XIV International PhD Workshop OWD 2012, October Axial flux brushless DC motor with rotors made of hybrid powder composites

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1 XIV International PhD Workshop OWD 2012, October 2012 Axial flux brushless DC motor with rotors made of hybrid powder composites Marcin Karbowiak, Tele and Radio Research Institute Warsaw Poland Abstract This paper presents a design of a disc-motor made from powder magnetic materials. For analyzed construction of a motor it was proposed multi-pole permanent magnet with soft magnetic composite as a material for a rotor. Composite material contains layers made of soft magnetic composite and a multipolarly magnetized permanent magnet. Analytical calculations and finite element method simulations of a motor were performed. 1. Introduction Axial flux permanent magnets machines (AFPM), also called disc-type machines, are an alternative to radial flux permanent magnets cylindrical machines (RFPM). In conventional machines magnetic flux density in the air gap has radial direction, in AFPM motors flux density in the air gap has axial direction. Disc type machines have much smaller an axial length than conventional motors at the same torque. They find many applications due to its pancake shape, compact construction and high power density. AFPM motors are dedicated to: electrical vehicles, pumps, machine tools, robots and industrial equipment. A large number of poles causes that these machines are used in low speed applications. AFPM machines can be designed with a single air gap, multiple air gaps, with slotted, non-slotted, or even with totally ironless construction. There are two constructions for slotted double-side AFPM motors. These topologies are: one stator and two rotors and two stators and one rotor [1-4]. In this paper the construction of a motor with one stator and two rotors are presented. An analyzed construction of motor was investigated and was used materials such as soft magnetic composites (SMC) and bonded permanent magnets. Three dimensional distribution of magnetic flux in this type of a motor cause necessity to use special materials. Widely used laminated sheets in construction of classical motors, in disc motors creates technological difficulties. Moreover, two rotors in a considered design can be made by use of hybrid multipolarly magnetized bonded magnets. These materials consist of two layers. One is soft magnetic composite, second is bonded permanent magnet. Both layers can be obtained in one pressing process, which greatly simplifies production of materials. A hard magnetic layer can be magnetized in one magnetization process in required distribution of magnetic poles. This allows to avoid necessity of gluing and possibility of detachment of a magnet during operation of a motor[5-8]. Field analyses of motor are investigated using Finite Element Method (FEM) by 2D FEMM 4.2 and 3D Maxwell 15 software. 2. Materials Magnetic cores of electric machines are more often produced from iron soft magnetic powders bonded by epoxy resin or other substances. Required shape of the core is obtained by compression of magnetic powder in a special form. Powder metallurgy is a technology almost without waste of material in production and also is friendly in recycling of its products. Epoxy resin insulates iron powder grains and allows to obtain high electrical resistivity of a core. Magnetization curve of Soft Magnetic Composite is presented in figure 1. Fig.1. Magnetization curve of Soft Magnetic Composite for 50Hz Permanent magnets from Nd-Fe-B melt spun powder are isotropic and can be magnetized in various directions with two or more magnetic poles. Demagnetization curves for bonded permanent magnet are presented in figure

2 Fig.2. Demagnetization curves for a bonded permanent magnet Hybrid magnetic composite with two magnetic layers is presented in figure 3a. This material can be magnetized in required distribution of magnetic poles. Figure 3b presents shape of magnetic circuit, in the rotor, which was simulated in 3D FEM software. Permanent magnets have axial direction of magnetization. Table 1 presents magnetic properties of a bonded permanent magnet. Fig.3. a) Hybrid magnetic composite b) magnetic circuit, in the rotor, which was simulated in 3D FEM software Tab.1. Magnetic properties of a bonded permanent magnet Symbol Quantity Value Unit B r Residual induction 0.67 [T] Coercivity of H cb magnetic induction 437 [kam] Coercivity of H cj magnetic polarization 719 [kam] 3. Design of axial flux brushless DC motor The designed motor is intended to drive light electric vehicles. The motor should be supplied from a 24 V rechargeable battery. In the process of the design these parameters were assumed: outer diameter, inner diameter, nominal speed, DC supply voltage and parameters of magnetic materials [9-11]. Concept construction of designed axial flux brushless DC motor is presented in figure 4. Table 2 presents main electrical parameters of motor. Dimensions of disc AFPM machine are presented in table 3. Tab.2. Main electrical parameters of the axial flux brushless DC motor Symbol Quantity Value Unit P Nominal power 32 [W] U DC DC Voltage 24 [V] I RMS Nominal current 0.91 [A] T em Nominal Torque (average value) 0.28 [Nm] f frequency 50 [Hz] n Nominal speed 1000 [rpm] p Number of poles 6 [-] B δm Peak magnetic flux density in air gap (D g ) 0.55 [T] m Number of phases 3 [-] K cu Winding factor 0.57 [-] Number of turns in one N c coil 50 [-] N s Number of turns per phase 300 [-] Tab.3. Dimensions of the axial flux brushless DC motor Symbol Quantity Value Unit D o Outer Diameter 72 [mm] D i Inner Diameter 40 [mm] D g Average Diameter 56 [mm] λ Diameter ratio 0.56 [-] L s Axial length of stator 22 [mm] L s1 5 [mm] L s2 Dimensions of stator 5 [mm] L s3 tooth and the space 2 [mm] L s4 filled by the winding 1 [mm] L s5 1 [mm] L r Axial length of rotor 7.5 [mm] L rc Axial length of rotor core 5 [mm] L r1 Length between PM 5 [mm] L PM Axial length of PM 2.5 [mm] L m Axial length of machine 38 [mm] δ Air-gap length 0.5 [mm] D w Diameter of wire 0.6 [mm] Axial section of a motor with marked symbols of length is presented in figure 5. Dimensions for stator tooth and for the space filled by the winding are presented in figure 6. Fig.4. Construction of axial flux brushless DC motor 443

