PERMANENT MAGNET SYNCHRONOUS MACHINES WITH … · 2011-09-22 · MACHINES WITH HALBACH ARRAY HH A ARRRRAAYY H ARRAY CONFIGURATIONS CONFIGURATIONS –––– A F.E.M ... de curent

PERMANENT MAGNET SYNPERMANENT MAGNET SYNPERMANENT MAGNET SYNPERMANENT MAGNET SYNCHRONOUS CHRONOUS CHRONOUS CHRONOUS MACHINES WITH HALBACMACHINES WITH HALBACMACHINES WITH HALBACMACHINES WITH HALBACH ARRAY H ARRAY H ARRAY H ARRAY

CONFIGURATIONS CONFIGURATIONS CONFIGURATIONS CONFIGURATIONS –––– A F.E.M. APPROACHA F.E.M. APPROACHA F.E.M. APPROACHA F.E.M. APPROACH

Leonard LIVADARU Gheorghe Asachi Technical University

of Iaşi

Florin LAZĂR Gheorghe Asachi Technical University

of Iaşi

Alecsandru SIMION Gheorghe Asachi Technical University

of Iaşi

Adrian MUNTEANU Gheorghe Asachi Technical University

of Iaşi

Adrian MALANCIUC Gheorghe Asachi Technical University

of Iaşi

Sorin VLĂSCEANU Gheorghe Asachi Technical University

of Iaşi

REZUMAT. REZUMAT. REZUMAT. REZUMAT. Utilizarea cUtilizarea cUtilizarea cUtilizarea configuraţiilor Halbach în construcţia maşinilor de curent alternativ cu magneţi permanenţi constituie o soluţie onfiguraţiilor Halbach în construcţia maşinilor de curent alternativ cu magneţi permanenţi constituie o soluţie onfiguraţiilor Halbach în construcţia maşinilor de curent alternativ cu magneţi permanenţi constituie o soluţie onfiguraţiilor Halbach în construcţia maşinilor de curent alternativ cu magneţi permanenţi constituie o soluţie relativ nouă ce urmăreşte îmbunătăţirea performanţelor şi, mai nou, eliminarea fierului din anumite zone ale circuitului magnrelativ nouă ce urmăreşte îmbunătăţirea performanţelor şi, mai nou, eliminarea fierului din anumite zone ale circuitului magnrelativ nouă ce urmăreşte îmbunătăţirea performanţelor şi, mai nou, eliminarea fierului din anumite zone ale circuitului magnrelativ nouă ce urmăreşte îmbunătăţirea performanţelor şi, mai nou, eliminarea fierului din anumite zone ale circuitului magnetic etic etic etic clasic. clasic. clasic. clasic. Înnnn aaaacecececeastă lucrare se face o analiză comparativă, bazată pe metoda elementului finit (M.E.F.), a unor topologii Halbachastă lucrare se face o analiză comparativă, bazată pe metoda elementului finit (M.E.F.), a unor topologii Halbachastă lucrare se face o analiză comparativă, bazată pe metoda elementului finit (M.E.F.), a unor topologii Halbachastă lucrare se face o analiză comparativă, bazată pe metoda elementului finit (M.E.F.), a unor topologii Halbach,,,, pentru pentru pentru pentru punerea punerea punerea punerea în evidenţă a modificărilor aduse de acestea asupra parametrilor magnetici (câmp, inducţii, armonici de ordin superior). n evidenţă a modificărilor aduse de acestea asupra parametrilor magnetici (câmp, inducţii, armonici de ordin superior). n evidenţă a modificărilor aduse de acestea asupra parametrilor magnetici (câmp, inducţii, armonici de ordin superior). n evidenţă a modificărilor aduse de acestea asupra parametrilor magnetici (câmp, inducţii, armonici de ordin superior). Sunt Sunt Sunt Sunt luate luate luate luate în discuţie structuri de maşini sincrone cu rotor interior respectiv exterior. Sn discuţie structuri de maşini sincrone cu rotor interior respectiv exterior. Sn discuţie structuri de maşini sincrone cu rotor interior respectiv exterior. Sn discuţie structuri de maşini sincrone cu rotor interior respectiv exterior. Siiiimulările efectuate mulările efectuate mulările efectuate mulările efectuate în regim magnetostatic şi n regim magnetostatic şi n regim magnetostatic şi n regim magnetostatic şi tranzitoriu tranzitoriu tranzitoriu tranzitoriu arată arată arată arată avantajele avantajele avantajele avantajele dar dar dar dar şi dezavantajeleşi dezavantajeleşi dezavantajeleşi dezavantajele acestor structuri.acestor structuri.acestor structuri.acestor structuri. Cuvinte cheieCuvinte cheieCuvinte cheieCuvinte cheie: analiza M.E.F., configuraţii Halbach, maşini sincrone cu magneţi permanenţi. ABSTRACT. The use of Halbach array configurations in manufacture of permanent magnet aABSTRACT. The use of Halbach array configurations in manufacture of permanent magnet aABSTRACT. The use of Halbach array configurations in manufacture of permanent magnet aABSTRACT. The use of Halbach array configurations in manufacture of permanent magnet a....cccc.... electric machines electric machines electric machines electric machines represents a represents a represents a represents a relative new solution, which has in intention an improvement of the performance and, lately, trelative new solution, which has in intention an improvement of the performance and, lately, trelative new solution, which has in intention an improvement of the performance and, lately, trelative new solution, which has in intention an improvement of the performance and, lately, the elimination of the iron in certain he elimination of the iron in certain he elimination of the iron in certain he elimination of the iron in certain areas of the magnetic circuit. This paper presents a FEMareas of the magnetic circuit. This paper presents a FEMareas of the magnetic circuit. This paper presents a FEMareas of the magnetic circuit. This paper presents a FEM----based analysis of some Halbach topologies in order to put in view based analysis of some Halbach topologies in order to put in view based analysis of some Halbach topologies in order to put in view based analysis of some Halbach topologies in order to put in view the the the the modifications brought by these structures upon magnetic parameters (field, flux densities, modifications brought by these structures upon magnetic parameters (field, flux densities, modifications brought by these structures upon magnetic parameters (field, flux densities, modifications brought by these structures upon magnetic parameters (field, flux densities, and highand highand highand high order harmonics). The study order harmonics). The study order harmonics). The study order harmonics). The study takes into takes into takes into takes into discussiondiscussiondiscussiondiscussion synchronous machines with inner and synchronous machines with inner and synchronous machines with inner and synchronous machines with inner and outerouterouterouter rotor. The magnetostatic and transient simulations show the rotor. The magnetostatic and transient simulations show the rotor. The magnetostatic and transient simulations show the rotor. The magnetostatic and transient simulations show the advantages but the drawbacks as well of these advantages but the drawbacks as well of these advantages but the drawbacks as well of these advantages but the drawbacks as well of these structuresstructuresstructuresstructures.... KeywordsKeywordsKeywordsKeywords: F.E.M. analysis, Halbach array configurations, permanent magnet synchronous machines.

