Н

the above-mentioned analogy with the magnetic characteristic PH (M), the total characteristics of all dynamo machines show an entirely similar type in their main features. But the form of the external characteristic is very materially affected by the method of winding. Thus the three principal types, 'series wound,' 'shunt wound,' and 'compound wound,' correspond to just as many kinds of external characteristic, upon the further details of which we cannot here enter.

This brief statement of the principal points of view which influence the pre-determination-that is, the estimation of the efficiency of a dynamo-lead us finally, therefore, to the determination of the total characteristic as the chief problem. And this, again, is essentially nothing more than the magnetic characteristic 62 PH (M), the discussion of which we shall continue after the above digression.

=

Н

§ 128. Investigation of Drs. Hopkinson.-As regards the magnetic circuit of the dynamo machine tested (fig. 28, p. 189), the following assumptions were first made in order to simplify

matters:

The total flux of induction in the upper yoke (4) is the same as that in the two limbs (3); let it therefore be called 63. In like manner, the 'useful flux of induction' in the armature (1) is equal to that in the air-gap (2) and the two pole-pieces (5); let this be G. 2.

These two values of the flux of induction are now unequal, and their ratio is defined by the Hopkinsons (p. 82) as the leakage-coefficient,

S
G 2

Starting now from the flux of induction in the air-gap, which, from what has been said, determines the electromotive force to be produced, the general equation (III) of § 100 will be in the present case

GRAPHICAL CONSTRUCTION

195

in which M is the total magnetomotive force produced by the field coils (§ 119), and fi, f3, fa, fs denote the functions.

H = ƒ (v)

for the corresponding ferromagnetic parts which form the magnetic circuit (cf. § 96).

40

The above equation (I) was experimentally tested by Drs. Hopkinson on the machine which has frequently been mentioned. The pole-pieces were separated from the cast-iron base-plate G by a magnetically indifferent piece Z of cast zinc. The principal dimensions of the machine may be estimated from the statement that fig. 28, p. 189, is on a scale of full size. The following data may be given in addition :1. The armature consisted of 1000 iron discs separated by sheets of paper and strongly pressed together. The section S was taken as = 810 sq. cm., the distance L1 = 13 cm. The winding was on the von Hefner-Alteneck system, and had 40 turns, each with a resistance of nearly 0.01 ohm. With a normal speed of 12.5 revolutions per second, the armature gave 320 amperes at 105 volts. The flux of induction 6, then amounted to 11 millions C.G.S. units, corresponding to an induction B1 = G1/S1 13,500 C.G.S.

2. Air-gap cross-section S2 = 1600 sq. cm.; width L

1.5 cm.

=

3. The limbs consisted of hammered and afterwards annealed

wrought iron. The rectangular cross-section was 22 × 44-5 sq. cm. For convenience of winding, the corners were somewhat rounded off, so that S, 980 square cm. The length of each The total number of turns on each limb

limb was L, 46 cm.

=

was n = 3260.

=

4. Yoke: S = 1120 sq. cm.; L1

4

=

49 cm.

5. Pole-pieces: S, 1230 sq. cm.; L = 11 cm.

=

The functions fi, fs, fa, fs were considered as identical, and taken from curves of induction previously determined by J. Hopkinson. The leakage-coefficient was experimentally determined in the manner to be afterwards described, and in accordance with this v was put equal to 1·32 (§ 130).

§ 129. Graphical Construction.-In the previous paragraphs all the necessary data are given, which are now simply to be

inserted in equation (I). According to the practice of Drs. Hopkinson, it is usual to make the calculation in question by the graphical method, as we have already done in the comparatively simple case of a toroid divided radially (fig. 25, p. 151).

The graphical construction for the Edison - Hopkinson dynamo just described is represented in fig. 29, p. 197, which is taken directly from Drs. Hopkinson's paper. The abscissæ represent the magnetomotive force M, the ordinates the flux of induction through the air-gap.'

