A light partial rub at a high rotating speed usually results in fractional sub-synchronous vibrations, along with the synchronous vibration (1×). In a machine with a relatively low rotating speed, the rotor bounces inside the contact point, producing multiple high harmonics in addition to 1×.
High radial (normal) and corresponding frictional (tangential) forces at the contacting surfaces during a rotor rub could lead to extremely severe damage of the seal and rotor surfaces in a very short time. In addition, the rotor operates under severe alternating stress with relatively high frequency.
Rotor-to-stationary-element rubbing actually is a very harmonic-rich vibration phenomenon, resulting in rapidly changing system parameters with a tendency for chaotic motions. The diagnosis of rotor rubbing from vibration data is based on the appearance of: 1) sub-synchronous fractional components (particularly ½×); 2) relatively high harmonics (2× and 3×); and 3) changes in shaft centerline position.
Rotating shafts generally operate in a fluid environment. An interaction between the rotor and the surrounding fluid becomes significant if the clearances between rotating and stationary parts are small and rotation is eccentric. Because of friction between fluid and machine components, the shaft rotation generates a circumferential fluid flow. This, in turn, produces a dynamic effect on the rotating machine parts. Such situations occur in lightly loaded fluid-lubricated bearings, seals, balance pistons, stator/blade tip clearances, rotor/stator peripheries, and rotors filled with fluids such as those in centrifugal pumps and compressors. Dynamic effects of rotor/fluid interaction are known as "fluid whirl" or "fluid whip" rotor self-excited vibrations.
The whirl frequency is generated purely by the fluid interaction and is related to the fluid film radial damping. The fluid involved in the circumferential motion transfers energy from rotation to lateral vibration. For well-balanced rotors, the whirl vibrations are quite persistent. At the beginning of a fluid whirl, the rotor vibrates as a rigid body.
When the rotating speed approaches the transfer speed (i.e., rotating speed×first critical speed/whirl speed), the rotor self-excited whirl vibrations get smoothly transformed into fluid whip, with a frequency asymptotically approaching the rotor high-eccentricity first critical frequency (i.e., the first critical frequency slightly modified by high-eccentricity nonlinearities). The fluid whip is usually persistent. At certain rotating speeds, however, it may disappear and then reappear again. Instabilities may cease and recur.
The main cause of the whirl/whip vibrations is the fully developed circumferential fluid flow. Reducing the circumferential-flow-related tangential force strength will make the rotor more stable. This may be accomplished either by moving the shaft to the higher eccentricities by applying a "friendly" external radial load force to the rotor, or by modifying the fluid flow pattern. Appropriately loaded noncircular bearings, bearings with lobes and grooves, and, particularly, bearings with tilting pads fulfill both objectives. Nowadays, tilting-pad bearings are very common in high-speed rotating machines. Seals with swirl brakes and anti-swirl injections achieve the goal of circumferential flow reduction, resulting in stable rotor operation. The shaft rotation at a higher eccentricity not only can reduce circumferential velocity ratio, but also may raise the fluid film's radial damping and stiffness, which are beneficial for shaft stability. Increasing the fluid pressure also can provide greater fluid radial stiffness. Some reports indicate externally pressurized bearings offer good stability features, but others point to operational problems and dynamic issues for some pressurized bearings. So, approach the use of such bearings with great care.