im Journal of JET v°iume 12 (2°19) p.p. 31-41 Issue 3, November 2°19 Type °f article 1.°4 Technology www.fe.um.si/en/jet.html INFLUENCE OF ROTOR STRUCTURE ON COGGING TORQUE IN A SURFACE-MOUNTED PM-GENERATOR VPLIV KONSTRUKCIJE ROTORJA NA SAMODRŽNI VRTILNI MOMENT GENERATORJA S POVRŠINSKO NAMEŠČENIMI TRAJNIMI MAGNETI Greconici Marian1, Madescu Gheorghe2, Milosevici Daniela3, Biriescu Marius4, Mot Martian4'* Keywords: cogging torque, electrical machines, FEM analysis, surface-mounted PM generator Abstract This paper deals with the analysis of the cogging torque in a surface-mounted permanent magnet generator in order to determine some techniques to minimize or eliminate the cogging torque. The simulation with finite element method (FEM) was carryout. A four-pole surface-mounted PM generator is investigated in the paper using FEM. The paper analyses the possibilities to reduce this type of torque by producing some asymmetry in the rotor structure. Two types of asymmetry were analysed: the PM pole arc with different widths, and the shifting of the PM. The numerical results obtained in the asymmetrical cases with symmetrical ones were compared and discussed. Finally, some conclusions are highlighted regarding the simulated results. R Corresponding author: Lecturer dr. ing, Mot Marxian Tel.: +40-256-40-3454, Mailing address: Timijoara, Romania, B.dul V. Parvan nr.2, E-mail address: martian.mot@upt.ro 1 Politehnica University of Timijoara, Fundamentals of Physics for Engineers Department, Timijoara, Romania, B.dul V. Par-van nr.2. 2 Romanian Academy - Timijoara Branch, Timijoara, Romania, B.dul M. Viteazul nr. 24 3 Faculty of Technical Sciences Cacak, Svetog Save 65, 32102 Cacak, Serbia 4 Politehnica University of Timijoara, Electrical Engineering Department, Timijoara, Romania, B.dul V. Parvan nr.2. JET 31 Greconici Marian, Madescu Gheorghe, Milosevici Daniela, Biriescu Marius,Mot Martian JET Vol. 12 (2019) Issue 3 Povzetek Članek obravnava analizo samodržnega vrtilnega momenta generatorja s površinsko nameščenimi trajnimi magneti z namenom določitve konstrukcijskih izboljšav oz. metod za zmanjšanje tovrstnega vrtilnega momenta. Obravnavan je štiri polni generator s površinsko nameščenimi trajnimi magneti pri čemer je analiza izvedena z uporabo metode končnih elementov (MKE). V prispevku so analizirane možnosti za zmanjšanje samodržnega vrtilnega momenta z uvedbo asimetrije na rotorju. Analizirana sta dva tipa asimetrije: spremenjena dolžina obodnega loka trajnih magnetov in zamik trajnih magnetov. Pridobljeni numerični rezultati za asimetrične primere so primerjani z simetričnimi. V zaključku sledi razprava v zvezi s pridobljenimi rezultati numeričnih simulacij. 1 INTRODUCTION The permanent magnet (PM) generator has many attractive characteristics, such as high efficiency and high torque/power density. Consequently, the use of PM machines has increased significantly in the previous two decades in different industrial applications, mainly due to the diminishing cost of the PMs. The absence of excitation currents and the high power factor make the PM machine a winning solution in many cases. That is why many papers deal with the design and optimization of such electrical machines using analytical and numerical methods, [19]. The air gap magnetic field density provides much information about estimating motor performance. Moreover, this magnetic field, as an analytical solution, also allows the calculation of some effects, such as cogging torque, ripple torque, back-EMF shape, etc., [7, 10,11, 12]. Paper [13] compares five analytical models for predicting the cogging torque in surface-mounted permanent magnet machines. The cogging torque is normally generated due to the presence of stator slots and