Stress on strap wrapped around a drum 3

[random_guy]

Sometimes it's the easiest problems that give you the most trouble...

I'm estimating the fatigue life of a thin load carrying strap that's .008" thick and .75" wide, wrapped around a Ø0.1 m drum.

Fatigue from axial loading is as expected (10^9, not a high axial load).

For stress due to winding around the drum, I'm using the simple flexural stress equation: σ = E*c/ρ
You can't screw that calc up.

Stainless steel material. E = 193 GPa
c = 1/2t = 0.5*.008"*25.4/1000 = .0001016m
ρ = .05m

σ = E*c/ρ = (193e9 Pa)*(.0001016m)/.05m = 392 MPa

Sy is 207 GPa
Sut is 517 GPa

According to this calc, I'm nearly double Sy, well into the plastic range, and I should be seeing ~5500 cycles to failure.

Testing, however, has demonstrated around 100k cycles.

I'm at a loss as to where I've steered wrong. I even dug out an old strengths textbook and there's nearly an identical example with the same results.

Thoughts? Thanks in advance.



Wise men learn more from fools, than fools do from the wise.

 

[btrueblood]

You sure about that? Stress relieved is a more likely condition for .008 thick stainless strip, fully annealed would be a lot more expensive than "as rolled"...

 

[random_guy]

Here is the material spec I have. It states annealed.

Wise men learn more from fools, than fools do from the wise.

 

[random_guy]

If I'm getting 50% more tensile strength, that bumps my fatigue calc up from 5500 cycles to 75,000. More in line with our failure rate.

I think the material properties are greatly understated.

What a rabbit hole this has become....

Wise men learn more from fools, than fools do from the wise.

 

[random_guy]

I spoke to the vendor. Those values are understated. Tensile as tested is 90-100ksi depending on the batch. Yield is around 40ksi. Coupled with conservative estimates in my fatigue calc, this solves my problem.

Big thanks to everyone for your input!

Wise men learn more from fools, than fools do from the wise.

 

[FACS]

[But there is a separate stress related to the bending of the material as it passes over the drum. That's where my discrepancy is.]

During the wrap around the drum, the strap will be split into three different zones. The outside (top) of the strap will be in tension at 2X the normal tension.
The center will be a neutral plane
The bottom will be in compression. All the tension that used to be in this section are transferred to the top of the strap.

The strap section that is not around the drum will have equal tension throughout the strap.

 

[dvd]

Neutral axis is not necessarily at mid-plane.

Also, could find good info on stresses related to bandsaw blades and wheels.

 

[btrueblood]

Random-guy: Good job bird dogging that data back to the vendor. It's why I joggled your elbow - full anneal is expensive (need a lot more time at temperature) relative to as-rolled or stress relieved or other monikers for run-of-the-mill material.

 

[random_guy]

The vendor states that the material is fully annealed. I asked if they considered stress-relieved to be annealed, and he said no, it's a full anneal.

Who knows.... I got my answer regarding higher tensile and yield strength, and that satisfied me.

Wise men learn more from fools, than fools do from the wise.

 

[btrueblood]

Hmm. "Full anneal" might be per spec., which might not be enough time to fully remove residual stresses in a coil of thin sheet. Or, like with spring wire, the thinner material gains strength from the winnowing process (stuff that breaks in the mill when rolling gets tossed out, leaving higher strength material to survive).