"We just guess it is nature frequency of some parts." Really, just guessing on an important machine!

The shaft speed indicates that measurement was not on the steam turbine, unless it is a very slow turbine or the speed is incorrect. You would have to provide a lot more information if you want a useful answer to your question: " Not clear which part can cause this failure frequency.".

Walt

Those numbers could relate to blade counts.  
Is there anything audible, like noise from a valve.  

How were the transducers fixed to the turbine?  
Cause a failure or relate to a failure:  Not clear that this could relate to a failure until you get a handle on the frequency.
At that frequency and with the large amplitude,  you might hear this.  Can you get a microphone and measure?

Normally the route data Fmax is around 2500Hz (50x)and can not see this high frequency peak. The shaft speed is about 2850rpm, sensor is put beside governor with Dual rail magnet. We noticed the G's value increased and then extend Fmax and found this peak at high frequency band.

No special noise observed, the things different for this turbine is we changed few carbon ring to float brush ring.

Turbine blade pass frequency should be much higher than this, gear mesh is lower.

Maybe consider to set Fmax as 70x or 80x and test other turbine to find if all have this component.

 

Consider doing a time synchronous average to see if the component remains or drops out. If it drops out, could be a mounting resonance as Walt mentions, in which case a significant change in the mounting method should make a significant change in the frequency.  Changing the mounting method might be the easiest thing accomplished in an attempt to learn something.

If the component remains, it could be what William Foiles mentioned ("...could relate to blade counts").

Generally, these high freq. components do not represent a mechanical issue.  Check the mounting - re-mount when you get the problem.  A change in frequency is possible, but the amplitude at the frequency of concern and/or other frequencies can change a lot if there is a mounted resonance.
Next to the governor, perhaps there is some coupling to the governor, accoustic or structural coupling.  At that frequency, a microphone may pick up the 'vibration' as sound, and you can check fruencies.

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