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factor Fs = 1.0 for the fully stressed profile. As Eq. (7.70) indicates, this profile has an infinite outer radius; truncating the profile reduces Fs substantially. Modifying the profile can improve the efficiency, increasing Fs to 0.97 (see Table 7.6), but that is the limit for a homogeneous isotropic design. To avoid this basic limitation and to take advantage of the higher strength-to-weight and stiffness-to-weight ratio of composite materials, recent efforts have concentrated on anisotropic designs ([7.1], [7.8]). Figure 7.7 describes a few of the many designs that are being developed.
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7.4.2 Special Considerations Energy-storage flywheels have special problems which are related to their high speed, flexibility, and anisotropy. The increased operational speed requires highspeed power transmission and bearings as well as special attention to drag forces and the critical vibration speeds of the torsional system. A continuously variable transmission and operation in a vacuum are usually required. Forward whirling is a potentially serious problem that may limit the operating range or require external damping [7.3]. The flexibility can cause flywheel vibration modes with frequencies in the operating range and can also cause significant imbalance to occur as the flywheel deforms with speed. Anisotropy can cause failure in the weak direction (matrix failure or delamination) before the full strength in the strong direction is utilized.
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7.5.1 Materials Neglecting gravity and other secondary loads, the stresses in a flywheel will be proportional to V 2 = (ro )2. Two flywheels of the same design but of different size will therefore have the same rim stress when their rim velocities are equal. Also, since the stress is proportional to V 2, a 10 percent increase in rotational speed will cause a 21 percent increase in stress. Although the strengths of flywheel materials are sometimes given in terms of their maximum rim velocities, these strengths include generous factors of safety to account for all the possible variations in the material properties, design details, and methods of manufacture. A rational approach would
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TABLE 7.6 Shape Factor for Several Isotropic Flywheel Shapes
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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FIGURE 7.7 Energy-storage flywheel designs. (a) Flywheel of helically woven fabric with variable properties in the radial and circumferential directions (exploded view) (Avco Systems Division); (b) filament-wound graphite/epoxy rim with laminated S2-glass/epoxy disk (General Electric Company); (c) subcircular multilayer rim of S-glass and Kevlar, with graphite/epoxy spokes (Garrett AiResearch Corporation); (d) bare-filament Kevlar rim with aluminum hub (Istituto della Motorizzazione, Torino, Italy, built by Industrie Pirelli S.p.A. and sponsored by the Italian National Research Council); (e) graphite/epoxy and steel-filament/epoxy rim with a woven graphite/epoxy overwrap (MAN Advanced Technology, Munich, Germany); (f) variable-thickness graphite/epoxy laminated disk (Lawrence Livermore National Laboratory).
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FIGURE 7.7 (Continued) Energy-storage flywheel designs. (g) bare-filament high-strength steelwire rim, as used in steel-belted radial tires, with fiberglass hub (The Johns Hopkins University Applied Physics Laboratory); (h) multilayer rim of S-glass and Kevlar, with catenary tensionbalanced spokes (William M. Brobeck and Associates); (i) graphite/epoxy-wound rim with overwrap over an aluminum liner with two contoured-aluminum hubs (Rockwell International/Rocketdyne Division); (j) vinyl-coated S-glass rim with Russian birch hub (The Johns Hopkins University Applied Physics Laboratory); (k) Metglas (amorphous steel) ribbon rim with aluminum spokes (The Johns Hopkins University Applied Physics Laboratory); (l) contoured graphite/epoxy filament-wound disk (Hercules Aerospace). (Kevlar is a registered trademark of E. I. du Pont de Nemours and Company, Inc.; Metglas is a registered trademark of The Allied Corporation.) (Photographs assembled with the assistance of W. Wilkinson, The Johns Hopkins University Applied Physics Laboratory, and S. Kulkarni, The Lawrence Livermore National Laboratory; by permission.)
Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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