Quote:
Originally Posted by jkelleyrtp
Does that mean ThunderHex by Vex is the best COTS option for weight savings and torque distribution?
By your numbers:
ThunderHex is 1/2" in size
.2" central bore
15% less weight by cross sectional area. ((.5^2)pi-(.2^2)pi))/((.5^2)pi)
The central .2" carries less than 2% of the total load?
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Those should be powers of 4, but the result is correct. A hollow round shaft with those parameters is just 2.56% less torsionally rigid than a solid shaft.
The existence of the hexagon-generating surface features complicates things if you care for precise numbers, but from this simplified situation, ThunderHex is the most efficient choice.
What is happening on a molecular level is, the atomic bonds on the outside edges of the shaft are being stretched in plane shear more than the atoms on the inside of the shaft for the same rotational displacement. In addition, there are more atoms on the outside edge than the inside near the center that are being stretched, and therefore resisting the displacement. Coring out the shaft removes the lightly-stretched central atoms while leaving the atoms actually seeing the most stress. Also, consider the stretched bonds on the edge are further from the axis of rotation and thus generate a higher moment.
Out of curiosity I wanted to find the internal radius of a hollow shaft that would maximize rigidity/weight. I calculated the moment of inertia ratio of the hollow shaft compared to a solid one, then calculated the mass ratio of the hollow shaft compared to a solid one. I then calculated inertia ratio/mass ratio. By setting the second derivative with respect to the inner radius equal to zero (maximizing), I found that the internal hole should have a radius equal to sqrt(3)/3 of the shaft radius (or 57.7%), which for a shaft of 0.5" diameter is 0.29" This shaft would have 66.6% the weight of a solid shaft, but maintain 88.9% the rigidity.