Damian R. Ludwiczak, Dzu K. Le, Anne M. McNelis, and Albert C. Yu

Glenn Research Center, Cleveland, Ohio

Sergey Samorezov

ZIN Technologies, Inc., Cleveland, Ohio

Dave S. Hervol

Analex Corporation, Brook Park, Ohio

Verification of a 2 kWe Closed-Brayton-Cycle

Power Conversion System Mechanical

Dynamics Model

NASA/TM—2005-213880

November 2005
The NASA STI Program Office . . . in Profile

Since its founding, NASA has been dedicated to

the advancement of aeronautics and space

science. The NASA Scientific and Technical

Information (STI) Program Office plays a key part

in helping NASA maintain this important role.

The NASA STI Program Office is operated by

Langley Research Center, the Lead Center for

NASA’s scientific and technical information. The

NASA STI Program Office provides access to the

NASA STI Database, the largest collection of

aeronautical and space science STI in the world.

The Program Office is also NASA’s institutional

mechanism for disseminating the results of its

research and development activities. These results

are published by NASA in the NASA STI Report

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major significant

phase of research that present the results of

NASA programs and include extensive data

or theoretical analysis. Includes compilations

of significant scientific and technical data and

information deemed to be of continuing

reference value. NASA’s counterpart of peerreviewed formal professional papers but

has less stringent limitations on manuscript

length and extent of graphic presentations.

• TECHNICAL MEMORANDUM. Scientific

and technical findings 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. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by

NASA.

• SPECIAL PUBLICATION. Scientific,

technical, or historical information from

NASA programs, projects, and missions,

often concerned with subjects having

substantial public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific

and technical material pertinent to NASA’s

mission.

Specialized services that complement the STI

Program Office’s diverse offerings include

creating custom thesauri, building customized

databases, organizing and publishing research

results . . . even providing videos.

For more information about the NASA STI

Program Office, 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 Access

Help Desk at 301–621–0134

• Telephone the NASA Access Help Desk at

301–621–0390

• Write to:

 NASA Access Help Desk

 NASA Center for AeroSpace Information

 7121 Standard Drive

 Hanover, MD 21076
Damian R. Ludwiczak, Dzu K. Le, Anne M. McNelis, and Albert C. Yu

Glenn Research Center, Cleveland, Ohio

Sergey Samorezov

ZIN Technologies, Inc., Cleveland, Ohio

Dave S. Hervol

Analex Corporation, Brook Park, Ohio

Verification of a 2 kWe Closed-Brayton-Cycle

Power Conversion System Mechanical

Dynamics Model

NASA/TM—2005-213880

November 2005

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

Space Technology and Applications International Forum (STAIF–2005)

sponsored by the University of New Mexico’s Institute for Space and

Nuclear Power Studies (UNM-ISNPS)

Albuquerque, New Mexico, February 13–17, 2005
Acknowledgments

The authors would like to thank Michael J. Barrett of the Thermo-Mechanical Systems Branch at NASA Glenn

Research Center for funding this work. This work was performed for NASA Headquarters, Science Mission

Directorate (Code S).

Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Trade names or manufacturers’ names are used in this report for

identification only. This usage does not constitute an official

endorsement, either expressed or implied, by the National

Aeronautics and Space Administration.

Available electronically at http://gltrs.grc.nasa.gov
Abstract. Vibration test data from an operating 2 kWe closed-Brayton-cycle (CBC) power conversion system (PCS) located at the 

NASA Glenn Research Center was used for a comparison with a dynamic disturbance model of the same unit. This effort was 

performed to show that a dynamic disturbance model of a CBC PCS can be developed that can accurately predict the torque and 

vibration disturbance fields of such class of rotating machinery. The ability to accurately predict these disturbance fields is

required before such hardware can be confidently integrated onto a spacecraft mission. Accurate predictions of CBC disturbance 

fields will be used for spacecraft control/structure interaction analyses and for understanding the vibration disturbances affecting 

the scientific instrumentation onboard. This paper discusses how test cell data measurements for the 2 kWe CBC PCS were 

obtained, the development of a dynamic disturbance model used to predict the transient torque and steady state vibration fields of 

the same unit, and a comparison of the two sets of data. 

INTRODUCTION 

The NASA Glenn Research Center conducted a first order analysis during the 2003 calendar year to determine the 

vibration effects that a simultaneously operating pair of rotor dynamic closed-Brayton-cycle (CBC) engines would 

have on a conceptual 100 kWe Nuclear Electric Propulsion (NEP) rigid spacecraft (Yu, 2003). This analysis 

concluded that the CBC engines would not impart significant dynamic loads (torque or vibration) to the overall 

spacecraft model. However, there is no test data to verify that the assumptions and methods used in the 2003 100 

kWe CBC engine model were satisfactory. 

