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electricpete

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Reply with quote  #16 
Warning - mind-numbing theory ahead. This may or may not help, feel free to ignore. 

Attached describes characteristics of common windows. (Its something I did a long time ago, also found in many signal processing textbooks).  It describes (among other things) the the degree to which leakage into adjacent bins is expected for various windows for a pure sinusoid.  If you look at the Hanning window you'll see a continuous curve where the horizontal axis is bin widths.  If the peak is perfectly centered, then the relative amplitudes are shown by reading off the curve the values corresponding to horozintal axis 0.0,1.0,2.0 etc.  In that particular case the values you read at 1.0, 2.0 etc are generally zero and there is no leakage (when we sample a pure sinusoid that is perfectly centered with the bin there is no leakage).   But the peak is rarely perfectly centered.  Let's say the actual peak is one tenth of a bin width above bin center. In that case you would have to read off values at maybe 0.1, 1.1, 2.1, 3.1 etc to see how much relative leakage is expected at the adjacent bins to the right.  You would have to read off -0.9, -1.9, -2.9 etc to estimate expected leakage to bins to eh left.  (we ready the negative values by flipping the curve abouto the vertical axix)   If the peak is centered about 0.9 = nine tenths of the way from the current bin center to the next bin center, then the main peak relative magnitude is going to show up at -0.1.    The worst case leakage is usually close to what you'd get reading off the values at 0.5 (main peak), 1.5, 2.5, 3.5 etc.  Regardless of whether it is exactly at 1.5, 2.5 etc you can read the worst case leakage from the peaks of the sidelobes. It's been awhile and I may have not described things 100% correctly, but I'm pretty sure I have the worst case leakage right and that worst case leakage is the most helpful / useful (leakage much worse than the worst case expected leakage could signal a resonance).  If you really want to fine tune your study of a given peak you could use peak interpolation frequency to try to figure out where you are within the bin but that gets tricky.  All this is for the ideal world.  Actually it's not a problem if the signal is non-sinusoidal but still periodic (then it is a sum of sinusoids and still applies). But if there are multiple peaks present close by or if there is changing frequency, then things don't work out right.

I know the theoretical stuff falls far short of convincing or illuminating for many folks.  If I have time I'll poke around and see if I can find some examples of obvious resonances that can be judged from a real world spectrum (maybe someone else has examples handy?).

 
Attached Files
pdf WindowCharacteristics5A.pdf (860.87 KB, 23 views)

MarkL

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Reply with quote  #17 
Alex,
I have seen it on a few articles by Jason Tranter, when I tried it myself I could see anything obvious on one or two machines I knew had resonance issues. Hence was asking if anyone else had used it with success.
electricpete

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Reply with quote  #18 

Here is an example where log scale shows very obviously a resonance that amplifies certain peaks in a non-synchronous pattern (this one happens to be a bearing defect pattern).  

Slides 1 and 2 are the same spectrum. The highest two peaks in the spectrum are 37.635 and 39.922 orders. They don't look that much higher on log scale but they (particularly 39.922) look far higher than the others on linear scale. 

Slide 1 shows us that 39.922 is the 1x sideband above 4th harmonic of BPFI.

Slide 2 shows us that 37.635 is the 5th harmonic of BPFO. 

Why are these two peaks the highest within the pattern?  A big factor is the resonance which is apparent looking at the noise floor which has a broad gentle peak in the vicinity of 38x or slightly higher.  

I'd say the resonance is pretty obvious in this spectrum.  exactly what kind is resonance I'm not sure (frequency is way to high to be first rigid body resonance of this vertical motor, ordinarily I'd say it's the bearing ring resonance but both inner and outer are amplified), but it's clearly resonance amplification. . Many are not quite that clear cut but they give you suspicions of where resonant amplification may be occurring. 


 
Attached Files
pdf OC11_LogScaleResonanceExample.pdf (392.60 KB, 29 views)

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