Effect of Collector Temperature on the Properties of a Sliding Brush Contact
Abstract Generated abstract
This paper examines how collector temperature affects the current, voltage characteristics, transition resistance, and voltage drop of sliding brush contacts in commutator electrical machines. Using an equivalent circuit model, the authors analyze experimental data for several brush grades by separating the temperature behavior of the blocking layer resistance, leakage resistance, and brush to collector film resistance. The results indicate that nonlinear film-related resistances decrease with rising temperature and dominate at low temperatures, while mechanical deterioration of the collector increases the brush to film resistance and becomes decisive above about 80°C. This framework explains the observed minimum in contact voltage drop near 70 to 80°C and supports calculation of contact behavior over a range of temperatures and current densities.
Full Text
EFFECT OF COLLECTOR TEMPERATURE ON THE PROPERTIES OF A SLIDING BRUSH CONTACT
R. F. Bekishev, B. I. Kostylev, A. I. Skorospeshkin
(Recommended by the seminar of the Departments of Electrical Machines and General Electrical Engineering)
The study of the influence of collector temperature on the form of the volt–ampere characteristics of a sliding contact and, as a consequence, on commutation is of considerable interest, since up to the present time there is no complete clarity in the solution of this question.
It has been established experimentally that the dependence of the voltage drop in a sliding brush contact on the temperature of the collector has a complex character. We consider this question from the standpoint of the semiconducting properties of the sliding brush contact, on the basis of the proposed equivalent circuit [1].
This article presents the results of a study of a sliding brush contact at different collector temperatures, using brushes of grades EG-8, EG-4E, EG-14. When taking volt–ampere characteristics, the collector temperature at each point of the characteristic was maintained constant by means of a heater. The constancy of the collector temperature was monitored by the thermoelectric method.
The static volt–ampere characteristic is completely described by the active resistances of the equivalent circuit shown in Fig. 1. Determination of the parameters of the indicated equivalent circuit is carried out according to the method proposed in [1]. The study of the influence of collector temperature on the properties of a sliding contact must be carried out in a differentiated manner, since each resistance of the equivalent circuit has a different physical nature.
Thus, the character of the change in the resistance of the semiconducting blocking layer \(R_{ac}\) with temperature is determined mainly by the semiconducting properties of the collector film. Proceeding from the physical properties of cuprous-oxide semiconductors [2], the change in the resistance of the blocking semiconducting layer with collector temperature is determined by the following expression:
\[ R_{acT} = R_{acT_0} e^{B\left(\frac{1}{T} - \frac{1}{T_0}\right)}, \tag{1} \]
where
\(R_{acT_0}\) — resistance of the blocking layer at a conditionally selected low temperature (in these experiments taken as \(40^\circ\text{C}\)) of the collector and a definite current density;
\(T_0\) — conditionally adopted absolute temperature of the collector in \({}^\circ\text{K}\);
\(B\) — rectifier constant, expressing, if one abstracts from po-
Fig. 1
constant coefficients, the work function (for EG-14 brushes \(B = 5 \cdot 10^3\).
In Fig. 2, dependences of the resistance \(R_{ac}\) on temperature are plotted for EG-14 brushes over a wide range of current-density variation (from \(4\ \mathrm{A/cm^2}\) to \(14\ \mathrm{A/cm^2}\)). The curves \(R_{ac} = f(t^\circ\mathrm{C})\) (Fig. 2—solid lines) were obtained from static volt-ampere characteristics for an anode-polarized brush. Having calculated, from expression (1), the change in the resistance \(R_{ac}\) with change in the absolute temperature of the collector (Fig. 2—dashed lines), we obtain quite satisfactory agreement. Analysis of the curves presented in Fig. 2 shows that at
Fig. 2. Solid lines—experimental; dashed lines—calculated.
at any constant collector temperature, but at different current densities, the value of the resistance \(R_{\mathrm{ac}}\) differs significantly. This is explained by the fact that the resistance of the locking layer \(R_{\mathrm{ac}0}\) changes with a change in the magnitude of the applied voltage.
