numerical analysis and evaluation of electromagnetic

156156156156156 QR of RTRI, Vol. 51, No. 3, Aug. 2010

PAPERPAPERPAPERPAPERPAPER

Numerical Analysis and Evaluation of Electromagnetic Forces in SuperconductingNumerical Analysis and Evaluation of Electromagnetic Forces in SuperconductingNumerical Analysis and Evaluation of Electromagnetic Forces in SuperconductingNumerical Analysis and Evaluation of Electromagnetic Forces in SuperconductingNumerical Analysis and Evaluation of Electromagnetic Forces in SuperconductingMagnetic Bearings and a Non-contact Permanent Magnetic ClutchMagnetic Bearings and a Non-contact Permanent Magnetic ClutchMagnetic Bearings and a Non-contact Permanent Magnetic ClutchMagnetic Bearings and a Non-contact Permanent Magnetic ClutchMagnetic Bearings and a Non-contact Permanent Magnetic Clutch

1. Introduction1. Introduction1. Introduction1. Introduction1. Introduction

We are currently developing a superconducting mag-netic bearing (SMB) and a non-contact permanent mag-netic clutch (PMC) applicable to flywheel energy-storagesystems for railways. The aim of this study was to im-prove driving efficiency by reducing frictional loss and tosolve maintenance-related problems for the bearing partsof flywheel energy-storage systems. The SMB consists ofa superconducting rotor and a stator to obtain a high loadcapacity [1]. A high-Tc bulk superconductor (HTS bulk)and a superconducting coil are adapted to the rotor andthe stator of the bearing. The SMB required the refrig-eration in the cryogenic temperature. On the other handheat generation in a motor/generator becomes large heatload in cryogenic temperature. For the reason of separa-tion of the heat of a motor/generator from refrigeratorheat load, a flywheel and a motor/generator are arrangedinside and outside the cryostat, respectively. The PMC isan element part that transfers the flywheel’s stored en-ergy to the motor/generator through the cryostat in a non-contact way. In this paper, we report on the basic study ofa magnetic bearing involving the coupling of supercon-ductors and the PMC. Electromagnetic forces generatedby the SMB and the PMC were calculated using 3D nu-merical analysis. Then, we compared the analytical re-sults with experimental results and confirmed the valid-ity of the analysis. Finally, we designed an enhanced

model representing the SMB and the PMC and their prop-erties according to the analysis.

2. 3D numerical analysis - a method of analyzing2. 3D numerical analysis - a method of analyzing2. 3D numerical analysis - a method of analyzing2. 3D numerical analysis - a method of analyzing2. 3D numerical analysis - a method of analyzingelectromagnetic forceelectromagnetic forceelectromagnetic forceelectromagnetic forceelectromagnetic force

We used the ELF/MAGIC 3D non-linear static mag-netic field solver for the electromagnetic force analysis.This is a software solver that adopts the integration ele-ment method to solve Maxwell's integral equations. It usesa network approach combining the magnetic momentmethod, the surface magnetic charge method and the sur-face current method for improved accuracy. The integralelement method is advantageous in terms of mesh gen-eration. The mesh partition is only necessary in mate-rial. Space meshes, and boundary conditions are not re-quired.

3. 3D numerical analysis of SMB and evaluation of SMB3. 3D numerical analysis of SMB and evaluation of SMB3. 3D numerical analysis of SMB and evaluation of SMB3. 3D numerical analysis of SMB and evaluation of SMB3. 3D numerical analysis of SMB and evaluation of SMBpropertiespropertiespropertiespropertiesproperties

3.1 SMB basic properties test (test SMB)3.1 SMB basic properties test (test SMB)3.1 SMB basic properties test (test SMB)3.1 SMB basic properties test (test SMB)3.1 SMB basic properties test (test SMB)

In this study, we developed a superconducting bear-ing (referred to as the test SMB) to allow examination ofthe load capacity and confirm practicality. In the first step

Hiroshi SEINO, Ph. D.Hiroshi SEINO, Ph. D.Hiroshi SEINO, Ph. D.Hiroshi SEINO, Ph. D.Hiroshi SEINO, Ph. D.Senior Researcher,

