[Illustration: FIG. 23.]
Wave-winding.
But for many purposes, especially where the voltage is high and the
current small, it is advantageous to add together the inductive effect
of the several poles of the multipolar machine by throwing the E.M.F's
of half the total number of elements into series, the number of
parallel circuits being conversely again reduced to two. This is
effected by the second method of winding the closed-coil continuous
current drum, which is known as "wave-winding." The front pitch is now
in the same direction round the armature as the back pitch (fig. 22),
so that the beginning of the second loop, i.e. element No. 15, lies
outside the first loop. After p loops have been formed and as many
elements have been traversed as there are poles, the distance covered
either falls short of or exceeds a complete tour of the armature by
two winding-spaces, or the width of two elements. A second and third
tour are then made, and so on, until finally the winding again closes
upon itself. When the completed winding is developed as in fig. 23, it
is seen to work continuously forwards round the armature in zigzag
waves, one of which is marked in heavy lines, and the number of
complete tours is equal to the average of the back and front pitches.
Since the number of parallel circuits from brush to brush is q = 2,
the _E.M.F. equation of the wave-wound drum_ is E_a = pZ_a (N/60)[tau]
x 10^(-8) volts. Only two sets of brushes are necessary, but in order
to shorten the length of the commutator, other sets may also be added
at the point of highest and lowest potential up to as many in number
as there are poles. Thus the advantage of the wave-wound armature is
that for a given voltage and number of poles the number of active
wires is only 1/p of that in the lap-wound drum, each being of larger
cross-section in order to carry p times as much current; hence the
ratio of the room occupied by the insulation to the copper area is
less, and the available space is better utilized. A further advantage
is that the two circuits from brush to brush consist of elements
influenced by all the poles, so that if for any reason, such as
eccentricity of the armature within the bore of the pole-pieces, or
want of uniformity in the magnetic qualities of the poles, the flux of
each field is not equal to that of every other, the equality of the
voltage produced by the two halves of the winding is not affected
thereby.
In appearance the two classes of armatures, lap and wave, may be
distinguished in the barrel type of winding by the slope of the upper
layer of back end-connexions, and that of the front connexions at the
commutator end being parallel to one another in the latter, and
oppositely directed in the former.
[Illustration: FIG. 24.]
After completion of the winding, the end-connexions are firmly bound
down by bands of steel or phosphor bronze binding wire, so as to resist
the stress of centrifugal force. In the case of smooth-surface
armatures, such bands are also placed at intervals along the length of
the armature core, but in toothed armatures, although the coils are
often in small machines secured in the slots by similar bands of a
non-magnetic high-resistance wire, the use of hard-wood wedges driven
into notches at the sides of the slots becomes preferable, and in very
large machines indispensable. The external appearance of a typical
armature with lap-winding is shown in fig. 24.
The commutator.
A sound mechanical construction of the commutator is of vital importance
to the good working of the continuous-current dynamo. The narrow,
wedge-shaped sectors of hard-drawn copper, with their insulating strips
of thin mica, are built up into a cylinder, tightly clamped together,
and turned in the lathe; at each end a V-shaped groove is turned, and
into these are fitted rings of micanite of corresponding section (fig.
19); the whole is then slipped over a cast iron sleeve, and at either
end strong rings are forced into the V-shaped grooves under great
pressure and fixed by a number of closely-pitched tightening bolts. In
dynamos driven by steam-turbines in which the peripheral speed of the
commutator is very high, rings of steel are frequently shrunk on the
surface of the commutator at either end and at its centre. But in every
case the copper must be entirely insulated from the supporting body of
metal by the interposition of mica or micanite and the prevention of any
movement of the sectors under frequent and long-continued heating and
cooling calls for the greatest care in both the design and the
manufacture.
Forms of field-magnet.
On passing to the second fundamental part of the dynamo, namely, the
field-magnet, its functions may be briefly recalled as follows:--It has
to supply the magnetic flux; to provide for it an iron path as nearly
closed as possible upon the armature, save for the air-gaps which must
exist between the pole-system and the armature core, the one stationary
and the other rotating; and, lastly, it has to give the lines such
direction and intensity within the air-gaps that they may be cut by the
armature wires to the best advantage. Roughly corresponding to the three
functions above summarized are the three portions which are more or less
differentiated in the complete structure. These are: (1) the magnet
"cores" or "_limbs_," carrying the exciting coils whereby the inert iron
is converted into an electro-magnet; (2) the _yoke_, which joins the
limbs together and conducts the flux between them; and (3) the
_pole-pieces_, which face the armature and transmit the lines from the
limbs through the air-gap to the armature core, or vice versa.
