Demonstration of a Turbojet Engine Using an Air Foil Bearing

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DEMONSTRATION OF A TURBOJET ENGINE USING AN AIR FOIL BEARING Hooshang Heshmat, Ph.D. (ASME/STLE Fellow) [email protected] Mohawk Innovative Technology Inc. Albany, NY 12205 James F. Walton II (ASME /SAE Member) [email protected] Mohawk Innovative Technology Inc. Albany, NY 12205 Michael J. Tomaszewski [email protected] Mohawk Innovative Technology Inc. Albany, NY 12205 ABSTRACT A test of the target drone main propulsion turbojet engine was recently conducted that demonstrated successful operation of a turbojet engine with a compliant foil air bearing. For this effort, the hot section rolling element bearing and the entire existing lubrication system was replaced with a compliant foil air bearing. This technology demonstration test showed the ability of the foil bearing to operate in the extremely challenging environment behind the turbine. Detailed engine integration studies, bearing component rig testing and hot engine simulator tests were completed prior to the successful engine test. The rig and simulator tests verified high temperature capabilities of the bearing and its surface coating, the bearing journal design, bearing dynamic performance, and rotor-bearing system dynamic stability, prior to engine integration and test. Based on these preliminary efforts, the engine and bearing were assembled and tests were conducted that included over 70 start stop cycles (including hot restarts), seven simulated mission cycles and more than 14 hours of run time. The foil bearing and engine operated flawlessly throughout the test. Vibrations were very low and all temperatures and pressures were as expected. A posttest tear down and hardware inspection revealed that the bearing, journal and all components remained in perfect condition. These data will be used to further the application of foil bearings to numerous other gas turbine engines for both military and commercial systems. INTRODUCTION There is a need for high specific thrust, fuel efficient, durable, affordable and maintenance free gas turbine engines for application to a wide range of both legacy and future engines in applications such as aerial targets, drones, Uninhabited Air and Air Combat Vehicles (UAV/UCAV), and powered munitions. For example, drone and target systems that are used in pilot training can benefit from improved performance and range to increase the quality of the training. By increasing system range and performance, more time is available to practice multiple intercepts using different weapons systems, or to practice runs by multiple aircraft before the target is destroyed. In turbojet powered munitions increased performance can be translated into greater standoff, greater loiter time and/or reduced time to target. In many cases, flight endurance of existing turbojet powered vehicles is limited due to restricted fuel load. Design of new engines or modification of existing engines to reduce engine volume and/or increase performance (e.g., reduced fuel consumption or increased thrust to weight) can have a significant impact on training as well as in weapon system capability. Simply reducing engine volume by eliminating the bearing lubrication system can be translated directly into increased fuel load. Operation at higher shaft speeds and turbine inlet temperatures can increase engine performance. To address the engine system development issues that will make these machines a reality with high performance, reliability and long term storability, this author has led the development and demonstrated of the needed supporting foil bearing technologies ranging from improved damping and load capacity to high temperature, long life and low friction coatings for compliant foil bearings [1-9]. These recent developments indicate that compliant foil air bearing (CFB) technology has the capability to be used as main rotor supports for a wide array of gas turbine engines, even engines up to and exceeding 5,000 pounds of thrust. Figure 1 and Figure 2 summarize the historical advancements in compliant foil bearing capabilities. This bearing technology foundation, successfully demonstrated in turboexpanders and turbochargers, has been instrumental in the successful turbojet engine test with a foil bearing placed directly behind the turbine [10-12]. 1 Copyright © 2005 by ASME Proceedings of GT2005 ASME Turbo Expo 2005: Power for Land, Sea and Air June 6-9, 2005, Reno-Tahoe, Nevada, USA GT2005-68404 Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/30/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use

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DEMONSTRATION OF A TURBOJET ENGINE USING AN AIR FOIL BEARING

Hooshang Heshmat, Ph.D. (ASME/STLE Fellow) [email protected]

Mohawk Innovative Technology Inc. Albany, NY 12205

James F. Walton II (ASME /SAE Member) [email protected]

Mohawk Innovative Technology Inc. Albany, NY 12205

Michael J. Tomaszewski [email protected]

