Investigation of the Influence of the Winding Manufacturing Process on Defects in the Ground Insulation of Induction Motors
Abstract Generated abstract
This study examines how operating parameters in stator slot insulation and winding manufacture affect through defects in the groundwall insulation of induction motors. Using statistical factorial experiment designs, the authors test varnished cloth specimens after processing on an IPS-3 slot-insulating machine and a WST-660 winding machine, treating defect occurrence with a Poisson model and deriving regression equations for defectiveness increments as functions of machine settings and incoming insulation quality. The resulting models indicate that winding tension, winding speed, punch-die clearance, insulation speed, and initial material defectiveness substantially influence insulation quality. Analysis of the models leads to recommended operating regimes that are reported to increase machine productivity while reducing groundwall insulation defectiveness by about 33% for slot insulation and 20% for winding.
Full Text
STUDY OF THE INFLUENCE OF THE TECHNOLOGICAL PROCESS OF WINDING MANUFACTURING ON DEFECTS IN THE GROUNDWALL INSULATION OF INDUCTION MOTORS
Yu. P. Pokhodkov, P. P. Besperstov, V. V. Lykhtin
(Presented by the scientific seminar of the Department of Electrical Insulation and Cable Engineering)
Analysis of failures of electrical machines during operation shows that the overwhelming majority of them are caused by the presence of hidden defects in the insulation, which are revealed during the running-in period [1—4].
Defects such as through punctures, tears, and cracks may appear in the insulation either during its manufacture or during the manufacture of windings [3].
The purpose of the present work is to study the influence of fluctuations in the technological operating mode of the WST-660 stator-winding machine of the GDR firm “Elektromat” and the IPS-3 slot-insulating machine on the quality of the groundwall insulation of windings.
As a criterion of the quality of the groundwall insulation we take the level of its defectiveness—$q$ [4].
The conversion of the defectiveness of the groundwall insulation to unit area can be carried out as follows. Assuming that a through defect of the specimen is a rare event, we take the distribution of defects over the area of the specimen to obey the Poisson law.
Then $(1-q)=e^{-a}$, where $a$ is the average number of defects over the area of the specimen $S$. The number of defects per unit area will be equal to
$$ q'=\frac{a}{S}\left[\frac{1}{\text{mm}^2}\right]. \tag{1} $$
The studies were carried out using mathematical methods of statistical factorial design of experiments [6].
According to preliminary studies, the principal factors exerting a substantial influence on defect formation in the groundwall insulation are:
1) on the winding machine—the tensile force ($P$) and the winding speed ($v$);
2) on the slot-insulating machine—the clearance between the punch and the die ($\delta$) and the insulation speed ($v$).
For studies on the winding machine, the experiment was planned according to a central composite rotatable second-order design (Table 1); the factor levels and intervals of their variation are presented in Table 2. For the insulating machine, the experiment was planned according to a first-order factorial design for two factors (Table 3); the factor levels and intervals of their variation are given in Table 4.
Table 1
| No. | $V$, strokes/min | $P$, kgf | $\Delta q_1 \cdot 10^{-3}$, $1/\mathrm{mm}^2$ | $\Delta q_2 \cdot 10^{-3}$, $1/\mathrm{mm}^2$ | $\Delta q_3 \cdot 10^{-3}$, $1/\mathrm{mm}^2$ |
|---|---|---|---|---|---|
| 1 | +1 | +1 | 1,63 | 2,83 | 5,36 |
| 2 | +1 | −1 | 0,95 | 1,59 | 2,52 |
| 3 | −1 | +1 | 1,33 | 2,40 | 4,72 |
