Composite Flywheel Development for Energy Storage 

by Jerome Tzeng, Ryan Emerson, and Paul Moy 

ARL-TR-3388 January 2005 

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Army Research Laboratory 

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ARL-TR-3388 January 2005 

Composite Flywheel Development for Energy Storage 

Jerome Tzeng, Ryan Emerson, and Paul Moy 

Weapons and Materials Research Directorate, ARL 

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Composite Flywheel Development for Energy Storage 

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622618H75 

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Jerome Tzeng, Ryan Emerson, and Paul Moy 

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14. ABSTRACT 

Composite flywheels for energy storage have been proposed and investigated for the past several decades. Successful 

applications are, however, limited due to the inability to predict the performance, especially the long-term durability. In this 

investigation, a comprehensive study was proposed with the intent to implement composites in high-performance flywheels. 

The potential failure mechanism of flywheels constructed with fiber composites was evaluated. Analytical codes for predicting 

elastic and viscoelastic (long-term) behavior were developed for flywheel design. Material characterization and test matrices 

were proposed to design flywheels with maximum performance. Component-level test methods and devices were developed to 

validate flywheel performance. Finally, a methodology incorporating these studies is presented for the design and manufacture 

of composite flywheels. 

15. SUBJECT TERMS

composite flywheel, filament winding, viscoelasticity, rotor strain measurement 

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19a. NAME OF RESPONSIBLE PERSON

Jerome T. S. Tzeng 

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iii

Contents 

List of Figures iv

1. Introduction 1

2. Analytical Models 3

3. Material Testing 7

4. Rotor Testing: Vibration and Strain Measurement 9

4.1 Improvements to ARL OESM System..........................................................................11 

4.2 Pattern Shape.................................................................................................................11 

4.3 Pattern Application........................................................................................................12 

4.4 Sensor Geometry ...........................................................................................................12 

4.5 Configuration and Control of the Sensor ......................................................................12 

4.6 OESM System at ARL ..................................................................................................12 

5. Conclusion 13

6. References 14

Distribution List 15 
iv

List of Figures 

Figure 1. Definition of coordinate systems and stress components in a rotating cylinder. ............2 

Figure 2. Stress profile in a hoop-wound composite cylinder with 3-in inner and 6-in outer 

radii, subjected to 50,000-rpm rotational load...........................................................................2 

Figure 3. Composite time-dependent unit ply properties. Transverse and shear properties are 

time-dependent and expressed with power forms......................................................................5 

Figure 4. Decrease of the preload (radial stress at 4.5-in radius) at the interface of a pressfit 

assembly due to creep and stress relaxation of composite.........................................................5 

Figure 5. Change of the radial stress profile in a rotating wheel due to creep and stress 

relaxation of composite..............................................................................................................6 

Figure 6. Change of the hoop-stress profile in a rotating wheel due to creep and stress 

relaxation of composite..............................................................................................................6 

Figure 7. Twenty-inch diameter composite cylinders fabricated at ARL facilities........................7 

Figure 8. Iosipescu test specimen represents the loading condition and rotor construction. 

Shear strength increases as the glass content increases. ............................................................8 

Figure 9. Fracture increases as the glass fiber content increases in the composite laminate. 

The glass is oriented to arrest the crack propagation.................................................................9 

Figure 10. Illustration of a pattern and sensor configuration with corresponding duty cycle 

(10)...........................................................................................................................................10 

Figure 11. Illustration of change in duty cycle at one radial location before and after 

deformation (10). .....................................................................................................................10 

Figure 12. Illustration of a four-lobe linear boundary and four-lobe spiral boundary pattern......11 

Figure 13. Picture of the rotor testing facility at ARL..................................................................13 
1

1. Introduction 

Composite flywheels are currently being developed for energy storage. The energy stored in the 

flywheel can be retrieved to supply power for electrical-drive machinery. To satisfy the 

high-performance and low-weight constraints, high-strength carbon fiber composites are the 

materials of choice for flywheel construction. Recently, several composite flywheels have been 

developed for commercial power generation and vehicles such as buses and trains. In the 

government sector, National Aeronautics and Space Administration (NASA) intends to have 

composite flywheels in the space station for energy storage. Flywheels have also been proposed 

for satellite attitude control. There are investigations of hybrid and all-electric combat vehicles 

and weapons. Composite flywheels are crucial components of the systems. There have been 

numerous research and development (R&D) programs on composite flywheels in the past (1–3). 

