C., “An Application of Newton's Method to the Lubrication Analysis of Air-Lubricated Bearing,” Tribology Transactions, 42, pp. 419–424 (1999).CrossRefGoogle Scholar
21. Strikwerda, J. C., Finite Difference Schemes and Partial Differential Equations, Pacific Grove: Wadsworth and Brooks (1989).Google Scholar
22. Morton, K. W. and Mayers, D. F., Numerical Solution of Partial Differential Equations, Cambridge: Cambridge University Press (2005).Google Scholar
23. Wang, N., Chang, S.-H. and Huang, H.-C., “Comparison of Iterative Methods for the Solution of Compressible-Fluid Reynolds Equation,” Journal of Tribology – Transactions of the ASME, 133, pp. 021702.1–021702.7 (2011).CrossRefGoogle Scholar
24. Wang, N. and Tsai, C.-M., “Application of Thread-Level Parallel Programming to Thermohydrodynamic Lubrication Computation,” Tribology Transactions, 49, pp. 473–481 (2006).CrossRefGoogle Scholar
25. Wang, N., Tsai, C.-M. and Cha, K.-C., “A Study of Parallel Efficiency of Modified DIRECT Algorithm Applied to Thermohydrodynamic Lubrication,” Journal of Mechanics, 25, pp. 143–150 (2009).Google Scholar
26. Wang, N., Tsai, C.-M. and Cha, K.-C., “Optimum Design of Externally Pressurized Air Bearing Using Cluster OpenMP,” Tribology International, 42, pp. 1180–1186 (2009).Google Scholar
27. Chapman, B., Gost, G., van der Pas, R. and Kuck, D. J., Using OpenMP: Portable Shared Memory Parallel Programming, Cambridge: The MIT Press (2008).Google Scholar
28. Chandra, R., Dagun, L., Kohr, D., Maydan, D., McDonald, J. and Menon, R., Parallel Programming in OpenMP, San Francisco: Academic Press (2001).Google Scholar
29. Ruscitto, D., Mc Cormick, J. and Gray, S., “Hydrodynamic Air Lubricated Compliant Surface Bearing for an Automotive Gas Turbine Engine I - Journal Bearing Performance,” NASA CR-135368 (1978).Google Scholar
30. Leonard, B. P. and Drummond, J. E., “Why You Should Not Use Hybrid, Power-Law or Related Exponential Schemes for Convective Modeling—There Are Much Better Alternatives,” International Journal for Numerical Methods in Fluids, 20, pp. 421–442 (1995).Google Scholar