Transverse Armature Reaction, the Reaction of Commutating and Eddy Currents in a Cross-Field EMA

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

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

In methods for determining the reaction of commutating and eddy currents in a cross-field EMA [1, 2, 4, 5], with the exception of [6], the influence of the transverse armature reaction is not taken into account, although this influence is very substantial.

In the present article a method is proposed for determining the resultant reaction from the current of the transverse circuit, as well as its individual components, taking into account the distinctive action of the transverse armature reaction for various control signals.

In the general case, when a cross-field electric machine amplifier is operating at no load, the equation of the m.m.f.’s acting along the longitudinal axis is written in the following form:

\[ F_d = F_y - F_k - F_c - F_{р я} + F_{ad}, \tag{1} \]

where

\(F_y\) — m.m.f. of the control windings,

\(F_k\) — m.m.f. of the commutating currents of the transverse circuit under delayed commutation,

\(F_c\) — m.m.f. from eddy currents and hysteresis,

\(F_{р я}\) — m.m.f. equivalent to the transverse armature reaction when the paths of the longitudinal flux are saturated by the transverse flux,

\(F_{ad}\) — m.m.f. of the longitudinal armature reaction, caused by the displacement of the transverse brushes from the neutral.

The magnitude of the m.m.f. \(F_{р я}\) in equation (1) can be neglected only in a linear consideration of the operating modes of the amplifier.

However, the actual no-load characteristic of the first stage of the amplifier is nonlinear (Fig. 1) and has two bends: concavity due to an increase in the magnetic permeability of the steel at low inductions, and convexity due to saturation.

Studies carried out by the method proposed below on a number of production amplifiers of the EMU-12A and EMU-12PM types and on amplifiers with a smooth armature showed that, when considering the operation of a cross-field EMA with various control signals, one cannot neglect either the magnitude or the distinctive nature of the action of the m.m.f. of the transverse armature reaction.

Figure 2 gives, in relative units, the dependence of the m.m.f. \(F_{р я}\) on the currents of the control and transverse circuits for the production EMU-12A, calculated by the method of [6].

From an analysis of this dependence it follows that:

1. when a cross-field EMA operates with various control signals, the m.m.f. of the transverse armature reaction may act as a magnetiz...

Fig. 1. No-load characteristic of the first stage of the EMU-12A

Fig. 2. Dependence of the m.m.f. \(F_{\mathrm{r}a}\) on the transverse-circuit current \(I_q\) and the control current \(I_y\)

... in a magnetizing manner, owing both to the concavity of the no-load characteristic in the initial part and to its demagnetizing action at saturation;

2) when the amplifier operates with a slowly varying control signal (for example, in automatic speed-maintenance, voltage-maintenance, etc., circuits), a regime is possible in which the magnitude and action of the m.m.f. of the transverse armature reaction will be minimal.

The complicated character of the dependence of the m.m.f. of the commutating currents, eddy currents, and transverse armature reaction on the current of the transverse circuit, and the distinctive action of the m.m.f. of the transverse armature reaction for different control signals, pose the problem of separating and determining each of these components so that, already at the design stage, it would be possible to estimate the influence of each of them on the control m.m.f.

In experimentally determining the individual components of the reaction from the current of the transverse circuit, one may proceed from the difference in the directions of their ac...

actions on the control m.m.f. when the transverse armature circuit is supplied from an external source and the polarity of the control field is changed.

When the polarity of the control field is changed and the direction of the current in the transverse circuit is maintained by supplying it from an external source, the following components of the reaction from this current remain the same in magnitude and direction:

1. the m.m.f. of the commutating currents, since the current of the transverse circuit retains its magnitude and direction;

2. the m.m.f. from eddy currents and hysteresis, since in both cases there is the same transverse current, the same transverse flux, and, consequently, the same iron losses from the transverse flux;

3. the m.m.f. of the longitudinal armature reaction, since in both cases there is the same brush position and the same transverse current.

In contrast to the other m.m.f. components constituting the reaction of the transverse current, the m.m.f. \(F_{r a}\), equivalent to the transverse armature reaction when the path of the longitudinal flux is saturated by the transverse flux, always acts demagnetizingly on the control m.m.f. It will be the same in magnitude, since in both cases there is the same current in the transverse circuit and practically the same saturation, but it will change its sign when the polarity of the control field is changed.

Equation (1), expressing the m.m.f. balance along the longitudinal axis, when the polarity of the control field is changed, is written in the following form:

\[ F_d = -F_y - F_k - F_c + F_{r a} + F_{ad}. \tag{2} \]

From equations (1) and (2) one can determine the m.m.f. \(F_{r a}\) and the sum of the m.m.f.’s \(F_\Sigma = F_k + F_c + F_{ad}\).