Several programs have been conducted in National Laboratories for nuclear applications. Some 

long-term programs were performed in academia and industry. In spite of much effort, few 

successful composite flywheels have been built and used in practical applications. The 

shortcomings that hinder the use of composite materials in flywheel applications will be 

illustrated and discussed. A new approach for design and testing is also proposed in the 

following sections. 

The inertial stresses in a flywheel during operation (high-speed rotation) are dominant in the 

circumferential direction and, consequently, composite flywheel rotors are usually filament 

wound with the fiber reinforcements oriented in this direction. However, tensile stress is also 

developed in the radial direction due to mismatches in the growth of the rotor as well as Poisson 

effects. Because filament wound composite rotors lack reinforcement through the radial 

thickness, these rotors generally fail by radial delamination prior to fiber breakage in the 

circumferential direction. An elastic thick-walled composite cylinder analysis was developed to 

determine the stress and strain profiles in a flywheel. Figure 1 shows the definition of stress 

components and coordinate systems used in the analysis. Figure 2 illustrates the stress profile in 

a graphite composite cylinder with 3-in and 6-in inner and outer radii, respectively, subjected to 

50,000 rpm rotational load. As shown in the analysis, the maximum hoop stress is ~95 ksi and is 

below the strength limit. However, the radial stress in this case is ~10 ksi—far exceeding the 

strength in that direction. These stresses were calculated using the model developed in 

reference (4). 

By assembling the rotor with a press fit or shrink fit, compressive radial stress is built-in, which 

helps to mitigate the radial stresses that develop during operation. Consequently, higher rotor 

performance is realized by avoiding premature failure by radial delamination. The press fit 

process, however, might induce significant banding and shear stresses along the axial direction 

of the cylinder during fabrication. Axial reinforcement might therefore be needed for a flywheel 
2

σθθ

u 

r,w

w

ω

a b 

“N” layers 

Figure 1. Definition of coordinate systems and stress components in a rotating 

cylinder. 

8.0 104

8.5 104

9.0 104

9.5 104

1.0 105

3 3.5 4 4.5 5 5.5 6

Hoop Stress (psi)

Radius (inch)

0.0 100

2.0 103

4.0 103

6.0 103

8.0 103

1.0 104

3 3.5 4 4.5 5 5.5 6

Radial Stress

Radial Stress (psi)

Radius (inch)

Figure 2. Stress profile in a hoop-wound composite cylinder with 3-in inner and 6-in outer radii, subjected to 

50,000-rpm rotational load. 

to achieve a higher speed or performance. With this in mind, a series of material tests were 

performed to determine the tensile and shear properties of laminates in this investigation. The 

test results will be used to design the layup of a composite rotor subjected to various loading 

conditions, including those induced by the manufacturing processes. 

To achieve high performance, the stresses in a composite rotor must be high during operation. 

Accordingly, the long-term behavior of the composite materials used in flywheel rotors is 

particularly critical. Over time, the stress and strain profiles can change in a composite flywheel 

significantly affecting the structural performance. Creep and fatigue crack growth are durability 
3

concerns that lead to unbalance in the rotor. To assist in evaluating the occurrence of such 

time-dependent phenomena, a viscoelastic analysis of flywheels was developed. Fracture 

properties of the composite laminates of interest were also evaluated in conjunction with the 

potential crack growth and failure mechanism (5). 

The rotor deformation needs to be monitored in order to validate structural design and integrity. 

