This paper compares the air-gap field distribution, cogging torque, back-electromotive-force waveform, and efficiency of brushless machines having a Halbach magnetization produced by either discrete magnet segments or a single ring magnet. Results deduced from finite-element analyses are compared with measurements, and the performance of Halbach magnetized machines is compared with that of machines equipped with radially magnetized magnets

Howe, D.

Xia, Z.P.

Zhu, Z.Q.

English

White Rose Research Online

This is a repository copy of Comparison of Halbach magnetized brushless machines based on discrete magnet segments or a single ring magnet .White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/871/Article:Zhu, Z.Q., Xia, Z.P. and Howe, D. (2002) Comparison of Halbach magnetized brushless machines based on discrete magnet segments or a single ring magnet. IEEE Transactionson Magnetics, 38 (5 (Pa). pp. 2997-2999. ISSN 0018-9464 https://doi.org/10.1109/TMAG.2002.803190eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002 2997Comparison of Halbach Magnetized BrushlessMachines Based on Discrete MagnetSegments or a Single Ring MagnetZ. Q. Zhu, Senior Member, IEEE, Z. P. Xia, Member, IEEE, and D. HoweAbstract—This paper compares the air-gap field distribution,cogging torque, back-electromotive-force waveform, and efficiencyof brushless machines having a Halbach magnetization producedby either discrete magnet segments or a single ring magnet. Resultsdeduced from finite-element analyses are compared with measure-ments, and the performance of Halbach magnetized is comparedwith that of machines equipped with radially magnetized magnets.Index Terms—Brushless machines, Halbach magnetization, per-manent-magnet machines.I. INTRODUCTIONHALBACH magnetized brushless machines have severalattractive features [1]. Most notably, they have an essen-tially sinusoidal air-gap field distribution and electromotiveforce (EMF) waveform, and exhibit negligible cogging torque.To date, however, Halbach magnetized machines have generallybeen fabricated from premagnetized magnet segments havingappropriate magnetization orientations [2], which approximatesthe Halbach magnetization, and, thereby, compromises theirperformance. However, Halbach magnetized ring magnets,in both sintered and bonded forms, are now available com-mercially [3], [4]. In this paper, bonded anisotropic Halbachmagnetized ring magnets, produced by orientating anisotropicNdFeB powder during the injection moulding process andsubsequently impulse magnetizing them with the requiredHalbach field distribution, are considered, and the performancewhich results when they are employed in a brushless motor iscompared with that which is obtained when the Halbach fieldis produced by discrete magnet segments and with radiallymagnetized segments.II. HALBACH MAGNETIZATIONIn an ideal Halbach magnetized magnet, the magnetizationdistribution, in polar coordinates ( and ), can be expressedas where and, being the number of pole-pairs, “” and “ ”being for internal and external field Halbach cylinders, respec-tively. However, when a Halbach magnetized magnet is realizedfrom discrete magnet segments, the ideal magnetization distri-bution is approximated, since the direction of magnetization isManuscript received February 13, 2002; revised May 21, 2002.The authors are with the Department of Electronic and Electrical Engi-neering, University of Sheffield, Sheffield S1 3JD, U.K. (e-mail: Z.Q.Zhu@sheffield.ac.uk; Z.P.Xia@sheffield.ac.uk; D.Howe@sheffield.ac.uk).Digital Object Identifier 10.1109/TMAG.2002.803190.Fig. 1. Angular relationship between and .(a) (b)Fig. 2. Segmented Halbach magnet machine. (a) Two segments/pole. (b) Threesegments/pole.fixed in each individual magnet segment bywhere is the angle between and the center of thethmagnet segment (Fig. 1). For example, the magnetization pat-terns with two and three magnet segments per pole in a 12-poleHalbach magnetized motor are illustrated in Fig. 2.III. COMPARISON OFALTERNATIVE HALBACHMAGNETIZED MACHINESIn order to demonstrate the relative merits of brushless ma-chines equipped with ideal and segmented Halbach magnetizedrotors, the influence of the number of magnet segments per poleon the field distribution, the cogging torque and the back-EMFwaveforms is investigated by finite-element analysis, the torquebeing obtained by Maxwell stress integration. The motors haveidentical stators, with an OD 90 mm, an ID 55 mm, anaxial length 13 mm, an air-gap length 0.5 mm, and 18 slotscarrying nonoverlapping windings [Figs. 2 and 5(a)]. The seg-mented Halbach magnet rotors employ sintered NdFeB mag-0018-9464/02$17.00 © 2002 IEEE2998 IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002(a)(b)(c)(d)(e)(f)Fig. 3. Radial air-gap field distributions, and phase and line back-EMFwaveforms. (a) Two segments/pole Halbach magnetized. (b) Threesegments/pole Halbach magnetized. (c) Four segments/pole Halbachmagnetized. (d) Five segments/pole Halbach magnetized. (e) Ideal Halbachmagnetized. (f) Radially magnetized (with back-iron).nets having a remanence of 1.0 T and a radial thickness of2.4 mm, while the single ring Halbach magnet rotor is an in-jection-moulded anisotropic NdFeB (NDA502E, 65% loading)magnet [4] having a radial thickness of 4.6 mm, and a rema-nence of 0.6 T. In this particular paper, the rotors were air-cored.In addition, however, an iron-cored rotor equipped with radiallymagnetized sintered NdFeB magnets, having a radial thicknessof 1.2 mm, was considered. All the motors were designed tomeet the same specification,viz. 0.71 Nm and 3000 r/min. Al-Fig. 4. Cogging torque waveforms.