MAGNETOSTRICTIVE OSCILLATIONS AND THEIR APPLICATIONS

N. N. Malov, Moscow.

As early as 1847 Joule1 discovered that, under the action of a constant magnetic field directed along the axis of a ferromagnetic rod, the dimensions of the latter change. This phenomenon, which was given the name magnetostriction, was subsequently studied in detail in constant magnetic fields.

It is natural to suppose that, under the influence of a magnetic field varying periodically in time, a ferromagnetic rod should periodically change its dimensions. Thus it is possible to obtain mechanical oscillations of a quite definite frequency.

If there is a straight rod of length \(l\) cm, fixed at the middle or hanging freely, then the frequency \(\nu\) of its natural longitudinal oscillations is determined, as is known, by the relation:

\[ \nu_n=\frac{v}{2l}n \qquad (n=1,2,3,4\ldots), \tag{1} \]

where \(v\) is the velocity of propagation of oscillations in the rod, and \(n\) is the overtone number.

Since the magnitude of magnetostriction does not depend on the sign of the field, the frequency of the magnetostrictive oscillations of the rod must be twice the frequency of the magnetic field; if

if the rod is magnetized sufficiently strongly, this doubling of the frequency, evidently, should not occur.

The amplitude of magnetostrictive oscillations is, generally speaking, small (the relative elongation is a quantity of the order of \(10^{-7}\)—\(10^{-6}\)).

However, in the case of “magnetostrictive resonance,” i.e., excitation of the rod at one of its natural frequencies, one must expect a considerable increase in the amplitude of its oscillations.

It is natural to expect that “resonance” can be produced both by the fundamental frequency of the magnetic field and by its overtones; in turn, the rod can resonate at various overtones of its natural oscillations; therefore it seems of interest to study in detail the possibility of exciting resonant ferromagnetic oscillations.

For obtaining magnetostrictive oscillations, the ferromagnetic rod \(S\) is placed1 in the coil of the oscillatory circuit \(L\) (Fig. 1), connected in such a way that, besides the oscillatory current, the constant component of the anode current also passes through it, creating a constant magnetization of the rod (this is done because, as experiment has shown, a magnetized rod gives more intense oscillations).

Fig. 1.

By continuous rotation of the capacitor \(C\), it was possible to vary smoothly the frequency of the electromagnetic oscillations, while observing the occurrence of resonant oscillations of the rod. These resonant oscillations, whose amplitude considerably exceeds the amplitude of ordinary oscillations—

oscillations, may be detected in various ways, for example:

1) If the rod is sprinkled with sand, then, under sufficiently strong excitation, at the moment of resonance the sand is thrown off the rod, remaining only at the nodal points; this makes it possible simultaneously to investigate the distribution of the amplitudes of oscillation along the rod (for example, when the fundamental frequency of a free rod, or of a rod clamped in the middle, is excited, the sand collects in its middle part and is completely thrown off the ends, etc.). 2) When working in the range of audio frequencies, a rod oscillating in resonance emits a strong sound, sharply distinguishable against the sound of the generator. 3) An objective determination of the presence of resonant magnetostrictive oscillations is possible, carried out as follows: between the side

Fig. 2.

surface of one of the ends of the rod (clamped in the middle) \(S\) and a rubber and cork roller \(K\), the axle \(R\), carrying a light mirror \(M\), is lightly clamped (Fig. 2); during the oscillations of the rod (which, evidently, occur in a direction perpendicular to the plane of the drawing), the axle together with the mirror is set in motion, which is recorded by means of a light beam from the source \(O\), reflected by the mirror onto the rotating drum \(B\) with photosensitive paper. With slow rotation of the drum and simultaneous variation of the oscillation frequency of the generator, a straight line is recorded on the paper, having in certain places sharp thickenings corresponding to the resonant oscillations of the rod (Fig. 3). If such a recording is made at the time when the rod is oscillating in resonance, while imparting to the drum a sufficiently rapid

rotation, then a zigzag-shaped curve of oscillations is obtained on the paper. Knowing the speed of rotation of the drum and measuring the distance between adjacent zigzags, one can determine the frequency of the recorded oscillations. From the amplitude of the recorded curve, the diameter of the axis, and the distance from the mirror to the drum, one can calculate the amplitude of the rod’s oscillations.

It turned out that, upon excitation of the fundamental tone (3850 oscillations/sec) of a nickel-silver steel rod of diameter 7.5 mm and length 653 mm (strength of the alternating field \(M = 100\) gauss), the amplitude of oscillations at the end of the rod reaches 0.007 mm, so that the relative elongation is \(20 \cdot 10^{-6}\) of the entire

Fig. 3.

length, i.e. exceeds by \(10^{-20}\) times the elongation arising in the absence of resonance.

