CHOICE OF THE COMPENSATING WINDING IN AN EMA WITH A SMOOTH ARMATURE

A. I. Skorospeshkin, A. I. Vilner, B. I. Kostylev

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

All modern transverse-field EMAs are made with compensation of the armature reaction of the output stage, since at the existing value of the amplification factor the magnetomotive force of the control winding is small, while the demagnetizing action of the armature reaction under load is very considerable, and obtaining a more or less stiff external characteristic without compensation is impossible.

The compensating winding in a transverse-field EMA with a toothed armature is made distributed, since with a concentrated compensating winding the reduction of the air gap is limited by the permissible distortion of the magnetic flux [1]. This complicates the design of the machine, but makes it possible to reduce the magnitude of the air gap and substantially increase the amplification factor.

When designing a transverse-field EMA, the number of turns and the distribution of the compensating winding are chosen as follows: from the conditions of minimum magnetic noise and pulsation losses as a function of the slot pitch of the armature, the pitch of the small slots is chosen; the stator bore is divided into equivalent divisions so that an integral number of equivalent divisions corresponds to each small, medium, and large slot. The number of turns of the compensating winding per pole is taken as

\[ W_{\mathrm{ko}} = k_{\mathrm{T}} W_{\mathrm{я}}, \tag{1} \]

where

\(W_{\mathrm{я}}\) is the number of series turns of the armature winding per pole,
\(k_{\mathrm{T}} = 1.03 \div 1.08\) is the transformation coefficient, making it possible to adjust the compensating winding for overcompensation. \(W_{\mathrm{ko}}\) is distributed among the slots according to the number of equivalent divisions [2].

Let us consider the distribution of the compensating winding in more detail. The magnetomotive force of a smooth armature has the form of a triangle (the actual curve of the magnetomotive force of the armature of a toothed machine is also reduced to a smooth armature); the magnetomotive force of the compensating winding is stepwise in character; consequently, even when adjusted for unit compensation (that is, equality of the areas of these two figures), uncompensated sections are necessarily present. It is obvious that the best distribution of the compensating winding is that in which the amplitudes of the magnetomotive forces of the uncompensated sections for the selected number of small slots are identical over the entire bore. In addition, it is advisable to consider compensation only in the zone of the partial and additional poles, since the air gap in the zone of the large and medium slots is at least an order of magnitude larger, and the magnetomotive forces

of the armature and the compensating winding will produce very small inductions there.

We neglect the analogous effect of small slots, since their opening is small; we take into account only the increase of the working air gap by Carter’s coefficient.

Figure 1 shows the superposition of the curves of the magnetomotive forces of the armature reaction and of the compensating winding (with the opposite sign) for \(\tau/2\), with pole overlap \(\alpha_i = 0.6\) and two small slots on the partial pole (\(N_{\mathrm{M}}=2\)); the width of the auxiliary pole is \(b_{\mathrm{d}}\).

Fig. 1

As can be seen, this picture is constructed on the basis of the considerations set forth above.

Considering in this superposition an entire system of similar triangles, we can obtain the magnitude of the magnetomotive force of the compensating winding falling on each slot, the total magnitude of the magnetomotive force of the compensating winding, and the amplitude of the pulsations of the magnetomotive forces of the uncompensated sections; and, taking the armature current equal to unity, the number of turns of the compensating winding in each slot. (The calculation formulas are written for unit compensation; overcompensation is specified within the usual limits.)

The number of turns of the large slot is

\[ W_{\mathrm{kB}} = W_{\mathrm{a}}\left(1 - \frac{\alpha_i N_{\mathrm{M}}}{N_{\mathrm{M}}+1}\right). \tag{2} \]

Number of turns of the small slot

\[ W_{\mathrm{ksm}}=\frac{W_{\mathrm{a}}\cdot \alpha_i}{N_{\mathrm{m}}+1}. \tag{3} \]

Number of turns of the middle slot

\[ W_{\mathrm{ks}}=\frac{W_{\mathrm{a}}}{2}\left(1-\frac{\alpha_i N_{\mathrm{m}}}{N_{\mathrm{m}}+1}-\frac{b_{\mathrm{d}}}{\tau}\right). \tag{4} \]

