Some Issues in the Study of Thermal Conductivity of Slot Insulation in Asynchronous Electric Motors
Abstract Generated abstract
This paper examines the measurement of thermal conductivity in slot insulation materials for asynchronous motor stators, emphasizing its importance for thermal design accuracy and for accounting for variability in winding heating. The authors describe an experimental flat-plate apparatus with a guard ring, estimate systematic and random measurement errors, and determine the number of measurements needed to achieve a stated confidence level. Tests on glass varnished cloth and a two-layer electrical cardboard and Lavsan insulation show substantial scatter in unimpregnated materials, while varnish impregnation increases equivalent thermal conductivity and markedly reduces scatter. The study suggests that thermal-conductivity scatter can serve as an indicator for monitoring insulation impregnation quality.
Full Text
Some Issues in the Study of the Thermal Conductivity of Slot Insulation in Asynchronous Electric Motors
L. N. Veresh, M. A. Sannikova
(Presented by the scientific seminar of the Department of Electrical Machines and General Electrical Engineering)
In the design of electrical machines, thermal calculations play an important role. Their accuracy depends mainly on the accuracy with which thermophysical constants are determined, in particular the specific thermal conductivity of insulating materials.
In addition to improving the accuracy of thermal calculation and the possibility of taking into account the conditions of heat removal from the winding when selecting insulation, studies of the thermal conductivity of insulation pursue one further goal.
The characteristics of materials, as is known, have a certain scatter. The scatter in thermal conductivity, along with other causes, leads to a scatter in winding heating. To prevent this scatter from causing premature failure of machines with a positive deviation of the operating temperature of the winding, it is necessary to reduce the permissible average overheating of the winding. A study of the thermal conductivity of insulation makes it possible to choose this margin on a more substantiated basis. The possibility opens up of reducing the margin through the introduction of monitoring of the thermal conductivity of insulation and rejection of batches with reduced thermal conductivity.
The task of the study at the first stage includes the experimental determination of the thermal conductivity of electrical insulating materials used as slot insulation of the stators of asynchronous motors, and an assessment of the accuracy of the result obtained.
Measurement of the coefficient of thermal conductivity is carried out with the aid of a flat apparatus by the method of one plate with a guard ring. The idea of this method is based on the simplest thermal regime of a solid body of the simplest form. As such a body, a plate of the material under study, bounded by parallel planes, was selected. In the specimen under study the isothermal planes are normal to the heat flow; consequently,
\[ P=\lambda(\Theta_1-\Theta_2)\frac{F}{\Delta_i}, \tag{1} \]
where \(P\) is the amount of heat passing per unit time through the surface; \(\Delta_i\) is the thickness of the specimen under study; \(F\) is the area of the specimen under study; \((\Theta_1-\Theta_2)\) is the temperature difference.
The installation developed by us is intended for the study of various sheet insulating materials and combined multilayer insulation. The amount of heat \(P\) is released by the main he—
by a heater consisting of a nichrome coil in a metal housing. To minimize heat leakage, a shielding ring equipped with a heater and an additional lower heater are used. Such a design ensures that the value \(P\), adopted in calculating \(\lambda\), i.e., the amount of heat that actually passes through the specimen per unit time, is equal to the power of the main heater.
The entire system is enclosed in a box filled with a good heat-insulating material, in this case glass wool. The heaters are supplied with direct current; the powers are regulated independently. To measure the temperatures of the various parts, 20 copper–constantan thermocouples are used.
The thermal conductivity of the insulation is determined on the basis of formula (1)
\[ \lambda=\frac{U \cdot I \cdot \Delta_i}{\Delta \Theta \cdot F}, \]
where \(U\) and \(I\) are the voltage and current of the main heater,
\[ U \cdot I=P\,[\mathrm{W}]. \]
The systematic error in measuring thermal conductivity is determined by the errors of the measuring instruments.
\(\delta_a\) and \(\delta_b\) are the relative errors of the ammeter and voltmeter in the circuit of the main heater;
\(\delta_\Delta\) is the relative error of the micrometer with which the insulation thickness is measured;
\(\delta_\Theta\) is the relative error in measuring the temperature difference
\[ \delta_\Theta=\frac{2(\Delta_p+\Delta_T)}{\Delta\Theta}, \tag{2} \]
where \(\Delta_p\) is the error of temperature measurement by the potentiometer;
\(\Delta_T\) is the error of the thermometer used in calibrating the thermocouples.
The error in measuring the specimen area \(F\), owing to its smallness, is not taken into account.
Under the experimental conditions \(\delta_a=0.5\%\); \(\delta_b=0.2\); \(\delta_\Delta=1.0\%\); \(\Delta_p=0.4^\circ\mathrm{C}\); \(\Delta_T=0.05^\circ\mathrm{C}\); \(\Delta\Theta=25^\circ\mathrm{C}\).
\[ \delta_\Theta=\frac{2(0.4+0.05)}{25}\cdot 100=3.6\%. \]
Thus, the systematic error of the measurements lies within the limits
\[ \delta=\delta_a+\delta_b+\delta_\Delta+\delta_\Theta=5.3\%. \]
The random error of the measurements is caused by inaccurate compensation of heat leakage from the main heater, by nonuniform heating of the plates between which the specimen under test is placed, by nonuniformity of the specimen thickness, and by other similar factors. The magnitude of the random error can be reduced to any specified value by increasing the number of experiments; however, this value must be balanced against the systematic error. It is sufficient to impose the following requirement on the guaranteed random error:
\[ \Delta x \leq \frac{\delta}{2}. \tag{3} \]
In this particular case, \(\Delta x=2.5\%\) may be adopted at confidence probability \(\alpha=0.95\).
