COMMUTATION OF DC MOTORS WITH VMK IN TRANSIENT MODES

V. A. IVANNIKOV, I. A. MILORADOV

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

Until now, the operation of motors with valve-mechanical commutation, with the valves loaded by part of the current of the brush set, has been investigated only in steady-state modes, for example, under slow changes of load, etc. [1]. However, in view of the special features of machines with VMK, it is of interest to consider the commutation of these machines in transient modes, in particular during starting, dynamic braking, and load surges.

As is known, in motors with VMK of the type under consideration, sparkless operation is ensured by the valves if the current of the commutator segment passes through zero between the instants at which the section is disconnected by the main and auxiliary brushes. This condition for sparkless operation is satisfied if the emf induced by the commutating poles in the short-circuited section lies within the limits

\[ e_2 < e_k < e_1, \tag{1} \]

where
\(e_2\) is the emf of the section at which sparking of the auxiliary brush begins, determining the lower boundary of the sparkless-operation zone;

\(e_1\) is the emf of the section at which sparking of the main brush begins, determining the upper boundary of the zone.

By selecting the magnetomotive force of the commutating poles, it is always possible to ensure that condition (1) is satisfied in any steady-state mode. But in transient modes the condition of normal commutation may be violated. This is due to the same causes as in ordinary DC machines: saturation of the magnetic circuit of the commutating poles; lag of the magnetic flux of the commutating poles because of the damping action of eddy currents in the solid cores of the commutating poles and in the frame; the appearance in the short-circuited section of transformer emf from the change in the main flux; and the influence of the active resistance of the section. All these factors, except for the influence of eddy currents, manifest themselves more sharply in machines with VMK than in machines with ordinary commutation, since the implementation of VMK leads to a reduction in the subdivision of the armature winding and to a certain increase in the number of turns of the commutating-pole winding. The damping of the commutating flux by eddy currents with an increase in the m.m.f. of the commutating poles, as is known, is relatively reduced [2].

All the subsequent analysis is carried out using as an example a motor with VMK, made on the basis of the P32M motor, with supply voltage of 220 V, \(I_a = 5.3\) A, \(n = 900\) rpm. The excitation is independent, with a slight series-

with a wave winding, the number of sections per slot \(u_n=1\), the number of turns in a section \(w_s=48\), the resulting inductance of a section \(L=0.0054\) H, the active resistance \(r=1\ \Omega\), the commutation periods at the upper and lower boundaries of the zone at \(n=900\) rpm \(T_1=0.00141\) s, \(T_2=0.00324\) s, the number of turns of the winding of the auxiliary pole \(w_d=270\), and the gap between the armature and the auxiliary pole \(\delta=1.6\) mm.

Let us consider certain operating modes in which commutation of machines with VMK may be disturbed.

Regulation of rotational speed at constant armature current

If the influence of eddy currents, saturation of the magnetic circuit of the auxiliary poles, transformer e.m.f., and the voltage drop in the brush contact is neglected, then the e.m.f. \(e_1\) and \(e_2\) can be written in the form [4]:

\[ e_{1(2)} = i_a \cdot r \frac{1 + e^{-\frac{r}{L}\cdot T_{1(2)}}}{1 - e^{-\frac{r}{L}\cdot T_{1(2)}}}, \tag{2} \]

where \(i_a\) is the current of the parallel branch.

The dependences of \(e_{1(2)}\) on the rotational speed \(\omega\) at \(i_a=\text{const}\), in relative units, i.e., in fractions of the nominal value of the commutating e.m.f. from the auxiliary poles, are shown in Fig. 1. The curves \(e_1\) and \(e_2\) cut off on the ordinate axis a segment equal in magnitude to the product \(i_a r\), and with increasing rotational speed asymptotically approach the straight lines 1, 2, which pass through the origin at the angles \(\alpha_1\) and \(\alpha_2\) and represent the dependences of the commutating e.m.f. \(e_1\) and \(e_2\) for \(r=0\). As can be seen from Fig. 1, the e.m.f. \(e_1\) and \(e_2\) for \(r\ne0\) are greater than for \(r=0\), i.e., the active resistance retards commutation, and the more so the smaller \(\omega\) is. At \(\omega=0\), \(e_1=e_2=i_a r\), i.e., the greater the armature current, the greater the degree of undercommutation.

Fig. 1. Rotational-speed regulation mode at \(i=\text{const}\).