The turns used to create the commutating magnetomotive force of the additional pole are not included in (4). The total number of turns of the compensating winding per pole is

\[ W_{\mathrm{ko}}=\frac{W_{\mathrm{a}}}{2}\left(2-\frac{b_{\mathrm{d}}}{\tau}\right). \tag{5} \]

Amplitude of the pulsations under a partial pole

\[ F_{\mathrm{p}}=\frac{I\alpha_i W_{\mathrm{a}}}{2(N_{\mathrm{m}}+1)}\;(\mathrm{A}). \tag{6} \]

Amplitude of the pulsations under the additional pole

\[ F_{\mathrm{pd}}=\frac{I b_{\mathrm{d}} W_{\mathrm{a}}}{2\tau}\;(\mathrm{A}). \tag{7} \]

As can be seen, the equality \(W_{\mathrm{ko}}=W_{\mathrm{a}}\) at \(k_{\tau}=1\), as given in [2], is not entirely correct. The number of turns in the middle slot, and consequently the total number of turns of the compensating winding, is somewhat smaller.

The effectiveness of turns located in different slots is not the same, since, as they approach the middle slot, they encompass an ever smaller cross section of the magnetic core.

The effectiveness coefficient of the middle slot is

\[ k_{\mathrm{es}}=\frac{b_{\mathrm{d}}}{b_{\mathrm{d}}+\alpha_i \tau}. \tag{8} \]

The effectiveness coefficient of the small slots and of the large slot is

\[ k_{\mathrm{e}}=\frac{(N_{\mathrm{m}}+1)b_{\mathrm{d}}+\alpha_i \tau n}{(N_{\mathrm{m}}+1)(b_{\mathrm{d}}+\alpha_i \tau)}, \tag{9} \]

where \(n=1,2\ldots,N_{\mathrm{m}}+1\); \(n=1\) is the small slot closest to the middle slot, and \(n=N_{\mathrm{m}}+1\) is the large slot.

From formula (6) it is evident that the amplitude of the pulsations under a partial pole, in addition to the magnitude of the armature current, is affected by the coefficient of pole overlap and the number of small slots.

For identical \(I\) and \(\alpha_i\), the magnitude of the pulsations with a distributed control winding is \(N_{\mathrm{m}}+1\) times smaller than with a concentrated one, while their number per partial pole is \(N_{\mathrm{m}}+1\) times greater.

In a transverse-field amplifier with a smooth armature, commutation is exceptionally good even under large overloads; there is no need for an additional pole. In Fig. 1, compensation should be considered only in the region of the partial pole; then expressions (2) and (3) are retained, while (5) takes the form

\[ W_{\mathrm{ko}}=\frac{W_{\mathrm{a}}}{2}\left(1+\frac{\alpha_i N_{\mathrm{m}}}{N_{\mathrm{m}}+1}\right). \tag{10} \]

Here \(W_{\mathrm{ko}}\) is already considerably smaller than \(W_{\mathrm{a}}\), and the effectiveness coefficient of a turn is determined independently of the geometric dimensions.

\[ k_{\mathrm e} = \frac{n}{N_{\mathrm m}+1}. \tag{11} \]

If, in designing an EMA with a smooth armature, we set ourselves the goal of obtaining the smallest pulsations of the uncompensated magnetizing forces, then we must choose the number of small slots per partial pole approximately the same as in an EMA with a toothed armature at an equal width of the partial pole. But since the winding on a smooth armature is distributed uniformly, we cannot be guided by the ratio of the slot pitches of the armature and the stator.

In this case we determine the total tooth width per partial pole as

\[ b'_z=\frac{B_{\delta\varphi}\tau\alpha_i}{B_{z\varphi}k_c}, \tag{12} \]

where \(B_{\delta\varphi}\) and \(B_{z\varphi}\) are the maximum induction in the air gap and in the stator teeth at the specified voltage forcing.

Taking \(B_{z\varphi}=1.7 \div 1.8\) T, and the tooth width \(b_z=3 \div 4\) mm on the basis of mechanical-strength conditions, then the number of small slots per partial pole is equal to

\[ N_{\mathrm m}=\frac{b'_z}{b_z}-1. \tag{13} \]

The further calculation of the compensating winding is carried out by formulas (2), (3), (10).

