Samuel A. Howard

Glenn Research Center, Cleveland, Ohio

Luis San Andres

Texas A&M University, College Station, Texas

A New Analysis Tool Assessment for Rotordynamic

Modeling of Gas Foil Bearings

NASA/TM—2010-216354

July 2010

GT2010–22508
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientifi c and Technical Information (STI) 

program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Offi cer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI program provides access 

to the NASA Aeronautics and Space Database and 

its public interface, the NASA Technical Reports 

Server, thus providing one of the largest collections 

of aeronautical and space science STI in the world. 

Results are published in both non-NASA channels 

and by NASA in the NASA STI Report Series, which 

includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or 

of specialized interest, e.g., quick release 

reports, working papers, and bibliographies that 

contain minimal annotation. Does not contain 

extensive analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

Specialized services also include creating custom 

thesauri, building customized databases, organizing 

and publishing research results.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question via the Internet to help@

sti.nasa.gov

• Fax your question to the NASA STI Help Desk 

at 443–757–5803

• Telephone the NASA STI Help Desk at

 443–757–5802

• Write to:

 NASA Center for AeroSpace Information (CASI)

 7115 Standard Drive

 Hanover, MD 21076–1320
Samuel A. Howard

Glenn Research Center, Cleveland, Ohio

Luis San Andres

Texas A&M University, College Station, Texas

A New Analysis Tool Assessment for Rotordynamic

Modeling of Gas Foil Bearings

NASA/TM—2010-216354

July 2010

GT2010–22508

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Turbo Expo 2010

sponsored by the American Society of Mechanical Engineers (ASME)

Glasgow, Scotland, United Kingdom, June 14–18, 2010
Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://gltrs.grc.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
NASA/TM—2010-216354 1 

A New Analysis Tool Assessment for Rotordynamic 

Modeling of Gas Foil Bearings 

Samuel A. Howard

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135 

Luis San Andres 

Texas A&M University 

College Station, Texas 77843 

Abstract 

Gas foil bearings offer several advantages over traditional 

bearing types that make them attractive for use in high-speed 

turbomachinery. They can operate at very high temperatures, 

require no lubrication supply (oil pumps, seals, etc.), exhibit 

very long life with no maintenance, and once operating 

airborne, have very low power loss. The use of gas foil bearings 

in high-speed turbomachinery has been accelerating in recent 

years, although the pace has been slow. One of the contributing 

factors to the slow growth has been a lack of analysis tools, 

benchmarked to measurements, to predict gas foil bearing 

behavior in rotating machinery. To address this shortcoming, 

NASA Glenn Research Center (GRC) has supported the 

development of analytical tools to predict gas foil bearing 

performance. One of the codes has the capability to predict 

rotordynamic coefficients, power loss, film thickness, structural 

deformation, and more. The current paper presents an 

assessment of the predictive capability of the code, named 

XLGFBTH (Texas A&M University). A test rig at GRC is used 

as a simulated case study to compare rotordynamic analysis 

using output from the code to actual rotor response as measured 

in the test rig. The test rig rotor is supported on two gas foil 

journal bearings manufactured at GRC, with all pertinent 

geometry disclosed. The resulting comparison shows that the 

rotordynamic coefficients calculated using XLGFBTH represent 

the dynamics of the system reasonably well, especially as they 

pertain to predicting critical speeds. 

Introduction 

Small, high-speed, lightly-loaded turbomachinery offers a 

class of applications with demands well-matched to the 

performance capabilities of Gas Foil Bearings. Examples of 

applications of commercial and industrial interest include: 

engines for turboshaft propulsion, general aviation propulsion, 

regional jet propulsion, turbo-generators, turbo-compressors, 

turbo-pumps, blowers, motors, etc. Successful machines, such 

as micro turbine generators, utilizing gas foil bearing 

technology demonstrate that the technology is feasible for 

turbomachinery of this size class. Design of such systems, 

however, is currently more of an art than a science because of 

a lack of accurate computational design tools and procedures. 

There have been some efforts to develop the tools and 

procedures necessary to design using minimal hardware and 

experimentation iterations. Several computational tools for 

predicting performance and rotordynamic coefficients to 

enable detailed design have emerged lately. This emergence 

exposes another deficiency in the lack of experimental data 

available to validate models and predictive capabilities. This 

paper seeks to assess the capabilities of a recently developed 

foil journal bearing analysis tool by comparison of predicted 

to measured response to accurately model the dynamics of a 

rotor bearing system. 

Nomenclature 

E Bearing eccentricity 

Cxx Damping coefficient (subscript denotes direction) 

Kxx Stiffness coefficient (subscript denotes direction) 

P Predicted pressure 

Pa Ambient pressure 

X Horizontal coordinate 

Y Vertical coordinate 

 Eccentricity angle 

 Rotational velocity 

Background 

A typical bump-type journal foil bearing is shown in 

Figure 1. The basic design consists of a compliant “foil” 

structure acting as the bearing surface inside a rigid shell. A 

hydrodynamic air film is generated in the space between the 

smooth top surface of the foil structure and a rotating 

shaft/journal inserted in the bearing. The compliant structure 

allows for deformation of the bearing to accommodate shaft 

centrifugal growth, thermal growth, misalignment, dynamic 

shaft motion, etc. The compliant structure also yields bearing 

performance characteristics that can be tailored to a specific 

application to some extent. Parametric design variations can 

result in more or less stiffness and damping, for example, to 

better match the demands of a particular application. The 

appeal of gas foil bearings lies in their ability to operate in the 

extreme environments of high temperature and high speed 
NASA/TM—2010-216354 2 

Figure 1.—Typical bump-type foil journal bearing cross-section. 

while eliminating the need for a lubricant supply and 

potentially exhibiting long life cycles with low maintenance 

and low power loss. Therefore, there is a strong desire to 

develop the ability to accurately model the bearings’ static and 

dynamic performance characteristics. There has been a fair 

amount of work done to characterize the structural stiffness 

and damping properties of the compliant structure in gas foil 

bearings. These analyses focus only on the mechanical 

properties of the bump foil strips and top foil, without the 

hydrodynamic film contribution due to journal rotation. The 

motivation for these studies comes from the fact that the 

overall gas foil bearing stiffness and damping coefficients are 

a series combination of the support structure (bump foil) 

stiffness and the hydrodynamic (gas film) stiffness. Therefore, 

these studies have the potential to elucidate some of the 

underlying physical behavior of the overall bearing. 

