Power spectral density
Power spectral density
(OP)
To compare measured vibrations with machine specifications, I need to convert acceleration-time signal in to power spectral density. I have FFT equipment available, but I have come up with different definition for PSD. Please help with a correct definition of PSD...
Thanks in advance
Wim
Thanks in advance
Wim





RE: Power spectral density
The FFT magnitude is squared.
Then multiply by (1/2) to convert G^2 to GRMS^2.
Next, divide by the spectral bandwidth, which is the frequency increment.
The result is a power spectral density in terms of GRMS^2/Hz. Note that by convention this unit is abbreviated as G^2/Hz.
I have posted some tutorials on the power spectral density function at:
http://www.vibrationdata.com
As disclosure, a small fee is required to access the materials at this site.
Sincerely, Tom Irvine
RE: Power spectral density
Also, is this FFT two sided?
Best regards
wim32
RE: Power spectral density
The Power Spectral Density is simply a method of scaling the frequency of the structure. It is more pronounced for random type of excitation.
RE: Power spectral density
I indeed measure random vibration, that is why I need to calculate PSD.
RE: Power spectral density
The instantaneous magnitude of any random vibration are specified only by probability distribution functions giving the probable fraction of the total time that the magnitude lies within specific range.
The Power Spectral Density is really the limiting mean-square value of the random parameter (e.g. acceleration, velocity, displacement, stress, etc.) per unit bandwidth.
As you can see, the PSD is the mean-square (see Tom Irvin message) and not Root Mean Square (RMS). The RMS value of any Sinusoidal Frequency amplitude is equal to the reciprocal of square root of 2 (0.707).
I hope that I am of help to you.
Take Care
RE: Power spectral density
I recently had some PSD data recorded over a very long period of time in real conditions. I need to experimentally test the equipment this data was originally recorded on, but the time period is unreasonable. Is there any way an accurate time experience of less duration can be made by "compressing" the data? Thanks.
RE: Power spectral density
(W0/W1) = (T1/T0)^(1/M)
where
W0 is the reference level in GRMS
W1 is the new level in GRMS
T0 is the reference time
T1 is the new time
M is the material constant, or slope of log-log S-N curve)
Typically, M=4 is assumed for aerospace vehicles.
(Reference: MIL-STD-1540C).
If you would like further information, I have posted a tutorial on time scaling at:
http://www.vibrationdata.com/tutorials.htm
As disclosure, a small fee is required to access the materials at this site.
Sincerely, Tom Irvine
RE: Power spectral density
The FFT sampling time (window) is probably not unreasonable long. If you can have the original time data still available, you could decrease the total measuring time to the sampling time width (if this is known). This way your frequency range stays intact. If the processes that are being measured are longer than your sampling time, you should increase the measuring time, so that it always contains complete samples.
Good luck, best regards
Wim32
RE: Power spectral density
RE: Power spectral density
RE: Power spectral density
I checked out the tutorial and I think I have a better handle on how to time scale, but I still have the same question: is there a limiting factor on the empirical time scaling formula? Theoretically, I could scale down the 2000hr data from the tutorial to a 1 second test, but this would not be practical. I realize that some limitations are determined based on equipment. However, assuming that my equipment can generate any new test levels at the appropriate frequencies, how is the largest, reasonable delta between actual time and test time (i.e., the shortest test time) determined?
RE: Power spectral density
The whole time-scaling method is highly empirical.
For example, the true S-N fatigue curves for the test item materials are seldom, if ever, known.
A further complication is that fatigue is only one of several failure mechanisms. Yielding, Ultimate failure, buckling, and excessive relative displacement are other examples. In addition, some failure modes such as creep are time-dependent.
I thus gave a moderate approach in the tutorial, where a 16 hour per axis test was used to represent 2000 hours of field service.
By the way, the tutorial paper was based on some work that I performed for an actual client.
Unfortunately, the testing project was cancelled due to the client's financial problems.
Sincerely,
Tom Irvine
http://www.vibrationdata.com