ANALYTICAL AND EXPERIMENTAL STUDY OF COMMUTATION IN A CROSS-FIELD EMU WITH A SMOOTH ARMATURE

A. I. Skorospeshkin, B. I. Kostylev, G. G. Konstantinov

(Recommended by the seminar of the departments of electrical machines and general electrical engineering)

Numerous studies of commutation in commutator electrical machines show that, among the large number of factors influencing the commutation process, the principal ones are electromagnetic. When the mechanical condition of the commutator-brush assembly is satisfactory, it is precisely the electromagnetic factors that lead to nonidentity of commutation of individual sections located in the same slot. This substantially limits the adjustment of commutation, since the action of the commutating field must not be the same for different sections. In addition, the placement of sections in slots leads to the sections having considerable inductance and, consequently, a reactive e.m.f. during commutation.

The indicated features can be eliminated or substantially weakened if the armature of the commutator machine is made smooth [1]. In this case the parameters of all sections will be identical, i.e., the electromagnetic causes of nonidentity are eliminated, and the inductances of the sections are considerably reduced.

Since the commutation process in a machine with a smooth armature proceeds in principle in the same way as in a machine with a toothed armature, methods verified on ordinary commutator machines may be applied to its study.

We carried out analytical and experimental studies of commutation in three models of cross-field EMU with a smooth armature. Some results of these studies are presented in the present work.

The models were made on the basis of a standard electric-machine amplifier of type EMU-12. Two of them, with an asynchronous drive, have a rotational speed \(n = 2900\) rpm, a minimum power of 0.7 kW, nominal voltages of 30 and 60 V, and, respectively, the number of turns in a section equal to 1 and 2. The third model, with a direct-current drive, has a rotational speed of 3500 rpm, power of 1 kW, voltage of 115 V, and 3 turns in a section. The commutator-brush assembly for all three models was taken from the standard EMU without changes; that is, the commutator has 87 laminations, brushes of grade EG-8 of size \(5 \times 15\) mm, two on each brush bolt, and brush overlap \(\beta = 1.5\). The winding for all models is a simple loop winding, since the amplifiers are of two-pole construction.

The analytical study of commutation in the EMU with a smooth armature was carried out according to the method [2] proposed for calculating the commutation of commutator machines with a toothed armature. Analytical methods for calculating commutation with allowance for mutual-inductive couplings and nonlinea-

properties of the brush contact, which, unfortunately, have not yet been worked out, are of very great importance in the design of commutator electrical machines. Such methods, providing sufficient reliability, would make it possible to predict the commutation reliability of the machine during design, to determine the electromagnetic loads, the parameters of the sections, and the brush grade from the standpoint of ensuring satisfactory commutation.

Taking into account the complexity of the commutation process, it may be stated with complete confidence that these calculation methods are feasible only with the use of electronic computers. Recently, works have appeared devoted to the calculation of commutation on analog and digital computers [2, 3, 4]. Naturally, a number of propositions of these calculation methods must be checked on many machines, and the methods themselves must be finally developed in such a way that they can be used by designers of commutator electrical machines.

The most objective assessment of calculation methods can be provided only by experiment. Therefore, at present numerous analytical and experimental studies of the commutation of various machines are necessary in order to complete the work that has been begun on the analytical solution of the commutation process.

The procedure for compiling the differential equations of commutation is, in principle, the same in all methods and is set forth in detail in [2, 3, 4]. The algorithm and program for calculating the commutation of an EMU, adopted in the investigations, are described in [2]. The program of Fig. 1 is very simple and universal; it can be successfully applied for calculating the commutation of both direct-current and alternating-current machines. The system of equa-

Figure 1 labels:

• Input of initial conditions
• Call to the Runge–Kutta subprogram
• To computation of the right-hand sides
• Computation of \(\Delta U\)
• Computation of determinants
• To processing of integration results
• Counting the number of steps
• Check for completion of the computation
• Input of initial conditions for the next section
• End of computation; printout of results

Fig. 1. Block diagram of the program for calculating the commutation process.

tions is solved by the Runge–Kutta method, since it is relatively simple, provides sufficient computational accuracy, and, in addition, there is a standard subroutine for the “Minsk-1” digital computer.

The volt-ampere characteristic of the brush contact is approximated by an exponential function of the form

\[ \Delta U = a j^k, \]

where \(\Delta U\) is the voltage drop in the brush contact,
\(j\) is the current density in the brush contact,
and \(a\) and \(k\) are coefficients of the approximating expression.

For the amplifiers under study, the time diagram of commutation is shown in Fig. 2. It is assumed here that commutation

Fig. 2. Time diagram of commutation:
\(T_{\text{c}}\) — calculated commutation cycle,
\(T_{\text{k}}\) — commutator period,
\(T_{\text{sh}}\) — time during which the sections are short-circuited by the brushes.

under the anode and cathode brushes proceeds identically. Since in a smooth armature it may be considered that the number of elementary slots is equal to the number of real ones, that is, \(u_{\text{p}} = 1\), then according to [2] the calculated cycle will be equal to

\[ T_{\text{c}} = U_{\text{p}} \frac{T_{\text{k}}}{2} = \frac{T_{\text{k}}}{2}, \]

where \(u_{\text{p}}\) is the number of section sides in a slot,
\(T_{\text{k}}\) is the time corresponding to rotation of the armature by one commutator division.

Indeed, in a smooth armature the commutation of all sections proceeds identically and, as follows from the time diagram in Fig. 2, it is sufficient to calculate the commutation-current curves of three sections over the interval \(\dfrac{T_{\text{k}}}{2}\), which gives a complete picture of the entire current curve over the time \(1.5T_{\text{k}}\).

