Factors Influencing the Performance of Foil Gas Thrust Bearings for Oil-Free Turbomachinery Applications

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FACTORS INFLUENCING THE PERFORMANCE OF FOIL GAS THRUST BEARINGS FOR OIL-FREE TURBOMACHINERY APPLICATIONS

BRIAN DAVID DYKAS

Submitted in partial fulﬁllment of the requirements For the degree of Doctor of Philosophy

Dissertation Advisor: Dr. Joseph M. Prahl

Department of Mechanical and Aerospace Engineering

CASE WESTERN RESERVE UNIVERSITY

May 2006 CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the dissertation of

______

candidate for the Ph.D. degree *.

(signed)______(chair of the committee)

______

(date) ______

*We also certify that written approval has been obtained for any proprietary material contained therein. Table of Contents

Table of Contents ...... iii ListofTables...... vi ListofFigures...... vii Acknowledgements ...... x Nomenclature...... xi Abstract...... xiii

1 Introduction 1 1.1Oil-FreeTurbomachineryApplications...... 1 1.2EnablingTechnologies...... 5 1.3 Present Work ...... 6 References...... 9

2 Background of the Art 11 2.1FoilAirBearingDevelopment...... 11 2.2CurrentStateoftheArtPractices...... 16 References...... 18

3 Gas Film Characteristics 20 3.1HydrodynamicFeatures...... 20 3.2 Thermal Behavior...... 21 3.3StructuralResponseandEﬀects...... 24 References...... 25

4 Methods 26 4.1ExperimentalMethods...... 26 4.1.1 ThrustBearingTestRig...... 26 4.1.2 TestSpecimens...... 31 4.1.3 CoolingTechniques...... 35 4.1.4 OperatingTorqueandPowerLossMeasurements...... 36 4.1.5 LoadCapacityTesting...... 38 4.1.6 WearMeasurements...... 38

iii 4.1.7 BearingTemperatureMeasurement...... 39 4.2NumericalTechniques...... 42 4.2.1 HydrodynamicModeling...... 44 4.2.2 ModelingofStructuralDeformation...... 45 References...... 46

5 Bearing Torque and Power Loss Results 48 5.1ExperimentalTorque/PowerLossMeasurements...... 48 5.1.1 BearingTorqueversusSpeedandLoad...... 48 5.1.2 Eﬀect of Runner Surface Roughness ...... 52 5.1.3 EﬀectofCoolingFlow...... 53 5.2NumericalPredictionsofBearingTorque...... 56 References...... 60

6 Load Capacity Results 61 6.1ExperimentalMeasurementofLoadCapacity...... 62 6.1.1 LoadCapacityasaFunctionofSpeed...... 62 6.1.2 EﬀectofCoolingAirFlow...... 64 6.1.3 Eﬀect of Runner Surface Finish ...... 66 6.1.4 ImpactofTopFoilCoating...... 67 6.2NumericalPredictionofLoadCapacity...... 70 6.3 General Observations...... 74 References...... 76

7 Compressibility Number and Film Thickness 77 7.1 Compressibility Number ...... 78 7.2 Film Thickness ...... 83 7.3 Relative Eﬀects of Thermal Management and Runner Surface Finish . 89 References...... 91

8 Physics of Thermal Management 92 8.1 Impacts of Runner Heat Transfer ...... 93 8.2MeasurementofBearingTemperatureGradients...... 97 8.3 Impact of Runner Convective Heat Transfer on Bearing Temperature Gradients...... 100 8.4 Runner Material Eﬀects ...... 104 References...... 106

9 Summary and Conclusions 108 9.1SummaryofResults...... 108 9.2Conclusions...... 110 9.3ImplicationsandFutureWork...... 111

iv A Discussion of Error 114

B Derivation of Characteristic Gas Film Parameters 117

C Runner Design Limitations 121

D Raw Experimental Data 126

Bibliography 132

v List of Tables

4.1 Test Bearing Parameters ...... 34 4.2 Material Properties of Test Runner Materials at 20◦C .... 37

8.1 Rotating Disk Convection Correlations ...... 101

vi List of Figures

1.1 Photographs of Modern Foil Bearings ...... 2 1.2 Disassembled Air Cycle Machine from a B-2 Aircraft ..... 3 1.3 Diagram of a Notional Closed Brayton Cycle Rotor ...... 4 1.4 Cross Sectional View of PS304 Solid Lubricant Coating ... 6

2.1 Examples of Rigid Thrust Bearing Geometries ...... 12 2.2 Cross Section of a Generation III Foil Journal Bearing .... 13 2.3 First Appearance of Bump Foil Type Thrust Bearing in Patent Literature ...... 15 2.4 Modern High Load Capacity Foil Thrust Bearing ...... 15

3.1 Exaggerated Cross Sectional View of Gas Film Control Volume 22 3.2 Deformed Top Foil Shape Under Hydrodynamic Pressure .. 25

4.1 Cutaway View of the Rotating Section of the High Speed Foil Thrust Bearing Test Rig ...... 27 4.2 Thrust Bearing Test Rig Loader Section ...... 28 4.3 Diagram of Thrust Bearing Loading Mechanism ...... 29 4.4 Thrust Bearing Test Rig Torque Measurement System .... 29 4.5 Photograph of Pneumatic Loading Arrangement ...... 30 4.6 Test Thrust Runner ...... 32 4.7 Photographs of Test Thrust Runner Surfaces ...... 33 4.8 Photographs of Test Thrust Bearings ...... 35 4.9 Sketch of Runner Assembly with Aluminum Annulus ..... 36 4.10 Time Trace of Typical Load Capacity Test ...... 40 4.11 Photograph of Optical Proﬁlometer ...... 40 4.12 Thrust Bearing Thermocouple Instrumentation ...... 43 4.13 Foil Wear Scar Due to Tack Weld Distortions ...... 43

5.1 Torque Versus Load From 25-55 krpm ...... 49 5.2 Power Loss Versus Load From 25-55 krpm ...... 50

vii 5.3 Bearing Torque vs Load with Chromium-Coated Runner and Cooling Flow ...... 51 5.4 Bearing Torque vs Load Showing Eﬀect of Runner Surface Roughness ...... 52 5.5 Eﬀect of Cooling Flow on Bearing Torque at 55 krpm Against PS304 Surface ...... 54 5.6 Power Loss at Load Capacity for Various Cooling Flow Rates 55 5.7 Comparison of Numerical Predictions of Bearing Torque to Experimental Data at 25krpm ...... 58 5.8 Comparison of Numerical Predictions of Bearing Torque to Experimental Data at 55krpm ...... 59

6.1 Thrust Bearing Load Capacity as a Function of Speed .... 63 6.2 Effect of Cooling Flow on Load Capacity ...... 65 6.3 Effect of Runner Surface Finish on Load Capacity ...... 68 6.4 Failure of Bearing with Uncoated Top Foils ...... 70 6.5 Thrust Bearing Surface Profile After High Load Operation .71 6.6 Comparison of Numerical Predictions of Bearing Load Ca- pacity to Experimental Data ...... 73

7.1 Load versus Compressibility Number at Various Speeds ... 79 7.2 Load Capacity Versus Compressibility Number ...... 80 7.3 High Speed Limit Behavior ...... 82 7.4 Load Versus Compressibility Number for Various Cooling Flow Rates ...... 83 7.5 Film Thickness Versus Load at Various Speeds ...... 85 7.6 Film Thickness near Load Capacity ...... 87 7.7 Film Thickness Versus Load at 25 krpm, 0.52 kg/min ..... 88 7.8 Load Versus Compressibility Number Showing the Eﬀects of Cooling and Runner Surface Roughness ...... 90

8.1 FEA Plot of Runner Axial Deflection due to Through-Thickness Heat Transfer ...... 95 8.2 PhotographofWearScaronBearingInnerRadius ...... 96 8.3 Thermocouple Locations Near Top Foil Trailing Edge ..... 98 8.4 Trailing Edge Temperature Gradients From 25-65 krpm ... 99 8.5 Estimated Convection Coefficient on Runner Backside at 35 krpm ...... 102 8.6 Trailing Edge Temperature Gradients versus Scaled Power Loss103 8.7 Runner Thermal Conductivity Effects on Temperature Dis- tributions ...... 106

viii C.1 Diagrams Showing Various Runner Design Features ...... 124 C.2 FE Model of Runner Face Axial Displacement at 60 krpm . . 125

ix ACKNOWLEDGEMENTS

The author extends his gratitude to Dr. Christopher DellaCorte of the NASA Glenn Research Center for his support and encouragement throughout this course of study. In addition, the author wishes to express his gratitude to Dr. Joseph Prahl of Case Western Reserve University for his counsel over the years, and for serving as the author’s academic advisor throughout his undergraduate and graduate studies. The members of the author’s committee, Dr. Edward White, Dr. Iwan Alexander, and Dr. Robert Mullen are also thanked. The author wishes to thank Dr. Robert Bruckner of NASA for his extensive help with numerical modeling and hydrodynamic analysis, as well as Kevin Radil of the Army Research Laboratory at GRC for his assistance with experimental methods. The author would also like to thank the rest of the members of the Oil-Free Turbo- machinery team of NASA Glenn Research Center for their advice and assistance. In particular, Brian Edmonds is thanked for his tireless effort in overseeing fabrica- tion and modification of experimental hardware. The author would also like to extend his gratitude to Donald Striebing of the Army Research Lab and Victor Lukaszewicz for their help around the lab. Furthermore, the author wishes to thank John Lucero for performing the profilometric analysis. Additionally, the author would like to acknowledge Dr. Hooshang Heshmat of Mohowk Innovative Technology, Inc. and Dr. Giri Agrawal of R&D Dynamics Corporation for supplying the test bearings used in this work. Finally, the author wishes to offer his very sincere appreciation to the National Aeronautics and Space Administration and the Case School of Engineering for gen- erous financial support of this research.

x NOMENCLATURE

Symbol Description h W Heat transfer coefficient, m2K h Gas film thickness, m h∗ Nondimensional gas film thickness, h hi

hc Characteristic (Couette) ﬁlm thickness, m hi Inlet gas ﬁlm thickness, hi k W air Thermal conductivity of air, mK Nu Local Nusselt number, hr kair P Local pressure, Pa P¯ Average load pressure, Pa P ∗ Non-dimensional pressure, P Pa

Pa Inlet pressure, Pa r Local radius, m R Outer radius of runner, m r∗ r Nondimensional radial coordinate, R

ri Inner radius of runner, m Re ωr2 r Rotational Reynolds number based on local radius, ν Re ωR2 R Rotational Reynolds number based on runner outer radius, ν

Retrans Rotational Reynolds number at transition to turbulence

To Experimentally measured bearing torque, Nm u m Circumferential velocity, s y Film thickness coordinate, m 6μωr2 2 Λ Compressibility number, Pah 6μωR2 Λ Characteristic compressibility number, 2 c Pahc

xi μ kg Dynamic viscosity of air, ms μ∗ Nondimensional viscosity, μ μa μ kg a Gas viscosity at inlet, ms ν m2 Kinematic viscosity of air, s ξ ri Bearing radius ratio, R ρ kg Air density, m3 ρ∗ Nondimensional gas density, ρ ρa ρ kg a Inlet gas density, m3

τw Wall shear stress, Pa ω rad Runner rotational speed, s2

xii Factors Inﬂuencing the Performance of Foil Gas Thrust Bearings for Oil-Free Turbomachinery Applications

Abstract

BRIAN DAVID DYKAS

The operating characteristics of foil gas thrust bearings are explored experimentally and analytically to ascertain the physical mechanisms that limit bearing performance. Measurements of bearing power loss and load capacity made in a variety of configurations highlight several important factors which influence performance. Consistent with conventional hydrodynamic theory, surface condition of the foil and surface condition of the runner have a large influence on bearing performance.

Furthermore, active thermal management via cooling air ﬂow and passive thermal management via conduction through the runner have a large inﬂuence.

Thermal eﬀects are shown to be more pronounced at higher loads where gas

film heat generation and resulting thermoelastic distortion are larger, but smooth lubricious surfaces are needed to achieve these loads. With non-optimal surface conditions such as high levels of roughness, it is shown that asperity contact dominates over thermal deformation. This dissertation quantifies the effects of these non-ideal surface conditions on the load capacity of foil thrust bearings.

xiii It is determined that both smooth, low friction surfaces combined with adequate thermal management are necessary to support large loads at high speeds. Further- more, analysis and modeling suggest that enhanced thermal management is possible by optimizing the thermal characteristics of the runner, an approach not yet exploited by the foil bearing community.

xiv Chapter 1

Introduction

Foil gas thrust bearings are self-acting, compliant-surface hydrodynamic bearings which operate on a thin lubricating gas ﬁlm. These bearings are in widespread use in oil-free microturbines and aircraft air cycle machines. While the gas ﬁlm prevents rubbing contact during normal operation, solid lubricants are applied to both foils and runners to prevent wear and galling during startup, shutdown, and overload conditions when sliding contact occurs. Despite their use for decades, theoretical understanding of foil thrust bearings remains incomplete. Models have been developed to predict hydrodynamic performance, but remain largely unvalidated. A major obstacle to improved modeling is a poor understanding of the phenomena that limit thrust foil bearing operation, particularly at high loads and speeds.

1.1 Oil-Free Turbomachinery Applications

The National Aeronautics and Space Administration currently supports a program to research advanced Oil-Free Turbomachinery technology in order to realize

1 improvements in the high speed rotating machinery for aircraft and space vehicles.

This program seeks to replace conventional oil-lubricated rolling element bearings with hydrodynamic foil bearings (Figure 1.1) lubricated by a gaseous working ﬂuid.

Foil bearings have seen service in some high speed turbomachines for several decades. The ﬁrst widespread commerical application of oil-free foil gas bearings was in air cycle machines (ACMs) for aircraft cabin pressurization and circulation in the 1970s1 (see Figure 1.2). Relatively low temperature and narrow operating range of the ACMs allow simple foil bearings with limited load capacity to operate with soft, low temperature polymeric solid lubricants. The beneﬁt of using oil-free foil gas bearings relative to oil-lubricated bearings was maintenance reduction and elimination of contamination of cabin air from oil emissions. Since their introduction, oil-free ACMs have accumulated millions of hours of reliable service, and achieved a mean time between failures (MTBF) in excess of 100,000 hours2.

Since the successful application of oil-free bearing to ACMs, foil bearing technol-

(a) Journal Bearing (b) Thrust Bearing

Figure 1.1: Photographs of Modern Foil Bearings

2 ogy advances have resulted in commercially available turbocompressors3, small gas turbine electrical generators (<100 kW)4, and the successful demonstration of an oil- free diesel truck turbocharger5 and small turbojet engine for a US Navy target drone6.

Auxiliary power units (APUs), gas turbine generators (>200 KW), small turbofan aeroengines, and closed-loop Brayton cycle generators for space nuclear power are all near-term applications for foil bearings enabled by the advancing state of the art.

In the case of typical turbofan aviation engines, studies show that with oil-free technology, total engine weight can be reduced by approximately 15% and engine maintenance lowered by 50%. Bearing temperature and shaft speed limits are increased, allowing for a 20% power density increase and an 8% reduction in direct operating costs7. A recent propulsion system study on a notional 50 passenger regional jet concludes that an improvement of 2.9% in take-oﬀ gross weight (TOGW) and 3.4% in block fuel can be achieved through oil-free engines8.

Figure 1.2: Disassembled Air Cycle Machine from a B-2 Aircraft (photograph reproduced from Agrawal2)

3 In the case of non-terrestrial power generation, the high energy density of nuclear power sources is attractive to spaceﬂight mission designers. Thermoelectric power generation with a nuclear heat source has been used in spacecraft for decades, but does not scale well to the power and eﬃciency requirements of future high-power missions9.

A closed Brayton cycle (CBC) dynamic power conversion concept requires oil-free rotor supports for long endurance. Foil bearings eliminate the problems associated with liquid lubricants including radiation incompatibility and contamination of the working ﬂuid, and will serve as the rotor supports for Brayton cycle space power conversion. Figure 1.3 shows a diagram of a candidate CBC rotor10.

Figure 1.3: Diagram of a Notional Closed Brayton Cycle Rotor

4 1.2 Enabling Technologies

The achievable reductions in weight, complexity, and maintenance that accompany

the use of the process ﬂuid as a lubricant have always been desirable for turboma-

chinery. While foil bearing development was still in its infancy, several unsuccessful

attempts were made at gas bearing supported turbomachines. These attempts failed

largely due to a few key deﬁciencies in gas bearing technology at the time.

The low load capacity of early thrust bearings limited their use to applications

with narrow operating ranges where thrust forces were low, and transient operation

at oﬀ-design conditions might require hydrostatic load sharing. A lack of appropriate

high temperature solid lubricants to reduce friction and wear during sliding contact

at startup and shutdown further hindered foil bearing adoption. Finally, modeling

of gas bearing behavior was mostly limited to simple cases of rigid geometry and

constant lubricant properties, requiring a rather expensive hardware-intensive testing

approach. These deﬁciencies in technology at the time contributed to the abandon-

ment of a United States Air Force project to develop an oil-free APU11. Recently however, these limitations have been partially addressed by industry, academia, and government researchers.

Within the past decade, advances in three key technology areas have resulted in renewed interest in oil-free rotor support systems. Foil air bearings have been developed with much higher load capacity than the previous state-of-the-art, and improved rotordynamic characteristics12. Analytical modeling has advanced with

increased computing power such that advanced numerical modeling can be con-

5 ducted relatively cheaply and quickly. Finally, the NASA-developed PS300 series

of plasma sprayed composite solid lubricant shaft coatings13,14 represents the most recent generation of high temperature, wear resistant solid lubricant coatings for this application (see Figure 1.4). The coatings have endured 100,000 start-stop cycles at temperatures from 93◦C up to 650◦C, representing a lifetime of twice that required for most turbomachinery applications15. Additionally, foil coatings are available to provide additional lubrication during the initial break-in period of turbomachines16,17.

Figure 1.4: Cross Sectional View of PS304 Solid Lubricant Coating

1.3 Present Work

While the advantages of foil bearings in high speed turbomachines have been

determined and feasibility demonstrated, much work remains to characterize bearing

behavior as it relates to system integration. There is currently a wealth of data

6 on foil journal bearing load capacity and rotordynamic characteristics, with work beginning on journal bearing thermal behavior and management. There is, however, comparatively little published data regarding even basic performance characteristics of foil thrust bearings.

Furthermore, the limited experimental data available for foil thrust bearings is provided by bearing manufacturers and is geared toward maximum attainable performance. Designers of next-generation oil-free turbomachinery require a comprehensive characterization of the bearings over a wide range of conditions in order to achieve workable and eﬃcient designs.

Current independent research on foil thrust bearings focuses on quantifying basic mechanisms that govern and limit their performance. Elucidating these phenomena is critical to advance understanding and guide modeling eﬀorts. The investigations presented herein also allow more objective evaluation of bearing design by quantifying the inﬂuence of various factors that are mostly independent of the foil design.

Providing this context will help turbomachinery designers understand the practices of the bearing community and design around their strengths and weaknesses.

With nominal gas film thicknesses on the order of tens of microns, gas bearings are very sensitive to flatness and roughness of the foil and runner surfaces. While compliant bearings provide tolerance to non-ideal runner surfaces, quantitative measurements of misalignment and runner distortion effects on bearing performance have not been reported, and these measurements are very difficult to make. Additionally, while surface roughness and lubricity effects have been studied in foil journal bear- ings17, the same has not been reported for their thrust bearing counterparts. This

7 dissertation quantiﬁes the eﬀect of surface condition (both foil and runner) on the load capacity of foil thrust bearings.

A further focus of study is the characterization of the bearing thermal environment. While bearing torque and power loss are typically less in foil bearings than rolling element bearings, the power loss is far more load-dependent in foil bearings. As a result, the thermal environment is more challenging to characterize over the operating envelope. Whereas heat generated in oil-lubricated bearings can be managed by circulating and cooling the lubricant, air bearings operate with a lubricant that has a much lower heat capacity and is not recirculated and cooled.

Instead, heat is removed through conduction in the support structure and through any net flow of the working fluid through the bearing cavity. With higher resistances to heat transfer, gas bearings are prone to significant temperature gradients within the structural components which can adversely affect performance.