results from the interaction between the permanent magnet MMF harmonics and the air gap permeance harmonics due to slotting. Some design parameters have a great influence on the cogging torque. In [14], the authors have introduced a factor that indicates the "goodness" of a slot and pole number combination with regard to cogging torque. There are several methods to reduce cogging torque, which may be adopted for rotor structure in surface-mounted PM motors, [15]: skewing of the stator slots (or of the PMs), notches in the stator teeth, the width of the PM pole arc, PM pole arc with different widths, shifting of the PMs. In the present paper, the last two techniques to reduce the cogging torque are analysed and compared using an FEM method. Some conclusions and discussions are made about these calculated results. 32 JET Influence of Rotor Structure onCogging Torque in a Surface-Mounted PM- Generator 2 GENERATOR TOPOLOGY A simple four-pole surface-mounted PM generator with the topology illustrated in Figure 1 was used for FEM analysis of cogging torque. The stator has a classical three-phase winding, star connected, with an integer number of slots per pole per phase (q=3) and single layer: six coil series connected per phase with 42 turns per coil. The cross-section area of conductor: 1.1 mm2. -60.0 -20.0 20.0 40 0 60 0 80 0 Figure 1: Cross-scctioo of synchronous surface-mounted PM generator The permanent magnets on the rotor surface are mounted. The main specifications of the generator are: power (4 kW); phase number (3); poles number (4); stator slots number (36); stator inner diameter (100 mm); stator length (120 mm); stator outer diameter (160 mm); airgap thickness (1 mm); permanent magnet thickness (5 mm); Permanent magnet material (NdFeB). Figure 2 introduces two parameters that are used in the analysis: the width of the PM pole arc (am) and the relative position of the magnets (aAB) in the cases of the unsymmetrical arrangement in which the relative positions are different by 90°. JET 33 Greconici Marian, Madescu Gheorghe, Milosevici Daniela, Biriescu Marius,Mot Martian JET Vol. 12 (2019) Issue 3 Figure 2: The width (am) rgd the relative position (aAam) cf the magnets 3 COGGING TORQUE ANALYSIS The finite element method (OPERA13-Vector Field-software) was used to analyse the cogging torque of a surface-mounted PM generator. Some aspects of these results are presented and discussed. 3.1 Symmetrical rotor structure In this case, the width of the PM pole arc (am) is the same for all the poles (A, B, C, D - Figure 2). Also, the relative position of the magnets present a symmetry, which means a,4c= acc= aco= ao,4=900 (mechanical degree). In these conditions, Figure 3 shows the air-gap flux density distribution due only to rotor magnets. The flux density in Figure 3 is provided only by PM with the rotor at standstill (without stator current). It is interesting to note here the same flux density distribution is obtained irrespective of the material placed in the spaces between the PM poles (soft-iron or air). In zone N (Figure 3), corresponding to the q-axis, the flux density is zero. 34 JET Influence of Rotor Structure onCogging Torque in a Surface-Mounted PM- Generator Figure 3: Air-gap flux density distribution dug to rotor magocts This air-gap flux density from Figure 3 generates the so-called "cogging torque" component part of the total developed torque. This torque component is due to the presence of stator slots, so that it is zero in slot-less structure. The following expression can be used to calculate this component, [16]: LRC f. C pm ' be,pm )• de (3.1) where integration surface is a cylindrical surface in the air-gap with radius Rc and length L (axial length of the stator), and Br,PM and Be,PM are, respectively, the radial and tangential components of the air-gap flux density generated by permanent magnets. Thus, using FEM (in Figure 4) simulated the cogging torque. Again, the same cogging torque waveform as in Figure 4 is obtained in the case with soft-iron pieces placed between the PM poles. The magnitude of cogging torque is about 4% of the working torque. 