Air gap permeance in doubly-slotted asynchronous machines

Irregularities in the air gap of asynchronous machines are sources of forces, torques, noise, and vibrations. A formal Fourier series solution for the variation in permeance is presented. It is assumed that the permeability of the iron portions of the magnetic circuit is infinitely great, the rotor slots are not skewed, and flux fringing is not considered as input information. The Fourier series for a rectangular gap varying between zero and unity is established, a key element in subsequent solutions for permeances. The Fourier series for variation in air gap due to stator slots opposite a smooth surface and a doubly slotted air gap are established. The reciprocals of these air gap variations are obtained.>