High speed PM motor with hybrid magnetic bearing for kinetic energy storage

D. Johnson, P. Pillay* and M MalengretDepartment of Electrical Engineering, University of Cape Town, Cape Town, South Africa

Tel: +27 21 650 3088, Fax: +27 21 650 3088, E-Mail: djohnso@powerelec.ee.uct.ac.za*ECE Department Clarkson University,Potsdam, NY, 13699

Abstract-This paper describes the design essentials of an out-side rotor Permanent Magnet Halbach array motor with a hy-brid magnetic bearing, intended for kinetic energy storage. Thetheoretical estimations are compared to Finite element analysisas well as an approximated model using standard shape magnets.A dipole Halbach array produces a uniform flux distribution in-side the cylindrical stator, where straight windings on an Iron-less stator are placed near the inner boundary. The position ofthe windings inside this field does not affect the efficiency of themotor. When the motor is operated continuously, these varia-tions become insignificant.

The motor is suspended on a hybrid magnetic bearing withoutactive control. Two radial repelling magnetic bearings are usedin combination with an axial journal bearing. The theoreticalvalues were found to be consistent to that of a working model.

For high speed kinetic energy storage it is essential that theflywheel, which incorporates the motor and hybrid magneticbearing, is operated in a vacuum. Under these conditions, themotor / bearing system approaches near 100% efficiencies e.g.the approximated Halbach array motor model showed an electri-cal to mechanical efficiency of 97%. The flywheel target storagecapacity was 150 W-h with a minimum power rating of 40 W ata maximum operating speed of 48000 rpm. It is intended thatmultiple modules of this basic unit can be used in parallel to in-crease the overall energy storage capacity for rural and isolatedpower supplies.

1. INTRODUCTION

Kinetic energy storage in general requires a high efficiencymotor, taking into account that this method of storage is stillexpensive, and the energy has to move through the device atleast twice, i.e. charging and discharging.

Being able to store the energy for a reasonable time furtherimposes that the frictional losses should be low. This consistsmainly of bearing and air friction losses. The air friction isadequately catered for by removal, i.e. operating in a vac-uum. Limiting bearing losses can be achieved by combining apassive magnetic bearing and dry lubricated journal bearing.

The design of this particular development was basedmostly on the work of R.F Post [1] and J. D. Steinmier [2],which were both developed for vehicle applications. Thereare few commercially available kinetic energy storage unitsand are very expensive. The commercial units are in the hun-dreds of kW range and intended for power quality applica-tions. New costs can be justified for power quality applica-tions in the developing world, but not for rural applications.

The above designs are both 1 kWh units, suspended onmagnetic bearings. The Steinmier [2] model used a hybridmagnetic bearing with an active bearing backup. Both incor-porates filament wound multiple rim graphite composite de-

signs, which was housed in a vacuum enclosure.

The objective of this exercise was to develop and evaluatethe viability of a unit economical enough for rural area andstand alone applications in the developing world.

2. MOTOR DESIGN

The heart of the motor, with an outside rotor design, is a di-pole Halbach array, establishing a uniform flux within the sta-tor area, as shown in figure 1. A uniform flux is needed foroperating the motor on a magnetic bearing, where slightmovement of the stator inside the air gap is inevitable. Hal-bach [3] describes the flux density for a dipole with the equa-tions :

B�Brem�log� r2

r1��� (1)

��

sin�2�M �

2�M

(2)

B = Resultant uniform flux, Brem = Remnant flux in perma-nent magnets, r2 = outer radius, r1 = inner radius and M =number of poles.

Inspection of (1) reveals that the wall thickness of the arrayhas a direct impact on the resultant flux density. Plotting theflux density versus the wall thickness results in figure 2. Thiswall thickness is limited by commercial magnet dimensions,strength considerations due to centrifugal forces, cost of ma-terials and dimensional constraints.

