High Temperature Superconducting Magnetic Levitation

336 Ë 9 HTS Maglev bearing and flywheel energy storage system

whereLis the length of PM rotor andkRis the radial stiffness of RSB. Ifl>0, the direc-
tion of dFRis left. Ifl<0, the direction of dFRis right. The corresponding moment of
dFRrelative to the horizontal line passing through pointAis

dM=dFR×l=

휃l^2 kR

L

dl. (9.13)

Based on the principle of balance of torque, the following equation can be obtained:

M=

0. 5 L

X

− 0. 5 L

dM=

0. 5 L

X

− 0. 5 L

휃l^2 kR

L

dl=휃kRL

2

12

. (9.14)

Thus, the angular deflection stiffness is

k휃=M

휃

=kRL

2

12

. (9.15)

A new parameter, the linear density of radial stiffness,휀, is introduced. This is the
radial stiffness per unit length of the PM rotor:

휀=kR

L

. (9.16)

When all the material characteristics of the HTS bulk and the PM ring, the dimensional
parameters of the HTSB (except the length of PM rotor and HTS stator) and the relative
position between the HTS bulk and the PM ring, are the same, then휀is a constant
value. From Eqs. (9.15) and (9.16), it is

k휃=kR

L

L^3

12

=휀L

3

12

. (9.17)

It is obvious that deflection angular stiffness is proportional to the cube of the length
of the PM rotor.

9.3 Application of HTSB

It is noticed that FESS is one of the most important and widespread applications of
HTSB (also see Section 9.4.2). Some new applications of HTSB are also significant.

9.3.1Typical applications

1. Rotor support for machine [19]: Utilization of a HTSB for rotor support can reduce
   rotational loss and increase total efficiency of a motor/generator, with no need to