Dynamo

Little practical use could be made of electrical energy so long as its only known sources were frictional machines and voltaic batteries. The cost of the materials for producing electrical currents on a large scale by chemical action was prohibitive, while the frictional machine only yielded very small currents at extremely high potentials. In the dynamo, on the other hand, electrical energy in a convenient form could be cheaply and easily obtained by mechanical means, and with its invention the application of electricity to a wide range of commercial purposes became economically possible. As a converter of energy from one form to another it is only surpassed in efficiency by another electrical appliance, namely, the transformer (see Transformers). In this there is merely conversion of electrical energy at a high potential into electrical energy at a low potential, or vice versa, but in the dynamo the mechanical energy which must be applied to maintain the relative movement of magnetic field and conductor is absorbed, and reappears in an electrical form. A true transformation takes place, and the proportion which the rate of delivery of electrical energy bears to the power absorbed, or in other words the efficiency, is the more remarkable. The useful return or “output” at the terminals of a large machine may amount to as much as 95% of the mechanical energy which forms the “input.” Since it needs some prime mover to drive it, the dynamo has not made any direct addition to our sources of energy, and does not therefore rank with the primary battery or oil-engine, or even the steam-engine, all of which draw their energy more immediately from nature. Yet by the aid of the dynamo the power to be derived from waterfalls can be economically and conveniently converted into an electrical form and brought to the neighbouring factory or distant town, to be there reconverted by motors into mechanical power. Over any but very short distances energy is most easily transmitted when it is in an electrical form, and turbine-driven dynamos are very largely and successfully employed for such transmission. Thus by conducing to the utilization of water-power which may previously have had but little value owing to its disadvantageous situation, the dynamo may almost be said to have added another to our available natural resources.

Not only does the toothed armature reduce the length of the air-gap to the minimum permitted by mechanical and magnetic considerations, and furnish better mechanical protection to the armature coils, but it also ensures the positive holding of the active wires against the mechanical drag which they experience as they pass through the magnetic field. Further, the active wires in the toothed armature are relieved of a large proportion of this mechanical drag, which is transferred to the iron teeth. The lines of the field, after passing through the air-gap proper, divide between the teeth and the slots in proportion to their relative permeances. Hence at any moment the active wires are situated in a weak field, and for a given armature current the force on them is only proportional to this weak field. This important result is connected with the fact that when the armature is giving current the distribution of the lines over the face of each tooth is distorted, so that they become denser on the “trailing” side than on the “leading” side;13 the effect of the non-uniform distribution acting on all the teeth is to produce a magnetic drag on the armature core proportional to the current passing through the wires, so that the total resisting force remains the same as if the armature had a smooth core. The amount by which the stress on the active wires is reduced entirely depends upon the degree to which the teeth are saturated, but, since the relative permeability of iron even at a flux density of 20,000 lines per sq. cm. is to that of air approximately as 33 : 1, the embedded wires are very largely relieved of the driving stress. An additional gain is that solid bars of much greater width can be used in the toothed armature than on a smooth core without appreciable loss from eddy-currents within their mass.

A disadvantage of the slotted core is, however, that it usually necessitates the lamination of the pole-pieces. If the top of the slot is open, and its width of opening is considerably greater than the length of the air-gap from the iron of the pole-face to the surface of the teeth, the lines become unequally distributed not only at the surface of the teeth, but also at the face of the pole-pieces; and this massing of the lines into bands causes the density at the pole-face to be rhythmically varied as the teeth pass under it. No such variation can take place in a solid mass of metal without the production of eddy-currents within it; hence if the width of the slot-opening is equal to or exceeds twice the length of the single air-gap, lamination of the pole-pieces in the same plane as that of the armature core becomes advisable.

If the wires are threaded through holes or tunnels pierced close to the periphery of the core, the same advantages are gained as with open slots, and lamination of the pole-pieces is rendered unnecessary. But on the other hand, the process of winding becomes laborious and expensive, while the increase in the inductance of the coils owing to their being surrounded by a closed iron circuit is prejudicial to sparkless commutation in the continuous-current dynamo and to the regulation of the voltage of the alternator. A compromise is found in the half-closed slot, which is not uncommon in alternators, although the open slot is more usual in continuous-current dynamos.

