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T. Magn. Soc. Jpn. (Special Issues)., 1, 66-69 (2017)<Paper>Demagnetizing Analysis of Ferrite Magnet Motor Based on RNA
Y. Yoshida, D. Momma*, and K. Tajima

Graduate School of Engineering Science, Akita Univ., 1-1, Tegata Gakuen-machi, Akita 010–5802, Japan* Graduate School of Engineering and Resource Science, Akita Univ., 1-1, Tegata Gakuen-machi, Akita 010–5802, Japan䢢

A method for analyzing the demagnetization of a surface permanent magnet (SPM) motor based on reluctancenetwork analysis (RNA) is presented. The validity of the proposed RNA model is demonstrated by comparing thecalculated results with 2D-FEA calculation results. The characteristics of the SPM motor determined by the RNAmodel were in almost complete agreement with the corresponding two-dimensional (2D) finite element analysis(FEA) calculation.
Keywords: reluctance network analysis, ferrite magnet, demagnetization analysis, two-line approximation

2. RNA model of SPM motor
Figure 1 shows the shape and specifications of theSPM motor under consideration. Stator and rotor corematerial is non-oriented electromagnetic steel sheet andthe relative permeability of 3000 is used to calculate the66

Stator core
100 mmIn recent years, high-performance permanent
magnet (PM) motors based on powerful rare-earthmagnets have emerged, and demand is consequently
expanding in various applications. However, rare-earthmagnets may be subject to price rises as the productionof such metals tends to be concentrated in a single
country.
Therefore,
thedevelopmentof
high-performance PM motors without rare-earthmagnets is required.
Although the maximum magnetic energy product offerrite magnets is one tenth that of rare-earth magnets1), high-efficiency ferrite magnet motors have beenreported 2). Ferrite magnets in motors are exposed to alarge reverse magnetic field to obtain performanceequivalent to that of rare-earth magnet motors.
Therefore,
ferritemagnets
areatriskofdemagnetization because of their low coercive force.
This
makes
it
necessarytoconsider
thedemagnetization of ferrite magnets for ferrite magnet
motor design.
Reluctance network analysis (RNA) is a useful
method to save calculation time in the estimation of thecharacteristics of PM motors, as reported in previousstudies 3)-6). In a previous paper, we proposed ademagnetization analysis method using RNA 7). In thatstudy, we presented an RNA model for determining theoperating points of ferrite magnets taking account of amagnet’s demagnetization. We demonstrated thecalculation accuracy of this model, which used a
two-line approximation of the demagnetization curve,by experiments and a comparison with two-dimensional(2D) finite element analysis (FEA). Therefore, in thepresent work, we apply this method to thedemagnetization analysis of a surface permanent
magnet (SPM) motor. To verify the accuracy of the
proposed model, the calculated results are compared tovalues obtained from 2D FEA.

Ferrite magnet

53 mm

1. Introduction

Rotor core
Number of slots

24

Number of poles

4Core materials

Non-oriented electromagnetic steel sheet(Relative permeability µs = 3000)

Permanent magnet materials

Ferrite magnet (SSR-420)

Number of winding turns per slot

100

Stack length

30 mm

Gap length

1.1 mmFig. 1 Shape and specifications of the SPM motor.
reluctance in the RNA model. The material of thepermanent magnet is ferrite (SSR-420).
Figure 2 shows a part of the RNA model of the SPM
motor. The SPM motor is divided into multiple
elements taking into consideration the motor shapes
and flux flow. Each element in the air gap is divided in
one-degree intervals in the circumferential direction
and the magnets are divided into three in the radialdirection. The stator tooth tip is divided into three
regions and reluctances in these regions are directlyconnected with air gap reluctances, as shown in thefigure.
Figure 3 illustrates the demagnetization curve ofSSR-420 at 20 °C used for the RNA model, which isapproximated by two lines. In the figure, Br, Br’, Hc, andHc’ are the residual magnetic flux density before
demagnetization, residual magnetic flux density after
demagnetization, coercive force before demagnetization,and coercive force after demagnetization, respectively.
Since the demagnetization curve of the magnet isapproximated by two lines, there is a slight error
around the knee point.
The elements of a ferrite magnet of the RNA modelTransaction of the Magnetics Society of Japan (Special Issues) Vol.1, No.1, 2017

