Why the vibration system from bentely nevda and pcb company using the voltage as a reference to measure on the rotating shafts and equipments?

This systems are using proximities which works under eddy current principle (measuring gap voltage) which is very stable during rotational

The systems you mentioned use what is known as a "proximity probe" or "eddy current probe" to measure shaft relative vibration (relative meaning relative to the bearing housing; the stator).

Without getting into unecessary details; the output of this probe is a signal known as a "dynamic voltage signal" which is basically an electrical signal which has a voltage which varies (almost) linerally with the distance between the probe tip and the shaft surface. As Mohamed mentioned, this signal has two components; the "DC" component which represents the "average" shaft position and the "AC" component which represents the shaft's vibration or its motion from the average position.

Hope this helps!

They using he voltage as a reference of the gap between the shaft and the sensor it depends on the induced EMF which is generated due to the magnetic filed generated by the sensor and it cut by the shaft o detect where the shaft is present  

So you can find that using a distance gap by a DC volt which will be the reference for the  mechanical shaft in the zero position and the moving shaft will be moving up and down around the reference line a round the gap. 

May be it Keep the SHaft Stable At that refernce Volatage and Output will be Without any Fluxtuation thank you