EXPERIMENTAL STUDIES OF COMMUTATION IN DC MOTORS WITH VMK IN THE MODE OF ROTATIONAL-SPEED CONTROL BY WEAKENING THE FIELD OF THE MAIN POLES

I. A. Volkomirskii, V. A. Ivannikov, V. V. Ivashin, I. A. Miloradov

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

Experiments were conducted on the following motors:
1) P32, 750–1300 rpm, 5.1–5.72 A; 2) P40, 1200–1875 rpm, 11.8–14.3 A. The excitation was shunt, with slight stabilization. The supply voltage was 175–320 V. Both machines were made with a VMK circuit with partial loading of the valve by the brush-holder current [1, 2].

Experimental Method

Since the aim of the work was to determine and verify the general regularities of commutation in machines with VMK in the mode of deep rotational-speed control by weakening the field of the main poles, the experimental machines were first used to take the dependences \(i_{\text{п}} = f(n)\) at \(U_{\text{я}}=\mathrm{const}\), \(i_{\text{в}}=\mathrm{var}\) (\(i_{\text{п}}\) is the current of the additional supply of the commutating poles, \(U_{\text{я}}\) is the armature voltage, \(i_{\text{в}}\) is the excitation current), in which all the factors affecting commutation when the rotational speed changes are reflected [1]. The shunt field winding was supplied from an independent source. On the armature, the minimum of the rated voltages—175 V—was set, since at this voltage the greatest limits of speed variation can be obtained by changing the excitation current. But even in this case the minimum speed at constant power remains rather high, which is caused by the peculiarities of the regulating characteristics of the experimental machines. A further reduction of speed was carried out by reducing the armature supply voltage at constant excitation current; that is, the dependences \(i_{\text{п}}=f(n)\) were taken at \(i_{\text{в}}=\mathrm{const}\), \(U_{\text{я}}=\mathrm{var}\). Such dependences make it possible to estimate the influence on commutation only of the active resistance of the section \((R_c)\) and of the brush contact (the average voltage introduced by the brush into the section, \(\Delta U\)) under a constant action of \(i_{\text{в}}\), since the share of \(i_{\text{в}}\) in changing the feed currents does not depend on the rotational speed [1].

The character of the action of \(i_{\text{в}}\) on the currents of the additional supply is best traced from the dependences \(i_{\text{п}}=f(i_{\text{в}})\) at \(n=\mathrm{const}\), \(i_{\text{в}}=\mathrm{var}\), which reflect the influence on \(i_{\text{п}}\) of the main field in the commutation zone and of the degree of saturation of the frame [1].

The data obtained in this way make it possible to determine the coefficients of static commutational stability of the experimental machines as a function of rotational speed and to compare them with analogous dependences for machines with traditional commutation.

Experimental results

The experimental curves \(i_p=f(n)\) for both machines at \(U_{\mathrm{a}}=\mathrm{const}\), \(i_{\mathrm{f}}=\mathrm{var}\) for several load currents are given in Fig. 1. As can be seen, the tendency toward relative strengthening of the interpoles with increasing rotational speed, which was pointed out in [1], is generally observed: with increasing \(n\), \(i_{p1}\) (the upper boundary of the zone) decreases, while \(i_{p2}\) (the lower boundary) increases somewhat.

An exception is \(i_{p1}\) of the P40 machine at small loads (curve 4, Fig. 1): \(i_{p1}\) first increases, and with a further increase in speed, as usual, decreases. This is connected with the special features of the effect of the excitation current magnitude on the emf in the commutation zone of this machine [1]. In Fig. 1, attention is also drawn to the sharper drop of \(i_{p1}\) with

Fig. 1. Dependence of the interpole currents on rotational speed.
1—1: P32, \(2i_{\mathrm{a}}=6\,\mathrm{A}\); 3—3: P40, \(2i_{\mathrm{a}}=13\,\mathrm{A}\);
2—2: P32, \(2i_{\mathrm{a}}=2\,\mathrm{A}\); 4—4: P40, \(2i_{\mathrm{a}}=3.9\,\mathrm{A}\).

increasing speed for the P40 motor, as compared with the P32. In our opinion, this is explained by two circumstances: a) a less favorable, than in the P32, ratio of the time constant of the short-circuited loop to the commutation period; b) a higher level of vibration. Both experimental machines are not designed for increased rotational speed, and balancing of their armatures was carried out at \(n<2000\) rpm. Therefore, with respect to vibration the machines left something to be desired, but since the P40 motor has greater shaft power and a higher peripheral speed of the commutator, the brush-vibration level in this machine was somewhat higher. Increased vibrations cause deterioration in the quality of current transfer into the valve and, as a consequence, a sharper decrease in the value of \(i_{p1}\) than would follow from purely electromagnetic causes.

