EXPERIMENTAL STUDY OF THE STABILITY OF LOW-SPEED SYNCHRONOUS MOTORS

A. A. BUCHMOV, E. V. KONONENKO, A. F. FINIK

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

Considering the physical model of the operation of synchronous motors with electromagnetic speed reduction, one can see their analogy with synchronous salient-pole motors. This makes it possible to write the voltage-balance equations of reduction motors along the longitudinal and transverse axes of the rotor and to apply research methods well developed for ordinary synchronous machines [1, 2]. The main difference in this case is that the longitudinal and transverse axes of the reduction motor are not rigidly connected with the rotor, but rotate synchronously with the first harmonic component of the permeance of the air gap. The wave of air-gap permeance, formed by the relative position of the stator and rotor teeth, in the synchronous mode of operation moves at the speed of the stator magnetic field. The angle \(\alpha\), which characterizes the mutual position of the axes of the field and of the permeance, may remain constant during operation or may change depending on the nature of the load and the ratio of the motor parameters. A change in the angle \(\alpha\) is the cause of nonuniform rotation of the rotor, since the permeance depends on the position of the stator and rotor teeth. Investigation of the equation of motion of the rotor, which includes the motor parameters and the nature of the load, makes it possible to determine the conditions under which speed oscillations arise, their frequency and amplitude, as well as the boundary of stable operation. In these investigations it is very important to measure and record the oscillations of the rotational speed of the rotor of a real machine, or to isolate and record the nature of the change in the angle \(\alpha\).

However, instruments for measuring this angle are not produced commercially, although several methods have been developed that can be used for these purposes. These include the frequency-optical [3], inertial [3], methods based on magnetic recording and those using photoelectric sensors [4]. Possessing a number of positive qualities, these devices are not without shortcomings. For example, the disadvantages of the frequency-optical method include the complexity of manufacturing the setup and the difficulty of processing the oscillograms obtained. The accuracy of measurement by the inertial method is affected by friction in the bearings on which the flywheel is mounted, as well as by the complexity of supplying power to the photodiode and incandescent lamps mounted on the rotating disk. When measuring the uniformity of rotation by means of magnetic recording, the accuracy of measurement is greatly affected by the external magnetic fields of the machine. Therefore, for meas—

To measure oscillations in the rotational speed of the rotor of synchronous geared motors, a method was applied based on the use of the stroboscopic effect and consisting of a light disk with teeth around its circumference and an adjustable source of light pulses. The disk is mounted on the shaft of the motor under test and is illuminated by light pulses with a frequency equal to the frequency at which the teeth pass. At a constant rotational speed the disk appears stationary to the observer. In the case of oscillations in the rotational speed, the teeth will move in the pulsed light. Thus the process of oscillations in the rotor rotational speed can be observed visually.

Fig. 1. Block diagram of the setup for measuring the angle $\alpha$

For a quantitative evaluation of the speed oscillations it is necessary to record the magnitude of the displacement of the teeth, which was done with the aid of the setup shown in Fig. 1. Light source 1 illuminates photodiode 3 with light pulses. Between them is a disk with teeth 2, mounted on the rotating shaft of the motor under test 4. The electrical signals of the photodiode are amplified by amplifier 5 and recorded on photographic film by loop oscillograph 6. The advantage of this method is that, at any constant speed, signals of identical amplitude are recorded on the film, since each time the light pulse illuminates the photodiode at some one position of a tooth relative to the photodiode. At a variable rotational speed, the photodiode is illuminated at different positions of the tooth; therefore a series of signals differing in amplitude is recorded on the photographic film, and their envelope reflects the character of the change in rotational speed. The amplitude of the oscillations of the angle $\alpha$ and its frequency are determined from the magnitude of these signals.

To determine the amplitude of the angle $\alpha$ in geometrical degrees, it is necessary to know the magnitude of the signals at different positions of the tooth relative to the photodiode. For this purpose, with uniform displacement of the teeth of the disk, a reference diagram is taken, shown in Fig. 2, a. In this case a series of increasing signals is recorded on the film,

Fig. 2. Oscillograms of the rotational speed of the rotor of a synchronous geared motor

the minimum of which corresponds to a tooth closed to the photodiode, the maximum to an open one, and the remaining ones to intermediate positions. Comparison of the oscillograms (Fig. 2, b, c) with the reference one (Fig. 2, a) makes it possible to determine the frequency and amplitude of the change in angle in each time interval.

Experimental studies carried out with the aid of this device confirm the theoretical conclusions that the magnitude of the active resistance introduced into the stator circuit affects the frequency and amplitude of the oscillations. Figure 3 presents the calculated and experimental boundaries of stable operation as a function of different values of the active resistance. The motor under test has the following parameters: \(x_d=816\ \Omega\); \(x_q=593\ \Omega\); \(R=53\ \Omega\). The supply voltage is \(120\ \mathrm{V}\) at a frequency \(f=50\ \mathrm{Hz}\). The oscillogram data (Fig. 2, b, c, d) clearly show the effect of resistance on the character of the oscillations. The oscillogram in Fig. 2, b was taken without introducing additional active resistance into the stator-winding circuit. In this case

Fig. 3. Boundary of stable operation of a synchronous reduction motor; a) calculation; b) experiment

the amplitude of the oscillations is \(\Delta\alpha=5.4^\circ\) and the frequency \(f_1=12.5\ \mathrm{Hz}\). At the same voltage, but with a resistance of \(20\ \Omega\) introduced into the stator-winding circuit, the oscillations decreased to \(\Delta\alpha=2.1^\circ\) and \(f_1=3.6\ \mathrm{Hz}\) (Fig. 2, c). An additional resistance of \(40\ \Omega\) completely smooths out the oscillations (Fig. 2, d).

Thus, the method considered can be used for measuring the amplitude and frequency of oscillations of the operating angle \(\alpha\).

REFERENCES

1. E. V. Kononenko, R. P. Laas, A. F. Fink. Basic equations of synchronous reduction motors of the reactive type (SRD-R). Izv. TPI, vol. 212, 1971.

2. V. V. Zhulovyan. Problems in the theory of reduction synchronous machines. In: Problems in the Theory and Calculation of Electrical Machines. Novosibirsk, 1970.

3. Edited by E. L. Lodochnikov and F. M. Yuferov. Micromotors for Automation Systems. Energiya, 1969.

4. G. M. Torbenkov, V. P. Skurigin, A. A. Yanko-Trinitskii. An instrument for oscillographing the operating angle of a low-speed synchronous motor during transient processes. Elektromekhanika, 1969, No. 1.