Oscillating Shaft Fatigue

[Farmboy71]

Hi. I'm designing a shaft that will be oscillating +/- 15 degrees and I'd like to determine the fatigue strength of the shaft. The problem is that all the equations and information that I can find(Shigley mostly) is for rotating beams with fully reversed stress, not oscillating motion.

Does anyone know how to approach this problem or other sources for info? Are there any endurance limit modifying factors specific for oscillating motion?

Thanks in advance.

 

[TVP]

Does this shaft rotate about its axis due to one side being driven by a gear, pulley, etc. upon which some type of oscillation is induced? I am having some difficulty understanding the problem, so perhaps you could provide a little further explanation of how this shaft moves through spacetime.

 

[Farmboy71]

Sorry for the confusion. Instead of the shaft revolving about it's axis continuously in the same direction (ex: motor shaft), this shaft rotates about it's axis forward 30 degrees and then back to the start position. I hope this helps clear up the confusion.

 

[dvd]

One of the issues with your analysis is going to be quantifying the accelerations due to the angular reversals. Is this oscillation produced by an indexer, or some other piece of purchased equipment? If yes, then the indexer manufacturer will be able to provide accel/decel data. If no, then you won't really know the magnitude of acceleration unless you can figure out how to calculate it.

Another issue that will affect your accel/decel is the backlash in the indexing gizmo, and the backlashes of the couplings, etc. If the assembly components aren't rigidly coupled there will be a slack period after the displacement reversal. Depending on the mass inertia of the machine the shock loading could be rather impressive..

If you can calculate the torsional moment and bending moments on the shaft then you should be able to size the shaft.

 

[gwolf2]

Just a gut feeling, but if all there is is a shaft oscillating +/- 15 degrees this will have an incredibly low rotational inertia/strength ratio unliss it is very very long. These things are usually only an issue if there is something with high rotational inertia like a wheel attached to the shaft. Possibly a non-problem?

 

[Farmboy71]

You guys both brought up good points. Yes, there are some components on the shaft that have inertia and are accelerating and decelerating against stops. I've got pretty good numbers for the dynamic loading on the shaft and have determined the stress. However, the problem I'm trying to wrap my head around is the realistic endurance limit for the material(4140HT) in an oscillating application. I don't think the equations for a fully rotating shaft with fully reversed bending will apply in my case. Sure it would be conservative, but I'd like to know how my calculated stress compares with a realistic endurance limit.

I hope this helps clarify the problem.

 

[MikeHalloran]

Applying a moment to a rotating shaft is just a convenient way to produce fully reversed stress within it. The metal doesn't know whether it's rotating or not, just that the stress reverses.



Mike Halloran
Pembroke Pines, FL, USA

 

[gwolf2]

In that case you need to get the max/min principal stresses from your torsion loads and use these as a stress range to compare against the rotating bending stresses, which are alternating tension/compression.

In your case for torsion you will have two principal stress ranges at 45 degrees to the shaft axis and 90 degrees to each other. You may have to stirr in some allowance for the fact that your stress field is biaxial and you are comparing it to a uniaxial tension/compression in the rotating bending.

Hope this helps.

gwolf.

 

[TVP]

Farmboy71,

Based on your last post, I suggest you review some of the work performed by Darrell Socie and others on multiaxial fatigue. Here are some links that you can start with:

http://www.fatiguecalculator.com/pdfs/MultiaxialFatigue.pdf

http://www.google.com/search?hl=en&...=&as_occt=any&cr=&as_nlo=&as_nhi=&safe=images

 

[Farmboy71]

Thanks for the links TVP...I'll check them out.

Mike, I'm not sure I understand what you mean. Let's imagine a horizontal shaft with a perpendicular load applied to the middle of the shaft. Are you saying that the shaft just oscillating back and forth only 30 degrees will fail just as soon as one completing full rotations with the same loading?

Thanks,
Farm

 

[MikeHalloran]

No, because the stress won't be fully reversed.

The rotating shaft fatigue test extracts data about the shaft material in a repeatable way, because the loading can be analyzed and controlled. For one thing, the rotation provides a controlled strain rate with no impact.
There is still a lot of scatter in the data, and it can be expensive to get enough data to be statistically significant.

With that data, and the math, one can estimate a fatigue life for other loading cases.

In your case, the stress associated with the oscillation per se should be computable. The extra stress associated with banging into hard stops is dependent on a lot of stiffness and inertia properties, and may not be so easy to compute.

For cases other than fully reversed stress, there are more than a few ways of estimating a fatigue life from the fully reversed stress data that's available, doing various machinations with stress range and mean stress and the phase of the moon.

All are subject to rather large inaccuracies, because of simplifying assumptions, the asymptotic nature of the material's S-n curves, scatter in the material test data, sensitivity to other influences like surface finish, notches, strain rate, chemical attack, and who knows what.

I.e., if you do it six different ways, you'll get six very different answers... probably all wrong. The only way to know the real answer is to suffer, investigate, and back- engineer a statistically significant number of field failures... and there are a lot of reasons why you want to avoid ever having that data.





Mike Halloran
Pembroke Pines, FL, USA