A 100 kWe CBC engine test bed unit does not exist and verifying the variables used in the 2003 analysis cannot be 

done until such test bed is available. However, an operating 2 kWe CBC engine test bed unit exists at NASA’s Glenn 

Research Center. This test bed was used to validate a dynamic model of the 2 kWe CBC engine and to show that an 

accurate, test verified model of a 2kW unit can be developed. This correlation effort will then be used to gain 

confidence in modeling the Brayton engine dynamic disturbances and in the assumptions needed for an accurate 100 

kWe model. 

Accurate torque and vibration disturbance prediction of a closed-Brayton-cycle (CBC) Power Conversion System 

(PCS) is important for two reasons. First, flexible on-orbit spacecraft control/structure interaction analyses will need 

to be performed for an NEP spacecraft such as the Jupiter Icy Moons Orbiter (JIMO) and the CBC torque and 

vibration disturbances are needed for such an analysis. Second, the vibration disturbance field affecting the scientific 

instrumentation onboard a spacecraft such as JIMO will also have to be characterized to ensure that accurate 

scientific measurements can be taken during the mission. A confident understanding of how to model the CBC torque 

and vibration disturbances is necessary to support the implementation of such a PCS onto a spacecraft mission. 

Verification of a 2 kWe Closed-Brayton-Cycle

Power Conversion System Mechanical 

Dynamic Model 

Damian R. Ludwiczak, Dzu K. Le, Anne M. McNelis, and Albert C. Yu 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Sergey Samorezov 

ZIN Technologies, Inc. 

Cleveland, Ohio 44142 

Dave S. Hervol 

Analex Corporation 

Brook Park, Ohio 44142 

NASA/TM—2005-213880 1
BRAYTON 2kWe CBC HARDWARE 

The Brayton 2 kWe PCU unit that was modeled and was used to acquire the test data is a modified version of a unit 

built for the Solar Dynamic (SD) Ground Test Demonstration (GTD). In the SD-GTD form, it compiled many 

hundreds of hours of operation in thermal vacuum with no failures or degradation. This hardware is shown in Figure 

1a. 

The operating Brayton Power Conversion Unit (BPCU) is run in a vacuum tank. Since the vacuum tank background 

vibration was assumed to be very high due to the operating vacuum pump systems, a vibration isolation test stand 

was developed for this task. The vibration isolation test stand was designed and built to utilize existing mounting pads 

within the vacuum tank and to suspend the CBC engine from a 2-cable suspension system in order to attenuate the 

high noise environmental vibration. The as tested hardware with the vibration isolation test stand is shown in Figure 

1b. 

 (a) Before Vibration Isolation (b) After Vibration Isolation

 

FIGURE 1. Brayton Power Conversion Unit Test Hardware 

DEVELOPMENT OF A BRAYTON 2kWe CBC ANALYTICAL MODEL 

The initial 2 kWe CBC engine analytical model, known as Model-1, was created with the Simulink software code and 

represented a generic model of the CBC engine test hardware. This model was created prior to any dynamic test data 

being taken on the actual test hardware. Model-1 assumed rough estimates for the bearing stiffness, rotor mass 

properties, rotor flexibility, rotor housing mass, and rotor housing mount stiffness. Imbalance forces (lumped at 

bearings in the model) due to mass imbalance and alternator electrical forces were assumed to be fixed at a 

conservative level for all rotor rotation speeds and only the fundamental imbalance (once-around) was modeled. Also 

included in this model were empirical estimates of test assembly mass, and suspension cable stiffness and tension. 

The model had three rigid elements: the CBC rotor shaft, shaft housing, and the support base and a representation is 

shown in Figure 2. In addition, the first fundamental bending mode of the rotor shaft was included. The support base 

encompassed all components of the engine external to the CBC shaft housing such as the heater, heat exchanger, 

cooler, and various plumbing and was the heaviest part of the test assembly. The shaft housing contained the CBC 

shaft. 

NASA/TM—2005-213880 2
FIGURE 2. Brayton Power Conversion Unit, Model-1, Representation

The CBC shaft and housing is assembled from several segments held together by a threaded rod and bolts. These 

segments are the turbine wheel, thrust bearing, foil bearings, alternator, and compressor wheel as shown in Figure 3. 

