Errors in Measuring the Diameter of Thin Wires by the Eddy-Current Method

V. K. Zhukov, V. E. Dreizin, I. G. Leshchenko

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

The use of the eddy-current method for monitoring the diameter of thin wires is associated with the need to register small changes in the inductance of the sensors, since their sensitivity cannot be made sufficiently high for the reasons set forth in [1]. This imposes stringent requirements on the stability and accuracy of the measuring circuits, which are mainly generator circuits. All causes that produce instability in the frequency of the generators will naturally be causes of measurement error. First of all this applies to the sensors themselves, whose instability is characterized by the magnitude of the temperature coefficient of inductance—TCI.

By taking measures to reduce the magnitude of the TCI, applying thermal compensation in the circuit of the measuring generator and stabilization of the supply voltages, it is possible to ensure a temperature coefficient of frequency not higher than \(10^{-5}\). In the case where frequency conversion is used in the circuit, it is better to use as the second generator a generator analogous to the first. In this way the measurement error associated with instability of the frequency caused by the sensor can be reduced. Still better results, as shown in [2], can be obtained when using one generator and two switched sensors, one of which is the measuring sensor and the other the reference sensor.

The use of two-generator circuits, or of single-generator circuits with switching, can ensure an error in monitoring changes in the sensor inductance, caused by a change in the controlled diameter, of the order of \(5 \cdot 10^{-5} \div 10^{-4}\). With a sensor filling factor of 0.01, it is evident from [1] that, when converted to microns, this will amount, for a wire of 0.1 mm, to no more than 0.5 µm.

Thus, the circuit error of monitoring can be made small and, in this respect, there are no significant difficulties in using the eddy-current method.

More substantial are the errors associated with the wire being measured, namely, errors due to displacement and skewing of the wire relative to the sensor and due to variation of its specific resistance.

For radial displacements of the wire, the error is determined by the fact that, first, owing to the nonuniformity of the field at the edges, the reactive and active resistances of the sensor will change and, second, if there is no electrostatic shield between the measured wire and

the interwinding capacitance of the latter to “ground” also will not be constant. With skewing (a condition in which the angle between the axis of the sensor and the axis of the wire is different from zero), the perimeter of the cross section of the wire by the plane normal to the sensor axis changes. The change in the perimeter, in its effect on the parameters of the winding, is equivalent to a certain increment in the wire diameter when it is arranged coaxially with the sensor winding.

By increasing the length of the sensor, or more precisely the ratio of the winding length to its diameter, it is possible to reduce the influence of displacement caused by the nonuniformity of the field. In practice, however, this is not always realized, since the dimensions of the winding, among other things, are also determined by the frequency of the measuring generator and by the requirement of convenient handling of the sensor in operation. Therefore, the principal means of combating displacements and skewing should be considered to be precise fixation of the wire in the sensor, which is achieved by using various kinds of guiding devices. The error due to the capacitive effect, i.e., due to the change in capacitance between the sensor winding and the wire being monitored, is considerably reduced when an open electrostatic shield placed between the winding and the wire is used. In the experiments carried out by us, the mechanical units of the sensor and of the guiding device were manufactured to accuracy class 2; diamond dies were used as the guiding device. For a sensor with a winding diameter of 1 mm and a monitored wire of 0.14 mm, displacement errors not exceeding 1 μm were observed.

The parameters of the sensor depend not only on the diameter of the monitored wire, but also on the magnitude of its resistivity $\rho$, determined by the quality of the copper from which the wire is made. This dependence is definitely related to the frequency of the current feeding the sensor. In [1] it is shown that the influence of $\rho$ decreases with increasing frequency, while the sensitivity of the sensor to a change in diameter increases. Consequently, the frequency must be selected with allowance for ensuring minimal sensitivity to a change in $\rho$.