| 4 | −1 | −1 | 0,35 | 1,12 | 1,76 |
| 5 | 1,414 | 0 | 1,02 | 2,13 | 4,43 |
| 6 | −1,414 | 0 | 0,42 | 1,33 | 2,24 |
| 7 | 0 | 1,414 | 1,72 | 3,22 | 5,68 |
| 8 | 0 | −1,414 | 0,28 | 0,92 | 1,52 |
| 9 | 0 | 0 | 1,00 | 1,99 | 3,98 |
| 10 | 0 | 0 | 1,10 | 2,02 | 3,56 |
| 11 | 0 | 0 | 1,04 | 2,08 | 3,62 |
| 12 | 0 | 0 | 1,07 | 2,08 | 3,62 |
Table 2
| Factors | Variation interval | Code designation | Factor levels −1,414 | Factor levels −1 | Factor levels 0 | Factor levels +1 | Factor levels +1,414 |
|---|---|---|---|---|---|---|---|
| $V$, strokes/min | 28 | $X_1$ | 40 | 52 | 80 | 108 | 120 |
| $P$, kgf | 0,7 | $X_2$ | 3 | 3,3 | 4 | 4,7 | 5 |
Table 3
| No. | $V$, slots/min | $\delta$, mm | $\Delta q_1 \cdot 10^{-3}$, $1/\mathrm{mm}^3$ | $\Delta q_2 \cdot 10^{-3}$, $1/\mathrm{mm}^2$ | $\Delta q_3 \cdot 10^{-3}$, $1/\mathrm{mm}^2$ |
|---|---|---|---|---|---|
| 1 | +1 | +1 | 0,589 | 0,700 | 1,16 |
| 2 | +1 | −1 | 0,345 | 0,300 | 0,560 |
| 3 | −1 | +1 | 0,520 | 0,548 | 0,880 |
| 4 | −1 | −1 | 0,328 | 0,168 | 0,280 |
Table 4
| Factors | Variation interval | Code designation | Factor levels +1 | Factor levels −1 |
|---|---|---|---|---|
| $V$, slots/min | 7,5 | $X_1$ | 92 | 77 |
| $\delta$, mm | 1,0 | $X_2$ | 3,5 | 5,5 |
After each technological operation, i.e., after insulating the stator slots and after winding the winding, the groundwall insulation was carefully removed from the slots. The specimens obtained were tested for breakdown in cylindrical electrodes of diameter \(20\) mm. In the implementation of one row of the design, 150 specimens were tested. From the value of the breakdown voltage, the increment in the defectiveness of the groundwall insulation was determined for various operating modes of the winding and insulating machines in accordance with the designs.
Varnished cloth LSK-0.17 was selected as the object of study. To assess the influence of the quality of the varnished cloth arriving at the plant on the increment in defectiveness during manufacture of the winding, three batches with different levels of defectiveness were selected for each machine:
a) for the winding machine
\[ q'_{1\text{п}} = 1.06 \cdot 10^{-3}\ \text{mm}^{-2}; \qquad q'_{2\text{п}} = 1.98 \cdot 10^{-3}\ \text{mm}^{-2}; \]
\[ q'_{3\text{п}} = 6.32 \cdot 10^{-3}\ \text{mm}^{-2} \]
b) for the insulating machine
\[ q'_{1\text{п}} = 1.4 \cdot 10^{-3}\ \text{mm}^{-2}; \qquad q'_{2\text{п}} = 2.42 \cdot 10^{-3}\ \text{mm}^{-2}; \]
\[ q'_{3\text{п}} = 4.68 \cdot 10^{-3}\ \text{mm}^{-2}. \]
As a result of implementing the designs and processing the experimental data [7], regression equations were obtained for the increment in defectiveness of the groundwall insulation as a function of the operating modes of the winding and insulating machines:
a) winding machine
for \(q'_{1\text{п}} = 1.06 \cdot 10^{-3}\ \text{mm}^{-2}\)
\[ \Delta q_1 = (1.05 + 0.218X_1 + 0.461X_2 - 0.119X_1^2 + 0.0865X_2^2 - \]
\[ - 0.075X_1X_2)\cdot 10^{-3}\ \text{mm}^{-2}; \tag{2} \]
for \(q'_{2\text{п}} = 1.98 \cdot 10^{-3}\ \text{mm}^{-2}\)
\[ \Delta q_2 = (2.07 + 0.254X_1 + 0.721X_2 - 0.14X_1^2 + 0.047X_2^2) \cdot 10^{-3}\ \text{mm}^{-2}; \tag{3} \]
for \(q'_{3\text{п}} = 6.32 \cdot 10^{-3}\ \text{mm}^{-2}\)
\[ \Delta q_3 = (3.67 + 0.56X_1 + 1.46X_2 - 0.141X_1^2 - 0.27X_1X_2) \cdot 10^{-3}\ \text{mm}^{-2}; \tag{4} \]
b) insulating machine
for \(q'_{1\text{п}} = 1.4 \cdot 10^{-3}\ \text{mm}^{-2}\)
\[ \Delta q_1 = (0.448 + 0.107X_2)\cdot 10^{-3}\ \text{mm}^{-2}; \tag{5} \]
for \(q'_{2\text{п}} = 2.42 \cdot 10^{-3}\ \text{mm}^{-2}\)
\[ \Delta q_2 = (0.468 + 0.071X_1 + 0.19X_2)\cdot 10^{-3}\ \text{mm}^{-2}; \tag{6} \]
for \(q'_{3\text{п}} = 4.68 \cdot 10^{-3}\ \text{mm}^{-2}\)
\[ \Delta q_3 = (0.72 + 0.14X_1 + 0.3X_2)\cdot 10^{-3}\ \text{mm}^{-2}. \tag{7} \]
The values of the increment in defectiveness are given in Tables 1 and 3.
