I have actually used vibration analysis to help troubleshoot a number of rotor problems over the years. But you can't use the vibration readings alone. I used to have a "test" DECS200 AVR to use along with other tools, and would try to compare a change in field output and ripple current to vibration levels. Was easier on units with stable loads or paralleled to grid, hardest ones to troubleshoot were on high cyclic loads like drill rigs. The 1st order magnitude usually doesn't change dramatically, but it can be measured in a lot of cases, at least on the units I have worked around. You just have to understand why it is changing.
Some times finding a problem was easy, both CAT and Stamford had issues with pole jumpers and their connections, both right after making rather large production changes, I guess someone tried to save a little money and it came back to bite them both in a pretty large way, once identified pretty easy to correct, but not cheap, pulling a rotor in the field sucks. Kato several years ago had problems on certain frame sizes after making changes to rotor production in their facility, as the rotor poles were being wound a part in the machine was nicking the wire, some affected units actually never failed, but several did, showing up as mostly internal shorts on a pole winding and in a few cases grounded windings.
A CAT generator like the OP has uses a packaged diode system, a heat sink plate with a positive diode pack, a negative diode pack and a surge suppressor. CAT only sells the assembly, if they are just changing a single diode pack they are using aftermarket parts. The packaged diodes were actually pretty rugged, only real issue we had was no one ever seemed to use heat sink compound when mounting them and over the years several failures all seemed to have excessive heating as root cause of the failure. CAT and LS made a decision to not provide individual parts and only sell the complete rectifier assembly, supposedly claims went down and problems reduced significantly. Actually there were some other issues going on at the time with suppliers and cost reductions, and at one point counterfeit parts, but lately diode problems on these types units don't seem to show up much anymore, at least in my experience.
Sometimes in cases like this it isn't actually the main rotor, I had one a couple of years ago that the rotor was both rewound and then replaced with new, but they kept reusing the PMG and Exciter stators because they tested "good", after several months of trying to figure it out, turned out to be a problem with the PMG stator, when a larger load would come in (in this case a larger motor with across the line starting)the PMG output would drop off (but not every time the load was applied), the AVR would go full field, hit the OEL and trip on under voltage, sometimes we would find a diode failed, sometimes a surge suppressor, something nothing was damaged and it would restart and work fine for hours, days or weeks. Changed the PMG stator and no more problems.
The nature of an intermittent problem, get lucky and find it early, or keep putting back into service and see where it fails, have customers who do it both ways and can't honestly which is really better in all cases, depending on the application and other factors that get involved.
Hope that helps, MikeL