[Illustration: FIG. 25.]
Of the countless shapes which the field-magnet may take, it may be
said, without much exaggeration, that almost all have been tried; yet
those which have proved economical and successful, and hence have met
with general adoption, may be classed under a comparatively small
number of types. For bipolar machines the _single horse-shoe_ (fig.
25), which is the lineal successor of the permanent magnet employed in
the first magneto-electric machines, was formerly very largely used.
It takes two principal forms, according as the pole-pieces and
armature are above or beneath the magnet limbs and yoke. The
"over-type" form is best suited to small belt-driven dynamos, while
the "under-type" is admirably adapted to be directly driven by the
steam-engine, the armature shaft being immediately coupled to the
crank-shaft of the engine. In the latter case the magnet must be
mounted on non-magnetic supports of gun-metal or zinc, so as to hold
it at some distance away from the iron bedplate which carries both
engine and dynamo; otherwise a large proportion of the flux which
passes through the magnet limbs would leak through the bedplate across
from pole to pole without passing through the armature core, and so
would not be cut by the armature wires.
[Illustration: FIG. 26.]
Next may be placed the "Manchester" field (fig. 26)--the type of a
divided magnetic circuit in which the flux forming one field or pole
is divided between two magnets. An exciting coil is placed on each
half of the double horse-shoe magnet, the pair being so wound that
consequent poles are formed above and below the armature. Each magnet
thus carries one-half of the total flux, the lines of the two halves
uniting to form a common field where they issue forth into or leave
the air-gaps. The pole-pieces may be lighter than in the single
horse-shoe type, and the field is much more symmetrical, whence it is
well suited to ring armatures of large diameter. Yet these advantages
are greatly discounted by the excessive magnetic leakage, and by the
increased weight of copper in the exciting coils. Even if the greater
percentage which the leakage lines bear to the useful flux is
neglected, and the cross sectional area of each magnet core is but
half that of the equivalent single horse-shoe, the weight of wire in
the double magnet for the same rise of temperature in the coils must
be some 40% more than in the single horse-shoe, and the rate at which
energy is expended in heating the coils will exceed that of the single
horse-shoe in the same proportion.
Thirdly comes the two-pole _ironclad_ type, so called from the
exciting coil being more or less encased by the iron yoke; this latter
is divided into two halves, which pass on either side of the armature.
Unless the yoke be kept well away from the polar edges and armature,
the leakage across the air into the yoke becomes considerable,
especially if only one exciting coil is used, as in fig. 27 A; it is
better, therefore, to divide the excitation between two coils, as in
fig. 27 B, when the field also becomes symmetrical.
From this form is easily derived the _multipolar_ type of fig. 28 or
fig. 29, which is by far the most usual for any number of poles from
four upwards; its leakage coefficient is but small, and it is
economical in weight both of iron and copper.
Materials of magnets.
As regards the materials of which magnets are made, generally speaking
there is little difference in the permeability of "wrought iron" or
"mild steel forgings" and good "cast steel"; typical (B, H) curves
connecting the magnetizing force required with different
flux-densities for these materials are given under ELECTROMAGNETISM.
On the other hand there is a marked inferiority in the case of "cast
iron," which for a flux-density of B = 8000 C.G.S. lines per sq. cm.
