DIAGNOSTICS OF SPARKING AT THE COMMUTATOR IN DC MACHINES

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

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

It is known that the limit of application of DC machines is determined by commutational reliability.

The main cause of sparking of electric brushes is the nonidentity of commutation cycles [1], caused by technological deviations and by the action of mechanical factors. The most important problem in increasing the reliability of DC machines is the development of an optimal system of tolerances for the indicated parameters, ensuring stable commutation during a prescribed period of operation.

The intensity of sparking cannot be assessed by any single parameter. With a one-dimensional assessment of sparking, it is also impossible to solve the problem of recognizing the causes of sparking, owing to the ambiguity of the vector of input factors at a given level of the output parameter, which makes it difficult to develop measures for increasing reliability. The need to solve these problems within reasonable time limits has led to the use of cybernetic methods of technical diagnosis as a means of analyzing commutation [2].

Diagnostics belongs to methods of indirect measurement of the parameters of machine elements that are not accessible to direct observation. Instead of them, the parameters of processes generated by the operating machine and accessible to measurement are measured.

We shall call the totality of the internal properties of a machine (the vector of input factors) its state. External processes that are carriers of diagnostic information will be called signals.

The signal space is a mapping of the state space. For diagnosis to be feasible, this mapping must be one-to-one, and this is possible only when the number of independent signal parameters is equal to the number of degrees of freedom of the machine, that is, to the number of input factors. Obtaining a multidimensional signal is possible both by installing the corresponding number of sensors and by using a single sensor that measures a complex signal having the character of noise. The latter is most convenient.

As the diagnostic signal we use an oscillogram of voltage pulses under the trailing edge of the brush, measured by means of an auxiliary brush. The oscillogram is photographed from an oscillograph and processed in order to determine the parameters of the distribution law of the heights of the voltage pulses. As the parameters, the first four moments of the distributions of the moduli of the heights are chosen.

pulses and heights with signs. The appeal to this type of signal is due to the following.

1. The oscillogram of voltage pulses under the trailing edge of the brush has the character of a noise signal and, consequently, can be represented by a large number of independent parameters. The method of commutation adjustment with the aid of such an oscillogram is widely used by researchers and practitioners [1]. The oscillogram carries information about the correctness of the adjustment of the auxiliary poles, about the condition of the commutator surface, and about the degree of identity of the commutation cycles. In fact, this method is already used for diagnostics of sparking, but it has not been formalized.

2. The possibility of a comparatively simple method of obtaining a signal on production machines under factory conditions.

The development of a diagnostic algorithm by experimental-statistical methods consists in finding an operator for transforming the space of signals into the space of state parameters, that is, in determining the dependencies:

\[ \begin{aligned} y_1 &= \varphi_1(x_1,\ x_2,\ \ldots,\ x_i,\ \ldots,\ x_n),\\ y_2 &= \varphi_2(x_1,\ x_2,\ \ldots,\ x_i,\ \ldots,\ x_n),\\ &\cdot\quad \cdot\quad \cdot\quad \cdot\quad \cdot\quad \cdot\quad \cdot\\ y_k &= \varphi_k(x_1,\ x_2,\ \ldots,\ x_i,\ \ldots,\ x_n),\\ &\cdot\quad \cdot\quad \cdot\quad \cdot\quad \cdot\quad \cdot\quad \cdot\\ y_n &= \varphi_n(x_1,\ x_2,\ \ldots,\ x_i,\ \ldots,\ x_n), \end{aligned} \]

where \(y_k\) is the \(k\)-th signal parameter;
\(x_i\) is the \(i\)-th input parameter;
\(n\) is the number of input parameters.

