Design Options for a Flywheel Energy Storage System

Design Options for a Flywheel Energy Storage System
Jed Firebaugh
A thesis submitted in partial fulfillment
of the requirements for the degree of
Master of Science in Mechanical Engineering
University of Washington
2007
Program Authorized to Offer Degree: Mechanical Engineering
© Copyright 2007
Jed Firebaugh
University of Washington
Graduate School
This is to certify that I have examined this copy of a master’s thesis by
Jed Firebaugh
and have found that it is complete and satisfactory in all respects,
and that any and all revisions required by the final
examining committee have been made.
Chair of Supervisory Committee:
__________________________________________________________
Brian C. Fabien
Reading Committee:
__________________________________________________________
Brian C. Fabien
__________________________________________________________
__________________________________________________________
Date: _____________________________________
In presenting this thesis in partial fulfillment of the requirements for a Master’s degree at
the University of Washington, I agree that the Library shall make its copies freely
available for inspection. I further agree that extensive copying of this theis is allowable
for only scholarly purposes, consistent with “fair use” as prescribed in the U.S. Copyright
Law. Any other reproduction for any purposes or by any means shall not be allowed
without my written permission.
Signature ___________________________
Date _______________________________
University of Washington
Abstract
Design Options for a Flywheel Energy Storage System
by Jed Firebaugh
Chair of Supervisory Committee:
Professor Brian C. Fabien
Department of Mechanical Engineering
A flywheel energy storage (FES) system with a hybrid magnetic bearing has been
developed at the University of Washington. Radial support of the flywheel is provided
by two sets of permanent magnetic bearings. The axial support is provided by a
mechanical point contact on the bottom of the flywheel. Actuation is accomplished by an
axial flux permanent magnetic motor/generator. The FES prototype has vacuum
containment, but not suitable to maintain ≤ 10-5 torr without continuous pumping. The
means to maintaining a containment chamber pressure of ≤ 10-5 torr without continuous
pumping are presented. Recommendations for future designs are proposed.
TABLE OF CONTENTS
List of Figures
ii
Chapter 1: Introduction
1.1 Energy Storage . . . . .
1.2 FES System . . . . . . .
1.2.1 Rotor . . . . . . .
1.2.2 Bearings . . . . .
1.2.3 Motor/Generator .
1.2.4 Containment . . .
1.3 Objective . . . . . . . .
Chapter 2: FES Prototype
2.1 Rotor . . . . . . . .
2.2 Bearings . . . . . .
2.3 Motor/Generator . .
2.4 Containment . . . .
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1
1
4
4
7
9
13
15
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16
17
19
20
24
Chapter 3: Future Design and Improvements
3.1 Rotor . . . . . . . . . . . . . . . . . . .
3.2 Bearings . . . . . . . . . . . . . . . . .
3.2.1 Eddy Current Dampers . . . . . . .
3.2.2 Contact Friction . . . . . . . . . .
3.3 Motor/Generator . . . . . . . . . . . . .
3.4 Containment . . . . . . . . . . . . . . .
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26
27
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32
33
36
36
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Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
i
LIST OF FIGURES
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14
1.15
Reduction of stress by multiple ring configuration . . . . . . . . . . . . . . .
0°/±45°/90° laminate stack . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hoop and radial reinforcement laminations . . . . . . . . . . . . . . . . . . .
Stacked-ply flywheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fiber pattern for optimized T1000 ply . . . . . . . . . . . . . . . . . . . . .
Magnetic bearing options . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Axially oriented magnet
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Axial flux motor geometry . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diametrically oriented magnet . . . . . . . . . . . . . . . . . . . . . . . . .
Radial flux motor, internal rotor and axially oriented magnet array . . . . . .
Radial flux motor, internal rotor and diametrically oriented magnet array . . .
Radial flux motor, external rotor and diametrically oriented magnet array . . .
Radial flux motor, external rotor and eight-magnet Halbach array . . . . . . .
Magnet orientations for an eight-magnet Halbach array . . . . . . . . . . . .
Basic geometry for an internal rotor . . . . . . . . . . . . . . . . . . . . . .
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5
6
6
7
7
9
10
10
11
11
11
12
12
12
13
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
Prototype flywheel energy storage system . . . . . . . . . . . . . . . . . . . .
Schematic of the FES prototype . . . . . . . . . . . . . . . . . . . . . . . . . .
Side view of the rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
View of the top of the rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . .
View of the bottom of the rotor . . . . . . . . . . . . . . . . . . . . . . . . . .
View of the ring magnet for the top bearing in the top disk . . . . . . . . . . .
Magnetically attractive axially-oriented ring magnets . . . . . . . . . . . . . .
Cross-section of attracting ring magnets with magnetic flux lines . . . . . . .
Portion of the bottom bearing in the bottom disk . . . . . . . . . . . . . . . . .
Motor magnet configuration . . . . . . . . . . . . . . . . . . . . . . . . . . .
View of top housing disk, showing the motor coils, bearing magnet, and sensors
Arrangement of motor coils and Hall effect sensors . . . . . . . . . . . . . . .
The three Hall effect sensors . . . . . . . . . . . . . . . . . . . . . . . . . . .
Optical position sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
View of the LED emitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Drawing of the LED emitter . . . . . . . . . . . . . . . . . . . . . . . . . . .
View of the photodiode detector . . . . . . . . . . . . . . . . . . . . . . . . .
Chamber gasket for the bottom disk . . . . . . . . . . . . . . . . . . . . . . .
Clear acrylic tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
17
17
18
18
19
20
20
20
21
21
22
22
23
23
24
24
25
25
3.1
3.2
3.3
3.4
3.5
3.6
3.7
FES system cross section showing the components
FES system cross section showing the components
Rotor cross section for no contact damper . . . .
Rotor cross section for contact damper . . . . . .
Rotor shaft . . . . . . . . . . . . . . . . . . . . .
Top view of the motor magnet mounting plate . .
Metal rotor . . . . . . . . . . . . . . . . . . . . .
26
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27
28
28
29
29
ii
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3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
Motor magnet mounting plate for metal rotor . . . . . . . . . . . . . . . . . .
Metal rotor with higher specific energy . . . . . . . . . . . . . . . . . . . . .
Schematic of top bearing from Figure 3.1, no mechanical contact damper . . .
Schematic of top bearing from Figure 3.2, mechanical contact damper . . . .
Section view A-A from Figure 3.10 . . . . . . . . . . . . . . . . . . . . . . .
Schematic of the bottom bearing from Figures 3.1 and 3.2 . . . . . . . . . . .
Geometrical layout of an eddy current damper . . . . . . . . . . . . . . . . .
Concentric ring magnets of the no contact damper of Figure 3.10 . . . . . . .
