ON SOME ISSUES OF COMMUTATION IN COMMUTATOR ELECTRIC MACHINES

A. I. SKOROSPELKIN, B. I. KOSTYLEV, Yu. P. GALISHNIKOV

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

Under present-day conditions in the development of commutator electric machines, the problem of commutation is becoming especially acute. This is connected with increased electromagnetic loading, higher rotational speeds, and the imposition of stricter operating requirements, with operation under the most varied conditions.

Although the problem of commutation is an old one, as a rule it always arises in a new aspect. This occurs because commutator electric machines have a complex system of circuits. Moreover, the commutation process is distinguished by complexity also because the operation of the sliding contact is affected by a wide variety of factors (the material of the brush and commutator, design features, the nature of the load, mechanical factors, etc.).

The equations of commutation contain nonlinearities. Therefore it is difficult to study them completely by analytical methods. In general, the complexity of the commutation process makes both analytical and experimental investigations difficult. Consequently, up to the present time there are no generally recognized analytical or experimental solutions to the problem of commutation. And, in all probability, they are difficult to obtain, since individual types of machines and the conditions of their operation have their own specific features, which must be taken into account in each particular case.

It should be noted that in many cases investigations of commutation have been carried out on models. Models imitate the commutation process and at the same time make it possible to separate the influence of individual factors, so that investigation of the commutation process is facilitated. The point, however, is that results obtained on models often diverge from results obtained on real machines. This gives rise to discussions that at times bring no tangible benefit.

In the analytical investigation of the commutation process, the main difficulty lies in the correct determination of the transient resistance of the brush contact.

The classical theory of commutation, which has found the widest application up to the present time and is based on the assumption of constancy of the specific transient resistance of the brush contact, has substantial shortcomings, which naturally leads to the need to seek new approaches in the investigation of commutation. Among these shortcomings are the difficulty and impossibility of calculations in the case \(v_{\mathrm{sh}} > v_k\), the failure to take into account the inequality of the actual and calculated perio-

…of commutation, etc. A consequence of this is the need for practical correction and adjustment of the commutation of machines after their manufacture.

Among other analytical regularities, which are slowly making their way, attention is deserved by the equations obtained by O. G. Wagner on the basis of the assumption \(\Delta U_{\mathrm{sh}}=\mathrm{const}\). These equations ensure the obtaining of a curve with a low-current stage. It is very tempting to achieve such a change in current when, at the final stage, the breaking current is absent and the trailing edge of the brush operates without current load. But the main difficulty lies in obtaining the low-current stage. For this, the corresponding distribution of the commutating field, the winding, and a definite type of brushes are necessary. Nevertheless, the assumption \(\Delta U_{\mathrm{sh}}=\mathrm{const}\) and the equations obtained on its basis have a physical and logical justification. Therefore, in our view, the equations of O. G. Wagner, as a special case, are applicable to a certain type of machine and operating conditions, but cannot claim to provide a comprehensive solution of the commutation problem.

In our opinion, the most promising approach, and the one that makes it possible to reflect more fully the physical aspect of the commutation process, is an investigation based on taking into account the dependence of the specific transient resistance of the brush contact on the current density.

What dependences \(r_{\mathrm{sh}}=f(j)\) occur in the axes of coordinates \(r_{\mathrm{sh}}, j\)? If a straight line 1, parallel to the abscissa axis (Fig. 1), is drawn, it can be seen that it corresponds to the classical theory, in which

Fig. 1. Types of possible dependences \(r_{\mathrm{sh}}=f(j)\).

it is assumed that \(r_{\mathrm{sh}}=\mathrm{const}\). Further, one of the possible dependences is the dependence that can be expressed by the equation of a straight line in intercepts

\[ \frac{j}{a}+\frac{r_{\mathrm{sh}}}{b}=1, \tag{1} \]

where \(r_{\mathrm{sh}}, j\) are the instantaneous values of the transient resistance of the brush contact and the current density,

\(a, b\) are constants.

Another possible dependence \(r_{\mathrm{sh}}=f(j)\) may be defined by an exponential

\[ r_{\mathrm{sh}}=r_m e^{-k j}, \tag{2} \]

where \(r_m\) is the maximum value of the transition resistance, \(k\) is a coefficient determined by the character of the exponent.

Another dependence is the hyperbolic one

\[ r_{\mathrm{ш}}=\frac{a'\cdot b'}{j}. \tag{3} \]

Here \(a'\), \(b'\) are constants.

The differential equation for the commutated circuit (Fig. 2) is written in the following form:

\[ L_c\frac{di}{dt}+i\cdot r_c+i_2\cdot r_2(j_2)-i_1\cdot r_1(j_1)=\pm e_k. \tag{4} \]

Fig. 2. Diagram of the commutated circuit.

The designations in (4) and in Fig. 2 are:

\(L_c, r_c\) — inductive and active resistances of the section;
\(i_a\) — current of the parallel branch of the armature winding;
\(i\) — current of the commutated section;
\(i_1=i_a-i\) — current corresponding to the entering part of the brush;
\(i_2=i_a+i\) — current corresponding to the leaving part of the brush;
\(t\) — time from the beginning of commutation;
\(T_k\) — commutation period;
\(e_k\) — commutating e.m.f.;
\(r_1(j_1), r_2(j_2)\) — resistances of the entering and leaving parts of the brush as functions of current density.