Currently, deformation of a rotating body can be measured by strain gage with a split ring at the 

spindle or a laser measurement. The strain gage works only up to a moderate speed then fails 

because of high centripetal force. The traditional laser device basically measures the distance 

change between the rotor surface and the device location. However, neither method will be able 

to satisfy the measurement required of a high-speed rotor. A noncontact optical-sensing 

technique was developed during the investigation. The method will enable a real-time monitor 

of rotor conditions and will be discussed in detail. 

Recent flywheel developments for energy storage of U.S. Army electric weapons and hybrid 

vehicles are discussed in this report. Technologies to achieve high-performance composite 

flywheels were developed during the course of this study. In the following section, those 

technologies will be presented, including analytical models, material characterization, 

component spin tests, and flywheel life assessment. 

2. Analytical Models 

An analytical model is necessary to predict creep and preload loss due to the time-dependent 

behavior of composites. A viscoelastic analysis has been developed that is relevant for 

thick-walled composite cylinders (6, 7). The Boltzmann superposition integral is used for the 

complete spectrum of increments of anisotropic material constants with respect to time. In the 

analysis, a thick composite cylinder is assumed to remain at a constant elevated temperature, and 

all boundary conditions are independent of time. Accordingly, the linear thermal viscoelastic 

problem can be derived from the associated linear elastic problem by employing the 

elastic/viscoelastic correspondence principle. In other words, the integral constitutive equations 

reduce to algebraic relations, which are essentially identical to those developed for elastic media 

when they are Laplace transformed by means of the rule for convolution integrals. The elastic 

analysis can thus be used to derive the transformed viscoelastic solutions in the time domain. 

The coordinate system used to model a rotor is shown in figure 1. The governing equation can 

be derived from the momentum equation with anisotropic constitutive material properties as 

follows: 

2

3

33 33

– –

2

2 2 13 12 o

2

d w dw ( ) C C

r + r w = r r ,

dr dr sC sC

ρω λ ε − % %

% % (1)
4

where w is radial displacement and r is radius, ω is angular velocity, ε is axial elongation, and s

denotes the Laplace transform variable. The Cij terms are material properties (4). 

Equation 1 is the governing equation in the Laplace domain. Here and henceforth, an overbar 

denotes functions of the Laplace transform variable. The elastic formulation has a similar form 

according to the correspondence principle. While this equation can represent any composite 

layer (with one set of material properties) within a multiple-layer composite cylinder, properties 

are allowed to vary from layer to layer. 

Solving equation 1 for w yields the complete solution as follows: 

– w Ar Ar w =+ + 1 2 p % λ λ , (2) 

where 1 2 A A and are coefficients determined from boundary and continuity conditions. The 

particular solution is obtained in the following expression: 

r . C

~ 9

1

r 

C

~ C - ~ C

~ C - ~

w

~ = 3

33

2

2

o

33 22

12 13

p

ρω

− λ

ε − (3) 

A set of simultaneous equations can be assembled for a multiple-layer composite cylinder. The 

total number of equations is determined by the number layers in the cylinder. A numerical 

technique was developed, which applies the continuity boundary condition during the assembly 

process of the equation set (6). This process reduces the total number of the equations to one half. 

Finally, traction-boundary conditions are applied to the assembly of equations that comprise the 

multiple-layer cylinder. 

The analysis previously described is used to simulate a composite press fit assembly. The 

simulation is composed of two concentric cylinders. The inner cylinder has a 3-in inner radius and 

a wall thickness of 1.5 in. The outer cylinder has a 4.5-in inner radius and also has a wall thickness 

of 1.5 in. Both cylinders are hoop wound and constructed of graphite/epoxy composite. The shear 

and transverse material properties (compliances) are treated as time dependent, and are given in 

figure 3. The fiber direction compliance and Poisson’s ratios are assumed to be elastic. 