Hitoshi HASEGAHitoshi HASEGAHitoshi HASEGAHitoshi HASEGAHitoshi HASEGAWWWWWA, Ph. D.A, Ph. D.A, Ph. D.A, Ph. D.A, Ph. D.Senior Researcher,

Cryogenic systems, Maglev Systems Technology Division

Masashi IKEDAMasashi IKEDAMasashi IKEDAMasashi IKEDAMasashi IKEDADepartment of Materials Science and Engineering,

Shibaura Institute of Technology

Ken NAGASHIMA, Ph. D.Ken NAGASHIMA, Ph. D.Ken NAGASHIMA, Ph. D.Ken NAGASHIMA, Ph. D.Ken NAGASHIMA, Ph. D.Senior Researcher, Laboratory Head,

Cryogenic systems,Maglev Systems Technology Division

Masato MURAKAMI, Ph. D.Masato MURAKAMI, Ph. D.Masato MURAKAMI, Ph. D.Masato MURAKAMI, Ph. D.Masato MURAKAMI, Ph. D.Professor,

Department of Materials Science and Engineering,Shibaura Institute of Technology

We are currently developing a superconducting magnetic bearing and a non-contactpermanent magnetic clutch applicable to flywheel energy storage systems for railways.This paper reports on electromagnetic force analysis concerning these developments. Inthe analysis, the electromagnetic force generated in superconducting magnetic bearingsand non-contact permanent magnetic clutches was estimated based on the magnetic fielddistribution ascertained through 3D numerical analysis. The validity of this analysis wasthen evaluated by comparing the results with experimental outcomes, and the two werefound to be consistent. It was therefore confirmed that the analysis was an effective way ofestimating the electromagnetic force of electromagnetic equipment containing the bulksuperconductor for use in application design.

KeywordsKeywordsKeywordsKeywordsKeywords: energy storage system, flywheel, magnetic bearing, superconducting magnet,bulk superconductor

157157157157157QR of RTRI, Vol. 51, No. 3, Aug. 2010

of the study, we selected a thrust rolling bearing for ap-plication. A liquid-nitrogen-cooled HTS bulk was adoptedas a rotor, and a superconducting coil was adopted as astator for the superconducting magnetic bearing. We veri-fied the load capacity of the SMB up to 10 kN in a staticload test. A rotation test with a thrust load of approxi-mately 5 kN added was then performed at a maximumrotation speed of 3,000 rpm [2]. We continued develop-ment aimed at increasing the thrust load to 20 kN, whichis considered a practicable load level. The 3D numericalelectromagnetic force analysis concerning the SMB isexplained below.

Figure 1 shows a schematic diagram of the test SMB.The dimensions of the cryostat are approximately 600 mm(outside diameter) and 500 mm (height). The rated mag-netomotive force is 1,032 kA, and the magnet consists oftwo superconducting coils vertically arranged in series.In order to generate a high magnetic force field, two su-perconducting coils are energized reversing the polarityto generate a cusp field. Consequently, a zero magneticfield space is generated at the vertical center of the twocoils; if the position is vertically shifted slightly from thecenter, the magnetic force field reaches its maximum. Amagnetic force field of 140 T2/m or more is produced inthis area with a magnetic field of under 2 T. The HTSbulks are set in this location. The gradient of the mag-netic field at a specific position of the HTS bulk is ap-proximately three times larger than that generated bythe same coil with single use. We adopted a dry-typemagnet and used Ni-Ti superconducting wire, then intro-duced a GM cryocooler for direct cooling. The diameter ofthe room-temperature bore was 120 mm, and a rotatableDewar with the HTS bulks installed was inserted into it.The analytical model and the element type used are asshown in Fig. 2 and Table 1, respectively. We analyzedthe electromagnetic properties of the SMB for two kindsof HTS bulk − one a disk shape and the other a ring shape.Table 2 shows the shape properties of the models.

A plane element that defined the magnetic field atthe center position of the element was applied to simula-tion of the HTS bulk. We calculated the magnetic fieldusing a current loop on the plane edge. The outside of thesimulated HTS bulk was enclosed by Maxwell’s stressevaluation planes. The electromagnetic force caused bythe shield current of the HTS bulk surface was evaluatedusing these stress evaluation planes.