The fundamental “electromotive-force equation” of the heteropolar alternator can now be given a more definite form. Let Za be the number of C. G. S. lines or the total flux, which issuing from any one pole flows through the armature core, to leave it by another pole of opposite sign. Since each active wire cuts these lines, first as they enter the armature core and then as they emerge from it to enter another pole, the total number of lines cut in one revolution by any one active wire is 2pZa. The time in seconds taken by one revolution is 60/N. The average E.M.F. induced in each active wire in one revolution being proportional to the number of lines cut divided by the time taken to cut them is therefore 2Za (pN / 60) × 10−8 volts. The active wires which are in series and form one distinct phase may be divided into as many bands as there are poles; let each such band contain t active wires, which as before explained may either form one side of a single large coil or the adjacent sides of two coils when the large coil is divided into two halves. Since the wires are joined up into loops, two bands are best considered together, which with either arrangement yield in effect a single coil of t turns. The average E.M.F.’s of all the wires in the two bands when added together will therefore be 4Za (pN / 60)t × 10−8. But unless each band is concentrated within a single slot, there must be some differential action as they cross the neutral line between the poles, so that the last expression is virtually the gross average E.M.F. of the loops on the assumption that the component E.M.F.’s always act in agreement round the coil and do not at times partially neutralize one another. The net average E.M.F. of the coil as a whole, or the arithmetical mean of all the instantaneous values of a half-wave of the actual E.M.F. curve, is therefore reduced to an extent depending upon the amount of differential action and so upon the width of the coil-side when this is not concentrated. Let k′ = the coefficient by which the gross average E.M.F. must be multiplied to give the net average E.M.F.; then k′ may be called the “width-factor,” and will have some value less than unity when the wires of each band are spread over a number of slots. The net average E.M.F. of the two bands corresponding to a pair of poles is thus eav = 4k′Za (pN / 60)t × 10−8.

The shape of the curve of instantaneous E.M.F. of the coil must further be taken into account. The “effective” value of an alternating E.M.F. is equal to the square root of the mean square of its instantaneous values, since this is the value of the equivalent unidirectional and unvarying E.M.F., which when applied to a given resistance develops energy at the same rate as the alternating E.M.F., when the effect of the latter is averaged over one or any whole number of periods. Let k″ = the ratio of the square root of the mean square to the average E.M.F. of the coil, i.e. = effective E.M.F. / average E.M.F. Since it depends upon the shape of the E.M.F. curve, k″ is also known as the “form-factor”; thus if the length of gap between pole-face and armature core and the spacing of the wires were so graduated as to give a curve of E.M.F. varying after a sine law, the form-factor would have the particular value of π/2 √2 = 1.11, and to this condition practical alternators more or less conform. The effective E.M.F. of the two bands corresponding to a pair of poles is thus eeff = 4k′k″Za (pN / 60)t × 10−8.

In any one phase there are p pairs of bands, and these may be divided into q parallel paths, where q is one or any whole number of which p is a multiple. The effective E.M.F. of a complete phase is therefore peeff/q. Lastly, if m = the number of phases into which the armature winding is divided, and τ = the total number of active wires on the armature counted all round its periphery, t = τ / 2pm, and the effective E.M.F. per phase is Ea = 2k′k″Za (pNτ / 60mq) × 10−8.

The two factors k′ and k″ may be united into one coefficient, and the equation then takes its final form

Ea = 2KZa (pNτ / 60mq) × 10−8 volts

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.

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 4Za (pN / 60) × 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′Za 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′Za (pN / 60) × 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 τ/2q, so that the total E.M.F. is Ea = 2(k′ / q) Za (pN / 60)τ × 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.

Ea = (2/q) (ZpN / 60) τ × 10−8 volts.

The fundamental equation of the electromotive force of the dynamo in its fully developed forms (1 a) (and 1 b) may be compared with its previous simple statement (I.). The three variable terms still find their equivalents, but are differently expressed, the density Bg being replaced by the total flux of one field Za, the length L of the single active wire by the total number of such wires τ, and the velocity of movement V by the number of revolutions per second. Even when the speed is fixed, an endless number of changes may be rung by altering the relative values of the remaining two factors; and in successful practice these may be varied between fairly wide limits without detriment to the working or economy of the machine. While it may be said that the equation of the E.M.F. was implicitly known from Faraday’s time onwards, the difficulty under which designers laboured in early days was the problem of choosing the correct relation of Za or τ for the required output; this, again, was due chiefly to the difficulty of predetermining the total flux before the machine was constructed. The general error lay in employing too weak a field and too many turns on the armature, and credit must here be given to the American inventors, E. Weston and T.A. Edison, for their early appreciation of the superiority in practical working of the drum armature, with comparatively few active wires rotating in a strong field.

