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TION GALVANOMETERS in the Vibration Galvanorneter

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TION GALVANOMETERS in the Vibration Galvanorneter A paper to be presented at the 29th Annual Con* vention of the American Institute of Electrical Engineers, Boston, Mass., June 25, 1912. Copyright, 1912. By Α. I. Ε. E. (Subject to final revision for the Transactions.) CHARACTERISTICS AND APPLICATIONS OF VIBRA- TION GALVANOMETERS BY FRANK WENNER In the vibration galvanorneter we have a type of synchronous motor which is distinctly different from all the ordinary types of dynamo electric machines. Further it does not have any of the characteristics of any of the ordinary galvanometers and except for the fact that it is used in the detection or measure­ ment of small currents and voltages, it should not be called a galvanometer. In galvanometers, except when used in the measurement of transient currents or quantity of electricity, the moving system is displaced until we have an equality of static couples acting on it. In the vibration galvanometer the equilibrium condition is an equality between integral values of the product of the current and generated voltage and the mechanical power dissipated in various ways as in ordinary electric motors when operated without a load. It therefore behaves more like an electric motor than like a galvanometer. Further, since it is used only with alternating currents and op­ erates in synchronism with the current it must necessarily have some of the characteristics of a synchronous motor. As a motor the efficiency of conversion was found in a particular case to be as high as 97J per cent while the power required to maintain an easily discernable amplitude of vibration was of the order of 10-11 watts. One of the large turbo-generators would therefore furnish the power necessary to operate a thou­ sand-million-billion such machines. While the vibration galvanometer will probably never be used in the ordinary way for driving other machines yet it is of con­ siderable interest from a theoretical standpoint and possesses 1073 1074 WENNER: VIBRATION GALVANOMETERS [June 25 certain characteristics which make it a most valuable instrument for use in a large number of alternating current measurements. A number of different forms of galvanometers have been and are being used. One form is very similar to an oscillograph except that in general the period is longer and the oil for damping is omitted. Another form is very similar to the D'Arsonval galvanometers of the marine type except that the coil is narrower and the suspensions tighter. In all cases provision is made for changing the period of the moving system. This is usually done by changing the length or tension of the suspensions. Where a large range in frequency is desired the suspensions are often made bifilar. Passing an alternating current through the coil causes it to vibrate back and forth past its equilibrium position, hence the name vibration galvanometer. The amplitude of the vibration, which is a measure of the current, is ordinarily determined by observing the broadening of a line image as seen in a small mirror attached to the moving system. As regularly used in the detection or measurement of current or voltage the natural or free frequency of the moving system is made to correspond with the frequency of the alternating current to be detected. As a result the amplitude of the vibration is much larger than it would be under almost any other condition. The sensitivity is large only to currents of the frequency to which the moving system of the galvanometer is tuned. It is therefore possible to use currents of almost any wave form, even in those null methods in which an exact balance can be obtained only with a current free from all higher harmonics. In all such measurements we may make our observations and calculations just as if we were using current having a sine wave form since the galvanometer responds only very feebly to the 3rd, 5th and higher harmonic components. It is this characteristic combined with its extremely high sensitivity at low frequencies which makes the vibration galvanometer a most valuable in­ strument in various kinds of alternating current measurements. Before we can make such progress in the design of an instru­ ment or machine it is necessary that we know definitely the re­ lation between its various constants. In some cases this knowl­ edge is necessary before we can even use a well designed and constructed instrument or machine to its best advantage. We shall therefore show the relation which exists between the ampli­ tude of the vibration and the impressed voltage in terms of the 1912] WENNER: VIBRATION GALVANOMETERS 1075 