Fully Analytical Dynamic Model of Permanent-Magnet Brushless DC Motor Considering Slot Effect

Permanent-magnet brushless DC motors (PMBLDCMs) are widely used in various industrial applications. This paper proposed a fully analytical dynamic model of PMBLDCMs based on the armature reaction and subsequent commutation phenomenon. First, it introduced the PMBLDCM prototype, including the stator currents, electromagnetic torque, and rotor position calculated via electromotive force balance equations, the Maxwell stress tensor method, and motion formulas. Then, it employed the subdomain method under load conditions to analyze magnetic flux densities in the airgaps and the stator slots. Finally, it established a field-circuit coupling finite-element model (FEM) to verify magnetic flux densities, back-EMF, torque and rotor-position predictions. A 1.5 kW PMBLDCM prototype was built with back-EMF and stator-phase currents validated through experiments. In addition, torque and rotor-position results are validated against FEM instead of physical experiments.