The resistance of the sections of bilateral conductivity of the collector film, called the leakage resistance \(R_{\mathrm{yt}}\), is due to film defects and graphite inclusions. As the collector temperature increases, the value of the leakage resistance at the same current density decreases substantially.
Figure 3 presents the dependence of the leakage resistance on the collector temperature over a wide range of variation in current density. The dependence \(R_{\mathrm{yt}}=f(t^\circ\mathrm{C})\) was obtained from static current-voltage characteristics for a cathode-polarized brush, taken on a short-circuited collector.
Fig. 3
It is seen from Fig. 3 that, at collector temperatures up to \(80^\circ\mathrm{C}\), the resistance \(R_{\mathrm{yt}}\) at constant current density changes practically according to a rectilinear law. The dependence \(R_{\mathrm{yt}}=f(t^\circ\mathrm{C})\) for the investigated brush grades (EG-8; EG-14; EG-4E) is described, with accuracy sufficient for practical calculations in the indicated temperature range, by the equation
\[ R_{\mathrm{yt}}=R_{\mathrm{yt}0}(1-\alpha t), \tag{2} \]
where
\[ \begin{aligned} R_{\mathrm{yt}0} &\text{ is the leakage resistance at the initial temperature and a specified current density,}\\ t^\circ\mathrm{C} &\text{ is the collector temperature,}\\ \alpha &\text{ is a coefficient depending on the brush grade.} \end{aligned} \]
At collector temperatures above \(80^\circ\mathrm{C}\), the linearity of the curves \(R_{\mathrm{yt}}=f(t^\circ\mathrm{C})\) is violated. In our opinion, this phenomenon is explained by the fact that, in this case, electrochemical phenomena [3] associated with a change in the structure of the adsorbed water film on the collector of the electrical machine become decisive.
The leakage resistance \(R_{\mathrm{yt}0}\) at the initial collector temperature
(in these experiments equal to \(40^\circ\mathrm{C}\)) depends nonlinearly on the current density in the sliding contact. Indeed, with an increase in current density, the spots of bilateral conductivity sharply increase their dimensions by means of \(B\)-fritting, and the resistance \(R_{\mathrm{uto}}\) falls according to a law close to hyperbolic.
Finally, the resistance between the brush and the collector film \(r_{\mathrm{sh}}\) depends on the type of brush and on the mechanics of the commutator-brush assembly. As studies of the thermal conditions on the commutator of an electrical machine have shown, the resistance \(r_{\mathrm{sh}}\) increases with increasing commutator temperature, which is explained by a deterioration of the mechanical state of the latter (an increase in the eccentricity and ellipticity of the commutator, as well as an increase in the level of protrusion and recession of individual commutator bars). Taking profilograms of the commutator with a profilometer with a capacitive sensor at different temperatures shows that the relief of the commutator undergoes substantial changes; moreover, beginning at temperatures of \(80\text{--}100^\circ\mathrm{C}\), these changes are irreversible. Profilograms processed according to the method set forth in [4] show that, with increasing temperature, the amplitude of disturbances of the commutator profile increases (in the range of reversible profile changes) practically linearly. As studies of profilograms at different temperatures have shown, the largest share of the total runout of the commutator is made up by the third harmonic. The change in the resistance \(r_{\mathrm{sh}}\), caused by an increase in the radial vibrations of the brushes when the commutator profile is distorted with increasing temperature, is determined, according to [4], by the amplitude and frequency of the most pronounced harmonic component of the profile.
Figure 4 presents the dependence of the resistance \(r_{\mathrm{sh}}\) on the commutator temperature for various brushes (EG-8; EG-49; EG-14), obtained using static volt-ampere characteristics taken on a short-circuited commutator. The decrease in the resistance
Fig. 4
\(r_{\mathrm{sh}}\), taking into account the small negative temperature coefficient of graphite \((\alpha=-0.00105\ \mathrm{1/^\circ C})\), is insignificant; therefore the decisive influence on the magnitude and nature of the change in the resistance \(r_{\mathrm{sh}}\) with increasing temperature is exerted by the mechanical state of the commutator. It is appropriate to note in this connection that, if the proposed equivalent circuit of a sliding brush contact is used to analyze the results of studies carried out by Volkmann [5] on a copper contact ring with axial channels, then the resistance \(r_{\mathrm{sh}}\) in this case remains po-
constant as the collector temperature increases, since the disturbance of the profile of the contact ring is insignificant.