This multi-body shaft is the only moving part of the engine. 

FIGURE 3. Brayton Power Conversion Unit, Model-1, Shaft Assembly Representation

In the Simulink model, the support base and housing subsystems contained equations of motion based on a second 

order damped mass-spring system. To have a reasonable representation of the disturbance created by the CBC shaft, a 

modified flywheel rotor model was implemented. The shaft had similar rotor dynamics as a flywheel rotor. The 

CBC shaft subsystem has the following dynamic features: the zero-spin dynamics, non-linear gyroscopic dynamics, 

mass imbalances, and bearing spring load offsets. The fundamental bending mode of the shaft as well as the speeddependent gyroscopic couplings between tilts and shaft bending were also included in this model version. 

To represent the test configuration, the whole CBC engine system was modeled as a pendulum system using isolation 

cables as shown in Figure 2. The cable system was very generic and could be quickly modified to reflect the actual 

test configuration. The mass, inertia, cables tension and linear stiffness used in the Simulink model were measured 

values of the test assembly. Details of inputs and assumptions for this model are provided in Table 1. 

Acceleration time history data predicted to occur at the geometric center of the shaft housing assembly was generated 

by the Model-1 Simulink model. This acceleration was the product of the predicted shaft assembly excitation acting 

on the test assembly model. Two rpm rates were investigated. The first was at 30,000 rpm and the second was 40,000 

rpm. This data was then converted into the frequency domain in the form of power spectra density (PSD) plots. 

These plots are shown in Figure 4 and Figure 5. 

CBC Shaft housing

Support Base 

Isolation Cable

Isolation Cable

X

Z 

Y

Turbine 

Compressor 

Thrust 

Bearing 

Foil 

Bearings 

Alternator 

Shaft 

Housing 

X 

Z 

NASA/TM—2005-213880 3
From Figure 4a and Figure 5a, the dynamics of the Simulink model can be seen for the X direction. Below 200 Hz, 

response due to the shaft backward whirl, bounce mode, and forward whirl are shown. Additionally, the once per 

revolution excitation frequency is obviously dominant. From Figure 4b and Figure 5b, the dynamics of the Simulink 

model can be seen for the Y direction. Below 200 Hz, response due to the housing and mount modes, shaft backward 

whirl, bounce mode, and forward whirl are shown. Additionally, the once per revolution excitation frequency is 

obviously dominant. These predicted excitations are tabulated in Table 2. It was expected that the PSD plots from 

actual testing would be somewhat comparable to the predicted results. Adjustments to Model-1 were expected to be 

required after comparison to the test data and that by adjusting the mass properties and various stiffness properties it 

would be possible to match the test up to 1000Hz. The model correlation task was also expected to be an iterative 

effort. 

 TABLE 1. Brayton Power Conversion Unit, Model-1, Properties

Property Model-1 Values 

Rotor Mass 2.627 lbm

Rotor Polar Moment of Inertia (Ip) 0.7044 lbm-in2

Rotor Transverse Moment of Inertia about C.G. (It) 16.303 lbm-in2

Flexible Shaft Modes Modeled Yes, Fundamental Mode (1974 Hz) 

Speed Dependant Gyro-Flex Dynamic Couplings Modeled Yes (cross-axis rigid body coupling = 

Ip/It = 0.0432) 

Bearing Model (Thrust and Radial) Spring Constant 3500 lbf/in per Bearing 

For All Speeds 

Bearing Viscous Damping (on shaft bounce and tilts) 3% of Critical 

Gyroscopic Destabilizing Rotating Damping (on gyroscopic 

motions) 3% of Critical 

Moment Arm From Rotor c.g. to Upper Bearing Center 

(towards turbine) 1.973 in 

Moment Arm From Rotor c.g to Lower Bearing Center 

(towards compressor) 1.680 in 

Housing and Mount Mass 30.56 lbm

Housing and Mount Mass Moment of Inertia About c.g. 11492 lb-in2 for all inertia-principal axes 

Mount Linear Stiffness 20000 lb/in 

Mount Torsional Stiffness 12000000 lb-in/rad 

Lumped Mass Imbalance and Electrical Effects (“Imbalance 

Forces”) Fundamental (Once-A-Round) 

Rotating Imbalance Force at Upper Bearing 0.667 lb (with 1350 phase offset from 

Lower Bearing) 