This dissertation investigates and compares thermal management phenomena to the magnitude of surface condition effects. Active flow of cooling air through the bearing foils is compared to passive thermal management achieved through conductive heat transfer design. Thermal effects are shown to be more pronounced at higher loads where gas film heat generation and resulting thermoelastic distortion are larger, but smooth lubricious surfaces are needed to achieve these loads. With non-optimal surface conditions including large roughness, it is shown that asperity contact dominates over thermal deformation. In that case, thermal management techniques are shown to have a lesser effect on bearing performance.

In this dissertation, the limiting factors for thrust foil bearings, namely surface

8 condition and thermal management, are investigated. Experimental results are compared with existing theory and analysis. It is anticipated that this characterization eﬀort will provide valuable guidance for the successful implementation of foil gas bearings to future more demanding oil-free turbomachinery systems.

References

[1] Agrawal, G., 1990. “Foil Gas Bearings for Turbomachinery”. In 20th Intersociety Conference on Environmental Systems, no. SAE Paper 901236, Society of Automotive Engineers.

[2] Agrawal, G. L., 1997. “Foil Air/Gas Bearing Technology An Overview”. In International Gas Turbine and Aerospace Congress and Exhibition, no. ASME paper 97-GT-347, American Society of Mechanical Engineers.

[3] Mohawk Innovative Technology, Inc., 2005. High-Speed, Oil-Free, Motorized Spindle. Press Release, January.

[4] Capstone MicroTurbine Corporation, 2000. Capstone Turbine Ships New Microturbine Product; New Capstone 60 Power System Generates Twice the Electricity of Current Models. Press Release.

[5] Heshmat, C., Heshmat, H., Valco, M. J., Radil, K., and DellaCorte, C., 2005. “Foil Bearings Makes Oil-Free Turbocharger Possible”. In Proceedings of WTC2005, World Tribology Congress III, no. WTC2005-63724, American Society of Mechanical Engineers/Society of Tribologists and Lubrication Engineers.

[6] Mohawk Innovative Technology, Inc., 2002. WJ24-8 Turbojet Engine Demonstration Testing with Air Foil Bearing. Press Release, December.

[7] DellaCorte, C., and Pinkus, O., 2000. Tribological Limitations in Gas Turbine Engines: A Workshop to Identify the Challenges and Set Future Directions. NASA TM 2000-210059, National Aeronautics and Space Administration, Cleveland, OH.

[8] Bruckner, R. J., 2004. A Propulsion System Analysis of Oil Free Turbomachinery for Aviation Turbofan Engines. AIAA 2004-4189, American Institute of Aeronautics and Astronautics, Reston, VA.

9 [9] Mason, L. S., 1999. Surface Nuclear Power for Human Mars Missions. NASA TM 1999-208894, National Aeronautics and Space Administration, Cleveland, OH.

[10] Howard, S. A., and DellaCorte, C., 2006. Gas Foil Bearings for Space Propulsion Nuclear Electric Power Generation. NASA-TM 2006-214115, National Aeronautics and Space Administration, Cleveland, OH.

[11] Suriano, F. J., 1981. Gas Foil Development Program; Final Report. AFWAL-TR 81-2095, Air Force Wright Aeronautical Laboratories, Dayton, Ohio.

[12] Heshmat, H., 1994. “Advancements in the Performance of Aerodynamic Foil Journal Bearings: High Speed and Load Capacity”. ASME Journal of Tribology, 116, pp. 287–295.

[13] DellaCorte, C., and Edmonds, B. J., 1995. Preliminary Evaluation of PS300: A New Self-Lubricating High Temperature Composite Coating for Use to 800C. NASA TM 107056, National Aeronautics and Space Administration, Cleveland, OH.

[14] DellaCorte, C., and Edmonds, B. J., 1999. Self-Lubricating Composite Containing Chromium Oxide. U.S. Patent 5,866,518.

[15] DellaCorte, C., Lukaszewicz, V., Valco, M. J., Radil, K., and Heshmat, H., 2000. “Performance and Durability of High Temperature Foil Air Bearings for Oil-Free Turbomachinery”. Tribology Transactions, 43(4), pp. 774–780.

[16] Radil, K. C., and DellaCorte, C., 2001. The Eﬀect of Journal Roughness and Foil Coatings on the Performance of Heavily Loaded Foil Air Bearings. NASA TM 2001-210941, National Aeronautics and Space Administration, Cleveland, OH.

[17] DellaCorte, C., Zaldana, A., and Radil, K. C., 2002. A Systems Approach to the Solid Lubrication of Foil Air Bearings for Oil-Free Turbomachinery. NASA TM 2002-211482, National Aeronautics and Space Administration, Cleveland, OH.

10 Chapter 2

Background of the Art

2.1 Foil Air Bearing Development

The foil gas bearings that enable oil-free turbomachinery systems are compliant, self-acting, hydrodynamic journal and thrust bearings which use ambient air or any other gas as a lubricant. During loaded operation, a very thin ﬁlm of air on the order of

10 μm1 is developed between the bearing foil surface and shaft or thrust runner, which results in no wear during operation2. Compliant foil structures consisting of a smooth top foil supported by an elastic foundation are tolerant to misalignment and distortion as well as allowing for design-tailored stiﬀness and damping characteristics3.They oﬀer improvements over rolling element bearings including higher shaft speed limited only by the burst strength of the rotating hardware, the ability to run from cryogenic temperatures to 650 ◦C (approximately the temperature of high pressure compressor

discharge in SOA gas turbine aeroengines), and low frictional losses. These charac-

teristics enable development of advanced turbomachinery with lower maintenance,

higher eﬃciency and power density, and reduced weight and complexity4.

11 Rigid geometry hydrodynamic bearings using gas as a lubricant have been around for decades, utilizing general designs that mimic oil-lubricated bearings, but with lower load capacity (Figure 2.1). In 1953, Blok and Van Rossum5 ﬁrst coined the term foil bearing to describe a thin cellophane foil, devoid of rigidity, wrapped around a rotating journal, lubricated with oil. They showed that the compliance of the foil surface allowed it to deform in the presence of hydrodynamic pressure, creating a more favorable geometry and increasing the minimum ﬁlm thickness at a given load, reducing torque and enhancing performance.

Figure 2.1: Examples of Rigid Thrust Bearing Geometries6

In the years and decades following the introduction of the foil bearing, new designs for bearings with compliant structures appeared, most focusing on journal bearings which support the shaft laterally and govern the most critical rotordynamic behavior.

Early patents for gas thrust bearings with compliant geometry claim that while foil journal bearings were advancing rapidly due to a geometry inclined to form a lubricating gas ﬁlm between the shaft and bearing, thrust bearings were progressing

12 more slowly due to a diﬃculty in creating an eﬃcient convergent wedge and load

carrying surface7,8.

Bump foil type journal bearings, whose conﬁguration is shown in Figure 2.2, emerged over the years to become the most advanced design available to date9,10.

In this style bearing there are three main components - the top foil, bump foil, and bearing housing. The top foil wraps around the journal, and can be reinforced with stiffener foil(s), outside of which are one or more compliant bump foils, that are contained within a solid bearing housing. The current state of the art designs are described by DellaCorte and Valco11 as Generation III foil bearings, which have stiffness properties that vary along the axial, radial, and circumferential directions in the bearing. Stiffness variation allows for bearings to be made with different stiffness, damping, and load capacity characteristics.

Figure 2.2: Cross Section of a Generation III Foil Journal Bearing

13 In response to the problems reported in foil thrust bearing development, bearings with rigid pads supported on compliant structures were introduced, but were ineffec- tive at light loads and high speeds7,12. Further research on compliant thrust bearings soon resulted in designs employing the bump foil structures that had proven successful in journal bearings. In this first appearance of this type of foil thrust bearing, the foil structure is comprised of a wave spring (bump foil) resting on a nonrotating backing plate. The wave spring supports a thick foil plate, on top of which is a thinner top foil (Figure 2.3). The thinner top foil provides an efficient wedge at low speeds and loads, while the underlying thicker foil supports the top foil and limits foil sag between bumps at high speed and load, where hydrodynamic pressures are higher13.

This load-tailored stiﬀness is notable in that bump foil style journal bearings did not generally include this type of advanced design feature until second generation designs emerged after years of development11.

Current advanced foil thrust bearings generally consist of an annular backing plate, to which a number of sector-shaped pads are tack welded. The pads consist of one or more underlying bump foils and a smooth top foil, between which one or more stiﬀener foils can be placed9. The foils which compose the pads are arranged and shaped so as to form an initial converging wedge with the runner, followed by a comparably ﬂat load carrying section. Nickel-based superalloys such as Inconel X-750 are the current material of choice for these foils due to, for example, their weldability, fatigue resistance, strength and modulus properties at high temperature, and creep resistance. A patent drawing of an advanced foil thrust bearing is shown in Figure

2.4. Other foil thrust bearing arrangements exist, but are not considered in this study.

14 Figure 2.3: First Appearance of Bump Foil Type Thrust Bearing in Patent Literature, adapted from Fortman13

Figure 2.4: Modern High Load Capacity Foil Thrust Bearing, adapted from Heshmat9

15 2.2 Current State of the Art Practices

Until recently, neither advanced thrust bearing hydrodynamic modeling nor high

speed high load test facilities existed to foster the rapid improvement of thrust bearing

design. With the construction of advanced test rigs14,15 and improved hydrodynamic modeling code16, accurate determination of thrust foil bearing performance and behavior is now possible across a wide range of operating conditions.

Over the course of decades of development, thrust bearing designers have come to rely on several methods to increase load capacity. Universally recognized as being critical to successful foil bearing systems are the tribological coatings on both foil and runner. These coatings form a system which must yield a low coefficient of friction, yet withstand high temperatures and exhibit low wear. These systems are often proprietary and not fully described in the open literature, which makes it difficult to evaluate bearing foil designs relative to one another when different tribological systems are employed.

Thrust runner coatings are typically hard, durable coatings with low surface roughness. Thin, dense chromium coatings 5-10 μm thick are common, yielding a surface with average roughness Ra=0.05-0.1 μm, but can only withstand on the order of 5,000-10,000 start-stop cycles and temperatures of 25 - 500◦C. By contrast, NASA- developed PS300 series coatings can withstand over 100,000 start-stop cycles at temperatures of 650◦C or more. However, the plasma spray deposition of PS304 coatings

results in porosity in the coating, with typical surface roughness of Ra=0.2-0.8 μm

after grinding and polishing. Until the coating achieves a lower surface roughness

16 through a break-in wear process, bearing performance can suﬀer signiﬁcantly17.

Foil coatings also play a central role in the load capacity behavior of “Generation I” foil thrust bearings, which are charaterized by simple foil structures with little spatial tailoring of stiffness properties (see DellaCorte and Valco11 for foil journal bearing classification). For the same foil design, tests have shown a remarkable increase in load capacity with the addition of a soft solid lubricant coating on the top foil. When a break-in procedure including low load start-stop cycles and near-load capacity tests at low speed is performed, the foil coating is seen to wear significantly in areas where the bump foil contacts the top foil. With further tests relatively little additional wear occurs, as determined by optical profilometry18. This indicates in addition to

its solid lubricant properties, the abradable nature of the top foil allows the surface

to compensate for foil sag16 at higher hydrodynamic pressures by allowing a more favorable foil geometry to develop through the wear process. As such, foil coatings can have a dramatic eﬀect on load capacity.

Another parameter that is seldom fully reported is the mass flow rate of cooling air forced through the bearing. Most high-load testing of thrust bearings is achieved using some amount of airflow through the bump foil structure to remove heat from the bearing and to reduce temperature gradients and corresponding thermal distortions within the structural elements. While effective at increasing load capacity in a laboratory setting, this practice is undesirable in the integrated system due to increased complexity and reduced thermodynamic efficiency. As a result of this practice, performance data on foil thrust bearings at high speed and high load often require contextual information about the cooling flow rates involved in the test.

17 It is desirable to lessen the need for foil coatings and cooling air as bearings develop. To some degree, the requirement for these techniques may be highly influ- enced by today’s rudimentary thrust foil bearing designs. It is anticipated that the fundamental studies carried out in the present work will improve understanding and enable future designs that lessen or eliminate the needs for cooling flow and sacrificial tribological coatings.

References

[1] Ruscitto, D., McCormick, J., and Gray, S., 1978. Hydrodynamic Air Lubricated Compliant Surface Bearing For an Automotive Gas Turbine Engine I - Journal Bearing Performance. NASA CR 135368, National Aeronautics and Space Administration, Cleveland, OH.

[2] DellaCorte, C., Lukaszewicz, V., Valco, M. J., Radil, K., and Heshmat, H., 2000. “Performance and Durability of High Temperature Foil Air Bearings for Oil-Free Turbomachinery”. Tribology Transactions, 43(4), pp. 774–780.

[3] Heshmat, H., Shapiro, W., and Gray, S., 1981. “Development of Foil Journal Bearings for High Load Capacity and High Speed Whirl Stability”. In Proceedings of the ASLE-ASME Joint Tribology Conference, no. 81-Lub-36, American Society of Lubrication Engineers/American Society of Mechanical Engineers.

[4] DellaCorte, C., and Pinkus, O., 2000. Tribological Limitations in Gas Turbine Engines: A Workshop to Identify the Challenges and Set Future Directions. NASA TM 2000-210059, National Aeronautics and Space Administration, Cleveland, OH.

[5] Blok, H., and vanRossum, J., 1953. “The Foil Bearing - A New Departure in Hydrodynamic Lubrication”. Lubrication Engineering, 9(6), pp. 316–320.

[6] Anderson, W. J., and Bisson, E. E., 1964. Advanced Bearing Technology. NASA- SP 38, National Aeronautics and Space Administration, Washington, D.C.

[7] Nemeth, Z. N., 1977. Experimental Evaluation of Foil-Supported Resilient-Pad Gas-Lubricated Thrust Bearing. NASA TP 1030, National Aeronautics and Space Administration, Cleveland, OH.

18 [8] Etsion, I., 1977. “A Cantilever Mounted Resilient Pad Gas Thrust Bearing”. Journal of Lubrication Technology, 99, pp. 95–100.

[9] Heshmat, H., 1999. High Load Capacity Compliant Foil Hydrodynamic Thrust Bearing. U.S. Patent 5,961,217.

[10] Heshmat, H., 2005. “Major Breakthrough in Load Capacity, Speed and Operating Temperature of Foil Thrust Bearings”. In Proceedings of WTC2005, World Tribology Congress III, no. WTC2005-63712, American Society of Mechanical Engineers/Society of Tribologists and Lubrication Engineers.

[11] DellaCorte, C., and Valco, M. J., 2000. “Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications”. Tribology Transactions, 43, pp. 795–801.

[12] Nemeth, Z. N., 1979. Operating Characteristics of a Cantilever-Mounted Resilient-Pad Gas-Lubricated Thrust Bearing. NASA TP 1438, National Aeronautics and Space Administration, Cleveland, OH.

[13] Fortmann, W. E., 1978. Dual Wedge Fluid Thrust Bearing Including Wave Spring. U.S. Patent 4,082,375.

[14] Hryniewicz, P., Locke, D., and Heshmat, H., 2003. “New-Generation Development Rigs for Testing High-Speed, Air-Lubricated Thrust Bearings”. Tribology Transactions, 46(4), pp. 556–559.

[15] Bauman, S., 2005. An Oil-Free Thrust Foil Bearing Facility Design, Calibration, and Operation. NASA TM 2005-213568, National Aeronautics and Space Administration, Cleveland, OH.

[16] Bruckner, R. J., 2004. “Simulation and Modeling of the Hydrodynamic, Thermal, and Structural Behavior of Foil Thrust Bearings”. PhD dissertation, Case Western Reserve University, Cleveland, OH.

[17] Radil, K. C., and DellaCorte, C., 2001. The Eﬀect of Journal Roughness and Foil Coatings on the Performance of Heavily Loaded Foil Air Bearings. NASA TM 2001-210941, National Aeronautics and Space Administration, Cleveland, OH.

[18] Lucero, J., 2006. Measured Foil Frequencies and Mode Shapes as a Function of Wear for a Gas Foil Thrust Bearing. NASA-TM (to be published), National Aeronautics and Space Administration, Cleveland, OH.

19 Chapter 3

Gas Film Characteristics

3.1 Hydrodynamic Features

Gaseous hydrodynamic lubrication is characterized by very thin ﬁlms which stem from the low viscosity of gasses relative to typical liquid lubricants. Gas lubrication is also characterized by compressible ﬂow, and viscosity that increases with, but is less dependent on, temperature than liquid lubricants.

In conventional gas lubrication analysis, the continuity equation and Navier-Stokes equations are scaled and reduced to a compressible form of the Reynolds equation.

The energy equation is often simplified by assuming an isothermal flow. Viscosity and heat capacity are often assumed constant. Traditional assumptions are often appropriate in bounding the behavior of the gas film, but cannot adequately predict behavior near the load capacity of the bearing where the gas film is in distress and near rupture.

The most advanced modeling of foil thrust bearings to date, including a rigorous derivation of the appropriate forms of the governing ﬂuid equations can be found

20 in a dissertation by Bruckner1. That analysis includes the effects of compressibility, density models, viscous heat generation, compliant structure, and temperature dependent fluid properties on the solution of the equations of the gas film.

Surfaces are assumed perfectly flat in numerical models, where real surfaces are characterized by some level of roughness and lubricity. As the film nears load capacity, the thinnest portion of the film may allow localized asperity contact as the bearing transitions to mixed (gaseous and solid) lubrication. This onset of contact generates large amounts of frictional heat due to the large relative surface velocity. This localized severe heating causes thermal expansion distortion of the foil and/or runner surfaces, leading to less favorable geometry (local thinning of film), which further increases localized heating. This type of thermal runaway is suspected to be the general mechanism of foil bearing failure.

3.2 Thermal Behavior

During steady-state operation, the heat generated in the gas ﬁlm must be trans-

ferred out at the same rate that it is generated. This can be illustrated by constructing

a control volume which encloses the gas ﬁlm between the top foil and runner surfaces,

and extending around the periphery of the top foil. Heat transfer occurring at the

boundaries includes conduction into the runner or bearing top foil as well as heat

advected (transport of heat energy in a vector ﬁeld) into and out of the control

volume in the gas flow. In general, gas flows into the film at the leading edge and is

heated due to compression and viscous dissipation from boundary work, then ﬂows

21 out at the trailing edge of the pad or at the sides due to leakage. Due to the thinness of the gas ﬁlm compared to radial and circumferential pad lengths, radiation heat transfer from within the control volume and conduction of heat through the gas at the control volume boundaries can be ignored. Therefore, heat is transported out of the control volume either by conduction into the thrust bearing foil and runner, or by advection of the bulk gas ﬂow, as shown in Figure 3.1.

Figure 3.1: Exaggerated Cross Sectional View of Gas Film Control Volume

The fraction of heat transfer that occurs by either conduction or advection has not been determined, however qualitative statements can be made about the system’s behavior. The bump foil support structure, made of thin metallic foils, effectively insulates the top foil from the bearing backing plate. Almost all heat that conducts into the top foil from the gas film must be removed by the air between the foils and the backing plate by convection. This mode of heat transfer is generally inefficient unless

22 a substantial ﬂow of air at a lower temperature is forced through the foil structure

to enhance convective heat transfer. Since a majority of heat in foil journal bearings

is transferred out of the gas ﬁlm via conduction through the metallic foil and runner

surfaces2, this may also be the case for thrust bearings.

Heat conducted into the thrust runner must be conducted down the shaft, or

removed from the exposed rotating surfaces by convection. The high surface speeds

of the thrust runner result in large Nusselt numbers, so the forced convection on

the runner is rather good considering the range of achievable Nusselt numbers for

convection in air. Since the thermal conductivity of nickel superalloys is poor relative

to many metals, the problem of heat transfer into and through the runner must

consider both the conduction through the runner and the heat transfer coeﬃcients at

the boundaries.

