Proceedings of the Tomsk Polytechnic Institute
awarded the Order of the October Revolution and the Order of the Red Banner of Labor
named after S. M. Kirov

Volume 267

1975

Study of Electromechanical Transient Processes in the Oscillatory Operating Mode of DID, ADP, and EM Series Electric Motors

S. A. Lukovnikova

(Presented by the scientific and technical seminar of the Department of Electrical Equipment)

It is known that when the windings of a two-phase asynchronous electric motor are supplied with currents of different frequencies, or with currents of the same frequency but with a phase shift between them continuously varying according to a linear law, a rocking magnetic field is created in the air gap and the motor shaft begins to perform torsional oscillations [1, 2]. Such an operating mode can be used in creating vibration drives for various machines and mechanisms, electric drives for certain types of scanning systems, for modeling alternating vibration forces developed in production mechanisms, and in a number of other cases. The use of an oscillatory electric motor may prove more effective if the expected character of the electromechanical transients in the motor during its starting is known.

Fig. 1. Block diagram of the model of an oscillatory electric motor, where
\[ M_v = 100\frac{b}{ed};\quad M_y = 100\frac{b}{ed};\quad M_f = \omega . \]

The equation of motion of the shaft of an oscillatory motor under the usual assumptions can be written in the form

\[ \dot{\gamma}=A\gamma^2\sin(\omega t+\beta)-B\gamma+C\sin(\omega t+\beta), \]

where \(v\) is the relative speed of the motor rotor; \(\omega\), \(\beta\) are the difference of the angular frequencies of the supply voltages and the initial phase shift between them. \(A, B, C\) are constants determined by the parameters of the motor equivalent circuit, as well as by the signal coefficient \(\alpha\) and the electromechanical time constant of the motor and load \(\tau\).

The analytical solution of the equation of motion is cumbersome and inaccurate, while the use of a digital computer requires large expenditures of machine time and labor in processing the calculation results [2].

In this connection, it is proposed that, in analyzing the electromechanical transients of the starting of an oscillatory motor, an analog computer be used.

Figure 1 presents a structural diagram of the electric-motor model, constructed in accordance with the equation of motion.

When setting up the model on an MN-7 electronic integrator, as was done in the present work, it is convenient to introduce a time scale equal to \(\omega\), thereby minimizing the number of model readjustments when varying \(\omega\), \(A\), \(B\), \(C\).

Using the indicated model, electromechanical transients arising during starting in the oscillatory mode of micromotors of the DID, ADP, and EM series were investigated. As a result of the calculation it was found that, for the indicated series, the constants vary within the following limits: \(0.035 \le A \le 2\); \(0.5 \le B \le 40\); \(0.2 \le C \le 50\). Here it was assumed that the signal coefficient and the electromechanical time constant of the motor and load would vary within the limits \(0.2 \le \alpha_e \le 1\), \(T_m \le \tau \le 5T_m\), where \(T_m\) is the electromechanical time constant of the electric motor itself.

The calculation was carried out according to the relations given in [2] and in accordance with the parameters of the motors of the indicated series set forth in [3].

The results of the modeling carried out for the indicated limits of variation of \(A\), \(B\), and \(C\), taking into account that under real conditions \(A\) is 10–40 times smaller than \(C\), and \(B\) cannot differ from \(C\) by more (or less) than a factor of two, showed the following:

1. The oscillatory mode is excited when \(\omega\) varies from 0.15 to 15 Hz.

2. The form of the angle and speed of the established oscillations is close to sinusoidal.

3. The impact torque is maximal at \(\beta = 90^\circ\) and large values of \(B\) and \(C\), but it does not exceed the value of the initial starting torque by more than 50%.

4. The displacement angle is maximal at \(\beta = 0^\circ\), large values of \(\omega\), and small values of \(B\) and \(C\), but does not exceed 3–4 amplitudes of the oscillation angle.

REFERENCES

1. A. M. Meistel, M. P. Rashkovich. Izv. vuzov. “Elektromekhanika”, 1967, No. 6.

2. V. I. Lukovnikov. In: Reports to the VI Scientific and Technical Conference on Problems of Production Automation. Tomsk, vol. III, 1969.

3. E. M. Lopukhina, G. S. Samykhina. Asynchronous Micromachines with a Hollow Rotor. Moscow, “Energiya,” 1967.