Mohawk Innovative Technology Inc. Albany, NY 12205

Proceedings of GT2005ASME Turbo Expo 2005: Power for Land, Sea and Air

June 6-9, 2005, Reno-Tahoe, Nevada, USA

GT2005-68404

ABSTRACT A test of the target drone main propulsion turbojet engine

was recently conducted that demonstrated successful operation of a turbojet engine with a compliant foil air bearing. For this effort, the hot section rolling element bearing and the entire existing lubrication system was replaced with a compliant foil air bearing. This technology demonstration test showed the ability of the foil bearing to operate in the extremely challenging environment behind the turbine. Detailed engine integration studies, bearing component rig testing and hot engine simulator tests were completed prior to the successful engine test. The rig and simulator tests verified high temperature capabilities of the bearing and its surface coating, the bearing journal design, bearing dynamic performance, and rotor-bearing system dynamic stability, prior to engine integration and test. Based on these preliminary efforts, the engine and bearing were assembled and tests were conducted that included over 70 start stop cycles (including hot restarts), seven simulated mission cycles and more than 14 hours of run time. The foil bearing and engine operated flawlessly throughout the test. Vibrations were very low and all temperatures and pressures were as expected. A posttest tear down and hardware inspection revealed that the bearing, journal and all components remained in perfect condition. These data will be used to further the application of foil bearings to numerous other gas turbine engines for both military and commercial systems.

INTRODUCTION

There is a need for high specific thrust, fuel efficient, durable, affordable and maintenance free gas turbine engines for application to a wide range of both legacy and future engines in applications such as aerial targets, drones, Uninhabited Air and Air Combat Vehicles (UAV/UCAV), and powered munitions. For example, drone and target systems that

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are used in pilot training can benefit from improved performance and range to increase the quality of the training. By increasing system range and performance, more time is available to practice multiple intercepts using different weapons systems, or to practice runs by multiple aircraft before the target is destroyed. In turbojet powered munitions increased performance can be translated into greater standoff, greater loiter time and/or reduced time to target. In many cases, flight endurance of existing turbojet powered vehicles is limited due to restricted fuel load. Design of new engines or modification of existing engines to reduce engine volume and/or increase performance (e.g., reduced fuel consumption or increased thrust to weight) can have a significant impact on training as well as in weapon system capability. Simply reducing engine volume by eliminating the bearing lubrication system can be translated directly into increased fuel load. Operation at higher shaft speeds and turbine inlet temperatures can increase engine performance.

To address the engine system development issues that will make these machines a reality with high performance, reliability and long term storability, this author has led the development and demonstrated of the needed supporting foil bearing technologies ranging from improved damping and load capacity to high temperature, long life and low friction coatings for compliant foil bearings [1-9]. These recent developments indicate that compliant foil air bearing (CFB) technology has the capability to be used as main rotor supports for a wide array of gas turbine engines, even engines up to and exceeding 5,000 pounds of thrust. Figure 1 and Figure 2 summarize the historical advancements in compliant foil bearing capabilities. This bearing technology foundation, successfully demonstrated in turboexpanders and turbochargers, has been instrumental in the successful turbojet engine test with a foil bearing placed directly behind the turbine [10-12].

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In the remainder of this paper the specific effort conducted that lead to the successful engine demonstration test will be presented. In particular, the rotor-bearing system design, system integration, simulator testing, high temperature materials testing, and finally engine test results will be presented.

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Figure 2. Advancement in compliant foil bearing damping.

TEST FACILITIES AND METHODS To minimize risk to the gas turbine engine, simulation rig

testing was completed prior to the start of engine testing. An existing simulator rig having size and dynamic characteristics similar to the candidate engine was selected to verify both bearing and system performance through out the expected operating speed and temperature range. The speed and temperature capability of the rig actually exceeded the requirements for the turbojet engine, which was deemed important as overspeed and high temperature conditions could be evaluated safely. Details of the experimental rig set up, rotordynamic analysis and experimental results are explained in the following sections.

Simulator Test Rig The simulator, shown in Figure 3 through Figure 5 consists

of a straddle mounted hollow rotor supported by an oil lubricated rolling element bearing at the forward end and a compliant foil bearing at the aft end. The compressor is simulated by the impulse air turbine drive, designed to have inertia properties very similar to the turbojet engine hardware.

