4894 IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 8, AUGUST 2013

A 2-D Finite-Element Analysis for a Permanent Magnet SynchronousMotor Taking an Overhang Effect Into Consideration

Dong-Kyun Woo, Dong-Kuk Lim, Han-Kyeol Yeo, Jong-Suk Ro, and Hyun-Kyo Jung

School of Electrical Engineering, Seoul National University, Gwanak-ro, Gwanak-gu, Seoul 151-742, Korea

In the two-dimensional (2-D) finite-element (FE) analysis, the overhang effect can be considered through an increase in the remanenceflux density of the permanent magnet in order to reflect the increment of the air-gap flux density due to the overhang structure. However,a repetitive 2-D FE analysis was performed in order to match the air-gap flux density with it in the three-dimensional (3-D) FE analysis.The proposed method accurately accounts for the overhang effect without trial and error. From the results of the 3-D FE analysis, thevalidity of the proposed method is verified.

Index TermsFerrite magnet, finite-element (FE) analysis, overhang effect, permanent magnet synchronous motor (PMSM).

I. INTRODUCTION

I N A permanent magnet synchronous motor (PMSM), arare-earth permanent magnet (PM) has been employedto ensure a high torque density and good efficiency [1][4].However, the increasing demand and uneven distribution forrare-earth materials has led to an undersupply and an increasein the cost of these materials. This has motivated many re-searchers to study the development of the PMSM using nonrare-earth material such as ferrite PM.The energy product of a ferrite PM is lower than that of a rare-

earth PM. Moreover, the coercive force and the remanence fluxdensity of ferrite PMs are much lower than those of rare-earthPMs. The magnet torque of a PMSM using a ferrite PM is muchlower than that using a rare-earth PM. Therefore, the overhangstructure for a radial-fluxmotor using a ferrite PM has been usedto improve the performance of the motor [5][8].By making the rotor longer than the stator in the axial direc-

tion [9], as shown in Fig. 1, the loss of leakage flux at the endof the stack could be offset, thus improving of the characteristicof the motor. This structure is termed the overhang.A two-dimensional (2-D) finite-element (FE) analysis is

much faster than a three-dimensional (3-D) approach in termsof the modeling and computation costs. However, the 2-D FEanalysis for an electromagnetic field analysis cannot guaranteeaccuracy when analyzing a PMSM which uses the overhangstructure, as overhang and end-winding effect cannot be takeninto consideration in a 2-D FE analysis [10]. 2-D character-istics such as the flux-linkage and air-gap flux density willbe overestimated, while 3-D FE analysis agrees well with themeasurement.The previous study addressed overhang effect in a 2-D FE

analysis according to the change in the material property usinga trial-and-error method through correction of the remanence

Manuscript received December 12, 2012; revised January 17, 2013; acceptedFebruary 18, 2013. Date of publication February 22, 2013; date of current ver-sion July 23, 2013. Corresponding author: J.-S. Ro (e-mail: jongsukro@naver.com).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMAG.2013.2248374

Fig. 1. Analysis model.

flux density in a PM [11]. In [11], in order to correct the air-gapflux density in models with and without the overhang structure,the remanence of the PM was increased according to the dif-ference in the air-gap flux density over the arc line in the axialcenter position of the air-gap. However, if the stack length of themotor (i.e., the motor aspect ratio) correspondingly increasesin comparison with the diameter of the motor, the change ofthe flux generated in the axial center position of the air-gap be-comes more insignificant than that of the flux produced alongthe axial direction. Moreover, if the motor has a small overhangand a high aspect ratio, the difference of the air-gap flux den-sity in a model between with and without the overhang struc-ture would be very small. In [9], an experimental design methodwas performed to consider the overhang effect in the design ofa motor. The experimental design method can be used to as-sess the screening activity and the polynomial regression ac-tivity. The screening activity involves finding the main factorsthat significantly influence the response [13][15]. However, theexperimental design method requires many analyses to find thefactors that are sensitive to the response.To address this problem, we propose a novel analysis method

that considers the overhang effect in a 2-D FE analysis. The pro-posed method determines the effective remanence flux densitythrough a single magneto-static FE analysis.

