IEEE TRANSACTIONS ON MAGNETICS, VOL. 43, NO. 6, JUNE 2007
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Optimization of the Magnetic Pole Shape of a Permanent-Magnet Synchronous Motor Ping Zheng, Jing Zhao, Jianqun Han, Jie Wang, Zhiyuan Yao, and Ranran Liu Harbin Institute of Technology, Harbin, 150001, China A kind of six-slot/four-pole permanent-magnet (PM) synchronous motor is very popular nowadays for the advantages of saving coppers and because it is easy to manufacture. The magnetomotive force (MMF) produced by the six-slot stator windings are not symmetrical under the four poles, and more harmonics exist in the air gap, which will increase the torque ripple and noise. In this paper the rotor structure is optimized from the aspects of magnetic-pole embrace, magnetic bridge, and magnetic-pole eccentricity to obtain better air-gap magnetic field distribution and torque curves. Index Terms—Finite-element method (FEM), magnetic pole, magnetic bridge, permanent-magnet synchronous motor (PMSM).
I. INTRODUCTION
D
UE TO THE excellent performance, permanent-magnet synchronous motors (PMSMs) are generally considered as the most promising motors and widely used in many fields [1]–[5]. Modifications and innovations are often made to the PMSMs to satisfy different applications. For the PMSMs used in the compressors of air conditioners, a kind of six-slot/four-pole structure is very popular nowadays for the advantages of saving coppers and easy to manufacture. Different from conventional windings, the six-slot stator windings cannot produce symmetrical magnetomotive force (MMF) under the four poles, and more harmonics exist in the air gap, which will increase the torque ripple and noise. In this paper, the finite-element method (FEM) is used to optimize the rotor from the aspects of magnetic-pole embrace, magnetic bridge, and magnetic-pole eccentricity to obtain better air-gap magnetic field distribution and torque curves [6]–[11]. The schematic diagram of the PMSM is shown in Fig. 1, and the main parameters are shown in Table I.
Fig. 1. Schematic diagram of the six-slot/four-pole PMSM.
TABLE I MAIN PARAMETERS OF THE PMSM
TABLE II CONTRAST OF TORQUE CHARACTERISTICS WITH DIFFERENT MAGNETIC POLE EMBRACES (1)
II. OPTIMIZATION OF THE MAGNETIC-POLE EMBRACE As to PMSM, both the amplitude and distribution of the air-gap magnetic field will be affected by the changing of the magnetic-pole embrace, which will further influence the average torque and torque ripple. With the volume of the permanent magnets kept unchanged, the magnetic-pole embrace varies from 0.67 to 0.92 by the step of 0.05, and the torque curves are obtained by time-stepping FEM. From the torque analysis, the average torque and torque ripple can be obtained, which are shown in Table II. As can be seen from Table II, with the increase of the magnetic-pole embrace, the average torque continues increasing, whereas the torque ripple decreases firstly and then increases. Since the changing of the torque ripple is much sharper than that of the average torque, the torque ripple is used as the criteria to determine the optimum point. The magnetic-pole embrace of 0.82 brings the lowest torque ripple, which is chosen as a reference point of a smaller range for further investigation.
The magnetic-pole embraces of 0.80 to 0.86 with the interval of 0.01 are further compared and the torque characteristics are shown in Table III. As shown in Table III, the magnetic-pole embrace of 0.85 is the optimum point, which gains the average-torque increase of 1.44% and the torque-ripple decrease of 4.07% compared to the magnetic-pole embrace of 0.82. In order to judge the degree of the air-gap magnetic field being close to the sine wave, the aberrance rate of air-gap magnetic field is introduced, which can be expressed as
% where Digital Object Identifier 10.1109/TMAG.2007.893631 0018-9464/$25.00 © 2007 IEEE
(1)
is the aberrance rate of air-gap magnetic field, are the harmonic components of the air-gap
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 43, NO. 6, JUNE 2007
TABLE III CONTRAST OF TORQUE CHARACTERISTICS WITH DIFFERENT MAGNETIC POLE EMBRACES (2)
TABLE V CONTRAST OF TORQUE CHARACTERISTICS WITH DIFFERENT MAGNETIC BRIDGE WIDTH (2)
TABLE IV CONTRAST OF TORQUE CHARACTERISTICS WITH DIFFERENT MAGNETIC BRIDGE WIDTH (1)
Fig. 2. Shape of the eccentric magnetic pole.
