Experimental Studies of the Uniformity of Rotation of Electric Machines
Abstract Generated abstract
The paper addresses experimental measurement of nonuniform rotation of electric machines within a single revolution, particularly under vibration where optical, magnetic, and inertial methods have practical limitations. It describes a photoelectric pulse sensor with amplification and frequency demodulation that converts shaft-speed-dependent pulse frequency into an output voltage proportional to instantaneous rotational speed, with reported accuracy no worse than 1 percent over 0.5 to 5000 rpm. Using this device, the authors study synchronous motors in a frequency-controlled vibration drive and compare measured load-angle oscillations with calculated results. The experiments support theoretical conclusions that rotational speed, unbalance static moment, and inertia ratios affect the magnitude and character of rotational nonuniformity.
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EXPERIMENTAL STUDIES OF THE UNIFORMITY OF ROTATION OF ELECTRIC MACHINES
A. Yu. Chernyshev, V. N. Dmitriev
(Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)
In recent years, the problem of ensuring high accuracy in the operation of electric drives has acquired topical significance. In this connection, the need has arisen for experimental determination of the uniformity of rotation of electric machines within one revolution. In practice, frequency-optical and inertial methods of speed measurement, as well as methods based on magnetic recording [1, 2], have found application. Along with positive qualities, these methods have a number of substantial shortcomings. For example, the disadvantages of known frequency-optical devices include the complexity of manufacturing the setups and the difficulty of processing the data obtained.
When measuring the uniformity of rotation by means of magnetic recording, external magnetic fields of the machine have a large influence on the accuracy of measurement. The use of the inertial method is difficult in electric drives whose nonuniformity of rotation is accompanied by significant vibrations of the electric machines.
A device with a linear characteristic \(U_{\text{out}} = f(\omega)\) has been developed for studying the uniformity of rotation of electric machines under conditions of vibration. The device (Fig. 1) consists of a photoelectric sensor, an amplifier, and a frequency demodulator.
The photoelectric sensor, consisting of a disk with teeth around its circumference, a light source, and a photodiode of type FD, is mechanically connected to the motor shaft. The light source and photodiode are arranged in such a way that, when the motor rotates, the teeth of the disk pass between them; in this case a pulsating voltage is taken from the photodiode, with a frequency proportional to the rotational speed (Fig. 2,A). This voltage is fed to the input of a two-stage amplifier assembled on transistors \(T_1\)—\(T_3\). The amplified voltage (Fig. 2,B) is supplied to the input of the frequency demodulator.
The demodulation cycle consists of two intervals: a nonworking interval (zero potential at the amplifier output) and a working interval (negative potential at the amplifier output).
During the working interval, under the action of the negative potential, transistors \(T_9\), \(T_{10}\) of the sawtooth-voltage generator open, and capacitor \(C_4\) is charged through resistor \(R_{15}\). The time constant of the charging circuit of capacitor \(C_4\) is numerically equal to the period of the voltage from the FD photodiode corresponding to the average rotational speed.
At the moment the working interval ends, transistors \(T_9\), \(T_{10}\) close and the charging of capacitor \(C_4\) stops; the logic element NOT
Figure 1. Schematic diagram of the device.
Fig. 2. Voltage diagrams
to transistor \(T_4\), inverting the amplifier signal, starts a one-shot multivibrator on transistors \(T_5, T_6\) through the differentiating circuit \(C_2R_6\). During the operation of the one-shot multivibrator, the OR-NOT logic element on transistors \(T_7\)—\(T_8\) inhibits triggering of the switching device on transistor \(T_{11}\) (Fig. 2, \(D\)). The voltage on capacitor \(C_4\) is stored (Fig. 2, \(V\)). This voltage is transmitted through an emitter follower on transistors \(T_{12}, T_{13}\) to the output storage device, made on transistors \(T_{14}, T_{15}\), the storage capacitor \(C_5\), and the discharge resistor \(R_{19}\). Transistor \(T_{15}\), opened during the operation of the one-shot multivibrator, discharges the storage capacitor \(C_5\). The parameters of the discharge circuit are selected in such a way that, by the moment the one-shot pulse ends, the voltage on capacitor \(C_5\) (Fig. 2, \(Zh\)) is proportional to the voltage on capacitor \(C_4\). The voltage on capacitor \(C_5\) is retained for one cycle; it is inversely proportional to the rotational speed of the electric machine.
The operating point of the amplifier on transistor \(T_{17}\) is selected in such a way that changes in the voltage at its input lead to such a change
...of the output voltage, for which in each cycle the value of the output voltage is proportional to the rotational speed of the motor.
At the moment when the single-vibrator action ends, transistor $T_{11}$ opens, discharging capacitor $C_4$, and as a result the circuit is brought to its initial state.
When the motor speed varies according to a sinusoidal law, the voltage at the output of the device also changes stepwise according to a sinusoidal law.
Thus, the device, based on converting the frequency of the photodetector pulses into a voltage proportional to the rotational speed, ensures measurement of the instantaneous rotational speed with an accuracy no worse than 1% over the speed range $0.5$–$5000$ rpm.
Experimental studies of the uniformity of rotation of synchronous motors in a frequency-controlled vibration drive, carried out with this device, confirmed the theoretical conclusions on the influence of the static moment of the unbalances $M_g$ and of the rotational speed of the motors on the magnitude and character of the nonuniformity of their rotation within a revolution [3].
Fig. 3. Dependence of the oscillation of the load angle of a synchronous motor on rotational speed: a — $M_d = 0.5$ N·m; b — $M_d = 2.5$ N·m; c — $M_d = 5.0$ N·m; ● — experimental results.
Figure 3 presents curves of the oscillation of the load angle of a two-pole synchronous motor $(P = 2.2\ \text{kW},\ n = 3000\ \text{rpm},\ J_p = 0.0048\ \text{kg·m}^2)$ over the range $30 \div 120\ \text{s}^{-1}$ for different static moments of the unbalances.
An increase in the rotational speed of the motor leads to a decrease in the oscillations of the load angle; at high speeds, the influence of the periodic component of the moment with double the rotational frequency increases (Fig. 4).
The growth of oscillations of the load angle of a synchronous motor when the static moment of the unbalances is increased depends to a significant extent on the ratio of the moments of inertia of the motor $J_p$ and the unbalanced masses $J_g$. The greatest increase in $\Delta \Theta$ with variation of the static moment of the unbalances is observed for the ratio $J_g = 1 \div 5J_p$.
The results obtained with the device considered are in good agreement with the calculated ones.
![Oscillograms labeled “a” and “b”]
Fig. 4. Oscillograms of the rotational speed of a synchronous motor:
a — $\omega = 40\ \mathrm{s}^{-1}$; b — $\omega = 100\ \mathrm{s}^{-1}$.
REFERENCES
-
Microelectric motors for automation systems. Technical handbook, edited by E. A. Londnikova and F. M. Iuferov. Moscow, “Energiya,” 1969.
-
G. M. Torbenkov, V. P. Skuridin, A. A. Trinitskii. An instrument for oscillographic recording of the working cycle of a low-speed synchronous motor during transient processes. Elektromekhanika, 1969, No. 1.
-
G. A. Sipailov, V. N. Dmitriev, V. F. Kulakov. Analysis of the operation of synchronous motors under vibrational load. Izvestiya TPI, vol. 200, Tomsk, TSU Publishing House, 1974.