CP011
MARCH 1972
Copy No. 96
APTD-1344
Air Pollution Control
HEAT-ENGINE/MECHANICAL-ENERGY-STORAGE
HYBRID PROPULSION SYSTEMS
FOR VEHICLES
FINAL REPORT
G. L. DUGGER, A. BRANDT, J. F. GEORGE, L L. PERINI,
D. W. RABENHORST, T. R. SMALL, and R. 0. WEISS
THE JOHNS HOPKINS UNIVERSITY • APPLIED PHYSICS LABORATORY
-------
CP 011
MARCH 1972
Air Poll ution Control
HEAT - ENGINE /MECHANICAl- ENERGY. STORAGE
HYBRID PROPULSION SYSTEMS
FOR VEHICLES
FINAL REPORT
G. L. DUGGER, A. BRANDT, J. F. GEORGE, L. L. PERINI,
D. W. RABENHORST, T. R. SMALL, and R. O. WEISS
PREPARED FOR THE ENVIRONMENTAL PROTECTION AGENCY,
OFFICE OF AIR PROGRAMS
THE JOHNS HOPKINS UNIVERSITY. APPLIED PHYSICS LABORATORY
8621 Georgia Avenue 0 Silver Spring, Maryland 0 20910
This report is printed on recycled paper.
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TME JOHNS MOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV€- S~_I"'G- Io4AATLA"'P
ABSTRACT
An analytical study indicated that a flywheel-only
propulsion system could satisfy the performance require-
ments specified by the Office of Air Programs, Environ-
mental Protection A gency, for a city bus, and that flywheel/
heat engine hybrids could meet the specified requirements
for cars, vans, and buses. In all cases substantial emis-
sion-free ranges could be achieved with hybrid systems
by using the engine only periodically (at constant load) to
recharge a large, high-energy flywheel. Experiments
verified the principle of the" superflywheel" by spin tests of
unidirectional materials in rod or bar rotor configurations.
The better results demonstrated energy densities greater
than 30 W-h/lb (max. = 48) for boron filaments and slender
rods of graphite and glass composites. High-speed photo-
graphs of rotor failure showed complete pulverization of
1 pound rods in O. 6 ms as they impacted steel containment
rings; only 1 to 2% of the initial stored energy was im-
parted to the rings. Thus, composite flywheels will be
much easier to contain than metal flywheels and are prom-
ising candidates for energy storage devices.
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THE .JC:'Ho'NS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
StLVI:. ~NG. NAIII't'LANO
CONTENTS
List of Illustrations ix
1. Summary 1
1.1 Experimental Study 1
1.2 Analytical Study 4
2. Introduction 9
3. Experimental Program 15
3. 1 Introduction 15
3. 2 Tests of Small-Diameter Rods at APL 15
3. 2. 1 Equipment and Instrumentation 17
3. 2. 2 Selection of Candidate Test Materials 21
3. 2. 3 Test Results and Discussion 22
3. 2.4 Conclusions from Small-Scale Tests 30
3. 3 Tests of I-Pound Bars at the Naval Air
Propulsion Test Center . 30
3. 3. 1 Facility Modifications 31
3. 3. 2 Selection and Procurement of Test
Materials 34
3. 3. 3 Test Results and Discussion 38
3.3.4 Mode of Failure 48
3. 3. 5 Energy Absorbed by the Containment
Ring 53
3.4 Conclusions 60
4. Flywheel System Design Considerations and
Performance 63
4. 1 Introduction 63
4.2 Rotor Configuration and Material
Considera tions 64
4. 2. 1 Simple Comparative Illustrations of
the Superflywheel Concept 64
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THII - HONINS UHIVIIII8ITV
APPLIED PHYSICS LABORATORY
8IL.vaa """NO. M.II'IUND
CONTENTS (cont'd)
4. 2. 2 Transverse Stresses in Bar Rotors
Made of Unidirectional Composite
Material 66
4. 2. 3 The Circular Brush Rotor 69
4.2.4 Radially-Fanned Brush Rotor 72
4. 2. 5 A Laminated Composite Disk' 77
4. 2. 6 Summary of Energy Characteristics 79
4.3 The Effects of Flywheel Rotor Speed 82
4. 3. 1 Bearings 82
4. 3. 2 Vacuum System 85
4. 3. 3 Power Losses and Run-Down Times 86
4.4 Factors Affecting the Allowable Stresses in
Composite Material Flywheels 89
4. 4. 1 Flywheel System Life Cycle and
Environment 89
4. 4. 2 Dynamic Fati.gue of Composite
Materials . 92
4.4.3 Creep and Stress-Rupture of Com-
posite Materials 95
4.4.4 Longitudinal Divergence 100
4.4.5 Future Improvements in Materials,
Fabrication, and Design Tech:-
niques 102
4.5 Vehicu1B.r Installation 107
4.5. 1 Heat Energy/Flywheel Hybrid Pro-
pulsion in a Commuter Car 107
4.5. 2 Flywheel Gyroscopic Torque 110
4.6 Closure 113
5. Preliminary Vehicle Evaluation Studies 115
5. 1 Introduction 119
5.2 Powerplants for the Hybrid-Flywheel
Vehicles 119
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THa .10M'" HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
8fLWIt ""'NO. ""IrYLANO
CONTENTS (cont'd)
5.2. 1 Otto (SIE) Cycle 120
5. 2. 2 Diesel Engine (CIE) 123
5. 2. 3 Gas Turbine (GT) Cycle 126
5. 2.4 Rankine Cycle 129
5. 2.5 Emissions 131
5. 2. 6 Engine Performance 134
5. 2. 7 Closure 139
5.3 Vehicle Requirements and Weight and Volume
Considera tions 140
5. 3. 1 Vehicles Specifications and Resulting
Flywheel Subsystem Weights 141
5. 3. 2 Rotor Weight and Flywheel Subsystem
Volume 148
5.4 Drivetrain Considerations 152
5.4. 1 General Considerations 152
5.4. 2 Engine-to-Flywheel (Charge)
Transmission 154
5.4.3 Flywheel-to- Wheels Drive
Transmission 155
5.4.4 Other Drivetrain Components and
Drivetrain Layout 160
5.4.5 Regeneration Efficiency and Operations
on the DHEW Cycle 163
5. 4. 6 Conclusions on Transmissions and
Regeneration Efficiency 172
5.5 Performance and Emission Estimates 172
5. 5. 1 Inputs 172
5.5.2 Method of Analysis . 176
5.5. 3 Re sults 178
5.5.4 Sensitivities of Performance and
Emission Estimates to Assumptions 188
5. 6 Closure 190
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THE .JOHN. HOPtlClNS UNIV£RSITY
."'PPLIED PHYSICS LABORATORY
"L.VE" ~"ING. "'."YLA""O
6.
CONTENTS (cont'd)
General
Rotor Configuration and Materials.
Containment of Rotors
Flywheel Systems
Evaluation Studies
193
193
194
196
197
201
Conclusions and Recommendations
6. 1
6. 2
6.3
6.4
6. 5
Appendices
A.
B.
C.
D.
E.
References
Flywheel Shape and Biaxial Stress
Considera tions
The Disk Flywheel. Configuration
Estimates of Windage Losses for Flywheels
Survey of Available Transmissions and
Proposed Concepts
Tire and Wind Resistance of Automobiles.
203
235
243
253
277
285
Acknowledgment
305
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THI: JOHN. ~INS UNIVPtSITY
APPLIED PHYSICS LABORATORY
"LV.. "'1tt1l8G. M.,I!tYLANQ
ILLUSTRA TIONS
3-1 Energy Storage Capability of the Straight
Filament 16
3-2 Spin Chamber for Small-Scale Tests Being
Installed in Test Cell at APL 18
3-3 Test Setup for Rotating Small Filaments or
Composite Rods Using High-Speed Motor
Inside Chamber 19
3-4 A lternative Setup with Speed Increaser Inside
Chamber and 1- HP Motor Outside 19
3-5 Schematic Diagrams of Spin Chamber
Setup at APL 20
3-6 Remains of Graphite/Epoxy Composite in
Spin Chamber after Test 28
3-7 Simulation of Circular Brush Configuration
and Test Results 28
3-8 General Arrangement for I-Pound Rod Tests
at NA PTC, Philadelphia 32
3-9 General View of APL' s Inner Chamber Sus-
pended from an Assembly Platform 35
3-10 Inside View of Spin Chamber 36
3-11 Typical Specimens for NA PTC Tests 36
3-12 S-Glass/Epoxy Fragments from Test JH-l 40
3-13 Graphite/Epoxy Fragments from Test JH-3 40
3-14 Containment RIngs after Tests, Compared
to Reference Circles 43
3-15 Static Tensile Test Specimens before and
after Test 46
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THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
Scl.n.. Sr"NG. ".,IIItYLANO
ILLUSTRATIONS (cont'd)
3-16 Kinematics of Rod Failure (Assuming Two
Equal Segments) 49
3-17 Photographs Taken before Run JH-4 and at 7
Times after Failure Tripped Photographic
System 49
3-18 Photographs Taken before Test JH-2 and at
Seven Intervals following Failure of
S-Glass/Epoxy Bar 51
3-19 Deformation of 3/8-Inch-Thick Steel Ring;
Rod Energy of 820 000 In-Lb 54
3-20 One of the Impact Arcs on the Containment
Ring 54
3-21 Radius of Curvature and Change in Curvature
for 3/8-Inch-Thick Ring (JH-4 Test) 56
3-22 A ssumed Initial Velocity Profile of Ring for
Use in Momentum Transfer Analysis 58
4-1 Specific Energy Coefficients, Relative
Specific Strengths, and Relative Specific
Energies for Various Flywheel Shapes 65
4-2 Specific Energy Degradation Caused by Biaxial
Stress Field in Wider Bars 68
4-3 Circular Brush Configuration 70
4-4 Radially Fanned Brush Rotor 73
4-5 Effects of Rotor Geometry and Material Prop-
erties on Specific Energy in a Radially-
Fanned Brush Rotor 76
4-6 Specific Energy and Energy Packaging Density
versus T I R for Radially-Fanned Brush
Rotors of S-Glass/Epoxy Elements 76
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TH. JOHN8 _IHe UNIY.MITY
APPLIED PHYSICS LABORATORY
kvnt -""1I8G. M.ItYLAND
4-7
4-8
4-9
4-10
4-11
4-12
4-13
4-14
4-15
4-16
4-17
4-18
5-1
ILLUSTRATIONS (cont'd)
Summary of Ultimate Composite Material
Flywheel Characteristics for Different
Rotor Configurations
Effect of Rotor Configuration on Tip Speed
80
83
Typical Flywheel Cycle Requirements for a
Commuter Car
Constant Amplitude Fatigue Tests of Boron-
Epoxy Composite at Room Temperature
(from Ref. 34)
91
93
Fatigue Tests of S-Glass and E-Glass/Epoxy
Laminates at Room Temperature (from
Ref. 33)
93
Probability Lines for Stress-Rupture of
S-Glass/Epoxy Strands (from Ref. 39)
Time of Failure for S-Glass/Epoxy Cylinders
under Pressure at Ambient and Liquid
Nitrogen Conditions (from Ref. 40)
Static Fatigue Data for Silica Fibers: in Vacuum
at -196°C, in Vacuum at Room Temperature,
and in A ir at Room Temperature (Refs. 41,
42)
97
97
99
Longitudinal Divergence of Rod-Type Rotors
Characteristics of Failure Mechanisms for
Metals and Composite Materials (from
Ref. 36)
101
108
109
Heat Engine/Flywheel Hybrid Commuter Car
Example of Family Car Encountering a Severe
Roadway Obstacle at 45 MPH with 5 kW-h
Hard - Mounted. Flywheel
112
Ideal Cycles (T-S Diagrams), Ideal Thermal
Efficiencies (17 ) and Simple Configurations
of Heat Enginet . . . .
121
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TH£ .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVE- S....,fII'G. WiA8YLANO
5-2
5-3
5-4
5-5
5-6
5-7
5-8
5-9
5-10
5-11
5-12
5-13
5-14
5-15
5-16
5-17
)
ILL USTRA TIONS (cont' d)
Spark- Ignition Engine Characteristics
Projections of HC, CO, and NOx (as N02)
Emissions
124
133
Specific Weight versus Brake Horsepower
for the Four Heat Engines
Comparison of Specific Weights of the Four
Engines
136
138
Brake Specific Fuel Consumption versus
Engine Size
Effect of Rotor Length on Rotor Weight and
Total Volume, T = O. 25 Inch, T /R = O. 125
c
Transmission Output Characteristics
138
149
156
Acceleration Parameters versus Time,
Family Car
Flywheel Hybrid Power Control System
158
162
Commuter Car Hybrid Operating on DHEW
Driving Cycle. Full Flywheel Charge at
Start of Cycle; Engine Is Off during this
Portion
168
Energy Disposition of Commuter Car on DHEW
Cycle without Air Conditioner; 0.247 HP-H/
Mile. (A 4-HP Air Conditioner Operating
Continuously Represents 32% of Above
Energy. )
Steady-State Wheel Horsepower Requirements
for the Four Vehicles
171
174
174
Dri ving Cycles
Flywheel Rotor Ma ss Fractions Assumed
174
187
Flywheel-Only Level Road Cruise Performance
Effect of Design Speed and Air Conditioner
Load for Otto Hybrid Commuter Car
189
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THE .JOHNS HOPJC.INS UNIVERSIT"f
APPLIED PHYSICS LABORATORY
St\...,~" SPtIIlNG "."''f\.A.HO
5-18
5-19
6-1
A-I
A-2
A-3
A-4
A-5
A-6
A-7
A-8
A-9
B-1
ILLUSTRA TIONS (coo t'd)
Effect of Flywheel Rotor Weight for Otto
Hybrid Commuter Car
Effect of Drivetrain Efficiencies and External
Resistance for Otto Hybrid Commuter Car
191
191
Details of Recommended Working Prototype
Structure
198
Constant Stress Flywheel Performance
Thickness Distributions for Constant Stress
Rod Flywheels. (t /t .2 = Thickness ot:
o 0/=
Uniform Rod with Same Weight as at = 2
Constant Stress Case. ) . .
209
209
Effect of End Mass on Constant Stress Flywheel
Performance
211
Stress Distributions in Various Rod Flywheel
Configu.rations
Formulation of Rotating Bar Problem. Note
that the Thin Plate or Bar Is.in Plane
Stress
211
214
Comparison of Rayleigh-Ritz Solution with
Finite-Difference Solution. The Solution Is
Shown as a Dashed Line (Symmetrical about
x and y Axes)(Ref. 125)
Stress Distribution for a Graphite/Epoxy
(Hercules 2002T) Bar
218
225
Geometric and Performance Parameters of a
Constant Stress Disk Flywheel
Performance Parameters for Hyperbolic Disks
(r ex: 1/ z) with a Central Hole. Inner-to-Outer
Radius Ratio Equals Inner-to-Rim Thickness
Ratio
229
229
Lamina Axes Rotation and Pseudo-Isotropic
Laminated Disk
237
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fHE X)HNS HOPK.NS UNIVERSIT'1
II,PPUED PHYSICS LABORATORY
StLYl:JIt S-OJltIHG. .....JltYLAHO
1)-1
0-2
D-~
0-4
0-5
D-6
D-7
D-8
D-9
E-1
E-2
E-3
ILLUSTRATIONS (cont'd)
Perbury, Hayes, or Toric Type CVT's
Beier CVT's
255
257
Hydrostatic Transmission
Efficiencies for Catalogued Hydrostatic Trans-
missions at 2800-RPM Input Speed
262
266
Fluid Coupling Diagram and Characteristics
Single-Stage Torque Converter Diagram and
Characteristics
268
268
Schematic Diagram and Wide-Open Throttle
(Acceleration) Efficiency of Sunstrand
Dual-Mode, Infinitely Variable Ratio
Transmission
272
Rear Axle Efficiency at Wide-Open Throttle
and Road Load
276
Overall Efficiency Comparisons of Roller
Traction versus Geared Planetary Drive
Units
276
Vehicle Drag Coefficients for a Frontal Area
of 25 ft2 and Drag Forces at 60 MPH
Experimental Rolling Resistance Coefficients
281
281
Steady Horsepower Requirements for Various
Drag and Friction Estimates
284
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THe JOHN":; HOPI< INS UNIV!lR9ITY
APPLIED PHYSICS LABORATOfH
!lII.VWII SP''''Hr.. N..YLA,NO
1.
SUMMARY
This experimental and analytical study of high-
specific energy flywheel systems for use in automotive pro-
pulsion systems had two main objectives:
1. Proof-of-principle demonstration of the use of.
filamentary or composite materials of high uniaxial tensile
strength in rotor configurations that would have significantly
higher specific energies than prior flywheels. The goal was
to demonstrate a specific energy storage capability of 30
W-h/lb of rotor material.
2. Theoretical evaluation of the performance of
such flywheels, alone and in combination with heat engines,
in four classes of vehicles: family car ,commuter car, van,
and intracity bus. The interest of the Office of A ir Pro-
grams (OA P) of the Environmental Protection Agency was
in the potential value of such propulsion systems for reduc-
ing air pollution from such vehicles.
1. 1 EXPERIMENTAL STUDY
The results of the experimental study may be sum-
marized as follows:
1. Several filamentary or composite materials
available today can exceed 30 W-h/lb at burst. The most
interesting spin test results for 30-inch-long specimens
spun around their mid-points are summarized in Table 1-l.
Boron filaments are outstanding (48 W-h/lb demonstrated
without failure) but probably will remain too costly
($100/lb) (Ref. 1) for automotive use. Glass and glass-
resin composites are most attractive from a co'st « $1 lIb)
(Ref. 2) and availability viewpoint. A slender (0. 1-inch-
diameter) R-glass/polyester rod failed at 31 W-h/lb. The
theoretical ultimate value for current S-glassl epoxy
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Table 1-1
. 1
Results of Small Rod (or Bar) Tests of Superflywheel Concept
.,
R d
[
[\.J
o or Ba r )escnption Values :\ttained at BUI'st-
Cross-Section, l\1aterial Dens itv We ight Rotational Calculated Specific
(source) (l b / i n 3') (pounds) Speed Stress Energy
(rpm) (ps i) (V,'-h/lb)
4-mil-diameter boron filament 38 0002 .H32
(;\ vca Corp. ) O. 094 O. 00004 424 000
20-mil-diameter boron/ magnesium
(General Technology Corp. ) O. 080 0.00075 31 500 254 000 33
1/16-inch-square graphite/epoxy
(Fothergill & Harvey, Ltd.) 0.056 0.00656 33 000 194 000 36
1/8-inch-square graphite / epoxy
(Hercules, Inc.) 0.057 0.0267 31300 180 000 33
O. 098-inch-diameter R-glass/polyester
(PPG Industries) O. 065 0.0147 30 700 195 000 31
O. 79-inch-square graphite/epoxy
(Hercules, Inc.) O. 054 1. 00 28 200 137 000 26
0.57-inch-square S-glass/ epoxy
(Hercules, Inc.) 0.075 O. 73 29 000 204 000 28
1 Each rod or bar was 30 inches long and was rotated about its mass center in an
evacuated chamber at pressures between 0.001 and 0.250 torr. (1 torr = 1 mm Hg abs. )
2The boron filament did not fail- value limited by spin test rpm limit; all other specimens
fa i led at ind ica ted rpm.
P-
.-
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....:
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HiE JOHNS HOPt(INS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVER SPRING MItIllTLAND
material is :38 W-h/lb, and O. 57-inch-square, 0.73-
pound, first-generation bars were spun to 28 W-h/lb at
failure. Because some questions remain about stress-
rupture and fatigue properties of glass for this applica-
tion, another family of materials of great promise and ex-
cellent fatigue properties, graphite and graphite/ resin
composites, is a leading contender. Very slender graphite/
epoxy bars ( 1 / 16-inch-square) achieved 36 W-h/lb, and
O. 79 - inch-square, I-pound, first-generation bars achieved
2fj W-h/lb. Costs of graphite composites are high at pres-
ent ($200/1b) but are expected to come down to the $20/lb
to $40/lb range in the next few years as applications in
new aircraft lead to more efficient production and quality
control, which will also raise performance (Ref. 1).
2. An encouraging finding from these tests with
respect to the use of filamentary or composite materials
for man-rated flywheel applications is the type of failure
mode observed. In all tests conducted, these materials
were ground to dust or small straw-like fragments upon
contact with the containing structure. Post-test analysis
of a containment ring used in the test of a I-pound graph-
ite / epoxy rod showed that only 1 to 2% of the kinetic
energy of the rod wa s imparted to the ring.
3. A s noted above and in Table 1-1, the burst
strengths of the larger (in cross-section) graphite / epoxy
and S-glass epoxy bars were lower than those of the very
slender bars or rods. This poorer performance is
attributed primarily to the inexperience of the supplier in
fabricating specimens of these greater thicknesses, but
basic factors related to size and flaw distribution proba-
bilities in composite materials may limit the optimal size
of individual elements used in a high-energy-density fly-
wheel rotor. Thus, brush-like rotors (see next paragraph)
comprising many slender elements may prove best from
both performance and containment (see previous paragraph)
viewpoints. It should be noted that the energy densities
quoted in Table 1 are burst values (except for boron fila-
ments) based on the weights of the bars or rods. In a
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11011 j(,"'H''''') HQPMH45 UNI'/EP611'1"
I-.J '1'1. 1i f) 1",1(",IC5 lABOR/I:I')!"1
~;I; V,.... ~'.""'4~J. ""."'''1 ,,'-to
flywhee 1 system, the rated value for the material used
will have to be lower than its burst value by some factor
of safety (including a factor for fatigue effects), and weight
of accessories (hub, bearings, seals, containment, and
mounting) will have to be included if one wishes to state an
overall flywheel subsystem energy density.
1. 2 ANALYTICAL STUDY
Theoretical studies were conducted on various po-
tential flywheel configurations. Of particular interest
are the calculated ultimate-stress performance capabili-
ties for four classes of "superflywheels": (a) composite
bars, (b) circular brushes comprising thousands of fila-
mentary spokes potted into a hub, (c) radially fanned
brushes comprising continuous filaments passed through
a potting hub, and (d) composite, pseudo-isotropic disks
made from many plies of uniaxial cloth cured together at
specified ply angles. Composite bars, such as tested ex-
perimentally, are simplest but are inefficient with re-
spect to packaging volume for a given stored e.nergy.
Composite disks would be far superior to bars with re-
spect to packaging volume and would have approximately
the same specific energy (E/W, W~h/lb) for a given mate-
rial. Such disks were assumed for the purposes of the
vehicle applications studies discussed below. The brush
configurations are intermediate to bars and disks with re-
spect to packaging volume and should require the lea st
containment weight, because very slender elements would
fail sequentially. The radially fanned brush is judged by
the authors to be particularly worthy of development, be-
cause its use of slender continuous filaments or compos-
ite rods pel m its slightly higher specific energy than a
composite disk, as well as a ready upgrading of specific
energy as better materials become available. '
The various materials problems (e. g., static and
cyclic fatigue) and fabrication and installation problems
(e. g., bearings, seals, and gyroscopic torques) for fly-
wheel systems are discussed in some detail, and an
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T1-4E JOHNS 1-40PKINS UN!VERSITY
APPLIED PHYSICS LABORATORY
SIl.V[R S..AINC- "'''''YL.lt.ND
example of major installation features of a flywheellheat-
engine hybrid propulsion system in a commuter car is
given.
The studies of performance of flywheel-only and
flywheel-hybrid propulsion systems in the four vehi c1e
classes were undertaken before the experimental worl,
was completed. At the outset of the program the antici-
pated vehicular operational date was 1980. For these
studies a -rated specific energy of 32 W-h/lb (at maximum
rated rpm) was assumed for the rotor, and the assumed
sizes and weights of the accessories and case (including
containment) were related to rotor size. A It.hough the
previously summarized experimental results demon-
strated with materials received early in 1971, when de-
graded for safety and fatigue effects, would lead to rated
rotor specific energies considerably lower than 32 W-h/lb,
the authors believe this value could be achieved by a pro-
totype flywheel subsystem using a brush or disk type rotor
after two or three years of active exploratory development.
If the rated specific energy achieved at any particular
point in time is different from 32 W-h/lb, the effect will
be simply to change all factors directly related to specific
energy (e. g., flywheel-only range) in proportion. With
this qualification in mind, and on the basis of the other
assumptions made (detailed in the report), the results of
the vehicle application studies may be summarized as
follows:
1. Of the vehicles studied, and within the specifi-
cations established for them by OAP, the city bus is the
only one for which a flywheel-only system would appear
to be able to meet all requirements. A van with approxi-
mately half of the specified 60-mile range might be possi-
ble.
2. It appears that all performance requirements
for all specified vehicles could be met with flywheel/ heat-
engine hybrid vehicles. Regenerative braking would re-
cover 15 to 200/0 of the total energy requirement on urban
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THE JOHNS HOPtotlNS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV!:IJ SPlitiNG "'...IIt'l'LAND
driving cycles. Compared to present vehicles with auto-
matic transmissions, however, approximately half of this
gain probably would be lost to the continuously variable
transmission and the clut~hes and speed changer postu-
1ated for the hybrids.
3. The most important aspect - the ability to re-
duce objectionable emissions - could not be assessed fully
because of a lack of a sufficient body of self -consistent
data on the optimization of heat engines to reduce emis-
sions near design points or over limited ranges of load
and speed. It is expected that substantial reductions
should be achievable by proper design and operation of
heat engines in these hybrid systems, where. the flywheels
would provide acceleration power. .
4. An important advantage seen for the use of
relatively large, high-specific-energy flywheels in hybrid
systems is the ability to provide significant ranges with
no emissions for travel through congested or specially
restricted areas such as may become necessary in the
future to meet air quality standards (Ref. 3). For this
reason an on-off mode of engine operation, whereby the
engine is used only about 20% of the time during urban
driving, to recharge the flywheel, is recommended. With
this mode of operation, there will be no emission penalty
for idling or rapid acceleration, and no drivability penalty,
if, for example, the engine is operated quite lean to re-
duce em iss ions. On the other hand, there will be an
emission penalty for the periodic engine restarts; an
a ssumption was made for this effect, but it could not be
assessed quantitatively.
5. With respect to transmission systems for use
in flywheel propulsion units, literature and technology
reviews were conducted, and it appears that the tech-
nology is a va ilable for direct engineering design and de-
velopment of a transmission for each of the vehicles
studied. \Vhile there are no off-the-shelf units that spe-
cifically satisfy the requirements, a leading contender
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THE JOI-iNS HOPKIN,S UNtVERStTY'
APPLIED PHYSICS LABORATORY
Sll""'(.. S~.I""G M"'''T~NO
feJr larger units appears to be the power-spli.tting, hydro-
mechanical system (see, e. g., Her. 4). V::uiable belt
drives, such as used by DAF on small cars (Ref. 5), may
be satisfactory for low power systems. A 72% overall
transmission efficiency (engine-to-flywheel-to-drive
wheels) is assumed in the foregoing studies.
6~ Among the heat engines considered - spark
ignition, diesel, gas turbine, and Rankine cycle - the gas
turbine appears most attractive because of its low speci-
fic weight and its low inherent hydrocarbon and CO emis-
sions. The diesel appeared unattractive for the cars and
van because o,f its weight and size (lea ving negligible
allowances for flywheels within given constraints) and
odor problems (Ref. 6). The diesel would remain attrac-
tive for the bus. Steam engines also appeared to rank
behind spark-ignition and gas turbine engines on the basis
of the limited available data, although their potentials for
low emissions cannot be denied. The spark-ignition en-
gine is a good short-term candidate by virtue of its pres-
ent use and the immense current efforts to reduce its
emissions.
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THE .JOHNS HOPKINS UNIY£RSITY
APPLIED PHYSICS LABORATORY
SrLw. SPtnfiC. MA,"L.AND
2.
INTRODUCTION
The objectives of this program were to conduct
proof-of-principle tests of the "superflywheel" concept
(Refs. 7 and 8) and to evaluate the use of such flywheels
in automotive vehicles, both alone and in combination
with heat engines, to reduce emissions of pollutants. A
superflywheel may be defined as. a rotor of novel design
that uses a material of high uniaxial specific strength
(i. e., ratio of tensile strength to density), such as glass
or graphite fibers or a composite of such a material in a
resin matri.x, in such a way as to take maximum advan-
tage of that uniaxial strength, and which is operated in a
chamber evacuated to 10-5 to 10-6 atmosphere pressure
to reduce material degradation caused by moisture or
oxygen, as well as windage loss and heating effects at
high rotational speeds. Such a rotor may take one of
several possible configurations, ranging from simple bar
shapes to various brush-like configurations.
The experimental program consisted primarily of
spinning small-diameter, 30-inch-Iong specimens at the
A pplied Physics Laboratory and approximately 1-pound,
3.D-inch-Iong bars of graphite/ epoxy and S-glass/ epoxy at
the Naval A ir Propulsion Test Center, Philadelphia. The
better results achieved during this program have been
summarized in Table 1-1 in the Summary; details of the
test equipment, testing techniques, and results are pre-
sented in Section 3. Considerations regarding design
and installation of flywheel systems are discussed in Sec-
tion 4. The latter section, supplemented by Appendixes
A -C, also presents results of theoretical studies of ad-
vanced rotor concepts.
The evaluation studies of the applications of ad-
vanced flywheels to automotive vehicles are covered in
Section 5. The objectives of this part of the program
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SIL Vir" $Pft,fr!tG ..... .."L.HO
were to explore the ways in which flywheels could be used
in propulsion systems that would have low HC (hydrocar-
bon), CO (carbon monoxide), and NOx (oxides of nitrogen)
emissions while meeting performance criteria specified
by the Office of A ir Programs (OA p) of the Environmental
Protection Agency (EPA) for each of four vehicle classes:
commuter car, family car, city bus, and van. For each
. vehicle class, four heat engine types (spark-ignition,
diesel, gas turbine, and Rankine cycle) were to be con-
sidered for the hybrid systems. The vehicles were to be
studied on their typical urban cycles, and estimated emis-
sion levels were to be compared to the OAP 1980 research
goal values that existed at the outset of this program.
This program was therefore intended to probe the poten-
tial value of advanced flywheels for applications in 1980.
However, Federal legislation has since established emis-
sions standards for 1976 (Ref. 9) that are essentially the
same as those earlier research goals.
Prior operational application of flywheel propul-
sion to land vehicles has been limited to mine engines
and to the Oerlikon Gyrobuses (Refs. 8 and 10) that were
used in Switzerland and Africa in the 1950' s. Experimen-
tal development of the Gyreacta system for cars and
buses was done in England in the 1950's (Ref. 10). All of
these applications had used steel flywheels of conserva-
tive design. Some research had been done on circum-
ferentially wound flywheels of composite materials for
naval applications (Ref. 11). A t the time this program
was begun, OA P also was sponsoring a study of the same
vehicular applications by Lockheed (Ref. 12), which was
to include demonstration of state-of-art technology by
testing shaped steel wheels and another type of flywheel
rotor. Thus, the present program was to study the
longer term prospects for advanced flywheels using the
aforementioned superflywheel concept.
Two advantages of using flywheels made of fila-
mentaryor composite ma terials in novel rotor configura-
tions. as contrasted to shaped metal flywheels, are seen:
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THE .JOHNS HOPtC.INS UNIVERSITY
APPLIED PHYSICS LABORATORY
S'LY~" SPwtNG. M".-vUHD
1.
The potential for significant improvement in
specific energy (stored-energy/weight ratio),
which would permit greater energy storage
within a specified weight allowance. for a pro-
pulsion system, and
2.
The lower safety hazard or lower contain-
ment weight requirement for a given energy
storage level that should follow because of
the. type of failure mode exhibited by such
materials (as discussed in Sections 3 and 4).
While Item 2 may prove to be of interest regard-
less of the propulsion system approach taken: Item 1 is of
particular interest in considering both flywheel-only sys-
tems and the propulsion system approach to be taken for
flywheel/heat-engine hybrids. There may someday be a
need to restrict operation of heat engines to certain por-
tions of cities or congested areas that have particular
difficulty in meeting air quality standards (see, e. g., Ref.
3). Therefore, a potential for dual-mode operation of a
flywheel/heat-engine hybrid, whereby in urban use1 the
engine. would be used only periodically to recharge the
flywheel, permitting substantial operating range on the
flywheel alone, is of interest. It follows that the largest
practical energy storage is of interest, and this, in turn,
calls for high specific energy in the flywheel. Therefore,
the authors concluded that the present study should em-
phasize the potential future performance with such systems,
thereby complementing the Lockheed study (Ref. 12), which
was covering the nearer term approach to the hybrids with
smaller flywheels used essentially in parallel with the heat
engine.
Important questions in optimizing a system using
the on-off mode of engine operation relate to the trade-off
1For automobiles, the engine still would be used continu-
ously for long-range highway cruise through unrestricted
areas.
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TH£ JOHNS HOPf< INS UNIV£RSlTv
APPLIED PHYSICS LABORATORY
SILVa:- SPilliNG "...,\...ND
between emission-free (engine-off) range available and
the total emissions produced per complete on-off cycle.
These questions include the reliability of engine starting
and what constitutes a IIcold start, II i. e., how much
penalty is paid' in emissions on each restart. The
answers undoubtedly will vary from one engine type to
another and may be affected by the particular emission
controls used on the engines. Data are needed on both
these points and the even more important question of just
how much is to be gained by operating the engine only at
nearly constant-load, constant-speed conditions so that
it can be truly optimized for those conditions. Until self-
consistent and pertinent sets of data become available in
these areas, these crucial points cannot be answered.
Another important feature of propulsion systems
using flywheels is the continuously variable transmission
needed between the flywheel and the drive axle. Considera-
ble progress is being made by industry in such transmis-
sions (see Section 5, Appendix D, and, e. g., Refs. 4, 5,
and 13 through 17) and OA P has contracted studies (follow-
ing Ref. 18) addressed specifically to flywheel-hybrid ve-
hicles. Finally, the questions of flywheel containment
design and gyroscopic forces must be addressed from a
safety viewpoint, and a little is said about each in Section
4.
Some features differentiating flywheels from elec-
tric energy storage systems should be kept in mind. The
nominal "depth of discharge" (DOD, or removal of energy
per discharge cycle) for the flywheel used in the present
studies is 75%. Since the stored energy is proportional
to the square of rotational speed, a 75% DOD requires
only a 2: 1 speed range for the flywheel (and a correspond-
ing' 2: 1 speed range for the normal, constant-load opera-
tion of the heat engine used to charge it). This nominal
DOD could be increased to 89%, if increasing the heat en-
gine's operating speed range to 3: 1 would not appreciably
affect its emissions of air pollutants. Neither a high DOD
nor a high rate of energy withdrawal for vehicle
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THE JOHNS HOPKINS UNIV~RSITY
APPLIED PHYSICS LABORATORY
SILVI[It S~.'NG "'."TL.""D
acceleration will affect the flywheel's life. A flywheel
system could easily provide as great a specific power
(w lIb or hp/lb) as a vehicle could profitably use. In con-
trast, the life, or number of useful cycles, of an electric
energy storage system depends strongly on either DOD
or rate of withdrawal, or both, depending on battery type
(see, e. g., Ref. 19) and a drawback in designing electric
propulsion systems is in determining the compromise in
acceleration capability that will be accepted in order to
improve range and obtain an acceptable life from the bat-
teries. It is likely that, for propulsion systems of com-
parable weight providing comparable acceleration and
emission-free range, a battery system would. have to be
replaced several times during the life of a vehicle (Ref.
20), whereas a flywheel system probably could be de-
signed for the full vehicle life (Refs. 2 and 20). However,
flywheel life will depend mainly on the life of seals and
bearings, which will be subjected to stresses and strains
caused by gyroscopic forces when the vehicle pitches up
or down (see Section 4.5. 2), and flywheel systems must
be developed and tested to confirm the potential life ad-
vantage compared to battery systems.
Detailed trade-off studies and cost comparisons of
mechanical and electric energy storage systems were be-
yond the scope of this program, and, indeed, much of the
da ta needed for such a task are yet to be developed. Sec-
tion 6 includes recommendations for some of the work
. .
needed to provide such information for flywheel energy
storage systems and their applications for automotive pro-
pulsion. .
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I
.
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY"
S'LV~A 8".'NG. ""."LAND
3.
EXPERIMENTA L PROGRAM
3.1 INTRODUCTION
The primary goal of the experimental program was
to prove the principle of the "superflywheel concept" (Ref.
8) by demonstrating that unidirectional composite or fila-
mentary materials can be spun about their centers of mass,
a s shown in Fig. 3-1, to develop high levels of specific
energy storage. This basic development effort was to pro-
gress from tests of single filaments and slender rods of
30-inch-length to rods or bars weighing approximately
1 pound each. A goal of 30 W-h/lb of rotor material (or
30 000 rpm for a 30-inch length) was established for a 1-
pound rod. This goal represented an order-of-magnitude
improvement over the past flywheel propulsion units such
as mentioned in Section 2. In addition, rod elongation,
creep, and fatigue were to be studied so as to estimate the
allowable, or rated, energy level for a vehicular system,
and the mode of failure was to be studied to permit esti-
mates of containment structure requirements for an opera-
tional system.
Thus, the experimental program was organized to
(a) construct equipment and instrumentation to spin test
specimens, (b) test small-diameter specimens of a variaty
of candidate materials, (c) sel~ct materials and spin" test
larger specimens (on the order of 1 pound), and (d) study
rod deformation and mode of failure so as to define the
problem of rotor containment in the event of structural
failure or vehicular accident.
3.2 TESTS OF SMALL-DIAMETER RODS AT APL"
This section describes the experimental program
conducted at A PL, including the spin equipment and its
instrumentation, the selection and testing of small-scale
rods, and static tensile tests of rod specimens.
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THE M'HNS HOPkiNS UNIVERSITY
APPLIED PHYSICS LABORATORY
51\..VIIt "'.'JiI8O- ".WyLAND
C£. SPIN AXIS
~
~~
I E/W = a/3p '= Iw212W I
~
E
= KINETIC ENERGY OF ROTATING ELEMENT ON-LB)
W = WEIGHT OF ROTATING ELEMENT (EXCLUSIVE OF
SHAFT AND HUB) (LB)
E/W = SPECIFIC ENERGY ON-LB/LB)
(MUL TIPL Y BY 0.314 XW-4 TO CONVERT TO W-H/LB)
w
= ROTATIONAL SPEED (RAD/S)
a
= STRESS AT ROTATIONAL SPEED w (PSI)
p'
= MATERIAL WEIGHT DENSITY (LB/IN3)
= MOMENT OF INERTIA ABOUT SPIN AXIS ON/LB/S2)
(FOR THIN ROD, I = R2W/3g)
= GRAVITATIONAL CONSTANT = 386IN/S2)
9
Fig. 3-1 ENERGY STORAGE CAPABILITY OF THE STRAIGHT FILAMENT
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THE JO~NS HO~kIN. UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVIE" S~"I"'G. ".""'LAND
3.2.1 EQUIPMENT AND INSTRUMENTATION
Fundamental to the superflywheel concept is the
provision of a very low pressure (and possibly a reduction
in gas molecular weight) to reduce the windage losses
. associated with the high tip speeds and high drag shapes
(see Appendix C). The spin-test chamber shown in Figs.
3-2 through 3-5 was designed and fabricated at APL for
testing small-scale rods at pressures near 10-3 torr
(i. e., 10-3 mm Hg abs, or approximately 10-6 atmo-
sphere). The chamber consists of 1/4-inch-thick, steel
tank closures. 32 inches in diameter, with flanges and an
"0" ring seal. Four sets of opposed viewing ports permit
observation of the rod tip regions. A 2-hp Heraeus
mechanical roughing pump reduces the. pressure to 5 x 10-2
torr. and a 500-watt Veeco diffusion pump (n.ot shown) in
series reduces it to 10-3 torr or less. Continuous pump-
ing is used. because the program schedule and funding did
not allow for development of a chamber that could main-
tain a vacuum over a long period.
Two methods of driving the rods were used. In
one a fractional horsepower electric motor was used in-
side the vacuum chamber to drive the rod directly or
drive a bearing-supported spindle holding the rod (Fig.
3-3). In the other. a I-hp electric motor. mounted out-
side the vacuum chamber, transmitted power through a
ferrofluidic vacuum seal to a 1: 10 planetary friction-drive.
speed increaser to the rod (Fig. 3 -4). Both systems
were capable of providing rod rotation. rates above 30 000
rpm.
A 11 spin tests were conducted remotely. The spin
chamber was located in a heavy-walled concrete test cell
with. bullet-proof glass .windows. The instrumentation was
designed to measure chamber pressure. rod rotation rate.
rod tip elongation. drive system vibrations. and to permit
visual observation of the rod and spindle.
Figure 3-5 shows the overall instrumentation
arrangement and system diagram. A s the rod rotates.
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THE J0I-1"'5 HOPKINS UNIVERSIT'r
APPUED PHYSICS LABORATORY
SILVER SPII'I""G MARYLAND
CHAIN HOIST
.-
BASE
Fig.3-2 SPIN CHAMBER FOR SMALL-SCALE TESTS BEING INSTALLED IN TEST CELL AT APL
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H
-------
THE JOHNS HOPKINS UNIVERSITV
APPLIED PHYSICS LABORATORY
SILVER S.-IIItING. MAIlltYL,AND
ROD
ROTATION
LASER PHOTO
BEAM
GENERATOR .. DIODE
1
AMPLI FIER FLASH
AND SIGNAL DE LA Y
DIVIDER
! 1
COUNTER STROBOTACH
LIGHT
(a) BLOCK DIAGRAM OF INSTRUMENTATION FOR TIMING
AND OBSERVING ROD
VACUUM
CHAMBER
TV CAMERAS (2)
PHOTO DIODE
VIEWING PORTS
(4 SETS)
MECHANICAL
VACUUM
PUMP
[yLASER
BEAM
GENERATOR
. (b) EXPERIMENTAL ARRANGEMENT
Fig.3-5 SCHEMATIC DIAGRAMS OF SPIN CHAMBER SETUP AT APL
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THE ..tOHNS HOPKINS UNIVEFISITY
APPLIED PHYSICS LABORATORY
SiLve:- SPRING, MA"YLAND
its tips interrupt the beam from a laser generator that
is focused on a high-response. photo diode. The diode
senses the change in energy. and the signa~ is amplified,
divided by 2, and displayed on a digital counter in rps.
The same signal triggers a strobotach flash unit, which
flashes in synchronization with the instantaneous rotation
rate of the rod. thereby freezing its image. which can be
viewed by TV cameras and displayed in the control room.
One TV camera is focused on a mirror which furnishes an
overall view of the rod and hub and can be used to observe
dynamic resonance of the rod and nutation of the drive
spindle. The other TV camera is focused through a micro-
scope with a. reticle. so that rod elongation can be observed
on the monitor. (This method of measuring elongation has
not yet been used because of circuit problems with the
flash delay unit, which was sent to. the factory for repair
and was returned to APL after the small-sca.le rod test
program ha.d been concluded. )
The digital counter signal activates a printer.
which provides a record of rotation rate versus time (rod
acceleration). Accelerometers were mounted on the drive
unit housing to detect excessive vibration and resonant
conditions. The chamber pressure was monitored with
two thermal-conductivity vacuum gauges. and two Hast-
ings meters. one covering the range from 1 atmosphere
to 10-2 torr and the other from 10-2 to 10-4 torr.
3.2.2 SELEC'rION OF CANDIDATE TEST MATERIALS
In order to aChieve a specific energy of 30 W-h/lb.
a rod must have a uniaxial-tensile-strength/ density ratio
(cr/fJ,)l in excess of 3 million inches. A number of com-
posite materials meet this requirement. including boron
filaments in.an epoxy or magnesium matrix, graphite
fibers in epoxy, and glass fibers in an epoxy or polyester
1In Sections 3 and 4, fJ' refers to the weight density of the
material (Ib/in3). The symbol p is used in the Appendix
for mass density (lb-s2/in4).
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THE JOHNS HOftKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
.'L.V.- ""1"". "..lrYLAIND
matrix. In addition, free-standing filaments of boron or
chemically strengthened glass satisfy the requirement
and would be suitable for certain brush-type rotors (see
Section 4~ 2). Table 3-1 lists the specimens tested at
APL.
While other materials might also have been suita-
ble, this group was selected because of the relatively
large amount of available test data. (Data for all com-
posites are sparse when compared to data for conventional
structural all()ys.) Though the costs of boron fibers and
graphite/epoxy broad goods are high (near $200 per pound),
fabricators and leading investigators of the field indicate
that order-of-magnitude reductions, at least for graphite
composites, are likely in the foreseeable future (Ref. 1).
While the glass composite prices are already low enough
for vehicular applications, some questions remain regard-
ing fatigue life, but the vacuum environment will be bene-
ficial (see Section 4.4). All of the selected materials
have the potential for dissipating large amounts of energy
by fractUring into very small segments at failure.
3. 2. 3 TEST RESULTS AND DISCUSSION
The drive system and rod mounting system used
for each test also are shown in Table 3-1, because in .
some cases it appeared that they had a direct effect on
the test results. The nominal length (spin diameter) for
all samples was 30 inches, but the minor length variations
have beEm included in the calculation of stress and stored
energy. The specific energy E/W and maximum stress
\J (at the center) are calculated from the equations (see
symbol definitions in Fig. 3 -1):
2 2
E / W = R (.&.). /6g
(3-1)
'R2 2
a=" UJ
2g
(3-2)
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THE JOHNS HOPKINS UNIVERSITV
APPLIED PHYSICS LABORATORY
SILV~" S~"IHG. M""YL.&ND
The calculated values do not include the effects of rod de-
formation as discussed by Brunelle (Ref. 21), which would
increase the maximum (j and E/w values by about 2% for
the glass composites but would have very little effect on
graphite and boron specimens (see Section 4. 4.5 for fur-
ther discussion of this point).
The boron filaments were tested with the small
)
Diehl motor (the only one available at the start of the pro-
gram) whose rated speed of 3600 rpm was increased .to
39 000 rpm under no-load conditions by raising the driving
voltage and frequency. The maximum speed attainable
with a test rod was strongly influenced by the mass of the
rod and the associated increase in bearing friction caused
by inherent imbalance. In fact, this drive. system was not
able to fail the boron test rods, all three types being in-
tact after spin-down. Therefore, the energy levels pre-
sented do not show the maximum capabilities of these
materials. The boron filament tests were conducted be-
fore the diffusion pump was added to the vacuum system,
and test pressures were 4.7 x 10-2 torr for the B-mil rod
and B. 0 x 10-2 torr for the4-mil rod; The test of the
boronl magnesium rod (a "preform" material from General
Technology Corp., Reston, Va.), and all subsequent tests
included the diffusion pump with nominal test pressures of
1xI0-3torr.
Graphite I epoxy composite specimens were fabri-
cated by Hercules, Inc., Cumberland, Md., and Fother-
gill & Harvey, Ltd., Lancashire, England. Both manu-
facturers used layers of composite tape to build up uni-
directional laminate plates 30 inches long. The Hercules
plate was lIB-inch thick, while the Fothergill and Harvey
material was 1/16-inch thick. These plates were cut
lengthwise with a diamond wheel to form the square rods.
For the most part the surface appeared smooth and free
from flaws; however, this type of fabrication will in-
herently impart more surface imperfections than a molding
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THE .IOH"'. HOfl'KINS UNIVa:RSITY
,f sIr RTV 26 200 124 2:1
6 I sIr RTV 22 100 88 16
7 GIS Epoxy 33 000 195 3(;4
PPG/RBr Type 525 E-Glass/Polyester (48"10 Fiber Volume)
0.098 Inch in Diameter Wr - 0.015 pounrl
I (;/5 Epoxy 23 600 11 (; In
2 cIs Epoxy 23 400 118 18
:1 GIS Epoxy 24 000 12:1 1:1
4 GiS RTV -19800 -114 -1:1 Counte.' ~lnpP('d .i\l~,t
\H~fon~ nht f:1i1un.'
~) r; Is RTV 24 000 12:1 1:1
r. (;/5 RTV 23 200 115 1 II
PPG/BfJl Type 1055 E-Glass/Polyester (58"10 Fiher Volume)
O. O!)I\ Inch in Diameter I Wr = 0.016 pounrl
I I C/5 I Epoxy 27 000 I 165 24
2 \.15 RTV 26 700 160 24
PPG/RBI R-Composition GlasslPolyester (55"/0 Fiber Volume)
O. 0!J8 rnch in Diameter Wr = 0.015 pound
1 GIS Epo~y 28 900 177 284
2 GIS Epoxy 30 700 In4 314
3 GIS RTV < 1 8 000 <65 <11 Fa i lure befot'e stroh"
synchronization
4 GIS RTV 26 400 \49 23
Columbia prorlucts (Shakespeare) E-Glassl
Epoxy. O. 250 Inch In Diameter W = 0.091 pound
r
I I sIr I RTV 14400 I 41 7 SOlne indications l"IHj
pull.-d olll of hold I:!'
2 Sl! RTV 14 600 42 7
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THE JOHNS H~INS UNIYERSITY
APPLIED PHYSICS LABORATORY
S.LV~" ~NG. "..YLAND
Table 3-1 (Cont'd)
Summary of Composite Materials, Rod Tests at A PL
Test ~ ~
Drive Moununf Max. Speed Max. Stress E/W Remarks
System I System (rpm) (ksi) (W-h/lb)
Corning Glass Rods. 0.106 Inch in Diameter.
30. fj Inches Long W.. = O. 026 pound
I GIS Acrylic 9 240 29 3
2 GIS Acrylic 9480 28 3
3 GIS Acrylic 9 780 26 3 Failed away from point
of max. stress
4 GIS Acrylic 9 900 32 4 d. o.
5 GIS Acrylic 9 540 30 3
6 GIS Acrylic 10 260 36 4
PPG Glass Rods in
Steel Holder (see Fig. 3-7) W la = 0.0015 pound; W I = 0.32 pound
I g ss stee
1 GIS Acrylic 25 100 165 I 14 Elv.. based on equivalent
full circular brush (see
text)
Drive System:
S/1:
GIS:
Diehl:
Speed increaser
Globe motor with spindle
Diehl motor
2
Mounting System:
RTV:
Epoxy:
Acrylic:
Tube:
Dow Corning Silastic 734, room temperature vulcanizing
Armstrong epoxy
A crylic cement
Stainless steel tube support wilh epoxy cement
.,
.J
Stress and specific energy calculations assume constant rod cross-section, uniform
mass distribution. and 30-inch length (spin diameter) except where noted; I ksi = 1000 Ib/in2.
For the graphitelepoxy and R-glass/polyester materials. the better results were obtained
with the Globe motor and epoxy mounting syslem.
4
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
StLYElit S"-'NG. MARYLAND
or pultrusion 1 process. Initial trials with Hercules rods
in brass holders (not listed in Table 3-1) led to early
fa ilure because of high acceleration and instability during
start-up. Motor operating procedures were changed to
avoid this problem. Tests of two Hercules rods and six
Fothergill & Harvey rods followed with the rod mounted
in the hub with Dow Corning 734 Silastic RTV. The as-
sumption was that this material was strong enough to
counter the nominal imbalance forces during spin-up but
would allow the segments of a failed rod to clear the rod-
holder quickly, before the resulting imbalance forces
would damage the bearings. These tests produced calcu-
lated stress levels at failure ranging from 66 to 151 ksi
for materials that were supposed to have 200 ksi strength.
To evaluate this problem further, some of the re-
maining Fothergill & Harvey rods were used for static
tensile tests. The ends of the test specimens were em-
bedded in aluminum rod grips and cemented with epoxy.
Table 3-2 shows that three of the specimens failed at
..... 80% of the quoted strength, while one nearly achieved it.
Table 3-2
Static Tensile Tests of 1/ 16-Inch-Square
Graphite /Epoxy Rods from Fothergill & Harvey, . Ltd.
S1
S2
S3
84
Failure Stress
(ksi)
158
154
163
195
Gauge Length
( inches)
5
5
5
2
Specimen
1 In the pult~sion process the fibers and resin are pulled
through a die into a mold, insuring a finished composite
with uniform properties along the length, correct fiber
alignment, and a smooth, dense surface.
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THE JOHNS MO..KINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVE. 5".''''0. M.""LAND
In general, the spin test results are lower than
the static test results. The manufacturer suggested that
fiber misalignment and surface flaws were responsible.
This hypothesis is somewhat verified by the higher
strength of the short-gauge-Iength specimen, a character-
istic of materials with random imperfections.
At this time in the program tests of O. 25-inch-
diameter glass/ epoxy rods gave evidence that the rods
may have pulled out of the RTV mounting and failed by
bending as they hit the side of the chamber. For this rea-
son, the remaining two graphite/epoxy rods were hard-
mounted with epoxy cement, and better performance was
indeed realized: both rods exceeded 30 W-h/lb. The cal-
culated stress was within 20% of the manufacturers. claim
for the 1/ 8-inch rod and within 3% for the 1/ 16-inch rod.
Twelve glass/polyester rods were furnished by
PPG Industries, Pittsburgh, Pa., as examples of the
kind of specimens that could be pultruded with the existing
equipment of BBI, Inc. of Pittsburgh. The fiber volume is
relatively low (45 to 55%) and could be increased to obtain
higher strengths. The E and R-glass fibers are formu-
lated for use in electrical applications, and the substitu-
tion of S-glass fiber, a high strength formulation, should
also raise the composite strength level by 10 to 20%.
Nevertheless, the tests of these glass/ polyester rods
were encouraging. The failure levels were quite con- .
sistent. For E-glass there is no clear-cut effect of using
an RTV mounting adhesive, though one rod did fail at a
low level. For R-glass rods, the epoxy mounting gave
better results.
The glass and graphite composite rods were com-
pletely destroyed after failing at high rpm. The graphite
rods were pulverized to fine particles, as shown in Fig.
