Vibration Fatigue

[izax1]

Can anyone direct me to articles, books etc. on fatige calculations on wide band random process?? I have already checked Steinberg, but that seems to cover only narrow band processes.

From my FE analysis, I have the random response (No. of positive crossings, rms stress, PSD stress etc.) I need to calculate the fatigue damage from three dominant freuency peaks.

Where can I look???

Thanks

bernt

 

[davefitz]

not sure this is exactly what you are looking for, but the latest, formalized method of calulating fatigue damage for engineering structures and pressure vessels is contained in the new European Union codes, for example prEN 13445.
The method of computing fatigue damage for complex cycles is either the rainflow cycle counting algorithm or the reservoir counting algorithm. I would assume that a monte carlo simulation of cycle sequences could be automated and the rainflow method would be used.

 

[izax1]

I know prEN 13445. That is not exactly what I am looking for. This has more to do with calculating fatigue life when a structure is operating at its resonant frequencies.

Thanks anyway.

Bernt

 

[dylan1450]

Hi, I know its been a while since this thread was started but I've only just signed up.

I do a lot of acoustic fatigue work which involves random vibration (evaluation of rms stresses and/or strains). The fatigue data I use is from the Engineering Sciences Data Unit (ESDU) series on Vibration and Acoustic Fatigue. The fatigue data is rms S-N data and it is possible you could do a Miner's rule calculation to determine the effect of the 3 predominant frequencies you refer to.

An alternative is to generate your own data by converting sinusoidal S-N data (like in the US Military Handbook) to "equivalent" rms S-N data. There are documented proceedures for doing this and I'm sure there is software available also.

I hope this helps.

 

[izax1]

Well,its never too late. And my thread hasn't got very many feedbacks. So thank you. I will check out your suggestions.

 

[Phatrick]

I have a similar question.
i have to pass MIL-STD 810f Random Vibration, consisting of a broadband PSD and 4 sinusoidal harmonics.
From FEA i have obtained the harmonic stress and used Minors rule with S-N data from the ASME Boiler Code to check for cumulative fatigue.
My question is how do i account for the spectral 1 sigma stress in my overall fatigue calculation?
I am assuming that i would need a different S-N curve than used for the sinusiodal and add that fraction into minors rule?
Thanks
Patrick

 

[dylan1450]

Patrick,

in my (aerospace) work I'm generally supplied 1/3 octave sound pressure levels from the engine manufacturer which suggests broad band random loading. In reality however the noise in the intake of a jet engine is narrow band random and the 1/3 octave levels are actually due to a single tone (until a band is reached where harmonics of the shaft speed lie within the same 1/3 octave band). The tone still produces a random behaviour and the prudent way of analysing this is to use the 1/3 octave level as the spectrum level for the calculations.

If you have the PSD I'd suggest putting the shaped spectrum into your FE model (give a triangular shape to your tones as opposed to a step change). As you are now dealing with a random vibration problem you will generate an rms response and you can use the relevant rms S-N data for your fatigue evaluation.

With the structures I'm involved with the sinusoidal excitation (representing unbalance) is supplied as seperate data and treated as a seperate load case from the acoustic excitation.

I hope this is of some use to you

David

 

[JTam]

dylan1450,

Could you (or someone else) please explain what is meant by "equivalent" rms S-N data and how to convert into it from sinusoidal S-N data?

Thanks
Jim

 

[dylan1450]

JTam,

the USAF document by Rudder and Plumblee (Rudder, F.F., Plumblee, H.E., (1975), "Sonic Fatigue Design for Military Aircraft," AFFDL-TR-74-112.) gives some rms S-N data and also provides detail on the conversion process. It also gives some useful references. The most relevant being by Fitch, G.E., et al., "Establishment of the Approach to and Development of, Interim Design Criteria for Sonic Design," ASD-TDR-62-26, AFFDL, USAF, Wright Patterson AFB, Ohio, June 1962.

Converting sinusoidal data to random is conservative and if possible I would advocate generating your own data using broad-band random loading on a shaker. If it is an acoustic load you are dealing with, you might want to consider a progressive wave tube (PWT) test on a panel of representative construction to your "real" structure - this way you test the correct stress concentration effects.

Hope this helps.

 

[BenGib]

I still dont get it...if I calculate the RMS stress from an output PSD (obtained from the transfer function and the input PSD of a random vibration test), why cant I just go to standard S-N data for R=-1 and apply miners rule for sigma 1, 2, and 3 with the cycles calculated from the positive crossings? If Im not mistaken this is what Steinberg does in his book in Chapter 8 (p226) for a simple example.

