MEASUREMENT SCHEMES FOR MONITORING THE DIAMETER OF THIN WIRES BY THE EDDY-CURRENT METHOD

V. K. ZHUKOV, V. E. DREIZIN, M. S. ROITMAN, I. G. LESHCHENKO

(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)

When measuring the diameter of thin wires by the eddy-current method, the sensing element is a through-type inductive transducer, in whose cavity the wire being measured is located. A change in the wire diameter leads to a change in the active and reactive resistances of the transducer, that is, to a change in its inductance and quality factor. The qualitative and quantitative relationships obtained in this case are analyzed in [1]. It follows from this analysis that, when measuring thin and very thin wires (50–300) μm, the optimum frequency is of the order of several tens of megahertz; moreover, for measuring the wire diameter it is most convenient to use changes in the reactive resistance of the transducer. In view of the fact that, when measuring thin wires, it is impossible, for design and operational reasons, to ensure a large filling factor (in practice it is of the order of 0.01–0.05), the sensitivity of the transducer is low, of the order of 0.015–0.08 percent change in inductance per 1% change in the wire diameter.

Under these conditions, generator-type measuring schemes are the most effective, in which the transducer is the main part of the oscillatory circuit of a self-oscillator. Bridge and resonance schemes are of little use for this purpose: the former because the measurement must be carried out at high frequency, and the latter because of the low quality factor of the transducer (not exceeding 10–20). In generator measuring schemes, changes in the inductance and quality factor of the transducer lead to changes in the frequency and amplitude of the generated oscillations. The subsequent measuring scheme may be constructed either to measure changes in amplitude or to measure changes in the frequency of oscillations. However, the amplitude method cannot provide the required accuracy for the following reasons. First, the accuracy will be determined by the stability of the generator amplitude. If only passive stabilization measures are used, it is difficult to reduce the instability of the generator to the required value; and active stabilization measures, i.e., amplitude feedback, cannot be used, since the measurement is performed precisely by the change in amplitude. Second, the measurement accuracy will depend on the error of the measuring scheme itself, that is, of the entire path from the generator circuit to the indicating instrument, which is also sufficiently large. The frequency method is far more promising, because the frequency stability of the generator, even if only passive stabilization measures are used, can be made much greater—

less high than in amplitude, and, moreover, frequency measurement can be performed with much greater accuracy than amplitude measurement. Therefore, in what follows we shall consider only frequency-type generator circuits.

In its most general form such a circuit will have the form shown in Fig. 1, where D is the sensor, G is the measuring generator, and FI is the frequency indicator.

The elements of the measuring circuit, in addition to the useful effect of the diameter \(d\) on the sensor, will be subject to the action of various destabilizing factors DF, which should first of all include: changes in ambient temperature, aging of elements, and instability of supply voltages (errors associated with the wire being measured are not included among circuit errors and therefore are not discussed). As noted above, the sensor has low sensitivity; therefore destabilizing factors, if no measures are taken, can lead to a large measurement error. The simplest way to increase measurement accuracy is to perform manual calibration of the generator frequency periodically. This variant is far from the best solution to the problem, since the introduction of manual adjustments into the circuit is undesirable, especially in the case of continuous measurement of the diameter under drawing conditions. Much better, both from the standpoint of measurement accuracy and from the standpoint of convenience in operation, is the introduction into the circuit of automatic calibration of the generator frequency, which will be carried out when the wire being measured is absent from the sensor. If calibration is performed according to the frequency indicator, then the error due to the action of destabilizing factors on the FI is thereby automatically eliminated.

Fig. 1.

A more complete functional circuit using automatic calibration of the frequency of the measuring generator is presented in Fig. 2a. When the measured wire is absent from the sensor, the generator voltage increases. This increase in voltage is transmitted through the amplitude detector AD and amplifier \(U_1\) to relay \(R_1\), causing it to operate. At the same time, contact K of the relay closes and connects motor \(Dv_1\) to the output of amplifier \(U_2\). If, in this state of the circuit, the voltage at the output of the frequency detector FD is different from zero, then through modulator M and amplifier \(U_2\) it will set in rotation the motor with which the axis of the tuning capacitor \(C\) is mechanically connected. The motor will rotate until the voltage at the output of the frequency detector becomes equal to zero. At this point the calibration process ends.

