# Fatigue Analysis problem

1. Jul 19, 2010

### ella_lei9

Hi everyone.

I'm working with a project about Fatigue Analysis now. I got some questions I'm stuck with at the moment. So I'm wondering if you have any idea about them.

The method people usually use to solve the fatigue problem at the moment is like this:

The first six plots shows the forces and torques of a wind turbine in x,y,z directions in 600s. From these 6 plot we find out 6 freedoms interact differently at each time step (see the orange line). Then methods resolve combined stress in a plane at each element (In simple terms, this means to combine these 6 vectors into a 3d plane), finally we can get a single stress history plot (which is combined from previous 6 plots). Next thing is using RAINFLOW COUNTING analysis to work out the fatigue using the S-N plot.

This method is quite good but the only problem is to combine those 6 plots into the plane take so long time to do, each of the single point combination need about 30 hours to process. So I'm asked to think another mathematical method to solve this problem.

At first I was thinking if I can combine the 3 forces and 3 torques in to resultant vector, but then i found that was wrong way. So now I'm thinking can we find out if there is a period exist for those 6 plot, or can we divide the plot into several time domain sections so that each section has its own individual period. If this can be done, instead of doing 600 points (say) combinations, we now only need to do 300 or even less because the periodic property.
Or are there some other ideas in your mind at all?

2. Jul 19, 2010

### john.phillip

You should not shorten your loading time history and fill out the gap with some "periodic property", as wind or wind+wave generates random loadings and should be handled stochastically. The pre-processing time is a common drawback with time domain analysis, one thing you could do is work with transfer functions in the frequency domain analysis or Time-Frequency domain analysis, depending on the software, knowledge, time and data available.

3. Jul 20, 2010

### ella_lei9

Thx John.

I got what you said. Well, I can definitely transfer these time domain plots into a frequency domain plots by Matlab FFT. But the thing is, what should I do next to find out the fatigue load from these frequency domain plots? The most annoying thing is this is not a simple 1d or 2d problem, it is 3D, which make the problem more complicated!

4. Jul 20, 2010

### john.phillip

With the loads translated to the frequency domain, you can do a modal analysis of the structure, and crosscheck with your loads frequencies to findout if your loads will potentialy excite it. If so, then you can get the transfer functions for stresses with a unitary load coupled with the harmonic analysis and later workout a random response analysis with the loads PSDF's to identify the dynamic amplification factors for each mode and the final stresses (this is the stage where you are getting after 30hrs processing of the time histories). At this moment, you can go back to the rainflow count or workout the zero-cross frequencies and get the Miner's sum for the structures damage due to the long term stresses, and therefore the final fatigue life, wich you can compare with your requirements.

5. Jul 20, 2010

### ella_lei9

Thank you so much for your quick reply John! I do appreciate it!

I went through your answer, still something there I don't quite understand. What do you mean by "crosscheck with loads frequencies to find out if loads will potentially excite it"? And also, could you explain a bit more about how to do the harmonic analysis from force and moment 3D data to give out an unitary load please.

6. Jul 20, 2010

### john.phillip

If the structure's first modes are within the loads excitation frequencies, you should check if the fluctuating part of your loads have the energy to amplify the structure's deflections, coupling with the structure's harmonics, as it happens with vortex induced vibrations (tacoma bridge effect). This is something a time domain analysis cannot do.
I am understanding that by 3D you mean you have a solid or a lattice structure with loads that change direction over time with a certain probability.
Distributed unitary loads for 6DOF are applied individually regardless of your data, but considering the appropriate direction, just to get the structure's transfer functions for stresses for each DOF, each load direction and each element.

7. Jul 21, 2010

### ella_lei9

Did spent quite a long time to think through what you said, sounds very interesting.

Well, the conventional method for doing the fatigue analysis at the moment is still the rainflow cycle counting in time domain. From what you said, we transfer time domain to the frequency domain, then do we have to transfer it back into time domain again to find out the results or can we doing rainflow cycle counting in frequency domain straight away? If we can do rainflow cycle counting in frequency domain, is that reliable?

8. Jul 21, 2010

### john.phillip

That will probably be your best option, changing back to the time domain for the rainflow cycle counting.
If you stick to the frequency domain, there are other stochastic approachs for keeping the analysis reliability when computing structural damage, like working with a Rayleigh distribution.

9. Jul 22, 2010

### ella_lei9

Morning John.

Yep that what I thought, But the thing is, when we doing the trnsfermation, time->frequency->time domain process, after all of them, is the data still gona be accurate?

10. Jul 22, 2010

### ella_lei9

I did some research then found out the transfer between FFT and IFFT is kind of accurate, so wouldn't be a problem then.

So the most difficult thing at the moment is, work out the random response analysis to identify the dynamic amplification factors for each mode and final stresses, as it will not only be static but dynamic. So it will take such a long time to finish, right?

11. Jul 22, 2010

### reta

I am looking for a engineering problem ( mech, chem, elec, bio or ... ) modeled by 2 order or higher ODEs or/and PDEs with solution method in analytical or numerical form. ( the physical problem and simplified model and basic equation(s) modeling the problem )

Please send me the article or journal paper, if possible.

Thank you in advance and best regards

12. Jul 22, 2010

### john.phillip

Don't expect to grab the results so fast, either learning your way trough a suitable hybrid analysis or sticking to the time domain will cost you some time.

About 15+ years ago, time domain analysis were almost unbearable even with relatively small load histories and simple models, so several workarounds and simplifications were created, like reliable techniques for frequency domain analysis and equivalent beam models. What I'm seeing today is, although computers got really productive and fast compared to that time, our data and model complexity have increased accordingly, and we are still in trouble with deadlines.

13. Jul 23, 2010

### ella_lei9

Thanks so much John. Thank you for all the replies and advices you gave me these few days. Have a nice weekend!