Fm ' ＋－＋－Air gap

1st layer (1.5 mm)
2nd layer (1.5 mm)
3rd layer (3.5 mm)＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－＋－Magnet

Rotor core
1 deg

Fig. 2 A part of the RNA model.
B   r  0 H  Br

(3)

3. Demagnetization analysis of SPM motor

Stator＋－Br ' l .
2 r 0Using the derived RNA model, the characteristics ofthe SPM motor are calculated taking demagnetization
into account. To verify the calculation accuracy of theRNA model, the calculated values were compared to theones obtained from 2D-FEA (JMAG-Designer Ver.15).
Figure 5 shows the 2D-FEA model of the SPM as acomparison object. Figure 6 shows the comparison of
the calculated waveforms of flux linkage. It is clear thatthe calculated values obtained from the proposed RNAmodel are in good agreement with the ones obtained
from 2D-FEA.

Br ’Parallel lines

Flux density (T)Br 1.32 10 6 H  0.420

Two-line approximation
Original

HcHc’

HcB0B  1.32 10 4 H  30.1

Magnetic field (A/m)

Fig. 5 2D FEA model of the SPM motor.

Fig. 3 Demagnetization curve of SSR-420 at 20 °C.

0.15
0.15
0.125
0.125
0.1
0.1
0.075
0.075
0.05
0.05
0.025
0.025
00
−0.025-0.025−0.05-0.05−0.075-0.075−0.1-0.1−0.125-0.125
−0.15
-0.15

l

Flux linkage (Wb)

RmaglFmcan be expressed as the reluctance and magnetomotiveforces (MMFs), Fm, shown in Fig. 4. The reluctance of aferrite magnet, Rmag, is expressed byl,2 r 0 l  ls (1)where r is the magnet’s recoil. If there is nodemagnetization in a ferrite magnet element, Fm isgiven byFm Br l .

2 r  0(2)When an operating point of a ferrite magnet is changedby an external magnetic field and becomes less than theknee point, the MMF after demagnetization, Fm’, can be
expressed as

V (RNA)W (RNA)U (2D-FEA)
V (2D-FEA)

W (2D-FEA)

00.0050.01
Time (s)

0.015

0.02

Fig. 6 Comparison of the flux linkage calculated by proposedmodel and 2D-FEA.
1212U-phase
V-phaseW-phase88
Current (A)Fig. 4 Unit magnetic circuit of magnet element.

Rmag U (RNA)4400-4−4−8-8-12−120

0.01

0.02

0.03
0.04
Time (s)

0.05

0.06

Fig. 7 Input current wave forms for calculating induced voltageof the SPM motor.

Transaction of the Magnetics Society of Japan (Special Issues) Vol.1, No.1, 201767

fundamental wave of the induce voltage after
demagnetization is decreased by 5.7 % and the phase of
the fundamental wave is shifted by 5.5 degrees
comparedtotheinducedvoltage
beforedemagnetization.
To compare the torque of the SPM motor before andafter demagnetization, three periods of input current

2020

101000RNA
2D-FEA-20−20-30−30-40−4000.005

0.010.015
Time (s)(a) Before demagnetization

12120.02

30
30
20
20-10
−10-20−20-30−30-40−400.04

RNA
2D-FEA-4
−430
30

0.500

00.06

RNA
2D-FEA
0Before (RNA)After (RNA)

0.005

0.010.015
Time (s)(a) Before demagnetization

0.02

1.50.005

Next, the induced voltages of the SPM motor beforeand after demagnetization are calculated. Figure 7
shows the three periods of input current wave forms. In
the first and third periods, the rotor rotates at the rotor
speed of 1500 rpm without supplying current. In thesecond period (0.02 seconds to 0.04 seconds), theovercurrent at the amplitude of 9.5 A is applied; rated
current amplitude of this SPM motor is 4.0 A.
Figure 8(a) and (b) shows the comparison of
calculated
inducedvoltagebeforeandafter
demagnetization between RNA and FEA, respectively.
In these figures, the calculated values obtained fromthe proposed RNA model are in good agreement withthe ones obtained from 2D FEA. Figure 9 shows thecomparison of calculated induced voltage by RNA before
and after demagnetization. The amplitude of the0.05

0.75-10−100.01
0.015
0.02
Time (s)Fig. 9 Comparison of U-phase induced voltage before and afterdemagnetization.

