Analytical Solution for Electromagnetic Torque in Surface Permanent-Magnet Motors Using Conformal Mapping

We present an analytical method for the calculation of electromagnetic torque in surface permanent-magnet (PM) motors. Our method uses conformal mapping to calculate the electromagnetic torque by integrating the Maxwell stress tensor inside the air gap. It uses the radial and tangential components of the flux density in the slotted air-gap produced by the currents flowing in the three-phase armature winding. We demonstrate our analytical solution on a 7-kW four-pole surface PM motor and compare the results with finite-element solutions. We present the results for various angular spans of permanent magnets and various sizes of the slot opening to confirm the validity of the analytical approach.