Toward a Method for Determining the Defectiveness of Winding Enamel Wires Used in Low-Voltage Electrical Equipment

V. I. Derevyanko, Yu. P. Pokholkov

(Presented by the scientific seminar of the Department of EIKT)

Insulation failures of the windings of various electrical devices are, for the most part, caused by the presence of defects in the insulation. Therefore, forecasting winding failures is impossible without a rigorous quantitative assessment of the magnitude of insulation defectiveness.

In the present case, defectiveness may be understood as the probability that a defect will occur over a certain area of insulation. With a certain degree of reliability, defectiveness may be regarded as the ratio of the number of specimens punctured by a voltage that we consider to be the maximum breakdown voltage of a defect of the given level, to the total number of specimens tested [2].

\[ q=\frac{n_{u\max \mathrm{def}}}{\sum_{i=1}^{n} n_i}. \]

With such an approach to the quantitative determination of defectiveness, the following problems must be solved:

1. Correctly select the maximum breakdown voltage of a defective place in the insulation.

2. Select electrodes for testing insulation for defectiveness in such a way that the detection of defects during testing corresponds to the conditions for detecting defects in the structure.

3. Correctly estimate the area of insulation that is tested for the purpose of determining defectiveness.

The present work is devoted to solving these problems for the enamel insulation of winding wires.

The operating voltages applied to insulation in low-voltage electrical devices, as a rule, are not dangerous for undamaged and even damaged insulation. Moreover, breakdown of undamaged insulation even under five- or sixfold overvoltages is an unlikely event, since the value of the insulation strength greatly exceeds the values of the field intensities that arise under overvoltages. In the manufacture of windings of low-voltage electrical devices, the enamel insulation of wires may be damaged, and the nature of the damage may beodaeth

various: deformation, surface scratches, abrasions, punctures, cuts, etc. Such insulation damage as deformations and surface scratches does not lead to a sharp decrease in the breakdown voltage of the insulation, since ultimately it is determined by the electric strength of the given insulation and by the thickness of it that remains undamaged. Through damage to the insulation (punctures, cuts, cracks) reduces its breakdown voltage to the level of the breakdown voltage of air over a thickness equal to the thickness of the conductor insulation. In addition, the condition of the insulation surface (moisture, dirt, etc.) has a substantial effect on the value of the insulation breakdown voltage at the defect location; therefore the breakdown voltage here must be determined not only from the insulation thickness and the electric strength of air, but also taking account of the surface flashover voltage.

In connection with the foregoing, it may be considered that breakdown of the insulation of low-voltage electrical devices occurs only in the presence of defects of the type of through punctures, cuts, cracks, etc. In this case the maximum breakdown voltage of the insulation at the defective point can be determined as follows:

\[ U_{\text{def}\cdot\max}=\overline{U}_{1}+3\sigma_{1}, \]

where

\(\overline{U}_{1}\) is the mean breakdown voltage of the enamel insulation of a wire having a through puncture (\(kv\ \max\));

\(\sigma_{1}\) is the root-mean-square deviation of \(\overline{U}_{1}\).

The distribution parameters of the breakdown voltage \(\overline{U}_{1}\) and \(\sigma_{1}\) can be estimated experimentally on artificially damaged enamel wires.

Tests of wires for defects may be carried out in various electrodes. One of the electrodes is always the metal of the wire; the other may be mercury, graphite, shot, or simply a flat metal electrode. When choosing electrodes it is necessary to bear in mind that, as a result of the test, in addition to the magnitude of the defectiveness, the distribution parameters of \(U_{\text{br}}\) of the defective insulation must be determined, and these parameters must not differ from the distribution parameters of the defective insulation in the structure. In this connection, such electrodes as graphite and mercury cannot be accepted for tests, since they give underestimated, in comparison with the structure, distribution parameters of \(U_{\text{br}}\) of the defective point. This is explained by the fact that both graphite and mercury can penetrate inside the defect, which leads to a reduction in the thickness of the air gap of the defect and, consequently, to a reduction in the mean breakdown voltage of the gap. In addition, graphite particles have different shapes and can create large nonuniformities of the electric field.

Shot also cannot be used as the second electrode, since the values of \(\overline{U}_{1}\) and \(\sigma_{1}\) in shot will depend on the diameter of the wire and the diameter of the shot. This is explained by the fact that the average distance between the metal of the wire and the shot depends on the diameter of the wire and the diameter of the shot.

