Shape factors for rotating machines [electromagnetic guns]

The ability to store as much energy as possible for the least weight is of paramount importance to the pulsed power supply of electromagnetic guns. One method of achieving high-energy density is with rotating machines made of composite materials with high shape factors. The shape factor F_s for rotating machines is defined to be a dimensionless factor which is the linear scaling factor between the stored energy density of a rotor and its strength-to-density ratio. A completely general derivation for the shape factor of thin spinning rotors of uniform thickness has been obtained and applied to various rotor geometries and properties. Four rotor configurations were evaluated in detail-anisotropic, isotropic, laminated composite, and nonlaminated composite and their relative optimum shape factors were compared. The rigorous mathematical analysis presented shows that the theoretical maximum shape factor for a uniform material rotor (isotropic or anisotropic) is F_s=1.0, and that for any composite rotor (laminated or not), it is F_s=0.5, whereas for all practical, well-designed thin rotors of uniform thickness, the maximum F_s appears to occur in a narrow range of 0.4-0.45. Comparisons between the shape factors of two composite rotor designs applicable to electromagnetic guns, a laminated disk (LD) rotor and a rim rotor (RR), are also presented