8/07/2011

Bode and Polar Plot

Vibration Vector

          A vibration vector plotted in the transducer response plane
           1x vector is 90 mic pp /220o
           Zero reference is at the transducer angular location
           Phase angle increases opposite to direction of rotation


 Polar Plot

           Polar plot is made up of a set of vectors at different speeds.

           Vector arrow is omitted and the points are connected with a line

           Zero degree is aligned with transducer location

           Phase lag increases in direction opposite to rotation

          1x uncompensated Polar Plot shows location of rotor high spot relative to transducer

           This is true for 1x circular orbits and approximately true for 1x elliptical orbits



8/06/2011

Shaft Orbit Plots (II)

Not- 1X Compensation of an Orbit

          At Left orbit is the uncompensated orbit
          At right is the same orbit with the 1X component removed
          The remaining vibration is primarily 1/2X from a rub


Measurement of peak-to-peak amplitude of an Orbit

X transducer measurement axis is drawn together with perpendicular lines that are tangent to maximum and minimum points on the orbit

Direction of Precession in Orbits

          In the orbit plot shaft moves from the blank towards the dot. In the plot on left the inside loop is forward precession
          In the right orbit the shaft has reverse precession for a short time at the outside loop at bottom


Effect of Radial Load on Orbit Shape


          Orbits are from two different steam turbines with opposite rotation. Both machines are experiencing high radial loads
           Red arrows indicate the approximate direction of the applied radial load.
           Red arcs represent the probable orientation of the bearing wall


Deflection Shape of Rotor Shaft


          When keyphasor dots of simultaneous orbits at various bearings along the length of the rotor are joined an estimate of the three dimensional deflection shape of the rotor shaft can be obtained
 *   This is a rigidly coupled rotor system 
 

 

8/05/2011

Shaft Orbit Plots (I)

The Orbit
          The orbit represents the path of the shaft centerline within the bearing clearance.
          Two orthogonal probes are required to observe the complete motion of the shaft within.
          The dynamic motion of the shaft can be observed in real time by feeding the output of the two orthogonal probes to the X and Y of a dual channel oscilloscope
          If the Keyphasor output is fed to the Z axis, a phase reference mark can be created on the orbit itself
          The orbit, with the Keyphasor mark, is probably the most powerful plot for machinery diagnosis

Precession

Once a gyroscope starts to spin, it will resist changes in the orientation of its spin axis. For example, a spinning top resists toppling over, thus keeping its spin axis vertical. If a torque, or twisting force, is applied to the spin axis, the axis will not turn in the direction of the torque, but will instead move in a direction perpendicular to it. This motion is called precession. The wobbling motion of a spinning top is a simple example of precession. The torque that causes the wobbling is the weight of the top acting about its tapering point. The modern gyroscope was developed in the first half of the 19th cent. by the

 
Construction of an Orbit

          XY transducers observe the vibration of a rotor shaft
          A notch in the shaft (at a different axial location) is detected by the Keyphasor transducer.
          The vibration transducer signals produce two time base plots (middle) which combine into an orbit plot (right)


 Probe Orientation and the Orbit Plot

          On the left side, when the probes are mounted at 0o and 90oR, the orbit plot and oscilloscope display show the same view.


           On the right, when the probes are mounted at 45oL and 45oR, the orbit plots are automatically rotated


           The oscilloscope, however, must be physically rotated 45o CCW to display the correct orbit orientation 








Examples of 1X and Subsynchronous Orbits
 
          Orbit at left shows subsynchronous fluid-induced instability. Note the multiple keyphasor dots because the frequency is not a fraction of the running speed
          The orbit at right is predominantly 1X. The keyphasor dots appear in a small cluster indicating dominant 1X behavior 

Slow Roll Vector Compensation of 1X Filtered Orbit

          Slow roll vector compensation can considerably change the amplitude and phase of the orbit

           Slow roll vectors of X= 1.2 mil pp /324o and Y= 1.4 mil pp /231o







Slow roll Waveform Compensation of a Turbine Orbit
Note how compensation makes the orbit (right) much clearer