If one looks more deeply into the essence of the question, one may come to the conclusion that the relation \(r_{\mathrm{ш}}=f(j)\) is the most general, while all the remaining equations are only special cases. Further, taking into account the dependence \(r_{\mathrm{ш}}=f(j)\), it appears possible to solve correctly the energy aspect of the problem of commutation.

It should be noted that, when such a dependence is taken into account, nonlinear differential equations are obtained, the solution of which requires considerable time and skill. But with the use of computing machines this shortcoming is eliminated. Examples of such use already exist (Department of Electrical Machines of the Novocherkassk Polytechnic Institute).

The question arises as to which dependences \(r_{\mathrm{ш}}=f(i)\) may be used for analytical investigations of commutation: static or

dynamic. An answer to this question can be given as a result of detailed studies.

Attention should also be paid to the following circumstance. All studies of the commutation process—both analytical and experimental—set themselves the task of finding ways to improve commutation conditions, to improve the characteristics of the machine, and to increase the machine’s commutational reliability. In our view, the solution of this problem can be carried out only by applying probability theory and the methods of mathematical statistics. This is prompted by the very nature of the commutation process, with all its complexity, many-sidedness, and interweaving of various factors.

No definitive word has been said on the question of selecting the grade of brushes and determining their commutating ability. This is explained by the very complex dependence of brush operation on various factors: material, manufacturing technology, operating conditions, etc.

In this respect, serious attention is deserved by the definition of the commutating ability of brushes, proposed by Prof. M. F. Karasev on the basis of the conditions of optimal commutation. The author gives a distinctive interpretation of brush operation, especially at the final stage. The meaning is seen in the fact that if, at the final stage, the trailing edge of the brush is not loaded with current, then no commutating properties are required of the brush. The brush leaves the commutator segment without sparking. This may occur in the case of normally accelerated commutation. The nature of the current variation at the preceding stage is not considered here. What is important is that the trailing edge should operate without load. But owing to the nonidentity of the commutation conditions of individual sections, some of them complete the commutation process either with retardation or with acceleration differing from the normal one. It is for these conditions that the commutating properties of the brush must manifest themselves. For these sections as well, the brush must ensure sparkless completion of commutation. In this interpretation of the question of the commutating ability of a brush, in our opinion, there is logical sense.

But the question naturally arises: “Why, then, must the commutating properties of a brush manifest themselves only at the trailing edge? What about the leading edge of the brush? Why is the change in current before the final stage of commutation not taken into account?” There are cases when the leading edge sparks. Moreover, the final stage is prepared by the change in current over nearly the entire commutation period.

Furthermore, instruments and methods for analyzing sparking and adjusting commutation are imperfect. Work is needed to improve them and to develop new instruments and methods. A special place should be assigned to the development of instruments that make it possible to measure commutator irregularities. It is known that commutator irregularities are one of the causes of brush sparking. With an increase in rotational speed from several thousand to tens of thousands, the problem of manufacturing a commutator that would retain a strictly cylindrical shape is at present the most urgent one. In order to give practical recommendations for manufacturing commutators, sufficiently accurate measurement of their irregularities is necessary. There exist some methods and instruments using various pickups and UKV, but they have not found application because of their imperfection and bulkiness.

Serious work is necessary, on the basis of which it would be possible to have a sufficiently clear idea of the influence of various factors, in particular electromagnetic and mechanical ones. This thought is suggested by the investigation of an electromechanical amplifier with a smooth armature that we have made. The influence of electromagnetic factors began—

is completely eliminated; only mechanical causes remain (vibrations, existing irregularities of the commutator, etc.). However, commutation under considerable loads proceeds entirely without sparking. Therefore the conclusion suggests itself that, since in most commutator machines it is impossible to exclude completely the influence of mechanical and electromagnetic factors, investigations should establish the optimum combination of them at which commutation will be satisfactory.

Conclusions

1. The most promising direction in solving the commutation problem is research that takes into account the dependence of the specific transient resistance of the brush contact on current density.

2. The equations of O. G. Wegner, obtained on the basis of the assumption \(\Delta U_{\text{sh}} = \mathrm{const}\), are acceptable, as a special case, for certain conditions and types of machines.

3. The use of probability theory and methods of mathematical statistics will make it possible to conduct versatile and deeper studies of commutation.

4. The idea of optimal commutation and the corresponding definition of the commutating ability of brushes, proposed by Prof. M. F. Karasev, and the work carried out in this direction are of great importance for theoretical and practical solutions to questions of commutation.

5. Further work is urgently needed to improve existing instruments and methods for analyzing and adjusting commutation, and also to develop new methods and instruments, in particular for determining the profilogram of the commutator.

6. Research must be carried out to establish the optimal combination of electromagnetic and mechanical factors under which the commutation of commutator machines is satisfactory.

LITERATURE

1. M. F. Karasev. Commutation of DC commutator machines. GEI, 1961.

2. Questions of commutation of commutator electric machines. Scientific Transactions of OMIIT, vol. XLIV, 1964.

3. O. G. Wegner. Theory and practice of commutation in DC machines. GEI, 1961.

4. A. I. Skorospeshkin. Commutation of a transverse-field EMU. 1960. Tomsk.

5. E. M. Sinelshchikov, A. G. Nazikyan, A. V. Kleimenov, F. I. Chernyavsky. Application of continuous-action calculating machines for investigating commutation of DC machines. Proceedings of Higher Educational Institutions, Electromechanics, No. 10, 1960.