0.030.04
Time (s)1101000.02

1.25

0.25

-20
−20-30−300.01

1.5

2020-40−400Fig. 10 Input current wave forms for calculating torque of theSPM motor.

0.045

4040
Induced voltage (V)00-12−120.05
0.055
0.06
Time (s)(b) After demagnetization
Fig. 8 Comparison of U-phase induced voltage between RNAand FEA.

68

44−8-8101000

Torque (Nm)Induced voltage (V)4040U-phaseV-phaseW-phase88

Current (A)-10−101.25

Torque (Nm)Induced voltage (V)

40
40
30
30

10.75
0.5

RNA

0.25
00.04

2D-FEA
0.045

0.05
0.055
0.06
Time (s)(b) After demagnetization
Fig. 11 Comparison of torque waveform of the SPM motor.
Table 1 Comparison of average torque.

RNA (Nm)

2D-FEA (Nm)Before

1.30

1.32

1.51

After

1.22

1.23

0.813

Transaction of the Magnetics Society of Japan (Special Issues) Vol.1, No.1, 2017

Error (%)

0.02
0.02

RNA

Torque (Nm)

0.015
0.015

2D-FEA

0.01
0.01
0.005
0.005
00−0.005-0.005
−0.05
-0.01
−0.01
-0.015−0.015

−0.02
-0.02

00.0050.01
Time (s)

0.015

0.02

(a) Before demagnetization
0.02
0.02

RNA

Torque (Nm)

0.015
0.015

2D-FEA

0.01
0.01
0.005
0.005
00−0.005-0.005
−0.05
-0.01
−0.01
-0.015−0.015

−0.02
-0.02
0.04

0.045

0.05
Time (s)

0.055

0.06

(b) After demagnetization
Fig. 12 Comparison of cogging torque before and after
demagnetization.

(a)
0150
Demagnetization factor (%)(b)

Table 1 lists the average torque before and after
demagnetization. The average torque calculated by theRNA model is decreased by 6.2 % compared to before
demagnetization. The errors of the average torquebetween the RNA model and 2D FEA are less than 2 %.
Figure 12(a) shows the cogging torque waveform
before demagnetization and Fig. 12(b) shows thecogging torque waveform after demagnetization
calculated using the input current waveforms shown inFig. 7. After demagnetization, there is a bit of adiscrepancy in the cogging torque waveforms between
RNAand2D-FEA.
Figure13shows
thedemagnetization factor calculated by RNA and 2D-FEA,
where the demagnetization factor, Dfac, is defined as B '
(4)
D fac  1  r   100 .
Br Comparing these results, the demagnetization factorof the surface of the magnet calculated by the RNA islarger than the one obtained from 2D-FEA. We conclude
that the discrepancy in the distribution of thedemagnetization factor affects the cogging torquewaveforms.
4. Conclusion
This study presented a method for demagnetizationof the SPM motor based on RNA. The validity of theproposed RNA model was demonstrated by comparing
the calculated results with 2D-FEA calculation results.
It is concluded that the characteristics of the SPM
motor determined by the RNA model are in almost
complete agreement with the corresponding 2D-FEM
calculated. Further studies will attempt to performdemagnetization analysis considering the effect of thedistorted current waveform by voltage input.
This work was supported by JSPS KAKENHI Grant
Number 26820093.
References0150

Demagnetization factor (%)

Fig. 13 Demagnetization factor of the ferrite magnet calculated
by RNA (a) and 2D-FEA (b).
wave forms are used, as shown in Fig. 10. In the first
period, the current amplitude of 4.0 A is applied to themotor to calculate the rated torque before
demagnetization. To demagnetize the rotor magnets,
the overcurrent more than double the rated current (9.5A) is supplied in the second period. Then, the current at
the amplitude of 4.0 A is applied again to calculate therated torque after demagnetization in the last period.
Figure 11 shows the comparison of the torque wave
forms of the SPM motor calculated by the proposed
RNA model and 2D-FEA. In the figures, the calculated
values obtained from the proposed RNA model are inalmost complete agreement with the ones obtained from
2D-FEA.

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Received October 20, 2016; Revised November 24, 2016;
Accepted January 4, 2017.

Transaction of the Magnetics Society of Japan (Special Issues) Vol.1, No.1, 201769