Methodology for Investigating Insulation Aging in Low-Voltage Electrical Machines
Abstract Generated abstract
This paper proposes a methodology for studying aging of insulation in low-voltage electrical machines by emphasizing crack formation rather than relying only on breakdown-voltage statistics. Using an AO2-32-4 asynchronous motor, the authors outline an accelerated experimental design that varies winding temperature, reversal frequency, and vibration, with repeated tests over several aging durations and response models for crack flux intensity and breakdown-voltage moments. The specimen preparation and testing procedure distinguish flashover between cracks from true insulation breakdown, enabling estimation of crack spacing and insulation defectiveness. Example results after 1000 and 4000 hours at 135°C show both reduced breakdown voltage and a marked increase in cracking, supporting use of crack counts as input for calculating failure-free operation probability.
Full Text
Methodology for Studying Insulation Aging in Low-Voltage Electrical Machines
A. P. Matyalis, E. K. Strelbitskii
(Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)
In the process of polymer aging, the structure changes and elasticity is lost. The probability of crack formation increases substantially.
The gradual decrease in breakdown voltage, approximately uniform throughout the volume, and the fairly rapid development of cracks together form the overall picture of changes in the electrical properties of insulation. However, it is precisely cracks that are the cause of failure, since operating overvoltages are insufficient to puncture the insulation.
In tests of aged insulation, the causes of breakdown are not identified, whereas at high test voltages both flashover between cracks and insulation breakdown may occur.
Introducing crack parameters (number and rate of formation) into consideration, instead of the mean and variance of the breakdown voltages of specimens, substantially increases the resolving power of measuring and information-gathering means by eliminating the interference created by undamaged areas, which have a large weight in the aggregate. This reduces the scatter in estimates of aging parameters and creates a physical basis for recalculating results obtained in accelerated tests of insulation systems. In addition, the introduction of a discrete principle for changing process parameters (the number of cracks), instead of a continuous one (breakdown voltage), makes it possible, first, to apply the well-developed apparatus for calculating the probability of failure-free operation and, second, to take into account in a uniform way defects of both technological and operational origin.
During the manufacture of the winding, scratches and dents appear on the insulation; these are sources of stress concentration and sites of crack initiation. Therefore, tests should preferably be carried out on real electrical machines, or on mock-ups with sufficiently accurate imitation of the technological process.
We set up an experiment with the aim of obtaining the dependence of crack-formation rates on operating conditions. The present work describes the experimental plan and the method for preparing test specimens. An AO2-32-4 asynchronous motor was taken as the object.
The levels of the influencing factors are given in Table 1.
The output parameters taken were the intensity of the crack flux and the first two moments of the insulation breakdown voltage. It is assumed that the response of the output parameters is described either in the form of
Table 1
| Factors | Unit of measurement | Code designation | Levels + | Levels 0 | Levels − |
|---|---|---|---|---|---|
| Temperature | °C | \(x_1\) | 145 | 135 | 125 |
| Reversal frequency | \(\text{min}^{-1}\) | \(x_2\) | 2.5 | 2 | 1.5 |
| Vibration | double amplitude, \(\mu\) | \(x_3\) | 260 | 180 | 100 |
\[ y=b_0(t)+\sum_{i=1}^{3} b_i(t)x_i+\sum_{i=1}^{3} b_{ii}(t)x_i^2, \tag{1} \]
or in the form
\[ \ln y=b_0(t)+\sum_{i=1}^{3} b_i(t)x_i+\sum_{i=1}^{3} b_{ii}(t)x_i^2 . \tag{2} \]
To obtain the response coefficients, an experiment was set up, implemented on a half-replicate of a central composite rotatable second-order uniform design [1]. The design matrix is given in Table 2.
Table 2
| Experiment No. | Factor levels \(x_1\) | Factor levels \(x_2\) | Factor levels \(x_3\) |
|---|---|---|---|
| 1 | + | + | + |
| 2 | + | − | − |
| 3 | − | − | + |
| 4 | − | + | − |
| 5 | \(+\sqrt{2}\) | 0 | 0 |
| 6 | \(-\sqrt{2}\) | 0 | 0 |
| 7 | 0 | \(-\sqrt{2}\) | 0 |
| 8 | 0 | \(+\sqrt{2}\) | 0 |
| 9 | 0 | 0 | \(-\sqrt{2}\) |
| 10 | 0 | 0 | \(+\sqrt{2}\) |
| 11–16 | 0 | 0 | 0 |
Determination of the kinetics of the aging process is carried out by repeating the design for four test durations: 1000, 2000 (3000), 4000 (5000) hours. As a result of the processing, equations can be obtained for the polynomial coefficients:
\[ \begin{aligned} b_0&=b_0(t),\\ b_i&=b_i(t),\\ b_{ii}&=b_{ii}(t). \end{aligned} \]
When preparing machines for tests, it is necessary to allow for a large scatter in characteristics. The preparation of machines for testing consists of the following. Before the winding is laid, certain pairs of turns, following the winding scheme, are connected at the end portions in eight places. The connections are made to ensure contact along the entire length of the turn and to identify pairs during testing. Between the layers of slot insulation, on both sides of each slot, electrodes made of stranded wire are laid at a distance of 50 mm along the axis. In each machine we thus obtain 150 samples of turn insulation and 72 of frame insulation. The end portion on the side of the subsequent separation was not impregnated.
After the planned aging time has elapsed, the unimpregnated end portion is cut open, and the turns are fixed in pairs. To prevent breakdown at locations damaged during separation of the pairs, the cut end portion is impregnated 5–6 times in varnish. During testing, the separated conductors are immersed in transformer oil.