Figure 3 shows an example of the analysis results formagnetic field distribution, and these outcomes were com-pared. The left-side figure is for an energizing coil only,and the center figure is for the HTS bulk in the energiz-ing coil. This bulk was defined with perfect diamagne-tism. The right-side figure is for the HTS bulk with asimulated 1 T magnetic flux passing. These figures showthe analytical results for magnetic flux distribution in aring-shaped HTS bulk. A high magnetic flux area wasvisible in the inside-diameter edge on the upper and lowerplates of the simulated bulk due to micro-pinholes. Thepinholes were installed for the sake of calculation con-vergence in the enclosed loop current elements. The mag-netic field distribution confirmed that perfect diamagne-tism or controlled magnetic flux (1 T) was maintained atinside the HTS bulk.

Fig. 1 SMB for basic properties test (test SMB)Fig. 1 SMB for basic properties test (test SMB)Fig. 1 SMB for basic properties test (test SMB)Fig. 1 SMB for basic properties test (test SMB)Fig. 1 SMB for basic properties test (test SMB)

TTTTTable able able able able 22222 Model shape propertiesModel shape propertiesModel shape propertiesModel shape propertiesModel shape properties

Fig. 2 Analytical model of the test SMBFig. 2 Analytical model of the test SMBFig. 2 Analytical model of the test SMBFig. 2 Analytical model of the test SMBFig. 2 Analytical model of the test SMB

TTTTTable 1 able 1 able 1 able 1 able 1 Element type for SMB simulationElement type for SMB simulationElement type for SMB simulationElement type for SMB simulationElement type for SMB simulation

Magnetic fieldevaluation element

Coil:3D current element

HTS bulk

z

yx

Coil

HTS bulk:Loop current

surface element

(inside)

(Outside)Maxwell s stress

evaluation surfaceelement

z

x

y

Simulationparts Type Functions

Superconductingcoil

Solid(3D) Current

Plane(2D)

　

　

HTS bulk Loop curent surface

Stress Maxwall's stress evaluationsurface

Magnetic field Magnetic field evaluationsurface

Shimulationmodel

　

　

Stress evaluation surface Stress evaluation surfaceOuter

diameter(mm)

Innerdiameter

(mm)

Thickness(mm)

Outerdiameter

(mm)

Innerdiameter

(mm)

Thickness(mm)

Disk chape 60 - 40 66 - 44Ring shape 60 20 40 66 18 44

Figure 4 shows a comparison between the analyticaland static load test results. For the ring-shaped HTS bulk,a difference between the analytical and experimental re-sults is seen, for a superconducting coil output exceeding70%. On the other hand, the analytical and experimentalresults correspond satisfactorily for the disk-shaped HTSbulk. It can be presumed that the increase in the rate oflevitation force in stronger magnetic fields decreases inhigh magnetic field conditions due to magnetic flux pen-

Rotatable Dewar vessel

HTS bulks

Rotor of bearingSuperconducting

coils (LTS winding)

Superconductingmagnet

SC-magnet

Stator ofbearing


Fig. 6 Illustration of the small-scale pilot machineFig. 6 Illustration of the small-scale pilot machineFig. 6 Illustration of the small-scale pilot machineFig. 6 Illustration of the small-scale pilot machineFig. 6 Illustration of the small-scale pilot machine

etration. In the case of the disk-shaped HTS bulk, it ispresumed that a nearly state of the perfect diamagne-tism was maintained at a superconducting coil output ofless than 60% (maximum magnetic flux under 2 T at theHTS bulk position).