Additionally, various models for the bump foil structure can 

be analyzed and compared to experimental results without the 

added complexity of the hydrodynamics in order to screen 

appropriate structural models for integration into a complete 

analysis tool. 

Ku and Heshmat (Refs. 1 and 2) were among the first to 

report such work. Their analysis and experimentation indicate 

that the distance between bumps in the support structure, or 

bump pitch, is an important parameter in dictating the 

structural stiffness. The number of bumps, types of surface 

coatings, and the presence of lubricant also influenced 

stiffness and damping, but to a lesser extent. A few years later, 

Ku and Heshmat (Ref. 3) extended their experiments to 

include applied load. Higher static loads were found to 

increase the structural stiffness of the bump foil strips. A 

frequency dependence was also identified. 

Recently, there has been more interest in this topic, Rubio 

and San Andres (Ref. 4) conducted experiments wherein a 

bearing was subjected to increasing static loads while the 

displacement was monitored. These so-called load-deflection 

curves show a dependence of the structural stiffness on load 

magnitude, amplitude of motion, dry-friction coefficient, 

radial clearance/preload, and bump geometry. Also present 

was hysteresis in the load deflection curve demonstrating that 

frictional forces do, in fact, provide significant mechanical 

energy dissipation or damping in oscillatory bearing motions. 

Le Lez, et al. (Ref. 5) advance a more detailed analytical 

study of support structure behavior by conducting a finite 

element analysis of the bump foil, including bump interactions 

with each other. Their findings again indicate that applied load 

and friction coefficient are important parameters, and to a 

lesser extent frequency of oscillation. They also point out that 

stick-slip occurs in foil bearing support structures leading to 

the hysteretic frictional damping observed by others. 

Lee, et al. (Ref. 6) studied the structural stiffness and 

damping coefficients using finite element analysis, as well. In 

addition, they included the effect of temperature. As with the 

others, they found bump geometry, including bump 

pitch/width and height, to affect stiffness. The effect of 

increased temperature was to decrease both stiffness and 

damping of the bump support structure due to a loss of 

material strength at higher temperature. 

All of the previous works serve to enable future advanced 

analysis tools for gas foil bearings including the 

hydrodynamic gas film. A brief summary of efforts to model 

foil bearings with coupled hydrodynamics and structural 

analysis follows: Heshmat, et al. (Refs. 7 and 8) present the 

first detailed analysis of gas foil bearings. Their model is 

among the simplest of models in the literature, applying a 

compliance parameter to the sub-foil structure. The 

compliance parameter, , is an analytic expression of the 

inverse of the bump foil stiffness based upon material and 

geometry. The foil deformation and fluid pressure are coupled 

through the film thickness relationship. In this manner, the 

stiffness of the bump foil structure is modeled as a continuous 

elastic foundation with local stiffness independent of global 

foil deflections. In other words, deflections in one location do 

not affect deflections in other locations. Dimensionless results 

of bearing performance characteristics are reported, but 

insufficient geometry information is provided to garner useful 

design data from the results. 

Iordanoff (Ref. 9) used a simple model with a linear 

compliance distribution in thrust bearings to solve for load and 

power loss. He developed a methodology to determine the best 

geometry for a given operating point and for a given operating 

range. He used his model to design a thrust bearing that 

demonstrated roughly a five-fold improvement in load 

capacity over previous designs. 

Heshmat, et al. (Ref. 10) used a commercial finite element 

code to model the structural bump foil supports coupled with a 

finite difference model of the gas film to predict steady state 

load performance of gas foil thrust bearings. Good agreement 

is shown between predictions and measurements for static 

load capacity. This method potentially can be used to model 

steady state performance, but its usefulness is limited due to 
NASA/TM—2010-216354 3 

numerical inefficiency and convergence issues for dynamic 

analyses. 

Bruckner (Ref. 11) analyzed foil thrust bearings using a biharmonic plate equation to model the top foil with a stiffness 

function representing the bump foil support structure. He also 

included a thermal analysis to determine the temperature field 

in the gas film. The thermal deformations of the foil structure 

are not included in this model. The structural equation and the 

Reynolds equation for the hydrodynamics were solved using a 

central differencing scheme, while the energy equation was 

solved using a type of shooting function for the temperature 

field. All three solutions are iterated upon until a converged 

solution is found. The results for predicted foil deflections 

show high spots in locations similar to wear scar patterns 

found in practice, and the temperature predictions are 

reasonably close to indicate that including thermal effects is 

important when modeling gas foil bearings. This is a steady 

state thrust bearing analysis, however, the methodology could 

be extended to predict dynamic coefficients of journal 

bearings, although it would likely be quite slow due to the 

multiple levels of iteration involved. It is important in that it 

shows it is necessary to include thermal effects in the 

modeling of gas foil bearings. 

Peng and Carpino (Refs. 12 and 13) use a finite difference 

solution technique to predict gas foil journal bearing stiffness 

and damping. The model uses an equivalent stiffness for the 

structure coupled with the Reynolds’ equation for the gas film. 

To model the frictional damping mechanism between the foils 

and between the foils and housing, they use a viscous damping 

model with the same energy dissipation as the dry friction 

mechanism. 

Carpino et al. (Refs. 14 and 15) developed a more 

sophisticated analysis using a finite element formulation. The 

gas film and structure are coupled via the pressure field and 

solved iteratively. In this model, the bending and membrane 

effects of the top foil are included as well as the deformations 

of the sub-foil structure. 

Carpino and Talmadge (Refs. 16 and 17) have developed a 

quite detailed model for foil journal bearings. The bending and 

membrane effects of the top foil are again included and are 

coupled through moment, tension, curvature, and strain 

equations. The model uses a single cylindrical shell finite 

element to represent both the gas film and the structural 

model. The top foil sag between bumps, and individual bump 

behavior are not included. An interesting result of this work is 

a prediction that damping decreases with increased friction 

coefficient due to the bump foil locking up above certain 

friction levels. 

