Natural Current-Voltage Characteristics of the Sliding Contact Between a Carbon Brush and a Commutator

Yu. P. Galishnikov, A. I. Skorospeshkin

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

Earlier [1, 2] the authors, using a physical model of a sliding contact for the simplest case \(b_k = b_{\mathrm{ш}}\), showed that the current-voltage characteristic of a brush is closely connected with the conditions under which contact conductance is formed, namely with the time of contact formation and the current density at which it occurs. From the experimental material presented below it is clear that this fundamental conclusion is also valid for more complex cases of commutation. If the question is considered from the standpoint of the theory of electrical circuits, a sliding contact is a nonlinear element whose characteristic depends on the current flowing through it. The dynamic characteristic exhibited by the sliding contact in each particular case of commutation was called by the authors the partial natural current-voltage characteristic of the contact. In [2] it was also noted that the partial characteristic does not describe the contact as a whole with respect to its electrical properties.

It is quite clear that this by no means exhausts the problem of the dependence of the current-voltage characteristics of a sliding contact on its operating conditions. However, at the present stage of the work the authors did not set themselves the goal of investigating the influence of such factors as the relative humidity of the surrounding medium, atmospheric pressure, the natural scatter of the physicochemical properties of the brush material, etc. This would have taken them too far afield. The task was to develop, experimentally verify, and test a qualitatively new method of interpreting and taking account of the electrical characteristics of a sliding contact as applied to direct-current machines, since the existing methods, in the authors’ opinion, are far from satisfactory. It is precisely to this question that the previously published works [1, 2], as well as the authors’ papers published in the present collection, are devoted.

Some results of an experimental investigation of the natural current-voltage characteristics of the brush–commutator contact are set forth below. The investigation was carried out on a two-pole direct-current motor of the P series, frame size 3, prepared for this purpose. The test setup is described in sufficient detail in [3]. The motor power was 2.4 kW at a supply voltage of 175 V. The nominal current density in the brush contact was then 12 A/cm². The specific mechanical pressure on the brush was standard, about 200 g/cm². The brush holder was of the radial type with a cylindrical spring. The number of commutator bars simultaneously covered by the brush was 3. The winding

the armature was a simple lap winding with a diametral pitch. Before the investigations described, the motor had been run in for approximately 3000 hours, after which the commutator was ground and the bearings were replaced. A profilogram of the commutator surface, taken at the operating rotational speed of 2200 rpm, shows that the steps between adjacent bars do not exceed 1 μm, and the amplitude of runout is 20 μm. Thus, mechanical effects on the sliding contact are minimal.

The procedure for recording current-voltage characteristics reduces to oscillographing the commutation-current curves of two adjacent armature sections and the voltage drop between the commutator bar common to these sections and the brush of the corresponding polarity during the commutation period. Then, by simple constructions, the bar current and the density of this current are determined for the entire time during which the given bar remains under the brush. Next, by comparing time-coincident points of the current-density and contact-voltage-drop curves, the desired characteristic is constructed. A similar method was also used by other investigators [4, 5]. However, in the present work, in order to improve the method, the authors used a circuit with a reference diode for measuring the contact voltage; this makes it possible to reduce the total armature voltage applied to the oscilloscope input to 9 V while retaining the useful signal. The measurement accuracy is thereby substantially increased, since otherwise the oscilloscope preamplifier is overloaded by a voltage exceeding the measured one by two orders of magnitude.

In addition, unlike the works mentioned, on the machine under investigation only one brush was installed on each bracket, which makes it possible to determine the true values of the instantaneous current densities in the contact. In the case where there are several brushes on one bracket, when determining the current density it is easy to make a gross error because of the nonuniform distribution of current among the individual brushes.

For the measurements an S1-8 oscilloscope was used, having a pass band from direct current to 25 MHz.

All tests were carried out after thorough seating of the brushes and with a well-developed patina on the commutator; for this purpose, immediately after installation of brushes of a given grade, they were run in for approximately 300 hours at rated load.

The oscillographing of the curves was carried out as follows. First, a 2-hour warming-up of the machine at rated load and at optimum excitation of the interpoles was ensured. Next, an interpole supply current was set corresponding to the lower boundary of the sparkless-operation zone. After the contact had reached a certain dynamic equilibrium (holding for 1 hour), the current and contact-voltage-drop curves were oscillographed in succession in as short a time as possible. The interpole supply current was then changed, and after the corresponding holding time the next series of oscillograms was taken. In this order the curves of interest were recorded for a number of interpole supply currents, so that the entire zone of sparkless operation of the machine was covered.

In all cases the relative humidity of the ambient air was maintained at 40 ± 5%.

We shall consider the main results of the investigation of the current-voltage characteristics using brushes EG-49 as an example. Figure 1 (a, b) presents the curves of current and contact voltage drop for an anode-polarized brush, obtained at the rated current density in the contact of 12 A/cm² and an interpole supply current of +10% of \(I_n\), which corresponds approximately to the middle of the sparkless-operation zone.