Figure 4 shows that the preload at the interface of cylinders decreases over a period of time. Stress 

relaxation is observed in the initial preload (radial stress at the interface between the inner and 

outer cylinders), which decreases over time from 5000 to 4000 psi. In response to this decrease in 

preload, it would be necessary to reduce the rotational speed of the rotor (i.e., knockdown the 

mechanical performance) because the preload is essential for preventing radial delamination. 

Figure 5 illustrates the change in the radial stress profile over a period of time for the flywheel 

subjected to constant rotation at 50,000 rpm. The hoop-stress profile changes also, as illustrated in 

figure 6. There is significant redistribution of stresses that should be considered in the design.
5

S (t)=7.553* 10 (t) -7 0.0175

22

S (t)=1.383* 10 (t) -6 0.06

66

S = 5.9*10 / psi -8

11

ν 12=ν 13=0.3,ν 23=0.36

1

2

3

Figure 3. Composite time-dependent unit ply properties. Transverse and shear properties are 

time-dependent and expressed with power forms. 

-5.0E+03

-4.0E+03

-3.0E+03

-2.0E+03

-1.0E+03

0.0E+00

3 3.5 4 4.5 5 5.5 6

Radius(in)

Radial Stress (psi) 

Initial 10 yrs Years Infinite

Figure 4. Decrease of the preload (radial stress at 4.5-in radius) at the interface of a pressfit 

assembly due to creep and stress relaxation of composite. 
6

Relaxation of Radial Stress

0.0E+00

2.0E+03

4.0E+03

6.0E+03

8.0E+03

1.0E+04

3 3.5 4 4.5 5 5.5 6

Radius (inch)

Radial Stress (psi)

Initial 10 Years Infinite

Figure 5. Change of the radial stress profile in a rotating wheel due to creep and 

stress relaxation of composite. 

Relaxation of Hoop Stress

7.00E+04

7.50E+04

8.00E+04

8.50E+04

9.00E+04

9.50E+04

1.00E+05

1.05E+05

3.0 3.5 4.0 4.5 5.0 5.5 6.0

Radius (inch)

Hoop Stress (psi)

Initial 10 Years Infinite

Figure 6. Change of the hoop-stress profile in a rotating wheel due to creep and stress 

relaxation of composite. 
7

3. Material Testing 

Composite cylinders with an inner diameter of 20 in were fabricated at the U.S. Army Research 

Laboratory (ARL) in-house facilities as shown in figure 7. David Spagnuolo, Robert Kaste, and 

Dennis Henry contributed to the fabrication of cylinders including mandrel fabrication, filament 

winding, and cure kinetics study. The details of manufacture will be documented in a separate 

report. The cylinder was made of T1000G graphite/epoxy composite. Several thin cylinders 

(0.1 in thick) were fabricated and sliced into 0.5-in-wide ring specimens for hydro-burst testing. 

A test matrix was conducted to measure the strength and stiffness of these composite ring 

specimens. This procedure works well for evaluating the circumferential strength of cylinders 

fabricated with various fiber volume fractions, matrix materials, and fabrication methods. High 

strength is obtained through careful engineering and manufacturing of the cylinders. The 

strengths measured from the ring samples were between 500 to 600 ksi for the fabrication 

methods and material systems used. 

ARL 20 inch diameter 

cylinder

Figure 7. Twenty-inch diameter composite cylinders fabricated at 

ARL facilities.
8

As discussed previously, the performance of a composite flywheel can be enhanced through a 

proper laminate architecture design with axial reinforcements. A series of tests was performed to 

evaluate the enhancement of S-2 Glass* axial reinforcement on the transverse, shear, and fracture 

properties of laminates. Effects of glass ply content on shear strength were evaluated using 

carbon/glass hybrid laminates. T1000G composite laminates with various axial glass contents 

were tested using Iosipescu shear tests. Figure 8 shows the trend of the enhancement of shear 

strength (τ23) of the T1000G laminate with increasing glass content. These results can be used in 

the design of laminated composite cylinders. An identical test matrix was also performed for 

transverse tensile tests. 