Section view A-A from Figure 3.11 . . . . . . . . . . . . . . . . . . . . . . .
Point contact geometry of the hybrid magnetic bearing . . . . . . . . . . . . .
Four-pole Halbach magnet array for the axial flux motor/generator . . . . . .
Schematic of the FES system with burst containment . . . . . . . . . . . . . .
iii
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30
30
30
31
31
32
32
33
33
34
36
37
ACKNOWLEDGEMENTS
The author wishes to express sincere gratitude to Professor Brian Fabien for his support,
guidance, and patience. Thank you Joseph Kay for wiring the motor and sensors of the
prototype. Many thanks to Kevin Soderlund for his time and effort invested to fabricate
parts for the prototype.
iv
1
Chapter 1
Introduction
1.1 Energy Storage
Energy exists in six major forms: mechanical, electrical, chemical, thermal,
electromagnetic, and nuclear. When supply exceeds demand, energy needs to be stored
efficiently in some recoverable form for use at another time.
Electromagnetic energy storage requires the use of superconductors. A
superconductor is a material that carries electric currents without resistive loss when
below a certain temperature. An electromagnetic field produced by an electric current
flowing through a wire can store energy [15]. If the wire is made of superconducting
material (no resistive loss), an electric current flowing through it can remain constant.
Electrical energy supplied as direct current to a superconducting wire coil can be stored
in the electromagnetic field. The stored energy can be recovered as electrical energy
(direct current) by attaching the coil to a load. This is the basis of the Superconducting
Magnetic Energy Storage (SMES) system that is under consideration for electric utility
use. Since no energy conversion is involved, SMES is highly efficient and can respond
rapidly, with a response limited by the time needed for conversion between DC and AC
power [36]. Rapid response is useful for load leveling and for frequency and voltage
control of the electrical utility grid. A drawback of superconductivity storage is the
operation of a cryogenic plant for producing the liquid helium or nitrogen required for the
low temperatures. Also special structures are needed to withstand the strong magnetic
fields produced by the large electric currents of large-scale applications.
Thermal energy can be stored as either sensible heat or latent heat. Sensible heat
refers to thermal energy that results in an increase in temperature when added to a
material or decrease in temperature when removed. Liquids, gases, and solids can store
energy as sensible heat provided they do not change phase by freezing, melting, boiling,
or sublimating. Water is the most common medium for thermal energy storage. Ceramic
bricks are also used for large-scale heat storage in industry, and water or a combination of
air and rock provide storage for heat derived from solar energy [15]. Latent heat is the
thermal energy that is stored in or released from a substance or mixture when it
undergoes a phase change while the temperature remains constant. The heat that can be
stored per unit mass in this manner is usually several times greater than for sensible heat
storage. Thus latent heat storage uses less space than cold-water storage but is more
expensive. The oldest phase change material used in thermal storage is ice. Other phase
change materials are saturated steam, inorganic salt hydrates, organics (such as paraffin
wax), fatty acids, eutectics, and aromatics. Latent heat storage systems have been
developed for ventilation systems using molecular adsorption and desorption of water
vapor on zeolites [36].
Mechanical energy storage is accomplished through pumped storage hydropower
storage, compressed air, and flywheels.
Hydropower uses electricity in excess of demand to pump water from a reservoir at a
lower level to a reservoir at a higher level. When the demand for power exceeds the
supply, the water flows back down through a hydraulic turbine, which drives an electric
2
generator. Unused power from intermittent sources, such as wind and solar, can be used
to power the water pumps. The overall efficiency for hydropower is 65−70% [36]. The
main weakness of hydropower is the small number of suitable sites for two reservoirs.
Compressed air energy storage uses electrical energy in excess of demand to
compress air in a reservoir for later use in a gas turbine to generate electricity. A gas
turbine compressor uses 50−60% of the total energy consumed by the gas turbine. The
storage facility for the compressed air is usually a man-made rock, salt, or porous rock
cavern, created either by aquifers, mining, or oil and gas extraction. In aquifers, the
compressed air will displace the water, creating a constant pressure storage system. For
compressed air energy storage, the overall efficiency is estimated to be 65−75% [15].
The concept of storing energy in a spinning a wheel has been known for about 6000
years [43]. Early forms of the flywheel include the potter’s wheel and spindle whorl.
Early steam engines and modern internal combustion engines use flywheels in a manner
similar to the potter’s wheel—discontinuous-in, continuous-out energy conversion. The
flywheel stores rotational kinetic energy usually in the form of a spinning disk or
cylinder, called the rotor.
Flywheels can be designed for a broad range of power ratings and can be charged and
discharged very rapidly, limited only by the transmission system capacity and the
maximum allowable torque. The ability to provide short bursts of power is utilized in
applications such as electromagnetic rail guns, inertial friction welding, inertial starters,
and hybrid electric vehicles, where the flywheel provides short bursts of power for
climbing hills and acceleration and is replenished directly by the engine through an
alternator or by regenerative braking [23]. Depending on the motor/generator design, the
charge/discharge efficiency of an FES system can reach 97 percent [12].
The total cost of generating electric power can be reduced by the use of flywheels to
bridge the gap between energy supply and demand through a procedure called load
leveling. Power plants are most efficient when operating continuously at the baseload
capacity. At night, the baseload capacity is typically underused, and during the daytime,
expensive and less efficient generating sources are used to meet the additional demand
for power. With the use of flywheels, excess electrical energy generated at night and
during weekends can be stored for use when the demand exceeds the baseload capacity.
Flywheel can also be used to feed the excess electrical energy from intermittent and
variable energy sources, such as solar and wind energy, into a utility grid.
Chemical energy storage is comprised of coal, refined petroleum oils and fuels,
natural gas, supercapacitors, hydrogen, biomass, and batteries.
The storage mechanism of capacitors is electric charge. A conventional capacitor
consists of a dielectric material between two conducting plates, one the anode, the other
the cathode. Dielectric capacitors have specific energies less than 1 Wh/kg.
Supercapacitors or electrochemical capacitors, which have 500,000 times more
capacitance than conventional capacitors, consist of carbon or high-surface area materials
as a conductor and an electrolyte. Supercapacitors can endure thousands of recharge
cycles, have a specific energy of about 5 Wh/kg, and can provide more than 1 kW/kg of
power output [36]. Batteries provide power densities of less than 0.2 kW/kg.
Supercapacitors can be used as an energy source, energy buffer (load leveling or peak
shaving), or a load equalizer for elevators.