When the number of magnets approaches infinity in (1), ithas a limit value of :

lim M l�

sin�2�M �

2�M

�1 (3)

This result is not practical, unless one such magnet couldbe manufactured. To use a large number of magnets is costly,because each magnet has to be magnetised in a unique direc-tion, the wedges become smaller and assembly becomes in-creasingly cumbersome.

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Fig.1: Magnet orientations for 8-magnet Halbach array

Fig 2: Effect of the number of magnets on resultant flux

An eight magnet array gives an acceptable result, shown infigure 3, which was used for this model.

Fig. 3: Finite Element analysis of 8-segment Halbach array

In order to reduce the cost of manufacture, the segmentsmay be replaced by commercially available rectangular mag-nets, embedded in a steel matrix, as shown in figure 4.

Fig. 4: Magnet segment and approximation with angledmagnetisation direction

The influence of the number of magnets used for an array isshown in figure 2.

Fig. 5: Effect of the ratio between the inner- and outer radii

The resulting design therefore reduces to a steel cylinderwith mass produced magnets oriented in the preferential di-rection as shown in figure 6.

To estimate the value of the remnant flux, Brem, in (1) forthe approximation, the flux has to be reduced in proportion tothe ratio of the actual volume of magnetic material to the totalvolume of the material. For unity depth, (2) becomes :

B�Brem

Amagnet

Asteel

�log� r2

r1��� (4)

Amagnet = cross sectional area of the magnets and Asteel =cross sectional area of the steel.

A prototype was constructed of readily available grade 28NdFeB magnets of dimensions 10 x 50 x 4 mm and mountedin an enclosure. A field strength of 0.39T was calculated. Thiscorrelates exactly with that of the finite element analysis re-sults and the measured values of the physical model. Thisconfirms the validity of using the magnet volume fraction in(4).

Fig. 6: Finite Element results of an approximated 8-seg-ment Halbach array

The three phase coils consists of copper windings woundonto an iron-less stator to eliminate iron losses. With the per-manent magnetic field moving, eddy currents will be gener-ated in magnetic and conductive circuits in the vicinity of the

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field.

The torque generated is directly proportional to the ampereturns and radius from the rotational centre in a Halbach array.

Fig. 7: Motor winding position

The armature windings are shown as single wires as oppos-ing pairs, as shown in figure 7. When a current is flowing in aphase, it exerts a force on the winding and the magnetic field,which are equal and opposite. Having a conductor in a uni-form flux, the air gap between the coils and the rotor insidethe perimeter is of no significance for this motor`s efficiency.The torque generated by the motor is proportional to the am-pere turns and radius from the rotational centre in a Halbacharray and are described by [4] :

T�B�l�i�r (5)

F = force, B = magnetic flux, L = length of conductor, i =current, r = radius and T = torque.

A full bridge converter acts as a solid state commutationdevice in this brushless DC machine, shown in figure 8.

TABLE 1

BRIDGE CONVERTER SWITCHING SEQUENCE FOR 3-PHASEOUTPUT

Angle 0 60 120 180 240 300

Positive TA+ TA+ TB+ TB+ TC+ TC+

Negative TB- TC- TC- TA- TA- TB-

By switching the MOSFETS / IGBTS of a full bridge con-verter, figure 8, in the sequence shown in table 1 results in asquare wave voltage fed to the 3-phase windings. The in-duced back EMF in the windings is sinusoidal. With the rotorbeing a fixed magnetic field and the windings on an iron-lesscore, the voltage equation for a DC generator, on the DC sideof the converter, applies [4] i.e.:

E�K ���I�R (6)

E = induced motor EMF, Φ = flux density, fixed for a per-manent Halbach array, ω = angular velocity in radians persecond, I = winding current, R = resistance measured over theMOSFETS and the windings and K = motor constant.

The induced voltage can be estimated by the the inductionlaw according to Fitzgerald [4] :

V i�Nd�

dt (7)

Vi = induced voltage, N = number of turns andd�dt

=

rate of change of magnetic flux.

