This paper presents an analytical subdomain model to compute the magnetic field distribution in surface-mounted permanent-magnet (PM) motors with semi-closed slots. The proposed model is sufficiently general to be used with any pole and slot combinations including fractional slot machines with distributed or concentrated windings. The model accurately accounts for armature reaction magnetic field and mutual influence between the slots. The analytical method is based on the resolution of two-dimensional Laplace's and Poisson's equations in polar coordinates (by the separation of variables technique) for each subdomain, i.e., magnet, air gap, slot-opening, and slots. Magnetic field distributions, back-EMF, and electromagnetic torque (including cogging torque) computed with the proposed analytical method are compared with those issued from finite-element analyses.

We propose an analytical computation of the magnetic field distribution in a magnetic gear. The analytical method is based on the resolution of Laplace's and Poisson's equations (by the separation of variables technique) for each subdomain, i.e., magnets, air gap, and slots. The global solution is obtained using boundary and continuity conditions. Our analytical model can be used as a tool for design optimization of a magnetic gear. Here, we compare magnetic field distributions and electromagnetic torque computed by the analytical method with those obtained from finite-element analyses.

This paper deals with an analytical method for magnetic field calculation in the air gap of cylindrical electrical machines including slotting effects. The analytical method is based on the resolution of the two-dimensional Laplace's equation in polar coordinates by the separation of variables technique. The originality of the proposed model is to take into account the mutual influence of slots on the air-gap magnetic field. The proposed method is sufficiently general to be used as a tool for air-gap magnetic field calculation of slotted electrical machines as reluctance or permanent magnet motors or actuators. Magnetic field and electromagnetic torque computed with the proposed analytical method are validated through finite-element analysis.

In this paper, a theoretical analysis of an axial magnetic coupling is presented, leading to new closed-form expressions for the magnetic axial force and torque. These expressions are obtained by using a 2-D approximation of the magnetic coupling geometry (mean radius model). The analytical method is based on the solution of Laplace's and Poisson's equations by the separation of variables method. The influence of geometrical parameters such as number of pole pairs and air-gap length is studied. Magnetic field distribution, axial force, and torque computed with the proposed 2-D analytical model are compared with those obtained from 3-D finite elements simulations and experimental results.

This paper compares the prediction of two independent methods for calculating electromagnetic torque and inductances of a synchronous reluctance machine under linear condition. One method is based on winding function analysis (WFA) and the other on finite-element analysis (FEA). Both methods take into account the rotor geometry, the stator slot effects and the stator winding connections. The simulation results obtained by the WFA are compared with the ones obtained by two-dimensional FEA. It is shown that the two methods give approximately the same results but require different computation times.

This paper presents an approach for quick calculation of steady-state and transient performances of an axial-field eddy-current coupling. Based on a 2-D approximation of the magnetic field distribution, a simple analytical expression for the transmitted torque is first developed. This expression is valid for low slip values, which correspond to the normal working area of such devices (high efficiency). The proposed torque formula is then used to study the steady-state (constant-speed operations) and the transient performances of the coupling (small variations of the slip speed). The results are compared with those obtained from 3-D finite elements simulations and tests. It is shown that good agreements are obtained.