PERMANENT MAGNET SYNCHRONOUS MACHINES WITH HALBACH ARRAY CONFIGURATIONS A F.E.M. APPROACH Leonard LIVADARU Florin LAZĂR Alecsandru SIMION Adrian MUNTEANU Adrian MALANCIUC Sorin VLĂSCEANU REZUMAT. Utilizarea configuraţiilor configuraţiilor 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 magnetic magnetic clasic. În n această ceastă lucrare se face o analiză comparativă, bazată pe metoda elementului finit (M.E.F.), a unor topologii Halbach, Halbach, pentru punerea în n evidenţă a modificărilor aduse de acestea asupra parametrilor magnetici (câmp, inducţii, armonici de ordin superior). Sunt luate în n discuţie structuri de maşini sincrone cu rotor interior respectiv exterior. Si n regim magnetostatic şi Simulările efectuate în tranzitoriu arată avantajele dar şi dezavantajele acestor structuri. Cuvinte cheie: cheie analiza M.E.F., configuraţii Halbach, maşini sincrone cu magneţi permanenţi. ABSTRACT. The use of Halbach array configurations in manufacture of permanent magnet a. a.c. electric machines represents a relative new solution, which has in intention an improvement of the performance and, lately, the the elimination of the iron in certain areas of the magnetic circuit. This paper presents a FEMFEM-based analysis of some Halbach topologies in order to put in view the modifications brought by these structures upon magnetic parameters (field, flux densities, and high order harmonics). The study takes into discussion synchronous machines with inner and outer rotor. The magnetostatic and transient simulations show the advantages but the drawbacks as well of these structures. structures. Keywords: Keywords F.E.M. analysis, Halbach array configurations, permanent magnet synchronous machines. Buletinul AGIR nr. 4/211 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-ironboron 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. 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 coercial 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 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 selfshielding propriety. 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. 18 Buletinul AGIR nr. 4/211 octombrie-decembrie
Fig. 2. PM configurations inner rotor (4 global magnetic poles): a - Radial magnetization (4 PMs); b - Halbach array with 9-45 magnetization (8 PMs) Type 1; c - Halbach array with 9-45 and intermediate magnetization (16 PMs) Type 2. 1 1.5 -.5.5 -.5.5 -.5 1 2 3 1 2 3 1 2 3 Spatial coordinate () Spatial coordinate () Spatial coordinate () 75 75 75 5 5 5 25 25 25 1 2 3 1 2 3 1 2 3 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 airgap 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 Buletinul AGIR nr. 4/211 octombrie-decembrie 19
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 airgap 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 selfshielding 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 15 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. d. Fig. 4. Flux density color map: a - Radial magnetization (4 PMs); b - Halbach array Type 1; c - Halbach array Type 2; d - Legend. Volt Volt 5 5 5 Line voltage (V) Line voltage (V) Line voltage (V) -5-5 -5 s. s..1.125.15.175.2.5 99.999E-3.15.2.5 99.999E-3.15.2 Time (s) Time (s) Time (s) Fig. 5. Induced line voltage : a - Radial magnetization (4 PMs); b - Halbach array Type 1; c - Halbach array Type 2. 2 Buletinul AGIR nr. 4/211 octombrie-decembrie
a. b. Fig. 6. PM configurations outer rotor: a - 8 PMs; b 16 PMs. 1 5.5 -.5 4 3 2 1 1 2 3 Spatial coordinate () 1 2 3.5 5 4 3 -.5 2 1 1 2 3 Spatial coordinate () 1 2 3 Fig. 7. Outer rotor Halbach array topologies (up - 8 PMs; down 6 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 Buletinul AGIR nr. 4/211 octombrie-decembrie 21
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 airgap 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,.52t, for the thin magnets structure but acceptable and improvable value,.3t for the thicker magnets structure). 5 99.999 4 3 2 1 1 2 3 3 1 2 3 5 2 1-5 1 2 3 1 2 3 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 nonferromagnetic 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. 28, Wuhan, pp.364-369. [2] Sadeghi S., Parsa L., Multiobjective Design Optimization of Five- Phase Halbach Array Permanent-Magnet Motor, IEEE Transactions on Magetics, June 211, Volume: 47, Issue: 6, pp. 1658666. [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 21, Volume: 37, Issue: 4, pp. 2827-283. [4] Gallo C.A., Halbach Magnetic Rotor Development, NASA/TM, Feb. 28. [5] Gieras J.F., Advancements in Electric Machines, Editura Springer Verlag, 28, ISBN 978 1 42 96 6. 22 Buletinul AGIR nr. 4/211 octombrie-decembrie