Results of a Refined Calculation of Commutation and Commutation Stability of a DC Machine Based on Accounting for a Family of Natural Current-Voltage Characteristics of a Sliding Contact
Abstract Generated abstract
This paper presents a refined calculation of commutation and commutation stability in a low-power DC machine using experimentally obtained families of natural current-voltage characteristics for EG-4E brush contacts under anode and cathode polarization. The authors solve the commutation differential equations iteratively on an M-20 digital computer and compare calculated section currents and brush contact voltage drops with experimental curves. The results show generally satisfactory agreement, with remaining discrepancies attributed mainly to approximations in mutual inductance and to magnetic-field effects near the end of commutation. The analysis indicates that brush-contact voltage effects can retard commutation under overcommutation and increase with commutation acceleration, supporting the need to include partial natural contact characteristics in analytical calculations.
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RESULTS OF A REFINED CALCULATION OF COMMUTATION AND COMMUTATION STABILITY OF DC MACHINES BASED ON ACCOUNTING FOR A FAMILY OF NATURAL CURRENT–VOLTAGE CHARACTERISTICS OF A SLIDING CONTACT
Yu. P. Galishnikov, A. I. Skorospelkin
(Recommended by the seminar of the Departments of Electrical Machines and General Electrical Engineering)
As was rightly pointed out in [1], in calculations of commutation in DC machines, “the calculation algorithm must follow from a definite scientific conception, and the reliability of its results is determined by the degree to which this conception corresponds to reality.”
The data presented below are the result of a refined calculation for a low-power DC machine, using partial natural current–voltage characteristics of the brush contact obtained experimentally over a wide range of variation of commutation conditions and represented in the form of analytical expressions that describe families of partial curves for anode- and cathode-polarized brushes of grade EG-4E.
The initial premises, as well as the method of writing the differential equations for the sections undergoing commutation, were considered in the preceding article on this question, published in the present collection.
The calculation was performed by the iteration method (calculation step \(1/100\)) for 4 calculation intervals, the duration of each of which is proportional to the commutator period, using the M-20 electronic digital computer.
Since the calculation used the actual characteristics of the brush contact, analysis of the calculated data shows their quite satisfactory agreement with the results of experiments.
Thus, in Fig. 1a the current curves of the 3rd and 4th slot sections are given when they are commutated by a brush of positive polarity. Both the calculated curves (solid lines) and the experimental curves approximately correspond to the middle of the sparkless-operation zone of the DC machine. As can be seen, the curves are sufficiently similar, especially in the first third of the commutation period. Some differences in the final phase of commutation are apparently due to the somewhat larger values of the mutual-inductance coefficients between the slot sections adopted in the calculation, as compared with their actual values. In addition, a certain error is introduced by the assumption we adopted that the emf induced in the section circuit by external magnetic fields remains constant throughout the entire commutation period. In reality, however, as our investigations show, there is an influence of the magnetic field of the main poles, which, acting opposite to the field of the interpole, leads to a certain slowing of commutation at its completion; this is revealed quite distinctly on the experimental commutation curve of the 4th slot section.
Further, Fig. 1b presents the curves of the voltage drop between the brush and the commutator bar, common to the 3rd and 4th sections.
Fig. 1. Anode-polarized brush:
a) commutation current curves;
b) contact voltage-drop curves.
groove. The solid line here shows the calculated curve, and the dashed line the experimental one. The discrepancies between these curves over most of their extent are very small; moreover, the experimental curve is more irregular than the calculated one, which is probably associated with the mechanical operating conditions of the sliding contact, as well as with certain of its physical characteristics that are difficult to take into account in the chosen method of approximating the current-voltage characteristics.
Somewhat larger discrepancies are found at the end of commutation. This is caused, as we said with respect to the current curves, by the influence of the magnetic field of the main poles.
The situation is analogous for commutation of sections under a cathode-polarized brush. The corresponding curves are given in Figs. 2a, b.
It is of interest to analyze the influence of the brush contact on commutation. The instantaneous values of this influence are determined, as is known, by the expression
\[ \left(U_{\mathrm{nb}} - U_{\mathrm{sb}}\right), \tag{1} \]
where
\(U_{\mathrm{nb}}\) is the voltage drop between the brush and the incoming commutator segment,
\(U_{\mathrm{sb}}\) is the voltage drop between the brush and the outgoing commutator segment.
Fig. 2. Cathode-polarized brush:
a) commutation-current curves,
b) contact voltage-drop curves.
Figure 3 presents curves showing the variation of the instantaneous values \(\left(U_{\mathrm{nb}} - U_{\mathrm{sb}}\right)\) for each of the four sections of one slot. The curves shown correspond to the current curves in Figs. 1 and 2. Since, as we see, in the present case appreciable overcommutation takes place, the difference in voltage drop \(\left(U_{\mathrm{nb}} - U_{\mathrm{sb}}\right)\) is directed oppositely with respect to the commutating emf and acts on commutation in a retarding manner.
