Centrifugal Pumps Design and Application 2nd ed - Val S. Lobanoff, Robert R. Ross (Butterworth-Heinemann, 1992)

Vibration and Noise in Pumps 453
Response To Unbalance
The location of a pump critical speed is defined by its response to unbalance.
It is important to recognize the difference between critical
speeds excited by unbalance and damped eigenvalues that are frequently
also called critical speeds [32]. Generally, the effect of damping is to
raise the frequency of the critical speed response due to unbalance; however,
the effect of damping on the damped eigen values is to lower the
frequency. The damped eigenvalues are primarily used for evaluating the
stability of the rotor system. For compressors and turbines with tilting
pad bearings, the damped eigenvalues are usually comparable to the unbalanced
response criticals. However, in a pump with a large number of
seals, the added damping to the system can be considerable, resulting in
large differences in the unbalanced response critical speeds and the
damped eigenvalues.
Rotor unbalance response calculations are the key analysis in the design
stage for determining if a pump rotor will be acceptable from a dynamics
standpoint. An accurate prediction of rotor unbalanced response
is difficult for centrifugal pumps because of the sensitivity to bearing and
seal clearances that may be at the tight or loose end of the tolerance
range.
Computer programs are available that can calculate the elliptical shaft
orbit at any location along the length of a rotor for various types of bearings,
pedestal stiffnesses, pedestal masses, seals, labyrinths, unbalance
combinations, etc. These programs can be used to determine the response
of the installed rotor to unbalance and accurately predict the critical
speeds over the entire range of variables. The actual critical speed locations
as determined from response peaks caused by unbalance are
strongly influenced by the following factors [33]:
• bearing direct stiffness and damping values
• bearing cross-coupled stiffness and damping values
» location of the unbalance
• location of measurement point
• bearing support flexibility
The normal unbalance used in the analysis would produce a force equal
to 10% of the rotor weight at operating speed. Usually the rotor response
to unbalance calculations are independently made for midspan unbal-