Influence of Technological Accuracy Indicators on the Quality of Low-Power Asynchronous Motors
Abstract Generated abstract
The paper examines how manufacturing accuracy affects the quality and acceptance testing of low-power asynchronous motors, whose technological parameter scatter may exceed existing standard tolerances. It develops probabilistic tolerance calculations linking deviations in motor output parameters to deviations in input parameters such as winding resistance, air gap, dimensions, rotor material resistivity, and capacitor characteristics, and applies these calculations to universal and capacitor motors. The authors show that, under the studied production conditions, existing rotor die-casting and related technologies cannot reliably meet standard tolerances for small motors, especially below 50 W. They also propose a method for deriving permissible acceptance-test zones from manufacturing accuracy indicators, enabling control-test limits to be estimated at the design stage and verified in production.
Full Text
INFLUENCE OF THE ACCURACY INDICATORS OF TECHNOLOGY ON THE QUALITY OF LOW-POWER ASYNCHRONOUS MOTORS
B. I. Burshtein, O. P. Muravlev, E. K. Strelbitskii
(Recommended by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)
In order to rapidly improve the quality of products, state quality certification has been introduced in our country; in carrying it out, primary attention is paid to technical characteristics and to the stability of quality. In the certification of products, standards are revised, scientifically substantiated quality requirements are established, and methods are developed for objective control of the quality level.
Existing standards [1, 2] establish tolerances for the output parameters of asynchronous motors, but they are not sufficiently substantiated, and the technological errors in the manufacture of low-power asynchronous motors considerably exceed the established tolerances [3]. These standards provide, during acceptance tests, for measurement of the current and power of no-load operation and short circuit. However, in the manufacture of asynchronous motors, for example at the Perm Electrotechnical Plant, because there is no reliable rule for converting the parameters of acceptance tests to the parameters of rated operation, tests have to be carried out in the rated mode.
For asynchronous motors we regard as output parameters the starting and maximum torques, starting current, rated slip, efficiency, and power factor; and as input parameters—the principal and local dimensions and the characteristics of the materials used (air gap, resistivity of the rotor-winding material, rotor and stator lengths, number of turns, etc.).
The scatter of the output parameters and of the acceptance-test parameters is due to one cause: the scatter of the input parameters, which characterizes the manufacturing technology. Using this proposition, we have developed methods for calculating tolerances on the output parameters and methods for determining the permissible values of the acceptance-test parameters, which take into account the actual accuracy indicators of the technology and are suitable for evaluating the quality of asynchronous motors in design and production.
The equations for calculating the tolerances and scatter of the output parameters by the probabilistic method have the form
\[ \delta_{y_i}^{2}=\sum_{j=1}^{m} c_{ij}^{2}\delta_{x_j}^{2}, \tag{1} \]
\[ i=1,2,\ldots,n;\quad j=1,2,\ldots,m, \]
where
\(\delta_{y_i}\) and \(\delta_{x_j}\) are the half-widths of the tolerance field, in percent, for the output and input parameters;
\(n\) and \(m\) are the numbers of output and input parameters;
\(c_{ij}\) is the coefficient of influence of the \(j\)-th input parameter on the \(i\)-th output parameter.
The calculation of influence coefficients for three-phase machines is set out in detail in [4, 5], while the formulas for calculating \(c_{ij}\) for single-phase machines were obtained by us on the basis of existing checking-calculation methods and were refined from experimental data.
The calculation of the influence coefficients was carried out for 13 frame sizes of UAD-series universal asynchronous motors with ratings from 1 to 70 W, as well as for AVE 0.71/4 and AVE 0.72/4 capacitor motors with ratings of 180 and 270 W.
The study of universal motors is of particular interest, since it makes it possible to compare the sensitivity of output parameters to deviations of input parameters in single-phase and three-phase modes.
Table 1 gives the values of the coefficients of influence of input parameters on the starting torque for several asynchronous motors: UAD 32(3) (three-phase mode, \(P = 7\) W), UAD 32(1) (single-phase mode, \(P = 4\) W), AVE 071/4 (\(P = 180\) W), and AO 32-4 (\(P = 1\) kW).
