Effect of the Mechanics of the Commutator–Brush Assembly on the Brush Short-Circuit Time of a Commutator Segment

A. I. Skorospelishkin, L. Ya. Zinner, R. F. Bekishev

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

It is known that the commutation time of an armature section is less than the time during which a commutator segment is short-circuited by a brush, and that complete contact between the brush and the commutator plate does not exist.

The factors affecting the commutation period may include the following: armature current, auxiliary-pole current, rotational speed, temperature of the brushes and commutator, brush pressure, brush grade, and the degree to which the brushes have been run in [1].

The apparent and actual time during which a segment is short-circuited by a brush is uniquely determined through the apparent and actual arc of contact of the brush with the commutator surface. It is obvious that the apparent length of the arc of contact, in the absence of intersegment height differences and with a cylindrical commutator, is determined from the expression:

\[ l_k = 4.375 \cdot 10^{-4} D_k \arcsin \frac{2b_{\mathrm{щ}}}{D_k}. \tag{1} \]

In real machines this equality is not satisfied because of the presence of intersegment height differences, eccentricity, and ellipticity of commutators; consequently, the actual arc of contact \(l_d\) is smaller than the apparent one.

Taking into account the circumstance that, in the presence of macroroughnesses, the brush is run in to the maximum radius of the commutator, we obtain an expression for the actual brush width:

\[ b_d = K b_{\mathrm{щ}} D_k \sqrt{\frac{2.3P(1 - K_{\mathrm{п}})}{E h \sin \omega t}}, \tag{2} \]

where

\[ \begin{aligned} P &\text{ — brush pressure, N;}\\ K_{\mathrm{п}} &\text{ — coefficient of pulsation of contact pressure;}\\ h &\text{ — height of the irregularity, mm;}\\ E &\text{ — modulus of elasticity of the electrobrush material, N/mm}^2. \end{aligned} \]

As can be seen from (2), in the presence of eccentricity and ellipticity of the commutator, the actual arc of contact does not remain constant, but is modulated with a frequency equal to the frequency with which the irregularities pass. The depth of modulation, in turn, is determined by the mass of the brushes, the pressure, the rotational speed, the maximum height of the irregularity, and the diameter of the commutator.

The influence of the factors listed on the short-circuit time of a segment by a brush was studied on a setup with a short-circuited commutator and two contact rings (Fig. 1).

Fig. 1. Experimental setup.
1 — short-circuited commutator; 2–3 — contact rings; 4 — brush; 5 — additional brush

Among the short-circuited segments there were three feeler plates insulated from the other segments. Two diametrically opposite feeler plates were short-circuited and had contact with one of the rings.

A voltage of 10 V from an accumulator battery was applied to the contact ring through the brush, the second terminal of which was connected to the brush on the commutator. When the feeler plate was closed by the brush, a current of 3 A flowed through the contact. At the same time, the voltage drop was oscillographed.

For synchronizing the oscilloscope sweep with the rotational speed, the second contact ring and the third feeler plate were used. During oscillography, characteristic current pulses are observed, the duration of which corresponds to the actual short-circuit time of the segment by the brush.

For calibrating the pulses by duration, a profilometer was used with a capacitive sensor specially developed for these purposes, having two plates. One of the sensor plates was installed on the approaching edge of the brush, the other on the trailing edge of the brush, so as to fix precisely the moment when the segment enters under the brush and the moment when it leaves it. The sensor itself was placed in the brush holder and was installed on one line with the brush along the commutator.

The signals from the feeler plate and the profilometer were fed to two beams of the C1-16 electronic oscilloscope.

The apparent short-circuit time of the plate by the brush was determined from the expression:

\[ T_k = \frac{60(b_{\text{щ}} + b_k)}{\pi D_k n}, \tag{3} \]

where

\[ \begin{aligned} T_k &\text{ — apparent short-circuit time;}\\ b_{\text{щ}} &\text{ — brush width, cm;}\\ b_k &\text{ — segment width, cm;}\\ D_k &\text{ — commutator diameter, cm;}\\ n &\text{ — rotational speed, rev/s.} \end{aligned} \]

In this case there is full contact of the brush with the commutator surface. The actual short-circuit time \(T_d\) is established with greater accuracy by superposing the current pulse and the profilogram. Figure 2 shows typical curves obtained by the method described above.

Fig. 2

In the course of the experiment four grades of brushes were tested: EG-49, EG-14, EG-74, and EG-8; the current density, rotational speed, and pressure were varied.