For a conductor loop the induced voltage becomes :

V i���max sin �� t (8)

ω = angular velocity in radians per second and Φmax= mag-netic flux given by the relationship[4] :

�max�B A (9)

B = calculated flux density in the Halbach array and A =area enclosed within a conductor loop.

For this motor running at 48000 rpm with a flux density of0.39 Tesla and a mean area 0.022 X 0.050 m per winding, the

induced Voltage reduces to: V i�2.43 N sin �� t perwinding, with N = number of turns. The RMS value for a si-

nusoidal wave shape has a value of [5]3

2������������������������1.7 volts

per phase per winding at maximum speed.

TABLE 2ESTIMATED VOLTAGES FOR DIFFERENT NUMBERS OF TURNS

Windings VL-L (Delta Con-nected)

VL-L (Star Con-nected)

14 24 41.6

20 34.3 59.4

25 42.9 74.3

Fig. 8: Full bridge converter

Substituting KΦ in (6), we get :

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E�K 1

900��I�R (10)

K1= maximum rated voltage of the motor and R = com-bined resistance of the semiconductor switches and the wind-ings. The constant, "900", is the maximum speed of the ma-chine in Hertz.

3. FLYWHEEL DESIGN

Benham et al. [6] defines the hoop and radial stresses in arotating cylinder by:

�

3��

4����2� �ro

2�1��

3����ri

2� (11)

r�3��

8����

2��ro�ri

2 (12)

σθ = maximum hoop stress, σr = maximum radial stress, ρ =density of the cylinder, ro, ri = cylinder outer and inner radii,ω = angular speed and υ = poisons ratio.

Fig. 9: Piecewise differential disk profiles

Berger and Porat [7] have shown that it is possible to ob-tain much higher specific energies when using a combinationof piecewise differential disk profiles, as shown in Fig 10.

By maximising the specific kinetic energy, it was shownthat an optimum is reached when points p3,p4 and p5 coincide,resulting in a profile disk as depicted in figure 10.

Fig. 10: Optimal flywheel shape

This shape results in a specific energy of 1.92 times that ofa thin cylinder whereas an exponential profile disk only yieldsan energy density of 1.49 times that of a thin cylinder.

For the experimental model, a dual rim approach was takenin order to simplify construction, shown in figure 11. From

(12) it is clear that the radial stress generated in the rotatingbody is a function of the cylinder wall thickness. This is re-quired for multiple rims, as the fibres in the composite arealigned in the hoop direction and only the matrix binds thelaminates in the radial direction.

The rims are inter-connected with a rubber compound totransmit the rotational-, but not the radial forces. The outerrim was constructed from a filament wound glass fibre/epoxycomposite, while the inner rim was moulded from choppedstrand short glass fibres. This is allowable because thestresses are much lower closer to the centre of the flywheel.

The maximum stress that an aligned continuous fibre com-posite material can withstand, as in the case of the filamentwound outer rim of the flywheel, can be estimated by [8] :

� m �1� f � f (13)

σ = composite tensile stress in the direction of the fibres,σm = tensile strength of a matrix, σf = tensile strength of afibre and f = fibre volume fraction.

Philips [8] describes the strength of a short fibre composite.This depends on the critical fibre length, i.e. the length atwhich fibre and the matrix fails at the same strain. This lengthis calculated by :

l c� f d

xy

(14)

lc = critical length, d = fibre diameter and σxy = shearstrength of the matrix.

Fig. 11: Dual Rim Composite flywheel

For a short fibre composite with fibres longer than the criti-cal length, the material strength can be estimated by [8]:

� f f � l�l c

2 l��1� f m (15)

l = average fibre length.

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The resulting flywheel parameters are listed in table 3.

