Influence Factor Analysis of PMSM Air Gap Flux Density
1
Chao-hui Zhao 1, Sui-liang Li 2, Yang-guang Yan1
Laboratory of Aeronautical Power system, Nanjing University of Aeronautics and Astronautics, Nanjing 210016,
China
2
College of Mechanical and Electrical Engineering, Henan Agricultural University, Zhengzhou 450002, China
method based on asymmetry air gap to improve wave
distribution of air gap flux density; Using resolution
method and finite element method (FEM), the literature [5]
analyzed air gap flux of PMSM and compared with induction machine; Under considered the assemble air gap and
saturated of stator, rotor instance, the literature [6] lodged
a sort of analysis method of IPM machine. Summarily the
air gap flux density of PMSM relate to many factor, in
relative literatures, however, it has not been reported.
To research the air gap densities influence factor of
PMSM, a Finite Element Analysis (FEA) was conducted.
The FEA analysis package used is ANASYS7.0’s Maxwell 2D model. This paper adopts the vector magnetism
potential to calculate the machines field, and some conclusion of practicality and palpability was presented.
Abstract-PMSM (permanent magnet synchronous machine) has high efficiency and torque. The influence of the
air gap flux density on torque and induced EMF is proverbial, thus it is very important to discuss influence factor of
PMSM air gap flux density. In relative literatures, however,
it has not been reported. This paper analyze the relative
factor of influence air gap flux density, and compare SPM
(surface mounted permanent magnet) with IPM (interior
permanent magnet) machine, then presents applied and intelligible conclusions: the machines air gap flux density
is changed with the air gap length varies, the air gap
flux density variety of IPM machine is bigger than
that one of SPM; To IPM, using non-magnetism shaft
is our advice; To SPM, in order to ease fabricate, we
suggest use magnetism shaft; To IPM, small pole arc
coefficient is suitable; To SPM, however, more bigger
pole arc coefficient is necessary; To IPM, the air gap
flux density has a suitable value due to the restriction
condition of rare earth magnet thickness; To SPM, the
restriction condition of rare earth magnet thickness is
not existence, the air gap flux density is enhanced with
the increase of the rare earth magnet thickness, then it
reaches a constant when the rare earth magnet thickness exceed some extent; IPM synchronous machine
bears “flux concentration function”, when its pole
pairs is more than or equal to 3,
Bδ
Br
Bδ
BM
II. THE STRUCTURE CHARACTERISTIC OF PMSM
Fig.1 show two structures of PMSM, which are similar to the conventional AC machine. Bases on placement
mode of PM, their rotors can be divided to SPM and IPM
type. PM strikes out slices commonly duo to its energy
product and coercive force are high.
Stator
Main pole
> 1 or 4,
Rotor
Air gap
> 1 ; To SPM, it has no “flux concentration
function”
I. INTRODUCTION
(a) SPM machine
Compared with conventional asynchronism machine,
permanent magnet synchronous machines (PMSM) have
several advantages, including the high torque/mass ratio
and efficiency [1][2]. Relative to electricity excitation
synchronous machine, due to there is a lack of excitation
winding, and cancel brush, slide loop equipment, PMSM
have some pop out merit, such as small loss, high efficiency and reliability, simple rotor structures. Thus, the
PMSM machine is widely used for electric household
appliances, OA, and electric vehicles.
In a way, the output torque and induction electricity
potential of PMSM depend on flux distribution of air gap.
The air gap flux density influences directly on machines
performance, so the research on air gap flux density for
PMSM is very important. The literature [3] lodged a sort
of magnetism field analytical method which immediacy
calculated no-load, full-load wave of air gap flux density
for PMSM; The literature [4] researched no-load wave of
air gap flux density for IPM, and brought forward a
Stator
Rotor
Main pole
Shaft
Auxiliary pole
Non-magnetism bush
Air gap
(b) IPM machine
Fig.1 Two structure of PMSM
In SPM machine, the PMs are drawn in gray and they
are characterized by radial magnetization. Two PM of
each pole pairs are series connection, and per pole flux is
supplied by one block PM, at the same time, the magnetism potential of circuit are supplied by two rare earth
magnet. Thus the air gap flux density of machine is approximately equal to flux density of PM work point.