Rotating Imbalance Force at Lower Bearing 1.334 lb 

Test Assembly Mass 1031 lb 

Test Assembly Mass Moment of Inertia about c.g. 350000 lb-in2

Cable Tension Front Cable = 745 lb 

Rear Cable = 297 lb 

Cable linear stiffness 500 lbs/inch for each cable 

Cable Length 33.00 in 

Number of Cables 2 

NASA/TM—2005-213880 4
 (a) Predictions in the X Direction (b) Predictions in the Y Direction 

 

FIGURE 4. Brayton Power Conversion Unit, Model-1, 30,000 RPM Vibration Predictions 

 (a) Predictions in the X Direction (b) Predictions in the Y Direction 

 

FIGURE 5. Brayton Power Conversion Unit, Model-1, 40,000 RPM Vibration Predictions 

STRUCTURAL DYNAMIC TEST MEASUREMENTS 

The objective of the structural dynamic test measurements was to obtain vibration measurements for an operating 2 

kWe CBC unit for comparison with analytically predicted values. This would help answer the question on what type 

and how much dynamic disturbances the CBC engine might impart into a spacecraft vehicle. The development of a 

dynamic test and measurement approach for the 2 kWe Brayton engine required a plan on where to place the 

measurement sensors and locations, identify and recommend test rig and vacuum chamber modifications necessary to 

enable accurate vibration, acquire dynamic data for several run conditions and to summarize the test data for use in 

correlating 2 kWe Brayton dynamic model. Because the analytical model predicted the CBC to be a very quiet 

machine, the Microgravity Emissions Laboratory at the NASA Glenn Research Center was given the structural 

dynamics test measurement task. The Microgravity Emissions Laboratory (MEL) performs testing services utilizing a 

highly sensitive acceleration measurement system to measure structure borne disturbances produced by the operation 

of electro-mechanical components, subassemblies, or assemblies such as the 2 kWe CBC. The vibration testing was 

conducted in Bldg 301, Vacuum Facility 6 (VF6) at the NASA Glenn Research Center. 

NASA/TM—2005-213880 5
Instrumentation 

Table 2 contains a list of the accelerometer instrumentation and location description that was recorded during the 

CBC testing. A total of 28 measurement channels were utilized. For this paper, accelerometer channels 13 and 14 are 

most important in that they were located on the CBC housing and measure accelerations at the same location of the 

CBC model predictions. 

 TABLE 2. Structural Dynamic Test Acceleration Measurement Channels

Measurement 

Channel No. Type (Model) Location 

1 PCB Seismic 393B05 Brayton Mounting Ring Base 

2 PCB Seismic 393B05 Brayton Mounting Ring Base 

3 PCB Seismic 393B05 Brayton Mounting Ring Base 

4 PCB Seismic 393B05 Brayton Mounting Ring Base 

5 PCB Seismic 393B05 Brayton Mounting Ring Base 

6 PCB Seismic 393B05 Brayton Mounting Ring Base 

7 PCB Seismic 393B05 Brayton Mounting Ring Base 

8 PCB Seismic 393B05 Brayton Mounting Ring Base 

9 PCB Seismic 393B05 Brayton Mounting Ring Base 

10 PCB Seismic 393B05 Brayton Mounting Ring Base 

13 B&K 4370 compr. plate 30Y14 B&K 4370 compr. plate 30X15 PCB 357B33 compr. bracket 20Y+ 

16 PCB 357B33 compr. bracket 20X17 PCB 357B33 compr. bracket corner Z+ 

18 PCB 357B33 recup. supp. bracket 20X+ 

19 PCB 357B33 recup. supp. bracket 20Y+ 

20 PCB 357B33 recup. supp. bracket Z+ 

21 PCB 357B33 chiller off 20deg X+ 

22 PCB 357B33 chiller Z+ 

23 PCB 357B33 cable supp. near Z+ 

24 PCB 357B33 cable supp. far Z+ 

25 B&K 4370 heater back bottom X+ 

26 B&K 4370 heater back bottom Y+ 

27 B&K 4370 heater back bottom Z28 B&K 4370 PTS ZData was acquired, as conditioned normalized voltage signals, using the Structural Dynamics Laboratory (SDL) 

multi-channel, HP E1432A measurement system. The measurement system is controlled with MTS IDEAS Test 

software. The test data was acquired as time history files for post processing by IDEAS. 

As data was acquired, the motion of the CBC on the isolation cables was as quiescent as ‘reasonably’ practical before 

test operations and measurements commenced. The ambient background was measured prior to the CBC being 

operated to insure that the environmental noise floor was below the expected measurement levels. Table 3 shows two 

of the operating CBC run conditions for which acceleration vibration data was recorded. 

