Method of Fatigue Life Prediction from Vibration Analysis 2

[CaptainCrunch]

Hello All,

I've been thinking about problems I've come across doing vibration analysis. Say I test a structure during operation and measure acceleration. Then I create an FEA model and input the acceleration to get stress as a function of frequency. If a have a case where stress at one freqeuncy in one location is much higher than all other frequencies then its pretty straight forward to use some simple fatigue life prediction equation to estimate the life of the component.

But say I have several high stress frequencies in a single location. The structure is experiencing all these frequencies simultaneously (but at different frequencies of course). Also to simplify the case, say that of all frequencies of interest will have enough cycles, N, to have infinite life.

So we have stress as a function of frequency and space (i.e. a location on a 3D structure), AND we have several significant stress frequencies. My questions are:

1. How would you come up with a composite stress level to predict fatigue life?

Assuming linearity we can superpose the stress solution at speocific frequenies. But:

2. Are the motion in phase form one frequency to another? You could imagine a situation where two frequencies were 180 degrees out of phase and cancel each other.

3. What if for shell elements in FEA, one frequency max occurred at one edge and a different frequency occurred at the other edge. How could yuou logically add those?

Sorry for the long winded post but I wanted to express myself clearly.

What I'm looking for is a references or ideas on how to come up with a "composite" stress level.

Thanks in advance for info,

George

 

[IRstuff]

What's missing is the power spectral density of the expected environment. In which case you could probably RSS all the components together.

TTFN

 

[CaptainCrunch]

Istuff,

Acceleration is related to PSD by PSD = G^2 /Hz. I don't see why PSD is better than aceeration.

I think in order to do some manipulation like RSS you have to make alot of assumptions which are probably not correct, because you are just adding the stresses (or squaring and adding then taking square rooting).

What if different freqeuncies are out of phase or happening at different layers of a shell element ?


My question is how to logically figure what is happening. Not to arbitrairily combine stress values at different frequencies.

Thanks for the feedback,

George
George

 

[electricpete]

Just a thought...

If the frequencies of interest are not harmonically related (not harmonics of each other), than I believe phase will be undefined and somewhat irrelevant. At least in the case of two sinusoids of non-harmonically related frequencies, the relative "phase" position (I use that term loosely) of the sinusoids will continuously shift relative to each other. If I shift one wavevorm by a certain time it has no effect on the long-term behavior of the sum of those two non-harmonically-related sinusoids.

 

[CaptainCrunch]

Excellent point pete, I think the phase shift doesn't matter. There will be loss of coherence unless frequencies were harmonics of each other and perfectly in phase. The question is still how do you add these stresses?

George

 

[IRstuff]

It seems highly unlikely that your initial measured acceleration from your equipment is random, therefore its PSD is unlikely to be white. It's more likely that your equipment is vibrating at one or more specifica frequencies plus associated harmonics.

If you still have your time-series acceleration data, you could FFT it to see what the actual frequencies are.

TTFN

 

[GregLocock]

You use a rainflow analysis to get a set of stress ranges, then you use Miner's rule to get the total damage.

Rainflow analysis is a time based method of finding the number of reversals of a given stress range in a signal.

That is, you CANNOT generally use a frequency domain solution for fatigue. One of the less thrilling parts of my job is generating very long time histories for the body guys to drop onto their FE models. If we could do it in the frequency domain we would, generating gigabytes of vibration is a pain.

You can use a frequency domain solution if the waveform is stable, but that is not really the point.

Incidentally please don't use the word coherent when discussing phase relationships between different frequencies, coherence is a very useful thing, but it is very accurately defined as function of each frequency. I don't know the techie phrase for 'the stability of the phase relationships between different frequencies' but it is a useful concept, witness the setting on your FFT analyser for triggered data capture. I think the electrical guys use group delay or some such expression.

Cheers

Greg Locock

 

[CaptainCrunch]

Greg,

I am familiar with rainflow analysis I dont think it can be used here. I am forced to work in the frequency domain. The test data is freqeuncy and the solvers ive used (NASTRAN and ABAQUS) perform moded based frequnecy response.


Granted, frequency stress values can be FFTed to time domain but that is simply not practical to meet my deadlines.

George

 

[GregLocock]

Then you can't get the right answer, in the general case. You could look at the fatigue life from each of your frequency components individually, if one is dominant then you may get a reasonable approximation, but with the typical relationship between fatigue life and stress range you wouldn't have to miss much to be out of luck.