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 Ea = Za (N / 60)τ × 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°/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.

Fig. 21.

Fig. 23.

Wave-loops Fig. 22.

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 Wave-winding. 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 Ea = pZa (N / 60)τ × 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.

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.

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.

Fig. 27.

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 Materials of magnets. (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).

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 Bg experience a force tending to draw them together proportional to the square of the density, and having a value of Bg² / (1.735 × 106) ℔ per sq. in. of surface, over which the density may be regarded as having the uniform value Bg. 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 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 lg and Ag be the length and area of the single air-gap in cm. and sq. cm., the reluctance of the double air-gap is 2lg / Ag, and the difference of magnetic potential required to pass Za lines over this reluctance is Za·2lg / Ag = Bg·2lg; 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 Xg = Bg·2lg / 1.257 = 0.8Bg·2lg. In the determination of the area Ag 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 = mlg, 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 ƒ(Bt) 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 Xt = ƒ(Bt)·2lt, where lt 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 (la) 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 Ba = Za / 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, Xp = Xg + Xt + Xa, where Xa = ƒ(Ba)·la; in order, however, to allow for the effect of the armature current, which increases with the load, a further term Xb, must be added.

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 λ, 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 Xa, Xt, and Xg, but also an item Xb, 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 cτ2λ / 360°, where c = the current carried by each of the τ active wires. Thus the term Xb, 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 (Xp = Xg + Xt + Xa + Xb), 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 zl = 1.257Xp × P, and this must be added to the useful flux Za, or Zp = Za + Zl. 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 Bm = Zm / Am 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 zn as traversing the entire length of magnet limbs and yoke (= lm), so that the density in the magnet has the uniform value Bm = (Zp + zn) / Am. The leakage flux added on actually within the length of the magnet core or zn 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 Xp, or X = Xp + Xm, where Xm = ƒ(Bm)lm. The final equation for the exciting power required on a magnetic circuit as a whole will therefore take the form

X = AT = 0.8Bg·2lg + ƒ(Bt) 2lt + ƒ(Ba) la + Xb + ƒ(Bm) lm.

Fig. 31.

If the magnet cores are of wrought iron or cast steel, and the yoke is of cast iron, the last term must be divided into two portions corresponding to the different materials, i.e. into f(Bm)lm + f(By)ly. In the ordinary multipolar machine with as many magnet-coils as there are poles, each coil must furnish half the above number of ampere-turns.

Since no substance is impermeable to the passage of magnetic flux, the only form of magnetic circuit free from leakage is one uniformly wound with ampere-turns over its whole length. The reduction of the magnetic leakage to a minimum in any Magnetic leakage. given type is therefore primarily a question of distributing the winding as far as possible uniformly upon the circuit, and as the winding must be more or less concentrated into coils, it resolves itself into the necessity of introducing as long air-paths as possible between any surfaces which are at different magnetic potentials. No iron should be brought near the machine which does not form part of the magnetic circuit proper, and especially no iron should be brought near the poles, between which the difference of magnetic potential practically reaches its maximum value. In default of a machine of the same size or similar type on which to experiment, the probable direction of the leakage flux must be assumed from the drawing, and the air surrounding the machine must be mapped out into areas, between which the permeances are calculated as closely as possible by means of such approximate formulae as those devised by Professor G. Forbes.

In the earliest “magneto-electric” machines permanent steel magnets, either simple or compound, were employed, and for many years these were retained in certain alternators, some of which are still in use for arc lighting in lighthouses. Excitation of field-magnet. But since the field they furnish is very weak, a great advance was made when they were replaced by soft iron electromagnets, which could be made to yield a much more intense flux. As early as 1831 Faraday18 experimented with electromagnets, and after 1850 they gradually superseded the permanent magnet. When the total ampere-turns required to excite the electromagnet have been determined, it remains to decide how the excitation shall be obtained; and, according to the method adopted, continuous-current machines may be divided into four well-defined classes.

Fig. 32.

