NASA/TM-2000-209782 ARL-TR-2334 

, Load Capacity Estimation of Foil Air 

Journal Bearings for Oil-Free 

Turbomachinery Applications 

Christopher DellaCorte 

Glenn Research Center, Cleveland, Ohio 

Mark J. Valco 

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio 

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NASA/TM-2000-209782 ARL-TR-2334 

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h-m-T& 

RESEARCHLABORATORY 

Load Capacity Estimation of Foil Air 

Journal Bearings for Oil-Free 

Turbomachinery Applications 

Christopher DellaCorte 

Glenn Research Center, Cleveland, Ohio 

Mark J. Valco 

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio 

Prepared for the 

International Joint Tribology Conference 

sponsored by the Society of Tribologists and Lubrication Engineers 

Seattle, Washington, October l-4,2000 

National Aeronautics and 

Space Administration 

Glenn Research Center 

October 2000 
.- 

Acknowledgments 

The authors wish to express their sincere gratitude and appreciation to Dr. Hooshang He&mat for his 

experience and historical insights in the field of foil bearings and for his assistance in 

recommending relevant reference materials. 

Available from 

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Available Available electronically electronically at htto: / /altrs.erc.nasa.eov/GLTRS /altrs.erc.nasa.eov/GLTRS 

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Springfield, VA 22100 

Price Code: A03 
. 

LOAD CAPACITY ESTIMATION OF FOIL AIR JOURNAL BEARINGS 

FOR OIL-FREE TURBOMACHINERY APPLICATIONS 

Christopher DellaCorte 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Mark J. Valco 

U.S. Army Research Laboratory 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

SUMMARY 

This paper introduces a simple “Rule of Thumb” (ROT) method to estimate the load capacity of foil air journal 

bearings, which are self-acting compliant-surface hydrodynamic bearings being considered for Oil-Free turbomachinery applications such as gas turbine engines. The ROT is based on first principles and data available in the 

literature and it relates bearing load capacity to the bearing size and speed through an empirically based load capacity coefficient, D. It is shown that load capacity is a linear function of bearing surface velocity and bearing projected 

area. Furthermore, it was found that the load capacity coefficient, D, is related to the design features of the bearing 

compliant members and operating conditions (speed and ambient temperature). Early bearing designs with basic or 

“first generation” compliant support elements have relatively low load capacity. More advanced bearings, in which 

the compliance of the support structure is tailored, have load capacities up to five times those of simpler designs. 

The ROT enables simplified load capacity estimation for foil air journal bearings and can guide development of new 

Oil-Free turbomachinery systems. 

INTRODUCTION 

Foil air bearings are self-acting compliant-surface hydrodynamic bearings that use ambient air (or any process 

gas) as their working fluid or lubricant. By utilizing this Oil-Free technology, foil bearing supported turbomachinery 

can benefit from design simplicity and reduced weight (no oil system), high speed and temperature capability, and 

reduced maintenance. Foil bearings have proven themselves in relatively small lightly loaded applications, like aircraft air cycle machines (ACM’s). Recent advances in foil air bearing design, high-temperature solid lubrication, 

and bearing and rotor system analytical modeling enable new applications in Oil-Free turbomachinery (ref. 1). 

Foil air bearings were first commercialized in the 1970’s in air cycle machines used for aircraft cabin pressurization (refs. 2 and 3). Since then, new applications in cryogenic turbo-expanders, turbo-alternators and turbochargers have been demonstrated (refs. 4 to 7). All of these applications relied on an experimental build and test development sequence. Although relatively time consuming and costly, this development approach is necessary due to the 

lack of accurate predictive performance analysis methods for a range of foil bearing sizes and designs. Despite the 

analytical and predictive shortcomings, experimental foil bearing characterization continues to add to the foil air 

bearing knowledge database. It is anticipated that as more applications are developed and ongoing research continues, an improved fundamental understanding of foil bearing performance characteristics will be developed to guide 

the engineering of new Oil-Free turbomachinery systems. 

Three key technical hurdles have impeded the application and widespread use of foil air bearings beyond air 

cycle machines into other turbomachinery systems such as gas turbine engines. These technical hurdles are: (1) 

adequate load capacity, (2) high temperature start/stop lubricants and (3) reliable predictive performance methods 

and design guidelines. 

Recent improvements in load capacity have been demonstrated. In a 1994 paper by He&mat, a twofold increase 

in load capacity was reported (ref. 8). This improvement was attributed to the better design of the compliant foil 

structure based on elastic and hydrodynamic analytical modeling. Other researchers have indicated similar load 

NASA/TM-2000-209782 1 
capacity improvements but have not yet published the data in the open literature. These demonstrated levels of load 

capacity help remove the first technical hurdle. 