TABLE 3DUAL RIM FLYWHEEL SPECIFICATIONS

Outer diameter 210 mm

Length 160 mm

Safe operating speed 48000 rpm

Safety factor 1.5 (on the outer rim)

Total Weight 6.234 kg

Capacity 157.42 W-h

Inertia 26.55 x 10-3 kg m/s

Specific energy 25.25 W-h / kg

4. HYBRID MAGNETIC BEARING

Steinmier et al. [2] describes the operation of a stable hy-brid magnetic bearing system. This system is constructed oftwo passive radial magnetic bearings (figure 12) and a journalthrust bearing, shown in figure 13. Steinmier [2] calculatedthe rotational frictional moment at the point of contact as:

T�0.9� r2 F� (16)

T = Torque, r = Ball diameter, F = vertical force and µ =frictional coefficient

Yonnet [9] shows that opposing ring and disk shapedNdFeB permanent magnets yield a stable radial bearing, butunstable in the axial direction, shown in figure 12. Likewise,opposing disk magnets will be stable in the axial direction,but not in the other five degrees of freedom. Using two pairsof ring and disk magnets removes the remaining degrees offreedom except for two i.e. one linear in the direction of theshaft and the rotation thereof. The radial stiffness in this ar-rangement is approximately linear with distance.

Determining the stiffness can be done analytically withgreat difficulty. Generally the Finite element method is usedand is verified experimentally. Steinmer et al. [2] determineda linear radial stiffness of 600 N/m for a disk and annularmagnet pair, shown in Table 1.

Fig. 12: Radial Magnetic Bearing

An experimental prototype magnetic bearing was con-structed out of commercially available NeFeB magnets. Thedimensions and stiffness are shown in Table 1. The total ra-dial stiffness for two pairs is 6000 N/m or 6 N/mm.

Fig.13: Axial journal bearing using synthetic gemstones

The remaining degree of freedom in the axial direction hasto be confined to allow rotation of the shaft only. Axial sup-port is achieved by resting the rotating part of the motor witha hard ball on top of a hard flat plate, as shown in figure 14.

TABLE 4

STIFFNES OF RADIAL MAGNETIC BEARINGS

Parameter Steinmier model [2] Prototype

ØINNER [mm] 44.5 30

ØOUTER [mm] 50.8 60

ØDISK [mm] 19.2 22

Height [mm] 10 10

Stiffness [N/m] 600 3000

A 5 mm stainless steel ball on a stainless steel surface willgive a frictional moment of approximately 1x10-4 Nm perkilogram of flywheel. For this flywheel it amounts to a run-down time of about 200 days, excluding any other losses,from a speed of 48000 rpm.

Fig. 14: Hybrid Magnetic bearing

For a flywheel exerting 60 N on a single ball the frictionallosses will be as indicated in Table 5 [10].

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TABLE 5

FRICTION VALUES FOR BEARING MATERIALS

Ball Plate Coefficientof Friction

[10]

Torque[Nm]

Power@ 50000

rpm [mW]

Ruby / sap-phire

Sapphire0.1

1.5 x 10-4

152

Hard Steel Hard Steel 0.42 6.0 x 10-4 628

Cast iron Cast Iron 0.15 2.2 x 10-4 230

Teflon Steel 0.04 6.0 x 10-5 63

3. MECHANICAL LOSSES OF THE FLYWHEEL SYSTEM

To determine the losses in the hybrid magnetic bearing, arundown curve was obtained while the containment was keptunder vacuum. The rundown curve is shown in figure 15.

At the resonant frequencies, especially the first, a large de-celeration is visible. The largest vibrations occurs at the firstresonant frequencies.

Fig. 15: Rundown Curve in a Vacuum

At these amplitudes the moving parts makes contact withthe stationary parts, resulting in large mechanical losses.

The almost linear sections between the natural frequencyand multiples thereof i.e. ±900 , 1800 etc. rpm, shows that theonly frictional force is the contact on the axial support, con-firming that the air friction has become negligible.

The motor was run at a constant current, which represents atorque, and allowed sufficient time to reach balance with thefrictional torque of the system. This speed which was reachedfor a constant input power is depicted in figure 16.

