COMMUTATION OF SHUNT OR COMPOUND-EXCITED DC MOTORS WITH VMK IN ROTATIONAL SPEED CONTROL MODE

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

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

Preliminary studies have shown that the relative width of the sparkless-operation zone in machines with valve-mechanical commutation (VMK), when the rotational speed of the armature is controlled, changes to a considerably lesser degree than in machines with traditional commutation [1]. In addition, the sparkless zone of machines with VMK is less prone to displacement relative to the armature-current axis, which is of decisive importance in speed control. In view of the expected prospects for the use of VMK circuits in motors with a wide range of control, it is of interest to consider the principal causes that determine the commutation of machines with VMK in this mode.

Such causes, on which the width and position of the sparkless zone depend, are:

a) the magnitude of the excitation current of the main poles, which affects the sparkless zone through the emf from the main field in the commutation zone and the change in the degree of saturation of the magnetic circuit in the path of the interpole flux (first of all, the part of the frame in which the fluxes of the main and interpoles are summed);

b) eddy currents in the iron and in the body of the conductors caused by the change in the slot leakage flux during phase-current commutation, which produce changes in the active and inductive parameters of the commutating sections. It is known that although, as the rotational speed increases, eddy currents contribute to a relative acceleration of commutation, their influence is small [2], especially in machines with a small conductor cross-section and laminated magnetic circuits. Therefore, in what follows the parameters of the sections are assumed to be constant;

c) the active resistance of the commutating sections;

d) the voltage drop in the brush contacts;

e) mechanical factors on which the quality of contact between the brushes and the commutator depends. VMK circuits are intended to combat sparking only of electromagnetic origin. Therefore, it is assumed here that, when the rotational speed changes, no disturbance of the mechanical contact occurs.

All the causes listed also act in machines with traditional commutation, but in machines with VMK, as will be seen below, they have their own specifics. Let us analyze separately the influence of each of the factors, assuming that in all cases, when the rotational speed changes, the armature current remains constant.

Influence of the excitation current of the main poles.

When the rotational speed is regulated, the emf induced in the commutating section by the field of the main poles of the machine changes both as a result of the change in rotational speed and as a result of the change in the excitation current of the main poles \((i_{\mathrm{в}})\), if the regulation is carried out at constant power.

As follows from [3], the auxiliary-supply current \((i_{\mathrm{n}})\) when the main field penetrates into the commutation zone can be written in the form:

\[ i_{\mathrm{n}} = k(U - e_0 \pm U_{\mathrm{r}}), \tag{1} \]

where \(U\) is the voltage in the commutating section at which sparking begins at the commutator; \(U\) is equal to the emf induced in the section by the field of the commutating poles if the other voltages in the section circuit are negligibly small; \(U_{\mathrm{r}}\) is a time-constant voltage equivalent, in the degree of its influence on the section current, to the effective emf from the main field in the commutation zone [3]; \(e_0\) is the emf from the commutating poles at \(i_{\mathrm{n}}=0\),

\[ k = \frac{1}{n} \]

is the proportionality coefficient.

According to (1), if the excitation current of the main poles remains constant and speed regulation is carried out by changing the voltage applied to the armature, then, provided that the voltage drops in the brush contacts and in the active resistances are negligibly small, \(i_{\mathrm{n}}\) does not change (both for the upper and for the lower boundary of the zone), since in this case \(U\), \(e_0\), and \(U_{\mathrm{r}}\) simultaneously increase or decrease in direct proportion to the armature rotational speed [3, 4], while \(k\) is inversely proportional. Consequently, with this method of regulation, possible changes in the outlines of the sparkless zone are not associated with the magnitude of the emf from the main field, but are caused by other reasons: the active resistance of the sections and the properties of the brush contact.

If, however, the excitation current of the main poles is changed at \(n=\mathrm{const}\), then the magnitude \(i_{\mathrm{n}}\), as is readily seen from (1), does not remain constant. In this case, the magnitude and sign of the change in \(i_{\mathrm{n}}\) depend primarily on the position of the commutation periods of the section at the boundaries of the zone relative to the geometrical neutral, that is, on the position of the brush traverse. In the case most probable for machines with VMK [3], one should expect an increase in \(i_{\mathrm{n1}}\) and approximate constancy of \(i_{\mathrm{n2}}\) when \(i_{\mathrm{в}}\) is decreased \((i_{\mathrm{n1}}, i_{\mathrm{n2}}\) are the auxiliary-supply currents corresponding to the boundaries of the sparkless zone). In real machines the picture is complicated by the fact that, when \(i_{\mathrm{в}}\) changes, the degree of saturation of the magnetic circuit in the path of the commutating-pole flux may change, and also, if a stabilizing series winding is used in the machine, by the nonlinear change of \(U_{\mathrm{r}}\) when the excitation current of the shunt winding is regulated.

