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) "o(oJ) 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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