3-6. The steel chamber was hardly scratched at impact,
suggesting that a significant portion of the rod energy was
dissipated by the microfracturing of the rod itself. The
low-level vacuum meter indicated a sudden rise in pressure
- 27 -
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i--
THE JOHNS HOPKINS UNfVERS't'V
APPLIED PHYSICS LABORATORY
SIL\I'£1It S~I.tlNG. MARYLAND
"-
}
Fig.3-6 REMAINS OF GRAPHITE/EPOXY COMPOSITE IN SPIN CHAMBER AFTER TEST
l'O.~150~+5001'G661
.:J
3IB-INCH DIAMETER 4340 HEAT-TREATED
STEEL ROD
1.4 ~ I
TYPICAL ~
-~
0.031-INCH DIAMETER GLASS ROD
BONDED TO STEEL WITH
ACRYLLIC CEMENT
t DRIVE SPINDLE
DIMENSIONS ARE IN INCHES
MAXIMUM SPEED AT FAILURE: 25100 RPM
AVERAGE DENSITY OF GLASS RODS: 0.090 LB/lN3
MAXIMUM STRESS AT ROOT OF GLASS ROD: 165000 PSI
EQUIVALENT CIRCULAR BRUSH ENERGY DENSITY: 14.3 W-h
LB
Fig.3-7 SIMULATION OF CIRCULAR BRUSH CONFIGURATION AND TEST RESULTS
- 28 -
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THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVER SP'..HG. MAlltYLANO
from 10-3 to> 10-2 torr. We did not determine the exact
magnitude of the pressure rise, since the continuous pump-
ing system quickly returned the chamber to the nominal
operating pressure. In fact, it is not certain whether the
increase in indicated pressure is a valid reading (result-
ing, probably, from heat generation and vaporization of
the matrix material) or whether the sudden increase in
small particles affects the thermal-conductivity vacuum
ga.uge so as to indicate an increase in pressure. The pre-
liminary indications were, however, that the break-up of
the composite materials occurred in a way that would
minimize damage to any surrounding chamber.
Another series of tests evaluated chemically-
strengthened glass for use in brush-type rotor configura-
tions (see Sections 4. 2. 3 and 4. 2.4). Six O. 100-inch-
diameter rods were furnished by the Corning Glass Com-
pany. They were chemically cleaned and etched to re-
move surface impurities and then covered with an acrylic
coating. A t A PL the rods were mounted in aluminum
holders with acrylic cement and spun to destruction. All
rods broke at low speeds with a maximum energy storage
of 4 W-h/lb. Two of them failed away from the hub at
points of lower stress, indicating flaws in the material at
these locations. The specimens were returned to Corn-
ing for examination, and their engineers reported that the
points of fracture were indeed flaws which should be cor-
rectable with better production controls.
PPG Industries supplied similarly coated glass
specimens that were O. 036-inch diameter and approxi-
mately 16 inches long. Two of these were cut to length
and cemented in opposite ends of a 10-inch-Iong, 3/8-
inch-diameter, hardened steel rod, as shown in Fig. 3-7.
This model simulated two opposite elements in a circular
brush rotor (see Section 4.2.3) which would have a steel
hub 10 inches in diameter and thousands of closely spaced
glass rods. The two-element model was spun to destruc-
tion at 25 OQO rpm. This speed produced a maximum
stress of 16.5 000 psi in the glass rods, which is equivalent
- 29 -
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THE X)HNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
StLYEIit S"'''ING: W"'''YLAHD
to a specific energy of 14 W-h/lb for a full brush rotor,
including the weight and energy of the steel hub. The
steel rod of the failed model impacted the vacuum chamber
with force sufficient to gouge a 1/ 4-inch-deep hole into the
2-inch-thick steel mating flange, damaging the "0" ring
seal.
3.2.4 CONCLUSIONS FROM SMALL-SCALE TESTS
These small-scale rod tests at APL provided
valuable information on selection of materials for later
tests as follows:
3.
1.
The spin and vacuum systems were adequate,
though a more powerful drive system, with
bearings on each side of the specimen, would
be desirable. The instrumentation system.
was versatile and well-suited to this explora-
tory program.
2.
The better test results for the composite
materials, obtained with the Globe motor/
spindle drive system and epoxy mounting,
demonstrated ultimate specific energy stor-
ages of 31 W-h/lb for R-glass/polyester and
33 to 36 W-h/lb for graphite/epoxy. A 4-mil
boron filament demonstrated 48 W-h/lb with-
out failure. The selection of materials for
scaled-up rotors will depend on specific sys-
tem requirements and rotor types.
Upon failure, the composite rods appear to
dissipate a significant portion of their kinetic
energy by microfracture or vaporization of
the matrix mate ria 1.
3.3 TESTS OF 1-POUND BARS A T THE NA VAL AIR
PROPULSION TEST CENTER
The Naval Air Propulsion Test Center (NAPTC)
operates a large vacuum spin chamber at the Philadelphia
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SlLYER SPORING. "AIIYL,AND
Naval Base. Under contract from the NASA Lewis Re-
search Center, they study the modes of failure of turbine
rotors and blades in order to develop design techniques
for sizing containment structures for turbojet enginesl.
Discussions with the NA PTC staff indicated that the facility
could be modified to test I-pound composite bars and to
observe the mode of failure and the consequent distortion
of a steel containment ring. The following sections dis-
cuss the facility modifications, the test results, and con-
tainment analysis.
3.3.1 FACILITY MODIFICATIONS
The main spin chamber at NAPTC has a 10-foot-
diameter test section, as shown in Fig. 3-8. In March
1971 it was operating at pressures near 1 torr. Its
photographic system (Ref. 22) consists of a high-speed
Beckman & Whitley camera with a loop of film, a high-
intensity strobe light system, and a large front-surface
mirror to reflect the light to the test section. The proce-
dure is to darken the test cell and bring the camera up to
speed before the spin test begins. Then the test rotor is
accelerated, and when failure occurs the first fragment
to strike the. containment ring closes a circuit between
the ring and a small trigger wire, activating the strobe
lights for a period just long enough to expose the loop of
film. This photographic system and operating technique
appeared directly applicable to the APL test program with
only a minor modification to the trigger wire to account
for the use of nonconducting rotor materials such as the
S-glass/ epoxy composite.
INASA also funds the Aeroelastic and Structures Research
Laboratory of MIT in a complementary program to de-
velop a computerized dynamic structural model of a con-
tainment ring for use in extending experimental results
and preliminary design. The program can compute defor-
mations of multilayer, multimaterial rings; however, cor-
. relation between results of tests and analyses has thus
far been limited to steel rings.
- 31 -
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I
I
,.-..., WINDOW I
I '..... "-
I \ . ...----- ../ APL'S INNER
\ DIFFUSION I --- CHAMBER
, PUMP /' ADDITIONS
...... .;
ROOM
AIR
w
~
o 1
.... . . .
2 3
. . . .
SCALE (feet!
4
.
DRIVE
TURBINE
HIGH VACUUM
5
.
Fig.3-8 GENERAL ARRANGEMENT FOR '-POUND ROD TESTS AT NAPTC, PHilADELPHIA
SOLENOID VALVE
CONTAINMENT RING
SPECIMEN
TIE BAR
LIGHT
~A
,.
11
"0..
r J:
-..
!l'a~
~ 1J %
; :r ~
.~~
~ (II
! -
~ ~ -
Eri
: > c
t~~
Z :II III
" ,. ~
-i-
O~
:II
~
-------
THE JOHNS HOPKINS UNIVIEASITY
APPLIED PHYSICS LABORATORY
SILVI[R S~AING MA"YLAND
There were two areas of concern about spinning
the I-pound rods with the NAPTC equipment. First the
pressure in the chamber would be 2 to 3 orders of mag-
nitude higher than that envisioned for a superflywheel
system. The temperatures at the tips of the rods would
reach 6000 to 800°F at the end of a rapid acceleration to
30 000 rpm (uj "'" 1500 rpm/ s). These temperatures would
be sufficient to start a charring process in .the ablative
resin materials, and in the high acceleration field
(400 000 g's at the tip) it is likely that pieces of the rod
would fly off, causing premature triggering of the lighting
system or destruction of the rotor by imbalance.
The second concern was one of critical speed of
the rotor itself. The NAPTC drive system consists of an
air turbine mounted on top of the vacuum chamber lid,
and a long, thin spindle shaft is cantilevered downward to
drive the rotor. In the case of symmetrical disk rotors
the critical speed (equivalent to the first lateral natural
frequency) is low, and the rotor is driven through it be-
fore excessive deflections develop. After passing this
critical speed the system is stable until the rotor fails.
However, NAPTC personnel pointed out that a rod-type
rotor might have different stability characteristics. Sim-
ple tests at APL of rods supported by thin, flexible drive
shafts confirmed this problem. The markedly different
inertias in the two directions perpendicular to the spin.
axis of a rod apparently create a "band" of critical speeds
that is difficult to traverse before developing unstable de-
flections, and the rod wobbles out-of -plane and bends the
dri ve spindle.
To solve these two problems a secondary, inner
chamber was fabricated (at APL) to permit the desired
higher vacuum and to provide support for additional bear-
ings on each side of the test rod to prevent instability dur-
ing spin-up. Figure 3-8 includes this secondary chamber
and the diffusion-type vacuum pump that was mounted
from it to exhaust through a flexibJe hose to a mechanical
roughing pump outside the main chamber (the same vacuum
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
StLVl[IIt $PRIJIitG. MARYL"NO
equipment used at A PL). To permit use of the existing
photographic system, a plexiglass window was used on
the bottom of the secondary chamber (canted 15° to re-
duce reflections), and tension tie bars were used to hold
the bearings in place. A solenoid valve was installed to
permit equalization of the pressure inside and outside the
secondary chamber during the initial evacuation of the
main chamber, thereby allowing the window to be designed
to resist only a small pressure differential.
Figure 3-9 shows APL's inner chamber while it
was suspended from an assembly platform at NAPTC.
Figure 3 -1 0 is a view through the window up into the
chamber, showing the specimen, bearing supports, tie
bars, containment ring, trigger wire, and drive spindle.
The containment ring rests on three metal tabs and is
constrained from vibration during spin-up by three small
C-clamps.
3. 3. 2 SELECTION AND PROCUREMENT OF TEST
MATERIA LS
In the small-scale tests at A PL, boron filaments
and boron/magnesium, graphite/epoxy, and R-glass/
polyester composites had achieved specific energies in
excess of 30 W-h/lb. After discussion with OAP it was'
, decided to test I-pound rotors of two material types
(rather than one as originally planned) to offer a com-
parison in strength levels and modes of failure. Glass
composites are, in general, the best documented and are
obvious candidates for operational systems because of
their low cost. Although they are prone to fatigue and
stress rupture, the vacuum environment proposed for a
flywheel system (10-2 to 10-3 torr, void of moisture and
oxidants that cause stress corrosion on the surface of
glass) will improve their fatigue and stress-rupture char-
acteristics (see Section 4.4). Therefore, this class of
material was considered the primary choice, and the
strongest and most fatigue-resistant ma terial in this class
is S-glass fiber in an epoxy matrix, which was selected.
- 34 -
-------
THE JOHNS MOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SIL.VEA SPAIJt.jG MAAYl,.AJt.jO
r
-. ::::-----. 1
. -
~
.
'
t
_ ....-.
! -
,
. . \
-.L.~ I .4! till1r I.
-. ,--~
~
~~--]
----~-~_.~--_.J
}..".c
.
;- ~ ~
-'II!
-
r-
"l.
Fig.3-9 GENERAL VIEW OF APL'S INNER CHAMBER SUSPENDED FROM AN ASSEMBLY
PLATFORM
- 35 -
-------
THE JOMNS HOPKINS UNIVERSIT'V
APPLIED PHYSICS LABORATORY
SILVEIII SPIII.NG "''''''YL'''ND
~
Fig. 3-10
INSIDE VIEW OF SPIN CHAMBER
(a) S-GLASS/EPOXY ROD POTTED INTO HUB
(b) GRAPHITE/EPOXY TEST ROD
Fig. 3-11 TYPICAL SPECIMENS FOR NAPTC TESTS
- :36 -
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV£III SPRING """ARYLAND
Boron and graphite composites were considered
for the second material. Both are excellent in their re-
sistance to fatigue and are logical alternatives to glass for
this reason. Boron has been in service longer, and its
properties are more completely characterized; however,
the trend in use appears to be toward the new graphite
fiber with its equal or superior strength and more rapidly
decreasing price. Therefore, graphite/epoxy composite
was selected as the second material for the I-pound tests.
Three bars of each composite material were
ordered from Hercules, Inc. Fabrication of the bars by
the process of net-moidingi was considered but discarded
because of the costs required for tooling. This process
eliminates machining of the part and usually results in
significant increases in strength compared to a machined
part. To meet the desired schedule at reasonable cost
Hercules elected to fabricate the bars by laying up the
composite tape to the required thickness and forming a
plate from which three square bars could be cut. A prob-
lem evolved because Hercules was in the process of shift-
ing production of composite materials from their Cumber-
land, Md.,. plant to their Magna, Utah plant. Their equip-
ment was expected to be in operation in Utah in time to
meet the schedule for this program, but it was not, and
they had to procure the tapes from another source. The
S-glass/ epoxy tape (Scotchply 1 009-26S) was procured
directly from 3-M Corporation. Hercules furnished the
graphite fiber and resin used in their 2002T system to
3-M, who made the graphite/ epoxy tape.
A 11 of the actual laying-up of the tape laminae,
curing, and machining of the bars was done by Hercules.
Lack of experience with the Scotchply tapes resulted in
the S-glass/epoxy plate curing-out at less than the de-
sired thickness, and the bars cut from it weighed only
1 A process where the part is pressurized and cured to
the final dimensions in a mold, eliminating the need for
final machining operations.
- 37 -
-------
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV«1It SPitiNG. MAItYL,AHD
3/4 pound each. The graphite/epoxy rods were of the
proper size and weighed 1 pound. The rods were cut with
a diamond wheel to minimize damage to the surfaces;
however, some bruising and scraping was evident, par-
ticularly with the glass composite. Tensile test speci-.
mens also were provided from the material used to make
the bars. The glass composite was expected to have an
ultimate tensile strength of 260 000 psi and a density of
0.075 lb/in3; the graphite, 200 000 psi and 0.054 Ib/in3.
If these strengths had been realized in the spin tests, the
specific energy storages would have been between 36 and
39 W-h/lb. Figure 3-11 shows one bar of each type
mounted in its spindle holder.
3. 3. 3 TEST RESULTS AND DISCUSSION
A shakedown test (designated JH-l) of the modified
equipment at NA PTC was conducted with a 1. I-pound,
O. 81-inch-diameter, pultruded E-glass/ epoxy bar that
was available as a free sample from PPG Industries, Inc.
Because of its glass type and its low fiber content this bar
was not expected to achieve 30 000 rpm but was useful
for a first test. It was cemented with epoxy into an alum-
inum adapter piece, which was cemented in the 2-inch-
diameter hole that runs through the center of the spindle
holder. This assembly was dynamically balanced at
NA PTC by drilling holes in the spindle (a procedure that
was modified later).
Because leaks in the main chamber system (proba-
bly in the turbine drive spindle seal) permitted large quan-
tities of humid ambient air to enter the secondary vacuum
system, large amounts of water were absorbed in the oil
in the pumps. It was necessary to clean and flush the
pumps between runs and to limit their operating times
during prerun preparation. During the pump-down for the
test of the trial specimen the solenoid valve remained
closed, though power was applied to open it. A s a result,
air trapped in the secondary chamber created an exces-
sive pressure differential across the plexiglass window,
- 38 -
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVER SPilliNG. W.lltYLAHD
and it burst downward, destroying the mirror. Fortu-
nately the test specimen was not damaged.. Tli.e test
procedure was revised to require verification that the
solenoid valve was in the open position before pump-down
of the main chamber was begun. In the next trial, with a
vacuum level of 1. 8 x 10-2 torr in the secondary chamber,
the bar was observed while it was accelerated to,.." 5000
rpm and then slowed down. No vibrations or instabilities
were observed. The bar was then spun to destruction at
19 900 rpm. All equipment worked well, and the check-
out run was considered successful. The 5/ 8-inch-thick
containment ring showed no damage other than mild abra-
sion where fragments of the bar co?tacted the trigger
strip. The bar disintegrated into straw-like fragments
upon impact.
The next test, JH -2, was of the S-glass/ epoxy
bar (Fig. 3-11a). A different balancing pro.cedure was
used on this and all subsequent specimens to minimize
forces that would tend to pull the bar out of the spindle or
adapter. First, the heavy .steel spindle was balanced by
drilling prior to insertion of the bar. The square bar was
clamped and cemented between the two halves of an alum.:
inum adapter that had been carefully sized to grip the
specimen. The adapter was then cemented into the steel
spindle, and the spindle-bar assembly was balanced by re.;;;
moving material from one end of the bar. During the five
tests there was no evidence that the bar had pulled from
the adapter before fracture, and the adapter always re.,..
mained in the spindle after bar failure.
The pressure in the secondary chamber was 6. 3 x
10-2 torr when the bar was accelerated at an average rate
of 335 rpm/ s. Failure occurred after 87 seconds at
29 100 rpm, equivalent to 28 W-h/lb for the bar. The
photographic system operated well, except that the light'"
colored bar did not offer sufficient contrast to produce
high-quality pictures. The bar fractured into a straw'"
like mass (Fig. 3-12).
- 39 -
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SlLVE" !WltIHG. MAltYL.,ANO
Fig.3-12 S-GLASS/EPOXY FRAGMENTS FROM TEST JH-1
Fig. 3-13 GRAPHITE/EPOXY FRAGMENTS FROM TEST JH-3
\
;
- 40 -
-------
THa. .JOHNS t-tOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
51L "''1'111 S~".""c. "'..AYLAND
~
Another S-glass/ epoxy bar was set up for test, but
after the main chamber vacuum pump had been operating
for about 15 minutes there was a sudden implosive failure
of the glass window that serves as the camera port.
Pieces from the window shattered the mirror and damaged
the lights. The small solenoid relief valve- could not com-
pensate for the large flow of air into the main chamber,
and after another 2 or 3 seconds the plexiglass window
imploded into the secondary chamber, breaking the speci-
men. Fortunately, there were no people near the camera
port at the time of failure, and only material damage re-
sulted. There was no explanation for the failure other than
possible fatigue of the window after many chamber evacua-
tions. The window was replaced with an identical unit,
and testing was resumed.
.
The next test, JH-3, was the first test of a graph-
ite I epoxy bar. In spite of cleaning and flushing the pumps,
the vacuum system could only evacuate the secondary
chamber to O. 17 torr. The bar accelerated smoothly for
71. 3 seconds, failing at 28 000 rpm (26 W-h/lb). The two
halves of the failed bar impacted a 1/ 4-inch-thick con-
tainment ring and were pulverized as shown in Fig. 3-13.
The ring suffered more damage than did the similar ring
in the glass-composite test, JH-2, as shown in Figs.
3-14a and 3-14b. This may be due to the fact that the
graphite bar fails suddenly and both ends impact the ring
simultaneously, whereas the glass bar breaks up more
slowly. Also, the graphite bar contained 28% more energy
by virtue of its greater mass.
In Test JH -4 the second graphite / epoxy rod
achieved 28 200 rpmJ or 26.5 W-h/lb. The pressure dur-
ing this test was O. 25 torr J the highest value experienced.
Continued attempts to seal possible leaks had no effect.
This vacuum was adequate, however, for the short-dura-
tion test, and the bending stresses induced in the rod by
aerodynamic drag were less than 50 psi. Since a 3/8-
inch-thick containment ring was used, the permanent de-
formation of the ring (Fig. 3-14c) was less than observed
in Test JH-3.
- 41 -
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THI: .JOHNS HOPKINS UNIYI['HUTV
APPLIED PHYSICS LABORATORY
"'.YI" ".,NO. ".."UU'D
The final test (JH-5) made use of the third S-glass/
epoxy bar, which was judged by Hercules to be the poorest
in quality of the three because of observable surface de-
fects. They applied an extra coating of epoxy over the en-
tire rod in an effort to improve its integrity, but the ef-
fectiveness of this treatment is doubtful. At the start of
this test the pressure was O. 19 torr. The rod was accel-
erated to 27 200 rpm (24. 7 W-h/lb), at which time the
camera lights were actuated, and the drive turbine was
decelerated. Visual inspection from outside the chamber
did not reveal rod damage, and it was concluded that
either the lights were actuated from a spurious signal, as
sometimes happens, or a small piece of the rod tip trig-
gered the system. Because a small film of oil was seen
on the inner surface of the plexiglass window, and the
drive shaft vacuum seal was its probable source, the
chamber pressure was checked and was found to be drop-
ping rapidly. Apparently the act of spinning the rod
caused the shaft seal to "wear in" and improve the seal,
though the result is not conclusive. The pressure finally
stabilized at 2. 6 x 10-3 torr, and the rod was accelerated
again. It failed at 24 200 rpm, somewhat verifying the
assumption that failure had begun at 27 200 rpm during
the previous run. The impact damage to the 1/4-inch-
thick ring is shown in Fig. 3-14d.
Results of these tests are summarized in Table
3-3. The calculated stresses at failure (and energy den-
sities) were less than expected. The best S-glass/ epoxy
test, JH-2, achieved 79% of the expected 260 ksi strength.
These differences can hardly be attributed to additive
bending stresses caused by aerodynamic drag and rod
acceleration, which were always quite small « 1%) com-
pared to the axial stresses resulting from centrifugal.
forces.
The tensile specimens mentioned earlier were
loaded to failure in a Universal Testing Machine at A PL.
Foil strain gauges were applied on opposite surfaces of
each specimen to detect bending stresses caused by eccentric
- 42 -
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r~
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVIE" SP'IItI~. "'''''YLJIt,ND
DEFORMED
RING
(a) JH.2 S.GLASS/EPOXY ROD (0.73 POUND)
29 100 RPM
1/4.INCH-THICK RING
(e) JH.4 GRAPHITE/EPOXY ROD (0.99 POU
2B 200 RPM
3/B.INCH.THICK RING
(d) JH.5 S.GLASS/EPOXY ROD (0.72 POUND)
24 700 RPM
1/4.INCH.THICK RING
Fig.3-14 CONTAINMENT RINGS AFTER TESTS, COMPARED TO REFERENCE CIRCLES
- 43 -
\
-------
Test
JH -12
JH-2
--
~
~
JH-3
JH-4
JH-S
Table 3-3
NA PTC Test Results: Speed, Stress, and Specific Energy at Failure
Material
E-Glass/ Polyester
S-Glass/Epoxy
S-Glass/Epoxy
Graphi te / Epoxy
Graphite / Epoxy
S-Glass/Epoxy
C ro s s
Section
13/16 inch diameter
Weight
(pounds)
1. 10
0.73
0.57 inch square
0.56 inch square
0.72
1. 00
O. 79 inch square
O. 78 inch square
0.99
O. 72
O. 57 inch square
1
Percentage of expected value quoted by Hercules
. 2Facility and instrumentation check-out
3 .
Test abo~ted at this speed. Rod subsequently failed at 24 700 rpm.
Speed
( rpm)
19 900
29 100
Stress 1
(ksi) (%)
89
204
--
No test (facility failure)
79
28 000
28 200
27 2003
136
137
178
68
69
69
E/W
(\V -hi lb)
13.2
28.2
26. 1
26.5
24.7
J>
1)
1) ..
r:l:
- '"
en rT1 '-
i' 00
< 1) :I:
; :I ~
\II -< :I:
~ !!! 0
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~-
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;u
-<
-------
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILYER S""I"'G. M""YL,AND
loading (see Fig. 3-15a); differences in strain readings
from the pairs of gauges remained less than 2% for all
specimens, and it was concluded that the specimens were
in proper alignment throughout the tests. Two of the
failed specimens are shown in Fig. 3-15b, and the results
are given in Table 3-4. .
Table 3-4
Failure Stresses for Tensile Test Specimens
Specimen Cross Sectional Load Stress
Area On2) (pounds) (ksi) (%)
Graphite -1 0.0187 3050 164 82
Graphite -2 0.0192 3220 168 84
Graphite -3 0.0187 3230 173 87.
S-Glass -1 O. 0218 5690 261 100
S-Glass -2 0.0218 6070 279 107
For graphite/epoxy, the average stress, 168 ksi, is 84%
of the expected value of 200 ksi, with a variation of :t:3%.
A probable explana tion for this lower strength is the fact
that the prepreg tape was produced by another firm (be-
cause of the previously discussed scheduling problems)
and yielded only 53% fiber volume instead of the normal
59%. The S-glass samples exceeded the requested ulti-
mate strength of 260 ksL
For graphite/epoxy, the average spin test stress
from Table 3-3 is 81% of the average tensile-test stress
from Table 3-4. For S-glass epoxy, this percentage is
71 % .
There are several possible reasons for the differ- .
ences in achieved strength between the bars and the ten-
sile specimens. First, the bars required the fabrication
of plates that were large, particularly in thickness, by
current composite material demands. As thickness in-
creases it is more difficult to maintain fiber alignment
- 45 -
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVE" S~"IHG. M""YLAHD
GRAPHITE SPECIMENS
.. - -
- .
.- r"
~;;;;:;;"";"~""'..'~. -
.--. "-.-'
- - ---
\ .
. .'
. ---:..~
-- .- .~~~ ." '
. . .
-'- ~l
~,,,.
~
STRAIN GAUGE
t
S-GLASS SPECIMENS
..~
. J):
(a) SPECIMENS BEFORE TEST
S-GLASS/EPOXY
I
f.~ -
~
.-. ...w;. ~
S~.-~. - .
'\
GRAPHITE EPOXY
(b) FAILEDTESTSPECIMENS .
Fig.3-15 STATIC TENSILE TEST SPECIMENS BEFORE AND AFTER TEST
- 46 -
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THE JO~NS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV~A' S~"I""G "'A.QTLAND
(a problE:m that could he overcome with the use of individual
har molds). Also, large sizes require special cure cycles
to achieve uniform properties, free of voids, and with the
desired fiber content. The current program involved only
a single fabrication and cure for each of the materials,
and it is not surprising that Hercules encountered some
difficulties, particularly with the use of different prepreg
tape material.
Another degrading effect on the bar strength was
the surface machining required to cut them from the
larger pIa te. This process is certain to damage or cut
fibers, and any vibration of the bars during spin testing
would aggravate the problem of stress transfer around
these discontinuities. The cut surfaces of the S-glass bars
were noticeably bruised and abraded, and the graphite bars
showed some delamination. Again, the use of an individual
molding process would eliminate the requirement for ma-
chining.
Another possible reason for the low spin test re-
sults is that the dynamic environment developed transient
vibrations that were damaging to the composite materials,
though the limited amount of instrumentation used was not
effective in detecting a problem of this type. A fourth.
possibility is that the differences result from a "size ef-
fect, II common to brittle structural materials, wherein the
probability of encountering a critical flaw increases with
the volume of material stressed. This is a real effect
that is observed in all structural materials, and it is true
that the strength of large elements will be less than that
of smaller ones. However, the principal flaws in compos-
ite materials are a direct result of manufacturing pro-
cesses, and it is judged that major differences in strength
with respect to size will be eliminated when the experi-
ence and control required to fabricate large pieces ap-
proaches the techniques now available to form tensile
specimens.
- 47 -
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TH£ JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
."..YI:II ~_'JIfG. "'."YLAND
3.3.4 MODE OF FAILURE
The photographic system at NAPTC gave us the
first definitive evidence of the mode of failure of the rods.
Because of the favorable indications for containment
(safety), the presentation of these data, their analysis,
and discussion is considered to be one of the more impor-
tant results of the current program.
It has been postulated that the kinematics of rod
failure would be as showh in Fig. 3-16. This behavior is
demonstrated clearly in Fig. 3-17 for a graphite/epoxy
rod test (JH -4).and Fig. 3-18 for an S-glass/ epoxy rod
test (JH-2). Figure 3-1Th shows the two halves of the
graphite/ epoxy rod impacting the containment ring, and
their orientations indicate forward angular velocities.
The fact that the two halves struck diametrically opposite
points of the ring at approximately the same time means
that (a) failure occurred near the spin axis and (b) maxi-
mum bending moments were imposed on the ring. The
subsequent frames show the pulverizing of the rod tips as
they grind into the containment ring.
For the S-glass/epoxy rod (Fig. 3-18) one end
failed first, possibly by fraying or interlaminar shear,
and the other end remained essentially attached to the hub
through one half of a revolution. The effect was to "spread"
the energy release over the perimeter of the containment
ring, reducing ring deformation. The effect can be judged
by comparing the deformations of the 1/4-inch-thick rings
shown in Figs. 3-14a and 3-14d (S-glass rods) with those
for the 1/4-inch and 3/8-inch-thick rings in Figs. 3-14b
and 3-14c (graphite rods).
A significant feature seen in both sets of failure
photographs is that the rod is essentially destroyed in .
less than 1 ms and before motion of the ring is detected.
This is in sharp contrast to failure of metal disks against
containment rings in which the ring "follows" the segments
of the disk until the ductile limit is reached (ring failure)
- 48 -
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV£III S~"ING, MAIII'I"LAND
FIRST
IMPACT
3O-INCH ROO
SEGMENT
CENTER OF MASS
CONTAINMENT
RING
Fig.3-16 KINEMATICS OF ROD FAILURE (ASSUMING TWO EQUAL SEGMENTS)
- - -
- - -
(a) PRETEST PHOTO
(b) TIME = + 41 /lS
Fig.3-17 PHOTOGRAPHS TAKEN BEFORE RUN JH-4 AND 7 TIMES
AFTER FAILURE TRIPPED PHOTOGRAPHIC SYSTEM
- 49 -
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVER SPRING ""ARYLAND
(c) TIME = + 123/..15
(e) TIME = + 287 /..IS
R!I
(g) TIME = + 451 Jls
(d) TIME = + 205 JlS
I""
. 1!1
(f) TIME = + 369 115
I
I
I
(h) TIME = + 533 Jls
Fig.3-17 (Cont'd) PHOTOGRAPHS TAKEN BEFORE RUN JH-4 AND 7 TIMES AFTER
FAILURE TRIPPED PHOTOGRAPHIC SYSTEM
- 50 -
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THE JOHNS HOPM;'NS UNIVE~SITY
APPLIED PHYSICS LABORATORY
SILV!£1It S~.rNG ~"'''YL'''NO
(a) PRETEST
(e) TIME = + 159/15
(bl TIME = + 53/15
(dl TIME = + 265/15
Fig.3-18 PHOTOGRAPHS TAKEN BEFORE TEST JH-2 AND AT SEVEN INTERVALS
FOllOWING FAilURE OF S-GlASS!EPOXY ROD
- 51 -
-------
THE JOHNS HOPKINS UNtVERSITY
APPLIED PHYSICS LABORATORY
S.LVI[IIt S~IItING. MAIIt"LAND
(e) TIME = + 371 1-15
(g) TIME = + 586 1-15
Fig. 3-18 (Cant'd)
.(f) TIIlAE = + 4761-15
(h) TIME = + 7951-15
PHOTOGRAPHS TAKEN BEFORE TEST JH-2 AND AT SEVEN
INTERVALS FOllOWING FAilURE OF S-GlASS!EPOXY ROD
- 52 -
-------
THE JOHNS HOP'KIN~ UNIVERSITY
APPLIED PHYSICS LABORATORY
SILYE" S~"ING. """YLAND
or until a sufficiently-resistive force field develops (con-
tainment) (Ref. 22). In all tests at NA PTC the rods were
completely destroyed, as shown in Figs. 3-12 and -13.
This is again contrasted with typical disk failures in
which no appreciable damage occurs to the large disk seg-
ments while the rings are being severely distorted or rup-
tured. In fact, the relative rates of rod destruction and
containment ring response limit the energy that can be
transferred from the rod to the ring. Techniques are
available to study the energy transfer by means of a com-
puter program (Ref. 23), but this is beyond the scope of
the current project.
3.3. 5 ENERGY ABSORBED BY THE CONTAINMENT RING
The graphite/epoxy Test JH-4, shown in Fig. 3-17,
resulted in a very regular pattern in the deformation of
the 3/B-inch-thick steel ring, as shown in Fig. 3-19.
Since the deformed shape was nearly a perfect ellipse, it
appeared that the theory of plasticity might be used to
estimate the energy dissipated during the deformat'ion
process. There was no detectable stretching of the nomi-
nal 31. 3B-inch-diameter mid-plane of the ring, only bend-
ing deformation. The deformed major axis measured
34. 62 inches, and the minor axis measured 2B. 62 inches.
There was very little bulging of the ring in the depth
direction at the points of impact, and the sides remained
essentially cylindrical. One of the impact points is shown
in Fig. 3-20.
Let us assume that the deformed ring is elliptical
and that the mid-plane can be defined by the polar coordi-
nate equation: .
r 2 = a 2b 2 /( a 2 s in 2 9 + b 2 co s 2 9) ,
(3-3)
where a = 14.31 inches, and b = 17.31 inches.
radius of curvature rD is defined by:
The
- 53 -
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THE JOHNS HOPKINS U""IVERSITY
APPLIED PHYSICS LABORATORY
SII,.VI[IIt S~.ING MARYLAND
.~~.
-f-Y \......
/ ' .
y ",
/ ~
,. t
7.
JH-4
\
\'........
"
'\
.~
.,,~
Fig.3-19 DEFORMATION ON OF 3/8-1 NCH-THICK STEEL RING; ROD ENERGY OF
8200001N-LB
I -
14INCHES~
9
"'-~ ...'" "'", if: ::
f...,. -...'11.,,' _I!',~ -""', .
oI'-"'~, '- ...-.:t...
. iIi-' .' . -~
~ """" *,he-M.GTH'OF IMPACT
III
Ii
TEST JH-4
INITIAL
IMPACT
Fig.3-20 ONE OF THE IMPACT ARCS ON THE CONTAINMENT RING
- 54 -
-------
THE JOHNS I-fOPKI,..S.UNIVERSITY
APPLIED PHYSICS LABORATORY
9ILVr.iIt g""'IJIojIG M.."L"'''''D
2 2 3/2
- . [r + (dr/dB) ]
rO - 2 2 2 2.
r + 2 (dr/dB) - r (d r/dB )
(3-4)
Figure 3-21 compares rD, calculated from these
equations, with the original radius of the undeformed ring.
In the theories of plasticity and limit analysis (Ref. 24)
the energy dissipated internally during the permanent de- .
formation of a beam by bending is assumed to be:
w. = S (Change in curvature) M ds,
1 S o.
(3-5)
where Mo is the "yield moment" of a "fully-plastic" beam
(i. e., the stresses in the beam do not vary linearly across
the depth of the beam as assumed in elastic theory, but
take on limit or yield values of tension and compression
on each side of the neutral axis). The yield moment is
determined from .
M
o
2
= bt a 14,
o
(3-6)
where b is the width of the beam, t is the thickness,
and a is the limit or yield stress of the material.
o
The rings were made from AISI C1018 cold drawn
steel plates whose static a 0 is 54 000 psi. Dynamic
straining usually results in some increase in yield strength,
though this type of steel should not be particularly strain-
rate sensitive. For b = 4 inches and t = 3/8 inch the static
yield moment given by Eq. (3-6) is 7600 in-lb.
The curvature is defined as the reciprocal of the
radius of curvature, and Fig. 3-21 includes a plot of the
absolute value of change in curvature of the ring. Inte-
grating the a rea under this curve and multiplying by 4 for
the other quadrants,
r (~Curvature) ds = 1. 25 (r:nd) (in) .
S
. (3 -7)
- 55 -
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SlLvt'" S-.'NCi. MARYLAND
~ 0.02
..II
----
I
W
a:
::>
I-
«
> 0.01
a:
::>
()
~
w
C)
z
«
:x:
()
o
-;;;
-5 20
.::
w
a:
::>
I-
«
>
a:
::>
()
u.
o
In
::>
o
«
a:
25
DEFORMED RADIUS
OF CURVATURE, rD
~
15
ORIGINAL RADIUS
OF CURVATURE, ro
--L
10
16 CURVATURE I
=Ir: - r;) I
5
o
0 5 10 15 20 25
ARC LENGTH (inches)
I I I I
o 30 60 90
QUADRANT ANGLE (degrees)
Fig. 3-21 RADIUS OF CURVATURE AND CHANGE IN CURVATURE FOR 3/8.INCH.
THICK RING (JH-4 TEST)
- 56 -
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THE JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
SILVER SPitiNG. MARYLAND
The energy dissipated internally during this plastic defor-
mation is, then.
E.
1 .
rmg
= 1. 25 (7600) = 9500 in-lb.
(3-8)
Undoubtedly there is residual elastic strain energy
in the ring which has not been accounted for, and dynamic
effects will increase the calculated values, but these in-
crements should be small compared to the energy dissi- .
pated in the permanent deformation process. Also, the
transverse bending energy at the points of impact has been
neglected, but this too should be small, as evidenced by
Fig. 3-20. The accuracy of the preceding assumptions
could be verified experimentally by loading a similar ring
at opposite points and measuring the force-deflection
function required to produce a permanent deformation of
this type. However, time did not permit this in the cur-
rent program.
A nother approach is to assume that a complete
transfer of momentum occurs when the rod strikes the
ring, an approach often used in ballistic studies. A ve-
locity profile of the ring is then assumed (Fig. 3-22) and
the total momentum is used to determine the velocity
values. (The assumed shape is often not too important
as long as it satisfies the physical conditions of the prob-
lem. )
For the rod in Test JH -4 the momentum at failure
was:
MV = WRw = (0.99) (15) (2950) = 57 lb-
2g 2(386) s .
(3-9)
The average velocity of the ring is 2/3 the maximum ve-
locity, Vo. Therefore:
~V
3 0
(W ~ing) "
57 lb-s ,
(3-10)
- 57 -
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THE JOH- 0401"11'''' UNIVVtIIITY
APPLIED PHYSICS LABORATORY
."n- "'1". "..-n...AND
kQV
(~ \ <. -<1~
. "-6/C
I\!C,y,
C!=',s-
VELOCITY PROFILE ASSUMED
PARABOLIC WITH RESPECT
TO ARC LENGTH, S.
Vis) = Vo (1 - 0.00165 $2)
Fig.3.22 ASSUMED INITIAL VELOCITY PROFILE OF RING FOR USE IN MOMENTUM
TRANSFER ANALYSIS
- 58 -
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THE JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
Sil vr.. 5..1It1"",.. ""'''Tt.''''''D
which yields V = 782 in/ s. The assumed velocity profile
(see Fig. 3-22fis:
2
V = 782 (1 - 0.00165 s ) .
(3-11)
The energy in the ring at th~ moment of impact is:
E.
i .
nng
1 2 1 bt I 24. 6 2
= - S V dm = 4 x - x -E... f V ds
2 Vol 2 g . 0
(3-12)
Substituting b = 4 inches, t= 3/8 inch, IJ' = 0.268 lb/in3,
g = 386 in/s2, and Eq. (3-11) for V, we find Ei' =
18 000 in-lb. rmg
Since the maximum kinetic energy of the rod at
failure was 820 OOOin-lb, the foregoing two estima,tes of
Ei. represent only 1. 2 and 2. 2% of this rod energy,
ring
respectively. Thus, only a small fraction of the energy
of the composite rod was transferred to the steel ring.
The momentum-transfer method shows that the
energy transferred to the ring is dependent on the relati ve
mass values of the rod and ring. Therefore, the very
low fraction of energy transferred may not hold as the
mass of the rod increases relative to the mass of the
ring. (This is somewhat borne out by Test JH-3 in which a
graphite/ epoxy rod with comparable mass and energy
impacted a 1/4-inch-thick ring (1/3 less mass) to produce
much larger deformations, as shown in Fig. 3-14b.) How-
ever, the momentum-transfer method does not include
the pulverizing process, which can account for a signifi-
cant portion of the energy absorption for brittle materials
(Ref. 25). The preferred approach would be to use the
computer program mentioned earlier (Ref. 23), with ve-
locity and deformation data measured in further experi-
mental studies.
- 59 -
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It-4[ JOkP"llS rlOPllf;lNS U¥'r\IIVERSI'TY
APPLIED PH'(SICS LABORATORY,
Sil vt. 6,.1t1..."'.. ~""YL"ND
3.4 CONCLUSIONS
The small-scale, materials test program in the
APL spin chamber demonstrated the principle of rotating
filamentary and composite materials to achieve high spe-
cific energy storage. It was observed that these materials
were likely to have a desirable mode of failure. The small-
s cale test chamber is a versatile arrangement that will con-
tinue to be useful in evaluating mp.terials for use in com-
posite flywheels.
The test program at NAPTC was successful in
demonstrating the use of a secondary vacuum chamber to
obtain required operating pressures (though some work
needs to be done with the drive shaft sea!). the use of a
dual bearing support to a void rod instability, the use of
high-'"speed photography to observe the mode of rod failure,
and the effect of composite rods striking steel containment
rings.
For the first set of laminated, wheel-cut. compos-
ite bars ever made by the supplier in these sizes. the best
demonstrated ultimate specific energy storage levels were
28 W-h/lb for 3/4-pound, 30-inch-long S-glass/epoxy bars
a.nd 26. 5 W-h/lb for I-pound. 30-inch-long graphite / epoxy
bars. The calculated stresses at failure were only 79 and
69%. respectively. of the values expected by Hercules.
who are confident that development and quality control in
the manufacturing process will raise the performance of
such bars above 30 W-h/lb.
The high-speed photography system at NAPTC
showed that the composite rods did indeed fail in a man-
ner that did minimum damage to the containment rings.
The bars initially parted into two segments by failure very
near the spin axis, and then each segment was pulverized
within O. 7 ms by rubbing against the containment ring.
This pulverization process was completed before ring
deformation caused by energy transfer began. Subsequent
approxima te analysis of the deformed rings by two ap-
proaches -:- plastic deformation and mon:entum transfer -
- 60 -
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TH( JOHNS HO,.kINS UNIVERSITY
APPLIED PHYSICS LABORATORY
g.'LV.. 6".,"0 M."Vl"""D
revealed that 1. 2 to 2. 2% of the kinetic energy of the rod
was transferred to the ring. This result, especially when
combined with the prospect of a brush-type rotor configura-
tion (two of which are described in Section 4. 2), is most
encouraging. . It offers the hope of developing high-energy
composite rotors that could be contained in the event of
failure or vehicle accident. The writers judge that if the
advantages seen for flywheel-only or flywheel-hybrid pro-
pulsion systems are ever adopted on an appreciable scale,
this safety aspect alone may lead to the choice of compos-
ite-material flywheels as opposed to all-metal ones.
- 61 -
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TH£ JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
Sn.VEA SPRINC MARYLAND
4.
FLYWHEEL SYSTEM DESIGN CONSIDERA TIONS
AND PERFORMANCE
4. 1 INTRODUCTION
The practical application of flywheel power in ve-
hicle propulsion will entail the design, development, and
integration of all of the components required in the energy
storage system in such a way as to me et both the perfor-
mance requirements and the constraints imposed by the
vehicle and its missions. Design constraints will tend to
lower the energy storage capacity of the flywheel system
relative to the ultimate values, but the amount of degrada-
tion will be highly dependent upon the particular applica-
tion. This section discusses the following major design
considera Hons:
1.
Rotor configuration and related material con-
siderations, including preliminary theoretical
(ultimate performance) analysis of four spe-
cific types of advanced rotor configurations
that would take advantage of the properties
of composite materials (supported by Appen-
dixes A and B).
2.
Effects of flywheel rotor speed, including
effects on bearings, the need for an evacuated
housing (supported by Appendix C), power
losses, and rundown times.
3.
Factors affecting the allowable stresses in
composite-material flywheels, including cy-
clic and static fatigue and related problems,
as well as the potential for improvements in
materials that will offset and may eventually
far outweigh these effects relative to the 32
W-h performance level that has been assumed
in the system studies subsequently discussed
in Se ction 5.
- 6:3 -
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THE JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
SILV!"R SPAIHG. MA.YLAND
4.
Vehicular installation. including an example
illustration for a commuter car and a brief
discussion of the gyroscopic torque problem
with an example for a family car.
Section 5 presents further discussion of weight and volume
considerations for the vehicles specified by OAP (commu-
ter ,car. family car. van. and city bus). and particularly
the effects of 'engine choice for hybrid systems on maxi-
mum allowable flywheel system weight, as well as power-
train installation. including the necessary continuously
variable transmission (supported by Appendix D). Section
6 includes the description of a flywheel demonstration sys-
tem. designed to establish operating parameters for an
energy storage unit of usable size.
4. 2 ROTOR CONFIGURA TION AND MA TERIA L
CONSIDERA TIONS
4.2. 1 SIMPLE COMPARA TIVE ILLUSTRA TIONS OF THE
SUPERFLYWHEEL CONCEPT
The simplest superflywheel rotor is a rod or bar
composed of a high-strength, unidirectional composite
material. Though the coefficient of specific energy stor-
age of such a rotor is lower than that of a more conven-
tional disk or rimmed flywheel, the ability to take advan-
tage of the ultra-high-strength/density ratio of uniaxial
composite materials more than offsets the geometric
penalty. This point is demonstrated in Fig. 4-1.
In all cases the ultimate specific energy, E/W, is
related to the ultimate specific strength (the ultimate-
tensile-strength/ density ratio cr / pI) by a geometric coeffi-
cient K. The coefficients shown in Fig. 4-1 for the shaped
disk and rod are not the truly optimal ones (see Appendix
A) but represent configurations that can be fabricated
easily. The values of relative specific strength assume
that the biaxial stress patterns in the disks require the
use of an isotropic material. such as steel or titanium,
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THE .IONNS HOPkiNS UNIVERSITY
APPLIED PHYSICS LABORATORY
SlLVDt SP1nNG. ""'.YLANO
It.
rR~R1
I I'
I
<::t=>
I
I
I
1
~
~
SHAPE
SPECIFIC
ENERGY
COEFFICIENT
RELATIVE
SPECIFIC
STRENGTH
RELATIVE
SPECIFIC
ENERGY
CONSTANT
THICKNESS
DISK
0.61 12 1.0
0.931 12 1.5
SHAPED
DISK
THIN
o 0 ROD OR
BAR
3.53
0.33
1.9
~
THIN
DOUBLE
PYRAMID
2.6
3.53
0.45
NOTES
1. THIS COEFFICIENT RELATES TO A SHAPED DISK WITH A HUB THICKNESS FOUR TIMES THE RIM
THICKNESS. SEE APPENDIX A.3.
2. ASSUMES ISOTROpic MATERIAL WITH alp' = 1 x 106 INCHES (STEEL OR TITANIUM).
3. ASSUMES UNIDIRECTIONAL MATERIAL WITH alp' = 3.5 x 106 INCHES IGRAPHITEOR S-GLASS
COMPOSITES).
Fig. 4.' SPECIFIC ENERGY COEFFICIENTS, RELATIVE SPECIFIC STRENGTHS, AND RE-
LATIVE SPECIFIC ENERGIES FOR VARIOUS FL.YWHEEL SHAPES
- 65 -
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THE .10M". HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILve-- SPItiNG. ""-YUNO
while the uniaxial rod stresses will permit the use of boron,
graphite. or glass composites. The performance of these
rotors in terms of ultimate specific energy storage (nor-
malized with respect to the constant-thickness disk) shows
the rods to be superior to the disks - which is the essence
of the 8uperflywheel concept. However, as discussed in
Section 3. 3. 4, another virtue of rotors made of composite
materials - an inherent ability to absorb the major portion
of failure energy by microfracture (and possibly vaporiza-
tion) of the matrix material and progressive fracturing of
the brittle filaments - may prove even more important.
4. 2. 2 TRANSVERSE STRESSES IN BAR ROTORS MADE OF
UNIDIRECTIONA L COMPOSITE MA TERIA L
Since the superflywheel is assumed to be encased
in a con~ainer evacuated t~ approximately 10-3 torr, fly-
wheel subsystem weight and volume will also include the
weights of the case, shaft, seals, and bearings. To mini-
mize weight of these items, one wants the rotor to be rela-
tively compact. Thus, one wishes to increase the lateral
dimensions of a bar-like rotor to improve the energy pack-
aging efficiency, E/V. However, a rotating bar of appre-
ciable width will be in a state of biaxial stress because of
the component of the centrifugal forces acting normal to
the bar centerline, and the transverse properties of the
composite material must be considered in determining the
energy storage capability.
The rotating bar is assumed to be in a state of
plane stress (no normal stresses perpendicular to the spin
plane), and the equations of elasticity have been formu-
lated for an anisotropic material (see Appendix A. 2). The
numerical method of collocation (see Appendix A. 2) was
used to obtain a solution to the governing equations and
thence the stresses acting in the bar1.
1 During the progress of this contract~another project
within APL was developing a capability to use the NASTRAN
program, a multipurpose, master structural analysis pro-
gram sponsored by the National Aeronautics and Space
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THE JOHNS MOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
SILV~A S~IIIING. ....RVLAND
When stresses exist in more than one direction it
is usually necessary to use some form of interaction rela-
tionship in order to use available materials test data to
predict structural failure because the majority of these
data are developed for a single state of stress. An often
used relationship is the Hill (Ref. 27) (or generalized
von Mises) criterion, which employs ratios of the actual
longitudinal, transverse, and shearing stresses to the.
allowable single-stress test data of these material prop-
erties. This criterion was used to predict the rotational
speed (.t) at which failure of the bar would occur. Figure.
4-2 shows the resulting specific energy degradation factor'
versus the bar half-width/ radius ratio T /R for three candi-
date composite materials. Here E/W is referenced to the
thin-rod, uniaxial stress value, [E/W] , for each mate-
o
rial. The absolute value of E /W forany T /R can be de-
termined by multiplying the appropriate [E/W]o by the
degradation factor. Therefore, the graphite/epoxy compos-
ite (Hercules 2002T system) is the superior performer
over the range of aspect ratios shown, though glass and
boron composites are near-equals for thfn-rods. A s an
example of the effect of the transverse stresses, a graph-
ite/ epoxy composite bar with width-to-length ratio of O. 10
will have an ultimate specific energy equal to..... 94% of that
of a thin rod of the same ma terial.
This analysis has considered only unidirectional
composite materials. Since the allowable transverse
stress for a material of this type is only a fraction (..... 1/17
for graphite/epoxy and..... 1/35 for S-glass epoxy) of the
allowable longitudinal stress, a modest number of cross
or angle plies might increase the transverse strength of
the laminate enough to overcome the attendant loss in
Agency. The bar flywheel was programmed as a trial
problem by members of the other project, and the result-
ing stresses were essentially identical to those obtained
by the numerical method of collocation. The NASTRAN
solution also develops a displacement function at all
points in the bar, and these data are referred to in later
sections on the design of the rotor hub.
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THE: .IOHHS HOPK'NS UNlvt;RS'TY
APPLIED PHYSICS LABORATORY
8rL.YEII ~ING. """VLA."D
0.9
o 0.8
~~
w~
0.7
0.6
1.0
-
[E/W] 0 = 40 W-h/lb. 2002T
= 38 W-h/lb, S-GLASS
= 31 W-hllb, 2002B
0.5 .---
0.08
0.10
0.16
0.12 0.14
(~)
0.18
Fig.4-2 SPECIFIC ENERGY DEGRADATION CAUSED BY BIAXIAL STRESS FIELD IN
WIDER BARS
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THE .JOto4HS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
s.L¥lEft SPRING. MA8t"rL.ANO
longitudinal efficiency. Since it has also been shown that
angle and/or cross plies improve the material resistance
to fatigue (Ref. 26), this seems to be a particularly fruit-
ful path to reduce the specific energy degradation while
improving volumetric efficiency.
4.2.3 THE CIRCULAR BRUSH ROTOR
A nother concept with theoretically improved energy
packaging efficiency (E/V) is depicted in"Fig. 4-3. The
II circular brush" rotor comprises a large number of in-
dividual elements mounted in a hub in a manner that allows
the free length of each element to lie along a radial line
from the spin center. The elements can be glass or graph-
ite / epoxy composite rods that are pultruded to avoid fiber
misalignment and fiber damage at the surface, or .they can
be individual filaments such as boron or chemically-
strengthened bulk glass rods. The relatively small size
of the elements and the controlled processing techniques
available for this type of element should result in maxi-
mum allowable strengths. The elements are imbedded
into the hub only as far as is required to develop a bond
strength sufficient to transfer the centrifugal forces to the
hub. The hub can be made of high-strength steel, or possi-
bly of layers of composite material that sandwich the
layers of rods. The ~ub diameter must be limited so that
the combination of loads transmitted from the brush and
the inertial body forces within the hub do not over-stress it.
The equations for maximum rod stress, rotor
energy, rotor specific energy, and energy packaging effi-
ciency follow. The subscripts Rand H refer to rod
and hub values, respectively. The parameter f'i. is the
ratio of hub diameter to brush diameter, while {3 is the
ratio of the sum of the rod cross-sectional areas to the
cross-sectional area of the perimeter of the hub (an index
of the brush element spacing at the hub interface). The
equations assume that the maximum stress in the rods'
governs the rotation speed, which is usually true for
f'i. ~ 1/3.
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TI4£ JOHNS I'IOPKINS UNlvERSIn
APPLIED PHYSICS LABORATORY
8tL v... """NG. MARYLAND
R
SIDE VIEW
CI RCULAR BRUSH
ELEMENTS
\EQUALL V SPACED
AROUND
PERIPHERY)
TOP VIEW
Fig.4-3 CIRCULAR BRUSH CONFIGURATION
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THE JOHNS HOPKINS UNlvlRSny
APPLIED PHYSICS LABORATORY
St'- vr- gp."IJtfC# "."YL"''''O
The equation for the stresses at the root of each
rod is similar to Eq. (3-2) for a simple rod, except that
it is modified to account for the hub radius.
2 2 2
p' (1 - t'i )R (.&)
R
(j R = . 2g
(4-1)
The stored energy in the brush flywheel is the product of
one-half the moment of inertia of the hub and elements
(taken about the spin center) and the square of the rota-
tion rate.
4 2
E = fTR (.&)
12g
Ep'iJ" (1 - ..3) + 3p' If ~
(4-2)
The specific energy (E/W) and the energy packaging effi-
ciency (E/V) can then be formulated by combining the.
weight and volume equations of the brush rotor with Eq.
(4-2), and using Eq. (4-1) to put them in terms of the rod
(j / p' ratio. . .
E
W
(jR
2
Bp' (1 - t'i )
R
3 3
4f3P'R(1 - t'i ) + 3P'Ifi
2~' R(1 - tit) + plif
(4-3)
E
V
(jR
2
6p I (1 - t'i )
R
rp'RiJ,,(1 - ..3) + 3P'Ifj . (4-4)
The above formulations include the energy and the
weight of the hub. It should be noted that these equations
include the effect of hub weight for the circular brush con-
figuration, whereas estimates for the other types of rotor
configurations discussed here in Section 4 have neglected
hub weight. Therefore, relative comparisons presented
later will be unfair to the circular brush to some degree,
even though its hub will probably be heavier than the hub
of a bar, fanned brush, or composite disk rotor.
