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外文翻译高性能磁齿轮的发展摘要：本文提出了一个高性能永磁齿轮的计算和测量结果。上述分析的永磁齿轮有5.5的传动比，并能够提供27 Nm的力矩。分析表明，由于它的弹簧扭转常数很小，因此需要特别重视安装了这种高性能永磁齿轮的系统。上述分析的齿轮也已经被应用在实际中，以验证、预测其效率。经测量，由于较大端齿轮传动引起的磁力齿轮的扭矩只有16 Nm。一项关于磁齿轮效率损失的系统研究也展示了为什么实际工作效率只有81。一大部分磁损耗起源于轴承，因为机械故障的存在，此轴承的备用轴承在此时是必要的。如果没有源于轴的少量磁泄漏，我们估计能得到高达96的效率。与传统的机械齿轮的比较表明，磁性齿轮具有更好的效率和单位体积较大扭矩。最后，可以得出结论，本文的研究结果可能有助于促进传统机械齿轮向磁性齿轮发展。关键词：有限元分析（FEA）、变速箱，高转矩密度，磁性齿轮。一、导言由于永久磁铁能产生磁通和磁力，虽然几个世纪过去了，许多人仍然着迷于永久磁铁。，在过去20年的复兴阶段，正是这些优点已经使得永久磁铁在很多实际中广泛的应用，包括在起重机，扬声器，接头领域，尤其是在永久磁铁电机方面。其中对永磁铁的复兴最常见于效率和转矩密度由于永磁铁的应用显著提高的小型机器的领域。在永久磁铁没有获取高度重视的一个领域是传动装置的领域，也就是说，磁力联轴器不被广泛用于传动装置。磁性联轴器基本上可以被视为以传动比为1：1磁力齿轮。相比标准电气机器有约10kN m/m的扭矩，装有高能量永久磁铁的磁耦有非常高的单位体积密度的扭矩，变化范围大约300400 kN 。研究磁性齿轮的基本思路，可以追溯到20世纪初。一个有趣的例子是1913年的美国专利申请1提出的的关于由两个突出的钢柱旋转轴组成的（电）磁齿轮的描述。两个磁性轴连接于固定磁极（电）之间。即使在专利方面齿轮技也术显得相当有效，但是这显然没有利用在商业领域的想法，而在专利方面的技术可能因此已被遗忘。另一个有趣的出版物提到有关磁性齿轮是从1940年，由美国专利Faus提交的。该专利描述了一种基于两个不同直径和不同数量的永久磁铁的磁盘的磁性齿轮，即，传动装置结构颇为相似于机械直齿圆柱齿轮轮齿的结构。在专利中，也对蜗轮与磁铁的变化进行了描述。在1940年，只有铁氧体磁铁是可用的，它每单位体积提供的力大约只有20世纪80年代的现代钕铁硼磁体的十分之一。当前市面上所推荐使用的齿轮传动装置仍然很落后，这是因为每个磁盘上只有一个磁体传输力矩，上述缺点都有可能在磁性齿轮的使用和研究方面使其受到使用限制，因此至今只有不到50本出版物被人所知。 在文献3 - 6中提到了磁性齿轮。 在文献3中，一个二维（2维）的计算方法已经发展了，比较于有限元分析（FEA）它具有非常好的认可度。如果把从文献3中所假设的齿轮得出结果推广到一个有（0.5毫米）气隙的齿轮，这个钕铁硼齿轮的单位体积扭矩大约是20 kN m/m左右。这样得出的结果并不是很可观，并且可以解释此齿轮为什么不能得到广泛应用。文献4 - 6中，通过有限元分析得出了齿轮的各项参数。一些有限元分析得出的结果也与已经被广泛接受的实验结果做了对比。磁蜗轮蜗杆和斜齿轮也已在文献78分析过了。再文献7中介绍了加有磁铁的实用蜗轮。磁蜗轮蜗杆有33：1的传动比，最大输出扭矩为11.5 N米。齿轮的体积没有描述，但是从这些数字和在文件中提出的主要数字可以得出它的实际体积量估计约为0.005立方米,，它所提供的单位扭矩是2.3kN m/m，也就是说磁齿轮的单位体积所受扭矩很小。 在文献8中提到，可以把实用齿轮修改为一个斜齿轮。这样可以使得磁性斜齿轮的扭矩比蜗轮蜗杆少五倍。因此，作者最终得出结论，此种变速箱齿轮可以应用到汽车上。上述所有文件提到的磁性齿轮都有比较低的永磁性，因此，单位体积提供的扭矩非常低。然而，9、10两份文件似乎提出了另一种磁齿轮，这种齿轮利用了更高性能的永磁铁，就像是行星变速箱上的齿轮一样，但相对文献1有了一些修改。在这两个文件，低磁阻的多级钢制部件传递了稳定的扭矩。这部分的想法来源于高速到多极低速永久磁极磁场整流的现象。另外，在两篇论文中齿轮的基本要素是相同的。在文献 9中，高速侧的永久转子也用于制造集成轴向永磁电机，并且扭矩传输是磁阻转矩的传动。在文献10中的传递扭矩是更传统的永久磁铁对准扭矩。 文献9中提出的齿轮，似乎有许多机械故障是由轴向布局和使用磁阻转矩引起的，由于这里需要一个非常小的空气间隙（40M）。在实际的情况下，传动是有机械摩擦的，因此，速度受到了限制。而同时装有电机和变速箱的先进样机所产生的转矩是相当可观的。如果安装的样机密度足够8000 kg/m ，那么文件中叙述的9 N m/kg就对用于72 kN m/m。 在文献10中提到，一个相对比较大的可用气体间隙（1毫米）是由永久磁铁的校准扭矩产生的。实际上于文献11中提到的相似，文献10中提到的齿轮箱的缺点是它只有理论上的单位体积的力矩。在文献中，对于活性材料单位体积的扭矩计算出来后超过100 kN m/m。所有的被引用的论文都说明由于能消除传统的机械变速箱的摩擦损失，磁变速箱有比较高的效率，但是这种说法既没有经过测量，也没有经过计算。因此，在文献缺少的是一种拥有高扭矩永磁性齿轮箱的实际例子，而这中齿轮箱具有与理论上计算上相等的扭矩能力。测量效率也是一个重要的参数，它是用来评估这个新型的有前途的技术，与传统的机械变速箱的优点。本文将着重提供上述缺失的材料。本文分为五节，第二节涉及一个总体的介绍和每体积密度高扭矩永磁齿轮的有限元分析。接着，在第三节，描述了实用齿轮箱的发展。在第四节中介绍了正在测试先进磁齿轮箱以及它于理论上预测的扭矩传输能力的比较。此后，在第五部分介绍了它于传统的商用变速箱的比较，在第五部分，最后，在第六节给出了结论。二、基本描述和有限元分析本文考虑的磁齿轮箱如图1。磁齿轮箱具有于文献10 在理论上所描述的相同磁极齿轮箱和定子的部分结构。这意味着，高速转子磁极对为Ph=4，低速转子磁极对为Pt=22，定子分类的数量是Ns=26。由以下公式得到的齿轮传动比为5.5 : 1。 公式：Ngear=Ph/（Ph-Ns）与文献10中的样机相比，此处提出的变速箱构造更加可行。不是像文献10中的在一个表面安装的类型，高速转子是一中常被谈到的类型。这样做，可以使用标准的矩形磁体，因而需要更少考虑所产生的的离心力和磁铁胶合。矩形永久磁铁也可用于低速转子侧弧段。事实上，整个结构通过使用许多相同的几何形状矩形的永久磁铁而变得先进了，这使每个低速转子横截面的上的磁铁实际上包括8块磁铁。在自由的有限元程序的帮助下我们对磁力齿轮显示图1进行了静态分析。所得的变速箱参数列于表一。应该指出，标准的矩形磁体的使用可使变速箱工作能力下降。 在图2，描绘了当达到最大档扭矩时，高速和低速转子被安置在同一位置时磁力线和感应线的分布情况。如果高速转子转速到达45（1/8转）而低速转子转速保持不变，那么变速箱就会产生最大档的负扭矩。由于低速和高速转子之间的相对转动可以得到可变的转矩，这就像一个传统的磁力联轴器的工作原理一样。在双方的耦合下扭矩相对于位移的关系呈现出一个半正弦的图像。在图2中值得注意的是轮辐磁铁在高速转子侧的磁力线。大约有1/4的磁能被泄漏于轴承附近了。这也表明永磁铁利用范围小的一个原因，同时暗示了在实际应用中较大端影响的效应是可能存在的。3764IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 3, MAY/JUNE 2005Development of a High-Performance Magnetic GearPeter Omand Rasmussen, Torben Ole Andersen, Frank T. Jrgensen, and Orla NielsenAbstractThis paper presents calculation and measurement re-sults of a high-performance permanent-magnetic gear. The ana-lyzedpermanent-magneticgearhasagearratioof5.5andisabletodeliver27N m.Theanalysishasshownthatspecialattentionneedsto be paid to the system where the gear is to be installed because ofa low natural torsion spring constant. The analyzed gear was