Buletinul AGIR nr. 4/2011 ● octombrie-decembrie_____________________________________________________________________________________________

17

1. INTRODUCTION

The permanent magnet a.c. machines have become lately a very attractive solution for electric drives. Certain advantages as higher efficiency, better dynamic performance or higher torque per volume values represent worthy reasons in considering the permanent magnet motors as significant competitors for induction machines in the range of fractional, small and even medium power applications. For a long time, the tender subject of the PM machines was the magnetic material itself, which was not capable to provide strong-enough fields. This problem has been solved with the development of rare-earth magnets. Firstly, samarium-cobalt and later, neodymium-iron-boron came with higher fields under acceptable costs. However, no matter the quality of the permanent magnet material, an important drawback holds over. The air-gap magnetic field is rather trapezoidal then sinusoidal and, as consequence, significant high order harmonics with negative effects inhabit the air-gap magnetic field spectrum.

In 1979, Klaus Halbach reported a PM configuration, which later has been denoted by his name, capable to inherently ensure a sinusoidal wave. Basically, the topology has magnet segments with distinct magnetization direction, Fig. 1.a. The Halbach’s researches had not in view a solution for electrical machines. It was a matter of time till R.F. post proposed a radial solution (Fig. 1.b) for an electric motor.

a.

b.

Fig. 1. Halbach array concept:

a – Linear arrangement; b – Circular arrangement.

Besides the sinusoidal wave created by this

structure, a second very important and challenging advantage defines the Halbach array. It is the self-shielding propriety.

In this paper, a comparison between a regular PM motor and a Halbach array topology is presented. The study consists in a F.E.M.-based analysis, which put in view the differences of the magnetic field quantities (mainly flux density). Finally, a few considerations regarding the use of Halbach array arrangement in the construction of electric motors are formulated.

2. FINITE ELEMENT ANALYSIS AND RESULTS

The study presented in this paper is signally a

simulation one. The analysis tool is commercial

software based on finite element method, which is

dedicated to the investigation of the magnetic field and

its derived quantities. Usually, the are different ways

that can be employed in simulation and they depend on

the state of the analyzed system, that is steady state or

transient operation. Since our intention is to give points

to the magnetic field created by permanent magnets, a

magnetostatic analysis is enough. It has to be pointed

out that this approach catches a certain moment of the

operation. As consequence, rotation, speed or

voltage/current variation is not considered. They are

represented by scalar values corresponding to the

analyzed moment. On the other hand, the evaluation of

the induced voltage due to the presence of the

permanent magnets required a transient analysis, which

supposes a rotation of the rotor at constant speed. In this

case, an equivalent electric circuit is coupled to the

considered geometry.

