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

454 Centrifugal Pumps: Design and Application
ance, coupling unbalance, and moment unbalance. An unbalance equal to
a force of 5 % of the rotor weight is usually applied at the coupling to
excite the rotor. For moment unbalance, an unbalance equal to 5 % of the
rotor weight is used at the coupling and another equal unbalance is used
out-of-phase on the impeller furthest from the coupling.
The unbalance response of a pump should be analyzed for several cases
to bracket the expected range of critical speeds. The first analysis should
include minimum seal and bearing clearances that represent the maximum
expected support stiffness and therefore, the highest critical speed.
The second analysis should consider the maximum bearing clearances
and seal clearances of twice the design clearance to simulate the pump
condition after long periods of service. The third analysis should simulate
the worn condition with no seal effects and maximum bearing clearances
that represent the overall minimum expected support stiffness for
the rotor (lowest critical speed).
The unbalanced response of the eight -stage pump with maximum bearing
clearances and no seals is shown in Figure 18*18. The peak response
at 1700 rpm was the minimum calculated critical speed. The unbalance
was applied at the rotor midspan to excite the first mode. The response
for the intermediate analysis (worn seals) is plotted in Figure 18-19. The
worn seals increased the predicted response peak to approximately 1800
cpni. With minimum clearances at the bearings and seals, the response
was lower and the frequency increased to 2200 cpm, as shown in Figure
18-20 (note scale changes).
Shop acceptance test data was available for the eight-stage pump which
was analyzed. The calculated unbalanced response is compared with the
measured vibration data from the test stand in Figure 18-21. For these
calculations, maximum bearing clearance and the design values of seal
clearance were used. Based on these results, Quids' finite length method
[28] provides favorable results compared with measured data. The
"shape" of the response curve using Childs' seal values compares
closely with the measured results, indicating that the damping contribution
of the seals is of the right magnitude.
The anticipated range of rotor response should be calculated with the
range of bearing values and various combinations of unbalance. This is
important because it is not possible in the design stage to know the exact
installed configuration with regard to bearings (clearance, preload) and
balance (location of unbalance). Usually a mechanical test will be limited
to one configuration (clearance, preload, unbalance) that may not show
any problem. Changes introduced later by spare parts during maintenance
turnarounds may change sensitive dimensions that may result in a
higher response. For this reason, the vibration characteristics of some
satisfactorily operating machines may change after an overhaul.