## Coil spring stress equation for tubular (vs. solid) wire?

## Coil spring stress equation for tubular (vs. solid) wire?

(OP)

Looked through my Wahl's

Tau = 16PR/(pi D

And a revised equation for a hollow section would be

Tau = 16PR Do/[pi(Do

Any comments regarding the substitution? Does anybody have a directly solved reference for such a beast (coiled tube spring)? Better, does anyone with access to the SMI software know if it can analyze springs wound from tube?

Thanks for any and all help.

__Mechanical Springs__text on how to compute the shear stress in a coil spring when the "wire" is actually a coiled tube. I finally decided to take the "J" (torsional area moment) in the standard spring equation, and replace it with a (Do^4-Di^4) term. More specifically, the "standard" coil spring shear stress equation isTau = 16PR/(pi D

^{3}) {(4c-1)/(4c-4)}And a revised equation for a hollow section would be

Tau = 16PR Do/[pi(Do

^{3}-Di^{3})] {(4c-1)/(4c-4)}Any comments regarding the substitution? Does anybody have a directly solved reference for such a beast (coiled tube spring)? Better, does anyone with access to the SMI software know if it can analyze springs wound from tube?

Thanks for any and all help.

## RE: Coil spring stress equation for tubular (vs. solid) wire?

It looks as if the substitution makes sense. I've searched around and can't find anything having to do with tubular springs.

V

## RE: Coil spring stress equation for tubular (vs. solid) wire?

Thanks for the reply. The reason (don't laugh) is to have a flexible hydraulic tube, in a place where a hose would be abraded and/or possibly subjected to collapse from external pressure. Thus, we need a rigid tube, but flexible enough to extend in the axial direction. The tube spring works, but I am trying to analyze for stresses and fatigue life, given different windings, preset conditions, etc.

## RE: Coil spring stress equation for tubular (vs. solid) wire?

Believe me, I don't laugh at anything (besides homework problems) . Your application makes sense to me.

My inclination would be to say that as long as you're very conservative as far as your axial extension/compression vs. the working length of the "spring", I can't see why they cannot be solved in the same manner.

I see it as being akin to bending a tube vs. bending a solid rod. In the linear elastic portion, they are very similar.

Maybe build in a higher safety factor for fatigue, just for that warm and fuzzy.

V

## RE: Coil spring stress equation for tubular (vs. solid) wire?

http:/

There have been some more recent studies on hollow springs fabricated from reinforced composites. The following are some links:

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The

Meccanicaarticle uses the following formula for maximum torsional stress:τ

_{max}= C_{f}· [16Mt/πd_{o}3(1 − a^{4})]where a = r

_{i}/r_{o}, d_{o}= 2r_{o}, and C_{f}= [4c-(1+a^{2})] / 4c-1. C = R/r_{o}and M_{t}is the torsion moment due to spring compression.## RE: Coil spring stress equation for tubular (vs. solid) wire?

## RE: Coil spring stress equation for tubular (vs. solid) wire?

V

## RE: Coil spring stress equation for tubular (vs. solid) wire?

I have this one, I think is the same as you have, but transformed for easiness of use:

Tmax = 16·Mt/[pi·(D^3)(1-((d^4)/(D^4))]

Where D is the outer diameter and d inner diameter.

Using the next formula you can calculate the tube section equally resistant in torsion to a solid section:

M^3 = D^3[1-(d^4)/(d^4)]

Where M is the diameter of the solid section and D & d have the same meaning as in the previous formula. So you can obtain Tmax for a determined solid section and then, "translate" it to a tube, with the thickness of your choice.

It is interesting to point that, in pure torsion, you always require less area with a hollow section vs. solid section (which translates into lighter components). The problem is that, in turn, higher outer diameters are required.

Localized failure (theoretically) can also be a problem when designing a hollow section spring (crippling of the wall), specially if the forming operation of the spring is not carefully carried out (deformed walls, roundness defects, non-concentricites...), which could not be so uncommon, as bending tube is somewhat more difficult than bending wire or bar.