(a) (b) (c)Fig. 5. Prototype motors. (a) 18-slot, unskewed, nonoverlapping windingstator. (b) 12-pole rotor having two sintered NdFeB magnet segmentsper pole. (c) 12-pole rotor having a Halbach orientated and magnetizedinjection-moulded NdFeB ring magnet.though the materials and the radial thickness of the magnets inthree motors are different, they result in a similar saturation levelin the stator, while the magnetic loading in the air gap is essen-tially the same, as shown in Fig. 3.Finite-element predicted results are shown in Figs. 3 and 4. Itcan be seen that, in addition to harmonics due to stator slotting,the approximation of the Halbach magnetization introduces sig-nificant harmonics in the air-gap field distribution when thenumber of magnet segments per pole is low. For example, withonly two magnet segments per pole, the air-gap field distribu-tion and the back-EMF waveform are much less sinusoidal thanthat with four or more magnet segments per pole, while the cog-ging torque is much larger, being similar in magnitude to thatwhich results with radially magnetized magnets. Predictably, asthe number of magnet segments per pole is increased, the fielddistribution and the back-EMF waveform become progressivelymore sinusoidal, and the cogging torque reduces. With a singleideally magnetized Halbach ring magnet, the motor should ex-hibit both a sinusoidal air-gap field distribution and a sinusoidalback-EMF waveform, as well as zero cogging torque. How-ever, as will be seen, stator slotting causes a slight distortion,while the resultant cogging torque is not zero (although it is verysmall) due to inaccuracies in the finite-element calculation, eachelement being assumed to have a fixed, rather than continuouslyvariable magnetization.IV. EXPERIMENTAL RESULTS AND DISCUSSIONMeasurements have been made on two brushless motorshaving the same stator [Fig. 5(a)] and full-load performance,ZHU et al.: HALBACH MAGNETIZED BRUSHLESS MACHINES 2999Fig. 6. Comparison of performance of alternative Halbach magnetizedmotors: two sintered NdFeB magnet segments/pole. (a) Air-gap fielddistribution. (b) Phase back-EMF waveform. (c) Cogging torque waveform.Fig. 7. Comparison of performance of alternative Halbach magnetizedmotors: anisotropic NdFeB injection-moulded ring magnet. (a) Air-gap fielddistribution. (b) Phase back-EMF waveform. (c) Cogging torque waveform.Fig. 8. Measured efficiency–torque characteristics of Halbach magnetizedmotors.as specified earlier, but different Halbach magnetized ro-tors—one having two sintered NdFeB magnet segments perpole [Fig. 5(b)], the other having a Halbach magnetizedinjection-moulded NdFeB ring magnet [Fig. 5(c)]. Figs. 6–8compare the measured and predicted air-gap field distribu-tions, the back-EMF, and cogging torque waveforms, and thetorque–efficiency characteristics. As will be seen, excellentagreement is achieved for both motors. The main reason for thedifference between predicted and measured waveforms for thetwo magnet segments per pole motor is assembly tolerances.As will be seen, the motor with the Halbach magnetized ringmagnet exhibits a very much lower cogging torque (5.5 mN(peak), 1% of rated torque, in contrast to 80 mN m (peak),11% of rated torque for the motor with two magnet segmentsper pole), as well as a higher efficiency, due to its sinusoidalair-gap field distribution, and, therefore, lower stator iron loss.V. CONCLUSIONThe finite-element method has been used to investigate theperformance of Halbach magnetized brushless machines havingdiscrete magnet segments or a single ring magnet. Predictedand measured air-gap field distributions, cogging torque andback-EMF waveforms, and efficiency, have been compared,and excellent agreement has been achieved. It has been shownthat since segmented Halbach magnets approximate the Hal-bach magnetization, they compromise the performance of themotors in which they are employed, although the use of ahigher number of magnet segments per pole improves the fielddistribution, albeit increasing the cost of fabrication.REFERENCES[1] K. Halbach, “Design of permanent magnet multipole magnets with ori-ented rare earth cobalt material,”Nucl. Instrum. Methods, vol. 169, pp.1–10, 1980.[2] M. Marinescu and N. Marinescu, “New concept of permanent magnetexcitation for electrical machines—Analytical and numerical computa-tion,” IEEE Trans. Magn., vol. 28, pp. 1390–1393, Mar. 1992.[3] K. Atallah and D. Howe, “The application of Halbach cylinders to brush-less ac servo motors,”IEEE Trans. Magn., vol. 34, pp. 2060–2062, July1998.[4] Z. Q. Zhu, Z. P. Xia, K. Atallah, G. W. Jewell, and D. Howe, “Powderalignment system for anisotropic bonded NdFeB Halbach cylinders,”IEEE Trans. Magn., vol. 36, pp. 3349–3352, Sept. 2000.

Comparison of Halbach magnetized brushless machines based on discrete magnet segments or a single ring magnet

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Comparison of Halbach magnetized brushless machines based on discrete magnet segments or a single ring magnet

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