0195136047.pdf

12.2 emf PRODUCED BY WINDINGS 515

−

+

N-turn coil on stator

Field winding

Magnetic flux path

Magnetic axis

of stator coil

Magnetic axis of rotor

e

a

S

−a

N

+

+

+

θ = ωt; θ = ω

β

(a)

Figure 12.2.1Elementary single-

phase two-pole synchronous ma-

chine.(a)Salient-pole machine.

(b)Nonsalient-pole or cylindrical-

rotor machine.

Air gap

(b)

Cylindrical rotor field winding

Teeth of laminated

armature core

Mean magnetic

flux path

Stator winding located

in armature slots

(not shown here)

+

+

+

+

+

+

+

S

N

φ=

∫+π/ 2

−π/ 2

Bmcosβlrdβ= 2 Bmlr (12.2.2)

and for aP-pole machine,

φ=

2

P

2 Bmlr (12.2.3)

wherelis the axial length of the stator andris the average radius at the air gap. For aP-pole
machine, the pole area is 2/Ptimes that of a two-pole machine of the same length and diameter.
The flux linkage with the stator coil isNφwhen the rotor poles are in line with the magnetic
axis of the stator coil. If the rotor is turned at a constant speedωby a source of mechanical power
connected to its shaft, the flux linkage with the stator coil varies as the cosine of the angle between
the magnetic axes of the stator coil and the rotor,

λ=Nφcosωt (12.2.4)

where timetis arbitrarily taken as zero when the peak of the flux-density wave coincides with
the magnetic axis of the stator coil. By Faraday’s law, the voltage induced in the stator coil is
given by