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The PM is parallel in the rotor structure of IPM synchronous machine (see Fig.1), and the per pole flux of
machine is supplied by two rare earth magnet, at the same
time, the magnetism potential of per pole pairs is supplied
by each rare earth magnet. Thus, the air gap flux density
of machine can enhance, and this is a flux concentration
structure. However, the leakage flux of it is bigger than
SPM machine. So, there are stainless steels (or aluminum)
non-magnetism bush between rotor yoke and shaft.
III. THE ANALYSIS AND CALCULATION METHOD
MAGNETISM FIELD
OF
negligible instance, the calculation of the machine flux
may predigest to two-dimension problem.
From the engineering view, the outer diameter of stator is a boundary of magnet field. So, the calculation
model of flux is shown in Fig.3, Fig.5.
With ANSYS7.0 software, we calculate magnetism
field of machine in the paper. For simplicity, the stator is
assumed to be slotless.
IV. INFLUENCE FACTOR ANALYSIS OF PMSM AIR GAP FLUX DEN-
MACHINE’S
SITY
The basis structure parameter of SPM and IPM machine is shown in TABLE.I. In TABLE.I, the material of
stator and rotor is silicon steel piece 1J22, and the material of rare earth magnet is NdFeB, which residual PM
flux density is Br=1.05T, and coercive force is
HC=827600A/m; the slot type is half hatch rectangle slot.
TABLE I
PARAMETERS OF TWO KINDS OF SYNCHRONOUS MACHINES
The name of machine
Inner diameter of stator (mm)
Outer diameter of rotor (mm)
Number of stator slots
Pole pairs
Thickness of magnets (mm)
Width of magnets (mm)
SPM
119.5
118
48
2
18
67.85
IPM
119.5
118
48
2
20.39
38.59
To build differential equation of machine interior field
and to ensure the region of account and the boundary
condition of FEA account, the following assumptions are
made[7][8][9]:
（1）End-effects are negligible, the machines field is
uniformity distributing in axial direction, viz: the current
density vector J and vector magnetism potential A has
only axial component, J=JZ,A=AZ;
（2）Iron core material is isotropy, and magnetization
curve is humdrum, namely, the effect of hysteresis is negligible;
（3）The magnetic field is negligible in the outer
shell of machine and shaft, that is: outer surface circumference of stator and the inner surface circumference of
rotor are zero vector potential surface;
（4）The effect of eddy current is negligible;
（5）The magnetization of each rare earth magnet is
uniformity. To rare earth permanent magnet material, it
means the remanent magnetization M is independent of
work point. In addition, if alnico is uniformity magnetization, its magnetism would maintenance all the time, due
to stuffs inner coercive force HC is very big.
（ 6 ） The magnets are modeled with parallel
magnetization.
The calculation of the machine flux distribution is a
non-linear three-dimension problem, however, considering physics process of energy transfer takes place inside
the air gap, and the length of the machine axis direction is
more than the length of air gap. Therefore, end-effects are
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A. The Influence of Air Gap Length’s Variety on Air Gap
Flux Density
1) The influence of air gap length’s variety on air
gap flux density in IPM: The length of the air gap affects
the shape of the air gap flux density distribution. This is
mainly due to the leakage flux around the end of the magnet, which increases with air gap length. Given magnet
type, the increase of air gap length will result in the reduction of the maximum flux density. Air gap flux density
distribution for various air gap lengths is showed in Fig.2
(a). Fig.3 is a distribution plot of machine flux when air
gap length is 0.5mm, 1mm, respectively, and it illustrates
of the leakage flux of magnets end when air gap length
increase.