The simplest method, and that which was first used, is separate excitation from some other source of direct current, which may be either a primary or a secondary battery or another dynamo (fig. 32). But since the armature yields a continuous current, it was early suggested (by J. Brett in 1848 and F. Sinsteden in 1851) that this current might be utilized to increase the flux; combinations of permanent and electromagnets were therefore next employed, acting either on the main armature or on separate armatures, until in 1867 Dr Werner von Siemens and Sir C. Wheatstone almost simultaneously discovered that the dynamo could be made self-exciting through the residual magnetism retained in the soft iron cores of the electromagnet. The former proposed to take the whole of the current round the magnet coils which were in series with the armature and external circuit, while the latter proposed to utilize only a portion derived by a shunt from the main circuit; we thus arrive at the second and third classes, namely, series and shunt machines. The starting of the process of excitation in either case is the same; when the brushes are touching the commutator and the armature is rotated, the small amount of flux left in the magnet is cut by the wires, and a very small current begins to flow round the closed circuit; this increases the flux, which in turn further increases the E.M.F. and current, until, finally, the cumulative effect stops through the increasing saturation of the iron cores. Fig. 33, illustrating the series machine, shows the winding of the exciting coils to be composed of a few turns of thick wire. Since the current is undivided throughout the whole circuit, the resistance of both the armature and field-magnet winding must be low as compared with that of the external circuit, if the useful power available at the terminals of the machine is to form a large percentage of the total electrical power—in other words, if the efficiency is to be high. Fig. 34 shows the third method, in which the winding of the field-magnets is a shunt or fine-wire circuit of many turns applied to the terminals of the machine; in this ease the resistance of the shunt must be high as compared with that of the external circuit, in order that only a small proportion of the total energy may be absorbed in the field.

Fig. 33.	Fig. 34.

Since the whole of the armature current passes round the field-magnet of the series machine, any alteration in the resistance of the external circuit will affect the excitation and also the voltage. A curve connecting together corresponding values of external current and terminal voltage for a given speed of rotation is known as the external-characteristic of the machine; in its main features it has the same appearance as a curve of magnetic flux, but when the current exceeds a certain amount it begins to bend downwards and the voltage decreases. The reason for this will be found in the armature reaction at large loads, which gradually produces a more and more powerful demagnetizing effect, as the brushes are shifted forwards to avoid sparking; eventually the back ampere-turns overpower any addition to the field that would otherwise be due to the increased current flowing round the magnet. The “external characteristic” for a shunt machine has an entirely different shape. The field-magnet circuit being connected in parallel with the external circuit, the exciting current, if the applied voltage remains the same, is in no way affected by alterations in the resistance of the latter. As, however, an increase in the external current causes a greater loss of volts in the armature and a greater armature reaction, the terminal voltage, which is also the exciting voltage, is highest at no load and then diminishes. The fall is at first gradual, but after a certain critical value of the armature current is reached, the machine is rapidly demagnetized and loses its voltage entirely.

Fig. 35.

The last method of excitation, namely, compound-winding (fig. 35), is a combination of the two preceding, and was first used by S.A. Varley and by C.F. Brush. If a machine is in the first instance shunt-wound, and a certain number of series-turns are added, the latter, since they carry the external current, can be made to counteract the effect which the increased external current would have in lowering the voltage of the simple shunt machine. The ampere-turns of the series winding must be such that they not only balance the increase of the demagnetizing back ampere-turns on the armature, but further increase the useful flux, and compensate for the loss of volts over their own resistance and that of the armature. The machine will then give for a constant speed a nearly constant voltage at its terminals, and the curve of the external characteristic becomes a straight line for all loads within its capacity. Since with most prime movers an increase of the load is accompanied by a drop in speed, this effect may also be counteracted; while, lastly, if the series-turns are still further increased, the voltage may be made to rise with an increasing load, and the machine is “over-compounded.”