Lee, et al. (Ref. 18) couple an elastic foundation model for 

the foil structure to the Reynolds’ equation including the 

effects of slip flow (high Knudsen number). The results 

indicate that for much of the operating regime, slip flow is 

negligible. However, at high load, low speed, and high 

temperature conditions, when the film thickness is small 

compared to the mean free path for air, slip flow can have 

significant influence on the load capacity and dynamic bearing 

coefficients. 

Peng and Khonsari advance isothermal (Ref. 19) and 

thermohydrodynamic (Ref. 20) analyses of gas foil journal 

bearings. In the isothermal model, the authors use a model 

similar to Heshmat’s (Refs. 7 and 8) to predict steady-state 

operating characteristics. They compare the load carrying 

capacity and stability to that of rigid gas bearings, and report 

that compliant gas bearings offer higher load capacity and 

better stability. In (Ref. 20), the authors extend their model to 

include the energy equation and therefore, can predict the 

temperature field in the gas film. While the model includes 

calculation of the temperature field, it does not include the 

thermal deformations of the foil structure, which is believed to 

detract significantly from the load capacity of gas foil 

bearings. The results indicate an increase in load capacity as 

temperature increases, which is in direct opposition to 

experimental data obtained at GRC (DellaCorte (Ref. 21)). 

Foil thermal deformations are thought to be the leading cause 

of decreased load capacity at high temperature, offering a 

plausible cause for the discrepancy between the analysis and 

experiments. 

Kim and San Andres (Ref. 22) use analytic expressions for 

foil structural stiffness linked to a Reynolds’ equation 

hydrodynamic gas film solution. Using an axially averaged 

pressure, they report good agreement with experimental data 

for journal attitude angle and eccentricity at high static load 

conditions. At low load conditions the agreement is poor, due, 

they claim, to manufacturing inaccuracy of the tested bearings. 

Kim and San Andres (Ref. 23) develop a concept to determine 

a theoretical minimum film thickness for implementation in 

more complex analyses. They use this model in the previous 

analysis (Ref. 22) and in a more advanced analysis (Ref. 24), 

wherein they model the top foil with 1-D and 2-D finite 

elements. They report that both advancements greatly increase 

computational efficiency, yet the 2-D model does not reap 

great benefits over the 1-D model. Forced axial flow has been 

identified as an effective mechanism for thermal management 

in foil journal bearings (Ref. 25). In Reference 26, San Andres 

and Kim identify an unintended beneficial byproduct of axial 

flow driven by end pressurization, enhanced rotordynamic 

stability. Their analytical results correlate well with 

experimentally observed delayed instability. 

Assessment of Analysis Capability 

The previous discussion is a review of the literature on foil 

bearing predictive techniques. While it is important to know 

the work that has been done to facilitate modeling of gas foil 

bearings, the desired end result is a comprehensive analysis 

tool designers can use to build foil bearing hardware. With 

that result in mind, the following discussion and assessment of 

one of the techniques listed above seeks to determine, by way 

of modeling an existing test rig, if hardware could reasonably 

be designed using current tools. 
NASA/TM—2010-216354 4 

The analysis tool being assessed is called XLGFBTH, and 

is based on the work of San Andres and Kim (Refs. 22 to 24). 

XLGFBTH uses a Microsoft Excel Graphical User Interface to 

make data entry and output easy and readily available for most 

users. The code gives the user control over all pertinent 

bearing parameters allowing analysis of most bump-type foil 

bearing designs. The sub-structure stiffness distribution is 

calculated separately, before the main analysis routine. Thus, 

with some programming skill, bearing designs other than 

bump-type designs may be possible. The program runs a 

number of operating conditions including multiple cases for 

journal speed and (a) applied load or (b) journal eccentricity, 

with selections of force coefficients evaluation for varying 

whirl frequency or fixed whirl frequency, usually synchronous 

with journal speed. 

The program graphical output includes plots for the 

pressure, film thickness and top foil deflection fields; and 

graphical and tabular output for the bearing journal 

eccentricity and attitude angle, minimum film thickness, 

torque and power loss, bearing structural stiffness, and 

stiffness and damping force coefficients versus the specified 

load and journal speed. Similar output parameters are found 

when the journal eccentricity is specified; however in this 

case, the program solves for the bearing reaction force. 

The output is easy to visualize using the spreadsheet 

interface. Some example output is shown in Figures 2 to 5. 

The major potential drawback to this code is its use of 

empirically derived characteristics used in the modeling of the 

structural stiffness and damping. There are two parameters, 

namely the sub-structure loss factor and the top foil stiffening 

factor, that must be input to the analysis. There are suggested 

values for these parameters, based upon empirical correlations. 

However, if one were to analyze bearings significantly 

different from those used in the correlations, these parameters 

would be relative unknowns, thus requiring experimental 

efforts to determine them. 

Figure 2.—Predicted pressure field in a 50.8 mm 

generation I gas foil bearing operating at 60,000 rpm, 20 n 

static load. 

Figure 3.—Predicted film thickness field in a 50.8 mm 

generation I gas foil bearing operating at 60,000 rpm, 20 n 

static load. 

Figure 4.—Predicted top foil deflection field in a 50.8 mm 

generation I gas foil bearing operating at 60,000 rpm, 20 n 

static load. 

Figure 5.—Predicted (synchronous speed) stiffness and 

damping coefficients versus journal speed for a generation I 

gas foil bearing with 20 n static load (y-direction). 

 

0

0.5

1

1.5

2

0 72 144 216 288 360

Axial Dir. 

(mm) Foil Deflection 

(m)

Angular Coordinate (deg)
NASA/TM—2010-216354 5 

Note that the structural loss factor is a measure of the 

mechanical energy dissipation characteristics of the bumps 

sliding against the bearing inner diameter. The loss factor is a 

function of the material characteristics and surface conditions, 

load amplitude and frequency, as well as the environmental 

conditions; including atmospheric pressure, gaseous content, 

and humidity. 

The top foil stiffening factor is a measure of the anisotropic 

elastic properties which depend on the forming process of the 

top foil. For example, annealed flat and conformed shells offer 

significantly different material properties along their principal 

axes. 