The commutating e.m.f. induced in the circuit of the short-circuited section by the auxiliary poles, under the assumptions made, in relative units is equal to

\[ e_k = i \cdot \omega, \tag{3} \]

where \(i\) is the armature current in relative units. Expression (3) is the equation of a straight line passing through the origin at an angle \(\alpha_k\) to the \(\omega\)-axis. In motors with VMK \(\alpha_1>\alpha_k>\alpha_2\), and the dependences \(e_k\) and \(e_2\) (Fig. 1) necessarily…

intersect positively, and only at one point—at a certain critical speed \(\omega_{\mathrm{cr}}\) (Fig. 1). At rotational speeds lower than the critical one, the commutating poles create too small an e.m.f. in comparison with that which is necessary to satisfy condition (1), i.e., in the interval \(0\)—\(\omega_{\mathrm{cr}}\) commutation has a delayed character, and sparkless operation of the motor can be ensured only by the properties of the brush contact.

Thus, even if proportionality is maintained between the current and the flux of the commutating poles at rotational speeds lower than the critical one, sparkless operation of the machine may be disturbed, owing to the action of the active resistance of the section. The available experience in adjusting machines with VMK shows that \(\omega_{\mathrm{cr}}\) at \(i=\mathrm{const}\), as a rule, does not exceed 25% of \(\omega_{\mathrm{n}}\).

During starting, braking, and load application, the armature current does not remain constant and often exceeds the rated value many times over. Therefore, in these modes the influence of the active resistance on commutation may prove to be stronger.

To evaluate commutation in the modes of starting, braking, and load application, it is necessary to know the character of the dependence of the current and rotational speed on time. These dependences were found under the following assumptions: a) the flux of the main poles in transient modes remains constant, i.e., it is assumed that changes in the modes occur with the separately excited winding switched on, while the armature reaction is compensated by a compensating series winding; b) the inductance of the armature circuit does not change; c) the dependence of the resisting torque on the motor shaft on the rotational speed is linear.

Under these assumptions the transient processes are described by a system of differential equations considered in detail in [3]. Therefore, only the final calculation results without intermediate derivations are given below.

Direct starting of an electric motor without load on the shaft

Neglecting saturation of the magnetic circuit of the commutating poles and the influence of eddy currents, the commutating e.m.f. \(e_k\), as in the case of speed regulation, will be determined by expression (3), but \(i\) and \(\omega\) in this case are functions of time and are found from [3].

Fig. 2. Direct starting of the motor
a)

Figure 2a shows the calculated dependences \(i\), \(\omega\), \(e_k\), \(e_1\), and \(e_2\), in relative units, as functions of \(t\) during direct starting of the P32 motor. As follows from Fig. 2a, the surge of the armature current under unsaturat-

of the magnetic circuit of the interpoles and the absence of eddy currents has practically no effect on the magnitude of the critical rotational speed \(\omega_{\mathrm{kr}1}\) (Fig. 2a), below which condition (1) is violated. However, it is well known that in uncompensated machines, especially of low and medium power, owing to saturation and increased leakage of the magnetic system of the interpoles at high current multiples, the linear relationship between the commutating current and the current is sharply disturbed, and the useful flux of the interpoles decreases as the current increases. Figure 3a shows the calculated magnetization curve of the interpoles of the P32 motor in relative units. As can be seen, the practically linear dependence of the interpole flux \(\varphi_d\) on the armature current \(i\) is retained only up to \(i = 2\). In addition, when the current changes abruptly by the value of the commutating current, eddy currents will be induced in the magnetic core, the action of which leads to a lag of the interpole magnetic flux behind the armature current. Saturation and eddy currents were taken into account in the same way as in [3]. The dependence of the commutating emf during direct starting, \(e_k(t)\), for this case is shown in Fig. 2a. The figure shows that the critical speed \(\omega_{\mathrm{kr}2}\) in this case is considerably greater than \(\omega_{\mathrm{kr}1}\) and amounts to \(0.7\omega_n\).

It should be noted that in this machine, as the calculation showed, the eddy currents in the magnetic circuit of the interpoles decay rapidly (the eddy-current decay coefficient \(\lambda_{\mathrm{vd}} = 31\ 1/\mathrm{s}\)), and although at the initial instant of starting the interpole flux, with saturation and eddy currents taken into account, \(\varphi'_d\), is considerably smaller than the flux without allowance for eddy currents \(\varphi_d\) (Fig. 2b), this has practically no effect on the magnitude of the commutating emf, since the rotational speed at this instant is very small.

