paper no. 4LPD-01A tubular linear magnetic gear is proposed, which newly utilizes high temperature superconductor (HTS) bulks for its field modulation. Compared to the conventional one, the proposed topology can significantly reduce the leakage flux, hence improving its force transmission capacity. By using the magnetic circuit modeling, the analytical formulae of air-gap flux density and thrust force are firstly derived. Then, the finite element method (FEM) is employed to validate the performance of the proposed linear magnetic gear. © 2010 IEEE.published_or_final_versio

Chau, KT

Li, J

Li, W

IEEE Transactions on Applied Superconductivity

Wenlong Li

K. T. Chau

Jiangui Li

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Simulation of a Tubular Linear Magnetic Gear Using HTS Bulks for Field Modulation

A tubular linear magnetic gear is proposed, which newly utilizes high temperature superconductor (HTS) bulks for its field modulation. Compared to the conventional one, the proposed topology can significantly reduce the leakage flux, hence improving its force transmission capacity. By using the magnetic circuit modeling, the analytical formulae of air-gap flux density and thrust force are firstly derived. Then, the finite element method (FEM) is employed to validate the performance of the proposed linear magnetic gear. © 2010 IEEE.published_or_final_versio

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Title Simulation of a tubular linear magnetic gear using HTS bulks forfield modulationAuthor(s) Li, W; Chau, KT; Li, JCitationThe 2010 Applied Superconductivity Conference (ASC 2010),Washington, DC., 1-6 August 2010. In IEEE Transactions onApplied Superconductivity, 2011, v. 21 n. 3, pt. 2, p. 1167-1170Issued Date 2011URL http://hdl.handle.net/10722/139249Rights Creative Commons: Attribution 3.0 Hong Kong LicenseIEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 21, NO. 3, JUNE 2011 1167Simulation of a Tubular Linear Magnetic Gear UsingHTS Bulks for Field ModulationWenlong Li, K. T. Chau, and Jiangui LiAbstract—A tubular linear magnetic gear is proposed, whichnewly utilizes high temperature superconductor (HTS) bulksfor its field modulation. Compared to the conventional one, theproposed topology can significantly reduce the leakage flux, henceimproving its force transmission capacity. By using the magneticcircuit modeling, the analytical formulae of air-gap flux densityand thrust force are firstly derived. Then, the finite elementmethod (FEM) is employed to validate the performance of theproposed linear magnetic gear.Index Terms—FEM, field modulation, HTS bulk, linear mag-netic gear, magnetic circuit.I. INTRODUCTIONC OAXIAL magnetic gears are becoming attractive insome niche areas such as electric vehicle propulsion andwind power generation [1], [2], since they take some distinctadvantages over the mechanical ones, such as higher efficiency,higher reliability, lower acoustic noise, inherent overload pro-tection, and free from maintenance. Moreover, they are readilyintegrated into various electric machines, hence creating theso-called geared machines which can simultaneously offerhigh-frequency machine design and low-speed rotating motion.Furthermore, the concept of coaxial magnetic gears has beenextended to the linear morphology [3] so as to improve theforce capability of a linear motor.The key of coaxial magnetic gears is the ferromagnetic seg-ments which locate between the inner rotor and the outer rotor.When the sum of the outer-rotor PM pole-pair number andthe inner-rotor PM pole-pair number equals the number offerromagnetic segments , torque transmission between theinner rotor and the outer rotor can be achieved without anymechanical contacts [4], [5]. The linear magnetic gear, flat ortubular, has a similar structure as its rotational counterpart. Asshown in Fig. 1, the tubular linear magnetic gear consists ofthree parts: the low-speed mover, the high-speed mover and thestationary field-modulation ferromagnetic rings. Due to prin-ciple of field modulation, the two movers with different PMpole-pair numbers interact with one another to achieve forcetransmission. However, because of the finite permeance of fer-romagnetic rings, it suffers from severe flux leakage, which sig-nificantly deteriorates the whole performance.Manuscript received August 03, 2010; accepted September 17, 2010. Date ofpublication October 28, 2010; date of current version May 27, 2011. This workwas supported by a Grant (HKU 710710E) from the Research Grants Council,Hong Kong Special Administrative Region, China.The authors are with the Department of Electrical and Electronic Engineering,The University of Hong Kong, Hong Kong (e-mail: wlli@eee.hku.hk).Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TASC.2010.2080255Fig. 1. Structure of conventional tubular linear magnetic gear.Fig. 2. Model of conventional tubular linear magnetic gear in cylindrical polarcoordinates.The purpose of this paper is to newly utilize high temperaturesuperconducting (HTS) bulks [6], [7] to shield the flux leakagebetween the ferromagnetic rings for field modulation. Hence,the resulting HTS tubular linear magnetic gear can achieve highforce transmission capacity. Both analytical formulation and fi-nite element analysis will be given to validate the performanceof the proposed magnetic gear.II. MATHEMATICAL MODELINGIn order to derive the analytical model, some assumptions aremade: the permeability of the back irons of two movers and theferromagnetic rings is assumed to be infinite, the permeabilityof the PMs is assumed to be equal to that of air, and the mag-netic field only varies in the longitudinal direction. Due to theMeissner effect of HTS materials, the use of HTS bulks canforce all PM flux passing through the ferromagnetic rings, thussignificantly decreasing the flux leakage. So, the relative perme-ability of HTS bulks is also assumed to be zero.In this modeling, the one-dimensional (1-D) path is adoptedso that the flux goes straightly up and down and close at theinfinite distance [6]. Fig. 2 shows the model of the tubular1051-8223/$26.00 © 2010 IEEE1168 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 21, NO. 3, JUNE 2011Fig. 3. Magnetic circuit excited by PMs on high-speed mover.Fig. 4. Magnetic permeance waveform.linear magnetic gear in the two-dimensional (2-D) cylindricalpolar coordinates. Based on the aforementioned assumptions,the magnetic circuit can be considered as linear so that theresultant magnetic field can be treated as the superposition ofthe fields separately excited by PMs on the two movers. Fig. 3shows the equivalent magnetic circuit when excited by PMs onthe high-speed mover only. Thus, the equivalent total magneticpermeance in the longitudinal direction can be expressed as:(1)where , , ,and are the magnetic permeances in the lon-gitudinal direction of the PMs on the high-speed mover, outerair-gap, inner air-gap and PMs on the lsow-speed mover, respec-tively; is the magnetic permeance in the longitudinal di-rection of the field modulation segment area which is a functionof the axial position ; and , , , and arethe longitudinal lengths of PMs on the high-speed mover, outerair-gap, inner air-gap, PMs on the low-speed mover and ferro-magnetic ring, respectively. When the segment area is the ferro-magnetic ring, the corresponding is infinite. On the con-trary, when the segment area is air space, ;and when it is the HTS bulk, .Fig. 4 shows the magnetic permeance waveform of the equiv-alent magnetic circuit of a conventional linear magnetic gear. Itcan be resolved into a Fourier series:(2)where is the DC offset of the total equivalent magnetic per-meance, is the amplitude of the th harmonic magnetic per-meance, is the number of ferromagnetic rings, and is theactive length of the linear magnetic gear which is also equal tothe total length of the high-speed mover.The magnetomotive force (MMF) of PMs on the high-speedmover can also be expressed in a Fourier series:(3)where is the coercive force of PMs on the high-speedmover, is the magnet thickness, is the number ofPM pole-pairs on the high-speed mover, is the axial positionof PMs on the high-speed mover with respect to , and isthe corresponding initial position as shown in Fig. 2. Thus, themagnetic flux density excited by PMs on the high-speed movercan be calculated:(4)where has the same pole-pair number with that of PMs onthe high-speed mover, and has the same pole-pair numberwith that of PMs on the low-speed mover. Thus, a thrust forcecan be produced by and PMs on the low-speed mover.In order to obtain the expression of the thrust force, an equiv-alent current sheet is used to substitute the MMF of PMs on thelow-speed mover. The fundamental MMF component of PMson the low-speed mover is given by:(5)where , and are the coercive force, thickness andpole-pair number of PMs on the low-speed mover, and isits initial position as shown in Fig. 2. Thus, the correspondingequivalent current sheet is given by:(6)Consequently, by using Lorentz force law, the thrust forceexerted on the low-speed mover can be obtained by:(7)LI et al.: SIMULATION OF A TUBULAR LINEAR MAGNETIC GEAR USING HTS BULKS FOR FIELD MODULATION 1169where is the angular displacement between the centers ofPMs of the two movers, hence written as, and is the diameter of the low-speed mover.The maximum thrust force occurs at equal to zero:(8)By using the same derivation, the magnetic flux density dueto PMs on the low-speed mover can be expressed as:(9)Then, the thrust force exerted on the high-speed mover can beobtained as:(10)where is the diameter of the high-speed mover.From (8), it can be found that the developed thrust force isdirectly proportional to , namely the fundamental harmonicof the magnetic permeance of the equivalent magnetic circuit,which is governed by the field-modulation segment area. Asshown in Fig. 4, the longitudinal magnetic permeance waveformof a conventional linear magnetic gear is a symmetrical squarewave. By using Fourier analysis, the analytical formula canbe expressed as:(11)where ,, is the length of ferromagneticring in direction, and is the pole-pitch of ferromagneticring. When equals one half of , achieves the peakvalue which is .In this analytical model, the HTS bulks are considered to bean ideal superconductor, in which the magnetic field is totallyejected. Thus, the corresponding permeability is zero so that thevalue of becomes zero. Consequently, it yields ,which physically means that the developed thrust forces of bothmovers can be improved from to. This theoretical improvement is then verified by ap-plying finite element analysis to simulate the thrust forces of theproposed tubular linear magnetic gear with and without usingHTS bulks.III. FINITE ELEMENT ANALYSISThe finite element method (FEM) is employed for analysis.In order to take into account magnetic saturation during anal-ysis, the permeability of back irons and ferromagnetic rings isbased on practical data of iron materials. On the other hand, thepermeability of PMs is a constant based on the Nd-Fe-B mate-rial, while the permeability of HTS bulks is set to zero.The key dimensions of the proposed gear are compared withthe conventional one as listed in Table I. The field-modulationsegments of the proposed gear adopts the zebra-striped design,TABLE IMACHINE PARAMETERSFig. 