Fig. 2.

When the wire being measured is inserted into the sensor, the voltage produced by the generator falls as a result of the decrease in the \(Q\)-factor of the circuit; contact \(K\) opens, and the automatic tuning circuit ceases to operate. The voltage developed at the output of the frequency detector is then determined only by the wire being measured.

A drawback of the circuit considered is that it does not eliminate the error due to changes in the conversion function of the frequency indicator, and is suitable only for recording absolute values of the diameter. In the case of measuring deviations of the diameter from the nominal value, the circuit will not provide high control accuracy.

The indicated drawback is eliminated if, along with frequency calibration, a compensation principle of measurement is used, as shown in Fig. 2,b. In this circuit, as in the preceding one, when there is no wire in the sensor, relay \(P\) operates; in this case contact \(K_1\) closes, while contact \(K_2\) opens. The circuit \(M_1—U_2—D_{v1}—C\) serves to tune the frequency of generator \(G_1\). As a result of the automatic tuning, the voltage at the output of the frequency detector is set equal to zero. When the wire is inserted into the sensor, contact \(K_1\) opens, thereby disconnecting the automatic tuning circuit, while contact \(K_2\) closes. If, in this case, the output voltage of the frequency detector is not equal to zero, motor \(D_{v2}\) begins to rotate. The shaft of motor \(D_{v2}\) is mechanically linked to the axis of the trimming capacitor \(C_2\). The system will remain in motion until the change in the frequency of generator \(G_1\) caused by inserting the wire into the sensor is compensated by the change in frequency caused by capacitor \(C_2\). A pointer \(I\), which moves along a scale graduated in microns, is mechanically linked to the axis of capacitor \(C_2\).

In such a measurement circuit, the error associated with changes in the transfer coefficients of the elements included in the frequency-indicator channel is eliminated. In addition, by connecting capacitors of constant capacitance in parallel with capacitance \(C_2\), one can select a measurement range of any width and at any point on the numerical axis of diameter values.

The use of frequency calibration is not the only way to eliminate the action of destabilizing factors. The use of differential measuring circuits also makes it possible to reduce their influence substantially. As an example, one may consider the operation of the differential measuring circuit shown in Fig. 3. Here \(d\) denotes the useful action on the circuit of the wire being measured, while \(DF\) denotes the action of destabilizing factors. The circuit consists of measuring generator \(G_1\) with diameter sensor \(D_1\) and frequency indicator \(FI\) (enclosed by the dashed line), which includes generator \(G_2\) with sensor \(D_2\), analogous to \(G_1\) and \(D_1\), frequency mixer \(C_m\), frequency meter \(Ch\), and output indicator \(I\). The measuring generator \(G_1\) and the reference generator \(G_2\), as well as sensors \(D_1\) and \(D_2\), are under identical operating conditions; therefore, to an equal extent, both qualitatively and quantitatively, they are subjected to the action of destabilizing factors. In the ideal case, that is, in the case when the gener—

Fig. 3.

...generators and sensors are absolutely identical, their response to the action of disturbing factors is the same, and thus the measurement error due to instability of the elements of the measuring circuit is eliminated. Indeed, the frequency of generator \(\Gamma_1\) carries information about the diameter \([d]\) and about destabilizing factors \([\Delta \Phi_1]\), while the frequency of generator \(\Gamma_2\) carries information only about destabilizing factors \([\Delta \Phi_2]\). In the mixer the frequencies are subtracted, so that the information contained in the difference frequency is equal to \([d]+[\Delta \Phi_1]-[\Delta \Phi_2]\). In the ideal case \([\Delta \Phi_1]=[\Delta \Phi_2]\), and a frequency carrying information only about the diameter is fed to the input of the frequency meter. In practice it is impossible to achieve complete identity of the measuring and compensating channels (meaning compensation for the influence of destabilizing factors), and therefore the monitoring error is reduced, but still remains significant.

An increase in the effectiveness of differential circuits can be achieved by reducing the number of elements that make up the measuring and compensating channels. For this purpose the circuit considered above can be modified by using one measuring generator and two switched sensors, one of which is the measuring sensor and the other the compensating sensor. The modified circuit is shown in Fig. 4a.

Fig. 4.