We identified the amounts of magnetic flux penetra-tion with levitation forces in the experimental resultsthrough numerical analysis. Figure 5 shows the simulatedlevitation force when magnetic flux penetration occurredin a high magnetic field. The magnetic flux penetration

Fig. 3 Analysis results for magnetic field distributionFig. 3 Analysis results for magnetic field distributionFig. 3 Analysis results for magnetic field distributionFig. 3 Analysis results for magnetic field distributionFig. 3 Analysis results for magnetic field distribution

Upper coil

HTS bulk

Only coil enegizing Perfect diamagnetism Simulated flux passing (1T)

Coil with HTS bulk

Lower coil

Fig. 4 Analysis results for magnetic field distributionFig. 4 Analysis results for magnetic field distributionFig. 4 Analysis results for magnetic field distributionFig. 4 Analysis results for magnetic field distributionFig. 4 Analysis results for magnetic field distribution

Fig. 5 Simulation of magnetic penetrationFig. 5 Simulation of magnetic penetrationFig. 5 Simulation of magnetic penetrationFig. 5 Simulation of magnetic penetrationFig. 5 Simulation of magnetic penetration

starts gradually from nearly 70% of the superconductingcoil output. It can be thought that magnetic flux penetra-tion of about 0.5 T occurred with a superconducting coiloutput of 100%.

3.2 Design of an SMB consisting of HTS coil and bulks3.2 Design of an SMB consisting of HTS coil and bulks3.2 Design of an SMB consisting of HTS coil and bulks3.2 Design of an SMB consisting of HTS coil and bulks3.2 Design of an SMB consisting of HTS coil and bulks

The second stage of the development was aimed atsupporting the flywheel magnetically through non-con-tact operation. To this end, one SMB coupling was madeto support thrust and radial loads simultaneously. Fig-ure 6 shows an illustration of a small-scale pilot machine.In the plan, a flywheel is supported magnetically by twoSMB couplings inside a cryostat. The SMB consists of HTSbulks and a high-Tc tape winding coil (i.e., an HTS coil).This new combination is referred to as an HTS-SMB. Ki-netic energy of the flywheel is translated from the insideto the outside through the cryostat using the PMC. Theflywheel mass was approximately 50 kg. The electromag-netic properties of the HTS-SMB to be applied to the pi-lot machine were designed using 3D numerical analysis.

As stable levitation in the SMB is difficult to achievewith a single-coil stator, a double-coil magnet that gener-ates a cusp field was adopted to provide stable levitationsimilar to that of the test SMB. In this case, the levita-tion force was approximately 2/3 that of the single coil,even using the double-coil winding. Accordingly, highercosts will inevitably be involved in making stator coilswhen the cusp magnetic field is adopted. Comparison ofthe HTS bulk compared with the HTS coil in terms ofproduction costs shows that the coil is more expensive.The HTS-SMB, which consists of a single HTS coil andHTS bulks to provide stable levitation, was found to beapplicable using 3D numerical analysis. The key to theanalysis is the combination of differently shaped HTSbulks.

Lev

itati

on f

orce

(k

N)

Output of superconducting magnet (%)

Fp=0TFp=0.1TFp=0.2TFp=0.3TFp=0.5T

Analytical value

Experimantal value

Lev

ita

tion

for

ce (

kN

)

Output of superconducting magnet (%)

Ring shape

Disk shape

Ring shape

Disk shape

Analysis value

Experimentalvalue

Refrigerator

Motor

Cryostat

PMC

SMBFlywheelSuperconductingmagnetic bearing

Non-contactpermanent

magnetic clutch


stable levitation force. When the relative displacement isover -18 mm and less than 18 mm, a stable levitation forcecan be achieved with an unstable radial force. Stablemagnetic levitation cannot therefore be achieved when asingle coil is used for a magnetic field source. On the otherhand, it is possible to achieve stable levitation using acombination of HTS bulks. A radial stabilization HTS bulkis located in the inner bore of the coil to generate a radialrestoring force, and a levitation HTS bulk is located onthe upper side of the coil. The levitation HTS bulk is setto be larger than the radial stabilization HTS bulk in or-der to prevent unstable levitation force generated by thelatter. The electromagnetic force properties were con-firmed using 3D numerical analysis.

