Analytical Calculation of the Magnetic Field Distribution in Slotless Brushless Machines With U-Shaped Interior Permanent Magnets

The aim of this article is to present a new analytical model developed for open-circuit magnetic field calculation in U-shape interior permanent magnet (IPM) machine. The model is developed based on the two-dimensional subdomain-model approach by solving Poisson's and Laplace's equations. The comprehensive theoretical derivations of the final analytical equations for the magnetic flux density distribution in the air gap and in the permanent magnets are explained in detail. We also provide the calculation algorithm in form of a flow diagram suitable for engineers to compute the radial and the tangential component of the magnetic flux density in all subdomains of slotless brushless machines with any possible number of rotor pole pairs of U-shaped IPMs. A slightly modified algorithm also applies to V-shaped IPMs.