(a)
IPM machine
(b) SPM machine
Fig.2 The air gap density waveforms when air gap variety
2) The influence of air gap length’s variety on air
gap flux density in SPM: Fig.2 (b) shows the influence of
air gap length’s variety on air gap flux density in SPM
machine. The value of air gap flux density will drop when
air gap length increase from 0.5mm to 1 mm, but its drop
range is more smaller than that one of IPM machine due
to the leakage flux of PM end is nonexistent in SPM machine.
In a word, the influence of air gap length on air gap
flux density is very serious. Because magnetism conductance of air is relative low, the ability which magnetic
force line get across air gap as air gap increase weaken,
i.e, the air gap flux density will be decreased. The drop
range of air gap flux density in SPM is more smaller than
that one in IPM machine.
Leakage
flux
(b)
Fig.3 The magnetic force lines distributing plot for IPM
B. The Influence of Shaft Material on Air Gap Flux Density
There are two types shaft material in machine, one is
nonmagnetic shaft, such as steel; and other is magnetizer
shaft, such as aluminum and stainless steel. The influence
of shaft material on air gap flux density is different when
the structure of machine is different. In our paper, the air
gap length is 0.75mm at simulink.
1) The influence of shaft material on air gap flux density in IPM: The influence of shaft material on air gap
flux density is different to IPM machine. Fig.3 (a) shows
the flux plot where the magnets are attached to the nonmagnetic shaft hence eliminating the leakage flux entirely
while in Fig.3(b) the leakage flux under the magnets is
illustrated very clearly. A comparison between two the
materials indicates that though the operating point of the
magnets has not changed, the flux density inside the machine with the non-magnetic shaft has risen significantly,
as shown in Fig.4.
So, the shaft material of IPM is usually the nonmagnetizer material, or the shaft made up with magnetizer
should be added a non-magnetizer bush. However, it
makes more complicated configuration and more difficult
fabrication.
2) The influence of shaft material on air gap flux density in SPM: Fig.5 shows the flux distribution of the SPM
with magnetizer shaft. Because PM is far away from shaft
and two PM with opposition polarity near shaft are attracted by one another. Therefore, magnetic force line PM
produced pass entirely through armature, and the shaft
material has no influence to air gap flux density.
Fig.4 The air gap flux density waveform of IPM machine which shaft is
different
(a)
(b)
Fig.5 The magnetic force lines distributing plot for SPM
(a)
So, for convenience, the shaft material is usually the
magnetizer in SPM.
C. The Influence of Pole Arc Coefficient on Air Gap Flux
Density
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τs
The pole arc coefficient α is ratio of pole arc width
to pole pitch τ p . That is:
α=
choice the smaller values in IPM machine, but no over
small, the reason is that the increase of air gap flux density will cause the saturation of rotor magnetizer when the
pole arc coefficient is very small.
τS
τP
With different structure PMSM, the restriction factor of pole arc coefficient is different. The variety of pole
arc coefficient reflects the change of permanent magnet
volume, therefore, the air gap flux density will take place
variety as pole arc coefficient’s variety. The air gap length
is 0.75mm when simulation calculation.
1) The influence of pole Arc coefficient on air gap
flux density in IPM: To IPM machine, the definition of
pole arc width τ s and pole pitch τ p is shown in Fig.6.
From Fig.6 we can find that pole arc width τ s will decrease as the increase of magnet thickness when pole
pairs number P and pole pitch τ p unchanged, it result in
Fig.8 The relation between pole arc coefficient and air gap flux density,
per-pole flux respectively for IPM machine
pole arc coefficient α decrease; Certainly, if pole pairs
number P change, α will vary as variety of τ s and τ p .
τP
So, the pole arc coefficient is restricted not only by magnet thickness, but also by the number of poles. Fig.8 illustrates the air gap flux density wave of IPM under different
pole arc coefficient. Fig.8 shows the relation between the
pole arc coefficient and the flux density, the per pole flux
respectively.