As is evident from Fig. 4, the dependence of the resistance \(r_{\mathrm{sh}}\) on the collector temperature for various grades of brushes is practically rectilinear and, in the range of reversible disturbances of the collector profile, can be determined by the expression
\[ r_{\mathrm{sh}} = r_{\mathrm{sh}0}(1 + k\Delta t), \tag{3} \]
where
\(r_{\mathrm{sh}0}\) — the resistance between the brush and the collector film at the initial collector temperature, depending on the brush grade and on the mechanics of the collector–brush assembly at the initial collector temperature;
\(k\) — a coefficient taking into account the disturbance of the collector profile when the temperature changes;
\(\Delta t\) — temperature increment in \({}^{\circ}\mathrm{C}\).
Thus, if the nature of the change in the individual parameters of the equivalent circuit with temperature is known, it is possible to determine the dependence of the total resistance of the sliding contact and of the voltage drop between the brush of the corresponding polarity and the collector on the change in the temperature of the latter.
Table 1 presents the results of calculating the transition resistance of a sliding brush contact when the collector temperature is varied over a wide range. The calculation was carried out separately for anodically and cathodically polarized brushes at different current densities.
Figure 5 presents the dependences \(U_{\mathrm{A}} = f(t^{\circ}\mathrm{C})\) and \(U_{\mathrm{K}} = f(t^{\circ}\mathrm{C})\), constructed from the calculation results, for EG-8 brushes at current densities in the contact of 3 and \(13\,a/\mathrm{cm}^{2}\). Analysis of the data obtained makes it possible to explain the complex nature of the change in the transition resistance of the brush–collector contact as the temperature rises. The initial decrease in resistance is due to a sharp decrease in the values of the resistances \(R_{\mathrm{ac}}\) and
Fig. 5
Table 1
| \(t^\circ\mathrm{C}\) | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | \(j,\ \mathrm{A}/\mathrm{cm}^2\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(R_{\mathrm{ac}}\), ohm | 0,03 | 0,15 | 0,1 | 0,08 | 0,05 | 0,035 | 0,03 | 0,027 | 0,025 | 0,023 | 0,021 | 0,02 | 3,3 |
| \(R_{\mathrm{ac}}\), ohm | 0,08 | 0,055 | 0,04 | 0,03 | 0,023 | 0,02 | 0,018 | 0,016 | 0,015 | 0,015 | 0,015 | 0,015 | 13,3 |
| \(R_{\mathrm{ut}}\), ohm | 0,18 | 0,12 | 0,085 | 0,07 | 0,057 | 0,052 | 0,05 | 0,049 | 0,045 | 0,044 | 0,043 | 0,042 | 3,3 |
| \(R_{\mathrm{ut}}\), ohm | 0,08 | 0,065 | 0,05 | 0,044 | 0,035 | 0,032 | 0,031 | 0,03 | 0,028 | 0,027 | 0,026 | 0,025 | 13,3 |
| \(\dfrac{R_{\mathrm{ac}}\cdot R_{\mathrm{ut}}}{R_{\mathrm{ac}}+R_{\mathrm{ut}}}\), ohm | — | 0,11 | 0,046 | 0,038 | 0,0266 | 0,021 | 0,018 | 0,017 | 0,016 | 0,015 | 0,014 | 0,013 | 3,3 |
| \(\dfrac{R_{\mathrm{ac}}\cdot R_{\mathrm{ut}}}{R_{\mathrm{ac}}+R_{\mathrm{ut}}}\), ohm | 0,04 | 0,03 | 0,022 | 0,018 | 0,014 | 0,012 | 0,011 | 0,0105 | 0,0098 | 0,0096 | 0,0095 | 0,0094 | 13,3 |
| \(r_{\mathrm{sh}}\) | 0,03 | 0,038 | 0,045 | 0,05 | 0,06 | 0,067 | 0,075 | 0,082 | 0,09 | 0,097 | 0,106 | 0,114 | — |
| \(R_{\lambda}\), ohm | 0,14 | 0,105 | 0,091 | 0,088 | 0,086 | 0,088 | 0,093 | 0,099 | 0,106 | 0,112 | 0,12 | 0,127 | 3,3 |
| \(R_{\lambda}\), ohm | 0,07 | 0,068 | 0,067 | 0,065 | 0,074 | 0,079 | 0,086 | 0,0925 | 0,0998 | 0,1066 | 0,1155 | 0,1234 | 13,3 |
| \(R_i\), ohm | 0,21 | 0,158 | 0,130 | 0,120 | 0,117 | 0,119 | 0,125 | 0,131 | 0,135 | 0,141 | 0,149 | 0,156 | 3,3 |
