CHAPTER 18 FLYWHEELS Daniel M. Curtis, . Senior Mechanical Engineer NKF Engineering, Inc. Reston, Virginia FLYWHEEL USAGE / SIZING THE FLYWHEEL / STRESS / FLYWHEELS FOR ENERGY STORAGE / STRENGTH AND SAFETY / REFERENCES / LISTOFSYMBOLS a A A5 Aj9 Bj, Cj b C5 Cu Dj fi F Fs g / ; J K n Nc N5 P r Constant, Ib • s • ft/rad (J • s/rad) Cross-sectional area of rim, in2 (m2) Cross-sectional area of spoke, in2 (m2) Difference coefficients Constant, Ib-ft (J) Coefficient of speed fluctuation Coefficient of energy fluctuation. | CHAPTER 18 FLYWHEELS Daniel M. Curtis . Senior Mechanical Engineer NKF Engineering Inc. Reston Virginia FLYWHEEL USAGE SIZING THE FLYWHEEL STRESS FLYWHEELS FOR ENERGY STORAGE STRENGTH AND SAFETY REFERENCES LIST OF SYMBOLS a A As Aj Bj Cj b cs cu Di 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 F Fs g I j J K Stress function ria lb kN Geometric shape factor Acceleration of gravity ft s2 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 2rt J rad W s n Nc Ns P Engine speed rpm rad s Number of cylinders Number of spokes Power hp W r Radial distance in m STANDARD HANDBOOK OF MACHINE DESIGN Ar Radial-distance increment in m rh Hub radius in m ra Average radius of rim in m H Inner radius of rim in m r0 Outer radius of rim in m R Specific energy in m Sy Yield strength psi MPa t Time s At Time increment s T Torque lb ft J Ta Angle-dependent torque lb ft J Ts Speed-dependent torque lb ft J Tj Torque at end of interval j lb ft J U Difference between the flywheel energy at maximum speed and at minimum speed lb ft J V Rim velocity ft s m s W Weight lb kN z Thickness in m z Radial derivative of flywheel thickness dzldr Zo Thickness at center in m Z Section modulus of rim in3 m3 Zs Section modulus of spoke in3 m3 2a Angle between adjacent spokes see Fig. rad P Angle rad 0 Angular position rad 0max Maximum angular deviation from constant-speed position rad 0o Angular position at start of machine cycle rad A0 Angular increment rad v Poisson s ratio Time s p Weight density lb in3 kN m3 g Stress psi MPa Go Stress constant psi MPa Gr Radial stress psi MPa c Tangential stress psi MPa co Rotational speed rad s comax .