Table 1
| Input parameter | UAD 32(3) | UAD 32(1) | AVE 071(4) | AO 32-4 |
|---|---|---|---|---|
| \(w_1\) | −1,134 | 1,251 | 2,032 | −1,543 |
| \(d_{\mathrm{pr}}\) | 1,540 | 0,782 | −0,092 | 0,904 |
| \(l_m\) | −0,975 | −0,401 | −0,100 | −0,634 |
| \(\rho_{\mathrm{Al}}\) | 0,518 | 0,885 | 1,083 | 0,748 |
| \(\delta\) | 0,369 | 0,036 | 0,054 | 0,703 |
| \(l_1\) | −0,097 | −0,010 | −0,013 | −0,462 |
| \(l_2\) | 0,116 | 0,766 | 0,940 | 0,030 |
| \(z_2\) | −0,505 | −1,752 | −2,380 | −0,203 |
| \(x_e\) | 0,000 | 1,072 | 1,470 | 0,000 |
Comparison of the influence coefficients shows that, in single-phase mode, the output parameters are more sensitive to changes in the specific resistance of the rotor winding. The working capacitance has a large influence coefficient.
The values of \(\delta_{x_j}\) are determined by the accuracy capabilities of the manufacturing technology and, for the Perm Electrical Engineering Plant, are given in [3].
As an example, Table 2 gives a calculation of the scatter of starting torque, starting current, and slip for a UAD 32 universal motor in three-phase and single-phase modes.
On the basis of the investigations carried out on parameter scatter, it may be concluded that, at powers below 50 W, the existing rotor die-casting technology cannot ensure scatter of starting torque and slip within the limits permitted by the standard. In motors with ratings below 10 W, a complete or partial break in one of the winding bars is possible; this is difficult to control, and the contribution of this defect to the scatter of the output parameters is significant. Deviations of the capacitance of the working capacitor from its nominal value have a substantial effect on the scatter of the starting parameters of single-phase motors.
Determination of the permissible values of the parameters of control tests is closely connected with calculation of the tolerances for the output parameters: based—
the same influence coefficients of the input parameters on the output parameters \(c_{ij}\) and the accuracy indicators of the technology \(\delta_{x_j}\) are used.
The deviations of the parameters of control tests are related to the deviations of the input parameters by the dependence
\[ \Delta \bar{v} = F \Delta \bar{x}, \tag{2} \]
where \(\Delta \bar{v} = (\Delta I_0,\ \Delta P_0,\ \Delta I_k,\ \Delta P_k)\) is the vector of deviations of the parameters of control tests, the components of which are the deviations of the current and losses of no-load operation and short circuit during control tests;
\(\Delta \bar{x} = (\Delta \rho_{\mathrm{Al}},\ \Delta(P_{\mathrm{st}} + P_{\mathrm{mech}}),\ \Delta \delta,\ \Delta x_c)\) is the vector of deviations of the significantly influencing input parameters;
\(F\) is the matrix of coefficients of the influence of input parameters on the parameters of control tests. The elements of this matrix \(f_{ij}\) are determined analytically [4—6].
Table 2
| \(j\) | Output parameter | Three-phase mode \(M_p\) | Three-phase mode \(I_p\) | Three-phase mode \(S\) | Single-phase mode \(M_p\) | Single-phase mode \(i_p\) | Single-phase mode \(S\) |
|---|---|---|---|---|---|---|---|
| \multicolumn{6}{c}{\(c_{ij}^{2}\delta_{x_j}^{2}\)} | |||||||
| 1 | \(w_1\) | 54 | 88,2 | 207 | 66,0 | 8,55 | 360 |
| 2 | \(d_{\mathrm{pr}}\) | 36,1 | 15,2 | 4,7 | 9,24 | 1,90 | 23,6 |
| 3 | \(l_m\) | 0,578 | 0,168 | 0,03 | 0,098 | 0 | 0,26 |
| 4 | \(\rho_{\mathrm{Al}}\) | 157 | 60,6 | 585 | 460 | 12,0 | 585 |
| 5 | \(\delta\) | 47,0 | 2,55 | 0 | 0,45 | 0,76 | 2,68 |
| 6 | \(l_1\) | 0,038 | 0,002 | 0 | 0 | 0 | 0,02 |
| 7 | \(l_2\) | 0,026 | 0,268 | 1,56 | 1,12 | 0,06 | 2,00 |
| 8 | \(z_2\) | 39,8 | 105,8 | 704 | 479 | 13,8 | 865 |
| 9 | \(x_c\) | 0 | 0 | 0 | 115 | 29,7 | 0 |
| \(\delta_{y_i}^{2} = \displaystyle\sum_{j=1}^{m} c_{ij}^{2}\delta_{x_j}^{2}\) | 334,5 | 272,8 | 1502 | 1131 | 66,7 | 1838 | |
| \(\delta_{y_i},\ \%\) | 18,3 | 16,5 | 38,8 | 33,4 | 8,15 | 42,9 |
On the basis of the fact that the deviations of the output parameters and of the parameters of control tests depend linearly on the same strongly acting input parameters, we have developed a method for transforming the limits of the output parameters into the limits of the control tests.