Investigations carried out by processing oscillograms of current pulses between the segment and the probe showed that, as the rotational speed of the commutator increases, the actual contact arc and the actual short-circuit time decrease. At the same time, contact of the segment with the brush becomes unstable both at the trailing and at the leading edges. Figure 3 gives the dependences of \(T_k\) and \(T_d\) on rotational speed at \(P=250\) g.

Fig. 3. Dependences of \(T_k\) and \(T_d\) on rotational speed.
1 — apparent short-circuit time of a segment by the brush \((T_k)\); 2 — actual short-circuit time \((T_d)\) of a segment by brush EG-49; 3 — the same, for brush EG-74; 4 — the same, for brush EG-14.

As a measure of contact efficiency, the ratio of the actual short-circuit time to the apparent time was taken,

\[ K=\frac{T_d}{T_k}\cdot 100, \tag{4} \]

where \(T_d\) is the actual short-circuit time of a segment by the brush.

Figures 4, 5, and 6 give the dependences of \(\dfrac{T_d}{T_k}\cdot 100\) as a function of rotational speed for three brush grades: EG-49, EG-14, and EG-74. As is seen from these curves, at low rotational speeds the contact of the brush with the commutator is stable, and shortening of the contact arc at the leading and trailing edges of the brush occurs only at the expense of wedge-shaped zones. In this case brushes with different moduli of elasticity are characterized by unequal shortening. Thus, for EG-49 the magnitude of the shortening is 10–12%, for EG-14 it is 16–18%, and for EG-74 it is 18–20%.

![Figure 4 graph]

Fig. 4. Dependence \(\dfrac{T_{\partial}}{T_k}\,100=f(n)\) for brush
EG-40.
1—2 scatter region

![Figure 5 graph]

Fig. 5. Dependence \(\dfrac{T_{\partial}}{T_k}\,100=f(n)\) for brush
EG-14.
1—2 scatter region

![Figure 6 graph]

Fig. 6. Dependence \(\dfrac{T_{\partial}}{T_k}\,100=f(n)\) for brush
EG-74.
1—2 scatter region

With an increase in rotational speed to 6000 rpm, the contact of the brush with the commutator becomes unstable both in the leading and in the trailing parts of the brushes. At the same time, a sharp reduction is observed in the actual short-circuit time of a segment and, consequently, a shortening of the contact arc. Thus, the reduction of the useful width of the brushes at \(n—6000\) rpm is 20–22 percent for EG-43, 26–28 percent for EG-14, and 32–36 percent for EG-74.

The curves in Figs. 3, 4, 5, 6 were plotted from the averaged values of ten equivalent measurements.

The error in determining \(T_{\partial}\), obtained by the least-squares method, is no more than 2 percent.

When the dependences presented are considered, one more interesting detail is revealed: at a fixed rotational speed of 3200 rpm there is a sharp increase in the effective short-circuit time of one of the commutator bars by the brush, whereas \(T_\mathrm{d}^{\circ}\) for the diametrically opposite probe plate decreases sharply. After oscillograms of the commutator had been taken at various rotational speeds, it was possible to establish that at a speed of 3200 rpm the experimental acceleration setup enters into resonance.

The latter completely determines the behavior of the brushes. Indeed, in the presence of resonance, the motion of one of the brushes is in phase with the motion of the commutator, which leads to weakening of the contact, whereas the motion of the diametrically opposite brush is in antiphase, shortening the contact. This follows from the following relations for the magnitude of the contact pressure between the brush and the commutator:

\[ N = m_{\mathrm{щ}} a_{\mathrm{щ}} - m_{\mathrm{щ}} a' \tag{5} \]

\[ N = m_{\mathrm{щ}} a_{\mathrm{щ}} + m_{\mathrm{щ}} a, \tag{6} \]

where

\[ \begin{aligned} N &\text{ is the magnitude of the contact pressure,}\\ m_{\mathrm{щ}} &\text{ is the mass of the brush,}\\ a_{\mathrm{щ}} &\text{ is the acceleration of the brush by the spring,}\\ a' &\text{ is the acceleration of the brush by the commutator.} \end{aligned} \]

An increase in the specific pressure on the brush, all other conditions being equal, promotes an increase in the effective short-circuit time and stabilization of the brush–commutator contact. Figure 7 shows the dependences of \(\dfrac{T_\mathrm{d}}{T_\mathrm{k}}\cdot 100\) as a function of pressure, obtained at a speed of 2500 rpm for brushes EG-4E, EG-14, and EG-74; from these it is evident that the effective arc and short-circuit time depend considerably on the pressure as the latter is varied from zero to 250–300 g/cm\(^2\).