3
Hydrogen, the most abundant element on the planet, can be used as chemical storage
compound. Through electrolysis or thermal input, water can be decomposed into
hydrogen and oxygen. These substances can be recombined when needed to release
energy. Renewable resources can be used to power the extraction of hydrogen from
water. Hydrogen can be combusted, like gasoline, in an engine or in a fuel cell; the fuel
cell being the more efficient of the two with about 55% percent efficiency. The challenge
of hydrogen is safe storage. It can be stored as a compressed gas in vehicles, cryogenic
liquid for transport, or in solid-state. Solid-state systems bind hydrogen to a solid
material such as carbon [36]. Lightweight metal alloy hydrides are a promising material
for hydrogen storage.
Biomass refers to harvested, waste, or residual plant matter. Chemical energy in
biomass fuels is stored within plants by photosynthesis. Gaseous or liquid fuels such as
methane, hydrogen, and alcohols or bio-oils can be produced from biomass [36]. Liquid
biofuels, such as ethanol and biodiesel, and biogas can be used as alternatives to fossil
fuels in internal combustion engines. Ethanol is produced by yeast and other bacteria in
the fermentation of crops including corn, sugarcane, wheat, and sugar beets [1]. Most
biodiesel is produced by the reaction of soybean oil with methanol in the presence of an
alkaline catalyst [1]. Biodiesel can also be made from other vegetable oils, oil seed,
animal fats, and waste grease [1]. Biomass is converted into electricity by either direct
combustion or integrated gasification combined cycle technology [36]. The major
problems with producing bioliquids are the cost and negative energy balance of
production. Also biofuels have smaller energy densities than gasoline or diesel.
The electrochemical battery is the prevailing means of short-term energy storage in
the world today. It supplies electrical energy to a seemingly endless variety of
applications. Batteries produce electrical energy through spontaneous electrochemical
reactions that are driven by the Gibbs free energy of reaction. In recent years, flywheels
have become a viable alternative means of energy storage to some batteries.
The major problems with electrochemical batteries are the relatively short life cycles
and the serious environmental concerns associated with manufacture, recycling, and
disposal. The contact free or minimal contact operation of magnetic bearings means
nearly no maintenance for FES systems and potentially more than 10,000,000
charge/discharge cycles for the life of the flywheel [2]. Unlike batteries, the life of the
flywheel is independent of the depth of discharge. Furthermore flywheels can be
fabricated from nontoxic materials with negligible disposal problems. Flywheels offer
several other significant advantages over batteries. As Hull states, “The power is limited
by the power electronics and the size of the [motor/generator] rather than by
electrochemistry. Second, the state of the charge of a flywheel battery is readily
determined from its rotational velocity, whereas determination of the state of charge for
an electrochemical battery is more difficult.” [23].
Specific energy is the energy stored by an object divided by its mass. Premium lead
acid batteries can attain a specific energy of about 45 Wh/kg [40]. Due to the
development of composite materials a filament wound flywheel can achieve a theoretical
specific energy of between 291 Wh/kg, roughly six times that of a premium lead acid
battery [42].
4
1.2 FES System
The basic components of an FES system are the rotor, bearings, power conversion, and
containment. The bearings either connect or exert a stabilizing force between the rotor
and the fixed platform. When the flywheel is used as a mechanical battery, a
motor/generator converts energy between rotating kinetic and electrical [23]. To reduce
energy loss from air friction, a flywheel is contained in a vacuum vessel, and often an
additional structure will surround the FES to contain debris if failure occurs.
1.2.1 Rotor
The purpose of the rotor of a flywheel is to provide moment of inertia. The kinetic
energy EK of a rotating rigid body is defined by
1 2
(1.1)
Iω
2
where I is the moment of inertia of the total mass of the rigid body about the center of
rotation and ω is the angular velocity. The maximum amount of kinetic energy that can
be stored in a rotating rigid body is determined by its geometry and the strength of its
materials. For a rotor composed of a single isotropic material, usually the case for most
metals, the maximum specific energy ES (kinetic energy per unit mass) is given by
EK =
ES = Kσ u / ρ
(1.2)
where K is a geometric factor of 1 or less, σ u is the ultimate burst strength, and ρ is the
density. The geometric factor K is associated only to shape, so the specific energy is
independent of size. Equation 2.1 can also represented as
2
ES = K (ωrb ) = Kvmax
2
(1.3)
where rb is the burst radius of the rotor for a given angular velocity and vmax is the
maximum rim speed. Thus the material with largest specific strength, σ u / ρ , can sustain
the fastest rim speed, enabling the storage of the most energy per unit of mass. The
maximum energy per unit of volume EV is
EV = Kσ u
(1.4)
So for a given rotor volume, the material with the highest ultimate strength will store the
most energy. When calculating the burst speed, tangential hoop stress and radial stress
must be taken into account independently. For isotropic materials, such as metals, hoop
stress dominates.
Flywheel rotors are normally made of either metal or fiber composites. Metallic
rotors are often made of moderate-strength steel because of low cost and manufacturing
experience. When higher specific energy is desired, metallic rotors are made from
maraging steel and titanium. Fiber composites consist of fibers embedded in a matrix
5
material, usually epoxy. Fibers typically used are E-glass, S-glass, graphite, and Kevlar.
The strongest fibers are made of graphite, a crystalline form of carbon. Carbon fiber
composites have higher specific strengths than metals, and are thus the material of choice
when trying to achieve the highest specific energy. Composite rotors are made in two
different configurations: filament-wound rings and stacked-ply.
A common method of producing a filament-wound composite flywheel is to wet the
fiber tow with matrix resin and spool the wetted fiber onto a mandrel, with fiber
reinforcement in the tangential direction only. Radial stress is produced from the
difference in expansion, caused by centrifugal force, between the faster moving outer
layers and slower moving inner layers [23]. Because of the low strength of the matrix,
the composite strength is weak in the radial direction, causing radial delamination and
prohibiting high energy densities.
A method of construction that improves the radial strength of filament-wound
flywheels and enables the achievement of higher energy densities is to press-fit different
filament-wound rings inside of one another. The maximum radial stress of a rotating ring
depends on the ratio between the inner and outer radii (rin/rout), and a larger rin/rout causes
a smaller maximum radial stress [41]. Therefore only a thin filament wound ring can
rotate at high speed because of low radial strength. If a thick ring is divided into multiple
rings, then the radial stress in each ring is lower than the stress in the thick ring during
rotation, but since the radial stress is tension during rotation, the rings will tend to
separate. If an inner ring is press-fit into an outer ring, then there is an induced
compressive stress at the interface that maintains structural integrity and reduces the
radial tensile stress during rotation. The multiple-ring structure can consist of either rings
of the same material or of rings with increasing ratio of circumferential Young’s modulus
to mass density, Eθ /ρ, with increasing radius, the latter better reduces the radial tensile
stresses (see Figure 1.2). The highest reported specific energy for a flywheel is 195
Wh/kg using press-fit filament-wound high strength carbon fiber rings [41].