In order to separate the m.m.f.’s \(F_k\) and \(F_c\), it is necessary, with the aid of a transverse bias winding, to create a flux along the transverse axis equal to the flux of the transverse armature circuit. The equality of these fluxes can be monitored by means of a voltmeter connected to the longitudinal brushes of the electric machine amplifier.

In amplifiers with a smooth armature, the transverse bias winding used for current unloading of the transverse circuit is employed to create the flux along the transverse axis. A similar winding is also used in other types of production amplifiers (for example, in the EMU-12PM).

As for the m.m.f. \(F_{ad}\), it may be neglected with sufficient accuracy by setting the brushes on the neutral.

For this case, the m.m.f. balance equations along the longitudinal axis take the form:

\[ F_d = F_y - F_{r.a} - F_c, \tag{3} \]

\[ F_d = -F_y + F_{r.a} - F_c. \tag{4} \]

From equations (3) and (4), the m.m.f.’s \(F_c\) and \(F_{r.a}\) are determined.

The m.m.f. \(F_k\) is now determined as the difference between the m.m.f.’s \(F_\Sigma = F_k + F_c + F_{ad}\) and the m.m.f. \(F_c\).

By the proposed method, the individual components and the resultant reaction of the transverse current were determined on a number of production amplifiers and amplifiers with a smooth armature. Figs. 3 and 4 give experimental (solid) and calculated (dashed) curves of the m.m.f.’s \(F_{r a}\), \(F_{r.a}\), \(F_k\), and \(F_c\) as functions of the transverse-circuit current \(I_q\) at rated control current for a production amplifier of the EMU-12A type and for an amplifier with a smooth armature having the following data:

EMU-12A: \(P_n = 1{,}2\ \text{kW}\), \(U_z = 115\ \text{V}\), \(I_z = 10{,}4\ \text{A}\), \(I_q = 3{,}7\ \text{A}\), \(i_y = 50\ \text{mA}\), \(n = 2950\ \text{rpm}\). The amplifier has no bias winding along the transverse axis;

EMU with smooth armature: \(P_n = 0{,}7\ \text{kW}\), \(U_z = 50\ \text{V}\), \(I_z = 14\ \text{A}\), \(I_q = 8{,}25\ \text{A}\),

\(i_y = 129\) mA, \(n = 2950\) rpm. The amplifier has a biasing winding along the transverse axis.

The curves are plotted in relative units. The control m.m.f. at the rated no-load voltage is taken as the unit of m.m.f.; the current in the transverse armature circuit at the rated amplifier voltage is taken as the unit of current.

As is seen from the curves in Figs. 3 and 4, in the series EMA the resultant m.m.f. of reaction from the transverse-circuit current \(F_{pq}\), at its rated value, is

Fig. 3. Experimental (solid) and calculated (dashed) curves of the m.m.f. \(F_{p.q}\), \(F_{p.a}\), \(F_k\), and \(F_c\) as functions of the transverse-circuit current at the rated control signal for a series amplifier of type EMU-12A

approximately half the control m.m.f. In this case almost the entire demagnetizing action is due to the m.m.f. \(F_k\) and \(F_c\), while the value of the m.m.f. \(F_{p.a}\) is approximately zero. This character of variation of the m.m.f. \(F_{p.a}\) fully confirms the theoretical conclusions given above concerning the distinctive action of the m.m.f. \(F_{p.a}\) when the amplifier operates with different control signals. In an amplifier with a smooth armature, the resultant reaction m.m.f. from the transverse current amounts to only about 20 percent of the control m.m.f., which is explained by the considerable magnitude of the air gap. The shares of the m.m.f. \(F_{p.a}\), \(F_k\), and \(F_c\) are each approximately 30 percent of the resultant reaction of the transverse-circuit current.

The calculation of the individual components of the reaction from the transverse-circuit current, carried out by the method of [6, 7, 8, 10], as is seen from Figs. 3 and 4, gives satisfactory agreement with experiment.

Conclusions

1. The proposed method makes it possible to separate and determine, with sufficient accuracy, each component of the reaction from the transverse-circuit current in amplifiers with a smooth armature and in series amplifiers.

2. When selecting the operating mode of a cross-field EMA, it is necessary to take into account the distinctive action of the transverse armature reaction on the control m.m.f. The m.m.f. \(F_{p.a}\), at certain values of the control current,

Fig. 4. Experimental (solid) and calculated (dashed) curves of the m.m.f. \(F_{p.q}\), \(F_{p.ya}\), \(F_k\), and \(F_c\) as functions of the transverse-circuit current at the nominal control signal for a cross-field EMA with a smooth armature.

can act both in a demagnetizing and in a magnetizing manner.

REFERENCES

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