EXPERIMENTAL STUDIES OF THE METHOD OF SEPARATE INSPECTION OF PRODUCTS WITH PARAMETRIC CONNECTION OF AN EDDY-CURRENT SENSOR

D. V. MILYAEV, A. M. NESTEROV

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

One of the main directions in the development of induction flaw detection (the eddy-current method) is the separate inspection of product parameters, since in some cases the product parameters are useful, while in others these same parameters may be interfering. At present, various methods have been developed for reducing the influence of interfering factors when using both parametric and transformer connection of an eddy-current sensor in inspection by the amplitude of the output voltage of the measuring circuit into which the sensor is connected. The phase, amplitude-phase, and two-frequency methods have become the most widespread.

A number of instruments for inspection by the eddy-current method are based on measuring the change in the fundamental frequency of the generator oscillatory circuit, whose inductance is determined wholly or partially by the inductance of the test coil. Until now it has been considered that such instruments cannot be used to carry out separate inspection of product parameters, since a change in inductance is caused not only by the parameter being inspected but also by an interfering factor. In inspection based on measuring the magnitude of the reactive resistance, it is considered that the quality factor of the coil \(Q\) is much greater than unity and the generator frequency is determined by the formula

\[ \omega_0 = \frac{1}{\sqrt{LC}}, \]

where \(L\) is the inductance of the coil;
\(C\) is the capacitance of the circuit.

In an experimental study of the method it was observed that the sensitivity to the inspected product parameter is different when the phase detuning \(\varphi_k\) of the oscillatory circuit is varied. The oscillation frequency of the circuit into which the phase shift is introduced is equal to

\[ \omega_k = \sqrt{\frac{1}{LC} - \left(\frac{R}{2L}\right)^2} - \frac{R}{2L}\operatorname{tg}\varphi_k, \]

where \(R\) is the active resistance of the sensor coil.

From this formula it is evident that the initial phase shift in the circuit determines the sign and magnitude of the frequency change when the parameters of the product change. With zero phase detuning, the frequency depends practically only on the inductance of the coil. As the phase detuning increases, the influence of the active resistance on the frequency increases. Within the range of \(\pm 90^\circ\) variation of the phase shift, one can find an angle at which the influence of one of the product parameters on the frequency will be practically equal to zero, while the influence of the other will remain unchanged. This method was called the frequency-phase method of detuning from interfering factors.

One of the advantages of the frequency-phase method of detuning from interfering factors is the possibility of carrying out inspection at any value of the generalized parameter.

The purpose of the experimental studies was to choose the initial phase shifts in the generator circuit corresponding to the optimal conditions for separate inspection of the diameter and electrical conductivity of nonmagnetic products. The block diagram of the installation is shown in Fig. 1. Changes in the frequency of the measuring generator with phase shift \(G.F.S.\) were monitored with the aid of a capacitor frequency meter \(F\). To obtain greater measurement accuracy and to isolate the signal from the increment of the sensor resistance, a reference-frequency generator \(R.F.G.\) was used. The difference-frequency signal was separated by the mixer \(M\) and fed through the amplifier \(A\) to the frequency meter. The operating excitation frequency of the eddy currents during testing was \(10\ \mathrm{kHz}\).

Fig. 1. Block diagram of the experimental installation

The sensor was connected into the oscillatory circuit of a self-oscillator with phase shift. Detuning of the oscillatory circuit was carried out by means of a bridge phase shifter connected into the generator feedback. The established value of the self-oscillator frequency is determined by the phase balance, i.e., the sum of all phase shifts must be equal to zero. Thus, if the feedback phase is changed by an angle \(\varphi_{\mathrm{fb}}\), then the circuit must be detuned by an angle \(\varphi_k=-\varphi_{\mathrm{fb}}\), and the oscillation frequency of the self-oscillator will be equal to

\[ \omega_g=\sqrt{\frac{1}{LC}-\left(\frac{R}{2L}\right)^2}+\frac{R}{2L}\tan\varphi_{\mathrm{fb}}. \]

With sufficient amplification, the phase shift in the circuit can be varied by means of a phase-shifting network within the limits of \(\pm 90^\circ\).

Copper, brass, and bronze rods with a nominal diameter of \(10\ \mathrm{mm}\) were used as specimens. The magnitude of the phase shift in the circuit was regulated within the range of \(\pm 80^\circ\). The experimental results are given in Fig. 2. At a phase angle close to \(60^\circ\), the frequency increment is caused mainly by the change in diameter and, conversely, at a phase angle of \(-60^\circ\) the frequency increment is related to a greater degree to the change in electrical conductivity.

To determine the initial shift angles corresponding to separate and independent inspection either of diameter or of electrical conductivity, Fig. 3 gives plots of the change in the self-oscillator frequency for relative changes in diameter or electrical conductivity as a function of the change in phase shift. With a considerable discrepancy between the values of diameter and electrical conductivity, the value of the phase

the angle at which the sensitivity to the interfering factor is equal to zero varies only slightly, within a few degrees. This makes it possible to detune from interfering factors over a wide range of their variation. Thus, in the experiments carried out, the electrical-conductivity values differed from one another by almost an order of magnitude.

To find the actual sensitivities of the monitored parameter and of the interfering one in the zone of their separate inspection, experimental studies used specimens with a small scatter of electrical conductivity. The latter is usually encountered in flaw-detection practice, when it is necessary to detect small changes in electrical conductivity or diameter.

Fig. 2. Dependence of the frequency increment on the magnitude of the phase detuning of the circuit for different values of diameter and electrical conductivity

Specimens with a small change in electrical conductivity were obtained by heating brass rods to a temperature of approximately \(900^\circ\mathrm{C}\) and then rapidly cooling them. Under different cooling conditions it was possible to obtain specimens with different electrical conductivities. The quenched and unquenched specimens differed in electrical conductivity by approximately 5%. The experimental data are shown in Fig. 4.

For a qualitative and quantitative assessment of the frequency–phase method of separation from the interfering factor, one can trace the change in sensitivity to the useful and interfering factors at phase angles close to the zones of separate inspection, and at a phase angle equal to zero, i.e., without using the detuning method. As shown in the graphs of Fig. 3, the sensitivities to diameter and electrical conductivity at a phase angle equal to zero, although they differ in magnitude from one another, but

Fig. 3. Dependence of the sensitivity to changes in diameter and electrical conductivity on the magnitude of the phase detuning of the circuit

Fig. 4. Dependence of the frequency increment on the magnitude of the phase detuning of the circuit for a small change in electrical conductivity

also differ significantly from zero, i.e., they cannot be determined separately. With a phase shift of \(66^\circ\), the sensitivity to diameter is maximal and averages \(40\) Hz per \(1\%\) change in diameter, while the sensitivity to electrical conductivity is close to zero. A similar picture is observed for the sensitivity to electrical conductivity at a phase angle of \(-55^\circ\). In this case, the sensitivity to electrical conductivity is maximal and amounts to \(4.5\) Hz per \(1\%\) change in electrical conductivity, while the sensitivity to diameter is zero.

The experimental studies carried out show the real possibility of detuning from interfering factors and the possibility of performing separate inspection of several parameters. Moreover, unlike all known methods of separate inspection, in which detuning from one of the uncontrolled electromagnetic parameters of the product is always accompanied by a decrease in sensitivity to the parameter being inspected, this method makes it possible to detune from interfering factors while maintaining high sensitivity to the useful parameter of the product. As can be seen from the experimental data, these sensitivities even increase by a factor of \(1.5 \div 2\).