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

448 Centrifugal Pumps: Design and Application
diameter, viscosity, load, speed, clearance, and the Sommerfeld number
that is defined as:
l*. = lubricant viscosity, Ib-sec/in.
N = rotor speed, rev/sec
D = bearing diameter, in.
L = bearing length, in.
R = bearing radius, in.
W = bearing load, Ibs
C = radial machined clearance, in,
The normal procedure in a design audit would be to calculate the bearing
characteristics for the range of expected clearances, preload, and oil
temperatures. The maximum clearance, minimum preload, and highest
oil temperature usually define the minimum stiffness. The other extreme
is obtained from the minimum clearance, maximum preload, and the
coldest oil temperature. This will typically define the range of expected
stiffness and damping coefficients for the bearings.
Preload is a configuration of the bearing clearances to promote a converging
wedge of oil that increases the oil pressure and consequently the
bearing stiffnesses. A preloaded bearing has its radius of curvature
greater than the shaft radius plus the clearance.
Seal Effects
The critical speed map for a eight-stage pump, including the effects of
seal and bearing stiffness, is given in Figure 18-15. Even though the
bearings and seals add considerable cross-coupling and damping, it is
still desirable to generate an undamped critical speed map to establish the
range of the undamped (dry) critical speeds.
Adequate experimental data exists that documents that the analytical
procedures used for simulating rotor response and stability for compressors
and turbines can accurately predict critical speeds and potential instabilities
from the design information. This is not true for pumps, especially
for pumps that use grooved seals, labyrinth seals, or screw type
seals with several leads. The accurate prediction of the stiffness and
damping properties of seals for different geometries and operating conditions
is a subject of on-going research [22, 27, 28]. The basic theories
presented by Black [29] have been modified to account for finite length