Permanent magnet synchronous motor: finite element torque calculations

The Maxwell stress tensor method is modified by the authors to yield an area integration which takes into account the field distribution in the airgap of a machine, resulting in an improvement in accuracy and the elimination of sensitivity to contour selection. A second technique, based on the co-energy derivative method, is also developed. This needs only one finite-element (FE) solution and eliminates the trial-and-error procedure of selecting a proper displacement for the derivative determination, thus shortening the computational time. The torque characteristics of a permanent magnet synchronous motor (PMSM) evaluated from the above methods compare favourably with each other as well as with those from the Lorentz method and an analytical model based on an equivalent circuit of the machine. The torque calculating techniques are used to select the geometry of the permanent magnets for the rotor of a 30 hp machine using a criterion which takes into account the torque per unit stator current, efficiency-power-factor product, overload capability of the machine, and volume (cost) of permanent magnet material.<>