High-temperature (>300 “C) bearing operation has always been a challenging technical hurdle because commonly used foil lubricant coatings rely on relatively low temperature materials (e.g., PTFE and MO&) (refs. 5 

and 9). These materials are used because, in addition to the good lubrication properties, they are flexible and as foil 

coatings they do not significantly alter the compliance and surface morphology of the top foil. These traditional 

solid lubricants are temperature limited to use under about 300 “C. Unfortunately, solid lubricants capable of operating above 300 “C are relatively rigid ceramic-like materials that are difficult to apply and their presence significantly 

changes the compliance of the thin and flexible foil members (ref. 10). 

Recent research on new high-temperature solid-lubricant coatings applied to bearing shafts (journals) appears to 

have overcome this second technical hurdle. Uncoated nickel-based superalloy foil bearings have been successfully 

lubricated with PS304 shaft coatings for over 100,000 start/stop cycles at temperatures as high as 650 “C (refs. 1 

and 7). PS304 is a plasma sprayed composite solid lubricant that has silver and fluoride eutectic lubricants in a 

metal/oxide matrix. During operation the lubricants transfer to the foils creating a thin but effective foil coating layer 

(ref. 1). By using PS304, or other similar coatings, high temperature operation with long life is achievable. 

The third technical hurdle, reliable predictive performance methods and design guidelines has not yet been 

overcome. The reason for this shortfall is that foil bearings are inherently nonlinear and very difficult to model using 

relatively simplistic first principle methods (refs. 11 and 12). This modeling difficulty is due to the complex nonlinear structural, hydrodynamic fluid, and thermal interactions between the compliant foils and the flmd film which 

are often influenced by stick/slip frictional contacts between foil elements and the elastic foundation support structure (e.g., bumps) (ref. 13). In more technologically mature systems, such as rolling element bearings, extensive 

experimental data and application based experience has led to empirically based design guidelines (refs. 14 and 15). 

For air foil bearings, extensive experimental measurements have not been made, especially at high temperatures, and 

thus similar experience based guidelines are not yet available. 

In this paper, an empirical or “Rule of Thumb” estimation of journal bearing load capacity is developed as an 

aid in feasibility assessments for foil bearing supported rotordynamic systems. The “Rule of Thumb” (ROT) is based 

on experimental data and fundamental first principles and is shown to be remarkably effective in making direct 

comparisons between bearing designs. 

A similar ROT analysis of thrust foil bearings is inhibited by the lack of available thrust bearing load capacity 

data. Future work in this area is expected to result in a thrust foil bearing load capacity ROT following a research 

path that parallels the one reported in this paper. 

Recognizing its limitations in scope and accuracy, the journal load capacity ROT serves as a first step for further work in developing similar ROT’s for thrust bearing load capacity and for bearing dynamic (stiffness and damping) characteristics. The successful development of additional ROT’s will help to overcome the third technological 

hurdle and foster the further successful application of foil air bearing technology to Oil-Free turbomachinery 

systems. 

FOIL BEARING BACKGROUND AND RULE OR THUMB DEVELOPMENT 

Foil air bearings operate under self-acting hydrodynamic principles in the same manner as conventional sleeve 

type rigid hydrodynamic bearings. However, a major difference is that foil bearings have compliant surfaces relative 

to rigid bearings; therefore, foil bearing geometry is not fixed. Figure 1 shows cross sections of two typical journal 

foil bearing designs, the overlapping leaf type foil bearing and the bump foil bearing. During operation, the hydrodynamic film pressure deflects or deforms the foils. The bearing geometry, therefore, is influenced by the operating 

conditions such as speed, load, and temperature. 

At rest, the top (or inner) foil is spring preloaded against the shaft. There is no clearance as in a rigid sleeve 

bearing. As the shaft rotates, viscous air is circumferentially dragged in between the top foil surface and the shaft 

generating hydrodynamic pressure. This pressure acts upon the top (inner) foil causing it to separate from or “liftoff’ the shaft surface and press against its compliant support structure. The fluid film pressure and foil compliance 

interact dynamically to seek an equilibrium state for a given set of conditions. Additionally, pressure changes in the 

shearing fluid film and viscous heating can lead to heat generation that may influence flmd film properties or foil 

mechanical properties. Because of these significant complex fluid/structural/thermal interactions, modeling of foil 

bearings must include fluid film and large deformation elastic effects. 

