Application of a Pareto Chart to Analyze Losses from Defects in the Manufacture of Induction Motors
Abstract Generated abstract
This paper proposes the use of Pareto analysis to identify and prioritize losses from defects in the manufacture of asynchronous motors. Using control test results for 40,000 AO2-series motor windings and defect cards containing repair and rejection costs, the authors rank defect types by frequency and cost, construct cumulative loss tables, and interpret Lorenz-type curves and defect diagrams. The analysis shows that a small number of defect categories account for a large share of total losses, especially defects associated with lead-end damage, interturn and frame short circuits, and poor contact. The method is presented as a simple practical tool for locating weak points in technological processes and for extending quality-improvement analysis to motor components, functional groups, and production units.
Full Text
Proceedings of the Tomsk Polytechnic Institute named after S. M. Kirov, Holder of the Order of the October Revolution and the Order of the Red Banner of Labor
Vol. 284 1974
APPLICATION OF THE PARETO CHART FOR ANALYZING LOSSES FROM DEFECTS IN THE MANUFACTURE OF ASYNCHRONOUS MOTORS
A. G. Veresh, O. P. Muravlev
(Presented by the joint seminar of the Departments of Electrical Machines and Apparatus and General Electrical Engineering)
Determining and analyzing losses from defects is a necessary part of quality-control work in the manufacture of asynchronous motors. An accurate and objective analysis of losses makes it possible to outline the most effective measures for improving product quality.
Table 1
| Defect number | Defect, failure: type | Loss indicator: number of defects, failures | Loss indicator: costs for defects and their correction, rub. |
|---|---|---|---|
| 1 | Lead ends damaged | 638 | 223.02 |
| 2 | Interturn short circuit | 384 | 855.02 |
| 3 | Frame short circuit | 130 | 57.78 |
| 4 | Operation on two phases (poor contact) | 118 | 657.64 |
| 5 | Winding damaged by burrs during impregnation | 144 | 175.12 |
| 6 | Different phase resistance | 54 | 122.16 |
| 7 | Turns damaged (during transportation) | 24 | 16.98 |
| 8 | Unidentified causes of winding short circuit | 88 | 244.66 |
| 9 | Poor soldering of lugs of lead ends | 182 | 38.10 |
| 10 | Rotor rubbing against the stator | 18 | 112.40 |
| 11 | Internal break of a turn | 74 | 70.74 |
| 12 | External break of a turn | 246 | 138.10 |
| 13 | Incorrect connection of the winding | 2 | 11.38 |
| 14 | Poor binding of end-winding parts | 60 | 9.56 |
| 15 | Winding damage when chips enter | 6 | 20.58 |
| 16 | Incorrectly selected winding wire | 2 | 6.02 |
In this work a method is proposed for analyzing losses from defects, based on the use of the Pareto principle [1]. The principal element of the analysis is the construction of a curve of cumulative losses for a set of units in which the losses are ordered by magnitude in descending or ascending order. In this case the losses and their carriers are divided into significant and insignificant ones, which is of great importance in establishing losses.
To estimate losses from defects, it is advisable to use the following indicators:
a) the number of defects of one kind or another;
b) the costs associated with eliminating defects or defective items.
Let us consider the method of loss analysis using a concrete example—for the winding of asynchronous motors of the AO2 series, third and fourth frame sizes.
On the basis of the results of control tests of 40,000 windings and defect cards, which indicate the costs of eliminating defects or the cost of final rejects, Table 1 was compiled. In Table 1 the types of defects and rejects are numbered and the loss indicators are determined. This table is the starting point for further analysis.
