Ironless permanent magnet synchronous machine stiffness calculations for flywheel energy storage systems

This paper describes an analytical method for determining the magnetic field and radial stiffness of an ironless permanent magnet synchronous machine, provided a geometrical description of conductor arrangements, off-centering value for the rotor magnet, and permanent magnet characteristics. A simple expression for calculating the magnetic field external to a uniformly magnetized parallelepiped is extrapolated to describe the macroscopic field surrounding a cylindrical rotor magnet. Sample calculations of the radial forces, stiffness, and cross-stiffness are provided within the context of a high-speed, two-pole ironless permanent magnet flywheel used in materials testing.