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Research on Two Manners of Magnetization in Surface-mounted Permanent Magnet Machine Deming Zhu,Caohui Zhao,Yangguang Yan Aero-Power Sci-tech Center, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016 ,China Abstract—Two manners of magnetization in surfacemounted permanent magnet (SPM) machine have been investigated. The 2D Finite Element Analysis model that is used to compute the field in this paper is first confirmed according to the parameters in a literature. Then the fields obtained from the accurate 2D Finite Element Analysis model are compared, and the differences between the field of the machine with two magnetization manners in both inner rotor and outer rotor are illustrated. The rules of air-gap flux varied with the pole number and thickness of magnet are further analyzed with different magnetization in both inner rotor and outer rotor at last. The conclusions derived from the outer rotor SPM machine are also suitable for DC permanent machine. This paper helps us choose the right manner of magnetization to bring into full play of the potential of the magnet and improve the performance of the machine. (a) The divisions of mesh Index Terms— SPM Machine, Radial Magnetization, parallel Magnetization. I. INTRODUCTION The SPM machine, especially the rare earth permanent magnet (REPM) machine, has been widely studied for its high efficiency advantage [1~2]. The SPM machine can be classified into inner rotor and outer rotor. The magnet in it has two manners of magnetization, which are parallel and radial magnetization. In the 90’s, the magnets are mostly magnetized parallel, while the radial magnetization manner is developed just recently. Many literatures have argued that the SPM DC machine has higher air-gap flux when it is magnetized radial, and the error became smaller if the pole number is larger. It’s also argued that in the SPM AC machine, the air-gap flux is larger when it is magnetized parallel, and the error is larger if the pole number is larger [3~7]. Two magnetizations are both studied by the 2D Finite Element Analysis model, which is verified according to the parameters in a literature. The effects on the magneto motive force, the field distribution, and the sharp of airgap density are discussed. Then the rules of air-gap flux varied with the pole number and thickness of magnet are further analyzed with different magnetization in both inner rotor and outer rotor. The situations of choosing which magnetization are illustrated and the range of the suitable magnet thickness is presented at last. This paper helps us choose the right manner of magnetization and the suitable thickness of the magnet to bring into full play of the potential of the magnet and improve the performance of the machine. (b) The waveform of the flux density under a pole Fig.1. The divisions of mesh and waveform of the flux density in the finite element analysis model solves the little areas by linear or non-linear interpolation individually, and totals each little area result to receive the universe solution. The Finite Element method has the high precision and the comparative advantage in analysis of performance of electric magnetic field [5]. A 2D finite element analysis model is created using the parameters in [8]. And the divisions of mesh are showed in fig.1 (a). The energy in the surface between the stator core and the air-gap is changed in large amount. So the meshes should be subdivided in order to get the accurate solutions. The waveform of the flux density under a pole of the motor calculated by finite element method is provided in fig.1 (b). The error between the model and the value listed in [8] is about 2.58%, which is acceptable and also verifies the model. Ⅲ. FIELD ANALYSIS A. Distribution characteristic of the field in the inner rotor permanent magnet machine Fig.2 shows the field of the inner rotor permanent magnet machine with two magnetizations separately. In order to discuss the air-gap flux with different pole numbers, the effect of the teeth is ignored, and the slotless model is used. Fig.2 (a) shows that the field in the magnet with parallel magnetization is nearly uniform. The flux lines II. THE 2D FINITE ELEMENT ANALYSIS MODEL The Finite Element Method is a numerical method, which divides the whole model into little areas, then 460 arc shape. If the magnet magnetizes by parallel field, the direction of the magnetic field strength is parallel with the centerline of the magnet. So the l PM equals to the value of ( Rm − Rr ) in the centerline of the magnet, and reduce after increasing to both sides ( Rm here is the outer radius of the magnet while Rr is the inner radius of the magnet). The l PM equals to the value of ( Rm − Rr ) , if the magnet is radial magnetization. In the centerline of the magnet, l PM is lager than that with radial magnetization. And the parallel magnetization has higher peak value of air-gap flux density than the radial magnetization, but not always the higher air-gap flux at the same time. Fig.3 compares the l PM along the arc the magnet with two magnetizations in the SPM machine. α m is the pole-arc coefficient in fig.3. The value of l PM is a constant in the radial magnetization machine, and the air-gap flux density is approximate of a rectangular waveform, which is very suitable for brushless DC motor. (a) Parallel magnetization B. Distribution characteristic of the field in the outer rotor permanent magnet machine Fig.4 compares the field of the outer rotor permanent magnet machine with two magnetizations. The inner surface of the magnet faces to the air-gap while the outer surface of the magnet faces to the air-gap in the inner rotor SPM machine. The field distribution is similar to the inner rotor SPM machine except that the leakage flux between the poles in parallel magnetization is much larger than that in the radial magnetization. As a result, choosing the radial magnetization in the outer rotor permanent magnet machine can get larger air-gap flux. (b) Radial magnetization Fig.2 Field distribution in the inner rotor PM machine Parallel magnetization R m − Rr Radial magnetization 1 − αm 1 + α m Electrical angle π π 2 2 Fig.3 Length of magnetization path are mostly cross through the air-gap and the leakage flux between the poles is also small. But the field in the magnet with radial magnetization is different, as shows in fig. 2(b). The flux density in the magnet increases along the