A detailed study of a number of rods showed that the occurrence of resonant oscillations is possible in all cases when the frequency of the magnetic field \(f\) and the natural frequency of oscillation of the rod \(\nu\) are related by:

\[ k f = n \nu \qquad \left( \begin{array}{l} k = 1, 2, 3 \ldots \\ n = 1, 2, 3 \ldots \end{array} \right), \tag{2} \]

i.e. that excitation of the fundamental tone of the rod or of one of its overtones is possible under the action of the fundamental frequency of the magnetic field or of one of its higher harmonics (see Tables 1 and 2).

MAGNETOSTRICTION OSCILLATIONS AND THEIR APPLICATIONS

TABLE 1.

Silver steel, diam. 7.5 mm, length 653 mm, $\nu_1 = 3850$ osc/sec.

TABLE 2.

Silver steel, diam. 7.5 mm, length 340 mm, $\nu_1 = 7470$ osc/sec.

The strongest resonance oscillations are obtained at $f = \nu$ and $f = \nu/2$, i.e., when the fundamental tone of the rod is excited by the first and second harmonics of the magnetic field; the oscillations weaken with increasing $n$; excitation of the higher overtones of the rod proves to be very weak.

The production of powerful low-frequency sounds (several thousand osc/sec) by means of magnetostriction rods proves possible. But on passing to frequencies lying at the limit of hearing (about 20,000 osc/sec), the thermal action of the Foucault currents excited in the rod becomes so considerable that it is necessary to use only weak magnetic fields (of a few gauss), which give not very intense oscillations.

However, even these weak sounds are of great interest, owing to their strictly definite frequency.

When the generator is switched off, the rod, strictioning in resonance, continues for some time to oscillate with decreasing amplitude; this phenomenon may serve for determining the damping decrement of various ferromagnetic materials.

Studying magnetostriction oscillations, Pierce1 found that the strictioning rod, like a piezoquartz crystal, is capable of exerting a stabilizing action on the frequency of the generator in whose coil it is placed.

The simplest scheme of such a generator is shown in Fig. 4; the coils \(L_1\) and \(L_2\) are wound in such a way that the field produced by them is in one direction. The rod \(R\) has a fixed point in the middle, but does not touch the inside of the coils, and hangs freely in them. When there is a large difference between the periods of the circuit and the rod, oscillations are absent. By changing the tuning of the circuit by rotating the capacitor \(C\), these periods can be brought so close together that generation suddenly begins; this will be noticeable by the sound which will begin to be emitted by the rod (if we are working in the range of audio frequencies), and also by the sharp increase in the magnitude of the anode current, indicated by the ammeter \(A\). With a further change of capacitance the current will gradually fall to its normal value, while the frequency of the oscillations during this time will remain unchanged until the resonant oscillations cease. In this case the rod is the exciter of the oscillations. It is also possible to use the ordinary generator circuit, placing in the coils of the circuit a rod which will stabilize the oscillations when the periods coincide. With a large difference of periods the generator will continue generation, but it will not be stable. It is necessary to note that stabilization is preserved regardless of whether the rod’s natural frequency is approached from the side of lower or of higher frequencies. In Fig. 5 curves are given which characterize the process of stabilization. Along the abscissa axis is plotted the value of the capacitance \(C\) (in divisions of the capacitor dial); the curves \(ABCD'E\) and \(EDCB'A\) give the dependence of the generator wavelength \(\lambda\) on the capacitance, the arrows indicating the direction of change

Fig. 4.

capacitance. From these curves it is evident that after the oscillations of the rod have arisen, the wavelength of the generator remains, despite the change in capacitance, unchanged, and then changes abruptly. Curve \(ABCDE\) shows the dependence of \(\lambda\) on \(C\) when the rod is damped (damping is achieved, for example, by clamping the end of the rod in the hand).

Fig. 5.

The middle curve shows the changes in the anode current during the stabilization process, while the upper curve shows the precisely measured (by the beat method) oscillation frequency of the generator (it maintains constancy with an accuracy up to \(0.01\%\)).

In view of the enormous importance of the discovery made, Pierce investigated a whole series of ferromagnetic materials, and found that rods of pure or carbon steel are little suited for stabilization, owing to their weak strictional capacity. Nickel, whose coefficient

although its magnetostriction is rather large, it nevertheless has little stabilizing ability. Nichrome alloys and invar (36% Fe + 64% Ni) prove to be the most applicable.

With changes in the anode voltage and filament current, or when tubes were replaced, the change in the stabilized frequency did not exceed 0.03%.