For generality, the selection of the top foil stiffening factor 

and bearing structural loss factor are left to the user. This 

enables flexibility in the code to analyze bearing designs 

different from those discussed here and benchmarked with the 

analysis tool. Experimental work may be required to arrive at 

appropriate values for these two parameters, however, for 

typical bump-type bearings resembling those in this paper, 

suggested values are given based on a significant volume of 

empirical work (Refs. 4, 27 to 29). 

The average user of this code will not have a bearing or 

rotor system in hand when using the code to design a 

turbomachine, and therefore will have no way to compare the 

results to measured response. Thus, the purpose of this paper 

is to determine if the analysis code adequately represents the 

physics of the particular problem class assessed herein while 

using recommended procedures and parameters where 

available, and reasonable assumptions elsewhere. For that 

reason, the recommended value for foil stiffening factor (4), 

and a reasonable guess at the loss coefficient (the code 

recommends using the friction coefficient, 0.2 is assumed) are 

used, and no attempt is made to evaluate the prediction 

sensitivity through parametric perturbation. 

Methodology for Assessment of 

Rotordynamic Predictive Capability 

The procedure used to evaluate the capability of XLGFBTH 

to predict the rotordynamic behavior of machinery is to first 

predict the rotordynamic response of a foil bearing test rig 

(Ref. 30) at GRC. The test rig, Figure 6, consists of a gas foil 

bearing supported rotor system capable of speeds ranging up 

to 60,000 rpm in any number of configurations with 

instrumentation and data acquisition to observe and record the 

rotor response. In this case, the rotor configuration is simple, 

as shown in detail below, for easy modeling in a 

rotordynamics analysis package. Two foil bearings 

manufactured at GRC are used in the rotor simulator for the 

evaluation of the bearing predictive tool. No specific break-in 

procedure was performed on these bearings because typical 

break-in procedures require many high-temperature start/stop 

cycles (Ref. 31), of which this test rig is incapable. It is worth 

noting, however, that the rotor was chrome plated resulting in 

a very smooth and consistent surface much like one would 

Figure 6.—Schematic of GRC foil bearing rotordynamic 

test rig. 

expect of the typical foil bearing shaft coatings after a break-in 

procedure. 

The first step, is to make the two foil journal bearings, and 

predict their rotordynamic coefficients using XLGFBTH. In 

order to predict their performance, the nominal bearing 

clearance must be known. One could ascertain the clearance 

by calculating the stack-up height of the bump and top foils, 

and subtracting that from the difference between the inner 

diameter of the bearing shell and the outer diameter of the 

shaft. There can be uncertainty in this method due to 

manufacturing variations, particularly in the bump foils. 

Therefore, in this case, a relatively new test rig at GRC, called 

the load deflection test rig and shown in Figure 7, is used to 

determine the nominal clearance. 

A foil bearing is mounted in the load deflection test rig and 

subjected to static loads in opposing directions. A cable pulls 

upward on the bearing using dead weights, while a cable 

connected through a load cell to a pneumatic cylinder pulls 

downward. By varying the pressure to the pneumatic loader, 

one can apply loads ranging from positive 178 N (upward) to 

negative 178 N (downward). This is done in a stepwise 

fashion while monitoring and recording the displacement of 

the bearing relative to the stationary (nearly rigid) solid shaft 

running through it. The result of this test is a curve of 

deflection versus load for a range of loads on both sides of 

zero, as shown in Figure 8 for a typical bearing. As the figure 

shows, the shape of the load deflection curve is typically 

somewhat like an “S” with a region near zero load where the 

slope is very steep denoting a large flexibility. This steep part 

of the curve is due to the fact that near zero load, the bearing is 

nearly centered on the shaft and it has very low stiffness in the 

radial direction. As the load increases, and the bearing moves 

further away from center, the bumps on the side opposite the 

load become active, deforming as the load increases. At that 

point, the stiffness of the bearing increases and the slope of the 
NASA/TM—2010-216354 6 

Figure 7.—Schematic of the GRC load deflection test rig. 

Figure 8.—A sample deflection versus static load test results 

for the right bearing. 

load deflection curve decreases. The region of the curve where 

the slope is steep is defined as the nominal bearing clearance, 

and the region where the slope is low is taken as the structural 

flexibility (1/stiffness) of the foil bearing. The load deflection 

curve also has some hysteresis, meaning that the bearing does 

not follow the same path during the unloading cycle as it does 

during the loading cycle. This well known behavior is 

indicative of material damping, and the size of the loop 

evidences the magnitude of the energy dissipation. It is 

important to note that a given foil bearing’s load versus 

deflection curve (and hysteresis loop) depends on the 

orientation of the load relative to the weld connection line for 

the top foil and bump foil strips. Hence, differing load 

orientations will lead to different ad-hoc clearances and 

substantially different loss factors. Thus, it is important to 

conduct the measurements with the bearing positioned in the 

same direction as the static load will act on the test rig. 

The clearance estimate is important because most foil 

bearing design tools typically assume there is some clearance 

between the rotor and the foil to define (initially) the air gap. 

Therefore, the clearance is an input needed to run an analysis. 

Using the results from the load deflection tests, the left bearing 

diametral clearance is estimated as 68 μm, and the right 

bearing diametral clearance is estimated as 100 μm, for the 

analysis. 

The most important realization from the load versus 

deflection data is that the structure of a foil bearing is highly 

nonlinear, with distinctive soft and hardening regions. In 

nonlinear dynamics, this structural behavior will give rise to 

forced sub- harmonic motions, not to be confused with 

instability associated to loss of damping (Ref. 32). 

In the interest of making the data useful to other 

researchers, the geometry of the test set-up must be presented. 

The general description of the test rig can be found in Howard 

(Ref. 30), and the specific geometry of the rotor is included in 

Figure 9 to enable others to model the rotor bearing system for 

assessment of future analysis tools. To make the data useful to 

a broad audience, the foil bearings used were of an opensource design, enabling the full details of the geometry to be 

reported. Dellacorte, et al. (Ref. 21) describe the 

manufacturing technique and basic geometry used for the 

journal bearings. Table 1 lists the specific geometry of the test 

foil bearings, whose bump geometry is identical to that in 

Reference 21. 