alsoconstructedinpracticeinordertovalidatetheanalysisandpredictthe efficiency. The measured torque from the magnetic gear wasonly 16 N m reduced by the large end-effects. A systematic anal-ysis of the loss components in the magnetic gear is also performedin order to figure out why the efficiency for the actual constructionwas only 81%. A large magnetic loss component originated in thebearings, where an unplanned extra bearing was necessary due tomechanical problems. Without the losses of magnetic origin in thebearings and less end-effects caused by relatively short stack, animpressive efficiency estimated at 96% can be obtained. Compar-ison with classical mechanical gears has shown that the magneticgear has a better efficiency and a comparable torque per volumedensity. Finally, it is concluded that the results in this paper mayhelp to initiate a shift from mechanical gears to magnetic gears.IndexTermsEnd-effects,finite-elementanalysis(FEA),gearbox, high torque density, magnetic gear.I. INTRODUCTIONPERMANENT magnets have fascinated and inspired manypeople though the ages because a permanent magnet pro-ducesafluxandmagneticforce.Itisexactlythesecharacteristicsthat have made permanent magnets useful in many applicationslike lifting mechanisms, loud speakers, and couplings, not tomention electrical machines, which have been going thougha renaissance the last two decades through the use of perma-nent magnets. This renaissance is most often seen in smallermachines where both efficiency and torque density have beenimproved significantly by the use of permanent magnets.An area where permanent magnets have not garnered muchattention is gearing purposes, that is, if a magnetic coupling isnot considered gearing. Magnetic couplings can basically beconsidered as a magnetic gear with a gear ratio of 1:1. Mag-netic couplings have a very high torque per volume density in aPaper IPCSD-05-009, presented at the 2003 Industry Applications SocietyAnnual Meeting, Salt Lake City, UT, October 1216, and approved for publi-cation in the IEEE TRANSACTIONS ONINDUSTRYAPPLICATIONSby the ElectricMachines Committee of the IEEE Industry Applications Society. Manuscriptsubmitted for review March 12, 2004 and released for publication March 14,2005. This work was supported by Elfor, by Grundfos A/S, by Danfoss DrivesA/S, and by Sauer Danfoss A/S.P. O. Rasmussen, T. O. Andersen, and F. T. Jrgensen are with the Instituteof Energy Technology, Aalborg University, DK 9220 Aalborg East, Denmark(e-mail: poriet.auc.dk).O. Nielsen was with the Institute of Mechanical Engineering, Aalborg Uni-versity, DK 9220 Aalborg East, Denmark. He is now at Frederikshjvej 36, DK9230 Svenstrup J, Denmark (e-mail: ullaogorlamail.gvdnet.dk).Digital Object Identifier 10.1109/TIA.2005.847319range of 300400 kN m/m with high-energy permanent mag-nets, compared to standard electrical machines with only about10 kN m/m .The basic idea of magnetic gearing can be tracked downto the beginning of the 20th century. An interesting exampleis a U.S. Patent Application filled in 1913 1 describing(electro)magnetic gears consisting of two rotational shafts withsalient steel poles. The two shafts were magnetically connectedwith stationary (electro)magnetic poles. Even though thegearing topology in the patent seems quite effective, apparentlynothing was done to utilize the idea in commercial applications,and the topologies in the patent may have been forgotten.Another interesting publication concerning magnetic gearsis from 1940, where a U.S. Patent by Faus was filed 2. Thepatent describes a magnetic gear based on two disks with dif-ferent diameters and different numbers of permanent magnets,i.e., a magnetic gearing