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Journal of Tribology | Volume 138 | Issue 4 | research-article
Research Papers: Hydrodynamic Lubrication

Starved Hydrodynamic Gas Foil Bearings—Experiment, Micromechanical Phenomenon, and Hypotheses

[+] Author and Article Information
Hooshang Heshmat

Fellow ASME
Mohawk Innovative Technology, Inc.,
1037 Watervliet-Shaker Road,
Albany, NY 12205
e-mail: hheshmat@miti.cc

James F. Walton, II

Mem. ASME
Mohawk Innovative Technology, Inc.,
1037 Watervliet-Shaker Road,
Albany, NY 12205
e-mail: jwalton@miti.cc

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 1, 2015; final manuscript received March 3, 2016; published online July 20, 2016. Assoc. Editor: Daejong Kim.

J. Tribol 138(4), 041703 (Jul 20, 2016) (14 pages) Paper No: TRIB-15-1235; doi: 10.1115/1.4032911 History: Received July 01, 2015; Revised March 03, 2016
Article
References
Figures
Tables

In this paper, a hypothesis for the operating tribological mechanisms and phenomena occurring in compliant surface gas foil bearings subjected to low ambient pressure conditions, such as occur at high altitude or in soft vacuum, will be presented and discussed. Both theoretical and experimental evidence supporting the proposed hypothesis will be presented to show that, under low ambient pressure conditions (i.e., something akin to starved fluid film lubrication), the shaft is supported by a combination of hydrodynamic and morphological elements. The theoretical treatment of the compressible fluid film in a simple gas bearing is highly nonlinear in-and-of-itself, and especially more so when combined with a compliant surface supported on a frictional-elastic foil foundation. Adding a “molecularly starved gas film” to this highly nonlinear system, one encounters a very interesting and complex system that, heretofore, has not been considered. When operating compliant foil gas bearings in a near or soft vacuum, the term hydrodynamic may be considered oxymoronic in that there is little or no apparent fluid/gas to provide “a full hydrodynamic” action. However, theoretical and experimental evidence of compliant surface foil gas bearings operating at low ambient pressures show that they do continue to work and, in fact, can do so quite well given the appropriate compliancy and other factors, as yet to be discussed. In this paper, the situation will be addressed based upon the experimental evidence that resulted in the essential hypothesis that there are elements at work that go above and beyond purely hydrodynamic phenomenon or so-called solid lubrication. These elements include both tribological and morphological interactions, which are at work at all times and it is the respective ratios of hydrodynamic and morphological elements that characterize operation. Evidence is presented to the effect that, even when hydrodynamic effects dominate, morphological interactions contribute to bearing performance and load-carrying capacity and that, when morphological effects dominate, third body and surface elements impart to the interface many of the characteristics and effects of a hydrodynamic film. Thus, by combining classical Reynolds equation modified for compressible media with the quasi-hydrodynamic/continuum equations and the appropriate rheological and morphological parameters, meaningful solutions for foil bearing operating with extreme low-pressure boundary conditions are possible, and which result in increased load-carrying capacity contrary to classical hydrodynamic theory.
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References

