2010 International Conference on Computer, Mechatronics, Control and Electronic Engineering (CMCE)

Analysis of simulation design of the disc eddy current braking device

Zhi-ding Ying, Xin-fu Xu, Jian-an Zhu Institute of Railway & Urban Rail Transit

Tongji University Shanghai, China

e-mail: yingzhiding@126.com .lovexxflove@163.com.zhujianan@126.com

Abstract-To analyze the mechanism of the high-speed train

eddy current braking device and optimize the design,

established the basic structural model and derived the

braking force equation. The magnetic circuit of it was

analyzed by the analysis method and the finite element

method (FEM). Mainly analyzed the influence of the air gap

and the thickness of the turntable on the eddy current brake

(ECB) electromagnetic field and the braking force, and the

corresponding braking performance curve was obtained.

There is some directive significance on the selection and

optimization of the structural parameters of the eddy

current braking device.

Keywords-eddy current brake (EeB); ffUlgnetic circuit;

eddy current braking force; electromagneticfleld

1. INTRODUCTION

Our China is researching on the over 350kmlh high­speed train braking system. The traditional mechanical friction brake is hard to bear the braking load of the high­speed train emergency braking due to its huge braking energy, and it is also hard to meet the needs of service braking owing to the frequent and vast replacement and refitment of the friction units according to the foreign technical documentation and computational analysis. No wear and tear, adjustable braking force are the prominent advantages of eddy current brake and it has excellent braking performance at high speed.

There are still some difficult points of the ECB technology in practice at home and abroad nowadays, but it has lots of technical superiorities over other brake modes. So it is a very urgent task to develop the practical eddy current braking device as the development as the high­speed trains.

II. THE STRUCTURAL MODEL OF THE DISC EDDY

CURRENT BRAKING DEVICE AND THE THEORETICAL

COMPUTATIONAL METHOD

On the foundation of the study of kinds of domestic and international electromagnetic force derivation models [1, 2], the eddy current braking device model is designed according to the braking force distribution of the express train, the estimation of the breaking force as well as the construction requirement of the bogie as indicated in Fig. 1.

978-1-4244-7956-611 0/$26.00 ©20 1 0 IEEE 309

Figure 1. The eddy current braking device model

Considering the electromagnetic field characteristics of the structural model that the electromagnetic field distribution is homogeneous on the circumference of the turntable, it can be proved by calculation that two­dimensional computus can obtain a relatively definite discipline of magnetic field distribution. In order to emphasize the analysis of the relationship between the electromagnetic field distribution and the structure of the turntable, and due to that two-dimensional computational model can largely save the computer resources and the structural relation in the model is clear, the two­dimensional simplified model is taken. It can be gained by splitting the model along the central longitudinal section of the magnetic pole and then spreading it into rectangle plane as shown in Fig. 2.

P 9 p 9 p 9 p 9 p g p g p

Figure 2. The two-dimensional simplified model

Assuming that the magnetic flux density, written as

B(x,y) , does not change according to the practical

operation condition in z-direction and taking a cuboid computational element as illustrated in Fig. 3

CMCE 2010

Figure 3. Computing element of the braking force

Induced electromotive force [3]

Resistance

& = BLv;

L R=-· as

'

Eddy current

i = � = avBS = avBdxdy· e R '

Braking force [4]

dF = BFi = avB2 Ldxdy . e '

(1)

It can be seen from (1) that the main influencing factors of the eddy current braking force are the electrical conductivity, the speed, the size and the flux intensity of the turntable. It primarily studies the influencing factors of the flux intensity and those on braking force through the analysis of magnetic circuit and the software computus.

m· ,

In the above:

B is the flux intensity vector, Wb/m2 or T; L is the length of the computing element in z-direction,

V is the velocity of the turntable, m/s; (Y is the electrical conductivity, S/m; S is the section area of the computational element on

2 xy plane, m n is the total area of the turntable on the xy plane

2 when spreaded, m In order to calculate the braking force, the flux density

B should be studied based on (1), so magnetic circuit of the simplified model is analyzed as shown in Fig. 4 [5, 6].

Here, Lj represents the length of every part and S; denotes

the area of every section.

310

2RII'II

4Rr.:: 4R ...

4NI

8Rm� 2Rm-4

(a) (b)

Figure 4. A sketch map of the magnetic circuit

By computing the vector potential with the subdomain integration function of the fmite element software FEMLAB, the flux density can be gotten. The equation adopted is as follows:

In the equation, Az is the vector potential in z­

direction; V is the scalar potential; v is the velocity; J; is

the energizing current density in z-direction; fio' fir' (Y

and L are material parameters; � V is the potential difference in z-direction [7]. Under the condition that all the other parameters are known, the distribution of A can

be gotten. And due to B = V x A , the distribution of B can also be gotten as shown in Fig. 5.