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T...e: JOH~S HOPKINS UNIVERSITY
APPLIED PHY$ICS LABORATORY
SILvER gPR'totG. M.IltYLA,ND
Table 4-1 presents values of ultimate specific
energy and energy packaging density as a function of rotor
geometry. For reference, a value of t3 = O. 20 is equiva-
lent to rods spaced in a square pattern 2 diameters on
center;fj = 0.35, a 1.5-diameter spacing; andfj = 0.50, a
1. 25-diameter spacing. E/W is a strong function of {3,
while E/V depends on both (1 and f3.
Table 4-1
Theoretical Ultimate Performance for Circular Brush Hotors
Using S-Glass/Epoxy Filaments and a Steel lIub 1
& =0. 2 &-0.3
Parameter ;3-0. 20 O. 35 0.50 0.20 0.35 0.50
E/w (W-h/lb) 17.!) 24.4 2!!.0 17. 6 24.0 28. 1
E/V (kW-h/ft3) 0.50 O. 84 1. 18 0.n7 1. 49 2. 01
]Assumptions: The small-diameter, pultruded filaments have cr 1'. = ~WO ksi
> I. 3 u ttma te
an(, p' = 0.075 Ib LO'; hub stresses do not control rotor speed.
A side from an improvement in theoretical energy
packaging density relative to a bar-type rotor, the circular
brush rotor offers two other advantages: (a) it should be
feasible, if required, to gimbal a steel hub at its connec-
tion to the shaft, permitting the vacuum case to ,pitch and
roll about the stable rotor; and (b) in the event of a rotor
failure or accident, the individual rods could fail suc-
cessively and distribute their energy over the entire con-
tainment case, which should permit a lighter containment
structure. '
4.2.4 RADIALLY-FANNED BRUSH ROTOR
This configuration is shown in Fig. 4-4. 1 The
elements are continuous from one side of the hub to the
1 A straight element, brush-type rotor was originally con-
sidered, but an analysis showed that bending stresses in
the rods were too high.
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THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SlLVE- Sfo~IHG. MARYLAND
R 6
5
4
r 3
aR
2
ELEMENTS CONTINUOUS
THROUGH HUB
o
o
0.2
0.4
0.6
T
O'R
Fig. 4-4
RADIALLY FANNED BRUSH ROTOR
- 73 -
0.8
1.0
-------
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVIER SPRING. "'ARYLAND
other, with balancing longitudinal components of centri-
fugal force. The transverse components of centrifugal
ferce must be reacted through the hub structure. The ele-
ments are held in the radially-fanned configuration by a
potting adhesive (such as epoxy) whose strength is suffi-
cient to transfer the normal components of force acting
on the elements.
The stress in the free-standing portion of an ele-
ment is pure tension; however. in the curved portion a
bending stress also exists and is additive to the tensile
stress. The resulting maximum stress in an element.
which controls the allowable speed of the rotor, is:
'R2 2 E d
(j _P W +~
max - 2g 2r
(4-5)
tensile
bending
where d is the element diameter. r is its radius of
curvature. and Em is its elastic modulus.
To achieve the radial alignment of the outermost
element at the edge of the hub. the hub radius of curva-
ture, r, becomes a direct function of the hub length,
2OtR, and width. 2T, as shown in Fig. 4-4. Thus, the
maximum operating speed (determined from Eq. (4-5»
and the specific energy are related to the rotor width and
packaging efficiency in a manner similar to the bar rotor.
Neglecting the weight and energy of the hub and the potting
material, the energy per unit thickness of the brush is:
3 2
E 2R w Tp'
T=-(O.91) 3g
(4-6)
where T is the half -width (transverse direction) of the hub
at the spin axis. The factor O. 91 assumes a dense. rod pack-
ing arrangement, and the energy formulation neglects rod
curvature. In terms of geometric parameters, the specific
energy is the same as for a thin rod,
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THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV£1Ir S~IIr!""C. "'''.'''LA''''D
~ = R2W2
W 6g
. (4-7)
However. in terms of materials properties the effect of
bending stresses modifies the thin rod values according to
fa - Em)
E~
W - 3p'
( 4-8)
The energy packaging density is given by:
~ = (0.91) (iw) (a - ~~) (~) .
(4-9)
The specific energy is shown in Fig. 4-5 as a func-'
tion of brush width-to-Iength ratio for four different rotor
configurations. All rotors have a 30-inch spin diameter
(R = 15 inches) and have a 12-inch-Iong hub (01 = 0.4), Re-
sults are given for a graphite/epoxy brush with 0.100-
inch-diameter rods and S-glass/epoxy brushes with rods
of three different diameters. The effect of the elastic
modulus of the rod is clearly shown by the rapid drop-off
in specific energy of the graphite/epoxy rod (Em = 21. 5 x
106 psi) when compared to the S-glass/ epoxy rod of the
same diameter (Em = 8 x 106 psi). Other things being
equal, a low-modulus material and small-diameter ele-
ments are desirable for the radially-fanned brush applica-
tion. Even with the small rod diameters, the energy stor-
age capacity drops off sharply as the geometric limit
(T/R ... 0/) is approached. Nevertheless, the energy degra-
dation with increasing width is not as severe as for the
wide bar.
Figure 4- 6 shows the effect of the hub length/ rotor
diameter ratio, 01, on the energy functions. The ,longer
hub results in a 50% improvement in energy packaging
density over the shorter one. It must be remembered,
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tHE ..fOHNS HQPt(\NS UNtV£ttS\TY
APPLIED PHYSICS LABORATORY
51LVllt ~NG. N"'.YLAHD
45
40
35
£ 30
?
~
~ 25
UJ
20
15
Q = 0.4
10
o
0.1 0.2 0.3
BRUSH WIDTH-TO-LENGTH RATIO, T/R
0.4
LEGEND:
- S-GLASS/EPOXY RODS
Gult = 300 KSI
p' = 0.075 LB/IN3
Em =8.0 x 106 PSI
-- GRAPHITE/EPOXY RODS
Gult = 225 KSI
p' = 0.054 LB/I N 3
Em = 21.5 x 106 PSI
d = ELEMENT DIAMETER
Fig.4-5 EFFECTS OF ROTOR GEOMETRY AND MATERIAL PROPERTIES ON SPECIFIC
ENERGY IN A RADIALLY-FANNED BRUSH ROTOR
45
40
35
~ ....
W
-E.
~ 30
~
~
W 25
/
/
/
. a = 0.4 ~""'-'""
/~a'O.3 E \
/ ~V
20
15
10
o
0.2
T/R
0.1
0.3
2.0
M...,
1.5 ?
~
:
>
W
1.0
0.5 .
0.4
NOTE:
1. ELEMENTS ARE 0.025
-INCH- DIAMETER
S-GLASS/EPOXY, GUlt =
300 KSI
2. HUB WE.IGHT NOT
INCLUDED.
Fig. 4-6 . SPECIFIC ENERGY AND ENERGY PACKAGING DENSITY VERSUS T/R FOR
RADIALLY-FANNED BRUSH ROTORS OF S-GLASS/EPOXY ELEMENTS
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Tt-tE JOHNS HOPKINS UNIVERSITV
APPLIED PHYSICS LABORATORY
SILVER S~RING. W""'YL,AND
however, that the weight of the hub and potting material
have not been included in this analysis, and the increase
shown would certainly diminish in an absolute comparison.
The outer elements, with their higher portions of
bending stress, control the speed (and energy) of the rotor.
It should be possible to shorten them to reduce the pure
tension portion of their stress. In fact, the lengths of all
of the rods could be adjusted so that their combined bend-
ing plus axial stresses would be equal. This would re-
duce the moment of inertia of the rotor but would allow
higher operating speeds; it is likely that shaping of this
type would result in some improvements in E/W for the
higher values of T /R.
4. 2. 5 A LAMINA TED COMPOSITE DISK
In Section 4. 2. 1 the geometric coefficients of spe-
c ific energy were discussed, and it was pointed out that
the biaxial state of stress. in disk rotors requires the use
of an isotropic material. By the very nature of the manu-
facturing process, composite laminae are nonisotropic,
however they can be oriented in patterns to produce lami-
nates whose properties are theoretically independent of
direction for plane stress applications. Composite lami-
nates of this type are referred to as quasi-isotropic, and
the lamina orientation patterns are usually +60/ 0/ ~60 or
+90/+45/0/-45 degrees. (Any pattern with three or more
equally spaced angles of orientation will give the same re-
sult by the method of analysis used, see Appendix B. )
The strength of such a laminate is only a fraction of the
unidirectional strength of the reinforced material, but
the biaxial stress capability may qualify it for use in a
disk rotor where the geometric energy coefficient is
nearly double that of a wide bar.
The finite-element, direct-stiffness method of
structural analysis was used to evaluate the stresses and
deformations in a constant thickness rotating disk, as
discussed in Appendix B. The results of the analysis
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THE JOHNS MOPJII;I....S UNIVERSITY
f,PPlIED PHYSiCS LABOr~ATORY
$1I.vr- S~";"'G ""."'LA...O
showed that all patterns except the 0/90 produced iso-
tropic-case stress resultants with zero shear stress~
The laminate properties of S-glass, graphite, and boron/
epoxy were determined from uniaxial tensile test data. in
the 0° and 90° orientations. These base data were trans-
formed and summed for different lamination patterns.
The ultimate material stresses for the biaxial stress
field were determined by the Hill criterion (Ref. 27), and
these values were used to establish the maximum rotor
speed and kinetic energy. The results are given in Table
4-2 for three composite materials.
Table 4-2
Theoretical Ultimate Performance of Disk Holor"s Made from
Quasi-Isotropic (+GO/O/-(jQ) Composite Laminate
Material Laminate Properties
01 0' a E/W E/V
u
Type (ksi) (lb/in:3) (ks i) (W-h/lb) :3
(kW-h/ft' )
Boron/Epoxy 212 O. 07S 112 :30 :3. 7
Graphite/ Epoxy 204 O. 054 105 37 :3. 4
S-Glass/ Epoxy 264 0.072 136 36 4. 5
The theoretical results are extremely good with
respect to both E/W and E/V. However, certain assump-
tions used in the analysis will require experimental veri-
fication: First, the method of transforming lamina prop-
erties and summing the values from all of the laminae to
form average laminate properties is a rational and neces-
sary approach because strength and deformation data are
available only for principal laminae directions. Some re-
searchers (Ref. 28) feel that the pseudo-isotropic allow-
able stress will be closer to 40% of the uniaxial value
rather than the,,-, 52% determined by the transformatioh.
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILvt:1t 5~"ING. ".."LAND
Secondly, the validity of the interaction criterion becomes
very important, since the radial and tangential stresses
are equal at the center of the disk. Third, a practical
method of attaching hubs to the disk will have to be de-
veloped. Finally,. the ability of the matrix to resist the
interlaminar shear forces that develop between the laminae
will have to be demonstrated. Nevertheless, this approach
offers the theoretical potential of achieving high specific
energy storage within a compact unit, while providing the
inhe rent. safety of composite construction (though this, too,
should be verified by experiment).
4.2.6 SUMMARY OF ENERGY CHARACTERISTICS
The superflywheel concept of using filamentary.
composite materials, stressed along the primary axis of
the material, has been presented, and examples of three
different configurations - the bar, the circular brush, and
the radially-fanned brush - ha ve been given. In addition,
the use of pseudo-isotropic composite laminates in con-
stant-thickness-disk flywheels has been investigated.
Figure 4-7 compares the specific energy (E/W) and
energy packaging density (E/V) characteristics of these
rotor configurations. As noted in Section 4.2.3, the E/W
values for the circular brush include hub weight, whereas
values for the other rotors (which would have somewhat
lower hub weight fractions) do not include hub weight and
should be lowered slightly for a 'fair comparison to the cir-
cular brush.
Bar rotor curves are shown for S-glass/epoxy and
graphite/epoxy unidirectional composites. For these con-
stant-crass-section bars, the results are nearly identical
for the two materials, yielding a maximum E/V of""' O. 65
kW-h/ft3 at an E/W of 32 W-h/lb. This is the simplest of
the superflywheel configurations and should be considered
for use in applications where the volume constraints are
not severe. Optimization of lamina orientation should im-
prove these values a modest amount, while also improving
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-------
TH8 JOHNS HOPt(INS UNIVI:A9ITY
APPLIED PHYSICS LABORATORY
Sn v... C:W-IHG. "'."YLAND
'1:
--
.c
~
..¥
>
W
0.8
0.6
0.4
0.3
15
Fig. 4-7
8
6
S.GLASS/EPOXY DISK.
4
GRAPHITE/EPOXY DISK.
(3 = 0.50
2
a = 0.4
S-G LASS/ EPO X Y
RADIALL Y-
FANNED BRUSH
30
E/W (W-h/lb)
SUMMARY OF ULTIMATE COMPOSITE MATERIAL FLYWHEEL
CHARACTERISTICS FOR DIFFERENT ROTOR CONFIGURATIONS
20
25
35
40
45
- 80 -
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TtotC .JOHNS t-fOP1UNS UNIVERSITY
APPLIED PHYSICS LABORATORY
fllL.VltI ""'HG. """"'UUiIIID
resistance to fatigue, thereby partially compensating the
probable derating needed for life 'and safety margin con-
siderations, as discussed 'in fol~owing subsections.
The radially-fanned brush has similar, though ap-
parently improved, characteristics. The "higher E/W at
low E/V is directly attributed to the assumption that small-
diameter, pultruded rod elements will achieve higher
strength than composite laminates.
However, it must be remembered that the hub and"
potting material weights are not included, and the hub
length of the best example (tt = 0.4) is probably 30 to 500/0
longer than the hub of a wide bar rotor. A Iso, the hub
must be strong enough to resist the transverse components
of centrifugal force. Nevertheless, a brush rotor should
achieve a 50 to 100% improvement in E/V .over a bar rotor
for a comparable E/W, and its containment requirements
probably would be lower because of both timewise and
spacewise distribution of failure energy of the thousands
of rod elements. A disadvantage is the increased com-
plexity of working with tJ:le many elements and fitting them
in the hub. Analysis and experiments must be conducted
to verify that the potting material will be capable of re-
sisting the lateral force components and maintaining the
fanned arrangement.
The circular brush is ideal for containment design
because of its intrinsic ability to distribute energy to the
absorbing structure. Its E/W is a strong function of the
rod element spacing, and a spacing no more than 1. 5
diameters ({3 = 0.35) is desirable. Though E/V improves
with increased hub diameter, Ci = O. 3 is an approximate
limit to prevent overstressin~ the hub. An arrangement
that gives E/V = 1. 5 kW-h/ft and E/W = 25 W-h/lb (in-
cluding hub weight) appears reasonable. Whether this
would prove superior to a fanned brush (tt = 0.4) would de-
pend on the latter's hub weight.
Finally, the use of composite materials, formed
into a quasi-isotropic, laminated, constant-thickness disk,
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THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
Sn..VI:" --MG. MARYLAND
may prove to be the most effective way of achieving high
E/V and E/W while retaining the inherent safety of the
composite materials. There are assumptions in the analy-
sis techniques used, but knowledge of the behavior of these
materials is steadily growing, and sufficient test data
should soon be. available to improve the estimates.
4. 3 THE EFFECTS OF FLYWHEEL ROTOR SPEED
The flywheels being considered in this program
have lower inertias but much higher rotational speeds than
those of previous flywheel systems. Figure 4- 8 shows
tip speed versus specific energy for constant-thickness
disk, thin rod, and circular brush configurations, and the
tip-speed scale is equated to the speed of rotation for a
30-inch-diameter rotor. These curves merely relate tip
speed (R(AJ) and specific energy according to the equation:
E K 2
- = - (R(AJ)
W g ,
(4-10)
where K is determined by the rotor configuration but not
the strength of the materials. However, each configuration
will be limited in E/W and tip speed by the materials used,
and data points from Fig. 4-7 have been added to indicate
the current limits of interest. The curve for a radially-
fanned brush will lie between those of the bar and circular
brush. It is probable that a disk rotor, with its higher
coefficient of E/v, would be smaller in diameter than a
bar, effectively increasing its relative rate of rotation
over the values shown. Some of the effects of these speeds
are discussed briefly in the following sections.
4. 3. 1 BEARINGS
The rotor bearings will be selected by the require-
ments of radial load capacity, operating speed, life, and
minimum no-load friction losses. Operating speeds of
interest will range between 20 000 and 40 000 rpm for the
rotor sizes of interest. If we assume the use of bearings
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TWI: JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
SU..VI" S~.I"'G. MAR\"L.AND
6
g
0
x
~4O 5
a:
w
r-
w ~
~
«
9 X
x ~
~30 :':4
~ 0
w
a: w
.IL
0 en
u.. IL
w r-
r-
«
a:
~ 20 3
r-
«
r-
0
a:
2
o
1C
20
EIW (W-h/lb)
CIRCULAR BRUSH
cr = 0.3; fJ c 0.35
STEEL HUB. .
FIBERGLASS RODS
30
40
Fig.4-8 EFFECT OF ROTOR CONFIGURATION ON TIP SPEED
- 83 -
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THE .-..... HOPto-machinery appear to be ade-
quate for flywheel rotors from the standpoint of DN rating.
The rated life of these bearings can exceed 10 000 hours
at maximum rpm, particularly when the fatigue-resistant,
high-temperature, M-50 tool steel is substituted for stan-
dard bearing material. Longer life would be expected
when the speed continually varies between full and 1/2 or
1/4 speed. Tests at DN values between 1. 25 and 1. 5 mil-
lion with bearings made from M-50 steel and using spe-
ciallubricants demonstrated an operating life at least 14
times the AFBMA 1 rated life for similar bearings of stan-
dard material (Ref. 30). A DN value of O. 5 million is
about the present limit for grease-lubricated bearings;
therefore, a flywheel system will probably have some type
of positive lubrication such as oil jet, spray, or mist
lubrica tion.
The principal drawback to the use of ball bearings
is that their no-load friction torque may reduce flywheel
run-down times to undesirable levels, as shown in Sec-
tion 4. 3. 3. An alternative is the use of air bearings with
lower power losses. Their use, however, has often been
limited by low load capacity and whirl instability. Tests
have been conducted to determine the effect of air supply
pressure ratio on bearing stiffness and fractional-fre-
quency whirl of a rotor (Ref. 31), and additional experi-
ments of this type would be required to determine similar
parameters for a flywheel rotor with large gyroscopic
effects. Another alternative to ball bearings is the magnetic
lAntifriction Bearing Manufacturer's Association.
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THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SaLVC- SPlitiNG. ".RYLAND
fluid bearing (Ref. 7), which also incorporates the vacuum
seals. These low-friction bearing systems, along with
conventional mechanical bearings, must be designed to re-
sist the intermittant radial loads resulting from flywheel
gyroscopic torques (though Section 4. 5. 2 illustrates that
this should not 'be a critical requirement for ball bearings).
4. 3. 2 VACUUM SYSTEM
The high rotation rates and blunt aerodynamic con-
figurations of most of the rotors dictates operating at air
pressures between ,10-3 and 10-2 torr (see Appendix C).
From a reliability and ma.intenance standpoint it would be
desirable to evacuate and seal the flywheel unit at the fac-
tory and never open it again.(or possibly just once for a
mid-life service at;~ 50 000 miles). After an initial period
of outgassing, while the unit is being maintained under
vacuum and a slightly elevated temperature at the factory,
a case with no rotating-seal penetrations could be sealed
and the system would maintain this pressure level (modest
by modern aerospace vapuum system standards) for an
acceptable period. This assumes an increase in the level
of mass-produced vacuum system technology, however.
The problem is that, for most power transmission
methods - and in order' to place the bearings outside of
the vacuum can to provide for active lubrication - we re-
quire a rotating vacuum seal(s). A seal that will satisfy
all of the requirements of the system is not available on
the market today. The Ferrofluidic Corporation produces
rotary vacuum seals that use a magnetic fluid to resist
the -pressure 'differential (a unit of this type was used in
the APL vacuum spin chamber, discussed in Section 3.2).
Currently Ferrofluidics has units that operate at DN = O. 3
million for> 5000 hours, and they are working on DN =
1. 0 million. These units require active water cooling,
which would be undesirable for an operational flywheel
system, but they feel there is a possibility of developing
a high-thermal-conductivity magnetic fluid that would
eliminate this requirement.
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THE .IOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
StLV!!. SPttING. """YLAND
DN values for the seals also could be reduced by
locally reducing the shaft diameter. Therefore, tech-
nology areas exist whereby rotor seal development for a
prototype flywheel system, with active cooling and reduced
seal life, appears to be possible. Friction drag of these
magnetic fluid seals is relatively high, equal or greater
than that of the bearings. This is a drawback for a fly-
wheel system where the reduction of parasitic losses is
very important. This type of seal, however, could be
acceptable in a demonstration model.
The use of magnetic couplings, harmonic drives,
or an electric motor inside the vacuum case would elimi-
nate the need for rotating vacuum seals if the bearings
could be placed inside the case. Again, the development
of a combination fluid bearing and seal would be highly de-
sirable. The use of a rubbing seal with an auxiliary
vacuum pump to make up for leakage around the seal is
a Iso a possibility, though it increases system complexity
and could present problems in spinning up the flywheel
after long periods of vehicle storage because of the small
pump displacement that would be used for economy.
4.3.3 POWER LOSSES AND RUN-DOWN TIMES
Windage losses are discussed in more detail in
Appendix C, and an example is shown where a O. 68-kW-h
bar-type flywheel would run down to one-half its maximum
speed of 30 000 rpm in 49 hours, assuming an air atmo-
sphere at 10-3 torr and no seal or bearing losses. This
does not account for the swirling of the air inside of the
can which will have the effect of reducing the relative ve-
locity between the bar and the air and could double the
value quoted above (i. e. , -- 4 days). The main purpose of
this section is to investigate the mechanical power losses
and their effect on run-down times, and therefore the
windage losses will be neglected for the time being.
The no-load bearing friction torque T, in ft-lb,
is given by Eq; (15) of the SKF Engineering Data Book
(Ref. 32) as follows:
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-------
rt-tE JOHNS MOPKINS UNIVERSl1Y
APPLIED PHYSICS LABORATORY
$ILV£" Bp".HO "''''''.I..'''''D
T = 1. 183 X 10-6 f (VN)2/3 d 3
om'
(4-11)
where
f
o
II
= viscous torque factor,
= lubricant kinematic viscosity in centi-
stokes at the operating temperature,
N
d
m
= speed in rpm, and
= bearing mean diameter in inches.
For single row, angular contact, ball bearings and oil
mist lubrication the torque factor fo = 1. O. This is the
minimum value for this type of bearing; an oil bath sys-
tem of lubrication results in a factor of 2. O. .
Equation (4-11) can be expressed as:
T = KIJ)2/3,
(4-12)
where U) = rotation rate in rad/s (= 21TN/60), and for a fly-
wheel rotor with n friction elements:
-6 2/3
K = 5. 33 x 10 f n v d
o m
3
(4-13)
The rate of run-down caused by the friction ele-
ments is expressed as:
2/3
dU) 1 d t = - T 1 I = - KUJ 1 I .
(4-14)
Solving this equation for t,
at t :: 0, we obtain:
with the condition that w = U)
o
t = 3I(w 1/3 - w 1/3) IK .
o
(4-15)
- 87 -
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THE .iOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SlLYER s..."~NG. W.UtYLAND
The time (in seconds) to run-down to half speed «(.&J = (.&J /2):
o
6t 1/2 = O. 62 fu> 0 1/3 /K .
(4-16)
Since:
E
o
= 2. T.. 2
2 iWO '
5/3
6 t 1 / 2 = 1. 2 4 Eo / Kw 0 '
(4-17)
where E is expressed in. ft-Ib.
o
If we now assume a rotor supported with two angu-
lar contact ball bearings (n = 2) of 30 mmbore (dm = 1. 81
inches) and lubricated with an oil mist (fo = 1), Eq. (4-13)
yields:
K = 63 x 10-6J12/3.
Standard bearings of this type operate at oil tem-
peratures near 125°F with JI = 85 centistokes. The use of
high-temperature M-50 tool steel for the bearing compo-
nents, and special lubricants operating near 300°F, will
reduce JI to...... 3 centistokes (Ref. 30). Using this value:
K = 63 x 10-6 (3)2/3 = 1. 31 x 10-4 (ft-Ib) (second)2/3
Then, assuming w = 3142 rad/ s (30 000 rpm):
o
1. 24 E
6.tl/2 = 0 /' = 0.0141 E (seconds)
1. 31 x 10-4 (3142)5 3 0
For a family car with a 163-pound rotor:
= (163 lb) (30 W-h/lb) (2656 ft-Ib/W-h) = 13 x 106 ft-Ib,
E
o
- 88 -
-------
THE JOHNS ~OPJoc;INS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILYER SPAtHG W.../lfYLAND
and
~tl/2 = 0.0141 (13 x 106) = 0.18 x 106 seconds = 50 hours
It may be seen that the run-down time is directly
proportional to the initial energy and inversely propor-
tional to the "number of friction elements. Therefore
smaller flywheel systems will run down faster, and the
inclusion of seal friction, which will likely be greater
than the bearing friction, will further reduce run-down
time. Thus bearing and seal friction are likely to be 0
more important than windage Josses for the types of com-
o ponents (and internal pressure, 10-3 torr) assumed in this
analysis. Again the need for a high-speed, low-friction
bearing/ seal unit is apparent, for the use of large fly-
wheel rotors in hybrid vehicles will be practical only if
friction losses can be minimized.
4.4 FACTORS AFFECTING THE ALLOWABLE STRESSES
IN COMPOSITE MATERIAL FLYWHEELS
For any structural applica tion, the allowable
stresses depend on (a) the prescribed life cycle and en-
vironment of the structure, (b) a criterion of desired reli-
ability of the structure (and this may be based on economics
of replacement, personnel safety. operational requirements,
etc.), and (c) the material characteristics, which, in addi-
tion to strength and physical properties, include manufac-
turing controls and size effects. The following sections
discuss the effects of these factors for flywheels made of
composite materials.
4.4.1 FLYWHEEL SYSTEM LIFE CYCLE AND ENVIRON-
MENT
A spresently envisioned. the flywheel system for a
hybrid vehicle would be factory-assembled, hermetically-
sealed, and operated under controlled vacuum conditions
at predictable stress levels. All of these factors will tend
- 89 -
-------
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
StLV.4It tiPPING "''''''''\...'''''D
to lower the efff:cti ve "factor of safety" applied to mat e-
ria.ls test data, particularly with respect to the vacuum en-
vironment. The flywheel life cycle is primarily a function
of the vehicle operational requirements and the size of the
flywheel. Rotor configuration (windage losses) and bearing
and seal friction have secondary influences.
As an example, a commuter car with a 2 kW-h
flywheel (70-pound. rotor with E/W =,... 30 W-h/lb) operat-
ing on the DREW driving cycle will cover,... 7 miles per
charge. For a vehicle design life of 100 000 miles this
equates to..... 14 000 charges, plus the additional charges
(full or partial) required because of run-down between
operating periods. If these amounted to an average of one
additional charge per day for 8 years (12 500 miles per
year), the total number of cycles would amount to,... 2 x 104.
If the flywheel stored only 0.5 kW-h, or 1/4 of the former
example (which is probably a minimum size to establish
history-independent performance; i. e., three complete
accelerations per charge without engine assist), the
number of charge cycles in a vehicle lifetime would be
4 x 14 000, plus possibly two additional charges per day
(because of faster run down), for,... 7 x 104 cycles. These
examples are shown in Fig. 4 -9a. A Iso shown (Fig. 4-9b)
is an example of emission-free driving in the central busi-
ness district, as discussed in Section 5. Note that the
charge and discharge rates are quite low compared to the
load i ng ra tes used in developing fatigue test data. This is
beneficial, for it eliminates heating of the composite mate-
rials caused by rapid straining, a factor which sometimes
results in loss of strength in the matrix. Also, the
stresses in the flywheel rotor range from the rated tensile
stress to zero, with no compressive stresses. Data of
composite materials tests by Boller (Ref. 33) show that
stress cycles involving only tensile stresses result in
much longer fatigue lives (orders of magnitude more) than
for stress cycles with alternating tension and compression.
.Another .material characteristic that interacts with
the rotor size and system losses is the stress-rupture or
- 90 -
-------
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
... ,... .'.
o-
w>
...l.:J
«cr
crW
z
U.W
o
*
MORNING COMMUTE
45 MINUTES, - 15 MILES
MID-DAY EVENING
RUN-DOWN CpMMUTEI
CHARGE
NIGHT TIME
RUN-DOWN
MORNING
COMMUTE
w
l.:J
cr
«
:r
u
...J
W
.W
:r
~
>
...J
~
100
75
50
DISCHARGE
25
o
l. 1 HOUR-1
~
1
l 1
TIME (hours)
(a)
EXAMPLE OF HYBRID COMMUTER CAR ON DHEW DRIVING CYCLE
(2 kW-h FLYWHEEL; AIR CONDITIONER OPERATING)
e CHARGE TIME (minutes)
e DISCHARGE TIME (minutes)
eASSUMED RUN-DOWN
TIME TO HALF SPEED (hours)
eLiFE REQUIREMENTS (cycles)
2 kW-h FLYWHEEL
(AS ILLUSTRATED)
6
16
0.5 kW-h FLYWHEEL
(ALTERNATIVE)
1.5
4
24
2 x 104
6
7 x 104
OVERNIGHT ~ORNIN~I-
FREE-COMMUTE
RUNNING 15 MI LES
(ELECTRIC
CHARGE
IF REQUIRED)
FR EE-RUNN ING
ELECTRIC CHARGE
(USING 1 HP MOTOR I
EMISSION-FREE
DRIVING
I EVENING I OVERNIGHT
.. ... .. ...
.COMMUTE FREE-
RUNNING
PARKING GARAGE
10 MILES OF
EMISSION-FREE
DRIVING IN CBD
~
AM
I
9
l 1
I
2
I
3
I
4
I
5
I
6
I
8
PM
TIME (hours)
(bl
EXAMPLE OF EMISSION-FREE DRIVING OPTION IN THE
CENTRAL BUSINESS DISTRICT (CBD) (COMMUTER CAR
WITH 2 kW-h FLYWHEEL; AIC NOT OPERATING)
Fig. 4-9
TYPICAL FLYWHEEL CYCLE REOUI REMENTS
FOR A COMMUTER CAR
- 91 -
-------
THa JOH... "OPIU"S UNIVa..DITY
APPl.IED PHYSICS LABORATORY
""YR. SPItf'I8G. ....IItYLAHD
static fatigue life of the material at various stress levels.
A large rotor with low system losses and long times to
run down will be stressed over this longer period even
though the vehicle is not operating. Conversely, a rotor
that has a short run-down period will be stressed pri-
"marily while the flywheel system is being used to propel
the vehi.cle. Since ~he allowable stress is a function of
time under load, a flywheel with the desirable character-
istic of low losses imposes operating stress limits be-
cause of the long time under load.
4. 4. 2 DYNA MIC FA TIGUE OF COMPOSITE MA TERIA LS
The high-modulus composite materials," graphite
and boron, have excellent resistance to fatigue loading,
and are superior in this respect to many of the high-per-
formance metals that are used in aerospace applications.
A notable example is the recent retrofit of a boron/epoxy
doubler panel to increase the fatigue resistance of the
D6A steel wing pivot structure on the FIll aircraft. In
general, boron and graphite/ epoxy composites endure
more than 107 cycles of tension-zero-tension at maximum
stress levels equal to 70% of their static ultimate values
(Refs. 34 q,nd 35). A data sheet from Ref. 34 is repro-
duced in Fig. 4-10, which shows that bo~on/ epoxy endures
105 cycles at,... 90% of the static ultimate. .
Conversely, glass-reinforced composites have
usually been characterized as having relatively poor
fatigue resistance. Data from Ref. 33 are reproduced in
Fig. 4-U, which show endurance to 107 cycles at,... 40%
of static ultimate stress, and endurance to 105 cycles at
,... 50% of static ultimate. These data clearly show the ef-
fect of compressive stresses (lower mean stress) in de-
grading the fatigue life of the material. The tests were
conducted at ambient temperature and 500/0 relative humid-
ity, which are typical cond~tions for fatigue tests reported
in the literature.
Thus, there apparently are large differences in the
abilities of the various composite materials to endure
- 92 -
-------
SILV!l:R SJI".'HG. M..YLAHO
THE .IOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
~ 180
L1J
d 160
>-
u
a: 140
L1J
11-
~ 120
L1J
a:
I- 100
en
~
::> 80
~
X
« 60
~
200
°MIN
R=-=0.1
°MAX
0- 30cpm
. - 1750 cpm
e-1800cpm
o - 2900 cpm
40
101
106
107
CYCLES TO FAILURE
Fig.4-10 CONSTANT AMPLITUDE FATIGUE TESTS OF BORON-EPOXY COMPOSITE AT
ROOM TEMPERATURE (FROM REF. 34)
100
90
80
S-GLASS
~ 70 ZERO MEAN STRESS
~ 60 I "i"
~. E-GLASS . ,
Ii; 50 25 000 PSI MEAN STRESS~
~ 40. I 'I"',
« a ult = 162 KS! FOR S-GLASS
~ = 120 KSI FOR E-GLASS
I I
o. t:. FOR 1f8-INCH
LAMINATE
o ZERO MEAN STRESS ON
1/4-INCH LAMINATE REDUCED
TO 1/S-INCH
30
/'
E-GLASS
ZERO MEAN STRESS
20
10
o
. 102
103
104
107
NUMBER OF CYCLES TO FAILURE
Fig. 4-11 FATIGUE TESTS OF S-GLASS AND E-GLASS/EPOXY LAMINATES AT ROOM
TEMPERATURE (FROM REF. 33)
- 93 -
-------
THE JOHNS HOPKI,.,S UNIVERSITY
APPLIED PHYSICS LABORATORY
StL~. $PlltING. MARYLAND
cyclic loading. These differences are often explained by
comparing the stiffness-to-strength ratios (ultimate strains)
of the materials (Hef. 36), as shown in Table 4-3.
Table 4-~
Ultimate Strains of Composite Materials
Ultimate Tensile Elastic Ultimate
Composite Material Strength (psi) Modulus (106 psi) Strain (in/ in)
Boron/ Epoxy 210 000 30.3 0.007
Graphite/ Epoxy
(high-strength type) 200 000 21. 5 0.009
S-Glass/Epoxy 260 000 7.6 0.034
The theory is that the matrix resin develops a non-
linear stress-strain behavior above strain elongations of
1/2 to 1%, and repeated cycles above these levels can
cause cracking or crazing of the matrix resulting in an
inability to transfer stresses from one fiber to another.
The values in the table show that the ultimate strain in the
glass composite is on the order of4 to 5 times the ulti-
mate strain in the high-modulus composite materials.
Therefore, the glass is usually limited to a lesser frac-
tion of its ultimate strength in order to reduce matrix
damage under cyclic loading. Another, and probably re-
lated reason for reduced endurance of the glass compos-
ites is that, when the resin matrix cracks or crazes under
stress, the glass fibers are exposed to atmospheric mois-
ture which is known to degrade their strength (Ref. 37).
There are no known dynamic fatigue test data of glass
composites in a vacuum, though static fatigue data for
glass and glass composites tested in the absence of air
and moisture (see Section 4.4. 3) show a marked improve-
ment over similar materials tested under ambient condi-
tions.
- 94 '7"
-------
THE JOHNS HOPKINS UNIV£RSITY
APPLIED PHYSICS LABORATORY
StLV!:A' SPRING MARYLAND
4.4. 3 CREEP AND STRESS-RUPTURE OF COMPOSITE
MATERIALS
Creep is a time- and stress-dependent phenomenon
in which the material continues to deform after the stresses
have reached a stable value. The rate of deformation i.s a
function of the stress level and the accumulated strain, and
the process terminates in rupture of the material. (Homo-
geneous, isotropic materials also are affected.) It is of
interest because {t generally limits the amount of stress a
material can resist for a specified time or the amount of
time a specified stress level may be endured. Stress-
rupture is sometimes referred to as creep-rupture or
static fatigue, and there are similarities between the be-
havior of materials under dynamic fatigue and long-term
loading.
There are not many data available on the stress-
rupture and creep characteristics of boron and graphite
composites, primarily because these materials have
usually been considered for applications where short-term
cyclic or vibratory loads are more important. The fibers
have very linear stress-strain relationships to failure,
and creep would not be expected to be a major concern.
Graphite/ epoxy composites were discussed by Soliman
(Ref. 38), and it was concluded that if the fibers are
aligned with the load direction, the creep strain will be
negligible compared to the instantaneous elastic deforma-
tion. Such is not the case for off-axis loading, where it
was found that fiber orientation is the most influential fac-
tor in determining the creep characteristics (i. e., the
fibers do not creep but the matrix does). The laminae
orientation effects the linearity of the stress-strain rela-
tions, which will be important for rotors with biaxial
stress states such as the wide bar and the pseudo-isotropic
disk. However, from the foregoing it seems reasonable to
assume that the high-modulus composites, graphite and
boron, can provide satisfactory endurance for long-term.
loading.
- 95 -
-------
rHe JOHN. HOPKIMI UNIVItRSITY
APPLIED PHYSICS LABORATORY
kV11IIt e..11I8Q. ""'.YLA"O
Boller (Ref. 37) and others have reported that
glass composites are susceptible to stress-rupture and
creep in a manner analogous to their problems in dynamic
fatigue. Very recently, . Chiao and Moore (Ref. 39) pub-
lished an interim report on their tests of the stress-rup-
ture of S-glass/ epoxy strands at Lawrence Radiation Labo-
ratory using 1500 specimens. .
Tests are being conducted at room temperature
and 20 to 600/0 relative humidity in air at six different load
levels, with the three highest levels completed. The re-
sults of the first series of tests are shown in Fig. 4-12,
where the cumulative percentage of strands failed is
plotted versus time-to-failure for these three load levels.
The spread in the data clearly illustrates a stress rupture
problem with this material. The time-to-break at any
given load level scatters over three orders of magnitude
with a coefficient of variation over 1000/0, while the ulti-
mate tensile strength data were reported to have had very
little scatter with a coefficient of variation of only 3. 60/0.
The spread in the data suggests that the stress-
rupture may be produced by progressive corrosion from
moisture in the atmosphere, with some strands being de-
graded, more rapidly than others. A study that lends sup-
port to this hypothesis is one by Hanson (Ref. 40), who
has tested glass filament-wound pressure vessels in both
ambient and cryogenic environments. Figure 4-13 shows
time-to-failure for 13 S-glass/ epoxy cylinders, 11 under
ambient conditions and 2 in liquid nitrogen. Both cryo-
genic tests were halted as the result of test equipment
malfunctions, but they sustained periods unde r load far
in excess of the other cylinders. The data are ratioed to
the single-cycle burst strength at test temperature, which
takes into account the increase in ultimate-tensile strength
of the glass composite at low temperatures.
A recent survey by Weiderhorn (Ref. 41) reviews
the large body of knowledge that has been accumulated on
- 96 -
-------
TME .JOHNS MOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV~. SPRI....e; JoIIAIIt't'LAHD
- 9O-nrrr-TTTfrTTlTr-Tll
1'; % OF SPECIMENS FAILED
~ 85 1- 510305070909599100
o
...J
~ 80
~
-------
THE ~HNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
S'LVE"" SP"lfirIfG. W.--VLAND
environmental stress corrosion cracking of glass. This
well-referenced document clearly states that (a) the ulti-
mate strength of glass is directly related to the perfec-
tion of its surface and not the size of the specimen, as
was once believed; (b) phenomenal increases in strength
can be obtained by the removal of surface flaws (for ex-
ample, bulk glass can be improved from 5000 to 500 000
psi by chemical polishing with hydrofluoric acid, and
silica rods can be flame-polished to obtain strengths to 2
million psi); (c) despite the inert character of glass and
its use to resist chemical attack, the material is highly
susceptible to stress-corrosion cracking, known as static
fatigue; (d) this phenomenon is caused by water in the en-
vironment; (e) glass that is baked out and tested in vacuum
shows little fatigue, and similar results are obtained for
tests conducted in liquid nitrogen; (f) tests conducted in
water or air can result in static fatigue failures within
time intervals as short as 10 ms at high stress levels;
and (g) comparison of cyclic and static tests demonstrate
that the time to failure depends on the magnitude and total
duration of the load, but not its cyclic nature. Reference
41 notes that the most extensive study of static fatigue of
silica glass fibers was conducted by Proctor, Whitney,
and Johnson (Ref. 42), and data from their experiments
are shown in Fig. 4-14. Static fatigue was observed in
air, but not in the liquid nitrogen environment. The
fatigue effects noted for the fibers tested in vacuum was
attributed to residual moisture adsorbed on the glass sur-
face.
It is the authors' opinion that the foregoing data
and discussion on the fatigue characteristics of glass
fibers are encouraging with respect to the application to a
flywheel system environment. Problems may still exist
in composite materials of glass fibers and a resin matrix
because of excessive ma:tri~ deformation; however, it
seems clear that controlled processing, fabrication, and
environment can significantly reduce fatigue degradation
of these materials.
- 98 -
-------
THE "tOHNS HOPKINS UNIVERSrTV
APPLIED PHYSICS LABORATORY
SILYKIt SPltINC. "'.ltYL."'O
1500
N
E
E
a.
:':£
'"
'"
w
a:
I-
'"
1000
o
uJ
:J
a.
a.
«
500
o
10-2
Fig. 4-14
xx
x
xx xxx xX)()( X>CXJ0
o 00 00 0 00000:>
o 0 000
o 0
o 0
c
o
o
o
-'-V""~ .
. . ...........--~ .
. . ..................... - .
8. . . ..~ .... ...
... ~..a... ~ . .. .
. .. . ,. ~............. -. .
............. .
. """""""......-. - .
--
+ -
1 month 1 year
...
+
1 day
.
10°
102
TIME TO FRACTURE (minutes)
104
106
STATIC FATIGUE DATA FOR SILICA FIBERS, x IN VACUUM AT -196° C, 0 IN
VACUUM AT ROOM TEMPERATURE,. IN AIR AT ROOM TEMPERATURE
(REFS. 41,42)
- 99 -
-------
THE JOHNS t-tOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
StLVJ:" SPORING. ""'.YL,AND
4.4.4 LONGITUDINAL DIVERGENCE
The theoretical upper limit to energy storage in a
rod-type flywheel has been discussed by Brunelle (Ref. 21),
who has shown that a condition of inertio-elastic instability
exists for certain combinations of rotor tip speed, elastic
modulus, and material density. He has termed this condi-
tion longitudinal di vergence, and the critical tip speed for
divergence (RUJD) is given by the equation:
. 1/2
RUJ D = ('IT / 2) (gE m / pi)
(4-18)
For rotational speeds higher than the critical value (wD),
the rod elongation becomes divergent. Also, using Eq.
(3-2), the maximum tip speed compatible with the ulti-
mate strength of the ma terial can be written: .
1/2
RUJ . = (2g cr / p' ) .
max max
(4-19)
Equation (4-18) is plotted in Fig. 4-15, and the
area below and to the right of the curve represents the
region of longitudinal divergence. A given material can
be located on the plot by fixing its ordinate with the elastic
modulus/ density ratio and its abcissa using Eq. (4-19).
Points for graphite/ epoxy, S-glass/ epoxy, boron fila-
ments, and a future high-strength fused silica material
are shown. The indications are that there is no problem
with longitudinal divergence for the range of materials
that we are considering. It would be desirable, once the
creep characteristics of the candidate materials are de-
fined more accurately for vacuum use, to extend this di-
vergence criterion to consider visco-elastic behavior of
the material, which may establish more practical limits.
Brunelle also pointed out that the extension of the
rota ting rod adds to its kinetic energy, and this increase
can be formula ted as:
- 100 -
-------
THE JOHNS HOPMINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV(R S~"IHG W."YL.AND
c
CI)
o
w1-~
o
j:
ex:
a:
>-
...
in
z
w
o
o
...
ch
::::I
..J
::::I
o
o
~
u
...
C/'J
ex:
..J
w
7
----r ----
"V BORON FILAMENT
6
5
4
GRAPHITE/EPOXY
o
CRITICAL TIP SPEED
3
(E ) 1/2
rr m9
Rw = - -
o 2 p'
(REF. 21)
2
o FUTURE FUSED
SILICA
o GLASS/EPOXY
DIVERGENCE
REGION
o
o
234
MAXIMUM TIP SPEED, RWO (105 in/s)
5
Fig.4-15 LONGITUDINAL DIVERGENCE OF ROD-TYPE ROTORS
- 101 -
"
6
-------
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVER SP"ING. MA"YLAND
E + ~E
E
=
3(2k - sin 2k)
3 2
4 k cos k
(4-20)
where
. 2 2/
k = pI R c.u gE .
m
(4-21)
For a 30-inch-long glass/epoxy composite rod spinning
at 30 000 rpm, this yields a kinetic energy increase of
only 2%, and the effect would be even smaller for the
higher modulus materials. Therefore, it has been ne-
glected in all energy calculations presented herein.
4.4. 5 FUTURE IMPROVEMENTS IN MA TERIA LS, <
FABRICATION, AND DESIGN TECHNIQUES
A study of the predicted future improvements in
materials indicates that there may be many with strength-
to-density ratios (a / p') several times the values of the
best materials currently available. These findings are
in part corroborated by work the Russians are doing in.
the field of mechanical energy storage, wherein they fore-
cast future rotor specific energies of 200 to 300 W-h/lb
(Ref. 43). Significant improvements are expected with
composites of glass and graphite, boron filaments, bulk
glass, high-purity fused silica, and other new materials,
as discussed in the following paragraphs.
Fiberglass. Improvements in a / pI of unidirectional
fiberglass will result from improved glass formulations,
increased glass-to-resin ratios, and (perhaps most of all)
improved manufacturing and handling techniques. With
the present techniques, the strength of the glass fibers in
the composite seldom reaches 500/0 of the virgin fiber
strength for two principal reasons: (a) the fibers are
physically damaged during manufacturing, and (b) they
are chemically damaged by the presence of water during
the manufacture of the filament and in .the ambient en-
vironment. The Russians apparently have developed a
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"THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
9'L VI''' S.....NG. ....."'LANO
method of protecting the glass filament from both physical
damage and water damage by applying a protective coating
of epoxy/polysulfide at the instant the glass filament is
formed at the bushing during drawing (Ref. 44). They
claim that with this procedure they can make unidirectional
composites wherein 900/0 of the virgin strength of the glass
is usable in the laminate. It is generally agreed that
future glass fibers will have virgin strengths of 800 000
psi. If 90% of this can be recovered in a unidirectional
laminate with 750/0 fiber volume, the resulting laminate
strength would be 540 000 psi. This is twice the strength
currently achievable with S-glassl epoxy systems.
Graphite/Epoxy. The strength of currently avail-
able graphite filaments has steadily improved with at
least two manufacturers quoting values of 400 000 psi
(Ref. 34). Bowman and Branan (Ref. 45a) report that
laboratory-produced samples of filament have exceeded
500 000 psi, and that graphite whiskers have been pro-
duced with strengths on the order of 3 million psi. Fabri-
cators are now beginning to talk about graphite/epoxy
laminates with tensile strengths of 250 000 psi, compared
to the 200 000 psi level seen in most data books. This
improvement is believed to result from the use of a super-
ior matrix material to increase the interlaminar shear
strength, which has been one of the weakest links in the
graphite / epoxy system. It seems reasonable to predict
at least a 50% increase in performance over current
laminates, including both fiber and matrix improvements.
The price of high-strength graphite fiber is", 50 times
the price of S-glass fiber, but it is expected to diminish
rapidly in future years as the rate of production increases
and plants are opened in different countries. Eventually
prices are expected to be less than $10/Ib. .
Boron. Line and Henderson (Ref. 45b) report that
the measured strength capability of pure boron is three
times the current production average of 450 000 psi for
the $250/1b boron/tungsten filament. Future boron fila-
ments are expected to be stronger and lower in cost,
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THE JOHNS HOP)( INS UNIVERSITY
APPLIED PHYSICS LABORATORY
g'LV'!- SfIIJtIHG ""''''TLAND
$100/ lb. The cost reduction is expected to result from a
faster plating method, plus the substitution of a silica sub-
strate for the more expensive and 10 times heavier tung-
sten substrate currently used. Thus, filament strength
may approach 800 000 psi while density is reduced to
,.... 0.083 (instead of the present 0.093), resulting in a 100%
improvement in (j / d.
A distinct advantage of boron is that the filaments
are large enough and stiff enough so that they can be used
alone without a matrix, which becomes an enormous advan-
tage in the brush type-configurations. For example, an
existing boron-magnesium composite only has a strength
of 300 000 psi, whereas the boron alone would have a
strength of 450 000 psi average, a 50% improvement.
Bulk Glass. About 10 years ago laboratory tests
demonstrated that common soda glass could be used to
make rods with a strength of 500 000 psi (Ref. 46) using
acid to etch away the micro-cracks on the surfaces. As
in any of the filament mater.ials, the principal reason the
finished product is only about 1/4 to 1/3 the theoretical
strength is because of the surface cracks and impurities.
In the case of the bulk glass rods these surface discon-
tinuities are smoothed out by the acid etch. High strength
can also be obtained by chemically treating the surface to
induce a compressive stress of greater magnitude than
the expected tensile stresses. Perry (Ref. 47) has fore-
cast strengths of 300 000 psi by 1980 and up to 500 000
psi in the future. This technique would be applicable to
a solid disk rotor.
Bulk glass has several intrinsic adval!tages over
fiberglass, which warrants interest. First~ the rods can
be used as is, without the need for a matrix rm. terial to
complicate the installation and reduce (j / p'. Its cost
should be much less than fiberglass/epoxy, because its
diameter is 100 times that of the glass fibers, which
means less assembly and handling is required, and
handling is much easier. .
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SIl,...,I:A SPR'''''G ""."YUJrojO
The glass rods would be made much the same as
the high strength fiberglass. They would be protected by
a polymer coating instantly when made, and, of course,
the flywheel vacuum environment would protect against
water damage, as well as against further mechanical
damage. The raw material from which these rods would
be made costs on the order of 15t/lb. Thus, the bulk
glass rods offer the potential of cr I pI of 5 to 9 million
(inch) for the least cost among the common materials
available.
Quartz and Fused Silica. High-purity, or high-
silica glass is generally agreed to be that which contains
95%+ Si02' Natural quartz has an even higher purity,
having about 99. 95% Si02' High-silica glass is chiefly
made by leaching impurities out of ordinary glass by ap-
propriate acid rinses. The leaching also reduces the
weight of the remaining glass, which can be as low as
O. 063 lbl in3, compared with O. 09 for S-glass. Quartz
is slightly heavier at O. .079 lb/in3.
Hillig of General Electric (Ref. 48) and a group of
scientists from Rolls Royce, Ltd, have tested fused
silica rods to greater than 1 million psi (some tests
approached 2 million psi). The theoretical strength of
this material is 4 800 000 psi, and it is reasonable to ex-
pect that future applications of high silica rods may dem-
onstrate strengths in excess of 2 million psi.
Other New Materials. New organic fibers are be-
ing produced that offer combinations of high strength and
high density. DuPont is in the process of documenting
data on a proprietary fiber material designated PRD49
Type 1, that is reported to have a simple filament cr I pI
of 7 to 10 million (inch) and an elastic modulus of 20 mil-
lion psi (3 to 4 times that of S-glass) (Ref. 49). This
material offers the promise of high energy storage per-
formance and good fatigue resistance due to its high
modulus. DuPont projects costs to $20/lb as demand in-
creases. In addit~on to new organic fibers, a large
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THE JOHNS ~O~KINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV'I:" 5~"ING. "''''''YLAND
variety of whisker-based materials should be applicable
to various superflywheel configurations. Milewski (Ref.
45c) projects widespread use of these materials, particu-
larly in conjunction with more conventional fibers to form
"whiskerized" systems. Plants having a capacity of
200 000 lb/yr are on the drawing board, and whisker
costs are projected at less than $5/lb for larger volumes.
Other Sources of Improvement. Along with im-
provements in the basic materials and their fabrication,
we can expect improvements in our ability to analyze the
composite materials and select allowable stresses that
will result in efficient, reliable, and safe structures. It
has been seen that considerable scatter exists in mate-
rials'property data (Figs. 4-10, -11, -12, and -13 for
example), and a simple factor-of-safety approach to de-
sign is no longer appropriate. However, using statistical
methods, reasonable reliability limits can be obtained on
properties such as fatigue life, stress endurance, and
ultimate strength. A s an example, Weibull statistics can
be used to describe the distribution of the measured data
(Ref. 39). A very extensive treatment of Weibull statis-
tics in structural design applications is gi ven by De Salvo
(Ref. 50), who determines allowable material strengths
and reliability factors for several structural problems.
The flywheel life cycle shown in Fig. 4-9 combines
effects of cyclic fatigue with long-term stress-rupture.
Broutman and Sahu (Ref. 51) are developing methods to
predict damage to composite materials resulting from
cumulative effects of this type.
It must be emphasized that the failure process of
most composite materials is quite different than that of a
metallic material. In the case of metals, most of the life
is spent in developing the first flaw, and there is little or
no change in strength or stiffness during this period.
After the flaw develops it usually propagates rapidly and
the metal fails. By contrast, composite materials may
exhibit several modes of damage, some occurring early
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THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SR..vER s...NG. ""'''YLAHD
in life and progressing at a very low rate until failure.
The damage can include delamination, matrix crazing and
cracking, void growth, fiber failure, or a combination of
these. These differences are shown qualitatively in Fig.
4-16 by Salkind (Ref. 36).
It is expected that composite materials will be
more damage-tolerant than metals. They exhibit good
fracture toughness and. unlike metals, increase in frac-
ture toughness with increasing tensile strength (Ref. 36).
The inspection threshold for composites occurs much
earlier in the life cycle and occupies a wider band; for
metals there may be little time between the threshold of
inspection and the propagation to fracture, requiring
more frequent inspections to assure reliability and safety.
In composites the stiffness oft~n changes during the life
cycle, and this offers a promising method of assessing
remaining life by nondestructively determining the static
resonances or dynamic damping of the structure.
4.5 VEHICULAR INSTALLATION
There are a number of concepts available for in-
stalling the propulsion equipment in each of the vehicles,
but this program has not dealt with this subject in much
detail, since the system factors described above have yet
to be selected. An example for a commuter car is pre-
sented to illustrate the fact that a flywheel hybrid propul-
sion system can be adapted to common vehicles in a
straightforward manner. Gyroscopic effects for large
flywheels also will require considerable study, and the
results of only a brief examination are presented here.