Figure 9 shows the model of the HTS superconduct-ing bearing (HTS-SMB). The relationships governing therelative displacement between the superconducting coiland HTS bulks and the generated electromagnetic forcein the axial and radial directions are as shown in Fig. 10.These results were obtained by 3D numerical analysis;they indicate that the levitation force decreased in posi-tive axial displacement and increased in negative axialdisplacement. A restoring force to adjust the position was

z

xy

Simulated HTS bulk:Loop current surface element

Stress evaluation surfaceelement (Maxwell s)

HTS coil:Current element

Fig. 7 3D analytical model of the HTS-SMBFig. 7 3D analytical model of the HTS-SMBFig. 7 3D analytical model of the HTS-SMBFig. 7 3D analytical model of the HTS-SMBFig. 7 3D analytical model of the HTS-SMB

Fig. 8 Analysis results for HTS bulk position versusFig. 8 Analysis results for HTS bulk position versusFig. 8 Analysis results for HTS bulk position versusFig. 8 Analysis results for HTS bulk position versusFig. 8 Analysis results for HTS bulk position versuslevitation forcelevitation forcelevitation forcelevitation forcelevitation force

Ra

dia

l re

stor

ing f

orce

Fr

(N)

Lev

ita

tion

for

ce F

z (N

)

Relative vertical displacement between HTS bulk and coil (mm)

Fz Fr

Stable levitation

Unstable levitation gUnstable guidance

uidanceStable guidance

Fig. 9 Analytical model of the HTS-SMB for the small-Fig. 9 Analytical model of the HTS-SMB for the small-Fig. 9 Analytical model of the HTS-SMB for the small-Fig. 9 Analytical model of the HTS-SMB for the small-Fig. 9 Analytical model of the HTS-SMB for the small-scale pilot machinescale pilot machinescale pilot machinescale pilot machinescale pilot machine

Rotor side Stator sideHTS bulk HTS coil

ShapeOuter

diameter(mm)

Thickness(mm) Amount

Outerdiameter

(mm)

Innerdiameter

(mm)

Thickness(mm)

Magnetomotive

force (kA)

Disk　

　

　

　56 270 30 314

60 20 146 15 2

We defined the HTS bulk for the disk shape. The di-ameter of the HTS bulk are 60 mm and 46 mm, respec-tively, and thickness of them are 20 mm and 15 mm. Themagneto motive force of the coil was defined as 314 kA.Figure 7 shows an example model of the 3D analysis. Therelationship between the position of the HTS bulk andthe electromagnetic force generated when it moves verti-cally (in the axial direction) is as shown in Fig. 8. TheHTS bulk is defined with perfect diamagnetism, and a 1mm displacement in the radial direction was given in thebulk to allow evaluation of the radial restitute force.

In Figure 8, the horizontal axis shows the relativeaxial displacement between the HTS bulk and the super-conducting coil in the axial direction. Relative position =0 means that the vertical center position of the HTS bulkcorresponds to the vertical center of the coil. When therelative position has a positive number, the HTS bulk islocated higher than the coil, and a negative number indi-cates a lower location. The axial-direction electromagneticforce becomes a levitation force for positive numbers (z >0 mm). When the relative displacement is less than 18 (z< 18 mm), the levitation force decreases in line with thereduced relative displacement. Conversely, the levitationforce increases in line with the relative displacement re-duction when the relative displacement is greater than18 mm (z > 18 mm). A stable levitation force will beachieved in this relative displacement area. The electro-magnetic force in the radial direction reaches its maxi-mum for a relative axial displacement of around 0 mm.However, the radial electromagnetic force will be unstablewhen the relative displacement is over 20 mm and under-20 mm. As the relative axial displacement exceeds thesevalues, a stable radial force can be achieved with an un-

Fig. 10 Relationship between HTS bulk displacement andFig. 10 Relationship between HTS bulk displacement andFig. 10 Relationship between HTS bulk displacement andFig. 10 Relationship between HTS bulk displacement andFig. 10 Relationship between HTS bulk displacement andelectromagnetic forceelectromagnetic forceelectromagnetic forceelectromagnetic forceelectromagnetic force

-500

-400

-300

-200

-100

0

100

200

300

400

500

0

1000

2000

3000

4000

5000

6000

Radia

l re

stori

ng f

orc

e F

r (N

)

Levit

ati

on f

orc

e F

z (

N)

Displacement from standard position (mm)

Levitation force: Fz

Radial force: Fr


generated when the levitation height changed. In the ra-dial direction, a restoring force to adjust the radial posi-tion was generated when there was radial movement. Wecan therefore conclude that it is possible to achieve stablelevitation in this way.