Fig. 2b)

On Fig. 2b are shown the dependences of the interpole fluxes \(\varphi'_d\) and \(\varphi_d\), as well as of the commutating emfs as functions of time: without allowance for saturation and eddy currents—\(e_k\), with allowance only for saturation—\(e_{kn}\), and with allowance for saturation and eddy currents—\(e'_k\).

Analysis of these dependences shows that during starting the magnitude of the commutating emf, and consequently also the magnitude of the critical speed, is influenced mainly by saturation of the magnetic circuit of the interpoles.

The critical speed below which condition (1) is violated, i.e., \(e'_k\) becomes less than \(e_2\), can be reduced by decreasing the current surge at the initial instant of starting. Calculations show that, for example, with single-step starting of the motor with a starting-current multiple of

of the first stage, \(2.7 i_{\mathrm{n}}\), the critical rotational speed is already \(0.32\omega_{\mathrm{n}}\).

A further reduction of the critical speed, i.e., a reduction of the speed range in which commutation during starting has a retarded character, can be achieved by special measures—for example, by connecting, for the starting period, a small capacitance in series with the valve, shunted by an active resistance [4]. It should be noted that sparking caused by undercommutation, owing to the small value of the rotational speed in the mode considered, is less dangerous than in modes with current surges at a rotational speed close to nominal and higher, for example during dynamic braking.

Dynamic braking of the motor with no load on the shaft

In Fig. 3, a, b, the dependences on \(t\) are given for \(i\), \(\omega\), \(e_{\mathrm{k}}\), \(e'_{\mathrm{k}}\), \(e_1\), \(e_2\), \(e_{\mathrm{kn}}\), \(\varphi_{\mathrm{dn}}\), and \(\varphi'_{\mathrm{d}}\) during dynamic braking of motor P32 with dis-

a

b

Fig. 3. Dynamic braking of the motor.

with a dynamic current of 4.2 \(i_{\mathrm{n}}\). Analysis of these dependences shows that the influence of eddy currents on the slowing of commutation during dynamic braking is relatively greater than in the direct-starting mode, since, with approximately the same rate of rise of the current in both cases, the rotational speed at the beginning of dynamic braking is close to nominal.

However, from the standpoint of the danger of sparking at the commutator, the principal slowing of commutation occurs because of saturation of the magnetic circuit of the interpoles, since the active resistance, as in the case of direct starting, leads to violation of condition (1) only at rotational speeds lower than \(\omega_{\mathrm{cr}1}\), when the magnitude of the dynamic armature current is small and cannot cause intense sparking of the brushes.

In conclusion it should be noted that in modes in which a relatively slow change of the armature current occurs and its magnitude does not lead to significant saturation of the magnetic circuit of the interpoles—for example, application of load up to \(2i_{\mathrm{n}}\)—condition (1) at \(\omega \ge \omega_{\mathrm{cr}}\) is not violated (Fig. 4), and the VMK circuit ensures sparkless operation of the machine. This is also confirmed by tests of motors with VMK carried out at the Elektromashina plant (Prokopyevsk) under overloads and load application up to \(2i_{\mathrm{n}}\).

Fig. 4. Load-application mode up to \(2i_{\mathrm{n}}\)

Conclusions

1. In transient modes, sparking at the commutator of machines with VMK is caused by the same principal reasons as in machines with conventional commutation and, above all, by saturation of the magnetic circuit of the interpoles at large multiples of the armature current.

2. The time intervals during which, in transient modes, the normal operation of the auxiliary valves is disturbed are, as a rule, small; therefore the sparking that arises, as experience shows, does not lead to destruction of the contact surfaces and does not affect the subsequent operation of the VMK circuit.

References

1. V. A. Ivannikov, V. V. Ivashin, I. A. Miloradov. Commutation of direct-current motors with shunt or compound excitation with VMK in the speed-control mode. Izv. TPI, vol. 212, 1971.

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

3. N. P. Ermolin. Transient processes in direct-current machines. GEI, 1951.

4. I. A. Miloradov. On valve-mechanical commutation of direct-current machines. Author’s abstract of a dissertation for the degree of Candidate of Technical Sciences. Tomsk, 1967.