HARMONIC ANALYSIS OF THE SIGNAL FROM A MEASURING COIL IN HARDNESS TESTING OF LONG RODS AND TUBES

V. D. Sartakov

(Presented by the scientific and technical seminar of the Department of Information and Measuring Technology)

The results of heat treatment of pressure-gauge springs are, to a certain extent, determined by the initial structure of the material, which makes its inspection necessary.

For reliable operation of metal-cutting equipment in the manufacture of pressure-gauge springs, it is necessary that the hardness of the blanks lie within the limits of the technical specifications. Increased hardness of the material leads to equipment downtime because of dulling and breakage of the cutting tool.

At a number of rolling mills in the USSR, electromagnetic instruments have been introduced for nondestructive testing of the microstructure and hardness of ferromagnetic rods and tubes of various profiles by magnetic permeability. In some cases, the absence of a good correlation between the physical and mechanical parameters of products, and the objectivity of assessing the state of the material by one of the electromagnetic parameters, require the development of new methods and instruments for quality control of long rods or tubes.

To increase the objectivity of inspection, the multifrequency method of forming a multidimensional signal from a number of product parameters and the method of harmonic analysis of the signal from a measuring coil, with subsequent processing of the signal by means of decision devices, may be applied [1, 2].

Magnetization of long rods by means of a short coil offers great possibilities for applying the method of harmonic analysis because of the nonuniform external field and the nonlinear properties of the ferromagnetic material.

Experimental and theoretical investigations carried out by R. I. Yanus and colleagues at the Institute of Metal Physics of the Academy of Sciences of the USSR made it possible to determine the distribution of the intensity and induction of the magnetic field along the length of a rod and to create, for testing the hardness and microstructure of long rods in a continuous process, an installation possessing a higher “resolving” capability with respect to the physicomechanical parameters of the products [3, 4, 5]. They showed that, at a certain distance from the magnetizing coil, the intrinsic field of the magnetized specimen changes from a “demagnetizing” one into a “magnetizing” one, which leads to equalization of the magnetic flux along the length of the specimen. This is especially pronounced in rods with higher magnetic permeability. If the measuring coil is placed at some distance from the ma...

magnetizing one and coaxial with it, the sensitivity of nondestructive testing of the microstructure and hardness of rods by magnetic permeability may exceed the maximum sensitivity in the case of a closed magnetic circuit.

The dependence of the magnitude of the specimen’s own field on the value of the magnetic permeability \(\mu\) and the nonlinear dependence of \(\mu\) on the magnetic-field intensity make it possible to obtain multidimensional information about the state of the material by means of harmonic analysis of the emf of a measuring coil displaced from the center of magnetization.

For a more detailed study of the magnetization of long rods by a short coil and for the development of more productive and more accurate instruments for nondestructive testing, we carried out experimental studies of the distribution of the emf (or induction) of the higher harmonics along the length of the rod, and also of the phase shift between the intensity of the external magnetic field at the center of the magnetizing winding and the induction of the higher harmonics at a specified value of the sinusoidal current of the magnetizing coil.

The arrangement of the setup for carrying out the experiments is shown in Fig. 1.

The magnetizing coil \((W_1 = 966\) turns, coil length \(l_1 = 30\ \text{mm}\), mean diameter \(d_{\text{av}1} = 45\ \text{mm})\), supplied from the industrial-frequency mains in a prescribed-current mode \((I_{\text{m}} = 0.4\ \text{A})\), creates an external alternating magnetic field that is nonuniform along the length of the specimen. The measuring coil \((W_2 = 5000\) turns, \(l_2 = 30\ \text{mm}\), \(d_{\text{av}2} = 30\ \text{mm})\) is placed

Fig. 1.

at various distances from the center of the magnetizing coil, and the emf induced in it is measured with the selective voltmeter V6–2. The output signal of the selective voltmeter is fed to the input of the electronic oscilloscope EO-7, synchronized by a voltage with a frequency of 50 Hz. The mode of synchronization from the mains makes it possible to make a rough estimate of the phase shifts of the emf harmonics relative to the intensity of the external field. For an accurate estimate of the phase shifts of the higher harmonics, the electronic phase meter F2–1 was used. To obtain a reference signal for the phase meter, a device was developed containing the nonlinear unit NU and the selective amplifier of the null indicator F550, tuned to the frequency of the corresponding harmonic.

The experiments were carried out on specimens of different hardness made of 50KhFA steel, 600 mm long and 16 mm in diameter.

The graphs (Fig. 2a, b, c) show the distribution curves of the first, third, and fifth harmonics of the emf along the length of the specimen (specimen hardness \(HV = 214\) units).

The distribution along the specimen length of the induction of the higher harmonics is determined by the magnitude of the magnetizing current, the geometric dimensions of the magnetizing coil, and the magnetic properties of the specimen. With

Fig. 2

constant magnetizing current and fixed length and diameter of the magnetizing coil, the amplitude of the higher harmonics, as the experiment showed, is the greater, the higher the value of the magnetic permeability of the rod. The character of the change in the induction of the higher harmonics along the specimen length is the same. No significant difference was observed in the attenuation decrements of the higher harmonics of the emf along the length of the rod. To assess the possibility of applying nondestructive testing of the hardness (heat treatment) of extended products (rods, tubes, bars) by the amplitude of the higher harmonics of the emf, in Fig. 3a a graph was constructed of the dependence of the ratio of the emf of the harmonics (1, 3, 5), corresponding to soft and hard specimens, on the distance between the measuring and magnetizing coils.

