PARAMETER SPREAD OF ASYNCHRONOUS MOTORS WITH POWER FROM 1 TO 70 W

B. I. BURSTEIN, O. P. MURAVLEV, E. K. STRELBITSKII

(Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)

The quality of low-power asynchronous electric motors is characterized by the accuracy with which the following indicators are maintained: starting and maximum torques, starting and rated currents, efficiency, and rotational speed, which we shall hereafter call output parameters. The spread of the output parameters is caused by fluctuations of the input parameters: the basic and local dimensions of the machine, and the characteristics of the materials used (the magnitude of the air gap, wire diameter, specific resistance of the winding material, etc.).

To calculate the influence of technological errors on the spread of the output parameters, it is necessary to know, on the one hand, the accuracy characteristics of the main technological processes in the manufacture of electrical machines, and, on the other, the system of equations relating deviations of the input and output parameters. This article presents the results of an investigation of the scatter of the parameters of motors of the UAD series with power from 1 to 70 W. The number of machines of each standard size was 12–30.

The necessary equations for calculating tolerances on the input and output parameters will be obtained after refining the calculation method for low-power asynchronous motors, the calculation error of which at present amounts to 30–50 percent or more.

Tables 1 and 2 present data from the statistical processing of the results of type tests and their comparison with the values specified according to the technical specifications. The notation is given in Appendix 1.

The ratio of the mean values of the output parameters to those specified by the technical specifications differs greatly for different parameters and machines. In some cases, for example, for the starting torque of the UAD-72 in single-phase operation, there is a margin of 5.4 times; in others, the mean value is very close to the permissible value and there is a high probability of rejects occurring (rated current in three-phase operation of the UAD-52, short-circuit current in three-phase operation of the UAD-42, efficiency in single-phase operation of the UAD-42, etc.).

The parameters of an electrical machine depend on a number of factors, including random ones. Consequently, the parameters themselves have a random character, which necessitates a statistical approach to their determination.

On the basis of a large number of type and acceptance tests, it has been established that all the input and output parameters considered by us obey the normal distribution law.

Table 1

The spread of the parameters will be evaluated by means of half the scatter field

\[ \delta_i=\frac{300\sigma_i}{\overline{x}_i}\,[\%], \tag{1} \]

where \(\sigma_i\) is the root-mean-square deviation;

Table 2

Values of half the scatter field \(\delta_i\) of the output parameters,
as percentages of the mean value

\(\overline{x}_i\) is the mean value of the parameter under consideration.

The quantities \(\sigma_i\) and \(\overline{x}_i\) are determined in the statistical processing of the test results.

As is evident from Table 2, in the single-phase mode the spread of \(\dfrac{M_{\text{п}}}{M_{\text{н}}}\), \(\dfrac{M_{\text{m}}}{M_{\text{н}}}\), and \(\eta\) exceeds the spread of these same quantities in the three-phase mode; i.e., these characteristics for the single-phase mode of an asynchronous motor are more sensitive to deviations in the technological process.

A comparison of the spread of the output parameters of low-power motors with the spread of analogous parameters of asynchronous squirrel-cage motors rated from 0.6 to 10 kW [1] shows that the former have a considerably larger spread—by a factor of 1.5–4.

The spread of the input parameters for the UAD series was determined by the method of [1], and for the air gap it was calculated from the permissible deviations in machining the rotor and stator:

\[ \delta_{w_1}=0\text{—}4.0\%;\quad \delta_{l_m}=0.44\text{—}0.52\%;\quad \delta_{l_1}=4.80-0.071l_1;\quad \delta_{l_2}=3.48-0.0529l_2; \]

where \(l_1\) and \(l_2\) are in mm, for variation limits of 20–60 mm.

\[ \delta_{\delta}=19\text{—}26\%;\quad \delta_{\rho A1}=20\text{—}40\%;\quad \delta_{z_{\text{н}}}=0 \]

The deviation of the wire diameter is determined according to GOST.

The spread of the input parameters of the asynchronous micromotors under consideration is practically the same as that of series-produced asynchronous motors rated at 0.6–10 kW. On the other hand, the spread of the output parameters is significantly greater in micromotors. This can be explained either by the fact that asynchronous micromotors are more sensitive to deviations of the input parameters, or by the fact that we do not take into account a number of factors specific to these machines. The fractional influence of each input parameter on the output parameters can be assessed with the aid of coefficients of influence of the input parameters on the output parameters, as was done for series-produced asynchronous motors of low and medium power [2]; but for this it is necessary to have a sufficiently accurate method for calculating the parameters of asynchronous micromotors. Therefore the creation of such a method for calculating asynchronous micromotors is a primary task, without solving which it is impossible to develop a methodology

calculation of tolerances for input and output parameters and to outline recommendations for reducing the spread of output parameters.

Conclusions

1. The spread of the output parameters of the asynchronous micromotors under consideration, with power from 1 to 70 W, is greater than that of asynchronous motors with power of 0.6–10 kW, with a practically identical spread of input parameters.

2. Reducing the scatter field of the output parameters is expedient from the standpoint of improving the quality of asynchronous micromotors and bringing the mean parameter values closer to the permissible values, which promises substantial savings of active and structural materials in the mass production of asynchronous micromotors. The solution of this problem must be preceded by work to refine the methodology for calculating asynchronous micromotors, which is currently being carried out.

Appendix 1

Notation

\(P_{\mathrm{n}}\) — rated power;
\(M_{\mathrm{n}}\) — rated torque;
\(M_{\mathrm{p}}\) — starting torque;
\(M_{\mathrm{m}}\) — maximum torque;
\(I_{\mathrm{n}}\) — rated current;
\(I_{\mathrm{k}}\) — short-circuit current;
\(n_{\mathrm{n}}\) — rated rotational speed;
\(\eta\) — efficiency;
\(\delta_i\) — half of the scatter field of the \(i\)-th parameter;
\(w_1\) — number of turns of the stator winding;
\(d_{\mathrm{pr}}\) — diameter of the stator-winding wire;
\(l_{\mathrm{m}}\) — mean length of a turn of the stator winding;
\(\delta\) — magnitude of the air gap;
\(\rho_{\mathrm{le}}\) — resistivity of the aluminum of the rotor winding;
\(l_1\) — stator length;
\(l_2\) — rotor length;
\(z_2\) — number of rotor bars.

References

1. O. P. Muravlev. Study of the influence of precision characteristics of the technological process on the quality and reliability of asynchronous electric motors. Dissertation, Tomsk, 1966.

2. O. P. Muravlev, E. K. Strelbitskii. Ensuring the necessary accuracy in the production of asynchronous motors, Elektrotekhnika, 1966, No. 7.