From the perspective of load capacity, it is helpful to view the moving shaft surface as a viscous pump and the 

top foil as a smooth impermeable membrane seal that traps the gas film pressure. The gas film pressure that is 

NASA/TM-2000-209782 2 
generated is a function of the effectiveness of the pump and the efficiency of the foil to act as a seal. Foil bearing 

load capacity is the integration of the fluid film pressure across the foil surface area. Consequently, foil bearing load 

capacity is a complex function of bearing design and operating condition as are the bearing stiffness and damping 

characteristics. 

On a fundamental first principles basis, the viscous pumping action of the shaft is proportional to surface velocity; therefore, the bearing diameter and rotational speed contribute to fluid film pressure and, hence, the bearing load 

capacity. The action of the foil is subtler. The foil surface must satisfy two seemingly conflicting requirements: 

maximize fluid film pressure and minimize leakage. In addition, local contact between the shaft and foil surfaces, 

i.e., high-speed rubs, must be avoided. This is accomplished by tailoring the foil support structure to provide a small 

but uniform fluid film thickness during operation taking into consideration that localized pressure decreases due to 

fluid leakage at the bearing edges. 

Foil bearing load capacity defined here from an engineering viewpoint, is the maximum constant load that can 

be supported by a bearing operating with constant speed and steady-state conditions. Theoretically, as the minimum 

hydrodynamic film thickness decreases, the gas pressure increases suggesting perhaps that no distinct or discrete 

load capacity limit exists. In practice, however, when the nominal hydrodynamic fluid film thickness approaches the 

average surface (foil or shaft) roughness, asperity contact and rubbing occurs causing local frictional heating, wear 

and damage. Thus, the permissible or engineering load capacity is reached when the minimum fluid film thickness is 

somewhat greater than the average surface roughness of the bearing component. 

Based upon these considerations, the permissible load that a bearing can support for a given working fluid is a 

function of design, bearing area and surface velocity. Put symbolically: 

W = D (LxD) (DxQ) 

Where: 

W is the maximum steady-state load that can be supported, N (Ibs) 

D is the bearing load capacity coefficient, N/(mm3.krpm) (lbs/(in3.krpm)) 

L is the bearing axial length, mm (in.) 

D is the shaft diameter, mm (in.) 

Q is the shaft speed in thousand rpm (krpm) 

This linear relationship should be reasonably accurate providing the fluid film is effectively incompressible with 

constant viscosity and the film thickness is nearly fixed (refs. 16 and 17). This is true for rigid gas bearings over a 

portion of their operating range as shown in figure 2 adapted from Faria and San Andres (ref. 17). In foil bearings 

the foils are purposefully designed to result in a near uniform film thickness across a broad operating range. In addition, since air viscosity, unlike many liquid lubricants, is a weak function of temperature a nearly linear relation 

between load capacity and surface velocity can be expected. In the above ROT, the empirically based load capacity 

coefficient, D, includes both fluid property and design effects. 

For the ROT model presented, it is recommended that non-S1 units (in. and Ibs) be used as a mnemonic aid. By 

using these units it is observed that modern design foil air bearings typically support “a pound of load per inch of 

bearing diameter per square inch of bearing projected area per thousand rpm.” While the authors clearly acknowledge that SI units are preferred, the units employed in using this Rule of Thumb (ROT) are easier to remember making the ROT more convenient. SI units will be used throughout this paper when discussing data and analysis and 

will be shown parenthetically with non-S1 units where appropriate. 

EXPERIMENTAL DATA 

For foil journal bearings there is a growing body of experimental data on load capacity available in the literature 

(refs. 7,8, 18 to 24). These references contain experimentally measured load capacity data for foil journal bearings 

ranging from 25 to 100 mm in diameter, operating over a wide speed and temperature range. 

Performance data is summarized in table I and plotted in figures 3,5,7 to 9. Figures 1,4 and 6 show representative bearing design details. It can be seen from the performance data that a nearly linear relationship exists 

between load capacity, surface velocity and projected area with the proportionally constant, D, which varies depending on bearing design. 

NASA/TM-2000-209782 3 
DISCUSSION 

The limited foil bearing experimental data available is consistent with the linear approximation assumptions 

made in the ROT equation. By using the ROT, a direct comparison can be made between the performance (load 

capacity coefficients, D’s) of different bearing designs operating at differing conditions. 

The data in table I shows that the earliest bearings (from the 1960’s and early 1970’s) had load capacity coefficient magnitudes, D ‘s, between about 0.1 and 0.3. These early bearing designs, defined here as “first generation,” 

had foil geometry’s that were essentially uniform in both the axial and circumferential directions (including uniformly periodic circumferential geometry). Figure 1 shows some typical examples of “first generation” bearings. 