Thanks for the help.
Erik

 

[dylan1450]

Hi BenGib

I'm not familiar with the text you quote so I'll not contradict you, but how do you account for the different probability from each environment? The random data has a peak value of 3 time the rms but only 3 times out of every 1000 cycles (you still rack up a lot of "peak" cycles if your fundamental frequency is a couple-of-hundred Hz). The USAF stuff is based on the peaks having a Rayleigh distribution.

Bob Blevins (author of Formulas for Natural Frequency and Mode Shape etc) wrote a conference paper a few years back entitled "On Random Vibration, Probability and Fatigue" it was at the Recent Advances in Structural Dynamics conference at the ISVR in Southampton in 1997. Blevins uses the Mil-Hdbk data but also accounts for non-Gaussian signals (the previous references I quoted I think assume the random signal is Gaussian with the peaks conforming to a Rayleigh distribution.......it's a while since I read it myself).

I hope I'm not steering you down the wrong path - the stuff I work on is generally assumed to be fundamental mode stuff. Have you a lot of modes contributing to your overall response, or is the fundamental prominant?

 

[BenGib]

Hi dylan1450,

If I am not mistaken the Steinberg reference assumes a gaussian distribution and hence the different probabality from each environment is taken into account as follows:

The sigma 1 RMS stress ocurrs 68.3% of the time, thus the total number of cycles is equal to .683 X (total time of test) X (positive crossings per unit time). The same method is applied to the sigma 2 RMS (27.1% of the time) and the sigma 3 RMS (4.33% of the time). Once you know the cycles to failure for each of the three RMS stresses you can just apply miners rule to get the damage.

 

[dylan1450]

Hi - I guess if the probability is accounted for, it seems fine; I'll try to check out the text to refer to - seems interesting.

Cheers for now

 

[izax1]

Hi all,

Suddenly this tread came to life again. Thank you.

BenGib. Steinberg method will work only if you have one resonnance to worry about. And that is what he explains in his book. If you have more peaks, how do you calculate the contribution to fatigue life from each peak? As I understand Phatrick, he has the same problem.

dylan1450: I have three modes contributing to my response. Is this case covered in Blevins paper?

 

[BenGib]

izax1,

Im not sure I agree with you...I think what Steinberg says is that for one resonance peak you can assume the positive crossings per sec is simply the resonance frequency, but I dont think there is anything in the post-process of problem 8.20 which is limited to single resonance.

The RMS stress can inherently include contributions from many different resonancies, you can see this clearly by doing a fourier transform of the transfer function to switch to the time domain (i.e. figure 8.14 on p222). I think that is the whole idea of the RMS stress, i.e. to convert a multi-peak response into a single series of average stresses (sigma 1 2 and 3) and cycles which can then be compared against S-N data.

 

[dylan1450]

Hi izax1

Blevins' paper is principally for obtaining a fatigue curve under random loading with any peak-to-rms ratio between 2^0.5 and infinity, from sinusoidal S-N data. It can cope with a single term (where the peak to rms ratio is 2^0.5) up to infinity.

I've not used this method, although I have used the USAF method in the past. In general however I use existing published data such as that in ESDU and the USAF design guide.

 

[izax1]

BenGib

We appearantly don't have the same edition of Steinbergs book. I am referring to "Vibration Analysis of Electronic Equipment" 3rd edition pp209-212. Here the Miner's cumulative fatigue damage is used to calculated the fatigue life for one frequency with life used at 1 sigma level, 2 sigma level and 3 sigma level. How could that be expanded to multiple peaks?

 

[JTam]

dylan1450, could you please tell me what ESDUs you mean?
Thank you
J

 

[dylan1450]

Hi JTam

its the series on Vibration and Acoustic Fatigue (Vol 1 has the endurance section - variety of curves for aluminium, titanium, carbon and Glare). USAF has data for steel, nickel and glass fibre.

 

[dampit]

Vibration fatigue - There are several methods. The simple approach is to generate SN data under Narrow band random condition - i.e generate a Srms vs. Cycle curve. Simply, predict a PSD using a analysis method, calculate the RMS and look up cycle to failure on your RMS Stress vs. cycles to failure curve. When you only have Constant Amplitude data, then use the Narrow Band Random method. I would recommend Ron Lamberts papers, "Analysis of Fatigue under Random Vibration, SHock and Vibration Bulletin 46 Aug 1976, and Fatigue Analysis of MDOF under Random Vibration, S&V Bulletin 47, Sep 1977. These papers also describe how to convert a constant amplitude SN curve into a random amplitude curve based on narrow band assumptions. For broad band vibration, the current accepted method is the Dirlik Method, which has been implemented into commercial CAE software like MSC/Fatigue. You could also regenerate a time history from a PSD, and then use rain flow cycle counting methods. Refer to WAFO Matlab Toolbox. In general, this is the preferred method for combined static and dynamic stress fatigue analysis.