Stress Concentration - Internal Shoulder 1

[TerribleTerryTate]

Hey all, first post here.

I am trying to put together some hand calculations for a stress analysis. I have a tube with a stepped internal shaft subject to a torsional load. See the attachment for a beautiful visual I put together.

Generally for some quick hand calculations, I crack open my copy of Shigley's and find the appropriate table. However, I have a seemingly simple case here that I cannot find a table for. I have browsed through Shigley's and through the Google books version of Peterson's to no avail.

How would someone go about determining the stress concentration factor at the stepped section of the tube? I have tried multiple Google searches for things like "internal step", "internal shoulder", "internal stepped shoulder", etc and have come up empty. I figure I can't be the first person in the universe to have designed a tube/shaft with an internal feature like this.

Any help greatly appreciated!

 

[dhengr]

I can’t see your attachment. More people would be able to open it if you used pdf, and that also prints better for me.

 

[TerribleTerryTate]

Hmmm, I uploaded a bitmap. I figured that would be simple. I've attached another version here in PDF in case others are having the same issue.

 

[rb1957]

would an internal shoulder by much different to an external shoulder (from a Kt point of view) ?

ESDU 89048 has a tube in torsion with an external step.

 

[dhengr]

TTT:
Thanks for the pdf, that truly is a beautiful visual, I’m glad I asked and patiently waited for the new attachment. My problem is that I don’t have every type of software on the market to up load attachments. But, I have already made a copy and plan on framing it this afternoon. Any chance of getting you to sign it, so that someday it’ll really be worth something? You know Rembrandt, and those guys... Now, for my take on your problem....

How is the shaft really loaded? Forces, moments, locations, stresses, etc.? That step would cause a stress raiser as related to bending or shear stresses in that region. But, much less so for torsional shear stresses which tend to flow with the shape of the round shaft, in a tangential orientation. They are max. out at the shaft surface D1 and less at D2 and at that shoulder/step. They also do not tend to cycle to the same extent or in the same way as bending stresses do. On the other hand a shear key could be a killer w.r.t. torsional shear stresses, and less so w.r.t. bending stresses, except where they try to bend around its square cut end. I would try to put a small radius at that shoulder/step, or an undercut radiused relief cut. I’d have to dig deeper to comment any further, and you would have to provide much more design info. too.

 

[TerribleTerryTate]

rb1957:

That's what I'm not sure about. I'm tempted to use the data for an external feature, but I haven't been convinced that the values will be the same. Close? I'd wager yes. The fact that I can't find tables for the internal features also makes me believe they might be the same.


dhengr:

I knew you would be impressed. I'd be more than happy to sign it. Who should I make it out to? Also, the original bitmap should be able to be opened by a wide array of fancy shmancy softwares, like MS Paint, and whatever image previewer Windows comes with.

But! Back to the problem!

The shaft really is loaded in pure torsion only, with the torque vector coaxial with the part. In my design I have a generous radius in the section where there would be a stress riser. What I'm designing is a torque tool for installing a locknut with a substantial amount of torque. I plan on FEA'ing the whole thing, but I'm required to have some hand calculations as a basis for comparison.

Is there any other info you would like to know about the design? The help is much appreciated.

 

[dwallace1971]

Why don't you FE the internal feature and a similar external feature, compare the Kt's. If they're similar use that as the basis for using the hand calcs for the external shoulder to analyze the internal shoulder. If they are not similar, at least you will have eliminated one possible solution to your problem.

"On the human scale, the laws of Newtonian Physics are non-negotiable"

 

[dhengr]

TTT:
Torques, dimensions, mat’l. props., all the info. I asked for in my earlier post. How is that large torque applied to this shaft, where, at the left end, and then what’s the torsional shear stress in the thinner walled length of shaft? What stress levels? Is it applied at or to the right of the shoulder/step and what’s the torsional shear stresses? Is the length of shaft with D2 just an aligning feature? Is the D2 length of shaft actually a broached square or hex female fitting? The corners btwn. the six flats would be thin spots and sensitive to torsional stresses. Still maybe not really serious stress raisers, witness the few failures of sockets we use every day, with a cheater pipe on the wrench handle. What’s the difference btwn. a std. hex socket and a heavy walled impact wrench socket, for our own edification? Any radius at those corners conforms with the outside dia. of the shaft and the generally smooth flow of the torsional shear stresses. I dare say, that the more likely failure force/stress at that location is due to a compressive force and bearing stresses which are primarily (almost) perpendicular to the outside surface of the shaft. And, finally a combined stress problem at that location. These forces times the dim. across the flats equals the torque applied. Your drawing, as beautiful as it is, doesn’t show any of this, or a generous radius anyplace. Get on the stick, you are not presenting your problem very well.

And, what are the consequences of a shaft failure, or of testing this device to failure to verify its strength? You can “FEA’ing” the hell out of this whole thing, and then your next question will be, what is a Von Miese stress, and why all those red and blue colors. And, nobody seems to be able to make much sense out of these either. And, you won’t be that much smarter about how this really works and fails. If in the process of using this shaft you can apply a lateral loading or moment, that will likely have a more detrimental effect.

 

[TerribleTerryTate]

dwallace:

Thanks for the suggestion. That's sort of where I'm headed at this point. I was hoping there would be a simple answer. But alas! I'll report back if I learn anything useful.

dhengr:

But, but, I'm not asking for help with the full analysis of the problem! I'm only presenting the very specific subset of my problem with my beautiful diagram because I think I have a good handle on the remainder of it, von Mises stresses and all. I was just surprised to find there seems to be no handy-dandy references on stress concentrations on internally stepped shafts.

Thanks again!

 

[rb1957]

i'd've thought the key geoemtry was the change in thickness (and the root radius) ... whether it's stepping in or out should be minor ... though i'd expect the internal shoulder would be slightly lower than the external shoulder as the stress increases away from the CL (no?) ... on 2nd thoughts maybe shear stress due to torque is constant through the thickness (and zero on both surfaces) (yes?) so then they'd be very similar ...