ASSESSMENT OF SPARKING AT THE COMMUTATOR IN DC MACHINES

E. K. Strelbitskii, V. S. Stukach, A. Ya. Tsirulik

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

At present, the state of commutation is assessed mainly by the level of sparking of the brushes, expressed in points according to GOST 183-66. The possibility of such an assessment is due to the fact that the intensity of sparking determines the intensity of destruction of the commutator and brushes. It is known that visual assessment of sparking is subjective; therefore, researchers attach great importance to the development of objective methods for assessing sparking at the commutator [1, 2, 3].

When determining the quantitative dependence between technological deviations of the parameters of the magnetic system and of the commutator-brush assembly and the commutation state of DC machines, the problem arises of an objective assessment of sparking on a continuous scale over the commutator as a whole. In this case, the signal selected for assessing sparking must be easily measured on production machines.

The sparking process has several degrees of freedom: the number of sparking points along the length of the brush edge, the intensity of the sparks, their color, etc. Therefore, an exact assessment of the sparking level can only be multidimensional. According to the cybernetic theory of technological diagnosis, the possibility of assessing and diagnosing sparking is determined by the choice of such a diagnostic signal as is generated by the processes subject to diagnosis. In this case, the signal must have a dimensionality no less than the number of degrees of freedom of the process under investigation. A multidimensional signal is one that has the character of noise, that is, one whose time realization has a sharply intersected, oscillatory character, like a noise oscillogram [4].

These requirements are best satisfied by an oscillogram of voltage pulses at the trailing edge of the brush, measured around the entire circumference of the commutator with the aid of an additional brush installed in the plane of the trailing edge of the main brush [2, 3]. This signal is generated by processes occurring under the brush at the final stage of commutation; therefore, it carries objective information about sparking at all commutator bars. It is used for diagnosing the state of the commutation system [2]: checking the state of the commutator, revealing the degree of nonidentity of commutation cycles, and the correctness of the adjustment of the additional poles.

Our task was to construct a sparking scale on the basis of selected signal parameters. This is a typical classification problem, which in mathematical language is formulated as a method of finding such a function.

\[ \hat{И}=\varphi(V), \tag{1} \]

which, over the entire specified space of realizations of \(И\), would approximate the unknown function

\[ И=\psi(V) \tag{2} \]

with a certain accuracy.

Here

\(И\) is the value of sparking obtained from experiment;

\(\hat{И}\) is the value of sparking, for the same values of the signal parameters, obtained from the approximating equation;

\(V=(v_1, v_2 \ldots, v_n)\) is the vector of parameters \(v_i\) of the diagnostic signal.

The actual function (2) is constructed from experimental data by dividing the set of values of the signal vectors into \(q\) classes, when to each \(i\)-th class a number \(И_i\) is assigned. Such a sequence of experimental values \(V\), divided into classes, is called a “training sequence.” In our case, when dividing the values of \(V\) into classes, it is natural to take as a basis the GOST 183-66 scale and to assign to the sparking classes \(1\), \(1^{1/4}\), \(1^{1/2}\), \(2\) the numbers, respectively, \(1\), \(1.25\), \(1.5\), \(2\).

The determination of the approximating function (1) can be carried out by various methods. In the present case this was done by the method of least squares (m.l.s.); in this method the unknown coefficients of the approximating polynomial are found by solving the system of “normal” equations compiled with allowance for minimization of the quadratic form

\[ \sum[\psi(V)-\varphi(V)]^2=\min. \tag{3} \]

The selected signal, like any phenomenon of nature, possesses qualitative infinity; however, practical needs make it possible, from the infinite set of signal parameters, to fix only those that carry the greatest information about sparking and its causes. Studies by L. L. Lavrinovich and K. Binder have established that the most essential parameters describing the oscillogram of the voltage at the trailing edge of the brush are the height \(h\) and duration \(\tau\) of the voltage pulses on individual commutator bars. Thus, an oscillogram interpreted as a complex signal, representing a multidimensional random function, can be represented in simplified form by a two-dimensional probability distribution law for the heights and durations of voltage pulses. The question of choosing a system of parameters for describing the signal when constructing the sparking scale cannot be resolved in advance. The criterion of sufficient resolving power of the selected system of parameters is the sufficient adequacy with which the obtained dependence describes the experimental “training sequence.”

In the present work the assessment of sparking is constructed on the basis of characteristics of the distribution law of pulse heights, that is, on the basis of a one-dimensional section of the two-dimensional distribution function of pulse heights and durations. The distribution of pulse heights carries a sufficient amount of information about the state of the commutation system and about sparking at the commutator. In addition, the duration of the pulses is correlated with their height.

The following characteristics were chosen as the signal parameters:

1. \(\bar{h}\) — the mean value of the heights of all (positive and negative) pulses. This is the value of the ordinate of the mean line

oscillograms characterizing the correctness of the adjustment of the commutating poles.

1. \(\overline{|h|}\) is the mean value of the moduli of the heights of all pulses, depending on the adjustment of the commutating poles, the condition of the commutator surface, and the contact pressure.

2. \(\sigma_{|h|}\) is the root-mean-square deviation of the moduli of the pulse heights, depending most strongly on the condition of the commutator surface.