Fig. 7. Dependence of \(\dfrac{T_\mathrm{d}}{T_\mathrm{k}}\,100\) on pressure at
\(n = 2500\) rpm.
1 — EG-4E; 2 — EG-14; 3 — EG-74

A further increase in \(P\) is not recommended, since, with the existing tolerances for the condition of the working surface of commutators, an increase in the specific pressure above 300 g/cm\(^2\) does not give any substantial improvement in the operation of the sliding contact, while leading, however, to a sharp increase in the rate of wear of the carbon brushes.

An increase in the temperature of the commutator also contributes to more stable operation of the brushes, which is partly explained by softening of the con-

the contact layer of the brush and, consequently, by better seating of it against the commutator.

With respect to loading the brushes with current, it should be noted that the influence of the current is manifested indirectly through a change in the temperature of the sliding contact. Thus, \(T_{\mathrm{b}}\) at a current through the contact of 3 A and 12 A, determined immediately one after the other, have one and the same value, since the contact temperature has not had time to change.

Investigations carried out according to the described procedure show that stable mechanical contact of the brush with the commutator occurs only in the zone \(0.5—0.85\, b_{\mathrm{sh}}\), symmetric about the brush axis, and, consequently, in the Hertzian zone. Instability of the short-circuit time and of the arc of contact is observed in the instability of the running-on and running-off edges of the brush.

In this respect one should point out a certain connection between the actual length of the arc of mechanical contact and the physical phenomena observed during commutation of an armature section. Thus, on careful examination of the superposed curves of the transient voltage drop and the current of the commutator segment (Fig. 8), it is found that

Fig. 8. Curves of the commutator-segment current and transient voltage drop.
1 — commutator-segment current; 2 — transient voltage drop; \(T_{\mathrm{k}}\) — period of short-circuiting of the segment by the brush; \(\varphi\) — phase shift.

there is a certain phase shift \(\varphi\) between the curves, consisting in the fact that at the instant when the current passes through zero the transient voltage drop is not equal to zero, but has a quite definite value. This shift can be explained by the influence of the capacitance of the brush–segment contact pair. In this case the capacitance of the section and the intersegment capacitance may be neglected as being of the second order of smallness in comparison with the contact capacitance.

Measurement of the contact capacitance by ordinary methods is difficult because of the active resistances connected in parallel, which form at the places of fretting of the patina.

For a more accurate determination of the contact capacitance and of its distribution along the arc of contact, we used the following method. After many hours of operation of the brush under current, the latter was placed on photographic film, and the film was exposed by a falling parallel beam of light. Subsequently, after 20-fold enlargement of the film, it was processed. In this process the actual contact zone of the brush with the commutator, the length of the wedge-shaped zones, the distribution of gaps between the commutator and the brush in the wedge-shaped zones, and, in addition, the distribution of capacitance along the apparent arc of contact were calculated. In the zone of actual mechanical contact, for the ...

for calculating the capacitance, the maximum approach of the brush–commutator-bar contact pair was taken to be \(0.5\,\mu\), on the basis of the limiting deformability of the brush projections under the action of the spring pressure.

The capacitance in the wedge-shaped zones was calculated by the refined formula for a flat nonparallel capacitor

\[ C=\varepsilon_0 \frac{S(t)}{d(t)} \left[1+\frac{L^2}{12a^2}\alpha^2\right]; \tag{7} \]

where

\[ \begin{aligned} S(t) &\text{— the instantaneous value of the area of the brush overlapped by the bar;}\\ d(t) &\text{— the instantaneous value of the gap between the plates;}\\ L &\text{— the length of the brush along the commutator;}\\ \alpha &\text{— the angle between the plates.} \end{aligned} \]

In the zone of established contact, the capacitance was calculated by the known formula

\[ C=\varepsilon_0 \frac{S(t)}{d}. \tag{8} \]

Figure 9 gives the curves of the distribution of the gap and the capacitance between the brush and the commutator bar, beginning from the moment of entry and ending with the moment when the bar leaves from under the brush. The curves were constructed for an EG-8 grade brush with an overlap equal to 1.5.

Fig. 9. Curves of the distribution of the gap and capacitance between the brush and the commutator bar.
1 — distribution of the gap under the brush; 2 — distribution of the contact capacitance

It is evident from the figure that the capacitance of the sliding contact is many times greater than the interbar capacitance and the capacitance between sections lying in one slot. The interbar and intersection capacitances, measured with a bridge, amount to \(80\text{–}100\) pF, whereas the contact capacitance reaches values of \((8000\text{–}10000)\) pF.

