an investigation of dual stator winding induction machines

The turn function of the th
i rotor loop is:
[ 0,
θi
)
[ θi
, θi
+ α r )
[ θ + α , 2π
)
⎧0
θ ∈
⎪
n i ( θ ) = ⎨1
θ ∈
(3.50)
⎪
⎩0
θ ∈ i r
The winding function can be expressed as:
⎧ α r
⎪−
θ ∈[
0,
θi
)
2π
⎪ α r
N i ( θ ) = ⎨1
− θ ∈[
θi
, θi
+ α r )
(3.51)
⎪ 2π
⎪ α r − θ ∈[
θi
+ α r , 2π
)
⎪⎩
2π
where, α r is the th
i rotor loop pitch. Since a symmetrical equally spaced rotor bar
structure is considered in the analysis, all the rotor loops have the same pitch α r .
None of the turn and winding functions shown in Figure 3.6 take the skew of the rotor
into the consideration. If the rotor is skewed, the turn function and winding function are
shown in Figure 3.7.
1
α
− r
2π
0
α
1 − r
2π
Figure 3.7 Rotor
β
θi
β
θi
θ i + α r
θ α − β
i + r
θ i + α r
θ i + α r − β
106
2π
2π
(a)
(b )
th
i rotor loop turn and winding function for skewed rotor, (a) turn function, (b)
winding function.