Using the bearing geometry from Table 1, the estimates for 

clearances, and the weight of the rotor (67.2 N), XLGFBTH 

was used to calculate the bearing synchronous rotordynamic 

force coefficients for use in the rotordynamic model 

predictions. Tables 2 and 3 give the calculated stiffness and 

damping coefficients for each bearing, and Figure 10 gives the 

resulting eccentricity and eccentricity angle. 

The geometry and physical attributes of the rotor must also 

be known to appropriately model the system rotordynamics. 

Figure 9 shows the geometry of the rotor, the solid middle 

section of which is 4140 steel, and the two disks attached to 

the ends are 17-4 stainless steel. The rotor assembly weighs 

67.2 N, and is symmetric about the center of mass except for 

small cutouts on the outside diameter of one disk for turbine 

buckets (the small effect of the buckets and the added mass of 

the bolts attaching the disks was neglected in the model). 

Load
NASA/TM—2010-216354 7 

TABLE 1.—FOIL JOURNAL BEARING GEOMETRY 

Diameter 50.8 mm 

Length 40.6 mm 

Foil thickness (bump and top) 0.102 mm 

Bump height 0.51 mm 

Bump pitch 3.17 mm 

Bump length 2.54 mm 

Bump foil angular extent 360

Foil material Inconel 718 

Structural loss coefficient 0.2 

Top foil stiffening factor 4 

Static load, each bearing 33.6 N 

TABLE 2.—STIFFNESS AND DAMPING COEFFICIENTS FOR LEFT BEARING. EVALUATED AT 

FREQUENCY = SYNCHRONOUS SPEED, STATIC LOAD = 33.6 N (IN Y DIRECTION) 

Speed, 

rpm 

Kxx, 

MN/m 

Kxy Kyx Kyy Cxx, 

kNs/m 

Cxy Cyx Cyy 

5000 2.55 –1.55 –2.46 5.89 2.58 –2.49 0.627 5.86 

10000 2.81 –1.06 –1.96 4.77 1.76 –1.19 0.621 2.57 

15000 3.09 –0.777 –1.61 4.38 1.38 –0.751 0.564 1.61 

20000 3.31 –0.538 –1.29 4.25 1.15 –0.550 0.506 1.16 

25000 3.57 –0.376 –1.03 4.20 0.986 –0.446 0.447 0.915 

30000 3.83 –0.265 –0.801 4.21 0.864 –0.385 0.393 0.757 

TABLE 3.—STIFFNESS AND DAMPING COEFFICIENTS FOR THE RIGHT BEARING. EVALUATED AT 

FREQUENCY = SYNCHRONOUS SPEED, STATIC LOAD = 33.6 N (IN Y DIRECTION) 

Speed, 

rpm 

Kxx, 

MN/m 

Kxy Kyx Kyy Cxx, 

kNs/m 

Cxy Cyx Cyy 

5000 1.53 –1.37 –2.11 5.79 1.16 –1.80 0.106 5.10 

10000 1.64 –1.08 –1.84 4.39 0.818 –0.962 0.157 2.23 

15000 1.76 –0.940 –1.68 3.78 0.661 –0.642 0.162 1.36 

20000 1.82 –0.803 –1.51 3.44 0.559 –0.465 0.168 0.953 

25000 1.91 –0.711 –1.39 3.22 0.489 –0.360 0.165 0.726 

30000 1.98 –0.629 –1.28 3.08 0.437 –0.291 0.161 0.583 

Figure 9.—Schematic of the rotor layout used in the 

rotordynamic model with dimensions in mm. 

Figure 10.—Plot of predicted eccentricity and eccentricity angle 

for the left and right foil journal bearings. 
NASA/TM—2010-216354 8 

Prior to running on the foil bearings, the rotor assembly was 

balanced with a residual imbalance of 4.2 g-mm at 46° on the 

left end and 7.5 g-mm at 87° on the right end, as determined 

by a balance machine at GRC. These two magnitudes were 

used as the unbalance distribution in the model. 

The rotordynamic model was used to calculate the 

synchronous response at each of the locations measured in the 

test rig to assess the capability of the predictive tool. A Bode 

plot presents the amplitude and phase of synchronous 

response. This is a convenient plot on which to focus attention 

because it relays information about the rotor response to 

unbalance as well as critical speeds of the system, both useful 

measures of a model’s capability to capture the physics of the 

system. The predicted Bode plots are shown in the following 

section in Figures 11 to 14 where they are compared to the 

experimentally observed response. 

Figure 11.—Bode plots: measured (solid) and predicted 

(dotted) amplitude and phase of rotor unbalance response at 

left bearing, vertical direction. 

Figure 12.—Bode plots: measured (solid) and predicted 

(dotted) amplitude and phase of rotor unbalance response at 

left bearing, horizontal direction. 

Figure 13.—Bode plots: measured (solid) and predicted 

(dotted) amplitude and phase of rotor unbalance response at 

right bearing, vertical direction. 

Figure 14.—Bode plots: measured (solid) and predicted 

(dotted) amplitude and phase of rotor unbalance response at 

right bearing, horizontal direction. 
NASA/TM—2010-216354 9 

Comparison of Predicted and 

Experimental Rotor Response 

After the load deflection tests were completed, the bearings 

and rotor were assembled in the rotor simulator test rig. 

Initially, the rotor was spun to a low speed (approx. 

10,000 rpm) slightly above its lift-off speed and checked out 

for smooth operation. This test was conducted to determine if 

the bearings were capable of supporting the weight of the 

rotor, and that nothing unusual, like thermal run-away, would 

prevent the test from reaching completion. Since bearing load 

capacity increases with speed, low speed conditions such as 

this are more likely to result in overload conditions and 

thermally unstable operation. So, while being 

rotordynamically less challenging, low speed operation is 

typically more stressful on the foil bearings in terms of load 

than moderate speed operation. The initial behavior of the 

bearings was acceptable, and the rotor was spun slowly up to 

30,000 rpm. After a short time, the air supply to the turbine 

was shut off and the rotor coasted to a stop. The speedup/coast-down cycle was repeated another time to observe the 

repeatability of the data. The maximum speed of 30,000 rpm 

was chosen as a result of data acquisition and dynamics of the 

system. Speeds higher than 30,000 rpm result in a twofold 

decrease in data resolution (32 samples per revolution 

compared to 64) and nothing of interest happens between 

30,000 rpm and the maximum speed of 60,000 rpm due to the 

bending critical speed occurring above that threshold. 

