USE OF LOW-POWER MOTORS IN ION ELECTRIC DRIVES WITH PULSE CONTROL OF ROTATIONAL SPEED

V. A. BEINAROVICH, Yu. M. ACHKASOV, A. I. ZAITSEV

(Presented by the scientific seminar of the Electromechanical Faculty)

At the present time, alongside continuous-action control systems, pulse-control systems are becoming widely used. The latter often have higher speed of response, better energy performance, simpler construction, and increased reliability, as well as lower weight, dimensions, and cost of the regulators. In addition, pulse-control systems allow control directly from digital computing machines and devices.

The operating principle of pulse-control systems is based on quantization of the energy supplied to the controlled object in such a way as to provide the prescribed law of control. The quality of control depends on the ratio of the time constant of the controlled object to the quantization period. If this ratio is large, the speed of response deteriorates; if it is small, the control process proceeds with considerable oscillation, which may be impermissible.

Pulse-control systems for electric drives are used to control rotational speed and angle of rotation, excitation of electric machines, force magnitudes in systems with elastic couplings, and for other purposes. Owing to the considerable mechanical inertia of electric motors, pulse control of electric drives can be used in a large number of cases.

The most widespread in industrial mechanisms and devices are DC electric drives with pulse control of rotational speed. Usually such electric drives contain an electric motor of standard design and a pulse regulator, which regulates the supply of electrical energy to the motor in the form of short current pulses with variable amplitude or duty cycle. The electric motor operates as an integrating element, converting the incoming pulses of electrical energy into a continuous value of power at the shaft.

The electric motor must be selected according to the maximum rotational speed and torque, taking into account heating and commutation conditions. However, the questions of heating and commutation of electric motors

in pulse-control systems, which are of great practical interest, have at present been studied quite insufficiently [1, 2, 3].

In the present work, questions are considered concerning the use of low-power separately excited direct-current electric motors in ion electric drives with pulse control of rotational speed, under the conditions of heating and commutation. This is part of investigations relating to the selection of an electric motor for a pulse follow-up feed system for belt-grinding machines, developed at the Department of Electrification of Industrial Enterprises of the Tomsk Polytechnic Institute [4, 5].

The follow-up feed system is based on a single-phase circuit for supplying a direct-current motor through a controlled valve—a thyratron (Fig. 1). The principle of operation of the regulator is based on keying control of the thyratron: when a certain specified value of the motor rotational speed is reached, the thyratron is locked and the speed begins to fall; the decrease in speed causes the thyratron to be unlocked, the motor receives power, and the speed increases. This process is repeated at a high frequency, so that the rotational speed acquires a practically constant value determined by the control voltage \(U_{\mathrm{ctrl}}\).

Fig. 1.

Because of the low power in such systems it is inadvisable to use multiphase rectifier circuits; therefore, the further consideration will apply only to single-phase circuits. However, with the appropriate recalculations all conclusions can also be successfully used for multiphase circuits (without allowance for anode overlap) [2].

Considering the possibilities of using standard motors in pulse-control systems under the conditions of heating and commutation, and without touching upon questions of control dynamics, we shall assume that the regulator ensures maintenance of a constant rotational speed at any point of the control range; that is, the value of the motor emf \(E\) is constant.

Let us introduce the following assumptions:

a) the times of ionization and deionization are not taken into account;

b) armature reaction, losses due to hysteresis, and eddy currents are not taken into account;

c) the voltage drop in the thyratron arc is constant;

d) the armature circuit consists of ohmic resistance and inductance that are constant in magnitude.

Under these conditions, the circuit (Fig. 1) can be represented by an equivalent circuit (Fig. 2), where

Fig. 2.

\(R\) — ohmic resistance of the circuit;
\(L\) — inductance of the circuit;
\(B\) — ideal valve;
\(\Delta E\) — voltage drop in the thyratron arc;
\(E\) — emf of the motor armature;
\(U\) — supply-source voltage;
\(i\) — instantaneous values of current;
\(K\) — automatic switch simulating the operation of the regulator.

