thin strip metal springs 2

[nigelt]

I posted this in Electromech Design forum some weeks back but nobody took up the gauntlet. Any clues from this group, please?

....A recurring issue is doing the engineering calculations for cantilever or beam type leaf springs, where the &quot;width&quot; of the spring cross section is large in relation to the &quot;height&quot; of the section. The standard formulae assume that deflection is small wrt the section, but in our case the deflections are typically large. As an example the strip from which the spring is stamped and formed might be 0.125in. wide, 0.015in. thick, maybe a 0.5in. cantilever and, in service, will go through say 5000 cycles of 0.1in. deflection. Material might be spring steel (plated), or, Ph/Bronze, or< Be/Cu or St. Stl ( all h. treat'd).
Any direction vis-a-vis the best approach, any texts etc that would help us?
Thanks folks!........

There you go. Any comments welcome &quot;The ideal client is one possessed of great good sense and perfect judgement;
that is to say, one who agrees entirely with the designer at all times and in every respect.&quot;
Fenwick Williams, Naval Architect.

 

[sancat]

One way is to way to go for finite element analysis. But this is too much for a so simple problem.
Another way would be to divide the beam in your own <<finite elements>>, by dividing your cantilever in several small pieces, and computing X,Y and slope at its beginning, and at its end. It is not actually finite elements calculus, since it will not use the energy approach, but, with some analytical geometry formulas and an excel spreadsheet, you could add the small deformations for this small pieces along the beam, and modify the acting forces direction.
Finally, you could use second order structural analysis. A Timoshenko's structural analysis book should have the formulaes.

Sancat

 

[TVP]

The following information is from the Associated Spring Design Handbook (1987 Edition):

&[ignore]sigma[/ignore]; = 6PL / bt²

where &[ignore]sigma[/ignore]; is maximum stress
P is force
L is length
b is width
t is thickness

P = fEBt³ / 4L³

where f is deflection
E is elastic modulus

For flat springs, as the width-to-thickness ratio increases, the lateral deformation that would normally accompany the longitudinal fiber stresses becomes restricted, effectively increasing rigidity of the spring. This increased stiffness is accounted for by replacing the elastic modulus (E) by:

E / 1-&[ignore]mu[/ignore];²

When the with-to-thickness ratio is greater than 10 and the length-to-width ratio is less than 5, this factor should be applied. &[ignore]mu[/ignore]; is given as 0.3 for spring steel.

These equations are satisfactory when the ratio of deflection to catilever length (f/L) is less than 0.3. For large deflections, another method is recommended that uses a correction factor and a chart. The source of this method is given as follows:

Bisshop, K. E. and D. C. Drucker, &quot;Large Deflections of Cantilever Beams&quot; Quarterly of Applied Mathematics, vol 3, no. 3, (1945), p. 272.

You can contact Associated Spring for more information using the following link:

http://www.asbg.com

 

[Speedy]

Nigelt,

Check out this thread, sounds very similar to your query;

Beam calculation doesn't add up.
thread404-28037 Speedy

&quot;Tell a man there are 300 billion stars in the universe and he'll believe you. Tell him a bench has wet paint on it and he'll have to touch to be sure.&quot;