Visible labels in the diagrams: \(a\), \(b\); \(d\); \(\Delta \Phi\); \(D_1\), \(D_2\); \(K\); \(\Gamma_1\), \(\Gamma_2\); \(S_m\); \(FD\); \(SD\); \(C\), \(C_1\), \(C_2\); \(AFC\); \(D_v\), \(D_{v1}\), \(D_{v2}\); \(U\), \(U_1\), \(U_2\); \(M\); \(\Phi\); \(50\ \mathrm{Hz}\); \(I\).

The sensors \(D_1\) and \(D_2\), by means of the commutator \(K\), are alternately connected to the measuring generator \(\Gamma_1\) as the inductance of its oscillatory circuit. In this case the generator delivers voltage packets whose frequencies are proportional to the values of the sensor inductances. The task of the subsequent part of the circuit is to extract the difference between the packet frequencies and to present it in a form convenient for observation. The frequency-difference meter, FDM (outlined in the circuit by a dotted line), consists of the auxiliary generator \(\Gamma_2\), the mixer \(S_m\), the frequency detector \(FD\), and the synchronous detector \(SD\) with indica-

…indicating instrument \(I\) at the output. To reduce the error in indicating the difference between the packet frequencies, an automatic frequency-control path is introduced into the PSC, including filter \(\Phi\), modulator \(M\), amplifier \(U\), motor \(D_v\), and tuning capacitor \(C\). In such a circuit, destabilizing factors acting on generator \(G_1\) do not change the difference between the packet frequencies and therefore do not cause monitoring error. The influence of the environment on the monitoring error will act mainly through the sensors, and it will be the smaller, the higher the degree of identity of the sensors. It is obvious that with this circuit a higher monitoring accuracy can be obtained than with the circuit shown in Fig. 3, since here there are fewer elements that must be identical.

To reduce the monitoring error introduced by the difference-frequency meter, one can use the compensation principle of measurement. The circuit shown in Fig. 4,b differs from the circuit in Fig. 4,a by the introduction of a circuit for changing the reactance of the compensating sensor \(D_2\). This circuit is connected to the output of the synchronous detector \(SD\) and contains: modulator \(M\), amplifier \(U_2\), motor \(D_{v2}\), and tuning capacitor \(C_2\). When a wire is inserted into the measuring sensor, its reactance changes, as a result of which a certain difference appears between the frequencies of the voltage packets of generator \(G_1\), leading to the appearance of a DC voltage at the output of the synchronous detector. This voltage is modulated at a frequency of 50 Hz, amplified, and fed to the control winding of motor \(D_{v2}\). The motor begins to rotate, turning the shaft of the tuning capacitor \(C_2\) and the pointer of indicator \(I\). The motor stops when the reactances of the sensors become equal. It is obvious that in such a circuit the difference-frequency indicator introduces practically no error into the measurement.

The instruments known to us from the literature for measuring the diameter of thin wires, using the eddy-current method, are made according to circuits with manual frequency calibration of the measuring generator. In particular, this is how it is done in the inductive micrometer IM-1 [2] and in the electronic micrometer [3]. For this reason, the circuit error of measurement in them constitutes a significant share of the total monitoring error.

Among the measurement circuits proposed by us, differential circuits assembled in accordance with the functional circuits shown in Fig. 3 and Fig. 4,a were investigated. The studies showed that the circuits can ensure a monitoring error of changes in the sensor inductance no greater than \(10^{-4}\). When an even smaller circuit error is required, it is necessary to turn to the circuits in Fig. 2,b or in Fig. 4,b.

The use of the proposed circuits in instruments for measuring diameter makes it possible to obtain a small circuit monitoring error, so that the measurement error as a whole will be determined by factors associated with the wire being measured.

LITERATURE

1. V. E. Dreizin, V. K. Zhukov, I. G. Leshchenko. Theory of a through-type sensor as applied to monitoring the diameter of thin copper wire by the eddy-current method. (The article is being printed in this collection.)

2. V. G. Gerasimov, V. G. Khlebnikov. Inductive Micrometer IM-1, Prospect of the MEI, 1961.

3. Jaensch Klaus. Wire gage provides continuous measurement, Electronics. 33, No. 7, 109–111, 1960.

4. V. E. Dreizin, V. K. Zhukov, I. G. Leshchenko. Errors in measuring the diameter of thin wires by the eddy-current method. (The article is being printed in this collection.)