334 Ë 9 HTS Maglev bearing and flywheel energy storage system
Fig. 9.6:Schematic diagram of PM rotor and HTS stator withn
pieces of HTS bulks.If the number of the HTS bulks in the stator isn(Fig. 9.6), each bulk is marked with
number 1 ton. The position angle of No. 1 HTS bulk is 0 and the position angle of No.i
(1⩽i⩽n) HTS bulk is
휙i=^2 휋(i−^1 )
n. (9.4)
The radial stiffness of No.iHTS bulk is
kR,휙i=k//cos^2 휙i+k⊥ 1 sin^2 휙i (if 0⩽휙i<휋) (9.5)or
kR,휙i=k//cos^2 휙i+k⊥ 2 sin^2 휙i (if휋⩽휙i< 2 휋). (9.6)The radial stiffness of RSB can be calculated as
kR=n
H
1kR,휙i. (9.7)Because the center angle of each HTS bulk is 2휋/n, so the angle density ofk//,k⊥ 1 and
k⊥ 2 isnk///2휋,nk⊥ 1 /2휋, andnk⊥ 2 /2휋. Based on Eqs. (9.5), (9.6), and (9.7), the radial
stiffness of a RSB can be calculated as
kR=휋
X
0¤
nk//
2 휋cos^2 휃+nk⊥^1
2 휋sin^2 휃¥d휃+2 휋
X
휋¤
nk//
2 휋cos^2 휃+nk⊥^2
2 휋sin^2 휃¥d휃=n(k⊥^1 +k⊥^2 )
4+
nk//
2.
(9.8)
With the data in Ref. 21, the values ofn,k//,k⊥ 1 , andk⊥ 2 are 8, 3.5 N/mm, 32.5 N/mm,
and 32.5 N/mm, respectively. The radial stiffness calculated with Eq. (9.8) is
kR=^8 ×(^32.^5 +^32.^5 )
4+^8 ×^3.^5
2
= 144 (N/mm). (9.9)