Static Airgap Magnetic Field of Axial Flux …Static Airgap Magnetic Field of Axial Flux Permanent...
Transcript of Static Airgap Magnetic Field of Axial Flux …Static Airgap Magnetic Field of Axial Flux Permanent...
Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor
1Xuanfeng Shangguan, 2Kai Zhang 1, School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo,
China, [email protected] *2, School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo,
China. [email protected]
Abstract Due to flat structure of the axial flux permanent magnet disc motor (AFPMDM), the airgap
magnetic field distribution is more complex. To study the static airgap magnetic field of AFPMDM, the conventional magnetic circuit method and the method of taking slice in finite element software Magnet are used respectively. Then axial airgap flux density distribution characteristics along circumferential direction and radial direction are analyzed. The accurate three-dimensional airgap magnetic field distribution can be gotten with the above methods. At last, analytical method, finite element method and average radius method are used to calculate the airgap magnetic flux of per pole respectively. Three results are approximate and can reflect per pole magnetic flux of AFPMDM generally. The research for airgap magnetic field of AFPMDM provides theoretical basis for its wide application.
Keywords: Airgap Magnetic Field, AFPMDM, Slice, Per Pole Magnetic Flux 1. Introduction
The disc axial flux permanent magnet motor, with advantages of axial compact structure, easy to heat dissipation, high efficiency, obviously energy saving effect, high torque - inertia ratio and power density and so on [1, 2], especially the size and weight of which is about 50% of the ordinary permanent magnet motor, is especially suitable for occasions demanding small size, low weight the low-speed drive system [3].
With flat structure, the airgap magnetic field distribution is along the axial direction, so the cross section of this motor can not be selected to create a 2D model simply the same as common radial motor is dealt with [4]. The axial airgap flux density of AFPMDM along the circumferential direction at different radius is different, and the axial airgap flux density along the radius direction in the same electrical degree is also different [5]. Therefore, in order to calculate airgap magnetic field distribution of AFPMM accurately, 3D finite element analysis is asked to use [6, 7]. In this paper, airgap magnetic field distribution only under permanent magnet excitation is studied. In order to save computing time, according to the symmetry of the magnetic field distribution, only a pair of poles 3D motor model [8-10] is built.
2. No-load airgap magnetic field calculation of AFPMDM by magnetic circuit method
The magnetic field analysis of axial flux permanent magnet disc motor is very complex. The main magnetic circuit contains two closed magnetic circuits shown in Figure 1: one magnetic circuit is starting from N pole, passing airgap and the magnetic yoke, through the airgap to reach S pole, at last, through the magnetic yoke returning to N pole; the other one is closed through the airgap, magnetic yoke and end cap [11, 12]. Due to the particularity of the permanent magnet magnetic circuit distribution, the length of the magnetic circuit at different radius is not the same, thus increasing the computational complexity of the magnetic circuit.
However, because the airgap length of AFPMDM is longer, and the main magnetic circuit is unsaturated, so for engineering, we often take the magnetic circuit of the average radius as the total magnetic circuit of AFPMDM to calculate.
Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang
International Journal of Digital Content Technology and its Applications(JDCTA) Volume7,Number7,April 2013 doi:10.4156/jdcta.vol7.issue7.139
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(a) (b)
Figure 1. Main magnetic circuit of AFPMDM (a) radial direction (b) circumferential direction 1-shaft 2-yoke 3-permanent magnet 4-cover
It’s assumed that the magnetic circuit is unsaturated, the magnetic potential drop of iron core and
the armature reaction are ignored. Thus, m MH H h (1)
1 2 (2)
Where is the total airgap length of motor, 1 is the distance between the surface of the
permanent magnet and armature plate surface namely the main airgap length of the motor, 2 is the
bond length between the permanent magnet and rotor disk, Mh is the length of the magnetization
direction of permanent magnet, H is airgap magnetic field strength, mH is the magnetic field strength
of PM. According to the magnetic flux continuity principle:
m mA B A B (3)
Where A and mA are respectively the effective area of per pole airgap and the area of one pole
magnetic flux provided by the PM, B and mB are the airgap magnetic flux density and the magnetic
flux density of the PM at the operating point, is the leakage coefficient. Assuming p is the number of pole pairs, miD and moD are the inner and outer diameter of PM,
p and i are the pole arc coefficient and the calculation pole arc coefficient. Thus,
2 21( )
8m p mo miA D Dp (4)
2 21( )
8 F i mo miA K D Dp (5)
Where FK is the airgap density distribution coefficient, is defined as the ratio of flux density
amplitude mean and flux density amplitude maximum in a group of airgap flux density curves distributed along with the circumference.
