Springback formula for bent laminations
This is nice, but hardly ideal, as it doesn't offer a way to calculate what radius to make the form in the first place to wind up with the desired finished radius after spring back.
By using a little trial and error in Auto CAD, I've been able to come up with the right answer. This approach, however, is as inelegant as it is time consuming.
Since the answer will probably involve some form of trigonometry, if the formula could be provided in spreadsheet form, well, how could it get any better than that?
What we normally do is build a bending form, laminate a test piece and then adjust the form as needed to compensate for the spring back.
We are making a part that will receive an aluminum extrusion and clamp it on a curve as it comes out of the extruder.
I asked the company doing the bending if they had a formula for spring back. They said they did but it was a very complex formula and then it was only a starting point and they ultimately had to just bend the material and measure the spring back. These guys specialize in dealing with bent metal parts for airplanes, etc.
Actually, there is a way around this problem in some circumstances.
We occasionally do a method I refer to as "steam/lam". We'll take our laminations and steam bend them to approximate radius prior to laminating. This simply takes the springback out of the strips so there is no springback issue in the final product.
Just yesterday I steam bent some 1/8" x 6" x 30" cherry to a 24" radius. It sprung back to about a 30" to 36" radius when I removed it from the form.
This morning I glued it up (Titebond 1) and put it back on the 24" radius form and placed it on the vac press. When I removed it there was no springback whatsoever.
It is a far cry from "straight" to a "slightly larger" radius when making the bend, and the effort of adding the steam bending step far outweighs the possibility of having to start the whole process over when the part comes out wrong.
Doesn't the species have something to do with this formula? What about when making curved reception desks, ie bandsaw or CNC plate on a radius and then add bender board and finally a layer of 1/4 MDF to glue veneers to successfully. After reading the responses I wonder if it really exists.
I have used a form of the formula "deflection=archeight/(lams*lams)" for years with varying results. It is not perfect but it is better than not using it at all.
The problem is that the formula does not tell you what radius to begin with. I tried every trig trick I know to come up with the corrected radius but was not successful. So I wrote a recursive program that "guesses" the initial radius before applying the springback formula and testing the result for the final radius. If the result does not match, it is adjusted by a calculated ratio and reapplied until the target radius is matched. The recursion takes from 8 to 20 loops to arrive at the correct answer and the initial radius is captured.
The comments below were added after this Forum discussion was archived as a Knowledge Base article (add your comment).
Comment from contributor A:
This is a working tool. CAD should detail the finished results as this is a fabrication method, not a design tool. The basic formula is y=x/n2 (n2 meaning n squared), (x is the vertical distance between the chord and the top of an arc), (n is the number of laminations) and y is the amount of springback, or the amount x will be reduced after the laminations come off the mold.
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