Generalized dynamic current-voltage characteristic of a carbon brush–commutator sliding contact

Generalized Dynamic Current–Voltage Characteristic of a Sliding Carbon Brush–Commutator Contact

E. K. Damm, L. Ya. Zinner, A. I. Skorospeshkin

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

The calculation of commutation and commutation stability of direct-current machines is possible only when exhaustive information is available on the behavior of the sliding contact under various conditions of its operation. Taking into account the diversity of factors affecting the electrical properties of a sliding contact, it is expedient to obtain its mathematical model by an experimental-statistical method.

Let us briefly recall the essence of the method [1].

A system under investigation, the mechanism of phenomena within which has not been fully studied (in the present case this is the sliding contact), is acted upon by factors \(x_i\) (in the present case these are factors that substantially affect the form of the current–voltage characteristic of the sliding contact). At the output, a quantity \(y\) is measured that quantitatively describes the current–voltage characteristic. The problem reduces to determining the function

\[ y = f(x_1, x_2, \ldots x_n). \]

Since the form of the function is unknown, it is represented by a polynomial of the form

\[ y = b_0 + \sum b_i x_i + \sum b_{ii} x_i^2 + \sum b_{ij} x_i x_j, \]

where the coefficients \(b_0, b_i, b_{ii}, b_{ij}\) are to be determined. The input factors \(x_i\) are varied according to a certain program; the coefficients \(b_0, b_i, b_{ii}, b_{ij}\) are determined on the basis of processing the experimental results by the method of regression analysis.

The experiment was carried out on an installation described in detail in [2]. The commutator, two opposite bars of which are short-circuited, is driven by a direct-current motor whose rotational speed can be varied within the range from 300 to 2500 rpm.

During the time when both working commutator bars are under the brushes, a current pulse from a special pulse installation is passed through the circuit that has been formed. The amplitude of the pulse, its duration, shape, and also its spatial position relative to the arc of contact of the bar with the brush can be varied within sufficient limits. During one revolution of the commutator, the installation delivers, at equal time intervals, 2 completely identical pulses, so that each bar is alternately anodically and cathodically polarized, as occurs in a real machine. In order not to introduce additional errors, the same brush was used in all measurements, while the polarity was changed by switching the pulse source.

The use of a special brush holder makes it possible smoothly to regulate the pressure on the brush; heating of the commutator and brushes is carried out at ...

using a spiral; the commutator temperature is measured by means of a thermocouple whose junction is placed in a hole at the end of one of the working bars.

Since in the present case the influence of various factors on the current–voltage characteristic of the sliding contact is considered, the coefficients of the approximating expressions were taken as the input parameters.

Fig. 1.

The current–voltage characteristics of the soft brush of grade EG-4E were approximated by the expression

\[ U = A \operatorname{arctg} Bj, \tag{1} \]

where \(U\) is the transition voltage drop in the contact;
\(j\) is the current density in the contact;
\(A\) and \(B\) are coefficients constant for the given characteristic.

Fig. 2.

The current–voltage characteristics of the hard brush of grade EG-74 are more correctly approximated by the expression

\[ U = A \operatorname{arch} Bj, \tag{2} \]

which has no asymptotes, since the voltage drop under the EG-74 brush increases without bound as the current density increases, in contrast to the EG-4E brush, for which at high current densities the transition voltage drop is practically stabilized.

Initially it was proposed to take the following as input factors:

\(x_1\) — average current density during the first commutator-bar period of contact between the bar and the brush,
\(x_2\) — temperature of the brushes and commutator,
\(x_3\) — specific pressure on the brush,
\(x_4\) — linear velocity of the commutator surface.

But subsequently it turned out that the velocity factor in this case did not exert a significant unidirectional influence on the form of the current–voltage characteristic.

[Figure: graph; vertical axis \(\Delta u\), V; horizontal axis \(i\), A/cm\(^2\).]

Fig. 3.

