338 Applied Electromagnetic Engineering for Magnetic, Superconducting, Multifunctional and Nano Materials

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1 Materials Science Forum Online: ISSN: , Vol. 792, pp doi: / Trans Tech Publications, Switzerland Torque Characteristic Analysis of an IM/PM Hybrid Motor by using Finite Element Method Shingo IWAO 1, a, Takashi TODAKA 1,b and Masato ENOKIZONO 1,c 1 Department of Electrical and Electronic Engineering, Faculty of Engineering, Oita University, 700 Dannoharu, Oita , Japan a v12e2003@oita-u.ac.jp, b todka@oita-u.ac.jp, c enoki@oita-u.ac.jp Keywords: Induction motor, permanent magnet motor, hybrid motor, finite element method, torque, electromotive force. Abstract. This paper presents torque characteristic analysis of synchronous induction motors called IM/PM hybrid motors by using the two-dimensional finite element method taking terminal voltage into account. The slip characteristics are analyzed by using multi-meshes corresponding to each rotor position, because the transient numerical analysis is quite difficult due to slip even two-dimensional analysis. There are many researches on IM/PM hybrid motors, however the torque characteristics when they are operating as an induction motor have not yet examined sufficiently. In this paper, we tried to explore how to improve the torque characteristics even operating as an induction motor by incorporating the embedded permanent magnets. The results show that the arrangement of the permanent magnets is very important to improve whole torque characteristics. Introduction The Ministry of Economy, Trade and Industry of Japan has reported that about 53% or more of the total electric power generated in Japan is consuming in motors. There are several kinds of motors, however induction motors (IM) are most popularly utilizing in factories. Therefore reducing losses and improving efficiency of the common induction motors are effective for saving energy. In this paper we focused on a synchronous induction motor (an IM/PM hybrid motor), which permanent magnets (PM) are embedded in the induction machine s rotor (IPM). This machine can improve the staring characteristic in comparison with that of synchronous permanent magnet motors. The torque and efficiency are higher at synchronous operation than that of induction operation of the same output power. The torque characteristics of the two types of IM/PM hybrid motors are numerically analyzed by using the finite element method and compared with that of IM. The results show that the arrangement of the permanent magnets is very important to improve whole torque characteristics [1-5]. IM/PM hybrid motors IM/PM hybrid motors are a kind of synchronous motors, which permanent magnets are embedded in the induction machine s rotor. IM/PM hybrid motors start as a squirrel induction motor by the torque generated by electromagnetic force between the currents flowing in the secondary conductors and the magnetic field. Therefore detecting the rotor position is needless at starting. As a result, IM/PM hybrid motors have a superior starting characteristic in comparison with that of the permanent magnet synchronous motors. When IM/PM hybrid motors are rotating at the synchronous speed, the torque is generated by the only permanent magnets. This means that IM/PM hybrid motors are independent from the secondary copper loss at the steady state operation. The torque characteristics when they are operating as an induction motor have not yet reported sufficiently, because the transient numerical analysis is quite difficult due to slip even two-dimensional analysis. In this paper, we tried to explore how to improve the torque characteristics when it is operating as an induction motor by incorporating the embedded permanent magnets. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-06/03/16,11:35:30)

2 338 Applied Electromagnetic Engineering for Magnetic, Superconducting, Multifunctional and Nano Materials Computation method Formulation of the magnetic field analysis [6]. From the Maxwell s equations, the governing equation of the electromagnetic field expressed with the magnetic vector potential A is given by 0 e 0 rot rota J J rot M, (1) A J e grad, (2) t divj 0, (3) e where, ν is the magnetic resistivity, J 0 the exciting current density, J e the eddy current density, ν 0 the magnetic resistivity of vacuum, M the magnetization of the permanent magnet, σ the conductivity, and the electric scalar potential. The two-dimensional finite element equation is written as the following equation by substituting the expression (2) into (1) and discretizing by using the Galerkin method. e 3 CieC je DieD je J z Gi y e x e Aje j e e Az t 3 z 1 1 2, (4) 0 M xdie M ycie 2 e 3 Aje, z 3S t (5) j1 where, A z (A je ) is the z-directional component of the magnetic vector potential, J z the z-directional component of the exciting current density, S the cross-sectional area of the conductor flowing eddy currents, Δ the area of the finite elements, k (k = x or y) the x- or y component of the magnetic resistivity, and M k (k = x or y) the x- or y component of the magnetization of permanent magnets. C ie, C je, D ie, and D je are the coefficients derived from the linear interpolation function. Because the exciting current is usually unknown and it changes depending on loads, the terminal voltage method is applied to solve the problem: di d R R I L V, (6) dt dt 0 0 c nc d dxdy S S A s, (7) c c nc J0 I 0n s, (8) Sc where, V 0 is the terminal voltage, I 0 the excitation current, Φ the flux linkage of the winding, L 0 the leakage inductance, R 0 the resistance of the primary winding in the finite element region, R c the resistance of the coil end, n c the number of turns of the primary winding, S c the cross-sectional area of the winding, ds the small element along the winding, and n s the unit vector of the direction of the exciting current. The finite element analysis considering the voltage source can be performed by solving (4) and (6) simultaneously.

