The number 0.47x applies to oil whirl in a lightly loaded plain bearing. For vertical pump I think it can have a wider range. I have heard people suggest 0.35x may be due to whirl in a cutlass-style water cooled bearing on vertical pump.
I also am by no means an expert on this subject and a book would be better.
Here is an excerpt from an EPRI report:
"Subsynchronous vibration is the most damaging and unstable type of vibration that can occur in
a rotating machine. Subsynchronous vibration amplitudes have been detected at frequencies
ranging from 0.3 to .9 times operating speed (Figure 3-1). The first and most difficult step in
troubleshooting subsynchronous vibration problems is making the distinction between rotor-dynamic
and hydro-dynamic, or hydraulic, induced instability. This is a very difficult task and
for years hydro-dynamic induced instabilities were not considered when a subsynchronous
vibration problem was investigated. Rotor-dynamics was considered to be the source of all
subsynchronous vibration frequencies, resulting in many elaborate and expensive rotor
modifications that did not solve the problem. When this occurred, the problem was considered a
phenomenon and was left unresolved. With the help of the utilities, hydraulic modifications were
made by ERCO that solved the problems and failures experienced, and the phenomena became
well-understood occurrences.
Frequency 3: This vibration component appears in the vicinity of 1/2 x RPM (0.3 to 0.6). It is a
self-excited, bearing-induced vibration instability. It is very damaging, and if it surfaces will
result in rotor destruction, often without warning. A basic requirement for this to develop is a
lightly loaded journal bearing, which is the case for most centrifugal pumps, particularly for
vertical applications such as reactor coolant pumps (RCP, PCP, or RRP).
Frequency 4: This vibration component appears in a wider range of frequencies, 0.35 to 0.9 x
RPM. It is the result of hydraulic forces developed when operating a centrifugal pump off or
away from its best efficiency point (BEP) flow. Examples are given below with distinct
frequencies as low as 0.35 and as high as 0.92 x RPM.
Combination of 3 and 4: This is the most difficult case to analyze. If the vibration frequency is
about 0.6 x RPM, it could be dynamic, hydraulic, or a combination of the two.
Vertical pumps, such as the RCP in nuclear applications, have very lightly loaded journal
bearings and, hence, are prone to bearing instability. If the hydraulic excitation is just right, it
will put the pump in the Frequency 3 category. The result of this phenomenon can be:
Frequent shaft seal failure (the most delicate part of the RCP)
Journal bearing damage
Shaft damage
Shaft breakage
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