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

1175

(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)


1176

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.


1177

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.


1178

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


1179

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.


1180

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


1181

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

Generator”, Electrical Machinery Technology, vol. 33, no. 3, pp.1-4, 2012. [2] Yongjuan Cao, Weifeng Chen, Li Yu, “Control and Simulation of a Novel Permanent Magnet

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.

[12] Longxin Zhen, Xiaogang Wei, “Structure and Performance Analysis of Regenerative Electromagnetic Shock Absorber”, Journal of Networks, vol. 5, no. 12, pp.1467-1474, 2010.


1182

static airgap magnetic field of axial flux …static airgap magnetic field of axial flux permanent...

Documents