an investigation of dual stator winding induction machines

( θ ) ⋅ g(
θ,
θ ) − H ( 0)
⋅ g(
0,
)
∫ H ⋅dl
= H A
C
rm A θ rm
(3.17)
where, g( , θ )
0 is the air gap length at the starting point and the value of θ at the
rm
starting point is assumed to be zero. ( 0)
while g( θ , θ ) and ( θ )
respectively.
rm
Substituting (3.17) into (3.15),
A
A
H is the magnetic field at the starting point
A
H are the air gap length and magnetic field at θ angle point
( θ ) ⋅ g(
θ θ rm ) − H A(
0)
⋅ g(
0,
θ rm ) = nA
( θ ) iA
H , ⋅
(3.18)
An expression for the magnetic field around the stator can be found from (3.18) as:
H
A
( θ )
n
( θ ) ⋅ iA
+ H A(
0) ⋅ g(
0,
θ rm )
g(
θ,
θ )
= A
(3.19)
rm
The H ( θ ) and ( 0)
A
applied to determine the unknown quantity.
as:
H are unknown and must be solved. Hence Gauss's Law is
A
If a cylinder passing through the air gap is considered, Gauss's Law can be expressed
2π
∫
0
( θ ) r l θ = 0
0 H is s
µ A d
(3.20)
where, ris is the radius of the inner stator surface; l s is the length of the machine.
Substituting (3.19) into (3.20),
2π
∫
0
( θ ) ⋅i
A + H A(
0)
⋅ g(
0,
θrm
)
g(
θ,
θ )
nA
µ 0 ris
ls
dθ
= 0
(3.21)
Rearranging equation (3.21) gives,
rm
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