Table 2
| Defect, failure number | Number of defects, failures | Cumulative number of defects: absolute | Cumulative number of defects: % |
|---|---|---|---|
| 1 | 638 | 633 | 29.4 |
| 2 | 384 | 1022 | 47.0 |
| 12 | 246 | 1268 | 59.3 |
| 9 | 182 | 1450 | 66.7 |
| 5 | 144 | 1594 | 73.5 |
| 3 | 130 | 1724 | 79.3 |
| 4 | 118 | 1842 | 84.8 |
| 8 | 88 | 1930 | 88.9 |
| 11 | 74 | 2004 | 92.2 |
| 14 | 60 | 2064 | 94.8 |
| 6 | 54 | 2118 | 97.5 |
| 7 | 24 | 2142 | 98.6 |
| 10 | 18 | 2160 | 99.5 |
| 15 | 6 | 2166 | 99.7 |
| 13 | 2 | 2168 | 99.9 |
| 16 | 2 | 2170 | 100.0 |
| Total | 2170 |
Table 3
| Defect, failure number | Costs, rub. | Cumulative costs: absolute | Cumulative costs: % |
|---|---|---|---|
| 2 | 955.02 | 955.02 | 28.9 |
| 4 | 687.64 | 1642.66 | 49.7 |
| 3 | 474.78 | 2117.44 | 63.9 |
| 1 | 244.66 | 2362.10 | 71.4 |
| 8 | 223.02 | 2585.12 | 78.2 |
| 5 | 175.12 | 2760.24 | 83.7 |
| 12 | 138.10 | 2898.34 | 87.6 |
| 6 | 122.16 | 3020.50 | 91.5 |
| 10 | 112.40 | 3132.90 | 94.8 |
| 11 | 70.74 | 3203.64 | 96.8 |
| 9 | 38.10 | 3241.71 | 98.2 |
| 15 | 20.58 | 3262.32 | 98.7 |
| 7 | 16.98 | 3279.30 | 99.3 |
| 13 | 11.38 | 3290.68 | 99.7 |
| 14 | 9.56 | 3300.24 | 99.9 |
| 16 | 6.02 | 3306.26 | 100.0 |
| Total | 3306.26 |
The data of Table 1, in order to make analysis possible, must be arranged by each indicator—the number of defects and the magnitude of costs. For this purpose, the types of defects are written out in descending order of one of the indicators. The results of the regrouping are presented in Tables 2 and 3. From these tables it is evident that the first three types of defects already include about 60% of all the defects encountered and losses in the winding.
This circumstance is shown still more clearly in the graphs presented in Figs. 1 and 2. Each figure contains two graphs that provide information on losses according to the Pareto system. In both graphs, the abscissa shows all 16 types of defects in the order determined by the magnitude of the corresponding loss indicators, and the ordinate shows the magnitudes of the losses. In the diagrams placed in the right-hand part of each figure, the course of the distribution is shown in descending order of the ordered values of the loss indicators.
The principal graph of Pareto analysis is the Lorenz curve of cumulative losses, which clearly reflects the proportional influence of each defect on the total losses. This curve has a distinctly pronounced character of a sharp rise in the initial left-hand part of the graph and a gradual slowing of growth in the right-hand part. Since the numbering order
... in the figures does not coincide with the defect number in the order of magnitude of the loss indicator; therefore, an additional scale is plotted beneath the main scale, reflecting this point. This makes it possible to compare individual magnitudes of losses in all the figures.
The curve of cumulative losses makes it possible to determine those winding defects on which attention must be focused in order to reduce the amount of rejects at the enterprise. On the basis of the curves of cumulative—
Fig. 1. Lorenz curve of cumulative losses and defect diagram
Fig. 2. Lorenz curve of cumulative losses and cost diagram
—losses and the diagrams, the defects are determined whose losses at the plant have the greatest specific weight in the total losses due to winding rejects. These are defects numbered 1, 2, 3, 4. The main causes of the increased number of turn-to-turn and frame faults in the winding are an insufficiently high standard of winding-and-insulation work. In addition, a large number of frame faults occurs because of the large size of burrs along the perimeter of the sheet punching. Failures due to defect number 4 occur because of poor contact of the lead-out...
ends with the winding, as well as poor soldering of the lead-out ends with the terminal lugs. In analyzing the causes of defect No. 1, it was established that the insulation of the lead-out ends is damaged mainly during the operations of pressing the stator stack into the frame and during the final machining of the frame locks on semiautomatic machines.
A Pareto loss chart can be used to analyze defects and motor failures as a whole. In this case it is necessary to prepare a logical set composed of the direct carriers of motor defects or failures. These may be so-called independent functional groups that provide a certain functional operation of the asynchronous motor. Seven such functional groups may be named for the asynchronous motor: winding, stator core, rotor, shaft, bearing shield, frame, bearing cover, and terminal box.
For this set of functional groups, tables and loss graphs are compiled according to the Pareto principle. On the basis of the conclusions developed with the aid of the tables and graphs, it is possible to establish a criterion for selecting the functional groups for which it is advisable, in the first instance, to develop measures to improve quality. In particular, the number of functional groups for the motor can be reduced to six, since statistics show that practically no defects are observed in bearing covers and terminal boxes.
Thus, the proposed method for analyzing losses from defects on the basis of the Pareto principle reveals weak points in technological processes that are the main sources of increased defects and makes it possible to intervene in a timely manner to reduce them. The clarity and simplicity of constructing cost diagrams make it possible to apply the method to the assessment of losses from defects in individual motor parts and assemblies, and also to use it practically for all electrical machines. In conclusion, it should be noted that the proposed method for analyzing losses from defects is not limited to solving only this problem. Pareto diagrams and graphs make it possible to solve a wide range of production problems associated with the manufacture of an asynchronous motor. In particular, using Pareto indexing, one can evaluate the effectiveness of the work of shops, departments, quality-control systems for manufacturing, etc.
References
- Quality management systems for products. Moscow, Standards Publishing House, 1972.