Awright you mechanical engineering and math types,
More on the high speed spindle, boys and girls. This boy calculated
the bursting speed of the ER collet nuts he want to spin up. It is
much higher than the speed I will be spinning the things. However, the
nut and holder will need to restrain the collet. Doing a very
conservative calculation on the centrifugal force (I know, centrifugal
force is imaginary) acting on one segment of the ER collet spinning at
32000 rpm I get the result of 176 Lbf acting on .05 square inches
which equates to 3520 PSI. There are 6 of these segments if that makes
any difference, though I don't think so. Not for the hoop stress calcs
that is. Anyway, using 3520 PSI as internal pressure, a mean diameter
of .635 and a wall thickness of .109 I get a hoop stress of 10253 PSI.
As near as I can tell this is well below the maximum stress for mild
steel and the nut is certainly stronger than mild steel. I have not
yet figured out how much the nut will tend to expand and I don't know
how, exactly, to go about figuring out what the bending stresses are
at the 12 places where the edges of the collet segments contact the
holder. I suspect this is something not to worry about since the space
between the segments is so small. So are my conclusions close to
correct so far? Please feel free to point out any errors.
Thanks,
Eric