Permanent magnetic material response curve is
0m r m rB H B (6)
According to the formula (1) ~ (6), assuming i p , the magnetic flux density of the PM at the
operating point mB and the airgap magnetic flux density B can be obtained .
F rm
F rM
K BB
Kh
(7)
Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang
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r
F rM
BB
Kh
(8)
Where r and rB are respectively relative magnetic permeability and remnant magnetization.
3. 3D airgap magnetic field analysis of single-side AFPMDM
Single-sided axial magnetic flux motor shown in Figure 2a is the simplest disc motor. It has only one rotor side and one stator side. The advantages of this motor are compact structure, short shaft and high torque but existing the great single-sided magnetic force. In this paper, the airgap magnetic field distribution of a pair of poles is analyzed by the 3D static magnetic field solver of Magnet. Figure 2b shows the flux density vector distribution of the motor excited by permanent magnet.
(a) (b)
Figure 2. Single-sided AFPMDM (a)structure (b)magnetic flux density vector distribution Taking a slice which is perpendicular to the shaft at the center of airgap, the airgap magnetic field is
reflected in this slice, and the airgap flux density contour map can be got as shown in Figure 3.
Figure 3. Airgap flux density contour map
Axial airgap flux density distribution curve of one pole shown in Figure 4 can be obtained through
taking the axial airgap flux density values along the circumferential direction respectively in the average radius, inner diameter and outer diameter from the slice as shown in Figure 3. Besides, the axial airgap flux density distribution curve along the radial direction can be got by taking a straight line in the center of the pole (electrical angle is 90°). It’s shown in Figure 5.
Comparison analysis between Figure 4 and 5 shows that the amplitudes of airgap flux density in different radius are not the same, that’s because the magnetic path length in different radius is different. Airgap flux density distribution in a certain radius is close to flat-top wave, the flux density amplitude in average radius is maximum, but due to the influence of the edge effect and the end flux leakage, the amplitude of airgap magnetic flux density near the inner and outer diameter of the magnetic poles decreases obviously.
Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang
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0 20 40 60 80 100 120 140 160 1800.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
air
ga
p m
agn
etic
flu
x d
en
sity
Bz(
T)
electrical degree(°)
1 average radius2 inner diameter3 outer diameter1
2
3
Figure 4. Axial airgap flux density distribution curve along the circumferential direction
30 35 40 45 500.40
0.45
0.50
0.55
0.60
0.65
0.70
air
ga
p m
ag
ne
tic fl
ux d
en
sity
Bz(
T)
radius(mm) Figure 5. Axial airgap flux density distribution curve along the radial direction
According to the above method, the axial airgap flux density is taken from the slice along the
circumferential direction and radial direction. The corresponding axial airgap flux density curve will be got. Then the cross-cutting airgap flux density curve nets can be obtained, namely, the accurate 3D airgap flux density space distribution graph in this airgap plane is shown in Figure 6.
30
35
40
45
0
60
120
180
2400
0.2
0.4
0.6
0.8
radius(mm)electrical degree( °)
air
gap
flux
desi
tyB
z(T)
0.1
0.2
0.3
0.4
0.5
0.6
Figure 6. The space distribution diagram of airgap magnetic field
Similarly, one slice is taken from the surface of permanent magnet; the airgap magnetic field
distribution of permanent magnet surfaces is shown in Figure 7.
Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang
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30
35
40
45
0
60
120
180
240-0.2
0
0.2
0.4
0.6
0.8
radius(mm)electrical degree(°)
air
gap
flux
dens
ityB
z(T
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Figure 7. The space distribution diagram of airgap magnetic field of critical the PM surface
Figure 7 shows that the magnetic field distribution of PM surface is flat-top shape. It’s impacted by
the shape of PM, and the permanent magnet is magnetized along the axis, therefore, the flux leakage is relatively small when the slice is taken from the PM surface.