Let us denote

\[ \varepsilon = \frac{E+\Delta E}{U_M}; \quad I_M = \frac{U_M}{R}; \quad I_{\mathrm{n}} = \frac{E+\Delta E}{R}; \quad T = \frac{L}{R}. \tag{1} \]

With switch \(K\) closed, current in the circuit arises at the firing angle of the thyratron \(\nu_3\), measured from the beginning of the sinusoid (Fig. 3),

\[ \nu_3 = \arcsin \frac{E+\Delta E}{U_M} = \arcsin \varepsilon . \tag{2} \]

The processes in the circuit are described by the differential equation

\[ U_M \sin(\nu_3+\omega t) = E+\Delta E+iR+L\frac{di}{dt}. \tag{3} \]

It is more convenient to count time in angular units

\[ \nu = \omega t. \tag{4} \]

The solution of differential equation (3), taking into account the notation (1, 4), valid only for \(i>0\), is written [6]:

\[ i = -I_{\mathrm{n}} + I_1 e^{-\frac{\nu}{\omega T}} - I_2 \cos(\nu-\Theta), \tag{5} \]

where

\[ I_1 = I_{\mathrm{n}} + I_M \frac{\omega T \cos \nu_3 - \sin \nu_3}{\omega^2 T^2 + 1}; \tag{6} \]

\[ I_{\mathrm{e}}=\frac{I_M}{\sqrt{\omega^2T^2+1}}, \tag{7} \]

\[ \Theta=\frac{\pi}{2}-\vartheta_z+\operatorname{arc\,tg}\omega T . \tag{8} \]

If in equation (5) we substitute \(i=0\), then we obtain the value of the thyratron extinction angle at \(\vartheta=\vartheta_p\) (Fig. 3). The duration of the current pulse, or the conduction angle of the thyratron (Fig. 3), is

\[ \lambda=\vartheta_p-\vartheta_z . \tag{9} \]

Fig. 3.

Diagrams of the conduction angle \(\lambda\) as a function of \(\varepsilon\) for different values of \(\omega T\) are given in Fig. 4 [2]. The duration of the current pulse increases with an increase in the time constant \(T\) and with a decrease in the relative voltage \(\varepsilon\).

Heating and commutation are strongly affected by the magnitude of the current amplitude \(i_M\), which can be determined from equation (5) by substituting \(\vartheta=\vartheta_M\) (Fig. 3). The angle \(\vartheta_M\) corresponds to the maximum current \(i_M\) and is found, as usual, by setting equal to zero the derivative of the expression for the current (5). Figure 5 gives diagrams of the dependence of the amplitude of current pulses, in relative units \(\iota_M\), on the value of \(\varepsilon\) for different values of \(\omega T\). The value of the current \(I_M\) (1) is taken as unity:

\[ \iota_M=\frac{i_M}{I_M}=i_M\frac{R}{U_M}. \tag{10} \]

The current amplitude \(\iota_M\) increases as the value of \(\varepsilon\) decreases. With an increase in the load parameter \(\omega T\), the amplitude of the current pulses decreases, since the influence of the circuit inductance increases and the current reaches its maximum with a delay relative to the maximum of the supply voltage.

Consideration of the diagrams (Figs. 4, 5) makes it possible to conclude that, at unchanged supply voltage, as the rotational speed decreases, the energy imparted to the motor by each current pulse increases owing to the decrease in the motor back emf. This leads to the appearance of undesirable pulsations at lower rotational speeds.

Fig. 4.

Fig. 5.

Heating, however, depends not only on the amplitude of the current pulses, but also on their frequency.

In a closed-loop control system, the pulses are supplied to the motor in such a way as to ensure the average torque on the shaft required to overcome the load and to impart the specified rotational speed to the motor. In steady-state operation the average current is determined by the load on the shaft

\[ I_{\mathrm{av}}=\frac{M}{K_m\Phi} =\frac{1}{t_2-t_1}\int_{t_1}^{t_2} i\,dt =\frac{K_T S_i}{2\pi}. \tag{11} \]

The number of current pulses falling within one period of the supply voltage is

\[ K_T=\frac{2\pi}{S_i}I_{\mathrm{av}}. \tag{12} \]

The area of one current pulse \(S_i\), taking into account expressions (5, 6, 7, 8, 9), is expressed as

\[ S_i=\int_{0}^{\lambda} i\,d\vartheta =\omega T I_1\left(1-e^{-\frac{\lambda}{\omega T}}\right) -\lambda I_{\mathrm{p}} -I_2[\sin(\lambda-\Theta)+\sin\Theta]. \tag{13} \]

The quadratic area of one current pulse, using expressions (5–9), is determined as

\[ \begin{aligned} S_k&=\int_{0}^{\lambda} i^2\,d\vartheta =\lambda I_{\mathrm{p}}^{\,2} -\frac{\omega T}{2}\left(e^{-\frac{2\lambda}{\omega T}}-1\right)I_1^{\,2} +\frac{1}{4}(2\lambda+\sin 2\lambda \cos 2\Theta \\ &\quad +2\sin 2\Theta \sin^2\lambda)I_2^{\,2} +2I_1 I_{\mathrm{p}}\omega T\left(e^{-\frac{\lambda}{\omega T}}-1\right) +2I_{\mathrm{p}}I_2[\cos\Theta\sin\lambda \\ &\quad +\sin\Theta(1-\cos\lambda)] -2I_1I_2\frac{\omega T}{1+\omega^2T^2} \Bigl\{\cos\Theta \times \\ &\quad \times \bigl[e^{-\frac{\lambda}{\omega T}}(\omega T\sin\lambda-\cos\lambda)+1\bigr] -\sin\Theta\bigl[e^{-\frac{\lambda}{\omega T}}(\sin\lambda \\ &\quad +\omega T\cos\lambda)-\omega T\bigr]\Bigr\}. \end{aligned} \tag{14} \]

Then the current equivalent with respect to heating is

\[ I_{\mathrm{e}}= \sqrt{\frac{K_T}{2\pi}\int_{0}^{\lambda} i^2\,d\vartheta} = \sqrt{\frac{S_k}{S_i}}\,I_{\mathrm{av}}. \tag{15} \]

A decrease in speed leads to an increase in heating, since in this case the amplitude and duration of the current pulses increase. An increase in the load \(I_{\mathrm{av}}\) also leads to a rise in the current equivalent with respect to heating. Physically, the increase in heating is caused by an increase in the frequency of the current pulses in the motor.

Calculation of the equivalent current from expression (15) is rather laborious.

For practical calculations it may be assumed that the current pulses have the form of a truncated sinusoid with the same amplitude \(i_m\) and duration \(\lambda\),

\[ i=i_m \sin \frac{\pi \vartheta}{\lambda}. \tag{16} \]

The area of one current pulse is

\[ S_i'=\int_0^\lambda i_m \sin \frac{\pi \vartheta}{\lambda}\, d\vartheta =\frac{2\lambda i_m}{\pi}. \tag{17} \]

The number of current pulses occurring during one period of the supply voltage is

\[ K_T'=\frac{2\pi I_{\mathrm{av}}}{S_i'} =\frac{\pi^2 I_{\mathrm{av}}}{\lambda i_m}. \tag{18} \]

The quadratic area of the current pulse is

\[ S_k'=\int_0^\lambda i^2\, d\vartheta =\frac{\lambda i_m^2}{2}. \tag{19} \]

The heating-equivalent current is

\[ I_e'=\sqrt{\frac{K_T' S_k'}{2\pi}} =0.886\sqrt{i_m I_{\mathrm{av}}}. \tag{20} \]

Comparison of the current values calculated from equation (20) and measured with an ammeter with a thermoconverter and by oscillography during experiments with the motors SL-521, MI-12F, and MI-21S showed that the discrepancies do not exceed 7%. Such accuracy is entirely satisfactory for practical calculations.

Taking into account that, in the motor, there are additional losses due to current pulsations, the rated current of the motor must be greater than the equivalent current by approximately 10–30%. The cooling conditions may be considered unchanged over the entire speed-control range, since low-power electric motors usually have an enclosed design without ventilation.

