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TABLE 6.28 Diameter and Out-of-Roundness Tolerances for Hot-Rolled Carbon-Steel Bars
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SPRINGS 6.69
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TABLE 6.29 Maximum Allowable Torsional Stress for Hot-Wound Helical Compression Springs in Static Applications
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TABLE 6.30 Maximum Allowable Torsional Stress for Hot-Wound Helical Compression Springs in Cyclic Applications
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used only for centerless ground alloy bars. Practical manufacturing tolerances for hot-wound springs can be found in ASTM A125.
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REFERENCES
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6.1 Leonard G. Johnson, The Statistical Treatment of Fatigue Experiments, Elsevier Publishing Co., New York, 1964. 6.2 R. E. Little and E. H. Jebe, Statistical Design of Fatigue Experiments, John Wiley & Sons, New York, 1975. 6.3 A. M. Wahl, Mechanical Springs, 2d ed., McGraw-Hill, New York, 1963. 6.4 W. R. Berry, Spring Design: A Practical Treatment, Emmot & Co., London, 1961. 6.5 J. O. Almen and A. Laszlo, The Uniform Section Disc Spring, ASME Transactions, vol. 58, no. 4, May 1936, pp. 305 314. 6.6 A. Blake, Design of Curved Members for Machines, Industrial Press, New York, 1966. 6.7 K. E. Bisshopp and D. C. Drucker, Large Deflections of Cantilever Beams, Quarterly of Applied Mathematics, vol. 3, no. 3, 1945, p. 272. 6.8 J. H. Maker, Steel Springs, Metals Handbook, 9th ed., vol. 1, American Society for Metals, Metals Park, Ohio, 1978, pp. 283 313.
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SPRINGS 6.70
MACHINE ELEMENTS THAT ABSORB AND STORE ENERGY
6.9 Design and Manufacture of Volute Springs, SAE, New York, 1945. 6.10 R. E. Peterson, Stress Concentration Design Factors, John Wiley & Sons, New York, 1953, p. 102. 6.11 Karl W. Maier, Dynamic Loading of Compression Springs, Product Engineering, January 1954, pp. 162 167; Dynamic Loading of Compression Springs, Product Engineering, March 1955, pp. 162 172; Surge Waves in Compression Springs, Product Engineering, August 1957, pp. 167 174.
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Source: STANDARD HANDBOOK OF MACHINE DESIGN
FLYWHEELS
Daniel M. Curtis, Ph.D.
Senior Mechanical Engineer NKF Engineering, Inc. Reston, Virginia
7.1 FLYWHEEL USAGE / 7.3 7.2 SIZING THE FLYWHEEL / 7.3 7.3 STRESS / 7.13 7.4 FLYWHEELS FOR ENERGY STORAGE / 7.20 7.5 STRENGTH AND SAFETY / 7.21 REFERENCES / 7.25
LIST OF SYMBOLS
a A As Aj, Bj, Cj b Cs Cu Dj fi F Fs g I j J K n Nc Ns P r Constant, lb s ft/rad (J s/rad) Cross-sectional area of rim, in2 (m2) Cross-sectional area of spoke, in2 (m2) Difference coefficients Constant, lb ft (J) Coefficient of speed fluctuation Coefficient of energy fluctuation Difference coefficient, lb (kN) Intermediate variable Stress function (= rt r), lb (kN) Geometric shape factor Acceleration of gravity, 32.2 ft/s2 (9.80 m/s2) Second moment of area, in4 (m4) Index Polar-mass moment of inertia, lb s2 ft (N s2 m) Coefficient, 33 000 lb ft rpm/hp [2 J rad/(W s)] Engine speed, rpm (rad/s) Number of cylinders Number of spokes Power, hp (W) Radial distance, in (m)
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FLYWHEELS 7.2
MACHINE ELEMENTS THAT ABSORB AND STORE ENERGY
r rh ra ri ro R Sy t t T Ta Ts Tj U V W z z z0 Zr Zs 2 max 0 0 r t max, min avg 0 j
Radial-distance increment, in (m) Hub radius, in (m) Average radius of rim, in (m) Inner radius of rim, in (m) Outer radius of rim, in (m) Specific energy, in (m) Yield strength, psi (MPa) Time, s Time increment, s Torque, lb ft (J) Angle-dependent torque, lb ft (J) Speed-dependent torque, lb ft (J) Torque at end of interval j, lb ft (J) Difference between the flywheel energy at maximum speed and at minimum speed, lb ft (J) Rim velocity, ft/s (m/s) Weight, lb (kN) Thickness, in (m) Radial derivative of flywheel thickness (= dz/dr) Thickness at center, in (m) Section modulus of rim, in3 (m3) Section modulus of spoke, in3 (m3) Angle between adjacent spokes (see Fig. 7.6), rad Angle, rad Angular position, rad Maximum angular deviation from constant-speed position, rad Angular position at start of machine cycle, rad Angular increment, rad Poisson s ratio Time, s Weight density, lb/in3 (kN/m3) Stress, psi (MPa) Stress constant, psi (MPa) Radial stress, psi (MPa) Tangential stress, psi (MPa) Rotational speed, rad/s Maximum and minimum speed, rad/s Average speed [= 0.5( max + min)], rad/s Speed at start of machine cycle, rad/s Maximum deviation of speed from average value, rad/s Speed at end of interval j, rad/s
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