The change in the degree of saturation of the frame sections on which the fluxes of the main and commutating poles act in the same direction manifests itself in machines with VMK, as in machines with conventional commutation, in the fact that, as \(i_{\mathrm{в}}\) decreases during speed regulation, the commutating poles become relatively stronger and the sparkless zone shifts toward negative auxiliary-supply currents. It is clear that this factor acts only if the induction in the frame is sufficiently large and the drop of magnetic potential in the steel cannot be neglected.

Thus, a change in \(i_{\mathrm{в}}\) may lead to directly opposite results: if, for example, a decrease in \(U_{\mathrm{r}}\) with a change in \(i_{\mathrm{в}}\) leads to an increase in \(i_{\mathrm{n1}}\), then, owing to a decrease in the degree of saturation of the frame, the current \(i_{\mathrm{n1}}\) should become smaller. The result depends on which factor proves predominant.

For example, Fig. 1 gives the dependences \(i_n=f\left(\dfrac{i_v}{i_{v0}}\right)\) at \(n=\mathrm{const}\) for motors P32 and P40 [5], obtained experimentally.

Active resistance of the commutating sections. If the active resistances of the commutating sections, like the voltage drops in the brush contacts, were equal to zero, then the dependences of the limiting section voltages corresponding to the boundaries of the sparkless zone on rotational speed would have the form of straight lines 3 and 4 in Fig. 2. It can be shown that, for \(R_c\ne0\), the dependences of the section voltages at the zone boundaries on rotational speed are represented by curves 1 (upper boundary) and 2 (lower boundary), which asymptotically approach straight lines 3 and 4 (respectively). This means that, starting from a certain rotational speed, the value of the limiting voltage does not depend on \(R_c\). As a rule, this occurs at \(n\ge n_N\), i.e., when investigating operating modes nominal with respect to rotational speed, one may proceed from the assumption \(R_c=0\) [3, 4].

Fig. 1. Dependence of the auxiliary-pole currents on the excitation current of the main poles.
P40: \(n=1200\) rpm, \(i_{v0}=0.5\) A,
\(1—1:\ 2i_a=13\) A, \(2—2:\ 2i_a=11.9\) A,
P32: \(n=750\) rpm, \(i_{v0}=0.1\) A,
\(3—3:\ 2i_a=6\) A, \(4—4:\ i_a=2\) A.

Straight line 5 in Fig. 2, a represents the dependence of the emf \(e_0\), produced in the section by the auxiliary poles in the absence of additional supply, on the rotational speed of the armature. The figure shows that, at rotational speeds lower than a certain critical value \(n_{\mathrm{cr}1}\), the sparkless-operation zone lies above the armature-current axis, since at \(n<n_{\mathrm{cr}1}\) the emf produced by the auxiliary poles is less than the voltage required for sparkless operation of the machine even at the lower boundary of the zone. As \(n\) increases, the zone descends into the region of “overcommutation” currents, and beginning with a speed \(n\approx n_N\), when the section resistance may be neglected, the value of \(i_n\) no longer depends on rotational speed. Consequently, if the “strength” of the auxiliary poles is chosen so that, at a speed close to the nominal one, the zone is symmetrical, then it remains symmetrical also at \(n>n_N\), i.e., the active resistance cannot cause the disappearance of the zone when the rotational speed is regulated. It only leads to its displacement into the region of undercommutation at low rotational speeds.

A more complete analysis makes it possible to establish that the nonzero active resistance of the sections somewhat reduces the value of the coef-

coefficient of static commutation stability of machines with a VMK, and to a greater extent the smaller the commutating emf, i.e., \(n\). But this decrease is fully or partially compensated by the effect of the brush contact on commutation.

