Beam Fatigue Deformation

[USMechE6]

Hi All,

We have a manipulator arm with a large central vertical shaft that after about 20 years of use has developed a slight bow to it. I don't know if this was due to some specific event or from cyclic loading, but it has the entire system skewed.

To replace it, I want to consider some sizing calculations. I can calculate the bending moment and cycles to fatigue failure well enough, but I don't know of any theory I can use to estimate plastic deformation over time/cycles of the entire shaft (not just local crack propagation). Does anyone know of anything like that?

There are no evident cracks, but perhaps there are some internally that are causing this. If so I have no way to translate that to the bulk deformation I am seeing and try to size against that moving forward.

 

[SwinnyGG]

There is no direct way to get what you're asking.

If it were me, I'd re-design the boom using an endurance limit based on the yield strength instead of UTS (i.e. 50% of Sy instead of 50% of UTS).

 

[israelkk]

This is probably due to creep or relaxation.

 

[USMechE6]

I didn't think so. That sounds reasonable, jgKRI. And israelkk I'm sure that's a part of it. Thank you both for your replies.

 

[EdStainless]

If this is structural the original design should have been bases on 25% of UTS or 33% of yield, whichever is lowest.
Often design for structures is based more on deflection than on load, and resulting load safety factors tend to be more like 6 or 8 to 1.

One key question is did the deflection of this gradually accumulate over time, of is it the result of a few severe overloads?

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P.E. Metallurgy, Plymouth Tube

 

[USMechE6]

Thanks for the additional info, EdStainless. This is structural in the sense that it is an overhead member supporting load.

On non-structural parts, I've used a FOS of 4:1 on the yield or 6:1 on the UTS, whichever is more conservative. But you're right that this does not necessarily account for deflection. In this case your range sounds about right to me.

Unfortunately I do not know the history of this machine. Based on its usage I can't think of how it could have been acutely deformed the way it is and so I'm suspecting the accumulation of micro-plastic deformation over time. Since it's at ambient temperature and undergoes loading-unloading I am doubtful that I can rely on general creep theory for a full answer.