4.5.1 HEAT ENERGY/FLYWHEEL HYBRID PROPUL-
SION IN A COMMUTER CA R
Figure 4 -1 7 shows the general deta Us of a hybrid
propulsion system for a commuter car. This car has a
curb weight of only 1400 pounds, and the loaded weight
of 1700 pounds accounts for the driver and one passenger.
This vehicle. is among those studied in Section 5. .
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THE ~ HOPKINS UHIVI:RtlITY
APPLIED PHYSICS LABORATORY
....v.... SP.,NG. MARYLAND
DAMAGE SI ZE
METALS
CRACK LENGTH
COMPOSITES
BROKEN FIBERS
DELAMINATION
MATRIX CRACKING
DE BONDS
VOIDS
COMPOSITE CRACKING
FRACTURE
!{
~"(~S r
O~v(ft
C FRACTURE
CRITICAL
DAMAGE
SIZE
METALS
FATIGUE CYCLES OR TIME
PROPAGATION
Fig.4-16 CHARACTERISTICS OF FAILURE MECHANISMS FOR METALS AND COMPOSITE
MATERIALS (FROM REF. 36)
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CURB WEIGHT:
lOADED WEIGHT:
HEAT ENGINE:
Fl YWHEEl SYSTEM:
1400 POUNDS
1700 POUNDS
32 BHP
70 POUND ROTOR
2 kW-h
......
o
CD
HEAT ENGINE
I
I
I
.1
I
. I
--- I
I' --J
(
I
I
I .
I
I
I
" CLUTCH
HATCH BACK DOOR
>
"
"..
rx
-,.
..PI",
~ 00
< 11 x
; J: :
I~x
anj
. 1/1 i
Erlll
; )10 c:
< ID Z
to"
Z ::0 ..
" > I
-t :;
0<
::0
-<
\
\
\
I
I
I
LUGGAGE DECK /
----r\..-----""
,-- ------,
I t SPARE TIRE I
L...:....--=====.-~-
CONTINUOUSL Y
VARIABLE
TRANSMISSION
AND DIFFERENTIAL
Fig.4-17 HEAT ENGINE/FL YWHEEL HYBRID COMMUTER CAR
-------
rH£ .JOHNS HOPKINS UNIVItROITY
APPLIED PHYSICS LABORATORY
Sn vUt ""'NO, M","VLAHD
For a series power train (discussed later in Sec-
tion 5.4.4 and shown schematically in Fig. 5-10) it is
desirable to locate the flywheel, gear box, and transmis-
sion in close proximity. This can be accomplished as
shown in Fig. 4-17 by placing the heat engine and asso-
c~ated equipment in the front of the car and the flywheel-
transmission system in the rear, essentially equalizing
the weight distribution. The continuously variable trans-
mission is integrated with the differential, and all of the
powertrain components in the rear of the car are rigidly
connected to one another and are shock-mounted on the
sprung mass, the rear wheels being independently sus-
pended. This arrangement will provide space for a disk
flywheel with Eo = 2 kW-h or a bar of approximately 1. 5
kW-h, though the use of a system with this amount of
energy will depend upon the ability to contain the rotor,
acceptable vehicle handling characteristics, and the de-
velopment of low-friction seals and bearings.
4.5. 2 FLYWHEEL GYROSCOPIC TORQUE
When the axis of a rotating element is pitched, a
torque is produced perpendicular to the axis of rotation
and the plane of the pitch according to the formula:
T = lu.>0 ,
(4-22)
Since E = Iw2/2, Eg. (4-22)
where 0 is the pitch rate.
may be written:
T = 2E0/w.
(4-23)
This equation shows that torque increases with the level of
flywheel system energy (vehicular operational criteria)
and pitch rate (a function of the vehicle suspension and
road characteristics), but reduces as rotor speed in-
creases. Therefore, all other things being equal, a fly-
wheel configuration with low inertia and operating at high
rpm will produce lower gyroscopic torques than a slower,
high-inertia system.
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THE .IOHN1S HOfII'KJNS UNiVERSITY
APPLIED PHYSICS LABORATORY
8k.VI(. 5~ft1HG. ....-n.ANO
Nevertheless, an attempt was made to assess the
degree of the problem associated with gyroscopic forces.
Dynamic data for a typical family car (a 1963 Ford Galaxie
4-door sedan) were obtained from McHenry (Ref. 52) and
used as inputs to the APL vehicle dynamics program
(APLDYN). This vehicle was assumed to have a 5 kW-h
flywheel system (164-pound rotor at...... 30 W-h/lb: see
Table 5-10b). The vehicle mass remained the same,
assuming that flywheel system weight additions were
balanced by heat engine and other weight reductions. The
flywheel system was (for simplicity) hard-mounted to the
sprung mass.
The vehicle was programmed over a 3~inch high,
transverse bump in the roadbed while traveling at 45 mph.
The bump profile and the resulting displacements are
shown in Fig. 4-18. In the upper graph, the dashed lines
are for a nonrotating flywheel, and it is seen that there is
no roll induced by the transverse bump. When the fly-
wheel is spinning at 30 000 rpm to produce 5 kW-h, the
pitching of the vehicle induces a roll component nearly
twice as large as the pitch. The vertical deflections are
the same for both cases. The maximum roll angle is
only 20.
It should be emphasized that these results arc
illustrative of the problem but not necessarily quantita,..
tively relevant. For instance, no shock mounting was
provided between the flywheel system and the sprung mass,
and this would be an obvious way to reduce flywheel system
rates. Also, the particular vehicle does not appear to
have much damping in the roll mode, and it would be ex-
pected that a flywheel-tailored suspension system would
improve the rideability. The bump is severe at this speed,
producing a pitch rate of 20 deg/ s. Rice (Ref. 53) notes
that pitch rates in excess of 20 deg/ s are rarely encoun-
tered on real-life roadways.
The peak value of the flywheel torque is 4000 ft-lb,
resulting in a radial bearing load of...... 4000 pounds. Other
- 111 -
-------
.......
.......
N
2.0 I
ROll
-- FLYWHEEL AT REST
1.5 - FL YWHEEL WITH 5 kW-h
1.0
-......
0.5 ............
"''''''''
......",
'"
o
-0.5
-1.0
-1.5
-2.0
45 MPH
-2.5 ==9 5 INCHES
~ L~ r-- VERTICAL DEFLECTION
3 ~ 0.. 3-1/2 INCHES ~ OF CG
REAR WHEELS
~ ~ 77"f 45° 4; / / HIT BUMP
2 1-1-
z-
OI
a:
u..'
0
-1
0.1 0.2 0.3 0.4 0.5 0.6
TIME (secondsl
>
"0
"0...
r :r
..Pi:
i' 0 I;)
< 1J :r
: I ~
!~6
- - 11
~ n"
. (II i
J:r"'
: » c:
~ ~ ~
z ::c ...
o > :
4 -
o ~
::0
-<
-.;
~
0>'
II>
~
W
..J
(,:J
Z
.t:.
'"
.S
z
o
t;
W
..J
u..
W
o
Fig.4-18 EXAMPLE OF FAMILY CAR ENCOUNTERING A SEVERE ROADWAY OBSTACLE
AT 45 MPH WITH 5 kW-h HARD-MOUNTED FLYWHEEL
-------
THE JOHNS HOPKINS UNIV£JtSIT'f'
APPLIED PHYSICS LABORATORY
$ILvt;" S~.I"'G- "'''''YL.AND
studies using this dynamic program have verified that the
induced roll is linear with respect to the flywheel mo-
mentum. Computer programs at Cornell Aeronautical
Laboratory, Inc. have the capability of assessing the
problem of flywheel gyroscopic torques with the use of
human response factors incorporated in the programs
(Ref. 52).
4.6 CLOSURE
Several flywheel rotor configurations offer the po-
tential of achieving high specific energy by using filamen-
tary or composite materials. These rotors are suffi-
ciently compact for use in vehicular propulsion systems.
System components such as bearings, seals, and
vacuum equipment demand development in order to realize
the full potential of the superflywheel concept.
Composite materials are rapidly emerging as prime
candidates for high-performance structural systems.
Their characteristics are improving and becoming more
reliable while costs are decreasing (Ref. 54). They have
the unique ability to match reinforcement to the structural
load paths. The apparently favorable aspects of operating
in a vacuum environment (Refs. 41 and 42) need further
definition for they could open the way to the use of low-
cost glass materials in flywheel systems. In any event,
forecasts indicate that materials will be developed that
will have performance characteristics superior to our cur-
rent exploratory materials. Predictions of specific energy
storage several times the values assumed in these studies
have already been made (Ref. 43).
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THE X)HNS HO"K'NS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILYER "'.1"'0. ".RYLANO
5.
PRELIMINARY VEHICLE EVALUATION STUDIES
5. 1 INTRODUCTION
The objective of the analytical evaluation studies
that are presented in this section was to investigate the
feasibility of using flywheels alone or in combination with
heat engines to reduce HC (hydrocarbon), CO (carbon
monoxide), and NOx (oxides of nitrogen) emissions from
vehicles, while essentially retaining current vehicle per-
formance as defined in criteria furnished by OA P at the
start of the program (July 1970). It should be empha-
sized that the purpose was to explore, in a broad ~ense,
the potential of a flywheel-only or flywheel-hybrid pro-
pulsion system for meeting this objective, and that most
of the inputs to the analysis were based on forecast im-
provements in flywheel system technology. Indeed, the
analysis effort conducted at APL was intended to be com-
plementary to the Lockheed effort (Refs. 2 and 12) in that
it would look toward future rotor materials and configura-
tions for advanced flywheels for application in the 1980
period, while the Lockheed work emphasized state-of-the-
art materials and an early prototype evaluation.
The studies are based on certain basic assumptions
of operating modes, engine emissions characteristics,
and flywheel system performance. First of all, it was
assumed that there was merit in a capability to operate
the vehicle in an emission-free mode all or part of the
time. This assumption is explicit in the flywheel-only
evaluation where the vehicle is charged between trips by
an outside power source, but the authors believe it to
have merit for the flywheel-hybrid case whereby a ve-
hicle with a large, high-specific-energy flywheel could
operate in an emission-free mode for a significant range
in the central business district or other severely polluted
regions of a large metropolitan area. The possible need
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THE JOHNS HOPKINS UNIVERSITY
APPLiED PHYSICS LABORATORY
S'LVER S""ING. "'''RYLAND
for limiting or banning emission-producing vehicles from
such areas has been discussed by others (Ref. 3), and the
ability for a flywheel-hybrid vehicle to provide such an
emission-free mode is a feature well worth considering.
Consistent with the above idea is the further
assumption of a serie~-type power train for a flywheel-
hybrid system whereby the heat engine would be operated
in an on-off mode; that is, all energy required to operate
the vehicle would come from the flywheel and the engine
would remain off while the wheel discharged 75% of its
stored energy (2: 1 speed range), at which time the engine
would be activated to recharge the flywheel to its maxi-
mum rated energy level before shutting down again. For
urban driving the engine would operate ......15 to 30% of the
time, depending on the type of vehicle and its driving re-
quirements. Alternatively, a hybrid vehicle could use a
parallel-type-power train in which the engine operated
continuously to power the vehicle with a much smaller fly-
wheel providing supplemental power during acceleration
(Ref. 12). The size of the heat engine would not be af...,
fected appreciably by the choice between these two ap-
proaches, since it must be large enough to provide con-
tinuous power for cruise conditions in both cases, and
cruise power is not strongly affected by modest weight
changes. .
The scope of this program did not include any
original work on emissions from heat engines, and OAP
supplied curves of emissions versus horsepower for each
type of engine (spark-ignition, diesel, gas turbine, and
Rankine cycle) to be considered in the hybrid studies.
These data were very preliminary and do not include
possible gains that may be achievable by optimizing a
heat engine to run only under the constant-load, limited-
speed-range conditions associated with on-off operation
for flywheel-charging in a hybrid system. No credit is
taken for such gains in the emission ratios presented
later, but the authors feel that they should be substantial.
In Ref. 55, 60% reductions in HC and CO and a 25%
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THI[ .IOH- HOPkiNS UN'_ITY
APPLIED PHYSICS LABORATORY
-".. _. ....~
reduction in NOx were obtained for an electric hybrid
"Minicar," and the first recommendation of that report
was: "Since the ICE (internal combustion engine) did not
operate at extremely high A IF ratios during the hybrid
mode, these tests should be repeated using an engine that
has been developed on a test stand for this type of opera-
tion." In Ref. 56 an appreciable effect of engine speed
on NOx emission from diesel engines was found, and this
effect of engine speed remained when water injection'
(which sharply reduced NOx) was used.
On the other hand, an on-off mode of operation
will result in start-up emission penalties, though data
have not been published on these effects for a typical 20-
minute cooldown period between engine charge cycles.
An allowance for HC and CO emission penalties has been
included in the analysis, but the effect of multiple starts
on NOx emission has been assumed to be negligible. The
large flywheel would be expected to have plenty of reserve
energy after overnight parking to use in restarting the
cold engine, and with flywheel "cranking' and properly
sequenced (computer-controlled) fuel injection, emission
penalties for the initial cold-start may also be reduced.
The evaluation studies were started at the same
time as the experimental, proof-of-principle, test pro-
gram began and, in fact, they were essentially com-
pleted at a time when only five of 41 rod tests (reported
in Section 3) had been made. Furthermore, studies of
rotor configurations, seals, and bearings, and contain-
ment had yet to be made. The assumptions on flywheel
system performance that were used in the evaluation
studies were not, therefore, based on test results or
studies of system components, but rather on the type of
system the authors believed achievable through active
development and the type of system that would be re-
quired to permit significant emission-free driving range.
The basic assumptions follow:
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1'HE X>HNS H~INS UNIVERSITY
APPLIED PHYSICS LABORATORY
Sla.y~. ~HG. M"-YLA,HD
1.
A rated specific energy capability of 32
W-h/lb of rotor material (at maximum rpm)
independent of rotor size.
2.
A 2: 1 operating speed range that will permit
withdrawal of 75% of the rated energy of the
system (24 W-h/lb per cycle).
3.
A disk-like rotor shape and a density equiva-
lent to a glass composite material for volume
considerations.
4.
A favorable failure mode that will permit a
containment case of nominal weight (equiva-
lent in weight to 3/8-inch of armor steel).
5.
Very low parasitic losses (windage and bear-
ing/ seal friction) which are negligible com-
pared to vehicle power requirements. .
6.
A weight allowance for the flywheel rotor
hub, bearings, and seals equivalent to 10%
of the rotor weight.
Results of the experimental program (Section 3) .
and the configuration and component studies (Section 4)
point to some problems that must be solved in order to
achieve the assumed performance; at the same time, how-
ever, projected increases in materials strength and re-
liability offer hope of realizing these characteristics for
use by 1980 if a vigorous development program is under-
taken. As a single example, researchers at the Naval
Ordnance Laboratory, White Oak, Md., forecast (Ref. 47)
the availability of surface-compressed silicate glass with
a strength of 300 000 psi by 1980. If this material were
used in a shaped disk rotor it would provide a compact
flywheel system with an ultimate specific energy density
of 96 W-h/lb of rotor material, allowing a factor of safety
of three compared to the rated value assumed in these
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THK -... -.... UHIVl:88m
APPLIED PHYSICS-L.ABOftATORY
........ --- ....-...-
studies. The radially fanned brush configuration discussed
in Section 4. 2 could take advantage of even more advanced
glass-like materiais (e. g., fused silica), if they become
economically feasible, and might produce an even safer
design (because of the favorable failure mode already
de~onstrated; see Section 3.3) with the rated specific
ene~gy assumed here. -
The flywheel system assumptions above have very
little direct effect on the calculated level of vehicle emis-
sions; however, the value of the on-off mode of operation
with respect to flywheel-only range would be diminished
if the usable rotor specific energy achieved were very far
below the assumed 32 W-h/lb, or the required net in-
crease in vehicle weight to assure rotor containment far
exceeded the estimates used. In such a case, the parallel
hybrid mode (Ref. 12) might be chosen, permitting use
of a flywheel of only 1/10 to 1/4 the weight considered
herein for any particular application while giving up the
possibility of appreciable emission-free range.
5.2 POWERPLANTS FOR THE HYBRID-FLYWHEEL
VEHICLES
This section presents. the characteristics of the
four heat engines considered in the flywheel-hybrid
studies:
1.
The spark..ignition, four-stroke Otto cycle
- engine (SIE),
2.
The compression-ignition, four-stroke
Diesel engine (CIE),
3.
The open-cycle gas turbine Brayton cycle
engine (GTE), and
4.
The steam Rankine cycle engine (SRE).
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THE JC»tNS HO"I(I...8 UNIVERSITY
APPLIED PHYSICS LABORATORY
SlLVlllit .",ItG. NAIitYLAND
..
For each, the ideal cycle efficiency, configuration, and
current characteristics are briefly'descz:'ibed, and, since
brake specific fuel.9pn#)Umption (bsfc, lbm/bhp-h) is In-
versely pr~portioqal to 'thermal. efficiencY,.11t, 'the maJor'
parameters affectiIjg,11i. are discussed., '1'hen,theemi,ssion
estimates supplied by the OAP are presepted. Finally,
the two performance parameters required for the analy-
sis, the ratio of specific weight to brake horsepower ratio
(lb I bhp), and the bsfc are. covered.
5. 2. lOTTO (SIE) CYCLE
The ideal Otto cycle is composed 6~ isentropic
compression ,and expansion with constant':'volume heat
addition and reJecfion (Fig. 5 -la). Its th~'rmal efficiency
(Fig. 5-1a) is given'by: '
11 =1-rl-y
tideal v'
(5-1)
where r v is the adiabatic compression ratio and y is the
ratio of specific heats. Increasing rv beyond 10 yields
only small improvements in 17tideal' which is theoreti-
cally independent of the load. A carburetor supplies a
fuel-air mixture to the engine intake at a relatively con-
stant fuell air ratio not far from stoichiometric. Engine
output (load) is controlled by varying (throttling) the air
flow. Combustion efficiencies are high (..... 98%). Average
cylinder temperatures are high, generally 5000oR, and
the combustion process can be described as a flame propa-
gating through the mixture. Final combustion pressures
are generally near 1000 psia, as the combustion is essen-
tially completed at constant volume before expansion be-
gins.
The engine, at a fixed throttle setting, delivers a
relati vely constant torque, and its output is roughly pro-
portional to en'gine speed (rpm). A typical (Ref. 57) wide-
open throttle (WOT) performance map is shown in Fig.
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THE .IOHNS ~INS UNI_'TY
APPLIED PHYSICS LABORATORY
.'LV." ~NG ....IItYLAND
la} OTTO ISlE)
(b) OIESEL (CIE)
J
2
3
w
a:
~
e(
a:
w
~
::E
w
I-
w
a:
::>
l-
e(
a:
w
Il.
::E
w
I-
2
4
ENTROPY ENTROPY
80
70 r=1
r=2
60
~ r=6
50 ~
.;- .;-
40
30
0 5 10 15
ADIABATIC COMPRESSION RATIO
20
8 12 16 20 24
ADIABATIC COMPRESSION RATIO
FOUR-CYCLE OTTO OR DIESEL
INT AKE IGNITION EXHAUST
VALVE VALVE
OPEN 111\\ OPEN
o
CONNECTING ROD
~ CRANKSHAFT
1
E.ND OF
EXHAUST
START OF
MIXTURE
INT AKE
1-2
START OF
COMPRESSION
2-3
HEAT
ADDITION
4
START OF
EXHAUST
Fig. 5-1 IDEAL CYCLES (T-S DIAGRAMS). IDEAL THERMAL EFFICIENCIES (TIt) AND
SIMPLE CONFIGURATIONS OF HEAT ENGINES .
- 121 -
\ 'p~
-------
THE X)HN$ HOPIUNS UN1Vl:RSITV
APPLIED p~.. .;, LABORATORY
StLv." SP1ttNG. MARYLAND
iC' BRAYTON (GTE) (d) RANKINE (SREI
3
3
w w
a: II:
:I ::>
..... .....
4; 4 4;
a: II:
~ 2 w
Q,. P=C
~ ~
W W
..... .....
ENTROPY
60
fir = 0.8
*
- 40
...
I:"
fir = HEAT EXCHANGE R
EFFECTIVENESS,
Ea. (5-4)
~
...
""
en
w
u
z
w
U
u..
u.
W
...J
4;
15 ~
a:
w
J:
.....
20
o
5 10
ADIABATIC COMPRESSION RATIO
SINGLE-SHAFT GAS TURBINE
CYCLE WITH REGENERATOR
REGENERATOR
COMPRESSOR
TURBINE
ENTROPY
45 T of T of
3, 4,
_.....----- 1000 70
--
--
.," .
,
,
.I'
/
35 I
1000 12\2
700
26
15
o
500
1000
1500
P2-3, BOILER PRESSURE (psis)
SIMPLE RANKINE CYCLE; EXPANDER IS EITHER
TURBINE OR RECIPROCATOR
2
PUMP
Fig. 5-' (Cont'd) IDEAL CYCLES n-S DIAGRAMS}, IDEAL THERMAL EFFICIENCIES (1}t) AND.
SIMPLE CONFIGURATIONS OF HEAT ENGINES . . .
- 122 -
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THE JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
S'LVI;A SPRING. ""'RYLAND
5-2a. The SIE characteristics normally quoted are the
maximum values of bhp and torque (at the output shaft)
and the minimum value of bsfc for the WOT conditions.
However, the engine seldom operates at those conditions
and is, in fact, not capable of sustained operation there;
the bhPmax indicates instead the acceleration capability
of the engine. A performance map of a six-cylinder SIE
(Ref. 58) for four throttle angle settings (800 throttle is
the WOT) is shown in Fig. 5-2b. Also shown, by a plus,
is the operating point for a 4500-pound vehicle cruising at
60 mph. The minimum bsfc curve generally corresponds
closely to the WOT curve, and the bsfc in<::rease (1]t de-
creases) as the throttle is closed. A s evident from the
60-mph point, the SIE generally is operated at relatively
low load; it may be operated at less than 10% full load for
90% of its life (Ref. 59).
Most of the current SIE's for vehicle application
(Ref. 60) use 4, 6, or 8 cylinders in in-line, opposed, or
V -type cylinder arrangements. Compression ratios
range from 8.3 to 11. 3; maximum powers from 90 to -160
bhp; and peak rotational speeds, from 4000 to 6000 rpm.
5. 2. 2 DIESEL ENGINE (CIE)
The ideal CIE cycle is characterized by isentropic
compression and expansion with constant-pressure heat
addition and constant-volume heat rejection (Fig. 5-1b).
For this cycle, 1]to 1 (Fig. 5-lb) is influenced by the
Idea "
compression ratio r and a parameter variously termed
the "fuel cutoff ra tioY; or "isentropic ratio" r, defined
as the heat-addition temperature ratio, r == '1'3/'1'2:
1] = 1 - r 1-y [r1-y ly(r-l)] .
t.d "I v
I ea
(5"- 2)
Thus, 1]tod" , differs from that for the Otto cycle by the
leaL
bracketed term in Eq. (5 -2), which is always greater
- 123 -
i -
I
-------
2000 3000
ENGINE SPEED (rpm)
(b) TORQUE, POWER, AND SPEED VERSUS THROTTLE ANGLE
THE .IOHNB HOPtCINS UNIVERSITY
APPLIED PHYSICS LABORATORY
_va. SPlhNQ.. MARYLAND
3: 120
IX)
280
240
200
:D
~
:= 160
w
::J
o
a:
o
....
w 120
~
<
a:
IX)
80
40
00
220
200
:.
160
80
40
0,6
u
0.5 ~
0.4
o
6000
40°
1000
4000
5000
Fig.5-2 SPARK-IGNITION ENGINE CHARACTERISTICS
- 124 -
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THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SlL.VER Sfl'FtING. M""YLANO
than one and is related to the load (i. e. , . heat addition).
For the equivalent rv the SI cycle is more efficient than
the CI cycle; however, in practice r v for the ClE is 15 to
20 as compared to 8-10 for the SIE, so that ClE's gen-
erally have the lower bsfc's.
Mechanically, the 4-cycle arrangement in Fig.
5 -1a also is used for the ClEo A ir only is inducted
through the intake valve (the air supply is unthrottled)
with fuel being injected into the cylinder at the end of the
compression stroke. The output is controlled by varying
the amount of fuel injected. Combustion is initiated by
self-ignition as a result of the high r v. . The combustible
mixture is heterogeneous, and the combustion process
can be described as one of localized burning at a number
of points (i. e., wherever the fuel is) throughout the cyl-
inder. The localized burning probably is at nearly
stoichiometric conditions although the overall air/fuel
ratios are quite lean, varying from 100 at idle to 20 at
full load.
The CIE is built heavier than the SIE because its
more rapid pressure rise results in higher stresses and
vibration (final pressures in the two engines are essen-
tially equivalent). It also has a higher initial cost be-
cause of its fuel injection system and its design for dura-
bility. For industrial vehicles its high initial cost is out-
weighed by its lower operating and maintenance costs.
Its marine use is attributed primarily to its lower fire
hazard (hence, lower insurance costs) because of the use
of less volatile fuels (Ref. 57). Its tendency to smoke can
be eliminated by proper fuel injector adjustment, but its
objectionable odor remains a problem (Ref. 6).
Current "off-the-shelf" ClE's (Ref. 60) have from
1 to 18 cylinders and are rated from 8 to 400 bhp. Com-
pression ratios vary from 10 to 34 with maximum engine
speeds up to 4200 rpm. Over 400 models are available.
Only eight production passenger cars (all European) are
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THE JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
SILV£~ SPAtNG. W".YL,.AND
offered with CIE' s. 1 The Mercedes Benz model 200 pas-
senger car can be purchased with a CIE (model 200D) or
SIE (model 200). Both are 4-cylinder, in-line engines,
and they have equal displacements. The CIE is rated at
65 bhp at 4200 rpm; the SIE, 116 bhp at 5000 rpm. The
CIE-powered car is 150 pounds heavier, takes 46% longer
to pass a 50 mph vehicle (Ref. 61), and has a 20-mph
lower maximum speed (Ref. 62).
5. 2. 3 GAS TURBINE (GT) CYCLE
The GT (Brayton) (Fig. 5-1c) is composed of isen-
tropic compression and expansion with constant-pressure
heat addition and rejection. For the simple Brayton
cycle:
17t
ideal
1
= 1 --
8 .
8 = r (1'-1)/1' .
v
(5-3)
The GT cycle, for aircraft and vehicular applica-
tions, is generally an open cycle and consists, in its sim-
ple form, of a compressor and turbine mounted on a com-
mon shaft with a combustion chamber between them. En-
gine output is reduced by reducing the amount of fuel,
thereby resulting in a lower heat addition, a lower rota-
tional speed, and hence a decrease in r v and thus in
17t. per Eq. (5-3). It is this unfortunate characteristic,
Ideal
the increase in bsfc as the load is decreased, that has
stymied the acceptance of the open-cycle gas turbine for
vehicular use. To increase 17t at part load, the waste
heat in the exhaust gas (at temperature T4) is transferred
via a heat exchanger (Fig. 5-1c) to the compressor exit
(temperature T 2). Defining the heat exchanger effective-
ness 17r as the fraction of the temperature difference
transferred:
IThe Land Rover (Great Britain), the Volga Rover, and
MZMA-Scaldia (Soviet Union), Mercedes 200-D (Germany),
Peugeot-204 (France), and the ISUZU-Bellett 1800D, .
Datsun 2L130 and Nissara Cedric Q130 (Japan) (Refs. 60
and 62).
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THIE .JOHNS HOPKfN& UNIVERSfTY
APPLIED PHYSICS LABORATORY
SILYER SPRING. MARVLAND
Tlr == (T4 - T2) I(T4 - T2)
tran max
(5-4)
the ideal thermal efficiency (Fig. 5-5b) for the regenera-
ti ve Brayton cycle is:
[ ]-1
I 2.
.. 1 Tlr(T3 T1)-a
TIt. = (1 - a) 1 - T (T IT ) - a . ,
Ideal 3 1
(5-5)
where T 3 is the combustor exit temperature, and T 1 is
the freestream ambient temperature. When TI = 0, i. e. ,
no regeneration, Eq. (5-5) reduces to Eq. (5-3). For
rv>' 10, regeneration is ineffective (TIt drops in Fig. 5...1c
for Tlr = O. 8).
Two types of heat exchangers have been developed,
recuperative (stationary) and regenerative (rotary). The
latter type is smaller but suffers from sealing difficulties.
Heat exchangers increase the complexity, cost, weight,
and size oi the engine but improve the fuel economy (par-
ticularly at part load) and reduce the exhaust tempera-
tures and hence the turbine noise (Ref. 63). Effective-
ness ratios Tlr are as high as O. 90 (Ref. 64).
I
The combustor is normally a simple can with fuel
being injected, in a cone-shaped spray, into the primary
air that enters through holes in the canIs head-end dome.
The local fuel-air equivalence ratios (ER' s) are gen-
erally from O. 8 to 1. 2 in the primary combustion zone.
Secondary air is injected into the burned mixture through
larger holes to reduce the combustor exit temperature to
a level (,..,. 1700°F) dictated by turbine material limitations.
Resulting overall ER's range from as low as O. 05 at idle
to O. 20 at full load. Combustion efficiencies are gen-
erally high (98 to 99%). Considerable research has been
done on emissions (Refs. 65 through 73).
Over twenty firms (Ref. 74) have developed GTE's
for vehicular application over the past decade, but not
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THIT ,JOHNG HoPKINS UNIVI'RBI"TY -
APPLIED PHYSICS LABORATORY
OllVI." ."'"IHO. ".."L."O
until 1971 was a plan for mass-prC?duction for trucks
and buses announced (Ref. 75). Various cycle modifica-
tions have been used to improve part-load economy. In
addition to a heat exchanger, all vehicular units developed
to date use a separate turbine (the power turbine) mounted
on an independent shaft, so that the main turbine is not
strongly influenced by load variation. Intercooling be-
tween multiple compressor stages and reheat between
multiple turbines have also been used (e. g., Ford, Ref.
76). The power turbine has also been equipped with
variable blades (e. g., Chrysler, Ref. 77) in an effort to.
improve acceleration response and for engine braking.
Great care is taken to reduce weights of rotating members
to improve acceleration response (i. e., minimize inertia).
The GTE is strongly influenced by the ambient tempera-
ture T 1 - the output drops sharply as T1 is increased, be-
cause compressor work is increased and the net work/
turbine work ratio is low (Ref. 57). General Motors
Corp., for example, designs and rates their engine at
100°F.
An added problem to the development of a small
GTE is the effect of small scale on component efficiencies,
which decrease as size is decreased, due largely to the
greater surface-area/mass-flow ratio, which increases
friction loss. In addition, rotational speeds increase as
size decreases, resulting in smaller manufacturing toler-
ances on the rotating parts to reduce unbalancing forces
(Ref. 78). Compressors are, in general, of the single-
stage radial type with r v = 3 -4 and efficiencies near 800;0.
Compressor and power turbines are generally of the
axial type and have efficiencies near 85%.
Williams (Ref. 79) has stated that GTE's for auto-
mobiles could be developed for mass production in a form
suitable for public acceptance by 1978, but others have
said .1980 (Ref. 59).
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THE ..JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
Su.V(1It Spollt'HG ""''''f'LAHO
5. 2.4 RANKINE CYCLE
The ideal Rankine cycle is a closed thermodynamic
cycle with constant-pressure heat addition (boiler) and re-
jection (condenser) and isentropic compression (pump)
and expansion (reciprocater or turbine). The previous
cycles have been discussed in terms of their idealized
behavior, and the question of a working fluid did not ap-
pear, although it was assumed for the efficiency relation-
ships that the fluid was an ideal diatomic gas with a spe-
cific heat ratio y of 1. 4. The Rankine cycle, in con-
trast, depends strongly on the heat of vaporization of the
working fluid and the boiler and condenser temperatures.
Figure 5-1d shows the cycle on the TS diagram for a
fluid with the characteristic dome-shaped phase diagram
(e. g., water). The region to the left of the dome repre-
sents the liquid state; to the right, superheated vapor.
The region enclosed by the dome is the "wet mixture'"
region. Heat a.ddition occurs at constant pressure
(2-21-3'-3). The left edge of the domed curve is the
saturated liquid line; the right edge, the saturated vapor
line. Heat addition occurs from 4 to 1. The thermal
efficiency of the cycle is given in terms of enthalpies:
17t = (h3 - h2 - h4 + h1)/(h3 - h2) .
(5-6)
For steam as the working fluid (Ref. 80), the favorable
effects of higher- boiler pressure P3 and boiler tempera- .
ture T 3' and lower condenser temperature T 4 are shown
in Fig. 5-1d.
The steam engine found an automotive application
in 1769 in France (Ref. 81) and reached its heyday in the
United States half a century ago. In 1930 the Doble Corp.
discontinued production of its steam automobile and ended
the" steamer era. 11 Although a Senate Committee pro-
nounced the Rankine cycle engine a "satisfactory alterna-
tive" to the 81 engine in 1969 (Ref. 82), citing its low
emissions of pollutants, low cost, simplicity, low noise ,
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THE JOHNS HOPKINS UNIVEASIT'f
APPLIED PHYSICS LABORATORY
S.L vt:a gPO.ING. MA.YLAHD
acceptable performance, no transmission required. and
acceptable packagability for automobiles. it is. to date.
the least developed of the four power plants. Only one
(GM-SE 101) (Refs. 83 and 84) working and completely
installed unit has been reported in detail.
Referring to Fig. 5-1d. an external combustor heats
the boiler. which is normally of a once-through monotube
construction. The condenser is quite large in relation to
the radiator on the 81E or CIE. mainly because of the re-
quirement to dissipate nearly all of the waste heat (81E
and CIE radiators handle only 1/3 to 1/2 of the waste heat).
Condenser size depends strongly on the condenser tem-
perature T 4. Both size and l1t increase as T 4 is de-
creased. Incorporation of a condenser in standard auto-
mobile bodies requires enlargement of the front end. Con-
denser fan horsepower requirements are large ('" 1 7 hp).
The condenser represents a sizable fraction of the weight
and cost of the powerplant. and. if it is located where
automobile radiators usually are located. a protective
structure will ha ve to be incorporated because of its sus-
ceptibility to damage in a low speed collision1. The ex-
pander can be of the reciprocating or turbine type. The
majority of paper studies and experimental hardware pro-
grams have selected the reciprocating type (Ref. 85).
The General Motors Corp. steam automobile. GM
8E-101 (Refs. 83 and 84). incorporates power steering,
air conditioning, and a novel continuously variable trans-
mission (Toric). The general conclusions with respect
to emissions. fuel economy, weight, size, complexity,
reliability.and performance are discouraging. American
Oil Co. (Ref. 87). investigating the possible impact of the
steam powerplant on the petroleum industry. has concluded
1The vapor cycle engine developed by Minto and pres-
ently being developed by Datsun for scheduled production
in 1972 (Ref. 86) uses a rotary condenser that results
in a reduced size. The boiler is located under the pas-
senger compartment.
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THE .JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
SILV(R S".'HG. M..YL.HO
that "they [automotive steam propulsion systems] would
probably consume 50% more fuel than conventional gaso-
line engines giving the same vehicle performance. "
Thermo Electron, with support from OAP and the Ford
Motor Co., is attempting to develop an organic Rankine
cycle with a reciprocating engine for automobiles.
Thermo Electron originally developed a smaller organic
reciprocating engine for military application (Ref. 88).
A full-scale working unit has not yet been demonstrated,
and the results to date (Ref. 89) have involved analytic
studies, testing of part- scale components and wood mo~k-
ups. Unfortunately, none of the strong vocal advocates
of the Rankine cycle engine (Lear, Williams, Keen,
Minto, etc., Ref. 85), has adequately documented his
results in the open literature.
5. 2. 5 EMISSIONS
The primary emissions of present concern are un-
burned hydrocarbons (HC), carbon monoxide (CO), and
oxides of nitrogen (NOx). In general the HC and CO emis-
sions result from many factors (rich combustion, pre-
mature qur::nching by walls, insufficient reaction times,
and poor mixing) all resulting basically in incomplete
combustion. Consequently, their concentrations can be
reduced in many ways (thermal reactors, afterburners,
catalytic converters, etc.). The NOx (basically NO) prob-
lem is a different story. Theoretically calculations
based on equiiibrium assumptions lead to high concentra-
tions (...... 3000 ppm) in the combustion zone at stoichiometric
conditions and very small values upon completion of the
expansion to ambient pressures. However, the formation
and dissipation of NO is kinetically controlled (Refs. 66
and 90); the NO equilibrium is generally not attained in
the burning region because of the relatively slow NO for-
ward reactions (Refs. 66, 73, 91, and 92). The amount
that is formed is "frozen" - the reverse reactions cannot
occur quickly enough upon early dilution or expansion to
reduce the NO concentration. Current research is
~I
1,- ,
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rHE JOHNS HOt'kINS UNiVERSITY
APPLIED PHYSICS LABORATORY
8ILV.. "'"'"0 MII,ItVl.AND
therefore directed toward methods of decreasing the effec-
tive flame temperature and the residence time. Lowering
of the flame temperature via lean or rich mixtures and/ or
dilution by recycling exhaust gas lowers the amount of NO
formed (Refs. 66, 70, and 91). Rich mixtures, however,
result in increased concentrations of CO and HC. Very
lean mixtures result in combustion instability with the
attendant inefficient combustion and again increased CO
and HC concentrations.
The use of premixed, prevaporized air-fuel mix-
tures (Ref. 92) and special fuel injection and mixing con-
figurations (Ref. 93) tend to decrease NOx emissions by
allowing lean operation (Ref. 66). For the closed com-
bustors (SIE and CIE), research is directed toward cyl-
inder redesign (Ref. 94), more efficient mixing and, for
the SIE, preheated -prevaporized fuel prepara tion (Ref.
95). Add-on devices (e. g., catalytic converters) are
under intense development for use on current power-
plants; however, questions of durability and reliability
remain (Ref. 96). It is difficult to relate the many labora-
tory experimental studies to a mass-produced vehicle in-
stallation.
The lowest emission estimates for HC, CO, and
NOx supplied by OAp are shown in Fig. .5-3. We have
used the lowest curves supplied (based on claims for
manifold reactor, carburetor modification, recirculation,
thermal reactor, combustor redesign, and modern com-
bustor technology) because of the presently conceived
mode of operation (1. e., constant-speed, constant-load,
on-off mode) of the heat engine. coupled with the assump-
tion that this allows minimum emissions, and the expected
time of application (1975 or later). The data are given in
brake specific units, BSPE, lb pollutant/bhp-h. - An at-
tempt was made, via the open literature, to verify the
supplied values, but it became apparent that one could
'pick a number' and locate a piece of data to support it.
The OAP estimates supplied are interpreted as steady-
state data applicable to different size powerplants.
- 132 -
-------
1
3 x 10'"4
N 3 x 10-2
o
Z-
(I)~
5~
(I)~
W N
o 0
xl
o=.
~ [;'
C> Z
OW
ocCL.
....~
Z 3 x 10-4 0
THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
S'LYER ~ING. ""RYLAND
.c
Z--
011.
CDI
oc!!:!
« u
gJ
oc-
a u
>UT
Ill.
(f)
eD
w7::
0--
- a.
XI
OeD
Z'o
o u
~:8
Z-
o 0
CD U
ocw
«a.
u~
10-3
B
6-
----OTTO
DIESEL
4
STEAM
OTTO
2
10'"4
8
6
STEAM
-------
-GASTURSiNE
DIESEL
-------
4
2
LEGEND
OAP
AEROSPACE
10"5
5 x 10" 4
STEAM AND OTTO
2
10-2
8
6
2
DIESEL AND GAS TURBINE
DIESEL
OTTO
10-3
8
6
STEAM
OTTO
------....
GAS TURBINE
-____~~A.M
4
100 200
BRAKE HORSEPOWER
300
Fig.5-3 PROJECTIONS OF HC, CO, AND NOx (AS N02) EMISSIONS
- 133 -
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TM£ JOHNS HOPkiNS UNIVERSITY
APPLIED PHYSICS LABORATORY
StLVEIit ""NG. MAIIt"L"AND
Allowances for transient emissions resulting from
startup have been incorporated in the computer studies as
follows. The TECO data (Ref. 89), based on a continuous
combustor expe riment for a Rankine cycle power plant ,
were used for the factors for these transient penalties,
and the same factors were used for all four engines. The
steady-state values of HC and CO are increased by fac-
tors of 10 and 5, respectively, for a 10-second period.
During the startup the engine is fuel-rich and relatively
cold, therefore not modified for the startup period. These
assumptions, it must be remembered, represent only
crude estimates for lack of better data; some engines
used in this mode may do better, others worse.
An intensive survey has recently been completed
by Aerospace Corp. (Ref. 97) on the available, published
and unpublished information on exhaust pollutants from
various powerplants. Their 'projected values' also are
shown (bydashed curves) in Fig. 5-3 and are generally
markedly lower than the values supplied by OA P, except
for HC from the Otto engine. The Aerospace projections
assume a fixed-speed, fixed-load operation. .
The projections of emission characteristics, for
the four powerplants under consideration, appear to be
open to conjecture. Reference 56 presents data on ways
to reduce emissions from the diesel engine. including
engine speed effects, and some of these trends may apply
for the 8IE. Reference 92 gives optimistic projections for
the 8RE and GTE. The potential probably is there for
each type to meet the 1975-76 standards; whether this po-
tential can be achieved in a mass-produced automobile
for the life of the vehicle, at a cost and with performance
acceptable to the customer, remains to be shown. The
major automobile manufacturers apparently are follow-
ing the course of cleaning up the present 81 engine as
opposed to developing another powerplant.
5.2.6 ENGINE PERFORMANCE
The two performance parameters required for the
analytic studies of the hybrid system are the engine
- 134 -
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVER S~RI""G. MARYLANO
specific weight (lb/bhp) and the brake specific fuel con-
sumption bsfc (lb fuel/bhp-h). Since the SIE's are
rated by manufacturers at the maximum bhp, we have
reduced the published bhp ratings by 40% to arrive at
"continuous" ratings for Fig. 5-4a. The engine weight
does not include the exhaust system, radiator, battery,
or fuel tank. Data (Ref. 60) for the CIE's are shown in
Fig. 5-4b; since CIE's are normally rated on a "con-
tinuous" bhp basis, the published values were not modi-
fied. For each engine, only the engine weight is included.
The GT data (Refs. 64 and 74) in Fig. 5-4c are for
single-shaft, double-shaft, and double-shaft-with-heat-
exchanger units. For the GTE and SRE, the methods of
horsepower and engine weight rating have not been defined.
We have assumed that the horsepower ratings are on a .
"continuous" basis and that the weight includes the com-
plete engine except for battery and fuel tank. Data for steam
engines are sparse and difficult to assess because of a
lack of documentation. The available information (Hefs.
8:~, e5, fJ8, and 99) for experimental hardware and paper
study predictions is shown in Fig. 5 -4d. The curves in
Figs. 5-4a - 5-4d are being used in the analytic studies;
they a re replotted, for comparative purposes, in Fig. 5-5.
The curves for the diesel and Sl engines represent the'
lower bounds of the data and reflect the assumptions that
the lower specific weights represent better designs and
that powerplants designed for a hybrid vehicle (fixed-
load, relatively narrow speed range operation) will re-
sult in improved specific weights. For the Rankine cycle
engines the three points quoted by Lear and Minto fall be-
low the chosen curve. . The curve for the GT specific
weights is assumed to represent single shaft engines with-
out a heat exchanger. The effects of control devices ha ve
not been considered, since it has not as yet been decided
what control techniques are to be adopted. It should be
emphasized that the values represent bare engine horse-
powers and weights. (They are modified in the analysis
to include power and weight requirements of auxiliary
- 135 -
-------
THE JOHHIS HOPKINS UNIVI:"SITV
APPU£D PHYSICS LABORATORY
SILV,,, ~"ltotG. M."VLAHD
15
~
X
IX)
-
~
r- 0
o 10
w
~
U
u.
U
~ 5
II)
w
2
(:J
2
w
o
25
~
X
~ 20
:9
r-
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W
~ 15
u
u.
U
w
a-
Il)
w
2
t3 10
2
w
o
2
o
o
000 00 0
0000 g
00 0
&:> 00
o 0
f
(al FOUR-CYCLE SPARK IGNITION ENGINES
RATING: 0 CONTINUOUS BHP, SMALL ENGINES
o TRUCKS - 60% OF BARE ENGINE MAXIMUM BHP
;~
~~fC
i~@
008
o cg
C() 0
o
o
'0
o
o
GMC-396
o
(b) DIESEL ENGINES
o
o
o
VEGA a
"'-
o
o
o
o 0 8
c5'
<0 0
o 0
0<% 0
00 8
c.90 ~
o
CO
o
o
o
OJ
o
cP 0
,0 00
0" CD
'b 00 ex:>
00
o
00 0 0 <9 00
o
o
08
o
500
Fig. 5-4. SPECIFICWF.!GHT VERSUS BRAKE HORSEPOWER FOR THE FOUR HEAT ENGINES
o
o
o
o
5
10 20 50 100
CONTINUOUS SUSTAINED HORSEPOWER BHP
200
- 136 -
-------
TH« JOHNS HOfI'K'. UN-VEIISITV
APPLIED PHYSICS LABORATORY -
Gt\. valt SPaIMG. MAItTLAND
"
+ SINGLE SHAFT, NO HEAT EXCHANGER
o DOUBLE SHAFT, NO HEAT EXCHANGER
6 DOUBLE SHAFT, WITH HEAT EXCHANGER
Ii: 15
:r
CD
~
I-
~ 10
IoU
~
~
II.
(3 5
IoU
a.
en
uJ
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ffi 0
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(3
W
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W
~ 5
CJ
z
w
It)
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.:
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o
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a:
w
::I
<{
V)
20
lei GAS TURBINE ENGINES
V)
w
a:
O!l2 0
..J >
0= 0
a:;: a:
I
~
g
~It)+
.....CJ
02
a:iU
00
II. CD
+
o
Idl RANKINE CYCLE ENGINES
o
o
o
2
o
o
~ LEAR
WILLIAMS MINTO-£)
200
1000
5
10
20 50 100
CONTINUOUS SUSTAINED BHP
500
- 137 -
Fig. 5-4 (Cant'd) SPECIFIC WEIGHT VERSUS BRAKE HORSEPOWER FOR THE FOUR
HEAT ENGINES
-------
THE JOHNS J-tO"KINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SIL ..,(IIt S~.I""G. MAIlfYLAHD
20
0-
ia 15
g
l-
X
"
W.
~
~ 10
~
U
W
0-
tJ)
W
Z
"
z 5
w
o
10
OTTO
DIESEL
GAS TURBINE
100 200
CONTINUOUS SUSTAINED BRAKE HORSEPOWER
500
1000
"
Fig.5-5 COMPARISON OF SPECIFIC WEIGHTS OF THE FOUR ENGINES
.r:.
ii:
X
!e
~ 0.6
u
~
tJ)
en
1.0
0.8
0.4
DIESEL
+ POINTS FROM PATTERSON AND BOLT. REF. 100
0.2
o
100 200 300
CONTINUOUS BRAKE HORSEPOWER
400
500
Fig.5-6 BRAKE SPECIFIC FUEL CONSUMPTION VERSUS ENGINE SIZE
- 138 -
-------
THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVER SP"'NG. W."YL,AND
devices, cooling, exhaust system, fuel, etc.) For a gi ven
bhp the CIE i.s heaviest, followed by the SRE, SIE, and GT.
For a 100-bhp engine, for example, the weights aTe 850,
460, 340, and 150 pounds, respectively.
The values for bsfc are more difficult to attain.
No comprehensive listing for any of the powerplants was
found. We are using the values reported in Ref. 100 and
plotted in Fig. 5-6 with the resulting curves. The values
are presumed to be minimum values for each engine and
can probably be improved because of the operating mode
(limited speed range at full load) envisioned for the hybrid
application. The curves reflect the lower efficiencies for
small engines. The gas turbine engines have the highest
bsfc's in the smaller sizes and show the grea test improve-
ment as siz.e is increased. Following the GTE in order of
decreasing bsfc are the steam, Otto, and diesel engines.
At 100 bhp, for example, the Otto, steam, and gas tur-
bine engines have fuel consumptions that arc by 10, 33,
and 40% higher, respectively, than the diesel engine
values. .
5. 2. 7 CLOSURE
A number of authors (e. g., Refs. 100 through
103) have attempted to compare various powerplants in
terms of emissions, cost, size, performance, weight,
feasibility, etc. The conclusions reached often depend
solely on the assumptions advocated for a particular en-
gine. The:;,' are subject to debate since the comparisons
normally involve comparing a paper study engine to a
mass-produced engine. In addition, it is difficult to
make valid comparisons since the SI and Clengines are
presently under intense study by automobile manufac-
turers as to methods of reducing emissions through en-
gine redes ign and / or emission control devices.
For the hybrid vehicles under study, it appears
that for the commuter car, family car, and delivery van
- 139 -
-------
THI JOHN. HOPKIN. UN I vlUtSIT Y
APPLIED PHYSICS LABORATORY
"LVIR "'.,HO. ""A RYLAND
the SIE is the first-choice powerplant for a near-term ve-
hicle (1975). For the bus, the diesel may be the first.
choice, but gas turbines also look very attractive. Smaller
engines suffice for the hybrid vehicles as compared to their
conventional current counterparts, but the relative specific
fuel consumptions of the gas-turbine and Rankine cycle en-
gines become even poorer in the small sizes. Oversize
GTE's may be of interest to improve bsfc, as discussed
in Section 5. 5. The potential for lower emissions from
current CI and SI engines may be enhanced by the pro-
posed fixed-load operation. The GTE is a clear seconrl
choice for all hybrid vehicles in 1978-80, and the hybrid
mode of operation might allow simplification of it, e. g. ,
elimination of the second shaft and possibly the regen-
erator. Improvements in both weight and volume would
appear to be needed for use of diesel or Rankine cyc1een-
gines in hybrid systems for the cars or the van, if appre-
ciable weight or volume is to be left for a flywheel system
by the approach described in the following subsections.
5. 3 VEHICLE REQUIREMENTS AND WEIGHT AND
VOLUME CONSIDERA TIONS
A primary premise to the approach in this section
is that it is desirable to maximize energy storage in order
to provide significant flywheel-only (nonemitting) ranges
for operation through cities. Therefore, the first step is
to establish the weight W s and volume Vols available for
propulsion in each vehicle type, within limits specified by
OAP (Ref. 104) at the outset of this study. Within these
limits, some modifications are used on the basis of prior
studies by others of present-day vehicles. The propulsion
system weight results herein are conservative in two re-
spects: they are generally below the OAP limits, and
they could be f:1rther increased in proportion to total ve-
hicle weight by increased use of lighter or more efficient
materials (plastics and composites) in the bodies and
accoutrements of future vehicles.
The next step is to break down W sand Vols to de-
termine the weight left for the flywheel subsystem itself
- 140 -
-------
THE .JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
5ILY"" SP"'N(; MA"YLAHO
(Wfwo) or in the case of hybrid propulsion systems, the.
sum of the weights of the heat engine (We) and the fly-
wheel subsystem (Wfw)' In the latter case, the heat en-
g me is sized by a certain critical performance require-
ment for each vehicle type (e. g., maximum sustained.
cruise speed) and by interpolation of data for current en-
gines to achieve that performance. Finally, assumptions
on other parts of the flywheel subsystem lead to a value
for the flywheel rotor weight Wr.
The situation is not really that simple, of course,
because certai!l items (e. g., fuel tank size) are iterated
even in the present, relatively simple computer program,
and many other items would be subject to iteration in the
detailed design of a specific vehicle. The greatest uncer-
tainties at present are flywheel containment weight (see
Section 4.4) and transmission weight, volume, and effi-
ciency. In these preliminary baseline studies, transmis-
sion weights and volumes are assumed to be comparable
to those of present-day automatic transmissions for given
horsepower requirements and vehicle duties, and con-
stant (average) efficiencies of 98. 5% for flywheel charging
(engine to flywheel) and 73% for the driv~train (flywheel
to vehicle drive wheels) are used. For some of the cases
covered, the transmission weight allowance may prove to
be too optimistic, but such factors on the optimistic side
are balanced somewhat by the aforementioned conserva-
tive approach to total propulsion system weight W s'
5. 3. 1 VEHICLE SPECIFICA TIONS AND RESULTING
FLYWHEEL SUBSYSTEM WEIGHTS .
The vehicle specifications supplied by OA P (Ref.
104) are listed in Table 5-1.
The total propulsion system is defined to include
the engine, battery, radiator, exhaust system, loaded
fuel tank, trarJsmission, and drive line (propeller shaft and
rear axle assembly). The values of W sand Vols supplied
- 141 -
-------
Table 5-1
Performance Specifications for the Four Vehicles
~
~
I:\J
Family Commuter
Parameter Carl Car Bus Van
V (mpb) 60 70 40 40
max
V d' rnph at Grade (0/0) 40 at 12 3 3 at 1 2 6 at 20 8 at 20
gra e .
R d (miles) 8 4 0.5 0.5
gra e
a (mph/ s) 4-6 5 3. 2 4
max
Jerk Rate (mph/ s) 6 5 2 4
R (miles) 200 50 18 60
W , Curb Weight (pounds) 3500( 4300) 1400 20 000 4500
c
WI' Fully Loaded Weight (pounds) 4000(5000) 1700 30 000 7000
CD' Drag Coefficient2 0.50 O. 35 O. 85 O. 85
2 18 80
A , Frontal A rea (ft ) 25 42
HP (with air conditioner) 12. 6 5.7 39. 3 2. 3 (
acc
HP AC' Air Conditioner (hp) 5.9 4.0 27.0 0
no A / C)
1 These values were given in the summer of 1970 (Ref. 104). Current OA P specifications
for the family car are much more complex and lead, among other things, to the higher
weights shown in parentheses.
2Aerodynamic drag only. A tire ;esistance coefficient, f = 0.01 + 1. 1 x 10-6V2, where
V is in mph, has been assumed to compute tire friction load (Ref. 108).
}>
1)
1)..
r J:
-..
