Thierry Lubin

2-D Exact Analytical Model for Surface-Mounted Permanent-Magnet Motors With Semi-Closed Slots

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 Laplaces and Poissons 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.

Exact Analytical Method for Magnetic Field Computation in the Air Gap of Cylindrical Electrical Machines Considering Slotting Effects

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 Laplaces 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.

Analytical Computation of the Magnetic Field Distribution in a Magnetic Gear

We propose an analytical computation of the magnetic field distribution in a magnetic gear. The analytical method is based on the resolution of Laplaces and Poissons 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.

Comparison Between Finite-Element Analysis and Winding Function Theory for Inductances and Torque Calculation of a Synchronous Reluctance Machine

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.

Simple Analytical Expressions for the Force and Torque of Axial Magnetic Couplings

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 Laplaces and Poissons 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.

Two-Dimensional Analytical Calculation of Magnetic Field and Electromagnetic Torque for Surface-Inset Permanent-Magnet Motors

The paper deals with a subdomain model for predicting the magnetic field distribution in surface-inset permanent-magnet (PM) motors with semi-closed slots under load conditions. Due to the presence of electrical current in the stator slots, a magnetic vector potential formulation is used. The magnetic vector potential distribution in each subdomain (air-gap, stator slots, and rotor slots with inset PMs) is obtained by solving two-dimensional Laplaces and Poissons equations by the separation of variables method. One of the main contributions of the paper concerns the magnetic vector potential expression in the PM region. Indeed, PMs are inset into the rotor iron which leads to solve Laplaces equation with nonhomogeneous Neumann boundary conditions. Magnetic field distribution and electromagnetic torque computed with the proposed analytical method are verified with those obtained from finite-element analyses.

Development of a 2-D Analytical Model for the Electromagnetic Computation of Axial-Field Magnetic Gears

This paper describes a two-dimensional (2-D) analytical model to predict the magnetic field distribution in axial-field magnetic gears by using the sub-domain method. The sub-domain method consists in solving the partial differential equations linked to the Maxwells equations in each rectangular region (magnets, air gaps, and slots) by the separation of variables method. The proposed model is based on a two-dimensional approximation for the magnetic field distribution (mean radius model) i.e. the problem is solved in 2-D Cartesian coordinates. One of the main contributions of the paper concerns the analytic solution of the magnetic field in a slot open on the two sides (space between the ferromagnetic pole-pieces). Moreover, it is shown that the analytical model and the 3-D finite elements simulations follow the same trends in the determination of the optimum values for the geometrical parameters. As the analytical model takes less computational time than 3-D numerical model, it can be used as an effective tool for the first step of design optimization.

Analytical Prediction of Magnetic Field in Parallel Double Excitation and Spoke-Type Permanent-Magnet Machines Accounting for Tooth-Tips and Shape of Polar Pieces

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 Laplaces and Poissons 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.

Analytic Calculation of Eddy Currents in the Slots of Electrical Machines: Application to Cage Rotor Induction Motors

This paper describes a two-dimensional analytic model for predicting the induced currents within conducting material placed in the slots of electrical machines. Slot-embedded conductors are subjected to a rotating magnetic field including space harmonics. The analytical method is based on the resolution of time-harmonic homogeneous Helmholtzs equation in polar coordinates by the separation of variables method. The global solution is obtained using boundary and continuity conditions between the different sub-domains (rotor slots and air-gap). The proposed model is applied for magnetic field and torque calculations in a rotor cage induction motor under steady state condition. The analytical results are verified with those obtained from finite element analyses.

General Subdomain Model for Predicting Magnetic Field in Internal and External Rotor Multiphase Flux-Switching Machines Topologies

This paper presents a general analytical subdomain model for the computation of magnetic field distribution in any number of stator slots and rotor poles with and without electrically excited, permanent magnet-excited and hybrid-excited multiphase flux-switching machine (FSM) topologies. The goal of this work is to elaborate an analytical general method based on the subdomain model for predicting the magnetic field in any FSM topology with defining in advance the number of subdomains and affect the general form of vector potential in each subdomain. The presented general subdomain method is comparable to the finite-element method (FEM) where the mesh elements can be compared with the number of harmonic terms used in each subdomain.