Statistical Analysis of the Manufacturing Accuracy of TVF-100 Turbogenerator Bars with Monolit-2 Insulation
Abstract Generated abstract
The paper examines manufacturing accuracy in TVF-100 turbogenerator stator bars with Monolit-2 insulation, focusing on how dimensional scatter affects winding reliability, calibration, and additional insulation requirements. Using statistical measurements of bar width and height at successive production operations, the authors estimate process centers, standard deviations, probabilities of calibration and extra insulation, and the distribution of insulation thickness under an assumed normal law. The analysis identifies pressing of the uninsulated bar and insulation operations as major sources of deviation, and process modifications reduced dimensional scatter, increased the probability of acceptable insulation thickness, and lowered the expected amount of calibration.
Full Text
Proceedings of the Tomsk Order of the Red Banner of Labor
Polytechnic Institute named after S. M. Kirov
Vol. 212 1971
STATISTICAL ANALYSIS OF THE MANUFACTURING ACCURACY OF TVF-100 TURBOGENERATOR BARS WITH MONOLITH-2 INSULATION
N. I. Shkolnikov, S. M. Kabanova, B. A. Itkin
(Presented by the scientific seminar of the Department of Electrical Machines and General Electrical Engineering)
The stator winding of a turbogenerator is one of the principal elements determining its reliability. Among the many factors affecting the potential reliability of the winding, alongside the type of insulation used, the main one is the thickness of the insulation and its actual scatter, determined by the accuracy of the technological process. In addition, the amount of calibration or additional insulation of the bars depends directly on the accuracy of bar manufacture; in a number of cases this amount is considerable and leads to additional costs, while at the same time worsening the quality of the winding.
The Department of EEM of NETI, together with SibNIIETI, carried out a statistical analysis of the accuracy of the technological process for manufacturing the bars of the TVF-100 turbogenerator with the new progressive Monolith-2 insulation.
Statistical methods for analyzing the accuracy of a technological process are usually understood as the comparison of the “scatter field” of the quality characteristic under study at a given operation with the tolerance specified in the drawing [1].
The task of the investigation was to determine the position of the setting center and the scatter of the geometric dimensions of the bars at various operations, and also to identify the principal causes determining them in the given technological process. The dimensions of the bar were determined with a caliper in terms of the width and height of the bar at several points on the slot and end-winding parts of it, at the following operations: before body insulation, after insulation before impregnation, and after impregnation.
The investigation was carried out in two stages. At the first stage, which was performed immediately after debugging the process of manufacturing bars with Monolith-2 insulation, 29 bars were measured at 8 points on the slot part of each. Statistical processing yielded the arithmetic mean (\(\overline{B}\)) and root-mean-square (\(\sigma\)) values of the dimensions of each bar and the distribution parameters of the dimensions of a hypothetical bar corresponding to the technology used. Analysis of the data showed that the setting center of the technological process was somewhat displaced from the nominal value of the bar width, while the dimensional scatter obtained in production relative to the drawing values was determined mainly by the scatter obtained in the operation of pressing the uninsulated bar. This led to a considerable amount of calibration and additional insulation of the bars.
Therefore, first of all, the old press dies, which determine the width dimension of the uninsulated bar, were replaced, and a number of changes were introduced in the insulation operations. The subsequent conducted...
Subsequent measurements on eight bars at 100 points in stage II of the investigation of the geometric dimensions of the bars showed a significant deterioration in the accuracy of the technological process.
Table 1 compares the drawing dimensions with the parameters of a hypothetical bar—the width of its slot portion after the pressing operation \((\overline{B}_1; \sigma_{1\mathrm{p}})\) and the impregnation operation \((\overline{B}_{1\mathrm{p}}; \sigma_{1\mathrm{p}})\), respectively, for stages I and II of the investigation. It also gives the values of the probability of calibration, \(P_{\mathrm{k}}\), and the probability of additional insulation, \(P_{\mathrm{d}}\), of the bar for distribution parameters corresponding to the initial technological process and to the process modified on the basis of the statistical analysis.
