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Force of a spring arround a tube

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ceblagu

Mechanical
Apr 30, 2012
3
I would like to calculate the force that a extension spring makes to a tube when is wrapped on it. Imagine a circular tube where you wrap a extension spring so it remains tensed up, pressing the tube surface like a clamp.
So I would like to calculate the force (knowing the K of the spring) that the spring makes on the tube walls.
Actually the tube is not circular but has a "hippodrome" secction, so in the "flat" zones of the hippodrome the spring does not make any clampling force. So I would like to study different tube sections in order to optimize it.

Thanks in advance!

 
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ceblagu:
It will be a compressive line of force applied in a spiral fashion around the tube. It will be a function of the tube and free spring diameters, and it will be resisting the spring’s tendency to decrease in I.D. as it is stretched. Friction will come into play. It will obviously be a function of the tension applied to the spring and of all of the spring dimensions and mechanical properties. Finally, at each of the flat spots on the tube, you will have some free length of spring with some nasty secondary bending stresses induced by the fact that the tube is not supporting the spring. These secondary bending effects will be a function of the internal spring stresses, the unsupported length of spring, the lack of the compressive load from the tube and some very complex partial end fixity at each end of the unsupported length of spring. A pretty interesting thesis problem, and not an easy one to resolve.
 
It is a simple problem, if you take the simplifying assumption of no friction, hence uniform elongation of the spring.
The tension T in the spring is determined of course by the difference in unstretched and stretched lengths.
Now for a circular tube, by a free body diagram of half tube (cut at a diameter) you'll determine that the force per unit length exerted radially by the spring on the tube wall is N=2T/D where D is the outer tube diameter.
For an obround tube (two flats joined by semicircles) you should have the same on the circular portions and zero on the flat. However this means that the radial force drops suddenly from a finite value to zero at the joint between the flat portion and the circular one, and this doesn't sound as very realistic.

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Thank you,
Yes I think the i should assume no friction to simplify. But are you sure the radial for would be 2T/D and not 2T/(Pi*r)?

For the oborund tube, on the flat part the force is zero, and that's the part I want to modify in order to have some force there. Maybe with a circular part or eliptical shape or something like that. But then I would like to calculate how much I increase the force in order to choose the optimal shape.



 
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