Spring rate of a single split cylinder

[nickjk]

I have a 1" O.D. cylinder with a 3/4" I.D. that is 1 3/4" long.
The cylinder has a slit on one side at full length.

Uniform force will be applied to the O.D. of the cylinder to make the cylinder close in.

I am trying to relate the uniform force to close-in the split cylinder to the change in the outer diameter of the cylinder. Like a spring rate.

Any help to create a formula or free body diagram would greatly be appreciated.

Thank you

Nickjk

 

[MikeHalloran]

You could get truly uniform force with hydraulic pressure on the outside of the cylinder, but that requires there be no slit. There are equations that will allow you to compute the shrinkage of a cylinder under uniform external pressure, as in submarines. But your cylinder will not be that stiff.
... until the slit closes.

So, how do you apply uniformly distributed force to the outside of a split cylinder? I'm drawing a blank on that.

For a first approximation, I'd mentally unwrap the cylinder, and think of the problem as a uniformly distributed load over a plate. ... but that gives a fictitious reaction force.

For a second approximation, I'd mentally unwrap the cylinder, and think of the problem as a uniformly distributed load over _half_ the plate, with the plate/cylinder fixed at the plane of symmetry.

This is starting to make my head hurt...


Mike Halloran
Pembroke Pines, FL, USA

 

[nickjk]

Hi Mike,

I was trying to simplify things a little.
The outside of the cylinder is actually a taper.
The inside of the cylinder is a bore.
The uniform pressure to the outside is applied by a mating detail with the same taper but no split. As the mating detail travels the tapered cylinder closes in.

What I am really trying to find out is how much force is required to make the mating detail travel a certain amount.
Think about it as a collet in a pre-loaded condition.

This makes my head hurt too, sorry.

I could draw a sketch if it would help.

Thanks,

Nick

 

[nickjk]

Below you will find a sketch for what I am trying to solve.

Thanks

Nick

 

[MikeHalloran]

Got it. Head still hurts.


Mike Halloran
Pembroke Pines, FL, USA

 

[sbozy25]

Why not treat the tapered split ring like a series of internal retaining rings. Start at the end and break it into however many pieces you wish, then run the calculation required to compress the ring from free to the ID of the bore. Plot the results on a graph and you should be able to find the force required at the location you need.

Make sense? My head now hurts....

Cabbages, knickers, It hasn't got A BEAK!

 

[bradleyelwood]

There are quite a few industrial taper lock collar assemblies that may come close to the split-tapered collet you describe. Look at b-loc or ringfedder or QD hubs or Dodge. Then look at their draw bolt loads necessary to provide a certain clamping force or torque on a shaft. This may not answer the exact question you are asking, but I think it may help.