00 5 0E03 001 0 015 0.02 0.025 0.03 time [s] Figure 4: FEM simulated cogging torque waveform (pole arc of magnets: 66°-mechanical degree). JET 35 Greconici Marian, Madescu Gheorghe, Milosevici Daniela, Biriescu Marius,Mot Martian JET Vol. 12 (2019) Issue 3 The number of periods of the cogging torque waveforms during a rotation (0.04 s) is 36, equal to the number of teeth (36 teeth). 3.2 PM pole arc with different widths The PM machine can be designed with PMs of different arc widths (am). However, all PM rotors of this kind of structure have the same relative position of the magnets. That means: aAB= aBC= aCD= aDA=90° (mechanical degree). A little asymmetry of the PM widths along the generator airgap can considerably reduce the cogging torque amplitudes. This asymmetry can be arranged in a different manner. The first type of arrangement is according to Table 1 and includes the FEM simulated cases. Table 1: First type of asymmetry Case am mechanical degree A B C D 1 70° 70° 2 74° 74° 3 78° 66° 78° 66° 4 82° 82° 5 86° 86° Figure 5 and Figure 6 represent the simulated cogging torque for Cases 1 and 2 of Table 1. One can see the influence of the magnets with different pole widths in these figures. Tco„ [Nm] (1 1 JUL hflnA* JHÎU h il Miil ' ffl 1 \m\m\ / Il M 1 -li] m II n 1 J1 y n i v « V m —pu il 5.0E-03 0.01 0.015 0.02 0.025 0.03 time [s] Figure 5: FEM simulated cogging torque waveform (case1, Table I) 36 JET Influence of Rotor Structure onCogging Torque in a Surface-Mounted PM- Generator Tcog [Nm] 1.0 -0.8 8.0 5.0E-03 0.01 0.015 0.02 0.025 0.03 time [s] Figure 6: FEM simulated cogging torque waveform (case2, Table I) In Figure 5, it is evident that a small increase in width of the magnets A and C (only 4° mechanical degree) reduces the cogging torque about 50% compared with symmetrical case in Figure 4. Also, from Figure 6, it can be seen that an additional increase in width of the both A and C magnets does not provide a further decrease of the cogging torque. Another type of asymmetry is presented in Table 2. Table 2: Second type of asymmetry Case am mechanical degree A B C D 1 70° 70° 2 74° 74° 3 78° 78° 66° 66° 4 82° 82° 5 86° 86° Figure 7 and Figure 8 show the cogging torque simulations in Cases 1 and 2 of Table 2. From this figure it comes out again that a small asymmetry in PM pole widths (around 4°) for two PM poles (magnets A and B) can reduce the cogging torque by 45% compared with the symmetrical case. JET 37 Greconici Marian, Madescu Gheorghe, Milosevici Daniela, Biriescu Marius,Mot Martian JET Vol. 12 (2019) Issue 3 Tcog [Nm] 1.0 0.8 -0.6 -0.8 0.0 5.0E-03 0.01 0.015 0.02 0.025 0.03 time [s] Figure 7: FEM simulated cogging torque waveform (casel, Table II) "1i8.0 5.0E-03 0.01 0.015 0.02 0.025 0.03 _ time [s] Figure 8: FEM simulated cogging torque waveform (case2, Table II) Consequently, this effect is obtained with a little increase of two PM poles arc (anyone of them), as can be seen in Figure 5 compared with Figure 7. 