348

ELECTRICAL APPARATUS

as the resistance of the brush contact, increasing when the arma-
ture coil begins to leave the brush, tends to reverse the current.
Such "resistance commutation" obviously can not be perfect;
perfect commutation, however, is produced by impressing upon
the motor armature at right angles to the main field, that is, in
the position of the commutator brushes, a magnetic field oppo-
site to that of the armature reaction and proportional to the
armature current. Such a field is produced by overcompensa-
tion or by the use of a commutating pole or interpole.
As seen in the foregoing, in the direct-current motor the counter
e.m.f. of self-inductance of commutation opposes the reversal of
current in the armature coil under the commutator brush, and
this can be mitigated in its effect by the use of high-resistance
brushes, and overcome by the commutating field of overcompen-
sation. In addition hereto, however, in the alternating-current
commutator motor an e.m.f. is generated in the coil short-cir-
cuited under the brush, by the alternation of the magnetic flux,
and this e.m.f., which does not exist in the direct-current motor,
makes the problem of commutation of the alternating-current
motor far more difficult. In the position of commutation no
e.m.f. is generated in the armature coil by its rotation through
the magnetic field, as in this position the coil encloses the maxi-
mum field flux; but as this magnetic flux is alternating, in this
position the e.m.f. generated by the alternation of the flux en-
closed by the coil is a maximum. This "e.m.f. of alternation"
lags in time 90° behind the magnetic flux which generates it, is
proportional to the magnetic flux and to the frequency, but is
independent of the speed, hence exists also at standstill, while
the "e.m.f. of rotation"—which is a maximum.in the position
of the armature coil midway between the brushes, or parallel to
the field flux—is in phase with the field flux and proportional
thereto and to the speed, but independent of the frequency. In
the alternating-current commutator motor, no position therefore
exists in which the armature coil is free from a generated e.m.f.,
but in the position parallel to the field, or midway between the
brushes, the e.m.f. of rotation, in phase with the field flux, is a
maximum, while the e.m.f. of alternation is zero, and in the posi-
tion under the commutator brush, or enclosing the total field
flux, the e.m.f. of alternation, in electrical space quadrature with
the field flux, is a maximum, the e.m.f. of rotation absent, while
in any other position of the armature coil its generated e.m.f. has