 

NASA/TM—2005-213880 6
 TABLE 3. Operating CBC Measurement Conditions

RPM Bandwidth 

(Hz) 

Data 

Sample 

Rate 

samples/sec 

Measurement 

Duration 

(min) 

30000 2000 5000 2 

40000 2000 5000 2 

INITIAL CBC MODEL AND TEST MEASUREMENT COMPARISIONS 

The data from measurement channels 13 (X direction) and 14 (Y direction) were post processed for both the 30000 

and 40000 rpm cases into power spectra density (PSD) data. Similarly, PSD data was generated by the CBC model, 

Model-1, at the same locations. A comparison of the data is shown in Figure 6. 

(a) 30000 RPM Comparison in the X Direction (b) 30000 RPM Comparison in the Y Direction 

 (Black Test Data, Grey Model Prediction) (Black Test Data, Grey Model Prediction) 

 (c) 40000 RPM Comparison in the X Direction (d) 40000 RPM Comparison in the Y Direction 

 (Black Test Data, Grey Model Prediction) (Black Test Data, Grey Model Prediction) 

 

FIGURE 6. Brayton Power Conversion Unit, Model-1 and Test Data Comparison 

NASA/TM—2005-213880 7
As can be seen in Figure 6 for the X and Y directions and for the 30000 and 40000 rpm cases, Model-1 does a very 

good job predicting the once per revolution excitation frequency. However, the Model-1 predicted magnitudes 

(G2

/Hz) do not compare favorably with the test data values. The first observance is that the predicted imbalance force 

at the once per revolution frequency was too high and that the as modeled values are too conservative. Additionally, 

the second harmonic excitation, most likely due to the alternator hardware interactions, was not predicted by Model-1 

for either rpm case. There also appears to be a random noise component across the entire spectrum. While there is yet 

no quantifiable explanation for this phenomenon, the leading candidate appears to be flow noise 

As stated in the introduction, accurate vibration disturbance predictions of a closed-Brayton-cycle (CBC) Power 

Conversion System (PCS) is important for two reasons. First, flexible on-orbit spacecraft control/structure interaction 

analyses will need to be performed for an NEP spacecraft such as the Jupiter Icy Moons Orbiter (JIMO) and the CBC 

torque and vibration disturbances are needed for such an analysis. Second, the vibration disturbance field affecting 

the scientific instrumentation onboard a spacecraft such as JIMO will also have to be characterized to ensure that 

accurate scientific measurements can be taken during the mission. For both of these concerns, vibration excitations 

below 600 Hz are of primary concern. Therefore, the underlying Grms value of both the predicted acceleration from 

Model-1 and the actual measured value from the test data were calculated. This value give the structural dynamics 

analyst an idea of the amount of excitation energy that exists which could be of concern for the spacecraft analyses. A 

comparison of this value for Model-1 and the test data is shown in Table 4. 

TABLE 4. Grms Comparisons of Model-1 and Test Data 

X Direction Y Direction 

Operating 

Condition Model-1 

Grms Value 

Test 

Grms Value 

Model-1 

Grms Value 

Test 

Grms Value 

0-600 Hz 

(30000 RMP Case) 0.026 0.0036 0.0267 0.0037 

0-600 Hz 

 (40000 RPM Case) 0.00007 0.0033 0.0001 0.0032 

Table 4 shows that Model-1 over predicts the excitation energy for the 30000 rpm case in both the X and Y directions 

due to the imbalance force being too conservative in addition to its frequency of excitation occurring below 600 Hz. 

Additionally, Model-1 under predicts the excitation energy for the 40000 rpm case in both the X and Y directions due 

to the imbalance force frequency occurring above 600 Hz. It was concluded that Model-1 needed to be adjusted. 

ADJUSTMENTS and ADDENDA to THE BRAYTON 2kWe CBC ANALYTICAL MODEL 

As previously discussed, Model-1 was created prior to any dynamic test data being taken on the actual test hardware. 

Model-1 assumed rough estimates for the bearing stiffness, rotor mass properties, rotor flexibility, rotor housing 

mass, and rotor housing mount stiffness. An imbalance force due to lumped mass and alternator electrical force was 

assumed to be fixed at a conservative value for all rotor rotation speeds and only the fundamental imbalance (oncearound) was modeled. Also included in this model were the best estimates of test assembly mass and suspension 

cable stiffness. 