This means that the stiffness characteristics of the foil structure are also more or less uniform. Thus, in operation, the 

foil surface deforms due to the fluid film pressure without support structure specifically accounting for localized 

effects such as edge leakage, thermal gradients, heat generation and other hydrodynamic phenomena. The relatively 

simplistic features of these “first generation” air foil journal bearings enabled application to high-speed and lightly 

loaded systems. However these “first generation” bearings were also restricted by their inherent limitations in low 

overall pressure rise and local film thickness reductions leading to low load capacity. 

For perspective it should be noted that “first generation” foil air bearings provided load capacities equivalent to 

circular, lobed or waved rigid gas bearings (refs. 22 and 25). Furthermore, these foil bearings provided greater 

damping, tolerance to misalignment and the ability to avoid high-precision manufacturing specifications and their 

associated costs. 

During the 1970’s and 1980’s, through further research, additional levels of refinement were added to bearing 

designs enabling the purposeful tailoring of the stiffness characteristics of the foil support structure. These bearing 

designs, defined here as “second generation,” are in commercial use in many air cycle machine applications. In these 

“second generation” bearings, the stiffness characteristics of the foil support structure typically vary either axially 

along the bearing length or in the circumferential direction, but not in both directions. Figure 4 shows some typical 

“second generation” bearing designs. 

By controlling, the foil support stiffness in one dimension (axial or circumferential) the bearing can better 

accommodate physical phenomena like edge leakage and, hence, yield improved performance. In leaf foil bearings 

this design flexibility is provided through the use of a “stepped” backing spring that contacts the backside of the top 

foils during bearing operation (ref. 20). In bump type foil bearings, the bump layers are sometimes split circumferentially to allow axial control of compliance or the bump pitch can be varied to allow circumferential compliance control. A further design refinement reported is the use of soft metal (e.g., copper) coatings at the bump layer/top foil 

interface to enhance frictional damping and thermal conduction (ref. 23). Another design features a second smooth 

foil, which enhances performance (ref. 4). 

Incorporating these “second generation” design features approximately doubled the bearing load capacity to 

coefficient magnitudes, D’s, to the range of 0.3 to 0.6. This level of performance represented substantial improvement over rigid gas bearing load capacity while retaining or further enhancing stiffness and damping characteristics. 

The enhanced performance resulted in successful commercial applications reported in the literature. 

Bearing development and research completed to this point has demonstrated a degree in understanding of the 

intricate relationship between load capacity and the details of the foil support structure design. Namely, the ability to 

control and design the support structure compliance properties to enhance bearing load capacity. Additionally, the 

geometrical design features also influenced the amount of Coulomb damping that the bearing is capable of producing, although the damping process is not as well studied or quantified. 

Advancements in foil bearings have continued the evolution into “third generation” foil bearing designs that 

tailor the foil support structure stiffness in axial (L), circumferential (0) and radial (r) (i.e., displacement sensitive) 

directions to enhance performance even further (refs. 29 to 31). In 1993, He&mat reported on a bearing design in 

which multiple bump layers, with spatially (L, 0, r) variable stiffnesses, are used to impart improved hydrodynamic, 

bearing stiffness and Coulomb damping properties (ref. 8). In this work, the calculated load capacity coefficient, D, 

has a magnitude of 1.4. This value is more than double that demonstrated a decade earlier and is the highest reported 

foil bearing load capacity the authors are aware of. Interestingly, the data reported for this bearing showed that 

damping and stiffness characteristics were also enhanced. The bearing design features described in the paper were 

matched with information available from the pertinent patents to produce the bearing illustration shown in figure 6 

(refs. 29 and 8). 

Recent work on “third generation” bearings includes high temperature (650 “C) load capacity tests on small 

bearings (25 mm length x 35 mm diameter) and room temperature tests on a large bearing (75 mm length x 100 mm 

diameter). Data from these tests have demonstrated bearing load capacity coefficient magnitudes, D’s, around 1.0 

(refs. 1 and 7). Figure 6 shows representative design features of these bearings in which the geometrical design has 

NASA/TM-2000-209782 4 
been tailored for the particular application (i.e., high temperature operation or large bearing size). Performance of 

these “third generation” bearings is shown in figures 7 to 9. 

Thus, despite significant changes in foil bearing support structural design, the simplified linear ROT introduced 

in this paper reasonably approximates bearing load capacity performance over the data range studied. It is expected 

that at extremely low speeds or high loads (e.g., the onset of film rupture) the model will not be accurate. However, 

for a “rule of thumb’ engineering type analysis and application feasibility study, the ROT model for load capacity is 

a useful design guide. 