~8o
~ 1) J:
': I I
~ -< %
! IE ~
~ () "
. III z
:~~
~ ~n
Z ;0 ..
o }> ~
-i-
0::
;0
~
-------
THe JOHNS H~IN. UNIVERSITY
APPLIED PHYSICS LABORATORY
aILV!", ."'''''NO. ""."LAHD
by OAP (Ref. 104) are listed in Table 5-2 and are based on
two previous OAP-funded studies (Refs. 105 and 106). The
values of Ws evidently are averages of the A. D. Little,
Inc. weight estimates (Ref. 106) based on "conventional"
and "lightweight" body construction (magnesium frames
and plastic panels), which would permit higher Ws for a
given vehicle curb weight WC' The "conventional" con-
struction weights from Ref. 106 were based on Hoffman's
(Ref. 107) data for 1966 automobiles and estimated values
for the van and bus. The Vols estima tes for the commuter
car and bus correspond to those from the Battelle study
(Ref. 105). .
The Ws values used herein are listed under "APL"
in Table 5 - 2. For the cars they are based on Hoffman's
(Ref. 107) average percentage weight distributions for
1966 cars of conventional construction. For the van, we
have modified the Hoffman results to account for the lower
powerplant mass fraction given for a van with the appro-
priate curb weight in Ref. 60. The bus weight fractions
have been derived from a weight breakdown for the Gen-
eral Motors T8H-5305A model bus (Ref. 110). Table 5-3
shows the corresponding weight breakdowns for the four
vehicles, and Tables 5-4 and 5-5 present breakdowns of
Ws and Vols for the first- and second-choice powerplants.
Radiator, exhaust system, and battery weights are related
to engine weight and are based on Hoffman's values (Ref.
107 and the OM bus data (Ref. 110); corresponding volumes
are based on data from Ref. 60 f6r the Diesel (Cn and Otto
(81) engines and from Ref. 74 for the gas turbine (GT) en-
gine. The fuel tank is sized for the amount of fuel re-
quired to travel the specified range at Vmax using gaso-
line with a density of 43 Ib/ft3. Transmission weights
are assumed to be equivalent to those for present vehicles,
and volumes have been derived from the Battelle study.
Table8 5-4 and 5-5 give the weights and volumes
available for the flywheel subsystem (rotor, hub, shaft,
seals, bearings, and case) for the hybrid (Wfw and Volfw)
- 143 -
-------
Table 5-2 -
Propulsion System Total Weight,apdyolume .'
.....
H:::>
H:::>
w W S' Total Propulsion System Wei~ht (pounds) Vol 1
c s
Vehicle (pounds) Conventional Lightweight OAP APL (ft3)
Family Car 3500 '1250 1750 1500 1138 . 3:0.9
Commuter 1400 500 700 600 455 16
Van 4500 1400 2000 1700 1323 42
Bus 20 000 5000 7000 6000 5940 175
1Vol = propulsion system total volumes (ft3) suggested by OAP; the value for the family
s was originally 28 ft3, but was raised by OA P to 30. 9 ft3 in January 1971; the vans
studied by Battelle (Ref. 105) gave 28 ft3, but OA P raised this allowance to 42 ft3.
. \,
:',
".
"
'0..
r%
-..
,,1'11\0
..Co
~ '0 %
: :I ~
\' -< %
! !!! ~
«n"
, 111 i
Krill
: ". c
.. 0:1 Z
~o<
~:u'"
".1
-1-
o~
:u
-<
-------
Table 5-3
Vehicle 'Weight Breakdowns
.....
~
CJ1,
~mmuter Fam ily City
Car (:ar Van Bus
B()dy, Trim, etc. 706 1763 2407 . 10 ,400
Suspension 84 210 270 1040
Wheels 35 88 113 660
Tires 45 112 144 700
Brakes 53 133 171 1120
Steering 22 56 72 140
Propulsion, Ws 455 1138 1323 5940
Hear Axle 60 151 194 1280
Transmission 1 66 165 212 520
Powerplant (= W f ) 329 822 917 4140,
, wo
Cur'b Weight W 1400 3500 4500 20 000
, c
Loaded Weight, WI. 1700 4000 7000 30 000
1For hybrid vehicles, powerplant includes engine, radiator, loaded fuel tank, battery, and flywheel
system weight (Wf~); for flywheel-only vehic1es,entire weight is available fer flywheel (Wfwo)'
>
11
11...
r:r
-..
!t'I'I>;
~ C f
: ~ I
f~%
~ Q ~
crl
~ » c
. III ,z
~ 0 <
. ;0 ..
"> I
d~
;0
-<
-------
~
~
Q)
Table 5-4
»
1)
1)...
rx
-,.
~a~
< 1) x
::d
f -< :r
JUIO
- - :
qJ -
& ~ .
; ~ c:
~ ~n
Z ;0 '"
o » ~
....-
O~
;0
-<
Breakdowns of Propulsion System Weight W s
. (pounds) for Hybrid Vehicles
Bus Family Commuter Van
. . 134 bhp1
94 bhp' . 33 bh 36bhp
. P
CI GT SI GT SI GT SI GT
Engine 1102 164 357 131 131 70 142 72
Battery 95 42 31 34 11 18 12 19
Fuel Tank 143 178 115 147 29 67 64 143
Radiator 102 0 33 0 12 0 13 0
Exhaust 95 0 31 0 11 0 12 0
Transmission
and Axle --1800-- -- 316-- -- 126-- - - 406--
Subtotal 3337 2184 883 628 320 280 649 640
OA P A Boca Hon, W --5940-- --1138-- -- 455-- --1323--
s
Left for Flywheel,
W 2603 3756. 255 510 135 175 674 683
fw
1Engine shaft output bhp; engine sized to sustain V max shown in Table 5-1.
-------
Table 5-5
Breakdowns of Propulsion System Volume Vol (ft3)
, ' s
»
"
"..
rJ:
-.,
,a~
;~i
r~1
~L1i
!~c
'~z
i~i
, -4-
o~
:0
-<
-
~
-.1
Bus Family Commuter Van
137 bbp 1 95 bbD 34 bbD 37 bbD
CI GT 51 GT SI GT SI GT
Engine, J Radiatc,r,
and Battcry2 31. 6 5.4 15.0 4.2 11. 1 2.3 13.6 2.3
Fuel Tank3 3.7 4.5 2.9 3. 7 0.7 1.7 1.6 3.6
3 1.9 0 0.6 0 0.2 0 O. ,2 0
Exhaust
Transmission 4 5. 8 -- 1.1-- -- 0.4-- -- 1. 4--
--
3 -- 12.8-- -- 1. 9--
Rear Axle -- 1. 5-- -- 0.6--
Total 55.8 I 28.5 21. 1 t 10.5 13.0 I 5.0 18.7 I 9.2
OAP Allocation, Vol --175.0-- --30.9-- --16.~- --16.0;.-
s
Left for Flywheel, 1
Volfw 119.2 146.5 9.8 17.5 3.0 11. 0 23.3 32.8
Flywheel-Only Case,
Volf --156.5-- --24.7-- --14.7-- --37.6--
wo
IAverage density of engines in Ref. 74, 31 Ib/ft3.
2CI and SI engine volumes increased ,by 100;'0 to account for radiator.
3 Ass1.imed overall densities (lb/n3): fuel tank, 50; exhaust, 40; rear axle, 100.
4Bus, 90 Ib/n3; oth~rs, 150 Ib/rt3 (Ref. 105).
-------
THIt JOHNS HOPKINS UNIVERSITY
APPLiED PHYSICS LABORATORY
.....v." 8~tHG. ""''''''LA,ffD
and the flywheel-only (Wfwo and V0lrwo) vehicles. It
should be noted from Table 5-4 that the heat engine system
subtotal weights for the GT and SI hybrid vans are almost
equal, 640 and 649 pounds, respectively, even though the
bare GT engine is 7Q pounds lighter, because such a small
gas turbine has a high bsfc (see Fig. 5-15) and requires
a larger fuel load (more than double the SI powerplant) to
attain the same range. The same characteristic is ob-
served for the commuter car hybrids.
5.3.2 ROTOR WEIGHT AND FLYWHEEL SUBSYSTEM
VOLUME
Let us represent the flywheel casing requirements
as equivalent to a steel casing with ,a uniform thickness
tc in the circumferential direction, which is left as a free
parameter. The top and bottom end plates, which are
parallel to the plane of rotation, are assumed to be equiva-
lent to 1 f8-inch-thick steel plates for all c~ses. The
rotor den,sity is assumed to be 0.073 lb/ in3, representa-
tive of a composite structure. Clearances of 1/8 inch are
allowed between the bar-shaped rotor and the casing. The
weights of the shaft, seals, bearings, and support struc-
ture are assumed to be equal in total to 10% of the rotor
weight. .
P~ior to settling on an equivalent to a disk configura-
tion a~d a case:'thickness tc of 3/8 inch, some param'etric
calcula:.tions,w~re done for bar rotors. For various values
of tc' 'TotOr'ha1f-width-t6~radius ratio T /R, and 1( = 2R),
the cor:rt!:Sp~nding rotor weight W r and total flywheel sub-
system vglume' Voli~'are"calculafedJor a fixed flywheel
subsyste~ we,~ht Wfw' Some consequences of the fore-
going ~s~uIIlpfibns for bar rotors are illustrated in Fig.
5-7. ror a"large Wf (917 pounds), with T/R apd tc
fixed at ,0. 1?5 'and O. ~5 inch, respectively, Wr and Volfw
increase .;slowly as 1. is increased, because the assumed
fixed Clearance and case thickness, as welLas the volume
and the; ~~eightof the cants end plates, have,"second-order
- 148 -
-------
THE JOHHS HOPKINS UNIV['RSITY
APpLIED PHYSICS .LABORATORY
.'L."'." ."''''''0. W..""LAHO
1:
~ 2.5
:::>
...J
o
>
...J
~
~
~
~
-.... 2.0
o
>
-...---
-..-..
......""",
~ -
~'" J
I """"""', 300
50
;;;
't:I
c:
~
!
~
z
C)4O
W
~
a:
o
I-
o
a:
--.......
--...........
.. ..........
.........
..........
"""'-
"
FLYWHEEL SYSTEM WEIGHT = 917 POUNDS
500
'"
"C
<:
~
o
E-
~
Z
400 ~
w
~
a:
o
I-
o
a:
25 . M.=
w
~
:::>
...J
o
>
...J
~
I-
o
I-
':i:
....
"0
>
20
Fig.5-7 EFFECT OF ROTOR LENGTH ON ROTOR WEIGHT AND TOTAL VOLUME.
T c = O.:l5 INCH, T/R = 0.125
30
3.0
--
--
--
---- FLYWHEEL SYSTEM WEIGHT = 133 POUNDS
1.5
24
27
30
BAR LENGTH /inches)
33
~5
36
- 149 -
-------
THE. JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
Sli..VlR 5""NG. M".YL,AHO
effects relative to Wfw' For a small Wfw' however,
effects of these parameters become significant and result
in reverse trends. (A s £ increases here, can height h
decreases.)
From such parametric studies, it has been con-
cluded that bar configurations would not exceed the volume
limits per s~; however, the physical dimensions for very
large bar rotors would pt'esent.installation problems.
For example, for the gas turbine/flywheelhybrip bus with
a 2960-pound bar rotor, and with 1. ='48 inches and T/R =
O. 188, the required height for the flywheel system would
be 9. 8 feet. The corresponding disk rotor requires 2. 1
feet. For the flywheel-only family car, with £ = 24 inches,
heights of 4.0and 1. 5 feet result for the bar (T/R = 0.188)
and disk, respectively; increasing 1. to 36 inches would
reduce these heights to 1. 8 and O. 42 feet, respectively.
For these reasons, as stated in Section 5. 1 (and
supported by the material presented in Section 4. 2, which
was actually developed later in the program), the flywheel
subsystem weights used in the system studies are equiVa-
lent to a disk configuration with a rated specific energy
E/Wr of" 3'2 W';;.h/lb.. Because of the lack of a definitive
case thickness design philosophy at this stage, a constant
3/8-inch wall thickness .has been used. This approach
may be considered compatible with a nominal.casing de-
sign philosophy wherein the external loads are of primary
concern. If further test results of the type described in
Se.~tion 3. 3. 5, together with safety specifications, estab-
lish that a constant percentage of the total energy is to be
contained, the case thickness requirements would in-
crease with increasing rotor energy per unit depth. Thus
for a disk configuration, tc would be proportional to the
square of the rotor diameter. (If a bar were used, e. g. ,
. in a commuter car, tc would be directly proportional to
the width and lengt'h of the bar.) The resulting flywheel
system weights and volumes used in the performance
studies are given in Table 5 - 6. It is noted again that the
- 150 -
-------
Table 5-6
Flywheel Rotor Length 1., Rotor Weight Voir- Can Depth h,
Can Volume Volfw' and Stored Energy EO for Each System of Table 5-51
.....
CJl.
.....
Bus Familv Car Commuter Car . Van
Parameter FO CI GT FO SI GT FO SI GT FO SI GT
1. (in.~hes) 48 48 48 24 24 24 24 24 24 24 24 24
h (inches) 25.3 15.8 22.9 18.2 5. 3 11. 2 7. 1 2.8 3. 6 20.3 14.8 15.0
3 0.8 5. 8 4. 2 4. 3
Volfw (it ). 27.6 17.2 25.0 5. 2 1.5 3. 2 2.0 1.0
W (pounds) 3278 2019 2964 584 163 353 217 74 103 655 474 481
r
EO (hp-h) 1431 880 1293 25.5 7. 1 15.4 9.5 3. 2 4.5 28.6 20. 7 21. 0
1Equivalent of composite disk flywheel configuration assumed throughout, with equivalent steel case thickness
tc of 3/8 inch. These required volumes are smaller than the available volumes in Table 5-5. FO = flywheel
only; first-choice powerplants for near term (Cl or S1) and longer term (GT) are listed for hybrid system for
each vehicle type (CI = compression ignition diesel, SI = spark ignition Otto, GT = gas turbine).
>
"
" ..
r r
-'"
~ rrI )r;
,. 0 'f
~ 1) z
. J: III
if -< r
. 1/1 0
- - ..
~ 0"
. 1/1 i
f ~ c:
~ ~ ~
z ;u 1:1
0> II
-1-
o ~
;u
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-------
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;/"'.>~( "~ ;"
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:p
THIE X)HHS HOPKINS UNIVERSITY
A.PPLIED PHYSICS LABORATORY
StLYl:A SPlitiNG, MARYLAND
>,
.k
. f~
overall weight limitations assumed are below the NA PCA
allowances (except for the bus), as was indicated in Table
5-2. .
5. 4 DRIVETRAIN CONSIDERA TIONS
5.4.1 GENERAL CONSIDERATIONS
,\ ~
In current vehicles the operator directly controls
the engine (hence the vehiCle) via the throttle and manual
or automatic transl11ission. Appropriate gears (3 to 15)
are selected depending o~ the engine / tire speed ratio and
torque requirements. Ciutches (torque converter in the
automatic) are used d~ririg the gear shifting to smooth the
transition. A 'rear axle gea,r reduction is usedl usually
about 3. 5: 1, 80 that at cru.ise conditions the transmission
speed ratio is essenti~lly,':unity. The powerplant operates
over a wide range of coricfitionsl particularly to attain
high accelerations. Current SI engines operate from 500
rpm at idle to 6000 ,rpm at maximum power (up to 300 bhp).
Manual gear box efficien~ies are 99% in high gear and 950/0
in low gear, and correspqn~ing automatic transmission
efficiencies are 93 and 870/0, respectively (Ref. 109). .
Specific weights are near 1/2 Ib/bhPmax for manual types
and 1 Ib/bhPmax for automatic types (Ref. 105). The effi~
ciency of the rear axle gear reduction is about 98% at
wide open throttle and varies from 85 to 95% at c
-------
TH. JC»fNS HOPKINS UHIV~"ITY
. APPLIED PHYSICS LABORATORY
"LoW.. ....ltlllfO, "'..YLAHD
factor of two (for a 75% DODI limit) or perhaps three
(890/0 DOD), so that the transmission speed range must be
able to accommodate this additional factor. To achieve
these objectives, a controllable, continuously variable
transmission (CVT) is required.
For hybrid systems (as well as flywheel-only sys-
tems), we assume that the vehicle is driven directly from
the flywheel, with the heat engine supplying energy to the
flywheel as needed. This approach may permit engine
design and operation to reduce emissions2. The vehicle
performance estimates presented herein are based on an
overall engine-to-drive-wheels transmission efficiency
of 72%. Overall transmission weights are assumed to be
comparable to those for current automatic units and amount
to 165 pounds for the family car and 66 pounds for the com-
muter car. These weights are optimistic for near-term
systems, but again it is noted that we have used total pro-
pulsion system weights considerably below the OA P allow-.
ances for al~ vehicles exc~pt the bus.
. An average regenerative recovery of 50% (of the
kinetic energ'.f to be removed during decelerations or down-
hill runs) is assumed for the bulk of th~se studies, based
on a detailed study of the DREW cycle (Section 5.4. 7). It
1DOD = depth of discharge, defined as percentage of total
energy already extracted, relative to that contained at
full rated speed and charge. In comparison, the DOD for
long-life batteries seldom exceeds 10%.
2An alternative dual-drive arrangement would be advan-
tageous for hybrid systems having relatively low energy
storage capabilities (smaller flywheels, as suggested
by Lockheed, Ref. 2) or limitations on energy with-
drawal rate (batteries) and thereby requiring dual or com-
bined drive systems (c. f., Ref. 19), but they require
additional controls or couplings to accomplish the dual
dri ving function.
;.. 153 -
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THE .IOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
s"..",..q s.'UNG. ""."\.AND
will be shown that this regenerative braking recovers
some 14 to 17"/0 of total urban cycle energy and thus com-
pensates the lower energy transfer efficiency as com-
pared to present automatic transmissions. Better CVT's
should become available over a longer term, and the pro-
posed programmer control (see Section 5.4.5), as oppo,sed
to unaided operator control on current vehicles, should
lead to gains. In any event, these studies, in agreement
with others (Refs. 10 and 111), indicate that the ultimate
advantage of using a flywheel for energy storage will de-
pend on the development of a suitable drivetrain with good
transmission and dynamic braking efficiencies.
5.4.2 ENGINE-TO-FLYWHEEL (CHARGE)
TRA NSMISSION
The engine-to-flywheel link may be as simple as a
mechanical clutch, provided that (a) a 2: 1 speed range for
the engine (corresponding to flywheel speed range) can be
tolerated without increasing emissions appreciably, and
(b) a satisfactory solution to the problem of start-up when
complete flywheel rundown (e. g., after several days of
parking) has been allowed to occur. One approach would
be to spin the flywheel up by an external electric motor.
These concepts are assumed herein. '(The 2: 1 engine
speed range might be a problem with gas turbine engines;
it might be necessary to reduce the speed range to 1. ;j;j: 1
by limiting the flywheel DOD to 44% instead of 75%. which
would require a 700/0 increase in flywheel rotor weight to
maintain a given flywheel-only range. )
If, however. it should prove that this energy trans-
fer, should be accomplished with a fixed engine speed to
minimize emissions, a variable-speed transmission will
be required. Since no external control is needed, a torque
converter or fluid' coupler would work, but the low overall
efficiencies (60 to 70%) of these devices make them unde-
sirable. Attainment of a high efficiency would require a
second CVT transmission similar to the flywheel~to:-wheels
- 154 -
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORAl"ORY
SILVI[R SPR''''G M,U'YL.AND
transmission discussed in the next section, but smaller,
since only half the power level is required. This choice
is llndesirabl e because of the penalties in efficiency,
weight, volume, and cost. .
~. 4. ~3 FLYWI-IEEL-TO-WHEELS DRIVE THANSMISSION
. The maximum n:quirements of the drive transmis-
sion are dictated by the vehicle acceleration requirements.
The s.chedule of torque and power supplied to the wheels
will depend on the particular capabilities of the transmis-
sion finally selected as well as specified vehicle perfor-
mance requirements. Figure 5-8 shows some transmis-
sion output characteristics, during accelerations, for
commuter and family cars using a simplified drivetrain
consisting of a speed changer (yielding a 10: 1 ratio for
charging the flywheel, or a 1:10 ratio for driving from it)
with 98% efficiency (in both directions), an undefined CVT
with a constant 76% efficiency, and a rear axle (to give
a 1: 1 overall ratio at Vm ) with 98% efficiency. The
ax
families of Golid lines represent constant-output-t.or<1ue
(Tn). The effects of rotating inertia (i. e., POW("l' rc:-
quired to aceelerate the vehicle components them sel ves)
and road wheel slippage have been neglected. Auxiliary
ordinate scales show transmission output speed W D (top)
and time scales (bottom) for acceleration from 0 to GO
mph at const8.nt T D and constant P . The dashed, con-
stant-PD line is at the level which ~oes provide the speci-
fied acceleration and similarly the constant Tn is shown
by a dashed curve (0 to 60 mph in 12 and 10 seconds for
the commuter and family cars, respectively).
For the 32.5 W-h/lb flywheels assumed for these
examples (73 pounds for the commuter car and 162 pounds
for the family car), the variation in flywheel speed is
small (3% decrease from full charge for both cases). How-
ever, if a small flywheel is used, the variation may be
large (e. g., for a 20-pound, O. 64-kW-h wheel the input
speed to the transmission would change by 52%). Figure
- 155 -
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THE JOHNS HOPKINS UNIVERSITV
. APPLIED PHYSICS LABORATORY
SILVER ""'NG. ....ItYLAND
100 0
4000
t
o
a.
~ 50
o
.r.
a
~
o
o
I
o
\
o
I
4
40
VELOCITY (mph)
I
8
60
80
20
\
4
TIME (seconds)
I
8
I T D = CONSTANT
12
I PD = CONSTANT
12
REAR
AXLE
."
r
-<
:E
J:
m
m
r-
(a) COMMUTER CAR
PD,T D,WD
o
200
DRIVElINE (rpm)
1000 2000
3000
-:"7;.
, '
..- ':: ..
~ .
o
a.
~ 100
o
.r.
20
40
VELOCITY (mph)
I
6
60
80
a
0.
~:J .
\1 ~
<' r::~.
'.
~
I
o
!
o
I
3
I
3
TIME (seconds)
I
6
I T D = CONSTANT
10 .
I PD = CONSTANT
10
(b) FAMILY CAR
J
,<1.
Fig.5.8 TRANSMISSION OUTPUT CHARACTERISTICS
- 156 -
-------
THE JOHNS HOPKINS UNlvt;ASITY
APPLIED PHYSICS LABORATORY
BILYKIII SPilliNG M.""'LAHC
5-8 shows that 37-hp at the output is required for the con-
stan t-power acceleration of the commuter car, with high
output torques (~ 130 ft-lb) for the first 3 seconds (at high
transmission speed ratios). In contrast, the con_stant
torque outp~t requires 134 ft-lb with higher powers
(~ 37 hp) during the last 6 seconds (at low transmission
speed ratios). The cruise horsepower curves fall well
below the acceleration requirements until the maximum
cruise speed requirements are approached. The trans-
mission requirements for the family car (Fig. 5-8b) arc
r- 2.5 times the values of the commuter car, roughly in
proportion to their loaded weights.
Figurc 5-9 shows variations with time of velocity,
acceleration, torque, horsepower, and transmission
speed ratio {NT) for the family car. The constant-torque
acceleration curve is essentially flat (constant accelera-
tion). The constant-power acceleration curve shows high
initial accelerations ('" 1 0 mph/ s or O. 5 g at 1 second), a
situation characterized by "squealing rubber!' and some
passenger discomfort. Note that an NT of 10 is required
at 10 mph. If the flywheel were at near the rundown con-
dition the NT required at 10 mph would be", 5. The ac-
celeration scnedule and consequent "jerk rate" are dic-
tated by the rate of change of NT and would be controllable
by the oper8.tor.
The overall requirements of the drive transmis-
sion may be summarized as follows:
1.
Continuous variation over speed range,
2.
2: 1 variation in input speed, but an essen-
tially constant speed input at any time, e. g. ,
during one acceleration period,
3.
Output speed range to match vehicle velocity
requirements, '" 5: 1 or higher,
4;
Control must go through the transmission,
to produce the required torque and speed,
- 157 -
-------
;
\
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'.:.:.
.' '.
~ ~.
:~
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'THE JOHNS HOPM,,..S UNIVERSITV
APPLIED PHYSICS LA80RAT()F
-r
-- '-"'---T----- ' .. .. r' ---' , .
--'1
,
"-
'--
--..-----
-----
-----
.,
,--- "-1
!
. --. ._-_..~.._.._.-
CONSTANT TORQUE (To) ACCELERATION
--- - CONSTANT HORSEPOWER (PO) ACCELERATION
o
1000
'1-U"-- -
1
,
......
. .....
'-
,,", --....--
~~~- ' I
------ '
-----------~
o
10
.....
.......,
"'-
5
--
--
---
-------------4
o
75
-.-l
U'l
50
25
---
-----------
--
..........-----
--
--
.--
--
--
,..-
",-
//
o
o.
8
2
4
6
10
TIME (seconds)
Fig.5-9 ACCELERATION PARAMETERS VERSUS TIME, FAMIL Y CAR
- 158 -
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THE .JOHNS t-tOPKlhlS UNivERSITY
APPLIED PHYSICS LABORATORY
SILVltit S""''''G MARYLAND
5.
Torque and horsepower requirements corre-
sponding to vehicle acceleration require-
ments, and
6.
High efficiency over operating range.
The limited use of CVT's in current vehicles is not
due to a lack of ideas. The recent patent rate on trans-
mission concepts has been near six per month, and a sig-
nificant portion of these are CVT's. Use of a CVT in any
automobile would allow the engine to operate in its mini-
mum bsfc region, and would reduce the speed range re-
quired of the engine (Ref. 112). The present lack of a
CVT for automobiles may mean mainly that the require-
ment has not been strong enough to force such an innova-
tion with its production development and changeover costs.
The general problem is low efficiency1 at off-design, non-
peak-load conditions, because most of the vehicles under
consideration seldom operate on the design curve (maxi-
mum cruise speed or maximum acceleration). However,
further development may lead to more satisfactory CV~I s.
A review of the literature on CVT's is given in Ap-
pendix D. For the commuter car the belt drive (Ref. 5) is
a candidate, . even though the combination of horsepower
(- 30 hp) and s~ced ratio (9: 1) requirements is difficult
relative to current belt applications, if one adheres
strictly to the present commuter car performance speci-
fications.
The needs of the family car, delivery van, and bus
probably will be best satisfied by a power-dividing device.
1 The transmission requirements for lower-energy fly-
wheels than we consider, perhaps operating in a dual
mode with the engine, would not be as stringent, but as
noted earlier, lower-energy systems give up the advan-
tage of flywheel-only (zero pollution) operating ranges
to alleviate local, in-town, emission levels.
- 159 -
-------
THE JOHNS MOPKINS U""JvEASITY
APPLIED PHYSICS LABORATORY
SIL.VIIIt S""'NO. """YLAND
The development of a power-dividing, hydromechanical
device [along the lines of Sundstrand's DMT (see, e. g. ,
Ref. 4) which they are now producing for trucks] should
be straightforward and appears promising for the van and.
bus because of their lower performance requirements and
relati vely higher propulsion system weight allowances.
A CVT for the family car will require a greater effort in
development because of the more stringent performance
specifications; the mechanical drives (Toric (Ref. 15) and
Beier (Ref. 16» appear to warrant further investigation,
and they may prove suitable. Pure electric or hydro-
static drives are least promising for any of the specified
vehicles because of their high weights and low efficiencies.
5.4.4 OTHER DRIVETRAIN COMPONENTS AND DRIVE-
TRA IN LA YOUT
A speed increaser (....... 1: 10) will be needed to match
the low-speed engines (i. e., all but the GTE) to the fly-
wheel speed, and in all cases a speed reduction (....... 10: 1)
will be needed to couple the flywheel to the vehicle drive
system. The ~apability for reverse operation must be in-
cluded. The. speed increaser and reducer functions can
be incorporated in a single unit, possibly at a savings in
weight and/or efficiency. Three clutches - engine/gear-
box, flywheel/gearbox, and gearbox/drive-transmission-
will be needed. A conventional drive axle (....... 3. 5: 1) is
assumed. Provisions for external (emergency) flywheel
charging must be made, and the ability to use the flywheel
to start the engine, particularly in the case of a GTE, may
be desired. .
A brake-regeneration system, providing for an
appropriate distribution of deceleration energy, must be
incorporated. . Finally, a control system is needed to:
monitor flywheel speed, start and stop the engine, inter-
pret and modulate driver commands, balance regenera-
tion and brake energy distribution, and operate drivetrain
clutches under appropriate conditions. .
- 160 -
-------
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATOR'.'
SILVER SPRING. MARYLAND
A driv~train schematic incorporating the foregoing
features is shown in Fig. 5-10. The power required for
accessories (power steering, power brakes, air condition-
ing, fans, pumps, and lights) is taken from the central
gearbox, and an input shaft is provided for externally sup-
plying power to charge the flywheel in the event of run-
down or while the vehicle is parked. The flywheel's clutch
is disengaged whenever the vehicle is parked to conserve
the stored energy. When the flywheel and drive clutches
are engaged, power can be transmitted from the gearbox
to the drive wheels, or vice versa (for regeneration).
The operator controls are analogous to those on
present vehicles. An" ignition" switch engages the fly-
wheel clutch, a selector lever positions the transmission
for drive, neutral, or reverse, and accelerator and brake
pedals corr.mand vehicle accelerations and decelerations.
(A conventional parking brake, not shown, would be pro-
vided.) A central control box, called the power program-
mer, translates operator commands into the desired me-
chanical responses. Its inputs are flywheel speed, drive-
wheel speed, and acceleration and deceleration rate com-
mands from the opera tor. It combines this information
to determine the appropriate, continuously varying trans-
mission rat.io. During deceleration it must also decide,
based on the flywheel charge status and the braking rate
demand, whether to use energy regeneration, the me-
chanical brakes, or a combination of both. It also con-
trols the on-off operation of the powerplant and clutch to
keep the flywhE:el speed within the design range. The same
programmer, using feedback data, could provide antislip
control of the brakes and drive wheels. It might also be
practical to provide a gain control to adjust the vehicle
response to operator preferences and driving conditions.
While the -arrangement shown in Fig. 5-10, with
the 10: 1 speed changer between the flywheel and its clutch
reduces the start-up clutching problem, it is undesirable
from the viewpoint of rundown time. Since a method of
- 161 -
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ELECTRICAL
FL YWHEEL
CHARGE UNIT
HEAT ENGINE
41: 1 . .
SPEED RANGE
(1500-30001
( 1500(3000)
EN.GINE
. ,Cl:YTCH .
(ONE-WAY)
......
C)
r-J
ON . OFF.
,
. I
I
I
I
I
I
I
I
~L~H~~C~R~C~M~D -
LEGEND
POWER LINKS
--- PRIMARY CONTROL LINKS
(REDUNDANT LINKS AND
INTERLOCKS NOT SHOWN)
) SHAFT RPM.TYPICAL VALUES
FOR FAMILY CAR
.,';
~
. GEAR BOX
,.
10: 1 SPEED
REDUCER
FL YWHEEL
(15 000-30 000).
- --
;.=!.~ "j" :."'. . .""
ACCESSORY
SYSTEMS
( 1500-3000)
FL YWHEEL
CLUTCH
1
,
VEHICLE I
START-UP ,
AND SHUT DOWN I
I
- - --
FL YWHEEL
SPEED
- --
MECHANICAL BRAKES
DIFFERENTIAL
CONTI NUOUSl Y
VARIABLE
TRANSMISSION
(DRIVE. ~EUTRAL.
REVERSE)
(0) '.
(-5001
I
I
I
I POWER
SETTI NG
I
I
I
WHEEL SPEED"
r- -
I
.1
"
I
,
,
I
J
POWER
PROGRAMMER
- ~
OPERATOR COMMANDS
VEHICLE ON-OFF
DRIVE,NEUTRAL,REVERSE
ACCELERATE
BRAKE
I
,
I
I
- --
,
Fig. 5.10 FLYWHEEL HYBRID POWER CONTROL SYSTEM
Ii
DRIVE
WHEELS
FREE
WHEELS
»
11
11..
r'"%
-PI
~1"I\r
~ 00
< 11 :t
; :r ~
f -< :t
! (II 0
In J
U1 -
J:i-i
: ~ c:
e ~ ~
Z :JJ PI
c » ~
-i :;
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-<
-------
THE: ,JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SlLv£1t SPJttNG. ".."'LAND
externally accelerating (via an electric motor) a rundown
flywheel probably will be needed in any case. it may prove ~
better to incorporate the speed changer within the gear-
box and, for normal operation after short-term k 18 hour)
parking, use the engine to match the flywheel clutch speed
within a few hundred rpm before engaging it at high speed.
A s previously noted, we have assumed for the fol-
lowing studies an average overall (engine to wheels) effi-
ciency of 72%. and this value is judged to be compatible
with the average efficiencies for CVT's that could be de-
veloped in the short term for use with these systems.
Over a longer term, better efficiencies should be achieva-
ble. The 72% value (which is used for all vehicle speeds
and power levels) is realistic for cars on urban cycles
but is pessimistic for freeway cruising at 40 to 70 mph.
The transmission weights assumed here,in, equivalent to
current automotive transmissions, are optimistic for
near-term flywheel-hybrid systems.
5.4. 5 REGENERA TIONEFFICIENCY AND OPERA TIONS
ON THE DHEW CYCLE
A study (Ref.115) of driving habits of selected
drivers indicated that of the total energy dissipated dur-
ing decelerations on a 'trip'. .as much as 70% is dissi-
pated by the br,ake/? . The remaining 30% evidently is dis-
sipated by v'ehicle drag (aerodynamic and frictional re-
sistance) and engine braking. For a 60 to 0 mph decelera-
tion. vehicle drag accounts for 3% (for a 3-second 'panic'
stop) to 15% (for a 15-second 'leisure' stop) of the kinetic
energy dissipation. If 10% is a reasonable average for
vehicle drag. then a maximum of 90% could go back from
the two drive wheels through the drivetrain to the fly-
wheel at 73% transmission efficiency. Thus. based on
this simple analysis. ~ maximum of 66% of all decelera-
tion energy might be recoverable. A more detailed analy-
sis follows.
- 163 -
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fM£ JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
S'LVI- SPlitiNG, MAlt""'."'!:)
To assess flywheel operation and regeneration on
the DHEW (Department of Health, Education and Welfare)
cycle, as detailed in the Federal Register (Ref. 113), a
numerical analysis was done. The DHEW cycle, which
is' being used by OA P for emission measurements, is
based on the accumulated experimentaldat:i for drivers
in the Los Angeles (Ref. 114) area and is defined by 1372
velocity (Vi, mph)-time (ti' second) points at I-second in-
tervals.' 'The analytical approach herein ,is as follows.
The ,net power required at the wheels (PN" hp) for
1
mass acceleration during the i th I-second time step is
computed from the equation of motion:
, 2
(3600) - -
a i = g( 5 5 0) 5280 P N JW I. V i = 831 0 P N .t WI. Vi'
1 1
(5-7)
-'
where ai and Vi are the arithmetic average acceleration
(mph/s) and velocity (mph) for the step, g is the gravi-
tational constant (32. 17 ft/ s2). and WI. is the loaded ve-
hicle weight (pounds). (The change in Wi. because of fuel
consUJppjion on one 7. 45-mile driving cycle is negligible. )
US~r)g,the prescribed drag coefficient ~D and 'frontal area
A for'thevehicle (Table 5-1), and assuming a tire fric-
tion fa:cf6~ (ft) relat'idnship (Ref. 1(8) (footnote 2, Table
5-1), the horsepower supplied to the wheel's during accel-
eraHon an~ cruise is given by: ' '
P~T = PN + PD '
(5-8)
where
P = (D + f W)V /375
D 't I.
= [0.00278 CDAV2 + (0.01 + 1.1 x 10-6V2) WflV/375,
(5-9)
- 164 - ,
-------
T).t£ JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVtA S~.ING "."VL."'O
where D = ~ P CDA V2 is the aerodynamic drag force.
ing deceleration the power regenerated at the flywheel
shaft is given by:
Our-
P R :-:( P N 17 R) ,
(5-10)
where 17R (= 17 D) is the average regeneration transmission
efficiency (0. 73 herein).
A ccnceptual schematic of the flywheel-hybrid sys-
tem analyzed is shown in Fig. 5-10. The engine is char-
acterized by its shaft power PES and cooling fan power
PCF. The net flywheel charging power PF. supplied by
the engine to the flywheel shaft is: In
PF. . = (PES - PCF) 17C '
In
(5-11)
where 17C is the charge transmission efficiency (O~ 985
herein). The net horsepower PF t extracted from the
ne
flywheel shaft is the difference between the vehicle re-
q~irement (PFout) and the horsepower supplied by the en-
gme:
PF =PF -kPF. =PW/17D+PAC+Pmisc-kPF.
net out In In
(5-12)
where 17D is the overall drivetrain efficiency from fly-
wheel to wheels (includes speed reducer, CVT,two
clutches, and rear axle); k = 0 if the engine is in the off
tnode and k = 1 during engine charging; and PAC and
Pmisc are the powers required for the air conditioner
and for the miscellaneous accessories - lights, radio,
windshield wipers, etc.
The maximum (and reference) flywheel energy
density Eo/Wr' maximum rotational speed ""0' and rotor
- 165 -
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
"LVI... .~"j"'Q. "".YL,e."'D
weight W r are input as initial conditions. A t each time
step an energy balance is made at the flywheel
AEi = 550 PF A\
net
(5-13)
and the rotational speed is found from:
l
W. = W (E./E )2 .
1. 0 1 0
(5-14)
When Wi has fallen to wo/ 2 (Ei = Eo/4), the powerplant is
turned on (k = 1), and when wi again reaches Wo it is
turned off (k = 0).
There is a fixed speed reduction ratio (NFR = 10)
between the flywheel and the main, variable speed trans-
mission. The rear axle gear ratio N A is based on the
assumption of a main transmission speed ratio of unity
(Nt = 1) at W = Wo and V = Vmax; thus:
N A = w~ r W/(14 NFR V max) ,
(5-15)
where rW is the drive-wheel radius (feet). The required
speed ratio Nt of the infinitely variable main transmission
is computed as a function Qf time from
Nt = U). rur/(14V.NANFR) = (w./w ) (V./V ) .
1 V\ 1 1 0 1 ma x
(5-16)
The foregoing cycle calculations have been made
for the family car and commuter car using SIE/flywheel
hybrid propulsion. The input conditions not already given
in Table 5-1 are shown in Table 5-7. The cycle is ~ 7.45
miles long with a time average velocity of 19.6 mph.
Maximum accelerations and decelerations are 3. 3 and
-3. 3 mph/ s, respectively. A peak speed of 56.7 mph is
a ttained, and 17. 3% of the total time is spent at idle
(V = 0). Each case was started with a fully charged.
- 166 -
-------
THE .JOHNS IotOPKINfI UNIV&RSITY
APPLIED PHYSICS LABORATORY
SILVa:" SP.ING. W...TLA,ND
flywheel and with all accessories and the air conditioner
operating continuously at full load. For the family and
commuter cars, the engines were on during 19.8 and
27.00/0, respectively, of a flywheel cycle (one period each
with k = 0 and k = 1). The ranges for a flywheel-only
operation (k = a period, Eo - E /4) were 6. 0 and 5.5
o '
miles for the family and commuter cars, respectively;
without the air conditioner operating the corresponding
ranges are approximately 8. 8 and 10. 1 miles. For the
commuter cc:.r the air conditioner power requirement is
a greater fraction of the total accessories load (0. 85)
than for the family car (0. '62).
The computer printout for each I-second interval
shows time t, velocity V, acceleration a, distance R, fly-
wheel shaft horsepower PFout' wheel gross horsepower
(PW = PN + PD), drag horsepower PD' flywheel rota-
tional speed (AJ., transmission speed ratio NT' energy in
flywheel E, and engine status (on or off). , Figure 5-11
shows the variation of PW' V, u), and NT for a 172 sec-
ond sequence for the commuter car as an example. Note
the very gradual decline in U) for the 73-pound rotor fly-
wheel.
The -resulting energy (W-h) balances are shown in
Table 5-8 for the two cars with and without their air con-
ditioners operating; The numbers in parentheses are
percentages of total cycle energy. For the commuter car,
398 W-h (28. 9% of the total energy) is used to accelerate
tht vehicle mass (excess over the external' resistance),
and this value also 'must represent the kinetic energy ex-
pended during decelerations. Figure 5-12 shows graphi-
cally the rtsulting energy balance for the commuter car.
In a conventional vehicle this kinetic energy is dissipated
through engine braking, mechanical brakes, and external
resistance. A ssuming a flywheel-to-wheels transmission
efficiency dUl'ing regeneration of 73% (i. e., 17R = 170)'
218 W-h (15. 8% of the total energy cycle) is returned to
the flywheel, while 100 W-h and 80 W-h are lost to
- 167 -
-------
~:
. .
»
1)
6 r-- "r -T'----r- 1)...
r %
-'"
I r!h
I < 1) %
=:d
I ,,-
-------
'HE JOHNS HOPKINS UNIV£R$I1',
APPliED PHYSICS LABORA10RY
Sll Vf" SPAIMC MAAYLANO
Table 5-7
Input Conditions for Family and Commuter
Hybrid Vehicles (see also Table 5-1)
Maximum RotatioMl Speed, U) :: U) rpm
max 0
Family Commuter
Car Car
30 30
158 72
30 000 30 000
1.5 1.0
73 7J
98.5 98. 5
73 73
10 10
92 33
3. 66 O. 71
3. 0 1.0
5. 89 4.0
Initial Energy Density E Iw (W-h/lb)
. 0 r
Rotor Weight, W (pounds)
r
Drive Wheel Radius, r (f eet)
w
Drive Efficiency,17D ({fa)
Charge Efficiency, 71 (%)
c
Regeneration Efficiency, ~R (0/0)
Flywheel Speed Reduction, NFR
Engine Shaft Horsepower , PES (bhp)
Miscellaneous A ccessories Power, P . (bhp)
mLSC
Engine Cooling Fan Power, P CF (bhp)
Air Conditioner Power, PAC (bhp)
- 169 -
-------
Table 5-H
Energy Disposition on DHEW Cycle (7. ;) miles)
»
"
" ...
r x
-'"
~~~
< " x
: :r 3
j -< x
- ~ ~
~ n "
. (/) Z
I: r"
: > c
. aJ Z
t: 0 ;:
Z AI '"
o » ~
~ -
0:::
AI
-<
.......
-J
o
l' .-
Energies (\,\ -h)
Family Car Commuter Car
Source . With A IC2 No AI C With A I G.2 No A I C
.-
in
-
Supplied by Powel'plant 4H75 .3178 2313 1160
Regenerated 523 523 218 218
Tota I 5398 3701 2531 1378
Out (%)1 (%) ('fa) (0/0)
Accessories 2712(50.2) 1 040( 28. 1) 1338(52.9) 202(14.7)
Engine Transmission Losses B1( 1. 5) 5 6( 1. 5) 38( 1. 5) 2l( 1. 5)
Main Transmission Losses 703( 13. 0) 703(19.0) 312(12.3) 312(22.6)
External Resistances (drag and friction) 954( 1 7. 7) 954(25,8) 445(17.6) 445(32.3)
Acceleration (kinetic energy) 3 948(17.6) 948(25.6) 39 8( 15. 7) 388(2B.9)
External Resistance 232(4.3) 232(6.3) 100(3.9) 1 OO( 7 . 3
Transmission Losses 1 9 3( 3. 6) 193(5.2) 80(3.2) 80(5.8)
Rp.generated Energy 523(9.7) 52 3( 14. 1) 218(8.6) 2 1 8(15.
- - - -
Total 5398 3701 2531 1378
8)
1 b .
?Num ers In parentheses are percentages.
;.'\/C = air.conditioner, operated at .100')0 load continuously.
AcceleratIOn kInetIc energy must equal the sum of external resistance,
losses, and regenerated energy during deceleration.
transmisSlOn
-------
ENERGY
SUPPLIED
BY
POWERPLANT
.....
-J
.....
ENERGY
REGENERATED
ACCELERATION IKINETlC)
ENERGY 128.9%1
I DECELERATION DRAG
~EGENERAT'ON TAI\NSMISSION LOSS
-~
EXTE RNAL RESISTANCES
(DRAG AND FRICTION) DURING
ACCELERATION AND CRUISE
ACCESSORIES - NO
AIR CONDITIONING
14.7%
MAIN
TRANSMISSION
LOSS
I.
~
TRANSMISSION LOSS
Fig.5.12 ENERGY DISPOSITION OF COMMUTER CAR ON DHEW CYCLE WITHOUT AIR
CONDITIONER; 0.247 HP.H/MILE. (A 4-HP AIR CONDITIONER OPERATING
CONTINUOUSL Y REPRESENTS 32% OF ABOVE ENERGY)
15.8%
>
1)
1)..
r %
101ii:'
;: 00
< 1) %
; I ~
10 -< %
: ~ ~
in"
C\ 1/1 -
z
!~~
e ~ ~
~ ~ S
~ -
0::
:u
-<
-------
,,~.; : "
. : f.V;~: ','
"
THE .K)HNS HOPKINS UNIVDI!IITY
APPLIED PHYSICS LABORATORY
SILva. ~. M..YLANO
external resistance and the transmission, respectively,
during decelerations. Thus, the regeneration efficiency
(H' defined as the recovery of kinetic energy during de-
celerations (or down-grade operation), is 218/398 :: 0.55,
or 55"/0 for the commuter car. The same value is obtained
for the family car: (R :: 523/948 :: 0.55. This value com-
pares with the maximum of 660/0 estimated earlier on the
basis of a driver study (Ref. 115) and a range of external
resistance losses for decelerations from 60 to Q mph.
For the broader but more. simplified analytic studies pre-
sEmted hereinafter, we have assumed an (R of 500/0.
I .
I
5.4. 6 CONCLUSIONS ON TRANSMISSIONS AND
REGENERA TION EFFICIENCY.
State-:of-the-art CVT's cannot meet the overall
flywheel system requirements, but short-term develop-
IJ?ent efforts probably would produce a satisfactory 'CVT,
slightly less efficient (especially at off-design conditions)
and heavier than current automotive transmissions. With
substantial long-term development, more competitive
CVT's could be developed. Mechanical or partly mechani-
cal (power dividing),transmissions provide high efficiency
and are the primary candidates.
. The overall transmission efficiency (720/0) and re-
g,eneration recovery (500/0) values assumed herein seem
cpmpatible with development for low emission vehicles
by 1975, especially for buses. Better efficiencies should
. he achievable over a longer term.
i.
5.5 PERFORMANCE AND EMISSION ESTIMA TES
5.5. 1 INPpTS
Since the vehicles appear to be weight-limited,
even when using bar-type flywheels, volumes are not
considered herein. The propulsion-system/vehicle-curb-
weight fractions (Ws/Wc) are 0.33, 0.29, and 0.30 for
- 172 -
-------
THE .10"''''5 t-tOPKIN9 UNIVIEASITY
APPLIED PHYSICS LABORATORY
SILVIER S~.IHG W".YLAND
the cars, van, and bus, respectively; these fractions cor-
respond to the" A PL" propulsion system weights in Table
5-2. Equations (5-8) through (5-12) are used, with the
vehicle characteristics given in Tables 5-1, 5-3, and 5-7.
Figure 5-13 shows Pw versus V for the four vehicles.
The ancillary requirements (Pmisc' PCF' and PAC) in
Table 5-7 were supplied by OAP (Ref. 104). The en-
gine cooling fan is not included in the flywheel-only ve-
hicles or the gas-turbine and stc8.m-enginc hybrids.
For e8.ch vehicle class, an appropriate driving
"cycle" is represented as the sum of a number of dis-
crete cruise, acceleration, and deceleration phases in
terms of the percentage of time spent in each (Fig. 5-14).
The operating mode of the flywheel-hybrid vehicles essen-
tially decouples the engine operation from the time se-
quence of operation of the vehicle. The engine is either.
on. (at full load and nearly fixed speed) to charge the fly-
wheel (from U,)r~'lin to wo) or off. For the cars the high
rotor energy densi ty allows energy storage for at least
seven accelerations from 0 to 60 mph, which, with re-
generation, allows the vehicle to negotiate with ease a
trip (of range RT as defined later) on any of the cycles
without the possibility of the energy use r:lte being gre;l!:el'
than the ch3.rge rate. Therefore, the timc sequence 01"
the modes is immaterial, and the resulting performance
and emission estimates are based on average horsepowl'I'S
and velociti.es for the various phases.
A cceleration rates also are not of primary concern
because, theoretically, energy can be extracted or sup-
plied to the nywheel system at any power level. The
power levels vdll be limited only by the powertrain
(transmission) capabilities. The energy required for an
acceleration is not strongly dependent on the rate (power)
at which it is accomplished. The acceleration rates
specified by OAP (Table 5-1) are used, and for the decel-
erations, rates 33% greater than these are used. The
low average velocities for the bus and van reflect the
- 173 -
-------
THE JOHNS HOPKINS U"'VERSITY
APPLIED PHYSICS LABORATORY
SIL VIE" SPoIIIING. "'.""L.UIIID
w 100
(I)
5
a:
u
a:
~ 75
a:
~
o
CL
w.
~ 50
o
:t
...J
W
w
J:
~
25
20 40 60 80
VEHICLE FORWARD VELOCITY (mph)
100
125
--r
o
o
Fig.5-13 STEADY-STATE WHEEL HORSEPOWER REQUIREMENTS FOR THE FOUR
VEHICLES.
50
::c
~
E
>
t: 25
u
o
...J
W
>
/
/
i
0.8
1.0
- (a) BUS - ~avg '" 9.95 mph
--- (b) VAN - ~avg '" 7.5 mph
-.- (c) CARS - Vavg '" 22.1 mph
o
o
0.2
Fig.5-14 DRIVING CYCLES
0.8
I BUS D = 48 INCHES 1
I
3
~- 0.6
~-
Eo/W, = 32.5 W hill;
0.4
o
1000 2000
FLYWHEEL ROTOR WEIGHT (pounds)
3000
Fig. 5-15 FLYWHEEL ROTOR MASS FRACTIONS ASSUMED
- 174 -
-------
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
S'LY(- s.-thNG. M..RY1...AND
large percentages of idling time (Fig. 5-14). The cycle
for the commuter and family cars (Fig. 5-14c) is the
Callfornia ten-mode cycle~ which is normally referred
to as the seven-mode cycle, since three of the modes
are not used in measuring emissions.
Flywheel rotor weights are computed as described
in Section 5. 3. 2, based on spin diameters (l) of 48 inches
for the city bus and 24 inches for the other vehicles.
With Eo/Wr '" '32.5 w-h/lb, these sizes yield (.&)0 = 15 900
rpm for the bus and 31 900 rpm for the other vehicles.
The resulting rotor mass fractions, Wr/Wfw' are plotted
in Fig. 5-.15 ",Fersus rotor weight Wr.
Emission results are nondimensionalized by divid-
ing by appropriate future standard values (Table 5-9).
For the light-duty vehicles (W c ~ 6000 pounds, van and
cars) the 1975-76 standards (I~ef. 3) are used, whereas
for the intracity bus the proposed 1973 California D~E'sel
Stand~rds (Ref. 116) are used. The former are expressed
iq gml mi; the latter in lb/bhp-h (BSPEx)'
Table 5-9
Light- and Heavy-Duty Vehicle Emiss'ion Standards
Pollutant
W ~ 6000 pounds
c
2
W > 6000 pounds
c
CO
HC
Emission standard, gm/mi
3.401
O. 411
0.401
lb/bhp-h
0.0770
0.0077
,', NOx (as N02)
0.0088
1Federal standards for 1976 (gm/mi) (Ref. 9).
2proposed 1973 California Diesel Standards (lb/bhp-h).
- 175 -
-------
THE JOH.,..S HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
""..,1. SPIlliNQ M"."LAND
5.5.2 METHOD OF ANALYSIS
For each portion (mode) of a vehicle's cycle, aver-
age acceleration (or deceleration) velocities (mph) and
horsepowers are defined by Vi = 6.s/6.t and Pw. = ViFw/375,
1
where F w is the constant wheel force required for the accel-
eration or deceleration, s is the distance (miles), and t
is time (hours). These wheel horsepowers are related to
the flywheel shaft horsepower by the specified efficiencies
with account taken for regeneration during deceleration.
The average flywheel shaft output horsepower PF for
. . out
the cycle is found by time-averaging the shaft horsepowers
over the modes, .
PF
out
t.
1
=~ t
. . T
1
PF
out.
1
(5 -1 7)
where ti is the time (hours) spent in the ith mode and tT
is the trip time (hours). Similarly, the time average
cycle velocity is: .
v = t t. V./ tT .
.11
1
(5-18)
The total energy expended on the cycle at the flywheel
shaft is:
6 -
EF =1.98xlO tTPF ,ft-Ib.
out out
(5-18)
The total engine-on time tea (hours) is related to the fuel
load Wf and engine output power (PE = PFin/17C) by:
t = W I (P . bsfc)
eo . [' E '
(5-20)
- 176 -
-------
THE" JOHNS HOPK"... UNIVERSITV
APPLIED PHYSICS LABORATORY
....YI- ~",...r. M"'''YLAHD
and the energy EF. (ft-Ib) delivered by the engine to the
flywheel shaft is: m
= 1. 98 x 106 Wf TJC/bsfc
EF.
1n
(5-21)
The total trip time (hours) is then found by equating
EF. and EF t' yielding:
1n ou .
tT = 11C Wff.bsfc '.
Ui-22)
and the total trip range (miles) is:
RT = tT V .
(5-23)
The fuel economy 'Y (mil gal) is:
'Y = RT "r/Wf .
(5-24)
where Pf is the fuel density, 5. 75 lb/ gal (for gasoline).
The ava1lable energy Ea (ft-Ib) in a flywheel charge is
75% of the maximum stored energy:
E
a
= O. 7!j (2655.3) (E /W)W = 64 730 W ,
o r r r
(5-25)
where Eo/Vir is the rated flywheel energy-density (32.5
W-h/lb), and 2655.3 converts ft-Ib to W-h. The number
of flywheel charges during the trip is:
n=E
F
out
/E
a
(5-26)
The flywheel-only (FO) range RFO on a single charge is:
R ::: n /n
FO T .
(5-27)
Similar calculations are used to estimate ranges and fuel
consumptions at constant speed or on a grade.
- 177-
-------
THE JOHNS 1010PKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV(Iit SPlitING. ".""",."'0
Emissivns Xi (gm/mi; i = NOx' CO, HC) are given by:
X. = 453, BSPE.' PE' t /RT = 453. BSPE.. PF / V TIc ' (5-28)
1 1 eo 1 .
ln
where BSPEi is the brake specific pollution estimate for
species i and is related to the engine's full-load brake
horsepower P from the curves supplied by OA P (Ref.