topology quite similar to mechanicalspur gears with different numbers of teeth on the two disks. Avariation of the worm gear with magnets is also described in thepatent. In 1940, only ferrite magnets were available, in whichthe force per unit volume is only about one-tenth of that whichcan be expectedfrom modern NdFeB magnets whichoriginatedin the 1980s. The proposed gearing topology was also weakin relation to the utilization of the permanent magnets becauseonly one magnet on each disk contributed to the transmission offorce. Both of the above disadvantages may have limited usageand research in the magnetic gearing area and to date less than50 publications are known. In 36, the magnetic spur gearis considered. In 3, a two-dimensional (2D) analytical cal-culation approach is developed and compared to finite-elementanalysis (FEA) with very good agreement. If the results fromthe hypothetical gear in 3 are extrapolated into a gear havinga small air gap (0.5 mm) the torque per volume of the two disksis around 20 kN m/m with sintered NdFeB. This is not too im-pressiveandexplainswhymagnetic“spur”gearingisnotwidelyused. In 46, parametric analysis is carried out with the helpof FEA. Some finite-element results are also compared to ex-periments where excellent agreement is seen.Magnetic worm and skew gears have also been analyzed inthe literature 7, 8. In 7, a practical worm gear with SMCOmagnets is presented. The gear has a gearing ratio of 33:1 andthemaximumoutputtorqueis11.5N m.Thevolumeofthegearwasnotstated,butfromthefiguresandmainnumberspresentedin the paper the active volume is estimated to roughly 0.005 m ,which gives a torque per volume of 2.3 kN m/m , i.e., a mag-netic gear with a very low torque per volume density. In 8, thepractical gear in 7 is modified to a skew gear. The torque fromthe magnetic skew gear was five times less than the worm gear,however, the authors somehow arrived at the wild conclusionthat the gear topology presented could be used in automotivetransmissions.0093-9994/$20.00 2005 IEEERASMUSSEN et al.: DEVELOPMENT OF A HIGH-PERFORMANCE MAGNETIC GEAR765The papers referred to above all deal with magnetic gearshaving a poor utilization of the permanent magnets and, thus,very low torque per volume density. However, two papers 9,10 seem to present magnetic gears with a much higher uti-lization of the permanent magnets with gearing topology sim-ilar to an epicyclic gearbox and also with some modificationsto the topologies in 1. In both papers, the torque is transmittedthoughastationarysegmentedsteelparthavingmanypoleswithlowmagneticreluctance.Theideawiththispartistocommutatethe magnetic field from the high-speed side with few perma-nent magnetic poles into the low-speed side with many poles.Other than the basic elements in the gearing topology in thetwo papers not much else seems to be equivalent. In 9, thehigh-speed-side permanent rotor is also used for an integratedaxial permanent-magnet motor and the torque transmission is areluctancetorque(PMtosteel)wherethetorquetransmissionin10 is the more traditional permanent-magnetalignment torque(PM to PM). The gear proposed in 9 seems to have numerousmechanical problems caused by the axial layout and the useof reluctance torque, which required a very small air gap (40m). In the practical prototype there was mechanical frictionand, thus, a limited speed. The torque density from the devel-oped prototype with both motor and gearbox was quite impres-sive. In the paper 9 N m/kg were stated which corresponds to72 kN m/m if the construction is assumed to be solid with amass density of 8000 kg/m . In 10, a relatively large air gap(1 mm) could be used caused by the permanent-magnet