The dependences \(i_p=f(i_{\mathrm{f}})\) at \(n=\mathrm{const}\) for several armature currents are given in [1]. For both machines, practical independence of \(i_{p2}\) from the magnitude of the excitation current is characteristic. This is connected with the fact that in machines with VMK the entire commutation brush and the commutation period at the lower boundary of the zone (\(T_2\)) are, as a rule, located symmetrically with respect to the geometric neutral (the axis of the interpole), and therefore the average value of the emf from the main field in the commutation zone over the commutation period \(T_2\) is close to zero. In this case \(i_p\) does not depend on the magnitude of \(i_{\mathrm{f}}\) [1]. In addition, at the lower boundary of the zone the drop of magnetic potential in the steel manifests itself to a lesser degree, since the interpole flux is small. As for the upper boundary of the zone (\(i_{p1}\)), the magnitude of \(i_{\mathrm{f}}\) affects it differently: in the P32, with increasing \(i_{\mathrm{f}}\), \(i_{p1}\) increases, while in the P40, on the contrary, it decreases. Apparently, in the P32 motor the influence

saturation of the steel sections in the path of the flux of the auxiliary pole is more significant, since this machine has \(2p=2\). The data obtained on the experimental machines at variable rotational speed and constant excitation current are considered in [1] and fully confirm the conclusions of the theoretical analysis: the influence of \(R_c\) and \(\Delta U\) on the “feed” currents, especially noticeable at low rotational speeds, decreases as \(n\) increases. The critical rotational speed, below which the sparkless zone passes into the region of undercommutation \((i_{p2}>0)\), lies for the experimental machines in the range 200–500 rpm.

Figure 2 shows the dependences of the relative width of the sparkless zones \(\Theta\)

Fig. 2. Dependence of the width of the sparkless zone on rotational speed: 1: P32, \(2i_a=6a\), VMK; 2: P40, \(2i_a=13a\), VMK; 3: P32, \(2i_a=6a\), OK; 4: P40, \(2i_a=13a\), OK.

\[ \Theta=\frac{i_{p1}+i_{p2}}{2i_a} \]

of the experimental machines on rotational speed. At \(n>700\) rpm for the P32 motor and \(n>1000\) rpm for the P40, \(\Theta\) was determined from Fig. 1, and at lower speeds from the functions \(i_p=f(n)\), \(i_v=\mathrm{const}\), \(U_a=\mathrm{Var}\) [1].

The same figure gives the curves \(\Theta=f(n)\) for machines of the same type with conventional commutation. As can be seen, \(\Theta\) for machines with VMK, although it also decreases with increasing rotational speed for the reasons indicated in [1], does not do so to the same degree as in machines with traditional, ordinary commutation (OK). For the latter, judging from Fig. 2, at the given armature currents one may generally expect the sparkless zones to disappear at a rotational speed of 2400–2800 rpm. It should be noted that no special experiment to determine the sparkless zones of a machine with traditional commutation in the range of speeds in which the experimental specimens with VMK were tested was carried out. The data for determining \(\Theta\) were taken from the routine test records of factory machines.

The curves in Fig. 2 were processed in order to determine the coefficients of static commutation stability [3], and \(k_c\) for machines with VMK was calculated taking into account the difference in commutation periods at the zone boundaries (see Appendix).

The dependences of \(k_c\) on rotational speed are shown in Fig. 3. The figure shows that the advantages of valve-mechanical commutation, as was assumed earlier, become especially evident at high loads and rotational speeds. Whereas in machines with traditional commutation \(k_c\) falls sharply with increasing rotational speed, for machines with VMK an approximate constancy of \(k_c\) over a wide range of variation of \(n\) is characteristic. The calculated values of \(k_c\) for the experimental ma-

Fig. 3. Dependence of \(k_c\) on rotational speed.
1 — P32, \(2i_a = 6a\), VMK; 2 — P40, \(2i_a = 13a\), VMK;
3 — P32, \(2i_a = 6a\), OK; 4 — P40, \(2i_a = 13a\), OK;
5 — P40, \(2i_a = 8a\), OK

are equal: for P32 — 0.77, for P40 — 0.473. These values are quite close to the experimental data (the value of \(k_c\) for the P32 motor is somewhat less than that indicated in [2], since in carrying out the present work the dimensions of some parts of the brushes were changed).

