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# Round Cylinder as a spring

## Round Cylinder as a spring

(OP)
If I have a round cylinder that I was to use as a holder for an object with clearance between the object and the cylinder I.D.

If I apply a uniform pressure to the outside of the cylinder to contract or close the I.D. to hold the object.

And I have calculated and confirmed during testing the amount of applied pressure needed to remove clearance.

I would like to look at the round cylinder as a spring in the sense of I.D. closing and be able to have a formula to calculate the efficiency of the spring so I can compare different designs.

The formula should take into account the wall thickness, material, pressure to remove clearance, clearance

Any thoughts or ideas where I could get information would greatly be appreciated.

Thank You,

Nick

### RE: Round Cylinder as a spring

Roark's Formulas for Stress and Strain, Warren C. Young, has formulas for cylinders under internal and external pressure loading, and for toroids and partial toroids under various loadings.  Beyond those resources, you may want to enter the realm of finite element models, especially as treating the end fixity of your cylinder will be difficult by classical formulas & methods.

Realize that, at some level of distortion, an inwardly-deflecting cylinder or toroid becomes unstable and may buckle.  Before it buckles, the distortion may not stay concentric to the original axis of the cylinder.  Both of those notes are from experience.  And the problem becomes even less tractable if you use elastomeric materials, with their own non-linear behavior, as the basis of your spring.

Good luck.

### RE: Round Cylinder as a spring

Several kinds of commercial metalworking chucks have used the same principle for decades, both for holding workpieces and for holding tools.

There's a lot of commercial value in good chuck designs, and a lot of fallacious claptrap that passes for 'lore', so you may want to triple check any magical equations that you come across.

Mike Halloran
Pembroke Pines, FL, USA

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