lnt J. mech. Sci.,
Vol. 19, pp. 223-231.
Pergamon Press 1977.
Printed in Great Britain
FLYWHEEL ENERGY STORAGE---I
BASIC CONCEPTS
JAMES A. KIRK
Mechanical Engineering Department, University of Maryland, College Park, MD 20742,
U.S.A.
(J
b
Ev~
Ew
1g
KE
Ks
N
Iv,
N,
P,.((o)
P,,~,(w)
R
t
T
t*
V
Vs
W(w)
3'
o"
o)
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WH
lbf
(Received
20
September
1976;
in revised form
24
January
1977)
Summary--The basic concepts of flywheel energy storage systems are described in the first
part of a two part paper. General equations for the charging and discharging characteristics of
flywheel systems are developed and energy density formulas for flywheel rotors are discussed.
It is shown that a suspended pierced disk flywheel is competitive with the super-flywheel
designs currently being suggested in the literature.
In Part I1 the details of a magnetically levitated spokeless ring flywheel design are
provided.
NOTATION
inner radius of flywheel rotor, m
outer radius of flywheel roton, m. Outer radius of single filament, m
kinetic energy per unit of swept volume, N/m 2
energy density, kinetic energy per unit of rotor weight, J/N
polar moment of inertia, kg m 2
stored kinetic energy, J
Flywheel shape factor, dimensionless
The number of individual single filament members rotating about a common axis, dimensionless
Final flywheel speed, rotations per minute
initial flywheel speed, rotations per minute
power input for flywheel systems, a function of angular speed, W
power output from flywheel system, a function of angular speed, W
radius of round single filament rod, m
time, sec
thickness of square single filament rod, m
time for flywheel to slow from N~ to Nt, sec
volume occupied by flywheel rotor, m 3
volume swept by flywheel rotor, m 3
parasitic losses in an energy storage system, a function of rotational speed, W
weight density of rotor material, N/m 3
maximum centrifugal stress in flywheel rotor, N/m 2
radial centrifugal stress, N/m 2
circumferential centrifugal stress, N/m ~
Angular velocity, rad/sec
efficiency of power converting elements in an energy storage system (dimensionless), a function of
rotational speed, ratio of output power to input power
Poisson ratio of contraction in the radial direction due to extension in the circumferential direction,
dimensionless
Watt hours
pounds of force
INTRODUCTION
The purpose of energy storage is to conserve petroleum resources through the
reduction in both dollar and environmental costs of providing energy to the consumer.
The
basic
problem
facing utility
companies
is, and will continue
to be,
hourly
variations in the daily demand for electric power. Kalhammer and Zygielbaum ~,
Keller 2 and Rabenhorst ~ point out that electric utilities use:
1. Base
load generators to serve the load which continues 24hr a day. This
function is served by the more efficient fossil fuel or nuclear generators which operate
nearly 100% of the time at full throttle. Typically, the base load is approximately 45%
of the peak load.

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