requires practically the same number of ampere-turns per centimetre
length as steel requires for B = 16,000. Whatever the material, if the
flux-density be pressed to a high value the ampere-turns are very
largely increased owing to its approaching saturation, and this
implies either a large amount of copper in the field coils or an undue
expenditure of electrical energy in their excitation. Hence there is a
limit imposed by practical considerations to the density at which the
magnet should be worked, and this limit may be placed at about B =
16,000 for wrought iron or steel, and at half this value for cast
iron. For a given flux, therefore, the cast iron magnet must have
twice the sectional area and be twice as heavy, although this
disadvantage is partly compensated by its greater cheapness. If,
however, cast iron be used for the portion of the magnetic circuit
which is covered with the exciting coils, the further disadvantage
must be added that the weight of copper on the field-magnet is much
increased, so that it is usual to employ forgings or cast steel for
the magnet cores on which the coils are wound. If weight is not a
disadvantage, a cast iron yoke may be combined with the wrought iron
or cast steel magnet cores. An absence of joints in the magnetic
circuit is only desirable from the point of view of economy of expense
in machining the component parts during manufacture; when the surfaces
which abut against each other are drawn firmly together by screws, the
want of homogeneity at the joint, which virtually amounts to the
presence of a very thin film of air, produces little or no effect on
the total reluctance by comparison with the very much longer air-gaps
surrounding the armature. In order to reduce the eddy-currents in the
pole-pieces, due to the use of toothed armatures with relatively wide
slots, the poles themselves must be laminated, or must have fixed to
them laminated pole-shoes, built up of thin strips of mild steel
riveted together (as shown in fig. 29).
[Illustration: FIG. 27.]
[Illustration: FIG. 28.]
However it be built up, the mechanical strength of the magnet system
must be carefully considered. Any two surfaces between which there
exists a field of density B_g experience a force tending to draw them
together proportional to the square of the density, and having a value
of B_g squared/(1.735 x 10^6) lb. per sq. in. of surface, over which the
density may be regarded as having the uniform value B_g. Hence, quite
apart from the torque with which the stationary part of the dynamo
tends to turn with the rotating part as soon as current is taken out
of the armature, there exists a force tending to make the pole-pieces
close on the armature as soon as the field is excited. Since both
armature and magnet must be capable of resisting this force, they
require to be rigidly held; although the one or the other must be
capable of rotation, there should otherwise be no possibility of one
part of the magnetic circuit shifting relatively to any other part. An
important conclusion may be drawn from this circumstance. If the
armature be placed exactly concentric within the bore of the poles,
and the two or more magnetic fields be symmetrical about a line
joining their centres, there is no tendency for the armature core to
be drawn in one direction more than in another; but if there is any
difference between the densities of the several fields, it will cause
an unbalanced stress on the armature and its shaft, under which it
will bend, and as this bending is continually reversed relatively to
the fibres of the shaft, they will eventually become weakened and give
way. Especially is this likely to take place in dynamos with short
air-gaps, wherein any difference in the lengths of the air-gaps
produces a much greater percentage difference in the flux-density than
in dynamos with long air-gaps. In toothed armatures with short
air-gaps the shaft must on this account be sufficiently strong to
withstand the stress without appreciable bending.
The magnetic circuit.
Reference has already been made to the importance in dynamo design of
the _predetermination of the flux_ due to a given number of ampere-turns
wound on the field-magnet, or, conversely, of the number of ampere-turns
which must be furnished by the exciting coils in order that a certain
flux corresponding to one field may flow through the armature core from
each pole. An equally important problem is the correct proportioning of
the field-magnet, so that the useful flux Z_a may be obtained with the
greatest economy in materials and exciting energy. The key to the two
problems is to be found in the concept of a magnetic circuit as
originated by H.A. Rowland and R.H.M. Bosanquet;[16] and the full
solution of both may be especially connected with the name of Dr J.
Hopkinson, from his practical application of the concept in his design
of the Edison-Hopkinson machine, and in his paper on "Dynamo-Electric
Machinery."[17] The publication of this paper in 1886 begins the second
era in the history of the dynamo; it at once raised its design from the
level of empirical rules-of-thumb to a science, and is thus worthy to be
ranked as the necessary supplement of the original discoveries of
Faraday. The process of predetermining the necessary ampere-turns is
described in a simple case under ELECTROMAGNETISM. In its extension to
the complete dynamo, it consists merely in the division of the magnetic
circuit into such portions as have the same sectional area and
permeability and carry approximately the same total flux; the difference
of magnetic potential that must exist between the ends of each section
of the magnet in order that the flux may pass through it is then
calculated _seriatim_ for the several portions into which the magnetic
circuit is divided, and the separate items are summed up into one
magnetomotive force that must be furnished by the exciting coils.
[Illustration: FIG. 29.]