Heat transfer is not currently modeled in foil bearing analysis, but appears to

play a significant role in the bearing performance at high speeds and loads3.Itis anticipated that future foil bearing analysis codes will begin to address this effect as experimental efforts map and characterize the thermal behavior of foil bearings. The present work investigates the effect of cooling on bearing performance, and begins to examine potential alternate methods of thermal management. Continuing research is beginning to investigate heat transfer out of the gas film and in the runner, which will provide a better understanding of the thermal limit in foil thrust bearings.

23 3.3 Structural Response and Eﬀects

The elastic nature of the thrust pad support structure gives the top foil some

compliance, which makes the bearing tolerant to misalignment and distortion of the

runner surface. This compliant surface also allows the bearing to run at higher loads

with thicker ﬁlm thicknesses than its rigid counterpart4.

Although compliance of the bearing surface is desirable for these various operational concerns, it complicates analysis. Since the gas film typically has a thickness on the order of tens of microns, very small distortions of the top foil or runner surfaces can have large effects on the gas film pressure distribution. This stiff coupling between the hydrodynamic and structural governing equations presents a challenge for the convergence of numerical models. Figure 3.2 shows a calculated top foil shape under hydrodynamic pressure1.

Additionally, heat transfer in the bearing and runner can cause thermoelastic distortions that exceed the nominal film thickness. This warping of the film boundaries can significantly alter the film thickness and pressure distributions in the bearing and influence load capacity. Modeling of structural heat transfer and the resulting deflections is currently limited to qualitative reasoning and rudimentary analysis due to large uncertainty in the thermal boundary conditions. The present work begins to characterize the heat transfer paths in thrust foil bearings with thermocouple instrumentation that will aid in the development and validation of numerical modeling which includes thermal effects.

24 Figure 3.2: Deformed Top Foil Shape Under Hydrodynamic Pressure, as calculated by Bruckner1

References

[1] Bruckner, R. J., 2004. “Simulation and Modeling of the Hydrodynamic, Thermal, and Structural Behavior of Foil Thrust Bearings”. PhD dissertation, Case Western Reserve University, Cleveland, OH.

[2] Salehi, M., Swanson, E., and Heshmat, H., 2000. “Thermal Features of Compliant Foil Bearings - Theory and Experiments”. In Joint Tribology Conference, no. 2000-TRIB-38, American Society of Mechanical Engineers/Society of Tribologists and Lubrication Engineers.

[3] Dykas, B., DellaCorte, C., Prahl, J., and Bruckner, R., 2006. “Thermal Management Phenomena in Foil Gas Thrust Bearings”. In Proceedings of Turbo Expo 2006: Power for Land, Sea, and Air, no. 2006-91268, American Society of Mechanical Engineers.

[4] Heshmat, H., Walowit, J. A., and Pinkus, O., 1983. “Analysis of Gas Lubricated Compliant Thrust Bearings”. ASME Journal of Lubrication Technology, 105, pp. 638–646.

25 Chapter 4

Methods

4.1 Experimental Methods

Because of the relatively complex interactions of the structural, thermal, and ﬂuid governing equations, modeling of foil bearings is a nontrivial task. Experimental data is needed on many fronts to guide and validate modeling eﬀorts in order to understand and predict foil bearing performance. The present work relies heavily on experimental data in the development of theories regarding the physical mechanisms that govern bearing performance.

4.1.1 Thrust Bearing Test Rig

Testing of foil thrust bearings for the current work is done on a high speed thrust bearing test rig at NASA Glenn Research Center which is described by Hryniewicz et al.1 and Bauman2. This newest generation test rig consists of a turbine-driven rotating shaft supported radially on foil journal bearings, with a magnetic thrust bearing to maintain axial position (Figure 4.1). A test thrust runner is bolted to the

26 shaft at the end opposite of the turbine. This oil-free shaft support system allows the rig to operate at speeds up to 80,000 rpm while supporting an axial load of up to

3100 N (700 lbs). In one conﬁguration, the test bearing can also be run at elevated chamber temperatures to 540◦C (1000◦F).

Figure 4.1: Cutaway View of the Rotating Section of the High Speed Foil Thrust Bearing Test Rig

A separate, non-rotating section of the rig, shown in Figs. 4.2, 4.3, was designed to load the test thrust bearing against the runner, while measuring bearing torque to within about 15% accuracy. As a major requirement, it is designed to allow access to the test bearing and runner for the measurement of temperatures and runner distortion. At the heart of the loader section, a test thrust bearing is mounted to a

16mm diameter hardened steel shaft supported by a pair of linear ball bearings to permit rotation and axial translation. With the thrust bearing mounted to this small diameter, linear bearing supported shaft, the resistance to rotation is small, such that

27 torque can be measured by a 250 gram force LVDT load cell attached to a torque arm

extending radially outward from the shaft (Figure 4.4). A pneumatic bellows-type

actuator loads the shaft through a ball contact on a pivoted arm (Figure 4.5). Due to care in aligning the ball contact with the center of the shaft, tests of repeatability and accuracy indicate that this method of measuring torque is suﬃcient for the required tests.

Figure 4.2: Thrust Bearing Test Rig Loader Section

The test rig shaft position is monitored by a displacement probe and serves as

a feedback for the magnetic bearing control system. Since the test bearing load is

applied through a mechanical/pneumatic system and not through a similar actively

controlled position system, the complex dynamic interactions of the test rig shaft

and test bearing shaft result in adverse rotor dynamics (large amplitude axial vi-

brations) at some operating conditions which precludes obtaining test data in this

28 Figure 4.3: Diagram of Thrust Bearing Loading Mechanism

Figure 4.4: Thrust Bearing Test Rig Torque Measurement System

29 Figure 4.5: Photograph of Pneumatic Loading Arrangement range of operation. Torque data is not given for conditions where this increased axial displacement is present. The minimum speed tested is 25 krpm, below which it is diﬃcult to maintain a constant shaft speed and some rig dynamic complications are present.

Shaft speed, bearing torque, and bearing load signals are acquired and recorded throughout these tests, along with additional bearing instrumentation such as thermocouples in the case of temperature testing. Various test rig operational parameters are also recorded. Tests are generally performed at a constant speed while varying axial load. Although speeds to 80 krpm are attainable, test speeds in most cases are limited to 55-65 krpm to reduce the probability of severe bearing damage when loaded to near capacity.

When using cooling air ﬂowing through the bearing foils, the cavity pressure in

30 the center of the thrust bearing is measured, as the increased pressure has the eﬀect

of hydrostatically unloading the test bearing. A correlation between cavity pressure

and hydrostatic unloading force is given by Bauman2, and used in this work to correct

for this eﬀect, where the cavity pressure is dependent on speed, cooling ﬂow rate, and

load. Measured cavity pressures approached 35 kPa (gauge) at the highest ﬂow rates

and loads.

4.1.2 Test Specimens

Thrust Runners

The basic thrust runner design for these tests is described as a central hub, extending radially out from which is an annular disk. The outer diameter of the hub section is 4.29 cm, and the outer diameter of the disk is 10.16 cm. A small

(14 mm diameter by 25 mm long) cylindrical protrusion extends from the hub and

ﬁts into a radially centered hole in the test rig shaft to ensure radially concentric positioning of the runner with respect to the shaft rotational axis. This is critical to attain a well balanced rotating group as the runners are component balanced independent of other rig hardware. The runner is bolted to the shaft through the hub (Figure 4.1), allowing for its removal and replacement with another specimen.

This basic runner conﬁguration is shown in Figure 4.6. The standard test runner for this research is constructed from Inconel 718, a nickel-based superalloy chosen for its high temperature strength. The annular disk portion of the runner has a nominal thickness of 1.27 cm and is coated on the bearing surface with a 250 μm thick PS3043

solid lubricant coating. The coating is plasma sprayed onto the runner surface and

31 Figure 4.6: Test Thrust Runner

ground to the desired thickness.

The plasma spray process is responsible for some porosity in the coating, leading

4 to an as-ground surface roughness of 0.2 - 0.8 μmRa . To achieve a better running

surface, a colloidal form of molybdenum disulfide (MoS2) in alcohol is sprayed onto the surface and then burnished to achieve a smooth glossy finish. This procedure is recommended by DellaCorte et al.5 as an overlay for the break-in of PS304-coated shafts for foil journal bearings, but its effectiveness is less apparent when used on a thrust runner.

Since thrust bearings run against unbroken-in PS304 coatings demonstrate a lower load capacity than when run against smoother chrome coatings, test data is taken using a standard runner with a thin dense chrome (TDC) coating rather than the baseline PS304. The chrome coating gives a smoother surface and results in

32 signiﬁcantly higher load capacity. However, the chrome coating is not as durable

as, and is more prone to heat checking (ﬁne cracks) than, the PS304. Because

of this, the chrome coating may be more typical of laboratory tests than high-

performance turbomachinery conditions, where high temperature capability and long life are necessary. Photographs of both the PS304 and thin dense chrome coated runners are given in Figure 4.7.

Surface roughness of the test thrust runners is measured using a contacting stylus- type surface proﬁler. Six 4 mm long radial scans were taken at various locations on each runner, and the Ra values for the scans were averaged. The thin dense chrome

coating roughness was measured to be Ra = 0.077 μm with a standard deviation of

σ = 0.012 μm. The “as-ground” post-test PS304 coating roughness was measured to

be Ra = 0.481 μm with a standard deviation of σ = 0.195 μm.

(a) PS304/MoS2-Coated Runner (b) Chrome-Coated Runner

Figure 4.7: Photographs of Test Thrust Runner Surfaces after being run in tests of bearing load capacity.

33 Parameter Bearing A Bearing B U.S. Patent 4,277,1116 4,462,7007 Inner Diameter 4.65 cm 4.62 cm Outer Diameter 9.02 cm 8.97 cm Pad Angular Extent 42◦ 41◦ Single Pad Area 5.47 cm2 5.28 cm2 Number of Pads 8 8 Total Pad Area 43.8 cm2 42.2 cm2 Top Foil Coating KorolonTM,8 800 PTFE

Table 4.1: Test Bearing Parameters

Thrust Bearings

Due to high specimen costs and limited availability, it is only possible to test a relatively small sample of different thrust bearings, which can vary in size, foil design, and foil coating thickness/composition. In this study, bearings are selected from two different manufacturers in the same size class. The top foil dimensions (inner radius, outer radius, and angular extent) are almost identical, but the design of the underlying bump foil structure and the top foil coatings differ between the bearings.

Table 4.1 lists relevant bearing parameters for the two test bearing types on which a bulk of the tests are performed. Figure 4.8 shows photographs of the two basic test bearing configurations. It should be noted that in this figure, bearing B has been run to high load while bearing A is shown in its unrun condition. The different conditions are unintentional, a consequence of limited available photographs.

34 4.1.3 Cooling Techniques

Thermal management, suspected to have a large inﬂuence on bearing behavior, is investigated in a rudimentary manner by selecting two methods of “cooling” for evaluation. A PS304-coated, standard Inconel 718 runner without any forced cooling air ﬂow is taken as the baseline “uncooled” case.

To simulate an active cooling method consistent with industry practices, air is forced through the bump foil structure from the inner diameter of the bearing and exhausting from the outer diameter. Cooling ﬂow rate is varied from 0 to 0.52 kg/min, with the hydrostatic unloading eﬀect of this method corrected for.

An alternative method of thermal management is a passive method relying on increased thermal conductivity of the runner to remove heat from the gas ﬁlm. In this case, the annular disk portion of the runner is constructed from an alloyed aluminum

(7075-T6) pressed onto an Inconel 718 hub. The aluminum has an order of magnitude

(a) Bearing A - never run, Au-coated (b) Bearing B - post-test, Au-coated

Figure 4.8: Photographs of Test Thrust Bearings

35 larger thermal conductivity, and a slightly lower thickness of 0.95 cm. A sketch of

the runner assembly is given in Figure 4.9. A comparison of the material properties

of Inconel 718 and 7075-T6 aluminum9 is given in Table 4.2. This runner has a

PS304/MoS2 coating with similar surface roughness to the baseline PS304-coated runner.

Figure 4.9: Sketch of Runner Assembly with Aluminum Annulus

4.1.4 Operating Torque and Power Loss Measurements

In order to characterize the thermal behavior of the thrust bearings and runners,

the bearing power loss (i.e. heat generation) must be determined for a wide range of

operating conditions. This is accomplished by directly measuring the torque on the

non-rotating bearing over the ranges of load and speed expected in turbomachinery

applications. Power loss is determined simply by multiplying the measured bearing

torque by the rotational speed of the shaft.

36 Property Inconel 718 Aluminum 7075-T6 Young’s Modulus (GPa) 200 71 Yield Strength (MPa) 1185 503 kg Density ( m3 ) 8220 2800 Poisson’s Ratio 0.29 0.33 W Thermal Conductivity ( m◦C ) 11.4 130 × −6 m Thermal Expansion Coeﬃcient ( 10 m◦C ) 12.1 21.6 J Speciﬁc Heat Capacity ( kg◦C ) 430 960

Table 4.2: Material Properties of Test Runner Materials at 20◦C9

The baseline power loss data is collected by incrementally increasing the load at constant speed until reaching a predeﬁned upper limit (typically 75-100% of load capacity, determined by a priori knowledge of the bearing limits). Load is generally held for two minutes or more to allow transient thermal phenomena to subside in the bearing/runner system. At low loads the torque tends to reach its steady state value immediately, while at loads nearer to the capacity of the bearing, the torque trace may exhibit settling times that can exceed a few minutes. These load increments are held longer to allow the torque to settle before recording the “steady state” value.

This process is repeated at various speeds of interest to obtain a family of curves depicting bearing power loss. Since cooling techniques can aﬀect the operating torque at a given set of conditions by changing the thermoelastic distortions and resulting

ﬁlm thickness distribution, power loss curves must be measured with each cooling condition and compared to the baseline case.

Although the experimentally measured bearing torque describes only the aggregate gas ﬁlm behavior and does not provide information on local ﬁlm characteristics,

37 a great deal of insight can be gained from these data. If a constant film thickness is assumed, bearing torque can be used to determine the characteristic film thickness and compressibility number, which are useful in analysis of the gas film. Appendix B gives a description of this analysis technique along with a derivation of these quantities.

4.1.5 Load Capacity Testing

Tests of load capacity are performed by incrementally increasing the bearing load at a constant speed, allowing one to two minutes of dwell time between successive load increments. This dwell time is consistent with the amount of time required for foil temperature gradients to approach steady state, and is characteristic of torque trace settling times. At loads close to the bearing capacity, the torque signal becomes noticeably erratic and more time between load intervals is allowed. This process attempts to capture steady state load capacity behavior.

Load capacity is reached when rapid increases in the torque signal occur with little or no additional load. With near-capacity operation characterized by unsteady torque and intermittent asperity contact, there is a signiﬁcant degree of variability in the measured load capacity (±5% or more). A data trace from a typical load capacity test is given in Figure 4.10.

4.1.6 Wear Measurements

In order to analyze wear of the foil coatings resulting from operation, an optical proﬁlometry system is used. The NewView 5000, manufactured by Zygo Corporation of Middleﬁeld, CT, uses scanning white light interferometry to image and measure

38 the top foil topography (see Figure 4.11) in post-test inspections.

Light directed through the microscope is split within an interferometric objective

(lens). One portion is reflected off a highly polished internal reference surface in the objective and the other is reflected off the part to be measured. The resulting fringes are analyzed to determine the surface topography of the part. Depths up to

100 μm can be imaged with 0.1 nm vertical resolution and 0.4 nm root mean square repeatability, regardless of objective magnification. Lateral resolution, which depends on the field of view of the objective in use, ranges from 0.45 μm at 100x magnification to 11.8 μm at 1x magnification.

Multiple scans of parts up to 13 cm in diameter can be stitched together to form a topographic image of the whole part. This procedure is used to produce the surface proﬁles of individual bearing top foils, which shows top foil coating wear from high- load operation. A detailed description of these thrust bearing wear measurements is given by Lucero10.

4.1.7 Bearing Temperature Measurement

The temperature field within the gas film is of interest to researchers in order to characterize the heat transfer where the heat is generated and temperatures are highest. Direct temperature measurements within the gas film would be difficult, if not impossible, due to its thinness. Therefore, representative measurements of film temperatures must be made by instrumenting the bearing foils or runner as close to the gas film as possible. Within the bearing, temperatures of the top foil are the most representative of gas film temperatures as it is the immediate boundary of the film

39 100 350 Speed 90 Torque 300 Load 80

70 250

60 200

150 Load (N) 40

30 100 Speed (krpm), Torque (N*mm) 20 50 10

0 0 0 1020304050 Elapsed Time (minutes)

Figure 4.10: Time Trace of Typical Load Capacity Test

Figure 4.11: Photograph of Optical Proﬁlometer

40 and has limited thermal conduction.

Due to the complex and relatively thin nature of the bearing foil structure, instrumentation of the foils is made diﬃcult by the requirement that this not deform the foils or interfere with the designed operation of the bearing. The bump foil support structure limits access to the top foil, so an alternate approach is to attach a thermocouple to a bump foil that is in contact with the top foil. Radil and Zeszotek11 used this method to measure foil temperatures in compliant journal bearings. They routed a thermocouple through an access hole in the bearing shell and tack-welded the junction to the backside of a bump at a point where it was in immediate contact with the top foil.

Although thrust bearings have different geometry, they can be instrumented in the same manner, as shown in Figure 4.12. A hole is made through the bearing plate by first drilling most of the way through the plate, finishing the hole using electric discharge machining (EDM). A thin flexible forty gauge (0.076 mm diameter), type

K, polymer-sheathed thermocouple wire is fed through the hole and the junction is attached to the backside of the bump foil where it is in direct contact with the top foil. Whereas the thermocouple junctions in Radil and Zeszotek’s test bearings were tack-welded to the bump foil, for this work they will be attached with a thermally conductive epoxy. Initial tests with tack welded thermocouples showed that highly localized foil distortions often occurred which had an adverse eﬀect on bearing performance, as was primarily evidenced by wear scars at the thermocouple locations

(Figure 4.13). The epoxy chosen has high thermal conductivity but is only rated to a temperature of 260◦C (500◦F). Although this temperature limit restricts testing to

41 low ambient temperatures, it represents a more reliable, non-intrusive instrumentation method for foil thrust bearings.

Thermocouple-instrumented thrust bearings are first used to provide baseline data on characteristic temperatures and temperature gradients within the bearing at various operating conditions. Bearing size and instrumentation techniques limit the number of thermocouples per pad to a maximum of about three to five. These can be arranged to provide information on temperature gradients of interest, such as radial gradients at a given angular location. The effectiveness of thermal management techniques is evaluated based on the reduction of temperature gradients and efficiency of heat removal. Those thermal management techniques investigated include active cooling, such as blowing air through the bearing, and passive cooling methods, such as runner assemblies with high thermal conductivity components.

4.2 Numerical Techniques

Because hardware-intensive approaches to foil bearing development are costly and time consuming, analytical and numerical methods to accurately predict bearing performance are desirable to reduce development costs. Although this study is largely experimental, two numerical techniques are employed to corroborate observations of foil thrust bearing operational characteristics. Finite diﬀerence (FD)-based hydrodynamic modeling and ﬁnite element (FE) structural modeling both support experimental observations.

42 Figure 4.12: Thrust Bearing Thermocouple Instrumentation

Figure 4.13: Foil Wear Scar Due to Tack Weld Distortions

43 4.2.1 Hydrodynamic Modeling

Numerical simulations of bearing operation to determine torque and load capacity

behavior are obtained using the the equations, methods, and codes described by

Bruckner12. His general thrust foil bearing model includes a total of nine unknowns, which include the three scalar velocity components, pressure, temperature, density, viscosity, speciﬁc heat capacity, and structural deﬂection.

A scaling analysis employing the traditional assumptions of hydrodynamic thin

ﬁlms permits the elimination of the three velocity components and associated momentum equations. Furthermore, for the purpose of simplifying the eﬀects present in the model, an isothermal assumption is made which eliminates the need to solve the energy equation. The heat capacity and viscosity relationships, which were assumed in the general model to be functions of temperature only, can be set as constants (equal to unity when expressed in nondimensional terms) with the isothermal assumption.