 

gage section

Glass

mean S.D. mean S.D. mean S.D. mean S.D.

0 12.72 0.51 1.78 0.22 4.88 0.38 0.91 0.10

7 12.65 0.39 1.5 0.08 7.2 0.51 1.18 0.08

10 12.71 0.41 1.68 0.12 8.67 0.24 0.93 0.13

G2-3 % (Msi)

S2-glass

τ 1-3 (ksi) G1-3 (Msi) τ 2-3 (ksi)

3

2 S-2 Glass

1 T1000

Figure 8. Iosipescu test specimen represents the loading condition and rotor construction. Shear strength 

increases as the glass content increases. 

Fracture toughness is a critical property for composite flywheels subjected to a very high 

operating stress. Microcracks developed in the matrix can propagate and cause delamination in 

the rotor. A composite system with high fracture toughness has a slow rate of crack propagation 

and, thus, a longer fatigue life. The fracture toughness of composite cylinders can also be 

enhanced by adding glass content in the rotor axial direction (5). Figure 9 shows how the glass 

content affects the fracture toughness. Reference (8) gives details of the test method, results, and 

fracture mechanism predicted for composite cylinders. The dependence of loading rate on the 

fracture toughness is also evaluated, which is useful for a high-rate loading condition. In 

conjunction with this study, a fatigue study on combined shear and compressive loading of 

composite laminates was performed (9). 

 *

 S-2 Glass is a registered trademark of Owens Corning. 

gage section 
9

0

1000

2000

3000

4000

5000

6000

0123456

load (N)

displacement (mm)

12% v.c.

6% v.c.

S2-Glass

IM7

Figure 9. Fracture increases as the glass fiber content increases in the composite laminate. 

The glass is oriented to arrest the crack propagation. 

4. Rotor Testing: Vibration and Strain Measurement 

Several techniques exist for measuring strains in the rotors of flywheels during operation, 

including strain gages with slip rings or telemetry, x-ray diffraction, and optoelectronic strain 

measurement (OESM). The OESM technique (described in detail in references [10] and [11]) is 

capable of simultaneously measuring and isolating flexible-body displacements (strain) and 

rigid-body displacements (vibration) in a noncontact fashion on flywheels rotating at several tens 

of thousands of rpm. In addition, the computer control of the OESM sensor enables the 

displacements to be measured in a quasi-continuous fashion (i.e., without postprocessing), and 

the OESM technique includes built-in compensation for drift/aging of the sensor. The 

combination of these previously-mentioned features, as well as its compact size, makes the 

OESM technique suitable for long-term autonomous operation in the field. 

The OESM technique consists of two components: a reflective pattern applied to the axial face 

of the flywheel, and a sensor that “looks at” the pattern as the flywheel rotates. The OESM 

sensor projects a stationary spot of light onto the axial face of a rotating disk. The reflective 

pattern on the axial face of the disk modulates the reflectivity of the light spot. This pattern, 

which deforms in unison with the disk, is designed such that the in-plane displacement of the 

disk is effectively “encoded” into a stream of reflected pulses of light. A photodetector on the 

sensor converts this stream of reflected light pulses to electrical pulses and sends these electrical 

pulses to the gate of a timer/counter circuit in a digital computer. The computer uses a 

6% v.c. 
10

tachometer signal to convert the (temporal) pulse widths to angular widths of the reflective 

features of the pattern. Figure 10 shows an illustration of a rotor with inner and outer radii, ri

and ro, respectively, with a pattern that has one reflective patch (the cardioid shape shown in 

white). Also shown in figure 10 is the corresponding swept-angle, φ, or so-called duty cycle, 

output from the sensor. 

φ

ri

ro

fixed

sensor

sensor

path

Top 

view

Oblique

view

0 π 2π

Logic 

Signal

on

off

π/2

π

3π/2

Duty Cycle

spot of 

light Azimuthal location

Figure 10. Illustration of a pattern and sensor configuration with corresponding duty 

cycle (10). 