There are four displacement sensors on the test rig, two 

near each bearing with one at 0 (horizontal) and one at 90

(vertical), resulting in four measured response plots. 

Figures 11 to 14 show four sets of two Bode plots (amplitude 

and phase) for the rotor supported on the two GRC made foil 

bearings. Each set of two plots contains first the predicted 

unbalance response (amplitude and phase) from above in 

dotted lines, and the measured unbalance response in solid 

lines (slow-roll compensated for mechanical and electrical 

run-out) for a given displacement sensor location. The 

experimental data does not extend below about 1000 rpm due 

to very rapid deceleration of the test rotor leading to unreliable 

keyphasor data. 

Discussion 

The first thing one might notice from comparison of the 

predicted response curves to the measured response curves is 

that both contain localized peak responses for the various 

directions at speeds between about 5,000 and 12,000 rpm. A 

closer look reveals that at the left end of the rotor, 

Figures 11 and 12, there is a mostly vertical resonance at 

around 12,000 rpm, and a mostly horizontal resonance with 

wider frequency content centered around 7,000 rpm. An 

immediate observation is that the predicted response captures 

the frequency content in both directions very well. However, 

the amplitude is off by a factor of as much as 3. The predicted 

phase lag agrees well in trend, but is shifted in both plots by a 

fairly constant amount. The amplitude and phase differences 

are consistent with incorrect unbalance magnitude and phase 

in the model. This is discussed in more detail later. 

The comparison between prediction and experiment at the 

right end is less favorable, yet when assessing the prediction 

as a design tool, not altogether terrible. Looking at the 

horizontal plot first, Figure 14, there is a predicted peak 

response around 8,000 rpm. Experimentally, the resonance 

occurs at around 9,000 rpm, with a much narrower peak. In 

the vertical direction, Figure 13, there is a predicted resonance 

at around 12,000 rpm. Experimentally, there is a 

corresponding peak to the horizontal resonance at 9,000 rpm, 

and interestingly, another small peak at 12,000 with similar 

amplitude to the prediction. As with the left rotor end, the 

predicted amplitudes are lower than those experimentally 

observed, with the exception of the right end horizontal 

direction, see Figure 14. The phase predictions still generally 

have similar shapes, but are less consistent in the shift amount 

than the predictions for the right end response. The most 

glaring difference between predicted and observed response 

for this rotor system is the horizontal peak observed at the 

right end at around 9,000 rpm. This frequency corresponds to 

the large vertical response at the right end, which was captured 

in the prediction, but the horizontal component was not. 

In summary of the predicted versus experimental unbalance 

response, there is general agreement between the two that two 

critical speeds exist in the speed range of 5,000 to 12,000 rpm. 

Experimentally, the first one occurs at around 9,000 rpm, and 

is elliptical in shape with larger horizontal amplitude on the 

left end, and larger vertical amplitude on the right. The second 

critical speed occurs at 12,000 rpm, and has a mostly vertical 

mode shape. In the predicted response, the first critical speed 

occurs around 7,000 rpm with large horizontal amplitude. The 

second critical speed agrees well with the experimental results, 

occurring at 12,000 rpm, with a mostly vertical mode shape. 

While the predictions are not an exact representation of the 

observed unbalance response, they are quite close, and 

importantly show the correct trends. The model correctly 

predicts the existence of two critical speeds, and that the 

horizontally oriented mode occurs at a lower speed than the 

vertically oriented mode. The predicted frequency of the 

higher critical speed is quite good, and the lower one, while 

not as accurate, is still reasonably close, considering the large 

speed range of the machine (0 to 60,000 rpm). 

As mentioned above, the model mostly under-predicts the 

amplitudes of the critical speeds by as much as a factor of 3. 

The amplitude error is likely due to a lack of certainty in the 

residual unbalance (amplitude and phase angle) from the 

balance procedure. 

Errors in the magnitude and/or phase of the unbalance 

vectors could come from several possible sources. 

Measurement uncertainty due to balance machine resolution 

accuracy and repeatability is one potential source. Another 

disassembly and re-assembly of the rotor required to mount it 

in the test rig. Small changes in angular position of the disks 
NASA/TM—2010-216354 10 

Figure 15.—Bode plots: measured (solid) and predicted 

(dotted) amplitude and phase of rotor unbalance response at 

left bearing, vertical direction using revised unbalance 

vectors in the rotordynamic model. 

relative to the shaft will result in changes to the unbalance 

condition. While these changes are small, the magnitude of the 

unbalance is small as well. Thus, it is conceivable that this 

could contribute to the discrepancies in response amplitude 

seen in the comparisons above. Whatever the source, it cannot 

be ruled-out that the unbalance vectors used in the model 

contain some level of uncertainty. 

The fact that the unbalance vectors used in the model are 

likely in error does not detract from the usefulness of the foil 

bearing predictive code as a design tool. To illustrate that a 

better match between predicted and observed unbalance 

response is possible, different unbalance vectors were used in 

the rotordynamic model to verify that good agreement is 

possible simply by using different unbalance inputs to the 

model. Figure 15 shows the same response data from 

Figure 11, but with a set of revised unbalance vectors to 

improve the agreement between predicted and observed 

unbalance response. The revised unbalance vectors are: 

8.5 g-mm at 150° on the left end, and 7.56 g-mm at 190° on 

the right end. Similar improvements were obtained for the 

other three probe locations shown in Figures 11 to 14, but are 

not shown here for brevity. It should be noted that the revised 

unbalance vectors are not presumed to be correct, they were 

simply intended to illustrate that the bearing rotordynamic 

coefficients calculated using XLGFBTH can result in quite 

good agreement to experimental data. 

Another contributing factor to the differences in the 

prediction to the experiment are the estimates used for bearing 

clearance. The load deflection tests described above were done 

with the bearings in two angular orientations, with the load 

direction in line with the bearing vertical direction and with 

the load direction oriented in the bearing horizontal direction 

resulting in slightly different clearance values. Also, as shown 

in Figure 8, due to the hysteresis effect, there is an upper load 

deflection curve and a lower curve. One could chose to use the 

upper, the lower, an average, or some other means to 

determine the clearance. Clearly, there is some subjectivity in 

modeling the clearance of a foil bearing, and the variations 

involved with which method chosen could lead to some 

variation in predicted bearing properties. 