flux density, and is the fundamental component of the air-gap flux density. The aberrance rates of air-gap magnetic field are respectively 25.54% and 24.63% with the magnetic-pole embrace of 0.82 and 0.85. It indicates that the optimization of magnetic-pole embrace can also improve the magnetic-field wave. III. OPTIMIZATION OF THE MAGNETIC BRIDGE The magnetic bridge, which is a part of the rotor core, can protect the permanent magnets from flying away from the rotor, but it also provides the path for the permanent-magnet leakage flux. The shape and size of the magnetic bridge are crucial for the leakage-flux factor, and also influence the torque, speed, and mechanical intensity, etc. The length of the magnetic bridge has little influence on the leakage flux, whereas the width of the magnetic bridge is much more important. The less width the magnetic bridge has, the better performance the machine can obtain. However, the width of the magnetic bridge can not be too small with the mechanical-intensity limit of the slice. Based on the above optimized model (six-slot/four-pole structure and 0.85 magnetic-pole embrace), the magnetic-bridge width varies from 0.5 to 1.75 mm by the step of 0.25 mm, and the corresponding torque characteristics are shown in Table IV, which are calculated according to the obtained torque curves by FEM. It can be seen from Table IV that the increase of the magnetic-bridge width reduces the torque ripple, but also causes the torque loss. So the choice of the magnetic-bridge width should follow the compromise principle: the torque ripple is effectively reduced but with the torque loss as little as possible. From the changing rate of the torque and torque ripple in Table IV, we can see that the torque ripple decreases sharply while the torque does tardily when the magnetic-bridge width varies from 0.5 to 1 mm. However, after 1 mm, the law of changing trend is opposite. So the magnetic-bridge width of 1 mm is preferred according to the compromise principle.
In order to get the optimum point, the torque characteristics with four new magnetic-bridge widths, i.e., 0.8, 0.9, 1.1, and 1.2 mm, are further investigated and compared with the case of 1 mm, as shown in Table V. The data of Table V show that the reduction rates of the average torque are at quite close range, but those of the torque ripple change notably, which can reach the peak value at the magnetic-bridge width of 0.9 mm. Based on the compromise principle, 0.9 mm can be regarded as the optimum point of the magnetic-bridge-width choice. By further analysis, the aberrance rates of the air-gap magnetic field with the magnetic bridge width of 1 and 0.9 mm are respectively 26.43% and 24.23%, which also shows the performance improvement. IV. OPTIMIZATION OF THE MAGNETIC-POLE ECCENTRICITY The eccentric magnetic-pole shape is adopted, as shown in Fig. 2. O is the center of the magnetic-pole outside arc, O’ is the is the thickness center of the magnetic-pole inside arc, and of the eccentric magnetic pole, which changes with the angular position. Owing to the use of the eccentric magnetic pole, the air-gap magnetic field can be more close to the sine wave and the cogging torque can be reduced. The machine is further optimized with the investigation of the magnetic-pole eccentricity. The eccentric distance, which is the distance between O and O’, varies from 0 to 2.5 mm with the interval of 0.5 mm, and the corresponding average torques and torque ripples are shown in Table VI. As shown in Table VI, with the increase of eccentric distance, the average torque firstly decreases and then increases, whereas the torque ripple keeps increasing. So it can be deduced that the better performance will appear at the point of small eccentric distance, and 0.5 mm is chosen as the reference point for a smaller range investigation. The eccentric distance changes from 0.3 to 0.7 mm by the step of 0.1 mm, and the corresponding torque characteristics
ZHENG et al.: OPTIMIZATION OF THE MAGNETIC POLE SHAPE
TABLE VI CONTRAST OF TORQUE CHARACTERISTICS WITH DIFFERENT ECCENTRIC DISTANCES (1)
TABLE VII CONTRAST OF TORQUE CHARACTERISTICS WITH DIFFERENT ECCENTRIC DISTANCES (2)
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V. CONCLUSION A PMSM of six-slot/four-pole structure used in the compressors of air conditioners is investigated in this paper. The magnetic pole shape of the rotor is optimized from the aspects of magnetic-pole embrace, magnetic bridge and magnetic-pole eccentricity by FEM. To obtain the optimum performance, the magnetic-pole embrace of 0.85, the magnetic-bridge width of 0.9 mm, and the magnetic-pole eccentricity of 0.45 mm is selected. The torque increases by 3.2%, and the torque ripple decreases by 8.7% after optimization. The air-gap magnetic field is more close to the sine wave with the aberrance-rate decrease of 6.1%. The PMSM performance can be effectively improved by the optimization of the magnetic-pole shape. ACKNOWLEDGMENT
TABLE VIII CONTRAST OF TORQUE CHARACTERISTICS WITH DIFFERENT ECCENTRIC DISTANCES (3)
This work was supported by National Natural Science Foundation of China under Project 50577011 and the 863 Plan of China under Project 2006AA05Z231. REFERENCES
Fig. 3. Torque curve after optimization.
are shown in Table VII. The result data show that the average torques are at quite close range, and the torque ripple is lowest at the point of 0.5 mm. So 0.5 mm can be regarded as the preferred eccentric distance among the compared ones. The average torque and torque ripple with two more eccentric distances, i.e., 0.45 and 0.55 mm are compared with the case of 0.5 mm for further optimization, as shown in Table VIII. It can be seen that the eccentric distance of 0.45 mm can be regarded as the optimum point with the larger torque and lower torque ripple. The further analysis shows that the aberrance rate of the air-gap magnetic field is 24.23% with the concentric magnetic pole and 23.97% with the 0.45 mm magnetic-pole eccentricity, which indicates the further performance improvement. When the finally optimized magnetic pole shape is employed, the torque curve is shown in Fig. 3.
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Manuscript received October 31, 2006; revised February 8, 2007 (e-mail:
[email protected]).
