Shark -new motor design concept for energy saving- applied to - VBN

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Chapter 2 Linear analysis of the Shark switched Reluctance Motor
From equations (2.6) and (2.27) the energy gain, k Wellipse , defined as the ratio of the change in coenergy
during one stroke in the elliptical Shark SRM to the same variable determined for the
CSRM, is given by:
∆Wellipse
kL
⋅ kellipse
− 1
k Wellipse = =
(2.28)
∆W0
kL
− 1
Variation as function of the dimensions of the elliptical Shark tooth is presented in Fig2.14 and it
exhibits similar features to the diagrams representing the saw-toothed profile.
2.2.4 Square wave profile
The inductance of the square wave profile, illustrated in Fig.2.6 consists of two components: a
radial component L 1 and an axial component L 2 :
L
square
= L
1
+ L
which means that:
L
square
2
µ 0 ⋅ N
=
µ 0 ⋅ N
=
g
2
ph
⋅
g
2
ph
1
⋅ A
1
µ 0 ⋅ N
+
g
2
ph
2
⋅ A
2
( l ⋅ l ) µ ⋅ N ⋅ ( 2 ⋅ n ⋅ h ⋅ l )
1
stk
pol
+
0
ph
g
2
2
t
shk
pol
(2.29)
(2.30)
Assuming that the axial and the radial air gaps are equal ( g 1 = g 2 = g ) the inductance associated
with the magnetic circuit of the square wave profile is given by the following expression:
L
square
=
µ 0
⋅ N
2
ph
( l ⋅ l ) ⋅ ⋅
⋅
g
stk
pol
⋅
2
1 +
which may be expressed as follows, in terms of dimensions of the Shark profile:
Lsquare
nt
l
stk
h
shk
(2.31)
l
2 ⋅
stk
⋅ hshk
l
⋅ h
= ⋅ + ⋅
shk
2
L
= L ⋅ +
shk
0 1 1
0 1
(2.32)
lstk
lshk
This means that the inductance gain of the square wave profile is determined by: