USE OF UNIVERSAL-SUPPLY MOTORS IN RELAY-TYPE TRACKING ELECTRIC DRIVES

V. A. BEINAROVICH

(Recommended by the scientific seminar of the Electromechanical Faculty)

A substantial simplification and reduction in cost of relay-type tracking electric drives, while simultaneously increasing their speed of response, can be achieved by using series-excitation motors instead of shunt and asynchronous motors. In such systems there is no need for a device to supply the excitation winding, and the considerably greater overload capacity of series motors (5–6 times), compared with shunt motors and asynchronous motors (2–3 times), makes it possible to obtain greater acceleration and to reduce the operating time.

As relay-type contactless elements in relay tracking electric drives supplied from an alternating-current network, thyristors or thyratrons may be used; in this case they perform the role of rectifier and regulator.

To reverse a series-excitation motor, four sets of relay elements are required, connected in a bridge circuit. In low-power tracking drives it is advisable to use universal-supply motors with a split excitation winding. This makes it possible to reduce the number of sets of relay elements to two. In addition, the universal commutator motor is designed for alternating-current supply, and its magnetic system is usually made unsaturated [1]. The first circumstance makes it possible not to take measures to reduce current pulsations; the second makes it possible to obtain a quadratic dependence of torque on current, i.e., the greatest maximum torque.

Despite the noted positive properties of universal motors, the latter are still not used widely enough in tracking electric drives. One reason for this situation is the limited study of converter electric-drive systems with series-excitation motors.

When designing low-power relay-type tracking drives supplied from an alternating-current network, it is advisable to recommend a single-phase rectification circuit (Fig. 1), which has the minimum number of controlled valves. The motor current in this system has

is of a pulsed character. The relay control device \(RYU\) ensures operation of the valves \(T_1\) and \(T_2\) in the “open—closed” switching mode. As a result, the motor operates in a switching mode on the principal mechanical characteristics “forward” or “backward” (in the absence of a dead zone of the \(RYU\)), or else the motor supply is disconnected in the matching position of the follow-up drive (when a dead zone of the \(RYU\) is present).

In the present article, current modes are considered and a method is proposed for selecting universal motors for relay follow-up electric drives operating according to the circuit of Fig. 1. The basic quantities for selecting the motor are the mean and rms values of the pulsed current.

For an approximate determination of these quantities, let us represent the motor circuit by an equivalent circuit (Fig. 2) and introduce the assumptions: the inductance \(L\) and ohmic resistance \(R\) are constant, the counter-emf \(E\) is proportional to the product of the current \(i\) and the speed \(n\), the valve commutation process occurs instantaneously, and the voltage drop \(U_v\) across the open valve is constant.

Fig. 1.

Fig. 2.

Introduce the following notation for dimensionless quantities:

\[ \Delta=\frac{U_v}{U_m}; \qquad \varepsilon=\frac{E}{U_m}; \qquad T=\frac{L}{R}; \qquad I_m=\frac{U_m}{R}, \tag{1} \]

where \(U_m\) is the amplitude of the supply voltage.

The equation of electrical equilibrium in the system of relative units, with sinusoidal voltage supply, is written as

\[ \sin(\omega t+\varphi)=\Delta+\varepsilon+\iota+T\frac{d\iota}{dt}; \tag{2} \]

\[ \varphi=\arcsin \Delta; \tag{3} \]

where \(\omega\) is the angular frequency of the supply voltage;

\(\varphi\) is the valve firing angle;

\[ \iota=\frac{i}{I_m} \]

is the instantaneous value of the current in relative units.

Since \(E=k_1 i n\), or, taking (1) into account,

\[ \varepsilon=k_2 \iota n, \tag{4} \]

equation (2) is written as:

\[ \sin(\omega t+\varphi)=\Delta+\iota(k_2 n+1)+T\frac{d\iota}{dt}. \tag{5} \]

The solution of equation (5) for the region \(\iota>0\) has the form

\[ i=\frac{\alpha \sin(\omega t+\zeta)-\omega T \cos(\omega t+\zeta)} {\alpha^{2}+\omega^{2}T^{2}}+Ae^{-\frac{\alpha}{T}t}-\frac{\Delta}{\alpha}; \tag{6} \]

where

\[ \alpha=k_{2}n+1, \tag{7} \]

\[ A=\frac{\Delta}{\alpha}- \frac{\alpha\sin\zeta-\omega T\cos\zeta}{\alpha^{2}+\omega^{2}T^{2}}. \tag{8} \]