After describing the coefficients of equations (2–7) as functions of the defectiveness of the groundwall insulation in the as-delivered condition [5] and replacing the coded values by natural ones [6], we obtain generalized models of the increment in defectiveness in the groundwall insulation after insulation on the IPS-3 machine:
\[
\Delta q = \left(0.7866 \cdot q_{\mathrm{p}}'^{-2.29} \cdot e^{0.655 q_{\mathrm{p}}'} + 0.014 \cdot q_{\mathrm{p}}'^{22} \cdot e^{-7.05 q_{\mathrm{p}}'} V -
\right.
\]
\[
\left.
- 0.092 \cdot q_{\mathrm{p}}'^{1.524} \cdot e^{-0.233 q_{\mathrm{p}}' \cdot \delta}\right) \cdot 10^{-3}\ \mathrm{1/mm^2};
\tag{8}
\]
and after winding the winding on the WST-660 machine—
\[
\Delta q = \left(-0.9753 \cdot q_{\mathrm{p}}'^{0.124} \cdot e^{0.42 q_{\mathrm{p}}'} + 0.02522 \cdot q_{\mathrm{p}}'^{-1.48} \cdot e^{0.657 q_{\mathrm{p}}'} \cdot V +
\right.
\]
\[
+ 0.0854 \cdot q_{\mathrm{p}}'^{-1.913} \cdot e^{1.183 q_{\mathrm{p}}'} \cdot P
- 0.000157 \cdot q_{\mathrm{p}}'^{0.376} \cdot e^{-0.079 q_{\mathrm{p}}'} V^{2} +
\]
\[
\left.
+ 0.1423 \cdot q_{\mathrm{p}}'^{-1.555} \cdot e^{0.284 q_{\mathrm{p}}'} \cdot P^{2}
- 0.000512 \cdot q_{\mathrm{p}}'^{-15.16} \times
\right.
\tag{9}
\]
\[
\left.
\times e^{1.94 q_{\mathrm{p}}'} \cdot V \cdot P
\right) \cdot 10^{-3}\ \mathrm{1/mm^2}.
\]
Analysis of equations (2–9) shows that the operating conditions of the winding and insulating machines have a substantial influence on the quality of the groundwall insulation.
Analyzing the generalized equations (8–9), one can recommend optimal operating conditions for the winding and insulating machines, achieve an increase in equipment productivity, and improve the quality of the groundwall insulation.
Figures 1–3 show lines of equal defectiveness level of the groundwall insulation after slot insulation and after winding the winding, for different defectiveness levels of the insulation in the delivery condition. Analysis of the dependences (Figs. 1–3) shows that the operating conditions of the insulating and winding machines that exist at the Sibelektromotor plant are not optimal.
Thus, on slot-insulating machines the insulation speed can be increased from 77 slots/min to 92 slots/min, while increasing the gap between the punch and the die from 0.35 mm to 0.55 mm. In this case the defectiveness of the groundwall insulation will decrease by approximately 33%.
On winding machines it is possible to increase the winding speed from 80 double strokes/min to 110 double strokes/min, while reducing the tension force from 4 kgf to 3.44 kgf. In this case the defectiveness of the groundwall insulation will decrease by approximately 20%.
Fig. 1. Lines of equal defectiveness level of the groundwall insulation of the winding:
a) \(q_{\mathrm{p}} = 1.06 \cdot 10^{-3}\ \mathrm{1/mm^2}\), b) \(q_{\mathrm{p}} = 1.98 \cdot 10^{-3}\ \mathrm{1/mm^2}\); winding machine WST = 660.
In Tables (5–6) the existing and recommended operating conditions of the technological equipment at the Sibelektromotor plant are given, and, correspondingly, for each condition the increment of defectiveness is given.
The results obtained in the work make it possible to draw the following conclusions:
- In this work, mathematical models have been obtained for defect formation in the groundwall insulation of induction motors when insulating slots on the IPS-3 insulating machine and when manufacturing windings on the WST-660 winding machine; these models take into account the quality of the insulation as supplied and the operating modes of the equipment.