Figure 1.1: Reduction of stress by multiple ring configuration [41]
6
The stacked-ply method of flywheel construction involves the laminating of diskshaped plies with unidirectional fibers oriented in the radial and tangential directions. It
is common to create a quasi-isotropic composite rotor from the stacking pattern
0°/±45°/90° [27] (see Figure 1.3). However the quasi-isotropic arrangement does not
provide the highest burst speed, thus not providing the highest specific energy. Curtiss et
al. showed that a flywheel with a majority of purely circumferential reinforcement versus
purely radial reinforcement performs better (see Figure 1.4).
0°
+45°
−45°
90°
Figure 1.2: 0°/±45°/90° laminate stack
Purely Circumferential
Reinforcement
Purely Radial
Reinforcement
Figure 1.3: Hoop and radial reinforcement laminations [8]
7
Thielman and Fabien et al. proposed a stacked-ply design of alternating plies of
tangential and radial reinforcement (see Figure 1.4). Classical lamination theory was
used to show that the stress/strain distribution in the disk is a function of the orientations
of the fibers in the radial reinforcement plies. The burst speed was maximized by
optimizing the orientation of the fibers in the radial reinforcement ply. An optimized
design using Toray T1000 fibers in an epoxy matrix was calculated to have a specific
energy of 291 Wh/kg, roughly six times that of a premium lead acid battery [42].
Figure 1.4: Stacked-ply flywheel [42]
Figure 1.5: Fiber pattern for optimized T1000 ply [42]
1.2.2 Bearings
A flywheel requires radial and axial support to perform useful work. The three general
types of bearings used in flywheels are mechanical, magnetic, and superconducting.
Mechanical bearings can be split into several categories: rolling-element bearings,
hydrodynamic journal bearings, gas bearings, squeeze-film bearings, and hydrostatic
bearings. Two general examples of rolling-element bearings are ball bearings and roller
bearings. Damping in rolling-element bearings is small but can be improved by squeezefilms. Journal bearings are comprised of a circular section of shaft (the journal) rotating
inside a bearing “bush,” which is nominally circular. The clearance gap between the two
8
is partially filled by the lubricating fluid, which is pressurized by the motion.
Hydrostatic bearings differ from hydrodynamic bearings in that the lubricant pressure
required to separate the bearings surfaces is supplied from an external pressure source not
journal rotation. Gas bearings are similar to oil-lubricated bearings but behave
differently because the gas is compressible. An advantage of gas bearings compared to
hydrodynamic bearings is that they tend to have much smaller rotational losses because
the viscosity of a gas is much smaller than that of a liquid. Squeeze-film bearings are a
special case of hydrodynamic bearings. This type of bearing consists of a conventional
rolling-element bearing with the outer race surrounded by a damper casing that dampens
radial motion. A small radial clearance between the outer race and the inner bore of the
casing contains a thin lubricating film. The fit is close enough to prevent the outer race
of the conventional bearing from rotating. The losses of mechanical bearings render
them suitable for FES storage times on the order of minutes to possibly an hour [23].
Viscous losses and friction from surface contact can be eliminated from an FES if the
flywheel is levitated by magnetic forces. However as Samuel Earnshaw proved in 1842
in his paper “On the nature of the molecular forces which regulate the constitution of the
luminiferous ether,” [10] there is no stable equilibrium position for a particle acted on by
any type or combination of 1/r2 forces. Magnetic, electrostatic, and gravitational forces
are 1/r2 forces. The Laplacian of any sum of 1/r−type energy potentials is zero, or
∇2 Σki/r = 0. So at any point where there is force balance (−∇2 Σki/r = 0), the equilibrium
is unstable because no local minimum exists in the potential energy [38]. In three
dimensions, the energy potential surface is a saddle. If the equilibrium is stable in one
direction, it is unstable in an orthogonal direction. Because of Earnshaw’s theorem, there
is no possible static configuration of permanent magnets that can stably levitate an object
against gravity, even when the magnetic forces are stronger than the gravitational forces.
Nevertheless stable levitation can be achieved by the use of electromagnets and
superconductors.
Active magnetic bearings levitate objects by the attractive force between an
electromagnet and a ferromagnetic body. Normally the electromagnet is stationary and
the rotor is a ferromagnetic body. Active magnetic bearings are inherently unstable since
they involve only 1/r2 forces. So active feedback is used to modulate the field of the
electromagnet corresponding to the position of the rotor. Position signals from gap
sensors are used by a controller power amplifier to set the suitable currents and voltages
of the electromagnets to attain stable levitation.
A superconducting magnetic bearing consists of a permanent magnet levitated over a
superconductor. Earnshaw’s theorem considers only hard fixed magnets. Werner
Braunbeck’s analysis in 1939 of static levitation showed that stable static levitation is
possible only if materials with ε < 1 or μ < 1 are involved, where ε is the dielectric
constant and μ is the permeability [6]. Diamagnetic materials, such as bismuth and
graphite, have μ < 1 and are repelled by magnetic fields. A superconductor acts like a
perfect diamagnet with μ = 0 (no magnetic flux penetrates the superconductor). Since the
superconductor is impermeable, a permanent magnet above a superconductor is repelled
by its mirror image in the surface of the superconductor. Superconducting bearings also
achieve stable levitation by flux pinning, where the motion of the flux lines is prevented
by their interaction with defects in the superconductor [13]. The material of choice for
superconducting bearings is YBCO (YBa2Cu3O7−x), which has a superconducting
9
transition temperature of 92 K. Certain oxides of copper called cuprates doped with
small amounts other elements become superconductive at temperatures to 134 K [35].
The magnetic strength of the mirror image of a permanent magnet above a
diamagnetic material is reduced by a factor of (1 + μ)/(1 − μ) [4]. Pyrolytic graphite has
the strongest diamagnetism of any solid with a susceptibility of 450 × 10-6 (μ = 0.99955)
when the magnetic field is perpendicular to its layers [38]. The reduction in the mirror
image strength for pyrolytic graphite is approximately 4443. A permanent magnet must
be minuscule to overcome its own weight above pyrolytic graphite. Consequently
flywheel levitation with diamagnets is not possible with current technology.
A permanent magnetic bearing can be stabilized with mechanical contact. There are
four distinct ways that a flywheel can be suspended by permanent magnets as shown in
Figure 2.1.
Magnetically Attractive
Magnetically Repulsive
Axially
Unstable
Radially
Unstable
Figure 2.5: Magnetic bearing options
Figure 1.6: Magnetic bearing options
The radially unstable case needs a minimum of two point contacts for stability. The
axially unstable case can be stabilized with a single point contact located on the axis of
symmetry of the flywheel.