104). The HCEand CO emissions are then increased for a
10-second period at the beginning of each of the n engine
startups as discussed in Section 5. 2.5 and ratioed to the
appropria te em ission standards.
5.5. 3 RESULTS
For the majority of the OA P estimates, BSPEi is
independent of horsepower, so that Xi is essentially inde-
pendent of the engine size, but a second-order effect is
introduced, in that as engine size (PE' bhp) and weight
are increased, Wr decreases, and therefore the number
of flywheel cycles (hence engine startups and correspond-
ing added emissions) on a fixed trip increases. In addi-
tion, for the smaller powerplants, thermal efficiencies
decrease, thereby resulting in larger bsfc's and subse-
quent increase in emissions (gm/mi).
The results that are discussed in the following para-
graphs do not include any credit for the fact that the en-
gines are operated over much smaller ranges of condi-
tions than conventional engines.
It should be noted, too, that the flywheel storage
systems do not suffer from the limitations of battery
storage systems (e. g., low depth of discharge for long
cycle life, and low power densities) and have the theo:-
retical potential for storing a larger amount of energy
than with a battery system of comparable weight. A 1-
though they will not offer reductions in total emissions.
over multihour periods compared to battery systems (or
- 178 -
-------
THIE JOHNS HO",INS UNIVERSITY
APPLIED PHYSICS LABORATORY
S'L ..,~. S-..NG. M"..,LAHD
lower energy flywheels used in parallel with heat engines),
the relatively large flywheel energy storage systems do
offer the possibility of operation for lengthy periods with-
out the heat engines, allowing limited operation in densely
populated areas (cities) with the flywheels only. The hy-
brid vehicles thus could serve as dual-mode vehicles,
with external (electrical) charging of the flywheels in
cities if necessary. The heat engines would be used for
longer intercity trips or for recharging of the flywheels.
outside the restricted city regions.
For these reasons, we consider relatively high
values of energy density and rotor weight to be desirable.
A s previously noted, the engines are sized in all cases
to permit cruise at V des' the maximum sustained ve-
locity specified by OA P, with all accessories operating.
Emissior.s, fuel economy, and ranges are quoted in
Tables 5-10 through 5-13 without the air conditioner
operating. The cruise range capabilities of the four fly-
wheel-only vehicles, with and without the air condit.ioner
operating are shown in Fig. 5-16. Results for each ve-
hicle ~re discussed in the following paragraphs. .
Commuter Car. Only three hybrids are presented
in Table 5-10, because the diesel engine weight ex- r
ceeded Ws' These hybrids have predicted emissions
levels'below the 1975-76 standards and can sustain the
specified grade of 12%, and the flywheel-only vehicle
attains the required 4 miles on a 120/0 grade. The fuel
tanks of the hybrid vehicles have been sized for a 100-
mile trip at 70 mph. (Larger fuel tanks coulcl be pro-
vider] at little penalty, of course.) The fuel consumption
of the small (33-bhp) gas-turbine-engine (GTE) hybrid is
high, almost three times that of the same-sized Otto en-
ginE: (SIE) hybrid, reflecting the poor performance of
smail GTE's. A second larger GTE hybrid (represented
by the numbers in parentheses) has been sized such that
the fuel economy is equivalent to that of theSIE hybrid.
This 80-bhp GTE leaves less weight for the flywheel,
- 1 79 -
-------
Table 5-10
Results for Commuter Car Without A ir Conditioner Operating
~
11
11 ...
r r
- ,.,
",1'1..
F 00
< 1J r
~ I ~
i~~
- - ..
qri~
z
Erin
: » c:
< (D Z
~ 0 ;:
z ::0 ,.,
o » ~
~-
O~
::0
-<
~
00
o
Hybrids
Fly:wheel Only Gas Turbine Otto Steam
Gross Engine Horsepower -- 32.2(09)1 33.2 32.2
W fw 1.0 0.53(0.33) 0.41 O. 25
fw. . {fw+E)
Flywp.eel Rotor Weig:1t, WR (pounds) 217 1 03( 64) 74 35
W Iw R (pounds) 112 72(45) 61 49
fw
Fuel Economy at V. (mpg) -- 10.9(25.5) 25.5 17.8
max
Flywheel Only Range at 40 mph (miles) 38.3 18.5(11.5) 13. 1 6. 2
Flywheel Only Range on Grade (miles) 4.9 2.3(1.4) 1.6 0.8
No. of Accelerations per Flywheel
Charge 42 20(12) 14 6
Flywheel Charge Time (minutes) -- 6.4(1. 2) 4. 6 2. 2
Cycle Performance
Fuel Economy (mpg) -- 13.0(30.6) 30.6 21. 2
HC Emission Ratio 2 0.01(0.01) O. 11 0.20
--
NO Emission Ratio - - O. 76(0. 76) 0.67 0.34
x
CO Emission Ratio -- O. 10(0.08) O. 22 0.24
Flywheel Cycles per 100 Miles 4. 7 9. 9( 15.8) 13.8 28.9
Flywheel Only Range (miles) 21. 5 10.2(6.3) 7.3 3. 5
% Time Engine on -- 23.1(6.8) 23. 1 23. 1
INumbers in parentheses are for a GTE sized for same fuel economy as Otto engine.
2Emissions ratioed to 1975-7G Federal Standards, Ii sted in Table 5-8.
-------
Table 5-11
Hesults for Family Car Witfiout .'\ir Conditioner Operating
Gross Engine Horsepower
\\', /\\'(f E\
1\\' w+-,
Flywheel Rotor Weight, \\ H (puunds)
\Yf /\\'R(pounds)
w
Fuel Economy at V (mpg)
. max
Flywheel Only Range at 40 moh (miles)
Flywheel Only Range on Grade (miles)
.......
co
.......
~o, .'\ccelerations per Flywheel Cbarge
Flywheel Charge Time (minutes)
Cycle Performance
Fuel Economy (mpg)
?
HC Emission Ratio-
NO Emission Rati02
x ?
(:0 Emission Ratio-
.r.'lywheel Cycles per 100 :\1 iles
Flywheel Only Range (miles)
0-0 Time Engine on
Flywheel On 1;:
Gas Turbine
H:'brids
Otto
~.;.o
O. 3;
1:i~
G?
11. 9
,'J ."\
1.5
13
3. 5
H. -4
O. 31
1. .3
0.53
16. ')
. .,
,J. -
21. 1
1 :-iumbers in parentheses are for a GTE si.zecl for s::J.me fuel economy :lS Otto e!1gine.
')
~Emissions ratioed to ID7(j F'deral Standards listed in T.1bk ~)_~1.
--
!J 1. O( '200. 0) i
0.82(0.52)
1.0
58-1
:3:) 3C2Sc»
159(143)
9.2(11. 8)
239
- -
42. 3
25.6(21.0)
:3. 3( 2. 7)
30U-1)
- -
;). .J
49
--
7. 7( 2.9)
--
11. 3( 14. -4)
0.02(0.01)
1.97(1.97)
0.20(0. 15)
--
--
- -
-1. 5
12.-1
7. -4(8. 0)
1:;' 5(11. 1)
- -
21,l(S'.G)
Stea m
J>
1J
\I ..
r :I
-'"
III fII..
r- 0 0
< \I :I
; I ~
f -< :I
. (J\ 0
- - ..
~ n"
~ (J\ -
z
~ r III
= > c
e ~ ~
~ ~ =
-4 -
o ~
:c
-<
91. 0
O. 27
138
85
10.0
10. 0
1.3
11
3.0
.','
12.2
0.-16
O. 88
0.57
18. e
5.3
21. I
-------
-
Table 5-12
»
1)
1J..
0%
-..
r~5
< " %
: J: i
.-<%
;~~
K 0"
. III i
J: 0 '"
: ~ c
n~n
z ;u ..
D » =
~-
O~
:0
-<
Results for Delivery Van with No A ir Conditioner
......
00
t\.:)
Hybrids
Flywheel Only Gas Turbine Otto Steam Diesel
Gross Engine Horsepower - - 34.3(110)1 36.3 34.3 36.3
Vi' /W LO 0.75(0.72) O. 73 0.67 0.-13
fw (fw-rE)
Flywheel Rotor Weight, WR (pounds) 655 481(465) 474 430 266
W . /W (pounds) 263 203(196) 200 185 129
fw R
Fuel Economy at V (mpg) -- 5.3(11. 9) 11. 9 8. 6 14.5
. max
Flywheel Only Range at 40 mph (miles) 25.4 18.6(18.0) 18.4 16. 7 10.3
Flywheel Only Range on Grade (miles) 2.4 1. 7( 1. 6) 1.7 1.6 O. 9
No. of Accelerations per Flywheel
Charge 30 2 2( 21) 21 19 12
Flywheel Charge Time (minutes) -- 28.0(8.4) 27.5 25.0 15.5
Cycle Performance
Fuel Economy (mpg) - - 6.2(13.9) 13.9 10.0 16.9
HC Emission Ratio 2 0.02(0.01) O. 20 0.28 O. 76
--
NO Emission Ratio 2 1. 67(1. 67) 1. 50 0.75
-- 1.77
x 2
CO Emission Ratio -- 0.19(0.15) 0.44 0.40 O. 18
Flywheel Cycles per 100 Miles 3.4 4. 6( 4. 7) 4. 7 5. 2 8.4
FlywheelOnly Range (miles) 29.6 21. 7(21. 0) 21. 3 19.4 12.0
0/0 Time Engine on - - 16. 1(5.0) 16. 1 16. 1 16. 1
1 .
Numbers in parentheses are for a GTE sized for same fuel economy as Otto engine.
2Emissions ratioed to 1976 Federal Standards listed in Table 5-~i.
-------
Table 5-1:\
J>
"U
"U..
r :r
iTi'"
~ 0 (5
< "U :r
: I ~
, -< :r
8 VI 0
- - ..
. n "
a VI z
~r"
: » c:
nn
z ;U '"
o » ~
~-
O~
;U
-<
Hesults lor Intracity Bus without Air" Conditioner Uperating
~
co
w
Hybrids
Flywileel Only Gas Turbine Otto Steam Diesel
Gross Engine Horsepower - - 1 '; f' " (" 7 0 0) 1 133. "/ 126. 6 133. 7
.;.. ). ,J ..~. .
W Iv...' 1.0 O. ~) [(0. tHH 0.81 0.8 i O. 63
fw . (fw+E)
Flywheel Rotor Weight, WR (pounds) 327~ 2964( 286(j) 2628 2628 2019
Wf IWR (pounds) 862 792( (66) 717 717 583
\\.
Fuel Economv at V (mpg) - - 4.5(5. 1) 5. 1 4. 7 5. 6
. max
Flywheei Only Range at 40 mph (miles) 43.9 39.7(38.4) 35.2 35.2 27.6
Flywheel Only Range on Grade (miles) 2.7 2.5(2.3) 2. 1 2. 1 1.6
No. of Accelerations per Flywheel
Charge 38 34(3:.n 30 30 23
Flywheel Charge Time (minutes) - - 46.6(21.1) 41.:3 41.3 31. 7
Cycle Performance
Fuel Economy (mpg) - - 3. 3( 3. 8) 3. 8 3. 4 4. 1
flC Emission Ratio 2 0.002(0.001) 0.03 0.04 O. 11
- -
:\0 Emission Ratio 2 0.2:)(0.23) O. 18 O. 10 O. 23
x 2
CO Emission Ratio - - 0.02(0.01) l;. lIC, 0.05 O. 01
Flywheel Cycles per 100 :\Iiles :3, 2 :L 3(:30 fj) I ., Q :3. ~, 5. 1
0. '.
Flywheel Only Range (miles) :31. 8 2f3. [)(27. :' .., - - 25.5 19. [)
-:). .J
0',. Time Eni;ine on - - :! fj. : j( I :!. (j) 2f:i. n Y' Q 2(j.9
-0. .
I
\llcnhers in parentheses 'ire for a GTE sized for same fuel ecnnorn\' 'lS (Jtt0 engine.
'J
"I.illissions ratioed to 1973 California heavy-dt.:ty vehicle :-itanrinrrJs.
-------
THI JOHN. HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SIL VI'- .""IIfG. .....It'YL,AHD
with a resultant 38% decrease in stored energy capability
compared to the 33-bhp GTE; nevertheless, the flywheel-
only (FO) range is near that of the SIE hybrid. The fuel
consumption of the steam-engine (SRE) hybrid is 44%
greater than the SIE hybrid.
The commuter car specifications list a maximum
trip range (range without supplementing the energy storage
system of the vehicle) of 50 miles. Although the flywheel-
only vehicle does not attain a 50-mile range on the lO-mode
cycle trip~ the 21. 5-mile range that it does attain is still
quite attractive for a specialized intracity vehicle. A
range of 50 miles can be attained at 30 mph without the
air conditioner operating (Fig. 5-16). A 50-mile range
on the cycle could be provided by increasing curb weight
Wc by-1/3 (450 pounds).
For a life of 100 000 miles of driving on the 10-
mode cycle, the total numbers of flywheel cycles vary
from 4700 for the flywheel-only vehicle to 28 900 for the
SRE hybrid; we would not expect these values to present
problems in terms of cyclic fatigue. From 6 to 42 accel-
erations from 0 to 60 mph can be provided by one flywheel
charge.
. The flywheel-only, Otto-hybrid, and larger GTE-
hybrid vehicles are the more prom ising commuter car
configurations. The GTE would necessarily be con-
sidered a longer term (i. e., 1978 rather than 1975)
choice. Note also the qualification about GTE speed
range mentioned at the end of Section 5.4. 3.
Family Car. Here, too, the Diesel engine is too
heavy to allow for a flywheel system and is omitted from
Table 5 -11. The larger engine requirement for cruise.
places the minimum GTE in a more competitive position
to the SIE, but its fuel consumption still is 20% greater
than the SIE's. Again, a larger GTE (numbers in paren-
theses) should provide nearly equivalent fuel economy to
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THE JO.....,S ~OPKIN. UNiVERSITY
APPLIED PHYSICS LABORATORY
SILVK. ~"I-.o. "."Y~ND
the SIE at smaller engine weight, with still nearly twice the
FO range. All of the hybrids can achieve the 12% grade
with the powerplant. The flywheel-only vehicle attains
5.5 miles on the 12% grade, which is short of the re-
quired a miles. The NOx emissions are approximately
double the 1976 goalJor the GTE and SIE hybrids; however,
~f the Aerospace projections (Ref. 97) are assumed, the
NOx emissions can be reduced by 60 and 670/0 for the SIE
and 9T:;E hyb,rids, respectively, and would result in emis-
sion levels below the 1976 goal. The flywheel-only ve-
hicle cannot meet the specified cruise (200 mile) and
grade (~'mile)ranges; however, as with the commuter car,
ran~~s available are attJ'active for specialized intracity
vehicles of this size.
The SIE would necessarily be the near-term en-
gine choice for a hybrid, but its FO cycle range would be
relatively low, so that the value of high energy storage
would be questionable. (The energy density or flywheel
rotor weight would have to be increased by a factor of
three to result in a desirable 15 to 20 mile range for a
,dup.l-m,?de vehicle.). In this case, a smaller flywheel
operating in parallel with the SIE simply to provide accel-
eration capability and smooth operation of an engine opti-
mized ~or low emissions at the higher engine speeds,
such as Lockheed (Ref. 2) has proposed, probably would
be'the correct choice. Nevertheless, the probable safety
advantages of composite-type rotors (as opposed to all-
metal rotors) could still dictate their choice.
Except for a doubt about NOx emission levels and
the aforementioned uncertainty about GTE speed range
and consequent engine-to-flywheel transmission require-
ments, the GTE has the greatest potential as a long-term
choice and does show promise for FO range. It is be-
lieved (~ee Section 7 and Appendix D) that NOx emissi,ons
from GTE's can be further reduced by proper combustor
design.
Delivery Van. With the exception of the eIE hy-
brid, all of the vehicles can attain approximately 20
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THE JOHNS HOPKINS UNIVERSITV
APPLIED PHYSICS LABORATORY
Sn..VE- -""NG. "'''.YI-APiCD
miles of FO range on the cycle trip. The performance
specifications are low when compared to the family car,
thereby resulting in a small (34-bhp) engine requirement;
the weight remaining permits packaging of a relatively
large rotor. The powerplant alone can sustain a 15.40/0
grade at 8 mph, and the required range of 1/2 mile on the
20% grade can be achieved by all the vehicles with the fly-
wheel alone. For a hybrid system, the SIE is the near-
term engine choice because of its lower fuel consumption
and low development costs. Again, a larger GTE (values
in parentheses) appears to be a good long-term choice,
because it cot..ld charge the flywheel in 8.4 minutes, and
21 miles of FO operation ('" 3 hours on the cycle) would
then be available. This larger engine also would allow
. .
the van to cruise at 60 mph on freeways.
A s with the family car the best-case OA P esti-
mates for NOx emissions (with no credit for engine opti-
mization for hybrid use) are double the 1976 goal for all
hybrids except the SRE. However, if the Aerospace pro-
jections can be attained through optimization, the 1976
goals can be met. The small GTE suffers from its high
fuel consumption, and the eIE suffers from its weight,
which reduces available FO range. The SRE hybrid, al-
though it 2.ppears promising, is the least developed power-
plant. The FO vehicle is attractive, since a cycle range
of 29. 6 miles is estimated. . From Fig. 5 -16 an FO range
of 60 miles (the range requirement specified by OAP) is
achievable at a constant speed of 15 mph. Many smaller
vans (e. g., postal, florist, druggist, etc.) could be de-
signed to achieve 60 miles on the van cycle if such ranges
are needed. .
t.
Intracity Bus. The intracity bus appears as the
most promising of the specified vehicles for a flywheel
system. The relatively large engine size permits a GTE
that is competitive with the eIE and SIE engines in terms
of fuel consumption. The OA P range requirement of 18
miles can be met with all vehicles in the FO mode of
- 186 -
-------
THf: .JOHNS HOPt(IHS UNIVERSIT"t
APPLIED PHYSICS LABORATORY
!I'L"'!:" SPlitiNG "'AAYLA..,O
80
60
..
~
E
w
"
Z
<{
c:
40
o
o
-:;;
!E
'e
w
<.:J
Z
<{
c:
WITHOUT AIR CONDITIONER
- - - WITH AIR CONDITIONER
--
. --
",..-
./
"
/
/
/
/
/
/
/
I
10
20
60
30
VELOCITY (mph)
40
50
40
60 -----
r--'-----r-
o
o
80
100
20
40 60
VELOCITY (mph)
Fig, 5-16 FLYWHEEL-ONLY LEVEL ROAD CRUISE PERFORMANCE
- 187 -
-------
THe JOHNS HOPKINS UN~VElltStTY
APPLIED PHYSICS LABORATORY
.LVI;8 8HttNG. MA""'L,ANO
operation. The FO vehicle attains a cycle range of 32
miles. For thG hybrids, .FO ranges of 26 (SRE) to 29
miles (GTE) are calculated. The larger GTE (values in
parentheses) would be able to charge the flywheel in 21
minutes (while the driver takes a rest break at a suburban
car barn having a high vent stack)*and would still give 27-
mile FO range (2.7 hours of service on the cycle); this
270-bhp engine also would raise V des to,.... 60 mph, making
this city bus useful on freeways. Such GTE's are ready
for introduction in heavy-duty vehicles before 1975 (Ref.
75).
The emissions for the bus, when compared to the
1973 Diesel proposed standards,are low; however, the
proposed standards are not particularly stringent and can
be met by the heat engines alone with the emission esti-
mates used h~re (best OAP values). The grade length re-
quirement of O. 5 mile can be met by all the vehicles with
the FO. The SIE hybrid has slight advantages over the
Diesel (CIE) in several parameters, but either would be
a good second choice behind the large GTE. The CIE
does, however, have an odor problem at present. The
steam engine also looks good, but its lower state of devel-
opment makes it an unlikely candidate.
5.5.4 SENSITIVITIES OF PERFORMANCE AND
EMISSION ESTIMA TES TO ASSUMPTIONS
The SIE hybrid commuter car was selected for the
purpose of investigating the influence of variations in vari-
ous parameters. The base case refers to the SIEhybrid
reported in Table 5-10 without the air conditioner operat-
i~g. The effects of vehicle (and engine) design speed
V des' and air-conditioner load, on FO range and fuel
economy are shown in Fig. 5-17. Reducing the design
speed to 60 G1.ph results in a 48% increase in FO range
(from 7.3 to 10.9 miles) with a 6% reduction in fuel
economy as a result of the lower bsfc for the smaller en-
gine. Since the BSPEi are assumed to be independent of
*
The vent stack could be equipped with both catalytic. con-
verters and continuous monitoring instrumentation.
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THE .JOkNS HOPKINS UN1V£RSIT.,
APPLIED PHYSICS LABORATORY
SILV£R S,.IItIHC M."YL."'D
120
w
~ 80
<
:J:
U
....
Z
w
u
ffi40
Go
o
MPG
-20
70
60 50 40
HYBRID ENGINE DESIGN SPEED (mph)
.30
60
40
~'"
",,,,\0
~~'
c\..~
c-<
w
C> 20
Z
<
J:
U
....
Z
w
u
ffi 0
Go
-20
/'vfPG
A.IIJO f:
l.YWH
eel. A
A.tvGe
-40
o
25 50 75
AIR CONDITIONER LOAD (%)
100
Fig.5.17 EFFECT OF DESIGN SPEED AND AIR CONDITIONER LOAD FOR OTTO HYBRID
COMMUTER CAR
- ] (1 ~!
-------
THE JOHNS HOPKI....S UNIVEftSI1'Y
APPLIED PHYSICS LABORATORY
51L VIU' S""ING. "",,,,,,"""'0
engine size and the total energy required is fixed, the
emissions will vary inversely with the fuel economy y
(mpg). Continuous operation of the 4-hp air conditioner
(100% load) requires an energy increase of 540/0. Accord-
ingly, the emissions increase by 540/0, while y and FO
range decrease by 35%.
Figure 5 -18 shows that as W r is increased, fuel
economy decreases and total emissions increase due to
the increased curb weight. The upswings in the HC and
CO emissions for the smaller rotors are due to the effects
of the start-up emission penalties. The Fa range in-
creases essentially directly with Wr. The effects of the
drivetrain efficiencies and the external resistance D
(drag and tire friction) on yare shown in Fig. 5-19.
(The emissions on a gm/mi basis vary inversely with y.)
Increasing the regeneration efficiency E R from 50 to 60%
(+20%) results in a 12% increase in y. The direct linear
effects of drive and charge efficiencies are equivalent: a
100/0 increase in either results in a corresponding 10% in-
crease in y. Because of the nature of the cycle (small
percentage of cruise time) the effects of drag variations
are not pronounced. A 200/0 drag decrease results in a
6. 2% increase in fuel economy.
5. 6 CLOSURE
With the assumptions stated in Section 5. 1, the
bus is the only vehicle that literally meets the OAP speci-
fications as an Fa vehicle. The 22-mile range of the Fa
family car is far short of the required 200-mile range.
The 21-mile range of the Fa commuter car on the 10-
mode cycle is 42% of the specified 50-mile range and
might be adequate for the second car of many two-car
families. A 20-mi/day average would be adequate for a
large percentage of cases, and a 7-mile reserve range
would always ne there for emergency, since only 75% of
E is used for 21-mile range. Likewise, for a van a 30-
o .
mile range would cover many types of delivery routes
- 190 -
-------
THE JOHNS HOPkiNS UNIVI[RSITY
APPLIED PHYSICS LABORATORY
SILVEIt S~I!tING Jrt4,aI!t,.L4NO
300
o
200
100
w
~ -100
«
I
U
....
Z
w
u
a:
uJ
0..
.~~ ~ :
eU~B ~IGHT :
~ ~
MPG
.~~ eo~~O' :
-100. 0 100
~
: He ~
200
300
400
CHANGE IN ROTOR WEIGHT (%)
Fig.5-18 EFFECT OF FLYWHEEL ROTOR WEIGHT FOR OTTO HYBRID COMMUTER CAR
20
REGENERATION
EFFICIENCY
10
~
E
w
t?
Z
<{ 0
I
U
....
Z
w
u
a:
w
0..
-10
CHARGE OR DRIVE
EFFICI ENCY
1",
I
I
\ EXTERNAL
RESISTANCE
I
I
I
I
-20
-20
-10
o
PERCENT CHANGE
10
20
Fig.5-19 EFFECT OF DRIVETRAIN EFFICIENCIES AND EXTERNAL RESISTANCE FOR
OTTO HYBRID COMMUTER CAR
- 191 -
-------
THI: JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
alLVrR ."R."'G. "'..YI,.","'O
before recharging. Smaller-payload vans could be de-
signed for 60-mile range if desired. A market certainly
exists in Britain for this type of vehicle; more than 70 000
battery-powered milk, parcel, and deli very vans are on
the road there (Ref. 117).
Heat-engine/flywheel hybrid propulsion looks
promising for all of the vehicles and definitely merits
further study. Estimated emissions based on the most
optimistic OAP projections indicate that the hybrid 'light-
duty' vehicles can meet the 1975 standards for CO and
HC. The NOxestimates for the SIE and GTE van and
family car hybrids are above the 1976 goals; however, if
the Aerospace projections (Ref. 97) for fixed-load, nearly-
fixed-speed operation can be attained, the NOx standard
will be met. It should be emphasized that the OAP projec-
tions for emissions did not consider engine optimization
for this type of operation. An SIE- or GTE-hybrid com-
muter car is attractive with 7 to 13 miles of emission-
free urban dri-ving, and these emission-free ranges could
be doubled by allowing a 10% increase in curb weight.
The GTE-hybrid bus looks very attractive, particularly
if it is given an oversized (300-bhp) GTE to permit 20-
minute flywheel recharging and 60-mph cruise on free-
ways.
These performance projections are based on a
number of assumptions that will require detailed investiga-
tion. Answers to questions regarding flywheel rotor con-
figuration, seals and bearings, gyroscopic forces, con-
tainment requirements, emission characteristics of power-
plants optimized for fixed-load, nearly-fixed-speed opera-
. Hon, powertrain component efficiencies, and weights and
volumes will have to await experimental investigations.
- 19 2-
-------
THE JOHN9 HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVI:A S~.ING. "".YLA""D
6.
CONCLUSIONS AND RECOMMENDA TIONS
6.1 GENERAL
The principal tasks of this program were an experi-
mental proof-of-principle demonstration of the superfly-
wheel concept and evaluation studies which considered a
matrix of four vehicles fitted with flywheel-only or fly-
wheel/heat-engine hybrid propuision systems. and four
heat-engine types.
Filamentary and composite rods of 30-inch length
have been rotated to high speeds. Energy storage ex-
ceeded the goal of 30 W-h/lb of rotor material for small-
scale rods of the better materials using the better experi-
mental drive/mounting systems. Larger 1-pound speci-
mens of glass and graphite / epoxy composite materials
came within 7 and 13%. respectively. of the goaL There
is good reason to believe that improved manufacturing
controls for the composite materials will lead to signifi-
cant improvements over these early experimental data.
High-speed motion pictures of the tests of the
larger rods confirm the hypothesized mode of failure.
The two halves of a failed composite rod were progres-
sively abraded as they struck (end-on) and moved along
opposite sectors (about 900) of the steel containment ring,
and this process was so rapid and complete as to mini-
m ize the energy transferred to the ring. This significant
finding offers the promise of rotor containment with mini-
mal system weight penalty. The most important task in
the future is to develop and test a flywheel system, com-
plete with vacuum capability. low-loss seals and bearings.
containment structure, and power take-out. .
The results of the evaluation studies indicate that
the city bus is the primary candidate for use of a large.
flywheel-only system. The delivery van, with reduced
- 193 -
-------
.~
THI! JOHNS "~IHa UNIVERSITY
APPLIED PHYSICS LABORATORY
81t.vl. ""'IIiIO. MAIltYUHD
range, is a secondary candidate for flywheel-only propul-
sion. All of the hybrid-propulsion vehicles would meet
all vehicle performance requirements and would meet or
nearly meet the 1975-76 emissions standards, based on
the "best" emissions estimates provided by OAP. How-
ever, studies have not taken into accoun~ the probable re-
ductions in emissions by the use of hybrid systems in
which the heat engine operates only under. constant-load,
nearly-constant-speed conditions. Investigation of the
latter area merits high priority, because it is fundamen-
tal to the value of the hybrid propulsion for reducing air
pollution.
A literature and technology review of transmissions
has shown that there are a number of systems that could be
developed to provide the continuously variable control re-
quiredby the flywheel system. The success in developing
such a system with a reasona1;>le production cost is also
. fundamental to the acceptance of flywheel propulsion sys-
tems.
The following sections delineate specific conclu-
sions of this program and the associated recommendations
for future work to develop flywheel propulsion systems.
6.2 ROTOR CONFIGURATION AND MATERIALS
We have demonstrated 48 W-h/lb (without failure)
with boron filaments, 36 W-h/lb at burst with small
graphite/ epoxy composite rods, and 31 W-h/lb at burst
with small R-glass/epoxy composite rods. These mate-
rials are candidates for brush-rotor configurations (the
glas~ composite should improve in strength by 15 to 200/0
with the substitution of:S-glass), and the use of pure fila-
ments or small,:",diameter, pultruded rods should insure
the highest strength,. uniformity,and freedom from surface
flaws.
. The large:!;' 1-pound composite rods did not come
up to expectations, showing only 28W-h/lb (S-glass/
- 194 -
-------
. THE ,JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATO~Y
SlLY." "'-'HG, "ARYLAND
epoxy) and 26 W -h/lb (graphite / epoxy). Tensile tests
show that the graphite/epoxy material was substandard,
while the S-glassl epoxy bars had many surface defects.
, The supplier is confident that bars of this same type and
material could be produced by a net-molding process (no
surface machining and more consistent cure conditions)
and would yield improvements in specific energy density
to> 30 W-h/lb. The unidirectional laminae should be in-
terspersed with angle plies to resist flaw propagation that
can lead to an early catastrophic failure.
With respect to rotor configuration, the simple
composite bar is still the most straightforward rotor de-
sign and is of interest for a commuter car application.
The analysis of a pseudo-isotropic composite disk has
shown outstanding potential for a compact. high-energy-
density device. The validity of these results must be
verified by experiment because of the lack of biaxial
stress-strain data for these materials. Finally. two
brush-type rotors comprising hubs and multiplicities of
individual filaments or rods of glass or fused silica .have
been conceived. Since these configurations may offer
the greatest safety in combination with good performance,
they merit experimental evaluation.
RECOMMENDA TIONS
1.
Evaluate the dynamic fatigue (tension-zero-
tension) and stress-rupture characteristics
of various types of glass or fused-silica rods
and of glass/ epoxy composites in a vacuum
. environment. This will determine whether
this low-cost. high-strength material is
applicable for flywheel systems.
2.
Fabricate and test larger bar-type rotors.
using improved processing techniqlies.
3..
Design, fabricate, and test a pseudo-iso-
tropic. glass / epoxy composite disk. .
- 195 -
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THE JOHNS HOJ8KINS UNIVaRSITY
APPLIED PHYSICS LABORATORY
BIL.v.II S~III"'O. W..IIYLJI,HD
4.
Fabricate and test simulations of both circular
brush and radially-fanned brush rotors to verify
the performance of these configurations.
6. 3 CONTAINMENT OF ROTORS
Experiments, both at A PL and at NA PTC, have
demonstrated that the filamentary and composite materiats
destroy themselves as they impact steel containing rings.
Photographic data from NAPTC have shown that the de-
struction of I-pound graphite / epoxy rods takes place in
approximately 600 Us, less than the response time of the
containment ring. Analyses by two methods have shown
that on this test only 1 to 2% of the kinetic energy of the
rod is transferred to the ring, the remainder being dissi-
pated by pulverization of the rod itself. This is in direct
contrast to the failure mode that has been observed for
steel disk rotors, which generally fracture into a small num-
ber (usually 2 to 4) of relatively large segments that in turn
transfer nearly all of their kinetic energy to the containment
ring, as evidenced by the minimal plastic deformation of the
segments and the severe distortions of the containment ring.
Therefore a conclusion based on data that are presently
a vailable is that it should be much easier to contain the frag-
ments of a composite material rotor than it is to contain the
fragments of a steel rotor, and this should be particularly
important for vehicular applications where public safety is
involved.
RECOMMENDA TIONS
1.
. Conduct an experimental program studying
the containment of larger rotors in order
to establish scaling laws for the ratio of con-.
tainment weight to rotor weight, to permit de-
sign estimates for various rotor sizes of
practical interest.
2.
Study the containment of configurations such.
as the pseudo-isotropic, composite disk and
the brush-type rotors.
- 196 -
-------
TJ'4E JOHNS HOPKINS UNIVE:RSITY
APPLIED PHYSICS LABORATORY
S'LVr.,. 51'1II1""G MAIII'I'L"""O
3.
Use computer programs that are available
to correlate experimental data with empirical
formulations of containment requirements.
6.4 FLYWHEEL SYSTEMS
The detailed study of system components such as
bearings, seals, and auxiliary vacuum pumps was not in-
cluded in the scope of the current program; however,
cursory review of these items indicates that the problems
are amenable to engineering development. The degree of
success may dictate the size and type of flywheel rotor
that can be used, which in turn will establish stress cycle
limits for dynamic and static fatigue rating. Gyroscopic
effects on vehicle ride and control were also outside the
scope of this program, though a simple simulation was
programmed as an example. Further studies of this area
could lead to the establishment of limits on flywheel size
for certa in vehicles.
RECOMMENDA TIONS
1.
. Conduct a detailed design, developm ent, and
testing program to qualify flywheel system
components such as bearings, seals, and
vacuum equipment. Integrate these items
and a scaled-up rotor weighing ~ 20 pounds
into a prototype demonstrator flywheel sys-
tem (Fig. 6-1, described below). Selection
of the material configuration for this rotor
would be based on results of experimental
work recommended under Sections 6. 2 and
6.3 if time and funds permit. However, be-
cause an early demonstration of flywheel
system performance, which also would illumi-
nate areas needing greatest attention, is highly
desirable, it is recommended that this work
proceed immediately with either a graphite /
epoxy or an S-glassl epoxy, bar-type rotor.
- 197 -
-------
...-
:.0
CX)
ALUMINUM
BEARING
BLOCK
ALUMINUM
END PLATE
/
J>
11
11..
rx
-,.
..1'11-
;: a 0
< 11 X
;: :I ~
UI- II
-4-
O=:
::0
-<
32 INCH DIAMETER
(a) STRUCTURE SIZED FOR BAR ROTOR TESTS
20 INCH DIAMETER
(b) STRUCTURE MODIFIED FOR DISK OR CIRCULAR BRUSH TEST
(BOLTS AND BEARING BLOCKS NOT SHOWN)
Fig. 6-' DETAILS OF RECOMMENDED WORKING PROTOTYPE STRUCTURE
-------
T"'£ .JOH~~ t-to.-K'NS UNIVERSITY
APPLIED PH 'SICS LABORATORY
!,IL"''''' 5"'''''''1; M""YL.AHn
BALL
BEARINGS
-----
COOLING
---..
WATER
IN
,.~
FERROFLUIDIC
VACUUM SEAL
SIDE PLATE DIMENSIONS
SELECTED TO
COMPRESS LAMINAE
AN AMOUNT GREATER
THAN EXPECTED
CONTRACTION OWING
TO AXIAL LOAD.
. (c) SEAL AND BEARING TEST BLOCK
t
~
TRANSVERSE
CLEARANCE
t
PROVISION FOR
ROTATING FLYWHEEL
UNIT DURING
RUN.DOWN
COMPOSITE BAR
1-3.INCH-50UARE
FOR 0.5 kW-h
DEMONSTRATOR
OIL MIST
OUT
~
---...
WATER
OUT
. ~ ,,'0-
AIR TURBINE FOR
DRIVE OR BRAKING
(e) OVERALL FLYWHEEL TEST UNIT
(dl HUB DETAILS FOR BAR ROTOR
J
Fig. 6.' (Cont'd) DETAILS OF RECOMMENDED WORKING PROTOTYPE STRUCTURE
- 190 -
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THE JOt'4NS ..-.OPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY, .
SIU'r:- S~"'I"'O, M....yl.""'o
2.
Conduct computer, simulations of flywheel
gyroscopi~ effects in a vehicle, including
driver response functions, to assess any
problems in r"ide comfort or control.
A concept for a flexible. working prototype model
to permit realistic evaluation of differen't types of bear-,..
ings. lubrication systems. shaft seals, ahd flywheel
rotors is shown .in Fig. 6-1. The vacuum chamber com-
prises two identical end ~lates separated by a cylindrical
segment as shown in Fig. 6-1a; "0" rings provide vacuum
seals between the parts. and are mechanically positioned
by grooves in the plates. Different size rotors. such as
required for a disk or circular brush, may be accommo-
dated by merely changing the cylindrical insert, as shown
in Fig. 6-1 b. In this way minimum radial and axial
clearance can be maintained.
Figure 6 -1 c shows the conceptual layout of the
bearing and seal attachment. A water-cooled ferrofluidic
seal is used on a reduced-diameter section of the shaft,
mounted inboard of the bearing. The bearing shown is
the angular-contact ball type, supplied with positive lubri-
cation. Thus the bearings and seals are accessible for
. inspection and replacement. .
Figure 6-1d shows a cross section of:th~ hub
attachment of a bar rotor. Numerical stress analysis of
. th~ rotqr has shown that the deformation near the hub is
quite complex. There is a positive deformation in the
directioh of the fibers, and this creates a contraction,
(Poissoni s ratio effect) in the transverse and spin-axis
directions. However, in the transverse direction centri-
fugal forces create a positive component of deformation
which. for wide bars, is greater than the contraction due
to Poisson's ratio. The net result is that the bar will con-
tract along the direction of the spin axis and contract,
s~y;tb~: same,or grow in the" transverseqi~ection depend-
ing on the bar aspect ratio. The.hub attachment accommo-
dates these deformatipns by (a) preloading the, bar in the
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVER SPRING. MARYLAND
spin-axis direction (squeezing) enough to counteract the
expected contraction, and (b) allowing the bar to expand
or contract in the transverse direction without constraint.
The overall arrangement is shown in Fig. 6-1e
with a bar-type rotor installed. The rotor is powered by
an air turbine, and the conical friction clutch can be dis-
engaged for free-wheeling operation. The flywheel unit
can be tilted to produce gyroscopic torques and radial
loads on the bearings. This working prototype system
could be used to evaluate seals and bearings and to demon-
strat~ flywheel run-down and power takeout.
6.5 EVALUATION STUDIES
The city bus is the only vehicle that can meet the
vehicle performance specifications using a flywheel-only
(FO) propulsion system. There still may be application
for FO propulsion in certain classes of central business
district delivery vans and for a small, personal runabout
or limited-range commuter car. Heat-engine/flywheel
hybrid propulsion systems satisfy the performance re-
quirements of all four classes of vehicles - commuter car,
fam ily car, city bus, and van. The near-term choice of
heat engine is the spark-ignition engine; however, the
gas turbine offers the greatest promise for the future be-
cause of its low specific weight, its potential for mini-
mizing emissions, and its operating speed, which is close
to that of the flywheel.
The results of emissions analysis of the hybrid
systems must be considered inconclusive because of the
lack of data on the operation of engines at single design
points or over a very limited speed range. . It is expected,
however, that restricted operation of a specially designed
engine will result in significant reductions in emissions,
and this mode of operation is recommended. The use of
on-off engine operation and relatively large flywheel sys-
tems will permit dual-mode operation of the veh icle, with
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THE JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
Su... ""1:" "".'"0. W.ttYl...ND
long periods of emission-free operation within congested
areas. This remains an attractive concept and should
not be discarded unless other studies show that a large
flywheel is undesirable or that start-up and shut-down
emissions are excessive.
RECOMMENDA TIONS
1.
Obtain emissions data for spark-ignition and
gas turbine engines operating at selected de-
sign points. The engines, which should be
of a size appropriate for use in a flywheel
hybrid system, should then be modified (tim-
ing, carburetion, manifold design, etc., or
corresponding features for gas turbines) to
minimize emissions at the selected operating
condition(s).
2.
Conduct basic combustion research to deter-
mine NO concentrations as a function of dis-
tance from the luminous zone of a flat flame,
thereby answering questions on the existence
of "prompt NO" (see Appendix E) that could
ha ve a fundamental effect on the ability to
meet the 19 76 NO~ standards.
3.
Develop a prototype continuously-variable
transmission and integrate it with an improved
heat engine (item 1 above) and a prototype fly-
wheel system (see Section 6.4). This propul-
sion system then should be installed. in a ve-
hicle to demonstrate heat engine/flywheel
hybrid propulsion. .
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'tHE x)HNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILY~" SPaIJIiIG. M"'.VLAHD
A PPENDIX A
FLYWHEEL SHAPE AND BIAXIAL STHESS
CONSIDERA TIONS
A.l FLYWHEEL PERFORMANCE CHARACTERISTICS
AND THE OPTIMAL SHAPE FOR A RIGID. UNI-
AXIALLY LOADED ROD
A. 1. 1 Constant-Thickness Flywheels of Isotropic
Material
As noted in Section 3. specific kinetic energy E/W
of a rotor of radius R and weight W at rotational speed
w is given by:
<) 2 2
E.rw'" R w
- =.- = k
W 2W I 2g
where
k =~
I WI{ 2 .
(1\ -1 )
and I is the mass moment of inertia about the axis of
rotation. If OJ is specified (for a given Rand W), maxi-
mum E/W can be achieved by using the flywheel configura-
tion with the highest I. and a rim-type flywheel is best.
However, if (J.) is allowed to vary. so that w is, in effect.
governed by the allowable stress of the material, it is not
directly apparent from Eq. (A-1) which flywheel configura-
tion is best. .
In general. the stress in a rotating rigid body can
be related to w through the equilibrium stress balance in
the radial direction. For conditions of plane stress in a
constant thickness flywheel (Ref. 118):
d 2 2
a - - (ra ) - pr w = 0
t dr r '
(A - 2)
where at. a r are the tangential and radial stresses,
p( = 'Y / g) the material mass density. and r the radial
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TMII: .10M... MOPIU", UNIVII:R8ITY
APPLIED PHYSICS LABORATORY
8IL.v." 8PttING. N.Jn"LAND
coordinate. . The last term represents the centrifugal
(inertial) force component. Solution of this equation for
particular configurations (using the appropriate boundary
conditions) permits the determination of the maximum
stress values for each configuration. Equating the maxi-
mum stress to the yield stress (allowable) (j a' given by a
suitable failure criterion - von Mises condition (Ref. 119):
2
2 2
=(J +0' -0' 0'
r t r t '
(A - 3 )
0'
a
determines the maximum speed allowable and. with Eq.
(A -1). the energy storage capability.
A s can be seen from dimensional considerations.
solutions for U)2 will be proportional to O'a/fJR2. so that
we can write:
E (Ja
-=kk-
W I fJg
where
2R2
k-U)
= 2cr IfJ .
a
(A -4)
Solutions of Eq. (A-l) for various standard con-
figurations. solid disk, disk with hole. thin rim. and
slender. uniform rods are readily available. c. f.. Ref.
118. For slender rods the terms involving crt in Eqs. (A-2)
and (A-3) crop out. The useof the failure criterion (A-3)
in these available solutions results in the performance
characteristics shown in the upper portion of Table A-l.
These computations assume that Rand 0' a are specified.
In particular. to determine the allowable U) for the solid
disk and the disk with a center hole. the maximum-stress
solutions given by Timoshenko (Ref. 118) were used. For
the thin rim alid the rod. solution of Eq. (A -2) follows
directly. In all cases 0' max = 0' a occurs at the innermost
radius (r = 0 with no hole; r = ro with a hole). It is ap-
parent from Table A-I that the solid disk is the best con-
stant-thickness flywheel configuration. For other payoff
criteria or other specified parameters (such as the fixed-
(.&.) case mentioned above) the relative merits of these con-
figurations would be different. .
- 204 -
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Tt-4£ JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVl'R SPAI"Kio. MAAYL...HO
T:thlf~ 1\-1
Effects of Shape on Flywhecl I'ropf'rtics
Hotor ConfigUl'ation
Rotational
Speecll
2 ' 2
UJ /('1 /pH )
a
I;;nergy
Storflge
EO/W
(0 IfJg)
a
Moment of
Inertifl
2
I/(WR /g)
(Iniform thickn"Rs rod
1/ :i
- 0
1/:i
1/ '2
2
"( Jpli ma I" rod
"C:onRtant-stress" fa mil)',
Q ~ '2:
-. '"
With ('nd rnress
IJ 0.120
H 0.117
I (j /:{ I /1 '2
!I I / I ()
'2.42 1/ '2
1. '21 I 1/ '2,- 1
h. CD - 0
B O. 2:n
4. 37 0.351
I. 31 0.58
1. 87 0.42
0,41
0.411
Without end rnress
0.4(;
'2/!I( =0.22)
I-II wedge (1\ 0: r)
'2
2-1J I.'.'f'''gf~ (pyramid) (/\ 'r I' )
{Jniform solid di:-;k
! II :~ II( ~,O. .1!»
II, (iO!i
11,:10 1/2
Uniform dm 0.... rholc --: H
Best conRt<1nt-stress solid
disk (theoretical limit)
Const<1nt-stress disk, k = 4
1
0.!)2c,
Hyperbolic (rim, q = 1), best
E/W, rO ~ 0.05
ilyperbolic, best E/V,
r 0 ~ 0, 50
Hye..erhoJic, 2/'/,1 = 4,
rO=I/4
0.77
0.38
1 Equal to 2k or ~2.
'2Rflsed on a rod radius =- 0.15 R (R = arm length);EO/W is degraded as EO/V
is increased (see Section A. 2).
3Rod also tapers almost hyperbolically (Fig. A-2) but still must effectively
occupy an almost drum-like packaging space.
4Hased on a maximum half-width ~ 0.15 R.
- 205 -
Packaging
Efficiency
EO/V
-------
THI[ .K)HHS _INS UHIVI[II8ITY
APPLIED PHYSICS LABORII.TORY
8tLva:. tlPltllIIQ. M.""~ND
A.1. 2 Optimal Rod Flywheels (Rotors) of Isotropic
Material
Consider a slender rod of variable cross-sectional
area, A = A(r) spinning about its center point (r = 0), and
having a specified R( = rl) and a given weight W. Because
of the variable area, the overall weight must be specified
as:
R
W = 2pg J Adr,
o
(A -5)
and the radial stress equation becomes:
d 2
- (Acr ) = - 1\1.\ rA cr(R) = 0 .
dr r ,.,- , .
(A -6)
The limitirJg stress relationship is cr ~ cr~, and the energy
to be maximized by optimization of r A(r} is:
R 2 2
E = p J UJ r Adr,
o
(A -7)
which is equivalent to maximizing E/W, since W is spe-
cified.
From the limiting stress relationship, cr r s; cr a' it
follows that the optimal configuration may consist of two
segments: crr < cra and crr = cra' The shape of the region
where the inequality holds is not ascertainable, since the
resulting Eq. (A-B) contains two unknown variables crr and
A. When cr r = cr a' Eq. (A -6) yields:
- 2(r/R)2 2 2R 2
A = A e a , where t:t == U,) .
o 2cr Ip'
a
(A -8)
and AO =.A(O), and the solution is specified when a,
the dimensionless rotational speed, is specified. . Physical
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THE JOMNS HOP,,"'N!) UNiVERSITY
APPLIED PHYSICS LABORATORY
SIL.VI!" ~RIHG ".A"'~ANO
reasoning suggests that the optimal rod should be in a
state of maximum stress throughout, since, if this were
not the case, some of the material existing in a region
where a r < 0a could be redistributed and therefore effec-
tively increase E Iw. On the other hand, if a I' ::: ° a over
the entire rod the boundary condition a(R) ::: 0 cannot be
satisfied. Thus, the optimal rod is one wherein ° I' ::: a a
throughout except for a small segment at each end of
length 6R and mass me' This end segment m::1,y be of any
shape as long as me is sufficient to give ar ::: Ga at I' ::: R - ~H.
(The end condition will be considered again below.) More-
over, to make me as small as possible, a2 should be as
large as possible. That this condition leads to the maximum
payoff is borne out by the following constant-stress flywheel
solutions.
A ssume now that the size, mass and energy of the
end mass are small. From Egs. (A -7) and (A -8) it follows
that:
W
2t)gA OR
::: J f( erf(a)
2 a
(A - 9)
]!:
a
( :!. v" rr .
Jf'i -1:'1'1(",)
l 2' 'L
- ..' rr
lex .r: erf(s)ds
- .I (Y. "t (' I' f( s) d s d t I j.
00'
t)/\OH
f)r'i
where s is:) dummy vadable, so that:
E/w ::: G(a)v It)g,
a
(A -1 0)
2
G(cd ::: a
a a t
2a 2
r erf(s)ds + f() J J erf(s)dsdt
erf(a) "0 er a 0 0 .
again indicating the independence of E Iw from the actual
dimensions of the flywheel. G(a) can be evaluated directly
using complementary error functions. In the limit as
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THIE .K)H1d _INS UNIVERSITY
APPLIED PHYSICS LABORATORY
"'LV.. "'NO. ",AIIYLAJIfD
a ... ft', G(a)... 1/2. Figure A-l shows E/W referenced to
E/W for the uniform rod (see Table A-l) versus a. The
area distribution for various values of a from Eq. (A-8)
is shown in Fig. A -2.
Although it would be difficult to construct the opti-
mal rod flywheel. various approximations to the optimal,
in the constant-stress family, a < co, can perhaps be con-
structed. For reference, the optimal case as well as a
possibl~ approximation (Q = 2) are included in the lower
portion of Table A-l. Other rod flywheels such as the
double pyramid [A/AO = (1 - r/R)2) also approach the
optimal. .
To complete the analysis it is necessary to show
that me ... 0 asa ... ft', i. e., the end mass is small for the
optimal rod. Moreover, for the solutions to be valid for
other values of a it must be demonstrated that the effects
of the end mass can correctly be neglected. Consider for
simplicity a concentrated end mass me located at r = R
(the subscript e refers to the end conditions at r = R). A
simple force balance at this location results in:
m . = (J A / CJJ 2R = fJA R / 2&. 2 ,
e a e e
(A -11 )
from which it is evident that as ex .... 00, me"" O. Using this
relation and the area distribution, Eg. (A -8), it follows
that:
W
e
--
W
aJ. /g
e
W
1
- 2/11
2
-ex E (j
e ~ = 2&.2 ~
ex erf(Q!) , W 2fJg
e
; (A-12)
E 2
e 2 -a
- =-e
W Iff
(j
a a
erf(ex) 2fJg .
(A -13)
Figure A -3 shows (Ee/W)/(E!W) as derived from Eg. (A -13).
For ex ~ 3 the concentrated-end-mass contribution is negligi-
ble. For the a = 2 case shown in Table A -1, the end mass
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SILV~R SP'It,...G MAAYLANO
THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
o
:!
<{ 0.5
o
~o
2.0
~Q
20
:>a: 0
~I~ 1.
ww
o
o
3.0
1.0
2.0
Q = WR/.J2o Alp
4.0
Fig. A.' CONSTANT STRESS FLYWHEEL PERFORMANCE
1.0
t It- (a" 2)
u 0
o
o
0.2
0.4
0.6
0.8
1.0
r/R
Fig. A.2 THICKNESS DISTRIBUTIONS FOR CONSTANT STRESS ROD FLYWHEELS.
(to/ta=2 = THICKNESS OF UNIFORM ROD WITH SAME WEIGHT AS a = 2
CONSTANl STRESS CASE.).
- 209 -
-------
THC X)HH8 -,. UNIVERSITY
APPLI/U) PHYSICS LABORATORY
"LY." .......... M.8YUNO
contains 4% of the total energy and about O. 3% of the mass.
While the solutions for large Q (including the optimal)
are therefore valid, solutions for Q < 2 using small values
are not, and a proper analysis of a rod for Q < 2 would en-
tail a combined set of computations considering both the
. constant-stress portion of the rod and the end mass. For-
tunately, such cases are of little interest. For large Q
the end mass becomes a very efficient energy storage por-
tion of the flywheel [Eg. (A -13»), but the magnitude of Ee
becomes very small. [Similar results can be obtained by
considering the end mass to be finite in extent. In this
case the constant-stress results would be somewhat in
error, since the constant-stress region goes only to
r = R - AR. If AR/R is assumed small a mass balance at
R - AR yields AR/R = 1/(2 Q2), confirming the conjecture.
For Q = 2, AR/R = 12.5%; and Q must be 5 to reduce
AR/R to 20/0. Thus, for end regions of finite length, the
analysis is more in error than for the "concentrated" end
mass case. )
The end mass given by Eg. (A-ii) need not have
any particular configuration so long as it is of a form which
does not violate the boundary condition, O'(R) = 0; however.
it must be present to give a constant stress throughout the
remainder of the rod. The saving grace in the actual con-
struction of such flywheels is the fact that the absence (or
incorrect value) of the end mass at large Q will only
slightly alter the stress distribution throughout the rod
and thus give an almost optimal value. This is illustrated
by the stress distributions shown in Fig. A-4 and the final
listing in Table A -1. .
A. 1. 3 Theoretical Performance Capabilities for
Isotropic Rotors
The optimal rod flywheel, while not feasible as an
actual design, represents a basis for comparison of other
candidate flywheel configurations. Using maraging steel
as an example of current high strength isotropic materials,
O'a = 400 ksi, Y = pg = O. 28lb/in3, it follows that the best
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f'H~ .JOtotNS H~INS UNIVERSITY
APPLIED PHYSICS LABORA.TORY
$ILYI:. ~"'HG. ""IIYLAND
Ee/W
-0.5
E/W
1.0
2.0
a:
3.0
4.0
o
o
1.0
Fig. A-3 EFFECT OF END MASS ON CONSTANT STRESS FLYWHEEL PERFORMANCE
a/a A 0.5
1.0
0.75
0.25
CD OPTIMAL (a = ~)
@ OPTIMAL SHAPE -
WIO END MASS, a = 2
@ OPTIMAL SHAPE.
