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

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26<br />

Chapter 2 Linear analysis of the <strong>Shark</strong> switched Reluctance Mo<strong>to</strong>r<br />

l<br />

l =<br />

shk<br />

t<br />

(2.15)<br />

2 ⋅ cos β<br />

and δ l is the length of the air gap which is not effectively crossed by the field lines:<br />

δ l = g ⋅ tan β<br />

(2.16)<br />

Fig.2.11 Geometry of the <strong>Shark</strong> teeth having different lengths<br />

From equations (2.14), (2.15), (2.16) the equivalent length of the stack used in the conversion is<br />

given by:<br />

l<br />

lshk<br />

= − g ⋅ tan β<br />

2 ⋅ cos β<br />

e (2.17)<br />

Under these considerations, the <strong>to</strong>tal active length ( <strong>to</strong>tal<br />

l e ) <strong>for</strong> a <strong>Shark</strong> SRM with the stack length,<br />

l stk is given by:<br />

l<br />

<strong>to</strong>tal<br />

e<br />

= 2 ⋅ n<br />

⋅ l<br />

lstk<br />

l<br />

= − 2 ⋅<br />

cos β l<br />

t<br />

e<br />

stk<br />

shk<br />

l<br />

= 2 ⋅<br />

l<br />

le1<br />

stk<br />

shk<br />

le<br />

⋅<br />

⋅ g ⋅ tan β<br />

l1<br />

lshk1<br />

l<br />

g g/cos<br />

lshk<br />

lshk<br />

− g ⋅ tan β<br />

2 ⋅ cos β<br />

(2.18)<br />

Equation (2.18) suggests that the effective conversion area is dependent on the length of the <strong>Shark</strong><br />

segment. There is a limit <strong>to</strong> the number of <strong>Shark</strong> teeth which may be built in a given stack length,<br />

<strong>for</strong> which the <strong>Shark</strong> air gap behaves similarly <strong>to</strong> the cylindrical air gap. This limit is obtained from

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