radius from outer to inner, reaching its max value at the inner radius of the magnet. As a result, the region near the inner radius of the magnet can be saturated easily, which limits the value of the air-gap flux. In addition, the leakage flux between the poles is larger than that with parallel magnetization. So the magnet with parallel magnetization in inner rotor PM machine has more potential to provide the air-gap flux. The magneto motive force in the magnet is also different, due to the different magnetizations. According to the law of Ampere, the magneto motive force can be described by: FPM = H c * l PM (a) Parallel magnetization (1) where l PM is the length of magnetization path, H c is coercive force of the magnet. For a fixed value of H c , FPM is proportional to the l PM . In the SPM machine, both of the outer and the inner surface of the magnet are (b) Radial magnetization Fig.4 Field distribution in the outer rotor PM machine 461 IV. THE EFFECTS OF MAGNETIZATION VARIED WITH THE STRUCTURE PARAMETERS The air-gap flux is a base parameter in SPM machine. And the magnetization has an effect on the air-gap flux as discussed above. The effect is varied with the structure parameters, which will be further studied here. In order to let the conclusions be general, we define: p ⎧ ⎪ φtotal = ∑ φi = f ( p, β ,α ) i =1 ⎪ Rm ⎪ ⎨β = Rr ⎪ g ⎪ ⎪ α=R m ⎩ (2) (c) Parallel magnetization Vs Radial magnetization Fig.5 The total air-gap flux varied with the structure parameters in the inner rotor machine the stator yoke in the model is so small that its effect on the air-gap flux can be ignored. The total air-gap flux varying with the structure parameters in the inner rotor machine with magnet parallel magnetization and radial magnetization are shown in Fig.5 (a)(b) separately. As the thickness of the magnet rising, the air-gap flux with parallel magnet closes in upon a constant. However, there is a peak value of air-gap flux with radial magnetization. So both of the magnets with different magnetization have an optimization value. The optimization value of β is between 0.085 and 0.9, under the conditions that α is from 0.024 to 0.072,and p is from 2 to 8.The length of the air-gap varies small, so the range of the parameter α here is wide enough for PM machine designing. Fig.5 (c) compares the two magnetizations. When the pole number is more than 2,the air-gap flux with magnet parallel magnetization is larger than that with magnet radial magnetization. And the phenomenon is more obvious if pole number is small, or the magnet is thick. The condition is more complex, when the pole number equals to 2, and will be illustrated in other paper. where g is the length of the air-gap, p is the pole number. Rm is the outer radius of the magnet while Rr is the inner radius of the magnet in the inner rotor SPM machine, and they are reverse in the outer rotor SPM machine. A. The inner rotor SPM machine For a fixed value of Rm , the thickness of the magnet is changed with the parameter β , which is defined in (2). And the length of the air-gap is changed with the parameter α , which is also defined in (2). The total airgap flux varied with the parameters p, β , α is calculated by the 2D finite element model, which is verified in part II. Fig. 5 clearly shows the results, and the flux density of B. The outer rotor SPM machine For a fixed value of Rm , the thickness of the magnet is changed with the parameter β , and the length of the air-gap is changed with the parameter α . (a) Parallel magnetization (a) Parallel magnetization (b) Radial magnetization 462 air-gap flux than that with radial magnetization when the pole number is more than 2. (2) The effect of the magnetization on the air-gap is more obvious when the pole number is small and the magnet is thick. (3) There is an optimization value of magnet thickness, no matter which magnetization is. The optimization value of the magnet thickness ( β ) is between 0.85 and 0.9. B. Outer rotor SPM machine (1) The machine with radial magnetization has a higher air-gap flux than that with parallel magnetization. (2) The effect of the magnetization on the air-gap is more obvious when the pole number is small and the magnet is thick. (3) There is also an optimization value of magnet thickness, no matter which magnetization is. The optimization value of the magnet thickness ( β ) is between 1.2 and 1.3 . (b) Radial magnetization REFERENCES [1] Gu Qishan. Gao Hongzhan. The Fringing Effectin PM electrical machines. ElectricMachines and Power Systems,vol.II: pp.159~169. 1986. [2] N. Boules. Prediction of No-load Flux Density Distribution in PM Machines. IEEE Trans. Industrial vo l. IA 221:pp. 633~643.App l., 1985. [3] Renyuan Tang.Modern permanent machine theory and design. Beijing. Publishing House Of the Mechanical Industry,1994. [4] Xiuhe wang, Yan Li,Yanzhong Wu, Renyuan Tang. Working poin determination of radial magnetized permanent magnet in PM machine. New Technique Of Electrician and Electrical Energy,pp.43～45. 1998,3. [5] Ruifang Liu. Research on analysis method for performance of permanent magnet electrical machine based on the electromagnetic field numerical calculation. Southeast university. pp.29～30, 2002,12. [6] Xu Yanliang Yao Flan Fang Jiancheng. Halbach Array Permanent Magnet Machine and Performance Comparison with the Normal Array One (I ). Transactions Of China Electro Technical Society. 19(2),pp.79～83.2004. [7] Chengyuan Wang,Meiwen Zhou,Dingqin Guo. Vector Control Of AC Servomotor. Beijing. Publishing House Of the Mechanical Industry,1994. [8] Zhongming Li ,Weiguo Liu. Rare earth permanent magnet machine. Beijing. National Defence Industry Press,1999. (c) Parallel magnetization Vs Radial magnetization Fig.6 The total air-gap flux varied with the structure parameters in the outer rotor machine Fig. 6 clearly shows the results. No matter what value p and α are, the magnets also have an optimization value. The optimization value of β is between 1.2 and 1.3, under the conditions that α is from 0.024 to 0.056,and p is from 2 to 8. The air-gap flux with magnet radial magnetization is larger than that with magnet parallel magnetization. And the phenomenon is more obvious if pole number is small, or the magnet is thick. V. CONCLUSIONS Two manners of magnetization in surface-mounted permanent magnet (SPM) machine have been investigated. The conclusions are shown as follows: A. Inner rotor SPM machine (1) The machine with parallel magnetization has a higher 463