As the oscillograms presented show, current reversal has time to occur mainly during the first commutator period, equal in this case

Fig. 1. Anode-polarized brush EG-49.
a) commutation-current curves of two adjacent armature sections,
b) curve of the contact voltage drop,
c) partial natural current-voltage characteristic at \(j_{\mathrm{n}} = 12\ \mathrm{A/cm^2}\).

in this case 450 μsec, while the subsequent change in current during the remaining commutation time proceeds considerably more slowly. The noted feature is, to a greater or lesser degree, characteristic of all the current oscillograms obtained. It is possible that it is not of general significance, but it is clear that the lower the specific resistance of the brush material, the faster the current changes at the beginning of commutation. Accordingly, the entry of a plate under the brush is characterized by a high current density. Depending on the degree of acceleration of commutation, the current density under the brush at the beginning of contact ranges from 90 to 500 A/cm². As the plate enters under the brush, the current density smoothly decreases from the maximum initial value, reaching values of 30–60 A/cm² by the end of the first commutator period. In the following very short time interval, when the adjacent section enters commutation, the current density in the contact drops sharply to 15–20 A/cm². Thereafter the contact current density changes more slowly in accordance with the bar current.

The oscillogram of the contact voltage drop (Fig. 1, b) can be divided into several characteristic regions. In the initial part

curve I there is always a short-duration peak of overvoltage, reaching 3–4 V and associated with the high current density. The next section of curve II, with a duration of about \(t_k\), is characterized by considerably lower voltages (1.2–1.5 V), despite the fact that the current density continues to remain relatively high. The decrease in contact voltage in this section is probably connected with the intensive formation or expansion of conducting spots by means of repeated frittage. The noticeable irregularity of the voltage curve in this part also points to frittage. In section III the curve is smoother, and the voltages here are lower than before. This means that the formation of contact spots in section III no longer takes place, except for the case when, owing to a certain undercommutation of the second adjacent section as the bar leaves from under the brush, the current density rises sharply, causing the contact voltage to increase to 3–4 V. During this very brief period there is also a definite decrease in the specific contact resistance. It should be noted, incidentally, that a voltage of about 4 V at the trailing edge of the brush causes sparking of grade \(1\frac{1}{4}\)—\(1\frac{1}{2}\).

Thus, it may be considered with complete justification that the time of formation of contact conductance in the given particular case is constant and equal to \(t_k\), and that the decisive influence on the current-voltage characteristic during this period is exerted by the current density, which varies over wide limits depending on the nature of commutation. As an indicator of the conditions of contact formation, in the general case one may successfully take the quantity

\[ \frac{j_0 + j_{t_k}}{2}\cdot t_k \frac{\mathrm{a}}{\mathrm{cm}^2}\cdot \mu\mathrm{s}, \tag{1} \]

where \(j_0\) is the current density at the beginning of contacting,

\(j_{t_k}\) is the current density after \(t_k\) microseconds from the beginning of contacting,

\(t_k\) is the commutator period.

The behavior of the brush contact under overcommutation is of interest. A change in the direction of the current causes the appearance of a contact potential of opposite sign, 0.5–0.7 V, which very actively contributes to sparkless completion of commutation. The corresponding oscillograms show that currents of opposite sign, both under positive and under negative brushes, are successfully brought to zero from 10 A and higher (the current density in the trailing bar reaches 45–60 A/cm\(^2\)).

On the contrary, with some retardation, the current density from values of 6–12 A/cm\(^2\) at the end of commutation rises sharply by the moment of rupture of the commutated circuit and, with sparking of grade \(1\frac{1}{4}\)—\(1\frac{1}{2}\), reaches on the order of 60–90 A/cm\(^2\). This, apparently, explains the fact that practically the entire zone of sparkless operation corresponds to overcommutation of greater or lesser degree.

In Fig. 2 (a, b) curves analogous to those considered are presented for the cathode-polarized EG-43 brush, which were obtained at the same current of excitation of the additional poles. Their general form is similar to those considered, but the level of the contact voltage is higher as a result of the polarity effect. The smaller relative magnitude of the overvoltage at the beginning of contacting indicates that, as was noted earlier [2], under a cathode-polarized brush there is a certain initial conductance, probably caused by copper particles deposited on the brush surface as a result of the transfer of positive ions through the contact gap.

The form of the experimentally obtained partial current-voltage characteristics (Fig. 1, c and 2, c) is very indicative. Each of them has

Fig. 2. Cathode-polarized EG-49 brush.
a) commutation-current curves of two adjacent armature sections,
b) curve of the contact voltage drop,
c) partial natural current-voltage characteristic at \(j_{\mathrm{n}} = 12\ \mathrm{A/cm^2}\)

a clearly expressed bend in the direction of the abscissa axis. It was noted earlier [2] that the current-voltage characteristic is the more strongly curved, the lower the specific resistance of the brush material. The characteristics, not presented here, for the EG-74 brush, which has an increased specific resistance, differ by having a significantly smaller curvature.