Estimation of the parameters \(\overline{U}_{1}\) and \(\sigma_{1}\) from the results of tests on a flat electrode corresponds to \(\overline{U}_{1}\) and \(\sigma_{1}\) obtained in a structure where the wires are in close contact with one another or fit closely against the insulated magnetic core. Figure 1 shows distribution curves of the breakdown voltage of wires damaged during winding placement.

into the slots of the stator winding. The tests were carried out with various electrodes (graphite, mercury, shot, flat electrode). The form of the distributions indicates that the parameters of the defect distribution vary depending on the type of electrode. Fig. 2 shows the curve for artificially and naturally damaged wires. The parameters of the left-hand

Fig. 1. Distribution curves of \(U_{\mathrm{br}}\) over wires damaged during placement of the winding in the stator slots.
Electrodes: 1 — graphite, 2 — mercury, 3 — shot,
4 — flat metal electrode

maximum of the distribution of the naturally damaged wire coincide with the parameters of the artificially damaged insulation. When testing the insulation of wires for defects, it is necessary to know the area over which defects are detected. In estimating the probability of breakdown over large

Fig. 2. Characteristic distribution curve of the breakdown voltages of winding enamel wires after placement in the stator slots

areas (in the construction), it is necessary to know the exact value of the ratio \(S_{\mathrm{total}}/S_{\mathrm{test}}\), since the probability of breakdown over a large area can be estimated by the formula

\[ Q = 1 - (1 - q_{\mathrm{test}})\frac{S_{\mathrm{total}}}{S_{\mathrm{test}}}. \]

The area of insulation tested for defects when testing the wire in graphite and mercury is determined simply: \(S_{\mathrm{test}} = \pi \cdot d_{\mathrm{ins}} \cdot l_{\mathrm{w}}\). However, for the reasons indicated above, these electrodes cannot be used. The area of the tested insulation when used as a

the shot electrode depends on the diameter of the shot and the diameter of the wire. The area of insulation tested when testing on a flat electrode can be determined with sufficient accuracy, taking into account the breakdown voltage.

We assume that defects located at a distance \(r_i\) from the flat electrode (Fig. 3) are detected by the voltage \(U_1+3\sigma_1\) with probability \(p_i(r_i)\). The probability of detecting defects by this voltage decreases with increasing distance of the defect from the electrode and, as is seen from Fig. 4, at \(r=2.4\) mm, \(p_i(r_i)\) is \(0.58\cdot 10^{-12}\). With a sufficient degree of accuracy the curve \(p_i(r_i)\) can be replaced by the rectangle OABC, provided that the area OABC is equal to the area under the curve, i.e., it may be assumed that all defects located in the interval \(0 \le r_i \le r_{\text{test}}\) are detected with probability equal to 1, while defects located from the flat electrode at a distance \(r_i>r_{\text{test}}\) are not detected at all. Proceeding from the above assumption, the area over which defects are detected with probability equal to unity will be

Fig. 3. Diagram for testing conductors for defects on a flat electrode

\[ S_{\text{test}} = 2 r_{\text{test}}\cdot l_{\text{spec}}, \]

where

\(l_{\text{spec}}\) is the length of the section of wire tested on the flat electrode.

An estimate of \(S_{\text{test}}\) was carried out for enameled wires of grade PETV-\(t\)-35. For this wire, with an insulation diameter of 1.64 mm, with through damage to the insulation applied in the form of point punctures, testing was carried out on a flat electrode. In this case the distance from the point of contact of the electrode with the wire to the defect was varied from 0 to 2.4 mm. At each distance, approximately 100 specimens were tested. At a distance of 0 mm, there were

Fig. 4. Dependence of the probability of defect detection on the distance of the defect to the flat electrode

the values \(U_1\) and \(\sigma_1\) were obtained. Then the probability of falling into the zone of defects located at \(i\)-th distances was estimated [1]:

\[ p_i(r_i)=F\left(\frac{\overline{U}_1+3\sigma_1-\overline{U}_i}{\sigma_i}\right). \]

Figure 4 shows the curve \(P_i(r_i)\). Using the formula

\[ r_{\mathrm{test}}=\sum_{i=1}^{i} r_i\cdot p_i(r_i), \]

it was established that \(r_{\mathrm{test}}=1.527\ \mathrm{mm}\). Assuming that, under normal conditions, \(r_{\mathrm{test}}\) for enamel wires may be regarded as constant, on a flat electrode the insulation of a wire with diameter less than \(d_{\mathrm{ins.crit}}\) is tested completely for defectiveness.

\[ d_{\mathrm{ins.crit}}=\frac{2r_{\mathrm{test}}}{\pi}. \]

When testing wires of large diameter, \(S_{\mathrm{test}}\) is determined by the formula

\[ S_{\mathrm{test}}=2r_{\mathrm{test}}\,e_{\mathrm{spec}}. \]

Conclusions

1. The parameters \(U_1\) and \(\sigma_1\), according to the results of tests for defectiveness on a flat metal electrode, correspond most accurately to the parameters \(U_1\) and \(\sigma_1\) obtained when testing close-fitting winding wires lying in the slots of the stator of asynchronous machines.

2. A method is proposed for determining the test area of a specimen when determining the defectiveness of the insulation of winding wires.

References

1. A. K. Mitropolsky. Technique of Statistical Computations. Moscow, “Nauka,” 1971.

2. V. P. Simensky. Classification of insulation defects in low-power electrical machines and apparatus. In: Electromechanical Devices and Systems. Electronic Instruments. Moscow, “Energiya,” 1967.