Interpreting PSD Displacement Results

[brysonc]

Many of you seem to have a lot of experience in this field, so hopefully you guys can make this a little clearer for me. I have been asked to reduce the "vibration" of a camera mount (not vague at all, yeah) using random vibration FEA studies. I have been analyzing the displacement, since I'm more concerned with image stability than failure of the electronics.


I understand the RMS value of the displacement, but I am having some trouble interpreting the displacement response graphs (PSD displacement?). I am returning a response graph for displacement (mm^2/Hz) against frequency. Here are some of my results for the peak displacement on these graphs:


Config 1: 0.509 mm^2/Hz at 27.1 Hz

Config 2: 0.150 mm^2/Hz at 36.0 Hz

Config 3: 0.060 mm^2/Hz at 35.8 Hz


I am trying to figure out how to compare these configurations. I hesitate to compare the peak response displacement, because each occurs at a different frequency. I tried "normalizing" these results by multiplying each PSD displacement result by the frequency and then taking the square root, but I don't quite understand what this value will represent. Will it be the RMS displacement value when the bracket is excited to that frequency?


I think that the difficulty I am having is with the units. I understand that RMS displacement is a statistical representation of actual displacement over the whole operating range, with units of length. I can quantify improvements by reduction in RMS displacement, but I also want to be able to interpret the meanings of the peaks on the graph of PSD displacement (mm^2/Hz) vs. frequency. Is there a physical meaning to these values? If I multiply the peak PSD displacement by the frequency at which it occurs, then take the square root, what will my results (which will have units of mm) mean?


I assume that the result will also be a statistical representation of the actual displacement, just at that given frequency. Still, this doesn't seem 100% concrete and I can't quite put my finger on why.


Thanks for your help!


Bryson Cook

 

[Twoballcane]

Well first what are you interpreting the input or output? RMS is dangers. This is really the area under the curve and it really gives you the flavor than actual. So I would not refer to this number other than comparing one curve to another. To get an estimate of deflection, you have to get the bandwidth from valley to valley with the peak in the middle and then multiply that number with mm^2/hz and then square root

I would attack this in a different way. If you know the frequency where you are getting image instability, you can try to change that frequency to somewhere in the valley of your profile instead of on the positive or negative slope or peak. This is easier said than done.


Tobalcane
"If you avoid failure, you also avoid success."

 

[BobM3]

Take the value of the PSD at each frequency and multiply it by the frequency resolution (not frequency). Then take the square root of that. You'll end of with the RMS of the value for that frequency. You'd have to know how the FFTs where generated. Say the data was sampled at 102.4 points per second and the FFT frame size was 1024 points. Your frequency resolution would be 102.4/1024 = .1 hz.

So, for your first case, the RMS at 27.1 hertz would be:

(.509 x .1)**.5 = .226 mm.

So the vibration at 27.1 hertz would be .226 mm RMS.