align-ment torque. The disadvantage with the gearbox proposed in10, which actually is similar to a topology in 11, was thatthe gearbox was only theoretically investigated with emphasison predicting torque per volume. In the paper, the torque pervolume was calculated to be more than 100 kN m/mfor theactivematerials.Allthecitedpapersstatemoreorlessthatmag-neticgearboxeshaveahighefficiencycausedbytheeliminationoffrictionallossesseenintraditionalmechanicalgearboxes,butneither measurements nor calculations were performed to vali-date this statement. Thus, missing in the literature is a practicalexample of a high-torque/density permanent-magnetic gearboxwith a measured torque capability equal to what was theoret-ically calculated. Efficiency measurement is also an importantparameterrequiredinordertoevaluatethisnewpromising tech-nology versus classical mechanical gearboxes. This paper willfocus on providing the above missing aspects.This paper is divided into five further sections, where Sec-tion II deals with a basic description and FEA of the perma-nent-magneticgearwithahightorquepervolumedensity.Next,in Section III, the development and construction of a practicalgearbox is described. In Section IV, the developed magneticgearbox is being tested and compared to the theoretically pre-dicted torque transmission capability. After this, a comparisonto classical commercial gearboxes is made in Section V and, fi-nally, a conclusion is given in Section VI.II. BASICDESCRIPTION ANDFEAThe considered magnetic gearbox in this paper is shown inFig. 1.The magnetic gearbox has the same pole and stator segmentstructure like the gearbox theoretically described in 10. ThisFig. 1.Cross section of the considered magnetic gear.means that the high-speed rotor haspole pairs, the low-speed rotor has, and the number of stator segments is. According to 10, the gearing ratiois given by(1)which yields a gear ratio of5.5:1.Thegearboxproposedhereinisconstructedinamorefeasiblemanner for prototyping when compared to the one in 10.The high-speed rotor is made as a spoke type instead of asurface-mountedtypeliketheone in10.Bydoingso,standardrectangular magnets can be used and less consideration needsto be given to the centrifugal forces and glue for the magnets.Rectangular permanent magnets are also used for the low-speedrotor side instead of arc segments. In fact, the whole structureis developed by using many rectangular permanent magnetswith the same geometry, whereby each spoke magnet on thelow-speed rotor actually consist of eight magnets in the crosssection.With help of the free FEA program FEMM 12 the magneticgear shown Fig. 1 is statically analyzed. The parameters for thegearbox are listed in Table I.It hasto be notedthatthe useof standard rectangularmagnetsresults in a gearbox which is not optimized.In Fig. 2, the flux lines and the induction are shown wherethe high- and low-speed rotors are placed in a position in rela-tion to each other where the maximum stall torque is achieved.If the high-speed rotor is rotated 45 (1/8 revolution) while thelow-speed rotor is kept fixed, then the gearbox is producingmaximum negative stall torque. The variable torque is obtainedby the relative position between the low- and high-speed rotorside like a classical magnetic coupling. Here, the torque hasa quasi-sinusoidal relationship to the relative displacement be-tween the two sides of the coupling. Worth noticing from Fig. 2are the flux lines from the spoke magnets on the high-speedrotor side. Approximately 1/4 of the magnet is used for leakagenear the shaft, which indicates both a poor utilization of the per-manent magnet and also that large end-effects may exist in theconstruction.766IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 3, MAY/JUNE 2005TABLE IPARAMETERS FOR THEANALYZEDMAGNETICGEARFig. 