Forward and Backward Whirl
For a symmetric rotor that is not rotating, all lateral vibration modes will appear in pairs with the same natural frequency. For the rotating system, the double natural frequencies will be split into two separate values, corresponding to forward and backward whirl. When vibrating at one of the natural frequencies, the corresponding mode shape will travel in an orbit due to the rotation of the rotor.
In a mode with forward whirl, the natural vibration mode travels in the same direction as the rotation of the rotor. For backward whirl, the situation is the opposite.
The orbit of the rotor actually consists of the summation of two rotating vectors: one is a forward circular motion and the other is a backward circular motion. When the forward amplitude is larger than the backward amplitude, the overall motion is forward. When the forward amplitude is smaller than the backward amplitude, the overall motion is backward. When both amplitudes are equal, the motion degenerates to a straight line.
When you have solved for the eigenfrequencies, you can plot a shape and directivity index variable, named <phys>.i_sd (for example, rotbm.i_sd). This variable has the range
A classification of the whirl can now be done using the following criteria:
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isd = −1: Backward circular planar motion
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−1 < isd < 0: Backward elliptical planar motion
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isd = 0: Straight line motion
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0 < isd < 1: Forward elliptical planar motion
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isd = 1: Forward circular planar motion
At points where the mode shape has a node (the lateral displacement is zero), the index cannot be determined, thus the value may be arbitrary.
Usually, the entire rotor has either forward or backward whirl. However, it is also possible that the complete rotor can have mixed whirling. In this case, the rotor can undergo forward and backward whirl simultaneously at different sections. Mixed whirling sometimes occurs in long, flexible rotors supported by fluid-film bearings.
For details about the shape and directivity index variable, see Identification of Whirl in the theory section.