Weibull Statistic in Hydrolytic Aging of Polyesterimide Used in Rotating Electrical Machine Windings

2.1 Specimens

A bobbin of copper wire enameled with polyesterimide was furnished by TREFICUIVRE, manufacturer in ALGERIA. The insulation, of class H (180℃), has a 35 μm coat. The diameter of the wire is 0.63 mm.

The samples were prepared as twisted pair conductors. Firstly, the insulated wire was cut into lengths of 400 mm. The samples were elaborated using a winding lathe. A weight of 7 N was hooked to the wire, then 12 turns were carried out. At the end, the weight was detached and the buckle located at the top part of the specimen was suppressed. The length of the realized samples is 125 mm. To avert bypasses during the test of dielectric failure, the extremities of the samples were separated. In order to avoid any attendance of defects, the specimens were inspected with a microscope. Figure 1 illustrates a performed sample.

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Figure 1. Photograph of an achieved specimen

2.2 Hydrolytic aging

A great number of samples was exhibited to moisture in a climatic chamber regulated at 93% relative humidity and 40℃. The aging was performed up to 12000 h (500 days). To obtain this humidity level, 1.215l of glycerin was mixed with 6.075l of distilled water. The glycerin volume represents 20% of that of distilled water. The enclosure is equipped by temperature regulator and a heating system. After each period of 500 h, 80 specimens were withdrawn from the climatic chamber.

2.3 Dielectric breakdown test

AC voltage, 50 Hz provided by a high voltage transformer, was applied to the extremities of the twists. The voltage was raised with a speed of 0.5 kV/s until a failure occurred. The breakdown voltage was registered. The experiments were executed in air and at ambient temperature. A number of 2000 specimens was tested.

2.4 Fournier Transform Infrared Spectroscopy

For the tests of FTIR, a powder of the polymer was mixed with a KBr amount. After blending, the whole was pressed, then the pellets were made. The infrared spectra were measured with JASCO FT/IR in the wavenumber range of 4000 - 500 cm^-1. The apparatus is equipped with a computer.

4.1 Statistical analysis

a) Table 1(a) depicts the values of V, P, X and Y before aging. The findings of confidence intervals of breakdown voltage are presented in Table 1(b). For 12000 h of aging, the results of V, P, X and Y, and confidence bounds are exposed in Tables 2(a) and 2(b), respectively.

Table 1(a). Values of V, P, X and Y before aging

Table 1(b). Confidence intervals of breakdown voltage before aging

Table 2(a). Values of V, P, X and Y after 12000 h of aging

Table 2(b). Confidence intervals of breakdown voltage after 12000 h of aging

b) Figure 2 shows the scatter diagrams of breakdown voltage before aging, and after 4000 h, 8000 h and 12000 h.

c) The values of V₀ and $\beta$, and the equations of Weibull plots are given in Tables 3-5. Some examples of Weibull graphs with confidence intervals are presented in Figures 3(a)-3(d). It is about virgin samples, and those aged after 4000 h, 8000 h, and 12000 h. The confidence intervals are marked with dashed lines.

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(a) Before aging

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(b) After 4000 h of aging

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(c) After 8000 h of aging

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(d) After 12000 h of aging

Figure 2. Scatter diagram of breakdown voltage

Table 3. Values of V₀ and confidence intervals

Table 4. Values of $\beta$ with confidence intervals

Table 5. Equations of Weibull graphs

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(a) Before aging: 11.176 < V₀ = 11.489 < 11.807; 6.054 < β = 7.179 < 8.220; Y = 7.179 X – 7.612

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(b) After 4000 h: 9.967 < V₀ = 10.255 < 10.548; 5.879 < β = 6.971 < 7.982; Y = 6.971 X – 7.048

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(c) After 8000 h: 10.196 < V₀ = 10.520 < 10.851; 5.343 < β = 6.336 < 7.255; Y = 6.336 X – 6.476

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(d) After 12000 h: 9.223 < V₀ = 9.561 < 9.907; 4.630 < β = 5.490 < 6.286; Y = 5.521 X – 5.413

Figure 3. Weibull plot of breakdown voltage

4.2 Variation of breakdown voltage versus aging time

Figure 4 displays breakdown voltage (V₀) against aging time. The curve shows a ragged variation with the attendance of several peaks. The variations can be depicted as follows:

• At the start of aging, V₀ decreases from 11.57 kV to 10.42 kV, raises to 11.15 kV and diminishes abruptly to 9.55 kV. Afterwards, V₀ increases to 10.75 kV and lowers to 10.25 kV corresponding to 4000 h.
• Beyond this time, V₀ increases a little to 10.50 kV and lessens until 9.75, then rises again to 10.67 kV. After it decreases to 10.10 kV, grows to 10.52 kV and remains somewhat constant until 8500 h.
• Last, V₀ augments to 11.19 kV and falls to 9.10 kV. After it increases to 10.18 kV and lessens again to 9.16 kV, then enlarges until 9.56 kV.