1.2.3 Motor/Generator
The motor/generator of an FES functioning as a mechanical battery has two different
permanent magnet configurations, both of which are brushless direct current (dc) motors:
axial flux and radial flux. Brushless configurations eliminate brush maintenance and
frictional loss from brush contact during flywheel idling. Also the configurations
presented will not have backing iron because it causes hysteresis and eddy-current losses
during flywheel idling. Neodymium Iron Boron (NdFeB) magnets are normally used
because they have the highest flux density, enabling the highest torque and power-toweight ratio.
An axial flux permanent magnet motor for an FES consists of two concentric circular
arrays of axially oriented magnets in the rotor and wire coils in the stator, usually copper,
10
separated by an air gap. The coils function as solenoids creating a magnetic flux that is
parallel to the direction vector of the helical path of the coils when energized. The
magnetic fluxes from the magnets and energized coils interact to produce the torque that
spins the flywheel. To maintain motion, the direction of the current needs to be reversed
(i.e., commutation) each time a permanent magnet pole encounters a different coil.
Commutation is most commonly executed by a controller that uses Hall effect sensors to
detect the shift of the magnetic poles as they pass by. A common sensorless method of
commutation is to use back emf. The movement of the permanent magnet rotor relative
to the stator induces a back emf (electromotive force) in the coils. This back emf can be
measured by the controller and used to calculate the position of the rotor. The drawback
of the back emf commutation method is that the rotor will likely move erratically at first
while the controller works to get a reading of the position of the rotor, reducing
efficiency.
Figure 1.7: Axially oriented magnet
Figure 1.8: Axial flux motor geometry
The torque quality of an axial flux permanent magnet motor is directly related to the
pulsating torque component. Pulsating torque consists of the cogging torque and torque
ripple components. Cogging torque is produced by the attraction between the rotormounted permanent magnets and the stator teeth. Stator teeth, typically made of iron, are
what the coils are wrapped around. The circumferential component of attractive force
tries to maintain the alignment between the rotor magnets and stator teeth. No stator
excitation is involved in cogging torque production. Cogging torque can be eliminated
11
by not using stator teeth in the motor design. Torque ripple is caused by the fluctuations
of the field distribution and the armature magnetomotive force (mmf). In surface
mounted permanent magnet machines, torque ripple is primarily created by the
interaction between the mmf created by the stator coils and the mmf caused by the rotor
magnets because there is no rotor reluctance variation. At high speeds, torque ripple is
typically filtered out by the system inertia [3].
The two basic types of radial flux permanent magnet motors are internal or external
rotor. The internal rotor type has two different magnet configurations: axially oriented
magnet array and diametrically oriented magnet array. The external rotor type has three
different magnet configurations: axially oriented magnet array, diametrically oriented
magnet array and Halbach array.
Figure 1.9: Diametrically oriented magnet
Figure 1.10: Radial flux motor, internal rotor and axially oriented magnet array
Figure 1.11: Radial flux motor, internal rotor and diametrically oriented magnet array
12
Figure 1.12: Radial flux motor, external rotor and diametrically oriented magnet array
Figure 1.13: Radial flux motor, external rotor and eight-magnet Halbach array
Figure 1.14: Magnet orientations for an eight-magnet Halbach array
13
The Halbach array of an external rotor design produces a uniform dipole flux through the
stator area, shown in Figure 1.14. Since there is a uniform flux, the air gap between the
coils and the rotor inside perimeter is of no significance for the motor’s efficiency [24].
For a given pole number in a Halbach array motor, a critical magnet thickness exists
beyond which rotor back iron brings no benefit in terms of increasing the air-gap field
and output torque [45].
As with axial flux permanent magnet motors, ironless radial permanent magnet motors
will have no cogging torque. Also torque ripple is filtered out at high speeds by the
system inertia.
The efficiency and power-to-weight ratio of axial flux motors are higher when the
diameter is greater than the axial bulk. The end-windings extend the radial direction,
implying good filling of the volume and reduced axial bulk [34]. A drawback to the axial
flux design is that in some cases a large force exists between rotor and stator. Since the
mean diameter of an axial flux motor is larger than an equivalent by volume of magnetic
material sized radial motor, it produces more torque [5].
Radial flux motors have some disadvantages. To have a high efficiency and power to
weight ratio, their length must be greater than their stator bore diameter, and the endwindings extend in the axial direction creating a big axial bulk [34]. This drawback leads
to a long and narrow structure with bad filling of the available volume, which leads to a
corresponding long and narrow magnet stack on the rotor. The geometry needed to
accommodate the magnet stack decreases the overall energy density of an internal rotor
because it has low inertia (see Figure 1.15).
Figure 1.15: Basic geometry for an internal rotor
1.2.4 Containment
The housing for a flywheel may need to maintain a vacuum and/or provide protection
from debris in the case of failure.
For high performance flywheels, reduction of aerodynamic drag is important for
reducing energy dissipation and preventing the flywheel from overheating. Aerodynamic
drag can be reduced by enclosing a flywheel in a vacuum vessel. Stienmier et al. showed
that a chamber pressure of 10-5 torr is sufficient to meet an energy dissipation rate of
14
0.1% per hour and a pressure of 10-6 torr would make the energy lost to air friction
negligible.
As a container is evacuated, its internal surfaces will begin to outgas. Outgassing is
the release of gas that was trapped, frozen, absorbed or adsorbed into some material into
the vacuum. It can include sublimation and evaporation, desorption, seepage from cracks
or internal volumes and gaseous products of slow chemical reactions. A gas molecule
attached to a solid surface by some bond is said to be adsorbed [7]. Desorption is the
release of the gas molecules attached to a solid surface by bonds. Hydrogen, oxygen,
nitrogen, and carbon oxides are dissolved into the bulk of materials during their
manufacture. They can arrive at the surface of the material of the vacuum wall by
diffusion. The rate of outgassing increases at higher temperatures because the vapour
pressure and rate of chemical reactions increases. For most solid materials, the method of
manufacture and preparation can reduce the level of outgassing significantly. Cleaning
surfaces or baking individual components or the entire assembly before use can drive off
volatiles. It is important that a composite rotor be properly cured to have low outgassing
at ambient temperature.
The ideal high performance flywheel system is evacuated to the required pressure,
then the pump is turned off to prevent parasitic power loss, and finally the system is
hermetically sealed. Vacuum pressure is maintained by a getter system that absorbs the
outgas products.
In cathode ray tubes, barium getters have been used for years. Powdered BaAl4 is
mixed with nickel powder and compressed together. The compound is then heated and
barium is released, evaporated, and deposited as a thin film onto the surface of the
evacuated tubes. The residual gases inside of cathode ray tubes consist largely of H2,
CO, CO2, N2, H2O, and CH4. Methane is not bound by a barium getter. In fact, methane
forms with the contribution of H2/H2O and CO/CO2, which are turned into CH4 on the
evaporated barium getter film through catalytic mechanisms [11]. Methane can be
removed from a barium gettered system by cracking it into hydrogen with a hot filament
(cathode switched on in a cathode ray tube), but this would be a parasitic power loss in an
FES system.