In carrying out the experiment it was observed that the resolving power of hardness testing of specimens by the amplitude of the first and higher harmonics increases with increasing distance between the measuring and magnetizing coils. However, the resolving power of testing by the higher harmonics is not the same. As the harmonic number increases, the resolving power of testing increases, reaches a maximum for the fifth harmonic, and then decreases monotonically. In Fig. 3b a graph is presented of the sensitivity of the hardness-testing method by higher harmonics as a function of the harmonic number.

The high sensitivity of hardness testing by the amplitude of the fifth harmonic makes it possible not to use a differential circuit for connecting the transducers.

To assess the possibility of amplitude-phase separation of information on the hardness of rods, measurements were made of the phase of the fundamental and higher harmonics of the emf along the specimen length. With increasing distance between the coils, the phase shift relative to the magnetizing current זיך

Fig. 3.

a)
Axis labels: \(L\); \(R\), cm.
Curve labels: 1st harmonic; 3rd harmonic; 5th harmonic.

b)
Axis labels: \(L\); harmonic No.

for all harmonics increases monotonically. Moreover, the phase lag relative to the magnetizing current is smaller for soft specimens than for hard ones.

Figure 4 shows a graph of the change in phase of the first, third, and fifth harmonics of the e.m.f. along the length of the specimen (specimen hardness \(HV = 214\)).

Fig. 4.

The dependences of the phase shift relative to the reference signal for the 1st, 3rd, and 5th harmonics on the hardness of rods at different positions of the measuring coil (\(0\ \text{cm}\), \(3\ \text{cm}\), \(15\ \text{cm}\), \(25\ \text{cm}\)) are presented in Fig. 5a, b, c, d, respectively.

It can be seen from the graphs that the maximum resolving power of rod-hardness testing by the phase of the harmonic signal is observed for the fifth harmonic. Moreover, the maximum resolving power occurs when the measuring coil is placed at a distance approximately equal to six lengths of the magnetizing coil (\(150 \div 200\ \text{mm}\)). The scatter of the experimental points in the graphs is explained by a certain inhomogeneity of the physicomechanical characteristics of the material along the length of the specimens.

Local inhomogeneities of the rods substantially affect the distribution of the amplitude and phase of the higher harmonics along the specimen, but jumps of induction at local inhomogeneities are somewhat smoothed.

The experimental results presented in Fig. 3a agree with the qualitative explanation that takes into account the influence of magnetic permeability on the magnitude of the specimen’s own field.

The appearance of higher harmonics of the e.m.f. is caused by the dependence of magnetic permeability on field strength. An increase in the amplitude of the magnetizing field will cause an increase in nonlinear distortions in the e.m.f. curve of the measuring coil.

a) b) c) d)

Fig. 5. — ● × ⊙ — the 1st, 3rd, and 5th harmonics, respectively.

The external field of the magnetizing winding appreciably magnetizes a ferromagnetic specimen whose length is considerably greater than the length of the winding only at the center of the winding [3].

At a considerable distance from the center of the magnetizing winding, only the specimen’s own field acts; its magnitude may, in simplified form, be related to the value of the magnetic permeability by

\[ H_0 = N \frac{\mu_0 H_i(\mu - 1)}{4\pi}, \]

where \(N\) is the demagnetizing factor;
\(H_i\) is the true field strength;
\(\mu_0\) is the magnetic permeability of free space;
\(H_0\) is the strength of the demagnetizing field.

An increase in the magnetic permeability of soft products causes an increase in the demagnetizing field and in the amplitude of the higher harmonics when the measuring coil is placed at a considerable distance from the magnetizing coil. In the central plane of the magnetizing winding, the demagnetizing field of the specimens almost balances the resultant field strength and, consequently, the amplitudes of the harmonics.

Conclusions

1. On the basis of experimental investigations of the distribution of the higher harmonics of the emf along the length of rods made of 50KhFA steel, magnetized by a short coil, the possibility has been shown of checking the hardness of rods differing in magnetic permeability by using harmonic analysis of the emf of the measuring coil.

2. A higher resolving power of hardness testing in terms of the amplitude and phase of the higher harmonics has been obtained when the measuring coil is located at a distance from the magnetizing coil and coaxially with it, as compared with testing by the fundamental harmonic.

3. For the particular case of testing, the optimal position of the measuring coil and the harmonic number for obtaining the greatest resolving power of the method have been determined.

Literature

1. V. G. Pustynnikov, S. D. Anisimov. Zavodskaya laboratoriya 10, 1964.
2. R. E. Ershov. Defektoskopiya, 1, 1966.
3. R. I. Yanus, V. S. Obukhov, L. A. Shubina. ZhTF, 11, 10, 936, 1941.
4. R. I. Yanus, P. A. Khalileev, V. V. Vlasov. Zavodskaya laboratoriya, IX, 10, 1103, 1940.
5. E. I. Popov, R. I. Yanus. Trudy IFM AN SSSR, issue 24, 140, 1965.