It is necessary, however, to note a certain straightening of the characteristic of the EG-49 brush in its initial part, which is the more pronounced the higher the current density during the period of contact formation. Unfortunately, this fact cannot be reflected with the chosen method of approximating the experimental curves.

The processing of the obtained current-voltage characteristics was carried out by the method of equal areas for a sequence of points. The empirical expression for the partial characteristic has the form:

\[ U = U_0 \cdot j^m, \tag{2} \]

where \(U_0\) is the contact voltage drop at unit current density \((j = 1 \text{ A/cm}^2)\);

\(m\) is a quantity depending on the general form of the characteristic.

The approximation was carried out under the condition \(m = \text{const}\) for all characteristics obtained with unchanged brush polarity. Otherwise, generalization of the experimental data is very difficult. The largest discrepancies for the curves of an anodically polarized brush are:

the mean linear discrepancy

\[ \Delta^{(1)} = \frac{\sum \Delta}{n} = 0.09, \]

the root-mean-square discrepancy

\[ \Delta^{(2)} = \sqrt{\frac{\sum \Delta^2}{n}} = 0.109 . \]

For the characteristics of a cathodically polarized brush the discrepancies are somewhat larger because of the greater irregularity of the curves.

The empirical dependence of \(U_0\) on the features of contact formation is expressed as follows:

\[ U_0 = \frac{C}{\left(\frac{j_0 + j_{tk}}{2} \cdot t_k\right)^n}, \tag{3} \]

where \(C\) and \(n < 1\) are constants. The corresponding graphs for the nominal current density in the contact of \(12 \text{ A/cm}^2\) are given in Fig. 3 \(a, b\) (curves 1). These curves, which have the form of a parabola, clearly show the dependence of the particular natural current-voltage characteristics on the conditions under which contact conductivity is formed. Indeed, at small values of

\[ \frac{j_0 + j_{tk}}{2} \]

the conducting spots under the brush are formed comparatively sluggishly, and the relative magnitude of the contact voltage drop, as shown by the curves in Fig. 3, increases noticeably in this case. Conversely, when

\[ \frac{j_0 + j_{tk}}{2} \]

increases with increasing degree of acceleration of commutation, a larger number of conducting spots is formed, or their dimensions increase, and as a result the contact voltage decreases.

The graphs presented show that the sliding contact tends to stabilize upon reaching sufficiently large values of

\[ \frac{j_0 + j_{tk}}{2} \, t_k . \]

This limiting state is reached when all possible contact points have already been realized.

Curves 2 in Fig. 3 were obtained at a nominal current density in the contact of \(6 \text{ A/cm}^2\). As can be seen, these curves are similar in general character to those considered above.

The regions enclosed between curves 1 and 2 describe the current-voltage characteristics for nominal current densities from 6 to \(12 \text{ A/cm}^2\) over a comparatively broad range of variation in the conditions of contact formation. If desired, one can, without particular difficulty, obtain a family of natural current-voltage characteristics for any intermediate current density.

On the basis of all that has been considered, the generalized current-voltage characteristic of the sliding contact for any nominal current density is represented by the expression:

Fig. 3. Dependences
\[ U_0 = U_0\!\left(\frac{j_0 + j_{tk}}{2}\cdot t_k\right) \]
for brush EG-4E:
a) anode-polarized brush,
b) cathode-polarized brush.

\[ U = \frac{C} {\left(\dfrac{j_0 + j_{tk}}{2}\cdot t_k\right)^n} \cdot j^m . \tag{4} \]

Expression (4) describes a family of partial natural current–voltage characteristics of the sliding contact and can be used in calculations of commutation and commutation stability of direct-current machines with various commutation conditions.

REFERENCES

1. A. I. Skorospeshkin, Yu. P. Galishnikov, E. G. Chebotkov. Electrodynamic properties of a sliding contact. Proceedings of the Second Scientific Session of Higher Educational Institutions, issue 5, 1966.

2. Yu. P. Galishnikov, A. I. Skorospeshkin. On the question of the instability of the dynamic current–voltage characteristics of the sliding contact carbon brush—commutator. Izvestiya TPI, vol. 160, 1966.

3. A. I. Skorospeshkin, Yu. P. Galishnikov. Investigation of commutation in machines of series “P.” Izvestiya TPI, vol. 145, 1966.

4. F. Jordan. Experimental investigation of commutation. ETZ, 30, 1909.

5. O. G. Vetner. Theory and Practice of Commutation in Direct-Current Machines. Gosenergoizdat, 1961.