Pump Vibration

What's the operating temperature? Bearings? Grease?

25' is not likely to be a single piece shaft, so take a look at the shaft-shaft coupling (I'm assuming it's a sleeve/key type.) A problem there could have symptoms of a bent shaft and an imbalance.

Is the 229 rpm a typo? What is the service? As far as explaining how a bent shaft gets progressively worse, would you expect it to get better?

"Extensive vibration and modal analysis has been done"

I picture the pump being constructed something like this -

So you are actually measuring vibration on the motor which is about all that is above ground, like this -

Do you have more detailed information about frequency and even phase of the predominant vibration?
Is it 1X the pump rpm, or some other frequency?
Have any resonance tests been made on the pump. looking for the first bending mode / "reed" frequency?

With almost no information given, this is completely guesswork. First I am guessing you are talking about a vertical pump. Then I'm guessing it is either a mixed flow or axial flow pump running at such a slow speed and at 450HP. I'm guessing this is basically a high flow, low head pump; a water mover. Probably one stage.

If my guesses are correct, then you should look at your bearings, in particular the bottom bearing (sometimes called a sand bearing). It is not at all unusual for a pump like this to experience crippling vibration with a small bit of imbalance. Typically (just guessing) you have a large weighted, high diameter impeller/propeller hanging on a shaft; once it starts to get unbalanced, things go awry quickly. If one of the lineshaft bearings gets worn, it will also degrade quickly.

Give us a little more information: Make, model, flow, head, shaft diameter, bearing arrangement, open/closed lineshaft. These details should be available in the pump's file folder, if you can find it.

A bent shaft probably would not get gradually worse over time. But, if the shaft had high run-out, the resulting vibration could get gradually worse as the bushing clearances increased. You should obviously check for shaft run-out. But, you should also check for issues with the rigid coupling that could cause high run-out. These couplings are notorious. Check for clearance in the upper bushing. You should be able to do this without pulling the pump. If you are pulling the pump for a complete tear-down, you will obviously check all the bushings, any line shaft couplers, etc.

Johnny Pellin