II. ANALYSIS MODEL

In a conventional PMSM, a hall sensor was used to detect theposition of the rotor and the rotational speed in response to amagnetic field [12]. In order to operate a hall sensor, an addi-

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WOO et al.: 2-D FE ANALYSIS FOR A PMSM TAKING AN OVERHANG EFFECT INTO CONSIDERATION 4895

TABLE ISPECIFICATION AND DIMENSION OF ANALYSIS MODEL

tional magnet or the use of the overhang structure to generatethe magnetic flux is required.When the overhang structure is used instead of an additional

magnet as the sensor magnet, the overhang protrudes from theside of the rotor, leading to a lack of balance. Therefore, thestructure of the motor becomes asymmetric. The asymmetricaloverhang structure of the motor creates Z-directional thrust dueto the asymmetrical flux density and the unbalanced mass dis-tribution in the Z-direction [12]. This Z-directional thrust gen-erates Z-directional vibration, which not only causes damage tobearings but also intense noise. In order to avoid Z-directionalthrust, the symmetrical overhang structure was applied in thisstudy.There are generally two types of PMSMs: the first with a

surface permanent magnet (SPM) motor in which the PMs aremounted on the rotor surface and the second with an interior per-manent magnet (IPM) motor in which PMs are mounted insidethe rotor. The size of the air-gap in the SPM motor is mainlydetermined by the thickness of the PM. The armature reactioneffect because of the large air-gap in the SPMmotor is less dom-inant than that of the IPM motor.When a rare-earth PM is used for the SPM motor, the air-gap

flux density is enough to saturate the teeth of the stator withoutthe overhang structure. The remanence magnetic flux densityof the ferrite PM is lower than that of a rare-earth permanentmagnet. Therefore, when the ferrite PM is used with the SPMmotor, the overhang structure is suitable for the rotor. In otherwords, the overhang structure is essential for a SPM motor,which uses the ferrite PM to ensure high torque and power.The specification of the analysis model and its structure are

shown in Table I and in Fig. 1, respectively. Parallel magneti-zation in the PM is used for the analysis model. To consider theend effect, the end winding was modeled in a 3-D FE analysis.

III. OVERHANG EFFECTFrom the overhang structure using a rotor longer in the axial

direction than a stator, the air-gap flux density at the end of thestack can be increased and the loss of the leakage flux can beoffset, which can effectively increase the torque of the motor.As shown in Fig. 2(a), a motor which does not use the overhangstructure shows a nonuniform magnetic field distribution in theaxial direction of the stator due to the leakage flux at the end ofstack. Moreover, the leakage effect presents an inefficient fluxdistribution in the motor. As shown in Fig. 2(b), it was verifiedfrom the 3-D FE analysis that the overhang structure increasesthe air-gap flux density at the end of the stack. This can increasethe performance of the motor. Fig. 2 shows that the leakage

Fig. 2. Increase of air-gap flux at the stack end by overhang effect. (a) Nonover-hang model. (b) Overhang model.

Fig. 3. Linkage-flux according to the overhang length.

effect is offset by the overhang effect. Fig. 3 shows that therelationship between the overhang length and the flux-linkageis proportional.However, the overhang effect does not only advance char-

acteristics. If the stator was already magnetically saturated, the

4896 IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 8, AUGUST 2013

overhang effect is not helpful for improving the performanceof the motor. Due to magnetic saturation, the shape of the elec-tromotive force (EMF) can be distorted if the flux increment isnot uniform according to the rotor position. Moreover, all of ad-ditional magnetic flux produced by the overhang effect cannotensure effective characteristics. Therefore, it is important to usethe overhang structure after a careful selection of its length. Inother words, there is an optimal length of the overhang that bestincreases of the performance of the motor [16].

