That looks to be developing into an interesting case study.
I’m stuck trying to think how the variation with flow might be related to what looks like looks to be a resonance during coastdown.
I came up with one half-baked idea (unrelated to hydraulic instability). It doesn't really pan out but maybe it could spark someone else to have ideas, so here it is in the bullets below:
- I’m assuming this is a horizontal multi-stage pump. Then it sometimes has a very long slender shaft (We have one that is about 8 feet between bearings, 2” diameter, 7000rpm), but the stiffness is well maintained by the interstage seals / wear rings.
- If there was really really severe wear on the interstage seals such that they didn’t contribute much stiffness, then in theory the resonant frequency of the shaft supported by only bearings (without any credit for the interstage seals) could drop in the neighborhood of 1-2hz (that's what I came up with when I tried a quick and dirty modeling of our long slender pump without taking credit for the seals).
- The Lomakin effect helps provides stiffness to the seals. At higher flows, there are lower DP's accross stages and lower seal flows and less Lomakin effect so even lower seal stiffness and lower resonant frequemcy. That's my idea to explain why the apparent resonant frequency decreases as flow increases.
- Three problems:
- 1 - It would have to be really severe degradation. Your pump performance would be severely impacted. I can maybe give my theory "a pass" because I don't think you talked about performance (although I'm sure it was looked at).
- 2 – why wouldn’t the resonant frequency go down when dp decreases during coastdown? I can’t explain. Seems to contradict my theory, but maybe I can stretch it in the name of open-mindedness and give my theory "a pass" by handwaving that there are other things going on during coastdown.
- 3 – where does the horizontal orbit come from? If so much flexibility comes from the shaft, the stationary bearing / support stiffness (where the horizontal/vertical differences appear) doesn’t affect the resonant frequency much and the postulated low frequency flexible rotor vertical/horizontal critical frequencies will be very close to each other resulting in circular orbit. I can't stretch it any further to give my theory a pass on this one. Flexible rotor is not going to give a flat orbit. My theory is officially dead.
- You may have other reasons to kill it (maybe it's not a multi stage pump, maybe it's not long and slender etc). Either way it's dead.
So your theory is hydraulic instability. I don’t know much about it. I looked up EPRI Pump Troubleshooting Volume 1. Since your vibration frequency is unusually low, I went to Chapter 8 which talks about very low frequency subsynchronous vibrations:
It starts out “The Gap A geometry has a very strong influence on almost all vibration and pressure pulsation components, particularly in the low flow operating range (below approximately 70% BEP). An improper Gap A will typically be picked up in the 4 to 10 hertz (Hz) range on the vibration spectrum and will be most dominant when monitoring the axial direction.”
I assume problems with the gaps resulting in subsynchronous vibration fall in the category of hydraulic instability. So it checks out that the lowest frequency vibration this reference is identifying (chapter 8) is talking about hydraulic instability. They mention axial vibration but of course that’s not available on prox probes and I’m not sure how much would get transmitted to the housing. And I have no doubt there are infinite varieties of hydraulic instabilities depending on the pump design that are much different than the particular one I looked up.
I’m curious if you have any ideas about whether and how the hydraulic instability indicated during the flow variation at full speed is related to the coastdown observations.