ON THE INSTABILITY OF DYNAMIC CURRENT–VOLTAGE CHARACTERISTICS OF A SLIDING CARBON BRUSH–COMMUTATOR CONTACT

Yu. P. Galishnikov, A. I. Skorospeleshkin

(Presented by the seminar of the departments of electrical machines and general electrical engineering)

The current–voltage characteristics of a sliding contact, depending on the method by which they are obtained, are divided into static and dynamic. According to the definition \[1, 2, 3\], each point of a static current–voltage characteristic, obtained on a short-circuited commutator or a smooth contact ring, reflects the established (static) state of the contact. In order to reach the established state, time intervals of up to half an hour are necessary at each fixed value of current. In this case the contact voltage drops corresponding to each current step reach their minimum value. Since, moreover, when a static characteristic is taken the current lines within the apparent contact surface are distributed uniformly, i.e., there is no forced increase or decrease of current density in any part of the face surface of the brush, as occurs with accelerated or retarded commutation, the curve obtained characterizes, with sufficient justification, the operation of the brush contact only under conditions of classical rectilinear commutation. At the same time, however, the actually existing difference in the operation of the entering and leaving edges of the brush remains unaccounted for. In addition, the use of static characteristics is unlawful for calculating the commutation of dc machines operating under transient conditions.

The use, in commutation calculations, of dynamic current–voltage characteristics, which represent the dependence of instantaneous values of the contact voltage drop on current under a comparatively rapid change of the latter, is difficult because of their extreme instability. The subject of the present article is one of the principal aspects of this instability, namely, the dependence of dynamic current–voltage characteristics on the magnitude, as well as on the rate and direction of change, of the current flowing through the carbon brush–commutator contact under the conditions of an electrical machine.

It is known that the actual mechanical contact of two touching surfaces is always smaller than the apparent macroscopic contact surface. The relation between the magnitude of the pressure on the brush and the surface that receives the pressure is expressed as \[2\]:

\[ P = \xi \cdot H \cdot S, \]

where \(\xi\) is the coefficient of compression of the material (usually \(0.25\)—\(0.5\)),
\(H\) is the hardness of the brush material.

The area of the electrical contact is still smaller in this case because of the presence, on the surface of the copper commutator, of a thin oxide film. According to [5], the initial oxidation of a copper surface in an atmosphere of atmospheric oxygen occurs extremely rapidly, so that within a few seconds an oxide film about 30 Å thick is formed. Although the surface film of Cu₂O is a semiconductor with a positive Hall coefficient (a \(p\)—\(n\) junction at the boundary with the metal), its intrinsic electrical resistance is large [2], and when the film has not been mechanically disrupted, the passage of current through it is effected by breakdown. Electrical breakdown of the Cu₂O film, called fritting, is a typical Zener breakdown of a thin semiconductor, associated with destruction of the crystal lattice of the film, and is characterized by a field strength of \(10^6\)—\(10^7\) V/cm. It is evident that the breakdown voltage is determined by the film thickness. For a thickness of the latter of 50–400 Å, it is 0.5–1.5 V [2, 4].

Destruction of the film as a result of fritting leads to the formation of metallic bridges or conducting spots of circular or elliptical shape. The constriction resistance for one of the contacting elements in the case of a circular conducting surface is determined as follows [2]:

\[ R_a=\frac{\rho}{4\cdot a}, \]

where

\(\rho\) — the resistivity of the contact material, in the present case graphite,

\(a\) — the radius of the circular conducting spot.

For the case of the carbon-brush—commutator contact, the quantity \(R_a\) is at the same time the contact resistance of a single spot, since the constriction resistance in copper may be neglected.