Conclusions

1. If the causes of sparking of a mechanical nature are not considered, then the main influence on the width and position of the sparkless zone, as expected from the data of the theoretical analysis, is exerted by \(R_c\), \(\Delta U\), and \(i_v\). The action of these factors does not lead to intersection of the boundaries of the sparkless zone at \(n > n_{\mathrm{cr}}\).

2. Valve-mechanical commutation makes it possible to obtain, in machines of the class under consideration, a range of variation of rotational speed up to 1:8 and higher without sparking at the commutator; the minimum rotational speed at which the machines still operate without sparking lies in the range 200–500 rpm, and the maximum possible speed is determined by the quality of the mechanical contact of the brushes with the commutator.

Appendix

Determination of \(\Theta\) and \(k_c\) of a machine with VMK, taking into account the unequal action of armature reaction at the boundaries of the sparkless zone

We assume that \(R_c=0\), \(\Delta U=0\), i.e., operating conditions close to nominal are considered.

The total magnetomotive force (m.m.f.) of the additional poles at the upper boundary of the sparkless zone, producing in the commutating section the emf \(e_1\), is equal to

\[ F_1 = F_d + F_{p1} - F_{ya1}. \tag{1} \]

Here

\[ F_d = I_y \cdot W_d \]

— the m.m.f. of the additional poles in the absence of their supplementary supply;

\[ F_{p1} = i_{p1}\cdot W_d \]

— the m.m.f. of the feed currents;

\[ F_{ya1} \]

— the m.m.f. of the additional poles compensating, on average, the action of the transverse armature reaction in the commutation zone at the upper boundary of the sparkless zone, i.e., during the commutation period of the current in section \(T_1\);

\[ W_d \]

— the number of turns of the additional pole;

\[ I_y \]

— the armature current.

Let us denote

\[ W_{01}\cdot I_y = F_d - F_{ya1}. \tag{2} \]

Then

\[ i_{p1}=\frac{F_1-I_y\cdot W_{01}}{W_d}. \tag{3} \]

In an analogous way, for the “inverse-feed” current we obtain:

\[ i_{p2}=\frac{I_y\cdot W_{02}-F_2}{W_d}, \tag{4} \]

where \(F_2\) is the m.m.f. of the additional poles at the lower boundary of the zone;

\[ I_y W_{02}=F_d-F_{ya2}, \tag{5} \]

\(F_{ya2}\) is the m.m.f. of the additional poles compensating the action of the transverse armature reaction at the lower boundary of the zone.

The relative width of the sparkless zone, taking (3) and (4) into account, is

\[ \theta=\frac{i_{p1}+i_{p2}}{I_y} =\frac{F_1-F_2}{I_y W_d} +\frac{W_{02}-W_{01}}{W_d}. \tag{6} \]

If, as is usually done, it is assumed that the relation between the m.m.f. of the additional poles and the commutating emf does not depend on the operating condition, that is,

\[ \frac{F_1}{e_1}=\frac{F_2}{e_2}=\frac{F_{00}}{e_{00}}=k, \tag{7} \]

then

\[ \theta=\frac{W_{00}}{W_d}\cdot \frac{e_1-e_2}{e_{00}} +\frac{W_{02}-W_{01}}{W_d}. \tag{8} \]

Here

\[ F_{00}=W_{00}\cdot I_y,\qquad W_{00}=\frac{W_{01}+W_{02}}{2}, \tag{9} \]

\(e_{00}\) is the EMF corresponding to the m.m.f. \(F_{00}\).

Introduce the notation:

\[ k_{\mathrm{d}}=\frac{W_{00}}{W_{\mathrm{d}}}\quad \text{— dynamic coefficient [3],} \]

\[ k_{\mathrm{c}}=\frac{e_1-e_2}{e_{00}^{*}}\quad \text{— coefficient of static commutation stability [3],} \tag{10} \]

\[ k_{\mathrm{p}}=\frac{e_{00}^{*}}{e_{00}}\quad \text{— coefficient for reducing the zone to a symmetrical one,} \]

\[ \Theta=\frac{W_{02}-W_{01}}{W_{\mathrm{d}}}. \]

Then

\[ \Theta=k_{\mathrm{d}}\cdot k_{\mathrm{c}}\cdot k_{\mathrm{p}}+\Delta\Theta. \tag{11} \]

Expression (11) was used to determine \(k_{\mathrm{c}}\) from the experimental data (Fig. 3).

