convert linear force to radial force for compression with O-Ring

[loughnane]

I'm using an O-ring as a belt (not a drive belt, like a waist belt), and I want to determine the compressive force that I am applying to the mandrel (or "waist" if we want to stick with that terminology).

I can easily take the length of the O-ring (if unraveled), the length (circumference) of the mandrel, and calculate a strain from those lengths. Where I have an issue is converting that linear load to a radial one.

I know I've seen this equation somewhere ( i thought it was in pressure vessel literature) but can't seem to find it.

Any + All help appreciated, thanks.

Chris Loughnane - Product Design

http://www.pdnotebook.com

http://www.twitter.com/DesignNotebook

 

[Denial]

Consider the free body diagram of a semicircle of your O-ring.

Eastbound you have two concentrated forces acting, these each being the tension (T) in the O-ring.

Westbound, you have the continuous "pressure" loading of the contact force (p – expressed as a force per unit length) directed radially. The vector integral, the "resultant", of this 180 degrees of radial force is easily shown to be equal to pD where D is the diameter of the O-ring, and this resultant has a direction due West. (If you have trouble with this result, think about Archimedes Principle and fluid pressure loadings.)

East-West equilibrium (a good thing in engineering as well as in politics) then tells you that
2T = pD
which is doubtless the formula you have at the back of your mind.

 

[GregLocock]

You probably remember it as the hoop stress

Cheers

Greg Locock


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