Thus, the conditions for normal operation with respect to heating will be

\[ I_{\mathrm{nom}} \geq (1.1-1.3) I_e'. \tag{21} \]

As numerous experiments have shown, when condition (21) was satisfied the motors operated without overheating.

From the expression for the equivalent current (20), it is seen that the latter is determined by the magnitude of the current-pulse amplitude \(i_m\) and the load \(I_{\mathrm{av}}\). The pulse amplitude \(i_m\) does not depend on the load and is determined only by the relative voltage \(\varepsilon\) and the load parameter \(\omega T\). This makes it possible to determine the maximum load allowable under heating conditions for the motor, \(I_{\mathrm{av,allow}}\), as a function of \(\varepsilon\) for different \(\omega T\). In the case of the limiting load with respect to heating, the condition must be satisfied

\[ I_{\mathrm{nom}}\simeq 1.2 I_e'. \tag{22} \]

Substituting (22) into (20), we obtain

\[ I_{\mathrm{nom}}=1.063\sqrt{i_m I_{\mathrm{av,allow}}}, \tag{23} \]

whence the load allowable with respect to heating is

\[ I_{\mathrm{avg,allow}}=\frac{I_{\mathrm{nom}}^{2}}{1.13\,i_m}, \tag{24} \]

or, in relative units,

\[ \frac{I_{\mathrm{avg,allow}}}{I_{\mathrm{nom}}} \left(\frac{U_m}{R I_{\mathrm{nom}}}\right) = \frac{0.885}{t_m}. \tag{25} \]

Using expression (25) and the graphs in Fig. 5, the dependences shown in Fig. 6 were constructed; they make it possible to determine the thermally permissible load of the motor for known circuit parameters and the amplitude of the supply voltage for various values of the relative voltage \(\varepsilon\), reflecting the magnitude of the rotational speed.

Fig. 6.

In the graph: vertical axis \(\varepsilon\); horizontal axis \(\dfrac{I_{\mathrm{avg,allow}}}{I_{\mathrm{nom}}}\left(\dfrac{U_m}{R I_{\mathrm{nom}}}\right)\); curves are marked \(\omega T=0\), \(1\), \(2\), \(4\), \(6\), \(8\), \(10\).

\[ \varepsilon=\frac{K_e\Phi n+\Delta E}{U_m}. \tag{26} \]

Analyzing the dependence of the permissible load on the circuit parameters, the voltage, and the frequency of the power source, the following ways of increasing the permissible load may be indicated:

1. Inclusion of an additional inductance in the motor armature circuit. As the time constant \(T\) increases, the permissible load increases, since the amplitude of the current pulses decreases, as discussed above. At the same time, the pulsation of the rotational speed also decreases and the range of speed regulation expands.

2. Rational selection of the magnitude of the supply voltage. The amplitude of the supply voltage \(U_m\) should not be selected higher than is required to obtain the maximum rotational speed \(n_m\) at the greatest load \(I_{\mathrm{avg}\,m}\).

The value \(U_m\) can be determined from equation (3) after substituting the motor e.m.f. corresponding to the maximum rotational-

i.e., the expressions for the current \(i\) and its derivative \(\dfrac{di}{dt}\) from equation (5) for the value of the angle \(\vartheta=\dfrac{\pi}{2}\). The expression for \(U_{\mathrm{m}}\) turns out to be very complicated. For practical purposes the magnitude of the voltage amplitude may be selected from the approximate empirical relation

\[ U_{\mathrm{m}} \approx \sqrt{2}\left(K_e \Phi n_{\mathrm{m}}+\Delta E+R I_{\mathrm{av\,m}}\right). \tag{27} \]

1. Introduction of additional resistances in series with the motor armature. This has a practical effect only when operating on ohmic loads and counter-emf, when \(\omega T \approx 0\) (Fig. 6). In circuits with \(\omega T>0\), the permissible load depends little on the magnitude of the resistance, since increasing \(R\), on the one hand, increases the permissible load (25), but, on the other hand, decreases the load parameter \(\omega T\), as a result of which the current amplitude \(i_{\mathrm{m}}\) increases and the permissible load decreases (25, Fig. 6). It should also be taken into account that the introduction of additional resistances reduces the maximum possible speed of rotation, and this leads to the need to increase the supply voltage.

