MEASUREMENT OF THE PERCENTAGE CONTENT OF COPPER IN A TIN–COPPER ALLOY BY THE EDDY CURRENT METHOD

V. K. ZHUKOV, G. V. USHAKOV

(Presented by the scientific seminar
of the Department of Measuring Technology)

In the practice of production control, determination of the composition of two-component alloys is carried out by various methods: chemical, physicochemical, thermoelectric, electrocontact, electromagnetic, and others. Thus, for a tin–copper alloy this problem at cable plants using the alloy is solved by the method of chemical analysis. Determination of copper in the Sn—Cu alloy by the chemical method requires a long time (several hours), and therefore the question arises whether some electrical method could be used for this purpose. We carried out investigations on determining the percentage content of copper in a tin–copper alloy by the eddy current method (ECM).

The essence of ECM is that, when a conducting body is introduced into the electromagnetic field of a coil, eddy currents are induced in it, creating their own electromagnetic field, which changes the magnitude and distribution of the original, exciting field. The degree of this change depends on the electromagnetic parameters of the body, its geometrical shape and dimensions, and the presence of various kinds of defects. By measuring, in some manner, the changes in the electromagnetic field, it is thereby possible to measure all the quantities listed above and, moreover, to measure other parameters of the body, such as composition, structural state, etc., which are related by a functional dependence to the electromagnetic properties of the material of the body.

As applied to the case under consideration, the task of investigating the possibilities of the method reduces, first, to establishing the functional dependence between the composition of the tin–copper alloy and its electrical conductivity and, second, to finding technical means capable of registering changes in the electrical conductivity of the alloy caused by a change in its copper content from 0 to 8%. The upper limit of the copper content is specified on the basis of the requirements of the cable industry.

The investigation of the dependence between the electrical conductivity of the alloy and its composition was carried out on an installation, the block diagram of which is shown in Fig. 1. The sensitive element of the installation was a two-winding eddy-current sensor with an outer coil diameter of 12 mm and a height of 6 mm. The sensor windings contained 450 turns each of PEV wire with a diameter of 0.12 mm. Inside the coil there was a ferrite core 8 mm in diameter. The coils were mounted in a bronze cup, co-

which was made in such a way that it served simultaneously as a high-frequency shield and as a fixture for the position of the specimen.

Fig. 1. Experimental setup for investigating the dependence between the electrical conductivity of the alloy and its copper content:
Г — driving generator;
М — phase-rotating bridge;
У — U2-4 amplifier;
И — indicating instrument;
Д — sensor.

Specimens of the alloys under investigation were cast in the form of short cylinders 65 mm in diameter and 5, 8, and 12 mm high. The required copper content in the specimens was obtained by melting calculated amounts of charge material (an alloy of 20% Cu and 80% Sn) and pure tin. The correspondence of the alloy compositions to the calculation was checked by chemical analysis. It was established that the difference between the calculated value of the alloy composition and the value obtained as a result of the analysis did not exceed \(\pm 0.5\%\) Cu. The specimens of the alloys under investigation were placed on the sensor.

The exciting winding of the sensor was connected to a generator of sinusoidal oscillations. Certain restrictions are imposed on the choice of the frequency of the exciting current: on the one hand, the current frequency must not be low, since this leads to a decrease in the sensitivity of the sensor to the electrical conductivity of the specimen material and to the need to increase the height of the specimen; on the other hand, the current frequency must not be too high, so as not to reduce the sensitivity to specific electrical conductivity and not to increase it with respect to surface microdefects. The optimum value of the frequency can be estimated using the concept of the “depth of penetration of the electromagnetic wave” \(\delta\). For the case of penetration of a plane electromagnetic wave into a conducting half-space,

\[ \delta = \sqrt{\frac{2}{\omega \cdot \gamma \cdot \mu}}, \]

where \(\omega = 2\pi f\) is the angular frequency of the exciting current;
\(\gamma\) is the specific electrical conductivity
and \(\mu\) is the magnetic permeability of the material of the product.

In practice, it may be assumed that at a depth of \(2\delta\) the electromagnetic wave is completely attenuated. If the height of the specimen of pure tin is taken to be equal to \(2\delta\), then one can find the current frequency at which this condition will be satisfied. It turns out to be equal to 3.74 kHz. On the basis of the above, the frequency of the exciting current in the experiment was taken to be 4 kHz.

The magnitude of the exciting current was chosen according to the permissible heating of the sensor winding wire.