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Likewise, the turbine rotor was sized to simulate the inertia properties of the engine hardware. The simulator turbine housing was kept separate from the drive turbine so that it could be insulated for high temperature operation. The turbine housing included electrical resistance heating elements and provision to accept air at temperatures up to 1200F (650C). Provision for displacement sensors and a speed pickup was also included.

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Figure 3. Simulator rig with key hardware elements

Figure 4. Simulator rig hardware setup.

Figure 5. Rig instrumentation plan

The simulator rotor was a hollow single-component shaft

with two end-caps that was approximately 327 mm (12.9 inch)

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long with a 3.2 mm (0.125 inch) wall thickness. The shaft was slightly longer than the engine shaft to make it easier to fabricate, and to facilitate instrumentation by presenting larger probe targets. The effects of the added length on the rotor’s inertial properties were compensated for by the size and locations of the disks. The wall thickness was chosen to be as thin as possible without causing fabrication obstacles. Most of the simulator rotor OD was 31.2 mm (1.23 in.), but was necked down to 25.4 mm (1 in.) at the forward end to reduce ball bearing DN.

The simulator rotor with two disks weighed approximately 30 Newtons (6.8 lbs). The forward disk was made of 17-4 stainless steel and served two roles: it simulated the inertial properties of the compressor, and it was the drive mechanism for the simulator. The aft disk, which simulated the turbine, was made of Inconel 718 to withstand the expected elevated temperatures. Due to the arrangement of the disks, the static or gravity load on the foil bearing was approximately 17.8 Newtons (4 lbs).

Bearing System Design And Analysis The overriding goal of the bearing design process was to

yield a bearing that had dynamic stiffness and damping properties that would enable the engine rotor (and the simulated hardware) to operate to at least a 25% overspeed conditions at bearing temperatures to 1200F (650C). While these criteria exceed requirements, the extra margin provided would enhance success and also demonstrate potential for growth engines. To achieve this bearing performance, the following specific design objectives were used:

1. Sufficient static load capacity 2. Sufficient dynamic load capacity 3. Stability throughout the rotor’s speed range 4. Reasonable lift-off speed for bearing life 5. Minimize journal deformation while maintaining

compatibility with flight hardware (i.e., lightweight). 6. Manufacturability of the bearing structures 7.Integration of the journal with the shaft, for assembly

procedures and fits to accommodate centrifugal and thermal effects.

Iterative bearing design and rotor-bearing system dynamic analyses were completed prior to hardware fabrication. Using the static load and known operating speed range, preliminary bearing dynamic coefficients were predicted for use in rotordynamic analysis to ensure adequate system critical speed margin during operation. Based on the nominal static load of approximately 17.8 Newtons, a 50 mm diameter by 25 mm long bearing was selected for the initial design. While the static loading only represented 13.8 kPa, the bearing was designed to provide a total load capacity of about 670 kPa.

To design the aft bearing to withstand changes in shaft diameter due to centrifugal and thermal growth that will occur during operation, a coupled elasto-hydrodynamic computer code was used to quantify the effects that speed changes would have on bearing dynamic coefficients. As seen in Figure 6, with the effect of journal centrifugal and thermal growth included, the variation in both direct and cross coupled stiffness can be substantial. To accommodate the high operating temperatures the a nickel base super alloy was used for the foils, the bearing surface was coated with a proprietary multi-layered composite dry film lubricant system capable of 730°C.

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While journal coating materials, such as PS304, were considered, the journal was coated with electrolysis nickel due to the limited testing planned for this demonstration program.

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Figure 6. Foil bearing speed dependent dynamic stiffness coefficients.

Using the bearing data and the finite element model of the rotor as shown in Figure 7 critical speeds and stability were predicted to assess the expected bearing and integrated system performance. The results of the rotordynamic critical speed whirl and stability analyses are presented in Figure 8 and Figure 9. These results, showing the operating range free of critical speeds/damped natural frequencies, were compared to engine predictions and found to adequately represent the engine.

With appropriate similitude between the simulator rig and

Figure 7. Simulator rotor bearing system model

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Figure 8. Simulator rotor critical speeds and mode shapes.

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the engine, testing of the hybrid bearing rotor support system (rolling element bearing in the forward end and compliant foil bearing in the aft end), would minimize engine integration risk.

