Predictions of Dynamic Behaviors for Gas Foil Bearings Operating at Steady-State Based on Multi-Physics Coupling Computer Aided Engineering Simulations

Authors: Tai Yuan Yu, Pei-Jen Wang

Abstract:

A simulation scheme of rotational motions for predictions of bump-type gas foil bearings operating at steady-state is proposed. The scheme is based on multi-physics coupling computer aided engineering packages modularized with computational fluid dynamic model and structure elasticity model to numerically solve the dynamic equation of motions of a hydrodynamic loaded shaft supported by an elastic bump foil. The bump foil is assumed to be modelled as infinite number of Hookean springs mounted on stiff wall. Hence, the top foil stiffness is constant on the periphery of the bearing housing. The hydrodynamic pressure generated by the air film lubrication transfers to the top foil and induces elastic deformation needed to be solved by a finite element method program, whereas the pressure profile applied on the top foil must be solved by a finite element method program based on Reynolds Equation in lubrication theory. As a result, the equation of motions for the bearing shaft are iteratively solved via coupling of the two finite element method programs simultaneously. In conclusion, the two-dimensional center trajectory of the shaft plus the deformation map on top foil at constant rotational speed are calculated for comparisons with the experimental results.

Keywords: Computational fluid dynamics, fluid structure interaction multi-physics simulations, gas foil bearing, load capacity.

References:

[1] Walowit, J. A., and Anno, J. N., “Modern Developments in Lubrication Mechanics, Applied Science”, London, (1975), Chap. 7.
[2] Heshmat, H., Walowit, J. A., and Pinkus, O., “Analysis of Gas-Lubricated Foil Journal Bearings,” ASME J. Lubr. Technol., 105, (1983), pp. 647–655.
[3] Ku, C. P., and Heshmat, H., “Compliant Foil Bearing Structure Stiffness Analysis: Part I—Theoretical Model Including Strip and Variable Bump Foil Geometry,” ASME J. Tribol., 114, (1992), pp. 394–400.
[4] Agrawal, G. L., “Foil Air/Gas Bearing Technology—An Overview,” ASME Paper No. 97-GT-347. (1997).
[5] Iordanoff, I., “Analysis of an Aerodynamic Compliant Foil Thrust Bearing: Method for a Rapid Design,” ASME J. Tribol., 121, (1999), pp. 816–822.
[6] DellaCorte, C., and Valco, M. J., “Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications,” NASA/TM, Report No. 2000-209782., (2000).
[7] Carpino, M., and Talmage, G., “A Fully Coupled Finite Element Formulation for Elastically Supported Foil Journal Bearings,” Tribol. Trans., 46, (2003), pp. 560–565.
[8] Peng, Z.-C., and Khonsari, M. M., “Hydrodynamic Analysis of Compliant Foil Bearings with Compressible Air Flow,” ASME J. Tribol., 126, (2004), pp. 542–546.
[9] Peng, Z. C., and Khonsari, M. M., “A Thermohydrodynamic of Foil Journal Bearings,” ASME J. Tribol., 128, (2006), pp. 534–541.
[10] Swanson, E. E., “Bump Foil Damping Using a Simplified Model,” ASME J. Tribol., 128, (2006), pp. 542–550.
[11] San Andres, L., and Kim, T. H., “Improvements to The Analysis of Gas Foil Bearings: Integration of Top Foil 1D and 2D Structural Models,” ASME Paper No. GT 2007-27249. (2007).
[12] Le Lez, S., Arghir, M., and Frene, J., “A New Bump-Type Foil Bearing Structure Analytical Model,” ASME J. Eng. Gas Turbines Power, 129_4_, (2007), pp. 1047–1057.
[13] Le Lez, S., Arghir, M., and Frene, J., “Static and Dynamic Characterization of a Bump-Type Foil Bearing Structure,” ASME J. Tribol., 129, (2007), pp. 75–83.
[14] Feng, K., and Kaneko, S., “A Numerical Calculation Model of Multi Wound Foil Bearing with the Effect of Foil Local Deformation,” Journal of System Design and Dynamics, JSME, 1, (2007), pp. 648–659.
[15] Lee, Y., Park, D., Kim, C. H., and Kim, S. J., “Operating Characteristics of the Bump Foil Journal Bearings with Top Foil Bending Phenomenon and Correlation Among Bump Foils,” Tribol. Int., 41, (2008), pp. 221–233.