τP
τS
a
Fig.6
b
τS τP
r
R
τS
Fig.9
τ s ,τ p
Sketch map of SPM
2) The influence of pole arc coefficient on air gap flux
density in SPM: To SPM machine, the pole arc
width τ s and pole pitch τ p are determined as Fig.9. With
bm
analysis we can find the pole arc coefficient is relative
unaided, it has no relation with the pole pairs number and
magnet thickness. Fig.10 shows the wave of air gap flux
density when pole arc coefficient are 0.78, 0.85, 0.9,0.95,
0.99 respectively, we can find that the influence of pole
arc coefficient on air gap flux density not too, due to under different pole arc coefficient, the maximum value of
air gap flux density much at one; It is seen form Fig.10
that flux increase as increase of pole arc coefficient, the
reason is the width of wave increase. Fig.11 shows the
relation between the pole arc coefficient and the air gap
flux density, per pole flux respectively, it also illustrates:
when pole arc coefficient vary, the air gap flux density of
SPM machine is hardly change, however, its per pole flux
increase with the increase of pole arc coefficient.
So, to enhance air gap flux density in SPM machine,
the pole arc coefficient should be at its maximum in order
to minimize the torque ripple.
D. The Influence of Magnet Thickness On Air Gap Flux
Density
The more thickness the magnet is, the more bigger the
magnetism potential force of magnetism circuit is, the air
gap flux density of the machine should be increase in the
theory. However, in practice, to increase of air gap flux
density, the structure of the machine may come into being
Sketch map of IPM
Fig.7 The air gap flux density distribution in IPM machine to various
pole arc coefficient
Fig.7 and Fig.8 shows the air gap flux density and
the per pole flux will decrease as the increase of pole arc
coefficient in IPM, this is because when pole arc coefficient increase, the PMs thickness became thin. Thus to
obtain a good performance, the pole arc coefficient should
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some restriction. Furthermore, the restriction cause of air
gap flux density is different with the different of machine
structure.
To SPM machine, it is seen from Fig.12 the air gap
flux density and the flux increase as the increase of magnet thickness. When magnet thickness reaches to a certainty value, however, the air gap flux density and flux is
basis constant. Therefore, the magnet thickness should be
reasonable choice when designing machine.
It is also seen from Fig.12 that the variety of air gap
flux density is very small when pole pairs number different, but the variety of per pole flux is very big. The per
pole flux decrease as the increase of pole pairs number,
this is because the per pole area decrease as the increase
of pole pairs number.
Fig.10 The air gap flux density distribution in SPM to various pole arc
coefficient
Fig.12 The relation between magnet thickness and air gap flux density,
per-pole flux respectively in SPM when pole pairs number are different
E. The Influence of Pole Pairs Number on Air Gap Flux
Density
The increase of pole pairs number of PMSM can boost
its air gap flux density, but there exists a suitable value.
When air gap flux reach to maximum, the pole pairs
number are different in different structure machine.
1) The influence of pole pairs number on air gap flux
density in IPM machine: To calculate the relation of pole
pairs number and air gap flux density accurately, the
model of Fig.1 was adopted, where the inner diameter of
stator is 152mm, the outer and inner diameter of rotor is
150mm, 60mm respectively, and the material of stator and
rotor are all choose 1J22; the material of shaft is 45# steel
which relative differential permeability µ r is 1500; the
material of rare earth magnet is NdFeB, which thickness
is 9mm, width is 42mm, residual PM flux density is
Br=1.07T and coercive force is Hc=827600A/m; the outer
and inner diameter of non-magnetizer bush is 60mm,
45mm respectively; the slot type is half hatch rectangle
slot.
Fig.13 reflects the relation of pole pairs number and
air gap flux density in IPM machine. The air gap flux
density has a maximum value as increase of pole pairs
number. So, the optimization of pole pairs number is a
value discussion question. To IPM machine, when pole
pairs number reach to 4, the air gap flux density is bigger
than the residual flux density of PM, i.e. IPM machine
have the flux concentration function.