EXPERIMENTAL TEST RIG RESULTS Having verified the suitability of the simulator rig, the first

task was to demonstrate stable operation to maximum rig speed. As seen in Figure 10, full speed operation was readily attained and that performance on acceleration and deceleration were very similar. Peak orbits observed at both ends of the rotor were less than 15 micron throughout the entire speed range. Of special note is the fact that rotor vibration amplitudes at the foil bearing, or aft end of the rotor, were less than 10 micron for much of the speed range.

Figure 10. Simulator rig rotor peak vibrations at forward and aft ends.

Following the system response and stability verification

tests, bearing thermal stability was evaluated. An assessment of axial thermal gradient in the bearing is important since the bearing performance can be adversely affected if a large gradient is encountered. A large thermal gradient results in uneven bearing and shaft growth thereby altering the local bearing clearance non-uniformly. During the thermal stability

Figure 9. Simulator whirl map showing damped natural frequencies

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tests the rotor was first spun to 60,000 rpm with an airflow rate of 566 l/min (20 CFM). Once bearing temperature stabilized, airflow was decreased incrementally until a high rate of temperature rise in sensor T3 was evident which did not appear to stabilizing. This qualitative assessment required considerable prior experience and familiarity with foil bearing thermal response, since thermal runaway could occur when very low flows were attempted. During initial reductions in airflow, bearing temperature would increase almost instantaneously with a decrease in airflow, but would begin to stabilize within a short time of between 30 seconds to 1 minute. Representative results of this testing are shown in Figure 11. Once the minimum flow was determined (i.e., that flow level where temperatures would stabilize), speed was then decreased and the cycle repeated. A typical test included 10 incremental stepwise decreases in airflow ranging from 40 to 10 L/min. From these tests, the minimum permissible flow was found to be about 140 L/min (5 CFM). Below 140 L/min bearing temperatures continued to rise with no indication of stabilizing. Rather than destroy the bearing, airflow would be increased to re-stabilize temperature and the next speed point would be evaluated.

Additional and more detailed thermal mapping was completed to assess foil bearing axial thermal gradients (see Figure 12). From these tests it was seen that for higher speed

Figure 11. Preliminary bearing thermal stability tests in simulator rig.

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operation, higher cooling flow rates resulted in higher axial gradients in the bearing. Sensors T1 and T2 were chosen for this evaluation since they were located in the loaded area of the bearing where the highest temperatures and gradients would be experienced. It was thus determined that, since the bearing can sustain operating temperatures to 1250F (675C), better bearing performance could be achieved with lower cooling flow. In essence it is better to let the bearing operate at a higher bulk temperature with a lower gradient. This has also been confirmed independently by Radil et.al [13]. Earlier testing by Heshmat [1] revealed that a bearing axial thermal gradient of 11 C/cm (50 F/inch) was the maximum permissible gradient across the bearing. As seen in Figure 12, the foil bearing has demonstrated an increase in thermal gradient capability up to 13 C/cm (up to 60 F/inch). Since a lower gradient minimizes bearing load carrying capacity reductions, lower cooling flows are used. Lower flows are beneficial since engine compressor performance is not compromised.

Following the baseline dynamic and thermal stability tests, high speed and high temperature testing was conducted. These tests and the results, as shown in Figure 13 through Figure 16, reveal the ability of properly designed Class IV foil bearings [11] and coatings to operate at high speeds and temperatures, both of which are crucial to successful engine application. In Figure 13, the simulator rig test cycle included steady operation at 40,000 rpm while the bearing compartment temperature was raised to approximately 538C (1000F). Once high temperature

Figure 13. Foil bearing temperature and speed versus time as recorded in simulator rig.

Figure 14. Measured simulator rig rotor motions versus foil bearing temperature and speed showing stable operation regardless of speed.

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was achieved speed was sequentially increased to 60,000 rpm and held constant to verify bearing thermal stability. Cooling airflow rates used for these tests were based upon the results of the earlier thermal stability tests. Having verified thermal stability at 538C, speed was decreased while bearing temperature was increased to 650C (1200F) and speed again increased to 60,000 rpm. Bearing temperature was increased by increasing the current to the electric resistance heaters and by increasing the inlet temperature of the air used for cooling the bearing. Once the desired temperature was achieved and operation demonstrated, the rig was rapidly shut down to simulate an operational condition.