The voltage of the measuring winding of the transducer, when a specimen of pure tin is placed on it, is compensated by a special device consisting of a phase-shifting bridge \(M\) and an additional resistance \(R_1\). The occurrence of compensation is indicated by a minimum deflection of the pointer of the output indicating instrument \(I\). It is not possible to bring the readings of the output instrument to zero at a large amplifier gain, even if a selective amplifier is used, and they are determined by the fundamental second harmonic of the voltages \(U_x\) and \(U_k\). After compensation had been carried out with the “zero” specimen, a specimen with a copper content of 10% was placed on the transducer, and the amplifier gain was selected so that the output instrument did not go off scale at any position of the specimen. Then all the specimens under investigation were placed on the transducer in succession.

At the first stage of the investigation the transducer had a symmetrical design; the coils of this transducer were arranged coaxially with the screen and therefore responded to the electrical conductivity of the regions of the specimen adjacent to its axis. With such a transducer, the dependence of interest to us was not found.

Fig. 2. Graphs of the dependence of electrical conductivity on the percentage content of copper in the alloy: 1, 2, 3—heat numbers.

An asymmetrical transducer was then made, in which the coils were displaced relative to the center of the screen. When working with such a transducer, the regions of the specimen located along a circumference with a radius equal to the distance between the coil axis and the screen axis were subjected to investigation. In the course of the investigation the specimen was rotated, which made it possible to obtain information on the value of the electrical conductivity at 12 local regions of the specimen located along a circumference with the radius indicated above. From readings taken at 12 points, the arithmetic mean values of the output-instrument readings were derived for each specimen. From the mean values a curve of the assumed dependence was plotted (Fig. 2). Next, the batch of specimens was remelted without changing the composition, and measurements were again carried out. The measurement results, po-

obtained after the 2nd and subsequent remeltings are presented in Fig. 2.

Analyzing the curves in Fig. 2, two conclusions may be drawn: first, the curves are not reproducible; second, a correlational dependence is noticeable between the electrical conductivity of the alloy and its copper content.

The correlation coefficient increases as the number of measurement points and the number of remeltings increase. From the same figure it is evident that the measurement result found from 12 points differs from the “true” value by no more than 1%. Thus, if the electrical conductivity of the specimens is measured at several points, it may be asserted that the mean value of the electrical conductivity of the Sn—Cu alloy is related by a correlation dependence to the percentage content of copper, and from the magnitude of the mean electrical conductivity, with an error of \(\pm 1\%\) Cu, one can judge the percentage content of copper in the alloy.

The conclusions obtained on the basis of the experimental investigations were used in developing an instrument. The block diagram of the instrument that was created is analogous to the block diagram of the experimental setup and contains: a generator, an eddy-current unbalanced sensor, a compensating device, a selective amplifier, an indication unit, and a stabilized rectifier (Fig. 3).

The generator unit serves to supply the primary winding of the eddy-current sensor and the compensating device with a voltage at a frequency of 4 kHz. The master oscillator of the unit is made according to the “capacitive three-point” circuit on transistor \(T_1\). The signal from the generator circuit is fed to the input of a resonant amplifier tuned to the first harmonic of the generator output voltage. The use of a resonant amplifier and the introduction of a negative-feedback loop make it possible to reduce the harmonic coefficient in the generator output voltage.

The compensating device includes a phase-shifting bridge and a variable resistor \(R_{10}\), and is intended for selecting the magnitude and phase of the compensating voltage, which is compared with the voltage on the secondary winding of the sensor coil. When \(|U_x| = |U_k|\) and \(\varphi_x = \varphi_k\), the undercompensation input signal will be absent.

The selective amplifier is intended for selective amplification of the undercompensation signal and is made on transistors \(T_3—T_6\). The stage on transistor \(T_6\) is selective, with an \(LC\) circuit in the collector circuit. The amplifier is covered by a negative-feedback circuit in order to improve the stability of the gain and reduce the magnitude of nonlinear distortions. The overall transfer coefficient of the amplifier is \(\sim 10\,000\).

The amplified voltage from the output stage (\(T_6\)) is fed to the mean-value detector (\(D_2, C_{20}\)) and then through the filter \(R_{32}, C_{21}\) to the input of the DC amplifier (\(T_7\)). Between the collector of the DC amplifier and the divider \(R_{37}, R_{38}\), used to compensate the quiescent current, an indicating instrument is connected. To protect the instrument against overloads arising when the article is removed from the sensor, a polarized relay \(P\) is used.

Additional investigations carried out with the developed instrument showed that it provides measurement of the percentage content of copper in the Sn—Cu alloy with an error of \(\pm 1\%\) Cu in the range \(0 \div 10\%\) Cu.

Fig. 3. Schematic circuit diagram of the developed device.