Method of Fatigue Life Prediction from Vibration Analysis
Method of Fatigue Life Prediction from Vibration Analysis
(OP)
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
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





RE: Method of Fatigue Life Prediction from Vibration Analysis
TTFN
RE: Method of Fatigue Life Prediction from Vibration Analysis
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
RE: Method of Fatigue Life Prediction from Vibration Analysis
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.
RE: Method of Fatigue Life Prediction from Vibration Analysis
George
RE: Method of Fatigue Life Prediction from Vibration Analysis
If you still have your time-series acceleration data, you could FFT it to see what the actual frequencies are.
TTFN
RE: Method of Fatigue Life Prediction from Vibration Analysis
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
RE: Method of Fatigue Life Prediction from Vibration Analysis
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
RE: Method of Fatigue Life Prediction from Vibration Analysis
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
RE: Method of Fatigue Life Prediction from Vibration Analysis
Cheers
Greg Locock
RE: Method of Fatigue Life Prediction from Vibration Analysis
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
RE: Method of Fatigue Life Prediction from Vibration Analysis
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
RE: Method of Fatigue Life Prediction from Vibration Analysis
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.
RE: Method of Fatigue Life Prediction from Vibration Analysis
RE: Method of Fatigue Life Prediction from Vibration Analysis
RE: Method of Fatigue Life Prediction from Vibration Analysis
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.