2) The influence of pole pairs number on air gap flux
density in SPM machine: The machine model adopts SPM
Fig.11 The relation between pole arc coefficient and air gap flux density,
per-pole flux respectively in SPM
1) The influence of magnet thickness on air gap flux
density in IPM machine: In IPM machine, the pole arc
coefficient is more and more small as magnet thickness
increase, and when point “a” and “b” in Fig.6 is superposition, the pole arc coefficient is most small, here the
magnet thickness reaches to the maximum.
Fig.8 shows the relation of pole arc coefficient and air
gap flux density, per pole flux respectively in IPM machine, and it also reflects variety instance of air gap flux
density when magnet thickness vary. As the increase of
magnet thickness, the pole arc coefficient will decrease,
while the air gap flux density will increase accordingly.
2) The influence of magnet thickness on air gap flux
density in SPM machine: In SPM machine, the pole arc
coefficient and the pole pairs number have not restriction
function to magnet thickness, thus, the magnet thickness
can randomly change inside the rotor radius under the
different pole pairs number. Fig.12 shows the relation of
the air gap flux density, the flux and magnet thickness
respectively under different pole pairs number in SPM
machine, the case which the magnets are parallel magnetization, the case which the ratio r/R denote magnet
thickness. The more the ratio is, the more thin the magnet
thickness, and the more small the ratio is, the more thick
the magnet thickness. We can find from Fig.9 r and R are
inner radius and outer radius of PM, respectively.
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machine in TABLE I. Fig.14 shows the relation of the
pole pairs number and the air gap flux density. It is shown
from Fig.14, the air gap flux density increase as the increase of pole pairs number when pole pairs number is
smaller than 3; the air gap flux density begin drop as the
increase of pole pairs number when pole pairs number is
more bigger than 3. When pole pairs number is 3, the air
gap flux density reach to the maximum value, however,
the value is smaller than the residual flux density of PM,
so SPM machine has no flux concentration function.
suitable for IPM; To SPM, however, more bigger pole arc
coefficient is necessary.
4) To IPM, the air gap flux density is enhanced with
the increase of the rare earth magnet thickness, but it has a
suitable value due to the restriction condition of rare earth
magnet thickness; To SPM, the restriction condition of
rare earth magnet thickness is not existence, the air gap
flux density is enhanced with the increase of the rare earth
magnet thickness, then it reaches a constant when the rare
earth magnet thickness exceed some extent.
5) The air gap flux density will produce the maximum
with the increase of pole pairs, that is, PMSM has a suitable pole pairs. IPM synchronous machine bears “flux
concentration function”, when its pole pairs is more than
or equal to 3,
Bδ
BM
> 1 or 4,
Bδ
Br
> 1 , where Bδ is
the air gap flux density; BM is the flux density of work
point of PM, Br is the residual flux density of PM. To
SPM, the air gap flux density is maximum when pole
pairs is 3, but its maximum is less than the residual flux
density of PM, thus SPM has no “flux concentration function”.
6) It is shown with the analysis of different diameter
machine that the above conclusions are generalized.
Fig.13 The relation of air gap flux density and pole pairs in IPM
ACKNOWLEDGMENT
This paper is partly supported by the National Science
of Chinese Foundation (No.50337030).
Fig.14 The relation of air gap flux density and pole pairs in SPM
V. CONCLUSION
Compared SPM with IPM machine, the main conclusions are put forward as follows:
1) The machines air gap flux density is changed with
the air gap length varies, the more the air gap length, the
more small the flux density. The air gap flux density variety of IPM machine is bigger than that one of SPM.
2) To different structure machine, the influence of
shaft material on air gap flux density is different. To IPM,
using non-magnetism shaft is our advice because of the
air gap flux density will increase 1 time or so than magnetism shaft; To SPM, in order to ease fabricate, we suggest use magnetism shaft due to the influence of shaft
material on air gap density is negligible.
3) The influence of pole arc coefficient on air gap flux
density is different for different structure machine. To
IPM, the air gap flux density decreases with the increase
of pole arc coefficient, hence, small pole arc coefficient is
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