Having said that, even the time based methods are pretty hopeless in my opinion, a factor of safety of 4 seems to give reasonable results most of the time, ie we have just the faintest idea of what is going on.

Could you synthesise time data using random phase for each frequency line, and repeat that until your rainflow estimates settled down to a stable figure?

Cheers

Greg Locock

 

[GregLocock]

Oddly enough they are just discussing Miner's rule on sci.engr.mech (a usenet group) and basically the more authoritative sounding guy there is saying that it has so little physical basis that you might as well not bother. A factor of ignorance of 4 gets mentioned there as well.


Cheers

Greg Locock

 

[markhgl]

Hi

I would suggest that the best approch a multi frequency input problem is to generate a PSD input for your model from your experimental data. PSD is better than accleration as it is a normalised energy input across the frequency range rather than acclerations at specific frequencies.

To do this you will have to identify where the inputs to your components, e.g. where the component is attached to the main structure, and measure the exication levels experimentaly and generate the PSD input levels for a forced response analysis.

Once you have a forced response analysis results from your model you will have the stresses from all the frequencies at the max stress point. You can then use a simple S-N material curve to calculate your fatigue life. The material in the component does not care about what frequencies the stresses occures at only the overall stress level.

I hope this makes sense,

Mark

 

[CaptainCrunch]

Mark,

yes I get all you said, most of it was in my original post. the question is which stress frequency do you use? If you have one dominant frequency, then you use that apply it to a S-N curve of use a fatigue method to *estimate* life, but what if you have multiple high stress frequecies ? The structure experiences them at the same time. How do these stresses combine?


George

 

[electricpete]

OK - here's another thought. I am not on the same plane with you guys in understanding this stuff (Miner who?) so be gentle if this is a stupid idea.

Part of the problem is that if we consider the displacement, each frequency has a different contribution to fatigue.

But if we consider velocity, then any frequency has the same contribution, depending only on the magnitude of its velocity (independent of frequency).

What if you use the overall velocity as an indicator of fatigue. The overall can be formed in a number of ways.

That may be overly conservative approach, but in any case I'm sure it's bounding. ie Fatigue of the combination of frequencies with overall velocity V0 won't exceed fatigue of a single frequency whose velocity is V0.

 

[electricpete]

I take back my statement: "I'm sure it's bounding". I'm not even sure of that. I don't have any rigorous basis for making that claim. It made sense intuitively when I said it but now I'm not so sure.

 

[electricpete]

I can see a whole lot of holes emerging in my suggestion. For one thing, my assumption that fatigue is dependent only upon the product of displacement and number of cycles is incorrect... that relation depends on what part of the S/N curve we are. For another thing I look in Mark's handbook and see a lot of references to empirical studies on this subject. That discussion quickly goes over my head. Leads me to believe my understanding and suggested approach was much too simplistic.

 

[PaulWeal]

I think I have an approach that works. Here are the requirements:
Contrained Modes (Static modes)
Normal Modes (eigen modes)
Time History
Fatigue Solver capable of Modal Superposition.

The steps:
1. Solve for constrained modes
2. Solve for normal modes
3. Compute modal participation factors (MPFs)
4. Compute fatigue life using modal superposition.

NASTRAN (and other FE solvers) can handle steps 1-3 using SOL101, SOL103 and SOL112. LMS FALANCS can handle step 4.

The Modal Superposition technique combines the stress mode shapes (items 1 & 2) with the MPFs to produce the multi-axial stress tensor time histories for each element.

Note: A special mode set called the Craig Bampton mode set is very useful here. This mode set is an orthoganalized mode set combined of the 2 - details too lengthy to explain here.

Automated time history reduction and nodal elimination techniques make it practical to perform a critical plane fatigue analysis in LMS FALANCS. The result is fatigue damage, hot spot and/or safety factor contours on the entire FE model. Please note that these results consider the frequency content and phasing of the loading and the resulting dynamic (modal) response of the structure; i.e.; dynamic fatigue solver. The phase in the loading environment is important particularily when stress tensors are rotating in critical areas of the FE model. The Critical Plane approach handles this.

An interresting outcome of this technique is that certain modes can be "left out" during superposition. Subsequently one can get an appreciation of which modes are causing the dynamic fatigue problem.