The form of the current pulses, and their average and effective values, can be calculated on the basis of (6), (7), and (8). However, these expressions can be simplified if it is taken into account that the voltage drop across the open valve is negligibly small in comparison with the amplitude value of the supply voltage, that is, \(\Delta\approx 0\). This is quite valid when thyristors are used and introduces a certain error into the calculation of a thyratron system. For \(\Delta=0\), the current from (3), (6), (7), and (8) is determined as

\[ i=\frac{\alpha\sin\omega t-\omega T\cos\omega t+\omega T e^{-\frac{\alpha}{T}t}} {\alpha^{2}+\omega^{2}T^{2}}. \tag{9} \]

To find the average and effective values of the current, we determine the duration of the current pulse \(t_i\) by equating expression (9) to zero:

\[ \frac{\alpha}{\omega T}\sin\omega t_i-\cos\omega t_i +e^{-\frac{\alpha}{T}t_i}=0. \tag{10} \]

Equation (10) is transcendental and is solved by numerical or graphical methods.

Figure 3 presents diagrams characterizing the dependence of the relative pulse duration \(\lambda=\omega t_i\) on the load parameter \(\omega T\) and the speed coefficient \(\alpha\) for a series motor, calculated from (10).

Fig. 3.

The average value of the motor current over the period of the supply voltage, taking (9) into account, is determined as

\[ i_{\mathrm{av}}=\frac{\omega}{2\pi}\int_{0}^{t_i} i\,dt = \]

\[ =\frac{1}{2\pi\left(\alpha^{2}+\omega^{2}T^{2}\right)} \left[ \alpha(1-\cos\lambda)-\omega T\sin\lambda +\frac{\omega^{2}T^{2}}{\alpha} \left(1-e^{-\frac{\alpha\lambda}{\omega T}}\right) \right]. \tag{11} \]

Figure 4 presents diagrams of the dependence of the average current of a series motor on the speed coefficient \(\alpha\) and the parameter \(\omega T\), constructed from (11) and (10). From the average current one can determine the mechanical characteristic of the drive with the relay element switched on for a specific system, which is subsequently used in calculations of the dynamic characteristics of the tracking system [2].

To estimate motor heating, it is necessary to know the root-mean-square current with the relay element switched on, which depends on the speed and the drive parameters and on the time cyclogram of the drive operation, determined in calculations of the dynamics of the tracking system. The root-mean-square

…the current when the relay element is switched on can be determined, taking (9) into account, as

\[ i_{\mathrm{rms}}^{2} = \frac{\omega}{2\pi}\int_{0}^{t_i} i^{2}\,dt = \frac{1}{2}\left( \frac{\lambda}{2} - \frac{\sin 2\lambda}{4} - \frac{2\omega^{2}T^{2}e^{-\frac{a\lambda}{\omega T}}}{a^{2}+\omega^{2}T^{2}}\sin\lambda \right) + \frac{\omega^{3}T^{3}\left(1-e^{-\frac{2a}{\omega T}\lambda}\right)} {4\pi a\left(a^{2}+\omega^{2}T^{2}\right)} - \frac{\omega T\sin^{2}\lambda} {2\pi\left(a^{2}+\omega^{2}T^{2}\right)} . \tag{12} \]

Fig. 4.

Fig. 5.

Figure 5 presents diagrams of the rms current of a series-excitation motor as a function of the speed coefficient \(a\) and the parameter \(\omega T\), constructed from (12) and (10).

Having the ability to calculate the average and effective values of the pulsed current, one may propose the following engineering procedure for selecting universal motors for electric drives with relay control using controlled valves:

1) a preliminary selection of the motor is made (by maximum power, speed, load, or other considerations);

2) the parameters of the motor circuit are determined, and the frequency and magnitude of the supply voltage are selected;

3) using the diagrams in Fig. 4, the dependence of the average current value on speed is determined and the mechanical characteristic of the drive is constructed;

4) using the mechanical characteristic and the characteristics of the relay system [2], a time cyclogram of the motor operation is constructed (current and speed as functions of time);

5) from the cyclograms and the diagrams in Fig. 5, a graph of the rms current versus time is constructed; the equivalent heating current is calculated from it, and the selected motor is checked by this current [3].

REFERENCES

1. Electric Machines of Low Power, edited by D. A. Zavalishin, GEI, 1963.

2. Ya. Z. Tsypkin, Theory of Relay Automatic-Control Systems, GITTL, 1955.

3. V. P. Andreev, Yu. A. Sabinin, Fundamentals of Electric Drive, GEI, 1956.