Since the presented study has a comparative

character, it evolves on three levels. It starts with a

regular PM synchronous motor, and its counterparts

with Halbach array configuration. Then, using a similar

structure, it is taken into discussion the outer rotor

topology. Finally, the iron core is removed and replaced

with non-magnetic materials.

2.1. Inner rotor configurations

The regular three-phase PM machine (Fig. 2.a) has 4

poles and rare-earth permanent magnets, sintered NdFeB – HS-38AV type, with radial magnetization. Both rotor and stator are iron cored structures. For the Halbach array configuration, two magnetization patterns have been chosen. The first has 8 magnet segments (Fig. 2.b) and the second has 16 magnet segments (Fig. 2.c). The difference between these two patterns consists in the angle between the magnetization direction of two adjacent segments.

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Buletinul AGIR nr. 4/2011 ● octombrie-decembrie

a. b. c.

Fig. 2. PM configurations – inner rotor (4 global magnetic poles):

a - Radial magnetization (4 PMs); b - Halbach array with 90°-45° magnetization (8 PMs) – Type 1; c - Halbach array with 90°-45° and

intermediate magnetization (16 PMs) – Type 2.

-1

-0.5

0

0.5

0 100 200 300

mm

Tesla

-1

-0.5

0

0.5

1

0 100 200 300

mm

Tesla

0

250

500

750

0 10 20 30

(E-3) Tesla

250

500

750

0 10 20 30

(E-3) Tesla

0

250

500

750

0 10 20 30

(E-3) Tesla

a. b. c.

Fig. 3. Air-gap flux density curve and content in high order harmonics:

a - Radial magnetization (4 PMs); b - Halbach array – Type 1; c - Halbach array – Type 2.

As it can be noticed, the number of magnet segments in the Halbach array configuration is not equal to the number of magnetic poles of the machine. This number depends on the magnetization pattern, which has to ensure the desired number of magnetic poles and an air-gap field

wave as sinusoidal as possible. Figure 3 presents the air-gap flux density curves for the three situations. Indeed, the magnetic field shape of the regular PM machine is trapezoidal (Fig. 3.a) with a rich content in high order harmonics (the greatest is the third but also the fifth and

-0.5

0

0.5

1

0 100 200 300

mm

Tesla

Flu

x d

ensi

ty (

T)

Spatial coordinate (mm) Spatial coordinate (mm) Spatial coordinate (mm)

Flu

x d

ensi

ty (

T)

Flu

x d

ensi

ty (

T)

Buletinul AGIR nr. 4/2011 ● octombrie-decembrie_____________________________________________________________________________________________

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the seventh are too significant). The presence of the Halbach configuration improves substantially the shape of the curves (Fig. 3.b, 3.c). It is interesting to notice and to state as well that a lower angle between two adjacent magnetization directions generates a more sinusoidal air-gap wave but requires a higher number of magnet segments per pole. In our case, the Type 2 configuration practically eliminates the high order harmonics that really counts upon machine operation.

A second interesting conclusion arises of the flux density map distribution (Fig. 4). There is a much lower loading of the rotor magnetic circuit in the Halbach topology. None the less that the rotor has a ferromagnetic core, an important amount of the flux lines tracks the permanent magnets (see the higher values of the flux density inside the magnet segments). Somehow, the self-shielding effect acts even for this topology.

Of high importance in the evaluation of the PM system of a synchronous machine is the shape of the back emf

voltage. For this purpose, a transient analysis corresponding to generating regime has been performed. In other words, it is taken into consideration the rotor movement (synchronous speed of 1500 rot/min) and an equivalent electric circuit (considered at no-load) of the stator winding. The results are presented in Fig. 5. It is again obvious that there is a slightly improved shape of the voltage for the Halbach structures.

2.2. Outer rotor configurations

The external position of the rotor requires a different

pattern of the magnetization directions, which guide the flux lines towards inside area. Figure 6 shows the new Halbach topologies together with the structures of the rotor and stator cores. For an accurate comparison, the outer rotor structures keep the geometrical dimensions of the air-gap and of the magnet segments.

a. b. c.

d.

Fig. 4. Flux density color map: a - Radial magnetization (4 PMs); b - Halbach array – Type 1; c - Halbach array – Type 2; d - Legend.

-500

0

500

0.1 0.125 0.15 0.175 0.2

-500

0

500

0.05 99.999E-3 0.15 0.2

s.

Volt

-500

0

500

0.05 99.999E-3 0.15 0.2

s.

