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

452 Centrifugal Pumps: Design and Application
Figure 18-17. Eight-stage pump—first mode response—seals included.
• The location of the critical speed relative to the support stiffness. If the
critical speed is near the rigid bearing criticals (flexible shaft region),
increasing the bearing stiffness will not increase the critical speed because
the weaker spring controls the resonant frequency. Vibration amplitudes
may be low at the bearings (first mode), and therefore, low
damping will be available. This can contribute to rotordynamic instabilities
that will be discussed later. If the critical speeds are in the area of
low support stiffness (stiff shaft region), the critical speeds are strongly
dependent upon the bearing stiffness and damping characteristics and
the critical speeds will be dependent upon bearing clearance. Bearing
wear could be a significant problem.
• The mode shape of the critical speed. The mode shapes are used to
assess the response of the rotor to potential unbalances. For example, a
rotor that has a conical whirl mode (second critical) would be sensitive
to coupling unbalance, but not strongly influenced by rnidspan unbalance.