OBTAINING A STATIC MAGNETIZATION REVERSAL LOOP OF A THIN SURFACE LAYER OF A SAMPLE

A. I. Gruznov, I. G. Leshchenko, B. B. Vinokurov

The distribution of the amplitude and phase of the magnetic flux in straight cylindrical samples of infinite length, located in an infinitely long solenoid, was calculated in [1]. The results of the calculations reduce, in the main, to the following:

a — directly beneath the surface of the sample there is no time lag between the induction and the magnetic-field strength;

b — the internal field is equal to the external field;

c — if at a given instant a constant internal field is applied to the sample, then the increase of the induction at some distance from the surface of the sample will occur with a definite time lag, and the induction reaches its final value throughout the entire volume asymptotically, without oscillations.

When a sample is magnetized in an alternating field, owing to the monotonic change in the amplitude and phase of the field strength into the depth of the sample, it is always possible to single out an upper layer of the sample of such depth that the field strength at any point of it is, with any arbitrarily small tolerance, equal to the field strength at the surface. The magnetization reversal of this layer at not too high frequencies, when the phenomenon of magnetic aftereffect may be neglected, will occur according to the static loop.

To obtain this loop on the screen of an oscilloscope it is necessary to have two voltages, one of which would be proportional to the field strength in the layer, and the other to its induction.

As the first voltage one may use the voltage drop across an active resistance due to the current of the magnetizing solenoid flowing through it. How to obtain the second voltage will be clear from the description of the proposed installation circuit and of the experimental results obtained on it.

The ferromagnetic sample (Fig. 1) is magnetized simultaneously in a low-frequency field, whose amplitude is sufficient for modulation of the magnetic permeability of the sample, and in a high-frequency field with so small an amplitude that, with respect to it, the sample is a linear element. The low-frequency field is produced by a solenoid powered from a 50 Hz mains supply, and the high-frequency field (200 kHz) by a narrow coil.

The filter plug serves to prevent the second-harmonic current (400 kHz) from passing from the generator; the resistance \(R\) provides a prescribed-current regime. The selective amplifier of the V6-1 voltmeter and the S1-19 oscilloscope make it possible to observe the time variation of the second-harmonic signal \(E_{2\omega}\), arising in the measuring coil \(W_2\) under the simultaneous action on the sample of the indicated fields.

The results of the experiments show that the envelope of the second-harmonic signal in the region of small magnetizing low-frequency fields represents the absolute value of the rate of change of the low-frequency induction in the layer into which the high-frequency component of the field penetrates. Indeed:

Fig. 1

1. The signal $E_{2\omega}$ passes through zero twice during the period of the low-frequency field. If a tube with a very thin wall and a longitudinal slit is used as the sample (the static and dynamic loops will be close to one another), then the following can be established. The instants at which the signal $E_{2\omega}$ passes through zero correspond to the points $\pm B_m$ on the dynamic (static) loop. At the points $\pm B_m$ the rate of change of the low-frequency induction $dB/dt$ is also equal to zero. At the same time we establish that the instants at which $E_{2\omega}$ passes through a maximum for the same sample on the loop correspond to the points $\pm H_c$.

When a solid cylindrical sample made of a conducting ferromagnetic material is remagnetized (the dynamic and static loops differ significantly from one another), the points $E_{2\omega}=0$ and $E_{2\omega}=E_{2\omega\max}$ are shifted relative to the points $B_{\text{dyn max}}$ and $H_{c\text{ dyn}}$ in the clockwise direction, as was to be expected. Indeed, the characteristic points on the magnetization-reversal loop of the surface layer are passed earlier than the same points for the dynamic loop.

This part of the experiment was carried out on two oscillographs. On the screen of one oscillograph the dynamic loop was obtained; on the screen of the other, the time sweep of the signal $E_{2\omega}$. The synchronous-illumination circuit made it possible to illuminate on the oscillograph screens points corresponding to one and the same instant of time.

1. The signal $E_{2\omega}$ is absent when the sample is magnetized by a constant field $(dB/dt=0)$ and appears when it is magnetized by an alternating field $(dB/dt \ne 0)$. Strictly speaking, the signal $E_{2\omega}$ also appears when magnetization is produced by a constant field, but its magnitude is several orders smaller. When nonferromagnetic samples are remagnetized in the indicated fields, no double-frequency signal arises.