In addition, the foil stiffening factor and the bearing 

structural loss factor are parameters that the user can change to 

fine-tune the results of the analysis. For example, the predicted 

bearing damping is overestimated as evidenced by the width 

of the peaks in the Bode plots. This is likely a result of the 

structural loss coefficient chosen. If this were an academic 

exercise to try to get the best agreement, the analysis could be 

iterated to find an optimum solution. Because of the nature of 

this paper, to assess the code as a typical user might exercise 

it, the sensitivity of the results to these parameters was not 

assessed. 

Summary 

A new analysis tool for gas foil bearings is assessed for its 

ability to predict dynamic response of a foil bearing supported 

test rig. Rotordynamic force coefficients are calculated for 

bearings made in-house and installed in the test rig, and a 

rotordynamic model predicts the unbalance response. The 

unbalance response is then measured experimentally, and 

compared to the prediction. 

Overall, the degree to which the predictive tool captures the 

critical speeds is impressive considering that there is some 

uncertainty in the way the clearance was determined for input 

into the analysis tool. The discrepancy between the observed 

and predicted amplitudes of motion are of concern, but are 

more likely related to modeling characteristics other than 

those predicted by the foil bearing analysis tool, such as 

residual unbalance and clearance. The usefulness of the 

predictive tool will be in its ability to help engineers design 

around critical speeds, which it appears to be reasonably 

capable of doing at the present. 

Of primary interest in this paper is the predictive capability 

of the code in regard to bearing rotordynamic coefficients. For 

discussion of other capabilities of the code with experimental 

validation see References 24, 26, 33 to 34. Reference 33 

extends the predictive gas foil bearing analysis to high 

temperature operation with thermal energy transport and 

management, as well as accounting for elastic and thermally 

induced changes in materials and operating clearance. 

Reference 34 provides temperature and rotordynamic 

measurements in a hot rotor-foil bearing system and 

comparisons to predictions from the extended 

elastothermohydrodynamic model. 

 
NASA/TM—2010-216354 11 

References 

1. Ku, C.P.R., and Heshmat, H., 1992, “Compliant Foil 

Bearing Structural Stiffness Analysis: Part I – Theoretical 

Model Including Strip and Variable Bump Foil 

Geometry,” ASME J. of Tribology, 114(2), pp. 394–400. 

2. Ku, C.P.R., and Heshmat, H., 1993, “Compliant Foil 

Bearing Structural Stiffness Analysis: Part II – 

Experimental Investigation,” ASME J. of Tribology, 

115(3), pp. 364–369. 

3. Ku, C.P.R., and Heshmat, H., 1994, “Effects of Static 

Load on Dynamic Structural Properties in a Flexible 

Supported Foil Journal Bearing,” ASME J. of Vibration 

and Acoustics, 116(3), pp. 257–262. 

4. Rubio, D., and San Andres, L., 2006, “Bump-Type Foil 

Bearing Structural Stiffness: Experiments and 

Predictions,” ASME J. of Eng. For Gas Turbines and 

Power, 128(3), pp. 653–660. 

5. Le Lez, S., Arghir, M., and Frene, J., 2007, “Static and 

Dynamic Characterisation of a Bump-Type Foil Bearing 

Structure,” ASME J. of Tribology, 129(1), pp. 75–83. 

6. Lee, Y-B., Jo, J-H., Park, D-J., Kim, C-H., and Rhim, YC., 2006, “Dynamic Characteristics of Bump Foils 

Considering with Thermal Effect in Air Foil Bearings,” 

STLE/ASME Paper No. IJTC2006-12189. 

7. Heshmat, H, Walowit, J.A., and Pinkus, O., 1983, 

“Analysis of Gas-Lubricated Foil Journal Bearings,” 

ASME J. of Lubrication Technology, 105(3), pp. 647–

655. 

8. Heshmat, H, Walowit, J.A., and Pinkus, O., 1983, 

“Analysis of Gas-Lubricated Compliant Thrust Bearings,” 

ASME J. of Lubrication Technology, 105(4), pp. 638–

646. 

9. Iordanoff, I., 1999, “Analysis of an Aerodynamic 

Compliant Foil Thrust Bearing: Method for a Rapid 

Design,” ASME J. of Tribology, 121(4), pp. 816–822. 

10. Heshmat, C.A., Xu, D.S., and Heshmat, H., 2000, 

“Analysis of Gas Lubricated Foil Thrust Bearings Using 

Coupled Finite Element and Finite Difference Methods,” 

ASME J. of Tribology, 122(1), pp. 199–204. 

11. Bruckner, R.J., 2004, “Simulation and Modeling of the 

Hydrodynamic, Thermal, and Structural Behavior of Foil 

Thrust Bearings,” Doctoral Dissertation, Case Western 

Reserve University, Cleveland. 

12. Peng, J-P., and Carpino, M., 1993, “Calculation of 

Stiffness and Damping Coefficients for Elastically 

Supported Gas Foil Bearings,” ASME J. of Tribology, 

115(1), pp. 20–27. 

13. Peng, J-P., and Carpino, M., 1994, “Coulomb Friction 

Damping Effects in Elastically Supported Gas Foil 

Bearings,” STLE Tribology Tansactions, 37(1), pp. 91–

98. 

14. Carpino, M., Medvetz, L.A., and Peng, J-P., 1994, 

“Effects of Membrane Stresses in the Prediction of Foil 

Bearing Performance,” STLE Tribology Transactions, 

37(1), pp. 43–50. 

15. Carpino, M., Peng, J-P., and Medvetz, L.A., 1994, 

“Misalignment in a Complete Shell Gas Foil Journal 

Bearing,” STLE Tribology Transactions, 37(4), pp. 829–

835. 

16. Carpino, M., and Talmadge, G., 2003, “A Fully Coupled 

Finite Element Formulation for Elastically Supported Foil 

Journal Bearings,” STLE Tribology Transactions, 46(4), 

pp. 560–565. 

