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# Hex torque strength

## Hex torque strength

(OP)
I have done mechanical testing on a set screw with a 4mm hex and its driver. I now have a set screw with a 3mm hex. Without the time and expense of making parts and testing, I want to know the percentage decrease in maximum torque that the set screw and/or driver will be able to withstand on the 3mm hex. I am getting a torque limiting device and I need it to be used for both set screws and I don't want it to strip the hex on the 3mm driver by being too large of a value.

If the materials and hex depth do not change (only change is 4mm to 3mm hex), what decrease do I expect to see in the 3mm hex?

Thanks,
sbbiomed

### RE: Hex torque strength

for the sress in the threaded section

the area of the 3mm divided by the area of the 4mm.

areas being f(d^2)

3^2/4^2 = 9/16 ~ 56%

but you state your limitation is in the key fit

### RE: Hex torque strength

If the manufacturer changed the hex from 4 to 3 mm but didn't change the size of the screw, I suspect he expects you to apply the same torque for the recommended screw tightness/load.

Or you could estimate that for the same force on the corners of the 3mm hex requires 75% of your 4mm test torque.  Guessing that failure is the rounding out of the hex socket in the screw or rounding over of the corners on the hex driver.  The force torque arm of the hex is reduced from 2 to 1.5mm.

Ted

### RE: Hex torque strength

Hi sbbiomed

The resistance of the plain circular section of the screw to
torsion is given by:-

J= 3.142 * d^4/ (32)

where d = root dia of thread

therefore if you have a 3mm dia and a 4mm dia then the ratio
of resistance to torsion is:-

3^4/4^4 = 81/256

desertfox

### RE: Hex torque strength

I don't think byrdj and desertfox answered the correct question - they are assuming torsional failure of a cylindrical shaft.  I think hydtools has identified the correct problem (rounding of the hex feature), but he assumes a linear relation, which I think is wrong also.  This is the only reference I have seen for torsional strength of a hexagon feature:

G. S. Case, "Stresses on Bolts-Nut Dimensions-Wrench Design:, Mechanical Engineer

This reference uses the equation:

TH = CH · WAF2 · WR.H · UTS · NC

where

TH is the hex torque capacity
CH is a constant (=0.103)
WAF is the width across flats
WR.H is the wrenching height
UTS is the ultimate tensile strength
NC is the number of pairs of driving contacts (NC = 3 for a hexagon)

So for your example, WAF goes from 4 mm to 3 mm, so TH,3 is reduced to 32/42, or 56 % of TH,4

Regards,

Cory

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### RE: Hex torque strength

(OP)
Thank you all for your help.  I was not concerned with the threads or the cylinder failing.  What I was concerned with is the hex tip of the hex driver only (the set screw is made of Cobalt Chrome and will not strip, whereas the driver is Stainless Steel).  The manufacturer did not change anything as I tested the 4mm hex and now need a 3mm hex for a different set screw, but don't want to spend the time and money to test the 3mm hex driver, but want to calculate its maximum torque based off the testing of the 4mm hex.

Corey and Bryjd both came up with 56% reduction in torsion resistance, but by different ways.  Hydtools has the correct problem, but simplified it too much as just a linear change.  I will use 50-56% and I should not go wrong.

Thanks

### RE: Hex torque strength

sbbiomed, your choice of 50-56% is conservative and should result in not causing your hex drive to fail.  Are you sure that the lower torque will result in the setscrew performance you expect or need?  We don't know what you expect the setscrew to do or what the failure mode you tested the 4mm for.

My linear approach relates to the load on the hex corners and not the loading across the crosssection of the hex.  Of course the stress on the crosssection varies as the square of the hex size as other responders noted.  The force on the hex corners varies directly as the size of the hex.  The corners transmit the torque from driver to screw socket.  Excess force on the hex corners causes hex socket rounding out or hex drive rounding over.

At 50-56% of the 4mm data you should not have the 3mm hex drive break or the hex drive corners rounding over.

Ted

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