WI UNIFORM END MASS, a = 2
@ UNIFORM BAR (a = 11
@ WEDGE (a = 1.631
CD
0.5
rlR
0.75
1.0
o
o
0.25
Fig. A.4 STRESS DISTRIBUTIONS IN VARIOUS ROD FLYWHEEL CONFIGURATIONS
- 211 -
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THE JOHNS HOPKINS UNtVERSITY
APPLIED PHYSICS LABORATORY
SIL"E." ~'"NG. "'''''''fLJ-'''O
rod flywheel configurations would approach E/W = 59 600
ft-Ib/lb = 22.7 W-h/lb, as compared to 15.3 W-h/lb for the
uniform rod and 27.5 W-h/lb for the uniform disk. (For
conventional steel (ja = 140 ksi, E/wlopt. rod = 7.9 \t\'-h/lb.
Values for other contlguratlons and properties can be com-
puted using the information in Table A-I.) Further im-
provements using isotropic materials can be achieved us-
ing optimal (nonuniform) shapes for other flywheel con-
figurations, e. g., the solid disk, as discussed in Section
A-3.
It is desired to use the increased uniaxial stress
properties of fibrous and fiber-composite materials in a
flywheel composed of rod type elements. Since E/W
-------
TH£ .JOHNS HOPKtNS UNiVERSITY
APPLIED PHYSICS LABORATORY
SILVIE- SPtttJi8G. ""''"LAHD
the energy storage capability. In this section a method of
solution based on collocation is used to provide approxi-
mate results for the biaxial stress field. Using Hill's yield
criterion (Ref. 120j for anisotropic materials, limiting
rotational speeds are determined as a function of bar
aspect ratio (width/length) for several fiber-composite
materials, and corresponding energy reduction factors
are presented.
A. 2.1 Method of Analysis
Among approximate ana'1ytical methods (Ref. 121),
weighted residual techniques are very effective. A trial
solution, in terms of undertermined parameters, is se-
lected and the parameters are determined in such a way as
to make a residual equation zero. Each method is classi-
fied according to the manner in which the residual equa-
tion is formed. One method in particular, collocation, is
most direct, requiring only a substitution of the trial solu-
tion in the governing differential equation, whereas other
methods require integrations. Collocation is analogous
to curve-fitting with the assumed solution sntisfying the
governing equation at all collocation points. The accuracy
attained depends critically on the selection of the form of
the trial solution. Problems in heat conduction (Ref. 122)
and elastic plate analysis (Ref. 123) have illustrated the
ease in application of the collocation method.
The conditions of equilibrium for an element of the
rotating bar in plane stress (Fig. A-5) are:
ocr
--=:. + oT + R = 0
or ot
ocr
oT +.-.! + T = 0 ,
or ot
(A ~ 14 )
where cr r' cr t,_and T ~re. the axial, transverse, and shear
stress and Rand T are components of the body-force
caused by rotation. With the body-force field obtained as -
the gradient of a potential V:
R =- oV / 0 r .
T=oV/ot.
(A -1 5 )
- 213 -
-------
ROTATING BAR
SOLUTION
-
-
AUXILIARY GAR
SOLUTION.
POTENTIAL FIELD
»
"'0
"'0...
r :t
-'"
co'" ..
rOo
< "D :t
: I 3
co -< :t
: (j) 0
- - ..
z n "
" (j) -
Z
J: r co
; > c
... aJ Z
~ 0 ;:
z ;u '"
o » =
en
;u
-<
~
......
~
T
x
1
_pw2(x2 + b2)
2
~
y
.y
~
b
x-
.!.PW2 (x2 + y2)
2
~a-1
Fig. A.5 FORMULATION OF ROTATING BAR PROBLEM. NOTE THAT THE THIN PLATE
OR BAR IS IN PLATE STRESS
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SU.VIA SPAING. "'AIltT!..AND
Equations (A-14) are identically satisfied when:
o~
a +V=-
r - 2 '
ot
o~
- -
°t+V=--:2,T=
or
2-
o\}r
i.Jri.Jt '
(A-iG)
--
where '¥ is a stress function and:
:-. 2 2 2
V ~ ip w ( r + t ).
(A -1 7)
For isotropic problems, the usual procedure is to
substitute the stress-strain relations into the compatibility
equation and use the definition of the stress function. When
body forces are absent, the solution of a biharmonic equa-
tion for ~ is required. However, for the anisotropic
p~oblem with body forces, a slightly different approach
will be used. The formulation follows from the use of an
artifice discussed by Flligge (Ref. ~4) known as Biot's
Theorem. The particular solution '¥ == 0 of the biharmonic
equation yields for the stresses:
o = 0t = - V , T = 0 .
r -
(i\-lS)
This represents the solution if the boundary c£.nditions
specify the application of a normal pressure V at all
points of the boundary, which is in equilibrium with the
body forces. Since forces different from this pressure
are prescribed at the boundary (namely stress-free con-
ditions), the solution is the sum of Eq. (A-iS) and a stress
system for zero .,£,ody forces and an edge load equal to the
normal tension V. Therefore, the stresses in a rotating
plate (or bar) can be derived from an auxiliary stress field
Sr, St' and S for a plate without body forces subjected to
T -
a normal stress V applied to all points of the boundary;
the actual stre sses are then:
a r = Sr - V , at = St - V , T = S7
(A -19)
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THE JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
SILva- s.--ING. M""YLAND
The situation is illustrated in Fig. A-5. With the body
forces removedJ the equilibrium equations:
as lor + as I~t = 0
r 'j'
aST lor + aSt/at = 0 .
(A - 20)
are satisfied by:
2 2 2 2 2
Sr = 0 /Plot. St = a fIllar . S'T = - a ~/arot . (A-21)
The stress-strain relations for an orthotropic
plane stress material are:
t = (S -II tSt)/E ; tt = (St -lit S )/Et;T = S IG t. (A-22)
r r r r . rr T r
where II r Er = II r Et. and the elastic constants Er. Et.
Grt. and IIrt are the Young's Moduli in the principal direc-
tions. the shear modulus. and the major Poisson's ratio.
When the constitutive equations [Eqs. (A -22)] are
substituted into the compatibility equation:
2- 2 2 2 2
o l' /orat = a tr/ot + 0 t/or .
(A-23)
and the stress function is introduced via Eqs. (A -21). we
obtain the following fourth-order equation:.
044> 044> 044>
L44> = ---:r + 2 P 2 2 + m 4 = 0 .
or or at at
(A -24)
where p == m[n + IIrt(n-l)). n == Er/2(1 + IIrt)G t' and
m == Et I Er' Note that for an isotropic materfal Eq. (A - 24)
reduces to the standard biharmonic form with p = n = m = 1.
In summary. to obtain the solution for the stress
field in a rotating anisotropic bar: (a) Eq. (A-24) is solved
according to the boundary conditions for the auxiliary
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TtotE JOHNS ~tNS UN'V~ASITY
APPLIED PHYSICS LABORATORY
SILV'. .....NO, M...YL."'O
problem, and (b) the stresses are determined by Eq. (A-10)
as the superposition of the potential field on the stresses for
the auxiliary problem, Eq. (A-21).
Some form must be assumed for the stress function.
Referring to Fig. A -5, the distribution of boundary stresses
on the auxiliary problem consists of a combination of uni-
form and parabolic components. A somewhat similar prob-
lem having a parabolic stress distribution on the boundaries
r = :t R was solved by Rivello (Ref. 125) using both finite-
difference and Rayleigh-Ritz solution techniques. (The
Rayleigh-Ritz procedure uses energy principles to obtain
approximate solutions.) This problem is illustrated .in
Fig. A -6 together with a comparison of the normal stresses
given by each approximate solution. The finite-difference
solution was based on a relatively crude mesh of 12 grid
points, but more important, the Rayleigh-Ritz solution
resulted from the following assumed form for the stress
function:
cZ> = ct4 + (r2 - R2)2 (t2 - T2)2 (a + a2r2 + a3t2) . (A-25)
12 . 1
The first term satisfies the essential (force boundary) con-
ditions, whereas the remaining terms are chosen to give no
stresses on the boundary. Since the loading is symmetrical
about the r- and t-axes, only even power terms were in-
cluded in the polynomial series. Although each method pro-
duces an approximate solution to the problem, because of
the form of Eq. (A -25), the Rayleigh-Ritz method gives ex-
act results for a r stresses at r /R = :t 1.
The similarity in boundary conditions between the
problem of Ref. 125 and.the auxiliary problem of the ro-
tating bar suggests the choice of Eq. (A-25) for the assumed
form of the stress function. To validate the collocation
method of solution for the rotating bar, the problem of Ref.
125 was resolved by collocation, and the results were com-
pared with the three-term Rayleigh-Ritz solution. For
collocation, up to 11 terms were included in polynomial
series:
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o
0 1/3 2/3
(a) ax
y/b
0
1/2
THE JOHNS HOPK ,,..,S UNIVERSITY
APPLIED PH',SICS LABORATORY
Sl~vt,. S~.''''G ~A.""\...ND
y/b
1/2
o
o
y
j..-a
a
I
X = cy2
EXAMPLE PROBLEM
X = cy2
SCA LE
~
2.0 ch2
x/a
~-~
a - 3
,.
SCALE
~
2.0 ch2
x/a
1/3
2/3
(bl 0y
Fig. A-6
COMPARISON OF RAYLEIGH-RITZ SOLUTION WITH FINITE-DIFFERENCE
SOLUTION. THE SOLUTION IS SHOWN AS A DASHED LINE (SYMMETRICAL
ABOUT X AND Y AXES) (REF. 125)
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THE .IOHfIIS HONIMS UNIVERSITY
APPLIED PHYSICS LABORATORY
8.....,." ~NG. """YLANO
~ ~ 22 4 4
F = a + a r -t a 'J t + a 4 r t + a r: r + a ,t
] 2.} ,) ()
24 42 44 6 6
+ a7r t + aSr t + a~/ t + a1 Or + a11 t .
(A-2())
To apply the collocation method, we select as many loca-
tions* as there are undetermined parameters ai' substi-
tute Eq. (A -25) into the biharmonic equation and solve the
linear algebraic system for the unknown coefficients ai'
For example, using the first four terms in the polynomial
would require four locations to evaluate the biharmonic
equation. Table A -2 summarizes the various solutions
corresponding to a specific number of terms in the poly-
nomHll for several collocation patterns. SelectE.d collo-
cation solutions are compared with the three-term Ray-
leigh-Ritz solution in Table A-3. For the parabolic
boundary stress distribution, very little accuracy is gained
by including more than six terms in ,the collocation solu-
tion.
A. 2. 2 Results for Fiber-Composite Rotating Bars
Based on the foregoing results, a six-term poly-
nomial was adopted in the solution for the stress-function
to evaluate rotating anisotropic bars:
"" 1 2(6R2t2 t4 6T2 2 4) (R2 - r2)2x
... = 12 pw + + r + r +
2 22 2 2 22 4 4
(T - t ) (al + a2 r + a3t + a4r t + a5r + a6t ). (A-27)
The first term in Eq. (A -27) satisfies the stress boundary
conditions of the auxiliary problem (Fig. A -5), whereas
the remaining terms vanish on the boundary. Using the
*
The collocation points, although arbitrary, . should be uni-
formly distributed over the domain to insure the best
possible results. .
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THE JOHNS HOPK INS UNIVERSITV
APPLIED PHYSICS L.A80RATCRY
SIL VIE" SP.ING h4."YLA"'O
Table A-2
SUMMARY OF COLLOCATION FOR CHECK PROBLEM4
F ~ a, ~ a?~2 + a3y2 + a4x2y2 + asx4 + asy4 + a7x2y4 + asx4y2
+ agx4y4 + a, ox6 + a'1 yS
a, a5 a7 a'0
COLLOCATION
PATTERN a2 a4 ag
a3 as as a"
A. 0 -0.06657
-0.03578
-0.00483
B. 0 -0.06961
-0.04392
-0.00476
C. EJ .0.0950
-0.03707
-0.00044
D. E] -0.06952
-0.04432 .0.01906
-0.00602
E. IJ -0.06941 .0.007529
-0.04597 .0.01467
.0.005504 0.000161
F. EJ -0.07005 .0.006854
.0.04757 -0.01890
.0.005672 0.00030
G. EJ -0.06564 -0.001248 0.03611 -0.00990
. -0.03' 34 0.020693 0.01896
-0.004177 0.000101 0.07883 -0.00078
H. 0 -0.070435 .0.00557 -0.0130 -0.00218
.0.04801 -0.02529 .0.01055
-0.006184 0.000219 0.00735 0.000228
I. b.. 1 -0.070241 -0.00862 -0.00230 0.000065
.0.04903 -0.02069 -0.00480
-0.005671 0.000262 -0.01246 0.000033
J. -0.070239 -0.ooB63 -0.00235 0.000064
Ii!] -0.049015 -0.02066 -0.00444
.. .0.005672 0.000260 .0.01237 0.000035
K. 0 -0.06914 -0.02040 0.04154 0.00839
.. -0.05216 -0.01765 -0.00972
Y .0.003581 0.000449 -0.09131 -0.00079
Lx
'NOTE: COEFFICIENTS AI ARE NON DIMENSIONAL WITH RESPECT TO x ~ x/a, y ~ y/b.
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Table A-3
Comparison of Collocation Solutions with the llhree-Term
Rayleigh-Ritz Solution from Ref. 8
Collocation 2
Rayleigh-
Ritz :\ 0 F H I
at -0.0700 -0.0666 -0.0698 -0.070 -0.0704 -0.0702
a2 -0.0557 -0.0358 -0.0443 -0.0476 -0.0480 -0.0490
a3 -0.00769 -0.00483 -0.0060 -0.00567 -0.00618 -0.00576
t\:)
l\j a (0,0) 0.1176 O. 1141 O. 1187 0.1195 O. 1197 O. 1198
.....
x .
a (0,0) 0.0333 0.0385 0.0376 0.0365 0.0367 0.0361
Y
a (0, n 0.1676 0.1906 0.1748 0.1763 0.1736 0.1756
.x
'J (1,0) -0.1986 -0.1618 -0.1804 -0.1967 -0.1994 -0.2020
Y
Notes:
lCoefficients ai are nondimensio~al with respect to x = ;'/a, y = y/b.
2 A 11 solutions, except .-\, have additional terms ai; refer to Table .'\-2.
)0
"
"..
'x
-..
!ITI~
~ 00
< " x
: J: ~
J~~
! n;1
. \11 i
~ > c
~ III Z
\:0<
";US
a )0
"'4-
o~
;u
-<
-------
THE JOHNS HOPkiNS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVEIIt S"!ltING. "'~.YLAHD
above assumed solution form, Eq. (A -24) was collocated
on pattern (F) of Table A-2. The coefficients ai were de-
termined with different values of width to length ratio T /R
for six fiber-composite materials. Table A -4 summarizes
the propertles corresponding to the indicated fiber volume
percent (vf). The stresses ° r' at, and 0 rt are the axial,
transverse and shear strengths, while the strength/ com-
posite density parameter 0r/fJ is proportional to E/W for
the uniaxial composite rod;
The biD,xial stresses in the anisotropic bar were
. computed, as discussed in Section A. 2. 1, by superimpos-
ing the stresses for the auxiliary problem on the potential
field caused by the body forces. Typical nondimensional-
ized distributions are shown in Fig. A -7 for a high-
strength graphite/epoxy (Hercules 2002T) composite for
various aspect ratios. For a uniaxial rod the limiting
axial stress is equal to IPw2R2, but for a biaxial situation,
or at the center of rotation> ifJW2R 2. The transverse and
shear stresses are two orders of magnitude less than or
and reach their maximum values for tiT > 0.50. Increas-
ing the aspect ratio T /R causes a moderate increase in
the maximum axial stress*. However, an 80% increase in
T /R causes more than three-fold increases in the trans-
verse and shear stresses.
Since the stress distributions are nondimensional-
ized with respect to tfJUJ2R 2, they are independent of w,
but to evaluate the E/W capability, an U,) must be speci-
fied to determine limiting stress conditions for the fiber-
composite bar. For an orthotropic material in plane
stress, a generalization of the von Mises isotropic yield
criterion, known as the Hill criterion, has the following
form: .
*
Note that as the aspect ratio increases the transverse
distribution of the axial stresses becomes more nonuni-
form, tending to decrease along the boundary tIT = 1.
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THIt JOHNS HOrKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
S.L~. ---ING. M...'fLA,ND
Table A -4
Properties of Fiber-Composite Materials
" E1 (11
E 1112 ";2 a Ip
2 1
G12 IIf ,) 12
106 ps i 1 O:~ psi 106 in
Boron/Aluminum 34.2 0.25 164 1. 80
23.4 0.50 13. 9
11. 0 15. 6
Boron / Epoxy 30.3 0.16 212 2.94
(Hercules 2002B) 3. 1 0.55 13
1.4 13. 5
Graphite / Epoxy 21. 5 0.25 204 3.78
(Hercules 2002T) 1. 44 0.59 11. 8
O. 61 14
'Graphite/Epoxy :W.1 0.28 13S 2. ;~~,
(Hercules 2002M) 1.0 0.58 7.6
0.61 13. 7
S-Glass/Epoxy 7. 65 0.27 264 3. 67
(Hercules 828-5994) 2.24 0.60 7.5
O. 78 8.5
E-Glass/ Epoxy 8.0 0.25 157 2.20
2. 7 , -0. 60 4. 0
1. 25 6. 0
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THE JOHNS HOPKINS UNIVERSITY
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S'LVE" SP"'NG. M....VL,AND
c:) 2 - g C;) G:) + G:) 2
( - )
+ -I-
0"12
2
-;1.
(A - 29)
where g = (j 2 (cr- l' and 0" r. 0" l' etc.. are actual stre s se s
divided by ,~",,2R2. For a uniaxial rod the rotational speed
(or specific energy) is directly obtained from the uniaxial
strength as:
2 2
""0 = 2crl/ ~a .
(A -30)
However. for a rotating bar, (.a,) is dependent upon the bi-
axial stress field through Eq. (A -29). That is. for a given
aspect ratio, an "" must be determined such that the
equality in Eq. (A-29) holds at some point in the bar. Com-
putations show'this point to be on the center of rotation.
For example. the limiting rotational speed (specific energy
storage) of a graphite/epoxy (Hercules 2002T) bar of aspect
ratio 0.10, is {94%)t of the"" computed on the uniaxial
composite strength. The stress-distributions are pre-
sented in Fig. A -7. This reduction in "" may be viewed
as an energy reduction factor owing to the biaxial loading
condition on the bar. Such a factor may be determined for
each fiber-composite material in Table A -4. as a function
of aspect ratio. Figure 4-2 shows the dependence of E /W
capability on aspect ratio for each composite material.
The glass/epoxy bars suffer the greatest percentage
degradations at large aspect ratios. while boron-com-
posites are the least affected. In terms of the largest
specific energy storage (E /W a: G a /~) the high-strength
graphite / epoxy is the superior composite material with a
wide bar configuration (T/R - 0.18). providing a Ga/p in
excess of 3 x 106 inches. .'
A.3 OPTIMIZATION OF DISK FLYWHEELS..
Classically two special cases of variable-thickness
disks have been studied (Refs. 126 and 127), the constant-
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TH£ .JOHNS HOPkiNS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVER ""'HG. MA.YLAHD
1.5
/ \ '"
\ 0
\ / "
1.0 '"
a:
/ \ -'"
\ ~ 3
Q.
rIA = 0.813 tIT = 0.60 / ~
III
'"
\ 0.5 0
x
I~
0
6.0
I = {0.10
A 0.18 '"
0
x
4.0 '"
r/R = 0.75 a:
- --- - "'\ ~N
I:> 3
".,- Q.
,/ \ ~
'"
/ lIT = 0 '"
2.0 0
/ "
-
II:>
/
0
I = { 0.1 0 1.5
R 0.18
r/R = 0
1.0
'N
o~
III
I~
0.5
--t/T=O
1.0
0.5
tIT
o
r/R
Fig. A-7 STRESS DISTRIBUTION FOR A GRAPHITE/EPOXY (HERCULES 2002T) BAR
- 22:1 -
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THI: .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
a'LVIU' Br'.'NG. ".IItTLAHD
stress and the hyperbolic- thickness-variation cases, be-
cause the use of either of these assumptions permits the
direct solution of the stress equilibrium equation(s), and
probably also because the resulting solutions give a family
of solutions which the designer can use to solve or "opti-
mize" his problem.
A. 3.1 Constant-Stress Solution for Disks.
For a rotating, variable-thickness disk the stress
equilibrium (radial direction com{X>nent and compatibility
(Hooke's law» equations are (c. f., Ref. 126):
d 2 2
dr (z r O'r) - z O't + z" ~ r = 0 ,
(A - 31 )
dO' t dO' r 1 + .
- - U - + ~ (0' - 0' ) = 0
dr dr r t r '
(A - 32)
where the radial displacement has been eliminated from
the radial anc tangential stress-strain equations to give
the stress compatibility relation, Eq. (A -32); 0' rand O't
are the radial and tangential stresses, respectively, r
is the radius, z is the thickness, and"" is Poisson's
ratio. These equations contain three unknown variables
(O'r, 0'1' and z) and an unspecified constant w. Generally,
~ can be deter-mined by the specification of an overall,
i. e., integral, disk property such as W or 0' a' depending
upon the specific problem; in any case solutions for the
variables, 3.S functions of r, can be made in terms of (1).
An additional relationship is needed to permit solution for
the three variables. Usually, as in most problems, this
relation is supplied by the assumed failure criterion. By
assuming that the stress is constant throughout the disk,
i. e., 0' r = 0' t = 0' , a direct solution of Eg. (A -31) is possi-
ble (Refs. 126 a~d 127), yielding:
k-2
- r
z = Ze ,
2 2 2
k =,,~ R /20' (=~ ),
a
(A - 3 3)
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THE: JOHNS HOPt(INS UNIVDtSITY
APPLIED PHYSICS LABORATORY
SILva:. Bf'It'NG. MA.V\.AND
where Z is the innermost disk thickness. and r == r fR.
Note that the compatibility equation is satisfied identically.
This result is similar in form to the uniform bar case, as
is the computation of E/W given below (which is in fact,
somewhat easier. since odd powers of r appear in the
I and W integrals. making their solutions straightforward;
i. e., error functions are not needed). Using Eqs. (A -1),
(A-4). and (A-33). it follows that the dimensionless weight,
moment of inertia. and Efw are given by:
W fl- -kr 2 - 1 -i
2 = r e dr = - 2k (e - 1) ,
2"gpZR 0 .
(A-34)
I 1 3 -kr 2 - 1 -k
4 = f 1" e dr =-(1 - (1 +k)e ), (A-35)
2'ITpZR 0 2k2
and
-k
~ = 1 - (1 + k)e
W (1 - 2-k)
(J
a
pg .
(A-36)
A s in the 1-D rod case. these solutions depend upon the
value assigned to k. which in effect sets the remaining
as yet unspecified geometric variable, say Z or W.
Moreover. an end-mass problem (analogous to that in the
I-D rod problem) exists. since at r = R the stress is not
equal to (Ja unless R ... CX>. Because the end thickness be-
comes exponentially smaller as r... R, the end mass is
probably of no consequence for large k, as shown for
the 1-D case. Evaluation of Eq. (A -36) shows that the
maximum Efw is achieved for k ... cx>, which is the best
value in the optimal family of constant-stress disks (dis-
cussed later) as well as for the rod. In this case as
k... cx>, E/W... 1 . (Ja/pg. With this use of (Ja' the allowable
stress, the constant-stress assumption is tantamount to a
failure criteria. and is similar to the 1-D failure criterion
(also constant stress). In this case, however, it has not
been fully demonstrated that the constant-stress-failure
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1'HE JOHNS HOPKINS UNIVlER91TY
APPLIED PHYSICS LABORATORY
SILV~" ~"'NG. ""'''Y\...AfoIO
'.
,
assumption is the most appropriate for 2-D problems (opti-
mization. or ot,herwise), but it is clear that the general re-
sult represents a possible, if not fully optimal, solution*.
To illustrate how closely more practical disk
shapes can approach the best constant-stress values, a
pl9t of dimensionless E/W and Z / Z versus k is shown
in Fig. A-B, where Zu is the thi~ness of the uniform-
thickness disk having the same weight as the disk in ques-
tion. For k = 4 [corresponding to the Cl::: 2 rod case Eq.
(A-8)], Z/Zu = 4.07, not too unreasonable a geometry,
and E/W is 92.5% of the best value obtainable. Thisdisk
and even other less drastically shaped disks are signifi-
cantly better than the uniform disk and I-D rod cases (see
comparisons in Table A-I). The packaging efficiency for
constant-stress disks is given by:
-k
E/V = (1 - e (1 + k)] (J /k.
a
(A - 3 7)
These values are also shown in Fig. A-I.
case, E/(J V = 0.227 (see Table A-I).
a .
For the k ::: 4
A. 3. 2 Hyperbolic-Thickness - Variation Disks
The other case of classical interest, the assump-
tion of a hyperbolic thickness variation, z = zl r -q (where
q is a positive number, and zl is a fixed edge reference
thickness at r = 1), when substituted into the combination
of Eqs. (A -31) and (A -32) formed by eliminating (J t, re-
sults in an integrable s~cond-order differential equation
in terms of the group zr(J r. The exact form of the results
*
Constant (J corresponds to the Tresca failure condition
and, in fact may be a suitable failure criterion (Ref. 119).
To account for a more appropriate biaxial failure criterion
an appropriate r.eduction (say, 10%) can be made in the
allowable maximum in the constant-stress case, and cor-
respondingly in the energy content levels (E/W, etc.) .
achievable.
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THE JOHNS HOPKINS UNiVERSITY
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S'Lva- 9~"IN(.. Iro4IAIltYL.a,,1O
1.0
0.2
4.0
5.0
0.8
0.6
0.4
k = pw2R2/2Ua
Fig. A.8 GEOMETRIC AND PERFORMANCE PARAMETERS
OF A CONSTANT-STRESS DISK FLYWHEEL
0.6
.5- / ~.a
- W 1'9
0.8
0.4
2 2
k = ~ x 10.1
w Ua
0.2
0.8
1.0
- rOo 21-
rO = R = Z
Fig. A.9 PERFORMANCE PARAMETERS FOR HYPERBOLIC DISKS (ra: 1/2) WITH
SMALL CENTRAL HOLE. INNER-TO-OUTER RADIUS RATIO EQUALS INNER.
TO-RIM THICKNESS RATIO.
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""'" JOHNS HO~KINS UNIVIEA81.,V
APPLIED PHYSICS LABORATORY
"LV'. S~"'HO "'..Y'LAHD
depends on the value of q (which can be chosen to give a
desired thickness variation),and a family of solutions is
obtained for each q selected. To maintain the hyper-
bolic shape there must be a central hole, for as r ... 0,
z / zl ... CD, thus hyperbolic solid disks are not possible.
Thus, the members of each family are characterized by
the yet to be specified inner radius (rO) and w, which in
turn are determined from the system parameters, such
as W or (J a' or other geometric parameters of interest.
By assuming the von Mises failure criterion (Ref. 119).
Eq. (A-3), the maximum E/W member of the family (vari-
able rO) "ordinary" hyperbolas, q = 1, z/z1 = 1/t:"was de-
termined. This was done by finding the maximum stress
point for each value of rO by algebraically locating the
maximum of Eq. (A-3) with respect to r and then numeri-
cally evaluating the expression for the maximum stress
point, rmax at each rOo The location of this point yields
the maximum stress in terms of w, i. e., yielding k
from Eq. (A-4), and permits evaluation of the flywheel
performance. For the ordinary hyperbola:
. 1
4 . -3--
1/( 2fTtJ R z 1) = S- r z dr = (1
rO
- 3
-rO)/3.
(A-38)
. 2
W / ( 2ft (J g H z 1 )
1
= S-
rO
r z dr = (1 - r 0) .
(A -39)
- 3
E 10-rO)
W - "6 (1 - r )
o
cr
k~
tJg ,
(A -40)
E 1 - -3
- = - k r(1 - r ) cr .
V 3 0 0 a
(A -41 )
The computations for the maximum stress for each
case (value of rO) have shown that, for all but the smallest
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THE ~HMS HOPt(INS UNIVERSITY
APPLIED PHYSICS LABORATORY
Sf Lvi. a."ING. MAlIIl"LANO
inner hole (i. e., for rO > 0.05), the maximum combined
stress occurs at the center. These results for k(.c) and
consequently Efw and E/V from Eqs. (A-40) and (A-41)
are shown in Fig. A-9. The best performance, E/W""'
O. 77 (Ja/pV occurs with a small (nonzero diameter) central
hole. The effect of the shift in the maximum stress point
to the interior is reflected in the shape of the E /W curve
at low rOo The packaging efficiency at the high E/W point
is quite low, reflecting the large Z/z1 ratio, where Z is
the (maximum) thickness at the r = rO location. The best
E/V occurs at E/W=-- 0.38 (Ja/pg and Z/zl = 2. For
Z/ zl = 4, whicr. equals the thickness r~io of the k = 4
constant-stress disk discussed above, rO = 1/4, possibly
a reasonable value, E/W = 0.39 (Ja/pg, and E/V = 0.15 (Ja.
These results are included in Table A-l. Thus, within
this family of hyperbolic flywheels, some reasonably per-
forming shapes can be found, and the best approaches that
of the best constant-stress case. .
Other simpler shapes such as the wedge-shaped disk
may prove advantageous, especially from the fabrication
point of view, but the foregoing examples are deemed suffi-
cient for the present exploratory studies.
A. 3. 3 Studies by Others of Optimal Disk Flywheels
Studies concerned with the optimization of flywheels
are relatively recent (Refs. 128 through 130)*. In all cases,
*
The only other optimization studies known to the writer
are those of Seirig and Surana (Ref. 131), and Sulkin et al.
(Ref. 132). The former numerically "optimizes" the thick-
ness of a rotating disk by dividing the radial dimension into
a finite number of subelements (rings) and applying a gra-
dient technique to the resulting algebraic equations. Be-
cause the assumptions going into the stress analysis, the
performance criteria chosen, and the numerical results
themselves seem to be of dubious validity or relevance to
practical applications, further discussion is not warranted.
The North American (Ref. .132) study apparently is based
on the constant-stress case but is difficult to follow.
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SlLV!:Jt S~"IJroiG. MARYLAND
moreover, . there are implicit assumpt.ions or conditions,
which result in an optimal-shape disk having a constant
stress throughout, i. e., cr r = crt:: cr, with the resulting
exponential thickness distribution. Ranta (Ref. 128) con-
sidered the optimal minimum-weight disk (presumably for
any suitable operating condition, e. g., given U) which
was assumed to occur when the stress is uniform through-
out. His analysis was concerned with showing that the
assumption cr t/cr r = constant also leads to the constant-
stress result; an assumption which has more validity when
materials having nonlinear stress-strain relations are
considered. This assumption also seems somewhat' more
appropriate for anisotropic materials, although in this
case the constituitive equations themselves would also
have to be modified. For shaped-disk flywheels, the de-
viations from t.he assumed 2-D stress distribution will in-
crease as the thickness variation increases (i. e., with in-
creased shaping), so that there may be an eventual trade-
off between the losses due to the triaxial stress distribu-
tion and the geometric improvement of E/W. Ranta (Ref.
128) considered the 3-D stress-strain problem in the con-
stant-stress (exponential thickness variation) disk and
obtained estimates of the errors incurred by assuming a
2-D stress field. The final results are a function of the
slope of the disk face [tan f3 :: d(z/2)/dr] and Poissons'
ratio ~. For O. 145 s; "" < O. 5, the maximum error is
o [2.72 (1 +.1")/(1 - u). max (tan2 ~)] giving values of 15.6
and 3. 8% for ~ = O. 3 and f3 = 10° and 5°, respectively. Ob-
viously, the errors could be even larger if f3 or U wer e
greater (as the effective value may be for some aniso-
tropic, materials), or if the true anisotropic problem were
considered.
Using the calculus of variations Chern and Prager
(Ref. 129) derived the optimality condition (i. e., suffi-
ciency condition) which gives the minimum-weight disk
ha ving a specified edge loading or displacement. This re-
sult, which is not completely relevant to the present objec-
tive, was applied to a disk having a specified edge dis-
placement> and the resulting stress distribution (numerically
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THE .IOHNtI HOP'U" UNIVERSITY
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SaLVI" s.-"...,. "A."'~"O
computed) was shown to be far from constant and thus
nonoptimal in this sense. Note that again (] = constant
was assumed to be optimal, and that the analysis did not
include a failure criterion as a constraint. Chern and
Prager also showed that the von Mises yield limit for an
elastic-plastic disk also results in the constant-stress
solution; a result of possible relevance to anisotropic,
composite materials.
Perhaps the study most relevant to the present ob-
. jective is that of de Silva (Ref. 130), who formulated the
minimum-weight problem in terms of Pontryagin's maxi-
mum principle. He included the Tresca yield condition as
a problem constraint and proved that the configuration
would have (] r .-:: constant (as opposed to (] t or (] r - (] 0 =
constant, the other branches of the Tresca condition).
This resulted in an exponential thickness distribution simi-
lar to the constant stress result, but here (] t is a function
of r:
~ 2 2J
- b -(1+~) p~ r
z - Z exp (1 + kJ r - 2(] ,
1.£ a a
(A -42)
where Z and. b are constants to be determined by the
geometry or by minimum-thickness requirements. This
result, which agrees with de Silva's previous numerical
computations, can be used to compute E/W and E/V; a
task which is at present not completed. His general ap-
proach can also be used to compute optimal shapes corre-
sponding to other yield criteria, such as the von Mises
condition, which may seem more appropriate, although for
such cases analytic results may not be attainable. .
A. 3.4 Disk Flywheels Constructed from Anisotropic
Materials
The properties of a flywheel constructed of an
anisotropic material depend on the material's properties,
its orientation, and the overall flywheel configuration. A
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IIf"-"'''. 8~"IHQ- "...yt..AMO
flywheel comprising fibrous or filamentary materials
which are structurally unbonded does not offer an attrac-
tive E/ V, because O'a will be significantly degraded by a
relatively small lateral displacement of filaments from
the center of rotation. However, circular brush (fila-
ments bonded into a hub) or rim-wound configurations can
also be analyzed using modifications of the closed-form
flywheel results. For a quasi-isotropic material formed
by alternating the layers of the oriented composite mate-
rials, the homogeneous solutions can be used. Although
such a flywheel does not take full advantage of the high-
strength filaments of which it is formed, the disk con-
figuration does give a high E/V with a moderately good
E/W(Table A-I).
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THE .tOHNS HOPKINS UNIVERSITV
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APPENDIX B
THE DISK FLYWHEEL CONFIGURATION
B. 1 CLASSICAL SOLUTION FOR AN ISOTROPIC
MATERIAL
The equation governing the plane stress condition
in a constant thickness disk flywheel was given in Section
1. 1 of Appendix A as:
d . 2 2
o t - dr(ro r) - pr w ::: 0 .
(A -2)
The solution to this equation for a solid disk flywheel is
known and is: .
a
..2:.:::3+V
a 4
o
(1 - :2)
(B-1)
at = 3 + ~ (1 - 1 + 3V
a 4 3+v
o
::) ,
where the reference stress ao = ipw2R2. The maximum
stress occurs at the center of the disk and depends solely
upon the value. of Poisson's ratio. v. Examination of the
failure condition [Eq. (A-3)] shows that at the center of
the disk a r = at = a a' and the maximum allowable speed is
easily determined when v. aa' P. and R are specified.
For example. when V =~. ar/ao = at/ao = 0.833. There-
fore if a a = 200 ksi and p = O. 30. * the reference stress
has a value of 240 ksi, from which w = 1265/R rad/ s. Be-
cause the isotropic-disk configuration presents a signifi-
cantly better packaging efficiency than the rod or bar
*
Values representative of steel.
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THE .IOHNS HOPkiNS UNIVERSITY
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configuration (Table A -1), it is desirable to evaluate the
use of fiber-composite materials in a disk-type configura-
tion. .
B.2 PSEUDO-ISOTROPIC/LAMINATED DISK
FLYWHEEL
B. 2. 1 Constitutive Relations
Consider a laminated disk constructed of several
individual layers* (or laminas). SinceJas shown in Fig.
B-1a, the lamina principal axes (1,2) are not coincident
with the reference axes for the laminate, (x. y), each
lamina constitutive relation must be transformed to the
laminate reference axes. Then, for the kth lamina (Ref.
27):
k Ql1 Q12 Q16 k k
(j £x
x
(j = Q12 Q 22 ~26 £y (B-2)
Y
Q16 Q26 Q66 'Yxy
where the tra:J.sformed lamina stiffnesses are given by:
Qll = U1 + U2 Cos 28k + U3 Cos 48k
Q22 = U1 - U2 Cos 28k + U3 Cos 48k
Q1 2 = U 4 - U 3 Co s 48 k
Q66 = U5 - U3 Cos 48k
Q16 = -iU2 Sin 28k - U3 Sin 48k
Q26 :: -iu 2 Sin 28k + U 3 Sin 48k
(B-3)
* .
The laminate is midplane symmetric so that warping
caused by inplane loads does not occur.
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THE .JOHNS HOPkiNS UNIVERSITY
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SILVER SP'.I"'G ""'''''L'''ND
3.Z
2
v
(a)
z
~v
o
+60
(bl
Fig. 8-1 (a) LAMINA AXES ROTATION AND (b) PSEUDO-ISOTROPIC LAMINATED DISK
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THE JOHNS HOPkINS UNIVERSITY
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SILVE,. S"'III'ING. M"_Yt".AND
and
Ul::~ (3Qll + 3Q22+ 2Q12+4Q66)
u2::i (Qll - Q22)
U3 ::; * (Qll + Q22 - 2Q12 - 4Q66)
U4 :: ~ (Qll + Q22 + 6Q12 - 4Q66)
U5 :: -~ (Qll + Q22 - 2Q12 + 4Q66)
(&4)
The unbarred quantities Qij are the stiffness coefficients
in the lamina coordinate system and can be defined in
terms of four elastic constants:
Qll = E 11 / (1 - II 1 211 21)
Q22 = E22/ (1 -11121121)
Q12 = II 21 Qll :: II 12Q22
Q66 = G12
Q1 6 = Q26 = 0
(B-5 )
where Ell and E22 are the Young's moduli in the 1 and 2
directions, G12 is the shear modulus, and 1112 is the major
Poisson's ratio. .
I .
The stresses in the laminated disk are evaluated
by requiring the stress resultants to satisfy the governing
equations. This leads to a resultant stiffness matrix for
the laminate which is the weighted sum of each lamina over
thickness of the laminate. That is:
(J :: l dz
x
n
cr =!; f (B-6)
Y k=l tk T xy ~ k
T
xy
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TI-t£ .JOHNS HOPKINS UNIV£RSITY
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SILVER s..'NG. IIU."YL.AND
and
n
Q.. = I:
IJ k=l
(~Ijt fk
(B-7)
where fk is the thickness fraction of the kth lamina relative
to the total laminate thickness. In general a laminated disk
composed of arbitrarily oriented laminas or plies is in-
herently anisotropic. However, several specific lamina
orientations will result in an equivalent isotropic disk with
an effective allowable stress.
B. 2. 2 The Pseudo-Isotropic Disk
With reference to Fig. B-1 b, the lamina orienta-
tions which produce pseudo-isotropic material properties
are +60/0/-60, +45/0/90/-45~and +60/+30/0/90/-30/-60,
where each lamina contribute s equally to the overall
laminate thickness. Furthermore, when the principal
lamina strengths are resolved into the laminate coordinate
system, an allowable laminate strength can be determined
which is the same for all pseudo-isotropic laminates:
n
a = ~
1 k=l
(k 2 k.2 k. )
a 1 cos 8k + a 2 sm 8k + T 12 2sm 8k cos 8k fk
(B-8)
cos 8k) fk
n (k.2 k 2 k.
a 2 = k~ 1 a 1 s:.n ~ + (] 2 co S 8 k - T 1 2 2 s in 8 k
and it follows that 0'1 = 0'2 = O'a for all laminate directions.
An energy storage capability can be computed for
the pseudo-isotropic disk once the equivalent isotropic
properties are determined. T3.ble B-1 summarizes re-
sults for three fiber /epoxy laminated disks. For example,
a laminated pseudo-isotropic disk constructed of .graphite/
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THE .K)HNS HOPKINS UNIVEMI'N
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SlLye" PlttNG. M.lltYLAHD
Table B-1
Energy-Storage Capability of Pseudo-Isotroplc1
Laminated Disks
"
S-Glass/Epoxy Boron/Epoxy Graphite / Epoxy
(828-5994) (2002B) (2002T)
6 6 6
7.65 x 10 30.3x10 21.5 x 10
6 6 6
2. 24 x 10 3. 10 x 10 1. 44 x 10
0.27 0.16 0.25
6 6 6
O. 78 x 10 1.4x10 0.64 x 10
264 x 103 212x103 204 x 103
3 . 3 3
7.5 x 10 13 x 10. 11.8x10
3 3 14 x 103
8. 5 )( 10 13.5 x 10
6 6 6
3. 92 x 10 12.27x10 .8.14x10
. 6 6 6
1.50x10 4. 76 x 10 3. 09 x 10
0.308 0.288 0.315
Item
Property: Ell
E22
"12
G12
A llowable Lamina
Stresses: C11
C12
T'12
Equivalent Isotropic
Property: E
G
Or C1e
- = - = K(,,)
cr (1
o 0
Ref. Stress
. 2 2
CJ = ipw a
o
0.827 0.822 0.829
. 3 3 3
135. 75 x 10 112.5 x 10 105.5 x 10
164x103 137')( 103 127 x 103
when r = 0
Allowable Disk Stress
2 2
CIJ 1 /CIJ, :
p y 1S0
Aluminum Ref. 2
3
Steel Ref.
6.33
2.85
5.30
2.38
6.55
2.94
1 Ply orie'ntations +60/0/-60, +45/0/90/-45, and +60/+30/0/90/-30/-60 produce'
the same equivalent isotropic disk.
20' = 30 ket, p = 0.1 pci, II = 1/3.
3 Y . . ,. ..
cr = 200 ksi, P = O. 3 pci, " = 1/3.
, Y ,
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THE" JOHNS HOPKINS UNIVERSITY
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SI\..V!:1t S~"I"'C. "AAT\..AND
epoxy plies can store 2.94 times the energy of a steel disk
and 6. 55 that of an aluminum disk, with a specific energy
of 37 w-hilb.
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TH~ JOHJfS HOPkiNS UNIVEA9ITY
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5ILY~1t ~IJrIfG. M"It'YL.AHD
APPENDIX C
ESTIMATES OF WINDAGE LOSSES FOR FLYWHEELS
C.1. INTRODUCTION
The purpose here is to present some gross trends
of effects of rotor shape, size, and speed and operating
pressure on Pwind' the power required to compensate the
windage drag. For example, a cylindrical rod will have
only 75% as much drag as a square bar of the same cross-
sectional area, arm-radius, and material. An S-glass/
epoxy rod having twice the energy density of a steel (music
wire)/epoxy rod of the same size and shape would also have
twice the windage loss, because both EO/Wand Pwind are
proportional to ClJ2, the square of the rotational speed.
Since mo st of the length of the rotor will be moving at
supersonic velocity relative to the surrounding gas, and
since form drag at supersonic speed is proportional to the
gas density, P wind can be reduced by a factor of 106 by
evacuating the container from 1 to 10-6 atmosphere.
It is emphasized that only the relative trends indi-
cated herein should be given any weight, inasmuch as two
major simplifying assumptions will be made:
1.
The relative velocity between rotor and gas is
equal to the rotor velocity; i. e., the gas sits
still as the rotor spins. This is a conserva-
tive assumption, because for rotors enclosed in
containers with appropriate clearance, the sur-
rounding gas will rotate at some speed, too, thus
reducing relative velocities and drag.
The degradation in allowable CIJ 2 as rotor width
is increased (caused by biaxial stress effects;
see Appendix A. 3) will be neglected. This
degradation will result in proportionate reduc-
tions in both EO/Wand P .. d.
wln
2.
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THa .JOHNS HOPKINS UNIVERSITY
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SILYER SPo.tlNG. M."TL"ANO
The examples presented herein are based on uni-
axially loaded rotors made of a composite material having
an allowable workin~ stress (J a of 200 000 psi and a den-
sity pg of 0.07 lb/in. For a rod or bar of uniform cross-
sectional area AO (in2), where the maximum loading F max
Obf) will occur at the spin axis and will be:
F = (J A 0 = 200 000 A 0 .
max a
(C-1)
The mass (slug) of each arm of the bar (of radial length R)
is:
m = AORp = 0.0327 AO (for R = 15 inches)
(C-2)
For our ref~rence case, the rotational speed U) that just
provides a centrifugal force equal to F max is:
U) = (F Ir m)t = 3130 radl s = 29 900 rpm
max cg
(r = R/2 = 0.625 foot) .
cg .
(C-3)
Here reg is the distance (feet) from the center of rotation
to the center of gravity of the mass being spun (one arm
of the total bar).
The maximum kinetic energy storage is:
. 2.
EO = Iw 12,
(C -4)
where I is the moment of inertia and varies with configu-
ra tion.
C. 2 WINDAGE LOSS FOR BARS AND RODS
.. Let us consider a bar of rectangular cross-section
with 2-to-l proportion .(2T I Z = 2). The half-width. T is
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THE JOHNS HOPKINS UNIVERSITY
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$M..Vft "'1". M"'''''LAND
2.3 inches (0.192 foot); the height Z of the flat face pre-
sented to the approaching airflow is 2. 3 inches (0. 192 foot).
The arm length R is 15 inches (1. 25 foot), so that T IR =
0.153, a reasonable value (see Appendix A. 3); and AO for
Eq. (C-2) is 10.58 in2, yielding m = 0.346 slug for each
arm. The rotor weight W (both arms) is 2mg, or 22. 3
pound s.
For UJ = 3130 radl s, the tip speed UJR is 3910 ftl s,
and most of the length of the bar is in supersonic flow.
For convenience, let us assume that the supersonic drag
coefficient, CD = 1.84, applicable for a flat, infinitely-
long plate, face-on to the approaching flow (Ref. 1013), can
be applied for the entire length of each arm for this case.
Then the drag force D (pounds) and moment Mare:
R
o = 2 C S qzdr
D 0
R
m =.r Dr dr ,
o
(C -5)
where q is the dynamic pressure, PgV2/2, for a flow
with 10cal velocity V and gas density pg. Using Eqs.
(C-5) for the moment, we can find the horsepower re-
quired to overcome windage loss:
UJM 2CDUJ. R
P wind = 550 = 550 So qzr dr .
(C-6)
where UJ is in. radls, and UJr is the distance (feet) through
which a local element of the drag force operates in 1 sec-
ond; UJr also is the local velocity (ftl s) at the radial dis-
tance r. Hence, the local q is simply t P (UJr)2. For
the rectangular bar, z = Z also is a constanf;. thus, inte.-
gration yields .
4 3 .3
P . d = P CDZR UJ 12200 = 0.00204 P UJ Z
Win g g
= 28 500 hp at 1 atmosphere'
(C-7)
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THE .JOHNS HOPKINS UNIVERSITY
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where Pg is O. 00238 slug/ft3 for air at 59°F and 1 atmo-
sphere. If we reduce the pressure from 1 atmosphere to
10-3 torr*, the air density becomes 3.13 x 10-9 slug/ft3,
and
-3
P . d = 0.0375 hp at 10 torr (2:1 bar) . (C-8a)
Win
If we replace the 2-to-:1 rectangular bar by a square
bar (2 = 2T = 3. 25 inches) of the same cross-sectional area
(10.58 in2), the face height 2 and the consequent Pwind
will be multiplied by.[2 for the same w (3130 radl s), or
-3
P . d = 0.052 hp at 10 .. torr
Win
(square bar) ~ (C-8b)
The diameter d of a cylindrical rod of the same
cross-sectional area will be (4I1r)t 2 = 1.128 2 = 3. 66
inches. However, the high-speed CD will be 2/3 that of a
flat-faced wall of equal frontal area, as can be shown by
integrating the Newtonian version of the expression for the
local pressure distribution around a circular section (a
result essentially confirmed by experiment) (Ref. 108).
Thus, the rod's windage loss will be (2/3) (1.128) = 0.752
times the square bar's value,
-3
P . d ~ O. 039 hp at 10 torr
Wln
(rod) .
(C-8c)
The crods-sectional shape does not affect the per-
missible rotati<;>n speed in Eq. (C-3) (neglecting trans-
verse stress effects); all that matters is AO' which is the
same for all three configurations examined so far. hence
the limiting UJ. is 3130 rad/ s for all three. However,
their energy-storage capabilities differ slightly. because
their I's differ. For a 2:1 rectangular bar:
2 .2 2
I = 2m(R + T }/3 = 0.369 slug-ft
( 2: 1 bar) .
(C -9)
*
1 torr = 1 mm Hg = 1/760 atmosphere = 0.001315 atmo-
sphere.
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THE JOHNS HOPKINS UNIV~ITY
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.~WIII Sl'thMG. ".~\.A"D
Here 2m is the rotor mass (both arms), 0.692 slug. Us-
ingthis I, and"" = 3130rad/s, Eq. (C-4) yields EO =.
1. 804 x 106 ft-lb, or 680 Wh, and EO/W = 30. 6 wh/lb.
For the square bar with its smaller T dimension,
I = 0.367 slug-ft2, and EO = 1. 79x 106 ft-lb.
For the circular rod,
222
I = 2m(3d 116 + R )/3 == 0.365 slug-ft
(rod, R = 1. 25 feet)
and EO = 1. 78 x 106 ft-lb.
(C-10)
If we reduce R for the rod from 15 to 12 inches
(800/0) but keep AO at 10.58 in2, we have 2m = 0.554 slug,
and rcg = 0.5 foot; the permissible Co\) per Eq. (C-3) is
increased to 3910 rad/ s. Note that the tip speed, (.&JR, re-
mains the same, 3910 ft/ s. Now we find I = O. 188 slug-ft2,
and EO = 1. 436 x 106 ft-lb, ...... 81 % of the original value.
The windage drag is 800;0 of the original value, hence:
-3
P . d = 0.031 hp at 10 torr
Wln
(rod, R = 12 inches) (C-Bd)
C.3 WINDAGE LOSS FOR A DISK OF ZERO THICKNESS
IN FREE AIR
For a disk of zero thickness experiencing only skin-
friction drag, . the relation analogous to Eq. (C-6) is:
(.&.1M 5 3
HP . d = 550 = CM(t fJ R Co\) )/550 ,
wm age g
(C-ll )
where CM is a nondimensional coefficient (including both
sides of the disk). A chart has been prepared in Ref. 133
(see Fig. 1 7) to facilitate rapid estimation of the horse-
power required to drive disks of various diameters at
speeds from 100 to 40 OOOrpm. A curve on this chart
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THri JOHNS HOPKINS UNIVERSITY
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shows the combination of Rand UJ at which boundary
layer transition from laminar to turbulent can be expected.
It is evident from this curve that for the configurations
and UJ's of interest for superflywheels, the turbulent-
boundary-layer analysis can be expected to apply. For a
turbulent boundary-layer, .
CM = 0. 146/Reo. 2 = 0. 146/(UJR2 P /1}. )0.2, (C-12)
g g
where Re is the Reynolds number and ~ is the gas vis-
cosity (3. 78 x 10-7 slug/ft-s for air at 39°F). This result
is confirmed by experiment (Ref. 134). Thus,
p = 0. 146 0. 8 R 4. 6 2. 8 0. 2
wind (550)(2) P g W ~g
(C-13)
Let us consider a 15-inch-radius disk, rotating at
2333 rad/ s, so that it will have the same EO/Was the rod
of the same R rotating at 3130 rad/s. Equation (C-13)
gi ve s:
-3
P . d = 497 hp at 1 atmosphere, or 0.0098 hp at 10 torr. (C-14)
wm
Thus, at 1 atmosphere the friction drag on the top and bot-
tom surfaces of a disk is only 1. 7% of the form drag on the
rod for equal EO/W, but at 10-3 torr it is 25%.
C.4 DEVIATIONS FROM SIMPLE FLOW PATTERNS
One thorough experimental investigation of disks
rotating inside cylindrical containers (Ref. 135) showed
that the thickness of the outer rimfaceof the disk has a
strong influence on the drag, so that any formula based on
the assumption of a vanishingly small disk edge is bound
to underestimate the friction drag of a thick~rim design.
In addition, surface roughriess could raise the drag ap-
preciably. However, the greatest factor (that is going to
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be ignored hereinafter) is the whirl-up of the body of air
in the container. If s is the separation distance in the
axial direction between the disk surface and the surface of
the can on each side, and if s exceeds the sum of the
boundary-layer thicknesses on the disk and can wall, the
"core" gas between the boundary layers will rotate approxi-
mately as a solid body. The relative velocity between the
disk and this core gas will be substantially less than the
disk velocity itself. Theoretically (Ref. 136), an enclosed
disk should have only 42.6% of the drag attributable to the
same disk spinning in the open in the same fluid. [If s
is much smaller than the sum of the boundary-layer thick-
nesses, on the other hand, .the drag can exceed the free-
air value (Ref. 137).] This finding of a constant fraction
of free-air drag, when a can of sufficient size is provided,
is used as the prime justification herein to ignore the
presence of any container entirely and to quote drag re-
sults for toe simpler condition of free-air operation.
C. 5 EFFECT OF CHANGING THE GAS IN THE CONT AINEH
Inasmuch as the drag of a rod or bar rotor is pre-
dominantly wa ve (form) drag, as opposed to skin friction
drag, the effect of a gas change is simply accounted for by
determination of the density ratio, which is proportional
to the molecul:3.r weight ratio. Thus, replacement of air
by hydrogen or by helium, under standard conditions, re-
sults in lowering the windage loss by a factor of 2/29 or
4/29, respectively.
In contrast, for a disk-type flywheel, the drag i.s
primarily due to skin friction, and Pwind will vary with
the product 1'0. 8UO. 2,as shown in Eq. (C-:-13); so that the
reduction factor ~roduced by a change from air to hydro-
gen is: (2~29)O. (1. 80/3. 78)0. 2 = 0.102, where the lJ,'s
are in 10- slug/ ft-s. Similarly, the reduction factor
attainable by supplanting air with helium is 0. 208.
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV~" 9~"IHG. M.IIYL,AND
C.6 RUNDOWN TIME CAUSED BY WINDAGE LOSS ALONE
The Pwind requirement can be used to make a rough
estimate of rU!1down time caused by windage loss alone
(neglecting seal or bearing friction loss). The rate o~ de-
crease of energy can be expressed as a function of time by
differentiating Eq. (C-4):
dE/dt :: -Iw(dw/dt) .
(C:-15)
where I i8 a constant for a given configuration. Accord-
ing to Eq. (C-7), Pwind is proportional to w3 for a given
system; i. e. ,
3
P . d :: Cw .