Recent experimental investigations fully confirm the described mechanism of the electrical conductivity of the contact. Examination of the surface of a copper commutator by means of an electrode made of gold wire [4] made it possible to establish that the surface film is speckled with small spots of elliptical shape, elongated along the direction of rotation of the commutator. The electrical resistance of such spots is practically equal to zero. Microscopic analysis of the commutator surface [5] likewise shows the presence of well-polished metallic spots 10–20 µ in diameter, the number of which, determined statistically using a brush of special shape, is approximately 30 for a \(5\times5\) mm brush. Finally, in measuring the temperature of the contact surface with the aid of a photoelement [6], it was found that the passage of current is accompanied by the appearance of clearly expressed heating spots, which indicates the local character of the current flow. The highest observed temperatures are 600–700°C.

A special feature of the sliding contact consists in the fact that the metallic contact spots formed while a given section of the commutator surface is under the brush, when moving from one brush to another of opposite polarity, have time to oxidize to a considerable degree as a result of friction of the commutator surface against the air. Frictional oxidation is accelerated by the action of the high temperatures occurring at the points of electrical contact. The mechanism of oxidation has been studied in detail by E. Holm. According to [7], oxidation due to friction against air during one or several revolutions of the commutator almost completely destroys the contact spots. However, during the time taken for the given commutator segment to pass from one brush to ...

spots of the opposite polarity of the brush only decrease in size. In this case, frittings again become necessary in order to bring into correspondence the sizes of the contact spots and the current flowing through the brush.

Thus, electrical conduction in the brush–commutator contact takes place under conditions in which two mutually opposite processes occur. This is, on the one hand, the process of destruction of the oxide film by mechanical abrasion and frittings, accompanied by the formation on the commutator surface of discrete metallic conducting spots, and, on the other hand, the oxidation of the conducting spots formed during fritting as a result of friction of the commutator surface against air. These processes are in a certain dynamic equilibrium.

As we see, an electrical sliding contact is a dynamic system and, like any such system, is characterized by a quite definite inertia. The inertia of the electrical properties of a sliding contact is due to the physical nature of the processes taking place. Indeed, the formation of conducting spots does not occur instantaneously. Formation of a fritting channel requires a time of about \(1/300\) sec [2], so that, at the values of lamellar frequency usually encountered, frittings do not have time to develop. For example, at a voltage frequency of the order of \(5\) kHz, fritting is completed over several half-periods (in the absence of oxidation in the intervals between applications of voltage). On the other hand, oxidation by friction against air likewise does not lead to instantaneous and complete destruction of the contact spots. Under certain conditions these spots are capable of persisting for several hours [4]. The commutator surface, so to speak, remembers the magnitude of the current that has flowed through the contact.

The artificial dynamic current–voltage characteristic shown in Fig. 1 convincingly confirms the inertia of an electrical sliding contact. The characteristic was obtained for an anode-polarized EG-4E brush sliding over a short-circuited commutator whose surface was covered with an oxide film. Formation of the film took place over \(4\)—\(6\) h at a current of \(8\) A (the average current density in the contact was \(6\) A/cm\(^2\)). The characteristic was recorded with a monotonic increase of the current through the contact over \(0.1\) sec from zero to \(8\) A and its subsequent decrease back to zero. Accordingly, the characteristic has an ascending and a descending branch. The divergence of these branches is evidence of the inertia of the sliding contact.

The process of formation of electrical conduction corresponds to the ascending branch of the characteristic (Fig. 1), which is clearly nonlinear.

Fig. 1. Artificial dynamic current–voltage characteristic of an EG-4E brush.

Fig. 2. a — commutation-current curves of two adjacent armature sections; b — current of the commutator bar; c — variation of the current density of the commutator bar. 1 — rectilinear commutation, 2 — normally accelerated commutation, 3 — retarded commutation.

because of the presence of an oxide film with high electrical resistance. As the current increases, the insulating film undergoes repeated fritting, as a result of which the contact resistance decreases considerably. The assumptions sometimes made that this decrease in resistance is connected mainly with a rise in temperature in the contact zone are untenable, since, according to [8], the resistivity of graphite, when the temperature is raised to \(2800^\circ\text{C}\), decreases only by a factor of 3 owing to its negative temperature coefficient. In the present case this decrease is greater, although the temperature at the points of direct contact, as was noted, does not exceed \(600\text{--}700^\circ\text{C}\). Thus, the nonlinearity of the ascending branch of the current-voltage characteristic is associated primarily with breakdown of the oxide film, which has a high electrical resistance. Experiments with various grades of brushes show that the nonlinearity of the ascending branch is the greater, the lower the resistivity of the brush material. This becomes understandable if one takes into account that the thickness of the film formed on the commutator when different brushes are used, and consequently also the breakdown voltage of this film, are on average the same.

