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
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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
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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
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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.
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[7] Chengyuan Wang,Meiwen Zhou,Dingqin Guo. Vector Control Of
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[8] Zhongming Li ,Weiguo Liu. Rare earth permanent magnet
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(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
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