On the Inhomogeneity of the Coercive Force Across the Cross-Section of a Ferromagnetic Sample
Abstract Generated abstract
This paper proposes and tests an experimental method for detecting variation of coercive force across the cross section of a ferromagnetic specimen. The method uses the frequency dependent penetration depth of an alternating component in a pulsating magnetic field and identifies mean coercive force at different depths from maxima in the induced secondary electromotive force during demagnetization. Experimental results on several specimens showed unequal coercive forces at different effective depths, with a marked increase near the surface, attributed plausibly to microcracks produced by cold drawing. The authors suggest that the approach can also help determine an optimal eddy current inspection frequency for surface layers when structural inhomogeneity has a distinct boundary.
Full Text
ON THE INHOMOGENEITY OF THE COERCIVE FORCE ACROSS THE CROSS SECTION OF A FERROMAGNETIC SPECIMEN
A. M. Gruznov, I. G. Leshchenko
(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)
The experimental method for proving the existence of inhomogeneity of the coercive force across the cross section of a ferromagnetic specimen is based on the following:
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The maxima of reversible permeability are located in the regions of the points \(+H_c\) and \(-H_c\) [1, 2].
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The modulus of the maximum reversible permeability is approximately equal to the modulus of the initial magnetic permeability [3].
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The coercive force is a magnetic characteristic that is extremely sensitive to the structural state of the specimen and does not depend on its geometrical dimensions [4].
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On the basis of item 2, the penetration depth of the alternating component of a simple pulsating field in the region of the point \(H_c\) and the penetration depth of only the alternating field into a previously demagnetized specimen are the same. Minor deviations from item 2 are not very significant, since the penetration depth is proportional to
\[ \sqrt{\frac{1}{\mu}} . \]
The experiment is carried out according to the scheme presented in Fig. 1. The dimensions of the solenoid are much larger than the dimensions of the specimen; in addition, the solenoid frame is made of a copper tube with a longitudinal slot, which acts as an electrostatic shield. All this indicates that the resistances introduced into the primary coil \(W_1\), first, are insignificant and, second, do not depend at all on the magnitude of the resistance of the external circuit of the solenoid. The resistance \(R\) provides the regime of a specified current. The modulus of the secondary EMF is directly proportional to the modulus of the reversible permeability. Therefore, the mean values of the coercive force at a depth from the surface determined by the generator frequency can be determined not by the maximum of reversible permeability, but by the maximum of the EMF through the corresponding values of the demagnetizing current.
Fig. 1. Block diagram of the experiment
To obtain a sharper maximum, the latter emf is determined from the maximum deflection of the light spot of a galvanometer connected into the measuring circuit of the tube voltmeter according to the circuit in Fig. 2. The tube voltmeter is connected to the mains through a voltage stabilizer. This reduces the effect of surges in the mains on the operation of the galvanometer.
After magnetic preparation has been carried out with the induction brought to limiting values, the magnetizing circuit is opened, and at point \(B\), by means of potentiometer \(R_5\), the current flowing through the measuring instrument of the voltmeter is compensated. Then switch \(P\) is opened and slow demagnetization of the specimen is begun by cutting out rheostats \(R_1\) and \(R_2\).
If the specimen were isotropic, then the coercive forces of any layer would be identical, and the dependence \(H_c=f(\omega)\) would be a straight line parallel to the abscissa axis.
If, however, the specimen is structurally inhomogeneous over the cross section, and the change in inhomogeneity occurs along the radius of the specimen, then the coercive forces obtained at different frequencies should turn out to be unequal.
Fig. 2. Circuit for connecting the galvanometer into the measuring circuit of the tube voltmeter
Fig. 3. Dependence of the magnitude of the demagnetizing current on frequency
The experiment confirmed these considerations. One of the results of a whole series of tests of various specimens is presented in Fig. 3.
The considerable increase in coercive force at the surface of the specimen is apparently explained by microcracks arising as a result of the cold drawing of the tubes from which the specimens were cut.
Conclusions
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The coercive force across the cross section of a specimen may be substantially inhomogeneous.
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If the structural inhomogeneity has a clearly defined boundary (hardening by high-frequency currents), then the method described will make it possible experimentally to establish the optimal frequency for controlling the quality of the surface layers of ferromagnetic products by the eddy-current method. The optimal frequency will be that at which the penetration depth...
of the field is equal to the depth of the controlled layer in the reference specimen. It may be said that the optimal frequency will be the frequency at which a sharp change in the coercive force begins.
REFERENCES
- K. M. Polivanov. Ferromagnets, Gosenergoizdat, 1957.
- G. Reinboth. Technology and Application of Magnetic Materials, Gosenergoizdat, 1963.
- L. I. Rabkin. High-Frequency Ferromagnets, Fizmatgiz, 1960.
- M. N. Mikheev et al. Magnetic inspection of the actively hardened layer of cold-rolled rolls hardened by industrial-frequency currents, Academy of Sciences of the USSR, Proceedings of the Institute of Metal Physics, no. 21, 1959.