A flywheel was supported by two sets of HTS-SMBand arranged with an upper and lower flywheel forma-tion as shown in Fig. 6. The flywheel was levitated at aheight balancing the flywheel mass. Twice the axis sup-port rigidity can be expected from this setup.

4. Analysis and evaluation of permanent magnetic4. Analysis and evaluation of permanent magnetic4. Analysis and evaluation of permanent magnetic4. Analysis and evaluation of permanent magnetic4. Analysis and evaluation of permanent magneticclutch (PMC) propertiesclutch (PMC) propertiesclutch (PMC) propertiesclutch (PMC) propertiesclutch (PMC) properties

In this chapter, we report on the results of 3D nu-merical electromagnetic force analysis and examinationin relation to a non-contact permanent magnetic clutch(PMC).

The PMC is an important element that transfers theflywheel’s stored energy to the motor/generator throughthe cryostat in a non-contact way. A permanent magnetis used to transmit the driving torque without contact.We estimated the characteristics of the magnetic clutchthrough 3D numerical electromagnetic force analysis. Inaddition, we evaluated the analytical results by compar-ing them with experimental results. Figures 11 and 12show the experimental clutch and analytical models, re-spectively. In the analysis, we examined a simulated ex-perimental model and a Halbach array model that con-centrated the flux of magnetic induction. A Halbach ar-ray is a special arrangement of permanent magnets thataugments the magnetic field on one side of the array.Additionally, magnetic field on the other side of the arrayis almost cancelled. Each model is composed of eight poles.In the simulated experimental model, permanent mag-nets are magnetized in the horizontal plane. In the

Halbach array model, permanent magnets magnetized inthe vertical direction are intermediately added betweenthe horizontally magnetized magnets. The permanentmagnets in both models are approximately the same sizeand are arranged at the same radius.

The residual flux density, magnetic coercive force andmaximum energy product of the permanent magnets weredefined as 12.85 kG, 12.217 Oe and 39.34 MGOe, respec-tively. Figure 13 shows example analytical results formagnetic field distribution. A comparison of the trans-mission torque between the analytical and experimental

Fig. 13 Analytical results for magnetic field distribution inFig. 13 Analytical results for magnetic field distribution inFig. 13 Analytical results for magnetic field distribution inFig. 13 Analytical results for magnetic field distribution inFig. 13 Analytical results for magnetic field distribution inthe PMCthe PMCthe PMCthe PMCthe PMC

Fig. 14 Comparison of transmission torquesFig. 14 Comparison of transmission torquesFig. 14 Comparison of transmission torquesFig. 14 Comparison of transmission torquesFig. 14 Comparison of transmission torquesFig. 12 Analytical model of two kinds of PMCFig. 12 Analytical model of two kinds of PMCFig. 12 Analytical model of two kinds of PMCFig. 12 Analytical model of two kinds of PMCFig. 12 Analytical model of two kinds of PMC

Fig. 1Fig. 1Fig. 1Fig. 1Fig. 11 Experimental PMC1 Experimental PMC1 Experimental PMC1 Experimental PMC1 Experimental PMC

Stress evaluation surface

Simulated experimantal model Hulbach array model (PM: Permanent magnet)

Unit PM

Unit PM (A)

Unit PM (B)

z

yx

Permanent magnet distributed disks

Tor

qu

e (N

m)

Gap between magnet surfaces (mm)

Experimental results

Analitical result(experimantal model)

Analitical result(Hulbach array model)


results is shown in Fig. 14. In the analysis, we calculatedthe maximum torque in an ideal position. The experimen-tal value was a measurement of the step-out torque inultra-slow rotation. The horizontal axis shows a gap be-tween the magnet surfaces. We confirmed the validity ofthe analysis through comparison between the analyticaland experimental values as shown in Fig. 14. In the analy-sis results, the transmission torque in the Halbach arraymodel is three times that of the experimental value.

