Analytical 2-D Calculations of Torque, Inductance, and Back-EMF for Brushless Slotless Machines With Surface Inset Magnets

In this paper, the electromagnetic torque, reluctance torque, inductance, and back-EMF are analytically calculated for brushless slotless machines with surface inset magnets. The calculations are based on the 2-D analytical magnetic field distributions. Although the expressions can be used for any magnetization patterns, the effects of three different magnetization patterns, i.e., radial, parallel, and Halbach, on the developed torque, back-EMF and inductances are examined. Besides, the influences of three types of armature current waveforms (sinusoidal, ideal rectangular, and six-step rectangular) on the mentioned quantities are investigated. The effects of pole arc per pole pitch ratio on the performance of slotless brushless machines are also studied. To evaluate the proposed 2-D analytical expressions, the analytical results are compared with those obtained by finite element analyses.