2. Increasing the frequency of the supply voltage and, consequently, the load parameter \(\omega T\) (Fig. 6).

Along with allowance for heating, when selecting a motor for pulse-control systems the commutation conditions must also be taken into account. Commutation of commutator machines in these systems has substantial features arising from the intermittent nature of the current. On the one hand, considerable reactive emfs arise, worsening the commutation conditions; on the other hand, the current to be commutated is absent during certain intervals of time, assumes a zero value, and in this case part of the commutator segments is not subjected to commutation processes, which reduces wear and burning of the commutator and brushes. Probably for this same reason, in the system under consideration no flashover is observed even at very large current overloads (more than 5).

A number of works [7, 8, 9, 10] consider questions of commutation of commutator machines when supplied by pulsating current, as applied to traction motors of electric locomotives. Thus, P. A. Zolotarev [7] indicates an increase in the permissible degree of sparking by a factor of \(\sqrt{2}\) when the motor is supplied by alternating current as compared with the degree of sparking on direct current; in the work of V. A. Khvostov [8] it is indicated that low-power dc motors operate satisfactorily, in terms of commutation conditions, without any design changes when supplied by pulsating current.

However, the questions of commutation of dc commutator machines when they are used in pulse-control systems have not been developed, and there are no methods or recommendations for the practical selection and checking of motors with respect to commutation. At the same time, in some cases, as practice shows, the load and the speed-control range are limited precisely by the commutation conditions and not by motor heating.

The intensity of sparking in motors of electric drives with pulse control depends on the amplitude and frequency of the current pulses and on the speed of rotation. As the amplitude of the current pulses increases, which determines the maximum power interrupted under the brush, the degree of sparking increases. An increase in the speed of rotation also

leads to an increase in the intensity of sparking, since the number of commutator segments commutating current in the range of amplitude values increases. As the load increases, the frequency of the current pulses increases and the intensity of sparking rises.

The wear of the commutator and brushes is determined both by the average value of the interrupted power \(P_{\mathrm{cp}}\), and by the amplitude and frequency of the pulses of the maximum interrupted power \(P_{\mathrm{M}}\). The nature of the distribution of the interrupted-power value (and of the degree of sparking) during operation of the motor in a pulse-control system is shown in Fig. 7.

The commutator and brushes will be subjected to the greatest effects at the maximum interrupted power; moreover, wear and burning of the commutator segments prove to be nonuniform around the circumference of the commutator.

To determine the permissible load under commutation conditions, comparative experimental investigations were carried out with

Fig. 7.

the motor supplied with direct current and during operation in a pulse speed-control system according to the circuit of Fig. 1. Three low-power motors of types MI-21S, MI-12F, and SL-521 were investigated. The load was varied so as to obtain approximately the same sparking intensity. The degree of sparking was evaluated visually by the appearance of visible sparking under diffuse illumination. As is known, a visual assessment corresponds to the maximum values of the interrupted power, at which the commutator and brushes undergo the greatest destruction. In addition, at maximum interrupted powers, hard particles of silicon carbide may form in the contact layer of the brushes, which subsequently greatly accelerate commutator wear and impair commutation. The appearance of sparking is recorded, as experiments have shown, with sufficient accuracy. The deviation of the current values at which visible sparking occurs does not exceed 10–20% for the indicated types of motors. Thus, visual assessment of commutation by the appearance of visible sparking may be considered satisfactory for comparative tests.

At the same time, the adoption of visual assessment is explained to some extent by the difficulties of applying objective methods of commutation assessment in the present case. Attempts to apply the method of M. F. Karasev—V. P. Suvorov [11] ended unsuccessfully because of the difficulty, under the experimental conditions, of manufacturing a miniature device with an auxiliary brush for small-size machines of the type

SL-521, MI-12F, and MI-21S. The application of the method recommended by L. L. Lavrinovich [12], based on measuring the mean value of the high-frequency components of the voltage between brushes of unlike polarity, encountered difficulties in separating the commutation voltages from a broad frequency spectrum, including the high-frequency spectrum that arises in pulsed ion electric-drive systems during operation. Finally, the study of commutation using a photoelectric sparking indicator of the II-1 type is made difficult by the fact that the mean value of sparking intensity measured by the instrument is in itself insufficient for evaluating commutation under pulsed operation; moreover, it is impossible to record the distribution of sparking over the commutator under pulsed supply, owing to the nonsynchronism of the current pulses passing through the motor armature. The problem can be solved by using a special device for photographing the indicator screen, or by other methods, so as to obtain a picture of the distribution of sparking intensity over the commutator for a considerable interval of time and thereby evaluate the commutation conditions.

