Page 677 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 663
A B C D
.
. .
2
1 . 1 .
2 .

H G F E

. .
. . . .

FIGURE 8.39: Progression of the magnetic field in a two-phase stator at eight different
instants.

In a P-pole motor, the electrical angle ( ) and mechanical angle ( ) are related by
e
m
(Figure 8.37),
= ∕(P∕2) (8.236)
m
e
Therefore, the frequency of the electrical excitation w , is related to the synchronous speed,
e
w (Figure 8.37)
syn
w = w ∕(P∕2) (8.237)
syn e
The difference between the electrical field rotation speed, w , and the rotor speed, w ,is
syn rm
called the slip speed or slip frequency, w
s
w = w − w (8.238)
s syn rm
= s ⋅ w (8.239)
syn
where s, slip, is defined as
w syn − w rm
s = (8.240)
w syn

If we consider the case that the rotor is locked (w rm = 0), then the slip is s = 1 and
w = w syn .
s
The AC motor operating principle is similar to a transformer. Stator windings serve
as the transformer primary winding. The stator structure serves as the transformer “iron.”
The rotor serves as the transformer secondary winding. The only difference is that the
secondary winding is the rotor conductor’s and it is mechanically rotating. The rotor sees
an effective magnetic flux frequency of w = w syn − w , slip frequency, due to the relative
s
rm
motion between the electrically rotating stator flux and mechanically rotating rotor. The
induced voltage in the rotor is analogous to the induced voltage in the secondary winding
of a transformer. The voltage in the primary winding generates a magnetic flux as follows.
Let P = 2, hence w = w . The stator AC voltage,
syn e
v (t) = V sin(w t) (8.241)
s s e
The resulting flux is
V s
Φ=− cos(w t) (8.242)
e
N ⋅ w
1 e