Based on the comparisons with the test data PSDs, some of the Model-1 properties were adjusted to develop Model2. Certain items were determined to have sufficient engineering justification to modify the Model-1 values. 

Additionally, it was determined that the bearing clock-spring (torsional) stiffness should be included in the model in 

addition to a random background noise to represent the CBC engine working fluid. A comparison of the property 

differences between Model-1 and Model-2 is presented in Table 5. 

As Table 5 shows, a majority of the changes made in Model-1 to create Model-2 were in the stiffness and damping 

properties. Additionally, a change was made in the amount of predicted imbalance force with the addition of the 

second harmonic excitation frequency. A comparison of the Model-2 predicted PSD values and the actual test data 

PSD values are shown in Figure 8 

NASA/TM—2005-213880 8
TABLE 5. Comparison of Model-1 and Model-2 Properties

Property Model-1 Model-2 

Rotor Mass 2.627 lbm 2.627 lbm 

Rotor Polar Moment of Inertia (Ip) 0.7044 lbm-in2 0.7044 lbm-in2

Rotor Transverse Moment of Inertia about C.G. 

(It) 16.303 lbm-in2

 16.303 lbm-in2

Flexible Shaft Modes Modeled Fundamental mode (1974 Hz) Fundamental Mode (1974 Hz) 

Speed Dependant Gyro-Flex Dynamic 

Couplings Modeled 

Yes (cross-axis rigid body coupling 

= Ip/It = 0.0432) 

Yes (cross-axis rigid body coupling = 

Ip/It = 0.0648) 

Bearing Clock-Spring (torsional) Stiffness Not Included 2900 lb-in/rad 

Bearing Model (Thrust and Radial) As Spring Constant of 3500 lbf/in 

per bearing for all speeds 

Spring Mass System Representing 

Airfoil/Bumpfoil/Bumpfoil 

Base/Base Support and Changes with 

Rotor Speed* 

Bearing Viscous Damping (on shaft bounce and 

tilts) 3% of critical 3% of critical 

Gyroscopic Destabilizing Rotating Damping 3% of critical 3% of critical 

Moment Arm from Rotor C.G.. to Upper 

Bearing Center (towards turbine) 1.973 in 1.973 in 

Moment Arm from Rotor C.G. to Lower 

Bearing Center (towards compressor) 1.680 in 1.680 in 

Housing and Mount Mass 30.56 lbm 30.56 lbm

Housing and Mount Mass Moment of Inertia 

about c.g. 11492 lb-in2

 11492 lb-in2

Mount Linear Stiffness 20000 lb/in 10000 lb/in 

Mount Torsional Stiffness 12000000 lb-in/rad 6000000 lb-in/rad 

Lumped Mass Imbalance and Electrical Effects 

(“Imbalance Forces”) Fundamental (Once-A-Round) Once -A-Round and Second Harmonic 

Rotating “Imbalance Force” at Upper Bearing 0.667 lb (with 1350 phase offset 

from Lower Bearing) 

0.200 lb (with 1350 phase offset from 

Lower Bearing) 

Rotating “Imbalance Force” at Lower Bearing 1.334 lb 0.355 lb 

Test Assembly Mass 1031 lb 1031 lb 

Test Assembly Mass Moment of Inertia about 

c.g. 

350000 lb-in2 350000 lb-in2

Cable Tension Front Cable = 745 lb 

Rear Cable 297 lb 

Front Cable = 745 lb 

Rear Cable 297 lb 

Cable Linear Stiffness 500 lbs/inch for each cable 500 lbs/inch for each cable 

Cable Length 33.00 in 33.00 in 

Number of Cables 2 2 

Random Background (internal) Disturbances None 

Yes-white noise force spectrum 

acting internally at each bearing 

(Frms = 0.016 lb for 0 to 2500 Hz) 

* See Figure 7 

NASA/TM—2005-213880 9
FIGURE 7. Brayton Power Conversion Unit Model-2 Bearing Stiffness Model 

(a) 30000 RPM Comparison in the X Direction (b) 30000 RPM Comparison in the Y Direction 

 (Black Test Data, Grey Model Prediction) (Black Test Data, Grey Model Prediction) 

(c) 40000 RPM Comparison in the X Direction (d) 40000 RPM Comparison in the Y Direction 

 (Black Test Data, Grey Model Prediction) (Black Test Data, Grey Model Prediction) 

FIGURE 8. Brayton Power Conversion Unit, Model-2 and Test Data Comparison 

NASA/TM—2005-213880 10
As can be seen in Figure 8 for the X and Y directions and for the 30000 and 40000 rpm cases, Model-2 does a very 

good job predicting the once per revolution excitation frequency in addition to the second harmonic. However, the 

