PSD(G^2/Hz) to time history for fatigue analysis 6

[ThetaJC]

I have a question concerning converting PSD random vibration levels into a representative block of time history. I am able to write a software code that converts G's vs. Hz in the frequency domain back into a G's vs. time in the time domain by including a random phase number. I have a specification for a military avionics unit which has a bracket that is of concern. We are convinced that the most appropriate way to perform a fatigue analysis on the bracket is by the strain life method, because we believe it is possible even w/ 3 sigma clipping that we may be experiencing periodic stresses that exceed yield for a small percentage of the time. The bracket material is aluminum 6061-T6 and we have the ability to produce an FEA model in Ansys. The following is the process I am considering using to generate an estimate of fatigue life

CAD model--->FEA model |
PSD spec--->Conversion to time history (?) |

------>
Input time history into FEA model as an inertial loading event and track the strain history in the area of interest (Multi-linear material model used).

-----> Rain flow counting ---> Strain life method coupled with Miner's cummulative damage-----> Result


The difficulty I am having is being able to convert the PSD in (G**2/Hz) into a (G/Hz) profile so I can perform an inverse FFT to calculate a time history block. Does anyone know of how to go about tackling this problem?


Thanks

 

[btrueblood]

Integrate the G^2/Hz curve with respect to Hz (G^2/Hz * Hz = G^2). Take the square root of the result to obtain G's.

 

[tomirvine]

I have posted a Matlab program to synthesize a time history to satisfy a PSD at:

http://www.vibrationdata.com/matlab.htm

The program is called: psd_syn.m

The program can be downloaded via:

Username: vibration
Password: quake

Tom Irvine

 

[Tunalover]

ThetaJC-
Note that when you go back to time history from the PSD profile you inevitably lose all history of acceleration sign changes (changes in direction). You will end up with only positive values. Now you may be able to INFER sign changes by cusps in the time plot...


Tunalover

 

[MikeyP]

btrueblood appears to have answered your question for you. However, you must be careful when using this sort of random-phase multisine for fatigue calcs.

The problem is with the crest factor of your reconstituded time signal. Crest factor is defined as the ratio of the maximum absolute value in the time history divided by the rms value of the time history. The crest factor using a random-phase multi sine will probably be 3 or more because at some time points you will find that (purely by chance) you get a very high amplitude.

The time data which was originally used to generate the PSD probably had a much lower crest factor (assuming it came from real measurements on a real structure). In this case your fatigue predictions will possibly be over-consevative (no bad thing, perhaps!). Ideally, if you had knowledge of the crest factor of the original measurement, you should ensure that the crest factor of your reconstituded signal is approximately the same. This crest factor optimisation is relatively easy to achieve (especially as you seem to have a good understanding of FFTs).

M

--
Dr Michael F Platten