When considering the effect of the contact capacitance on commutation, it is advisable, in our opinion, to take into account not the magnitude of the capacitance itself, but the ratio between the active and capacitive resistances of the contact at each stage of the commutation process. Let us consider this in more detail. Figure 10 presents the distribution of the transition resistance between the brush and the commutator bar, constructed from the curves of the transition voltage drop and bar current (Fig. 7) for the case of normally accelerated commutation (curve 1). In addition, the distribution of the capacitive resistance over the width of the brush has been constructed (curve 2).

From Figs. 8 and 9 it is evident that, at the initial stage of the commutation process, the capacitance of the brush–segment contact is small, and the transient capacitive resistance is large because of the presence of a wedge-shaped zone at the entering edge of the brush and the small overlap area, whereas the transient active resistance of the contact is comparatively small. Consequently, the contact capacitance at the initial stage has no appreciable effect on the commutation process.

Fig. 10. 1 — transient resistance between the brush and the segment; 2 — capacitive resistance of the contact

At the middle stage, the influence of the capacitance also does not manifest itself, owing to the extremely small transient resistance of the brush–segment and the large value of the capacitive resistance. Here the contact capacitance is charged up to the amplitude value of the transient voltage drop. The situation is different in the final phase of commutation, where, as a result of the decrease in current density, the transient resistance of the brush–segment increases sharply, becoming “commensurable” with the capacitive resistance. At the same time, at the moment when the segment current falls to zero, the trailing edge of the brush maintains for some time a definite voltage value \(\Delta U_{\text{sh}}\) by virtue of the charge on the contact capacitance, preventing a change in the segment current. The time during which the contact capacitance damps the change in the segment current is determined by the discharge time of the capacitance through the parallel-connected resistance of the a-spots. From Fig. 7 it is evident that this time is sufficiently large and reaches 15–20 percent of the commutation period for various degrees of acceleration.

The foregoing is valid for accelerated commutation. In the case of retarded commutation, the influence of the contact capacitance on the commutation process is insignificant because the moment at which commutation ends is shifted to the trailing edge of the brush, where the capacitance is small.

It should be noted that the capacitance of the sliding contact largely determines the commutating ability of electrical brushes. The greatest influence of capacitance on the commutating ability is observed in hard grades of brushes EG-8, EG-74, and others. The latter is due to the fact that, in the final phase of commutation, the transient resistance of these brushes is comparatively large at a low current density, which helps preserve for some time the charge on the contact capacitance, damping the reversal of the current. When using soft

for various brush grades the effect of capacitance on commutation is insignificant, although its magnitude is greater than for hard brushes. The increase in the capacitance of the sliding contact when soft brushes are used is explained by their better bedding-in and by the greater convergence of the contacting surfaces.

However, because of the extremely small transition resistance, the capacitance is constantly short-circuited, which leads to its instantaneous discharge at the moment when the current passes through zero. Subsequently, during current reversal, the capacitance has no effect on the commutation process.

The studies carried out on the influence of the parameters of the commutator–brush assembly, rotational speed, specific pressure, temperature, and current on the instability of the arc of contact between the brush and the commutator, and on the time during which a segment is short-circuited by the brush, make it possible to draw the following conclusions:

1. The presence of substantial eccentricity leads to instability of the contact arc and to a reduction in the time during which a segment is short-circuited by the brush, owing to incomplete bedding-in and to the resulting radial accelerations of the brushes.

2. A change in rotational speed, like eccentricity, leads to a reduction in the contact arc and in the short-circuit time. Thus, at a speed from 0 to 500 rpm, the reduction of the arc amounts to 10–12 percent for EG-49, 16–18 percent for EG-14, and 18–20 percent for EG-74. Increasing the speed to 6000 rpm leads to a reduction of 20–22 percent for EG-49, 26–28 percent for EG-14, and 32–36 percent for EG-74.

3. Increasing the specific pressure promotes stabilization of the contact arc and an increase in the actual short-circuit time. Increasing the pressure above 250–300 g/cm² is not recommended, since any further increase has no appreciable effect on improving the operation of the sliding contact and leads to increased brush wear.

4. A method and an experimental setup are proposed for investigating the actual contact arc and the actual time during which a segment is short-circuited by the brush.

5. A photographic method is proposed for determining the gaps between the brush and the commutator, for calculating the capacitance and its distribution along the contact arc. It is shown that the magnitude of the capacitance reaches 10,000 pF and more.

6. The investigations have shown that the presence of capacitance in the sliding contact makes it possible to maintain a certain voltage at the trailing edge. The commutating ability of electric brushes is directly related to the magnitude of this capacitance.

REFERENCES

1. N. Kluge. The commutation period of an armature section and the stepped character of the commutation curve. ETZ-A, 22, 1955.