Using an experimental apparatus incorporating a hollow cylindrical rotor (partially filled with liquid) fitted to a vertically suspended shaft, we clarified the pressure mode shape, frequency, etc. of the liquid by directly measuring the pressure fluctuation while varying the amount of liquid and the rotating speed, and studied in detail the relationship between whirling vibration of the rotor and fluctuation of the liquid inside the rotor.
On that basis, we propose a practical method for estimating the region of unstable vibration. Results of estimation by this method were checked against the results of an experiment conducted using three types of differently shaped rotor.
According to many studies conducted in the past, the frequency of unstable vibration is almost constant. In the present experiment, however, the frequency of unstable vibration showed a characteristic tendency to increase with increasing rotational speed. The vibration that was observed in the experiment was found to be an unstable vibration caused chiefly by axial fluctuation of the liquid inside the rotor. It was also found that in the rotational speed range where the difference between the rotor rotating speed and the natural frequency of fluctuation of the free surface of the liquid becomes almost equal to the natural frequency of the rotor, a resonance occurs that causes the unstable vibration. Concerning the vibration studied here, we developed a practical method of estimating the region of unstable vibrations and showed that the method should be universally applicable.
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