After these steady state tests, transient conditions tests were conducted as shown in Figure 14 through Figure 16. The purpose of the transient tests was to verify the ability of the bearing to accommodate the varying centrifugal and thermal bearing journal growth conditions under simulated operating conditions. The final thermal testing was completed with the bearing temperature held at 538C during numerous start stop cycles to simulate hot restarts and assess bearing wear under elevated temperatures. As seen in Figure 17 and Figure 18, the condition of the bearing and journal after numerous tests at speeds to over 60,000 rpm, temperatures to 650C and numerous start stop cycles, remains in excellent condition. No evidence of rubs or surface degradation was observed, although the bearing coating color changed to light grey from its original black color.

Figure 15. Bearing thermal response while heating simulator rig and cycling speed.

Figure 16. Simulator rig bearing start-stop cyclic testing at 400°C

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With the successful completion of simulator and bearing testing showing that stable high speed and high temperature was achieved, engine integration and testing was initiated.

Figure 17. Foil bearing surface condition after high temperature operation in simulator rig.

Figure 18. Condition of journal surface after high temperature testing in simulator rig.

ENGINE TEST RESULTS As shown in Figure 19 the engine aft end housing and rotor

were modified to accommodate the compliant foil bearing. In an effort to reduce the engine modification costs for these initial engine tests, externally supplied cooling air was used. This approach simplified the engine modifications and provided for more precise control over test conditions.

Instrumentation in the modified engine included thermocouples to measure bearing temperature; pressure sensors to measure pressure drop and flow across the foil bearing; displacement sensors to measure relative shaft-to-housing vibrations; accelerometers to measure case vibrations; and instrumentation to measure engine thrust were all included. Once the engine was assembled and installed in the test cell (see Figure 20), a series of engine air starts were conducted to verify bearing lift off and engine low speed operation. Typical speeds achieved during the engine restarts were on the order of

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13,000 rpm. Following these initial low speed tests, the engine was started and operated to full speed and thrust.

Figure 19. Turbojet engine aft cone, foil bearing and turbine rotor.

Figure 20. Turbojet engine installed in test cell.

Once engine full speed engine operation was verified, a total of 70 engine start stops, including, hot restarts, were completed to verify bearing integrity and life. Other tests included a total of seven simulated mission cycles. Figure 21 and Figure 22 present data acquired during the first simulated mission cycle. During subsequent mission cycles nearly identical performance was observed. As seen in Figure 21, the differential pressure across the axial length of the bearing was 7 kPa (1 psig), a very small amount to affect the needed cooling flow. Additionally, it was noted that the differential temperature gradient in the bearing was consistent with the simulator rig testing, mirroring shaft spin speed. During the mission cycle testing, the engine case vibrations were below those typically observed for the engine with a rolling element bearing installed, see Figure 22. Figure 23 is a composite plot of the relative housing-to-shaft motions during a series of cyclic engine tests. As seen a high degree of repeatability was achieved over seven different engine cycles. Even though it appears that the vibrations increase with subsequent cycles in the 100 and 104% tests, it should be noted that the variation in signals is on the order of sensor resolution for the 104% speed testing. Additionally, the housing motions and structural vibrations do influence the readings of the aft end sensor reading, especially since the data was not filtered and

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instantaneous data signals were used. After more than 14 hours of engine operation and seventy start stop cycles the engine was disassembled and the bearing and journal inspected. As seen in Figure 24 the condition of both components was excellent.

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CONCLUSION AND SUMMARY The operation of a turbojet engine simulator with a hybrid

support bearing system of a ball bearing and foil bearing was successfully completed at speeds and temperatures to 60,000 rpm and 650C respectively. The successful simulator rig testing was followed by installation of a foil journal bearing into a 1070 to 1330 N thrust class turbojet engine directly behind the single stage turbine rotor. Full speed operation and numerous engine simulated flight mission profiles were successfully completed with the hybrid rotor support system. Based on this very successful demonstration, the feasibility of developing a truly oil-free gas turbine engine for flight has been established. Additional testing is planned to demonstrate operation using compressor bleed air and further quantify the benefits to be gained with foil bearings in gas turbine engines.

Based on the engine configuration tested, it is estimated that engine weight reductions as high as 30% and cost reductions of up to 20% may be possible by eliminating the entire bearing lubrication system and using foil bearings.

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Figure 24. Condition of bearing and journal after engine testing.