Wln
(C -16)
Equating (C-15) and (C-16) we obtain:
Cw3 :: -Iw(dw/dt),
(C-17)
which we can integrate between any two values of t, tl'
and t2:
t2 .
S dt:: ~t . d
t Win
1
I w2 1
:: - C J 2" dw
(1.)1 (I.)
I 1 (1.)2 I (1 1 )
Atwind::-cl~wl(l.)1 -C (l.)2-wl
(C-18)
Now i£we multiply and divide by wI 3/2, we obtain
At . d ::
Wln
2
2 OWl / 2 )(1.)1
3
CU'1
(~2 - ~J
::
2E1
P .
wind1
(:> 1)
, (C-19)
where El and Pwind are in. consistent units, e. g., ft-Ib
and ft~lb/s. For rundown to half speed (W1/W2:: 2,
Er /E2 :: 4); this reduces to: .
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THE .tOHHS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
S'Ly~1It !WIlING. M."YLAND
6t . d = 2E1/P . d
Win .WIn 1
(UJ1/UJ2 = 2)
(C-20)
For the 2:1 bar, starting from a full charge (E1 = EO) and
using results from (C-8a) and (C-9), this gives:
6t . d = 2(1. 804 x 106 ft-lb)/(o. 0375' 550 ft-Ib/s)
Win
5
= 1. 75 x 10 s, or 49 hours
Starting from half speed (UJ1 = UJOI 2, E1 = Eo/4, and
Pwind1 =P wind 18) and running down to one-quarter speed
. . 0
(w1/UJ2 = 2 again), ~twind would be twice as great, or 98
hours, because E1 IPwind1 would be twice as great. The
total time from full speed to 1 14 speed would be 49 + 98 =
147 hours, or 6+ days, neglecting seal and bearing losses.
Again, it should be remembered, as noted in Section C. 4,
that the true windage 108S probably will be about half as
large as the estimates given here, because the air will
tend to turn with the rotor, reducing the air drag.
C.7 WINDAGE LOSSES FOR PYRAMIDAL AND HALBERD
CONFIGURA TIONS
A s was shown in Appendix A. Table A -1, a rotor
comprising two square-based Plramids base-to-base would
have 4. 5 times the allowable w compared to a rod of the
same materiql and would thereby provide 35% more spe-
cific energy capability, even though the moment of inertia
is considerably lower for the pyramidal configuration.
Some rather complicated analytic geometry and integra-
tion were required to resolve velocity vectors and forces
relative to the advancing sloped and tapered face, and
these details will not be given here. The basic principle
indicated by Eq. (C-6) was retained. However, some re-
sults of comparisons between bars, pyramids, and cones
of equal volumes and equal R' s (20 inches for the.se ex-
amples) may b~ summarized as follows:
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THE JOHNS H~K'NB UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVI. 8~IItIHG. MAIIIIYLAHD
1.
At a given(&), a double pyramid with 2:1 base
dimensions (narrower dimension facing the
wind) would have 33% of the drag of the cor-
responding 2: 1 bar.
However, at the higher permissible UJ for
the pyramid, it would have 3. 2 times the
drag of. the 2:1 bar.
2.
3.
A square-based pyramid would have 1.46
times the drag of the 2:1 pyramid, or 3. :3
times the drag of the corresponding square
bar.
A double-cone rotor of the same volume
would have 75% of the drag for the square-
based double-pyramid rotor, just as the rod
had 75% of the drag of the square bar. The
energy density for the cone would be 5% less
than that of the square pyramid.
4.
5.
If the square-based pyramid is rotated
through 45° to present a wedge profile to the
wind, its drag will be reduced by 50%. This
result implies that the drag of bar rotors
also might be halved by presenting wedge
profiles to the wind, but no specific calcula-
tions were made.
A n interesting concept for low drag is to. form a
halberd design by using a stack of thin bars and staggering
them like a fanned deck of cards. By sweeping the upper
half of the set one way and then reversing the sweep on the
lower half, a wedge profile with a sharp leading edge can
be developed on each side of the spin axis. A halberd con-
figuration with a 7.8° half-angle would have only 8.6% of
the drag of the corresponding 2:1 bar of the same total
material volume.
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fH€ JOHNS HOPKINS UNIVERSITV
APPLIED PHYSICS LABORATORY
.'&..vl- ""'HG MAItTL""HC
APPENDIX D
SURVEY OF AVAILABLE TRANSMISSIONS AND
PROPOSED CONCEPTS
The information presented here has been gathered
from technical literature. Further information, especially
regarding recent developments and research on transmis-
sions, can only be obtained from the manufacturers, and
it often is proprietary. . .
D.l CONTINUOUSLY VARIABLE TRANSMISSIONS
(CVT's)
The large number of CVT concepts can be cate-
gorized broadly as to their method of attaining the varia-
bility: mechanical (belt or other friction types), electri-
cal, hydrostatic, hydrokinetic, and aerodynamic torq ue
converters. In addition, combinations of these can be
used as discussed later. At the outset let us note that the
use of a CVT in present day vehicles could provide
smoother performance and improved thermal efficiency,
a fact recognized by automobile manufacturers (Ref. 14).
However, to the authors. knowledge, only two production
vehicles have been sold with a CVT: a Hayes friction
drive was used on Austin cars in 1932-1936 (Ref. 13~',
and a belt drive is still in productiori by DAF (Ref. 5).
In general, the CVT's have not attained a sufficient com-
bination of reHability, durability, efficiency, and power
capabilities in combination with acceptable size, cost, and
weight, to dis;:>lace the current well-developed automatic
transmissions. 'The emerging importance of control of
emissions may change this' picture.
D. 1. 1 Mechanical (Belt or Friction) CVT's
There are many schemes for attaining a variable
speed drive with belts (Ref. 16). In general, however,
belt drives are restricted to the low horsepower « 30)
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THE JOHNS HOPKINS UNIVERSITY
/l,PPLIED PHYSICS LABORATORY
S'L\I(R ~"I"'G. M"'''''LAND
. regime. Variable speed is obtained by variable-pitch
pulleys, and speed adjustment can only be made while the
drive is running. When both pulleys have variable pitch,
speed changes up to 9:1 are possible. The major advan-
tages to belt drives are low cost and simplicity. The
major problems normally associated with them for high-
horsepower (>25), and high-rpm (>3000) CVT's are short
belt life, poor speed regulation under varying load, and
high maintenance requirements. Regenerative braking is
inherently possible with all mechanical CVT's.
Belt drives are widely used in snowmobiles and
other small equipment (Ref. 16). The only production
automobile currently sold with an "infinitely variable
drive" - a belt drive with a 4. 2: 1 speed ratio - is the DAF,
manufactured in Holland. The DAF models vary in curb
. weight from 1460 to 1700 pounds with powerplants rated
from 32 bhPmax at 4200 rpm to 66 bhPmax at 5600 rpm.
The manufacturer suggests that the belts be. changed when-
ever tires are changed and inspected every 2000 miles.
Two belts are used, one per drive wheel, and the transmis-
sion is bulky, occupying a large portion of the rear of the
automobile.
General Motors, in a small (950-pound) experimen-
tal urban car (Ref. 139), used a variable-ratio, V-belt
. transmission and a two-cylinder 81 engine rated at 13.9
bhPmax' The car had a top speed of 25 mph and an aver-
age acceler2.tion rate of 1. 6 mph/ s from 0 to 30 mph.
Of the many variations of friction drives (Ref. 16)
only two will be considered here. The Toric (Ref. 15)
drive, known previously as the Perbury (Ref. 140) or the
Hayes (Ref. 138) transmission, was first patented in 1899
by W. D. Hoffman. The drive uses disks with toroidal
surfaces on the input and output shafts with speed varia-
tion by control of tiltable roller disks between the shaped
shaft disks (Fig. D-1). Power is transmitted through the
oil film separating the surfaces and controlled by axial
loading. The Hayes transmission was fitted to the Austin
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TH~ .IOHNS HOPkiNS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILviE- SJ"ttlNG- """"LAND
ROT./HABLE
DISCS
INPUT
SHAFT
OUTPUT
SHAFT
(a) PRINCIPLE OF OPERATION OF PERBURV, HAYES,
AND TORIC TRANSMISSIONS
.94
"*
>-
u
~ 92
u
u.
u.
w
j 90
c:(
IX:
w
>
o 88
0.5
200 HP AT 5000 RPM INPUT
1.0
RATIO OUTPUTIINPUT SPEEDS
1.5
(b) EFFiCIENCY VERSUS
SPEED RATIO, PERBURY CVT (REF. 140)
Fig. D.l
PERBURY,HAYES, OR TORIC TYPE CVT'S
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THE JOHNS HOPkiNS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILVI[IIII ~IItING. ""'''YLAND
car in 1933 and evidently was abandoned in 1936, "owing
to teething problems" (Ref. 141), i. e., bugs. Recent
interest (l9S6-1964) has resulted in the perbury tr:lnsmis-
sion, actually built from old Hayes parts. Labor8 tory
tests were conducted for a test unit designed for a nominal
100 hp and reported in Ref. 140. Figure D-1 shows the
results for 200-hp input at 5000 rpm (input torque = 210
ft-Ib); efficiencies from 91 to 92% are attained over a 3:1
speed ratio. A hypothetical automotive Perbury trans-
mission with clutch, gearbox, and Perbury drive was out-
lined in Ref. 140. Further studi"es were to be conducted
on the life of the unit; however, we have found no more
recent information in the literature.
General Motors' Toric transmission (Ref. 15.) is a
furthe r development of the Perbury drive. Reference 15
quoted 96% efficiency, 800 ft-lb of torque and 275 hp. A
visit to G. M. produced some additional general informa-
tion but relatively little in the way of design information.
Mr. Paul Vickers and other members of the Research
Laboratories indicated that the unit is capable of a G:1
(possibly 7: 1) speed variation, and useful efficiencies 3re
nearer 92% and evidently do not include oil pumping re-
quirements. One main problem has been to obtain satis-
factory hardened rIB terials that could be produced at
acceptable cost, but some progress has been made in
recent years, and use in less capital:";cost-critical appli-
cations (buses with GT's) may be approaching. The unit
has been fitted to the experimental GM steam car (the
SE 101) and a gas-turbine-powered bus, the RTX. No
published ~nformation is available on size, weight, or
durability as a function of power requirements. The GM
Research people suggested that information for a specific
requirement might be provided on request to the Trans:"
mission Division, to whom all GM work on the Toric has
been transferred.
The second friction-type CVT under consideration
is .the Beier drive, in which many tapered disks are
spring-.mounted on a rotating drive shaft (Fig. D-2). The
,
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THE .JOHNS HO",IH8 UNIVaatllTY
APPLIED PHYSICS LABORATORY
g'L V£- 8I-1t1NG. ""."LAND
INPUT
SHAFT
100
~ 90
>
o
ffi 80
U
L4. 70
L4.
W 60
o
MOVEMENT FOR
5'000 OO~~L
(a) PRINCIPLE OF OPERATION
FULL LOAD
1/4 LOAD
40 50
OUTPUT SPEED (%)
(bl EFFICIENCIES (REF. 16)
. Fig. D-2 BEIER CVT'S
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OUTPUT SHAFT
100
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TNt: .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS lABORATORY
e'lYI" .""'HG. W...,n'l"""O
driven shaft is fitted with flanged disks, and speed control
.is obtained by varying the depth to which the flanged disks
are inserted into the tapered disks. Power is transmitted
by the viscous drag of thin oil films between the disks.
Metal-to-metal contact (hence wear) of the power trans-
mitting surfaces is prevented. Catalogued industrial units
employ a 4:1 speed ratio with minimum output speeds of
650 rpm, and a ~ximum input speed of 1800 rpm. Units
UP' to 300-hp capac.ity are 'aVailable. Efficiency (Fig. D-2)
increases with the power capability and ranges from 85%
at the low speed ratio (4.:1) to 91% at 1:1 for a 300-hp unit.
The Beier transmiss.ion,:ev.id~ntly was under development
(1957) in Germany a's an auto'mobile transmission (Ref. 16);
however, no further information has been located. No in-
formation is aYlailable'as to size and weights.
D.1. 2 Electric CVT's
The application of electric transmissions to elec-
tric vehicles was analyzed at length in the A. D. Little,
Inc. study (Ref. 106). What follows here is largely a sum-
mary of those results, as related to our interests. (Refer-
ence 106 did not discuss the potential of high-energy-
density flywheels or flywheel-hybrids.) The electric trans-
mission as applied to a flywheel hybrfd comprises a gen-
erator to comrert the shaft'mechantcal energy to electrical
energy, a motor to convert the electrical energy to
mechanical energy, and a controller. Numerous con-
trollers are available for each type. Losses in electrical
machinery a.I"e due to bearing losses, windage losses of
the rotor, and I2R losses. Overall efficiency increases
as power rating increases.
A DC motor provides the required high perfor- .
mance and is easier to control than an AC motor, but has
brush-wear problems and is heavier. A DC motor pro-
vides essentially a constant horsepower throughout its
speed range. DC motors have been used in electric loco-
motives and have been selected for the drives of a number
. .
of proposed urban transportation systems. Regenerative
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THE .IOHN8 HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
8"..YK" ~.'NG 1III"""'L4ND
braking can be accomplished witp both AC and DC motors.
DC motors were selected for the vehicle drives in Ref. 106.
To reduce weight, high-speed (13 000 to 16 000 rpm) motors
were assumed, hence speed reducers were required in
the drives. For the generators, however, AC units were.
selected because they have no brush maintenance, can be
run at high speeds, are compact, and are mass-produced
now (alternators); consequently, Ac/DC rectifiers also
were required.
Table D-1 shows the estimates from Ref. 106 for
the electrical transmissions as applied to the commuter
and family cars. It was not stated whether the quoted
efficiencies were maximum values or averages over a
driving schedule. Inclusion of the motor speed reducers
and generator efficiencies would result in an overall drive
transmission efficiency 11D of", 70% in contrast to the 73%
we are presently assuming. The weights in Table D-1
are larger by factors of 2. 7 and 2. 25, respectively, for'
the family and commuter cars than the values we have.
assumed in the analytic studies.
General Motors, under contract to the U. S. Army
Tank Automotive Command, has equipped a 2i-ton M-35
Army truck with an all-electric drive system (Ref. 142).
A six-cylinder, 140-net-hp, SI engine drives a 15 000-
rpm, 75-hp, brushless homopolar induction alternator.
The six motors (one per wheel) are brushless synchronous
units rated at 20 hp each over a 16: 1 speed range (1000 to
16 000 rpm) with 33/9:1 gear reducers from motor to
wheel. Overall efficiencies are not given. Specific
weight for the complete drive train (alternator, motors,
and controls) is 19.1 lb/hp. After installation of the
electric drive train the "electric drive test bed is 873
pounds heavier than the original M-35 truck with mechani-
cal drive. "
An excellent discussion of the various types of
electrical devices available for power transmissions can
be found in Ref. 143. .
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THt: .JOHNS HQP'ClNS UNIV£RSITY .
APPLIED PHYSICS LABORATORY
SILVI[" s..tNG. "&',"'-AHO
Table 0-1
Electric Drivetrain Characteristics (Ref. 106)
Parameter
Commuter
Car
Family
Car
Maximum Output of Hybrid Power Source (hp)
Curb Weight (pounds)
Weight of Generator, Rectifiers, Speed in-
creaser and Voltage Regulator (pounds)
Maximum Power Delivered to Wheel Speed Re-
ducers (hp)
Motor Weight (pounds)
Motor Efficiency (0/0)
System Voltage, v
Controller Weight (pounds)
Controller Efficiency (%)
Weight of Speed Reoucers (pounds)
Weight of Cables, Mounting, etc. (pounds)
Weight of Cooling System (pounds)
Overall Efficien(:y (Excluding Speed Re-
ducers and GenErator) (%) .
Overall Weight of Electrical System (pounds)
Specific Weight (lb/hp)
114
3500
70
94
228
88
500
50
93
15
45
10
82
418
3.68
39
1400
30
30
66
86
250
30
91
6
12
4
77
148
3. 80
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THE JOHNS Ha.IC.'MS UN'VUtS.,...,
APPLIED PHYSICS LABORATORY
S'LV..1It ~.... "".n.AND
D. 1. 3 Hydrostatic Drives
A hydrostatic transmission consists basically of a
pump mounted on the input shaft that converts mechanical
power to hydraulic' power and a motor on the output shaft
that converts hydraulic power to mechanical power. The
pump and motor are positive displacement devices (they
trap and discharge fluid in discrete segments). They are
classified as to their method of fluid displacement (piston
or rotary) and their controllability (constant or variable
displacement). The piston type is better developed be-
cause of its high efficiency, ease of controllability, and
capability of operating at high pressures. Figure D-3 de-
picts one with a variable-displacement axial piston pump
and a fixed-displacement axial piston motor. The pump
(input) consists of axial pistons mounted on a plate (swash-
plate) attached to the input shaft. The pistons and cylin-
der block rotate with the shaft, and through suitable port-
ing valves at the cylinder base, fluid is pumped under
pressure from the 'low' end to the 'high' end. Defining
the displacement D of a pump or motor as the volume of
fluid (in3) displaced per revolution of the shaft, the fluid
delivery Q(in3 / min) for a given shaft speed N (rpm) is
Q=DN.
For an ideal pump the mechanical power input (torque x
rpm) equals the hydraulic power output (~elivery x pres-
sure). The torque (in-Ib) is then given~:
j
T = pD/21r ,
and the horsepower by:
p = p D N/396 000.
Speed control is accomplished by varying the piston stroke,
i. e., swashplate angle, to vary Q. Pressure levels are
dictated by the power input and can be monitored compared
to a'reference pressure determined by operator controls.
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T...' JOHNS ~OPKINS UNI'VERSITV
APPLIED PHYSICS LABORATORY
51LVlUi a"'.'NG M....YL.NO
OUTPUT
MOTOR
Fig. 0-3
"..
~ LOW~
HIGH ....
LOW
LOW
..
HIGH ..
FORWARD
NEUTRAL
REVERSE
~
PUMP
.
LOW
HYDROSTATIC TRANSMISSION
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THE .JOHNS HOPt(tNS UN1V£A$ITY
APPLIED PHYSICS LABORATORY
SILVE''' ""'NG. "...nAND
If the pressure is used to adjust the swash-plate angle,
control is effectively established. Such a system has been
proposed for vehicle control. The motor operates on the
same principle as the pump.
Neutral with a hydrostatic transmission (Fig. D-3)
is not free-wheeling (i. e., the tractive wheels are not
disconnected from the power train). To permit free-
wheeling, say for towing. a special provisIon must be
made. connecting the high- and low-pressure motor parts.
Otherwise. the unit must be disconnected from the drive
wheels or the pump will be damaged.
The advantages claimed for hydrostatic drive are:
(a) infinite and smooth variability from full design speed
in one direction, down to zero speed and to full design
speed in the reverse direction. (b) precise controllability.
(c) flexibility of installation and capabilities for (d) ex,-
tremely fast acceleration or deceleration, (e) dynamic
or regenerative braking. (f) developing a constant-torque
or constant-power output, and (g) developing a constant
speed independent of the load. Offsetting these features
are its high specific weight (lbl hp) and volume. low over-
all efficiency, noise, cost, close manufacturing toler-
ances, and cooling requirements.
The earliest reference to an application was in a
1908 White Motor Co. truck (Ref. 144'). No hydrostatic
drive has, to our knowledge. been offered on a production
automobile. although its applicability has been suggested
(Ref. 145). Current usage is centered in industrial v~-
hicles, e. g., grade and power rollers (Ref. 60.) and farm
tractors (Ref. 146). A hydrostatic drive has been pro-
posed for a 6000-pound-Ioaded-weight vehicle in a mass.
transportation system. The top speed is 27. 5 mph with
a 2.75 mphls acceleration capability. The proposed hy-
drostatic unit is estimated to weigh 320 pounds with an
1]D of 65%.
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THC[ JOHNS HOPKINS UNIVCR91TY
APPLIED PHYSICS LABORATORY
.IL.V~. s....tJlIrfG. "."TL.AHO
Some characteristics of three catalogued units are
listed in Table D-2. The "48-hp"* Sta-Rite unit is a com-
pact:, integral, motor-pump transmission. An efficiency
map,' computed from data in Ref. 147, at an input speed of
. 2800 rpm is shown in Fig. D-4a. The unit is too small to
meet the acceleration requirements specified by OA P
for tHe 1400-p'ound commuter car; its maximum output
power actl~ally is 32 hp at ~ 1. 2:1 speed ratio. Maximum
acceleration would occur along the 3000-psia line with an
average efficiency of,... 70%, which would be further re-
duced by inclusion of rear axle and speed-reducer effi-
ciencies. The efficiency map of the "120-):1p" Hydreco
model 60 (ReI. 148) is shown in Fig. D-4b at an input
speed of 2800 rpm. .Its peak output power actually is 77 hp
at ~ 1.5:1 speed ratio, and its efficiencies are somewhat
poorer; than those of the smaller Sta-Rite unit. Its accel-
e~ation' cap~bility exceeds the requirement for the com-
muter vehicle, but is inadequate for the family car. In
addition to the pump and motor weight of 220 pounds,
another 100 pounds or so will be required for controls and
cooling.
. Hydrostatic transmissions evidently are noisy
(Ref. 149). possibly caused by fluid vaporization, which
would be evident at high rotational speeds and high pres-
sures. Current units operate at pressures up to 5000
psia. Maximum rotational speeds are limited by cavita-
tio,n problems, and catalogued units operate at 3000 rpm.
High power capability is obtained by increasing the size
of"the'\.H~it (i. e., Q). One manufacturer offers a 4000-hp
unit with Q = 2300 g~l/ min at 4000 rpm (Ref. 150). . As
nQtE7d above, hydrostatic transmissions are relatively in-
effi~ient, and because of hydraulic fluid temperature limi-
tations must be cooled to r~move the lost power.
, 'i4,1." .
~ ' .' ,". .
"-ni~cu~Sion with Sundstrap4 representatives brought out
the fact that ratings a~e based on "corner horsepower, "
i. e., the result of maximum torque and maximum speed.
The units are incapable of operating over a speed range
at this power. '
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THE JOH- HOPkiNS UNIYP!S'TY
APPLIED PHYSICS LABORATORY
SlL.ftlt SPtttNG. MA,"UJlfO
Table D-2
Characteristics of Catalogued Hydrostatic
Transmissions
Manufacturer Sta-Rite Hydreco Hydreco
Model Number C3 60 110
Displacement (in 3 I rev) 1;8 6 11
Input Power: Maximum (hp) 48 120 175
Conti,nuous (hp) 80 125
Weight, Dry (Pump and Motor) (pounds) 50 220 482
Maximum Pressure (psia) 3500 5000 5000
Continuous Pressure (psia) 3000
Maximum Input Speed (rpm) 3000 2800 2500
)"Iaximum Output Speed (rpm) 3000 3200 3200
~laximum Output Torque (ft/lb) 83 370 685
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TME JOIooINS kOPH:INS UNIVERSITY
APPLIED PHYSICS LABORATORY
Stl..v(1II: Sfr.''''G M,,""UNO
~
>-
U
Z 70
w
S!
u..
u..
w
50
80
INPUT
HP
110
80
~ 60
>- 60
u
z
w
u
u..
u..
w 40
90
INPUT
HP
40 ,..
30 ~..........-
20 r -'..... 1\1
, ,.....4>( PlY
" ESSU
I ""'....IYE" J
I ',.....OoOPS/
I .....-
10 V "--
I ~'"
.-1___L_.__- .1-._---
(a) STA.RITE "48 HP" UNIT
2800.RPM INPUT SPEED
(REF. 147)
---i
. .1 - ..
(b) HY~REC~ "120 HP"l
MODEL 60
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TH£ .IOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SaLVe''' ""'NG. .....RYLAND
Battelle Memorial Institute, under contract to the
U. S. Army Tank-Automotive Command, is investigating
the possibility of developing a 600-hp, variable-displace-
ment vane-type pump (Ref. 151) for possible use in a tur-
bine-powered vehicle. Because of its hj,gh speed (22 '000
rpm), it may be suitable for direct connection to' the fly-
wheel shaft. Discussions with Battelle personnel, how-
ever, disclosed that development effort is minimal, and
the desired goals have not yet been attained in a test unit.
D. 1.4 Hydrokinetic Drives
Hydrokinetic devices (Ref. 150) comprise an im-
peller (pump) connected to the drive shaft and a turbine
(motor) connected to the driven shaft, between which is a
viscous fluid, oil. The impeller causes fluid to travel
radially under centrifugal forces and thence into the tur-
bine. The angular momentum imparted to the fluid by the
impeller is transferred to the turbine. Two types of
drives are considered: (1) variable speed hydraulic cou-
plings and (2) torque convertors. Variable speed is at-
tained by controlled slip, an inefficient method of control
that is analogous to using a resistor in an electric motor
for speed control; hence, waste heat rejection is a design
cons idera t ion.
A hydraulic coupling is depicted in Fig.. D -5. Since
the velocities leaving and entering the impeller are the
same as those entering and leaving the turbine, 'respec-
tively, the torque is the same on the i.mpeller and turbine,
i. e., output torque is equal to input torque. The trans-
mission of torque depends on slippage; for zero slippage,
no torque is transmitted as the centrifugal forces in the
turbine are equal to the centrifugal forces in the impeller
(i. e., pressures are equal), thereby preventing the circu-
lation of fluid. The normal slip loss is 2 to 40/0 at the maxi-
mum turbine speed and torque. Speed control of the tur-
bine is accomplished by bleeding fluid from the unit,
thereby reducing the quantity of fluid circulated. This,
however, also results in a lowe.:r; capacity for torque
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THE .lOW". HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SII..¥EIIt ""rNO. ""RYLAND
SPEED RATIO (output/input)
0 0.2 0.4 0.6 0.8 1.0
100
w
::J 80
TURBINE 0
a:- 80 -
o E ?fi.
to-E60 >-
0.- 60u
INPUT W)( /
~ E z
. SHAFT ,,4. / LJ.J
~ ~ '0 40 «,~ / 40 !:!
CI)* ~"/~ u..
z- u..
e:( ««./ l;J
a: 20 ~/ 20
to- /
0
0.8 0.6 0.4 0.2 0
SLIP
(REF. 152)
Fig. D-6 FLUID COUPLING DIAGRAM AND CHARACTERISTICS
STATIONARY
HOUSING.
100
5
-,
~
c
,
:;
&
"
.E
o
2 to-
e:(
a:
w
::J
o
a::
o
to-
1.00
~
;:60
u
z
w
Q 40
u.
u.
w
0.2 0.4 0.6 0.8
SPEED RATIO (output/input)
(REF. 152)
Fig.D-6 SINGLE STAGE TORQUE CONVERTER DIAGRAM AND CHARACTERISTICS
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THE .JOHNS HOPKINS UNIVPIS.TY
APPLIED PHYSICS L.ABORATORY
StLV£. SPtI\NG. "".YLAHO
transmission; Torque and efficiency curves for a typical
unit with a fixed impeller (input) speed are shown in Fig.
D-5. "
In a torque converter, a stationary "reaction mem-
ber" (stator) is inserted between the impeller and turbine
for torque multiplication (Fig. 0-6). For steady flow the
torques acting on the device must sum to zero; i. e., the
output torque equals the input torque plus the torque de-
veloped on the reaction member. Maximum I stall torque'
(i. e., stationary output shaft) varies from 2:1 to 6:1 de-
pending on the design. The efficiency of a single-stage
(one set of blades on the turbine) torque converter as a
function of speed ratio is shown in Fig. D-6 (Ref. 152) as
the bell-shaped curve. " Mounting the reactor on a one-way
clutch, thereby allowing the reactor to rotate freely in one
direction, converts the torque converter into a fluid cou-
pler. At the high-speed ratios the forces on the reactor
reverse and it therefore rotates with the impeller. The
higher efficiency of the fluid coupler results. Figure
D-6 shows the release (coupling) point occurring at the
speed ratio where the torque converter and fluid coupler
efficiencies cross. This type of unit is referred to as a
, converter-coupler'.
D. 1. 5 Aerodynamic Torque Converter
An aerodynamic torque converter (A TC) is pres-
ently under development by Power Technology Corp. (Refs.
153 and 154). The first unit tested (lOO-hp capacity) re-
sulted in a peak efficiency of 770/0. The A TC is, in prin-
ciple, similar to a hydraulic torque converter except that
a compressible fluid 1S used as the working fluid, with
control accomplished by the fluid density. The unit is
envisioned as operating with a GT, whereby the fluid for
the A TC is bled from the turbine compressor output and
then returned to the main GT flow, thereby recovering
a portion of the transmission losses. This recovery capa-
bility has not been considered in the reported 77% effi-
ciency. For a GT-flywhe"el hybrid vehicle, the ATC may
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THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV.. s...'NG. M"_"LAND
be. suitable for the drivetrain from the GT to the flywheel.
However, wi.th our present hybrid concept of on-off opera-
tionof the engine, use of an A TC for the main transmis-
sion is not 'feasible.
D. 2 POWER - DIVIDING TRA NSMISSIONS
Attempts have been made to alleviate the deficien-
cies of CVT's by dividing the power between two subsys-
tems, one of which (e. g. , a hydrostatic subsystem) gen-
erallyperforms the control function, the other (e. g. ,
mechanical gearing) giving a high efficiency power transfer.
The power split is generally a function of the speed ratio
and -power level. It is obviously desirable to transmit
most of the power through the high efficiency unit.
The hydromechanical transmission invented by
Ebert (Ref~ 150) in Germany incorporates hydrostatic cir-
cuits in combination with constant-mesh gearing. It was
(1964) under development under the name DB "Transmatic"
for cars, bus~s, and trucks by David Brown Industries
Limited in England. One unit for a car was designed to
fit in the same volume as the standard gearbox. A 6:1
maximum to:::'que ratio is claimed, of which one unit is
mechanical and five. units are hydrostatic. At the 1:1
speed ratio the drive is purely mechanical. . The trans-
mission uses a small variable-displacement pump and
three small variable-displacement motors operating at
less than 3006 psi. - Features claimed are 17D > 90%, re-
duction in noise levels, and small size. Prototype units
evide~ly have been.-built and tested in trucks. . It has been
heard- that ths Army Automotive Tank Command has sup-
ported "'effort. on development of this unit, but its status
is"uncertain; :further information is be ing sought.
Ahycro-mechanical transmission now under de-
velopment for large trucks by the Sundstrand Corp., called
*.. .
Private discussions with Sundstrand Corp. representa-
ti ve s.
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THE .JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
5ILVt:.. 9NtNG "A"VI-AND
the Dual Mode Transmission (DMT) (Ref. 4), uses a vari-
able-displacement pump and a fixed-displacement motor
in combination with gears. During startup, all power is
transmitted hydraulically. A t a fixed, preset, power
level the mechanical gears are placed in, so that for high-
speed cruise, most of the power is transmitted mechani-
cally. Control is obtained through this hydrostatic unit
(see Section D. 1. 3). The prototype units (1968) used a ir-
craft-type (expensive) materials and construction, were
rated at 250 hp input, and weighed 225 pounds. The DMT
250 production units scheduled for 1972 also will be rated
at 250 hp input but will weigh 675 pounds when made of
conventional materials. The transmission is advertised
for both on- and off-highway vehicles. Full-load effi-
ciencies (acceleration) are shown in Fig. D -7. Efficien-
cies during cruise are expected to be somewhat lower.
Sundstrand representatives* feel that the concept can ulti-
mately be applied to flywheel vehicles, but that their cur-
rent DMT design is not ideally suited for FW systems,
and tha t significant development efforts will be necessary.
The main problem areas of the simple hydro-mechanical
transmission are weight and low efficiency at low vehicle
speeds k 25 mph) encountered over most of the typical
operating cycles. A simple hydro-mechanical transmis-
sion adapted for a family car FW system (Ref. 155 ) is
estimated to weigh -- 280 pounds and would have peak effi-
ciencies similar to those shown in Fig. D-7. Advanced
design concepts such as multimechanical modes are possi-
ble, but ha ve not been demonstrated.
General Electric, under sponsorship of the Army
Tank-Automotive Command, is developing a hydromechani-
cal transmission (Ref. 13) called the XMl. It has been
-"
-rA cursory study of the applicability of their hydro-
mechanical transmission design concept to the APL fly-
wheel vehicle systems was performed by Sundstrand
Corp. as a result of their interest and our informal re-
quest at a recent meeting.
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T"'I: JOHNS ~'HS UNIV£RSITY
APPLIED PHYSICS LABORATORY
.,L via -""'NG M"a"'LAND
I
HYDRO~CHANICA~--
MODE CLUTCH
HYDROSTATIC MODE
INPUT
OUTPUT
: "-
Ij!-- ::-s
HYDROMECHANICAL
MODE CLUTCH
I
I
--~
PLANETARY
DIFFERENTIAL
HYDROMECHANICAL MODE
SCHEMATIC DIAGRAM
90
~
>-
()
z 80
w
U
u.
u.
w
70
o
20
40
60
80
100
VEHICLE SPEED (% of maximum) (REF. 4)
Fig. D.7
(a) SCHEMATIC DIAGRAM AND (b) WIDE.OPEN THROTTLE (ACCELERATION) EFFI.
CIENCY OF SUNSTRAND DUAL.MODE, INFINITELY VARIABLE RATIO TRANSMISSION
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THE JOH..,.S f10PkINS UNiVERSITY
APPLIED PHYSICS LABORATORY
!lILyr" 8~.IHG MA.YLANO
tested in the.M113A1 Armored Personnel Carrier, a
tracked vehicle, and it is claimed that'the concept can be
applied to wheeled vehicles as well. Performance char-
acteristics of the XM1 have not been reported. A IIre-.ro-
lutionary new car transmission II has been tested success-
fully by the National Engineering Laboratory in Glasgow,
Scotland, in a small family car (Ref. 156). It is not clear
whether the unit uses power-splitting or is a pure hydro-
static. It is claimed that the unit IIproduces a tiny power
loss and can be mass-produced economically. II No other
information on this unit has been located.
An electromechanical transmission (EMT) for a
hybrid battery vehicle is under development by TRW, Inc.
(Ref. 17). It is a parallel-type configuration and operates
in two modes. Mode 1 is used for urban operation, with
the powerplant operating at fixed load and fixed speed,
providing the average power needed on the cycle. Extra
power for acceleration is supplied by the batteries, and
excess power during idle is used to charge the battery.
Mode 2 is used for highway cruise. The engine is directly
coupled to the rear wheels, and the engine is throttled
(speed change) to maintain the desired cruise condition.
The transmission is capable of regeneration in mode 1.
and the batteries are not used in mode 2. Dynamometer
emission measurements of a breadboard proof-of-prin-
ciple model were performed on the LA-4 driving route
and compared to those for two standard automobiles - a
1970, 6-cylinder, 120 hp, 3000-pound car, and a 1969,
V8, 190 hp, 3500-pound car - driven on the same schedule.
The emissions reported for the two test comparisons
showed reduction factors of 2. 7 and 3. 1 for HC, 10. 4 and
6. 0 for CO and 6. 2 and 3. 2 for NOx, all for hot starts.
Fuel economy of the EMT was 4% poorer than that of the
6-cylinder car - but 27% better than that of the V8 car.
The fixed-speed EMT engine was operated lean at a/f::.. 18,
and it was necessary to operate the engine at a power level
approximately twice that of the road power demand be-
cause of the low overall EMT efficiency.k 50%). They
(Ref. 17) concluded that regenerative braking does not
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TW£ JOHNS HOPKINS UNIVER$ITV
APPLIED PHYSICS LABORATORY
S'LYt:R S~NG. """"LAND
contribute substantially,to the total charging process, but
they believe that the transmission efficiencies can be im-
proved significantly by design refinement.
D.3 THE GYREACTA MECHANICAL TRANSMISSION
The Gyreacta (Ref. 10) transmission was developed
and tested by Clerk, King, Poynter & Co., Ltd. spe-
cifically for a flywheel-hybrid vehicle and is discussed
separately, since it isa unique unit. !tis a purely me-
chanical dl..ive using meshing gears and clutches. Speed
control is accom.p~isheQ' by the spark ignition engine with
appropriate gear. shifting, to. cover the operating range.
The unit has provisionsJor regenerative braking, charg-
ing the flywheel, and powering from the power plant and I
or flyw,heel. Efficiencie.s of 98. 5% are claimed. Because
of the metQod of control, i. e., via the powerplant, the
unit is not suitable for the mode of operation presently
under consideration, Le., a hybrid using a constant-
speed powerplant and capable of flywheel-only operation
in congested areas.
D.4 SPEED REDUCERS
A speed reducer is required between the flywheel
and the transmission. The current state-of-the-art
should be adequate. Garrettl A iresearch, for instance,
uses a speed redu;cer of -20:1 from the high-speed (58 000
rpm) TSE 36-1 gas turbine that develops 240 shaft horse-
power (Rtf. 157).
. Catalogued (Ref. 158) herringbone units with 15:1
reduction and pitchline velocities of 30 000 ftl min are
quoted as 98% efficient at rated power with the efficiencies
decreasing at less than full power.
Rear axle reduction boxes operate nominally at a
3.1: 1 ratio and use planetary gear configurations.
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THE )0"'''''9 HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
alL.vr- s.o.ING, ""'''YL....ND
Figure D-8 shows the rear axle efficiency of an installed
unit (Ref. 109) operating at wide-open throttle (i. e.. ac-
celeration) and road load conditions. Note that at low
cruise speed. 20 mph. the efficiency is reduced to 87%.
The low efficiency under light load is attributed to seal
friction, oil churning losses. and bearing losses.
A new development in planeta ry speed reducers is
the roller traction type of device (Refs. 159 and 160)
which is more efficient, reliable. durable, and quieter
than planetary gears. Figure D-9 shows its significant
efficiency advantage at part load. It is suited to high-
speed (and high-power) applications. Tests on a 500-hp,
~j5 OOO-rpm unit and a 5-hp, 480000-rpm unit are re-
ported in Ref. 159. Weights and volumes are claimed to
be equivalent to planetary gear trains.
A unique speed reduction mechanism is the
harmon"ic drive (Ref. 161). The units use a "deflection
wa ve transmitted to a nonrigid member to produce a high
mechanical advantage between concentric parts." Advan-
tages cited are high speed ratios. high efficiencies, low
weight. and hermetic sealing. The last feature is par-
ticularly attractive for flywheels in evacuated cases. .
Maximum shaft-to-shaft efficie'ncies of 90% are reported.
The units are employed where high reduction ratios are
required, i."e.. greater than 60:1. For a 30 OOO-rpm
fully charged flywheel speed and a 60: 1 reduction, input
transmission speeds would vary from 250 to 500 rpm re-
quiring high levels of input torque. For speeds ~ 20 mph
a t low flywheel charge. the transmission would be re-
quired to operate at over 1:1 speed ratio. reaching 1:5 at
80 mph.
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THE JOMNS HOPKINS UNIVERSITy
APPLIED PHYSICS LABORATOR"
SILVEIit 5""1""4 MARYLAND
100
~
>- 95
u
2
w
U
u. 90
u.
w
85
J 40 60
Fig. 0.8
100
SPEED (mph)
REAR AXLE EFFICIENCY AT WIDE-OPEN THROTTLE
AND ROAD LOAD (REF. 109)
TRACTION DRIVE
~
90
;;.
>-
U
~ 80
u
u.
u.
UJ
70
60
o
---L-
I
40
3000 RPM INPUT
3.5:1 SPEED RATIO
I
80
INPUT TORQUE (ft-Ib)
I
120
--_1-.
160
Fig.D.9 OVERALL '::FFICIENCY COMPARISONS OF ROLLER TRACTION VERSUS
GEARED PLANETARY DRIVE UNITS (REF. 160) .
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. - . ~------" -- -~~--
THE .JOHNS HOPKINS UNiVERSITY
APPLIED PHYSICS LABORATORY
SILV(. g".'NG """."\"""0
APPENDIX E
TInE AND vVIND RESISTANCE OF AUTOMOBILES
The major external resistance to vehicle propul-
sion are the aerodynamic resistance and the rolling con-
tact resistance between the tires and the road. The aero-
dynamic drag force D is. related to th~ drag coefficient
CD by:.
_l 2 A- .A2
D - 2 fJV Co - 0.00257 CD V , pound
(E-l)
where sea-level density has been assumed, A is in ft2 and
V in mph. The rolling friction FF is related to the roll-
ing resistance coefficient f (Ib/Ib) by: .
F = f W
F l'
(E - 2)
where W1 is the loaded vehicle weight. With the forces
given in pounds and the velocities in mph, the conversions
to horsepower are given by:
p . = DV /375 .
o
P = F V /375 .
F F
(E-3)
The values given by Eqs. (E-l) - (E-3) are wheel
forces. To relate these to the power plant shaft requires
consideration of the driveline efficiency.
E.1 AERODYNAMIC DRAG COEFFICIENT
Bowman (Ref. 162) reported wind-tunnel measure.-
ments of 21 models of automobiles, 17 of which were "pre-
cise scale duplicates of production vehicles" ranging in
size from subcapacity and small, high-performance rac-
ing coupes to the large high-production volume sedans.
Three were models of production car proposals, and one
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l'H(: JOHNS HOPKIJt\lS UNIVERSITV
APPLIED PHYSICS LABORATORY
S'LV'" 9""."'0. "","VL"''''O
was a "highly streamlined experimental body shape" (Ref.
162. p. 609\. The measured CD's are listed in Table E-l.
Hoffman (Ref. 107) plots drag force at 60 mph (88
ft/ s) versus Wi. for 1960 automobiles. In Fig. E-1. force
is shown on the right-hand scalefand the left-hand scale
shows the corresponding drag coefficients for vehicles
with 25-ft2 frontal areas per Eq. (E-l).
In the North American study (Ref. 132). values of
CD = O. 45 for II conventional 1966 cars" and CD = O. 25 for
"advanced veh icles" were used.
Hoerner (Ref. 108) reports values of CD for a num-
ber of production vehicles of 1920-1950 vintage. In addi-
tion. values for smooth wind-tunnel models are also docu-
mented. These values are given in Table E-2. .
The Battelle (Ref. 105) and Little (Ref. 106) studies
t1employed optimistic values for the drag coefficients"
(Ref. 106.. p. 15). The values used (along with frontal areas)
for a small commuter car and a family car are shown in
Table E-3. Also shown in Table E-3 are the corresponding
values proposed by OAP for the hybrid-.flywheel vehicle
specification.
E-2 ROLLING RESISTANCE COEFFICIENT
Experimental values of the rolling resistance coef-
ficient. f. as a function of speed (0 to 70 mph). tire pres-
sure (25 and 30 psi) and material (nylon and rayon cords)
for 8.00-15 4-ply passenger tires are reported in Ref.
163. The results are shown in Fig. E-2:
Various equations have been proposed by tire manu-
facturers, automobile manufacturers. and analysts. A
number of thesE: are: .
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THE JOHNS HOPKI...,S UNIVERSITY
APPLIED PHYSICS LABORATORX
SILV[1It SP-,IIr,U;; MAIitYLANO
Table E-l
Measured Frontal Areas and Drag
Coefficients from Bowman
Specimen 1 A(ft2) CD
Make
A Ford Fairlane-500 (1963) 21. 55 0.529
B A nglia (English Ford) 16.95 0.508
C 1955 Ford 24.80 0.508
D Unknown 20.8 0.502
E 1965 Ford 23.7 0.500
F Unknown (no photo) 24.2 0.499
G Datsun 18.5 0.473
H 1962 Ford 24. 1 0.466
I Edsel 22. 3 0.458
J Volkswagen 19.65 0.445
K 1960 Ford Falcon 20.75 0.445
L Ford Station Wagon (1962) 24. 70 0.4307
M Unknown 20.1 0.429
N Vauxhall 20.0 0.4258
o Unknown 17.3 0.3996
P Renault Dauphine 17.8 O. 3938
Q Unknown 18.9 O. 369
R Unknown 14. 7 0.324
S Proposed 17.56 0.307
T Proposed 17. 15 0.288
U Experimental, highly stream-
lined vehicle 21. 53 O. 272
1 .
Photographs were shown 10 Ref. 162, but the makes were
not specified; the identifications listed here are opinions
of "car buffs" at APL.
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THE JOHNS HOPK,U..S UNIVERStTY
APPLIED PHYSICS LABORATORY
a'L'III:" SPRING "..RYl.AND
Table E- 2
\'ehicle Orag Coefficients from
Hoerner (Ref. 108)
Car or wind-tunnel model
CD
1920 open car
1940 German DKW
1949 Chrysler Windsor
1949 -53 Hudson
1949 Nash
Box shape
Basic car body with sharp lateral edges
With sharp edged windshield
With long tapering tail .
Streamline cal' shape
Extreme streamline shape
0.95
O. 64
0.60
0.51
0.45
0.86
O. 24
O. 35
0.12
0.16
0.13
Table E""3
'lehicle Drag Coefficients Assumed
. for Recent Studies
Vehicle
Wipound)
3500
] 400
A (ft 2 )
Family Car
Commuter Car
28
18
CO(Ref. 106)
0.35
O. 25
CD(OAP)
0.50
O. 35
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THE: JOHfirr(S HOPKtNS UN-IVERSITV
APPLIED PHYSICS LABORATORY
SILVI"IIt S~.ING ".IItYLAND
150 . -
0.6 E
o
w
u
a::
o
N 0 U.
~ 0.4 100 C)
u. a::
N 0
U
-
o
STYLING 0
a::
w
o 0
-------
TH~ .K)HNS HO~IN5 UNIVERSITY
APPLIED PHYSICS LABORATORY
.'LV... ""ING. W.""LAND
Heference
f = 0.0120
f=0.0148
f = 0.0168 + 13~L 5 x 10-6V
f:= 0.0116 + 165.0 x 10-6V
-G
f=0.0146+100.0xl0 V
f = 0.0061 + :~6. 0>. 10-6V
-G
+ 50.0 x 10 V
-G
f = 0.02 + 28. 0 x 10 V + O. 24 x
57
57
~)7
'.)7
1 :~2 ("conventional 1966 cars")
I :~2 ("advanced v"ehicles")
f = O. 01
107
10~6V2 .10fi (includes bearing and axle
losses)
f = O. 005
0.;'5 :{!) fj 2
+ -+-xl0 V
P p
lOB (P = tire pressure in psia)
where V is i:1 mph. Values of the rolling resistance
coefficient were not specified by OA P for the current
study; however, it was recommended that current values
only be used*. Current APL studies use the equation
given by Hoe:cner (Ref. 1(8), with a tire pressure P = 30
psia (last equation in list above), as used in Eq. (5-9).
E.3 DISCUSSION AND CONCLUSIONS
It can be seen that the drag coefficients and rolling
resistance quoted and measured by various authors differ
by factors of 7 and 2.7 respectively (0. 13 ~ Co ~ 0.89 and
*
"Any calcula [ions of rolling resistance caused by tires
should be made on the basis of currently available tires
and include the effect of tire width. Decreasing the roll-
ing resistance caused by the tires by. assuming a type of
tire that has unsafe traction characteristics by virtue of
low rolling resistance is not allowed" (Ref. 104).
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THE JOHNS HOPKINS UNIVERSITV
APPLIED P>-IYSICS LABORATORY
Su..vt:Jf S~"I"'G WARYLAND
0.0065 s; f s; 0.0182 at 10 mph). The drag coefficients
are mainly a function of body styling. Current values of
production vehicles vary from 0.4 to O. 5 (independent of
frontal area); the attainment of CD::" O. 3 seems feasible.
Rolling friction coefficients are sensitive to tire mate-
rial, construction, and pressure. Advanced projections
based on higher pressures and more favorable construc-
tion and materials seems tenuous. The arguments ad-
vanced in Ref. 106 for discarding highly.optimistic values
of f are of interest.
"We have taken a cautious approach for the
following reasons: (1) much of the reduction in
rolling resistance of improved tires is lost if
correct inflation pressures are not maintained;
(2) a soft ride may be demanded by buyers of
automobiles, . and on rough roads this would re-
quire that energy be absorbed either in the tires
or by the suspension system; (3) Federal safety
requirements for tires cannot at present be met
by tires with very low rolling resistance" (Ref. 106,
p. 17).
Based on the above considerations the following
ranking of values seems appropriate:
Co f
Conservative 0.50 0.0168 + 139. 5 x 10-6V
Optimistic 0.30 0.010 + 50.0 x 10-6V
Highly Optimistic 0.20 O. 00612 + 36 x 10-6V
Steady state horsepower requirements based on the above
assumptions are plotted in Fig. E-3 for a 1400 pound (curb
weight) commuter automobile. Also shown for comparison
are the values currently in use. (CD = O. 35 and Hoerner's
equation for the resistance with P = 30 psia.) It can be
summarized. tha t the values currently in use can be con-
sidered as reasonably optimistic.
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Tt4E JOHNS HOPKINS UNIVERSI1'V
APPLIED PHYSICS LABORATORY
SI1.VU' S'-"11'ifG W"'''YLAHD
80
CURB WE I GH",. = 1400 POUNDS
.::,'<.1
,,'
::.'"
$
R
uO
60
ex:
w
~
o
a.
w
(f)
~ 40
:J:
oJ
w
w
:J:
~
20
I
i
o 0
20
40 60
VELOCITY (mph\
80
100
Fig. E.3 STEADY HORSEPOWER REQUIREMENTS FOR VARIOUS DRAG AND FRICTION
ESTIMATES
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S'LVEIit ~'''''G. ""WYLAND
THE JOHNS HOPKINS UNiVERSITY
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Sixteen," Automotive Industries, Vol. 69, 18
November 1933, pp. 604-607.
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APPLIED PHYSICS LABORATORY
139.
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Cars," SAE Paper No. 690461, 1969.
T. G. Fellows, et aI., "Per bury Continuously
Variable Ratio Transmission," from Advances in
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MacMillan Co., 1964. .
C. K. J. Price and S. A. Beasley, "Hydrostatic
Transmissions," from Advances in Automobile
Engineering II, Carter (Ed.), Vol. 5, MacMillan
Co., 1964.
C. W. King, et aI., "Electric-Wheel Vehicle Pro-
pulsion System," SAE Paper No. 690071, pre-
sentedat Inter Auto. Engineering Congress,
Detroit, Mich., 13-17 January 1969.
E. R. Laithwaith, "Electrical Variable-Speed
Drives," Engineers' Digest, Survey No. 17, Vol.
25, No. 10, October 1964, pp. 113-165 (see also
Survey No.2, Vol. 18, No. 12, December 1957,
pp. 533-568).
P. C. Mortenson, "Hydrostatic Transmissions,"
SAE Transactions, Vol. 68, 1970, pp. 243-247.
E. H. Bowers, "Hydrostatic Transmissions for
Vehicles," SAE Transactions, Vol. 68, 1960, pp.
248-256. .
R. H. Eshelman, "Hydro-Tractors: Reality in
Iron," Automotive Industries, Vol. 143, No.7,
1 Octob er 1970.
Hydraulics, C3 Series Hydrostatic Transmissions,
Sta-Rite Industries, Inc., Racine, Wis., Bulletin
FP 26-2, April 1969.
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S'LYI'R' SP_'''''G. "4""'YLANO
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APPLIED PHYSICS LABORATORY
148.
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No.9 -002-13. '
J. H. Hobbs, "The Small Car - Why Not Automatic, II
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(Ed.), Vol. 5, MacMillan Co., 1964.
C. V. Lezard, "Hydraulic Variable-Speed Drives, "
Engin0ers' Digest Survey No. 18, Engineers'
Digest, Vol. 25, No. 12, December 1964.
J. C. ~wain, et al., "A Turbine-Speed Pump for
Vehicle Transmission Use, II SAE Paper No.
670954, 1967. .
H. L. Dougherty and A. C. Ingersoll, Fluid
Mechanics, McGraw-Hill Book Co., N. Y., 1954.
C. C. Hill, "Aerodynamic Torque Converter from
Gas Turbines," ASME Paper No. 69-GT-108, 1969.
C. C. Hill, et al., "Design and Test of the First
Aerodynamic Torque Converter for Gas Turbines, "
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T. E. Hamsey, Sundstrand letter to Dr. A. Brandt
A PL! JHU), Sundstrand A viation, Rockford, Ill.,
AE No. 421-78, 28 December 1970.
Industrial Research, December 1970, p. 17.
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duct Literature, MS 2101, 20 March 1970.
"1970 Fluid Power Reference Issue, II Machine
Design, Vol. 42, No. 22, 10 September 1970.'
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THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
159.
160.
161.
162.
163.
A. L. Nasvytis, "MultirollerPlanetary Friction
Drives," SAE Paper No. 660763, October 1966.
L. O. Hewko, "Roller Traction Drive for Quiet,
, High-Speed Power Transmission," SAE Paper
No. 690572, September 1969.
"Harmonic Drive, Mechanical Power Transmis-
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Brochure.
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namic Characteristics of Sedan Type Automobile
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ing Temperature of Tires," Journal of Research
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Vol. 64C, No.1, January-March 1960.
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TH£ JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SIL¥!"R SPlitiNG. WAIltVLAND
ACKNOWLEDGMENT
The authors would like to acknowledge the contribu-
tions of the many persons associated with this program and
to others who gave freely of their knowledge and experi-
ence. In particular, we acknowledge the support and pro-
gram guidance of Dr. Jalal Salihi, Mr. David Dawson,
and Dr. Karl Hellman of the Office of A ir Programs, En-
vironmental Protection Agency; the experimental tech-
niques for rotating the rod flywheels and photographing
the failure process developed by Mr. Guy Mangano of the
Naval Air Propulsion Test Center; the efforts of Mr.
Robert Randolph and Mr. James Burns of Hercules, I!1c.,
in developing the processes required to fabricate the 1-
pound test rods; the cooperation of A VCO Corp., General
Technology Corp., Fothergill and Harvey, Ltd., PPG
Industries, Hamilton Standard Corp., Corning Glass,
Columbia Products Co., and the Whittaker Corp., for
furnishing test samples of filamentary and composite mate-
rials; the information and suggestions offered by Mr. D. M.
Latson of the U. S. Army Tank Automotive Command and
Mr. R. H. Guedet of Sundstrand Corporation in the field
of transmission design; the analysis of rotor drag and
windage losses conducted by Mr. R. H. Cramer of APL;
and t~e counsel and guidance of Dr. W. H. Avery and
Messrs W. B. Shippen and R. W. Blevins of A PL, and
the experimental assistance of Mr. A. J. Klaunberg, Jr.,
of A PL.
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