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
where: A ellipse is the area of the elliptical air gap and
'
l stk is the equivalent length of the Shark
'
SRM air gap. l stk may be determined from the semi perimeter of the ellipse multiplied by the
number of Shark segments n t :
( ) ( ) t n
' π
lstk = ⋅ a + b ⋅ − 43
he
⋅−
2
where
(2.21)
2
2
a − b 1 − tan β
h e = =
(2.22)
a + b 1 + tan β
From (2.20), (2.21) and (2.22) the inductance in the aligned position becomes:
L
L
L
ellipse
ellipse
ellipse
µ 0 ⋅ N
=
µ 0 ⋅ N
=
2
ph
2
ph
2
ph
µ 0 ⋅ N
=
g
⋅
⋅
⋅ l
n
n
t
t
stk
π
⋅ ⋅
2
π l
⋅ ⋅
2 2
⋅
π
⋅
4
( a + b)
⋅ ( 3 − 4 − h )
shk
g
⋅
( 1 + tan β ) ⋅ ( 3 − 4 − h )
g
( 1 + tan β )
⋅
3 −
e
⋅ l
4 −
pol
e
⋅ l
pol
1 − tan β
1 + tan β
From (2.23) and (2.3) the inductance gain, k ellipse , of the elliptical Shark profile is given by:
2
(2.23)
Lellipse
π
1−
tan β
kellipse
= = ⋅ ( 1+
tan β ) ⋅ 3 − 4 −
(2.24)
L 4 1+
tan β
0
The inductance gain of the elliptical profile depends on the angle β only. The elliptical profile
produces a higher aligned inductance compared with the saw-toothed profile for the whole range of
angle β .
To express the inductance gain as a function of the length and the height of the Shark segment,
tan β is replaced by an expression in terms of h shk and l shk . Using this expression the variation of
inductance gain with the length, l shk , is presented in Fig.2.13, for different heights, h shk , of the
Shark profile. The variation is quite similar in shape to that in the case of the saw-toothed profile.
The change of the co-energy of the elliptical toothed air gap may be determined as:
2