Improved method for field analysis of surface permanent magnet machines using Schwarz–Christoffel transformation

Abstract

Air gap field solution for an outer rotor permanent magnet (PM) machine is derived based on numerical Schwarz-Christoffel (SC) transformation of a single slot geometry and analytical solution of a point wire field in the rectangular canonical domain. This approach takes into account geometrical distortions of PM edges and field evaluation points located along the air gap centre, which occur due to conformal mapping of the slotted air gap into a slotless domain and impair the accuracy of the existing analytical field solutions using SC transformation and complex relative air gap permeance. The increased accuracy of the improved solution is confirmed by comparing the air gap flux density waveforms produced by the PMs and armature winding, cogging torque, and total torque with the results of time-stepping transient finite element simulation.

On-Load Field Prediction of Surface-Mounted PM Machines Considering Nonlinearity Based on Hybrid Field Model

“…It is simple and fast because Schwarz-Christoffel (SC) transformation is required only once, but it neglects the deformation of magnets and path for airgap field prediction. To eliminate this error, exact conformal mapping based on SC Toolbox can be used to accurately calculate the magnetic field in the SPM machines [7]- [8]. SC Toolbox was developed to construct a SC map from the machine geometry at first and then numerically evaluate the position of PM equivalent current in the canonical domain at every rotor position [10].…”

Analytical model for armature reaction of outer rotor brushless permanent magnet DC motor

“…Many scholars have made their contributions to the analytical calculation of the armature reaction magnetic field in PMBLDCM [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. In order to solve the problem of analytical calculating the air-gap magnetic field of slot effect, there are two main methods used by scholars: direct method and indirect method.…”

“…The accuracy of the direct method is relatively high, but the analytical formula is not simple and intuitive. The latter, indirect method, refers to the analytical formula of the air-gap magnetic field of the slotting by multiplying the simple analytical formula of the slotless magnetic field by the air-gap late permeance [8,10,11,17]. Compared with the direct method, the indirect method has obvious advantages in the simplicity of the formula, but the accuracy of the result depends on the accuracy of the air-gap late permeance function.…”

Computational-Time Reduction of Fourier-Based Analytical Models

“…Although some authors of FB models have reported on numerical issues [3], [7], [8], to date no extensive study of the computational time of such models has been presented. The only available literature that discusses computationaltime reduction was presented by Ramakrishnan et al in [9]. However, that discussion is limited to a specific class of Fourier-based models that uses Schwarz-Christoffel mapping.…”