17. Carpino, M., and Talmadge, G., 2006, “Prediction of 

Rotor Dynamic Coefficients in Gas Lubricated Foil 

Journal Bearings with Corrugated Sub-Foils,” STLE 

Tribology Transactions, 49(3), pp. 400–409. 

18. Lee, N.S., Choi, D.H., Lee, Y.B., Kim, T.H., and Kim, 

C.H., 2002, “The Influence of the Slip Flow on SteadyState Load Capacity, Stiffness and Damping Coefficients 

of Elastically Supported Gas Foil Bearings,” STLE 

Tribology Transactions, 45(4), pp. 478–484. 

19. Peng, Z.-C., and Khonsari, M.M., 2004, “Hydrodynamic 

Analysis of Compliant Foil Bearings with Compressible 

Air Flow,” ASME J. of Tribology, 126(3), pp. 542–546. 

20. Peng, Z.-C., and Khonsari, M.M., 2006, “A 

Thermohydrodynamic Analysis of Foil Journal Bearings” 

ASME J. of Tribology, 128(3), pp. 534–541. 

21. DellaCorte, C, Radil, K.C., Bruckner, R.J., and Howard, 

S.A., 2007, “Design, Fabrication and Performance of 

Open Source Generation I and II Compliant 

Hydrodynamic Gas Foil Bearings,” NASA/TM—2007-

214691/ARL–TR–4102. 

22. Kim, T.H., and San Andrés, L., 2005, “Heavily Loaded 

Gas Foil Bearings: A Model Anchored to Test Data,” 

ASME Paper No. GT2005–68486. 

23. Kim, T.H., and San Andrés, L., 2006, “Limits for High 

Speed Operation of Gas Foil Bearings,” ASME J. of 

Tribology, 128(3), pp. 670–673. 

24. San Andrés, L., and Kim, T.H., 2007, “Improvements to 

the Analysis of Gas Foil Bearings: Integration of Top Foil 

1D and 2D Structural Models,” ASME Paper No. 

GT2007–27249. 

25. Radil, K., DellaCorte, C., Bruckner, R., and Zesotek, M., 

2007, “Thermal Management Techniques for Oil-Free 

Turbomachinery Systems,” STLE Tribology Transactions, 

50, pp. 319–327. 

26. Kim, T.H., and San Andrés, L., 2009, “Effect of Side Feed 

Pressurization on the Dynamic Performance of Gas Foil 

Bearings: A Model Anchored to Test Data,” ASME J. of 

Eng. Gas Turbines Power, 131(1), pp. 012501. 

27. Rubio, D., and San Andrés, L., 2007, “Structural 

Stiffness, Dry Friction Coefficient, and Equivalent 

Viscous Damping in a Bump-Type Foil Gas Bearing,” 

ASME J. of Eng. Gas Turbines Power, 129(2), pp. 494–

502. 

28. Kim, T.H., Breedlove, A.W., and San Andres, L., 2008, 

“Characterization of Foil Bearing Structure for Increasing 

Shaft Temperature: Part I-Static Load Performance,” 

ASME Paper No. GT2008–50567. 
NASA/TM—2010-216354 12 

29. Kim, T.H., Breedlove, A.W., and San Andres, L., 2008, 

“Characterization of Foil Bearing Structure for Increasing 

Shaft Temperature: Part II-Dynamic Force Performance,” 

ASME Paper No. GT2008–50570. 

30. Howard, S.A., 2007, “A New High-Speed Oil-Free 

Turbine Engine Rotordynamic Simulator Test Rig,” 

NASA/TM—2007-214489. 

31. Radil, K.C., and DellaCorte, C., 2002, “The Effect of 

Journal Roughness and Foil Coatings on the Performance 

of Heavily Loaded Foil Bearings,” Triboloy Transactions, 

45(2), pp. 199–204. 

32. San Andrés, L., and Kim, T. H., 2008, “Forced Nonlinear 

Response of Gas Foil Bearing Supported Rotors,” 

Tribology International, 41(8), pp. 704–715. 

33. San Andrés, L., and Kim, T. H., 2010, 

“Thermohydrodynamic Analysis of Bump Type Gas Foil 

Bearings: A Model Anchored to Test Data,” ASME J. 

Eng. Gas Turbines Power, 132(4), pp. 10. 

34. Kim, T.H., and San Andrés, L., 2010, 

“Thermohydrodynamic Model Predictions and 

Performance Measurements of Bump-Type Foil Bearing 

for Oil-Free Turboshaft Engines in Rotorcraft Propulsion 

Systems,” ASME J. Tribol. 132(1), pp. 11. 
REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB 

control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

01-07-2010 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

A New Analysis Tool Assessment for Rotordynamic Modeling of Gas Foil Bearings 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Howard, Samuel, A.; San Andres, Luis 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 877868.02.07.03.01.01.04 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-17290-1 

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

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2010-216354 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Categories: 07 and 37 

Available electronically at http://gltrs.grc.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

Gas foil bearings offer several advantages over traditional bearing types that make them attractive for use in high-speed turbomachinery. 

They can operate at very high temperatures, require no lubrication supply (oil pumps, seals, etc.), exhibit very long life with no maintenance, 

and once operating airborne, have very low power loss. The use of gas foil bearings in high-speed turbomachinery has been accelerating in 

recent years, although the pace has been slow. One of the contributing factors to the slow growth has been a lack of analysis tools, 

benchmarked to measurements, to predict gas foil bearing behavior in rotating machinery. To address this shortcoming, NASA Glenn 

Research Center (GRC) has supported the development of analytical tools to predict gas foil bearing performance. One of the codes has the 

capability to predict rotordynamic coefficients, power loss, film thickness, structural deformation, and more. The current paper presents an 

assessment of the predictive capability of the code, named XLGFBTH (Texas A&M University). A test rig at GRC is used as a simulated 

case study to compare rotordynamic analysis using output from the code to actual rotor response as measured in the test rig. The test rig 

rotor is supported on two gas foil journal bearings manufactured at GRC, with all pertinent geometry disclosed. The resulting comparison 

shows that the rotordynamic coefficients calculated using XLGFBTH represent the dynamics of the system reasonably well, especially as 

they pertain to predicting critical speeds. 

15. SUBJECT TERMS

Gas bearings; Foil bearings; Rotor dynamics 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

18 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18