We develop analytical models for predicting the magnetic field distribution in Halbach magnetized machines. They are formulated in polar coordinates and account for the relative recoil permeability of the magnets. They are applicable to both internal and external rotor permanent-magnet machines with either an iron-cored or air-cored stator and/or rotor. We compare predicted results with those obtained by finite-element analyses and measurements. We show that the air-gap flux density varies significantly with the pole number and that an optimal combination of the magnet thickness and the pole number exists for maximum air-gap flux density, while the back iron can enhance the air-gap field and electromagnetic torque when the radial thickness of the magnet is small.
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