2.Calculated flux lines and induction for magnetic gear.In Fig. 3, the calculated torque versus relative positiondisplacement is shown. The curve is obtained by evaluatingMaxwells stress tensor in the air gap on the low-speed sidewhere the low-speed rotor is incrementally rotated while thehigh-speed side is kept fixed.FromFig.3it is possibletosee thatthemaximumstall torqueis 27 N m, which, with the use of the diameter and stack lengthin Table I, gives a torque per volume density of 92 kN m/m . Ifthehigh-speedrotorwasmadewithsurface-mountedpermanentmagnets with the same volume as the spoke magnets, the stalltorque is then calculated with the help of finite-element method(FEM) to be 32 N m.Fig. 3.Torque on low-speed side versus relative position displacement on thehigh-speed rotor side.If a radial magnetic coupling were built with the same low-speed rotor and a matching inner rotor, the stall torque can beestimated to 117 N m by the method given in 13. This corre-sponds to a reduction of approximately four which is caused bythe segments where approximately half of the available area islost. The other half seems to be lost by the fact that not all seg-ments and low-speed poles react with maximum torque and thatthere are double air gaps.The curve in Fig. 3 can be interpreted as an internal torsionspring in the magnetic gear. In the relatively linear part from20 to 20 N m a displacement of 25is seen, which trans-formed to the low-speed side will correspond to 0.08 rad. Thetorque difference of 40 N m is, thus, giving a static torsionalstiffness constant on 500 N m/rad. For a rough comparison, aminiature double-disk flexible coupling with medium torsionalstiffness and rated at 22 N m has a static torsional stiffness con-stant of 2500 N m/rad. Therefore, seen from the low-speed sidethe magnetic gear is about five times more flexible than a clas-sical mechanical coupling and more concern needs to be givento vibrations and resonances in the system where the magneticgear may be used. The torsion spring seen from the high-speedside is even worse because the static torsional stiffness con-stant has to be divided by the gearing ratio squared, which gives16.5 N m/rad.III. DEVELOPMENT OF THEFIRSTPROTOTYPEThe basic idea with the magnetic gear is to make a con-servative design for what is believed to be the first prototypeever of this type of magnetic gearbox. The stack length is keptsmall in order to have fewer bearing problems with this double-sided construction and to limit the consumption of the perma-nent magnets. In Fig. 4, a photograph of the constructed mag-netic gear is shown. The photograph shows the outer low-speedrotor together with the stator having the high-speed rotor inside.From Fig. 4, it can be noticed that the stator segments arefixed by a nonmagnetic and dielectric nylon housing. The alu-minum shaft of the low-speed rotor is mounted by adding eightholesto theoutside of thelow-speed rotor yoke.Thehigh-speedrotor shaft is also made of aluminum. The magnetic field insidethe shaft does not seem to vary much, so the eddy currents inthe high-speed shaft should be inconsequential. Extra bolts andRASMUSSEN et al.: DEVELOPMENT OF A HIGH-PERFORMANCE MAGNETIC GEAR767Fig. 4.Photograph of the constructed gear.nuts are also used to secure the high-speed rotor stack. Further,it is worth noting in the photograph that the stack is made bydoubling the amount of standard magnets.The outer diameter of the whole construction is 160 mm andthetotallengthis 90mm,whichyieldsatotaltorquepervolumeof only 15 kN