The three remaining variables are the gas pressure and density, and the structural deﬂection. The system of equations which allows for the solution of these variables consists of the compressible Reynolds equation, an equation of state, and a structural model. Under the isothermal conditions assumed, the ideal gas equation of state allows the nondimensional pressure to be set equal to the nondimensional density. As such, the Reynolds equation and structural model may be solved for the pressure and

ﬁlm thickness distribution.

The structural model used consists of a bending-dominated top foil reinforced by a supporting bump foil structure. The bump foil structure is modeled as a set of

44 discrete bumps with an aggregate stiﬀness equal to that of a test bearing. This model

permits the mechanism of foil sag between bumps to be shown in the deformed top

foil shape, within the limits inherent to a bending-dominated top foil model. Further

detail of this structural model is given by Bruckner12.

The exact foil thicknesses and other geometric details of the test bearings are not given here, as they may be considered proprietary. However, a cursory review of the patent literature shows that foil thicknesses on the order of 0.1mm are typical. The numerical results presented herein are based on the actual (measured) geometry of the test bearings in order to closely approximate the deformation behavior. They are intended to demonstrate that this previously developed code is validated by the experimental data now available.

4.2.2 Modeling of Structural Deformation

In order to examine the ﬂatness of the runner surface against which the bearing

operates, mechanical and thermal stresses are modeled in a commercially available

ﬁnite element (FE) analysis software. A three dimensional model of a standard thrust

runner is created as an input to an automatic meshing routine, which generates a close

representation of the runner geometry with linear tetrahedral elements. Material

properties for Inconel 718 at 25◦C, shown in Table 4.2, are used.

The model is constrained by fixing the cylindrical outer surface of the cylindrical protrusion to prevent nodal displacement axially or circumferentially. Radial growth is not restrained however, and since the portion of the runner in which deflections are of interest is sufficiently far away from the static constraint, the difference between

45 this imposed constraint and the physical system has a vanishingly small impact on the displacements of interest. Centrifugal loads are applied to the model and a static analysis is run to determine resulting displacements.

Thermal modeling assumes all exposed faces of the runner are insulated unless another boundary condition is imposed. Boundary conditions applied in this work are speciﬁed heat ﬂux (Neumann) and Newton’s law of cooling (Robin) conditions.

Heat flux is specified at the bearing running surface on the front of the runner and a convection condition is applied to the rear, exposed face. For convective heat transfer on the back face, a constant, average assumed convection coefficient is imposed, leading to a purely axial heat flux in the case of an axisymmetric runner with an insulated outer rim.

To determine the runner thermoelastic behavior, the temperature distribution is used as an input to a static analysis of runner stress and displacement, with the temperature of the backside of the runner is used as a reference for zero thermal strain. Displacement plots for mechanical, thermoelastic, or combined stresses can be generated in parametric studies of runner behavior at various operating conditions

References

[1] Hryniewicz, P., Locke, D., and Heshmat, H., 2003. “New-Generation Development Rigs for Testing High-Speed, Air-Lubricated Thrust Bearings”. Tribology Transactions, 46(4), pp. 556–559.

[2] Bauman, S., 2005. An Oil-Free Thrust Foil Bearing Facility Design, Calibration, and Operation. NASA TM 2005-213568, National Aeronautics and Space Administration, Cleveland, OH.

46 [3] DellaCorte, C., 1998. The Evaluation of a Modiﬁed Chrome Oxide Based High Temperature Solid Lubricant Coating for Foil Gas Bearings. NASA TM 1998- 208660, National Aeronautics and Space Administration, Cleveland, OH.

[4] Radil, K. C., and DellaCorte, C., 2001. The Eﬀect of Journal Roughness and Foil Coatings on the Performance of Heavily Loaded Foil Air Bearings. NASA TM 2001-210941, National Aeronautics and Space Administration, Cleveland, OH.

[5] DellaCorte, C., Zaldana, A., and Radil, K. C., 2002. A Systems Approach to the Solid Lubrication of Foil Air Bearings for Oil-Free Turbomachinery. NASA TM 2002-211482, National Aeronautics and Space Administration, Cleveland, OH.

[6] Gray, S., and Heshmat, H., 1981. Support Element for Compliant Hydrodynamic Thrust Bearing. U.S. Patent 4,277,111.

[7] Agrawal, G., 1984. Hydrodynamic Fluid Film Thrust Bearing. U.S. Patent 4,462,700.

[8] Heshmat, H., Hryniewicz, P., Walton, J., Willis, J., Jahanmir, S., and DellaCorte, C., 2005. “Low Friction Wear-Resistant Coatings for High- Temperature Foil Bearings”. Tribology International, 38.

[9] Davis, J., ed., 1998. Metals Handbook Desk Edition. ASM International.

[10] Lucero, J., 2006. Measured Foil Frequencies and Mode Shapes as a Function of Wear for a Gas Foil Thrust Bearing. NASA-TM (to be published), National Aeronautics and Space Administration, Cleveland, OH.

[11] Radil, K. C., and Zeszotek, M., 2004. “An Experimental Investigation into the Temperature Proﬁle of a Compliant Foil Air Bearing”. Tribology Transactions, 47(4), pp. 470–479.

[12] Bruckner, R. J., 2004. “Simulation and Modeling of the Hydrodynamic, Thermal, and Structural Behavior of Foil Thrust Bearings”. PhD dissertation, Case Western Reserve University, Cleveland, OH.

47 Chapter 5

Bearing Torque and Power Loss Results

5.1 Experimental Torque/Power Loss Measurements

Bearing torque and power loss are measured over a wide range of operating conditions in the test thrust bearings. A number of factors which aﬀect bearing torque including speed, load, cooling ﬂow rate, and surface conditions are varied and torque measured. The plots of torque and power loss data in this section are single measurements and are plotted without error bars for clarity. Generally speaking the data are very repeatable (±3Nmm). The raw experimental data presented in this section can be found in tabular form in Appendix D.

5.1.1 Bearing Torque versus Speed and Load

Very little foil thrust bearing torque data is available in the open literature over a range of applicable speeds and loads. This lack of information remains a hurdle for turbomachinery designers, who are concerned with the power loss in the bearing and

48 the corresponding eﬀect on thermal management requirements for stable operation.

To look at the eﬀects of speed and load on bearing torque and power loss, bearing

B is tested against an Inconel 718 runner with a PS304/MoS2 surface as described in

Chapter 4, without any cooling air ﬂow. At speeds from 25-55 krpm, the measured bearing torque is given in Figure 5.1, and the corresponding power loss is given in

Figure 5.2, as reported by Dykas et al1. The torque and power loss measurements shown include measurements up to near the measured load capacity as detailed in

Chapter 6.

80 25 krpm 30 krpm 70 35 krpm 40 krpm 45 krpm 60 50 krpm 55 krpm

Torque (N mm) 30

0 0 1020304050607080 Load (kPa)

Figure 5.1: Torque Versus Load From 25-55 krpm of bearing B against a PS304- coated runner, showing that torque generally increases with larger loads and higher speeds. It is notable that the eﬀect of a doubling speed from 25 to 50 krpm has the eﬀect of increasing torque only by about 35%, as measured at approximately 65 kPa.

49 100 25 krpm 90 30 krpm 35 krpm 40 krpm 80 45 krpm 50 krpm 70 55 krpm ) 2

40 Power Loss (kW/m 30

0 0 1020304050607080 Load (kPa)

Figure 5.2: Power Loss Versus Load From 25-55 krpm of bearing B against a PS304-coated runner, showing the same data as in the previous ﬁgure, but multiplying torque by speed to obtain power loss on the ordinate. Power loss is shown to increase with both speed and load.

It can be seen in these plots that for the conditions tested, the bearing torque and power loss are relatively small for low to moderate loads. Power loss on the order of hundreds of watts is typical for this range of operation. The bearing torque and power loss increase with both speed and load, which both tend to increase shear rate within the gas ﬁlm.

Based on tests of load capacity discussed in Chapter 6, the sustainable axial loads using a rougher runner surface without cooling air are somewhat lower than with smoother surfaces and active thermal management. Figure 5.3 shows the eﬀect of

50 speed and load on bearing torque when bearing B is run under more ideal conditions

of surface roughness and thermal management. Again, the torque is given over the

full range of bearing operation, from light loads to near the load capacity for a given

speed. It is notable that with these more ideal surface and thermal conditions, the bearing is able to support signiﬁcantly more load and run at higher rates of heat generation, due to a smaller attainable ﬁlm thickness.

180

25 krpm 160 40 krpm

140

) 120 2

100

Power Loss (kW/m 60

0 0 20 40 60 80 100 120 140 160 Load (kPa)

Figure 5.3: Bearing Power Loss vs Load with Chromium-Coated Runner and Cooling Flow for bearing B, showing the bearing behavior when a smoother runner and active cooling ﬂow are used to allow it to operate with larger axial loads.

51 5.1.2 Eﬀect of Runner Surface Roughness

Bearing torque is measured with both the PS304 and chromium coatings to determine the extent to which the surface roughness aﬀects the torque over the range of average runner surface roughnesses to be expected in a real turbomachine.

Figure 5.4 shows torque versus load for both runner coatings at 25 krpm with 0.52 kg/min of cooling flow. The lower speed and higher cooling flow rate is chosen for this comparison in order to minimize any thermal management effect on the torque curves.

PS304 80 Chromium

40 Torque (N mm) 30

0 0 102030405060708090100 Load (kPa)

Figure 5.4: Bearing Torque vs Load Showing Effect of Runner Surface Roughness, using bearing B at 25 krpm and 0.52 kg/min cooling air flow. Torque vales differ slightly, with the rougher surface showing evidence of less torque than the smoother surface at otherwise identical operating conditions.

52 It is notable that the smoother chromium surface results in a higher bearing torque given the same operating conditions as compared to a PS304-coated bearing.

However, the curves are obtained from two bearings of identical design, but the operation of each may differ slightly. As a result, any effect that roughness has on performance may be overwhelmed by the variations of the bearings. Since the flow in the gas film is likely laminar due to the thin gap, roughness may be expected to have no noticeable effect on shear stress provided it is small compared to the film thickness.

Although it is diﬃcult to draw a strong conclusion based on this experimental data, it is presented for the sake of completeness.

5.1.3 Eﬀect of Cooling Flow

Since cooling air ﬂow is able to increase load capacity and tolerable rates of heat

generation, it is desirable to determine if varying the cooling ﬂow rate at a given

speed and axial load condition aﬀects the bearing torque. This secondary eﬀect, the

result of cooling eﬀects on ﬁlm thickness distribution and/or viscosity variation, may

be signiﬁcant if wide ranges of cooling ﬂow rates and heat generation are considered.

Figure 5.5 shows the measured bearing torque for bearing B at 55 kprm over a

range of loads and cooling air ﬂows. For the range of cooling ﬂows tested, it appears

that the ﬂow rate does have an eﬀect on bearing torque, but at high loads where heat

generation is largest, this eﬀect is a modest percentage of absolute torque (∼25%).

Figure 5.6 shows the maximum attainable power loss over a speed range from 25-

55 krpm with cooling ﬂow rates up to 0.52 kg/min. A rather large amount of scatter is

present in these data due to erratic torque behavior near the bearing load capacity and

53 70 Cooling Flow Rate 0 kg/min 60 0.17 kg/min 0.35 kg/min

30 Torque (N mm)

0 0 1020304050607080 Load (kPa)

Figure 5.5: Effect of Cooling Flow on Bearing Torque at 55 krpm Against PS304 Surface for bearing B, showing a small effect of cooling air flow on the resulting bearing torque. For a given load, torque appears to decrease as cooling flow is increased.

54 corresponding difficulty getting accurate steady state torque measurement, but this plot shows a general trend of larger attainable heat generation rates with increased speed. The absolute power loss values are relatively small, particularly compared to the values of heat generation in Figure 5.3, owing to unbroken-in PS304 surface used to generate these data. For the flow rates tested, cooling flow does not appear to have a large effect on the maximum sustainable bearing power loss.

100 Cooling Flow Rate

90 0 kg/min 0.17 kg/min 0.35 kg/min 80

70 ) 2 60

40 Power Loss (kW/m 30

0 0 102030405060 Speed (krpm)

Figure 5.6: Power Loss at Load Capacity for Various Cooling Flow Rates for bearing B run against a PS304-coated runner at various speeds. Tolerable power loss near load capacity is shown to increase with speed, but cooling appears to have little eﬀect.

55 5.2 Numerical Predictions of Bearing Torque

Experimental data is used to validate numerical models of the gas film. While standard thin film assumptions are clearly applicable in foil gas bearings, the isothermal assumption noted in Section 4.2.1 may not be appropriate for some or all regions of bearing operation. In physical terms, numerical results presented here represent a highly cooled bearing where any heat generated by compression or dissipation is immediately removed through the gas film boundaries (foil or runner surfaces).

In Figure 5.4, the effect of runner surface roughness was compared for a bearing operating at 25 krpm and with 0.52 kg/min of cooling air flow. Since this speed is the lowest tested in this study, the bearing heat generation is the lowest of any speed, as shown in Figure 5.2. This in conjunction with a relatively large cooling flow rate yields gas film conditions that more closely approximate isothermal conditions than would higher speeds and lower cooling flow rates. Furthermore, the torque data obtained for a runner coated with thin dense chrome more closely approximates the perfectly smooth surfaces assumed in a numerical model.

A numerical analysis of an isothermal bearing operating at 25 krpm is performed over a range of loads, where the deformed foil shape at the previous iteration is used as an input to the subsequent iteration. The bearing torque, pressure distribution, and resulting deflected foil shape are then calculated to determine the load/torque data and a deflected foil shape. At each successive iteration the runner surface is brought slightly closer to the bearing to increase the load. While this iteration scheme does not provide a self-consistent solution at each iteration, sufficiently small steps reduce

56 the bias error in the solution.

Figure 5.7 is a plot of the data which appears in Figure 5.4, along with a numerical calculation of a torque/load curve at 25 krpm. The calculated curve gives torque magnitudes that closely approximate those obtained experimentally with a smooth runner. Agreement between experimental and numerical results is better at moderate bearing loads, where a thrust foil bearing would be designed to operate.

At lower loading, the bearing foils may not have fully seated on the bump foils and manufacturing variations between pads and bearings may have large eﬀects on the measured torque. At higher loading, the eﬀects of foil sag between bumps may not be accurately accounted for in the numerical model. Furthermore, increasing heat generation at higher loads may render the isothermal assumption in the numerical model less valid.

A higher speed simulation of bearing load/torque behavior is calculated at 55 krpm, where heat generation is larger. In this case, the calculated data are plotted against experimentally measured torque curves from a PS304-coated thrust runner with varying amounts of cooling ﬂow (Figure 5.8). Based on the previous ﬁgure, it is expected that the data generated from the numerical study more closely approximates the behavior of a bearing running with a smoother coating. However, limited experimental data with the thin dense chrome-coated runner restricts plotting options.

The isothermal model can be thought of as having a large (tending toward infinite) cooling flow rate, and so it appears that the numerical results continue the trend of decreasing torque with increasing cooling flow rate. In general, this numerical model is able to predict with reasonable accuracy the magnitude and character of the

57 90 Chromium 80 PS304 Numerical

40 Torque (N mm) 30

0 0 102030405060708090100 Load (kPa)

Figure 5.7: Comparison of Numerical Predictions of Bearing Torque to Experimental Data at 25krpm for bearing B operating against both smooth TDC and as-ground PS304 runner surfaces. The numerical simulation shows generally good agreement with the torque magnitude for a bearing operating against a smooth runner surface, particularly at moderate loading conditions.

58 load/torque curves for a simple thrust foil bearing geometry.

70 0 kg/min (Experimental) 0.17 kg/min (Experimental) 60 0.35 kg/min (Experimental) Isothermal (Numerical)

30 Torque (N mm)

0 0 1020304050607080 Load (kPa)

Figure 5.8: Comparison of Numerical Predictions of Bearing Torque to Experimental Data at 55krpm where experimental data is obtained from bearing B running against an as-ground PS304 runner with various cooling ﬂow rates and over a range of loads. The isothermal case studied numerically shows good agreement with the trending evident in the experimental data.

In both Figures 5.7 and 5.8, the plot of torque versus load contains an inflection point at moderate loads. This behavior is not observed in the experimental data, and its exact cause is not fully understood. However, as previously noted, under very lightly loaded conditions where the top foil has not been fully seated in the experimental configuration, the numerical model overpredicts the bump foil support stiffness and may not capture the real film thickness distribution. At higher loads

59 beyond the inflection point, both the experimental and numerical data exhibit positive curvature. As the film thickness decreases at high loads, the amplitude of top foil waviness due to foil sag becomes large relative to the film thickness, and any inadequacies of the structural model can have a large effect on the calculated torque.

Irrespective of the extreme ends of bearing loading, the previously developed model2 appears to predict bearing torque with reasonable accuracy at moderate loads.

References

[1] Dykas, B., DellaCorte, C., Prahl, J., and Bruckner, R., 2006. “Thermal Management Phenomena in Foil Gas Thrust Bearings”. In Proceedings of Turbo Expo 2006: Power for Land, Sea, and Air, no. 2006-91268, American Society of Mechanical Engineers.

[2] Bruckner, R. J., 2004. “Simulation and Modeling of the Hydrodynamic, Thermal, and Structural Behavior of Foil Thrust Bearings”. PhD dissertation, Case Western Reserve University, Cleveland, OH.

60 Chapter 6

Load Capacity Results

Load capacity is a performance metric used to determine the effectiveness of the foil structure in maintaining an adequate gas film. Over the past few years, load capacity has risen with advanced bearing designs1,2 and by employing adequate cooling air and very smooth runner surfaces. Of interest is the effect that cooling has on the load capacity of the bearing, which is an indicator of the importance of thermal management design relative to the physical design of the bearing. Furthermore, since high temperature, durable coatings such as PS304 may require special application and

finishing techniques3 or overlay coatings to achieve highly smooth surface finish at entry into service, it is also necessary to quantify the effect of typical surface finishes on foil thrust bearing performance.

61 6.1 Experimental Measurement of Load Capacity

6.1.1 Load Capacity as a Function of Speed

Until recently, even basic estimates for achievable load capacity in foil bearings

were not readily available to turbomachinery designers. To address this particular

need, DellaCorte and Valco1 proposed a “rule of thumb” model to predict foil journal bearing load capacity. This simple tool matches experimental data well over a wide range of bearing sizes and speeds. Their model predicts a linear relationship between journal speed and load capacity for the speed range of engineering interest. They extended the rule of thumb concept to thrust foil bearings, but their complementary model has not been corroborated due to a lack of suﬃcient experimental data.

Figure 6.1 shows a plot of load capacity versus speed for bearing A running against a PS304-coated runner. The load capacity is given in units of pressure, where the largest supported axial load has been divided by the total top foil area to give an average pressure at capacity. Note that this diﬀers from the bearing swept area based on inner and outer foil diameters by about 10%. Tests are performed from 25-55 krpm

(89-196 m/s runner surface velocity based on mean bearing diameter). Load capacity is not measured below 25 krpm because of test rig operational complications, but it should be noted that the load capacity tends toward zero as the speed is reduced to the liftoﬀ speed of the bearing.

In contrast to the behavior of foil journal bearings in DellaCorte and Valco’s study, this thrust foil bearing does not exhibit a load capacity that increases linearly with speed. The highest recorded load capacity is found to occur at the lowest speed

62 80

30 Load Capacity (kPa)

0 0 102030405060 Speed (krpm)

Figure 6.1: Thrust Bearing Load Capacity as a Function of Speed for bearing B running against a PS304-coated runner in the absence of cooling air ﬂow, showing a decreasing trend in load capacity with increased speed. Load capacity is said to approach zero at zero speed.

63 tested, with the lowest load capacity occurring at the highest speed tested. Load capacity therefore is shown to trend downward with speed over this range when the thrust bearing is run against a PS304-coated runner without any cooling air ﬂow. It has been suspected that this behavior is related to inadequate thermal management of the bearing-runner system.

6.1.2 Eﬀect of Cooling Air Flow

In general, larger loads on the bearing result in a thinner gas film, which in turn leads to increased shear rate. This leads to increased shear stress and more heat generation. Reduced volume of gas in the thinner film results in a lower total heat capacity of the film. The higher temperatures which result tend to increase the viscosity of the gas, which theoretically should increase load capacity. This is in contrast to the temperature dependence of liquid lubricants, which lose effectiveness with increasing temperature due to reduced viscosity.