To implement the “training sequence,” an experiment was carried out in which 30 machines of the P series, of frame sizes 1, 2, and 3, were investigated. Different sparking conditions at the commutator were obtained by varying the excitation current of the commutating poles, the contact pressure, and the mechanical operating conditions of the brushes. In each test, a group of observers consisting of five persons visually recorded the sparking class in points, and at the same time an oscillogram of the signal was photographed from the oscilloscope screen. To determine the scale, an oscillogram of a reference sinusoidal voltage was also photographed. The signal parameters were computed after measuring the oscillogram on a Promin digital computer. In all, 270 oscillograms were processed \((N=270)\). The “training sequence” is written in a table of the following form:

The approximating function was preliminarily specified by a first-degree polynomial:

\[ \hat{И}=a_0+a_1\cdot x_1+a_2\cdot x_2+a_3\cdot x_3. \tag{4} \]

By the method of least squares, the system of normal equations for finding the regression coefficients \(a_i\) has the form:

\[ a_0\cdot X_0\cdot X_j+a_1\cdot X_1\cdot X_j+a_2\cdot X_2\cdot X_j+a_3\cdot X_3\cdot X_j=X_j\cdot И, \tag{5} \]

where

\[ X_i\cdot X_j=\sum_k^N x_{ik}\cdot x_{jk} \]

is the scalar product of the column vectors of the parameters \(x_i\) and \(x_j\) of the table of experimental data.

\[ X_j\cdot И=\sum_k^N x_{jk}\cdot И_k \]

is the scalar product of the column vectors of the parameter \(x_j\) and the sparking \(И\).

Solving the system leads to the following dependence of the brush sparking level on the selected signal parameters:

\[ \hat{И}=0{,}9925-0{,}0256\cdot \overline{h}-0{,}0683\cdot \overline{|h|}+0{,}158\cdot \sigma_{|h|}. \tag{6} \]

To check the adequacy of the equation, the residual sum of squares \(S_R\) and the multiple correlation coefficient \(R\) were computed:

\[ S_R=\sum_k^N И_k^2-\sum_{i=0}^3 a_i\cdot \sum_{k=1}^N x_{ik}\cdot И_k=1{,}0887. \tag{7} \]

\[ R=\sqrt{1-\frac{S_R}{\sum (И-\bar{И})^2}}=0.992. \]

The lower confidence limit for \(R\) at a 99 percent confidence probability is \(R_{\mathrm{n}}=0.986\) [5].

Since \(R\) is close to unity, the adequacy of the equation obtained is high.

For greater confidence in conclusions about the possibility of assessing sparking by means of the parameters of the distribution law of pulse heights, one more relationship was found in which the area \(S\) (Fig. 1) under the curve \(F_1(h)=1-F(h)\) was taken as the signal parameter, where \(F(h)\) is the integral distribution curve of pulse heights:

\[ F(h)=P\{H<h\}. \tag{8} \]

The parameter \(S\) characterizes the probability that pulses fall in the region \(h>h_{\mathrm{cr}}\), and depends on the height and on the length of the “tail” of the function \(F_1(h)\). The height of the tail ordinates depends on the number of pulses, and the length on the pulse heights. Therefore the parameter \(S\) must be objectively related to the intensity of sparking.

Fig. 1.

The ordinates of the curve \(F_1(h)\) are easy to determine from an oscillogram by counting the accumulated frequencies of pulses \(Q_h\) for various values of \(h\). The accumulated frequency is the number of pulses exceeding the level \(h\). The area \(S\) is determined from a certain critical voltage \(h_{\mathrm{cr}}\), at which the first sparking visible to the eye may appear. Observations showed that for EG74 brushes this voltage is equal to 6 V. To verify this conclusion, three “training sequences” were constructed for \(h_{\mathrm{cr}}=2\) V, 4 V, and 6 V. It turned out that nonoverlapping estimates occur only at \(h_{\mathrm{cr}}=6\) V.

The values of the function \(F_1(h)\) were determined discretely at \(h=2, 4, 6, 8, 12, 16, 20, 24,\) and \(28\) V.

Processing the experiment by the least-squares method made it possible to obtain the following formula:

\[ \hat{И}=1.14+0.00515\cdot S. \tag{9} \]

Here the parameter \(S\) is expressed in volts. The multiple correlation coefficient characterizing the adequacy of the formula (taking into account the influence of the discreteness of the sparking estimate according to the GOST scale) is \(R=0.998\), with a lower confidence limit \(R_{\mathrm{n}}=0.997\) at a 99 percent confidence probability.

The constant 1.14 in expression (9) corresponds to the boundary between

sparkless commutation and commutation with sparking on a continuous scale.

The high adequacy of the obtained dependences of the sparking level on the signal parameters indicates the possibility of an objective assessment of sparking by means of the parameters of the distribution law for the heights of voltage pulses at the trailing edge of the brushes. The dependences obtained are valid for EG74 brushes. Similar dependences can be found for brushes of other grades.

Although in the experiment sparking was assessed visually, the subjectivity of the assessment was nevertheless smoothed out by averaging the assessments of individual observers. The construction of an approximating function completely eliminates subjectivism and makes it possible to assess sparking directly on the basis of the signal parameters.

REFERENCES

1. L. L. Lavrinovich. Sparking in a sliding contact, Vestnik elektropromyshlennosti, 1957, No. 2.

2. M. F. Karasev. Commutation of DC Machines, GEI, 1955.

3. M. F. Karasev, V. P. Paramzin, I. V. Senkevich. Sparking indicator, Proceedings of OMIIT, issue 54, Omsk, 1965.

4. B. V. Pavlov. Cybernetic Methods of Technical Diagnosis, “Mashinostroenie,” Moscow, 1966.