Wax: 2.154

� _________________________________ �o

Figure 5. Magnetic flux density

Fig. 6 provides the comparison diagram of the computed braking performance curve and the domestic test curve and Germanic Knorr-Bremse corporation test curve.

100%

90%

80%

70%

60%

50%

40% Force' (

30%

20%

10%

0%

r1- � � � 1 i--

� - �;: ......

i--........-:::: �

d If

F l/e/F( ce •• ) - Domestic test

-- Foreign test --+-- Simulation and

Calculation

50 100 150 200 250 300 350 Ve loci ty (km/h)

Figure 6. The calculated curve and trial curves

The braking forces are different due to diverse test conditions, in order to make the test data endowed with

comparability, the longitudinal coordinate employs the relative braking force F', namely the ratio of the braking force at various speeds and that at the critical velocity, in the braking performance curve diagram. In order to get the ideal braking efficiency, the flux distribution in the magnetic circuit should be reasonably designed. In the following, the optimization analysis and simulation of the air gap and the turntable thickness that influence the ECB device are conducted.

III. ANALYSIS OF THE INFLUENCE OF STRUCTURAL

PARAMETERS ON MAGNETICFIELD AND BREAKING FORCE

Given different air gaps, the flux density and the braking force variation curves can be gotten as shown in Fig. 7 and Fig. 8 by computing with FEMLAB.

1.2 -I �--�----'���----+--����

-2 �--�----+-\r�-+----+----+--�

-3 L-__ -L ____ L-___ ,�( ,�,,) ---L----�--�

Figure 7. Influence of the air gap on magnetic field

18 16 14 12

� 10

1_5111111 _7111111 _10111111 -1201ml -..... -t--1/ ---

/ -/ 1/

I I II V

/!�V II#' V'

10 20 30 40 50 60 v (m/s)

Figure 8. Influence of the air gap on braking force

It can be seen from the graph above that not only the braking force declines, but the variation trend of the braking characteristic curve also becomes flatter. Consequently, in order to enlarge the braking force of the ECB device, the minimum air gap should be taken in a reasonable scope.

Fig. 9 provides the influence curve of turntable thickness on braking force. L::r.:...: ___ - 2-0 .-'",-�-3-om'-. --o--4 0;]-Dlm ....,

20 18 16 14

'2 12 -==- 10

� ..L

l?4 ---......, /I II ---

II III

II. /II

/1

10 20 30 40 v (m/s)

---

-

50 60

Figure 9. Influence of the turntable thickness on braking force

Clearly, with the increase of the turntable thickness, the whole trend of the braking force declines. However, at

311

lower speed, the braking force increases when the thickness of the turntable decreases. To interpret the phenomenon, Fig. 10 gives the distribution of magnetic lines in turntables with 20mm and 40mm at lower (a, b) and higher (c, d) speed. , -==----���====

(.)

(b)

(,) •

(d)

Figure 10. Influence of the turntable thickness on magnetic field

At lower speed, the difference between the flux density is very small, according to the (I), the determinant of the braking force is the area of the turntable section Q .However, at higher speed, magnetic lines are not so

easy to penetrate the thicker one, then B( x, y)2 diminishes and the braking force becomes smaller.

CONCLUSION

(1) The basic structure of the eddy current braking device was designed and the braking force analysis equation was simply derived. It was compared with the domestic and foreign test data, and it verifies that the structural model of the disc eddy current braking device and the theoretical computational method fit the actual situation well.

(2) The influence of the air gap and the turntable thickness on magneticfield and braking force was studied on the foundation of the analysis of the ECB magnetic circuit, and the braking characteristic curve was obtained. There is some directive significance on the selection and optimization of the structural parameters of the eddy current braking device.

(3) Influence of the dynamic factors and the static structural parameters on eddy current braking force can be analyzed through finite element simulation, and the cognition of the ECB character is deepened.

REFERENCES

[I] 1. H. Wouterse. Critical torque of eddy current brake with widely separated soft iron poles. lEE Proceedings-B, 1991, Vol. 138 (4): pp.153-158

[2] W. R. Smythe. On eddy currents in a rotating disk.AIEE Transaction, 1942, Vol. 61: pp.681-684

[3] MA Zhan-shan, ZHANG Ji-shi, WANG Ping. Theory of electromagnetics. BeiJing: Tsinghua University Press, 1995

[4] Nannapaneni Narayana Rao. Elements of engineering electromagnetism. Beijing; Machine Press, 2006

[5] GUO Qi-Yi, CHEN Peng, LUO Ting-yong, LI Wei-gang. Study on electro-magnetic mechanism in eddy current brake (ECB) based on analytical method. Electric drive for locomotives, 2006 (I): pp.30-32

[6] SUN Wei-min, ZHANG Yue-ming, WU Bing-bo. A new calculation method of brake torque for eddy current retarder. Modem Machinery 2005 (4): pp.21-29

[7] MENG Qing-Iong, Y AN Wei-Ii. Numerical analysis of electrical appliances. Beijing: Machine Press, 1993