In practice however, foil bearings do not exhibit higher load capacities if temperature is allowed to increase. Heat transfer within the bearing systems has the undesirable eﬀect of producing thermoelastic distortions within the structural components.

Temperature gradients within the bearing and runner can result in deformations larger than the gas ﬁlm thickness, which is typically on the order of tens of microns or less. These deformations can then lead to local gas ﬁlm rupture as described by

Dykas and Howard4.

The determination of the effect of cooling on load capacity is a first step to understanding the degree to which thermal phenomena influence bearing operation.

64 In this work, cooling air is used ostensibly to reduce structural temperature gradients and the consequent thermoelastic distortion.

Figure 6.2 shows a plot of load capacity versus speed with varying amounts of cooling ﬂow through the bearing. Tests are performed with cooling ﬂow rates of 0,

0.17, 0.35, and 0.52 kg/min against a PS304-coated runner.

120 Cooling Flow Rate 0 kg/min 0.17 kg/min 100 0.35 kg/min 0.52 kg/min

Load Capacity (kPa) 40

0 0 102030405060 Speed (krpm)

Figure 6.2: Effect of Cooling Flow on Load Capacity for bearing B running against a PS304-coated runner with various cooling flow rates. Load capacity is seen to increase with cooling flow rate.

It is shown that at 25 krpm, load capacity is relatively insensitive to cooling

ﬂow rate, indicating that thermal management may not be critical at speeds below this. Diﬀerences in measured load capacity at this speed are within the estimated

65 uncertainty of approximately ±5 kPa. Above 25 krpm however, load capacity is seen

to increase with increasing cooling ﬂow beyond the estimated uncertainty, indicating

that at speeds greater than the lowest tested, thermal management is needed to

achieve the highest possible performance.

Furthermore, it is notable that at each cooling condition, load capacity tends to

ﬂatten or trend downward with increasing speed. This decrease in load capacity with

increasing speed is contrary to current understanding of foil gas bearings. It may be

postulated that this decrease in load capacity is due, at least partly, to the increase

in heat generation and thermoelastic deformation with increasing speed (see Chapter

5 for the eﬀects of speed and load on heat generation). Based on this hypothesis, a

reduction of temperature gradients in the structural elements would yield increased

load capacity, a result which suggests that alternate thermal management methods

including passive structural features may be possible.

6.1.3 Eﬀect of Runner Surface Finish

Since SOA numerical modeling assumes a perfectly smooth runner surface, the

eﬀect of real surfaces on load capacity is of interest. The thin dense chromium coatings

used in laboratory tests typically have surface roughness of Ra = 0.05-0.10 μm, which is small compared to estimated film thicknesses. The unbroken-in PS304 surface by comparison has surface roughnesses of 0.3-0.8μm, closer to the estimated film thicknesses. Quantifying the effect of surface roughness on the load capacity behavior of the bearing is needed to determine the requisite surface condition of production thrust runners.

66 The two runner coatings (PS304 and TDC) are compared in load capacity tests of bearing A with 0.52 kg/min of cooling flow. A cooled configuration is chosen in order to reduce the thermal effects and to lessen the risk of destructive failure. Load capacity of the chromium-coated runner is tested at 25, 35, and 40 krpm, while the

PS304-coated runner is tested only at 25 krpm in this configuration. A plot of load capacity for the two surface roughnesses is given in Figure 6.3. Although the rougher surface is tested at only one speed, the difference in performance can be clearly seen from these data. The load capacity against PS304 at 25 krpm, where cooling air has been shown to have little effect, is only 64% of that when a smooth chromium-coated runner is used. This difference in load capacity of the two runner surfaces is consistent with the results obtained by Radil and DellaCorte5 in foil journal bearings.

6.1.4 Impact of Top Foil Coating

Almost invariably, bearing top foils are coated with a thin (on the order of 25

μm thickness) solid lubricant coating. The addition of this coating is intended to

improve tribological properties from the baseline foil material5. The improved friction coeﬃcient can be veriﬁed in pad-on-disk or equivalent tests. However, it is notable that these foil coatings are typically soft materials which do not exhibit particularly long wear life.

In a series of checkout runs with the test rig described herein, uncoated thrust bearings demonstrated severely limited load capacity relative to their expected performance. Bearings with identical foil design which had a solid lubricant coating applied to the top foil were found to have dramatically higher load capacity in comparison

67 200

Chromium 180 PS304

160

140

120

100

80 Load Capacity (kPa) 60

0 0 5 10 15 20 25 30 35 40 45 Speed (krpm)

Figure 6.3: Effect of Runner Surface Finish on Load Capacity for bearing A running against both PS304 and chromium runner coatings with 0.52 kg/min of cooling air flow. The smoother chromium surface is able to support significantly more load compared to the as-ground PS304 surface.

68 tests. This result underscores the importance of advanced coating systems for bearing

foils.

To explore the function of a thick solid lubricant foil coating, load capacity was

tested in a bearing with a much thinner low friction top foil coating. A bearing

identical to bearing B was subjected to a high temperature environment to burn

oﬀ the foil coating. After the coating was removed, a colloidal form of molybdenum

disulfide (MoS2) in alcohol was sprayed onto the surface and lightly polished. This was done to provide a low friction coefficient in the event of asperity contact or light dry rubbing. The replacement of a comparatively thick (25 μm) solid lubricant coating with a thin (∼3 μm) MoS2 film is significant in that the low friction characteristics

of the foil are retained, but the coating thickness and adhesion to the surface is much

reduced.

A load capacity test was then performed on the bearing at 30 krpm with 0.69

kg/min of cooling air ﬂow. Based on tests of a coated bearing at these conditions,

the expected load capacity was more than twice that at which the uncoated bearing

failed. Figure 6.4 shows the wear scars on the failed bearing. In this photograph the

large, shiny area on the foil in the three o’clock position is unrelated to the failure.

A conclusion drawn from these results is that the foil coating may serve a function

beyond improved lubricity. A low friction foil coating is a necessary but not suﬃcient

condition for maximum performance from a given bearing design. Visual evidence

and proﬁlometric data of coating wear from previous tests suggest that an additional

function of thick (∼25μm) top foil coatings is to provide an abradable surface that,

when run-in, compensates for foil sag between bump foils. A post-test proﬁle of a

69 Figure 6.4: Failure of Bearing with Uncoated Top Foils with wear scars visible toward the inner diameter of the top foils. These scars are most pronounced where the bump foils are in contact with the top foil. bearing that has been highly loaded is given in Figure 6.5.

6.2 Numerical Prediction of Load Capacity

Experimental observations of load capacity behavior in foil thrust bearings show a dependence on speed and cooling flow rate which can be examined further in a numerical model. It is hypothesized that thermoelastic distortions play a role in limiting the bearing load capacity, a theory supported by the increase in capacity with increased cooling flow rate. The tendency for load capacity to decrease with increasing speed (and corresponding increase in heat generation) also supports this theory, and suggests that the bearing requires a larger average film thickness near load capacity when thermoelastic distortions are larger.

70 Figure 6.5: Thrust Bearing Surface Profile After High Load Operation, showing the topography of a top foil coating after being worn by high load testing. A profile along a line extending from the leading edge to the trailing edge as indicated is given in the lower portion of the figure. The deepest wear troughs are located where the bump foils support, and are in contact with, the top foil.

71 Figure 6.6 contains the load capacity data previously shown in Figure 6.2, with the addition of some load versus speed curves generated by a numerical analysis.

The numerical curves are obtained by setting an initial bearing-to-runner spacing at a low speed and increasing speed in small increments, calculating the resulting pressure distribution and foil deﬂection at each step. The hydrodynamic pressure increases with speed, and the foil deﬂects slightly with the increased pressure load.

In this iteration scheme, the film thickness is not exactly constant, but calculations of bearing torque at each iteration enable the calculation of a Couette film thickness that is very nearly constant. This scheme tends to produce a load-speed curve with a slight negative curvature as the structure relaxes to allow increased film thickness at higher speeds.

In order to demonstrate the eﬀect of the ﬁlm thickness on the hydrodynamic bearing load, three initial gaps are set between the bearing and runner, while using the same foil geometry. The load curve obtained using the smaller initial gap yields higher bearing loads in response to the larger contraction ratio. This can be seen in

Figure 6.6, while the curve at lower loads is obtained from a larger initial (low speed)

film thickness. Note that the negative curvature of the curves increases as the film thickness decreases. In addition to the contribution of foil deflection to the curvature, this behavior is consistent with high speed behavior (large compressibility number) in gas bearings.

The nature of the experimental data compared to the numerically-determined load curves supports the theory that thermoelastic distortion has the eﬀect of increasing the required average ﬁlm thickness at load capacity. A family of curves for various

72 120 Experimental (0 kg/min) Experimental (0.17 kg/min) Experimental (0.35 kg/min) Experimental (0.52 kg/min) 100 Numerical (small gap) Numerical (moderate gap) Numerical (large gap)

60 hc = 6.3 Pm Load (kPa)

h = 9.4 Pm 40 c

hc = 12.4 Pm

0 0 102030405060 Speed (krpm)

Figure 6.6: Comparison of Numerical Predictions of Bearing Load Capacity to Experimental Data using experimental data from bearing B and an isothermal numerical model of a simple thrust bearing. The load capacity behavior described by the numerical model is based on an initial prescribed bearing-to-runner gap with speed increased in small increments. Curves based on three diﬀerent initial gaps are given, with the smallest gap giving rise to higher loads due to a larger contraction ratio.

73 average ﬁlm thicknesses can be drawn between the small-gap and large-gap curves

in Figure 6.6, and it is demonstrated in this ﬁgure that for a given cooling ﬂow

rate (tracing one of the experimental curves), the maximum load supportable by

the bearing occurs at larger ﬁlm thicknesses as speed (and heat generation) increase.

Alternatively, to reach the same characteristic ﬁlm thickness at load capacity (tracing

one of the numerical curves with roughly constant hc), cooling ﬂow rate must be increased with speed.

It should be further noted that in the numerical simulations, top foil sag between bumps results in a wavy bearing surface. As demonstrated earlier in this chapter, experimental observations show that in practice, the foil coating can be abraded at high loads in order to compensate for foil sag, resulting in a bearing surface that under hydrodynamic pressure, is ﬂatter with respect to the runner. This phenomenon is not accounted for in the numerical simulations, and the wavy surface can create nonsensical artifacts at very high loads where the ﬁlm thickness in portions of the bearing tend toward zero (see the highest loads in the hc =6.3μm curve in Figure

6.6).

6.3 General Observations

Based on this series of load capacity tests, it is shown that factors other than

the particular bearing design are critical to achieving maximum performance in a

foil thrust bearing system. These factors include thermal management and surface

condition of both the bearing and runner, previously studied to some degree in foil

74 journal bearings, but perhaps more critical in foil thrust bearings which typically

operate at a higher percentage of their rated load capacity.

Considering its demonstrated eﬀect, very little quantitative data is reported for

the eﬀect of thermal management in foil bearings. It is now obvious that this is an

important consideration, in particular because it is desirable to minimize parasitic

cooling ﬂows in turbomachinery. Further, since bearing manufacturers typically

employ cooling air for foil bearing thermal management in laboratory testing, reported

data should be considered within the context of any thermal management technique

used.

The eﬀects of runner surface condition and foil coatings, while not yet reported

in thrust foil bearings, have been examined to some degree in foil journal bearings5,6.

When compared with a thin dense chromium coating, the reduced performance associated with a rougher as-ground PS304 surface is consistent with reported results for journal bearings. However, to the author’s knowledge the use of a thick abradable foil coating as a wear surface for in situ optimization has not been reported. The need for foil coatings to perform this function may be minimized with better a priori design and manufacturing methods.

The result that these bearings are limited thermally and by surface condition presents a challenge for turbomachinery designers, who must design a rotor support system around issues such as these. In the following chapters these eﬀects are discussed on a more fundamental level in an attempt to understand how to overcome their limitations.

75 References

[1] DellaCorte, C., and Valco, M. J., 2000. “Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications”. Tribology Transactions, 43, pp. 795–801.

[2] Heshmat, H., 2005. “Major Breakthrough in Load Capacity, Speed and Operating Temperature of Foil Thrust Bearings”. In Proceedings of WTC2005, World Tribology Congress III, no. WTC2005-63712, American Society of Mechanical Engineers/Society of Tribologists and Lubrication Engineers.

[3] Kim, J. H., Blanchet, T., and Calabrese, S., 2004. “High Velocity Oxyfuel Deposition for Low Surface Roughness PS304 Self-Lubricating Composite Coatings”. Tribology Transactions, 47(1), pp. 157–169.

[4] Dykas, B., and Howard, S. A., 2004. “Journal Design Considerations for Turbomachine Shafts Supported on Foil Air Bearings”. Tribology Transactions, 47(4), pp. 508–516.

[5] Radil, K. C., and DellaCorte, C., 2001. The Eﬀect of Journal Roughness and Foil Coatings on the Performance of Heavily Loaded Foil Air Bearings. NASA TM 2001-210941, National Aeronautics and Space Administration, Cleveland, OH.

[6] DellaCorte, C., Zaldana, A., and Radil, K. C., 2002. A Systems Approach to the Solid Lubrication of Foil Air Bearings for Oil-Free Turbomachinery. NASA TM 2002-211482, National Aeronautics and Space Administration, Cleveland, OH.

76 Chapter 7

Compressibility Number and Film Thickness

While load capacity measurements are eﬀective in demonstrating bearing per-

formance, they alone are not able to describe bearing operation and limits in a

fundamental way. In order to evaluate the gas ﬁlm behavior, experimentally measured

6μωR2 bearing torque is used to estimate a compressibility number (Λ = 2 )anda c Pahc characteristic ﬁlm thickness (hc). In the context of hydrodynamic theory, these parameters are more meaningful than a simple load capacity.

Both compressibility number and characteristic film thickness (Λc and hc, respec- tively) are determined by assuming uniform Couette flow in an annular film that is given by the inner and outer diameters of the bearing pads. This assumed flow field permits the calculation of the film characteristics given an experimentally measured torque. The derivation and significance of these parameters is detailed in Appendix

B. Unless otherwise noted, all data presented in this section is from bearing B running against a PS304-coated thrust runner.

77 7.1 Compressibility Number

Translating experimentally measured torque data into a characteristic bearing number is a way to compare laboratory test data to ﬁrst principles analysis and modeling results. This method of data reduction is useful for conveying the basic physics of thrust bearing operation, and are shown to agree well with theory.

Figure 7.1 is a plot of experimentally measured combinations of load and characteristic compressibility number. Data are taken at several speeds, and are shown to demonstrate similar behavior. Although some bias is visually evident in the various speed curves, speed appears to have little eﬀect on the curves of load versus compressibility number.

Figure 7.2 incorporates all of the load capacity data points shown in Figure 6.2, but are plotted versus the experimental bearing number rather than the speed. It is shown that cooling air has the effect of increasing the load capacity of the bearing at a given compressibility number. Since the compressibility number calculated here is proportional to the bearing torque squared, these data indicate that increased cooling allows the bearing to operate at a higher “hydrodynamic efficiency.” In this context, additional load supported by the bearing at a given Λ is an indication of increased hydrodynamic efficiency.

Furthermore, it can be seen that at 0.52 kg/min cooling flow, the bearing is able to operate at significantly higher bearing numbers than in the cases with lesser cooling. While this allows increased performance, it appears to be more expensive in terms of cycle efficiency (cooling flow is typically bled from a compressor stage within

78 120 25 krpm 30 krpm 35 krpm 100 39 krpm 42 krpm 45 krpm 48 krpm 80 55 krpm

60 Load (kPa)

0 0 20 40 60 80 100 120 140 160 180 200

Figure 7.1: Load versus Compressibility Number at Various Speeds showing a general curve of load versus characteristic compressibility number in a gas foil thrust bearing with 0.52 kg/min of cooling air ﬂow. The load behavior for a given compressibility number appears to be somewhat insensitive to speed such that data from multiple speeds can be incorporated in a single curve.

79 120 Cooling Flow Rate 0 kg/min 0.17 kg/min 100 0.35 kg/min 0.52 kg/min

Load Capacity (kPa) 40

0 0 20 40 60 80 100 120 140 160 180 200

Figure 7.2: Load Capacity Versus Compressibility Number comparing data taken at different cooling flow rates. Increased cooling flow is shown to increase achievable loads and compressibility numbers.

80 the turbomachine) to implement. It can be seen that the load capacity increases

with bearing number over the range shown, but that as bearing number continues to

increase, the curve ﬂattens so that large increases in bearing number are needed to

support additional load. This ﬂattening of the curve is a characteristic of the “high

speed limit” in gas bearings1, which is described in more detail in Appendix B.

In order to more closely examine the high speed limit behavior of the bearings,

the average load pressure is multiplied by the apparent ﬁlm thickness, a quantity

that for isothermal rigid step bearings with ﬁxed contraction ratio and inﬁnite width,

becomes constant with Λ for suﬃciently large values of Λ.

Figure 7.3 gives a plot of this quantity versus bearing number for various speeds

with a cooling ﬂow rate of 0.52 kg/min. Data is taken from low loads up to near the

load capacity at each speed in order to show the behavior throughout the operational

envelope. The largest ﬂow rate is used for this test in order to more closely approxi-

mate an isothermal case than would be achievable with an uncooled test. These data ¯ show a rapid increase in (Phc) with increasing bearing number followed by a levelling ¯ oﬀ and slight decrease in (Phc) with further increases in Λc.

When torque data are taken over a wide range of speeds, loads, and cooling flow rates, it can be plotted as in Figure 6.2, but showing the behavior throughout the operating range rather than just near the load capacity. As shown in Figure 7.4, the result is a smoother curve that includes data at lower bearing numbers, where typical operation might be expected to occur. Note that with increasing cooling flow rate the bearing supports more load for a given compressibility number, except for the largest value of cooling flow. It is unknown why this trend reverses, but the effect

81 1.2 25 krpm 30 krpm 35 krpm 1.0 39 krpm 42 krpm 45 krpm 48 krpm 0.8 55 krpm

0.6 (N/m) c Ph

0.4

0.2

0.0 0 20 40 60 80 100 120 140 160 180 200 /c

Figure 7.3: High Speed Limit Behavior of bearing B against a PS304-coated runner with 0.52 kg/min cooling ﬂow, which shows asymptotic behavior ¯ of the quantity Phc at large values of Λc, in accordance with the so-called high-speed limit behavior in gas bearings

82 is relatively small and is suspected to be related to the relatively high ﬂow rate and

ﬂow patterns within the bearing chamber. A more interesting feature of this plot is, as stated in reference to Figure 7.2, at 0.52 kg/min of cooling ﬂow, the bearing is able to run at higher Λc, which increases the load capacity.

120 Cooling Flow Rate 0 kg/min 0.17 kg/min 100 0.35 kg/min 0.52 kg/min

60 Load (kPa)

0 0 20 40 60 80 100 120 140 160 180 200 /c

Figure 7.4: Load Versus Compressibility Number for Various Cooling Flow Rates including data from lightly loaded conditions to near load capacity, over a speed range from 25-55 krpm. Most signiﬁcant is the increased compressibility numbers and loads achievable at the maximum cooling ﬂow rate.

7.2 Film Thickness

Gas ﬁlm thickness (and in particular the minimum thickness) is typically used in numerical modeling of hydrodynamic bearings to determine load capacity. This is

83 somewhat arbitrary since corroborative experimental gas ﬁlm thickness measurements

are particularly difficult to make on account of the thinness of the film, high rotational speeds, and flexible nature of the bearing geometry. To the author’s knowledge, the only reported experimental measurement of gas film thickness in foil bearings is given by Ruscitto et al.2, whose work concerns foil journal bearings.

Without experimental measurement of limiting ﬁlm thickness behavior, numerical models have little hope of accurately predicting the load capacity of foil thrust bearings in the near future. The eﬀort and expense of making direct measurements of

film thickness can be avoided, however, by making use of the experimentally measured bearing torque and simple analysis to determine a characteristic film thickness that can aid the modeling effort.

