ALTERNATING-CURRENT MOTORS

319

Fig. 151 gives, with the speed, S, as abscissae: the current, J0,
the power output, P, the torque, D, the power-factor, p, the
efficiency, ??.

3. POLYPHASE SHUNT MOTOR

181. Since the characteristics of the polyphase motor do not
depend upon the number of phases, here, as in the preceding, a
two-phase system may be assumed: a two-phase stator winding
acting upon a two-phase rotor winding, that is, a closed-coil
rotor winding connected to the commutator in the same manner
as in direct-current machines, but with two sets of brushes in
quadrature position excited by a two-phase system of the same
frequency. Mechanically the three-phase system here has the
advantage of requiring only three sets of brushes instead of four

FIG. 152.
as with the two-phase system, but otherwise the general form
of the equations and conclusions are not different.
Let $o and — j$6 == e.m.fs. impressed upon the stator, $1 and
— j]$i = e.m.fs. impressed upon the rotor, 00 = phase angle be-
tween e.m.f., -B0 and $1, and 0i = position angle between the
stator and rotor circuits. The e.m.fs., $0 and — jEQy produce the
same rotating e.m.f. as two e.m.fs. of equal intensity, but dis-
placed in phase and in position by angle 0o from EQ and j$o,
and instead of considering a displacement of phase, 0o, and a dis-
placement of position, 0i, between stator and rotor circuits, we
can, therefore, assume zero-phase displacement and displacement
in position by angle 0o + 0i = #• Phase displacement between
stator and rotor e.m.fs. is, therefore, equivalent to a shift of
brushes, hence gives no additional feature beyond those pro-
duced by a shift of the commutator brushes.