Electrical Properties of a Sliding Contact

Electrical Properties of a Sliding Contact

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

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

A thorough study of the physical properties of a sliding contact is an indispensable condition for further development and for solving theoretical and practical questions associated with the problem of commutation. In the present work, the physical processes occurring in the sliding contact of a brush—commutator segment are investigated with allowance for the capacitance in the contact layer; a method for determining it is proposed; natural dynamic volt-ampere characteristics are considered, and their mathematical approximation is given.

It is known that the actual mechanical contact between two bodies (brush—commutator segment) takes place only over a comparatively small fraction of the apparent macroscopic contact surface [1]. In this case, direct electrical contact exists only on the part of the surface that bears the pressure, which corresponds to the actual mechanical contact. The areas of direct electrical contact, the so-called a-spots, have dimensions not exceeding 30–40 μm, and their shape and origin are associated with the microrelief of the commutator surface. In the case where the entire contact surface is covered with an oxide film, electrical conduction in the contact occurs by breakdown of the film; in this case the electric-field strength reaches values on the order of \(10^6\)—\(10^7\) V/cm.

It has been shown that when there are level differences of the commutator plates on the commutator surface, \(\Delta_{\min} < 0.5\) μm, uninterrupted contact is ensured by the elastic properties of electrobrush materials. Thus, during rotation of the latter, the brush and commutator are separated by a small gap whose magnitude may vary within the limits 0.01—1 μm.

Considering the oxide film on the commutator, which according to [2] has a thickness of \(40\)—\(500 \mathring{A}\), as a dielectric, and taking into account the separation of the brush—segment contacts, the physical model of the sliding contact may be represented as in Fig. 1.

Since contact is made only at several points whose dimensions are much smaller than the distance between the contacting points, the equivalent circuit of the sliding contact may be represented as a parallel connection of the differential capacitance of the contact and the variable active resistance of the contacting points (Fig. 2).

The capacitance between the contacting elements of the brush—commutator segment depends on the distance between the contacts (the latter includes

Fig. 1. Physical model of a sliding contact

Fig. 2. Equivalent circuit of a sliding contact

includes the thickness of the oxide film and the separation of the contacts) and of the apparent contact area. In this case the area of the actual electrical contact may be neglected, since the latter is much smaller than the apparent one.

The capacitance between two parallel contacts, of area \(A\) and separated by a distance \(h\), for \(\varepsilon = 1\), is determined by

\[ c_k = \varepsilon_0 \int \frac{dA}{h}\, |\phi| . \]

In a particular case, for an apparent contact area \(A = 1\ \text{cm}^2\) and a distance between the contacts \(h = 0.01\ \mu\), the maximum value of the capacitance of the sliding contact reaches

\[ c_{\max} = 0.0885\ \mu\text{F}. \]

With a constant distance between the contacts, the capacitance varies from \(0\) to \(c_{\max}\) according to the law of variation of the apparent contact area during rotation of the commutator. If one takes into account that the separation between the contacts also does not remain constant, it can be seen that determining the law of variation of the capacitance of the sliding contact is very difficult.

In turn, the active resistance of the contact, which depends on the current density, is also variable.

The main difficulty in this case consists in determining the relationship between the active and capacitive resistances of the sliding contact.

The capacitive reactance at the frequency of the commutated current

\[ f_1=\frac{1}{T_k} \]

of the order of 3–4 kHz is

\[ X_{C_k}=\frac{1}{\omega C_k}\ [\Omega] \]

and amounts to 400–300 ohms, which may be comparable with the active resistance of the contact at low current density.

An experimental verification of the propositions set forth was carried out in a study of the commutation of an EMU-12A electric-machine amplifier equipped with EG-8 brushes. Oscillograms were taken of the commutation-current curves of two adjacent armature sections, and also of the voltage drop between the commutator bar common to these sections and the brush of the corresponding polarity during the period of their contact. For the measurements a two-beam oscillograph C1-16 was used, having a sweep common to the two beams. External synchronization and triggering of the triggered sweeps is effected by a signal obtained electromagnetically and rigidly connected with the rotational speed of the armature. The design of the synchronizing device makes it possible to trigger the oscillograph at any required instant of time during each revolution of the commutator.

The lamella current is determined for the entire time it remains under the brush by geometrical constructions.

Figure 3 gives oscillograms of the commutation-current curves of two adjacent armature sections and of the voltage drop in the contact; the lamella-current curve is also constructed.

Fig. 3. Oscillograms of the section currents and voltage drop.
\(i_1, i_2\) — section currents; \(i_l\) — lamella current; \(\Delta U\) — contact voltage drop; \(T_k\) — period of short-circuiting of the lamella by the brush.

