This paper deals with the nonlinear analytical harmonic modeling (HM) of three phases, and 6/4 conventional switched reluctance machine (SRM). The proposed model consists in computing magnetic field distribution and electromagnetic performances of an SRM with conventional winding. Because an SRM has inherently nonlinear characteristics, the analytical subdomain model that does not take into account the saturation has a limited accuracy. This is due to the assumption of infinite tooth permeability. The new analytical model (AM) based on the HM technique, which overcomes this limitation, is presented with the consideration of the local magnetic saturation on the stator and rotor teeth. The results obtained with the nonlinear AM have been compared with the linear AM based on the subdomain method (i.e., without the saturation effect) and nonlinear finite-element method solutions.

In this paper, we apply an original numerical Schwarz-Christoffel (SC) transformation to analyze magnetic field originating from permanent magnets and the armature winding currents in a slotted air gap of an inset permanent-magnet synchronous motor. We obtained the solution of the SC integral numerically using Matlab SC Toolbox. We used this field solution to calculate both cogging torque and electromagnetic torque by integrating the Maxwell stress tensor inside the air gap. The case without inter-polar piece, which is equivalent to a surface-mounted permanent-magnet motor, is also treated. The accuracy of the developed method is verified by comparing its results with those obtained from the developed numerical finite-element models.

This paper presents analytical and numerical conformal mapping (CM) to analyze magnetic fields originating from permanent magnets and armature winding currents in a slotted air-gap of a surface mounted radial permanent-magnet synchronous motor (SPM), taking into account the effect of arbitrarily curved motor surfaces. We also studied the slotless configuration of the external rotor permanent-magnet motor for the purpose of calculating the complex relative air-gap permeance. The model is able to predict the air gap field and torque with high accuracy, which cannot be achieved using the previously available analytical methods in both cases: internal and external rotor permanent-magnet motor. We obtained one of the conformal mappings used in this study, the numerical solution of the Schwarz-Christoffel (SC) integral, by using the Matlab SC Toolbox. We used this field solution to calculate cogging torque and electromagnetic torque by integrating the Maxwell stress tensor inside the air gap. We verified the accuracy of the developed method by comparing its results with those obtained from the developed numerical finite-element (FE) model.

An analytical model is presented, which uses two-dimensional field theory in polar coordinates to determine the flux density distribution, cogging torque, back EMF and electromagnetic torque in the slotted air gap of permanent-magnet motors with surface mounted magnet bars which are magnetized in shifting direction. The magnet arc to pole pitch ratio in the motor is not necessarily equal to unity like in the case of Halbach array magnetization. The effect of stator slots is introduced by modulating the magnetic field distribution in the slotless stator by the complex relative air-gap permeance. With this complex permeance, the radial and tangential components of flux density are calculated. In the analytical and numerical study a finite number of magnet bars, which is considered sufficient to get a sinusoidal magnetization, is used. The influence of the number of magnet bars on magnetization is also investigated. The accuracy of the developed model is verified by comparing its results with those obtained from experimental measurement and previously validated linear and nonlinear numerical finite element code.

This paper presents an analytical method based on subdomain method for the computation of open circuit, armature reaction, and on-load magnetic field distribution in integer slot winding parallel double excitation and spoke-type tangential permanent-magnet machines. The proposed model takes into account for stator and rotor slots tooth tips and shape of polar piece. A 2-D exact analytical solution of magnetic field distribution is established. It involves solution of Laplace's and Poisson's equations in semi-closed stator and rotor slots, air-gap, buried permanent magnets into rotor semi-closed slots, and nonmagnetic region under magnets. Obtained exact analytical results of open circuit, armature reaction, and on-load magnetic field distribution are verified with those issued from the finite element method.

The most significant assumptions in the subdomain technique (i.e., based on the formal resolution of Maxwell’s equations applied in subdomain) is defined by: Theiron parts(i.e.,theteeth and the back-iron are considered to be infinitely permeable, i.e., µiron → +∞, so that the saturation effect is neglected. In this paper, the authors present a new scientific contribution on improving of this method in two-dimensional (2-D) and in Cartesian coordinates by focusing on the consideration of iron. The subdomains connection is carried out in the two directions (i.e., x-andy-edges). Forexample,the improvement was performed by solving magnetostatic Maxwell’s equations for an air- or iron-cored coil supplied by a direct current. To evaluate the efficacy of the proposed technique, the magnetic flux density distributions have been compared with those obtained by the 2-D finite-element analysis (FEA). The semi-analytical results are in quite satisfying agreement with those obtained by the 2-D FEA, considering both amplitude and waveform.