[b]Finding amplitude from PSD data?[/b] 1

[Parsnip]

A question to those of you who probably have a far greater knowledge about this than me!
I have a PSD plot (g2/Hz) against frequency, there are very distinct peaks at certain frequencies. Very simply I want to find out what the displacement of the object would be at these frequencies.
I am sure this must be easy but.....
Thanks alot in advance
Parsnip

 

[Twoballcane]

Hello,

What do you mean, the travel of the vibration head or the deflection on the part due to Fn?

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

 

[Parsnip]

Afternoon,
Basically the accelerometer was mounted on the vertical axis of the excited part, the PSD was 0.004 g2/Hz at 504Hz, what I want to try and find out is how much has that part moved. Does that make sense?
Cheers
Parsnip

 

[IRstuff]

If these frequencies are continuously present, then the double integral of A*sin(2pi*f*t) will give you the maximum displacement of a sinusoidal motion with that acceleration.

BUT, unless the random background is VERY low, the total random displacements might exceed the contribution from any single line.

TTFN

FAQ731-376

 

[IRstuff]

Oh, I should mention that it's usually easier to assume a sinusoidal displacement d*sin(2pi*f*t) and differentiate twice: d*(2pi*f)^2, which you set equal to the acceleration and solve for d

TTFN

FAQ731-376

 

[GregLocock]

504 Hz~ 3000 rad/s

a~0.6 m/s^2 rms

x~5*10^-6 m rms

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[electricpete]

"PSD was 0.004 g2/Hz at 504Hz"

How do we convert that PSD into acceleration in g's?

I would assume two steps:
1 - Integrate over a certain frequency band.
2 - Take the square root.

What frequency band should be used for step 1?

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[BobM3]

Yes, you have to know the frequency band. If the data was taken digitally then the band width = sample rate/frame length. If the frequency band is small enough then you would just multiply instead of integrate.

So for instance, in this case, suppose the sample rate was 8192 pts/sec and the frame length was 1024 points, then the frequency resolution would be 8192/1024 = 8 hertz. Then, using the OP's data:

Average amplitude = sqrt[.004 g2/hz* 8 hz] = .179 g
Peak Displacement = (.179 * 386 )/((2*pi*504)**2) = .00000689 inches

 

[GregLocock]

Sorry, yes I got the wrong units. Again.
that should be m/Hz


Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Parsnip]

Thanks for all your help - I reckon that should do me great.
Cheers
Parsnip