A Novel Analytical Model for No-Load, Slotted, Surface-Mounted PM Machines: Air Gap Flux Density and Cogging Torque

An analytical model for prediction of air gap flux density and cogging torque in slotted surface-mounted permanent magnet (SPM) machines is presented in this paper. The proposed method is based on superposition theorem, the concept of equivalent magnetization currents (EMCs), and analytically solving of Poisson’s equation. To solve Poisson’s equation easily, the air gap flux density of the slotted SPM machine is stated as superposition of the air gap flux density functions of two slotless machines. The first slotless machine is excited by PMs, while the second one is excited by surface EMCs. Therefore, the concept of EMC is used in an iterative algorithm which converges quickly with a negligible computation time. Using the obtained analytical model and Maxwell’s stress tensor, cogging torque of the slotted SPM machine is predicted. This analytical model provides a quick tool to study the effect of leading design parameters on the machine cogging torque. Finally, the validity of the proposed model and the obtained results are verified with finite element analysis.