Other important bearing parameters for rotor systems include stiffness and damping that must also be considered when assessing foil bearing feasibility for turbomachinery. These parameters directly influence rotordynamic 

stability and cannot be ignored. Foil bearing stiffness is derived from a combination of the fluid film compression 

and elastic deformation of the foil structure both with potentially substantial non-linearity. In contrast to the limited 

damping capability in rigid gas bearings, significant damping can and does occur in foil air bearings in both the fluid 

film (viscous effects) and in the foil support structure (Coulomb friction damping). Data in the literature as well as 

research underway at the author’s laboratory suggests that advanced design bearings can provide adequate load 

capacity, damping and stiffness properties for many Oil-Free turbomachinery systems (ref. 6). Experimental results 

and theoretical analyses also suggest that load capacity performance can be “traded” for stiffness and damping 

enhancement through proper design compromises. Thus a bearing with excess load capacity for a given application 

can be tailored to provide better stiffness and damping at a lower load capacity (ref. 29). Because of this, further 

development of bearing load capacity remains an important research ,goal. With additional experimental and 

analytical work it may be possible to develop similar design ROT’s for stiffness and damping characteristics of foil 

bearings. 

CONCLUSION 

This paper introduces the foil journal bearing load capacity estimation Rule of Thumb (ROT) concept. The experimental data published in the literature combined with experimental data collected at the author’s laboratory was 

used to validate the ROT model. The enhancement of the load capacity coefficient magnitudes, D, over the last three 

decades can be correlated to the geometric details in the bearing foil support structures and the ability to tailor the 

design features to optimize bearing performance. With this concept in mind, it may be possible to assess or predict a 

foil bearing’s performance potential based upon its design. Demonstrated improvements in bearing performance 

coupled with the development of suitable ROT’s for thrust bearing load capacity, stiffness and damping will assist in 

the development of Oil-Free turbomachinery systems. 

REFERENCES 

4. 

5. 

6. 

7. 

8. 

9. 

DellaCorte, C., Lukaszewicz, V., Valco, M.J., Radil, K.C., and Heshmat, H.: “Performance and Durability of 

High Temperature Foil Air Bearings for Oil-Free Turbomachinery,” NASA/TM-1999-209187. 

Barnett, M.A., and Silver, A.: “Application of Air Bearings to High-Speed Turbomachinery,” SAE Paper 

700720, Sept. 1970. 

Emerson, T.P.: “The Application of Foil Air Bearing Turbomachinery in Aircraft Environmental Control Systems,” ASME Proceedings of the Intersociety Conference on Environmental Systems, San Diego, CA, 

July lo-13,1978, Paper #780-ENAS-18. 

Agrawal, G.L.: “Foil Gas Bearings for Turbomachinery,” Presented at 20* Intersociety Conference on Environmental Systems, Williamsburg, VA, July 9-12,1990, SAE Paper Number 901236,199O. 

O’Donner, L.: “Fluid-Film Foil Bearings Control Engine Heat,” Mechanical Engineering, ASME, May 1993, 

pp. 72-75. 

Howard, S.A.: “Preliminary Development of Characterization Methods for Compliant Air Bearings.” STLE 

Tribology Transactions, Vol. 42 (1999), 4, pp. 789-794. 

DellaCorte, C.: “A New Foil Air Bearing Test Rig for Use to 700 “C and 70,000 rpm,” STLE Tribology Transactions, Vol. 41, #3, 1998, pp. 335-340. 

Heshmat, H.: “Advancements in the Performance of Aerodynamic Foil Journal Bearings High Speed and Load 

Capability,” ASME Journal of Tribology, Vol. 116, pp. 287-295, April 1994. 

Newman, P.: “Surface Coating for Machine Elements Having Rubbing Surfaces,” U.S. Patent #4,005,914, 

Feb. 1, 1977. 

NASA/TM-2000-209782 5 
10. Laskowski, J.A. and DellaCorte, C.: “Friction and Wear Characteristics of Candidate Foil Bearing Materials 

from 25 “C to 800 “C,” STLE Lubrication Engineering, Vol. 52, No. 8, pp. 605-612,1997. 

11. Arakere, N.K.: “Analysis of Foil Journal Bearings with Backing Springs,” STLE Tribology Transactions, 

Vol. 39, No. 1, pp. 208-214, 1996. 

12. Carpino, M., Peng, J.P., and Medvetz, L.: “Misalignment in a Complete Shell Gas Foil Journal Bearing,” STLE 

Tribology Transactions, Vol. 37, No. 4, pp. 829-835, 1994. 

13. Heshmat, C.A., Xu, D.S., and He&mat, H.: “Analysis of Gas Lubricated Foil Thrust Bearings Using Coupled 

Finite Element and Finite Difference Methods,” ASME Paper No. 99-TRIB-34, 1999. 

