Open-circuit Magnetic Field Distribution Research Articles

Analytical Model for Cogging Torque Calculation in Surface-Mounted Permanent Magnet Motors With Rotor Eccentricity and Magnet Defects

This article proposes a novel analytical model which combines subdomain method and magnet equivalent circuit (MEC) method to predict the cogging torque of surface-mounted permanent magnet (SPM) motors with rotor eccentricity and magnet defects in any slot-pole combination cases. Firstly, the general solution of open-circuit magnetic field distribution in a slotless SPM motor with magnet defects is derived. Then, the motor is divided into several subdomains along the air-gap circumferential direction to consider the non-uniform air-gap caused by rotor eccentricity, where the air-gap lengths of each subdomain are considered to be uniform. Finally, the methods of conformal mapping and MEC combined with equivalent current is used to consider the effect of slotting and saturation, which is beneficial to improve the calculation precision. The magnetic field distributions and cogging torque calculated by the proposed model are consistent with the results of finite element analysis (FEA). Compared with the FEA, the proposed model can perform fast calculations of air-gap flux density and cogging torque under rotor eccentricity and magnet defects for SPM motors, which can be utilized for optimizing the motor towards fault tolerance.

Design and Analysis of Permanent Magnet Homopolar Machine for Flywheel Energy Storage System

This paper presents the design and analysis of a 4-poles-24-slots permanent magnet (PM) homopolar machine for the flywheel energy storage system (FESS), and the operating principle is investigated. Due to the unconventional flux distribution in this machine and the goal of the design is to minimize the torque ripple while maximizing the torque density, the parameter of this machine was obtained by the 3-D finite element global optimization genetic algorithm method. In addition, the air-gap flux density of double stator, open-circuit magnetic field distribution, flux linkage, back electromotive force stator, core loss, external characteristic were analysis, and the operating principle is verified by open-circuit magnetic field distribution. It was found that core loss can be reduced almost 34% by comparing with a heteropolar PM machine, which demonstrated that the homopolar machine is a promising candidate for the FESS. A prototype has been manufactured and tested to validate the finite-element and theoretical analyses.

A Hybrid Field Model for Open-Circuit Field Prediction in Surface-Mounted PM Machines Considering Saturation

This paper presents a nonlinear hybrid field model to predict the open-circuit magnetic field distribution in surface-mounted permanent-magnet machines. It combines the complex permeance model (CPM) with the magnetic equivalent circuit (MEC). The saturation effect is accounted for in the CPM by considering the magnetic potential distribution on the stator bore, which is calculated by the MEC and can be transformed to the virtual current on the slot. The proposed model significantly improves the calculation accuracy for saturated machines, which is verified by the finite-element analysis and the experimental results.

Analytical Modeling and Optimization for Electromagnetic Performances of Fractional-Slot PM Brushless Machines

This paper presents a closed-form solution to optimize surface permanent magnet (PM) machines using concentrated windings. An analytical model is developed to predict the electromagnetic performances of fractional-slot PM machines. The model can be used to evaluate open-circuit magnetic field distribution with stator slotting effects, armature reaction field distributions, back-EMF waveform, winding inductance, cogging torque, electromagnetic ripple torque, efficiency, specific power, radial force density, and vibration mode order. Particle swarm optimization technique is applied to the proposed model in order to search for solutions that are a good compromise between conflicting objectives. The performances of the optimized machine are verified using finite element analysis. Finally, the analytical and finite element results have been validated with the experimental data, demonstrating a strong correlation between key machine parameters.

Research on the Field-Modulated Tubular Linear Generator With Quasi-Halbach Magnetization for Ocean Wave Energy Conversion

A field-modulated tubular linear generator (FMTLG) with quasi-Halbach magnetization is proposed for ocean wave energy conversion. The FMTLG, which is equipped with field-modulated technology and quasi-Halbach arrays, can overcome the disadvantages of heavy weight and inefficiency caused by low-speed ocean waves to some extent. To design and optimize the FMTLG in a short time, the open-circuit magnetic field distribution is established with an analytical method. Results of a finite-element method show that the back EMF of the FMTLG is 43% higher than that of a tubular linear permanent magnet generator (TLPMG) with quasi-Halbach magnetization. A novel assistant tooth of the FMTLG makes the cogging force eight times smaller than that generated by the TLPMG. Finally, a prototype is manufactured to verify the simulation results by experiments.

3-D Performance Analysis and Multiobjective Optimization of Coreless-Type PM Linear Synchronous Motors

This paper presents a three-dimensional (3-D) performance analysis and multiobjective design optimization of coreless-type permanent magnet linear synchronous motors. The average of open circuit magnetic field distribution is analytically predicted by solving two Laplace's equations. The winding factor calculation, which requires an approach different from conventional slotted motors, is provided to evaluate the motor performances. As a result, average thrust and thrust ripple can be obtained without loss of accuracy compared with results of 2-D finite element analysis (FEA). The 3-D leakage influences are subsequently incorporated into the analysis using lumped parameter magnetic circuit model because end effects are not neglected due to a relatively large air gap. Consequently, two meaningful contributions of this paper are summarized as follows: first, 3-D electromagnetic performances can be accurately predicted by the proposed analytical method. Second, with no need for the time-consuming 3-D FEA, differential evolution, a practical approach to global optimization, can simply be employed to search for solutions which belong to the Pareto optimal set. Finally, the validity of the analytical results is confirmed with the experimental results.

