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Rotor vibrations can be generally categorized into two groups: synchronous and non-synchronous vibrations. The frequency of synchronous vibrations matches the rotor rotational frequency. A shaft spinning at 3600 rpm (60 Hz) will have a synchronous vibration of 60 Hz. Synchronous vibration is largely caused by imbalance. The force created by an imbalance increases as the shaft rotational speed increases and is proportion to the square of the speed.  Mathematically, F = mrw^2 where F is the imbalance force, m is the imbalance mass, r is the radius of the imbalance mass and w is the rotational speed of the shaft. The animated graphic below shows a synchronous orbit. This orbit shows the rotor rising to a peak after exactly a single rotations.


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Non-synchronous orbits do not have the same frequency as the rotational frequency. Sub-synchronous vibrations occur at frequency less than the rotational frequency.   Below is an animated graphic showing a simple sub-synchronous orbit. The key phasor line shows that rotor rises to a peak after two rotations.

When these vibrations are combined, you get the following pattern