IV. PROPOSED METHODIn the 2-D FE analysis, the overhang effect was taken into

consideration through an increase in the remanence flux densityof the PM or the stack length. This method requires a repetitive2-D FE analysis to match the analysis result of the 3-D FE anal-ysis with much effort. To address this problem, we propose anovel parameter which takes the overhang effect into account.We term this the overhang parameter in this study.In order to derive the overhang parameter, we use the dif-

ference in the permeance coefficient in the PM caused by theoverhang effect. The permeance coefficient is referred to as theoperating slope on the demagnetization curve on which a PMoperates. The permeance coefficient allows a designer to deter-mine the operating point of a PM.The operating point of a PM changes according to the oper-

ating environment, such as the type of material that is locatednear the PM. A PM exposed to air by the overhang structure hasrelatively high magnetic reluctance compared to that of an inte-rior PM. Therefore, the operating point of a PM with the over-hang structure should be decreased. Due to overhang structure,the magnetic reluctance which a PM takes on is different de-pending on the measuring position in the magnet. Therefore, inthis paper, the permeance coefficient refers to the average valuein a magnet.From (1) to (3), we calculate the permeance coefficient Pc in

one pole of a PM

(1)

(2)

(3)

where and are the - and -axis components of the mag-netic flux density, and are the - and -axis componentsof the magnetic field intensity, and and are the magneticflux density and magnetic field intensity in the magnetizing di-rection, respectively. In addition, denotes the number of ele-ments within a PM in the FE analysis, is the magnetizationangle, is the permeability and is the permeance coefficientof a PM. Fig. 4 shows the magnetization angle. The permeancecoefficient depends on both the shape of the magnet and themagnetic circuit of the PMSM. The variation in the magneticcircuit caused by the overhang structure will give the perme-ance coefficient a new value. Fig. 5 shows the variation of thepermeance coefficient caused by the overhang structure. Due tothe overhang structure, the magnetic reluctance in the magnetic

Fig. 4. Magnetization angle .

Fig. 5. Permeance coefficient of the PM. (a) Nonoverhang model. (b) Over-hang model.

Fig. 6. Permeance coefficient is moved to .

circuit is increased. Thus, the permeance coefficient , whichis used for the nonoverhang structure becomes for the over-hang structure, as shown in Fig. 6.We can define the variation of the operating point in a

PM by (4)

(4)

WOO et al.: 2-D FE ANALYSIS FOR A PMSM TAKING AN OVERHANG EFFECT INTO CONSIDERATION 4897

Fig. 7. Demagnetization curve of the PM (the original demagnetization curveis modified to by overhang parameter ).

Fig. 8. Comparison of the cogging torque. (a) 1 mm overhang. (b) 3 mm over-hang.

where and are the operating points in PMs with thenonoverhang and the overhang structure, respectively. By mul-tiplying the number of poles and end winding factor by theresult of (4), the total variation of the reluctance over the entirePM caused by the overhang effect, the overhang parametercan be induced by (5), for which the effect on the BH curve isillustrated in Fig. 7.

(5)

In (5), the end winding factor guarantees the accuracy of theresults in the case of a large overhang structure. In a PMSMwith a large overhang structure, there is a possibility of theflux-linkage flowing into the end winding. Therefore, the endwinding factor should be adjusted. If the overhang length iswithin 10% of the stack length, the value of the end windingfactor becomes 1. To the guarantee of the analysis result, the-axis shown in Fig. 4 should be aligned with the reference axis.

Fig. 9. Comparison of the back EMF. (a) 1 mm overhang. (b) 3 mm overhang.