5. Proposed tubular linear magnetic gear using HTS bulks.Fig. 6. Comparison of inner air-gap flux densities excited by PMs on high-speed mover. (a) Waveforms. (b) Spectra.namely the HTS bulks are inserted between the ferromagneticrings while they have the same pole-pitch. Fig. 5 shows theproposed gear, in which the HTS bulks are located in the sta-tionary rings, thus facilitating the cooling arrangement. Also, itcan achieve the thrust force density of 3.2 MN/m .Firstly, the inner air-gap flux densities of the two magneticgears are analysed when only PMs on the high-speed moverserve as field excitation whereas PMs on the low-speed mover1170 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 21, NO. 3, JUNE 2011Fig. 7. Comparison of outer air-gap flux densities excited by PMs on low-speedmover. (a) Waveforms. (b) Spectra.are set as air space. Fig. 6 shows the corresponding waveformsand harmonic spectra. It can be found that by using the HTSbulks, the amplitude of air-gap flux density can be improvedgreatly. By using spectrum analysis, it can also be found thatthe 6th and 15th harmonic components improve dramaticallyby using the HTS bulks. The largest asynchronous space har-monic which has 15 pole-pairs interacts with the 15 pole-pairnumber PMs on the low-speed mover, hence developing the de-sired steady thrust force.Secondly, the outer air-gap densities are analysed when onlyPMs on the low-speed mover serve as excitation whereas PMson the high-speed mover are set as air space. Fig. 7 shows theirwaveforms and spectra. It can be also found that the 6th and15th harmonic components improve greatly. The correspondinglargest asynchronous space harmonic which has 6 pole-pairsinteracts with the 6 pole-pair number PMs on the high-speedmover, hence developing the desired thrust force.Thirdly, when their low-speed movers travel at 1 m/s whiletheir high-speed movers are fixed, the static thrust force char-acteristics of the low-speed mover are analysed. As shown inFig. 8, the maximum thrust force of the proposed magnetic gearis improved by 1.8 times than that of the conventional one,which agrees with the theoretical 2.1 times as predicted by (8).Finally, the thrust force transmission capacity of the proposedmagnetic gear is obtained as shown in Fig. 9, which confirmsthat it can offer the force amplification by 2.5 times.Fig. 8. Comparison of static thrust force characteristic of low-speed mover.Fig. 9. Thrust force transmission capacity of proposed magnetic gear.IV. CONCLUSIONA new tubular linear magnetic gear using HTS bulks forfield modulation has been proposed. By using magnetic circuitmodeling, the corresponding air-gap flux density and devel-oped thrust force are analytically derived, which is essentialto provide physical insight for machine design. Also, by usingfinite element analysis, the use of HTS bulks to greatly improvethe thrust force density is verified.REFERENCES[1] K. T. Chau, D. Zhang, J. Z. Jiang, C. Liu, and Y. J. Zhang, “Design ofa magnetic-geared outer-rotor permanent-magnet brushless motor forelectric vehicles,” IEEE Transactions on Magnetics, vol. 43, no. 6, pp.2504–2506, 2007.[2] L. Jian, K. T. Chau, and J. Z. Jiang, “A magnetic-geared outer-rotor per-manent-magnet brushless machine for wind power generation,” IEEETransactions on Industry Applications, vol. 45, no. 3, pp. 954–962,2009.[3] K. Atallah, J. Wang, and D. Howe, “A high-performance linearmagnetic gear,” Journal of Applied Physics, vol. 97, no. 10, pp.10N516:1–10N516:3, 2005.[4] K. T. Chau, D. Zhang, J. Z. Jiang, and L. Jian, “Transient analysis ofcoaxial magnetic gears using finite element comodeling,” Journal ofApplied Physics, vol. 103, no. 7, pp. 07F101: 1–07F101: 3, 2008.[5] X. Liu, K. T. Chau, J. Z. Jiang, and C. Yu, “Design and analysis of inte-rior-magnet outer-rotor concentric magnetic gears,” Journal of AppliedPhysics, vol. 105, no. 7, pp. 1–3, 2009paper no., 07F101.[6] L. Jian, K. T. Chau, W. Li, and J. Li, “A novel coaxial magnetic gearusing bulk HTS for industrial applications,” IEEE Transactions on Ap-plied Superconductivity, vol. 20, no. 3, pp. 981–984, 2010.[7] G. Krabbes, G. Fuchs, W.-R. Canders, H. May, and R. Palka,High Temperature Superconductor Bulk Materials. Weinheim:Wiley-VCH Verlag GmbH & Co. KGaA, 2006.

Simulation of a tubular linear magnetic gear using HTS bulks for field modulation

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Simulation of a tubular linear magnetic gear using HTS bulks for field modulation

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