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