Figure 15 shows analytical values for the maximumtransmission torque between a PMC coupling when thenumber of poles in the models is enhanced to 16 and 24.The gap between the surfaces of the facing permanentmagnets was set to 16 mm. The Halbach array magnet,which consists of a combination of permanent magnetsas shown in Fig. 13, and simulated experimental modelwere adapted to the analytical model. The number of polesin the PMC was increased by enhancing the arrangedradius of the permanent magnets. The rated torque in a22 kW motor that was applied to the SMB test stand andthe estimated rated torque in the IHI-developed flywheelsystem [3] are indicated in this figure. From the analysisresults, it was confirmed that a practicable torque couldbe transmitted by multi-polarizing.

5. Conclusions5. Conclusions5. Conclusions5. Conclusions5. Conclusions

We are currently developing a superconducting mag-netic bearing (SMB) and a non-contact permanent mag-netic clutch (PMC) applicable to flywheel energy storagesystems for railways. The SMB consists of a supercon-

Fig. 15 Analytical results for enhanced torque modelsFig. 15 Analytical results for enhanced torque modelsFig. 15 Analytical results for enhanced torque modelsFig. 15 Analytical results for enhanced torque modelsFig. 15 Analytical results for enhanced torque models

ducting rotor and a stator to obtain a high load capacity.A high-Tc bulk superconductor (HTS bulk) and a super-conducting coil are adapted to the rotor and the stator ofthe bearing. A flywheel and a motor/generator are ar-ranged inside and outside the cryostat, respectively. ThePMC is an important element that transfers the flywheel’sstored energy to the motor/generator through the cryostatin a non-contact way. The electromagnetic forces gener-ated by the SMB and PMC were calculated using 3D nu-merical analysis. We used the ELF/MAGIC 3D non-lin-ear static magnetic field solver for the electromagneticforce analysis. A plane element that defined the magneticfield at the center position of the element was applied tothe HTS bulk. We calculated the magnetic field using acurrent loop on the plane edge. The results can be sum-marized as follows:(1) The analytical and experimental results corresponded

sufficiently. It was demonstrated that the electromag-netic properties for a coupling of HTS bulks and acoil or a coupling of permanent magnets could beevaluated accurately using 3D numerical analysis.

(2) An SMB consisting of a single coil and HTS bulksachieving stable levitation was considered using 3Dnumerical analysis. The key to the analysis was a com-bination of differently shaped HTS bulks. The analy-sis results showed that it was possible to achievestable levitation.

(3) We estimated the PMC’s characteristics through 3Dnumerical electromagnetic force analysis. The resultsconfirmed that a practicable torque could be trans-mitted by multi-polarizing.

6. Acknowledgement6. Acknowledgement6. Acknowledgement6. Acknowledgement6. Acknowledgement

This study was financially supported by Japan’s Min-istry of Land, Infrastructure, Transport and Tourism.

ReferencesReferencesReferencesReferencesReferences

[1] Ken NAGASHIMA, Hiroshi SEINO, YoshikiMIYAZAKI, Yuuki ARAI, Naomichi SAKAI andMasato MURAKAMI, “Force Density of MagneticBearings Using Superconducting Coils and Bulk Su-perconductors,” Quarterly Report of RTRI, Vol. 49, No.2, pp.127-132, 2007.

[2] Hiroshi SEINO, Ken NAGASHIMA, YoshichikaTANAKA and Masahiko NAKAUCHI, “Study of aHigh-temperature Superconducting Magnetic Bear-ing for Flywheel Energy Storage Systems,” QuarterlyReport of RTRI, Vol. 50, No. 3, pp.179-184, 2008.

[3] Kuwata, Sugitani, Saito, “Development of Low LossActive Magnetic Bearing for Flywheel UPS,” Proceed-ings of The 10th international Symposium on MagneticBearings(ISBM 10), 2006.

Tor

qu

e (N

m)

Arranged radius of PM (mm)

Alalitical (Experimental model)

Analitical (Hulbach array model)

Torque requirement (500kg, 22kW)

Torque requirement (2000kg, 75kW)

Torque requirement (IHI:2.3kWh, 200kW)

8 poles8 poles

16 poles16 poles 24 poles24 poles

ExperimentalExperimentalmodelmodel

numerical analysis and evaluation of electromagnetic

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