Fig. 2. Lines of equal level of defectiveness of the winding groundwall insulation:
c) WST-660 winding machine, \(q'_{\mathrm{p}} = 6.32 \cdot 10^{-3}\ \text{1/mm}^2\);
d) IPS-3 insulating machine, \(q'_{\mathrm{p}} = 1.4 \cdot 10^{-3}\ \text{1/mm}^2\).
Fig. 3. Lines of equal level of defectiveness of the winding groundwall insulation:
e) \(q'_{\mathrm{p}} = 2.42 \cdot 10^{-3}\ \text{1/mm}^2\);
f) \(q''_{\mathrm{p}} = 4.68 \cdot 10^{-3}\ \text{1/mm}^2\), IPS-3 insulating machine.
-
On the basis of an analysis of the mathematical models obtained, optimal operating modes of the IPS-3 and WST-660 machines have been proposed, making it possible to increase the productivity of the IPS-3 machine by 20%, that of the WST-660 machine by 37%, and at the same time to reduce defectiveness by 33% and 20%, respectively.
-
The results of the studies performed show that deviations in the operating modes of the winding and insulating machines have a substantial influence on the quality of the groundwall insulation of induction-motor windings.
Table 5
Winding machine WST-660
| \(q'\) as delivered | Recommended regimes | Existing regimes |
|---|---|---|
| \(1.06\cdot10^{-3}\ \text{1/mm}^2\) | \(V=110\ \dfrac{\text{rev}/\text{h}}{\text{min}}\) \(P=3.44\ \text{kgf}\) \(\Delta q=0.85\cdot10^{-3}\ \text{1/mm}^2\) |
\(V=80\ \dfrac{\text{rev}/\text{h}}{\text{min}}\) \(P=4.00\ \text{kgf}\) \(\Delta q=1.05\cdot10^{-3}\ \text{1/mm}^2\) |
| \(1.98\cdot10^{-3}\ \text{1/mm}^2\) | \(V=110\ \dfrac{\text{rev}/\text{h}}{\text{min}}\) \(P=3.58\ \text{kgf}\) \(\Delta q=1.77\cdot10^{-3}\ \text{1/mm}^2\) |
\(V=80\ \dfrac{\text{rev}/\text{h}}{\text{min}}\) \(P=4\ \text{kgf}\) \(\Delta q=2.07\cdot10^{-3}\ \text{1/mm}^2\) |
| \(6.92\cdot10^{-3}\ \text{1/mm}^2\) | \(V=110\ \dfrac{\text{rev}/\text{h}}{\text{min}}\) \(P=3.51\ \text{kgf}\) \(\Delta b=2.67\cdot10^{-3}\ \text{1/mm}^2\) |
\(V=80\ \dfrac{\text{rev}/\text{h}}{\text{min}}\) \(P=4\ \text{kgf}\) \(\Delta q=3.67\cdot10^{-3}\ \text{1/mm}^2\) |
Table 6
Insulating machine IPS-3
| \(q'\) as delivered | Recommended regimes | Existing regimes |
|---|---|---|
| \(1.4\cdot10^{-3}\ \text{1/mm}^2\) | \(V=92\ \text{slots/min}\) \(\delta=0.55\ \text{mm}\) \(\Delta q=0.4\cdot10^{-3}\ \text{1/mm}^2\) |
\(V=92\ \text{slots/min}\) \(\delta=0.35\ \text{mm}\) \(\Delta q=0.6\cdot10^{-3}\ \text{1/mm}^2\) |
| \(2.42\cdot10^{-3}\ \text{1/mm}^2\) | \(V=92\ \text{slots/min}\) \(\delta=0.55\ \text{mm}\) \(\Delta q=0.336\cdot10^{-3}\ \text{1/mm}^2\) |
\(V=77\ \text{slots/min}\) \(\delta=0.35\ \text{mm}\) \(\Delta q=0.6\cdot10^{-3}\ \text{1/mm}^2\) |
| \(4.68\cdot10^{-3}\ \text{1/mm}^2\) | \(V=92\ \text{slots/min}\) \(\delta=0.55\ \text{mm}\) \(\Delta q=0.54\cdot10^{-3}\ \text{1/mm}^2\) |
\(V=77\ \text{slots/min}\) \(\delta=0.35\ \text{mm}\) \(\Delta q=0.9\cdot10^{-3}\ \text{1/mm}^2\) |
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