The curve (H) corresponds to the pole-pieces, (4) to the armature, (G) to the yoke, (C) the limbs of the magnet, the straight line (B) to the air-gap. The latter claims, as is obvious-especially for small values of the induction—by far the greater part of the total magnetomotive force.

From the five partial curves which correspond to the five members of equation (I), the resultant curve (D) is ultimately found by adding the abscissæ. (C) and (G), moreover, are not simple curves, but loops corresponding to hysteresis of the ferromagnetic parts in question. The ascending or descending branches are denoted by arrows. This, on addition, is also transferred to curve (D), which thus appears as a loop, and represents 6, PH (M) for the whole magnetic circuit of the machine.

=

In the experiments made to test the theory, the fieldmagnets were excited by a current I, separately generated and measured. From this there was found, by means of the number of turns mentioned,

M = 0.4 × 3260 IM

= 4100 I

K

M

The corresponding difference of potential E at the terminals, for the normal speed of rotation and no current in the armature, was determined; it was therefore equal to the electromotive force. It was plotted on a suitable scale as a function of M.

The numbers on the scale of abscissæ represent (as with Hopkinson) C.G.S. units; multiplied by 0.8 (which is very nearly equal to 1/04π); this gives M in ampere-turns, as is also usual. The numbers of the scale of ordinates represent millions of C.G.S. units.

The highest values of M or of G in this machine were about as follows:

M: 50,000 C.G.S. = 40,000 ampere-turns. 6: 15 x 10o C.G S. units.

EXPERIMENTAL DETERMINATION OF LEAKAGE

197

The points thus obtained are denoted for ascending currents by +, and for descending by, and are also entered in fig. 29.

The agreement, as will be seen, is as good as can at all be expected with such measurements on a working machine. It is true that the points observed for higher magnetomotive forces lie somewhat below the theoretical curve (§ 132). The approximate correctness of the theory, and the utility of the graphical construction depending on it, are, however, on the whole, confirmed by the experiments.

FIG. 29

§ 130. Experimental Determination of the Leakage. The coefficient of leakage v was determined by Drs. Hopkinson by special experiments with exploring coils (§ 2).

In the first case, a single turn of wire was passed round the middle of the limb of the magnet, the ends of the wire being connected with a ballistic galvanometer. A short circuit was then connected with the field coils, on opening or closing which a throw was observed in the galvanometer. This measured the

The general objection may indeed be raised against such ballistic measurements on dynamo machines, &c., that the period of the galvanometer can scarcely be assumed to be long enough as compared with the very long time which, owing to their considerable self-induction, the limbs required for their magnetisation, demagnetisation, or reversal of magnetisation. That assumption is, however,

total flux of induction through the limbs, in so far as residual induction may be disregarded.

In the second case, the throw of the ballistic galvanometer was determined when its leads were soldered to those segments of the commutator, corresponding to that armature winding which lies in what is called the plane of commutation. In the machine examined, fig. 28, this is the vertical plane. This throw gave a measure of the 'useful flux of induction' through the armature (§ 128).

The ratio of the first throw to the second, is also that of the total flux of induction to the useful flux-that is, it is equal to the leakage-coefficient, whose value for the machine in question was thus found to be 1:32. The leakage-coefficient was here found to be almost constant-that is, independent of the value of the induction-which is not surprising considering the small value of the latter (§§ 95, 126).

If, therefore, we put the total flow of induction equal to 100, the effective flux through the armature becomes 100/1·32=75·8. The difference 24-2 is equal to the 'stray field.' The question now arises how this latter is distributed in the various air-spaces. Drs. Hopkinson have investigated this question also by placing loops of wire in various places and directions, and observing as above, the induced throws with the same ballistic galvanometer. They thus found:

In fig. 28, p. 189, the dotted lines of intensity give, according to Silv. Thompson, an approximate idea of the leakage in the entire air-space. The base-plate, notwithstanding that a

an essential condition for applying the ballistic method. Moreover, in the present case it would have been better to wind the test coil round the upper part of the limb than about the middle. (See the calculations of Forbes, § 132.)