The frequency found in this way turns out to be considerably higher than that which is needed to ensure high sensitivity of the sensor to a change in diameter. Thus, in [1] it is indicated that the sensitivity to diameter reaches its maximum value when the ratio of the radius of the wire being measured to the penetration depth of the eddy currents is equal to 8–10, whereas to ensure insensitivity of the sensor to a change in $\rho$, it is recommended in [3] that this ratio be chosen greater than 100. Fulfillment of the latter condition for thin wires requires the use of the UHF range, which cannot be done for design reasons. Thus, the monitoring error associated with resistivity is determined by how strongly the value of $\rho$ will vary under real conditions and by how well the condition of sensor insensitivity to a change in $\rho$ is fulfilled.

Measurement under drawing conditions is accompanied by an increase in monitoring errors due to changes in $\rho$ and due to displacement. This is explained by the fact that, as a result of the deformations experienced, the resistivity of the wire, especially of its surface layer, can vary over wider limits, and by the fact that it is more difficult to fix the wire in the sensor because of wear of the guiding devices. In addition, measurement under drawing conditions is accompanied by errors caused by copper dust and heating. Indeed, the wire leaves the drawing machine in a heated state and, passing through the measuring sensor, will heat it to some extent.

...zero, as a result of which, when the TKI is not equal to zero, the inductance will change. In this case the temperature conditions of the reference sensor and of the other elements of the generators remain unchanged; that is, the change in the inductance of the measuring sensor caused by heating is not compensated in any way and, consequently, leads to an error. This component of the error can be reduced only by lowering the TKI of the winding. Experiments show that thermal equilibrium in the sensor is reached approximately 10 minutes after the first start of the machine. During repeated starts of the machine after short stops \((1 \div 3)\) min, this time is considerably shorter. During tests of instruments for measuring the diameters of thin wires, changes in the inductance of the sensor during warm-up were observed (at a filling factor of 0.01) reaching \(5 \cdot 10^{-4}\), which is equivalent to a change of 5 μm for a wire of diameter 0.2 mm. The degree of influence of heating depends on many factors, in particular on the design of the sensors and, naturally, on the temperature difference between the wire being measured and the surrounding medium. As the filling factor of the sensor increases, the influence of heating increases.

The presence of copper dust on the wire being measured, in the absence of sufficiently effective cleaning, leads to gradual deposition of the dust on the walls of the sensor. In its effect on the sensor parameters this process is equivalent to an increase in the diameter of the wire being monitored, i.e., to the appearance of an error. Obviously, the influence of dust is reduced when wire cleaning is used and when the working aperture of the sensor is periodically cleaned.

From what has been said above, the following conclusions can be drawn:

1. The use of the eddy-current method for monitoring the diameters of thin wires \((50 \div 300)\) μm encounters no difficulties on the part of the measuring circuits, since the generator-circuit variants most acceptable for this case can ensure an error in monitoring changes in the sensor inductance caused by the wire being monitored on the order of 0.01%. Converted to diameter, for example, at a filling factor of 0.01, this will amount to no more than 0.01 of the nominal value.

2. The measurement error during the drawing process is determined mainly by heating, copper dust, and displacement. By adopting appropriate measures, the errors due to the listed causes can be substantially reduced, but nevertheless they remain fairly high. Therefore, for small diameters it is unlikely that an error of less than \((2 \div 3)\) μm can be obtained.

3. The diameters of stationary wires can be measured with higher accuracy, since in this case the errors associated with copper dust and heating are eliminated. In addition, errors due to displacement and skew are reduced owing to better axial fixation of the wire.

REFERENCES

1. V. K. Zhukov, V. E. Dreizin, I. G. Leshchenko. Theory of a pass-through sensor applicable to the monitoring of the diameter of thin copper wire by the eddy-current method using a pass-through single-winding sensor. (The article is published in the present collection.)

2. V. K. Zhukov, V. E. Dreizin, M. S. Roitman, I. G. Leshchenko. Measuring circuits for monitoring the diameter of thin wires by the eddy-current method. (The article is published in the present collection.)

3. V. P. Grabovetskii. A contactless method for measuring resistivity and geometric dimensions by means of eddy currents. Avtomatika i telemekhanika, vol. XX, No. 7, 1959.