3 magnetic flux density and flux lines are presented in figure 8. Distribution of magnetic induction in air gap is presented in figure 9. Fig.5. Axial section of motor Fig.8. Distribution of magnetic flux density and flux lines in analyzed layer Fig.6. Dimensions of stator tooth and the space filled by a winding 4. 2D FEM calculations First computer calculations of a motor were performed in 2D software. In this case, model was divided and only one part from six, was analyzed. A thickness of analyzed layer, on average diameter, is 1 mm. Fig.7. Method of transformation the 3D geometry of an axial-flux machine to a 2D geometry, which can be used in quasi-3d computation By performing of 2D simulation it is possible (in some approximation) to determine distribution of magnetic induction in an air gap. By changing the value of parameter L r1 and analysis parameters such as: cogging force, maximum force, minimum force, and the average value of force - the parameter L r1 was chosen to achieve minimum pulsation of the force. A position of the rotor was changed and functions F=f(rotor position) were obtained (for each value of parameter L r1). Displacement at about 30 mm with step 1 mm corresponds to rotation of rotor with angle 60 with step 2. For obtained curves only 20 was taking into account. For one rotation of rotor a switching sequence of phases is 20 (18 times for one rotation). Distribution of Fig.9. Magnetic induction in air gap (simulation on average diameter Dg = 56 mm ) Table 4 presents optimization process to obtain optimal value of parameter L r1. Tab.4. Optimization of dimension Lr1 - in the rotor of the axial flux motor L r1 Cooging force Force F max F min F ave F max F min F ave ε mm mn mn % L r1 length of air gap between magnetic poles ε - electromagnetic torque ripple factor F Fmin 100[%] max F ave Graphics interpretation of optimization process is presented in figure 10. Fig.10. Relationship between: F ma x F a ve F min and value of parameter L r1 444

4 B (mt) The lowest value of pulsation, ε = 15 %, was obtained for value of parameter L r1 = 5 mm. Further calculations were performed for the value of parameter L r1 equal 5 mm. 5. 3D FEM simulations Symetry of model allows to split the motor to 12 parts. In 3D software only 1 part from 12 parts was analyzed, which accelerated time of simulations. Figure 11 presents view of generated mesh for 1/12 part of the model. Distribution of magnetic induction on the surface of 1/12 part of motor is presented in figure 12. Figure 13 presents distribution of flux lines inside of a magnetic circuit. Distribution of magnetic induction in the air gap (Fig.13.) obtained by 3D simulation is slightly greater than magnetic induction obtained by 2D simulation. Nevertheless, it is confirm the validity of the analysis presented in Section B = f ( l ) l (mm) Fig.14. Distribution of magnetic induction in air gap (simulation on average diameter Dg = 56 mm ) Maximum value of magnetic induction in air gap is T. Simulation was conducted on average diameter Dg = 56 mm for one magnetic pole - 60º. Electromotive forces e in phases of motor are presented on figure 15. Fig.11. View of generated mesh for 1/12 part of the model Fig.12. Distribution of magnetic induction on the surface of 1/12 part of the motor Fig.15. Electromotive force e induced in phase_a phase_b and phase_c as a function of angle of rotation n=1000 obr/min Shape of electromotive forces is trapezoidal, which satisfies the assumptions of design but generates higher harmonics. The percentage content of harmonics with respect to the first harmonic, for electromotive force in phase_a, is presented on figure 16. Fig.13. Distribution of flux lines for 1/12 part of the motor Fig.16. The percentage content of harmonics with respect to the first harmonic of electromotive force in phase_a Distribution of flux linkage in phases of motor is presented in figure

