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12.2 emf PRODUCED BY WINDINGS 519

S

N
b

c

−b

−c

a

(a) (b)

−a

+

+

b 1

c 1

−b 1

−c 1

a 1

(c)

−a 1

b 2

c 2

−b 2

−c 2

a 2

−a 2

+ +

+ + N

N S

S

(d)

c 1 b^1

−c (^1) −b 1
a 1
−a 1
c 2 b 2
−c 2 −b 2
a 2
−a 2
b 1
c 1
−b 1
−c 1
a 1
−a 1
b 2
c 2
−b 2
−c 2
a 2
−a 2
Figure 12.2.3Elementary three-phase synchronous machines.(a)Salient two-pole machine.(b)Salient
four-pole machine.(c)Phase windings connected in wye.(d)Phase windings connected in delta.
action of the commutator (even though the closed armature winding on the rotor is rotating), so
the commutator winding becomes pseudostationary.
The action of slip rings and that of a commutator differ in only one way. The conducting coil
connected to the slip ring is always connected to the brush, regardless of the mechanical speedωm
of the rotor and the rotor position, but with the commutator, the conducting coil conducts current
only when it is physically under the commutator brush, i.e., when it is stationary with respect to
the commutator brush. This difference is illustrated in Figure 12.2.5.
A dc machine then operates with direct current applied to its field winding (generally located
on the salient-pole stator of the machine) and to a commutator (via the brushes) connected to the
armature winding situated inside slots on the cylindrical rotor, as shown schematically in Figure
12.2.4. In a dc machine the stator mmf axis is fixed in space, and the rotor mmf axis is also fixed in
space, even when the rotor winding is physically rotating, because of the commutator action, which
was briefly discussed earlier. Thus, the dc machine will operate under steady-state conditions,

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