Maximum Vibration

There is no such thing as a "maximum allowable" vibration. (By vibration I guess you are measuring velocity?)

There are of course guidelines of acceptable limits etc from ISO et al. There are also acceptance criteria for pump and motor vibrations given in standards such as API.

Below are some charts that have been around for many years which you may find helpful - there are many many more. The first one I think is from Technical Associates of Charlotte, the other two show their origins.

None of these should be seen as absolutes, they are guidelines. The best indication of condition is change, as no two pumps or installations are the same. If you are more specific about your requirements we may be able to help.

That about sums it up.