m/m . This number can, of course, be optimizeddue to the fact that both the layouts of the magnetic and the me-chanical parts are conservative in this design. The stack lengthis very small which means that the end-shields play a domi-nant role in the total volume. The extra holes in the yoke onthe low-speed side also play a significant role. If, for instance,the low-speed side of the gearbox was integrated into a wheel,the total volume would have been much lower.IV. TEST ANDVALIDATIONIn order to see the torque capability of the constructed mag-netic gear, static torque measurement with the system describedin14wasdone.Thestatictorque-positioncurvewasmeasuredon both the high- and low-speed sides with the opposite sidelocked.Themeasuredtorque-positioncurvefromthelow-speedside can be seen in Fig. 5.FromFig.5,itisquiteobviousthatthetorquecalculatedfromthe 2-D FEM model was not archived. Only 60% of the 2-DFEM calculated stall torque is measured. The reason for thatmay be caused by large end-effects, which, for the spoke-typemagnets more or less also could be interpreted from the 2-DFEMresultsifthestackisshort,whichactuallyisthecase.Also,the salient stator segments may participate with large end-ef-fects. Large end-effects with salient poles are commonly knownfor switched reluctance machines.The measured torque-position curve on the high-speed rotorside is shown in Fig. 6 together with measured low-speed-sidetorque-position curve divided by the gearing ratio of 5.5. Thetwocurvesarequitesimilarexceptthatthemeasuredtorque-po-sition curve on the high-speed side has a smaller ripple com-ponent. These ripple components harmonic order is 26 timeshigher than the fundamental component seen in Fig. 6 and iscaused by the salient stator segments.Fig. 5.Measured torque on low-speed side.Fig. 6.Measured and ideal geared torque on high-speed side.Measurement of accurate efficiency is quite difficult whena large efficiency is expected, whereby it is attempted to finda simple but reasonably accurate method to generate some in-dications. It is quickly realized that the losses in the gearboxare mechanical and iron losses, which in classical electrical ma-chines are measured by a no-load test. At load, the iron lossesmay change a little, which is caused by another flux distribu-tion in the magnetic components, where the major magneticloss components are expected to be in the stator segments, inthe low-speed rotor yoke and in the permanent magnets. Eventhough there may be some inaccuracies the choice was made touse the simple no-load test with a dc motor acting as an actu-ator and torque transducer utilizing the machine constant andthe knowledge of dc motors no-load losses.During the initial dynamic test of the magnetic gear, it wasrealized that there were some mechanical bearing problems andan extra bearing was installed in the open end between the high-speed rotor and the nylon housing having the stator segments.With the extra bearing installed a new static torque characteri-zation was performed. The new measured static torque-position768IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 3, MAY/JUNE 2005Fig. 7.Measured magnetic gear losses.Fig. 8.Extraction of different loss components in the magnetic gear.curves did not show any visible deviation from the curves inFigs. 