14. Zaretsky, E.V.: “Life Factors for Rolling Element Bearings,” STLE Special Publication. 

15. Zaretsky, E.V., Poplowski, J.V., and Peters, S.M.: “Comparison of Life Theories for Rolling-Element Bearings,” STLE Tribology Transactions, Vol. 32, No. 2, pp. 237-248, 1996. 

16. Gross, W.A.: Gas Film Lubrication, John Wiley and Sons, Inc., 1962, p. 4. 

17. Faria, M.T.C. and San Andres, L.: “On the Numerical Modeling of High Speed Gas Bearings,” ASME paper 

99-TRIB-2. Presented at the 1999 ASME/STLE Joint Tribology Conference, Kissamee, FL, Oct. 1999. 

18. Ma, J.T.S.: “An Investigation of Self-Acting Foil Bearings,” ASME, Journal of Basic Engineering, Dec. 1965, 

pp. 837-846. 

19. Koepsel, W.F.: “Gas Lubricated Foil Bearing Development for Advanced Turbomachines,” U.S. Air Force 

Report #AFAPL-TR-76-114 Vol. 1, March 1977, p. 23 1. 

20. Suriano, F.J.: “Gas Foil Bearing Development Program,” U.S. Airforce Report #AFWAL-TR-81-2095, 

September 1981. 

21. Advanced Gas Turbine (ACT) Technology Development Project-Final Report, NASA CR-180891, December 

1987. T. Strom Program Manager. 

22. Ruscitto, D., McCormick, J., and Gray, S.: “Hydrodynamic Air Lubricated Compliant Surface Bearing for an 

Automotive Gas Turbine Engine - I - Journal Bearing Performance,” NASA CR-135368, April 1978. 

23. Heshmat, H., Shapiro, and W., Gray, S.: “Development of Foil Journal Bearings for High Lead Capacity and 

High Speed Whirl Stability,” ASME Journal of Lubrication Technology, Vol. 104, No. 2, pp. 149-156,1982. 

24. Kirschmann, A.E., and Agrawal, G.L.: “High Temperature Foil Air Bearings Development for a Missile/UAV 

Engine Application,” Proceedings of JANNAF Conference, Cleveland, Ohio, July 15-17,1998. 

25. Dimofte, F., Addy, H.E., and Walker, J.F.: “Preliminary Results of a Three Wave Journal Air Bearing,” Proceedings of the Advanced Earth-to-Orbit Propulsion Technology Conference,” NASA CP-3282, Vol. II, 

pp. 285-294,1994. 

26. Walton, J.F.: “Mohawk Innovative Technology Newsletter-Winter 1998,” Mohawk Innovative Technology, 

Albany, NY, 1998. 

27. Gray, S. and Bhushan, B.: “Support Element for Compliant Hydrodynamic Journal Bearings,” U.S. Patent 

#4,274,683, June 1981. 

28. Saville, M.P. and Gu, A.L.: “High Load Capacity Journal Foil Bearing,” U.S. Patent #5,116,143, May 1992. 

29. He&mat, H.: “High Load Capacity Compliant Foil Hydrodynamic Journal Bearing,” U.S. Patent #5,988,885, 

Nov. 1999. 

30. He&mat, H.: “A Feasibility Study on the Use of Foil Bearing in Cryogenic Turbopumps,” Presented at the 

AIAAISAEIASMEIASEE 27” Joint Propulsion Conference, June 24-26,1991, Sacramento, CA, AIAA 

Paper No. 91-2103. 

31. Bosley, R.W.: “Compliant Foil Hydrodynamic Fluid Film Radial Bearing,” U.S. Patent #5,427,455, June 1995. 

NASA/TM-2000-209782 6 
. 

Bearing type 

Tension dominated 

tape type 

Rigid type circular 

profile 

Rigid type wave 

profile 

Leaf type 

Bump type w/single 

bump layer 

Bump type w/single 

bump layer (Cu 

coated) 

Leaf type w/backing 

springs 

Leaf type w/backing 

springs 

Bump type w/single 

bump layer (Cu coated 

and circumferentially 

split) 

Bump type reverse 

multiplayer twin top 

foils and single bump 

layer 

Bump type w/multiple 

bump layers, split 

circumferentially and 

axially 

Bump type w/single 

top foil, staggered 

bump foil (split axially 

and circumferentially) 