4. Study for the variation regular of axial airgap flux density amplitude
In order to research the relationship between flux density amplitude and pole arc coefficient, the
motor model is built by selecting the pole arc coefficient p =0.8,0.7,0.6,0.5, respectively. And the
slice is taken from the center plane of airgap to solve the 3D static magnetic field, and then the axial airgap flux density distribution curve of one pole along the circumferential direction at the average radius corresponding to different pole arc coefficient can be got that is shown in Figure 8.
0 20 40 60 80 100 120 140 160 180 2000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
air
ga
p flu
x d
ens
ity Bz
(T)
electrical degree(°)
pole arc coefficient 0.8 pole arc coefficient 0.7 pole arc coefficient 0.6 pole arc coefficient 0.5
Figure 8. Airgap flux density change curves corresponding to different pole arc coefficient
It can be seen from Figure 8 that the airgap flux density amplitude at the average radius keeps a
constant. It is nothing to do with the pole arc coefficient. Next, the factors that affect the airgap flux density amplitude at the average radius will be studied.
Firstly, the magnetization length of the permanent magnet is changed while keeping the airgap length that is 4mm unchanged. Secondly, the length of the airgap is changed while keeping the magnetization
Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang
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length of the PM a constant 6Mh mm . According to the above two methods, the airgap flux density
amplitude curve at the average radius is shown in Figure 9.
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.40.3
0.4
0.5
0.6
0.7
0.8
air
gap
flu
x de
nsi
ty a
mpl
itude
B(
T)
hM/
=4mm hM=6mm
Figure 9. The change curve of airgap flux density amplitude at the average radius
It can be seen from the above figure that the airgap flux density amplitude is related to the size
of Mh , but the flux density amplitude corresponding to the same value of Mh in different
situations is not the same. As can be seen from the formula (8), considering the flux leakage, magnetic saturation and so on, the flux leakage will become larger with the increase of airgap length when the value of Mh is a constant. That is to say, the flux leakage coefficient becomes larger and the
amplitude of airgap flux density will decrease. Overall, the amplitude of airgap flux density is mainly determined by the size of Mh .
5. Calculation of per pole airgap magnetic flux with different methods
Whether static characteristic or dynamic characteristic is considered, the airgap magnetic flux is an important parameter for motor, and it affects electromagnetic torque and back electromotive force directly. So it is very necessary to calculate per pole airgap magnetic flux.
Firstly, using the analytical method to calculate the per pole airgap magnetic flux. For non-sinusoidal magnetic flux density waveforms, the per pole airgap magnetic flux formula is as follows [9]:
2 22( )
2 2
out
in
R
f i mg i mg out inRB rdr B R R
p p
(9)
Where, mgB is the amplitude of airgap flux density, outR is the outer radius of PM, inR is the inner
radius of PM. Per pole airgap magnetic flux can be calculated combining the equations (8) and (9) with motor
parameters, and FK are respectively approach to 1.4 and 0.88 according to their characteristic curves.
Secondly, the magnetic field integrator of finite element software is used to calculate per pole airgap magnetic flux. Taking a slice at the airgap center of one pole and completing the static simulation of 3D magnetic field, airgap flux density distribution of one pole can be got as shown in Figure 10. Then the airgap magnetic flux of per pole can be calculated by magnetic field integrator on this slice.
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Figure 10. Magnetic flux density distribution of one pole
Finally, using the average radius method to calculate the per pole airgap magnetic flux. Taking the
axial flux density values of one pole in the average radius along the circumferential direction from the slice in Figure 10 and the default interpolation in the software is 1001 points, so per pole magnetic flux can be calculated by putting these flux density values into formula (10).