To find the maximum speed of this curve, the mechanicalfriction in (16) is equated to the electrical resistive loss , giv-ing:

0.9� r2 F�����I 2 R (17)

The theoretical maximum speed from the motor can now berewritten as:

Fig. 16: Motor speed vs. Power in vacuum

��I 2 R

0.9� r2 F�� (18)

Applying this to the prototype flywheel results in a fric-tional coefficient of: µ = (82 * (2* 0.055 + 0.516))/(0.9π(0.01)2*60) *261) = 0.16 , using 2500 rpm as the maximumspeed (see figure 16) and a current of 8 Amperes.

This value correlates with the coefficient of friction of CastIron on Cast Iron and lies in between those of hard steel onhard steel and hard steel on Teflon. The slight increase overthat of the steel on Teflon lubricated steel surface, used in thisprototype, is due to the steel surfaces not being entirelysmooth, flat and aligned. This causes the ball to slide over thesurface, in small circular movements, instead of rotating onone point.

5. SYSTEM OVERVIEW

Shown in figure 17 is a schematic, illustrating a solar arrayapplication of a kinetic energy storage system.

Fig. 17: Discrete logic controlled Electromechanical stor-age schematic

The solar array provides DC power to a user, sharing acommon bus with a bidirectional DC-DC converter, perma-nently connected to a kinetic energy storage unit. The controllogic limits the current flow in and out of the motor and moni-

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Input Power [Watt]

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tors the voltage, representing the speed of the motor.

The 3-phase, full bridge converter is synchronised with themotor by an optical encoder.

When the voltage of the solar array is higher than that ofthe DC bus, current flows into the flywheel system which ac-celerates the flywheel. When a consumer starts demandingpower, which the solar panel may not be able to supply at thetime, the DC bus voltage reduces slightly and the currentstarts flowing out of the electromechanical storage system,slowing down the flywheel.

6. CONCLUSION

The design procedure of a high efficiency motor / generatorwith a hybrid bearing system, built with off-the-shelf compo-nents, has been described. High efficiencies were obtained,using standard manufacturing techniques available in SouthAfrica, for a kinetic energy storage application.

It is concluded that the manufacture of efficient, low costkinetic energy storage devices is not only possible, but shouldbe pursued in order to develop an affordable and competitivecommercial unit for rural and isolated applications, as com-petitor to the electrochemical battery.

7. REFERENCES

[1] R.F Post, S.F. Post, "A high-efficiency electromechanicalbattery", Proceedings of the IEEE, Vol. 81, No 3, March1993.

[2] J. D. Steinmier, S.C. Thielman, B.C. Fabien, "Analysis

and control of a flywheel storage system with a hybridmagnetic bearing.", Transactions of the ASME, Vol. 119,December 1997.

[3] K. Halbach, "Design of permanent multipole magnets withorientated rare earth cobalt material", Nuclear instrumentsand Methods, Vol. 169, 1980, North Holland PublishingCo.

[4] A.E Fitzgerald, D Higginbotham, A Grabel, "Basic Elec-trical Engineering", 5th edition, 1981, Mc Graw Hill Kuga-kusha Ltd.

[5] N. Mohan, T.M. Undeland, W.P. Robbins, "Power Elec-tronics, converters, applications and design", Second Edi-tion, 1995.

[6] P.P. Benham, F.V Warnick, "Mechanics of solids andstructures", 1982, Pitman Publishing Inc.

[7] M. Berger, I. Porat, "Optimal design of a rotating disk forkinetic energy storage", Transactions of the ASME, Vol55, March 1988.

[8] LN Philips, "Design with Advanced Composite Materi-als", 1989, Biddles Ltd.

[9] JP Yonnet, "Passive magnetic bearings with permanentmagnets", IEEE Transactions on magnetics, Vol 14, Sep-tember 1978.

[10] E.A. Avallone, T Baumeister III, "Marks Standard hand-book for Mechanical Engineers", 9th edition, 1987,McGraw-Hill Inc.

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