SINGLE-PHASE COMMUTATOR MOTORS 357

and from e\ = 0o it then follows that:

$' = ./* ( ;

119)

that is, the commutating field of the single-phase motor must
be in quadrature behind and proportional to the main field, pro-
portional to the frequency and inversely proportional to the
speed; hence, at synchronism, /o = /, the commutation field
equals the main field in intensity, and, being displaced therefrom
in quadrature both in time and in space, the motor thus must
have a uniform rotating field, just as the induction motor.

Above synchronism, /0 > /, the commutating field, $', is less
than the main field; below synchronism, however, /0 < /, the
commutating field must be greater than the main field to give
complete compensation. It obviously is not feasible to increase
the commutating field much beyond the main field, as this would
require an increase of the iron section of the motor beyond that
required to do the work, that is, to carry the main field flux. At
standstill & should be infinitely large, that is, compensation is
not possible.

Hence, by the use of a commutating field in time and space
quadrature, in the single-phase motor the short-circuit current
under the commutator brushes resulting from the e.m.f . of alter-
nation can be entirely eliminated at and above synchronism,
and more or less reduced below synchronism, the more the nearer
the speed is to synchronism, but no effect can be produced at
standstill. In such a motor either some further method, as re-
sistance leads, must be used to take care of the short-circuit cur-
rent at standstill, or the motor designed so that its commutator
can carry the short-circuit current for the small fraction of time
when the motor is at standstill or running at very low speed.

The main field, <1>, of the series motor is approximately inversely
proportional to the speed, /o, since the product of speed and field
strength, /0$, is proportional to the e.m.f. of rotation, or useful
e.m.f. of the motor, hence, neglecting losses arid phase displace-
ments, to the impressed e.m.f., that is, constant. Substituting

therefore
equation (19):

= >- <$>o, where <$o == main field at synchronism, into
Jo

m

If

(20)