intrinsic constants of the instrument and of the electric circuit in which it may be used. Since here we have a mechanical and an electrical oscillating system so connected that they must necessarily operate at the same frequency we shall make free use of the analogy existing between such systems. Passing a current through the winding produces a mechanical torque tending to displace the moving system of the galvanometer from its equilibrium position. The torque is proportional to the current and we shall let G be the proportionality factor or the displacement constant. In addition we shall use the follow­ ing notation, in which vectors are designated by bold faced type and make use of the following well known relations: IN THE ELECTRICAL SYSTEM IN THE MECHANICAL SYSTEM L = inductance κ = inertia constant r = electrical resistance D = damping constant or mechanical resistance C = capacity U = restoring constant anal- agous to 1/C ef = impressed voltage Gi = displacing torque i = current s = rate of displacement or angular velocity q = charge = / i δ t Φ = displacement = f sτ t Ε' (D ef G I (2) I ê*1 (3) i S s (4) a Q ë*1 (5) Φ φ ηiPt (6) 1 r + i(pL-l/Cp) (7) c GJi s = (R D + i(Kp-U/p) W or if we let X represent the electrical reactance and M represent the mechanical reactance 0) 1076 WENNER: VIBRATION GALVANOMETERS [June 25 s = <10> G I Φ = ip(D + iM) (12) Here £7' is the total voltage available for producing current or the sum of the impressed voltage Ε and generated voltage Et. The voltage generated by the relative motion of the magnet and winding is proportional to the amplitude and in quadrature with the vibration. It is also proportional to the frequency and proportional to the displacement constant and it is easily shown that Eg = - ip G Ö (13) therefore j E-~ipG$ 1 = r + iX (14) This value of / substituted in equation (12) gives GE Φ = p [(-rM-D X) + i{Dr-MX + G2)] (15) or GE Φ = ρ V(-rM-'DX)* + (Dr-MX+ G2)2 (16) or G Ε €»<*"+<•> p VJ-r M -D Χ)2 + (Dr-M X + G2)2 (17> where -(Dr-MX + G2) tan a = Mr + DX : (18) Equation (16) gives the relation between the amplitude of the vibration, the impressed voltage, the displacement constant, the frequency, and the other constants of the electric and me­ chanical systems expressed as resistances and reactances. Where the instrument is to be used in precise measurements we usually desire as high a sensitivity as can conveniently be obtained, i.e. we wish as large an amplitude of the vibrations for a given small impressed voltage as we can conveniently get. An inspection of equation (16) does not at once suggest the 1912] WENNER: VIBRATION GALVANOMETERS 1077 relations which should be made to exist between the various quantities D, r, M, X, and G to give the best sensitivity. Since power is absorbed or converted into heat proportional both to D and to r the most natural beginning is to make both small. The mechanical resistance or damping constant D is a definite constant of the galvanometer and as we shall see later one of the most important points to be looked to both in the design and the construction is to make this constant as small as possible. The electrical resistance r is the total resistance of the circuit in which the galvanometer is used. As the resistance of a part of this circuit is usually fixed from other considerations the particular value of the resistance of the galvanometer is of little importance providing it is less than say \ the total resistance of the circuit. As vibration galvanometers are usually constructed provision is made for varying the free period of the moving system so that the mechanical reactance can be adjusted to zero for any frequency in the range over which it is expected that the gal­ vanometer will be used. The electrical reactance is usually very small in comparison with the electrical resistance. It can however, be varied by placing capacity or inductance in series with the winding of the galvanometer. If the galvanometer is so constructed that the displacement constant G can be varied; and all instruments intended for use in circuits of different resistances should, if a high sensitivity is desired, be so constructed; we can then adjust each or all of the remaining quantities, the electrical reactance X, the me­ chanical reactance Af, and the displacement constant G. If M, is adjusted to zero and if ζ is small or adjusted to zero it will be seen that the sensitivity is a maximum when G2 = Dr Under these conditions we have Φ = 27Wr (19) or since we observe the total amplitude of the vibration and measure the root mean square value of the voltage Ρ V 2 Dr • (20) as has been shown by the author.1 1. Bulletin, Bureau of Standards, Vol. VI, p. 376; reprint 134; 1909.
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