Returning to stable subsynchronous vibration, another example is rotating stall in a compressor or pump (and sometimes in fans). The stall field involves one or more vortical zones (i.e. like mini tornadoes or typhoons) that rotate in the direction of the rotor, but at a lower rotational speed than the rotor (usually 60 to 95% of 1x rpm). If the rotating static pressure field of the stall field rotates at the same frequency as a natural frequency of the structure or (more likely) rotor, a significant vibration may occur. Depending upon the level of damping, the vibration may violate standards or even be damaging, but it is stable. As in the case of the submersible pump, running the machine at increased speed will “drive through” this resonance, such that low vibration results at the higher operating speed. There is no cross-coupling or other phenomenon that tends to cancel the damping, and therefore there is no instability. The fix is not bearings with lower cross-coupling, but operating outside the zone of rotating stall (may require guide vane modification if that operating point is a plant requirement).
Another example of subsynchronous vibration that is in fact stable is a rotor rub. This situation can cause what is known as a “parametric resonance”. The analogy is dribbling a basketball, where the dribbler moves the hand twice or three times for each bounce. To achieve significant vibration, the key is to nearly perfectly synchronize the strikes with the top of the bounce. In this manner, rubs are the most likely cause of rotor vibration at exactly ½ x, or sometimes 1/3x, running speed. But beware, although unusual it is certainly possible for a fluid whirl instability mechanism to occur at exactly 1/2x rpm.
The final contrary examples are actually true rotor instabilities, but are not at “half running speed”. One case is steam whirl in a steam turbine with excessively worn labyrinth seals. The typical construction of these machines leads to the leakage of steam starting out near the rotor rim, and maintaining a large percentage of the rotor tip speed as it migrates toward the smaller diameter labyrinth “packing”. Typical fluid whirl that results in the packing clearances has been observed to be 60 to 70% rotor speed. This whirl then can drive rotor whirl at the same frequency, with the rotating close clearance portion of the packing clearance causing whirl-induced cross-coupling, and potentially unstable rotor vibration at 60 to 70% rotor speed.
The second case is a supersynchronous (i.e. faster than rotor speed) unstable vibration. This has been encountered in centrifugal pumps with unusual wear ring designs that encourage leakage flow to whirl at speed not only faster than the typical half-speed, but faster than 1x rpm. The mechanism is that fluid near the impeller rim is revolving close to running speed, but as it migrates toward the smaller diameter of the wear ring, to conserve angular momentum its whirl velocity must increase as diameter decreases. This is like a spinning skater drawing in her arms, and thereby spinning faster. Like the steam turbine case, and all classical rotordynamic instability cases, the whirling fluid within the close clearances (of the complex wear ring passages in this case) causes a cross-coupled force acting to cancel damping, but in this case both the cross-coupling and damping forces rotating at 130% rotor speed.
So, is “half-speed” whirl always an instability? The answer is that this is FICTION. However, great caution is still recommended whenever you encounter a half-speed vibration. Those that did not know what rotor instability was, or assumed they didn’t have it, sometimes ended up with broken machine parts as unintentional boat anchors, as souvenirs.
