Environmental Engineering Reference
In-Depth Information
Figure 4.12
Induction machine with cage rotor (1, shaft; 2, cage rotor; 3, stator three- phase winding;
4, terminal box; 5, stator iron core; 6, cooling fan; 7, motor frame). (Reproduced with permission of
Asea Brown Boveri Ltd)
The difference between
ω
s
and
ω
r
is expressed as a ratio with respect to
ω
s
and is known
as
slip
s
where
(
)
ωω
ω
−
s
r
s
=
(4.15)
s
Therefore
(
)
ω
=−
1
s
ω
(4.16)
r
s
The relative motion between the stator's and rotor's RMFs determines how frequently the
stator RMF cuts the rotating rotor conductors, so the frequency of the rotor induced voltages
and currents
f
r
is
f
=
sf
(4.17)
r
where
f
is the mains frequency. The frequency of the rotor currents determines
ω
rr
, the speed
of the rotor RMF with respect to the rotor:
ωπ
=
2
f
p
=
2
π
s f p
=
s
ω
(4.18)
rr
r
s
The speed of the rotor RMF with respect to the stationary stator is the rotor speed plus the
rotor RMF's speed with respect to the rotor:
(
)
1
s s
s s s
It can be concluded that the rotor and stator RMFs rotate together at synchronous speed
as required for a uniform torque to be developed as in the synchronous machine. However,
in contrast to the synchronous machine, the rotor RMF is produced through
induction
from
ωω
+=−
ω
+=
ωω
r
rr