In this section, a characteristic ﬁlm thickness is examined by assuming Couette

ﬂow in a uniform annular gap between the runner and bearing over a range of conditions, particularly near the measured load capacity. While ﬁlm thickness varies over the pad, this characteristic value is an important parameter for the corroboration of numerical models.

Figure 7.5 gives curves of experimentally determined characteristic film thickness versus load at several different speeds, and with 0.52 kg/min of cooling air running against a PS304 coated runner. It is shown that as load is increased, the film thickness is decreased, as expected. Furthermore, at a specified load, the film thickness generally increases with increased speed. These results are entirely consistent with traditional hydrodynamic theory.

When ﬁlm thickness behavior near load capacity is examined however, a somewhat

84 60 25 krpm 35 krpm 45 krpm 50 55 krpm

20 Film Thickness (micron)

0 0 20406080100120 Load (kPa)

Figure 7.5: Film Thickness Versus Load at Various Speeds, verifying that the bearing operates with a larger characteristic ﬁlm thickness as speed is increased at conditions of constant load. When load is increased at a constant speed, the characteristic ﬁlm thickness decreases. These results are in accordance with hydrodynamic theory

85 unexpected trend appears. Measurements of the maximum sustainable (steady)

torque on the bearing before load capacity is reached are used to determine the

characteristic thickness at which ﬁlm rupture is imminent.

In conventional hydrodynamic analysis, the ﬁlm’s capacity is said to be reached

when the minimum ﬁlm thickness approaches (or is some ﬁxed multiple of) the

bearing/runner surface roughness3, regardless of shaft speed. At this point, intermittent asperity contact occurs at high relative speeds and the heat dissipated in these contacts can quickly lead to thermal runaway. Contrary to this reasoning,

Figure 7.6 shows the characteristic ﬁlm thickness at maximum load to increase with increased speed, and to decrease with increased cooling.

The non-constancy of minimum achievable (characteristic) film thickness suggests that a simple asperity contact model may not be adequate to describe the physical mechanism responsible for film rupture. Since the characteristic film thickness near load capacity increases with increasing heat generation (increasing speed and load capacity), the implication may be that thermoelastic distortion of the runner face exceeds the magnitude of the surface roughness and therefore dominates the load capacity behavior at high speeds. Since existing hydrodynamic models do not account for structural heat transfer and the resulting thermoelastic effects, they do not predict this type of effect.

To compare the eﬀects of surface roughness on the characteristic ﬁlm thickness, data from tests of bearing B at 25 krpm with 0.52 kg/min is plotted as an apparent

ﬁlm thickness versus load. This is shown in Figure 7.7, where it can be seen that the ﬁlm thickness behavior is similar for both runner surfaces, with the smoother

86 18 Cooling Flow Rate 0 kg/min 16 0.17 kg/min 0.35 kg/min 14 0.52 kg/min 0.52 kg/min (Chromium)

6 Film thickness (micron)

0 0 102030405060 Speed (krpm)

Figure 7.6: Film Thickness near Load Capacity, demonstrating that both active thermal management and smoother runner surfaces allow the bearing to operate at smaller characteristic ﬁlm thickness.

87 60

PS304 Chromium 50

20 Film thickness (micron)

0 0 102030405060708090100 Load (kPa)

Figure 7.7: Film Thickness Versus Load at 25 krpm, 0.52 kg/min, showing the rougher as-ground PS304 surface to result in a slightly larger characteristic ﬁlm thickness at otherwise identical operating conditions. chromium surface showing a slight bias toward a thinner ﬁlm for the same operating conditions.

It is noted that due to the rudimentary nature of the film thickness estimation, inferences of film behavior should be carefully scrutinized. The use of experimentally measured film thickness is described here to suggest potential modeling efforts and to verify assumptions about the typical film thicknesses experienced in these bearings.

88 7.3 Relative Eﬀects of Thermal Management and Runner Surface Finish

It has been deﬁnitively shown that smoother runner surfaces and active thermal management can increase the load capacity of foil thrust bearings. As a demonstration of the relative magnitudes of these eﬀects, a plot of bearing load versus compressibility number is shown in Figure 7.8 comparing data from an uncooled test with a “rough” runner to data from cooled tests with both smooth and rough runners.

The baseline data is taken at multiple speeds against a PS304-coated Inconel 718 runner with no active cooling. Compared to this, the data from the same runner with

0.52 kg/min of cooling ﬂow demonstrates higher attainable compressibility numbers and correspondingly large attainable loads. These data points are the same as given in Figure 7.4. However, an additional series of data points has been added, those taken from a 40 krpm load capacity test of a bearing against a smoother, chrome- coated runner with 0.52 kg/min of cooling ﬂow. These data show a further increase in attainable load and compressibility number.

This plot shows definitively that the performance potential of a given thrust foil bearing design is highly dependent on both thermal management and surface condition. Furthermore, as shown in Figure 7.6, the limiting Couette film thickness is also dependent on thermal management and surface finish, where lower attainable

film thicknesses correspond with the higher observed load capacities. Beyond the treatment of thermal and surface effects in Chapters 5 and 6, characteristic film thickness and compressibility number better describe the implications of the observed

89 140 0 kg/min (PS304) 0.52 kg/min (PS304) 120 0.52 kg/min (Chromium)

100

60 Load (kPa)

0 0 50 100 150 200 250 300 /c

Figure 7.8: Load Versus Compressibility Number Showing the Effects of Cooling and Runner Surface Roughness, with a PS304-coated runner and no cooling flow corresponding to the lowest achievable loads and compressibility numbers. A bearing run against a PS304- coated runner with 0.52 kg/min of cooling air is able to run at higher compressibility numbers than achievable with any lesser amount of cooling flow. Finally, the smooth chromium runner coating used in conjunction with 0.52 kg/min cooling flow allows the bearing to achieve higher loads and compressibility numbers than with the other tested configurations.

90 raw load capacity and torque data.

References

[1] Hamrock, B. J., 1994. Fundamentals of Fluid Film Lubrication. McGraw-Hill, Inc., New York.

[2] Ruscitto, D., McCormick, J., and Gray, S., 1978. Hydrodynamic Air Lubricated Compliant Surface Bearing For an Automotive Gas Turbine Engine I - Journal Bearing Performance. NASA CR 135368, National Aeronautics and Space Administration, Cleveland, OH.

[3] Lu, X., and Khonsari, M., 2005. “On the Lift-Oﬀ Speed in Journal Bearings”. Tribology Letters, 20, pp. 299–305.

91 Chapter 8

Physics of Thermal Management

The data obtained from tests of bearing load capacity are consistent with the theory

that thermoelastic distortions within the bearing/runner system are responsible for

performance loss. This decreased performance is most notable with increased speed

and load, which tend to increase bearing power loss.

Work by Dykas and Howard1 highlights the need for consideration of structural temperature distributions in foil bearing systems. The current work includes discussion of thermoelastic eﬀects in thrust bearings. While these theories have not been fully tested, they are presented to the bearing community as considerations that warrant further investigation, and are the subject of ongoing research. In understanding thermal expansion eﬀects on geometric distortion, bearing and system design can be advanced and parasitic cooling requirements reduced.

92 8.1 Impacts of Runner Heat Transfer

One mechanism of thermal distortion is related to the transfer of heat through

the thrust runner. Some of the heat generated in the gas ﬁlm conducts through

the thrust runner, with heat ﬂow components in both axial (through-thickness) and

radial directions. The low thermal conductivity of many high strength alloys used to

fabricate the runners renders them vulnerable to larger temperature gradients needed

to conduct the heat through the thickness.

Higher temperatures in the bearing face of the runner results in thermal expansion

greater than that of the back (exposed) face, assuming a positive coeﬃcient of thermal

expansion. The resulting thermoelastic stresses tend to bend the runner face away

from the operating bearing, leaving a convex running surface with respect to the

bearing.

Pan and Sternlicht2 investigated this phenomenon in spiral groove gas bearings as a load capacity-limiting factor inherent to bearing operation. They conclude that for spiral groove bearings, the realizable load capacity may be only half the theoretical capacity. From a material properties standpoint, runner distortion is proportional to the coeﬃcient of thermal expansion, and inversely proportional to the thermal conductivity.

The compliant nature of foil bearings makes them more tolerant of, but not im- mune to, thermal and centrifugal distortion than their rigid counterparts. Tolerance to predictable distortions can theoretically be tailored in the bearing by spatially varying the support stiﬀness3, but the bearing must be able to accommodate a wide

93 range of operating conditions where distortions may vary signiﬁcantly.

For the bearing and runner geometry in this work, an analysis is performed

to determine the peak-to-peak magnitude of the surface deﬂection due to an axial

heat load, as reported by Dykas et al4. A ﬁnite element model of the runner is constructed from the three dimensional geometry. The analysis is axisymmetric, and room temperature properties of Inconel 718 are used.

A uniform distributed heat input of 100 W is applied to the bearing surface of the runner. The temperature of the back face of the runner annulus is set to zero, with the hub surfaces insulated. The heat input is forced to conduct axially through the

1.27 cm thick annulus, resulting in a temperature diﬀerence between the bearing and exposed surfaces of 17◦C.

This temperature distribution is input to a structural simulation of the resulting deformation. For this case of 100 W of axial heat flux, the amplitude of the convexity is approximately 10 μm from the inner diameter of the bearing surface where it joins the hub, to the outer diameter of the bearing surface (Figure 8.1). This deviation from flatness is approximately the same magnitude as a characteristic film thickness, and indicates the potential for this mechanism to alter bearing operation. It is notable that in some failed bearings, wear scars near the inner radius of the bearing after load capacity tests provide anecdotal corroboration of this particular mode of failure. An example of this is shown in Figure 8.2.

Given that power loss at low to moderate loads has been measured to be a few hundred watts or less over the speed range tested, the 100 W assumed axial ﬂux would appear to be a large proportion of generated heat. This number is somewhat

94 Figure 8.1: FEA Plot of Runner Axial Deﬂection due to Through-Thickness Heat Transfer, showing that the runner takes on a convex shape with respect to the bearing. This forces a larger portion of the load to be supported on the inboard portion of the bearing.

95 Figure 8.2: PhotographofWearScaronBearingInnerRadiusafter a load capacity test. The presence of wear on the inner radius with little to no wear on the outer portion of the bearing supports the convex runner theory. arbitrary, but is more appropriate for higher speeds and loads than shown in Figure

5.2, with associated larger total power loss.

Actual runner temperature distributions will certainly deviate from this simplified case, with radial variation in the annulus and heat flux through additional surfaces, however this analysis demonstrates the potential for modest axial heat flux in the runner to significantly affect the flatness of the runner. Furthermore, large centrifugal stresses may also contribute to a distorted runner face. Cumulative effects of thermal and rotational distortions are not considered here, but are noted for their importance in runner design.

For this thermoelastic phenomenon, cooling air forced through the bearing foils should lessen the deformation of the runner by reducing the temperatures at the bear-

96 ing face and the axial temperature gradients through the runner thickness. Because

this convexity eﬀect is qualitatively consistent with experimental observations of load

capacity and wear scars, it is presented as a potential performance-limiting mecha-

nism. Introducing cooling air to the bearing reduces thermal distortions, leading to

observed increases in load capacity.

8.2 Measurement of Bearing Temperature Gradi- ents

As moderate through-thickness temperature gradients in the thrust runner can be

shown to result in substantial deformation of the bearing surface, radial temperature

gradients within the bearing and runner can also exist, with similar potential for

harmful thermoelastic distortion.

An investigation by Dykas and Radil5 measured radial temperature gradients at the trailing edge of thrust pad over a range of speeds and loads when running against an Inconel 718 runner with a PS304 coating. Measurements of the temperature distributions are performed in the absence of a cooling air flow, which would flow over the thermocouple junctions and degrade accuracy of the measurement. Here the gradient is determined by the temperature difference across the inner and outer thermocouples (8.3), though the temperature profile is close to linear across the the three thermocouples on the bearing. These radial gradients increase with increasing bearing power loss, as expected (Figure 8.4). Furthermore, it is clear from this data that at a given value of power loss, radial temperature gradients decrease with

97 increasing speed.

Figure 8.3: Thermocouple Locations Near Top Foil Trailing Edge in bearing A. The thermocouples are secured to the underlying bump foil where it is in contact with the top foil, as described in Chapter 4.

These measured temperature gradients are not necessarily the largest within the

bearing, but the thermocouple locations are chosen based on accessibility to instru-

mentation. The temperature gradients measured in a foil thrust bearing are similar

in magnitude to those measured by Radil and Zeszotek6 in foil journal bearings.

While it is difficult to predict the thermoelastic stresses in bearing foils without having a more detailed understanding of the overall temperature distribution, these data show significant temperature gradients within the bearing, which at the very least will need to be addressed in the hydrodynamic modeling of foil thrust bearings to pinpoint the most performance-critical thermal effects in foil thrust bearing systems.

98 3.0 25 krpm 32 krpm

2.5 35 krpm 45 krpm 55 krpm C/mm) o 65 krpm 2.0

1.5

1.0 Radial Temperature Gradient ( 0.5

0.0 0 50 100 150 200 250 300 350 400 450 500 Heat Generation (W)

Figure 8.4: Trailing Edge Temperature Gradients From 25-65 krpm for bearing A, showing that the temperature gradient increases with the bearing power loss at any given speed. It also shows that for a given amount of bearing power loss (heat generation), the temperature gradient decreases as the shaft speed increases.

99 8.3 Impact of Runner Convective Heat Transfer on Bearing Temperature Gradients

The decrease in temperature gradients with speed for a given rate of heat generation (noted in Figure 8.4) may be attributed to increasing convective heat transfer at the root of the runner annulus. Increasing speed results in a larger Reynolds number at a given radial location, and a corresponding increase in Nusselt number, and inﬂuences the heat transfer characteristics of the thrust runner.

The test runner has more complex geometry than a plain disk/cylinder, and ro- tates within a test rig-specific cavity geometry. Furthermore, the high runner surface speeds result in a large Reynolds number, compressible flow. These characteristics make a detailed analysis of runner heat transfer difficult due to uncertainty in the

ﬂow physics and convective heat transfer.

A simpliﬁed, ﬁrst order analysis is presented here to address the type of study needed to understand heat transfer within the runner and how this might be exploited as a thermal management technique. Convective heat transfer on the back side

(exposed to air) is assumed to behave as a simple rotating disk exposed to an inﬁnite quiescent medium, and heat transfer correlations for that conﬁguration are used.

Correlations for local heat transfer in a ﬂow induced by a rotating disk are given in

a terms of the local Reynolds number, Rer,intheform,Nu = cRe ,wherec and a are constants speciﬁc to the ﬂow regime and geometry. Here a constant Prandtl number has been assumed for air, allowing the Prandtl number dependence of the Nusselt number to be accounted for in the constant c. The generally accepted value for the

100 Flow Regime Convection Correlation Applicable Region 0.5 5 Laminar Nu =0.33Re Rer < 1.95 × 10 −20 4 5 5 Transition Nu =10× 10 Re 1.95 × 10 2.5 × 10

Table 8.1: Rotating Disk Convection Correlations

exponent a is 0.5 for laminar ﬂow and 0.8 for turbulent ﬂow, based on an analytical

solution with experimental veriﬁcation. Transition from laminar to turbulent ﬂow on

5 a rotating disk usually takes place at around Rer ≈ 2 × 10 .

For laminar ﬂow below Retrans the heat transfer coeﬃcient h is independent of

radial location on the disk. However, for turbulent ﬂow h is radially dependent, and

is proportional to r3/5. As a result of the heat transfer coeﬃcient increases with radial location on the disk face, there is less resistance to convective transfer of heat out of the disk backside at the outer diameter.

5 BasedonthistransitionRer ≈ 2×10 , it would appear that under some conditions inner portions of the runner backside might experience laminar flow, with a transition to turbulence occurring at some radial location, outboard of which the heat transfer coefficient increases with radius. Figure 8.5 shows a plot of calculated convection coefficient on the runner backside versus radial location based on the heat transfer correlations given by Popiel and Boguslawski7, with a transition region from 1.95 ×

5 5 10

The observed decrease in radial temperature gradient with increased speed at a given rate of heat generation may be considered in the context of the convective heat

101 400

350

°C 300 2 m W 250 h

200

150

0.025 0.03 0.035 0.04 0.045 0.05 Radius m

Figure 8.5: Estimated Convection Coefficient on Runner Backside at 35 krpm for a disk rotating in still air, showing a constant convection coefficient for a laminar region near the inner radius. Outboard of this the convection coefficient increases rapidly in a transitional region of the flow, with a fully turbulent region on the outer radial portion of the disk.

102 transfer on the exposed backside of the runner. With increasing speed the inner radial portion of the exposed runner face experience a transition to turbulent ﬂow and increasing heat transfer coeﬃcient.

If the bearing power loss is scaled with respect to the runner convection coeﬃcient, a revised plot of the data in Figure 8.4 appears as Figure 8.6. Here the parameter scaling the bearing power loss is Re4/5, a measure of turbulent heat transfer.

3.0 25 krpm 32 krpm 35 krpm 2.5 45 krpm 46 krpm C/mm)

o 55 krpm 2.0 65 krpm

1.5

1.0 Radial Temperature Gradient ( 0.5

0.0 0.0E+00 1.0E-03 2.0E-03 3.0E-03 4.0E-03 5.0E-03 6.0E-03 7.0E-03 8.0E-03 Heat Generation/Re0.8 (W)

Figure 8.6: Trailing Edge Temperature Gradients versus Scaled Power Loss Re0.8 for bearing A, where the speed is scaled by R , and the various speed curves lie roughly within a single curve.

Note that the temperature gradient curves for the range of speeds tested tend to collapse into a single curve when plotted in this manner. This result allows

103 temperature gradients at the trailing edge to be estimated for conditions of heat generation and speed that are not tested in this study. The degree to which this behavior applies to other aspects of the temperature distribution within the foils has not yet been determined. However, as further research into foil temperature distributions is undertaken, it is anticipated that the behavior shown here will become more clear.

Re0.8 Nonetheless, it is demonstrated by this plot of temperature gradients versus a R scaled bearing power loss that the temperature distributions in the bearing can be expressed over the range of speeds tested with a single curve. This is useful for simple estimations of thermal behavior based on expected operating conditions, and further study may demonstrate that the applicable speed range can be extended to lower and higher speeds. In the case of a thermal failure mechanism that is temperature- gradient dependent, this curve could predict the rate of heat generation corresponding to the onset of failure for a given bearing speed.

8.4 Runner Material Eﬀects

The positive influence of cooling air flow on the load capacity of foil thrust bearings demonstrates a need for thermal management to achieve maximum performance. As previously noted, active cooling with a bleed flow is undesirable, so passive methods of thermal management which take advantage of the rotating hardware to induce flow or sink heat are preferable. In order to investigate the potential use of runner heat sinking, a runner assembly was fabricated with a high thermal conductivity annulus

104 as detailed in Section 4.1.3. The aluminum portion of the runner has an order of

magnitude larger thermal conductivity, resulting in less resistance to internal heat

conduction.

Figure 8.7 shows a plot of trailing edge temperature gradients versus a scaled

speed parameter as in Figure 8.6, but here the data from a baseline Inconel 718

runner is compared to that from the aluminum runner. It is clear that increased

thermal conductivity of the runner material results in smaller temperature gradients

for the same scaled speed parameter, but the diﬀerence is within a factor or two

rather than an order of magnitude. This may stem from the relative magnitudes of

conductive and convective resistances to heat transfer or from the degree of thermal

coupling between the gas ﬁlm and runner.

This result indicates that the temperature gradients within the bearing foils can

be reduced by using a runner material with higher thermal conductivity, but the

achievable reduction in temperature gradients is modest compared to the ratio of

thermal conductivities. Furthermore, freedom in design and material selection is very limited for thrust runners, as detailed in Appendix C. This eﬀect is nonetheless demonstrated to be signiﬁcant and should be considered in product design.

