On-Load Field Component Separation in Surface-Mounted Permanent-Magnet Motors Using an Improved Conformal Mapping Method

This paper introduces an improved conformal mapping (ICM) method for the separation of the on-load air-gap magnetic field components in surface-mounted permanent-magnet (SPM) motors under loading conditions. The ICM method can model the magnetic induction inside a permanent magnet (PM) due to the armature reaction and the relative recoil permeability. The ICM method can also consider the simultaneous influences of the armature reaction, the slotting effect, the magnetic saturation, and the relative recoil permeability in the determination of operating points of the PM in its different parts. Therefore, this proposed method can be useful for an on-load performance analysis of SPM motors. Three conformal mappings are used to reach the main canonical domain: two logarithmic complex functions and the Schwarz-Christoffel (SC) mapping. The field solution in the slotless domain is then mapped back into the slotted domain using the complex air-gap permeance. The field solution in the slotted domain is used to calculate the on-load air-gap field components due to the PMs and the armature reaction. These on-load field components allow the calculation of the on-load PM flux linkage, the on-load PM back-EMF, and the on-load torque components. The influences of electric loading on the on-load torque components and the on-load PM back-EMF are studied using the ICM method. The on-load cogging torque periodicity is confirmed to change due to the magnetic saturation, and the harmonic content of torque components and the PM back-EMF is also altered due to the electric loading. The accuracy of this developed model is verified by comparing the results obtained through the ICM method with the respective results obtained through the finite-element analysis and the frozen permeability method.