These data and experience gained in this test program is being used to assess the application of foil bearings to numerous other applications ranging from near MEMS scale to man rated engines for both military and commercial systems.

ACKNOWLEDGMENTS The engine testing presented in this paper was funded

independently by MiTi® and Williams International. The background technology work presented herein was the result of numerous Small Business Innovation Research efforts funded by the U.S. Air Force, the U.S. Army and NASA, as well as MiTi® internal research and development funds. The authors would like to thank those individuals within government and industry that have had the vision and patience to pursue the efforts that have resulted in this demonstration. Special thanks are reserved for Dr. John Willis for his efforts in developing the high temperature coatings and Mr. David Slezak for his fabrication of the foil bearings used in this effort.

REFERENCES 1. Heshmat, H. and Hermel, P. "Compliant Foil

Bearing Technology and Their Application to High Speed Turbomachinery." Proceedings of the 19th Leeds-Lyon Symposium on Thin Film in Tribology - From Micro Meters to Nano Meters, Leeds, U.K.,

Sep. 1992.

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2. Heshmat, H. "Analysis of Compliant Foil Bearings with Spatially Variable Stiffness." AIAA/SAE/ ASME/ASEE 27th Joint Propulsion Conference, June,1991, Sacramento, CA, Paper AIAA-91-2102.

3. Heshmat, C.A. and Heshmat H. "An Analysis of Gas Lubricated, Multi-Leaf Foil Journal Bearings with Backing Springs." ASME Paper No. 94-Trib-61.

4. Heshmat, H. and Ku, C-P R., ”Structural Damping of Self-Acting Compliant Foil Journal Bearings,” ASME Trans., J.of Trib., Vol. 116, No.1, January 1994, pp. 76-82.

5. Salehi, M., Heshmat, H., 2001, “Frictional Dampers Dynamic Characterization-Theory and Experiments” The 28th Leeds-Lyon Symposium on Boundary and Mixed Lubrication, Sep. 3rd to 7th , Vienna, Austria, Elsevier Science Publishers B.V., 2001, pp: 559-575.

6. Heshmat, C.A., Xu, D. and Heshmat, H., “Analysis of Gas Lubricated Foil Thrust Bearings Using Coupled Finite Element and Finite Difference Methods,” presented at ASME/STLE Joint Tribology Conference Orlando, Fl October 10-13,1999, Transaction of ASME, Journal of Tribology, Vol. 122, pp: 199-204, January 2000.

7. Heshmat, H., “The Integration of Structural and Fluid Film Dynamic Elements in Foil Bearings- Part I: Past Approaches to the Problem,” Proceedings of the 1999 ASME Design Engineering Technical Conferences, 17th Biennial Conference on Mechanical Vibration

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and Noise, ASME Paper No. DETC/VIB-8271, September 12-15, 1999 Las Vegas, Nevada

8. Salehi, M., Heshmat, H., Walton, J., 2003, “The Frictional Damping Characterization of Compliant Bump Foils”, Accepted for publication in ASME journal of Tribology, Vol. 125, No. 3.

9. Heshmat, H. “Operation of Foil Bearings Beyond the Bending Critical Mode,” presented at ASME/STLE Joint Tribology Conference Orlando, Fl October 10-13,1999, Transaction of ASME, Journal of Tribology, Vol. 122, pp: 192-198, January 2000.

10. Walton, J.F. and Heshmat, H., “Application of Foil Bearings to Turbomachinery Including Vertical Operation,” Presented at ASME Turbo Expo, Land, Sea and Air, June 1999, Indianapolis, IN. ASME Paper 99-GT-391

11. Della Corte, C., and Valco, M.J., 2000, “Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery.” NASA/TM-200-209782 and AR-TR-2334.

12. Heshmat, H., Walton,J.F., DellaCorte,C. and Valco,M.J., “Oil Free Turbocharger Demonstration Paves Way to Gas Turbine Engine Applications” Paper 2000-GT-0620, presented at ASME Turbo Expo, Land, Sea and Air, International Gas Turbine Conference, Munich, Germany, May 8-11, 2000.

13. Radil, K. and Zeszotek, M. “An Experimental Investigation into the Temperature Profile of a Compliant Foil Air Bearing.” Trib. Transactions, 47, 4, pp 470-479,Oct. 2004.

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