From the moment that a dynamo begins to run with excited field, heat is continuously generated by the passage of the current through the windings of the field-magnet coils and the armature, as well as by the action of hysteresis and Heating effects. eddy currents in the armature and pole-pieces. Whether the source of the heat be in the field-magnet or in the armature, the mass in which it originates will continue to rise in temperature until such a difference of temperature is established between itself and the surrounding air that the rate at which the heat is carried off by radiation, convection and conduction is equal to the rate at which it is being generated. Evidently, then, the temperature which any part of the machine attains after a prolonged run must depend on the extent and effectiveness of the cooling surface from which radiation takes place, upon the presence or absence of any currents of air set up by the rotation of itself or surrounding parts, and upon the presence of neighbouring masses of metal to carry away the heat by conduction. In the field-magnet coils the rate at which heat is being generated is easily determined, since it is equal to the square of the current passing through them multiplied by their resistance. Further, the magnet is usually stationary, and only indirectly affected by draughts of air due to the rotating armature. Hence for machines of a given type and of similar proportions, it is not difficult to decide upon some method of reckoning the cooling surface of the magnet coils Sc, such that the rise of temperature above that of the surrounding air may be predicted from an equation of the form t° = kW / Sc, where W = the rate in watts at which heat is generated in the coils, and k is some constant depending upon the exact method of reckoning their cooling surface. As a general rule the cooling surface of a field-coil is reckoned as equal to the exposed outer surface of its wire, the influence of the end flanges being neglected, or only taken into account in the case of very short bobbins wound with a considerable depth of wire. In the case of the rotating armature a similar formula must be constructed, but with the addition of a factor to allow for the increase in the effectiveness of any given cooling surface due to the rotation causing convection currents in the surrounding air. Only experiment can determine the exact effect of this, and even with a given type of armature it is dependent on the number of poles, each of which helps to break up the air-currents, and so to dissipate the heat. For example, in two-pole machines with drum bar-armatures, if the cooling surface be reckoned as equal to the cylindrical exterior plus the area of the two ends, the heating coefficient for a peripheral speed of 1500 ft. per minute is less than half of that for the same armature when at rest. A further difficulty still meets the designer in the correct predetermination of the total loss of watts in an armature before the machine has been tested. It is made up of three separate items, namely, the copper loss in the armature winding, the loss by hysteresis in the iron, and the loss by eddy currents, which again may be divided into those in the armature bars and end-connexions, and those in the core and its end-plates. The two latter items are both dependent upon the speed of the machine; but whereas the hysteresis loss is proportional to the speed for a given density of flux in the armature, the eddy current loss is proportional to the square of the speed, and owing to this difference, the one loss can be separated from the other by testing an armature at varying speeds. Thus for a given rise of temperature, the question of the amount of current which can be taken out of an armature at different speeds depends upon the proportion which the hysteresis and eddy watts bear to the copper loss, and the ratio in which the effectiveness of the cooling surface is altered by the alteration in speed. Experimental data, again, can alone decide upon the amount of eddy currents that may be expected in given armatures, and caution is required in applying the results of one machine to another in which any of the conditions, such as the number of poles, density in the teeth, proportions of slot depth to width, &c., are radically altered.

It remains to add, that the rise of temperature which may be permitted in any part of a dynamo after a prolonged run is very generally placed at about 70° Fahr. above the surrounding air. Such a limit in ordinary conditions of working leads to a final temperature of about 170° Fahr., beyond which the durability of the insulation of the wires is liable to be injuriously affected. Upon some such basis the output of a dynamo in continuous working is rated, although for short periods of, say, two hours the normal full-load current of a large machine may be exceeded by some 25% without unduly heating the armature.

In all large central stations it is necessary that the dynamos should be capable of being run in parallel, so that their outputs may be combined on the same “omnibus bars” and thence distributed to the network of feeders. With simple shunt-wound machines this is easily effected by coupling together terminals of like sign when the voltage of the two or more machines are closely equal. With compound-wound dynamos not only must the external terminals of like sign be coupled together, but the junctions of the brush leads with the series winding must be connected by an “equalizing” lead of low resistance; otherwise, should the E.M.F. of one machine for any reason fall below the voltage of the omnibus bars, there is a danger of its polarity being reversed by a back current from the others with which it is in parallel.

Owing to the necessary presence in the continuous-current dynamo of the commutator, with its attendant liability to sparking at the brushes, and further, owing to the difficulty of insulating the rotating armature wires, a pressure of 3000 volts has seldom been exceeded in any one continuous-current machine, and has been given above as the limiting voltage of the class. If therefore it is required to work with higher pressures in order to secure economy in the transmitting lines, two or more machines must be coupled in series by connecting together terminals which are of unlike sign.19 The stress of the total voltage may still fall on the insulation of the winding from the body of the machine; hence for high-voltage transmission of power over very long distances, the continuous-current dynamo in certain points yields in convenience to the alternator. In this there is no commutator, the armature coils may be stationary and can be more thoroughly insulated, while further, if it be thought undesirable to design the machine for the full transmitting voltage, it is easy to wind the armature for a low pressure; this can be subsequently transformed up to a high pressure by means of the alternating-current transformer, which has stationary windings and so high an efficiency that but little loss arises from its use. With these remarks, the transition may be made to the fuller discussion of the alternator.

