Page 127 - Improving Machinery Reliability

Machinery Reliability Audits arid Reviews 99

values comparable to the bearing stiffnesses. This information will show how sensi-
tive the rotor critical speeds and responses are to pedestal stiffnesses. Generally,
pedestal stiffnesses may vary from approximately 1 million to 20 million Ib/in. The
horizontal stiffnesses are usually less than the vertical stiffnesses; therefore, the hori-
zontal critical speeds will be lower than the vertical. Pedestal stiffnesses are impor-
tant in the analysis of large rotors such as induced draft fans where the pedestal and
foundation stiffnesses will be lower than typical bearing stiffnesses.

Special Lateral Response Analyses
Liquid Pump Lcrteral Response Analyses. Pump rotordynamics are dependent on a
greater number of design variables than are many other types of rotating equipment.
Besides the journal bearing and shaft characteristics, the dynamic characteristics of
the seals and the impeller-diffuser interaction can have significant effects on the crit-
ical speed location, rotor unbalance sensitivity, and rotor ~tability.~~’~
For modeling purposes, seals can be treated as bearings in the sense that direct and
cross-coupled stiffness and damping properties can be calculated based on the seal’s
hydrostatic and hydrodynamic properties. Seal clearances, geometry, pressure drop,
fluid properties, inlet swirl, surface roughness, and shaft speed are all important in
these calculations. Since the pressure drop across seals increases approximately with
the square of the pump speed, the seal stiffness also increases with the square of the
speed. This increasing stiffness effect is often thought of as a “negative” mass effect,
which is usually referred to as the “Lomakin effect” or the “Lomakin mass.”” In
some cases the theoretical Lomakin mass or stiffness effect can be of sufficient mag-
nitude to prevent the critical speed of the rotor from ever being coincident with the
synchronous speed.
The accurate prediction of the stiffness and damping properties of seals for differ-
ent geometries and operating conditions is a subject of ongoing re~earch.’~.’~ The
basic theories presented by Black14 have been modified to account for finite length
seals, inlet swirl, surface roughness, and other important parameters. However, a
universally accepted procedure to accurately predict seal properties is not available
for all the types of seals in use today. This is particularly true for grooved seals.
Unless seal effects are correctly modeled, calculated critical speeds can be signifi-
cantly different from actual critical speeds.
Grooved seal designs used in commercial pumps have been tested recently, and
techniques have been developed whereby the seal geometry can be specified and the
characteristics calculated for specific assumptions with regard to inlet swirl, groove
design, et^.'**'^
The rotordynamic analysis of an eight-stage centrifugal pump using serrated
(grooved) seals was discussed by Tisong and will be used to illustrate a design audit of
a pump.” The first step in a rotordynamic analysis of a pump is to model the basic
rotor, using the lumped parameter techniques. A sketch of the rotor with the location of
the seals and bearings is given in Figure 3-15. Note that the pump shaft is analyzed as
a rotor with 11 bearings (2 cylindrical bearings, 8 impellers, and the balance piston).