Volt

a. b. c.

Fig. 5. Induced line voltage :

a - Radial magnetization (4 PMs); b - Halbach array – Type 1; c - Halbach array – Type 2.

Lin

e volt

age

(V)

Lin

e volt

age

(V)

Lin

e volt

age

(V)

Time (s) Time (s) Time (s)

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Buletinul AGIR nr. 4/2011 ● octombrie-decembrie

-1

-0.5

0

0.5

1

0 100 200 300

mm

Tesla

a. b.

Fig. 6. PM configurations – outer rotor: a - 8 PMs; b – 16 PMs.

100

200

300

400

500

0 10 20 30

(E-3) Tesla

-1

-0.5

0

0.5

0 100 200 300

mm

Tesla

100

200

300

400

500

0 10 20 30

(E-3) Tesla

a. b. c.

Fig. 7. Outer rotor Halbach array topologies (up - 8 PMs; down -16 PMs):

a - Air-gap flux density curve; b - High order harmonics content; c – Boundary flux density vectors.

For the both structures, the air-gap flux density curve has a rather strange variation, which is definitely improper for an efficient machine. The explanation becomes easy with the inspection of flux lines distribution (Fig. 7.c). There are magnet segments that allow a sort of “return” of the magnetic field and consequently a distorsion, which

distort the air-gap curve. Two main reasons are responsible for this phenomena. The first and the most important is due to the magnetization direction of the segments. A proper correlation of the magnetization angles is mandatory in order to avoid these returning intermediary routes of the magnetic lines. The second

Flu

x d

ensi

ty (

T)

Spatial coordinate (mm)

Spatial coordinate (mm)

Flu

x d

ensi

ty (

T)

Buletinul AGIR nr. 4/2011 ● octombrie-decembrie_____________________________________________________________________________________________

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reason, less important but still countable refers to the modality of placing the permanent magnets. Usually, the magnet segments are disjointed and their orthoradial length is much smaller. At any hand, an optimization of these two design elements is mandatory for a good solution.

2.3. Air-cored topologies

To push the Halbach array to its limits, we have

removed the back iron both in stator and rotor. Consequently, there is no more ferromagnetic material and

the flux lines distribution is determined by the magnets themselves. Since we have anticipated that the magnetic field decrease dramatically, the outer rotor structure has higher magnets. Moreover, there are no rotor slots but there is a flat winding placed on the surface of the inner stator. Figure 8 show the flux lines distribution and the air-gap magnetic field curves.

It is obvious the self-shielding propriety for both structures. It is also noticeable the effect of the thicker PMs on the value of the flux density (useless value, 0.052T, for the thin magnets structure but acceptable and improvable value, 0.3T for the thicker magnets structure).

-100

0

99.999

0 100 200 300

mm

(E-3) Tesla

10

20

30

40

50

0 10 20 30

(E-3) Tesla

-500

0

500

0 100 200 300

mm

(E-3) Tesla

100

200

300

0 10 20 30

(E-3) Tesla

a. b. c.

Fig. 8. Ironless topologies (up – 16 PMs inner rotor; down – 16 PMs outer rotor and increased magnet volume):

a – Flux lines distribution; b – Air-gap flux density curve; c – High order harmonics content.

3. CONCLUSION

No doubt, the Halbach array configuration brings

important advantages in electric machines

performance. The air-gap magnetic field can be

brought to a quasi sinusoidal shape by means of a

carefully magnetization of the segments. For certain

applications where high speed or miniaturization is a

constraint, the back iron can be replaced with non-

ferromagnetic and lighter materials. But a price has

to be paid. The machine needs powerful PMs

(preferable super high energy NdFeB) with particular

magnetization directions.

REFERENCES

[1] Hongfeng Li, Changliang Xia, Halbach Array Magnet and its

Application to PM Spherical Motor, Int. Conf. on Electrical

Machines and Systems, Oct. 2008, Wuhan, pp.3064-3069.

[2] Sadeghi S., Parsa L., Multiobjective Design Optimization of Five-

Phase Halbach Array Permanent-Magnet Motor, IEEE

Transactions on Magetics, June 2011, Volume: 47, Issue: 6,

pp. 1658-1666.

[3] Jang S-M., Jeong S-S., Ryu D-W., Choi S-K., Design and

Analysis of High Speed Slotless PM Machine with Halbach

Array, IEEE Transactions on Magetics, July 2001, Volume: 37,

Issue: 4, pp. 2827-2830.

[4] Gallo C.A., Halbach Magnetic Rotor Development, NASA/TM,

Feb. 2008.

[5] Gieras J.F., Advancements in Electric Machines, Editura

Springer Verlag, 2008, ISBN 978 – 1 – 4020 – 9006 – 6.

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