A piezoquartz stabilizer maintains (under unchanged generation conditions) frequency constancy with an accuracy up to 1/500%; but if the potentials of the anode and filament circuits are changed, or the tube is replaced, the oscillations of the stabilized frequency reach 0.07%, i.e. the quality of stabilization of a rod and of quartz is almost the same.

Fig. 6.

However, piezoquartz has a negligible temperature coefficient of frequency (the relative change of frequency for a temperature variation of 1° C), amounting to from 1/200 to 1/1000%; determination of the temperature coefficient of nichrome rods showed that it reaches 1/93%. To reduce the temperature coefficient of frequency, Pierce constructed a compound vibrator consisting of a nickel tube (which has a negative temperature coefficient of frequency) filled with invar (with a positive temperature coefficient of frequency). Such a compound vibrator gave frequency changes not exceeding 1/500%, i.e. it approached a quartz stabilizer in constancy.

Obtaining very low stabilized frequencies with the aid of magnetostricting rods presents no difficulties; in practice they can conveniently be used up to frequencies of the order of 2000–2500 oscillations/sec (in this case the length of the rod will be approximately 110–90 cm, if the speed of sound is taken in the calculation as 4500 m/sec, as the mean between the speed in invar—4160 m/sec—and in nichrome—4980 m/sec).

Using a compound vibrator consisting of a nickel tube filled with lead, Pierce obtained 1000 oscillations/sec with a vibrator length of 94.5 cm.

Fig. 7.

Oscillations with frequencies up to 100,000 (the rod length in the latter case is close to 2 cm) are obtained very easily by using rods of various lengths.

Further shortening of the rods makes it difficult to fasten them and to install them in coils. Using a rod of complex shape, made of high-grade steel and turned as shown in Fig. 6, with two adjacent projections entering the coil, Pierce obtained 295,480 oscillations/sec.

The construction of compound vibrators presents certain difficulties; as for simple straight rods, they can easily be cut in any laboratory, and the problem of stabilizing oscillations with a frequency from several thousand to 100,000 oscillations/sec is solved very simply and economically. The use of quartz for stabilizing such low frequencies, however, is very difficult and requires large expenditures, since the dimensions of the plates must be very considerable.

In Pierce’s work the results are given of the application of a magnetostrictive generator for measuring the frequency of oscillations, calibrating a wavemeter, etc. The method is entirely analogous to the method of using piezoelectric generators; the results obtained are just as good.

At the present time the production of magnetostrictive generators has already been established abroad on a factory scale.

Fig. 8.

By measuring the natural frequency of magnetostrictive oscillations, one can determine the velocity of sound and Young’s modulus for various ferromagnetic materials, as well as their dependence on the composition of the alloy and on temperature. The determination of Young’s modulus \(E\) is of considerable interest, since it is carried out at much smaller elongations of the rod than those that have to be produced in the usual determination of Young’s modulus.

In Fig. 7 is shown the variation of the velocity of sound \(V\) and of its temperature coefficient \(f: \dfrac{\Delta V}{\Delta t^\circ}\) as a function of the percent—

of the chromium content in the alloy \(Fe—Cr\). Fig. 8 presents the same quantities in the alloy \(Fe—Cr\).

These studies led Pierce to the conclusion that in binary metallic alloys the extreme values of the velocity of sound and of its temperature coefficient are obtained simultaneously.

The dependence of Young’s modulus \(E\) and of its temperature coefficient \(\varepsilon: \dfrac{\Delta E}{E t^\circ}\) on the nickel content in the alloy \(Fe—Ni\) is given in Fig. 9.

Fig. 9.

Curve \(E\) gives the results obtained by Pierce, while curve \(B\) gives the values of Young’s modulus according to Bureau of Standards data, obtained by the ordinary method. The difference in absolute values may be explained by the different magnitude of the extensions of the rod, but the possibility is not excluded of attributing these changes to different heat treatment or to the influence of an impurity of \(0.3\%\) manganese.

The above results show how broad a scientific and technical application magnetostrictive oscillations may find—oscillations to which researchers, until recently, had not paid due attention.

A theoretical substantiation of magnetostrictive oscillations may be found in the above-mentioned work of Pierce and in Black’s article.^1

^1 K. Ch. Black. Proceed. Amer. Acad. 63, 49, 1928. Since this article was submitted for publication, a number of further studies on strictional oscillations have appeared; see Friedman, Telegraphy and Telephony without Wires, No. 3, 1929.

1. W. Pirce. Proceed. Amer. Acad. of Arts and Sciences, 63, 1, 1928. ↩↩↩