My problem involves calculating spring back in a laminated setup. I've found a formula on the web, but it only tells you how much spring back you can expect if you use X number of plys and bend them over a given radius.
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?
I have done a great deal of bent wood laminations over the years for circular stair handrails and to my knowledge no such formula exists. It has been my experience that the amount of spring back is influenced by the number of laminates, thickness of the laminates, species of wood, cut of the grain (plain sawn, quarter sawn, etc.), type of glue, and the radius of the bend.
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.
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.
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.
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.
Comment from contributor A:
I have used a very simple springback formula in building laminated ribs and frames in boat building for several years. At first I was dubious and tested with scrap. In perhaps a dozen different laminations from two layers up to six I have had success so I now use my best wood with no fears that the finished piece will come out as intended. Thickness and species of wood do not affect the results, only the number of laminations.
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.