The system of differential equations has the form:

\[ L \frac{dx}{dt} + M_{\text{vn}} \frac{dy}{dt} + M \frac{dz}{dt} = \sum e - R_x - \Delta U_1 + \Delta U_2, \]

\[ L \frac{dy}{dt} + M_{\text{vn}} \frac{dx}{dt} + M \frac{dz}{dt} = \sum e - R_y - \Delta U_3 + \Delta U_4, \]

\[ L \frac{dz}{dt} + M_{\text{vn}} \frac{dy}{dt} + M \frac{dx}{dt} = \sum e - R_z - \Delta U_5 + \Delta U_1. \]

where \(R\) is the resistance of a section;
\(L\) is the inductance of the commutated sections;
\(M_{\text{vn}}\) is the mutual inductance between sections commutated by opposite brushes;
\(M\) is the mutual inductance between sections commutated by the same brush;
\(\sum e\) is the total rotational emf of the commutated section;
\(\Delta U_1 \div \Delta U_5\) are the voltage drops in the brush contact.

The calculations are carried out on the basis of approximate initial conditions, which are determined from the rectilinear commutation-current curve.

The computed current values at the end of an interval serve as the initial conditions for the next interval or, in the example considered, as the initial conditions of the second approximation. The calculation is carried out several times (not more than 3–4) until sufficient convergence is obtained between the results of two successive identical intervals.

Fig. 3. Calculated (dashed lines) and experimental (solid lines) commutation-current curves:
a — for the transverse circuit at \(I_q = 5.6\) A;
b — for the longitudinal circuit at \(I_d = 8.7\) A.

Figure 3 gives the calculated and experimental commutation-current curves in the longitudinal and transverse circuits of the third EMU model. The initial data for the calculation are:

\[ R = 0.19\ \Omega;\quad L = 4 \cdot 10^{-6}\ \text{H};\quad M = 3.4 \cdot 10^{-6}\ \text{H};\quad M_{\mathrm{vn}} = 1.29 \cdot 10^{-6}\ \text{H}; \]

\[ \Delta U = (0.5 i)^{0.5} \]

\[ \sum e = 0 \]
for the commutated sections of the longitudinal circuit,

\[ \sum e = -0.935 \]
for the sections of the transverse circuit.

The current of the longitudinal circuit is \(I_{d\mathrm{n}} = 8.7\) A; that of the transverse circuit is \(I_{q\mathrm{n}} = 5.6\) A.

The expression for the volt-ampere characteristic was obtained by approximating the experimental characteristic for EG-8 brushes, taken on the short-circuited commutator of a standard EMU-12A. The remaining parameters were determined by calculation according to existing methods, since in designing the machine this is the only way to determine them. Determination of the parameters experimentally is possible in a manufactured machine, which does not correspond to the main task of calculating commutation during the design process.

Oscillographic recording of the current curves of the commutated sections and of the field was performed with the aid of bifilar turns.

Comparison of the current curves in Fig. 3 shows satisfactory agreement between calculation and experiment, especially in the character of the curves. The discrepancies are mainly due to the mismatch between the actual commutation period and the calculated one, owing to contact instability at the final stage. Therefore, in further work it is proposed to introduce into the calculation a reduction of the contact time on the basis of probabilistic methods. The disturbance of the smoothness of the current-variation curve is caused by magnetic coupling between sections and corresponds to the moment at which another section enters or leaves the commutation process.

It is also seen from the current curves in Fig. 3 that the character of the current variation in the sections is close to rectilinear. A somewhat greater deviation of the curves toward retardation is observed for the transverse circuit, which

This is explained by the action of the rotational emf from the armature-reaction field. Judging from the current curves, commutation should proceed quite satisfactorily. Observations of sparking and of the state of the brush contact during the experiment also confirm this. At the rated load of the amplifier, sparking under the brushes is completely absent. Even under repeated overloads, sparking is absent in the first two models, and in the third it does not exceed grade 1 on the GOST scale, although the current density under the brush considerably exceeds the rated value.

The studies showed that in the amplifiers considered, with a smooth armature, there is no need for additional poles along the longitudinal axis; therefore, in the first and third models they were removed. In this case, too, the compensating winding does not play the role of a factor substantially affecting commutation, as it does in standard amplifiers [5].

The analytical and experimental investigations once again confirmed that electromagnetic factors are among the principal ones. Therefore, in commutator machines, first of all, the appropriate electromagnetic conditions of commutation must be ensured, and the proposed calculation method, in our opinion, can fully contribute to this.

Conclusions

1. The investigations carried out confirm the possibility of applying the proposed method for calculating commutation in the process of designing commutator electric machines.

2. The electromagnetic conditions of commutation are decisive, and they must be ensured when designing the machine.

3. Replacing the toothed armature of commutator electric machines with a smooth one undoubtedly considerably increases their commutation reliability, both from the standpoint of reducing the inductance of the sections and from the standpoint of the identity of the commutation cycles.

References

1. A. I. Skorospeshkin, Yu. A. Stepanov. A cross-field EMU with a smooth armature, Elektromekhanika, No. 10, 1964.

2. B. I. Kostylev. Studies of a cross-field EMU operating with a variable control signal. Dissertation, Tomsk, 1965.

3. E. M. Sinelnikov, A. G. Nazikyan, V. V. Kleimenov, F. I. Chernyavsky. Application of continuous-action computing machines to the study of commutation in direct-current machines, Elektromekhanika, No. 10, 1960.

4. O. G. Wegner. Calculation of the commutation process and the width of the sparkless-operation zone of direct-current machines using an electronic digital computer, Elektromekhanika, No. 4, 1966.

5. A. I. Skorospeshkin. On the commutation of cross-field electromechanical amplifiers, Elektromekhanika, No. 6, 1959.