The first experimental determination of the shape of the E.M.F. curve of an alternator was made by J. Joubert in 1880. A revolving contact-maker charged a condenser with the E.M.F. produced by the armature at a particular instant during Shape of E.M.F. curve. each period. The condenser was discharged through a ballistic galvanometer, and from the measured throw the instantaneous E.M.F. could be deduced. The contact-maker was then shifted through a small angle, and the instantaneous E.M.F. at the new position corresponding to a different moment in the period was measured; this process was repeated until the E.M.F. curve for a complete period could be traced. Various modifications of the same principle have since been used, and a form of “oscillograph” (q.v.) has been perfected which is well adapted for the purpose of tracing the curves both of E.M.F. and of current. The machine on which Joubert carried out his experiments was a Siemens disk alternator having no iron in its armature, and it was found that the curve of E.M.F. was practically identical with a sine curve. The same law has also been found to hold true for a smooth-core ring or drum armature, but the presence of the iron core enables the armature current to produce greater distorting effect, so that the curves under load may vary considerably from their shape at no load. In toothed armatures, the broken surface of the core, and the still greater reaction from the armature current, may produce wide variations from the sine law, the general tendency being to give the E.M.F. curve a more peaked form. The great convenience of the assumption that the E.M.F. obeys the sine law has led to its being very commonly used as the basis for the mathematical analysis of alternator problems; but any deductions made from this premiss require to be applied with caution if they are likely to be modified by a different shape of the curve. Further, the same alternator will give widely different curves even of E.M.F., and still more so of current, according to the nature of the external circuit to which it is connected. As will be explained later, the phase of the current relatively to the E.M.F. depends not only on the inductance of the alternator itself, but also upon the inductance and capacity of the external circuit, so that the same current will produce different effects according to the amount by which it lags or leads. The question as to the relative advantages of differently shaped E.M.F. curves has led to much discussion, but can only be answered by reference to the nature of the work that the alternator has to do—i.e. whether it be arc lighting, motor driving, or incandescent lighting through transformers. The shape of the E.M.F. curve is, however, of great importance in one respect, since upon it depends the ratio of the maximum instantaneous E.M.F. to the effective value, and the insulation of the entire circuit, both external and internal, must be capable of withstanding the maximum E.M.F. While the maximum value of the sine curve is √2 or 1.414 times the effective value, the maximum value of a Λ curve is 1.732 times the effective value, so that for the same effective E.M.F. the armature wires must not only be more heavily insulated than in the continuous-current dynamo, but also the more peaked the curve the better must be the insulation.

Since an alternating current cannot be used for exciting the field-magnet, recourse must be had to some source of a direct current. This is usually obtained from a small auxiliary continuous-current dynamo, called an exciter, which may Excitation. be an entirely separate machine, separately driven and used for exciting several alternators, or may be driven from the alternator itself; in the latter case the armature of the exciter is often coupled directly to the rotating shaft of the alternator, while its field-magnet is attached to the bed-plate. Although separate excitation is the more usual method, the alternator can also be made self-exciting if a part or the whole of the alternating current is “rectified,” and thus converted into a direct current.

The general idea of the polyphase alternator giving two or more E.M.F.’s of the same frequency, but displaced in phase, has been already described. The several phases may be entirely independent, and such was the case with the early polyphase Quarter-phase alternators. machines of Gramme, who used four independent circuits, and also in the large two-phase alternators designed by J.E.H. Gordon in 1883. If the phases are thus entirely separate, each requires two collector rings and two wires to its external circuit, i.e. four in all for two-phase and six for three-phase machines. The only advantage of the polyphase machine as thus used is that the whole of the surface of the armature core may be efficiently covered with winding, and the output of the alternator for a given size be thereby increased. It is, however, also possible so to interlink the several circuits of the armature that the necessary number of transmitting lines to the external circuits may be reduced, and also the weight of copper in them for a given loss in the transmission.21 The condition which obviously must be fulfilled, for such interlinking of the phases to be possible, is that in the lines which are to meet at any common junction the algebraic sum of the instantaneous currents, reckoned as positive if away from such junction and as negative if towards it, must be zero. Thus if the phases be diagrammatically represented by the relative angular position of the coils in fig. 39, the current in the coils A and B differs in phase from the current in the coils C and D by a quarter of a period or 90°; hence if the two wires b and d be replaced by the single wire bd, this third wire will serve as a common path for the currents of the two phases either outwards or on their return. At any instant the value of the current in the third wire must be the vector sum of the two currents in the other wires, and if the shape of the curves of instantaneous E.M.F. and current are identical, and are assumed to be sinusoidal, the effective value of the current in the third wire will be the vector sum of the effective values of the currents in the other wires; in other words, if the system is balanced, the effective current in the third wire is √2, or 1.414 times the current in either of the two outer wires. Since the currents of the two phases do not reach their maximum values at the same time, the sectional area of the third wire need not be twice that of the others; in order to secure maximum efficiency by employing the same current density in all three wires, it need only be 40% greater than that of either of the outer wires. The effective voltage between the external leads may in the same way be calculated by a vector diagram, and with the above star connexion the voltage between the outer pair of wires a and c is √2, or 1.414 times the voltage between either of the outer wires and the common wire bd. Next, if the four coils are joined up into a continuous helix, just as in the winding of a continuous-current machine, four wires may be attached to equidistant points at the opposite ends of two diameters at right angles to each other (fig. 40). Such a method is known as the mesh connexion, and gives a perfectly symmetrical four-phase system of distribution. Four collecting rings are necessary if the armature rotates, and there is no saving in copper in the transmitting lines; but the importance of the arrangement lies in its use in connexion with rotary converters, in which it is necessary that the winding of the armature should form a closed circuit. If e = the effective voltage of one phase A, the voltage between any pair of adjacent lines in the diagram is e, and between m and o or n and p is e √2. The current in any line is the resultant of the currents in the two phases connected to it, and its effective value is c √2, where c is the current of one phase.