A nonevaporable getter that does not produce methane and can effectively pump H2,
CO, CO2, N2, and H2O at room temperature is St707 alloy (Zr 70%, V 24.6%, Fe 5.4%).
Nonevaporable getters do not pump the inert gases helium, neon, and argon. St707 does
not pump methane measurably at room temperature, but can pump it at low speed at
temperatures above 100 °C [22]. So at room temperature with proper St707 gettering and
no pumping, methane outgassing will determine the level of maintainable vacuum.
When a flywheel bursts, the total angular momentum of the debris cloud is the same
as before the burst, and this moment must be resisted by the containment structure. The
motion of individual debris fragments is translational and rotational. Very small particles
have almost entirely translational energy. Composite rotors usually produce tiny
fragments in the form of long needle-like shards or small grains. Permanent magnets and
metallic components usually produce larger fragments in the debris cloud. These
fragments can produce large localized loads in the containment shell.
15
1.3 Objective
The objective of this research is to design an FES system that has energy dissipation due
to friction of < 0.1% of maximum charge per hour. This thesis provides the bearing and
containment architecture that compliment an axial flux motor/generator that can meet this
goal. In the course of this study, a lab prototype was constructed that incorporated the
chosen bearing design and addressed some of the containment issues.
16
Chapter 2
FES Prototype Description
Figure 2.1 shows the assembled prototype FES device.
Figure 2.1: Prototype flywheel energy storage system
The flywheel is supported inside of the housing with the axis of symmetry in a vertical
orientation. The housing contains the flywheel, portions of the bearings, position sensors,
motor/generator, and functions as a vacuum vessel. The top and bottom disks of the
housing are made from polycarbonate and fixed in position by four aluminum rods with
threaded ends. Four rubber-coated knobs are screwed onto the threaded ends of the
aluminum rods and provide support for the housing on the work surface. A clear acrylic
tube serves as the wall for the vacuum vessel. It is pressed into two butyl rubber gaskets
that rest on grooves in the top and bottom disks by brass nuts on the threaded ends of the
aluminum rods. Raising and lowering the flywheel with a mechanism in the bottom
housing can adjust the air gap between the motor magnet in the top of the flywheel and
the coils of the motor/generator in the top disk.
17
Figure 2.2: Schematic of the FES prototype
2.1 Rotor
Figure 2.3: Side view of the rotor
18
NdFeB ring
magnet
Motor magnet
Figure 2.4: View of the top of the rotor
NdFeB ring
magnet
Ruby ball tip
indicator
Figure 2.5: View of the bottom of the rotor
The prototype rotor is made of 6061-T6 aluminum. The rotor geometry was chosen to
reduce the weight compared to a solid cylinder of the same outside diameter and length.
The rotor geometry has low rotational inertia for the cylindrical envelope it fits in. A
geometry with approximately the same weight, better specific energy, and fitting within
19
the same envelope is provided in chapter 3. The aluminum 6061-T6 rod protruding from
the top of the rotor provides vertical separation between the pair of NdFeB axially
oriented ring magnets and the coils and motor magnet, which produce magnet fields that
tend to interfere with interaction between the two ring magnets.
2.2 Bearings
To minimize friction and have a passive system, the bearing design developed at the
University of Washington consists of an axially unstable magnetic bearing that is
mechanically stabilized with a point contact (hybrid magnetic bearing). The contact
consists of a spherical point on the axis of symmetry of the flywheel and a stationary, flat
plate. This configuration does not require any active control, power, or cryogenic
temperatures. Also the point contact causes the flywheel to behave like a top rendering
the system asymptotically stable in all directions. The challenge of this configuration is
to minimize the friction of the point contact to meet the efficiency goal.
The attractive force between two axially oriented NdFeB ring magnets at the top of
the flywheel (see Figures 2.2 and 2.7) produces a centering force when the rings are out
of vertical alignment. Figure 2.8 shows that horizontal components of force are
introduced by the bending of the magnetic flux when the ring magnets are out of vertical
alignment, providing radial stiffness to the bearing. The radial stiffness is useful for
keeping the flywheel upright when at rest and providing support at low speeds. At high
speeds, gyroscopic forces become dominant. So the flywheel does not require high radial
stiffness in the top bearing for adequate stability throughout its operating range.
The bottom bearing has two magnetically attractive axially oriented NdFeB ring
magnets that provide radial stiffness for the point contact. The radial stiffness resists the
precession of the contact point improving stability. The point contact of the bottom
bearing is a ruby ball tip indicator screwed into the bottom of the flywheel (see Figure
2.5). The disk magnet of the bottom bearing serves as the bearing surface for the point
contact (see Figure 2.9).
Figure 2.6: View of the ring magnet for the top bearing in the top disk
20
Figure 2.7: Magnetically attractive axially-oriented ring magnets
Figure 2.8: Cross-section of attracting ring magnets with magnetic flux lines
NdFeB disk
magnet
Figure 2.9: Portion of the bottom bearing in the bottom disk
2.3 Motor/Generator
The motor/generator of the FES prototype is an axial flux design and consists of a foursector permanent ring magnet slip fit into the top of the flywheel, copper coils, and Hall
effect sensors bonded onto the top housing disk. The four sectors of the motor magnet
are axially oriented NdFeB ring sections bonded onto an aluminum disk mounting plate.
The stator windings consist of 12 individual coils located in grooves machined into the
top housing disk. Each coil spans a 90° arc and consists of 31 winding turns. For
21
motor/generator operation, the coils are connected in three phases in a wye configuration
with four coils per phase. Three Hall effect sensors are bonded onto the top housing disk
between the winding grooves. These sensors detect the edges of the magnet poles as they
move past. They are used by the motor controller as position sensors to switch the phases
for motoring operation. The three sensors are spaced approximately 30° apart, providing
a resolution of 30° throughout the full rotation of the flywheel [28]. Two sets of LED
emitters and photodiode detectors are used to measure radial displacement of the
flywheel.
Figure 2.10: Motor magnet configuration, see Figure 2.4
Figure 2.11: View of top housing disk, showing the motor coils, bearing magnet, and
sensors
22
Figure 2.12: Arrangement of motor coils and Hall effect sensors [28]
Figure 2.13: The three Hall effect sensors
23
Figure 2.14: Optical position sensors
LED emitter
Figure 2.15: View of the LED emitter
24
Figure 2.16: Drawing of the LED emitter
Photodiode
detector
Figure 2.17: View of the photodiode detector
2.4 Containment
The top disk must be nonmetallic to avoid eddy currents being created by the motor
magnet. Polycarbonate was chosen as the material for the top and bottom disks because
it is an inexpensive plastic with good structural strength and moderate outgassing. The
25
clear acrylic tube was chosen as the vacuum chamber wall because it is inexpensive and
readily available. Acrylic has high outgassing rates. So the chamber will likely require a
long pumpdown time to reach a low vacuum pressure. The chamber gaskets are rings cut
®
from a flat sheet of 40-durometer butyl rubber. Viton is normally the elastomer of
choice for vacuum applications. Butyl has an outgassing rate that is comparable to
®
Viton and is cheaper.