Each sample of turn and frame insulation is subjected to breakdown twice. From the magnitude of the difference between the primary and secondary voltages
…by voltage, flashover and breakdown of the insulation are recognized. It has been experimentally established that flashover corresponds to a voltage difference of up to 0.6 kV.
Tables 3 and 4 give the distributions of breakdown voltages of the turn insulation of motors that had operated at a winding temperature of 135°C for 1000 and 4000 hours, respectively. The breakdown voltages of the specimens located in the first column characterize the distance—
Table 3
Results of testing the turn insulation of a motor that had operated for 1000 hours at a winding temperature of 135°C
\[ \Delta U_j = U_{1i} - U_{2i}\;(\text{kV}) \]
| \(U_{1i}\) (kV) | up to 0.6 | 0.6–1.6 | 1.6–2.4 | 2.4–3.2 | 3.2–4.0 | 4.0–4.8 | 4.8–5.6 | 5.6–6.4 | 6.4–7.2 | 7.2–8.0 | 8.0–8.8 | \(\sum n_i\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0–0.8 | — | — | — | — | — | — | — | — | — | — | — | — |
| 0.8–1.6 | — | — | — | — | — | — | — | — | — | — | — | — |
| 1.6–2.4 | 1 | — | — | — | — | — | — | — | — | — | — | 1 |
| 2.4–3.2 | 1 | — | 1 | — | — | — | — | — | — | — | — | 2 |
| 3.2–4.0 | 1 | 1 | — | — | — | — | — | — | — | — | — | 2 |
| 4.0–4.8 | 2 | — | — | — | 1 | 2 | — | — | — | — | — | 5 |
| 4.8–5.6 | 2 | — | 1 | — | — | 1 | 3 | — | — | — | — | 7 |
| 5.6–6.4 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 5 | — | — | — | 14 |
| 6.4–7.2 | — | 2 | 2 | 3 | 1 | 1 | 2 | 4 | 10 | — | — | 25 |
| 7.2–8.0 | 1 | 1 | 1 | 1 | 2 | 1 | — | 3 | 2 | 5 | — | 17 |
| 8.0–8.8 | — | — | — | — | 1 | 1 | — | 1 | 2 | 1 | 3 | 9 |
| 8.8–9.6 | — | — | — | 1 | — | — | 2 | — | — | 1 | 1 | 5 |
| 9.6–10.4 | — | — | — | — | 1 | — | — | — | — | — | — | 1 |
| 10.4–11.2 | — | — | — | — | — | 1 | — | — | — | — | — | 1 |
| \(\sum n_j\) | 9 | 5 | 6 | 6 | 7 | 9 | 9 | 13 | 14 | 7 | 4 | 89 |
\[ \overline{U}=6.735\ \text{kV} \qquad \sigma=1.5428\ \text{kV} \]
\[ \overline{x}=444.9\ \text{mm} \]
Table 4
Results of testing the turn insulation of a motor that had operated for 4000 hours at a winding temperature of 135°C
\[ \Delta U_j = U_{1i} - U_{2i}\;(\text{kV}) \]
| \(U_{1i}\) (kV) | up to 0.6 | 0.6–1.6 | 1.6–2.4 | 2.4–3.2 | 3.2–4.0 | 4.0–4.8 | 4.8–5.6 | 5.6–6.4 | 6.4–7.2 | 7.2–8.0 | 8.0–8.8 | \(\sum n_i\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.0–0.8 | — | — | — | — | — | — | — | — | — | — | — | 0 |
| 0.8–1.6 | 1 | — | — | — | — | — | — | — | — | — | — | 1 |
| 1.6–2.4 | 3 | 1 | 1 | — | — | — | — | — | — | — | — | 5 |
| 2.4–3.2 | 3 | 1 | 2 | 3 | — | — | — | — | — | — | — | 9 |
| 3.2–4.0 | 5 | 2 | 2 | — | 6 | — | — | — | — | — | — | 15 |
| 4.0–4.8 | 4 | 1 | 2 | 1 | 1 | 4 | — | — | — | — | — | 13 |
| 4.8–5.6 | 2 | 1 | 1 | 4 | 2 | — | 7 | — | — | — | — | 17 |
| 5.6–6.4 | 1 | — | 1 | 2 | 1 | 1 | 3 | 3 | — | — | — | 12 |
| 6.4–7.2 | — | — | 1 | 1 | 1 | 1 | 1 | 1 | 3 | — | — | 9 |
| 7.2–8.0 | — | — | — | 1 | — | 1 | — | 1 | 1 | — | — | 4 |
| 8.0–8.8 | — | — | — | — | — | — | 1 | — | — | — | 1 | 2 |
| \(\sum n_j\) | 19 | 6 | 10 | 12 | 11 | 7 | 12 | 5 | 4 | 0 | 1 | 87 |
\[ \overline{U}=4.8024\ \text{kV} \qquad \sigma=1.6010\ \text{kV} \]
\[ \overline{x}=230.49\ \text{mm} \]
...the distance between cracks and defects. The defectiveness of the insulation is determined from the average distance between cracks [2]. The breakdown voltages of the remaining specimens are the minimum breakdown voltages of the insulation over the corresponding lengths or areas.
A comparison of the data in Tables 3 and 4 shows that, in the process of insulation aging, along with a decrease in the breakdown voltages of defect-free insulation, there is a sharp increase in the number of cracks. The number of cracks is used as the initial data for calculating the probability of failure-free operation over a specified time.
REFERENCES
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V. V. Nalimov, N. A. Chernova. Statistical Methods for Planning Extreme Experiments. Nauka, Moscow, 1965.
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A. P. Matyalis, E. K. Strelbitskii. Method for determining the defectiveness of insulation in low-voltage electrical machines. Izv. TPI. Present collection.