Analytical Methods for Springs

[treddie]

Howdie.
Would anyone happen to know of a good book that explains the dynamics (and statics) of springs?

This is all for a visual I need to build; it's not for building an actual spring, although I will be building it in ProE, nonetheless. That is, once I can get a fairly accurate plan view of the spring windings, by building a VB program to generate it. I'll then save out as a DWG to import into ProE for a trajectory, along which the spring will follow.

Here's the problem:
Visualize a flat spiral spring of, say 20 turns. It has an axle, ofcourse, perpendicular to the direction of the spring's turns. Put one end of the spring axle in a hole in a tabltop so that the axle is sticking straight up out of the tabletop. The plane of the spring turns is now parallel to the tabletop. Now, push on the spring itself, pushing parallel to the tabletop, using your finger. The windings compress on that side of the spring, and expand on the other. That is the shape I am trying to model.

Although it is easy to find general equations for springs, it seems to me that any deformations that
are forced on the spring requires an analytical approach. That is the kind of info I can’t seem to locate.

Thanks in advance,
treddie

 

[sreid]

This is pretty "Primitive Pete" but I'll bet that the deflection at the end of the sprial is close to being the same as if you treat ther length of the spring wire as a straight cantilever beam.

 

[treddie]

That makes sense to me, but doesn't that modelling grow more and more inaccurate as you look at the areas approaching 90 degrees to the applied force (where the spiral arms begin to wrap around to the other side of the spring)? In other words, if I take a thin metal, circular loop (or a hollow cylinder for that matter), lay it on a table and compress it from above, the top and bottom seem to act as reverse cantilever beams, but the sides act as their own cantilever beams as well. But the sides are decreasing their average radius of curvature while the top and bottom are increasing their average radius of curvature. To make that model more accurate I could break the spring up into a zillion cantilever beams, but my experience with numerical integration falls way short of my differential calculus. I really want to learn this, but just can't seem to find the articles that solve this type of problem.
treddie