Lap-winding.
The development of the modern drum armature, with its numerous coils
connected in orderly sequence into a symmetrical winding, as
contrasted with the earlier Siemens armatures, was initiated by F. von
Hefner Alteneck (1871), and the laws governing the interconnexion of
the coils have now been elaborated into a definite system of winding
formulae. Whatever the number of wires or bars in each side of a coil,
i.e. whether it consist of a single loop or of many turns, the final
connexions of its free ends are not thereby affected, and it may be
mentally replaced by a single loop with two active inducing sides. The
coil-sides in their final position are thus to be regarded as separate
primary elements, even in number, and distributed uniformly round the
armature periphery or divided into small, equally spaced groups by
being located within the slots of a toothed armature. Attention must
then be directed simply to the span of the back connexion between the
elements at the end of the armature further from the commutator, and
to the span of the front connexion by which the last turn of a coil is
finally connected to the first turn of the next in sequence, precisely
as if each coil of many turns were reduced to a single loop. In order
to avoid direct differential action, the span of the back connexion
which fixes the width of the coil must exceed the width of the
pole-face, and should not be far different from the pole-pitch; it is
usually a little less than the pole-pitch. Taking any one element as
No. 1 in fig. 20, where for simplicity a smooth-core bipolar armature
is shown, the number of winding-spaces, each to be occupied by an
element, which must be counted off in order to find the position of
the next element in series, is called the "pitch" of the
end-connexion, front or back, as the case may be. Thus the back pitch
of the winding as marked by the dotted line in fig. 20 is 7, the
second side of the first loop being the element numbered 1 + 7 = 8. In
forming the front end-connexion which completes the loop and joins it
to the next in succession, two possible cases present themselves. By
the first, or "lap-winding," the front end-connexion is brought
backwards, and passing on its way to a junction with a commutator
sector is led to a third element lying within the two sides of the
first loop, i.e. the second loop starts with the element, No. 3, lying
next but one to the starting-point of the first loop. The winding
therefore returns backwards on itself to form each front end, but as a
whole it works continually forwards round the armature, until it
finally "re-enters," after every element has been traversed. The
development of the completed winding on a flat surface shows that it
takes the form of a number of partially overlapping loops, whence its
name originates. The firm-line portion of fig. 21 gives the
development of an armature similar to that of fig. 18 when cut through
at the point marked X and opened out; two of the overlapping loops are
marked thereon in heavy lines. The multipolar lap-wound armature is
obtained by simply repeating the bipolar winding p times, as indicated
by the dotted additions of fig. 21 which convert it from a two-pole to
a four-pole machine. The characteristic feature of the lap-wound
armature is that there are as many parallel paths from brush to brush,
and as many points at which the current must be collected, as there
are poles. As the bipolar closed-coil continuous-current armature has
been shown to consist in reality of two circuits in parallel, each
giving the same E.M.F. and carrying half the total current, so the
multipolar lap-wound drum consists of p pairs of parallel paths, each
giving the same E.M.F. and carrying 1/2p of the total current. Thus in
equation 1.b we have q = 2p, and the special form which the _E.M.F.
equation of the lap-wound armature_ takes is E_[alpha] = Z_a
(N/60)[tau] x 10^(-8) volts. All the brushes which are of the same
sign must be connected together in order to collect the total armature
current. The several brush-sets of the multipolar lap-wound machine
may again be reduced to two by "cross-connexion" of sectors situated
360 deg./p apart, but this is seldom done, since the commutator must then
be lengthened p times in order to obtain the necessary brush
contact-surface for the collection of the entire current.
[Illustration: FIG. 21.]
[Illustration: FIG. 22.