Practical Solutions to Machinery and Maintenance Vibration Problems
Chapter 4, Rotor Resonance and Corrections
Section 1, Resonant Whirl
Resonant whirl is the condition whereby a rotor is resonating at a frequency equal to its own running speed (1 x rpm). Rotors can resonate to frequencies other than those equal to their operating speeds (they would be resonant, not in resonant whirl). Resonant whirl is very uncommon in such rotors as armatures, pump rotors and other relatively short-length, relatively rigid rotors. Even long, relatively slender shafted multistage pumps are not subject to resonant whirl as, when they are operating, the individual wear rings between each of the stages act like bearings (when the liquid being pumped flows through them), adding considerable rigidity (even though the non-running rotor can have a resonant frequency equal to its operating speed).
Almost all normal electric motor and generator armatures are designed to not be subject to resonant whirl. Though rare, occasionally a relatively long, smaller diameter, higher speed armature is subject to resonant whirl. Such armatures usually have operating speeds of approximately 3600 rpm or higher (60 Hz electrical current), or approximately 3000 rpm or higher (50 Hz electrical current). Fans with relatively long distances between bearings, heavier fan wheels, or several fan wheels between bearings, also have much greater potential for resonant whirl.
All the above suggests that resonant whirl should be rare. But certain machinery types are very prone to resonant whirl. These tend to be variable speed machines operated at higher speeds than when originally commissioned, such as steam turbines, centrifugal compressors and smaller diameter papermachine rolls. In such situations, the rotor produces the same exaggerated flexing or "curling" mode shape as for non-rotating part resonances. But instead of flexing back and forth and reversing its stresses, the rotor simply rotates with this continuously "bent" shape. There is no flexing back and forth and, therefore, no reversible stresses. For example, if a rotor is running resonant to its own 1st critical speed, its mode shape will be the same as for any other part resonating at its 1st resonance frequency. To visualize this, mentally bend a wire into that shape, then rotate it.
If a rotor's 2nd critical is equal to its own rotating rpm, then the characteristic double bend mode shape will result. Again, the rotor or shaft will not flex back and forth but will, instead, rotate as a rotor with two bends. To show this, mentally bend a wire into two bends, 180° opposite each other. Now rotate the wire. The wire will not show flexing back and forth. Therefore, it will not experience cracking due to fatigue.
However, if the rotor's 2nd critical on up is resonated, not by a vibration at its own rpm, but instead by a vibration at a frequency other than its own rpm, then the usual flexing back and forth occurs. This is not called resonant whirl, and fatigue cracking at a node can eventually occur. To resonate a rotor at its 2nd or 3rd critical on up, and at frequencies above 1 x rpm, usually requires a relatively high vibration frequency source, such as gearmesh frequency, blade or vanepass frequency and so on.
As resonant whirl is a resonance phenomenon, expect the same types of phase changes that occur between resonant and non-resonant conditions. If means are available for phase measurements at various rotor speeds, phase relationships for the non-resonant rotor will simply reveal the symptoms that are the source for the 1 x rpm vibration, such as 1 x rpm from unbalance or 1 x rpm from misalignment, etc. However, as the rotor reaches its speed for resonant whirl, not only will all phases shift, but they will also have different phase relationships with each other. At a speed below that for resonant whirl, the phase symptoms may, for example, point to misalignment as the source; but when the rotor is in full resonant whirl, the phase symptoms will approximate those of a bent shaft. [See section, "To Determine A Bent Shaft (Using Phase)."]
This textbook contains only part of the information in our Practical Vibration Analysis seminar.