Figure 2.18: Chamber gasket for the bottom disk
Figure 2.19: Clear acrylic tube
26
Chapter 3
Future Design and Improvements
A schematic of an FES system that can meet the design objective is shown in Figure 3.1.
Figure 3.1: FES system cross section showing the components
Two different eddy current dampers for the upper bearing of the proposed FES device are
presented. Figure 3.1 shows the top bearing with eddy current damper that uses only
repulsive magnetic force, no mechanical contact, to move a magnet relative to a
conductor. Figure 3.2 shows the top bearing with eddy current damper that uses
mechanical contact to move a magnet relative to a conductor.
Figure 3.1 shows a slot cut into the top housing disk that has magnetic shielding. The
magnetic shielding is needed to attenuate the magnetic fields generated by the coils and
the motor magnet. These fields can adversely affect the interactions of the magnets in the
®
top bearing. The magnetic shielding consists of layers of either Metglas 2714A alloy
®
film or Finemet alloy film wrapped around a plastic tube, which is then inserted into the
slot of the top housing disk. The maximum magnetic permeabilities of 2714A alloy and
®
Finemet film are 1,000,000 and 70,000 respectively, and their maximum flux densities
are 0.57 T and 1.23 T respectively [98, 99].
27
Figure 3.2: FES system cross section showing the components
3.1 Rotor
Figure 3.3: Rotor cross section for no contact damper
28
Figure 3.4: Rotor cross section for contact damper
Figure 3.5: Rotor shaft
The motor magnet for the proposed FES device will have the same configuration as that
of the prototype device (see Figure 2.3). However the mounting plate will have different
geometry (see Figure 3.6). A filament wound carbon fiber composite ring is press-fit
around the motor magnet to induce a compression stress. This compression stress offsets
the hoop and radial stresses that develop as the rotor spins, enabling the rotor to spin
faster before the magnets fail. The ply stack is the design proposed by Thielman and
Fabien (see section 1.2.1), and uses Toray T1000 fibers in an epoxy matrix. If the shaft,
motor magnet mounting plate, and/or the bottom bearing cap are made of aluminum, they
will need to have a coat of paint because they are in contact with the ply stack.
29
Aluminum experiences galvanic corrosion when it is in contact with carbon composite
materials and there is moisture present.
Figure 3.6: Top view of the motor magnet mounting plate
A cheaper but lower specific energy option to the ply stack is to make the rotor out of
metal. Titanium has the highest specific strength of metals, and thus would be the metal
of choice for achieving the highest specific energy. Two different metal rotor geometries
that are compatible with the motor/generator and bearing designs are displayed in Figures
3.7 and 3.8.
Figure 3.7: Metal rotor
30
Figure 3.8: Motor magnet mounting plate for metal rotor
Figure 3.9: Metal rotor with higher specific energy
3.2 Bearings
Figure 3.10: Schematic of top bearing from Figure 3.1, no mechanical contact damper
31
Figure 3.11: Schematic of top bearing from Figure 3.2, mechanical contact damper
For both bearing designs, the two axially oriented ring magnets at the top of the rotor and
in the top housing disk provide radial stiffness. The axial touchdown ball and axial
touchdown disk prevent any critical components from touchdown in the event of a
vertical disturbance lifting the rotor off of the point contact, and they should be a low
friction and low wear material combination. The radial touchdown balls and radial
touchdown ring prevent any critical components from touchdown in the event of a large
horizontal disturbance or large vibration of the rotor, and they should also be a low
friction and low wear material combination (see Figure 3.5).
Figure 3.12: Section view A-A from Figure 3.10
32
Figure 3.13: Schematic of the bottom bearing from Figures 3.1 and 3.2
For the bottom bearing, the two axially oriented NdFeB ring magnets provide radial
stiffness for the point contact. The contact ball and bearing disk comprise the point
contact for the hybrid magnetic bearing.
3.2.1 Eddy Current Dampers
The relative motion between a conductor and a magnetic field generates eddy currents in
the conductor that interact with the magnetic field producing a force in the direction
opposite to the relative motion [14]. Since the currents in the conductor are dissipated as
heat from electrical resistance, energy is being removed from the system, thus allowing
the magnet and conductor to function like a viscous damper. Eddy current dampers for
rotating machinery generally consist of an axially oriented permanent magnet ring(s)
connected to a shaft and a conductor disk connected to the stator; an example is shown in
Figure 3.9. These eddy current dampers produce continual damping as the shaft rotates.
For efficient flywheel energy storage, it would be ideal to have no damping when the
rotor is rotating and the vibration magnitude is below some tolerable limit.
Figure 3.14: Geometrical layout of an eddy current damper
33
Both of the proposed eddy current damper configurations are designed to allow a
certain amount of vibration before damping occurs. For both damper designs, a copper
ring that is bonded onto the top housing disk is the conductor, and the relative motion of a
permanent ring magnet underneath it produces the eddy currents in the copper ring. In
the damper of Figure 3.5, the ring magnet underneath the copper ring moves in response
to the motion of the ring magnet bonded onto the bearing cap; the ring magnets are
magnetically repulsive (see Figure 3.9). In the damper of Figure 3.6, the ring magnet
underneath the copper ring moves when the damper contact ball, embedded in the bearing
cap, makes contact with the damper contact ring. The ring magnet above the copper ring
is magnetically attracted to the ring magnet underneath the copper ring, producing a
centering force for the ring magnet underneath the copper ring that keeps its aligned with
the principal axis of the flywheel at nominal position. This damper will performed the
best with the lowest friction and wear material combination for the contact balls and
contact ring.
Figure 3.15: Concentric ring magnets of the no contact damper of Figure 3.10
Figure 3.16: Section view A-A from Figure 3.11
3.2.2 Contact Friction
The energy lost to friction of the point contact is quantified by calculating the torque
due to the sliding friction. The contact geometry is that of a sphere in contact with a flat
plate as shown in Figure 2.10.
