Practical Solutions to Machinery and Maintenance Vibration Problems
Chapter 7, Misalignment
Section 18, Using Understanding of Vectorial Addition for Vibration Analysis
For a rotating machine, the rotor shaft reacts to several forces at the same time. There are forces that produce 1 x rpm vibrations, 2 x rpm and other frequencies. A vector diagram can represent all the vibration forces at the same frequency, that are present at the same time.
For example, a vector diagram can show how the 1 x rpm force due to unbalance vectorially combines with the 1 x rpm force due to coupling misalignment. These 1 x rpm forces also combine vectorially with other 1 x rpm forces that may also be acting simultaneously on the same part of the rotor shaft, such as due to armature or gear eccentricity, bent shaft and so on. Fortunately, there is usually just one major source for the resultant excessive vibration. The contributions of the secondary sources to the total resultant vibration are usually small enough so that they don't alter the symptoms very much, leading to easier analysis of the prime source of the trouble. However, these secondary sources do affect the symptoms enough that basic understanding is required.
Example: A machine experiences its greatest vibration severity at a frequency of 1 x rpm of the rotor. The 1 x rpm measurement at each bearing is given in amplitude and phase. If, for example, there is only one source for the vibration, such as rotor unbalance, and no contribution from other possible sources, such as misalignment, bent shaft, etc., then for a specific vibration measurement, the amplitude and phase are both due to that of unbalance only. As measured at one bearing, its resultant provides the instrument and the analyst relatively clear symptoms of its source unbalance. Assume that the resultant of all forces gives a phase response as it passes the phase pickup.
Now to the same unbalance, add at another angle a 1 x rpm vector due to a small amount of misalignment. Notice that the resultant of the two vectors has a different amplitude and phase than before the small misalignment vector was added. As the effect of the misalignment vector changes the resultant's amplitude and phase by only a small amount, the symptoms for analysis are still relatively clearly and designate unbalance as the primary source for the vibration (but this time not as clear as when no misalignment was present).
Most machines with excessive vibration have only one major defect that
provides only one major vector. The other forces that are within their
tolerances would contribute only minor sized vectors that alter the
resultant's phase and amplitude slightly. However, sometimes a machine
has more than one source for major vectors at the same frequency, such
as due to a large unbalance and large shaft/coupling misalignment. Analysis
for such machines becomes much more difficult. Sometimes the symptoms
are so unclear that the analyst may simply first check and correct the
possible misalignment (to eliminate one vector) and then analyze the
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