As an example, Figs. 1 and 2 show oscillograms of the current and transient voltage drop of a cathode-polarized EG-74 brush for circumferential speeds respectively equal to 2.09 m/s and 8.4 m/s at \(x_1 = 55\ \frac{\text{A}}{\text{cm}^2}\), \(Q_k = 70^\circ\text{C}\), \(p = 250\ \frac{\text{g}}{\text{cm}^2}\). The corresponding current–voltage characteristics are shown in Figs. 3 and 4. Comparison shows their almost complete coincidence.

[Figure: graph; vertical axis \(\Delta u\), V; horizontal axis \(i\), A/cm\(^2\).]

Fig. 4.

It should be noted in passing that, before the experiment was carried out, the commutator surface was very carefully treated with a P30 abrasive block, with simultaneous observation of the oscillogram of the commutator profile obtained using a profile meter [3]. The total runout of the commutator did not exceed 4–5 microns, and the steps between adjacent commutator plates did not exceed 1 micron. The relative humidity of the air was, as far as possible, maintained constant, equal to 55%.

Table 1

In accordance with the foregoing, a plan was drawn up for rotatable uniform planning of the second order for three independent variables varied at three levels (Table 1). The limits of variation of the input parameters were chosen from the operating conditions of real machines (Table 2).

Table 2

The experiment was carried out in the following order. After mechanical treatment of the commutator surface, all bars were short-circuited, and a normal commutator film was formed by direct current over the course of 100–150 hours. After this the commutator was opened, two working plates were selected, and the brushes were connected to the pulse installation. First all experiments were performed at one brush pressure, then at another, and so on. After the brush pressure was changed, the latter was again carefully run in to the commutator for 10 hours. At a given pressure, the experiment was first performed for the smallest value of $x_1$, then for a larger value, and so on. In each test the curves of the bar current and of the contact voltage drop for both brush polarities were photographed from the screen of a dual-beam oscilloscope. After processing, for the volt-ampere characteristics obtained, the coefficients of the approximating expressions were found; for an EG-74 grade brush these are given in Table 1. As output parameters, $A$ and the product $AB$ were adopted, since the latter has a definite physical meaning. $AB$ is numerically equal to the specific contact resistance at zero current density.

Below are given expressions for the generalized characteristic of an EG-74 grade brush, obtained as a result of processing the experimental results presented in Table 1.

\[ U_{\mathrm{k}}=A_{\mathrm{k}}\operatorname{arsh}\frac{A_{\mathrm{k}}B_{\mathrm{k}}}{A_{\mathrm{k}}}\,j \tag{3} \]

\[ U_{\mathrm{a}}=A_{\mathrm{a}}\operatorname{arsh}\frac{A_{\mathrm{a}}B_{\mathrm{a}}}{A_{\mathrm{a}}}\,j, \tag{4} \]

where $U_{\mathrm{k}}$ is the contact voltage drop between the bar and the brush of cathodic polarity;

$U_{\mathrm{a}}$ is the contact voltage drop between the bar and the brush of anodic polarity;

\[ \begin{aligned} A_{\mathrm{k}}={}&0.44+0.05563x_1-0.052x_2-0.08238x_3+0.0203x_1^2\\ &-0.0125x_2^2-0.004x_3^2+0.029x_1x_2+0.014x_1x_3+0.01781x_2x_3; \end{aligned} \tag{5} \]

\[ \begin{aligned} A_{\mathrm{k}}B_{\mathrm{k}}={}&0.0767-0.0207x_1-0.01208x_2-0.0235x_3+0.0039x_1^2\\ &-0.00589x_2^2+0.0043x_3^2+0.0008625x_1x_2+0.0000375x_1x_3+0.00136x_2x_3; \end{aligned} \tag{6} \]

\[ \begin{aligned} A_{\mathrm{a}}={}&0.3755-0.01449x_1-0.05257x_2-0.03016x_3-0.0059x_1^2\\ &-0.0378x_2^2+0.0103x_3^2-0.0416x_1x_2-0.07375x_1x_3-0.04062x_2x_3; \end{aligned} \tag{7} \]

\[ A_{\mathrm{a}}B_{\mathrm{a}}=0.0521-0.01103x_1-0.008439x_2-0.00762x_3-0.002x_1^2- \]

\[ -0.00031x_2^2 + 0.00167x_3^2 - 0.00297x_1x_2 + 0.000925x_1x_3 + 0.00405\,x_2x_3. \tag{8} \]

