Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov

Vol. 212　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1971

Calculation of Dynamic Current-Voltage Characteristics of a Sliding Contact

R. F. Bekishev, B. I. Kostylev, A. I. Skorospelkin

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

As is known, under normal operating conditions of the commutator-brush unit of an electrical machine, the dynamic current-voltage characteristics reflect the properties of the sliding brush contact quite completely. Therefore, in calculating commutation it is necessary to use precisely the dynamic current-voltage characteristics. The main difficulty in using dynamic current-voltage characteristics in commutation calculations consists in the fact that the latter have been obtained only experimentally during operation of an electrical machine. However, in order to ensure high reliability of a commutator machine, which is determined mainly by commutation factors, it is necessary to know the dynamic current-voltage characteristics of the sliding contact of the electrical machine at the design stage.

Thus, the question of developing a method for calculating dynamic current-voltage characteristics using certain parameters of the sliding brush contact obtained on models or artificial installations arises with full necessity.

As the analysis of the equivalent circuit of the sliding brush contact of a commutator electrical machine proposed in [1] shows, dynamic current-voltage characteristics can be calculated from the indicated equivalent circuit using parameters obtained when recording static current-voltage characteristics on a short-circuited commutator. The method for determining the parameters of the equivalent circuit is set forth in [1]. By this method the parameters of the equivalent circuit of the sliding brush contact were determined for various brush grades (EG-49, EG-14, EG-8, EG-74), which are given in Table 1.

Table 1

The static current-voltage characteristics needed to determine the parameters of the equivalent circuit were taken on a short-circuited collector while maintaining a constant temperature \((50^\circ\mathrm{C})\) at each point of the characteristic.

Radial and tangential oscillations of the brushes have a substantial effect on the magnitude of the mean resistance between the brush and the collector film. Using the data of studies [2], the resistance \(r_{\mathrm{sh}}\) in the presence of oscillations can be determined from the expression

\[ r_{\mathrm{sh}} = r_{\mathrm{sh}0}(1 + m \sin \omega t)(1 + m' \sin \xi \omega' t); \tag{1} \]

where

\[ \begin{aligned} r_{\mathrm{sh}0} &\text{ is the resistance between the brush and the collector film, corresponding to a given pressure in the absence of brush oscillations and depending on the brush grade;}\\ m \text{ and } m' &\text{ are the depths of resistance modulation by, respectively, tangential and radial oscillations of the brushes.} \end{aligned} \]

The current-voltage characteristic of the nonlinear leakage resistance \(R_{\mathrm{ut}}\) is determined for the brushes studied by a dependence of the form

\[ i_{\mathrm{ut}} = f(SU_{\mathrm{sl}}) = aSU_{\mathrm{sl}}^{\,n}, \tag{2} \]

where \(a\) and \(n\) are constants characterizing the brush grade,

\(S\) is the contact area of the lamella with the brush,

\(U_{\mathrm{sl}}\) is the voltage across the blocking layer.

The current-voltage characteristic of the resistance of the semiconducting blocking layer \(R_{\mathrm{ac}}\) for brushes EG-49, EG-14, EG-8, EG-74 can be represented by the expression

\[ i_{\mathrm{ac}} = \varphi(U_{\mathrm{sl}}) = bU_{\mathrm{sl}}^{\,k}, \tag{3} \]

where \(b\) and \(k\) are constants characterizing the semiconducting properties of the collector film.

The dependence of the capacitance of the blocking layer, formed between the semiconducting cuprous-oxide film and the copper of the collector, on the magnitude and polarity of the applied voltage can be represented by expression (4), characteristic of cuprous-oxide semiconductors,

\[ C = S_{\mathrm{l}}\frac{A}{2 - U_{\mathrm{sl}}}, \tag{4} \]

where

\(S_{\mathrm{l}}\) is the total contact area of the lamella \((\mathrm{cm}^2)\),

\(A\) is a rectifier constant.

The calculation of the dynamic current-voltage characteristics is carried out by the method of [1] for a specified lamella current. The voltage drop in the sliding contact for brushes of both polarities is determined from the expression

\[ U = U_{\mathrm{sl}} + U_{\mathrm{sh}} = \int_{0}^{T} \left[ \left( i_{\mathrm{l}} - aS_{\mathrm{t}}U_{\mathrm{sl}}^{\,n} - bU_{\mathrm{sl}}^{\,k} \right) \frac{(2 - aU_{\mathrm{sl}})^2}{S_{\mathrm{l}}A} \right]dt + \frac{r_{\mathrm{sh}}}{S_{\mathrm{t}}}\cdot i_{\mathrm{l}}, \tag{5} \]

where

\(i_{\mathrm{l}}\) is the instantaneous value of the lamella current,

\(T\) is the period of the lamella current,

\(S_{\mathrm{t}}\) is the instantaneous value of the contact area of the lamella with the brush.

Since the resistance of the semiconducting layer \(R_{\mathrm{ac}}\) under a cathode-polarized brush may be taken as infinitely large, for calculating the contact voltage drop between the brush of the given polar-

… and the commutator; in expression (5) the coefficients $b$ and $a$ are set equal to zero.

The influence of radial and tangential vibrations is taken into account on the average through the resistance $r_{\mathrm{sh}}$. The procedure for calculating dynamic current-voltage characteristics was verified both on actual electrical machines [1] and on artificial installations of the short-circuited-commutator type.