Analyzing the indicated oscillograms, it is easy to see that the lamella current reaches zero earlier than the voltage drop; in other words, there is a phase mismatch between the current and the voltage drop, which is confirmed by the presence of capacitance in the sliding contact.

In order to determine whether the capacitance of the contact is due to the presence of thin oxide films on the commutator or to separation of the contacts during rotation of the commutator, the following experiment was carried out. Oscil-

the commutation-current curves of adjacent sections and the voltage drop in the contact were oscillographed after prolonged running-in of the polish, and the time shift between the bar current and the voltage drop was determined. Then the polish was removed with glass paper and oscillography was again carried out. In this case the time shift decreased. As a result of the experiment it was found that the high capacitances of the contact are due mainly to the presence of an oxide film, although the gap between the contacts also participates in this process.

Parker’s experiments [3] also showed that, for contacts having no oxide film—gold—graphite and graphite—graphite—high contact capacitances also occur.

When oscillographing the current and voltage curves on a short-circuited commutator using high-frequency alternating current corresponding to the commutation-current frequency, no time shift between the bar current and the voltage drop was observed. This is explained by the entirely different character of the change in the load of the sliding contact. Indeed, on a short-circuited commutator there is a change only in time of the current passing through the brush, whereas in the commutation process on the commutator of an electric machine a periodic redistribution of current over the individual regions of the brush contact surface takes place.

Analyzing the oscillograms obtained (Fig. 3), we see that the character of the change in the bar current and the voltage drop in the contact depends on the relation between the variable \(r\) and \(c\) of the sliding contact. Thus, under accelerated commutation at the entering edge, the current density is high and the capacitance is insignificant, owing to the small area of overlap of the bar by the brush, and contact is effected entirely through the active resistance. As the plate moves under the brush, the current density decreases to zero, and the area of the brush—bar contact and, correspondingly, the capacitance become maximal. Since the corresponding energy is stored in the capacitance, when the current reaches zero a certain magnitude of voltage drop in the sliding contact occurs.

Under retarded commutation at the entering edge, the current density is close to zero, but the capacitance is small; therefore the reactance of the contact manifests itself more weakly than under accelerated commutation at the corresponding current density. At the leaving edge, with an insignificant capacitance of the contact layer, there is a high current density and the reactance of the sliding contact practically does not manifest itself.

The magnitude and relation between the capacitance and the active resistance of the sliding contact are directly connected with the change in the actual commutation period. This question is considered in detail in [4].

Accurate measurement of the capacitance of a sliding contact in a real machine involves great difficulties, since the magnitude of the capacitance depends on two variables, \(A\) and \(h\).

The only method that can be accepted for this purpose is an indirect one, based on measuring the phase-shift angle between the bar current and the voltage drop in the contact.

Figure 4 presents the circuit for measuring capacitance. The measurement was carried out by the method of comparing the capacitance of the sliding contact with the capacitance of a standard capacitor \(C_{\mathrm{e}}\), with the connection of the standard capacitance in parallel with the contact capacitance being made only during the time of contact of the brush with the commutator plate under investigation by means of contact \(K\). For this purpose, on the shaft of the current collector a ring made of textolite was mounted, and on its surface

Fig. 4. Circuit for measuring the maximum value of the capacitance

In the axial direction a copper plate was placed, with a width equal to that of a collector lamella. Two contacts slide over the surface of the ring; they close at the moment when the lamella is under the brush. Oscillograms of the commutation-current curves and of the voltage drop in the contact are recorded with switch \(P\) open, and the phase shift is estimated. Then, after closing \(P\), the standard capacitance \(C_e\) is connected and, by varying its value, an increase of the phase shift by a factor of two is obtained. Obviously, in this case the magnitude of the contact capacitance is equal to the magnitude of the standard capacitance, since \(C_e\) and \(C_k\) are connected in parallel. By this method one can determine only the value of the maximum capacitance of the sliding contact. Naturally, the external synchronization of the oscillograph in this case must be well adjusted. The value of the maximum capacitance measured by this method is \(0.03\)—\(0.05\ \mu\mathrm{F}\).

For a comparative estimate of the capacitance of the contact layer, it was measured in the case of stationary contacts at different separations. The capacitance of a stationary contact pair—brush/collector lamella—can be measured by coulomb-static methods, widely used in electrochemistry. From electrochemistry it is known that, if the distance between two surfaces carrying opposite charges is vanishingly small, the totality of these surfaces has the character of an electric double layer, where there is a potential jump proportional to the charge density on the plates of the double layer. The jumps of the electrode potentials at the phase boundary are directly associated with the formation of boundary double layers. The mechanism of formation of the double layer consists in the fact that dipolar molecules adsorbed at the phase boundary—for example, water molecules—are oriented in a definite way.

