Rotordynamic Instability

Rotordynamic instability refers to the phenomena whereby the rotor and its system of reactive support forces are able to become self-excited, leading to potentially catastrophic vibration levels even if the active, stable excitation forces are quite low. The most common form of Rotordynamic instability is known as Shaft “Whip,”?

The fluid rotational speed becomes the whirl speed. The most common cause of whirl is fluid rotation around the impeller front or back shrouds, in the wear rings, or in journal bearing clearances. Such fluid rotation is typically about 45% of running speed, because the fluid is stationary at the stator wall, and rotating at the rotor velocity at the rotor surface, such that the bulk of the fluid rotates at roughly half speed in the running clearance. (Due to boundary flow condition)

The pressure distribution which drives this whirl is generally skewed such that the cross-coupled component is potentially strong and positive in sign, able to “pump” energy into the rotor whirling motion. If somehow clearance is decreased on one side of the gap, due to eccentricity the resulting cross-coupled force increases further.

The cross-coupled force acts perpendicular to any clearance closure. In other words, the cross-coupling force acts in the direction that the whirling shaft minimum clearance will be in another 90 degrees of rotation. If the roughly half speed frequency at which the cross coupled force and minimum clearance are whirling becomes equal to a natural frequency, a 90-degree phase lag shift occurs, which is typical when force frequency equals natural frequency. This phase shift means that the motion in response to the cross-coupling force is delayed from acting for 90 degrees worth of rotation. By the time it acts, therefore, the gap which caused the force has rotated 90 degrees such that the cross-coupled force tends to act in a direction to further close this minimum gap. As the gap closes in response, the cross-coupled force which is inversely proportional to this gap increases further. The cycle continues until all gap is used up, and the rotor is severely rubbing. This final process is shaft whip, and is a dynamic instability in the sense that the process is self-excited once it begins.

One method of overcoming Rotordynamic instability is to reduce the cross-coupling force which drives it. A complementary solution is to increase system damping to the point that the damping vector, which acts exactly opposite to the direction of the cross-coupling vector, overcomes the cross-coupling.

Typical design modifications which reduce the tendency to rotor dynamic instability involve bearing changes, to reduce cross-coupling and hopefully simultaneously increase damping. The most unfavorable type of bearing in this regard is the plain journal bearing, which has very high cross-coupling.

Other bearing concepts, with elliptical or offset bores, fixed pads, or tilting pads, tend to reduce cross-coupling, dramatically so in terms of the axially grooved and tilting pad style bearings. Even more effective and controllable, but much more expensive, are the hydrostatic bearing and the actively controlled magnetic bearing. Another bearing effective in reducing cross-coupling relative to damping is the pressure dam bearing.

If Some one has more articles related to Cross Coupling force kindly share with us.

Reference: Pump Handbook by Igor J Karassik

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