Thus, on an artificial installation developed by the authors [3], pulsed dynamic characteristics were obtained for a brush contact formed by brushes of different polarity sliding along a common track on a short-circuited commutator. The duration of the current pulse was varied within the range of 100–1750 $\mu\mathrm{s}$, and the amplitude from 5 to 30 A. During the study, the current pulse and the curve of the contact voltage drop between the brush and the selected commutator segment, insulated from the other plates, were recorded simultaneously using a two-beam C1-16 oscillograph.

The segment-current pulse obtained by oscillography was used to calculate the curve of the contact voltage drop. The voltage drop between the brush of the corresponding polarity and the commutator plate during contact was determined from expression (5) by a numerical method. In the calculation, the changing area of contact between the segment and the brush was used; the nature of its variation is determined by the brush overlap $b_{\mathrm{sh}} = 3 b_{\mathrm{k}}$. The calculation was performed for EG-4E and EG-74 brushes of both polarities.

Figures 1 and 2 show the pulses of segment currents obtained by oscillography on the experimental installation, as well as the experimental and calculated (dashed lines) curves of the contact voltage drop.

Fig. 1. Solid lines—experimental; dashed lines—calculated

The analysis of the experimental curves of contact voltage drop and of those obtained as a result of calculation shows their sufficiently good agreement. The root-mean-square error is 12%. Attention is drawn …

Fig. 2. Solid lines are experimental; dashed lines are calculated.

a significant irregularity of the experimental curves of the contact voltage drop is observed, which is not found on the calculated curves. This is explained by the influence of mechanical factors, which are taken into account by the resistance \(r_{\mathrm{sh}}\) only as an average over the commutator. As can be seen from Fig. 2, the contact voltage drop for EG-74 brushes is subject to larger oscillations. Indeed, as studies [2] have shown, when EG-74 brushes are used, tangential and radial oscillations have a significant effect on the modulation of the contact voltage drop. Therefore, when calculating the contact voltage drop for hard brushes, it is necessary to take into account the influence of the mechanics of the commutator–brush assembly by means of expression (1).

When soft brushes (EG-49) are used, the influence of brush oscillations is weaker, and, with the commutator in satisfactory mechanical condition, the oscillograms show no noticeable irregularities in the curves of the contact voltage drop (Fig. 1). Therefore, in this case the mechanical factors can be taken into account by the average resistance \(r_{\mathrm{sh}}\) over the commutator, which is determined from the static current–voltage characteristics.

In addition, using the indicated method, calculations were carried out for dynamic current–voltage characteristics under a symmetric triangular current pulse of constant duration and with different types of variation in the apparent area of contact between the lamella and the brush.

Figure 3 presents the current pulses with amplitude \(10\,a\) and duration \(600\,\mu\text{s}\), adopted for the calculation, as well as the curves of the contact voltage drop between the brushes of both polarities and the commutator lamella, obtained as a result of the calculation. As can be seen from the curves (Fig. 3), the contact voltage drops \(U_{\mathrm{k}}\) and \(U_{\mathrm{a}}\) considerably exceed the magnitude of the voltage drop across the resistance \(r_{\mathrm{sh}}\). Only in the case of high current densities at the trailing or leading edges of the brush is the voltage drop across the blocking semiconducting layer insignif-

Fig. 3

… and the contact voltage drop is determined mainly by the value \(U_{\mathrm{sh}}\).

The dynamic current–voltage characteristics \(U_{\mathrm{sh}} = f(i_{\mathrm{l}})\), obtained as a result of the calculations performed for different patterns of variation of the apparent contact area of the lamella with the brush, are presented in Fig. 4.

The analysis shows that the outline of the current–voltage characteristics is determined by the magnitude and the nature of the variation of the current density in the contact. If the pulse of the lamella current corresponds in time to the pattern of variation of the contact area of the lamella with the brush, the contact voltage drop is constant during the period of the lamella current, and the ascending and descending branches of the characteristic coincide. When the current pulse of the lamella corresponds in time to the increase in the contact area of the lamella with the brush, which is characteristic of accelerated commutation, the ascending branch of the characteristic lies above the descending branch (Fig. 4, б). Finally, in the case of delayed commutation, when the current pulse of the lamella corresponds in time to the running-out of the collector plate from under the brush, the descending branch of the current–voltage characteristic lies above the ascending branch (Fig. 4, в).

Comparison of the pulsed current–voltage characteristics obtained experimentally [4] and those calculated by the proposed method gives complete qualitative agreement.

Fig. 4

Thus, the results of the work clearly show that the proposed method makes it possible to determine the parameters of a sliding brush contact and to calculate the dynamic current-voltage characteristics at the design stage of an electrical machine.

REFERENCES

1. B. I. Kostylev, R. F. Bekishev, A. I. Skorospeshkin. Current-voltage characteristics of a sliding contact in static and dynamic operating modes. Izvestiya TPI, vol. 190, 1968.

2. L. Ya. Zinner. Investigation of the influence of mechanical factors on commutation in collector electrical machines. Dissertation, Tomsk, 1968.

3. L. Ya. Zinner, A. I. Skorospeshkin, E. K. Damm, V. P. Karataev. Apparatus for the experimental investigation of the sliding brush–collector contact. Izvestiya TPI, vol. 212, 1969.

4. Z. B. Vartanov. Pulsed current-voltage characteristics of a brush contact. VEI, 1957, No. 2.