Table 1
| \(\overline{B}_1\), mm | \(\sigma_1\), mm | \(\overline{B}_{1\mathrm{p}}\), mm | \(\sigma_{1\mathrm{p}}\), mm | \(P_{\mathrm{k}}\) | \(P_{\mathrm{d}}\) | |
|---|---|---|---|---|---|---|
| According to drawing | \(15.8^{+0.3}\) | — | \(23.9^{-0.5}\) | — | ||
| Stage I | 16.03 | 0.31 | 23.7 | 0.381 | 0.30 | 0.10 |
| Stage II | 15.81 | 0.178 | 23.6 | 0.248 | 0.111 | 0.052 |
The following procedure was adopted for determining \(P_{\mathrm{k}}\) and \(P_{\mathrm{d}}\). Preliminary investigations showed that the distribution densities \(f(B_1)\) and \(f(B_{1\mathrm{p}})\) may be assumed to obey the normal law. Then the possible values of the insulated bar lie within the limits
\[ B_{1\mathrm{p}\,\max}=\overline{B}_{1\mathrm{p}}+3\sigma_{1\mathrm{p}};\qquad B_{1\mathrm{p}\,\min}=\overline{B}_{1\mathrm{p}}-3\sigma_{1\mathrm{p}}. \tag{1} \]
According to the technology, bars with \(B_{1\mathrm{p}}\geq 23.9\) mm are calibrated (the “go” size of the gauge is \(B_{\mathrm{k}}=23.9\)), and with \(B_{1\mathrm{p}}\leq 23.2\) mm they are given additional insulation (the “no-go” size of the gauge is \(B_{\mathrm{d}}=23.2\)).
The probability of calibration and additional insulation of a bar is calculated from the formulas
\[ P_{\mathrm{k}}=(B_{\mathrm{k}}<B_{1\mathrm{p}}<B_{1\mathrm{p}\,\max}) = \Phi\!\left(\frac{B_{1\mathrm{p}\,\max}-\overline{B}_{1\mathrm{p}}}{\sigma_{1\mathrm{p}}}\right) - \Phi\!\left(\frac{B_{\mathrm{k}}-\overline{B}_{1\mathrm{p}}}{\sigma_{1\mathrm{p}}}\right), \tag{2} \]
\[ P_{\mathrm{d}}=(B_{1\mathrm{p}\,\min}<B_{1\mathrm{p}}<B_{\mathrm{d}}) = \Phi\!\left(\frac{B_{\mathrm{d}}-\overline{B}_{1\mathrm{p}}}{\sigma_{1\mathrm{p}}}\right) - \Phi\!\left(\frac{B_{1\mathrm{p}\,\min}-\overline{B}_{1\mathrm{p}}}{\sigma_{1\mathrm{p}}}\right), \tag{3} \]
where \(\Phi\) is the Laplace function, the values of which may be taken from the appendix [2].
Of practical interest is the determination of the actual distribution of the insulation thickness, \(b_{\mathrm{i}}\), of the bars. Direct measurement of \(b_{\mathrm{i}}\) is very difficult and, moreover, is usually associated with damage to the bar. The insulation of the bar is the difference \(B_{1\mathrm{p}}-B_1\). It is known that if two quantities are distributed according to the normal law, then the other quantity representing their sum (difference) will also be distributed according to the normal law, with mathematical expectation equal to
\[ \overline{b}_{\mathrm{i}}=\overline{B}_{1\mathrm{p}}-\overline{B}_1, \tag{4} \]
and with standard deviation [3]
\[ \sigma_{\mathrm{i}}=\sqrt{\sigma_{1\mathrm{p}}^{2}-\sigma_1^{2}} \tag{5} \]
or
\[ \sigma_{\mathrm{i}}^{2}=\sigma_{1\mathrm{p}}^{2}-\sigma_1^{2}-2r\sigma_1\sigma_{\mathrm{i}}, \tag{6} \]
where \(r\) is the correlation coefficient between \(B_1\) and \(b_{\mathrm{i}}\).
When the quantities \(B_1\) and \(b_i\) are independent, formula (5) is used; if they are correlated, then (6) is used. From physical considerations, for the technological process under study—especially in the case of mechanized insulation of bars—it may be assumed that there is a very weak positive correlation between \(B_1\) and \(b_i\), and \(r=0\) may be taken approximately.
Having determined from the statistical data, according to (4) and (5), the parameters of the normal law, one can calculate the probability of obtaining the thickness within specified limits \((b_i \div b_{i+1})\). Without allowance for calibration, this probability is determined by
\[ P_b(b_i < b < b_{i+1}) = \Phi\left(\frac{b_{i+1}-b_p}{\sigma_p}\right) - \Phi\left(\frac{b_i-b_p}{\sigma_p}\right). \tag{7} \]
Assuming that the deviation in the geometrical dimensions over the width of the bar must not exceed \(0.5\) mm [4], then for the limit \((7.5 \div 8.5)\) mm, respectively for stages I and II of the study, from (7) we obtain \(P_{bI}=0.778\) and \(P_{bII}=0.953\).
The use of statistical methods for analyzing the accuracy of the technological process of manufacturing turbogenerator bars made it possible to identify the main causes leading to deviations of dimensions from the drawing specifications. Elimination of these causes led to a significant reduction in the scatter of insulation thickness, and to a 2.8-fold reduction in the amount of calibration.
This demonstrates the effectiveness of using statistical methods in heavy electrical-machine building. Their further introduction is necessary for the analysis of technological processes not only in winding manufacture, but also in the entire production process of large electrical machines.
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