In (10), \(e_{00}^{*}\) is the EMF \(e_{00}\) corresponding to the symmetrical zone.

\[ e_{00}^{*}=\frac{e_1+e_2}{2}. \tag{12} \]

For \(k_{\mathrm{p}}\), after transformations we obtain

\[ k_{\mathrm{p}}=1+\frac{W_{\mathrm{d}}}{W_{00}}\cdot \frac{\Delta i_{\mathrm{p}}}{I_{\mathrm{a}}}, \tag{13} \]

where

\[ \Delta i_{\mathrm{p}}=\frac{i_{\mathrm{p}1}-i_{\mathrm{p}2}}{2}. \]

The quantities \(e_1\) and \(e_2\), required in (10) for calculating \(k_{\mathrm{c}}\), are found by the method set forth in [4]. In order to determine \(k_{\mathrm{c}}\) from experimental data using (11), it is necessary to know the quantities \(W_{01}\) and \(W_{02}\), which, according to (2) and (5), depend on \(F_{\mathrm{ra}}\) and are equal to:

\[ W_{01}=W_{\mathrm{d}}-\frac{F_{\mathrm{ra}1}}{I_{\mathrm{a}}};\qquad W_{02}=W_{\mathrm{d}}-\frac{F_{\mathrm{ra}2}}{I_{\mathrm{a}}}. \tag{14} \]

Usually, when calculating commutation, the m.m.f. of armature reaction is determined by the formula

\[ F_{\mathrm{ra}}=A\frac{\tau}{2}, \tag{15} \]

which gives a correct result only when all sections of the slot begin commutation simultaneously and the current in the sections changes instantaneously by \(2i_{\mathrm{a}}\). For a more accurate accounting of \(F_{\mathrm{ra}}\), it is necessary to take into consideration the duration of current commutation in the sections [5]. This is all the more valid for a machine with VMK, in which the periods of current commutation in the sections at the upper (\(T_1\)) and lower (\(T_2\)) boundaries of the zone are not the same. The value of \(F_{\mathrm{ra}}\) can be determined simply if it is assumed that the total slot current changes linearly (in machines with VMK at \(n\approx n_{\mathrm{N}}\) this assumption is especially justified). Simple calculations, omitted here, show that in this case the average value of the armature-reaction m.m.f. over the commutation period is equal to:

\[ F_{\mathrm{ra}}=A\cdot \frac{\tau}{2}\left(1-\frac{3}{4}\frac{T}{\tau}\right). \tag{16} \]

In (16), \(T\) should be understood either as the period of commutation of the phase current, if the phase sections begin commutation simultaneously, or as the period of commutation of the section current.

Substituting (16) into (14), with the corresponding value of \(T\), we determine the values \(W_{01}\) and \(W_{02}\).

Correct allowance for armature reaction in machines with VMK is of great importance. For example, for the P32 motor (\(T_2 = 2.21T_1\)), calculation performed by the formulas given yields, for the relative width of the symmetrical sparkless zone, a value of 25.1%, whereas when (15) is used, i.e., when \(T = 0\) is assumed, the calculated value is \(\Theta = 18.6\%\).

The experimental data in Fig. 2 show that the first result is much closer to reality.

REFERENCES

1. V. A. Ivannikov, V. V. Ivashin, I. A. Miloradov. Commutation of DC motors of shunt or compound excitation with VMK in the mode of regulating the rotational speed. See the present collection.

2. V. V. Ivashin, I. A. Miloradov, V. L. Gromok. Some results of a study of valve-mechanical commutation. Proceedings of the Fourth All-Union Conference on Commutation, MIT, Omsk, 1968.

3. V. V. Ivashin, I. A. Miloradov. Commutation stability of DC motors and its relation to the sparkless-operation zone. Izvestiya TPI, vol. 190, 1968.

4. V. V. Ivashin, I. A. Miloradov. Investigation of the zones of sparkless operation of a DC motor with brush-and-valve commutation. Izvestiya TPI, vol. 172, 1967.

5. R. Richter. Electrical Machines, vol. 1, ONTI, 1935.