# Analysis of Fatigue due to random vibration

1. Apr 20, 2012

### fettapetta

Hi!

I'm trying to find a good way to predict fatigue caused by a random vibration (given PSD).

I know at least 2 ways of doing it but i'm questioning them both.
One of them is using the rain flow count algorithm at a simulated acceleration/time signal to generate a certain amount of cycles at a certain loadfactor. A Wöhler(S/N)-curve and Miners rule is used to calculate the fatigue.

This one does not take the fact that a great part (even though most of them of very small amplitudes) of the cycles having a mean value inequal to 0.
In classic fatigue analysis one usually talks about an R-factor (smax/smin) giving other properties to the wöhler-curve.

A very large amount of different R-values is found in a random vibration. Is it possible to say that since the mean value of all "R-values" are -1 one can treat all cycles as they where acting around 0? Is it possible to find any sources on this?

Next question concerns the fatigue caused at different vibration modes. Let us take a cantilever beam with given natural frequenc-y/ies and damping. The first frequency(fn1) concerns the mode close to the fastening and the second one(fn2) a point a bit from the middle.

Is it possible to not take the second natural frequency into account by saying that the stresses acting on the second mode(due to the excitation in fn2) is so much smaller than in the first mode? Sources/references at this?

I'm sorry if the text is badly written and hard to understand!

Thank you!

2. Apr 20, 2012

### Pkruse

Who worries about random vibrations? We look at the first ten modes, and then make sure that nothing is exciting them under operating conditions. Then we test to make sure that we captured all the excitation sources. Aero buffeting is still very difficult to predict with available software.

3. Apr 20, 2012

### fettapetta

and if some modes are excited? Lets say a white noise. I guess that is hard to make sure that a component will not be excited here?

4. Apr 20, 2012

### Pkruse

I've never heard of anyone worrying about white noise in fatigue analysis. Anything that is transitory is not normally considered. As an example, a customer might specify that an engine have no modes between 80% and 130% of the operating rpm. So we would have to certify that to be so in the final design.

I think perhaps we are confusing high cycle fatigue with low cycle fatigue. In HCF, we are looking at vibrations. Even though the fatigue life might be many millions of cycles, we will reach it very quickly if something gets excited. So that is not an acceptable situation and we must design it out of the system, because you can get many millions of HCF cycles in just a few minutes of operation.

But LCF is different. That is basically one duty cycle of the machine. In an airplane, for example, that would normally be counted as one take off and one landing, at least for airliners in which cruise is at idle power. A military fighter might use up a number of fatigue cycles in a single flight. A customer might specify 1000 LCF cycles, which is normally fairly cheap and easy to meet. But if he specifies 10,000 cycles, then he is going to pay much more money for it. Most customers have by now figured out that for an operational system, it pays to invest in more cycles in the design phase; but if it is a test rig maybe they don’t need so many.

Fatigue normally is a concern at stress risers, where you have a high KT. You can estimate that from Peterson’s work, or you can model it on the computer to figure out what it is. The old rule was that if your stress at the KT point was less than yield, then you had an infinite fatigue life. But some will now specify perhaps only 85% of yield at the KT for infinite life. Apparently, they have collected enough data by now to suggest that is the right thing to do.

It may very well be that you might have a HCF mode at perhaps 40% rpm, but the plan is to pass through it as quickly as possible so as to minimize damage. Then that gets combined with the LCF data to plan an overhaul cycle for the equipment, during which all parts subject to fatigue are replaced.

5. Apr 20, 2012

### AlephZero

Google has about 188,000 hits on the topic, so I guess some people do.

This might give you some clues how to get started (but I don't claim any particular expertise in this). http://www.ansys.com/staticassets/ANSYS/staticassets/resourcelibrary/article/AA-V2-I3-Random-Vibration-Fatigue.pdf [Broken]

Last edited by a moderator: May 5, 2017
6. Apr 22, 2012

### Pkruse

AlephZero: As a mechanical design engineer, I'm backed up by our whole analysis department. They are the ones who do the detailed analysis. But I'm expected to feed a design to them that is in the ball park, and I work with them in their analysis to tweak the design for better results. Much of this tweaking is for the purpose of changing vibration modes to move them outside of the operating envelop, so that we don’t have to worry about them. That requires adding or subtracting mass, stiffness, and damping where ever I’m able to.

I do an ANSYS Workbench model of my design to look for hot spots. Then I tweak the mesh around those spots and determine the actual stresses. That gives me my KT, a number I use just for reference and no other reason. The number that I really look at is the real stress, and I compare that with a requirements number that was given to me by the analysis group or from a similar group in the customer's company. I'm not a hundred percent sure what all goes into that number, but I know that input from our metallurgist weighs in heavily. They also have access to a massive amount of actual test data for that particular material in that particular condition and under those particular operating conditions. Much of that data is proprietary, so it is not published anywhere.

We always need a quick and dirty means of getting into the ball park in a few minutes. Much of what you might learn on those 180K hits on random vibration fatigue analysis would be useful for that, especially if you did not have a means of knowing your modes with some degree of precision. But that really is not a problem anymore, with the advent of such excellent software. The design engineers can get close with Workbench very quickly, but the analysis group will run a full up ANSYS and pretty much nail it down. That eliminates the need to worry much about random vibration. The difference between what I run in Workbench and what they run is that I can get a close number in a few minutes of processing time on a cheap computer. They run on a monster server and sometimes will tie it up for eight hours or more before their solution converges.

The really important thing to remember is that fatigue comes in two flavors: High Cycle and Low Cycle. Since we must and do eliminate the HCF that is caused by vibration, I’m normally only focused on LCF as my design develops. Vibration is only “random” when we don’t fully understand it. Once we understand it, we no longer concern ourselves with random vibrations and focus completely on those specific frequencies and modes that actually exist in the machine. The state of art in airplane and engine design would have ended its evolution at about 1950 without the ability to do this. We would have given up on developing jet engines for civilian use and the airlines would still be flying reciprocating engines. There is not a single engine flying today which is not stressing critical components beyond yield during every flight. They also creep. Turbine inlet temperatures far exceed the melting point of all available alloys. None of this would be possible without a massive amount of very sophisticated analysis that was not available to our fathers and grandfathers.

I find it interesting that many of the wonderful “super-alloys” we use today were available for turbocharger design during WWI, an art that was fully developed by the beginning of WWII. New alloys that have been introduced since then are mostly just minor tweaks of those alloys, often only for the purpose of avoiding a patent dispute or to obtain some small incremental improvement in the properties. The only thing that is many orders of magnitude better today and which enables us to put these advanced designs out are our analysis tools. I’ve set a mobile crane from 1964 next to a modern crane. Both were the same size and physical weight, but one had a rated capacity of 140 tons and the other of 500 tons. The only difference between the two are the design tools that enable us to make much better utilization of our materials.

7. Apr 22, 2012

### AlephZero

It's always nice to learn something about how far behind the curve one's competitors are - but I don't see what any of the above has to do with the OP's question.

Really????? Even if WWI was a typo for WWII - Really??

8. Apr 23, 2012

### fettapetta

AlephZero: Thenk you, the link is pretty much one method i use to do the analysis but as i told you i'm questioning it.
I would like to know why it's possible to not considirate the mean value differences. They do not mention it there, neither is it mentioned by their reference. Even if it probably has a very small effect i would like some proof.