Frequency Converter for Powering the Electromagnetic Drive of Vibratory Machines

M. A. Zhitkov, B. A. Zakharov

(Presented by the Scientific and Technical Seminar of the Research Institute of Electrical Machines under TPI)

At present, in metal machining, in foundry production, in mining and ore-processing, and in other branches of industry, vibratory machines of various types are widely used. Vibrators with mechanical, hydraulic, pneumatic, or electromagnetic drive are known. Vibratory machines with electromagnetic drive are the most advanced, since in them the required reciprocating motion is obtained directly, without any intermediate mechanisms.

Fig. 1.

As a rule, electromechanical frequency converters (FCs) are used to power the traction coils of the electromagnets of vibrators; these provide operation both at constant and at variable frequency. The disadvantages of electromechanical FCs are well known; therefore, from the standpoint of compactness, economy, and reliability of vibratory machines, it is advisable to use static FCs for their power supply.

A large group of vibratory machines consists of screens, conveyors, crushers, and other mechanisms requiring alternating-current energy at a frequency of 25 Hz for their power supply. In such cases, it is possible to use known FCs with direct coupling, which perform division of the supply-network frequency.

The essence of dividing the frequency of the supply network by two can be clarified by considering the operation of a known FC with natural commutation, whose basic electrical circuit is shown in Fig. 1.

With an active load, the output voltage is formed from two half-waves of the supply-network voltage, through the alternating operation, in rectifier mode, of the valve groups \(1'—3'\); \(1—3\); and \(2'—4'\); \(2—4\). The output-voltage curve is shown in Fig. 2. When operating into an active-inductive

Fig. 2.

load, the valves of the group entering operation will not conduct until the lagging load current has fallen to zero. In this time interval the valves of the group leaving operation operate in inverter mode. Thus, with an active-inductive load, the operating duration of the valves belonging to one group is not the same. At low values of the load power factor, the valves of the incoming group will

Fig. 3.

conduct over the interval \(\frac{\omega_1}{2}T_1 - \varphi_{\mathrm{n}}\), which may amount to only a few degrees. Obviously, in this case the use of all the valves is inexpedient, and the FC circuit considered above can be reduced to the circuit shown in Fig. 3.

The power section of the FC contains commutating reactors and two groups of thyristors \(T_1—T_3\) and \(T_2—T_4\), to whose control electrodes control pulses are supplied from the output of a push-pull power amplifier assembled on transistors \(PP2\) and \(PP3\). The power amplifier is synchroni-

Fig. 4.

is synchronized by the frequency of the supply mains by means of an amplifier on transistor \(PP1\). The voltage waveforms in the circuit of Fig. 3 are shown in Fig. 4.

The output voltage (graph б) is applied to the base of transistor \(PP1\) in antiphase with the mains voltage (graph а). The rectangular voltage (graph в) from its collector is differentiated (graph г) and fed to the input of a two-stroke

…of the amplifier. The duration of the control pulses (plots d, e), taken from the output windings of the pulse transformer 2TP, is determined by its parameters. When the transformer saturates, the collector current of transistors PP2 and PP3 is limited by resistances \(R_4, R_7\). The voltage and current curves in the load are shown in (plots zh, z).

For a qualitative assessment of the voltage formed across the load, let us determine its spectral composition, using the expansion of nonsinusoidal functions into a Fourier series. The curve of the output voltage (plot zh) is symmetric with respect to the abscissa axis; therefore its Fourier-series expansion has the form

\[ f(t)=\sum_k^{\infty}\left[a_k\cos K\omega t+b_k\sin K\omega t\right] =\sum\left[F_k\sin\left(K\omega t+\theta_k\right)\right], \tag{1} \]

where

\[ K=1,\,3,\,5 \text{ is the harmonic number.}\quad F_k=\sqrt{a_k^2+b_k^2};\quad \theta_k=\operatorname{arctg}\frac{a_k}{b_k}; \]

The expansion coefficients are determined by the formulas

\[ a_k=\frac{2}{\pi}\int_0^\pi f(\omega t)\cos K\omega t\,d(\omega t), \tag{2} \]

\[ b_k=\frac{2}{\pi}\int_0^\pi f(\omega t)\sin K\omega t\,d(\omega t). \tag{3} \]

The function \(f(\omega t)=U_{\mathrm{n}}(\omega t)\) is defined as follows:

\[ U_{\mathrm{n}}(\omega_2 t)=U_m\sin 2\omega_2 t \quad \text{for } 0\leq \omega_2 t\leq \varphi;\quad \varphi\leq \frac{\pi}{2}; \]

\[ U_{\mathrm{n}}(\omega_2 t)=-U_m\sin 2\omega_2 t \quad \text{for } \frac{\pi}{2}\leq \omega_2 t\leq \pi. \]

Solving equations (2), (3), taking into account that \(\omega_1=2\omega_2\), we obtain:

\[ a_k=\frac{2U_m}{\pi}\left[ -\frac{1-\cos(2+k)\varphi+\cos(2+k)\pi}{2(2+k)} +\frac{1-\cos(2-k)\varphi+\cos(2-k)\pi}{2(2-k)} \right], \tag{4} \]

Table 1

\[ b_k=\frac{2U_{\mathrm{m}}}{\pi}\left[-\frac{\sin(2+k)\varphi+\sin(2+k)\frac{\pi}{2}}{2(2+k)} +\frac{\sin(2-k)\varphi+\sin(2-k)\frac{\pi}{2}}{2(2-k)}\right]. \tag{5} \]

The current spectrum corresponds to the voltage spectrum, and the amplitudes of the current harmonics are determined through the total load impedances for each harmonic:

\[ I_k=\frac{U_k}{Z_k}. \tag{6} \]

The results of calculating the amplitudes of the voltage harmonics are given in Table 1, for the case in which the supply network has the parameters: \(U=220\ \mathrm{V}\), \(f=50\ \mathrm{Hz}\). Analysis of the calculated data makes it possible to conclude that the output voltage of the frequency converter according to the circuit of Fig. 3 differs only slightly from the voltage at the output of the frequency converter assembled according to the circuit of Fig. 1. Thus, at \(\cos\varphi=0.5\) the amplitude of the first voltage harmonic at the output of the simplified frequency converter decreases by 18.7%, while the total content of higher harmonics in the spectrum increases by only 5% in comparison with the voltage of the frequency converter according to the circuit of Fig. 1. It is therefore obvious that at \(\cos\varphi=0.5\) the use of the simplified frequency-converter circuit is entirely justified. At the same time, the installed power of the valves is reduced by half, the control circuit is simplified to the utmost, and the weight-and-size characteristics of the frequency converter are reduced to a minimum.

Thus, the simplified frequency converter can be used to supply a load with a low power factor, when strict requirements are not imposed on the waveform of the output voltage. In the electric-drive laboratory of the Scientific Research Institute of Electromechanics, such frequency converters were successfully used in the development of power supplies for the electromagnetic drives of vibrating screens with ratings of 5 and 7 kW at an output frequency \(f=25\ \mathrm{Hz}\).