Helical Compression Spring with Elliptical X-Sxn

[ivymike]

Hello all,

Does anybody have a reference that gives spring rate (stiffness) of helical compression springs (valve springs) made of wire with an elliptical cross-section? I've derived a formula on my own, but it doesn't agree with a formula that I found in an ASME paper. The ASME paper doesn't give any background (it is primarily concerned with stress levels in the wire), it simply states that the formula is obtained by modifying standard formulae. When the major and minor radii are set equal, our formulae are mathematically identical, but for truly elliptical sections they are not.

I'm currently awaiting measurement info from the hard parts. That should tell me who's right, but I'd like to have another "theoretical" reference to compare with, especially in the case that I'm wrong. The elliptical wire case is just a stepping stone towards my true goal, which is to develop a formula for springs with a peculiar wire cross-section, so it is important that I gain an understanding of the physical principles involved. I thought I had the problem all worked out, but then I couldn't reconcile my formula with the reference material.

A derivation would be particularly appreciated. If anyone is interested in looking over my calculations, I can pdf the sheet and send it via email. I can be reached at ivymike1031@yahoo.com for this purpose.

Any help would be appreciated...

 

[GregLocock]

i think I understand how a round wire coil spring works - I've designed many sets of road-springs (not valve springs) and have generally found the standard references fine for round wire, with a slight modifier. On the other hand I've never derived the formula from scratch - I think Timoshenko does.

So, guessing - basically the spring is a torsion spring, therefore you should be looking at the torsional properties of the cross section, and the torsional modulus of the material. You may need at the least to add a deflection related term to account for the additional bending contribution of a flattened ellipse as it twists into a new orientation.... quite scary. Can you compare your results to a non linear FE model?


Cheers

Greg Locock

 

[ivymike]

Thanks for the suggestion Greg, I'll have to check my Timoshenko book when I get home. The FE guys here balked at the suggestion (it was one of the first things that came to mind) so I guess I'm out of luck on that route. Here's a link to a pdf showing the method I used, and the trouble I'm having:

http://www.geocities.com/compact_enthusiast1/spring_eqns.html