I believe it is a very complex subject above my head and you have already gotten input from two people I respect highly sms and vanstoja.
Here is an excerpt from EPRI Pump Troubleshooting
"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 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."
Roughly speaking how I interpret it is that there are two broad categories
"Frequency 3" - a whirl phenomenon related to bearing parameters and loading as described by vanstoja
"Frequency 4" - hydraulic forcing fucntion similar to described by sms.
Some ways to help distinguish:
#4 - Should be sensitive to system configuration. We have had 0.35x on vertical machines and it repeatably becomes worse when we go to the left on the curve, which would seem to confirm a hydraulic forcing fucntion.
#3 - Should be sensitive to oil temperature. Vary oil cooling and temperature and look for change in vibraiton.
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