Study of Operating Modes of Electric Motors of Universal Metal-Cutting Machines
Abstract Generated abstract
This study examines the actual load conditions of electric motors installed on widely used 1K62 universal metal-cutting machines, with attention to data needed for insulation reliability, protection selection, efficiency, and power-factor calculations. Load records from A61-4 motors were obtained with self-recording wattmeters and statistically processed on an M-20 computer, converting input power into output power, efficiency, and power factor by polynomial approximations derived from standard motor tests. The results show low average motor loading, with mean output power about 1.33 kW and average efficiency and power factor of 0.68 and 0.43, respectively, and indicate that 45 second sampled power values may be treated as independent. The output-power histograms could not be represented by a single distribution law, suggesting a mixture of probable operating modes at low loads and overload behavior at higher loads.
Full Text
Study of the Operating Modes of Electric Motors in Universal Metal-Cutting Machines
Yu. M. Bashagurov, A. S. Gitman, E. K. Strelbitskii
(Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)
This article presents the results of studies of the load conditions of electric motors in universal machine tools of the most widespread model, 1K62.
Knowledge of the statistical characteristics of the random process represented by the load diagram of the motors of universal machine tools is necessary for solving the following important applied problems:
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For calculating insulation reliability. Aging of insulation occurs as a result of thermal and mechanical effects. The statistical parameters of these effects can be determined only on the basis of knowledge of the actual load conditions. In addition, when selecting and calculating protection, it is necessary to know the probability of overloads that lead to operation of the protection.
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For calculating the average values of efficiency and power factor. At present these indicators are calculated for average load values, which leads to errors owing to the nonlinear dependence of efficiency and \(\cos \varphi\) on power in the range of actual variation of useful power. It should be noted that the average load values used in economic calculations are overestimated by a factor of \(2 \div 2.5\) in comparison with the actual values.
Studies carried out at ENIMS and NIIMASH showed that the average loading of the motors of universal machine tools does not exceed 27% of the rated value [1]. The cited works dealt mainly with the loading of machine tools. Therefore, they lack a number of important data required by electrical-machine designers: the distribution of pause times, idle-running times, the correlation function, etc. In connection with this, we began more detailed investigations aimed at obtaining complete information on the actual operating conditions of the electric motors of the machine-tool fleet.
The object of the study was the fleet of universal machine tools of model 1K62 at the 5th State Bearing Plant, on which A61-4 motors are installed.
For recording, self-recording wattmeters N 383 were used, with a maximum chart-feed speed of 5400 mm/h. The processed array of numbers consisted of values of the primary power taken at intervals of 45 s. As a result of statistical processing, two moments (the mean and the variance) of the secondary power \(P_2\) were obtained,
efficiency coefficient $\eta$ and power factor $\cos\varphi$. An M-20 digital computer was used for the processing.
The conversion of the values of $P$ into the values of $P_2$, $\cos\varphi$, and $\eta$ was carried out on the digital computer. For this purpose, from the results of standard tests of the motor, the dependences
\[ P_2=f_1(P_1), \qquad Q=f_2(P_1), \tag{1} \]
where $Q$ is the reactive power, were calculated.
The dependences (1) are approximated quite well by second-degree polynomials. The coefficients of the polynomials were calculated by the method of least squares:
\[ P_2=-0.4412+1.0229P_1-0.0104P_1^2 \]
\[ Q=2.8698+0.2005P_1+0.0125P_1^2 . \tag{2} \]
Analysis of the correlation functions obtained gives grounds for disregarding the correlation relation and for considering that, with a step of 45 sec, the power values may be regarded as independent random variables.
The results of the remaining calculations are given in Table 1.
Table 1
| Quantities | $P_2$, kW | $\cos\varphi$ | $\eta$ |
|---|---|---|---|
| Mean $m_1$ | 1.33 | 0.43 | 0.68 |
| Variance $m_2$ | 1.71 | 0.0198 | 0.0122 |
| Root-mean-square deviation | 1.30 | 0.14 | 0.11 |
The histograms of the secondary powers are shown in Figs. 1 and 2. Fig. 2 presents the beginning of the histogram of Fig. 1 with an interval reduced by a factor of 4.
Attempts to approximate the histograms by a single distribution law proved unsuccessful. This leads to the idea that here there is a mixture of distribution laws, namely: in the interval [from 0 to 2 kW]—the distribution law of the most probable operating modes, and in the interval [from 2 to $\infty$]—the distribution law of overloads. This does not cause difficulties in using the results. Indeed, the mean values of $\eta$ and $\cos\varphi$ are determined mainly by the most probable modes shown in Fig. 2, while the probability of operation of the protection is determined by the right-hand branch of histogram 1.
LITERATURE
- R. M. Pratusevich. Operating load conditions of universal machine tools. Stanki i instrument, No. 6, 1960.
Fig. 1 and Fig. 2. Histograms of output powers
Fig. 1
Vertical axis: Time (in fractions of the total operating time)
Horizontal axis: \(P_2,\ \mathrm{kW}\)
\[ P_{2n}=10\ \mathrm{kW} \]
\[ P_{2\mathrm{avg}}=0.13\,P_{2n} \]
Fig. 2
Vertical axis: Time (in fractions of the total operating time)
Horizontal axis: \(P_2,\ \mathrm{kW}\)