We have experienced this same kind of problem on a 27,000 HP centrifugal air compressor in our nitric acid plant. The vibration would rise and fall on a regular cyclic pattern over approx a 230 minute period. Amplitude variation was 1.2 mils max with over a 200 deg phase shift. The pattern would repeat day and night for weeks on end between runs. Frequency was primarily at 1xRPM, with a significant subsynch vibration at the rotor natural frequency. Vibration could be decreased with speed reductions, axial thrust position shifts, and discharge temperature changes.
This is a two stage compressor running at 11,100 to 12,600 RPM with overhung steam turbine and hot gas expander at opposite ends. Rotor components are connected through highly tensioned curvic couplings.
Problem was corrected on two rotors by opening up axial clearance on 2nd stage, converting to honeycomb shaft seals, and mininmizing mechanical runout in shaft segments.