586
DYNAMO
circuit into such portions as have the same sectional area j quadrant on one side of DC, but opposed to it in the other on the same side of DC ; hence in the resultant field and permeability and carry approximately the same total quadrant due to the combined action of tiux • the dili'erence of magnetic potential that must exist the field-magnet and armature between the ends of each section of the magnet in order ampere-turns, the flux is as much that the flux may pass through it, is then calculated strengthened over the one half seriatim for the several portions into which the magnetic of each polar face as it is weakover the other, and the circuit is divided, and the separate items are summed up ened total number of lines is uninto one magnetomotive force that must be furnished by affected, although their distribution is altered. The armature the exciting coils. ampere-turns are then called The chief sections of the magnetic circuit are (1) the air-gaps, cross - turns, since they produce a cross-field, which, when (2) the armature core, and (3) the iron magnet. , The air-gap of a dynamo is partly filled with copper and partly combined with the symmetrical with the cotton, mica, or other materials used to insulate the core field, causes the leading pole-corners ll to be weakened and the and inductors ; all these substances are, however, sensibly non- trailing pole-corners tt to be strengthened, the neutral line of zero magnetic, so that the whole interferric gap between the iron of the field being thus twisted forwards in the direction of rotation. But pole-pieces and the iron of the armature may be treated as an air- when the brushes and diameter of commutation are shifted forspace, of which the permeability is constant for all values of the ward, as shown in Fig. 31, it fiux-density, and in the C.G.S. system is unity. Hence in the will be seen that a number of simple bipolar machine with single horse-shoe magnet, if lg and ampere-turns, forming a zone An be the length and area of the single air-gap in cm. and sq.cm., between the lines Dn and mC, are in effect wound im21 the reluctance of the double air-gap is r'Ji and the difference of mediately on the magnetic '0 magnetic potential required to pass 7jg lines over this reluctance is circuit proper, and this belt of ampere-turns is in direct ^ • r7 = Bg. 2lg; or, since one ampere-turn gives 1‘257 C.G.S. opposition to the ampereof the field, as shown units of magnetomotive force, the exciting power m ampere-turns turns by the dotted and crossed required over the two air-gaps is Xg= 1.257°^0* -A bi wires on the pole-pieces. The armature ampere-turns are then divisible into the two bands, the determination of the area Ag a small allowance must be the back-turns, included within twice the angle of lead X, made for the fringe of lines which extend beyond the actual weakening the field, and the cross-turns, bounded by the polar face ; and in the ring machine, as already mentioned, Zg is lines Dm, nC, again producing distortion of the weakened syma few per cent, more than Za, owing to the leakage across the metrical field. If, therefore, a certain flux is to be passed through interior of the core. the armature core in opposition to the demagnetizing turns, the In the armature core the length of path continually shortens as difference of magnetic potential between the pole-faces must include we pass from the middle of the pole towards the centre line of not only Xa and Xg, but also an item X&, in order to balance the symmetry. On the other hand, as the lines gradually accumulate “back” ampere-turns of the armature. The amount by which in the core, their density increases from zero midway under the brushes must be shifted forward increases with the armature the poles until it reaches a maximum on the line of symmetry. current, and in corresponding proportion the back ampere-turns are The two effects partially counteract one another, and tend to 2 equalize the difference of magnetic potential required over the also increased, their value being c.t.-—0, where c = the current 3oO paths of varying lengths ; but since the reluctivity of the iron carried by each of the r inductors. Thus the term X& takes into increases more rapidly than the density of the lines, we may ap- account the effect of the armature reaction on the total flux; it proximately take for the length of path {la) the minimum peri- varies as the armature current and angle of lead required to avoid pheral distance between the edges of adjacent pole-faces, and then sparking are increased ; and the reason for its introduction in the assume the maximum value of the density of the lines as holding place (Xp = X? + Xa+X&), is that it increases the magnetic throughout this entire path. In ring and drum machines the flux third of potential which must exist between the poles of the issuing from one pole divides into two halves in the armature difference and to which the greater part of the leakage is due. The core, so that the maximum density of lines in the armature is dynamo, 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 Ba=—, where a = the radial depth of the discs in centimetres 2ab flux at the commencement of the iron-magnet path. If P = their and 6 = the net length of iron core parallel to the axis of rotation. joint permeance, the leakage flux due to the difference of potential A distinction must be made between the gross length of the core at the poles is 1-257 Xp x P, and this must be added to the useful and the net length of iron, owing to the waste of space through flux Zg, or Zp~Zg+zl. There are also certain leakage paths in the insulating varnish or paper between the discs, and the presence parallel with the magnet cores, and upon the permeance of these of ventilating air-ducts, which are sometimes introduced at inter- a varying number of ampere-turns is acting as we proceed along vals along the length of the core, especially in multipolar arma- the magnet coils ; the magnet flux therefore increases by the adtures of large diameter. The former deduction may be said to dition of leakage along the length of the limbs, and finally reaches average about 7 to 10 per cent, of the gross length. Reference a maximum near the yoke. Either, then, the density in the magnet has now to be made to a (B H) or flux-density curve, from which V f~ will vary if the same sectional area be retained throughout, may be found the number of ampere-turns required per centimetre . . . length of path. This may be expressed asT a function of the or theAmsectional area of the magnet must itself progressively assumed density Ba, and the total exciting pow er required between increased. In general, sufficient accuracy will be be obtained by the pole-pieces is tlnrefore, at no load, Xp^X^ + Xa, where Xa = assuming a certain number of additional leakage lines as travers/(Ba). la ; in order, however, to allow for the effect of the armature ing the entire length of magnet limbs and yoke ( = lm), so that the current, which increases with the load, a further term X& must be added. density in the magnet has the uniform value Bw= - J’+—• The In the continuous-current dynamo it may be, and usually is, necessary to move the brushes forward from the interpolar line of leakage flux added on actually within the length of the magnet symmetry through a small angle in the direction of rotation, in core or will be approximately equal to half the total M.M.F. of order to avoid sp irking between the brushes and the commutator the coils multiplied by the permeance of the leakage paths around (vide infra). Whim the dynamo is giving current, the inductors one coil. The corresponding value of H can then be obtained from on either side of the diameter of commutation form a current-sheet the (B H) curve of the material of which the magnet is comflowing along the surface of the armature from end to end, and posed, and the ampere-turns thus determined must be added to whatever the actual end-connexions of the wires, the inductors Xp, or X = Xp + Xm, where Xm=f (Bm). lm. The final equation the exciting power required on the magnetic circuit as a whole may be imagined to be joined together into a system such that the for two sides of each loop are carrying current in opposite directions. will therefore take the form Thus a number of armature ampere-turns are formed, and their X = AT = 0'8B(7. 270+/’(Ba) . ?a +X&+/’(Bm) • effect on the entire system of magnet and armature must be taken Since no substance is impermeable to the passage of magnetic flux, into account. So long as the diameter of commutation coincides with the line of symmetry, the armature may be regarded as a the only form of magnetic circuit 1'ree from leakage is one uniformly cylindrical electromagnet producing a flux of lines, as shown in wound with ampere-turns over its whole length. The reduction Big. 30. The direction of the self-induced flux in the air-gaps of the magnetic leakage to a minimum in any given type is thereis the same as that of the lines of the external field in one fore primarily a question of distributing the winding as far as