Model-2 predicted magnitudes (G2

/Hz) do not compare favorably with the test data values for the 30000 rpm case at 

these frequencies. This is because the imbalance force is fixed in the model (i.e. is not speed dependent) and is more 

representative of the force that would be present at the 40000 rpm condition. It was also observed that the predicted 

imbalance force at the once per revolution frequency was still slightly conservative for the 40000 rpm X direction 

PSD value. The other frequency bands show a better comparison to the random noise background noise suspected to 

be the result of fluid dynamic excitation of the CBC engine working internal fluids. It is also believed that the 

excitation energy in the 300-600 Hz band was a result of CBC airfoil-bearings dynamics and should be included in 

the model. The airfoil-bearings dynamics (as a spring-mass system) were added to the model to capture the effects of 

fluid dynamics disturbance at least up to 600 Hz. All other frequency bands for which there is a magnitude difference 

is expected to be the result of structural modes of the vibration test stand structure and the CBC working fluid random 

excitation at higher frequencies. 

However, as stated previously, accurate vibration disturbance predictions at least up to 600 Hz for a closed-Braytoncycle (CBC) Power Conversion System (PCS) is important for flexible on-orbit spacecraft control/structure 

interaction analyses and for understanding the vibration disturbance field affecting the scientific instrumentation 

onboard a spacecraft such as JIMO. Therefore, the underlying Grms value of both the predicted acceleration from 

Model-2 and the actual measured value from the test data were calculated. This value give the structural dynamics 

analyst an idea of the amount of excitation energy that exists which could be of concern for the spacecraft analyses. A 

comparison of this value for Model-2 and the test data is shown in Table 6. 

 TABLE 6. Grms Comparisons of Model-2 and Test Data

X Direction Y Direction 

Operating 

Condition Model-2 

Grms Value 

Test 

Grms Value 

Model-2 

Grms Value 

Test 

Grms Value 

0-1500 Hz 

(30000 RMP Case) 0.012 0.010 0.016 0.007 

0-1500 Hz 

(40000 RPM Case) 0.018 0.019 0.025 0.020 

Table 6 shows that Model-2 still over predicts the excitation energy for the 30000 rpm case in both the X and Y 

directions due to the imbalance force being too conservative (i.e. is not speed dependent) in addition to its frequency 

of excitation occurring below 1500 Hz. Additionally, Model-2 shows very good comparison for the excitation energy 

for the 40000 rpm case in both the X and Y directions. The results from Model-2 show that if the model predictions 

were used in spacecraft analyses, an overly conservative response would be expected for the 30000 rpm run 

condition, but a fairly accurate spacecraft response would be expected for the 40000 operating condition. Further 

improvements such as speed dependent imbalance force and improved CBC engine working fluid random vibration 

excitation could be made to Model-2 in the future. 

It is also important to recognize the low vibration magnitudes reported in Table 4 and Table 6. The operating 2 kWe 

CBC engine was predicted to be a quiet machine, and this was proven with test data. It is expected that in any future 

spacecraft analyses, the predicted response of the spacecraft system to the disturbance caused by an operating CBC 

engine would be negligible regarding spacecraft control authority and effects on scientific instrumentation. 

CONCLUSION 

Analytical models of an operating 2kWe CBC engine were created and refined based on operational test data. 

Through a single refinement stage, the analytical model showed very good comparison to the test data vibration 

energy for the specific imbalance rpm case modeled. There are still several areas in which the existing model could 

be improved. These are speed dependent imbalance force, high-frequency airfoil-bearings dynamics, and improved 

CBC engine working fluid random vibration excitation. These additional improvements were not implemented for 

NASA/TM—2005-213880 11
this paper but will be pursued in the future in order to gain possible additional understanding of how to model a 

working CBC engine for spaceflight application. 

Note that, the effects of rotating machinery and airfoil-bearing dynamics were conservatively modeled (by necessity), 

because these internal disturbances alone already manifested the vibration level of the actual system. Even on the 

frequency band of 0 to 1500Hz, the actual system vibration must have been the result of many more complex 

disturbances 

Furthermore, the final model developed predicted very minimal excitation energy in the frequency band of interest, 0-

600Hz, which was validated by test data. This is important information in that the understanding of the on-orbit 

spacecraft control/structure interactions for a large, flexible spacecraft such as the Jupiter Icy Moons Orbiter (JIMO) 

will be required and the CBC disturbances will be of primary concern. With such expected low disturbances coming 

from an operating 2 kWe CBC engine, issues with spacecraft control/structure interactions are not expected. 

