CHAPTER XIV

ELECTRO-MAGNETIC MACHINES

525. Barlow's Wheel.-One of the simplest arrangements for converting electrical energy into mechanical energy is that known as Barlow's wheel, and is shown in section in Fig. 502. A copper disc, A, is mounted on a horizontal axle, the bottom edge of the disc just dipping into some mercury placed in a small dish D. The disc A turns between the poles of a magnet, NS, and a current is passed through the disc between the mercury dish D and the axle. Thus in the portion of the disc A between the poles of the magnet we have an electric current flowing at right angles to the lines of force of the field, and therefore the conductor conveying the current, that is, the disc, is acted upon by a force tending to move it at right angles to the lines of force and to the direction of the current, i.e. to rotate the disc about the axle.

FIG. 502.

If the wheel is rotated by mechanical means, and the wires E and F are joined together, a current will be produced in this circuit, for the portion of the circuit which is formed by the radius of the disc between the axle and the mercury-cup will be moving at right angles to the lines of force of a magnetic field, and hence will be the seat of an induced E. M.F. The direction of the rotation of the wheel in the first case, and that of the induced current in the second, can easily be obtained by means of the rule given in § 519.

526. Induced Currents produced by Rotating a Coil in a Magnetic Field.-Suppose that a rectangular circuit of length a and breadth bis rotated about an axis AB, Fig. 503 (a), which is at right angles to the lines of force of a uniform field of strength H, and that the ends of the rectangle are connected with a stationary circuit, the resistance of this circuit and of the rectangle being R. Let us start with the rectangle in the position CD, Fig. 503 (6), in which it is at right angles to the lines of force of the field, so that the number of tubes passing through the rectangle is ab. H. Suppose now that the rectangle is turned into the position C'D', making an angle with CD. The number of tubes which now pass

through the rectangle is evidently equal to the apparent area of the rectangle, as seen in the direction of the tubes, multiplied by H. But the area, as seen in the direction of the tubes, is equal to a. EF or 2a.EA. But EA=AC Cos @=b2.cos 0. Hence the number of tubes of induction passing through the rectangle in its new position is abH cos 0. If the angular velocity of the coil is uniform and equal to w, and if is the time since the coil started from the position AB, we have = wt. Now suppose that in the small time & the coil turns through the angle 80. The number of tubes now passing through the circuit will be abH cos (0 +80). Hence in the small time at the number of tubes has decreased by-abH{cos(+80) - cos 0}. Now cos (0+80) = cos cos 80 - sin @ sin 80. If do is very small cos 80=1 and sin 80=80, so that the decrease in the number of tubes in the time &t is abH sin 0.80. Now the decrease in the number of tubes divided by the time during which this decrease takes place is, if the decrease goes on at a constant rate, and since dt is very small, we

may consider that at any rate during this time that this is so, equal to the rate of decrease of the number of tubes, and, as we have seen, this is equal to the induced E.M.F. Hence the induced E.M.F. is equal to ab Hồ sin 0/st, or abHw sin 0. Hence the induced electromotive force is at any time proportional to the sine of the angle which the plane of the coil makes with the lines of force of the field. Thus if E is the induced E.M F. at a time after the instant when the coil passed through the position CD, we have

E=SH∞ sin 0=SHw sin wt,

where S has been written for the inductive area of the coil. Since the resistance of the coil and its connected circuit is R, an electromotive force E will produce a current C given by the relation C=E/R. Hence if the current in the coil at a time t is C, we have

Thus, as the coil rotates, a periodic current and E. M.F. will be pro

duced, the maximum current occurring when =90°, so that sin (=1, the maximum value of the E.M.F. being wSH, and that of the current @SHR. When the plane of the coil is at right angles to the lines of force of the field 0=0 or 180°, and sin 0=0, so that the induced E.M.F. and also the current is zero. While changes from 180° to 270°, the induced E.M.F. changes from zero to -wSH, and the current increases from o to wSH|R. The minus sign shows that the current is in the opposite direction to what it was while increased from o° to 90°. For 0=270° the current is again a maximum, but, as we have pointed out, in the negative direction. As changes from 270° to 360°, the current decreases to zero, while as changes from o° to 90° the current is again

in the positive direction and increases from o to wSH|.R.