2. On a ferromagnetic sample of toroidal shape, a magnetizing winding of thick copper wire is wound. On a small section of the sample free of winding, two short coils $W_1$ and $W_2$ of the high-frequency sensor are placed. The magnetizing winding

is connected to a sinusoidal-voltage source. In this case the magnetization reversal of the upper layer of the specimen takes place in the regime of sinusoidal induction. If the envelope of the second-harmonic signal is the rate of change of the low-frequency induction in the surface layer of the specimen, then it must have a sinusoidal form. Indeed, after detecting the signal \(E_{2\omega}\), we feed it to the \(Y\) channel of the oscilloscope, and to the \(X\) channel—the voltage from the power source of the magnetizing winding, the phase of which can be varied. At a certain phase of this voltage, the screen gives an image of a straight line broken in half (\(V\)). The break in the line occurs because the detected second-harmonic signal has the form of unipolar half-waves of a sinusoid.

Fig. 2.

1. Keeping the magnitude of the magnetizing current unchanged in experiment 3, we shall vary its frequency. In this case the rate of change of the low-frequency induction in the surface layer should increase linearly with frequency. If the signal \(E_{2\omega}\) is the rate of change of the induction of the surface layer, then the value of this signal, measured with the selective voltmeter V6-1, should also depend linearly on frequency. The data of this experiment are shown in Fig. 2. From the graphs it is evident that up to a magnetizing frequency of about 200 Hz the dependence is indeed linear. The presence of a maximum and the subsequent drop in the signal is explained by the fact that its side frequencies, of the form \(\pm k\omega\), at high magnetizing frequencies \((\Omega)\) begin to fall outside the passband of the selective amplifier of the voltmeter. As a result, only the carrier frequency \(2\omega\) may remain within the transparency band of the amplifier.

2. Unfortunately, it is not possible to measure the actual value of the static coercive force of the specimen surface with which one could compare the instantaneous values of the magnetizing current corresponding to the maximum of the second harmonic, i.e., the values which, as we believe, characterize the static coercive force of the surface layer. True, one may expect the presence of a correlation between the coercive force of the surface and, consequently, between the instantaneous values of the indicated current, and the coercive force of the entire specimen. Indeed, such a relationship was observed (Fig. 3).

3. The magnetization-reversal loop of the upper layer, obtained on the oscilloscope screen according to the block diagram shown in Fig. 4, always turned out to be narrower than the corresponding dynamic loop. The following designations are used in the block diagram:

\(I\)—electronic integrator, AD—amplitude detector, SA—selective amplifier, SS—synchronous switch.

The circuit made it possible to obtain on the screen either the static or the dynamic loop.

1. It is known that the static coercive force of a nickel specimen increases under tension [2]. By successively obtaining on the screen the static loop of the surface layer and the dynamic loop of a nickel specimen and subjecting it to tension, we note that the static loop expands, while the dynamic loop narrows. The decrease in the dynamic coercive force, associated with losses due to hysteresis and eddy currents, occurs as a result of the reduction of eddy-current losses caused by the decrease in the magnetic permeability of nickel under tension.

Fig. 3

The static coercive force often has an unambiguous relationship with various metallurgical and physical characteristics of a product. Having the possibility of measuring the static coercive force on the surface of a product, it will be possible to monitor the indicated characteristics exclusively for the upper layer of the product.

Fig. 4

REFERENCES

1. K. L. Scott, Proc. Inst. Radio Eng. 18, 1750 (1930); Bell Syst. Techn. Publ. B 620.

2. K. P. Belov. Elastic, Thermal, and Electrical Phenomena in Ferromagnetic Materials. GTTI, Moscow–Leningrad, 1951.

3. A. M. Gruznov, B. B. Vinokurov, I. G. Leshchenko. Influence of elastic stresses on the magnitude of the second harmonic of a high-frequency field under superposition of parallel fields of different frequencies and amplitudes. Izv. TPI, vol. 194 (in press).