However, this still requires validation by adapting this model to a model of the full-scale system (50-kWe unit). 

Additionally the vibration disturbance field from an operating CBC engine is not expected to negatively affect the 

scientific instrumentation onboard a spacecraft. 

The performance of the CBC engine models at other operating condition will also need to be investigated. Of 

particular interest will be transient torque conditions and emergency shutdown transients.

NOMENCLATURE 

CBC Closed Brayton Cycle 

GTD Ground Test Demonstrator 

JIMO Jupiter Icy Moons Orbiter 

kWe kilo Watt electric 

MEL Microgravity Emissions Laboratory (at NASA Glenn Research Center) 

NEP Nuclear Electric Propulsion 

PCS Power Conversion System 

PSD Power Spectral Density 

RPM Rotations Per Minute 

SD Solar Dynamic 

SDL Structural Dynamics Laboratory (at NASA Glenn Research Center) 

REFERENCES 

Yu, A., “Preliminary Torque Analysis of Closed Brayton Cycle Rotor Dynamics on a Conceptual Nuclear Electric 

Propulsion Vehicle”, NASA GRC EDAD Internal Task Report #69037; January 21, 2003. 

NASA/TM—2005-213880 12
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

REPORT DOCUMENTATION PAGE

2. REPORT DATE

19. SECURITY CLASSIFICATION

 OF ABSTRACT

18. SECURITY CLASSIFICATION

 OF THIS PAGE

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 Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson

Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

Form Approved

OMB No. 0704-0188

12b. DISTRIBUTION CODE

8. PERFORMING ORGANIZATION

 REPORT NUMBER

5. FUNDING NUMBERS

3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE

6. AUTHOR(S)

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

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

13. ABSTRACT (Maximum 200 words)

14. SUBJECT TERMS

17. SECURITY CLASSIFICATION

 OF REPORT

16. PRICE CODE

15. NUMBER OF PAGES

20. LIMITATION OF ABSTRACT

Unclassified Unclassified

Technical Memorandum

Unclassified

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135–3191

1. AGENCY USE ONLY (Leave blank)

10. SPONSORING/MONITORING

 AGENCY REPORT NUMBER

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

National Aeronautics and Space Administration

Washington, DC 20546–0001

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

November 2005

NASA TM—2005–213880

E–15251

WBS–22–973–80–10

18

Verification of a 2 kWe Closed-Brayton-Cycle Power Conversion System

Mechanical Dynamics Model

Damian R. Ludwiczak, Dzu K. Le, Anne M. McNelis, Albert C. Yu, Sergey

Samorezov, and Dave S. Hervol

Closed Brayton cycle; Power generation; Dynamic loads

Unclassified -Unlimited

Subject Categories: 20 and 44

Prepared for the Space Technology and Applications International Forum (STAIF–2005) sponsored by the University

of New Mexico's Institute for Space and Nuclear Power Studies (UNM–ISNPS), Albuquerque, New Mexico, February

13–17, 2005. Damian R. Ludwiczak (currently at NASA Kennedy Space Center), Dzu K. Le, Anne M. McNelis, and

Albert C. Yu, NASA Glenn Research Center; Sergey Samorezov, ZIN Technologies, Inc., 3000 Aerospace Parkway,

Brook Park, Ohio 44142; and Dave S. Hervol, Analex Corporation, 1100 Apollo Drive, Brook Park, Ohio 44142.

Responsible person, Dzu K. Le, organization code DEI, 216–433–5640.

Vibration test data from an operating 2 kWe closed-Brayton-cycle (CBC) power conversion system (PCS) located at the

NASA Glenn Research Center was used for a comparison with a dynamic disturbance model of the same unit. This effort

was performed to show that a dynamic disturbance model of a CBC PCS can be developed that can accurately predict

 the torque and vibration disturbance fields of such class of rotating machinery. The ability to accurately predict these

disturbance fields is required before such hardware can be confidently integrated onto a spacecraft mission. Accurate

predictions of CBC disturbance fields will be used for spacecraft control/structure interaction analyses and for

understanding the vibration disturbances affecting the scientific instrumentation onboard. This paper discusses how test

cell data measurements for the 2 kWe CBC PCS were obtained, the development of a dynamic disturbance model used to

predict the transient torque and steady state vibration fields of the same unit, and a comparison of the two sets of data.