Bump type w/staggered bump foil (large 

bearing) ^~ 

,-Ls. I.-k-“DLWIZCY I-“L fun J”“RlYlUl DCnllu*” wrlu b.nrrlLll I unln 

Generation Date Size, Speeds, Load capacity References and comments 

number mm (in.) Krpm coefftcient,a D, 

Ibs/in.3.Rrpm 

n/a 1965 J-=13 (0.5) to 14.4 0.016 Reference 17, early magnetic tape 

Dg50 (2) bearing 

n/a 1977 to G-38 (1.5) 5, 10, 14 4.3 Reference 21, not a foil bearing, 

1978 D=38 (1.5) unstable above 14 krpm 

n/a 1994 L=58 (2.3) 15 4.24 Reference 24, not a foil bearing, staD=51 (2.0 ble above 15 krpm 

1”’ 1973 to L=150 (6) 20, 23, 0.07 Reference 18, early leaf type bearing 

1976 D=ll4 (4.5) 28,33 without backing springs, (US 

Pat. #3,215,479) 

15’ 1977 to L.=38 (1.5) 30,45, 55 0.3@25 “C Reference 21, simple bump foil bear1978 D=38 (1.5) 30,39,45 0.24@315 “C ing, (US Pat. #4,208,076) 

IS’ 1980 L=44 (1.7) to 40 0.43 Reference 22, (US Pat. #k&277,1 13) 

D=35 (1.4) 

2nd 1979 to J-=107 (4.2) 12,33.2 0.4025 “C Reference 19, load capacity at 25 “C 

1981 D=89 (3.5) 0.30500 “C may be higher, (US Pat. #4,153,315) 

20d 1979 to L=27 (1.1) 75,100 0.06 to 0.2 Reference 20, bearings not optimized 

1987 D=34 (1.4) for maximum load capacity 

2nd 1982 L.=44 (1.7) to 68 0.50 Reference 22, (US Pat. ##4,277,112) 

D=35 (1.4) 

2nd 1998 L;40 (1.6) to 55 =0.6b Reference 23, bearing tested with 

D=40 (1.6) (estimated) dynamic load, (US Pat. #4,414,280), 

(US Pat.#4,414,281) 

3rd 1994 L=31 (1.2) 29.7, 50, 1.4 Reference 8, bearing optimized for 

D=35 (1.4) 59.7 load capacity, (US Pat. #4,300,806) 

3’d 1998 L=27 (1.1) 5 to 40.0 0.8 to 1.0 Reference 7, shaft coated with slightly 

D=35 (1.4) CO 25 to 650 “C porous high temperature lubricant, 

(US Pat. #5,902,049) 

3rd 1998 L=76 (3.0) 10, 22, 30 0.8 Reference 25, bearing design for large 

D=102 (4.0) size, (US Pat. #5,988,885) 

. . . . . . “Data taken at room temperature unless otherwtse mdrcated. 

bBearing tested with 10 N static load plus an additional 600 N imbalance load. 

NASA/TM-2000-209782 
Figure 1 .-Schematic example of first generation foil 

bearings with axially and circumferentially uniform 

elastic support elements. (a) Leaf-type foil bearing. 

(b) Bump-type foil bearing. 

NASA/TM-2000-209782 8 
NASA/TM-2000-209782 9 

I c 

Bearing number (surface velocity) 

Figure 2.-Non-dimensionalized, theoretical load 

capacity for circular rigid gas bearing. Adapted 

from Faria and San Andres reference 17. 

A Simple bump foil bearing 

0 Circular rigid gas bearing 

220 (unstable above 14,000 rpm 

W) L = D = 38.1 mm (1.5 in.) 

2? 0 Lobed (wave) non-circular 

4 180 rigid gas bearing. Data 

T 

(40) from reference 25. 

10 20 30 40 

Bearing speed, krpm 

Figure 3.-Foil bearing load capacity for first generation bump foil type bearing at 25 “C. Data from 

reference 21. 
r Bearing housing 

(4 

Circumferentially 

split bump foil 

Figure 4.--Selected details illustrating elastic support components of 

second generation foil air bearings offering variable circumferential 

or axial compliance characteristics. (a) Variable pitch backing springs, 

references 11 and 28. (b) Circumferentially split bump foil, reference 27. 

NASA/TM-2000-209782 10 
A Load capacity 

L = 44.5 mm (1.72 in.) 

D = 35 mm (1.37 in.) 

0= 

0 10 20 30 40 50 60 70 

Bearing speed, krpm 

Figure 5.-Foil bearing load capacity for second 

generation bump foil bearing having a single 

circumferentially split bump foil. Data from 

reference 23. 

NASA/TM-2000-209782 11 
12 

NASA/TM-2oot-782 

Variable pitch 

Figure 6 &elected details of third generation foil air 

bearings elastic support mechanisms which allow 

both axial and circumferential tailoring of compliante, Bump foil from reference 29. 
NASA/TM-2000-209782 

5340 

B 

(1200) 

c. 4450 t 

2 

? 