The instantaneous displacement, u, of the rotor at the location of the projected spot of light is 

determined by comparing the instantaneously measured angular widths to a calibration record of 

pulse width vs. radial location on the rotor. Figure 11 shows the duty cycle before deformation, 

φ 1, and after deformation, φ 2, for a sensor fixed in space at a location corresponding to an initial 

radial location r1 on the under-formed rotor. 

 

u r

1

= r

1− r2

before

deformation:

after

deformation: 

φ1

φ2

2π

0

ri r2 r1 ro 

φ2

φ1

r

Duty 

Cycle,

φ

radial position 

Calibration Record of φ (r)

Figure 11. Illustration of change in duty cycle at one radial location before and after 

deformation (10).
11

4.1 Improvements to ARL OESM System 

Recent changes have been made to many aspects of the OESM system since the original system 

was developed. These changes encompass improvements to the pattern shape, the technique for 

applying the pattern to the rotor, the sensor geometry, and configuration and control of the 

sensor. 

4.2 Pattern Shape 

While the shape of the pattern shown in figures 10 and 11 is a spiral boundary shape (10, 11), the 

pattern shape used in practice possessed geometric features with linear boundaries. Figure 12 

shows a comparison of these two types of pattern shapes on an identical annular rotor. Note that 

the patterns shown in figure 12 possess four reflective lobes, while the patterns shown in 

figures 10 and 11 have only one lobe (for illustrative purposes). 

0

0.4

0.8

1.2

1.6

0.7 0.8 0.9 1

Normalized Radius, r/ro

Duty 

Cycle,

φ 

(rad)

Linear Boundary

Spiral Boundary

Calibration Records for Linear Boundary and

Spiral Boundary Patterns

ri

ro

ri

ro

lobe

Linear boundary 

Spiral boundary 

Figure 12. Illustration of a four-lobe linear boundary and four-lobe spiral boundary pattern. 

A linear boundary pattern possesses a region near the inner radius where the duty cycle exhibits a 

large change with respect to radial position. This large change corresponds to a large “slope” of 

the calibration record and, therefore, is a pattern with favorable sensitivity to radial displacement 

(figure 12). It has been found, however, that the portion of the linear boundary pattern near ri

(where this large slope is an advantage) is not practical to use. In the usable radial locations in a 

linear boundary pattern, the duty cycle of a spiral boundary pattern exhibits equivalent or better 

sensitivity to radial displacement than a linear boundary pattern. The sensitivity of a linear 

boundary pattern quickly decays away from the inner radius, while the sensitivity of a spiral 

boundary pattern remains essentially constant over the entire radial region. Based on these 

findings, the current rotor-testing protocol employs a spiral boundary reflective pattern.
12

4.3 Pattern Application 

The reflective pattern in the OESM system is essentially analogous to a strain gage in as much as 

the pattern must not significantly reinforce the rotor, and it must deform with the rotor. With the 

previous OESM technique, the pattern was applied to the axial face of the rotor with a spray-on 

photographic emulsion. The emulsion was developed in a contact-print fashion using a mask 

with computer-generated geometric features. The main drawbacks of this pattern application 

technique are that it is very laborious, and it results in a delicate pattern. The new technique for 

applying the reflective pattern uses a thin layer of reflective paint followed directly by a thin 

layer of ink that is applied using a pen and compass. The resulting pattern is able to be applied 

faster and is much more resistant to damage that may occur during handling of the rotor. 