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Figure 4. Breakdown voltage versus aging time

4.3 Variation of shape parameter in function of aging time

The variations of shape parameter (β) against aging time are represented in Figure 5 that shows, like Figure 4, an uneven evolution indicating several peaks. The evolutions can be summarized as follows:

• During the first 3000 h, β decreases from 7.18 to 5.22, rises to 5.94 and lessens again to 4.44 corresponding to 1500 h. Afterwards β increases to 6.29, decreases to 4.92 and grows until 7.52 after 3000 h.
• Later, it falls to 4.92, augments to 7.21 and lowers to 6.24 after 5000 h. Then it grows a little to 6.49, shortens to 5.47 and remains somewhat invariable until 7500 h.
• After this time, β increases to 6.34, decreases to 5.77 and raises to 6.89 corresponding to 9000 h. Afterwards β lessens to 5.28 and raises again reaching 8.15. Then, it drops until 4.15 and heightens to 5.52 for 12000 h.

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Figure 5. Shape parameter as a function of aging time

4.4 Infrared spectra

Table 6 shows the significant infrared absorbance bands of polyesterimide. The IR spectra, in the range 4000 cm^-1 - 500 cm^-1, are presented in Figures 6-9.

Table 6. Absorbance bands

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(a) Wavenumber between 4000 cm^-1 to 2000 cm^-1

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(b) Wavenumber between 2000 cm^-1 to 500 cm^-1

Figure 6. FTIR spectrum before aging

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(a) Wavenumber between 4000 cm^-1 to 2000 cm^-1

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(b) Wavenumber between 2000 cm^-1 to 500 cm^-1

Figure 7. FTIR spectrum after 4000 h

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(a) Wavenumber between 4000 cm^-1 to 2000 cm^-1

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(b) Wavenumber between 2000 cm^-1 to 500 cm^-1

Figure 8. FTIR spectrum after 8000 h

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(a) Wavenumber between 4000 cm^-1 to 2000 cm^-1

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(b) Wavenumber between 2000 cm^-1 to 500 cm^-1

Figure 9. FTIR spectrum after 12000 h

4.5 Discussion

1. After several hours of aging, water can diffuse into the polymer. Water plasticizes the material leading to the decrease of mechanical properties as ductility. This phenomenon has been reported by Merdas et al. [15].
2. The hydrolytic aging causes a lessening in viscosity expressing a weakening of molecular bonds and a raise in free volume. Therefore, the mean free path and the mobility of charge carriers enlarge inducing a reduction of breakdown voltage. While the increase of the breakdown voltage is due to the arrangement in the structure producing, in the contrary, a shortening of mean free path and the mobility of charge carriers. The maximum variation of V₀ is 21.34%.
3. The breakdown voltage is linked to the presence of defects which can be voids, metallic inclusions, electrode asperities and laminations at the electrode-polymer interface. These defects can exist within the insulations during the manufacturing or created by the hydrolytic aging.
4. As it can be shown, the dispersion of data alters from a distribution to another.
5. The change of β is assigned to the size distribution of defects. The reduction is ascribed to the size raise of defects. On the other hand, the increase is due to the arrangement in the molecular structure. The maximum variation β is 42.20%.
6. The dielectric breakdown of polymeric materials is related to the presence of space charge as indicated by Chen et al. [16]. Indeed, in the present work, the average maximum value of electrical field is about 100 kV/mm and the space charge can be shaped due to the injection of electrons/holes from the conductors (electrodes).
7. The interpretation of FTIR spectra is presented as follows:

1. Before aging

It arises an absorbance band at 3036 cm^-1 allotted to the stretching vibration of hydroxyl groups (OH) [17]. We notice two absorption peaks at 1774 and 1716 cm^-1 attributed to the asymmetrical stretching vibration and symmetrical stretching vibration of carbonyl (C=O) on the imide ring, respectively [18]. The absorbance band, detected at 1701 cm^-1, matches to the C=O vibration of ester groups [19, 20]. The absorbance band at 1655 cm^-1 corresponds to stretching vibration on the C=O ester bond [18]. The absorbance band at 1486 cm^-1 is allotted to C-C stretching vibration on benzene ring skeleton [18]. The C-N stretching vibration of aromatic-imide is shown at 1396 cm^-1 [18].

2. After aging, we remark a change of the spectra. The absorbance band at 1396 cm^-1 disappears after 4000 h. After 8000 h, the vanishing of the absorbance band at 3036 cm^-1 is noted. After 12000 h, we notice the disappearance of two absorbance bands at 1486 and 1396 cm^-1.

8. Depending on the investigation yielded by Araki and Taguchi [21], copper was detected in the polyesterimide layer. Oxygen can easily diffuse into the polyesterimide and attack the copper leading to formation of copper oxide. This latter grows into the insulation. The formation and the growth of copper oxide was confirmed by Lukas Korcak and Culliton [22]. The degradation of polyesterimide is a result of scission reaction of imide bond and ester bond at the copper – polyesterimide interface. The dissolution of copper can accelerate the decomposition of the polymer.
9. In a previous work, we studied the influence of hydrolytic aging on breakdown voltage of wire enameled including two layers of insulations [23]. The samples are twisted pair copper conductor insulated by polyesterimide (class H) covered with a film of polyamide imide (class C). By comparing the results obtained in the preceding work and the present study, we can conclude that:

• Before aging, the breakdown voltage is 12.709 kV in the precedent study. On the other hand, its value is 11.489 kV in the actual work. Therefore, the breakdown voltage is greater in the prior work; that is a difference of 9.6%.
• After a same aging time, the breakdown voltage corresponding to the current work is higher than that matching to the anterior investigation. The difference attains 36.58%.
• In the antecedent work, the degradation did not occur after 15000 h of aging. On the contrary, in the actual work, the degradation takes place after 12000 h.