Thus in the circuit attached to the coil a current will be produced which changes its direction twice in each revolution of the coil, the maximum current in each direction being the same. Such a current is called an alternating current.

al

By

b

By suitable arrangements this alternating current in the circuit attached to the coil can be changed into a current which always flows in the same direction. Under these circumstances the alternating current is said to be rectified. A method of rectifying the current consists in fitting a copper ring on the axle on which the coil turns, which is insulated from the axle, and is in addition split along two generating lines which are on opposite sides of the ring as shown at abcd, Fig. 504. Two copper springs, B1 and B called brushes, rest against the copper ring, and are connected to the two ends of the external circuit. One end of the coil is connected to ab and the other to cd. The positions of the two brushes, B1, B2, are so arranged that as the coil revolves the brushes cross the gaps ad and be in the ring, just as the coil is passing through the position in which its plane is perpendicular to the lines of force of the field, and hence the induced current is zero. Suppose that when the coil is in the position C'D' (Fig. 503) the end of the coil connected with ab is at the higher potential, so that the current in the external circuit is going from B1 to B. When the coil has passed through the position in which its plane is at right angles to the lines of force of the field, the direction of the induced E.M.F. will be reversed; thus dc will now be at the higher potential. The copper conductor de will now be in contact with the brush B1, and hence the current in the external circuit will still flow from B1 to B. Although the current in the external circuit is now always in the same direction, it is not a constant current, but twice in every revolution it is zero, and twice reaches a maximum value of wSH|R. The difference between this rectified current and the

B2

FIG. 504.

alternating current can most clearly be seen from Fig. 505, where A represents the manner in which the alternating current varies with the

CURRENT

OR E. M. F.

TIME

FIG. 505.

time, which is taken as abscissa, while at B the corresponding A curve in the case of the rectified current is shown.

If a second coil of the same dimensions as the first were fixed to the same axle, so that its plane B was at right angles to that of the first, and it were supplied with its own commutator, the brushes being connected to the same circuit as the first in such a way that the currents produced by the two coils in the external circuit were in the same direction,

then the actual current in the circuit would be obtained by combining two such curves as that in Fig. 505 B. From the fact that one coil is placed a quarter of a revolution in advance of the other, the two curves must be displaced by a time equal to a quarter of a revolution, the one with respect to the other. In Fig. 505 C the dotted curves represent the currents due to the two coils separately, and the full-line curve the actual current due to the combined action of the two. It will be noticed how much more nearly uniform is the current than in the case where only one coil is used, and hence it will be understood how, by increasing the number of coils, what is practically a uniform current can be obtained.

527. Machines for the Conversion of Mechanical Energy into Electricity. The arrangement described in the last section, although from its extreme simplicity it was useful as a means of explaining the production of the currents induced in a coil when rotated in a magnetic field, yet, on account of the weakness of any uniform field of the extent we there supposed and one produced in a space which was quite free from iron, the currents induced would only be very weak. In order to obtain stronger currents, it is necessary to have recourse to the use of iron in order to increase the induction through the rotating coil. Although the systematic description of even one or two of the different forms of machine which are used in practice for obtaining the strong currents which are now used is quite beyond the scope of this book, yet it may be of use to devote a few pages to considering the more general features which are more or less common to all.

In the first place, from a historical point of view rather than a practical one, such machines can be divided into two classes according to the means adopted for the production of the magnetic field in which the conductor in which the currents are induced is moved. Machines

in which the field is produced by means of permanent steel magnets are called magneto machines, while those in which the field is produced by electro-magnets are called dynamos.

The small machines which are used for the production of the currents of electricity used in medicine are examples of magneto machines. The field is produced by a horse-shoe magnet, while the coils in which the induced currents are generated are wound on soft iron cores. The coils and their cores are rotated near the poles of the magnet in such a way that the ends of the cores are brought alternately near the north pole and the south pole of the magnet. The result is that the cores become magnetised alternately in one direction and the opposite, and hence the induction through the coils which are wound over the cores is changed, being in one direction when the core is opposite the north pole, and in the opposite direction when the core is opposite the south pole. If required, the alternating currents thus produced are rectified by means of a commutator, such as was described in the last section.

528. Dynamo Electrical Machines.—In dynamo electrical machines the magnetic field is produced by means of electro-magnets which are magnetised by sending either the whole or part of the current produced by the machine round the coils of these magnets. The coil in

which the current is induced is called the armature, while the electromagnets are called the field magnets. There are a great number of different forms of armatures in use, and we shall only describe the principles on which the action of three of these forms depend.

The Siemens armature consists of a coil of insulated wire wound longitudinally on a cylinder of soft iron as shown in Fig. 506. This armature is rotated between the poles of the field magnet NS, and as it rotates the induction through the coil changes in very much the same way as occurs in the simple coil considered in § 526, only the presence of the soft iron core on which the coil is wound very much increases the induction through the coil when it is placed in a given magnetic field. If a continuous current is required, a commutator is used to rectify the alternating current.

The Gramme armature is shown diagrammatically in Fig. 508, and the construction of an actual armature is shown in Fig. 507. This armature consists of a soft iron ring AA' (Fig. 508) on which is wound a