105 3.0

25 krpm (aluminum) 32 krpm (aluminum) 2.5 40 krpm (aluminum) 48 krpm (aluminum) 25 krpm (inconel) C/mm) o 32 krpm (inconel) 2.0 35 krpm (inconel) 45 krpm (inconel) 46 krpm (inconel) 1.5 55 krpm (inconel) 65 krpm (inconel)

1.0 Radial Temperature Gradient ( 0.5

0.0 0.0E+00 1.0E-03 2.0E-03 3.0E-03 4.0E-03 5.0E-03 6.0E-03 7.0E-03 8.0E-03 Heat Generation/Re0.8 (W)

Figure 8.7: Runner Thermal Conductivity Eﬀects on Temperature Distri- butions in bearing A, where temperature gradients are plotted versus the scaled power loss parameter for several speeds. Data obtained with a standard Inconel 718 runner is compared to that of an aluminum runner, showing the higher thermal conductivity of the 7075-T6 results in a decrease in bearing temperature gradients.

References

[1] Dykas, B., and Howard, S. A., 2004. “Journal Design Considerations for Turbomachine Shafts Supported on Foil Air Bearings”. Tribology Transactions, 47(4), pp. 508–516.

[2] Pan, C., and Sternlicht, B., 1967. “Thermal Distortion of Spiral-Grooved Gas- Lubricated Thrust Bearing Due to Self Heating”. ASME Journal of Lubrication Technology, 89(2), pp. 197–202.

[3] DellaCorte, C., and Valco, M. J., 2000. “Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications”. Tribology Transactions, 43, pp. 795–801.

106 [4] Dykas, B., DellaCorte, C., Prahl, J., and Bruckner, R., 2006. “Thermal Management Phenomena in Foil Gas Thrust Bearings”. In Proceedings of Turbo Expo 2006: Power for Land, Sea, and Air, no. 2006-91268, American Society of Mechanical Engineers.

[5] Dykas, B., and Radil, K., 2005. “Experimental Measurement of Thrust Foil Bearing Temperature Proﬁles”. In Proceedings of WTC2005, World Tribology Congress III, no. WTC2005-63564, American Society of Mechanical Engineers/Society of Tribologists and Lubrication Engineers.

[6] Radil, K. C., and Zeszotek, M., 2004. “An Experimental Investigation into the Temperature Proﬁle of a Compliant Foil Air Bearing”. Tribology Transactions, 47(4), pp. 470–479.

[7] Popiel, C. O., and Boguslawski, L., 1974. “Local Heat-Transfer Coeﬃcients on the Rotating Disk in Still Air”. International Journal of Heat and Mass Transfer, 18, pp. 167–170.

107 Chapter 9

Summary and Conclusions

9.1 Summary of Results

In order to address the inadequacy of the body of knowledge concerning foil gas thrust bearings, a comprehensive experimental study is undertaken. Measurements of bearing torque and load capacity are made over a wide range of rotational speeds, axial loads, cooling ﬂow rates, and surface conditions. First principles analysis and numerical modeling, where appropriate, are used to interpret and understand the experimental results. Generally good agreement between experimental and analytical/numerical results is obtained.

The experimental measurements serve to characterize the bearing behavior throughout the operational envelope, and highlight critical areas that further development work should address in order to improve foil thrust bearing performance and adoption.

All of these factors have been previously suspected as able to enhance performance, but the level of understanding remains largely anecdotal and limited to a small number of foil bearing specialists. Furthermore, this study shows that many factors

108 inﬂuencing bearing performance (bearing design and foil coating, surface topography and tribological characteristics, thermal management) have similar magnitudes and must all be considered to achieve high load capacity.

Load capacity data demonstrate that foil coatings may be needed not only to provide a low friction foil surface, but can also serve as abradable surfaces to allow the bearing to correct for non-optimal geometry when deformed under hydrodynamic pressure. Predictions of foil sag between bumps correlate well with observed foil coating wear, and suggest that improved bearing design may be needed, and is being enabled through this more fundamental understanding.

In addition to coatings on the top foil, two runner surface coatings are investigated.

A smooth chromium coating is shown to have significantly higher load capacity than a somewhat rougher and higher friction as-ground PS304 surface with a molybdenum disulfide overlay. This behavior is consistent with the reported results for foil journal bearings, but this effect had not yet been verified for thrust bearings. In service,

PS304 coatings are expected to break in and provide a surface comparable to the TDC coatings, but the as-ground condition is shown here to be an important consideration for entry into service.

Cooling air flow is shown to enhance load capacity at high speeds, but is shown to have little effect at the lowest speed tested. This behavior indicates an interplay between hydrodynamic behavior and thermal behavior where the relative magnitudes vary over the speed range of interest. While shown to increase the capacity of the bearing, the use of bleed flows for thermal management in turbomachines incurs a thermodynamic penalty and should be minimized.

109 Finally, preliminary studies of thrust bearing temperature distributions show that large radial temperature gradients, present near the trailing edge of the pad, may correlate with a thermal limit in the bearings. Increased thermal conductivity of the runner is shown to decrease these temperature gradients signiﬁcantly in the absence of cooling air ﬂow.

9.2 Conclusions

Two basic mechanisms are shown to limit thrust foil bearing performance. The

absence of suﬃcient thermal management and non-optimum geometry of the foil and

runner surfaces both reduce achievable capacity in foil thrust bearings, and further

study is warranted on these eﬀects to enhance the operation of the bearings.

In the case of inadequate thermal management, the physical mechanism suspected

for reduced performance is thermoelastic distortion of the runner and foil surfaces.

This distortion causes a redistribution of the gas ﬁlm pressure ﬁeld, causing some

portions of the ﬁlm to shoulder a higher portion of the axial load than intended.

Thinning of the ﬁlm occurs in certain areas at lower loads than intended, resulting in

lower load capacity and potentially higher viscous friction.

The roughness of the foil and runner surfaces also represent non-optimal geometry

since current hydrodynamic modeling assumes perfectly smooth surfaces. Surface

roughness reduces the eﬀective gas ﬁlm thickness for a given mean separation distance,

and decreases the load at which surface asperities begin to contact.

Waviness of the top foil surface as a result of foil sag between bumps is also

110 classiﬁed as a non-optimal geometry eﬀect. The wear of the foil coating where

the bump foil supports the top foil implies that the top foil becomes wavy under

hydrodynamic pressure and the top foil wear allows the deformed top foil to attain a

ﬂatter surface with respect to the runner plane.

At a fundamental level, these factors all entail deviation from optimal geometry.

Hydrodynamic modeling which tends to idealize the surfaces, has not included these eﬀects. Since they have been shown to inﬂuence bearing operation, the implication is that current modeling methods for foil thrust bearings cannot accurately predict their limits with appropriate physical principles.

9.3 Implications and Future Work

The results of this study show that beyond the speciﬁc foil design of a given

bearing, a number of other factors can inﬂuence bearing performance. These factors,

which include surface condition and thermal/elastic distortion, can easily erode much

of a bearing’s potential performance capability. In a general sense, these can be

categorized as system-level design issues whereas the particular foil structure can be

considered a component-level design.

It is now clear that continuing development work on foil thrust bearings must

include these eﬀects in order to properly evaluate the adequacy of the system design.

Further study will be needed on several fronts to improve the capability of thrust foil

bearings, particularly with respect to turbomachinery integration.

Current, ongoing research on foil and runner tribological coatings is addressing

111 the need for robust, high-temperature, abradable foil coatings and smooth, lubricious runner coatings. It is expected that with improved understanding of these factors, optimized thrust bearing designs are likely to result. The conclusions of this dissertation emphasize the importance of coating research to address composition and surface characteristics.

Increased attention will need to be paid to thermal management issues, particularly as the applied load and associated power loss are expected to increase.

Tacit awareness of the importance of thermal management exists in the foil bearing community, but there remains a fundamental lack of understanding of the specific thermal mechanism (e.g. thermomechanical, thermoelastic, heat transfer) that limits capacity. Continued experimental work in this area is necessary to develop more efficient thermal management techniques which may involve runner heat sinking and tailored, flow-inducing geometries.

In addition to this experimental evaluation of thermal management techniques, it will be necessary to consider thermal eﬀects in numerical models. It is becoming apparent that modeling which ignores heat transfer inadequately describes the behavior of bearings at high rates of heat generation. Even simple structural heat transfer models should improve the accuracy of numerical models and aid in the design of eﬃcient thermal management techniques.

Research in these key areas will complement the development eﬀort being conducted by bearing manufacturers and facilitate the design of integrated systems.

Some aspects of these research topics are currently being addressed in various studies, but this dissertation demonstrates their relative importance and begins to quantify

112 attainable improvements. Furthermore, it provides a context for turbomachinery designers to understand the importance of factors beyond bearing design in achieving eﬃcient, high performance oil-free rotor support systems.

113 Appendix A

Discussion of Error

Error and uncertainty are present in both the experimental measurements and the numerical simulations presented in this text. In the case of numerical modeling, accuracy is limited not by the numerical method employed, but by the physical model input to the analysis. The assumptions and simpliﬁcations made in the numerical simulations are treated in the body of this dissertation. This appendix addresses the largest sources of experimental error present and the relative magnitudes.

Experimental Measurements

Four primary types of measurements are made in this research study - speed, load, torque, and temperature. These quantities are all subject to error and uncertainty, which in some case is diﬃcult to quantify.

Speed measurements are made by a transistor-based ﬁber optic sensor, and the digital output signal is fed to a frequency-to-voltage converter. The bias error in this signal conditioning arrangement is small compared to the degree with which the

114 speed can be controlled during a test. Generally, the speed can be controlled within

±150 rpm, which is ±0.6% at the lowest speed tested.

Axial load measurements are made from a strain gauge-based load cell that is placed in line with the test bearing shaft. Direct calibration of this load cell demonstrates the ability to measure load to the greater of ±10 N or ±4%. However, when cooling air is used, the elevated pressure in the bearing cavity leads to a hydrostatic eﬀect on the test bearing that acts to share the axial load imparted through the shaft.

A calibration of cavity pressure versus hydrostatic unloading is used to account for this phenomenon, but this adds an addition uncertainty of perhaps ±10 N. Note that this largest uncertainty applies at the highest cooling ﬂow rate of 0.52 kg/min and is less at smaller ﬂow rates.

Uncertainty in the torque signal is perhaps the most diﬃcult to quantify. The

LDVT load cell and signal conditioning arrangement used to measure torque has far less inherent error than the physical torque being transmitted. The reactionary torque of the test thrust bearing is transmitted through the shaft to the load cell, but the linear rotary bearings supporting this shaft have a small breakaway torque that may support some of the torque. Furthermore, the load is applied through a ball contact at the end of the shaft, and the small contact area can also contribute a small amount of error to the torque measurement, also through a static friction eﬀect. However, repeatability tests at similar conditions show little variation in the measured torque at identical operating conditions. In a test where load is increased slowly and constantly, followed by a slow and constant unloading of the bearing gives a plot of torque that shows little hysteresis. This suggests the restraining torque of

115 the linear bearings and ball contacts is small. The tests designed to determine the

error in torque suggest an uncertainty of about ±3Nmmor±15%.

Temperature measurements taken from the Type K thermocouples are expected to have bias error of up to ±2.2◦C for the relatively low temperatures tested. This is based on the voltage-to-temperature polynomial ﬁt, and further error is introduced due to precision (±0.3◦C), and also small errors due to installation (cold junction

compensation) and signal noise. Since temperature gradients rather than absolute

temperature values are given, these error values are expected to be overly conserv-

ative. Due to close positioning of thermocouple junctions and the small diﬀerences

in measured temperature (up to roughly 20◦C), the largest contribution to error in the temperature gradient measurements should come from a lack of precision. A reasonable estimate for the error in these measurements based on these assumptions

± . ◦C is 0 12 mm . Aside from errors present in the process signals, it is important to note that

the bearings tested are subject to manufacturing variability which may be large due

to the very low volume production of the particular designs tested. It is diﬃcult

to quantify the degree of expected variability in the bearings because of a lack of

suﬃcient operational experience, but it is expected to be in the tens of percent.

For this reason, comparative measurements are made from the same bearing when

possible. Where data from diﬀerent bearings are presented together, it is noted

in the text. While the issue of large suspected variation between test specimens

is signiﬁcant, it is speculated that this will decrease with increase production vol-

ume.

116 Appendix B

Derivation of Characteristic Gas Film Parameters

Compressible Reynolds Equation

Scaling analysis of the mass and momentum conservation equations in gas bearings

produces the compressible Reynolds equation, shown below in cylindrical coordinates

(starred notation denotes a dimensionless quantity):

1 ∂ ρ∗h∗3 ∂P∗ ∂ ρ∗h∗3 ∂P∗ ∂(ρ∗h∗) + r∗ =Λ r∗ ∂θ μ∗ ∂θ ∂r∗ μ∗ ∂r∗ ∂θ

In this nondimensional form of the Reynolds equation, the terms on the left hand side represent the divergence of the radial and azimuthal ﬂow rates, and the term on the right hand side is an expression of the variation of height and density in the azimuthal direction, sometimes referred to as the advection mass transport term.

It is notable that the mass transport term on the right hand side of this equation is scaled by the bearing compressibility number, Λ. As the compressibility number becomes very large (as in a high speed and/or highly loaded bearing), the right hand

117 side term dominates the gas ﬁlm behavior since terms on the left hand side are O(1).

The resulting form of the Reynolds equation is:

∂(ρ∗h∗) Λ ∂θ =0 which implies that:

(ρ∗h∗)=constant

In many analyses of gas ﬁlm lubrication, the gas is assumed to be isothermal, which simpliﬁes the analysis by allowing the energy equation to be ignored. Further assuming an ideal gas allows the substitution of pressure for density:

(P ∗h∗)=constant which is the result for isothermal ideal gas lubrication in the high speed limit.

Characteristic Film Thickness

In addition to calculation of bearing power loss and apparent friction coeﬃcient, speed/torque data can be used to characterize the nature of the gas ﬁlm to corroborate and guide numerical modeling.

The torque that is measured on the bearing is the integral of the quantity shear stress multiplied by the radius, acting over the surface of the bearing:

2π R To = (τw r) r dr dθ 0 ri

Substituting in the expression for wall shear stress:

2π R ∂u To = rμ r dr dθ 0 ri ∂y

118 In order to solve this integral using experimentally measured speed and torque, the

flow field is assumed to be a Couette flow with uniform film thickness extending from

the inner bearing radius to the outer bearing radius, and extending a full 360 degrees

around the bearing: 2π R ωr To = rμ r dr dθ 0 ri hc

Integrating this expression to get hc in terms of experimentally measurable parameters yields:

πμω R4 − r4 ( i ) hc = 2To

Note that the Couette film thickness is a simple estimate of gas film behavior requiring only geometric information, the viscosity of air, and experimentally measured speed and torque be known in order to calculate a film thickness.

Characteristic Compressibility Number

The compressibility number, Λ, appears in the Reynolds equation scaling the mass transport term and is a measure of the compressibility of the ﬂuid relative to the surface speed of the runner:

6μωR2 Λ= P h2 a c

In order to determine the characteristic compressibility number of the bearing given experimentally measurable quantities, the Couette ﬁlm thickness derived above

119 is substituted into the expression for Λ to give:

T 2 24 o Λc = 2 6 4 2 Paπ μωR (1 − ξ )

This expression represents the experimentally measured characteristic compressibility number of the bearing, which allows inferences to be made about the region in which the gas ﬁlm is operating.

120 Appendix C

Runner Design Limitations

Materials

Rotating hardware in gas turbine engines can be subjected to severe conditions of stress and temperature which in many cases require that components be made of advanced superalloy metals. Because of the large rotational stresses and high temperatures, components must retain strength at high temperature, have good creep resistance, and have at least moderate toughness.

There is some freedom in the design of the thrust runner since it will not be subjected to stress and temperature levels as severe as those experienced by the turbine blades, and there may be some choice of where the thrust bearings are located within a turbomachine. This may permit the thrust bearings and runner to operate at moderate temperatures (a few hundred degrees Celsius), which would provide an expanded envelope of potential runner materials. SOA high pressure compressor discharge temperatures can approach 650◦C in modern aeroengines.

Of particular interest may be maximizing the thermal conductivity of the runner

121 to increase its heat sinking capabilities and to reduce temperature gradients which

cause structural distortion. A small coeﬃcient of thermal expansion is also desirable

to minimize thermoelastic deformation. In terms of thermophysical properties, an

important material consideration is then the distortion parameter of the runner,

αQ Π= kLc

where:

k = thermal conductivity of runner

Lc = characteristic length

α = coeﬃcient of thermal expansion

Q = heat input

Although limited freedom may exist to increase the value of this nondimensional parameter, it is nonetheless a consideration in runner design. High strength at operating temperature, toughness, and compatibility with tribological materials are all essential considerations that may limit the ability to reduce the distortion parameter.

A characteristic value of this parameter using the baseline 1.27 cm thick Inconel 718 thrust runner with 100 W of heat input is Π = 8.4 × 10−3.

Physical Dimensions

The physical size of the thrust runner is limited by mass, stress, rotordynamic, and power loss considerations. In general, it is desirable to have the smallest runner possible to limit mass, stress, and power loss. However, since bearing load capacity is a function of both surface area and speed, the minimum required thrust runner size

122 is dictated by axial load requirements.

Turbomachines currently under consideration for oil-free operation are relatively small and operate at speeds from roughly 50-100 krpm. These machines may require thrust bearings that have load capacities in excess of a few hundred pounds, so bearings with outer diameters of 10 cm or more are required. Larger bearings would result in increased power loss, as well as larger mass, stress, and rotordynamic complications.

In addition to the outer diameter of the thrust runner, the thickness is also a critical design parameter for the same reasons as for the diameter. A runner must be thick enough to resist bending under large axial loads, which for loads on the order of a few hundred pounds is no thinner than about 5 mm. However, the disk must be as thin as possible to reduce mass and inertia. As a result of these competing requirements, there will be a rather narrow envelope of possible runner dimensions for any given design.

Features

In order to enhance heat transfer out of the thrust runner, a multitude of features can be included on various parts of the runner. Surface roughness, holes, vanes, and ﬁns in various conﬁgurations can all be used to enhance heat transfer from the rotating disk. The design and placement of these features can be tailored to control temperature distributions within the bearing and runner, based on knowledge of the thermal phenomena that govern bearing limitations.

However, particular attention must be paid to any undesirable structural defor-

123 mation caused by these features, particularly when the features are not axisymmetric.

A variety of features have been explored in a ﬁnite element (FE) numerical model of the runner to determine the resulting deformations at various operating conditions.

Features such as radial holes and vanes were seen to cause a rippling of the running surface which is generally viewed as detrimental to the performance of the bearing.

While numerous notional designs have been examined in FE models to determine structural response to various combinations of centrifugal, axial load, and thermal conditions, these design-speciﬁc results are mostly beyond the scope of the current work. Figure C.1 shows a few examples of designs that include ﬂow-inducing geometries that may be characteristic of passive thermal management features.

Figure C.1: Diagrams Showing Various Runner Design Features where the runner on the left incorporates radial cooling air channels, the middle runner is designed with a weakened backside to counteract thermally- induced convexity, and the right runner incorporates a centrifugal pumping design.

124 It is noteworthy that the addition of non-axisymmetric features has the potential to affect the flatness of the runner face at high rotational speeds and corresponding centrifugal stresses. An example of this is shown in Figure C.2, where radially extending cooling holes in the runner are spaced periodically around the circumference and extending to the center of the runner hub. The face shows a waviness caused by these radial channels, with an amplitude of approximately 2.5 μm. This example highlights the potentially deleterious effect of non-axisymmetric geometry, and demonstrates another limitation on runner design freedom.

Figure C.2: FE Model of Runner Face Axial Displacement at 60 krpm, showing the eﬀect of radial cooling holes on the ﬂatness of the runner face. Peak-to-peak amplitude of the circumferential waviness is approximately 2.5 μm.

125 Appendix D

Raw Experimental Data

This appendix contains much of the raw experimental torque and power loss data presented in Chapters 5-7 for bearing B running against an as-ground PS304-coated

Inconel 718 thrust runner. Measured bearing torque, power loss, and characteristic compressibility number and ﬁlm thickness are given for speeds from 25-55 krpm, cooling ﬂow rates up to 0.52 kg/min, and loads up to the bearing load capacity.