| \(R_i\), ohm | 0,11 | 0,103 | 0,095 | 0,094 | 0,085 | 0,099 | 0,106 | 0,112 | 0,118 | 0,124 | 0,132 | 0,139 | 13,3 |
$R_{\mathrm{ut}}$ with increasing temperature, which is most characteristically expressed at low current density. At a collector temperature above 80–100°C, these resistances remain practically constant and are insignificant in magnitude. Therefore, the change in the resultant resistance of the sliding brush contact at high collector temperatures is determined mainly by the resistance $r_{\mathrm{sh}}$. Indeed, with increasing temperature the current–voltage characteristics tend to straighten and at a temperature of 80–100°C approach a straight line. In this case the resistances $R_{\mathrm{ac}}$ and $R_{\mathrm{ut}}$, which determine the nonlinearity of the current–voltage characteristic, are so small even at low current density that they exert no substantial influence. The conducting properties of the collector film are impaired upon further increase in the collector temperature, and the contact voltage drop between brushes of both polarities and the collector is determined by the magnitude of $r_{\mathrm{sh}}$. It is therefore no accident that the difference in the current–voltage characteristics caused by polarity is most sharply manifested at low collector temperatures. It should be noted that the significant increase in contact resistance at high collector temperatures (above 100–120°C) is explained only by an increase in the resistance $r_{\mathrm{sh}}$, since in this case not only does intensive formation of the collector film fail to occur, as indicated in [6], but the existing film also “burns out.”
Thus, the investigations carried out of the parameters of the sliding contact under variation of the collector temperature, on the basis of the proposed equivalent circuit, make it possible not only to explain the complex character of the transition resistance and voltage drop in the sliding contact, but also to calculate them.
Conclusions
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The proposed equivalent circuit of the sliding brush contact makes it possible to determine the influence of collector temperature on the form of the current–voltage characteristics.
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At low collector temperature (up to 50°C), the current–voltage characteristic of the sliding contact is determined mainly by the nonlinear resistances $R_{\mathrm{ac}}$ and $R_{\mathrm{ut}}$, whose magnitude decreases with increasing temperature.
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The resistance $r_{\mathrm{sh}}$ increases with increasing temperature (which is explained by disturbances of the mechanical state of the collector) and at temperatures above 80°C becomes the determining factor. Therefore the contact voltage drop, having reached a minimum value at a temperature of 70–80°C, increases with further increase in temperature.
References
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L. Ya. Zinner. Investigation of the influence of the mechanics of a sliding contact on commutation in commutator electrical machines. Dissertation, Tomsk, 1968.
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Volkmann W. Halbleitereffekte beim kohlebürsten—Gleitkontakt. ETZ-A, 89, No. 17, 1968.
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M. F. Karasev, V. A. Seregin, V. V. Turkin. Influence of temperature on the magnitude of the voltage drop in a brush contact and on commutation conditions. Scientific Works of OMIIT, vol. 88, issue 2, Omsk, 1968.