The scenario in previous installments described resonance versus classic rotordynamic instability. Rotordynaic instability is recognized by its typical roughly half running speed vibration becoming dominant, growing quickly once initiated. Unlike a forced response resonance, where vibration is excessive only when the exciting force frequency is at or close to the natural frequency, increasing the rotor speed to “drive through” the situation does not work. Increasing speed only enables the self-excitation of the whirl at the natural frequency to “lock on” to the natural frequency, and to more severely stress the machine. Increasing rotor speed beyond this point does not result in any change in the frequency of the whirl. Instead, the whirl becomes large enough to severely rub the bearings and seals, and in this form is typically termed “whip”. An example of whirl becoming unstable whip is shown in the figure, for a multistage centrifugal compressor, as speed is gradually increased.
But can also occur in other rotating machines including turbines and pumps
This situation sounds pretty bad, and it is. But when subsynchronous vibration occurs, it is not always time to trip the machine, or run for the door. The first time it is encountered, yes, better safe than sorry. But if such vibration is chronic, an expert assessment may demonstrate that, in fact, the below running speed vibration is actually a perfectly stable resonance, probably driven by fluid whirl like an instability, but not an instability. This would very likely be the case, for example, if as speed is further increased the vibration begins to drop with further speed increase. While this procedure is NOT recommended without expert observation and ability to immediately trip the machine, in many cases such information is already available because of accidental or (in hindsight) imprudent operation by the plant.
An example of where such a situation has been seen is in submersible pumps, in which water or oil surrounds the motor rotor, within generous radial clearances. The fluid in the motor casing whirls at roughly half running speed, but has no opportunity to cause a cross-coupling force at all competitive with the system damping. However, the imbalance of the large mass of whirling fluid can drive a resonance of the cantilevered structure of the pump and motor, causing a simple (and stable!) resonance, although at an unusual 0.45x running speed rather than 1x rpm. If the plant attempts to run the rotor above the resulting resonant frequency, the pump and motor will operate quite well once the resonance is passed. Stiffening of the cantilever structural support can move the problem natural frequency out of the operating range.
Real-life examples of both stable and unstable vibration initiated by rotor whirl is provided in the accompanying video animations. The first shows vibration of a particularly flexible vertical pump casing (column piping), driven by fluid whirl as the pump speed is gradually increased. The roughly half speed whirl drives resonant vibration response as the 40 to 50% running speed whirl force moves through a casing bending natural frequency. The vibration peaks out, due to net damping being positive, and then decreases again as speed (and whirl frequency) increase further. This is classic (and stable) resonant behavior.
The second example is the same pump, but before the excessive cross-coupling of the bearings was reduced to be less than the damping. Rotordynamics-driven instability occurred, as can be seen. Trying to drive the whirl frequency through the natural frequency did not succeed, and in fact only made the vibration worse. The vibration frequency “locked-on” to the casing natural frequency. This would have been a typical rotordynamic instability, except that it was an unusual situation in which the casing, rather than rotor, natural frequency was excited unstably by the whirl.
More examples of stable subsynchrous vibration, as opposed to the ustable kind, will beprovided in the next installment. Stay tuned!