3 Materials Science Forum Vol Torque Calculation. The Maxwell stress method is used to obtain the torque characteristics: 1 1 n Bn Hn Bt Ht, (9) 2 2 t BH n t, (10) where, σ n and σ t are the Maxwell stress tensor. B n and B t are the normal and tangential component of the magnetic flux density, respectively. H n and H t are the normal and tangential component of the magnetic field strength, respectively. Because σ t contributes to the torque, T is given by the following equation. T BB n t r l D, (11) 0 where, r is the radius from the center of the rotating body to its surface, l the unit length in the tangential direction, D the product thickness of the rotating body, and μ 0 the permeability in vacuum. IM/PM hybrid motor models and condition used in the analysis Fig. 1 shows the analyzed models including two types of IM/PM hybrid motor models. Fig. 1 (a) shows the fundamental induction motor model and Figs. 1 (b) and 1 (c) are IM/PM hybrid motors named Model A and Model B, respectively. The stator winding of these motors was assumed to the two-layer winding with a short-pitch. Table 1 shows the condition used in the analysis. These data were kept to be constant during the investigations. Table 1 Conditions used in the Analysis Number of phase, pole 3 phase, 6 pole Frequency 60 [Hz] Stator Outer diameter 590 [mm] Number of slots 36 Rotor Outer diameter 376 [mm] Number of slots 24 Air gap length 2 [mm] Lamination thickness 440 [mm] Electrical steel sheet 50A470 Voltage 400 [V] Number of turns of coil 18 [turns/slot] Coil resistance [Ω/phase] Revolution speed 1200 [min -1 ] Residual magnetization 1.2 [T] (a) IM (b) Model A (c) Model B Fig. 1 Analyzed models

4 340 Applied Electromagnetic Engineering for Magnetic, Superconducting, Multifunctional and Nano Materials Analyzed results Fig. 2 shows the magnetic flux lines for each model: (a) the IM at slip equals 0.1, (b) the Model A without excitation, and (c) the Model B at without excitation. The magnetic fluxes at the magnet ends of the Model A often made a closed loop and those fluxes were not use effectively to generate electromagnetic force. The magnetic fluxes of the Model B pass through well into the stator. (a) IM (b) Model A (c) Model B Fig. 2 Magnetic flux lines Fig. 3 Comparison of torque characteristics Fig. 3 shows torque characteristic of the each model. Induction motors are usually operated at a low slip around the slip equals 0.2. The torque of the IM was higher than that of IM/PM hybrid motors when the machines were operating at slip = 0.2. The starting torque of IM/PM hybrid motors at slip = 1.0 was higher than that of the IM. However at slip = 0.4, the Model B showed the highest torque. The starting torque of the hybrid motors was larger than that of the IM. Here, we names Model A without magnet Model A 0 and Model B without magnet Model B 0, respectively Fig. 4 shows the magnetic flux lines of the Model A 0 and the Model B 0. There is no magnetic flux generated by the magnets and the magnetic fluxes avoided the air regions where the magnets were removed. Fig. 5 shows torque characteristic of the IM, Model A 0 and Model B 0. The torque characteristics of the Model A 0 and the Model B 0 did not change from the one of the IM. In other words, it can be said that the torque characteristics were changed by the embedded permanent magnets in the Model A and Model B. At asynchronous, induction motors generates a torque. On the other hand permanent magnet synchronous motor obtains a torque whit a load angle at synchronous. Because the two phenomena are the relationship conflicting, it is necessary to devise another construction for effectively using the magnet torque at asynchronous operation. Fig. 6 shows the components of the magnet torque depending on the slip derived by Fig.3 and Fig.5. Figs. 6 (a) and (b) show the torques of the Model A and A 0, and ones of the Model B and B 0, respectively. The magnet torque was varied as a function of the slip, and it became negative as the slip became smaller. The magnet torque of the Model B worked as positive at slip = 1.0 and slip = 0.4. Because r, l, D and μ 0 in Eq. (11) are constant, B n and B t are important parameters. We therefore focus on value of B n times B t (B n B t ). Figs.7 and 8 show B n B t value at slip = 0.4 and slip = 0.1, respectively. The maximum value of B n B t in the air gap of Model B was larger than that of IM. This is because magnetic flux increases by the permanent magnets. Average value of B n B t in the air gap of IM