Each of the functions \(y_k\) is determined by the method of regression analysis in a statistically planned experiment [3, 4]. The form of the function \(y_k\) is specified by a second-degree polynomial. Using formal linearization, equations (1) can be written in matrix form as a system of linear equations:

\[ Y = B \cdot X, \]

where \(Y\) is the column vector of signal parameters;
\(X\) is the column vector of state parameters;

\[ B = \left\| \begin{array}{ccccc} b_{10} b_{11} & \ldots & b_{1i} & \ldots & b_{1n} \\ b_{20} b_{21} & \ldots & b_{2i} & \ldots & b_{2n} \\ \cdot\ \cdot\ \cdot\ \cdot & \cdot & \cdot & \cdot & \cdot \\ b_{k0} b_{k1} & \ldots & b_{ki} & \ldots & b_{kn} \\ \cdot\ \cdot\ \cdot\ \cdot & \cdot & \cdot & \cdot & \cdot \\ b_{n0} b_{n1} & \ldots & b_{ni} & \ldots & b_{nn} \end{array} \right\| \]

is the matrix of influence coefficients;

\(b_{ki}\) is the coefficient of influence of the \(i\)-th factor \(x_i\) on the \(k\)-th signal parameter \(y_k\).

Finding the dependencies (1) reduces to determining the influence coefficients.

The diagnostic algorithm is written as the system of equations

\[ X = B^{-1} \cdot Y. \tag{3} \]

The set of signals is infinite and even uncountable; one level of sparking corresponds to an uncountable set of signal vectors in the signal space, and hence also to state vectors in the state space. Therefore, the further task in the study is to solve the classification problem, that is, to partition the signal space and

of the state space into regions corresponding to different sparking levels, for example, according to sparking scores.

The experiment was carried out on series P machines of the third frame size, having the following rated data: voltage—220 V, current 12.2 A, rotational speed 1500 rpm.

The following were adopted as input factors: brush pressure, eccentricity and ellipticity of the commutator surface, the root-mean-square deviation of the differences in the heights of the commutator segments, and the excitation current, whose optimum value should characterize the deviation from the optimum setting of the commutating pole for each machine.

Screening experiments were first conducted in order to identify and discard insignificant factors. Analysis of the experimental results made it possible to regard, at the specified rotational speed, the eccentricity and ellipticity of the commutator as insignificant and, at the first stage of the study, to confine consideration to three factors: excitation current \(J_p\), brush pressure \(P\), and the root-mean-square deviation of segment differences \(\sigma\).

Table 1 gives the ranges of variation by means of which the transition from the natural variables \(J_p, P\), and \(\sigma\) to the coded variables \(x_1, x_2, x_3\), respectively, is specified.

Table 1

The experiment was carried out according to a central composite rotatable uniform plan with \(n = 3\) [3]. The machines tested were selected so that the parameter \(\sigma\) varied in accordance with the plan. Complete orthogonality of the plan could not be achieved because of the limited possibilities of selecting machines with the required values of \(\sigma\).

The experimental design matrix is presented in Table 2. To determine the influence coefficients \(b_{ki}\), systems of normal equations are solved

\[ X'X \cdot B = X'Y_k, \tag{4} \]

where \(X'\) is the transposed matrix \(X\),
\(Y_k\) is the column vector of the values of \(y_k\) in the experiment.

The calculation of the signal parameters and the coefficients of the normal equations was carried out on a “Promin” digital computer, and the solution of systems (4) on a “Minsk-1” digital computer. The solution of system (4) is presented in Table 3 for the influence coefficients of the linear and quadratic terms and pairwise interactions for each signal parameter. Here \(y_1, y_2, y_3\), and \(y_4\) are, respectively, the mean, the root-mean-square deviation, and the third and fourth central moments of the distribution of pulse heights, while \(y_5, y_6, y_7\), and \(y_8\) are the same for the distribution of the moduli of the pulse heights.

The sparking diagnostic system being developed, in addition to its primary purpose, will serve as a basis for constructing an optimal system of tolerances for the input parameters and for developing a system for objective assessment of sparking.

Table 2

Table 3

References

1. M. F. Karasev. Commutation of DC commutator machines. Gosenergoizdat, Moscow–Leningrad, 1961.

2. B. V. Pavlov. Cybernetic methods of technical diagnosis. Mashinostroenie, Moscow, 1966.

3. V. V. Nalimov, N. A. Chernova. Statistical methods for planning extreme experiments. Nauka, Moscow, 1965.

4. Design of experiments. Nauka, Moscow, 1966.