Analytical magnetic field distribution of slotless brushless permanent magnet motors – Part 1. Armature reaction field, inductance and rotor eddy current loss calculations

Two-dimensional analytical armature field calculations are presented for slotless permanent magnet brushless motors. The proposed method is applicable to both brushless AC and DC motors with any number of phases. The problem is formulated for eight annular regions: shaft, rotor back-iron, magnets, retaining sleeve, airspace, winding, stator back-iron and exterior. A general armature current density distribution is expressed as a function of spatial angle and time for any number of phases, any current waveform and any winding distribution. The governing partial differential equations of all the regions subject to a set of boundary conditions are represented and solved analytically for both internal and external rotor motors. Self- and mutual-inductance calculations as well as expressions for the calculation of rotor eddy current losses in the magnets, retaining sleeve and rotor back-iron are also represented. In the second part of these two papers, the open-circuit magnetic field is presented for different magnetisation patterns and subsequently the electromagnetic torque is calculated. The effectiveness of the analytical model is validated by comparing the results with those obtained from finite-element analyses as well as an experimental set-up which presented in the second part of the series.