(100) 

3560 

$ (800) 

4 2670 

; 6300) 

B 1780 

1J) (400) 

.E 

% 890 

i (200) I 

A Load capacity 

L = 76 mm (3.0 in.) 

D = 102 mm (4.0 in.) 

0’ I * 

0 10 20 30 

Bearing speed, krpm 

Figure 7.-Foil bearing load capacity for large, third 

generation foil air bearing. Data from reference 26. 

t 

710 

(140) t 

530 

2 (120) t 

=, 440 

3 (100) 

.z 

8 360 630) 

O 270 

1 (‘33 

F 180 

‘5 (40) 

m” 

: 

A Load capacity 

L = 31 mm (1.22 in.) 

D = 35 mm (1.37 in.) 

t 

0 10 20 30 40 50 60 70 

Bearing speed, krpm 

Figure 8.-Foil bearing load capacity for third 

generation bump foil bearing with axially and 

circumferentially varying bump foil design. 

Data from reference 8. 

13 
NASA/TM-2000-209782 14 

z 180 

2 (40) 

8 p 130 

g (30) 

B 

= 90 

.z (20) z 

2 40 

Load capacity @ 25 “C 

Load capacity & 315 “C 

Load capacity Q 650 “C 

L = 27 mm (1.06 in.) /’ 

D = 35 mm (1.375 in.) ,/ 

= 0.8 

Bearing speed, krpm 

Figure O.-Foil bearing load capacity for third 

generation bump foil bearing operating against 

PS304 coated shaft from 25 to 650 “C. Data 

from reference 7. 
REPORT DOCUMENTATION PAGE Form Approved 

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED 

October 2000 Technical Memorandum 

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS 

Load Capacity Estimation of Foil Air Journal Bearings 

for Oil-Free Turbomachinery Applications WU-523-18-13-00 

6. AUTHOR(S) 

Christopher DellaCorte and Mark J. Valco 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS 

National Aeronautics and Space Administration 

John H. Glenn Research Center 

Cleveland, Ohio 44135-3191 

and 

U.S. Army Research Laboratory 

Cleveland, Ohio 44135-3 191 

8. PERFORMING ORGANIZATION 

REPORT NUMBER 

E-12067 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS 

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

and 

U.S. Army Research Laboratory 

Adelphi, Maryland 20783-l 145 

11. SUPPLEMENTARY NOTES 

10. SPONSORlNG/MONlTORlNG 

AGENCY REPORT NUMBER 

NASA TM-2000-209782 

ARL-TR-2334 

Prepared for the International Joint Tribology Conference sponsored by the Society of Tribologists and Lubrication Engineers, Seattle, Washington, October l-4,2000. Christopher DellaCorte, NASA Glenn Research Center; and Mark J. Valco, 

U.S. Army Research Laboratory, NASA Glenn Research Center. Responsible person, Christopher DellaCorte, organization 

code 5960, l-216-433-6056. 

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE 

Unclassified -Unlimited 

Subject Category: 07 Distribution: Nonstandard 

Available electronically at httu://eltrs.mc.nasa.gov/GLTRS 

This publication is available from the NASA Center for Aerospace Information, l-301-621-0390. 

13. ABSTRACT (Maximum 200 words) 

This paper introduces a simple “Rule of Thumb” (ROT) method to estimate the load capacity of foil air journal bearings, 

which are self-acting compliant-surface hydrodynamic bearings being considered for Oil-Free turbomachinery applications such as gas turbine engines. The ROT is based on first principles and data available in the literature and it relates 

bearing load capacity to the bearing size and speed through an empirically based load capacity coefficient, D. It is shown 

that load capacity is a linear function of bearing surface velocity and bearing projected area. Furthermore, it was found 

that the load capacity coefficient, D, is related to the design features of the bearing compliant members and operating 

conditions (speed and ambient temperature). Early bearing designs with basic or “first generation” compliant support 

elements have relatively low load capacity. More advanced bearings, in which the compliance of the support structure is 

tailored, have load capacities up to five times those of simpler designs. The ROT enables simplified load capacity estimation for foil air journal bearings and can guide development of new Oil-Free turbomachinery systems. 

14. SUBJECT TERMS 15. NUMBER OF PAGES 

Foil air bearings; Gas bearings; Journal bearings; Load capacity; Turbomachinery 20 

16. PRICE CODE 

A03 

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT 

OF REPORT OF THIS PAGE OF ABSTRACT 

Unclassified Unclassified Unclassified 

-. .- --- .- - --. NSN 7540-01-280-5500 Standard Form 298 (Hev. 2-83) 

Prescribed by ANSI Std. 239-18 

298-l 02