In the alternator q is most commonly 1, and there is only one circuit
per phase; finally the value of K or the product of the width-factor
and the form-factor usually falls between the limits of 1 and 1.25.
We have next to consider the effect of the addition of more armature
loops in the case of dynamos which give a unidirectional E.M.F. in
virtue of their split-ring collecting device, i.e. of the type shown in
fig. 7 with drum armature or its equivalent ring form. As before, if the
additional loops are wound in continuation of the first as one coil
connected to a single split-ring, this coil must be more or less
concentrated into a narrow band; since if the width becomes nearly equal
to or exceeds the width of the interpolar gap, the two edges of the
coil-side will just as in the alternator act differentially against one
another during part of each revolution. The drum winding with a single
coil thus gives an armature of the H- or "shuttle" form invented by Dr
Werner von Siemens. Although the E.M.F. of such an arrangement may have
a much higher maximum value than that of the curve of fig. 7 for a
single loop, yet it still periodically varies during each revolution and
so gives a pulsating current, which is for most practical uses
unsuitable. But such pulsation might be largely reduced if, for example,
a second coil were placed at right angles to the original coil and the
two were connected in series; the crests of the wave of E.M.F. of the
second coil will then coincide with the hollows of the first wave,
and although the maximum of the resultant curve of E.M.F. may be no
higher its fluctuations will be greatly decreased. A spacial
displacement of the new coils along the pole-pitch, somewhat as in a
polyphase machine, thus suggests itself, and the process may be carried
still further by increasing the number of equally spaced coils, provided
that they can be connected in series and yet can have their connexion
with the external circuit reversed as they pass the neutral line between
the poles.
[Illustration: FIG. 15.]
[Illustration: FIG. 16.]
Given two coils at right angles and with their split-rings displaced
through a corresponding angle of 90 deg., they may be connected in series by
joining one brush to the opposite brush of the second coil, the external
circuit being applied to the two remaining brushes.[14] The same
arrangement may again be repeated with another pair of coils in parallel
with the first, and we thus obtain fig. 15 with four split-rings, their
connexions to the loops being marked by corresponding numerals; the four
coils will give the same E.M.F. as the two, but they will be jointly
capable of carrying twice the current, owing to their division into two
parallel circuits. Now in place of the four split-rings may be employed
the greatly simplified four-segment structure shown in fig. 16, which
serves precisely the same purpose as the four split-rings but only
requires two instead of eight brushes. The effect of joining brush 2 in
fig. 15 across to brush 3, brush 4 to brush 5, 5 to 6, &c., has
virtually been to connect the end of coil A with the beginning of coil
B, and the end of coil B with the beginning of coil A', and so on, until
they form a continuous closed helix. Each sector of fig. 16 will
therefore replace two halves of a pair of adjacent split-rings, if the
end and beginning of a pair of adjacent coils are connected to it in a
regular order of sequence. The four sectors are insulated from one
another and from the shaft, and the whole structure is known as the
"commutator,"[15] its function being not simply to collect the current
but also to commute its direction in any coil as it passes the
interpolar gap. The principle of the "closed-coil continuous-current
armature" is thus reached, in which there are at least two parallel
circuits from brush to brush, and from which a practically steady
current can be obtained. Each coil is successively short-circuited, as a
brush bridges over the insulation between the two sectors which
terminate it; and the brushes must be so set that the period of
short-circuit takes place when the coil is generating little or no
E.M.F., i.e. when it is moving through the zone between the pole-tips.
The effect of the four coils in reducing the percentage fluctuation of
the E.M.F. is very marked, as shown at the foot of fig. 15 (where the
upper curve is the resultant obtained by adding together the separate
curves of coils A and B), and the levelling process may evidently be
carried still further by the insertion of more coils and more
corresponding sectors in the commutator, until the whole armature is
covered with winding. For example, figs. 17 and 18 show a ring and a
drum armature, each with eight coils and eight commutator sectors; their
resultant curve, on the assumption that a single active wire gives the
flat-topped curve of fig. 4, will be the upper wavy line of E.M.F.
obtained by adding together two of the resultant curves of fig. 15, with
a relative displacement of 45 deg.. The amount of fluctuation for a given
number of commutator sectors depends upon the shape of the curve of
E.M.F. yielded by the separate small sections of the armature winding;
the greater the polar arc, the less the fluctuation. In practice, with a
polar arc equal to about 0.75 of the pitch, any number of sectors over
32 per pair of poles yields an E.M.F. which is sensibly constant
throughout one or any number of revolutions.
[Illustration: FIG. 17.]
[Illustration: FIG. 18.]
The fundamental electro-motive-force equation of the
continuous-current heteropolar machine is easily obtained by analogy
from that of the alternator. The gross average E.W.F. from the two
sides of a drum loop without reference to its direction is as before
4Z_a(pN/60) x 10^(-8) volts. But for two reasons its net average
E.M.F. may be less; the span of the loop may be less than the
pole-pitch, so that even when the brushes are so set that the position
of short-circuit falls on the line where the field changes its
direction, the two sides of the loop for some little time act against
each other; or, secondly, even if the span of the loop be equal to the
pole-pitch, the brushes may be so set that the reversal of the
direction of its induced E.M.F. does not coincide with reversal of the
current by the passage of the coil under the brushes. The net average
E.M.F. of the loop is therefore proportional to the algebraic sum of
the lines which it cuts in passing from one brush to another, and this
is equal to the net amount of the flux which is included within the
loop when situated in the position of short-circuit under a brush. The
amount of this flux may be expressed as k'Z_a where k' is some
coefficient, less than unity if the span of the coil be less than the
pole-pitch, and also varying with the position of the brushes. The net
average E.M.F. of the loop is therefore
4k'Z_a(pN/60) x 10^(-8).
In practice the number of sections of the armature winding is so large
and their distribution round the armature periphery is so uniform,
that the sum total of the instantaneous E.M.F.'s of the several
sections which are in series becomes at any moment equal to the net
average E.M.F. of one loop multiplied by the number which are in
series. If the winding is divided into q parallel circuits, the number
of loops in series is [tau]/2q, so that the total E.M.F. is E_a =
2(k'/q)Z_a(pN/60)[tau] x 10^(-8) volts. Thus as compared with the
alternator not only is there no division of the winding into separate
phases, but the form-factor k' disappears, since the effective and
average E.M.F.'s are the same. Further whereas in the alternator q may
= 1, in the continuous-current closed-coil armature there can never be
less than two circuits in parallel from brush to brush, and if more,
their number must always be a multiple of two, so that q can never be
less than two and must always be an even number. Lastly, the factor k'
is usually so closely equal to 1, that the simplified equation may in
practice be adopted, viz.