converting g/Hz to g^2/Hz 2

[Tomliu]

Can anybody help me with convert g/Hz to g^2/Hz.
I have data curve that has data .616g at 289Hz and in the PSD plot, it become .0243g^2/Hz, how is that converted?

Thanks for the help

 

[franck]

Hi Tomliu,

I am not sure if it is really the answer since the description of the problem is very limited but here is a try. Basically I guess this is finding the equivalent sine vibration for equal random damage.

A PSD of 0.0243g2/Hz at 289Hz gives you an equivalent static acceleration of 18 grms using a Q of 30 and the Miles equation:

sqrt(Pi/2*289*30*0.0243)=18 grms

Now, the damage produce by this random environment assuming the 3 sigma value (3*grms) occurs for only 4.33% of the time and an exponent of 3 for fatigue damage you get a random damage of:

random damage = 0.0433*(3*180^3=4692

Now the peak value from a sine input to get the same damage during a sine test is (still assuming a Q of 30 and the same exponent):

(Input_Sine*30)^3=4692 gives Input_Sine= 0.616g

This approach is defined in 'Vibration Analysis for Electronic Equipment' -Dave Steinberg-Wiley Interscience-

Franck

 

[electricpete]

I thought about the question for awhile and couldn't figure it out. I vote a star to Franck.

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[CESSNA1]

TOMILIU: They are two different things. The Power Spectral Density (PSD) is sometimes called the autospectral function. The PSD is obtained basically by taking the Fourier Transform or more frequently the Fast Fourier Transform of the time domain signal. For accelerometers the time domain signal is acceleration (usually g's) plotted against time. Since Fourier's law says that "any repeating signal can be decomposed into the sums or sines and cosines" The Fourier Transform converts the time domain signal to the frequency domain signal. That is "acceleration vs.time" to "frequency vs. time". The PSD curve is a slight modification of the tme doamin signal to plot (G(rms))^2/ Hertz. In this curve we are baiscally looking at sines and cosine functions edgewise. To convert the PSD curve to G's at a designated frequency. Selct a frequency on the PSD curve and look at the corresponding amplitude. Take the square root of that amplitude and you wind up with G(rms) at that frequency. To convert this to peak multiply the rms value by 1.414. If you do this for each frequency and plot the results you wind up with a G(rms) or G(peak) verses frequency.

Rememher that most, if not all raw data signals contain a DC Offset and noise. That must be removed. Also before taking the PSD remove the DC offset and noise (or at least what noise you can)and then window the data (usually the Hanning window is used) It is also necessary to know the anit-aliasing filter frequency, the sampling rate which should be at least 5, preferably 10 times the highest frequency of interest, and whether the accelerometers were calibrated in G(rms) or G(peak). It is best to take the PSD of points in powers of 2 such as 1024, 2048, 4096 etc.

Hope this helps

REGARDS
Dave

 

[CESSNA1]

tomiliu: One thing I forgot that is very important is that digital signal acquisition and analysis hase a lot of pitfalls and shortcomings. I suggest anyone involved in this take a few courses. One souce that I use, and there are probably others is

http://www.ttiedu.com

Regards
Dave