In expressions (5)—(8)

\[ x_1=\frac{j_{\mathrm{av}(t_k)}-50}{17.2};\quad x_2=\frac{\theta_k-70}{10};\quad x_3=\frac{p-250}{50}, \]

where

\(j_{\mathrm{av}(t_k)}\) — average current density in the contact during the first lamellar period of contact of the lamella with the brush, \(\dfrac{a}{\mathrm{cm}^2}\);

\(\theta_k\) — commutator temperature, °C;

\(p\) — specific pressure on the brush, \(\dfrac{G}{\mathrm{cm}^2}\).

The expressions obtained make it possible to obtain the current-voltage characteristics of the sliding contact when the conditions of its operation vary within the limits defined by Table 2.

To make sure that, in planning the experiment, all factors substantially affecting the form of the current-voltage characteristics were taken into account, one can calculate the multiple-correlation coefficients for the output parameters.

\[ R=\sqrt{1-\frac{\sum (y-\hat{y})^2}{\sum (y-\bar{y})^2}}, \]

where \(y\) — mean value of the output parameters;

\(\hat{y}\) — values of the output parameters determined from the regression equation obtained;

\(\bar{y}\) — values of the output parameters obtained from the experiment.

Table 3

The values of the indicated coefficients are given in Table 3. If \(R=1\), this means that all factors affecting the output quantity have been taken into account. The values of the coefficients \(R\) obtained in the present case indicate that all substantially affecting factors were taken into account. The share of unaccounted and uncontrolled factors is no more than 9%, which is quite satisfactory for such an object as a brush contact.

Consideration of the equations for generalized current-voltage characteristics shows that the factor \(x_1\) has a very substantial influence. The form of the contact current-voltage characteristic depends to a large extent on the conditions under which the contact conductance is formed in the first lamellar period of contact. This was first pointed out in [4].

In Fig. 5, curve II represents the static characteristic of an EG-4E anode brush, taken on a short-circuited commutator at \(\theta_k=70^\circ\mathrm{C}\), \(p=250\,\dfrac{G}{\mathrm{cm}^2}\), with increasing current density. Curve I represents the dynamic characteristic taken on the above-described experimental setup at the same values of \(\theta_k\) and \(p\). The only difference was that the current density in the contact at the initial moment of contact of the lamella with the brush was approximately \(90\,\dfrac{a}{\mathrm{cm}^2}\), decreasing by the end of the contact period to zero, as occurs in accelerated commutation.

Comparison of curves I and II shows their significant divergence at relatively small current densities. The contact resistance at small

at current densities under the real conditions of its operation (curve I′) proves to be significantly smaller than that determined by the static characteristic (curve II′).

Thus, the result of the investigation carried out is the development of a method for calculating the generalized dynamic current–voltage characteristic of the brush contact. This method makes it possible to take into account the principal factors (temperature, current load and the nature of commutation, the change in contact pressure in the presence of radial vibrations of the brushes) that determine

Fig. 5.

the current–voltage characteristic of the brush contact, and to introduce it into the commutation calculation with sufficient reliability.

REFERENCES

1. V. V. Nalimov, N. A. Chernova. Statistical Methods for Planning Extremal Experiments. Nauka Publishing House, Moscow, 1966.

2. A. I. Skorospeshkin, L. Ya. Zinner, E. K. Damm, V. P. Korotaev. Installation for experimental investigation of the sliding brush–commutator contact. Izv. TPI, vol. 212 (in press).

3. L. Ya. Zinner, A. I. Skorospeshkin. Instrument for measuring small displacements. Izv. TPI, vol. 172, 1967.

4. Yu. P. Galishnikov, A. I. Skorospeshkin. Natural current–voltage characteristics of the sliding contact carbon brush–commutator. Izv. TPI, vol. 172, 1967.