The essence of this method consists in determining the limits of the significantly influencing input parameters at which the output parameters are made to conform to the standard tolerances. Then, from equation (2), the permissible limits for the parameters of the control tests are determined.
The advantage of this method is that the parameters of the control tests can be calculated at the motor design stage, taking into account the features of a particular production process.
The equations for determining the permissible values of the input parameters have the form
\[ c_{i4}\Delta \rho_{\mathrm{Al}} + c_{i5}\Delta \delta + c_{i9}\Delta x_c + c_{i10}\Delta(P_{\mathrm{st}} + P_{\mathrm{mech}}) = \Delta y_i \pm \delta_i, \tag{3} \]
where
\[ \delta_i=\sqrt{c_{i1}^{2}\delta_{w_1}^{2}+c_{i2}^{2}\delta_{d_{\mathrm{pr}}}^{2}+c_{i3}^{2}\delta_{l_m}^{2}+c_{i6}^{2}\delta_{l_2}^{2}+c_{i7}^{2}\delta_{l_2}^{2}+c_{i8}^{2}\delta_{z_2}^{2}}; \]
\[
\Delta y_i
\]
is the standard tolerance of the \(i\)-th input parameter;
\[
\delta_i
\]
is one half of the scatter range of weakly influencing input parameters. The sign of \(\delta_i\) is taken opposite to the sign of \(\Delta y_i\).
For a number of universal and capacitor-type low-power asynchronous motors, the zones were calculated. Verification of the applicability of these zones was carried out at the Perm Electrotechnical Plant and gave positive results. It was established that, for motors operating in single-phase mode, in acceptance tests it is possible to measure only the no-load and short-circuit currents, while universal asynchronous motors need only be tested in any one mode.
Figure 1 presents the zones of permissible values of the no-load current and the short-circuit current for the universal motor UAD 32.
Fig. 1
The polygon \(ABCD\) bounds the zone of permissible values of the control parameters for the three-phase mode, and the polygon \(A'B'C'D'\) for the single-phase mode. For the single-phase mode, the following current is plotted:
\[ I_{k(1)}=I_{\kappa(1)}+\Delta, \tag{4} \]
where
\[
I_{\kappa(1)}
\]
is the short-circuit current in single-phase mode, measured during acceptance tests,
\[ \Delta=I_{\mathrm{kp}(3)}-I_{\mathrm{kp}(1)}; \]
\[
I_{\mathrm{kp}(3)}
\]
is the calculated short-circuit current in three-phase mode;
\[
I_{\mathrm{kp}(1)}
\]
is the calculated short-circuit current in single-phase mode.
The polygon KLMN defines the zone for motors satisfying the requirements of single-phase and three-phase operating modes.
Thus, the scatter of output parameters and the permissible values of the parameters of acceptance tests can be calculated at the design stage of asynchronous motors on the basis of the accuracy indicators of the proposed manufacturing technology.
Comparison of the scatter fields of output parameters with the tolerances according to GOST 183-66 shows that, with the existing technology, it is impossible to ensure the standard tolerances.
The results of the studies have made it possible to develop a scientific approach to constructing zones of permissible values for the parameters of acceptance tests.
REFERENCES
-
GOST 183—66. “Electrical machines. General technical requirements.”
-
GOST 10799—64. “Single-phase capacitor asynchronous motors with a squirrel-cage rotor, from 10 to 400 W. Basic parameters and technical requirements.”
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B. I. Burshtein, O. P. Muravlev, E. K. Strelbitskii. Scatter of parameters of asynchronous motors with power from 1 to 70 W. Izvestiya TPI, vol. 190, 1968.
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O. P. Muravlev, E. K. Strelbitskii. Ensuring the required accuracy in the production of asynchronous motors. Elektrotekhnika, 1966, No. 7.
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O. P. Muravlev, E. K. Strelbitskii. Calculation of tolerances for the parameters of asynchronous motors. Elektrotekhnika, 1968, No. 11.
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O. P. Muravlev, E. K. Strelbitskii. Calculation of zones of permissible values for the parameters of acceptance tests of three-phase asynchronous motors. Izvestiya TPI, vol. 172, 1967.