Practical Solutions to Machinery and Maintenance Vibration Problems
Chapter 2, Mechanical Resonance
Section 8, Resonating a Rotor's First Critical Speed that is Twice its Operating Speed
It's easy to think that the rotor's primary vibration should be the usual 1 x rpm. However, certain rotors that have unequal bending flexibilities produce another vibration which can cause mystifying trouble, unless understood. For example, a relatively flexible shaft may have two long keyways 180° from each other. When the keyways are in the vertical plane, the shaft is deflected more due to the rotor's weight than when the keyways are in the horizontal plane. As the shaft rotates a full revolution, it receives two stiffening impulses. When it rotates at half its critical speed, it receives two stiffening impulses per revolution, thereby resulting in resonance. Extra keyways, cut 90° from the original two, will cure such a condition by doubling the frequency of impulses, causing them to no longer correspond to the resonant frequency.
The above situation is rare enough to warrant little concern beyond an awareness of its solution, if and when it does occur. However, with papermachine rolls, this is a much more common problem, especially when the machine's speed has been increased so that the 2 x rpm impulses correspond to the roll's critical speed. Although a hollow roll looks as if its flexibility would be equal regardless of its position, it really is not. The difference in flexibility is due to the relatively unequal wall thicknesses of the hollow shell from which it was fabricated. The pipe from which it was machined could have been either eccentric or slightly bent. Machining the roll straight necessarily results in unequal wall thicknesses. All papermachine rolls have some 2 x rpm vibration due to reasons indicated above, but at amplitudes that are usually very small. However, there are some relatively rare situations whereby this frequency matches the roll's resonant frequency. Also, it could instead excite the resonant frequency of one of the non-rotating parts of the support structure or machine frame.
Sometimes a roll can be subject to excessive vibration at 2 x rpm, due not to unequal flexibility but to misalignment of non-parallel rolls. The same could occur due to misalignment of a jackshaft or coupling that is driving the rolls. Usually this is caught when the misalignment is great enough to cause a major problem, but when it is only slight, it goes unnoticed. Yet, if the 2 x rpm vibration it creates matches frequencies of some resonance in the support structure, then correction is in order. Usually this is accomplished through better alignment of the rolls.
This textbook contains only part of the information in our Practical Vibration Analysis seminar.