Sharp Radius and Peterson's Stress Concentration Factors

[Penguineer]

Hello All,

I am investigating the safety factor for a keyed shaft under constant torsion and reversed bending, but questions keep coming up:

Our keyways are machined using an end mill, which produces a very sharp radius at the fillet. I know there is no such thing as a zero radius, but this is at least 1/256" if not smaller (

http://files.engineering.com/getfil...48bd-a4fc-589ad4cfefe4&file=Radius_Gage.PNG).

The r/d ratio here works out to be 0.0016 at the most, perhaps even 0.0008 or lower. The charts in Peterson's Stress Concentrations bottom out at a r/d ratio of 0.005 (see attached). How does one determine a Kt in such a case? It's greater than 4, but by how much?

If torsion is constant and bending is fully reversed, does the charts for combined torsion and bending need to be referenced or would only the bending charts be referenced? I ask because the stress concentration is more of a concern in cyclic loading, so I imagine a constant torsion doesn't really impact the life of the shaft. Furthermore, in reversed bending the peak stress will be at the end of the keyway whereas the peak torsion is along the side of the keyway.

In calculating the nominal bending stress in the shaft, is the maximum moment used in the stress equation (32M/pi*D^3) or the moment at the x-position on the shaft that's being analyzed? For example, they keyway fillet in the shaft does not reside in the same x-position of the maximum bending moment on my moment diagram, do I still go with the max moment even though they're out of alignment?

I'm producing an FEA model to review the "true" stress concentration by converging on the peak stress in the fillet (assuming a 1/256" radius). Again, would it be best to look at bending only in this case given that the shaft sees reverse bending and constant torsion? Also, which stress would be most appropriate in determining the peak stress? Von Mises? Max Principle? Normal with respect to the shaft axis? Lastly, in determining nominal stress, would that value be derived from the hand calculation discussed earlier or should it be somehow extracted from the FEA model? If from the FEA model, then where would be a good spot to probe?

Many questions, thank you all in advance for any assistance provided.

 

[rb1957]

there are key-way design standards, no?

it sounds like your fillet rad is much smaller than standard ? why so tight ??

i wouldn't try to FEA the stress concentration; i'd use Neuber (sp?) to account for local plasticity.

appliciable bending stress ? ... design analysis should be clear, to could use the extreme fiber stress (as a baseline, like your Petersen figures do) or it could use the local stress.

another day in paradise, or is paradise one day closer ?

 

[RolMec]

Hello,

- sharper edge radii than standard? --> DONT, & perhaps you don't need that as the key shall be a standard item with resp. radii of its own (am I right there?).
- any kt or other factors "of your own making" would need to be benchmarked against tests, at least if used for serious business (mass prod., safety relevance)
- confirmation / derivation from FEA - solution: Well, there's a challenge. This is a complex geometry, w. overlay effects from contact pressure from key, deflection effects & effects from the hub (stiffness, friction, seat etc.). Surroundings need to be considered.
- somewhere out there this little piece of standard equipment gets full blown calc. standards of its own, e.g. DIN 6892 (G-mny)
- due to the complex geometry, the effects of overlaying bending + statical torsion tau /sigma are not evident: There's a region where lifecycle might even improve. But there's conditions (lots)
- if you're out of bounds of "standard geometry", imo the nominal stress philosophy cannot apply anymore, you need to do a local stress investigation (It's the factors, as you found, which in themselves depend on conditions)
- when i saw cracking, i found cracks start at the transition from head radius to the length of the keyway, at the bottom of the keyway. But this might not be a general rule.

Wish you all the best / success @ your task!
Regards
R.

 

[Penguineer]

Thanks for your input. Could you advise which standard is being referenced in regards to the radius of the keyway of a profile cut? ANSI B17.1?

 

[geesamand]

According to several shops I work with, radiused broaches and keyway mills are now a special order item. Most shops that do keyways do them with sharp corners.

IME the internal radius is critical only for harder materials. For materials with ductility the effect is small.