Statistical Characteristics of the Sparking Process at the Commutator in P-Series Machines
Abstract Generated abstract
This paper examines the statistical characteristics of commutator sparking in P-series electrical machines for use in estimating commutator service life under electro-spark erosion. Using service-life test observations from 23 machines of frame sizes 1 to 6 operated at rated load, the authors process sparking frequencies by class, estimate the probability of sparkless commutation, and relate sparking levels to spark-discharge duration. The observed mean sparking level corresponds to class 1.5, with sparkless commutation probability 0.35, mean discharge duration about 4 microseconds, and discharge-duration variance estimated at 1.78 square microseconds. The paper also gives a general relation between mean discharge duration and variance for applying these parameters in commutator life calculations.
Full Text
STATISTICAL CHARACTERISTICS OF THE SPARKING PROCESS ON THE COMMUTATOR IN P-SERIES MACHINES
V. S. Stukach, A. Ya. Tsirulik, V. N. Popov
(Presented by the joint seminar of the Departments of Electrical Machines and Apparatus and General Electrical Engineering)
When calculating the service life of commutators under sparking conditions, in order to determine the rate of the electro-spark erosion process it is necessary to know the mean value and variance of the duration of spark-arc discharges during sparking for machines of a given series. This article presents the results of a study of the statistical characteristics of sparking for P-series machines, obtained on the basis of data from service-life tests carried out at the Elektromashina plant (Prokopyevsk). Observations were processed for sparking in 23 machines of frame sizes 1–6, which had operated at rated load: more than 20 thousand hours—2 machines, from 15 to 20 thousand hours—2 machines, from 10 to 15 thousand hours—7 machines, from 5 to 10 thousand hours—5 machines, and less than 5 thousand hours—7 machines. Observations of sparking were carried out at equal time intervals. The frequencies and probabilities of occurrence of sparking of each level are given in Table 1.
Table 1
| Sparking class | 1 | $1\frac{1}{4}$ | $1\frac{1}{2}$ | 2 |
|---|---|---|---|---|
| Frequency, $n_i$; Probability, $p_i$; |
549 0.35 |
128 0.082 |
890 0.567 |
2 0.001 |
Sparking is a stationary random process in which the intensity of sparking varies within certain limits, at times disappearing completely. For the machines under study, the probability of sparkless commutation is $\xi = 0.35$. This probability is determined from the observation results as the ratio of the number of observations in which dark commutation was recorded to the total number of observations.
As can be seen from the data in Table 1, the mean sparking level of P-series machines corresponds to class $1\frac{1}{2}$ according to GOST 183-66. To determine the variance of the sparking level, a histogram of the distribution of sparking levels was constructed (Fig. 1), in which the classes are denoted by decimal numbers; a corresponding scale of sparking in points was also assigned to the sparking scale.
a scale of the duration of spark-discharge events on the basis of the function relating the duration of discharges to the sparking level in points, having the form [1]
\[ \tau_{\mathrm{i}}=\frac{I-1.14}{0.089},\ \mu\text{sec}, \tag{1} \]
where
\(I\) is the sparking level in points.
The multitude of factors leading to scatter in the sparking levels of individual machines in the series and to drift of the sparking level over time for one and the same machine makes it possible to regard the distribution of sparking levels of machines in the series as normal; this is also not contradicted by the histogram in Fig. 1. For a normal distribution law, practically all values of the random variable \((99.73\%)\) lie within the interval \(6\sigma\), where \(\sigma\) is the root-mean-square deviation of the random variable. According to Fig. 1, the six-sigma interval for the discharge duration \(\tau_{\mathrm{i}}\) is equal to \(8\ \mu\text{sec}\), whence the variance of the durations is
\[ D\{\tau_{\mathrm{i}}\}=\sigma^2=\left(\frac{8}{6}\right)^2=1.78\ \mu\text{sec}^2. \]
Fig. 1. Histogram of the distribution of sparking levels of machines of the P series, sizes 1–6
The mean value of the discharge duration on the commutator for the machines studied is equal to \(\overline{\tau}_{\mathrm{i}}=4\ \mu\text{sec}\).
The obtained parameters of the spark discharges should be used in calculating the service life of the commutators of machines of the P series.
The variance of the discharge duration increases with increasing sparking intensity, that is, with increasing mean discharge duration \(\overline{\tau}_{\mathrm{i}}\). In the general case one may use the relation
\[ D\{\tau_{\mathrm{i}}\}=\left(0.18+0.287\cdot \overline{\tau}_{\mathrm{i}}\right)^2,\ \mu\text{sec}^2, \tag{2} \]
found on the basis of a study of the relationship between discharge durations and sparking intensity in points [1].
REFERENCES
- A. Ya. Tsirulik, V. S. Stukach, Z. F. Idrisov. Study of the relationship between the parameters of spark-discharge events on the commutator and sparking intensity in points. Izvestiya TPI. Present collection.