The descending branch of the characteristic, while being flatter, is at the same time distinguished by greater linearity. From the point of view of the theory of electrical contact this is explained as follows. When the current reaches its maximum value, metallic conducting spots are formed on the surface of the commutator, sufficient for the passage of the given current. The number and dimensions of these spots are determined by the magnitude of the current and by the time of contact formation. With a subsequent decrease in current, the contact spots, not having time to oxidize appreciably, continue to operate, thereby ensuring the linearity of the return branch of the current-voltage characteristic.

Thus, along with the ability to provide electrical conductivity of a metallic character by breakdown of the insulating oxide film, the sliding contact possesses another most important property, namely inertia.

Turning to the clarification of the causes of instability of the dynamic current-voltage characteristics, let us consider the features of the formation of the electrical conductivity of a sliding contact, taking into account its inertia under different conditions of variation of the commutation current. In Fig. 2, a are shown the commutation-current curves of two adjacent armature sections. In this case the current in the commutator bar directly connected with these sections is determined as the algebraic sum of the instantaneous values of the section currents and, with a brush width equal to one commutator pitch, has the form of a pulse of symmetric triangular shape (Fig. 2, b). With deviations of commutation in one direction or the other

toward the rectilinear one, the current pulse of the commutator segment is somewhat distorted, but its general form—in particular, the greatest instantaneous value of the current—remains unchanged.

The dynamic current-voltage characteristics obtained experimentally under real operating conditions of a sliding contact are called by the authors natural, in contrast to artificial dynamic characteristics, which are recorded when the brush operates on a short-circuited commutator or ring, when the total contact current is distributed more or less uniformly over the face surface of the brush. The natural characteristics of a contact are usually represented as the dependence of the contact voltage drop on the current of the commutator segment (coil) [9]. In such a representation, the differences in the current-voltage curves caused by the different character of commutation have the appearance of a greater or lesser random scatter. The physical nature of this scatter remains unexplained.

In reality, as will be shown below, the formation of electrical conductivity under the brush is determined by the magnitude and the character of the change in current density in the contact, and not by the magnitude of the current. Indeed, in the process of commutation there occurs not only a change with time in the current of the section being commutated, but also a spatial displacement of the commutator segments associated with this section, so that the contact surface of a given segment and the brush is constantly changing, correspondingly changing the current density in the contact even when the current magnitude is unchanged. The current-density curves shown in Fig. 2, c are constructed by relating the instantaneous values of the current in the contact to the instantaneous values of the apparent area of contact between the segment and the brush. It is assumed here that the entire face surface of the brush is active.

For comparison of natural current-voltage characteristics, let us consider the formation of the contact under normally accelerated and somewhat retarded commutation, when, however, sparkless operation of the brush is still ensured. Operation of the brush contact with sparking is not considered within the scope of the present article, since in that case the conductivity of the contact is associated with electrical breakdown of air gaps, and the current-voltage characteristic of the contact, at least in the sparking region, is described by the specific laws of a gas discharge, for which constancy of the voltage at the electrodes is characteristic, irrespective of the discharge intensity.