5 6. 3D simulation vs. analitical calculation In tables below there are presented comparison between 3D simulation and analytical calculation (Tab 5-6). The results are almost on the same level. This confirms the correctness of the calculation. Some mathematic formula to perform analytical calculation are presented on equation 2-5. Fig.17. Distribution of flux linkage in phase_a, phase_b and phase_c as a function of angle of rotation Nominal RMS value of current is I RMS=0.91 A and ideal switching sequence of phases is shown in fig. 18. Tab.5. Comparison of torque between 3D simulation and analitical calculation J 3D simulation Analytical calculation A/mm 2 I m T max T a ve I RMS T [A] [m Nm] [A] [m Nm] , , I RMS I m (2) 3 Fig.18. Current in phases A B C of axial flux brushless DC motor as a function of angle of rotation Relationship between current density and maximum torque is presented in figure 19. With on increase of current, the maximum value of torque increases linearly. Electromagnetic torque of motor as a function of angle rotation is presented on figure 20. A 3N I s RMS (3) 2 2 r i 3 o 2 T 2 B m Ar (1 ) (4) A - electrical loading [A/m] r i - inner radius = D i/2 [mm] r o - outer radius = D o/2 [mm] Tab.6. Comparison of magnetic induction in the air gap between 3D simulation and analitical calculation Kind of analisys 3D simulation Analytical calculation B δm [T] B L B PM m r L (5) PM Fig.19. Relationship between current density and maximum torque I m J (1) S In figures were presented characteristics showing the impact of changes value of parameters such such as: magnetic induction in the air gap and the diameter ratio λ on the value of the torque. Fig.20. Electromagnetic torque of motor as a function of angle rotation Fig.21. Impact of changes values: of the magnetic induction in the air gap and the diameter ratio λ on the value of the torque. Calculations were performed for I R M S=0.91 [A] ; A=4608 [A/m] 446

6 Fig.22. Relationship between diameter ratio λ and value of torque. Calculations were performed for I R M S=0.91 [A] ; A=4608 [A/m] and B δm = 0.55 [T] Fig.23. Relationship between magnetic induction in the air gap B δm and value of torque. Calculations were performed for I R M S=0.91 [A] ; A=4608 [A/m] and λ = 0.56 [-] 7. Conclusions Electromagnetic torque, of axial flux brushless DC motor, calculated by 3D simulation is slightly lower than that obtained from analytical calculations. The analysis of motor showed that induced electromotive force has trapezoidal shape that causes the generation of higher harmonics. The harmonic analysis of the course of the electromotive force shows that the highest value of amplitude has third harmonic and its value is up to 20% amplitude of the fundamental harmonic. Decrease in the amplitude of the third harmonic requires additional design steps: application of skew magnets or special kind of magnetization. This allows to achieved more sinusoidal distribution of magnetic induction in the air gap of the motor. The presented results show that it is possible to design axial flux motor with hybrid magnetic composite as a material on rotor and soft magnetic composites as a material on stator core. In order to verify the results of simulation a physical model will be manufactured and measured. Bibliography [1] S. Gholamian, M. Ablouie, A. Mohseni, S. Jafarabadi: Effect of Air Gap on Torque Density for Double Sided Axial Flux Slotted Permanent Magnet Motors using Analytic and FEM Evaluation Journal of Applied Sciences Research, 2009 [2] A. Darabi, H. Moradi, H. Azarinfar: Design and Simulation of Low Speer Axial Flux Permanent Magnet (AFPM) Machine World Academy of Science, Engineering and Technology [3] R. Huzlik, J. Lapcik, S. Fialova, AXIAL DISC MOTOR FOR TOTAL ARTIFICIAL HEART Zeszyty Problemowe Maszyny Elektryczne Nr 84/2009 [4] S.Huang, J.Luo, F.Leonardi, T.Lipo, A General Approach to Sizing and Power Density Equations for Comparison of Electrical Machines Department of Electrical and Computer Engineering University of Wisconsin-Madison U.S.A [5] B. Ślusarek, B. Jankowski, D. Kapelski, M. Karbowiak, M. Przybylski: The influence of connecting method of hybrid magnetic elements on their physical properties, Materiały konferencyjne z Advances in Powder Metallurgy & Particulate Materials , May 2011, San Francisco, USA [6] B. Ślusarek, B. Jankowski, D. Kapelski., M. Karbowiak, M. Przybylski: Influence of environmental condition on physical properties of hybrid elements prepared by compression moulding Euro PM2011 Congress and Exhibition, 9-12 October 2011, Barcelona, Spain. [7] D. Kapelski, B. Jankowski, M. Karbowiak, M. Przybylski, P. Maciejewski, B. Ślusarek Hybrydowe elementy obwodu magnetycznego wytwarzane metodą klejenia, Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych Politechniki Wrocławskiej Nr 65, Studia i materiały 31, 2011 r., ISSN , str [8] D. Kapelski, B. Jankowski, M. Karbowiak, M. Przybylski, B. Slusarek Research of magnetic properties of hybrid composite elements Przegląd Elektrotechniczny - Electrical Review, ISSN , R. 88 Nr 5a/2012, str [9] S. Wiak, H. Welfle: Silniki tarczowe w napędach lekkich pojazdów elektrycznych, Wydawnictwo Politechniki Łódzkiej ISBN [10] T. Glinka: Maszyny elektryczne wzbudzane magnesami trwałymi, Wydawnictwo Politechniki Śląskiej, 2002 [11] D. Hanselman: Brushless Permanent Magnet Motor Design, Second Edition, Magna Physics Publishing, 2006 Author: Marcin Karbowiak Tele And Radio Research Institute ul. Ratuszowa Warszawa tel. (22) ex. 265 fax (22) marcin.karbowiak@itr.org.pl 447