5 and 6.Withthenewbearinginstalled,theno-loadlossesforthegearwere measured against speed (see Fig. 7).At a nominal speed of 1500 r/min, the losses were predictedto be 104 W, which seems enormous due to the fact that only1.9 kg is used in active materials, i.e., an indicated loss of morethan 54 W/kg if the bearing losses were ignored.Duetothehugeamountoflosses,themagneticgearwasmoresystematically analyzed in order to separate the loss compo-nents. The gear was separated into the two parts shown in Fig. 4and the losses as a function of speed were measured on bothsides. A test without the stator segments was also performed toidentify the influences from these and “frictional” losses fromthe high-speed side. In Fig. 8, the results are shown for the threetests together with the difference between the two tests with andwithout stator segments.FromFig.8isitquiteclearthatthehigh-speedsidehasexten-sivelosses.Whenthesegmentsareremoved,thelossesare80Wat1500r/min,wherethelossesonthelowsideatthesamespeedare only 12 W. The high-speed side has three bearings while thelow-speed side has only two, which are equal to two of the threeFig. 9.Estimated magnetic gear losses without “magnetic” bearing losses.bearingsonthehigh-speedside.Therefore,iflosseswerepurelymechanical bearing losses, the third bearing should have a me-chanical loss of 68 W, which is impossible. The big differenceseems to be caused by the end-fields from the spoke-magnetrotor which gives rise to extra friction and iron losses mainlyin the extra installed bearing. The extra bearing was necessaryin the construction because of mechanical problems. The influ-ence of the stator segments also seems significantly higher thanexpected. The stator segments consist of 0.21 kg grain-orientedsteel with 0.89 W/kg at 50 Hz and 1 T. Even though the fun-damental frequency is 100 Hz at 1500 r/min, is it difficult tounderstand that the losses in the segments are 18 W. Some maybe explained by the fact that the flux may cross the laminationplane and give higher eddy-current losses.In order to have an idea of the magnetic gear losses withoutthe unwanted “magnetic” bearing losses the measured losses onthe high-speed side without the segments plus the low-speedside losses (real bearing losses measured on low side) can besubtracted from the total measured losses in Fig. 7. This givesthe estimated result in Fig. 9.The efficiency of the magnetic gear can be estimated as if itdidnothavetheproblemswiththemagneticfieldinthebearingsand was able to deliver the expected torque on 27 N m withoutincreasing the iron losses by a required lower leakage field. At1500 r/min and with the help of Fig. 9, the estimated efficiencyis calculated to be 96%.From the experience gained developing the prototype, it isquite clear that more care must be taken if a new magnetic gearis to be constructed to render higher efficiency. A longer stacklength is interesting in order to reduce the end-effects and alsoa surface-mounted high-speed rotor seems more preferable. Ifpossible, the stator segments have to be stacked in the axiallength with a stiffer material than nylon to secure them. Morecare has to given to the bearing layout in order to avoid cou-plings to the magnetic field. Bearing support in both ends forboth the high- and low-speed rotor may solve some of the me-chanical problems.RASMUSSEN et al.: DEVELOPMENT OF A HIGH-PERFORMANCE MAGNETIC GEAR769TABLE IICOMPARISION OF THEMAGNETICGEARWITHCOMMERCIALMECHANICALGEARS. (a) 2-D FEM COMPUTATION. (b) MEASUREDFROM THECONSTRUCTEDMAGNETICGEAR. (c) ESTIMATEDEFFICIENCY FOR A“PROBLEM-FREE” CONSTRUCTIONV. COMPARISONWITHMECHANICALGEARBOXESThe magnetic gear seems to have the following advantageswhen compared to classical mechanical gears:no mechanical fatigue;no lubrication;overload protected;no mechanical contact losses;no mechanical contact acoustic noise;potential for very high efficiency (only a little core lossand bearing loss);high torque per volume ratio (ten times standard motors).Even though the general advantages above give the magneticgear a plus, it is