However, the study of commutation in commutator machines under pulse regulation, the development and creation of apparatus for an objective evaluation of commutation conditions, and the substantiation of criteria for evaluating commutation during operation in pulsed systems lie outside the scope of the present work and should be the subject of an independent investigation.

In the present work a visual method is used, giving only an approximate estimate of the permissible load according to commutation conditions in a pulsed system, as compared with the permissible load on direct current, which is specified in the nameplate data of the machines.

The results of the experimental determination of equal sparking intensities on direct current and in a pulsed automatic-control system are presented in Figs. 8, 9, and 10. The solid curve shows the dependence of the armature current at which visible sparking occurs on the rotational speed under direct-current supply. The dashed curve shows the dependence of the mean current in the pulsed-control system; the dash-dotted curve shows the amplitude values of the current.

From the graphs in Figs. 8, 9, and 10 and from the nameplate data of the motors tested, Table 1 was compiled.

Table 1

Fig. 8.

Vertical axis: \(n\), rpm.
Horizontal axis: \(I\), A.

Scale markings shown: vertical axis \(0, 500, 1000, 1500, 2000, 2500, 3000, 3500\); horizontal axis \(10\).

Inset label:

SP-521
110 V; 1.1 A
3000 rpm
77 W

Fig. 9.

Vertical axis: \(n\), rpm.
Horizontal axis: \(I\), A.

Scale markings shown: vertical axis \(500, 1000, 1500, 2000, 2500\); horizontal axis \(0, 5, 10, 15, 20, 25, 30\).

Inset label:

MI-12F
110 V; 1.46 A
2000 rpm
120 W

The current admissible under commutation conditions in a pulse-control system may be taken as equal to

\[ I_{\text{dc}} = K_i I_{\text{n}} . \tag{28} \]

Or, in relative units,

\[ \frac{I_{\text{dc}}}{I_{\text{nom}}} = K_i \frac{I_{\text{n}}}{I_{\text{nom}}}. \tag{29} \]

Fig. 10.

On the basis of the graphs in Figs. 8, 9, 10 and Table 1, Fig. 11 gives the dependences of the permissible load on motors of the indicated types as a function of rotational speed, under the condition that the amplitude of the supply voltage is chosen so as to ensure the nominal rotational speed at nominal load and with no thyratron ignition omissions (i.e., in the mode of an ordinary uncontrolled rectifier). Figure 12 presents the permissible amplitudes of current pulses as a function of rotational speed.

Commutation is proposed to be considered satisfactory if, at a given rotational speed, the average current \(I_{\text{av}}\) and the current amplitude \(i_{\text{m}}\) do not exceed the permissible values

\[ I_{\text{av}} \leqslant I_{\text{dc}}, \tag{30} \]

\[ i_{\text{m}} \leqslant i_{\text{mc}} . \tag{31} \]

The values of the currents \(I_{\text{av}}\) and \(i_{\text{m}}\) are obtained in the motor heating calculation; the values \(I_{\text{dc}}\) and \(i_{\text{mc}}\) are readily determined from the graphs in Figs. 11 and 12. When motors of other types are used, one may be guided by the dependences for one of the listed motor types whose parameters are closest to those of the motor being used.

Thus, commutation of motors depends on the same quantities as heating—on load, rotational speed, and the amplitude of the current pulses. Consequently, the selection and verification of low-power motors for heating and commutation conditions, when they are used in systems for pulse control of rotational speed, can be carried out on the basis of a unified calculation method.

Fig. 11.

