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
generalization of the saw-toothed and square wave Shark SRMs. As the dimension l top , shown in
Fig.2.7, varies, the inductance gain assumes values varying between those of the saw-toothed and
square wave Shark SRMs. The inductance gain of the elliptical profile exceeds that of the sawtoothed
profile but it is smaller than that of the square wave profile.
In Fig.2.19, the curves showing the inductance ratio variation with angle β are presented for the
saw-toothed, square wave, elliptical and trapezoidal Shark profiles. A similar variation is observed
for the energy ratio, presented in Fig.2.20
These curves show that:
• the influence of the Shark profile on the performances of the magnetic circuit increases with
the angle β
• the saw toothed and the square waved profiles represents respectively the lower and the
upper limits for the inductance and energy gain
• the trapezoidal profile may be considered to be a generalisation of both the saw-toothed and
the square wave profiles.
Table 2. 1 Inductance gain for saw-toothed, square-wave, ellipsoidal and trapezoidal Shark profiles
Profile type Inductance gain in the aligned position in terms Inductance gain at
of
=45 [deg]
Saw-toothed profile
1
k saw =
cos β
1.41
Square wave profile k square = ( 1+ tan β )
2
Ellipse profile
π
kellipse
= ⋅ ( 1+
tan β ) ⋅
4
3 − 4 −
2
1−
tan β
1+
tan β
1.57
Trapezoidal profile
( ) ( ) 2
2
ktrap = 2 ⋅ +
1.41 (k=0)
1−
2 ⋅ kk
+ tan β ,
1.48 (k=0.1)
ltop
k = ;
lshk
k ≤ 0.
5
1.67 (k=0.3)
2.00 (k=0.5)
According to this idealised analysis (2.13), the number of Shark teeth in a given machine does not
affect the performances of the Shark configuration if the ratio of the Shark tooth height to its length
remains constant ( β =const.). This is contradicted by equation (2.18), which shows that if there are
many Shark profiles much active area of the air gap is lost. This is due to the fact that the flux
density is not uniformly distributed along the Shark air gap. This subject will be discussed in
chapter 3 as it may be decisive in choice of Shark profile for further considerations.