Let us begin the consideration with the case of accelerated commutation. Curve 2 in Fig. 2, c represents the change in current density in a given commutator segment on the surface of its contact with the brush. As noted, when a segment passes from one brush to another the contact spots are oxidized to a considerable extent, and when the segment enters under the brush the comparatively large voltage drop caused by the considerable current density is almost entirely applied to the film. Under the action of this voltage drop, a series of frittings of the oxide film occurs, as a result of which the former contact spots expand or new contact spots are formed. The contact resistance thereby decreases in jumps. Owing to the inertia of the measuring instruments, the voltage drops characteristic of fritting are not directly observed, manifesting themselves only as a noticeable irregularity in the initial part of the curve of the contact voltage drop. With further motion of the segment, the contact voltage drop, owing to the considerable current density, continues to remain sufficient for fritting.

After the segment has completely entered under the brush, beginning with a certain current density, the contact voltage is realized as a voltage drop across the constriction resistance; therefore fritting-

… the formation of the oxide film ceases, and no expansion of the contact spots occurs. From this time on the contact is formed, and the contact resistance reaches its lowest value under the given conditions and is determined as the constriction resistance in the brush material. It is clear that the higher the maximum current density, which depends on the degree of commutation acceleration, the larger the number of conducting spots formed under the brush and, correspondingly, the lower the resulting contact resistance. On the other hand, the time of contact formation is also closely connected with the degree of commutation acceleration.

Thus, beginning with a certain current density, the operation of the sliding contact is carried out with the use of already existing contact spots, whose number and dimensions remain unchanged, since oxidation of the spots does not occur because air has no access to them. The resistance of the adhesive films always present on metallic surfaces, through which current flow is ensured by the tunnel effect, is practically constant over a wide temperature range [2]. Thus, from a certain moment the current–voltage characteristic of the contact is ohmic in character.

It would be incorrect to suppose that, under accelerated commutation, the sliding contact has a linear current–voltage characteristic only at low current densities [11]. Experiments by the authors on a short-circuited commutator show that, when the current is dynamically decreased from some steady value to zero, the sliding contact exhibits comparative linearity of the current–voltage characteristics at current densities of \(10—12\ a/cm^2\). Linearity of the contact characteristic should also be expected in the case of a change in the direction of the current in the coil to the opposite one under considerable commutation acceleration, again because of the ohmic character of the conductivity.

The linearity of the current–voltage characteristic of the contact during a decrease in current density (accelerated commutation) is disturbed only by abrupt changes in the contact resistance due to individual spots emerging from under the brush in the final phase of commutation, since the total number of these spots on the surface of the plates overlapped by the brush is limited. However, according to the data of [10], the amplitude of these jumps is approximately 2.5 percent of the total voltage drop.

Let us next consider the formation of the contact conductivity under delayed commutation (curve 3 in Fig. 2, \(в\)). As follows from the curve, the entry of the commutator plate under the brush occurs at current densities close to zero. Therefore the developing contact voltage is not capable of producing effective fritting of the oxide film. Frittings nevertheless do occur, however, since the minimum breakdown voltage of the film is \(0.02\ v\) [4]. An exception is the cathode-polarized brush, beneath which there is a certain initial conductivity.

The current density, increasing as the plate moves, leads to an increase in the contact voltage drop. As a result, the motion of the plate is accompanied by successive frittings, expanding the contact spots. This process continues until the commutator plate has completely emerged from under the brush. Thus, under delayed commutation, contact formation occurs throughout the entire time the commutator plate remains under the brush. The consequence of this is a smaller, other conditions being equal (including the value of the greatest current density), magnitude of the resulting specific contact resistance than in the case of accelerated commutation. The latter, incidentally, explains the well-known practical fact that, under accelerated commutation, the brush contact

exerts a greater effect on the current of the commutated section through its voltage drops. Returning to the form of the current-voltage characteristic of the contact under delayed commutation, let us note that in this case there is no constancy of the specific contact resistance.