4.4 Sensor Geometry 

During testing of the original OESM system, it was found that when the vertical distance 

between the rotor and the sensor changed more than ~50 μm, significant errors were introduced 

into the measurement of the apparent duty cycle. It is believed that some of this sensitivity was 

attributable to drifting of the spot in the active area of the photodetector, as the original OESM 

sensor projected the spot of light onto the rotor surface at an angle that was ~10° away from 

perpendicular. Also, the original sensor had a stand-off distance between the sensor and the 

rotor surface of ~4.5 mm; thus, vertical displacements resulted in defocusing of the projected 

spot. With these design issues in mind, the current OESM sensor has a stand-off distance of 

~50 mm and projects the light perpendicularly to the surface. 

4.5 Configuration and Control of the Sensor 

The OESM system described in references (10) and (11) was configured with 10 positions 

equally spaced along a radial line at which a sensor could be located. The sensors in this 

configuration remained stationary during operation. The displacements measured at these 10 

locations, therefore, were only useful for constructing a rather coarse full-field “picture” of the 

state of strain in the rotor. The current OESM setup uses a single sensor, which is bolted to a 

linear stepper motor stage. The stroke length of this linear stage is capable of scanning a large 

radial range (125 mm) in radial increments as small as 1 μm, thus enabling the construction of a 

very fine full-field “picture” of the state of strain in the rotor. Also, a new algorithm for 

controlling the inevitable drift of the sensor (12) will be employed in the current OESM system 

at ARL. 

4.6 OESM System at ARL 

Measurement of radial growth is an essential piece of data for validating the structural design 

and analysis of the flywheel rotor. It is unlikely that any rotor will be accepted for operation in 

the field without validation by testing. The previously developed OESM technique was capable 

of measuring displacements with 1-μm sensitivity on a disk rotating at 20 krpm. While not yet 
13

fully tested, the improvements embodied in the current OESM system as previously described 

should enable a several-fold increase in the sensitivity to displacement. Figure 13 shows a 

picture of the spin test facility at ARL, which is ready to be used in the component tests in 

support of the efforts for developing a pulsed power rotating machine. 

Acrylic 

vacuum 

enclosure 

Optoelectronic 

sensor 

Glass 

window 

Rotor with new 

reflective 

pattern 

Figure 13. Picture of the rotor testing facility at ARL. 

5. Conclusion 

A comprehensive research program has been conducted to develop high-performance composite 

flywheels for energy storage applications. Modeling techniques including elastic, viscoelastic, 

and fatigue analyses were developed for design as well as prediction of rotor behaviors. A 

laminate architecture for achieving high mechanical performance of flywheels was proposed 

based on lessons learned from previous programs. A material test matrix at the laminate level 

was also proposed from a design point view of high-performance flywheels. The optical strain 

measurement technique can be used to validate flywheel design and construction. Particularly, 

the proposed design and test procedure indeed considers the long-term behavior of flywheel such 

as creep, stress relaxation, fatigue, and fracture of composites. 
14

6. References 

1. Stone, R. G. Fiber-Composite Flywheel Program: Quarterly Progress Report; 

UCRL-50033-76-4; Lawrence Livermore National Laboratory: Livermore, CA, 1976. 

2. Pardoen, R.; Nudenberg, D.; Wartout, B. E. Achieving Desirable Stress States in Thick Rim 

Rotating Disks by Variation of Properties. Proceedings of the 1980 Flywheel Technology 

Symposium 159, Dayton, OH, October 1980. 

3. Acebal, R. Energy Storage Capabilities of Rotating Machines Including a Comparison of 

Laminated Disk and Rim Rotor Design. IEEE Transactions on Magnetics 1999, 35 (1). 

4. Tzeng, J. T.; Chien, L. S. A Thermal/Mechanical Model of Axially Loaded Thick-Walled 

Composite Cylinders. Journal of Composite Engineering 1994, 4 (2). 

5. Tzeng, J. T.; Moy, P. Composite Rotor Design for Fatigue Crack Growth Resistance. 

Proceedings of the 16th Technical Conference, American Society for Composites, 

Blacksburg, VA, September 2001. 

6. Tzeng, J. T. Viscoelastic Analysis of Composite Cylinder Subject to Rotation. Journal of 

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