The operation of the contact pair brush—collector lamella under real conditions fully corresponds to the mechanism of formation of a double layer.

For measuring the capacitance, a circuit was adopted that is used in electrochemistry for determining the parameters of an electrochemical reaction [5].

The schematic diagram of the measuring setup is shown in Fig. 5.

Measurement of the charge of the electrode under investigation (i.e.) is carried out by discharging onto it a capacitor \(C_1\), previously charged from battery \(B\). Capacitor \(C_1\) must be of high quality and without leakage, so that the change in charge can be calculated from the equation

\[ \Delta Q = C_1 U_B . \]

Switching capacitor \(C_1\) to the electrodes under investigation is carried out by means of a relay, which simultaneously starts the oscillograph. The charge of the electrode changes over a time of \(0.1\)—\(1\ \mu\mathrm{s}\), in

Fig. 5. Schematic diagram of the measuring setup for determining \(C\)

during which it is necessary to monitor the change in potential. The potential \(\varphi\) reaches its maximum value \(\varphi_{\max}\), after which it begins to fall to zero. Knowing the value of the potential \(\varphi_{\max}\), the capacitance of the double layer can be determined from the formula

\[ c_k = c_d = \frac{c_1 \varphi_{\max}}{U_B}. \]

In the measuring circuit, potentiometer \(P\) serves to compensate the equilibrium potential, so that on the oscilloscope, before the electrode charge changes, the voltage must be equal to zero. In order that the resistance of the potentiometer not increase the charging time of the double layer, the potentiometer is shunted by a large capacitance \(C_2\).

The method described makes it possible simply to determine the capacitance of a stationary contact, which is difficult to do with an AC bridge because of the presence of a pseudo-capacitance that increases the true value of \(C_k\).

However, by this method one can only establish the presence of contact capacitance or determine its order of magnitude, since before the measurement a definite separation of the contacts is set in advance. Thus, when an average gap of \(0.5\ \mu\) is set, the capacitance is \(0.03—0.05\ \mu\mathrm{F}\).

The results of an experimental study of the natural dynamic current–voltage characteristics of the brush–commutator sliding contact confirm the validity of the adopted physical model of the sliding contact.

As oscillographic recording of the commutation current curves when using EG-8 brushes showed, the actual commutation period differs significantly from the theoretical one, even when satisfactory mechanical operating conditions of the commutator are ensured. The condition of the commutator surface was monitored by taking a profilogram of the commutator using a profilometer with a capacitive transducer [6].

The construction of natural dynamic current–voltage characteristics is carried out by comparing in time the points of the curves of current density and voltage drop [7].

The current–voltage characteristics of cathodically and anodically polarized brushes, respectively for the longitudinal and transverse circuits of the EMU-12A, are given in Figs. 6 and 7.

In analyzing the natural dynamic current–voltage characteristics, it is necessary to note that their form is completely determined by the nature of commutation. The magnitude of the voltage drop between the brush and the commutator bar in contact with the brush of a given polarity depends on the magnitude and rate of change of the current density and on the reactance of the contact. The latter is appreciable only

Fig. 6. Volt–ampere characteristics of the cathode- and anode-polarized brushes of the longitudinal circuit of the EMU-12A.
1 — volt–ampere characteristic of the cathode-polarized brush at the lower boundary of the sparkless zone; 2 — the same at the upper boundary of the sparkless zone; 3 — volt–ampere characteristic of the anode-polarized brush at the lower boundary of the sparkless zone; 4 — the same at the upper boundary of the sparkless zone

Fig. 7. Volt–ampere characteristics of the cathode- and anode-polarized brushes of the transverse circuit of the EMU-12A

at current densities close to zero, and the magnitude of the voltage drop \(\Delta U_0\) at this moment in time may reach values of 1.0–1.5 V. Thus, under accelerated commutation the moment at which the current density reaches zero corresponds to the greatest value of the capacitance of the sliding contact, and the magnitude of the voltage drop \(\Delta U_0\) is maximal. With the subsequent change in the nature of commutation from strongly accelerated to rectilinear and then to retarded, the moment at which the current passes through zero shifts increasingly toward the trailing edge of the brush (the actual commutation period tends toward the theoretical one). In this case, the instantaneous value of the contact capacitance corresponding

by the instant when the lamella current passes through zero, is significantly reduced. This, naturally, entails a decrease in the magnitude of the voltage drop \(\Delta U_0\). If, by regulating the current of the interpoles, such a degree of retardation of commutation were achieved that the lamella current becomes zero at the moment when the lamella leaves from under the brush, while the beginning of contact coincides with the moment when the plate enters under the brush, the reactance of the sliding contact would have no effect either at the trailing or at the leading edges of the brush. However, such conditions cannot be attained in real machines.

