High speed spindle force calc question

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.
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Eric - 2 possible considerations. First, the collet is retained by the tapered section of the spindle, radially that is, ie it is the spindle around the collet that keeps the collet from flying into peices (?) in all directions perpendicualr to spindle's axis. The nut keeps the collect from shooting out the front (bottom?) of the spindle. Now the nut hasn't much to do since the force along the axis is due to the angle along the sides of the collet, which, if memory serves, is 8 degrees. The outward force on the collets pieces whould be multiplied by the tangent of that angle, again if memory serves. Assuming the nut retains the collet via the tapered section on the front of the collet, which is, by eye, roughly 45 degrees, the resulting axial force due to centrifugal forces will push the collect back into the spindle with noticeably greater authority than the other force bearing fordward or out. Anyone who likes to piddle with detail might find the threads retaining the retaining nut to have all sorts of possible considerations. There usually comes a time, however, where the best course is simply doing and see what happens.
snipped-for-privacy@whidbey.com wrote:
Reply to
Hul Tytus
Thanks for the reply Hul, The collet is indeed retained in the tapered spindle. The spindle in turn bears against the nut. When the nut is tightened it not only draws the collet in it also centers on the threads on the spindle OD. So this means if the spindle tries to expand it does so against the nut which then tries to expand. I didn't think about the collet expanding and then pushing against the nut which then makes it tighter. This is good thanks again for the reply. Cheers, Eric
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