8/04/2011

Full Spectrum Plots

Full Spectrum

          Half Spectrum is the spectrum of a WAVEFORM
          Full Spectrum is the spectrum of an ORBIT
          Derived from waveforms of two orthogonal probes
        These two waveforms provide phase information to determine direction of precession at each frequency
        For phase accuracy they must be sampled at same time
          Calculated by performing a FFT on each waveform
          These FFT’s are subjected to another transform
        Data converted to two new spectra – one for each direction of precession – Forward or Reverse
        Two spectra are combined into a single plot
Forward to the right, Reverse to the left


Calculation of Full Spectrum Plot



 
First
Waveform and its half spectrum



Second
Waveform and its half spectrum



Combined orbit and its full spectrum






 
Circular Orbits and Their Full Spectra


<-- Forward Precession        
         Spectrum on forward side of plot


 <--    Reverse Precession
         Spectrum on reverse side of plot
         Direction of rotation – CCW

<--   Forward Precession
        Spectrum on forward side of plot
        Direction of rotation – CW

<--   Reverse Precession
        Spectrum on reverse side of plot
        Direction of rotation - CW



Full Spectrum of Elliptical Orbit
Orbit is generated by two counter rotating vectors

Forward spectrum length is twice the length of forward rotating vector

Reverse spectrum length is twice the length of reverse rotating vector

Major axis of ellipse = a +b
Minor axis of ellipse = a - b

Original orbit cannot be reconstructed from full spectrum because there is no phase information.

3 possible orbits are shown




Circular & Elliptical 1x Orbits

         Direction of precession is indicated by dominant line of “Forward” and “Reverse” components. 

          Flatness of ellipse is determined by the relative size of forward and reverse components

          When orbit is circular there is only one spectrum line

          When orbit is a line the spectrum components are equal.

          Therefore, the smaller the difference between components, the more elliptical the orbit. 







Orbit and Spectrum of a ½x Rub

         Orbit and spectrum of  a steam turbine with a ½ x rub
          Full spectrum clarifies the complex orbit which is a sum of ½ x, 1x and their harmonics.
          From the ratio of forward ad reverse components
          1x is the largest, forward and mildly elliptical
          ½ x and 2x orbits are nearly line orbits
          Small component of 3/2 x is third harmonic of ½ x fundamental

Half and Full Spectrum Display of a ½ x Rub

 
Differentiating ½ x Rub and Fluid Instability from Full Spectrum Plots
         Half and full spectrum display of a ½ x rub (red data) and fluid induced instability (blue data)
         Note similarity in appearance of the two half spectrum plots
         The full spectrum plots clearly show the difference in the subsynchronous vibration
        The ½ x rub orbit is extremely elliptical – small difference between forward and reverse components
        The fluid induced instability orbit is forward and nearly circular – large difference between forward and reverse 1x and ½ x components.
         The unfiltered orbits are at the bottom
Full Spectrum Cascade Plot of Machine Start Up
         Horizontal axis represents precession frequency

          Rotor speed is to the left and amplitude scale is on the right

          Order lines drawn diagonally from the origin show vibration frequencies that are proportional to running speed


         Display of spectra plots taken at different speeds during start up
          Base of each spectrum is the rotor speed at which the sample was taken
          Diagonal lines are “Order” lines. Usually 1x, 2x and ½ x are plotted
          Resonances and critical speed can be seen on 1x diagonal line
          Sudden appearance of ½ x indicates rub which can produce harmonics.
          Phase relationships cannot be seen on cascade plot.
          Many harmonics at low speed usually due to scratches on shaft

 
·         Horizontal ellipse shows rub second balance resonance (critical)

·         Vertical ellipse shows ½ x rub frequency is almost equal to first critical. Slight shift to right is due to stiffening of rotor system from rub contact.





Full Spectrum Waterfall Plot
         Displays spectra with respect to time

         Used for correlating response to operating parameters

          Time on left and Running Speed on right. Amplitude scale is at extreme right

          Plot of compressor shows subsynchronous instability whenever suction pressure is high (red). 1x component is not shown on plot. 

          Full spectrum shows subsynchronous vibration is predominantly forward.




Waterfall of Motor with Electrical Noise Problem


         High vibration at mains frequency (60 Hz) during start up (red). 1x is low.

          Vibration reduces when normal speed and current are reached (green)

          When motor is shut down (blue) 60 Hz component disappears suddenly.

          1x component reduces gradually with speed.



Summary

          Conventional spectrum is constructed from the output waveform of a single transducer
         Full Spectrum is constructed from the output of a pair of transducers at right angles.
        Displays frequency and direction of precession
        Forward precession frequencies are shown on right side
        Reverse Precession frequencies are shown on left side
         Full spectrum is the spectrum of an orbit
        Ratio of forward and reverse orbits gives information about ellipticity and direction of precession
        However, there is no information about orientation of orbit
         Cascade and Waterfall plots can be be constructed either from half or full spectra



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