Going from Time Domain to PSD in shock questionà

[Tobalcane]

A question was posed to me about shock. In the time domain (G vs time) at the beginning of the time window, it would show high amplitude (high Gs) for the higher frequencies (The number of crossings at the beginning of the time window is more than later in the time window) and lower amplitude (lower Gs) for the lower frequencies (later in the time window). But, when the PSD is calculated, it appears that at the higher frequencies (right of the profile), G^2/hz is going lower instead of going higher.

What gives? I would expect that since we have high Gs in the beginning of the time domain that you would guess that you would have high G^2/hz at the right of the PSD profile.


Go Mechanical Engineering
Tobalcane

 

[Skogsgurra]

Tobalance,

All systems with a mass are more or less low-pass filters. Sometimes with one or two resonance peaks. So it is only natural that your PSD falls off at higher frequencies.

Also, the initial shock has a DC component (that is why a loose object moves when hit - cf golf ball hit by club) and this DC component and its associated components are very much low-frequency and will be mapped to the left of your PSD.

Also, if you examine your time domain trace, you will find that the rise-time is finite. And you can probably also find that the rise-time is about 1/3 of the highest frequency in your PSD (do not count spurious frequencies, just those with some energy in them).

Actually, with a square wave with a finite rise-time, one calculates that the band-width is about 0.35 divided by tr. Example: an oscilloscope with 10 MHz BW will show perfect square waves with a 350 ns tr.

I think that the important thing is to remember that the rise-time is finite - and that puts a limit to how high frequencies there will be in your spectrum.

 

[tomirvine]

The power spectral density (PSD) function is not well-suited for shock data. Typical shock events are very brief. As result, there is usually only a small number of statistical-degrees-of-freedom available.

Another concern is whether a Hanning, rectangular, or some other type of window was used. A rectangular window is appropriate for transient data.

A better function for analyzing the frequency content of shock is the shock response spectrum (SRS).

Tom Irvine

http://www.vibrationdata.com

 

[Tobalcane]

Thanks guys for responding.

Skogsgurra (forest gunnar): I looked back at my time domain profile and I don’t see any rise time (if you mean a rise “before” the first big peak from left to right), but I looked in my text books to see a typical shock profile and I do see a rise. But, are you saying that if there was a rise leading up to the first big spike and that rise is calculated first for the tail end of the PSD profile that would make sense. So that would mean that the “high energy spike” would be hypothetically ¼ (just for argument sake) from the right of the PSD profile?

Tomirvine: I’ve started with a SRS and I agree that this is the best profile to use for shock, but for my application, I could not determine if there was a natural frequency in the frequency range that is causing me problems. It’s funny. The SRS is actually doing what I expected it would do. That the high Gs in the beginning of the time domain is showing up at the tell end of the SRS profile. I would think that the PSD profile would follow suit. Now about the windows that I used, to be honest I’m not sure what window I used. What is the difference? I’m using a B&K analyzer and it gives me the time domain.

Thank you for your time and effort.




Go Mechanical Engineering
Tobalcane

 

[IRstuff]

Are you really comparing apples to apples?

A PSD is a spectral DENSITY. Since the high frequency components occupy only a small portion of the time duration of the data, you might expect that the spectral density to be somewhat lower than that of lower frequency components.

TTFN

 

[Tobalcane]

IRstuff,

You may be right, but in my simple thinking the PSD is in G^2/hz and this is defined as the analyzer dividing the amplitude of the measured G at each frequency by the band width of each frequency bin (of the analyzer) in hertz. The band with can be constant so it is just G at each frequency. In the time domain G is the amplitude and the number of crossings per time is the frequency (am I thinking this correctly?). So when I look at the time domain window we have high amplitude with a lot of zero crossings and the further you go right the amplitude is ramping down and less zero crossings, but when I look at the PSD from left to right you would see the normal resonances and then the profile will start to ramp down. It’s just that I would have expected that at the right of the profile would start to ramp up instead of ramping down. If the beginning of the time domain window started high in high frequency then this should correspond in the PSD. In the SRS I do see this, I just though the PSD would do the same thing.

Thank you IRstuff for you comments.


Go Mechanical Engineering
Tobalcane