1001 1001
1 1
( )out
in
R
f i i out inRi i
B ldr B l R R
(10)
The calculation results of the above three methods are listed in Table 1:
Table 1. The calculation results of the above three methods Calculation method Analytic method FEM Average radius methodPer pole magnetic flux 4.83×10-4Wb 5.21×10-4Wb 5.35×10-4Wb
It can be seen that calculation results of per pole magnetic flux are close to each other with the
above three methods. The result calculated by the finite element method is the most accurate in the three methods, because the 3D static solver of Magnet is used. This method will take long computing time. Besides, the calculation gap between analytic method and FEM is 0.38×10-4Wb. So the error of analytic method is relatively large because the leakage flux coefficient is from experience curve. However, the gap between average radius method and FEM is only 0.14×10-4Wb, the error of average radius method is very small. Therefore the AFPMDM can be equivalent to linear motor to model and analyzed by using the average radius method. 6. The main parameters of the motor in this paper
Table 2. The main parameters of the motor Motor parameters Value Motor parameters Value
Rated voltage Rated power
Number of phases Number of pole pairs
PM material Remnant magnetization density
one pole angle
48V 168W
3 3
NdFeB 1.2T
48°
Inner diameter of PM Outer diameter of PM
Thickness of PM thickness of stator core
air gap length Thickness of magnetic yoke
60mm 105mm
6mm 15mm 4mm 5mm
7. Conclusion
By taking slice in airgap center, airgap magnetic field spatial distribution of AFPMDM is obtained. In this way, the complex axial airgap magnetic field distribution can be displayed simply, conveniently, and accurately. Axial airgap magnetic field distribution is close to flat-top wave. Due to the influence of the edge effect and the end flux leakage, the airgap flux density decrease gradually near the inner and outer diameter of the magnetic poles. The airgap flux density amplitude is maximum at average
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radius and it is determined by the size of Mh . Then, the analytic method, finite element method and
average radius method are adopted to calculate per pole magnetic flux of AFPMDM. In general, the above three methods can calculate per pole magnetic flux of AFPMDM with certain accuracy. The above research has achieved anticipated effect and provided a basis for the research of AFPMDM airgap magnetic field. 8. References [1] Zhao Rubin, Feng Lingling, “Design of Disk Type Coreless Permanent Magnet Synchronous
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Brushless DC Wheel Motor based on Finite Element Method”, IJACT, AICIT, vol. 4, no. 13, pp. 279-286, 2012.
[3] De Donata G., Giulii Capponi F., Caricchi F., “Fractional-Slot Concentrated-Winding Axial-Flux Permanent-Magnet machine with Core-wound Coils”, Industry Applications, IEEE Transactions on, vol.48, no.2, pp.630-641, 2012.
[4] Mei Ying, Pan Zaiping, “Research on a Novel Axial Field Disk Type Switched Reluctance Motor”, Micromotors, vol. 44, no. 1, pp.4-6, 2011.
[5] Zhang Dilin, “The Calculation of the Performance of Axial Flux PM Synchronous Generator Based on ANSOFT”, Marine Electric & Electronic Engineering, vol. 28, no. 4, pp.222-224, 2008.
[6] Xia Bing, Jin Mengjia, Shen Jianxin, “Design of Axial Flux Permanent Magnet Machines with Segmental 2D Finite Element Method”, Small & Special Electrical Machines, vol. 39, no. 4, pp.1-3, 2011.
[7] Wang Yan-fang, Su Yan-ping, “Simulation and Analysis of Electromagnetic Field for Moving-coil Permanent Magnet Motor”, JDCTA, AICIT, vol. 6, no. 13, pp.185-191, 2012.
[8] Tang Renyuan, “Theory and Design of Modern Permanent Magnet Machines”, China Machine Press, Beijing, 2011.
[9] J. F. Gieras, R. J. Wang and M. J. Kamper, “Axial Fulx Permanent Magnet Brushless Machines”, Springer Science + Business Media B.V., Norwell, 2008.
[10] Tze-Yee Ho, Mu-Song Chen, Lung-Hsian Yang, Jia-Shen, Lin, Po-Hung Chen, “The Design of a High Power Factor Brushless DC Motor Drive”, IJACT, AICIT, vol. 4, no. 18, pp.141-149, 2012.
[11] Shoucheng Ding, Wenhui Li, Shizhou Yang, Jianhai Li, Guici Yuan, “The Motor Virtual Experimental System Based on Matlab Web Technology”, Journal of Networks, vol. 5, no. 12, pp.1490-1495, 2010.
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