Consideration of the process of formation of contact conductivity, taking its inertia into account for two cases of commutation that are opposite in a certain sense, leads to the conclusion that the scatter of the natural current-voltage characteristics of a sliding contact is not accidental, but is due to different conditions of contact formation. Indeed, depending on the degree of acceleration or delay, the value of the maximum current density first of all varies within wide limits, and the concentration of current lines falls now on the entering, now on the leaving edge of the brush. This, as follows from what has been considered, has a decisive influence on the contact characteristic. Further, the time of contact formation also does not remain constant. Thus, under accelerated commutation it is considerably smaller than under delay of the same degree. Finally, the very form of the natural current-voltage characteristics is very different.

Thus, the natural current-voltage characteristic obtained for a definite character of commutation, by virtue of its features, describes only one particular case of operation of the sliding contact and, given the existing variety of electrical conditions on the commutator of an electric machine, cannot characterize the sliding contact as a whole. In this connection one cannot recognize as valid the proposals to adopt, as a criterion of the commutating properties of an electric brush, certain parameters of particular current-voltage characteristics [9]. From our point of view, the commutating ability should be assessed on the basis of the totality of properties of the brush material, the principal ones being its specific resistance, its ability to form a stable patina on the commutator, and also its hardness and elastic properties.

From the physical point of view, the use in commutation calculation of any particular current-voltage characteristic is likewise unjustified. The currently intensively developed theory of optimal commutation [11] considers somewhat accelerated commutation to be the best. Similar considerations have been expressed earlier as well, and theoretically they are, of course, justified. An approximate calculation of commutation is possible in this case also when using a particular contact characteristic. However, as the oscillographic investigation of commutation of low-power direct-current machines carried out by the authors shows, alongside the random influence of mechanical factors there is a nonidentity of the commutation conditions of armature sections caused by electromagnetic reasons. The point is the difference between commutation of nonsingle and single sections, associated with a redistribution of electromagnetic energy. In this case the worst position is occupied by single sections of the first order, that is, sections completing commutation in the absence of magnetically coupled short-circuited circuits. The absence of damping leads to the commutation of such sections being clearly delayed even when the setting of the interpoles is optimal with respect to the other armature sections. The commutation calculations now widely practiced using electronic digital computers, based on accounting for the instantaneous values of the self- and mutual inductances of the sections, do not allow one to neglect the indicated feature, which is apparently inherent in all direct-current machines regardless of power. Under these conditions, introducing into the calculation a single particular characteristic of the sliding contact is inadmissible. From all that has been considered it follows that the only correct course in refin—

... in commutation calculations is the introduction into the calculation of a family of current–voltage characteristics describing the operation of the sliding contact under wide deviations of commutation, say, from rectilinear commutation. Mathematical processing of the family of current–voltage characteristics of the sliding contact by means of regression analysis makes it possible to obtain sufficiently simple approximation expressions.

References

1. R. E. Hellmund, L. R. Ludwig. Sparking under the brushes of commutator machines, Electrical Engineering, 1935.

2. R. Holm. Electrical Contacts, IIL, 1961.

3. H. A. Schultze. On the dynamics of a sliding contact, ETZ-A, 8, 1964.

4. E. Shobert. Electrical resistance of a carbon brush on a copper ring, AIEE Transactions, Part II-A, 1954, 73.

5. A. E. Stebbens. Processes of wear of the contact surface and the flow of current in it between carbon and copper, Conf. Commut. Rotat. Mach., London, 1964.

6. D. A. Parker. Surface properties of the sliding contact of a copper–graphite pair, Conf. Commut. Rotat. Mach., London, 1964.

7. E. Holm. On the theory of contact between a carbon brush and a copper contact ring, Journal of Applied Physics, vol. 28, 1957, 10.

8. F. Schröter. Transient resistance of a sliding contact, ETZ-A, 14, 1955.

9. O. G. Wegner. Theory and Practice of Commutation in Direct-Current Machines, GEI, 1962.

10. F. Schröter. Commutating ability of carbon brushes, ETZ-B, 3, 1962.

11. M. F. Karasev, V. N. Kozlov. Optimal commutation in direct-current machines, Proceedings of OMIIT, vol. 44, 1964.