1
Heshmat, H. , and Hermel, P. , 1992, “ Compliant Foil Bearing Technology and Their Application to High Speed Turbomachinery,” 19th Leeds-Lyon Symposium on Thin Film in Tribology—From Micro Meters to Nano Meters, Vol. 25, pp. 559–575.
2
Heshmat, H. , 1993, “ Advancements in the Performance of Aerodynamic Foil Journal Bearings: High Speed and Load Capability,” ASME J. Tribol., 116(2), pp. 287–294. [CrossRef]
3
Walton, J. F. , and Heshmat, H. , 1994, “ Compliant Foil Bearings for Use in Cryogenic Turbopumps,” Advanced Earth-to-Orbit Propulsion Technology, Vol. 1, pp. 372–381.
4
Heshmat, H. , and Ku, C.-P. R. , 1994, “ Structural Damping of Self-Acting Compliant Foil Journal Bearings,” ASME J. Tribol., 116(1), pp. 76–82. [CrossRef]
5
Ku, C.-P. R. , and Heshmat, H. , 1993, “ Structural Stiffness and Coulomb Damping in Compliant Foil Journal Bearings: Theoretical Consideration,” STLE Annu. Meet., 37(3), pp. 525–533.
6
Heshmat, H. , Walowit, J. , and Pinkus, O. , 1983, “ Analysis of Gas-Lubricated Foil Journal Bearings,” J. Lubri. Technol., 105(4), pp. 647–655. [CrossRef]
7
Heshmat, H. , 1991, “ Analysis of Compliant Foil Bearings With Spatially Variable Stiffness,” AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference, Paper No. AIAA-91-2102.
8
Heshmat, C. A. , and Heshmat, H. , 1994, “ An Analysis of Gas Lubricated, Multi-Leaf Foil Journal Bearings With Backing Springs,” ASME J. Tribol., 117(3), pp. 437–443.
9
Heshmat, H. , Ren, Z. , Hunsberger, A. Z. , Walton, J. F. II. , and Jahanmir, S. , 2010, “ The Emergence of Compliant Foil Bearing and Seal Technologies in Support of 21st Century Compressors and Turbine Engines,” ASME Paper No. IMECE2010-40598.
10
Jennings, S. , 1988, “ The Mean Free Path in Air,” J. Aerosol Sci., 19(2), pp. 159–166. [CrossRef]
11
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Van Bramer, S. E. , 1998, “Mean Free Path Versus Pressure and Altitude.”
13
Walton, J. F. II. , Heshmat, H. , and Tomaszewski, M. J. , 2012, “ Power Loss in High-Speed Micro Turbomachinery—An Experimental Study,” ASME Paper No. GT2012-69558.
14
Heshmat, H. , 2010, Tribology of Interface Layers, CRC Press, Taylor and Francis Group, LLC, Boca Raton, FL, pp. 187–190.
15
Heshmat, H. , 1992, “ The Quasi-Hydrodynamic Mechanism of Powder Lubrication—Part I: Lubricant Flow Visualization,” Lubri. Eng., 48, pp. 96–104.
16
Heshmat, H. , 1992, “ The Quasi-Hydrodynamic Mechanism of Powder Lubrication: Part II: Lubricant Film Pressure Profile,” Lubri. Eng., 48, pp. 373–383.
17
Heshmat, H. , 2010, Tribology of Interface Layers, CRC Press, Taylor and Francis Group, LLC, Boca Raton, FL, pp. 317–328.
18
Einstein, A. , 1906, “ On a New Determination of Molecular Dimensions,” Ph.D. thesis, University of Zurich, Zurich, Switzerland.
19
Acrivos, A. 1995, “ Bingham Award Lecture 1994: Shear-Induced Particle Diffusion in Concentrated Suspensions of Noncolloidal Particles,” J. Rheol., 39(5), pp. 813–826. [CrossRef]
20
