Re: Break down, go ahead and give it to me.
“johnfoss” <johnfoss@NoEmail.Message.Poster.at.Unicyclist.com> writes:
> Based on all of this, it looks like bolt-on cranks may not be a good
> idea for unicycles. I was surprised at the size of the hole in that
> first picture. There’s a lot less metal there to take up the stress
> compared to a solid axle.
Oops. Should have read this before my last post. In response to your
question, I calculated the (relative) strength of the axle.
The short answer is tubes are really quite strong and you only lose
about 8% of the strength by hollowing out the axle. Any loss of
strength of standars square taper axle may be unacceptable for
hardcore use, but then the square taper (in standard materials) may be
unacceptable anyway.
Now, the question I have is whether cutting threads into the axle
weakened it.
[GEEK WARNING: Read on at your own risk]
The long answer is that bending strength is limited by the maximum
stress exterted on the axle, which will be at the outside of the bend
(in a smooth walled tube). For hollow axles, that stress is
proportional to
T / (od^4 -id^4),
where T is torque (from the crank), od is the outside diameter and id
is the inside diameter of the axle. For solid axles, it is just
1/od^4. Looking at the picture of the failed axle, I estimate od=4.3w
and id=2.3w, where w is the wall thickness at its narrowest. Fixing
maximum stress and cancelling terms yields:
T_solid/0.0029 = T_hollow/0.0032, so
T_hollow = 0.92*T_solid
The maximum torque for the hollow axle is 92% of that for the solid.
In reality, the situation for the hollow axle is even better. This
calculation is for a round axle, and doesn’t take into account the
extra material forming the square taper. That material effectively
increases the outside diameter, making the max torques even closer.
Cutting threads inside the hollow axle is an unknown to me. But I
know for sure that stresses love to concentrate at sharp corners and
if the threads go deep and are sharp, they could easily weaken the
axle. My earlier suggestion of using a longer bolt might actually
make matters worse if threads have to be cut as deep as the crank
sits.
Ken
P.S. I’m Chief Inspector of the Climbing Physics Police (ret.), not an
engineer.