The overhang effect can be taken into consideration in the2-D FE analysis using the proposed overhang parameter withouta trial-and-error process. Specifically, during the first step, theoperating point of a PM with the overhang structure shouldbe calculated by means of 3-D magnetostatic analysis. In thenext step, the operating point is analyzed in a 2-D magneto-static analysis in which the overhang cannot taken into account.With the data calculated through the first and the second step,we can calculate the overhang parameter. Finally, by adding theoverhang parameter term via (6), the remanence flux den-sity of the PM in the transient model of the 2-D FE analysis canbe increased considering the overhang effect.In this paper, the proposed overhang parameter repre-

sents the extent of magnetic compensation by the overhangeffect

(6)

where is the original demagnetization curve andis the demagnetization curve corrected by the overhang param-eter OP as shown in Fig. 7.

V. RESULTSIn the first example, the characteristics of the analysis model

shown in Fig. 1 were calculated. Its validity was verified bycomparing the results of the 2-D FE analysis which was calcu-lated by the proposed method and results of the 3-D FE analysis,as shown in Figs. 810 and in Table II. The analysis results con-tain models with and without overhang and including no loadand load characteristics.The proposed method was verified through two different

overhang lengths. The resultant tooth flux density is not sat-urated (below 1.2 T). Table III shows the increment of the

4898 IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 8, AUGUST 2013

Fig. 10. Comparison of the load torque in the analysis model. (a) 1 mm over-hang. (b) 3 mm overhang.

TABLE IICHARACTERISTIC RESULTS

TABLE IIIINCREMENT OF REMANENCE FLUX DENSITY IN THE 2-D FE ANALYSIS

remanence flux density of the PM in the 2-D FE analysisconsidering the overhang length. According to the results,the overhang effect enhanced the performance of the motor.Moreover, it is clear that the overhang effect is a function ofthe overhang length. When an overhang length was 1 mm, theload torque increased by 2.6%. When an overhang length was3 mm, the load torque increased by 6.8%.More specific results are shown in Table IV. It was verified

by comparing the results of the 2-D FE analysis using the pro-posed method and results of the 3-D FE analysis. The proposedmethod is applied with different poles and slots. As expected thegreater overhang length was, the higher load torque and EMFwas obtained.When the overhang effect for a radial-flux motor is applied,

an additional flux is generated both along the in-plane and the

TABLE IVCOMPARISON BETWEEN 2-D AND 3-D FE ANALYSIS WITH COMBINATION OF

DIFFERENT POLES AND SLOTS

lamination direction. In order to evaluate effects by overhang,those caused by the flux generated in the in-plane and the lami-nation direction need to be separated. The flux generated alongthe lamination direction than the in-plane influences magneticflux density. This effect increased characteristics such as cog-ging, EMF, and generating torque as shown in Figs. 810 andTable IV.The proposed method is still effective and accurate in case

the PMSM has the combination of different poles and slots. Thismeans that the proposed model is valid and suitable for the pur-pose of motor design with overhang structure.For the overhang model in which mild saturation was con-

sidered, the overhang parameter without distortion of the EMFshape could be applied to the 2-D FE analysis. From the pro-posed overhang parameter OP, the overhang effect can be takeninto account in the 2-D FE analysis. Through the proposedmethod, the computational problem associated with the 3-D FEanalysis can be mitigated.

VI. CONCLUSIONThe design of a motor with the overhang structure is compu-

tationally expensive because it requires a 3-D FE analysis. Themain feature of the proposedmethod is that the overhang param-eter can consider the overhang effect precisely in a 2-D FE anal-ysis while reducing the computational cost. Many researchershave tried to take the overhang effect into consideration in a 2-DFE analysis. Most of the approaches have considered the over-hang effect as the change in the material property via correctionof the remanence flux density using a trial-and-error method.Therefore, this study is significant in that the correction of theremanence flux density can be adjusted precisely and quicklyusing the proposed method.The validity of the proposed method is confirmed by a com-

parison between results of the 2-D FE analysis and results of the3-D FE analysis result with different models.

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