Voltage drop in the brush contacts: assume that \(R_c=0\); then, as indicated above, the voltages at which the machine begins to spark at the boundaries of the zone will be linear functions of the rotational speed (Fig. 2, б). A feature of the VMK circuit under consideration is that the average voltage \(\Delta U\), introduced by the brush into the circuit of the short-circuited section, always acts opposite to the commutating emf [4]. Therefore, in order that the resulting, total voltage of the section be equal to \(U\), i.e., to the voltage at which sparking begins, the commutating emf created in the section by the interpoles must be equal to

Fig. 2. Influence of section resistance and voltage drops in the brush contacts on the sparkless zone:
а) \(R_c \ne 0,\ \Delta u=0\), б) \(R_c=0,\ \Delta u \ne 0\)

\[ e=U+\Delta U . \tag{2} \]

If it is assumed that, at \(2i_a=\mathrm{const}\), \(\Delta U=\mathrm{const}\) independently of the rotational speed, then when the speed changes the emfs corresponding to the boundaries of the zone must vary as shown in Fig. 2, б (\(e_1, e_2\)). It is accepted that the retardation of commutation at the upper boundary of the sparkless zone is greater than at the lower one, i.e., \(\Delta U_1>\Delta U_2\), which is also the case in reality.

It is evident that, as in the case \(R_c\ne0,\ \Delta U=0\), there always exists a rotational speed \(n_{\mathrm{kr}2}\), below which the sparkless zone is located above the armature-current axis, since for \(n<n_{\mathrm{kr}2}\), \(e_0<e_2\). The figure shows that when the rotational speed is increased above \(n_{\mathrm{kr}2}\), the straight lines \(e_0\) and \(e_1\) (or \(e_2\)) do not intersect. This means that although, as \(n\) increases, the zone descends into the region of overcommutation (the interpoles become relatively stronger under the action of \(\Delta U\)), nevertheless always \(i_{n1}>0\) and \(i_{n2}<0\). It also follows from Fig. 2, б that, under the influence of \(\Delta U\), the width of the sparkless zone and \(k_c\) increase, i.e., in this respect the action of \(\Delta U\) is opposite to the action of active resistance. At the same time, as \(n\) increases, the influence of the brush contact relatively decreases, since with increasing speed the commutating emf increases proportionally, whereas the value of \(\Delta U\) at \(2i_a=\mathrm{const}\) does not change. How \(k_c\) will change under the simultaneous action of \(R_c\) and \(\Delta U\) depends on the specific parameters. The combined action of \(R_c\) and \(\Delta U\) always leads to a displacement of the zone toward the relative strengthening of the interpoles with increasing \(n\), and also, as

it is not difficult to establish, by comparing Figs. 2a and 2b, a certain increase in the critical rotational speed, below which \(i_{n2}>0\).

Figure 3 shows the experimentally obtained dependences \(i_n=f(n)\) at \(i_{\mathrm{в}}=\mathrm{const}\) on the P32 and P40 machines, which precisely characterize the effect on \(i_n\), \(R_c\), and \(\Delta U\), since in this case, owing to the constancy of the excitation current, the action of the field of the main poles and the degree of saturation of the frame remain constant.

Fig. 3. Dependence of the auxiliary-pole currents on rotational speed at \(i_{\mathrm{в}}=\mathrm{const}\),
\(1\)—1: P40, \(2i_a=13\ \mathrm{A}\), \(i_{\mathrm{в}}=0.45\ \mathrm{A}\),
\(2\)—2: P32, \(2i_a=6\ \mathrm{A}\), \(i_{\mathrm{в}}=0.18\ \mathrm{A}\)

Conclusions

The sparkless zone of a machine with VMK, with the magnetomotive force of the commutating poles properly selected, at rotational speeds greater than the critical speed, never shifts completely into the region of over- or under-commutation. The factors considered above, which distort the sparkless zone in machines with VMK, unlike in machines with traditional commutation, cannot lead to the disappearance of the sparkless zone, to the crossing of its boundaries as the rotational speed of the armature increases.

LITERATURE

1. V. V. Ivashin, I. A. Miloradov, V. L. Gromok. Some results of research on valve-mechanical commutation. Abstracts of reports of the Fourth All-Union Conference on Commutation, MEI, Omsk, 1968.

2. M. F. Karasev et al. Further development of the theory of optimal commutation. Proceedings of OMKITA, vol. 78, 1967.

3. V. V. Ivashin, I. A. Miloradov. Investigation of the influence of the main field on the commutation of machines with auxiliary valves. Izvestiya TPI, vol. 172, 1967.

4. V. V. Ivashin, I. A. Miloradov. On valve-mechanical commutation of direct-current machines. Izvestiya TPI, vol. 160, 1966.

5. I. A. Volkomirskii, V. A. Ivannikov, V. V. Ivashin, I. A. Miloradov. Experimental studies of the commutation of direct-current motors with VMK in the rotational-speed control mode (see the present collection).