High Temperature Superconducting Magnetic Levitation

7.4 Calculation of the magnetic field of PMG Ë 225

Fig. 7.2:Schematic drawing of the equivalent surface current of a rectangular PM (g: half of the gap
between the adjacent PMs;l: length of the PM;tPM: height of the PM).

dBy=

4

H

i= 1

dByi=Kdy耠Œ

0

X

−tPM

(휓 1 (x−(L+g),y−y耠,z−z耠)

+휓 1 (g−x,y−y耠,z−z耠))dz耠+

L+g

X

g

(휓 3 (x−x耠,y−y耠,z)+휓 3 (x−x耠,y−y耠,−z−tPM))dx耠, (7.29)

dBz=

4

H

i= 1

dBzi=Kdy耠

L+g

X

g

[휓 2 (x−x耠,y耠−y,z)

+휓 2 (x−x耠,y−y耠,z+tPM)]dx耠. (7.30)

Furthermore, the 3D analytical expressions in Fig. 7.2 can be given by the following
form, taking into account Eqs. (7.26) and (7.27),

Bx=K

2

(훤(x−(L+g),y−y耠,z+tPM)−Γ(x−(L+g),y−y耠,z)

−Γ(x−g,y−y耠,z+tPM)+Γ(x−g,y−y耠,z))儨儨儨儨ww^21 , (7.31)

By=K(휓(z,y−y耠,x−(L+g))−휓(z+tPM,y−y耠,x−(L+g))

−휓(z,y−y耠.x−g)+휓(z+tPM,y−y耠,x−g)

+휓(x−(L+g),y−y耠,z)−휓(x−g,y−y耠,z)−휓(x−(L+g),y−y耠,z+tPM)

+휓(x−g,y−y耠,z+tPM))儨儨儨儨ww^21 , (7.32)