Speed Cooling Flow Load Torque Power Loss Λc hc (krpm) (kg/min) (N) (N mm) (W) (µm) 25 0.00 44 20 53 14 22.8 25 0.00 89 26 68 23 17.9 25 0.00 133 32 83 34 14.7 25 0.00 178 38 101 50 12.1 25 0.00 222 44 115 65 10.5 25 0.00 267 49 127 79 9.6 25 0.00 289 52 136 91 8.9 25 0.00 311 55 145 103 8.4 30 0.00 44 19 59 9.7 29.9 30 0.00 89 24 75 16 23.5 30 0.00 133 31 96 26 18.3 30 0.00 178 37 117 39 14.9 30 0.00 222 43 135 52 13.0 30 0.00 267 50 156 69 11.2 30 0.00 289 52 163 76 10.7

126 Speed Cooling Flow Load Torque Power Loss Λc hc (krpm) (kg/min) (N) (N mm) (W) (µm) 35 0.00 44 19 70 8.8 33.8 35 0.00 89 25 91 15 26.1 35 0.00 133 31 112 22 21.3 35 0.00 178 37 137 33 17.4 35 0.00 222 44 161 47 14.7 35 0.00 44 24 87 14 27.4 35 0.00 89 29 108 21 22.1 35 0.00 133 35 128 29 18.6 35 0.00 178 41 149 40 16.0 35 0.00 222 49 178 57 13.4 35 0.00 245 52 190 65 12.5 35 0.00 267 55 203 74 11.7 40 0.00 44 26 109 14 28.6 40 0.00 89 33 137 23 22.7 40 0.00 133 41 170 35 18.3 40 0.00 178 47 199 47 15.7 40 0.00 222 53 222 59 14.0 40 0.00 245 58 241 70 12.9 40 0.00 267 61 256 78 12.2 40 0.00 289 66 274 90 11.3 45 0.00 44 24 112 11 35.2 45 0.00 89 31 144 17 27.4 45 0.00 111 34 160 21 24.7 45 0.00 133 36 170 24 23.1 45 0.00 156 42 197 33 20.0 45 0.00 178 44 208 36 19.0 45 0.00 200 49 229 44 17.2 45 0.00 222 52 245 50 16.1 45 0.00 245 57 266 60 14.8 45 0.00 267 61 287 69 13.7 45 0.00 289 68 319 86 12.3 50 0.00 44 26 136 11 35.7 50 0.00 89 33 172 18 28.3 50 0.00 111 37 195 23 24.9 50 0.00 133 41 213 28 22.8 50 0.00 156 43 225 31 21.6 50 0.00 178 46 243 36 20.0 50 0.00 200 51 266 43 18.3 50 0.00 222 55 290 51 16.8 50 0.00 245 61 319 63 15.2

127 Speed Cooling Flow Load Torque Power Loss Λc hc (krpm) (kg/min) (N) (N mm) (W) (µm) 50 0.00 267 66 343 72 14.2 50 0.00 289 71 373 85 13.0 55 0.00 44 29 169 13 34.8 55 0.00 89 36 208 20 18.2 55 0.00 133 43 247 28 23.8 55 0.00 178 50 286 38 20.5 55 0.00 222 59 338 53 17.4 55 0.00 245 64 371 63 15.9 25 0.17 40 12 33 5.2 37.3 25 0.17 111 21 56 15 21.6 25 0.17 156 26 68 23 17.9 25 0.17 178 29 77 29 15.8 25 0.17 200 33 86 36 14.2 25 0.17 222 36 95 44 12.8 25 0.17 245 40 104 53 11.7 25 0.17 267 45 118 69 10.3 25 0.17 289 50 130 83 9.3 35 0.17 44 18 66 7.8 35.9 35 0.17 89 24 87 14 27.4 35 0.17 133 31 112 22 21.3 35 0.17 178 36 133 31 18.0 35 0.17 222 44 161 47 14.7 35 0.17 267 51 186 62 12.8 35 0.17 289 55 203 74 11.7 35 0.17 311 60 219 86 10.9 35 0.17 333 66 240 103 9.9 45 0.17 44 19 91 6.9 43.5 45 0.17 89 26 122 13 32.2 45 0.17 133 32 149 19 26.4 45 0.17 178 38 181 28 21.8 45 0.17 222 45 213 38 18.5 45 0.17 266 53 250 53 15.7 45 0.17 288 58 272 62 14.5 45 0.17 311 62 293 72 13.4 45 0.17 333 67 314 83 12.5 55 0.17 44 24 137 8.6 43.0 55 0.17 89 31 176 14 33.5 55 0.17 133 37 215 21 27.4 55 0.17 178 44 254 30 23.2 55 0.17 222 52 299 41 19.6

128 Speed Cooling Flow Load Torque Power Loss Λc hc (krpm) (kg/min) (N) (N mm) (W) (µm) 55 0.17 266 61 351 57 16.7 25 0.35 38 11 30 4.3 41.1 25 0.35 82 17 44 9.6 27.4 25 0.35 126 23 59 17 20.5 25 0.35 170 28 74 27 16.4 25 0.35 215 35 92 41 13.3 25 0.35 259 42 109 59 11.1 25 0.35 281 47 123 74 9.9 25 0.35 303 50 132 85 9.2 35 0.35 38 13 48 4.0 50.0 35 0.35 82 17 62 6.9 38.3 35 0.35 126 23 83 12 28.8 35 0.35 170 28 104 19 23.0 35 0.35 215 35 128 29 18.6 35 0.35 258 42 153 42 15.5 35 0.35 303 47 174 54 13.7 35 0.35 325 52 190 65 12.5 35 0.35 347 55 203 74 11.7 35 0.35 369 61 224 89 10.7 35 0.35 391 67 244 107 9.7 45 0.35 39 18 85 6.1 46.2 45 0.35 83 23 106 9.5 37.0 45 0.35 127 28 133 15 29.6 45 0.35 171 34 160 21 24.7 45 0.35 215 41 192 31 20.5 45 0.35 259 47 224 42 17.6 45 0.35 304 55 261 57 15.1 45 0.35 347 63 298 75 13.2 45 0.35 370 68 319 86 12.3 55 0.35 39 21 124 7.0 47.6 55 0.35 83 27 156 11 37.7 55 0.35 127 33 189 16 31.2 55 0.35 171 41 234 25 25.1 55 0.35 215 47 273 34 21.5 55 0.35 259 55 319 47 18.4 55 0.35 304 64 368 62 16.0 25 0.52 22 9 24 2.7 51.4 25 0.52 59 14 35 6.2 34.2 25 0.52 101 19 50 12 24.2 25 0.52 143 24 62 19 19.6

129 Speed Cooling Flow Load Torque Power Loss Λc hc (krpm) (kg/min) (N) (N mm) (W) (µm) 25 0.52 187 29 77 29 15.8 25 0.52 229 36 95 44 12.8 25 0.52 274 44 115 65 10.5 25 0.52 297 49 127 79 9.6 25 0.52 319 53 139 95 8.7 30 0.52 41 11 35 3.6 49.3 30 0.52 120 23 71 14 24.7 30 0.52 187 32 99 28 17.6 30 0.52 231 38 121 41 14.5 30 0.52 276 46 146 60 12.0 30 0.52 320 55 174 86 10.1 30 0.52 364 64 202 116 8.6 30 0.52 385 69 217 133 8.1 30 0.52 406 77 241 165 7.3 30 0.52 430 81 256 185 6.8 35 0.52 38 17 62 6.9 38.3 35 0.52 78 21 79 11 30.3 35 0.52 120 26 95 16 25.0 35 0.52 162 32 116 24 20.5 35 0.52 207 38 141 35 16.9 35 0.52 250 44 161 47 14.7 35 0.52 294 52 190 65 12.5 35 0.52 339 60 219 86 10.9 35 0.52 383 69 253 114 9.4 35 0.52 411 75 273 133 8.7 35 0.52 439 81 298 159 8.0 39 0.52 27 14 55 4.0 53.4 39 0.52 84 21 88 9.9 33.7 39 0.52 165 33 134 23 22.1 39 0.52 229 43 175 40 16.9 39 0.52 273 50 203 53 14.6 39 0.52 316 58 235 71 12.6 39 0.52 360 64 263 89 11.2 39 0.52 401 76 309 123 9.6 39 0.52 426 81 332 142 8.9 42 0.52 22 17 75 5.7 46.0 42 0.52 78 25 109 12 31.4 42 0.52 163 37 164 28 20.9 42 0.52 229 47 209 45 16.4 42 0.52 272 54 239 59 14.4

130 Speed Cooling Flow Load Torque Power Loss Λc hc (krpm) (kg/min) (N) (N mm) (W) (µm) 42 0.52 315 62 273 77 12.5 42 0.52 357 69 303 95 11.3 42 0.52 401 77 338 118 10.2 42 0.52 422 84 368 140 9.3 45 0.52 34 19 91 6.9 43.5 45 0.52 125 32 149 19 26.4 45 0.52 190 41 192 31 20.5 45 0.52 232 47 224 42 17.6 45 0.52 276 54 256 55 15.4 45 0.52 319 61 287 69 13.7 45 0.52 364 68 319 86 12.3 45 0.52 390 75 351 104 11.2 45 0.52 57 26 122 13 32.2 45 0.52 143 38 181 28 21.8 45 0.52 185 44 208 36 19.0 45 0.52 228 51 240 48 16.4 45 0.52 272 58 272 62 14.5 45 0.52 314 64 303 77 13.0 45 0.52 357 73 346 101 11.4 48 0.52 28 20 102 7.2 43.8 48 0.52 100 31 153 16 29.2 48 0.52 161 37 187 24 23.9 48 0.52 226 47 239 39 18.8 48 0.52 271 54 273 51 16.4 48 0.52 314 62 312 68 14.3 48 0.52 358 71 358 89 12.5 48 0.52 381 76 380 100 11.8 48 0.52 403 80 403 113 11.1 48 0.52 422 84 420 122 10.7 55 0.52 58 29 169 13 34.8 55 0.52 143 42 241 27 24.4 55 0.52 184 47 273 34 21.5 55 0.52 227 57 325 49 18.1 55 0.52 41 25 143 9.4 41.1 55 0.52 103 33 189 16 31.2 55 0.52 145 40 228 24 25.8 55 0.52 187 47 273 34 21.5 55 0.52 229 55 319 47 18.4 55 0.52 273 63 364 61 16.1

131 Bibliography

Agrawal, G., 1984. Hydrodynamic Fluid Film Thrust Bearing. U.S. Patent 4,462,700.

Agrawal, G., 1990. “Foil Gas Bearings for Turbomachinery”. In 20th Intersociety Conference on Environmental Systems, no. SAE Paper 901236, Society of Automotive Engineers.

Agrawal, G. L., 1997. “Foil Air/Gas Bearing Technology An Overview”. In International Gas Turbine and Aerospace Congress and Exhibition, no. ASME paper 97-GT-347, American Society of Mechanical Engineers.

Anderson, W. J., and Bisson, E. E., 1964. Advanced Bearing Technology. NASA- SP 38, National Aeronautics and Space Administration, Washington, D.C.

Bauman, S., 2005. An Oil-Free Thrust Foil Bearing Facility Design, Calibration, and Operation. NASA TM 2005-213568, National Aeronautics and Space Administration, Cleveland, OH.

Blok, H., and vanRossum, J., 1953. “The Foil Bearing - A New Departure in Hydrodynamic Lubrication”. Lubrication Engineering, 9(6), pp. 316–320.

Bruckner, R. J., 2004. A Propulsion System Analysis of Oil Free Turbomachinery for Aviation Turbofan Engines. AIAA 2004-4189, American Institute of Aeronautics and Astronautics, Reston, VA.

Bruckner, R. J., 2004. “Simulation and Modeling of the Hydrodynamic, Thermal, and Structural Behavior of Foil Thrust Bearings”. PhD dissertation, Case Western Reserve University, Cleveland, OH.

Capstone MicroTurbine Corporation, 2000. Capstone Turbine Ships New Microturbine Product; New Capstone 60 Power System Generates Twice the Electricity of Current Models. Press Release.

Davis, J., ed., 1998. Metals Handbook Desk Edition. ASM International.

132 DellaCorte, C., 1998. The Evaluation of a Modiﬁed Chrome Oxide Based High Temperature Solid Lubricant Coating for Foil Gas Bearings. NASA TM 1998- 208660, National Aeronautics and Space Administration, Cleveland, OH.

DellaCorte, C., and Edmonds, B. J., 1995. Preliminary Evaluation of PS300: A New Self-Lubricating High Temperature Composite Coating for Use to 800C. NASA TM 107056, National Aeronautics and Space Administration, Cleveland, OH.

DellaCorte, C., and Edmonds, B. J., 1999. Self-Lubricating Composite Containing Chromium Oxide. U.S. Patent 5,866,518.

DellaCorte, C., Lukaszewicz, V., Valco, M. J., Radil, K., and Heshmat, H., 2000. “Performance and Durability of High Temperature Foil Air Bearings for Oil-Free Turbomachinery”. Tribology Transactions, 43(4), pp. 774–780.

DellaCorte, C., and Pinkus, O., 2000. Tribological Limitations in Gas Turbine Engines: A Workshop to Identify the Challenges and Set Future Directions. NASA TM 2000-210059, National Aeronautics and Space Administration, Cleveland, OH.

DellaCorte, C., and Valco, M. J., 2000. “Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications”. Tribology Transactions, 43, pp. 795–801.

DellaCorte, C., Zaldana, A., and Radil, K. C., 2002. A Systems Approach to the Solid Lubrication of Foil Air Bearings for Oil-Free Turbomachinery. NASA TM 2002-211482, National Aeronautics and Space Administration, Cleveland, OH.

Dykas, B., DellaCorte, C., Prahl, J., and Bruckner, R., 2006. “Thermal Management Phenomena in Foil Gas Thrust Bearings”. In Proceedings of Turbo Expo 2006: Power for Land, Sea, and Air, no. 2006-91268, American Society of Mechanical Engineers.

Dykas, B., and Howard, S. A., 2004. “Journal Design Considerations for Turbomachine Shafts Supported on Foil Air Bearings”. Tribology Transactions, 47(4), pp. 508–516.

Dykas, B., and Radil, K., 2005. “Experimental Measurement of Thrust Foil Bearing Temperature Proﬁles”. In Proceedings of WTC2005, World Tribology Congress III, no. WTC2005-63564, American Society of Mechanical Engineers/Society of Tribologists and Lubrication Engineers.

Etsion, I., 1977. “A Cantilever Mounted Resilient Pad Gas Thrust Bearing”. Journal of Lubrication Technology, 99, pp. 95–100.

133 Fortmann, W. E., 1978. Dual Wedge Fluid Thrust Bearing Including Wave Spring. U.S. Patent 4,082,375.

Gray, S., and Heshmat, H., 1981. Support Element for Compliant Hydrodynamic Thrust Bearing. U.S. Patent 4,277,111.

Hamrock, B. J., 1994. Fundamentals of Fluid Film Lubrication. McGraw-Hill, Inc., New York.

Heshmat, C., Heshmat, H., Valco, M. J., Radil, K., and DellaCorte, C., 2005. “Foil Bearings Makes Oil-Free Turbocharger Possible”. In Proceedings of WTC2005, World Tribology Congress III, no. WTC2005-63724, American Society of Mechanical Engineers/Society of Tribologists and Lubrication Engineers.

Heshmat, H., 1994. “Advancements in the Performance of Aerodynamic Foil Journal Bearings: High Speed and Load Capacity”. ASME Journal of Tribology, 116, pp. 287–295.

Heshmat, H., 1999. High Load Capacity Compliant Foil Hydrodynamic Thrust Bearing. U.S. Patent 5,961,217.

Heshmat, H., 2005. “Major Breakthrough in Load Capacity, Speed and Operating Temperature of Foil Thrust Bearings”. In Proceedings of WTC2005, World Tribology Congress III, no. WTC2005-63712, American Society of Mechanical Engineers/Society of Tribologists and Lubrication Engineers.

Heshmat, H., Hryniewicz, P., Walton, J., Willis, J., Jahanmir, S., and DellaCorte, C., 2005. “Low Friction Wear-Resistant Coatings for High-Temperature Foil Bearings”. Tribology International, 38.

Heshmat, H., Shapiro, W., and Gray, S., 1981. “Development of Foil Journal Bearings for High Load Capacity and High Speed Whirl Stability”. In Proceedings of the ASLE-ASME Joint Tribology Conference, no. 81-Lub-36, American Society of Lubrication Engineers/American Society of Mechanical Engineers.

Heshmat, H., Walowit, J. A., and Pinkus, O., 1983. “Analysis of Gas Lubricated Compliant Thrust Bearings”. ASME Journal of Lubrication Technology, 105, pp. 638–646.

Howard, S. A., and DellaCorte, C., 2006. Gas Foil Bearings for Space Propulsion Nuclear Electric Power Generation. NASA-TM 2006-214115, National Aeronautics and Space Administration, Cleveland, OH.

134 Hryniewicz, P., Locke, D., and Heshmat, H., 2003. “New-Generation Development Rigs for Testing High-Speed, Air-Lubricated Thrust Bearings”. Tribology Transactions, 46(4), pp. 556–559.

Kim, J. H., Blanchet, T., and Calabrese, S., 2004. “High Velocity Oxyfuel Deposition for Low Surface Roughness PS304 Self-Lubricating Composite Coatings”. Tribology Transactions, 47(1), pp. 157–169.

Lu, X., and Khonsari, M., 2005. “On the Lift-Oﬀ Speed in Journal Bearings”. Tribology Letters, 20, pp. 299–305.

Lucero, J., 2006. Measured Foil Frequencies and Mode Shapes as a Function of Wear for a Gas Foil Thrust Bearing. NASA-TM (to be published), National Aeronautics and Space Administration, Cleveland, OH.

Mason, L. S., 1999. Surface Nuclear Power for Human Mars Missions. NASA TM 1999-208894, National Aeronautics and Space Administration, Cleveland, OH.

Mohawk Innovative Technology, Inc., 2002. WJ24-8 Turbojet Engine Demonstration Testing with Air Foil Bearing. Press Release, December.

Mohawk Innovative Technology, Inc., 2005. High-Speed, Oil-Free, Motorized Spindle. Press Release, January.

Nemeth, Z. N., 1977. Experimental Evaluation of Foil-Supported Resilient-Pad Gas-Lubricated Thrust Bearing. NASA TP 1030, National Aeronautics and Space Administration, Cleveland, OH.

Nemeth, Z. N., 1979. Operating Characteristics of a Cantilever-Mounted Resilient- Pad Gas-Lubricated Thrust Bearing. NASA TP 1438, National Aeronautics and Space Administration, Cleveland, OH.

Pan, C., and Sternlicht, B., 1967. “Thermal Distortion of Spiral-Grooved Gas- Lubricated Thrust Bearing Due to Self Heating”. ASME Journal of Lubrication Technology, 89(2), pp. 197–202.

Popiel, C. O., and Boguslawski, L., 1974. “Local Heat-Transfer Coeﬃcients on the Rotating Disk in Still Air”. International Journal of Heat and Mass Transfer, 18, pp. 167–170.

Radil, K. C., and DellaCorte, C., 2001. The Eﬀect of Journal Roughness and Foil Coatings on the Performance of Heavily Loaded Foil Air Bearings. NASA TM 2001-210941, National Aeronautics and Space Administration, Cleveland, OH.

135 Radil, K. C., and Zeszotek, M., 2004. “An Experimental Investigation into the Temperature Proﬁle of a Compliant Foil Air Bearing”. Tribology Transactions, 47(4), pp. 470–479.

Ruscitto, D., McCormick, J., and Gray, S., 1978. Hydrodynamic Air Lubricated Compliant Surface Bearing For an Automotive Gas Turbine Engine I - Journal Bearing Performance. NASA CR 135368, National Aeronautics and Space Administration, Cleveland, OH.

Salehi, M., Swanson, E., and Heshmat, H., 2000. “Thermal Features of Compliant Foil Bearings - Theory and Experiments”. In Joint Tribology Conference, no. 2000- TRIB-38, American Society of Mechanical Engineers/Society of Tribologists and Lubrication Engineers.

Suriano, F. J., 1981. Gas Foil Development Program; Final Report. AFWAL-TR 81-2095, Air Force Wright Aeronautical Laboratories, Dayton, Ohio.

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