34
Figure 3.17: Point contact geometry of the hybrid magnetic bearing
Assume the contact pressure is distributed over a circular area. The diameter of the
circular contact area is given by Shigley and Mischke [37] as
((
)
(
) )
a = 3 3Fd 1 − ν 12 / E1 + 1 − ν 22 / E2
(3.1)
where F is the total normal force supported by the point contact, d is the diameter of the
sphere, ν 1 is Poisson’s ratio of the sphere, E1 is the modulus of elasticity of the sphere,
ν 2 is the Poisson’s ratio of the plate, and E2 is the modulus of elasticity of the plate. The
contact pressure has a semielliptical distribution with the maximum pressure at the center
of the contact area given by
6F
pmax = 2
(3.2)
πa
So the pressure anywhere in the contact area can be determined by
p=
6F
4x2
1
−
a2
πa 2
(3.3)
where x is the distance from the center of the contact area. If the frictional stress at any
point of the contact area is μp, then the total torque due to friction is found by integrating
throughout the contact area, A,
24 μF
T = ∫ μpxdA = 2πμ ∫ px dx = 3
a
0
0
A
a/2
2
a/2
∫
0
x2
a2
3πμFa
− x 2 dx =
4
32
(3.4)
The energy dissipation per second due to friction is
Pd = Tω
(3.5)
where ω is the angular velocity of the flywheel. So the energy dissipation per hour is
Ed = 3600Tω
(3.6)
35
The energy dissipation is largest at the maximum charge of the flywheel when the
angular velocity is the highest. The energy dissipation decreases from this state to zero
when the flywheel comes to rest. The rotational kinetic energy of the flywheel at
maximum charge is
Emax =
1 2
Iωmax
2
(3.7)
where I is the moment of inertia of the total mass of the flywheel about its axis of
symmetry and ωmax is the angular velocity of the flywheel at maximum charge.
Therefore the energy dissipation rate in percent of maximum charge per hour due to the
friction of the contact point is
7.2 × 105 T
Ed
=
R=
Emax
Iωmax
(3.8)
If R < 0.1, the dissipation goal is met. If the contact point is not coincident with the
principal axis of the flywheel, it will trace out a circular path of radius equal to the
misalignment, which increases the torque due to friction at the contact point. So it is
imperative that the contact point be as precisely aligned as possible when fabricating the
flywheel.
The contact friction can be reduced by decreasing the normal force, the contact ball
diameter, and/or the coefficient of friction. The normal force can be decreased by
shortening the length of the air gap between the ring magnets in the upper bearing,
increasing the length of the air gap between the ring magnets in the lower bearing, using
more powerful ring magnets in the upper bearing, and by using less powerful ring
magnets in the lower bearing. The contact ball diameter can be decreased only so much
before there is Brinelling of the plate material or plastic flow and grooving of the ball
material [19]. Choosing a material combination for the point contact could involve a
compromise between desired dissipation rate and cost. Some options for low coefficients
of friction in a vacuum are: a Si3N4 ball sliding on a carbon nitride (CNx) coating on a
silicon wafer substrate has a coefficient of friction of about 0.05 [25], a JIS type 304
stainless steel ball sliding on a CuO coating on a JIS type 304 stainless steel substrate has
a coefficient of friction of about 0.05 [17], a 440C steel ball sliding on a WC/DLC/WS2
coating has a coefficient of friction of about 0.03 [44], a ring of JIS SUS 304 stainless
steel sliding on a cubic boron nitride film has a coefficient of friction of 0.009 [46], a
pure platinum pin sliding on an alumina disk has a coefficient of friction of 0.005 [20], a
440C stainless steel ball sliding on a hydrogenated diamond-like carbon (H-DLC) film
has a coefficient of friction of 0.004 [26], a hemispherical diamond pin sliding on a silver
film has a coefficient of friction of 0.004 [16], and a diamond ball sliding on an Hterminated silicon surface has a coefficient of friction of 0.003 [30].
36
3.3 Motor/Generator
Two modifications can be made to the motor/generator design of the prototype FES
device that will improve the performance. The first modification is to replace the
standard copper wire with twisted strands of Litz wire to improve efficiency. Litz wire is
a bundle of individually insulated fine wire used to replace a single conductor. In
ironless motors, the stator copper is exposed to the full magnetic field, and so to prevent
excessive eddy currents in the windings, Litz wire is used [18]. A motor efficiency of
greater than 97% can be achieved when using Litz wire [29]. The second modification to
the motor/generator design is to replace the four-pole axially oriented motor magnet array
with a four-pole Halbach array. The maximum air-gap flux density per unit rotor magnet
mass can be maximized by using a Halbach array [29]. Lovatt, Ramsden, and Mecrow et
al. found that using more than four magnets per pole provides only a marginal increase in
performance. So to maintain a reasonable balance between complexity (or cost) and
performance, the Halbach array should consist of four magnets per pole as shown in
Figure 3.12.
Figure 3.18: Four-pole Halbach magnet array for the axial flux motor/generator
3.4 Containment
The two most commonly used structural materials for vacuum vessels are type 300
stainless steels and type 6061/63 aluminum alloys. These materials are chosen for
vacuum applications because of their low outgassing, corrosion resistance, machinability,
weldability, and low cost [9]. The most frequently used stainless steel is type 304.
Aluminum has vacuum characteristics approximately equal to 304 stainless steel, and has
the added advantages of lower material and machining costs, but compared to steels, has
37
less strength and weldability. So the bottom housing disk and vacuum chamber wall
components for the FES devices shown in Figures 3.1 and 3.2 should be made from
either 6061 or 6063 aluminum.
The top housing disk component should not be made of metal to avoid eddy current
losses due to the motor magnet. PEEK (polyetheretherketone) is a good candidate for the
®
top housing disk material. Its outgassing rate is comparable to Vespel SP1
(condensation-type polyimide), but it is stronger and costs about 15-16 times less [33].
PEEK is also a good candidate for the support disk material. The support disk is
embedded in the bottom housing disk, and it holds a ring magnet and the bearing plate of
the bottom bearing. The purpose of the support disk is to prevent eddy current losses in
the bottom bearing.
To seal the chamber wall between the housing disks, metal wire should be used;
®
copper, indium or aluminum are cost effective options for the sealing wire. Viton or
butyl rubber should not be used because of gas permeation over an extended period of
time.
The components that are within or constitute the vacuum containment structure can be
®
properly cleaned with an alkali detergent (i.e., Alconox or equivalent) in deionized
water [9].
St707 alloy getter should be used to maintain proper vacuum pressure. The gettering
of methane will become an area of research for the future if methane outgassing poses a
problem with the proposed FES device.
If the flywheel needs burst containment, the bottom housing disk can be changed to
304 stainless steel if the aluminum is not strong enough. If either or both of the PEEK
top housing disk and aluminum vacuum chamber wall are not strong enough to contain
debris from a rotor burst, then a burst containment shell can be used as shown below in
Figure 3.10. Since the containment shell is not involved with vacuum containment,
material outgassing is not a concern.
Figure 3.19: Schematic of the FES system with burst containment
38
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