As studies of commutation along the longitudinal and transverse axes of the EMU-12A under various commutation conditions within the sparkless zone have shown, the magnitude of the voltage drop \(\Delta U_0\) caused by the reactance of the sliding contact varies over wide limits: \((1.5—0.6)\) V for a cathode-polarized brush and \((1.1—0.4)\) V for an anode-polarized brush.

The nature of the change in the voltage drop of the sliding contact at high current densities is determined mainly by the magnitude and rate of change of the current density. Thus, with accelerated commutation the current density decreases sharply, and the formation of contact conductance proceeds rapidly through intensive expansion of the contact spots by means of fritting. In this case the level of the voltage drop is somewhat lowered. With retarded commutation, the magnitude and rate of change of the current density are insignificant at the beginning of contact, increasing only toward the end of the commutation period; therefore the formation of contact conductance proceeds sluggishly and the level of the voltage drop rises sharply. This explains the small inclination of the volt-ampere characteristics to the current-density axis under accelerated commutation and the considerable inclination under retarded commutation.

A large number of experiments carried out using EG-8 brushes showed that, for this grade of brushes under real operating conditions of the sliding contact, the dependence of the transient voltage drop on the current density in the contact is expressed by a straight line. It should be noted that with rectilinear commutation, which can be ensured by regulating the interpoles, the natural dynamic volt-ampere characteristic degenerates into a point, since the current density and the voltage drop in the contact are constant.

The difference in the volt-ampere characteristics of anode- and cathode-polarized brushes is explained by the known polarity effect.

The natural dynamic volt-ampere characteristics obtained can, with accuracy sufficient for practical calculations, be approximated by an expression of the form

\[ \Delta U = \Delta U_0 + K j . \]

For cathode- and anode-polarized brushes, respectively, the expression has the form

\[ \Delta U_k = \Delta U_{0k} + K_k \cdot j, \]

\[ \Delta U_A = \Delta U_{0A} + K_A \cdot j, \]

where

\[ \begin{aligned} \Delta U_{0k},\ \Delta U_{0A} &\text{— voltage drops at a current density equal to zero, for cathode- and anode-polarized brushes,}\\ K_k,\ K_A &\text{— tangents of the angles of inclination of the volt-ampere characteristic to the current-density axis, respectively for cathode- and anode-polarized brushes.} \end{aligned} \]

In conclusion it should be noted that in works [8, 9, 10, 11] an attempt was made, in calculations of commutation, to take into account the capacitance between adjacent commutator plates and the distributed capacitance

sections. In this connection, the influence of capacitance on current commutation is noted as a factor reducing the probability of sparking. The capacitance between the brush and the commutator segment, however, is not taken into account, although in fact it is the principal one both in magnitude and in its role in the commutation process.

Moreover, in the scheme proposed by the authors of [12], a determination is made of the capacitance between the sections of the armature winding and the armature core, which is then introduced into the calculation of commutation, whereas this capacitance, in essence, does not take part in the commutation process.

Studies carried out by us using brushes of various types have revealed the following feature. Brushes exhibiting a high reactance of the sliding contact (EG-8, EG-74) possess, as a rule, high commutating properties.

Thus, it may be considered that one of the important characteristics of brushes from the standpoint of commutation is the ratio between active resistance and capacitance at a current density reaching zero value. At the same time, taking account of the reactance of the sliding contact makes it possible to answer the question of how brushes possessing high commutating properties maintain a certain voltage value in the transition layer at the leaving edge.

As a result of the investigations carried out, the following conclusions may be formulated:

1. A physical model of the sliding contact in electrical machines has been constructed, according to which the brush–commutator-segment contact must be regarded as a nonlinear circuit with parallel connection of the variables \(r_k\) and \(c_k\).

2. The proposed method for determining the capacitance of the sliding contact by comparison with the capacitance of a standard capacitor makes it possible to measure the value of the maximum capacitance of the sliding contact under real operating conditions of commutator electrical machines.

3. Natural dynamic volt-ampere characteristics, taking into account the reactance of the sliding contact, are approximated by an expression of the form

\[ \Delta U = \Delta U_0 + K \cdot j . \]

1. The commutating properties of brushes are inseparably associated with the presence of capacitance in the brush–commutator-segment contact and, correspondingly, with the magnitude of the voltage drop that the brush maintains at the leaving edge under accelerated commutation.

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