Vand, V. , 1948, “ Viscosity of Solutions and Suspensions,” J. Phys. Chem., 52(2), pp. 277–299. [CrossRef]
21
Paul, E. L. , Atiemo-Obeng, V. A. , and Kresta, S. M. , 2004, Handbook of Industrial Mixing—Science and Practice, John Wiley and Sons, Hoboken, NJ.
22
Heshmat, H. , 2010, Tribology of Interface Layers, CRC Press, Taylor and Francis Group, LLC, Boca Raton, FL, pp. 83–86.
23
Sutherland, W. , 1895, “ The Viscosity of Mixed Gases,” Philos. Mag. Ser. 5, 40(246), pp. 421–431. [CrossRef]
24
Bi, H. T. , Ellis, N. , Abba, I. A. , and Grace, J. R. , 2000, “ A State-of-the-Art Review of Gas–Solid Turbulent Fluidization,” Chem. Eng. Sci., 55(21), pp. 4789–4825. [CrossRef]
25
Heshmat, H. , 1991, “ The Rheology and Hydrodynamics of Dry Powder Lubrication,” Tribol. Trans., 34(3), pp. 433–439. [CrossRef]
26
Heshmat, H. , and Brewe, D. E. , 1992, “ On Some Experimental Rheological Aspects of Triboparticulates,” 18th Leeds-Lyon Symposium on Wear Particles: From the Cradle to the Grave, Vol. 21, pp. 357–367.
27
Heshmat, H. , Hryniewicz, P. , Walton, J. F. II. , Willis, J. P. , and Jahanmir, S. , 2005, “ Low-Friction Wear Resistant Coatings for High-Temperature Foil Bearings,” World Tribology Congress III, pp. 399–400.
28
Heshmat, H. , Hryniewicz, P. , Walton, J. F. II. , Willis, J. P. , and Jahanmir, S. , 2005, “ Low-Friction Wear Resistant Coatings for High-Temperature Foil Bearings,” Tribol. Int., 38(11), pp. 1059–1075. [CrossRef]
29
Heshmat, H. , and Jahanmir, S. , 2006, “ Evaluation of Coatings for a Large Hybrid Foil/Magnetic Bearing,” ASME Paper No. IJTC2006-12328.
30
Hunsberger, A. Z. , Jahanmir, S. , Heshmat, H. , Eryilmaz, O. , and Erdemir, A. , 2007, “ Performance Evaluation of Half-Wetted Hydrodynamic Bearings With DLC Coated Surfaces,” ASME Paper No. IJTC2007-44207.
31
Heshmat, H. , Jahanmir, S. , and Walton, J. F. II ., 2007, “ Coatings for High Temperature Foil Bearings,” ASME Paper No. GT2007-27975.
32
Jahanmir, S. , Heshmat, H. , Heshmat, C. A. , Eryilmaz, O. , and Erdemir, A. , 2007, “ Evaluation of DLC Coatings for Foil Bearing Applications,” ASME Paper No. IJTC2007-44035.
33
Jahanmir, S. , Heshmat, H. , and Heshmat, C. A. , 2009, “ Assessment of Tribological Coatings for Foil Bearing Applications,” Tribol. Trans., 52(2), pp. 231–242. [CrossRef]
34
Jahanmir, S. , Heshmat, H. , and Heshmat, C. A. , 2008, “ Evaluation of DLC Coatings for High-Temperature Foil Bearing Applications,” ASME J. Tribol., 131(1), p. 011301. [CrossRef]
35
Heshmat, H. , Walton, J. F. II. , and Jahanmir, S. , 2011, “ Tribological and Thermal Properties of a New Flexible Ceramic Coating,” STLE Annual Meeting & Exhibition, pp. 12–14.
36
Heshmat, H. , Walton, J. F. II. , and Jahanmir, S. , 2012, “ Evaluation of a New Coating for Application to Ramjet Engine Combustion Chamber,” ASME Paper No. GT2012-68725.
37
Kaur, R. G. , and Heshmat, H. , 2002, “ 100mm Diameter Self-Contained Solid/Powder Lubricated Auxiliary Bearing Operated at 30,000 rpm,” Tribol. Trans., 45(1), pp. 76–84. [CrossRef]

