The directivity of vibration fault diagnosed by using the general frequency spectrum analysis method was not clear

hence

in order to interpret the information of vibration measurement more accurately

and determine the basic nature of vibration faults

the differential equations of rotor vibration and their solutions of displacement on x and y direction as well as the corner have been given in the fixed Cartesian coordinate system

the cross-correlation functions at different measuring points along the axial direction

and along x

y directions at a same point

can be obtained.Based on these

the characters of cross-correlation and phase-difference of the rotor vibration under typical excitation and hinged by ideal supports have been analysed

and the phase-difference diagnosing method of shaft vibration being put forward.Practical application shows that the said theory tallies very well with reality

and can be used as an effective diagnosis method for shaft vibration of turbo-generator sets.