The chief sections of the magnetic circuit are (1) the air-gaps, (2)
the armature core, and (3) the iron magnet.
The _air-gap_ of a dynamo with smooth-core armature is partly filled
with copper and partly with the cotton, mica, or other materials used
to insulate the core and wires; all these substances are, however,
sensibly non-magnetic, so that the whole interferric gap between the
iron of the pole-pieces and the iron of the armature may be treated as
an air-space, of which the permeability is constant for all values of
the flux density, and in the C.G.S. system is unity. Hence if l_g and
A_g be the length and area of the single air-gap in cm. and sq. cm.,
the reluctance of the double air-gap is 2l_g/A_g, and the difference
of magnetic potential required to pass Z_a lines over this reluctance
is Z_a.2l_g/A_g = B_g.2l_g; or, since one ampere-turn gives 1.257
C.G.S. units of magnetomotive force, the exciting power in
ampere-turns required over the two air-gaps is X_g = B_g.2l_g/1.257 =
0.8 B_g.2l_g. In the determination of the area A_g small allowance
must be made for the fringe of lines which extend beyond the actual
polar face. In the toothed armature with open slots, the lines are no
longer uniformly distributed over the air-gap area, but are graduated
into alternate bands of dense and weak induction corresponding to the
teeth and slots. Further, the lines curve round into the sides of the
teeth, so that their average length of path in the air and the air-gap
reluctance is not so easily calculated. Allowance must be made for
this by taking an increased length of air-gap = ml_g, where m is the
ratio _maximum density/mean density_, of which the value is chiefly
determined by the ratios of the width of tooth to width of slot and of
the width of slot to the air-gap between pole-face and surface of the
armature core.
The _armature core_ must be divided into the teeth and the core proper
below the teeth. Owing to the tapering section of the teeth, the
density rises towards their root, and when this reaches a high value,
such as 18,000 or more lines per sq. cm., the saturation of the iron
again forces an increasing proportion of the lines outwards into the
slot. A distinction must then be drawn between the "apparent"
induction which would hold if all the lines were concentrated in the
teeth, and the "real" induction. The area of the iron is obtained by
multiplying the number of teeth under the pole-face by their width and
by the net length of the iron core parallel to the axis of rotation.
The latter is the gross length of the armature less the space lost
through the insulating varnish or paper between the disks or through
the presence of ventilating ducts, which are introduced at intervals
along the length of the core. The former deduction averages about 7 to
10% of the gross length, while the latter, especially in large
multipolar machines, is an even more important item. Alter calculating
the density at different sections of the teeth, reference has now to
be made to a (B, H) or flux-density curve, from which may be found the
number of ampere-turns required per cm. length of path. This number
may be expressed as a function of the density in the teeth, and f(B_t)
be its average value over the length of a tooth, the ampere-turns of
excitation required over the teeth on either side of the core as the
lines of one field enter or leave the armature is X_t = f(B_t).2l_t,
where l_t is the length of a single tooth in cm.
In the core proper below the teeth the length of path continually
shortens as we pass from the middle of the pole towards the centre
line of symmetry. On the other hand, as the lines gradually accumulate
in the core, their density increases from zero midway under the poles
until it reaches a maximum on the line of symmetry. The two effects
partially counteract one another, and tend to equalize the difference
of magnetic potential required over the paths of varying lengths; but
since the reluctivity of the iron increases more rapidly than the
density of the lines, we may approximately take for the length of path
(l_a) the minimum peripheral distance between the edges of adjacent
pole-faces, and then assume the maximum value of the density of the
lines as holding throughout this entire path. In ring and drum
machines the flux issuing from one pole divides into two halves in the
armature core, so that the maximum density of lines in the armature is
B_a = Z_a/2ab, where a = the radial depth of the disks in centimetres
and b = the net length of iron core. The total exciting power required
between the pole-pieces is therefore, at no load, X_p = X_g + X_t +
X_a, where X_a = f(B_a).l_a; in order, however, to allow for the
effect of the armature current, which increases with the load, a
further term X_b, must be added.
[Illustration: Fig. 30.]