To determine the necessary number of experiments, the root-mean-square error of a single measurement was first found. For
this one insulation specimen was tested several times; before each experiment it was removed from the device and then reinstalled, moreover in a different position; the heater power in the different experiments was different. As a result of a sufficiently large number of measurements, the root-mean-square scatter was found to be \(S = 5.5\%\).
Using the table of the required number of measurements [2], for
\[ \varepsilon=\frac{\Delta x}{S}=\frac{2.5}{5.5}=0.45 \quad\text{and}\quad \alpha=0.95 \]
with interpolation, the required number of experiments was found to be \(n=23\).
Thus the total guaranteed error, with reliability 0.95, does not exceed
\[ \Sigma=\Delta x+\delta=2.5+5.3=7.8\%. \]
Table 1 gives the results of measuring the specific thermal conductivity for two types of slot insulation of electrical machines:
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Single-layer insulation made of LES-grade glass-escapon varnished cloth, \(0.165\ \mathrm{mm}\) thick, in the unimpregnated state.
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Two-layer insulation made of EV-grade electrical cardboard, \(0.199\ \mathrm{mm}\) thick, and Lavsan film, \(0.051\ \mathrm{mm}\) thick. This type of insulation was tested in the unimpregnated state and after impregnation in ML92 varnish; the quality of impregnation of the test specimens was checked by the absence of bubbles between the layers. During testing, the equivalent thermal conductivity of the layered insulation was determined.
The test specimens had the form of \(10 \times 10\ \mathrm{mm}^2\) squares. Each specimen was tested once.
Table 1
Distribution of the thermal conductivity of slot-insulation specimens by classes
| Class interval \(\left(\Delta\lambda=0.01\ \dfrac{\mathrm{W}}{\mathrm{m\,deg}}\right)\) | Number of measurements in the class: glass-escapon cloth | Number of measurements in the class: two-layer insulation, electrical cardboard—Lavsan, before impregnation | Number of measurements in the class: two-layer insulation, electrical cardboard—Lavsan, after impregnation |
|---|---|---|---|
| 0.05–0.06 | – | 3 | |
| 0.06–0.07 | 1 | 0 | |
| 0.07–0.08 | 1 | 1 | |
| 0.08–0.09 | 1 | 3 | |
| 0.09–0.10 | 2 | 1 | 2 |
| 0.10–0.11 | 2 | 3 | 11 |
| 0.11–0.12 | 0 | 6 | 6 |
| 0.12–0.13 | 4 | 5 | 3 |
| 0.13–0.14 | 3 | 1 | 1 |
| 0.14–0.15 | 4 | ||
| 0.15–0.16 | 2 | ||
| 0.16–0.17 | 1 | ||
| 0.17–0.18 | 0 | ||
| 0.18–0.19 | 1 | ||
| 0.19–0.20 | 1 | ||
| Total number of measurements | 23 | 23 | 23 |
As a result of the measurements, the mean value of the thermal conductivity \(\overline{\lambda}\), the root-mean-square scatter of the thermal conductivity, and the error in determining the mean value were found:
\[ \sigma_{\lambda}=\frac{\sigma}{\sqrt{n}}\cdot\frac{100}{\overline{\lambda}}\% \tag{4} \]
owing to the scatter of the characteristics of the specimens.
The results of processing the experimental data are given in Table 2.
Table 2
Thermal conductivity of insulation and its scatter
| Type of insulation | $\lambda$, $\dfrac{\mathrm{W}}{\mathrm{m}\cdot\mathrm{deg}}$ | $\sigma$, % | $\sigma_{\bar{\lambda}}$, % |
|---|---|---|---|
| Single-layer insulation LSE (glass-mica varnished cloth without impregnation) | 0.13 | 25 | 4.9 |
| Two-layer insulation: electrical cardboard—lavsan, before impregnation | 0.10 | 25 | 5.2 |
| After impregnation in ML-92 varnish | 0.16 | 6.2 | 1.3 |
Analysis of the experimental data makes it possible to draw the following conclusions:
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Impregnation in varnish not only increases the equivalent thermal conductivity, but also substantially reduces its scatter—in the example given, by a factor of 4; moreover, the scatter of the thermal conductivity obtained on different specimens approaches in magnitude the scatter obtained in repeated measurements on a single specimen.
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The indicators of scatter in thermal conductivity may be used to monitor the quality of insulation impregnation.
REFERENCES
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V. A. Osipova. Experimental Study of Heat-Transfer Processes. “Energiya,” 1969.
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A. N. Zaidel. Elementary Estimates of Measurement Errors. “Nauka,” 1968.