5 Materials Science Forum Vol and Model B was and at slip = 0.4, respectively. Average value of B n B t in the air gap of IM and Model B was and at slip = 0.1, respectively. The B n B t value of Model B increased at slip = 0.4 in comparison with that of IM, however it decreased at slip = 0.1. If we can enlarge the B n B t value by optimizing the embedded permanent magnet arrangement, the total torque can be improved like the torque of Model B at slip = 0.4. It seems there is a possibility to increase total torque by utilizing the permanent magnet torque effectively or controlling the residual magnetization of the permanent magnets. (d) Model A 0 (e) Model B 0 Fig. 4 Magnetic flux lines Fig. 5 Comparison of torque characteristics (a) Model A (b) Model B Fig. 6 Components of the magnet torque depending on the slip (a) IM (b) Model B Fig. 7 B n B t value at slip = 0.4.

6 342 Applied Electromagnetic Engineering for Magnetic, Superconducting, Multifunctional and Nano Materials (a) IM (b) Model B Fig. 8 B n B t value at slip = 0.1. Conclusion The torque characteristics of IM/PM hybrid motors, which have different embedded permanent magnet structure in the induction operation mode, have been compared. We have clarified the torque characteristics of the hybrid motor in asynchronous operation mode. Because the permanent magnet sometimes induced breaking torque due to the slip, the whole torque characteristics could not be improved with the IPM rotor. Near the synchronous speed, the magnet torque acted as a braking force. It was found that the permanent magnets were useful in order to increase the starting torque, also at the middle slip around 0.4, the magnet torque of the Model B worked as positive. Therefore, there is a possibility to increase total torque by effectively utilizing the permanent magnet torque. References [1] K. Yamazaki, Y. Kawase, T. Yamaguchi, K. Miyata, T. Yamada, T. Fujioka, H. Kaimori, H. Yano, M. Nakamura, in: Electromagnetic Field Analyses of an IPM Motor : Comparisons between Methods of Analysis in Case of a Benchmark Model (Papers of Joint Technical Meeting on Static Apparatus and Rotating Machinesof IEEJ, SA-07-25, RM-07-25, pp.45-50,2007). [2] N. Sakamaki, I. Morita, in: Study on Synchronous Induction Hybrid Motors (Papers of Joint Technical Meeting on Static Apparatus and Rotating Machinesof IEEJ, RM-09-54, pp.19-24, 2009). [3] K. Kurihara, Starting Performance Analysis for Induction Motor and Self-Starting Permanent Magnet Synchronous Motor by FEM (Papers of Joint Technical Meeting on Static Apparatus and Rotating Machinesof IEEJ, RM , pp , 2003). [4] T. Sano, T. Watanabe, K. Sawa A Study on Magnetic Circuit Design of Self-start Interior Permanent Magnet Synchronous Motor (Papers of Joint Technical Meeting on Static Apparatus and Rotating Machinesof IEEJ, RM-04-66, pp , 2004). [5] A. Takahashi, S. Kikuchi Line-Starting Permanent Magnet Synchronous Motor for IE4 Efficiency Classification (Papers of Joint Technical Meeting on Static Apparatus and Rotating Machinesof IEEJ, RM , pp , 2010). [6] T. Nakata, N. Takahashi in: Finite Element Method in Electrical Engineering (Morikita Publications, Japan 1982).

7 Applied Electromagnetic Engineering for Magnetic, Superconducting, Multifunctional and Nano Materials / Torque Characteristic Analysis of an IM/PM Hybrid Motor by Using Finite Element Method /