In the continuous-current dynamo it may be, and usually is, necessary
to move the brushes forward from the interpolar line of symmetry
through a small angle in the direction of rotation, in order to avoid
sparking between the brushes and the commutator (_vide infra_). When
the dynamo is giving current, the wires on either side of the diameter
of commutation form a current-sheet flowing along the surface of the
armature from end to end, and whatever the actual end-connexions of
the wires, the wires may be imagined to be joined together into a
system of loops such that the two sides of each loop are carrying
current in opposite directions. Thus a number of armature ampere-turns
are formed, and their effect on the entire system of magnet and
armature must be taken into account. So long as the diameter of
commutation coincides with the line of symmetry, the armature may be
regarded as a cylindrical electromagnet producing a flux of lines, as
shown in fig. 30. The direction of the self-induced flux in the
air-gaps is the same as that of the lines of the external field in one
quadrant on one side of DC, but opposed to it in the other quadrant on
the same side of DC; hence in the resultant field due to the combined
action of the field-magnet and armature ampere-turns, the flux is as
much strengthened over the one half of each polar face as it is
weakened over the other, and the total number of lines is unaffected,
although their distribution is altered. The armature ampere-turns are
then called _cross-turns_, since they produce a cross-field, which,
when combined with the symmetrical field, causes the leading
pole-corners ll to be weakened and the trailing pole-corners tt to be
strengthened, the neutral line of zero field being thus twisted
forwards in the direction of rotation. But when the brushes and
diameter of commutation are shifted forward, as shown in fig. 31, it
will be seen that a number of ampere-turns, forming a zone between the
lines Dn and mC, are in effect wound immediately on the magnetic
circuit proper, and this belt of ampere-turns is in direct opposition
to the ampere-turns of the field, as shown by the dotted and crossed
wires on the pole-pieces. The armature ampere-turns are then divisible
into the two bands, the _back-turns_, included within twice the angle
of lead [lambda], weakening the field, and the cross-turns, bounded by
the lines Dm, nC, again producing distortion of the weakened
symmetrical field. If, therefore, a certain flux is to be passed
through the armature core in opposition to the demagnetizing turns,
the difference of magnetic potential between the pole-faces must
include not only X_a, X_t, and X_g, but also an item X_b, in order to
balance the "back" ampere-turns of the armature. The amount by which
the brushes must be shifted forward increases with the armature
current, and in corresponding proportion the back ampere-turns are
also increased, their value being c[tau]2[lambda]/360 deg., where c = the
current carried by each of the [tau] active wires. Thus the term X_b,
takes into account the effect of the armature reaction on the total
flux; it varies as the armature current and angle of lead required to
avoid sparking are increased; and the reason for its introduction in
the fourth place (X_p = X_g + X_t + X_a + X_b), is that it increases
the magnetic difference of potential which must exist between the
poles of the dynamo, and to which the greater part of the leakage is
due. The leakage paths which are in parallel with the armature across
the poles must now be estimated, and so a new value be derived for the
flux at the commencement of the _iron-magnet_ path. If P = their joint
permeance, the leakage flux due to the difference of potential at the
poles is z_l = 1.257X_p x P, and this must be added to the useful flux
Z_a, or Z_p = Z_a + Z_l. There are also certain leakage paths in
parallel with the magnet cores, and upon the permeance of these a
varying number of ampere-turns is acting as we proceed along the
magnet coils; the magnet flux therefore increases by the addition of
leakage along the length of the limbs, and finally reaches a maximum
near the yoke. Either, then, the density in the magnet B_m = Z_m/A_m
will vary if the same sectional area be retained throughout, or the
sectional area of the magnet must itself be progressively increased.
In general, sufficient accuracy will be obtained by assuming a certain
number of additional leakage lines z_n as traversing the entire length
of magnet limbs and yoke (= l_m), so that the density in the magnet
has the uniform value B_m = (Z_p + z_n)/A_m. The leakage flux added on
actually within the length of the magnet core or z_n will be
approximately equal to half the total M.M.F. of the coils multiplied
by the permeance of the leakage paths around one coil. The
corresponding value of H can then be obtained from the (B, H) curve of
the material of which the magnet is composed, and the ampere-turns
thus determined must be added to X_p, or X = X_p + X_m, where X_m =
f(B_m)l_m. The final equation for the exciting power required on a
magnetic circuit as a whole will therefore take the form