Figures

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Fig. 1

Complaint surface foil bearing schematic diagram and coordinate system

+Complaint surface foil bearing schematic diagram and coordinate system
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Complaint surface foil bearing schematic diagram and coordinate system
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Fig. 2

Foil bearing analysis calculation procedure

+Foil bearing analysis calculation procedure
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Foil bearing analysis calculation procedure
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Fig. 3

Generated pressure profiles for foil journal bearing and single thrust foil bearing pad

+Generated pressure profiles for foil journal bearing and single thrust foil bearing pad
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Generated pressure profiles for foil journal bearing and single thrust foil bearing pad
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Fig. 4

Predicted thrust top foil deformations under the influence of hydrodynamic pressure and corresponding experimental evidence under 390 N loading per pad (1560 N total load) during 40,000 rpm operation

+Predicted thrust top foil deformations under the influence of hydrodynamic pressure and corresponding experimental evidence under 390 N loading per pad (1560 N total load) during 40,000 rpm operation
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Predicted thrust top foil deformations under the influence of hydrodynamic pressure and corresponding experimental evidence under 390 N loading per pad (1560 N total load) during 40,000 rpm operation
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Fig. 5

Increasing gas molecular mean free path with decreasing ambient pressure at a constant temperature

+Increasing gas molecular mean free path with decreasing ambient pressure at a constant temperature
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Increasing gas molecular mean free path with decreasing ambient pressure at a constant temperature
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Fig. 6

Increasing gas molecular mean free path with increasing altitude and corresponding change in pressure and temperature

+Increasing gas molecular mean free path with increasing altitude and corresponding change in pressure and temperature
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Increasing gas molecular mean free path with increasing altitude and corresponding change in pressure and temperature
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Fig. 7

Normalize windage loss for rotor system as a function of speed and ambient pressure

+Normalize windage loss for rotor system as a function of speed and ambient pressure
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Normalize windage loss for rotor system as a function of speed and ambient pressure
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Fig. 8

Characteristic properties of air as a function of ambient pressure

+Characteristic properties of air as a function of ambient pressure
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Characteristic properties of air as a function of ambient pressure
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Fig. 9

Foil bearing characteristics as a function of Λ for variable viscosity and ambient pressure at a fixed bearing geometry and speed

+Foil bearing characteristics as a function of Λ for variable viscosity and ambient pressure at a fixed bearing geometry and speed
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Foil bearing characteristics as a function of Λ for variable viscosity and ambient pressure at a fixed bearing geometry and speed
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Fig. 10

Simulated velocity profile representations: (a) no-slip Reynolds boundary, condition 1; (b) slip at bearing, condition 2; (c) slip at runner, condition 3; and (d) slip at both surfaces, condition 4

+Simulated velocity profile representations: (a) no-slip Reynolds boundary, condition 1; (b) slip at bearing, condition 2; (c) slip at runner, condition 3; and (d) slip at both surfaces, condition 4
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Simulated velocity profile representations: (a) no-slip Reynolds boundary, condition 1; (b) slip at bearing, condition 2; (c) slip at runner, condition 3; and (d) slip at both surfaces, condition 4
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Fig. 11

Identification of starved lubrication region with slip at the boundary as a function of ambient pressure

+Identification of starved lubrication region with slip at the boundary as a function of ambient pressure
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Identification of starved lubrication region with slip at the boundary as a function of ambient pressure
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Fig. 17

Test system instrumentation and data acquisition layout

+Test system instrumentation and data acquisition layout
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Test system instrumentation and data acquisition layout
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Fig. 16

Assembled flywheel and motor/generator being installed in the vacuum chamber

+Assembled flywheel and motor/generator being installed in the vacuum chamber
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Assembled flywheel and motor/generator being installed in the vacuum chamber
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Fig. 15

Cross section view of a chamber and modular flywheel simulator with motor/generator

+Cross section view of a chamber and modular flywheel simulator with motor/generator
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Cross section view of a chamber and modular flywheel simulator with motor/generator
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Fig. 14

Impact of particulate/powder and gas mixture viscosity on load capacity

+Impact of particulate/powder and gas mixture viscosity on load capacity
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Impact of particulate/powder and gas mixture viscosity on load capacity
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Fig. 13

Chrome plated disk after testing with Korolon® coated thrust foil bearing pad under load showing accumulated wear debris powder and small particles distributed on the wear track

+Chrome plated disk after testing with Korolon® coated thrust foil bearing pad under load showing accumulated wear debris powder and small particles distributed on the wear track
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Chrome plated disk after testing with Korolon® coated thrust foil bearing pad under load showing accumulated wear debris powder and small particles distributed on the wear track
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Fig. 12

Theoretical and experimental values of viscosity of slurry mixture as a function of solid fraction

+Theoretical and experimental values of viscosity of slurry mixture as a function of solid fraction
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Theoretical and experimental values of viscosity of slurry mixture as a function of solid fraction
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Fig. 18