Fig. 41.

When we pass to machines giving three phases differing by 120°, the same methods of star and mesh connexion find their analogies. If the current in coil A (fig. 41) is flowing away from the centre, and has its maximum value, the Three-phase alternators. currents in coils B and C are flowing towards the centre, and are each of half the magnitude of the current in A; the algebraic sum of the currents is therefore zero, and this will also be the case for all other instants. Hence the three coils can be united together at the centre, and three external wires are alone required. In this star or “Y” connexion, if e be the effective voltage of each phase, or the voltage between any one of the three collecting rings and the common connexion, the volts between any pair of transmitting lines will be E = e √3 (fig. 41); if the load be balanced, the effective current C in each of the three lines will be equal, and the total output in watts will be W = 3Ce = 3CE / √3 = 1.732 EC, or 1.732 times the product of the effective voltage between the lines and the current in any single line. Next, if the three coils are closed upon themselves in a mesh or delta fashion (fig. 42), the three transmitting wires may be connected to the junctions of the coils (by means of collecting rings if the armature rotates). The voltage E between any pair of wires is evidently that generated by one phase, and the current in a line wire is the resultant of that in two adjacent phases; or in a balanced system, if c be the current in each phase, the current in the line wire beyond a collecting ring is C = c√3, hence the watts are W = 3cE = 3CE / √3 = 1.732 EC, as before. Thus any three-phase winding may be changed over from the star to the delta connexion, and will then give 1.732 times as much current, but only 1/1.732 times the voltage, so that the output remains the same.

Fig. 42.

The “armature reaction” of the alternator, when the term is used in its widest sense to cover all the effects of the alternating current in the armature as linked with a magnetic circuit or circuits, may be divided into three items which are Armature reaction in alternators different in their origin and consequences. In the first place the armature current produces a self-induced flux in local circuits independent of the main magnetic circuit, as e.g. linked with the ends of the coils as they project outwards from the armature core; such lines may be called “secondary leakage,” of which the characteristic feature is that its amount is independent of the position of the coils relatively to the poles. The alternations of this flux give rise to an inductive voltage lagging 90° behind the phase of the current, and this leakage or reactance voltage must be directly counterbalanced electrically by an equal component in the opposite sense in the voltage from the main field. The second and third elements are more immediately magnetic and are entirely dependent upon the position of the coils in relation to the poles and in relation to the phase of the current which they then carry. When the side of a drum coil is immediately under the centre of a pole, its ampere-turns are cross-magnetizing, i.e. produce a distortion of the main flux, displacing its maximum density to one or other edge of the pole. When the coil-side is midway between the poles and the axes of coil and pole coincide, the coil stands exactly opposite to the pole and embraces the same magnetic circuit as the field-magnet coils; its turns are therefore directly magnetizing, either weakening or strengthening the main flux according to the direction of the current. In intermediate positions the ampere-turns of the coil gradually pass from cross to direct and vice versa. When the instantaneous values of either the cross or direct magnetizing effect are integrated over a period and averaged, due account being taken of the number of slots per coil-side and of the different phases of the currents in the polyphase machine, expressions are obtained for the equivalent cross and direct ampere-turns of the armature as acting upon a pair of poles. For a given winding and current, the determining factor in either the one or the other is found to be the relative phase angle between the axis of a coil in its position when carrying the maximum current and the centre of a pole, the transverse reaction being proportional to the cosine of this angle, and the direct reaction to its sine. If the external circuit is inductive, the maximum value of the current lags behind the E.M.F. and so behind the centre of the pole; such a negative angle of lag causes the direct magnetizing turns to become back turns, directly weakening the main field and lowering the terminal voltage. Thus, just as in the continuous-current dynamo, for a given voltage under load the excitation between the pole-pieces Xp must not only supply the net excitation required over the air-gaps, armature core and teeth, but must also balance the back ampere-turns Xb of the armature.