38 JET Influence of Rotor Structure onCogging Torque in a Surface-Mounted PM- Generator 3.3 Shifting of the PM The PM generator can be also designed with the same pole arc widths (am) and different relative position of the magnets along the airgap. Table 3 includes five cases of this asymmetry type analysed with the FEM method. Table 3: Third type of asymmetry Case Pole arc width (am) Position of the magnets A B C D aAB O.BC acD Oda 1 68 68 68 68 88 92 88 92 2 70 70 70 70 86 94 86 94 3 72 72 72 72 84 96 84 96 4 74 74 74 74 82 98 82 98 5 76 76 76 76 80 100 80 100 Figure 9 shows the simulated cogging torque in Case 1 of Table III. A small asymmetry by shifting of the PM by 2° produces a decrease of the cogging torque by 52% compared with the symmetrical case. A greater shifting in the PM poles distribution along the airgap cannot provide further a smaller cogging torque. -0-6 -0.8 S.O 5.0E-03 0.01 0.015 0 02 0.025 0.03 time [s] Figure 9: FEM simulated cogging torque waveform (casel, Table III) JET 39 Greconici Marian, Madescu Gheorghe, Milosevici Daniela, Biriescu Marius,Mot Martian JET Vol. 12 (2019) Issue 3 4 CONCLUSIONS A four-pole surface-mounted PM generator is investigated in the paper, using FEM. Two methods for minimizing the cogging torque have been analysed. The simulated results show that a small asymmetry in PM pole arc between 4-5% for half of the number of PM poles (anyone of them) is enough to reduce the cogging torque by around 50%. Furthermore, a small asymmetry by shifting of the PM by 2° (mechanical degree) can produce a decrease of the cogging torque by 48%-53%. These two techniques for reducing the cogging torque in a surface-mounted PM generator a very simple and easy to apply. References [1] Yao Duan, D. M. lonel, "A review of recent developments in electrical machine design optimization methods with a permanent magnet synchronous motor benchmark study," IEEE Transactions on Industry Applications, 2013, Volume: 49, Issue 3, pp. 1268-1275, DOI: 10.1109/TIA.2013.2252597 [2] S. V. A. Simion, L. Livadaru, N.D. Irimia, F. Lazar, "FEM analysis of a low speed permanent magnet synchronous machine with external rotor for a wind generator," Proceedings of OPTIM 2012, 24-26 May 2012, pp. 624-629, DOI: 10.1109/OPTIM.2012.6231940 [3] M. 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Effect of stator slotting", IEEE Transactions on Magnetics, 1993 Vol.: 29 , Issue: 1, pp: 143 - 151 40 JET Influence of Rotor Structure onCogging Torque in a Surface-Mounted PM- Generator [11] A.B. Proca, A. Keyhani, A. El-Antably, Wenzhe Lu, Min Dai, "Analytical model for permanent magnet motors with surface mounted magnets", IEEE Transactions oo Energy Conversion, 2003 Vol.: 18 , Issue: 3, pp. 386 - 391 [12] Z. J. Liu, J. T. Li, "Accurate Prediction of Magnetic Field and Magnetic Forces in Permanent Magnet Motors Using an Analytical Solution", IEEE Transactions on Energy Conversion, 2008 Vol. 23, Issue: 3, Pages: 717 - 726 [13] L. J. Wu, Z. Q. Zhu, D. Staton, M. Popescu, D. Hawkins, "Comparison of analytical models for predicting cogging torque in surface-mounted PM machines", The XIX International Conference on Electrical Machines - ICEM 2010, Pages: 1 - 6 [14] Z.Q. Zhu, D. Howe, "Influence of design parameters on cogging torque in permanent magnet machines", IEEE Transactions on Energy Conversion, 2000, Vol. 15, Issue: 4, Pages: 407 - 412 [15] N. Bianchi, S. Bolognani, "Design techniques for reducing the cogging torque in surface mounted PM motors" IEEE Transactions on Industry Applications, 2002, Vol. 38, Issue: 5, pp. 1259-1265 [16] A. Rahideh, M. Mardaneh, T. Korakianitis, "Analytical 2-D Calculations of Torque, Inductance, and Back-EMF for Brushless Slotless Machines with Surface Inset Magnets", IEEE Transactions on Magnetics, 2013, Vol. 49, Issue 8, pp. 4873-4884, DOI: 10.1109/TMAG.2013.2242087 Nomenclature (Symbols) (Symbol meaning) r, 8 polar coordinates Rc air-gap radius L axial length of the stator Br,PM radial component of the air-gap flux density generated by PM B8,PM tangential component of the air-gap flux density generated by PM Po vacuum permeability JET 41