Summary of coast down tests at ambient pressures to 7.6 kPa (1.1 psi)

+Summary of coast down tests at ambient pressures to 7.6 kPa (1.1 psi)
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Summary of coast down tests at ambient pressures to 7.6 kPa (1.1 psi)
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Fig. 19

Deceleration rates for different ambient pressure conditions time synchronized to ending condition

+Deceleration rates for different ambient pressure conditions time synchronized to ending condition
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Deceleration rates for different ambient pressure conditions time synchronized to ending condition
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Fig. 33

Modified Stribeck curve showing lubrication regimes

+Modified Stribeck curve showing lubrication regimes
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Modified Stribeck curve showing lubrication regimes
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Fig. 20

Motor power for required to operate the flywheel at 30,000 rpm as a function of ambient pressure

+Motor power for required to operate the flywheel at 30,000 rpm as a function of ambient pressure
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Motor power for required to operate the flywheel at 30,000 rpm as a function of ambient pressure
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Fig. 21

Torque and coast down time versus speed

+Torque and coast down time versus speed
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Torque and coast down time versus speed
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Fig. 22

Variation in bearing temperature during low ambient pressure coast down test

+Variation in bearing temperature during low ambient pressure coast down test
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Variation in bearing temperature during low ambient pressure coast down test
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Fig. 23

Experimental evidence of increasing morphological effect in foil bearing subject to depressurization and increasing mean free path length

+Experimental evidence of increasing morphological effect in foil bearing subject to depressurization and increasing mean free path length
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Experimental evidence of increasing morphological effect in foil bearing subject to depressurization and increasing mean free path length
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Fig. 24

A 76 mm diameter foil journal bearing subjected to abusive overload conditions without failure. Polished/burnished areas correspond to apex of bump spring elements and are indicative of a high-speed rub.

+A 76 mm diameter foil journal bearing subjected to abusive overload conditions without failure. Polished/burnished areas correspond to apex of bump spring elements and are indicative of a high-speed rub.
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A 76 mm diameter foil journal bearing subjected to abusive overload conditions without failure. Polished/burnished areas correspond to apex of bump spring elements and are indicative of a high-speed rub.
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Fig. 25

Bearing journal after abusive overload showing lightly adhered material from Korolon® coating

+Bearing journal after abusive overload showing lightly adhered material from Korolon® coating
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Bearing journal after abusive overload showing lightly adhered material from Korolon® coating
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Fig. 26

Journal with Korolon® coating transfer film

+Journal with Korolon® coating transfer film
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Journal with Korolon® coating transfer film
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Fig. 27

Journal foil bearing with loose Korolon® wear debris on surface

+Journal foil bearing with loose Korolon® wear debris on surface
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Journal foil bearing with loose Korolon® wear debris on surface
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Fig. 28

A 50 mm diameter journal after high-temperature and high-speed testing showing film transfer from bearing to journal

+A 50 mm diameter journal after high-temperature and high-speed testing showing film transfer from bearing to journal
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A 50 mm diameter journal after high-temperature and high-speed testing showing film transfer from bearing to journal
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Fig. 29

A 50 mm diameter journal bearing after high-temperature and high-speed testing showing bearing surface and dry powder film

+A 50 mm diameter journal bearing after high-temperature and high-speed testing showing bearing surface and dry powder film
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A 50 mm diameter journal bearing after high-temperature and high-speed testing showing bearing surface and dry powder film
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Fig. 30

High-speed flywheel demonstrator system built for operation in soft vacuum

+High-speed flywheel demonstrator system built for operation in soft vacuum
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High-speed flywheel demonstrator system built for operation in soft vacuum
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Fig. 31

Foil bearing load-carrying capacity and film height as a function of ambient pressure

+Foil bearing load-carrying capacity and film height as a function of ambient pressure
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Foil bearing load-carrying capacity and film height as a function of ambient pressure
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Fig. 32

Contribution of hydrodynamic and morphological elements in tribological process

+Contribution of hydrodynamic and morphological elements in tribological process
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Contribution of hydrodynamic and morphological elements in tribological process

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