Fig. 12

For practical purposes, the following engineering procedure is recommended for checking low-power motors for heating and commutation in ion electric-drive systems with pulse control of rotational speed and a single-phase rectifier circuit:

1. Compute, for the minimum rotational speed, the values of the relative voltage and the load parameter

\[ \varepsilon_{\min}=\frac{K_e\Phi n_{\min}+\Delta E}{U_m};\qquad \omega T=2\pi f\frac{L}{R}. \]

1. From the diagrams in Fig. 5, determine, from \(\varepsilon_{\min}\) and \(\omega T\), the amplitude of the current pulses \(i_m\).

2. For the specified load \(I_{\mathrm{av}}\), compute from expression (20) the current equivalent with respect to heating

\[ I_{\mathrm{e}}'=0.886\sqrt{i_m I_{\mathrm{av}}}. \]

1. Check the motor for heating according to expression (21)

\[ I_{\mathrm{nom}}\geq (1.1\text{--}1.3)I_{\mathrm{e}}'. \]

1. Using the graphs in Figs. 11 and 12, check the motor for commutation conditions according to expressions (30), (31).

\[ I_{\mathrm{av}}\leq I_{\mathrm{dc}}, \]

\[ i_m\leq i_{mk}. \]

The motor is first selected according to the maximum rotational speed and torque. Next, the supply-voltage value is selected (27), and then a check for heating and commutation is made according to the procedure indicated above.

In conclusion, it should be noted that the ion electric-drive system considered, with pulse control of rotational speed, is intended for low-power installations (from tens to several hundred watts) and can be used in various servo drives, tracking systems, and so on. In these systems the electric motor cannot be used at its full power because of the severe heating and commutation conditions. However, the need to overrate the motors does not have any significant effect on the cost and dimensions of installations at such low powers, and is fully justified by the simplification of the control systems and by the increased reliability of their operation.

Conclusions

The investigations carried out permit the following conclusions to be drawn:

1. Low-power motors can be used in pulse-control systems at loads below the rated load without any additional devices.

2. The permissible load on the motor increases when additional inductances are inserted, the frequency is increased, and the amplitude of the supply voltage is reduced.

3. The heating and commutation conditions of the motor in a pulse-control system depend on the load and on the amplitude of the current pulses.

4. An engineering procedure has been proposed for selecting motors for pulse-control systems.

References

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2. A. A. Bulgakov. Electronic Devices for Automatic Control. GEI, 1958.

3. P. M. Morozov, M. G. Chilikin, N. G. Lysenkov, and A. M. Tverdin. A new circuit for high-speed pulse control in systems with ion converters. Electricity, No. 2, 1958.

4. V. A. Beinarovich, A. I. Zaitsev. Automation of flute-grinding machines. Proceedings of TPI, Vol. 115, 1960.

5. V. A. Beinarovich, A. I. Zaitsev. Device for automatic control of the transverse-feed speed of the grinding wheel of a flute-grinding machine. Inventor’s certificate No. 131716; Bulletin of Inventions, No. 1, 1961.

6. A. A. Sirotin. Automatic Control of Electric Drives. GEI, 1958.

7. P. A. Zolotarev. On the permissible degree of sparking of the brushes of pulsating-current traction motors. Proceedings of Higher Educational Institutions, Electromechanics, No. 11, 1959.

8. B. S. Khvostov. Commutation of a pulsating-current traction motor during operation from a single-phase rectifier. Proceedings of Higher Educational Institutions, Electromechanics, No. 11, 1959.

9. V. E. Skobelev. Physical characteristics of commutation of traction motors with pulsating current. Proceedings of Higher Educational Institutions, Electromechanics, No. 8, 1958.

10. V. L. Dudenkov. Investigation of commutation in single-phase industrial-frequency commutator traction motors. Proceedings of Higher Educational Institutions, Electromechanics, No. 11, 1959.

11. M. F. Karasev. Commutation of DC Commutator Machines. GEI, 1961.

12. L. L. Lavrinovich. Adjustment of commutation by means of measuring instruments. Bulletin of the Electrical Industry, No. 4, 1959.

Received by the editors
in May 1962.