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



8/03/2011

Half Spectrum Plots

Spectrum Plot-1

          Machines can vibrate at many different frequencies simultaneously  1x, 2x, 3x, vane passing etc.
          Timebase  and orbit have frequency information but only a couple of harmonics can be identified – impossible to identify nonsynchronous frequencies
         Using an analog tunable analyzer the amplitude and phase at each individual frequency can be identified but only one at a time. 
        All frequencies cannot be seen simultaneously.
        Trend changes in individual frequencies cannot be followed
        Each frequency sweep may take one minute during which short duration transient events may be missed
   •          A Spectrum Plot by a FFT Analyzer shows all frequencies instantaneously.

Spectrum Plot-2  
          Spectrum plot is the basic display of a Spectrum Analyzer. It the most important plot for diagnosis
          Spectrum plot displays the entire frequency content  of complex vibration signals in a convenient form.
        It has frequency on X-axis and amplitude on Y-axis
        It is constructed from sampled timebase waveform of a single transducer – displacement, velocity or acceleration
          Fast Fourier Transform (FFT) calculates the spectrum from the sample record which contains a specific number of waveform samples
          Spectrum plots can be used to identify harmonics of running frequency, rolling element bearing defect frequencies, gear  mesh frequencies, sidebands 

Periodic motion with more than one frequency

Above waveform broken up into a sum of harmonically related sine waves
 
Illustration of how the previous signal can be described in terms of a frequency spectrum.
Left        - Description in time domain
Right      - Description in frequency domain 



 
Spectrum Frequency as a Function of Pulse Shape

Construction of Half Spectrum Plot - 1
          Raw timebase signal (red) is periodic but complex.
           Fourier transform is equivalent to applying of a series of digital filters
           Filtered frequency components are shown as sine waves (blue)
           Phase for each signal can be measured with respect to trigger signal
           We can see components’ amplitude, frequency and phase 
  
Construction of Half Spectrum Plot - 2
          If we rotate the plot so that the time axis disappears we see a two dimensional spectrum plot of amplitude v/s frequency
           Component signals now appear as  series of vertical lines.
           Each line represents a single frequency
           Unfortunately, the phase of the components is now hidden.
           It is not possible to see phase relationships  in spectrum plot.

 
These plots show why it is impossible to guess the frequency content from the waveform.
Vertical lines in top plot show one revolution
It is clear that 2x and higher frequencies are present
But 3x and 6x could not be predicted from the waveform.
A Fourier spectrum shows all the frequencies present


Linear and Logarithmic Scaling
          Amplitude scaling can be Linear or Logarithmic
          Logarithmic scaling is useful for comparing signals with very large and very small amplitudes.
        Will display all signals and the noise floor also
          However, when applied to rotating machinery work
        Log scale makes it difficult to quickly discriminate between significant and insignificant  components.
          Linear scaling shows only the most significant components.
        Weak, insignificant and low-level noise components are eliminated or greatly reduced in scale
          Most of our work is done with linear scaling

 
Illustration of Linear and Log scales
           Log scale greatly amplifies low level signals
           It is impossible to read 1% signals in linear scale
           It is very easy to read 0.1% signals on the log scale

Limitations of Spectrum Plots
          FFT assumes vibration signal is constant and repeats forever.
          Assumption OK for constant speed machines .
        inaccurate if m/c speed or vibration changes suddenly.
          FFT calculates spectrum from sample record
        Which has specific number of digital waveform samples
        FFT algorithm extends sample length by repeatedly wrapping the signal on itself
        Unless number of cycles of signal exactly matches length of sample there will be discontinuity at the junction
        This introduces noise or leakage into the spectrum
          This problem is reduced by “windowing”
        Forces signal smoothly to zero at end points
        Hanning window best compromise for machinery work

Effect of Windowing
          Figure shows a timebase plot with a mixture of 1/2x and 1x frequencies. 
 Two examples of half spectrum plots are shown below



          Without window function the “lines” are not sharp and widen at the bottom
           This “leakage” is due to discontinuity at sample record ending



          When “Hanning” window is applied to the sample record 1/2x spectral line is narrower and higher
           Noise floor at base is almost gone.