Evidently therefore the characteristic curve connecting armature current and terminal volts will with a constant exciting current depend on the nature of the load, whether inductive or non-inductive, and upon the amount of inductance already possessed by the armature itself. With an inductive load it will fall more rapidly from its initial maximum value, or, conversely, if the initial voltage is to be maintained under an increasing load, the exciting current will have to be increased more than if the load were non-inductive. In practical working many disadvantages result from a rapid drop of the terminal E.M.F. under increasing load, so that between no load and full load the variation in terminal voltage with constant excitation should not exceed 15%. Thus the output of an alternator is limited either by its heating or by its armature reaction, just as is the output of a continuous-current dynamo; in the case of the alternator, however, the limit set by armature reaction is not due to any sparking at the brushes, but to the drop in terminal voltage as the current is increased, and the consequent difficulty in maintaining a constant potential on the external circuit.

The joint operation of several alternators so that their outputs may be delivered into the same external circuit is sharply distinguished from the corresponding problem in continuous-current dynamos by the necessary condition that they The coupling of alternators. must be in synchronism, i.e. not only must they be so driven that their frequency is the same, but their E.M.F.’s must be in phase or, as it is also expressed, the machines must be in step. Although in practice it is impossible to run two alternators in series unless they are rigidly coupled together—which virtually reduces them to one machine—two or more machines can be run in parallel, as was first described by H. Wilde in 1868 and subsequently redemonstrated by J. Hopkinson and W.G. Adams in 1884. Their E.M.F.’s should be as nearly as possible in synchronism, but, as contrasted with series connexion, parallel coupling gives them a certain power of recovery if they fall out of step, or are not in exact synchronism when thrown into parallel. In such circumstances a synchronizing current passes between the two machines, due to the difference in their instantaneous pressures; and as this current agrees in phase more nearly with the leading than with the lagging machine, the former machine does work as a generator on the latter as a motor. Hence the lagging machine is accelerated and the leading machine is retarded, until their frequencies and phase are again the same.

Authorities.—For the further study of the dynamo, the following may be consulted, in addition to the references already given:—

General: S.P. Thompson, Dynamo-Electric Machinery—Continuous-Current Machines (1904), Alternating-Current Machinery (1905, London); G. Kapp, Dynamos, Alternators and Transformers (London, 1893); Id., Electric Transmission of Energy (London, 1894); Id., Dynamo Construction; Electrical and Mechanical (London, 1899); H.F. Parshall and H.M. Hobart, Electric Generators (London, 1900); C.C. Hawkins and F. Wallis, The Dynamo (London, 1903); E. Arnold, Konstruktionstafeln für den Dynamobau (Stuttgart, 1902); C.P. Steinmetz, Elements of Electrical Engineering (New York, 1901).

Continuous-Current Dynamos: J. Fischer-Hinnen, Continuous-Current Dynamos (London, 1899); E. Arnold, Die Gleichstrommaschine (Berlin, 1902); F. Niethammer, Berechnung und Konstruktion der Gleichstrommaschinen und Gleichstrommotoren (Stuttgart, 1904).

Alternators: D.C. Jackson and J.P. Jackson, Alternating Currents and Alternating Current Machinery (New York, 1903); J.A. Fleming, The Alternate Current Transformer (London, 1899); C.P. Steinmetz, Alternating Current Phenomena (New York, 1900); E. Arnold, Die Wechselstromtechnik (Berlin, 1904); S.P. Thompson, Polyphase Electric Currents (London, 1900); A. Stewart, Modern Polyphase Machinery (London, 1906); M. Oudin, Standard Polyphase Apparatus and Systems (New York, 1904).