• 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
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Periodic motion with more than one frequency |
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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.
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