Analytical Method for Open-Circuit Air Gap Magnetic Field Calculation in Surface-Mounted Permanent Magnet Motors with Rotor Eccentricity

Analytical method with vector magnetic potential is proposed to calculate the open-circuit air gap magnetic field distribution in surface-mounted permanent magnet motors with rotor eccentricity, and the method is applicable to both internal and external rotor eccentric structure. The Laplace’s or Poisson’s equations and associated boundary conditions are formulated. The analytical expressions of eccentric air gap flux density are deduced by a perturbation method; and the perturbation quantity  is dimensionless. The analytical results are compared with the finite element method analysis results which verify the correctness and the effectiveness of the perturbation method.

Analytical calculation of open-circuit magnetic field distribution of slotless brushless PM machines

A comprehensive analytical open-circuit magnetic field distribution of slotless brushless permanent magnet machines with surface mounted magnets is presented for six different magnetization patterns. The stator and rotor back-irons are assumed to be finite permeable. Therefore, the analytical model covers five annular regions: rotor; magnet; air–gap/winding; stator; and exterior. The expressions of the five regions are presented in a convenient form to ease the numerical computation for both internal and external rotor motors. The induced back-EMF is also expressed analytically. The efficacy of the analytical model is validated by comparing the results with finite element analyses (FEAs).

Analytical magnetic field distribution of slotless brushless PM motors. Part 2: Open-circuit field and torque calculations

This study presents the open-circuit analytical magnetic field distribution of slotless brushless permanent magnet motors equipped with surface-mounted magnets. Although the focus of the study is on open-circuit magnetic field analysis, by augmenting the open-circuit magnetic field distribution with the armature reaction field distribution obtained from the first part of the series of two studies, the electromagnetic torque is calculated. The electromagnetic torque is calculated for both internal and external rotor motors with six different magnetisation patterns and three different armature current waveforms. The analysis domain consists of eight annular concentric regions: motor shaft, rotor back-iron, magnets, retaining sleeve, air-gap, winding, stator back-iron and exterior regions. Based on the open-circuit magnetic field distribution, the induced back-electromotive force (EMF) is also calculated. The validity of the proposed model is confirmed by comparing the analytical results with those obtained from the finite element method and an experimental set-up.

Analytical Prediction of Open-Circuit Eddy-Current Loss in Series Double Excitation Synchronous Machines

This paper describes an analytical technique for prediction of open circuit eddy-current loss in armature windings and permanent magnets (PM) of series double excitation synchronous machines. First, a 2-D exact analytical solution of open circuit magnetic field distribution in idealized geometry of series double excitation synchronous machine is established. It involves solving Maxwell's equations in stator slots, air gap, PM region, and rotor slots. Then, magnetic vector potential solutions in the stator slots and PM regions are respectively used for prediction of resistance limited eddy currents in armature windings and permanent magnets. This analytical model is then used to estimate eddy-current loss in armature windings and permanent magnets. The validity of the developed model, which is also applicable to conventional designs of permanent-magnet machine, is verified by time-stepped transient finite-element analysis (FEA). The developed model is then used to quantify the effectiveness of segmenting the magnets and armature windings in reducing the eddy-current loss.

Analytical Magnetic Field Distribution of Slotless Brushless Machines With Inset Permanent Magnets

An analytical open-circuit magnetic field distribution for slotless brushless machines with inset permanent magnets is presented. Three different magnetization patterns (radial, parallel, and Halbach) have been considered and their results compared with each other. The induced back-electromotive force (EMF) is also presented for each magnetization pattern. The effects of iron inter-pole on the magnetic flux density and back-EMF have been studied. To verify the model, the results have been compared with those obtained from finite element analyses (FEA).

Tubular modular permanent-magnet machines equipped with quasi-Halbach magnetized magnets-part I: magnetic field distribution, EMF, and thrust force

This paper describes the analysis, design, and experimental characterization of three-phase tubular modular permanent-magnet machines equipped with quasi-Halbach magnetized magnets. It identifies feasible slot/pole number combinations and discusses their relative merits. It establishes an analytical expression for the open-circuit magnetic field distribution, formulated in the cylindrical coordinate system. The expression has been verified by finite-element analysis. The analytical solution allows the prediction of the thrust force and electromotive force in closed forms, and provides an effective tool for design optimization, as will be described in Part II of the paper.

Open-circuit field distribution in a brushless motor with diametrically magnetised PM rotor, accounting for slotting and eddy current effects

An analytical model has been developed for calculating the open-circuit time-varying magnetic field distribution in the airgap/magnet/retaining sleeve region of a brushless permanent magnet motor equipped with diametrically magnetised magnets. It accounts for the stator slotting and curvature, as well as for parasitic eddy currents induced in the retaining sleeve and magnets. The analytically predicted time-varying field distribution in the different regions is compared with corresponding finite element predictions.

Instantaneous magnetic field distribution in brushless permanent magnet DC motors. II. Armature-reaction field

For pt.I see ibid., vol.29, no.1, p.124-135 (1993). An analytical technique for predicting the open-circuit magnetic field distribution in the airgap/magnet region of a brushless permanent-magnet DC motor equipped with a surface mounted magnet rotor and a slotless stator was presented in Pt.I. In the present work, the analysis is extended to the prediction of the armature reaction field produced by the three-phase stator windings. As before, th motor model is formulated in polar coordinates and accounts for the large effective airgap, but it is not developed further to consider the effect of winding current harmonics on the airgap field distribution. Predicted instantaneous armature reaction field distributions are validated by a comparison with corresponding finite element calculations. >