Section 1
\[ \frac{1}{t_1}\int_{0}^{t_1}(U_2-U_1)\,dt=0.292\,\mathrm{V} \]
\[ \frac{1}{T_k-t_1}\int_{t_1}^{T_k}(U_2-U_1)\,dt=0.564\,\mathrm{V} \]
\[ \frac{1}{t_1}\int_{0}^{t_1}(U'_2-U'_1)\,dt=0.403\,\mathrm{V} \]
\[ \frac{1}{T_k-t_1}\int_{t_1}^{T_k}(U'_2-U'_1)\,dt=0.570\,\mathrm{V} \]
Section 2
\[ \frac{1}{t_1}\int_{0}^{t_1}(U_3-U_2)\,dt=0.557\,\mathrm{V} \]
\[ \frac{1}{T_k-t_1}\int_{t_1}^{T_k}(U_3-U_2)\,dt=0.587\,\mathrm{V} \]
\[ \frac{1}{t_1}\int_{0}^{t_1}(U'_3-U'_2)\,dt=0.690\,\mathrm{V} \]
\[ \frac{1}{T_k-t_1}\int_{t_1}^{T_k}(U'_3-U'_2)\,dt=0.545\,\mathrm{V} \]
Section 3
\[ \frac{1}{t_1}\int_{0}^{t_1}(U_4-U_3)\,dt=0.440\,\mathrm{V} \]
\[ \frac{1}{T_k-t_1}\int_{t_1}^{T_k}(U_4-U_3)\,dt=0.280\,\mathrm{V} \]
\[ \frac{1}{t_1}\int_{0}^{t_1}(U'_4-U'_5)\,dt=0.480\,\mathrm{V} \]
\[ \frac{1}{T_k-t_1}\int_{t_1}^{T_k}(U'_4-U'_3)\,dt=0.476\,\mathrm{V} \]
Section 4
\[ \frac{1}{t_1}\int_{0}^{t_1}(U_1-U_4)\,dt=0.477\,\mathrm{V} \]
\[ \frac{1}{T_k-t_1}\int_{t_1}^{T_k}(U_1-U_4)\,dt=0.992\,\mathrm{V} \]
\[ \frac{1}{t_1}\int_{0}^{t_1}(U'_1-U'_4)\,dt=0.678\,\mathrm{V} \]
\[ \frac{1}{T_k-t_1}\int_{t_1}^{T_k}(U'_1-U'_4)\,dt=1.12\,\mathrm{V} \]
Fig. 3. Effect of brush contact on commutation.
When considering the curves in Fig. 3, it seems advisable to express the effect of the brush contact in the form of its effective value
\[ \frac{1}{t}\int_{0}^{t} (U_{\mathrm{nb}} - U_{\mathrm{sb}})\cdot dt. \tag{2} \]
In this case the following interesting features are revealed. First, when the direction of the current in the commutator bar changes to the opposite one (with substantial overcommutation), in most cases there is no sharp increase in the effect of the brush contact on commutation. Only when an independent section is being commutated is there an increase in this effect by no more than a factor of 2. Thus, for example, for the 4th section (Fig. 3) during the period of commutation proper (anode brush),
\[ \frac{1}{t_1}\int_{0}^{t_1}(U_1 - U_4)\,dt = 0.477\ \mathrm{V}, \tag{3} \]
and after the direction of the current in the bar changes,
\[ \frac{1}{T_k - t_1}\int_{t_1}^{T_k}(U_1 - U_4)\,dt = 0.992\ \mathrm{V}, \tag{4} \]
where \(t_1\) is the instant at which the direction of the current in the commutator bar changes.
An analogous relation also holds for a cathode-polarized brush.
The increase in \((U_{\mathrm{nb}} - U_{\mathrm{sb}})\) when the direction of the current in the bar changes is not so large, since, despite the change in sign of \(U_{\mathrm{sb}}\), there is a decrease in \(U_{\mathrm{nb}}\) owing to the reduction of current density in the contact, and as a result the increase in \((U_{\mathrm{nb}} + U_{\mathrm{sb}})\) is not very significant.
Another interesting feature is that, with an increase in the degree of acceleration of commutation, the effect of the brush contact increases substantially both during the period of commutation proper and after the direction of the current in the loop changes. This known circumstance leads to the fact that the middle of the zone of sparkless operation, strictly speaking, corresponds not to optimal commutation as defined in [2], but to a more accelerated commutation in comparison with it.
In general, the proposed method provides quite satisfactory accuracy in calculating commutation and commutation stability of DC machines and thereby confirms the necessity, in the analytical study of commutation, of taking into account the family of partial natural current-voltage characteristics of the brush contact.
REFERENCES
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O. G. Vegner. Calculation of the commutation process and of the width of the sparkless operating zone of DC machines using a digital computer, IVUZ, Electromechanics, 1966, No. 4.
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M. F. Karasev, V. N. Kozlov. Optimal commutation in DC machines, Scientific Transactions of OMIIT, vol. 44, 1964.