still interesting to compare the practical proto-typewithsomestandardgearboxeswithsimilarmajorratingsinthe form of torque and gearing ratio. In Table II four commer-cial mechanical gearboxes are compared to the prototype wherethe practical problems are more or less ignored. The compar-ison parameters are technical performance parameters in formof efficiency and volume (weight). Price also could have beenan interesting parameter, but the magnetic gearing technologyis too early in the development stage to give a good estimate.FromTableII,itisseenthatthemagneticgearwithonlyactiveparts is favorable when the efficiency and volume are comparedto all the mechanical gears. Also, the total assembled magneticgear has advantages even when the assembly is far fromoptimized. The efficiency is comparable to a single-stage spurgear and, yet, the assembly occupies less than half the volume.The estimated efficiency of the total assembled magnetic gear ismuchhigherthantherestofthemechanicalgears,butthevolumeseems higher. However, it is believed that an optimization maymake comparable volumes. An aspect which is favorable forthe magnetic gear is the compared torque rating. The stalltorque is used as the comparison parameter, which, in practice,never will be the case because of safety. A safety factor of70% will probably be a reasonable choice.VI. CONCLUSIONA high torque per volume density magnetic gear was de-scribedandanalyzedwiththehelpof2-DFEA.Thecalculationshave shown that the magnetic gear with a gearing ratio of5.5 and a stall torque of 27 N m has a torque per volumedensity on 92 kN m/m . In order to validate the 2-D FEA,a practical gear, which is believed to be the first of its kind,was constructed. Tests with the gear have shown that the stalltorque is only 16 N m. The reduction seems to be caused bylarge end-effects in the short practical construction. No-loadtests were performed on the constructed magnetic gear in orderto predict efficiency. For the actual construction the efficiencywas only 81%. The low efficiency was mainly caused bylosses of magnetic origin in an extra installed bearing, whichwas necessary due to mechanical problems. If the constructionwere improved with lower end-fields and no losses of magneticorigin in the bearings, the efficiency is expected to be 96%.Themagneticgearboxwasalsocomparedtovariousclassicalmechanical gears. Here, it is seen that the magnetic gear has asignificantly improved efficiency with a comparable or smallervolume than the classical gears.In the future, more care must be given to the mechanicalconstruction. Single-sided bearing supports may not be veryadvantageous if the gear box has a long stack. Further, it maybe interesting to explore the gear with other gearing ratiosand fully optimize its construction. However, indications of apossible shift from mechanical gears to magnetic gears seemeven more realistic with the results of this paper.ACKNOWLEDGMENTThe authors will like to thank B. Kristensen for making theprototype.REFERENCES1 A. H. Neuland, “Apparatus for transmitting power,” U.S. Patent1171351, Feb. 1916.2 H. T. Faus, “Magnet gearing,” U.S. Patent 2243555, May 27, 1941.3 E. P. Furlani, “A two-dimensional analysis for the coupling of magneticgears,” IEEE Trans. Magn., vol. 33, no. 3, pp. 23172321, May 1997.4 Y. D. Yao, D. R. Huang, C. M. Lee, S. J. Wang, D. Y. Chiang, and T. F.Ying, “Magnetic coupljng studies between radialmagnetic gears,”IEEETrans. Magn., vol. 33, no. 5, pp. 42364238, Sep. 1997.5 Y. D. Yao, D. R. Huang, C. C. Hsieh, D. Y. Chiang, and S. J. Wang,“Simulation study of the magnetic coupling between radial magneticgears,” IEEE Trans. Magn., vol. 33, no. 2, pp. 22032206, Mar