A feature of an EMA with a smooth armature is the rather substantial nonmagnetic gap, determined, in addition to the actual air gap, by the diameter of the winding conductor and by the insulation.

In amplifiers with a smooth armature of power \(1 \div 2.5\) kW, for example, the gap is \(\delta=1.6 \div 2\) mm, whereas in analogous EMAs with a toothed armature \(\delta=0.35 \div 0.5\) mm. Consequently, equal pulsations in magnitude of the magnetizing force of the uncompensated sections will produce in an EMA with a smooth armature considerably smaller induction pulsations \(B=\frac{F}{\delta}\) than in an amplifier with a toothed armature.

For example, the induction pulsations for identical \(I\) and \(\alpha_i\) in an amplifier with a toothed armature at \(\delta=0.4\) mm and \(N_{\mathrm m}=4\), and in an amplifier with a smooth armature at \(\delta=2\) mm and a concentrated compensating winding \(N_{\mathrm m}=0\), are equal.

A pattern analogous to Fig. 1 for a concentrated compensating winding is given in Fig. 2.

In this case the number of turns of the compensating winding per pole is

\[ W_{\mathrm{ko}}=\frac{W_{\mathrm a}}{2}. \tag{14} \]

In the large slot

\[ W_{\mathrm{kB}}=W_{\mathrm a}. \tag{15} \]

The amplitude of the pulsations of the magnetizing force is

\[ F_{\mathrm p}=\frac{I\alpha_i W_{\mathrm a}}{2}\;(\mathrm a). \tag{16} \]

The absence of teeth on the partial poles makes it possible to use the armature steel much better, to increase substantially the induction in the air gap, to obtain greater output power in the same volume, to increase voltage forcing, to simplify the machine design, and to reduce the copper consumption for the compensating winding.

Fig. 2

The character of the resultant field in the air gap differs substantially in the case of a distributed compensating winding (Fig. 3a) and a concentrated one (Fig. 3b). (The dashed line shows the field pattern in the no-load mode of the amplifier.) In the first case, \(N_{\mathrm{M}}+1\) induction peaks are superimposed on the interpole, but the slope of the induction curve remains as it is at no load; in the second case, the slope of the curve on the leading edge increases, and on the trailing edge, at a sufficiently large current, it even changes direction, rotating about the center of the interpole, but the induction changes monotonically, without pulsations.

Fig. 3a.     Fig. 3b

To verify the influence of the distribution of the compensating winding on the operation of an EMA with a smooth armature, a machine was made with leads of the compensating winding brought out from each slot.

When connecting the compensating winding, starting with the large slot and then adding one small slot at a time, unit compensation was adjusted and the field in the air gap was oscillographed. The oscillograms are given below:

Fig. 4 — no-load mode \(I = 0\),
Fig. 5 — distributed winding \(N_M = 4,\ I = I_n\),
Fig. 6 — concentrated winding \(I = 0.25\,I_n\),
Fig. 7 — concentrated winding \(I = I_n\).

Fig. 4

Fig. 5

As can be seen, the oscillograms agree well with Figs. 3a and 3b. A certain discrepancy is explained by the not entirely correct distribution of the turns of the compensating winding in the experimental amplifier. At the same time as the field was oscillographed, all the characteristics of the amplifier were recorded; with different distributions of the compensating winding they practically did not change. Sparkless commutation was preserved.

Fig. 6

Fig. 7

The results of the work may be formulated as follows:

1. Simple design formulas have been obtained for determining the number of turns and the distribution of the compensating winding in a transverse-field amplifier with a smooth and a toothed armature.

2. An amplifier with a smooth armature can be manufactured with a concentrated winding without impairing its characteristics. This makes it possible to create an electric-machine amplifier of simpler design, with better utilization of steel, higher voltage forcing, and lower consumption of winding copper.

REFERENCES

1. M. Sey. Electric-Machine Amplifiers. GEI, 1959.
2. F. A. Goryaninov. Electric-Machine Amplifiers. GEI, 1962.