Dedicated Clamping Cauls

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Quite some time ago I had Morris make me up a clamping caul "template". Basically it's a 48" long piece of Masonite with a curve cut on one edge to a radius of 2000.5 (inches, I believe). The goal was to have the ends be 1/8" higher than the center when place on a flat surface. Well just recently I got around to making the actual cauls themselves. I had a bunch of baltic birch rippings left over, so I laminated three pieces together and template routed the curve into one edge. The finished dimensions are 1.5 x ~3 x 40". I made them 40" because that maximized usage of material, and because I needed them for a 36" round table top. I ended up making six of them, and they really worked like a charm. I used them in pairs, top and bottom, but I suppose if you had a really rigid bench you could just use one on top to push it flat. In that case, though, maybe you'd want them a bit wider - say 4" or so.
And, for those who think it ridiculous to go through the trouble of obtaining a CNC'd template to make a clamping caul.....you're probably right! To me a fair curve seems like it should apply more even pressure across the width of the panel, so that's why I wanted it.
Thanks, Morris!
JP
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Jay Pique wrote:

I'm glad they did the job. The nice part about having a good template is that it can be used over and over.
Afterward I wondered if a catenary with that same 1/8" chord height might apply more even pressure...
Thank /you/ for helping keep the lights on. :)
--
Morris Dovey
DeSoto Solar
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Hmmm...that's a question for the engineeers, but I like the way you think. Is that sort of formula easily input into your CNC language?
JP
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Jay Pique wrote:

It's not difficult, but I usually write a simple C language program to write the bulk of a part program - so as to take advantage of the increased precision available.
The mathematical description (actually, several of 'em) can be seen at
http://www.answers.com/topic/catenary
I'm not sure the difference in behaviors of arc and catenary would be significant, tho.
--
Morris Dovey
DeSoto Solar
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Morris Dovey wrote:

Take your choice, a catenary is a special case of a parabola where only the weight of the cable, chain, rope, etc defines the curve.
x^2/a^2 + y^2/b^2 = 1 is the basic formula for a parabola. where the values chosen for a & b define the curve.
Lew
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On Mon, 8 Jun 2009 17:48:21 -0700 (PDT), Jay Pique
...

Assuming a caul with uniform stiffness - EI is constant along the length of the caul - to get uniform pressure along the clamping surface, the shape of the caul should be:
Y = Ymax * ( 1 - 3.20 * [ (X/L) - 2*(X/L)^3 + (X/L)^4 ])
where X is distance along the caul, L is the length of the caul between the clamps at each end, Y is the chord height at any point along the caul before applying the clamps, and Ymax is the maximum chord height at the clamp location at each end.
The clamping pressure exerted by the caul - force/unit length. - is given by
Q = 76.8 * EI * Ymax / L^4
where Q is the clamping pressure, EI is the caul stiffness (E Young's Modulus of the caul material, I is the cross section moment of inertia) and Ymax is the maximum chord height of the unloaded caul at the clamp positions.
Increase the pressure exerted by the caul by any combination of: 1) increase the maximum chord height 2) increase the caul stiffness 3) decrease the length of the caul between clamp positions.
Tom Veatch Wichita, KS USA
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Tom Veatch (Wichita KS US) wrote:

This is information I can use (and I've already backed it up for safekeeping).
Thank you!
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Morris Dovey
DeSoto Solar
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<snip of complex formulas and other stuff I don't understand>
Sweet fancy Moses, Tom - did you just pull that off the top of your head?! Thanks for sharing - I may have to get Morris to translate it into a real live caul sometime!
JP
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"Jay Pique" wrote:

head?!
Now that you see what a total PITA beam deflection calculations are along with the incorrect assumption that the beam is supported on knife edges unless cantilevered, you can understand why stress calculations are used with a serious safety factor derate to CTA, for beam design.
Lew .
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On Tue, 09 Jun 2009 22:40:52 GMT, "Lew Hodgett"

Plus the fact that the algebraic equations result from integration of the governing differential equations which are themselves linearized because the actual non-linear equations frequently do not have a closed form solution in any but the most trivial cases.
All of engineering mathematics is an approximation of the real world but the nice thing about it is that the linearized versions of the equations generally yield conservative results when compared to numerical solutions of the non-linear equations. One of the linearizing simplifications that is non-conservative with respect to deflections is ignoring the contribution of shear deformation. That particular effect isn't usually introduced in undergraduate level courses.
Your point about the assumptions underlying the model is well taken. The simplifying assumptions are rarely a true and exact picture of the real world. That's why it's called "Engineering Approximation" and why "Safety Factors" (civil engineering) or "Margins of Safety" (aeronautical engineering) are always applied to any critical stress analysis.
In response to a question asked in another post: No, I didn't recall that from memory. I believe Albert Einstein is credited with the advice to never try memorizing something that you can easily look up. I went back to an old Strength of Materials text from my undergraduate days in the '60s. The case of a uniform beam, simply supported, with a uniform distributed load is one of the introductory examples of beam analysis..
Tom Veatch Wichita, KS USA
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"Tom Veatch" wrote:

The most dominant design factor is the eyeball.
It's got to look good in the shower.
Look at the columns on some of the monuments in Washington DC.
Ever see a school building with anything smaller than an 8WF35 floor beam.
Still remember my design engineer's comment about bracing ribs on the bed of a threading machine used in a steel mill to thread seamless drill pipe.
"I could use 3/4 thick ribs, they are certainly strong enough, but 1-1/4 ribs look better, and after all, we sell this equipment by the pound".
Lew
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On Wed, 10 Jun 2009 04:09:45 GMT, "Lew Hodgett"

I hear you!
But since I spent most of my working life in the aircraft industry, the "pound" was the arch-enemy! Had to be "hell-for-stout" and light as goose down. Which is why we talked in terms of safety margins rather than safety factors and tested all major structure to failure to verify/validate the analysis.
Tom Veatch Wichita, KS USA
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"Tom Veatch" wrote:

Supplied a lot of front end equipment used for data acquisition systems in wind tunnels, etc.
As I remember, had a couple of customers in Wichita.
Lew
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Tom Veatch wrote:

Who was it, Ed Heinemann? that said "Simplify and add lightness"?
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Morris Dovey wrote: ...

...
OTOMH, don't think so (if I understand the question).
_IF_ the caul were perfectly rigid, the force would be distributed normal to the surface uniformly between the two ends irregardless of the shape.
The real-world difference is how much flexure is in the caul and the mold and how much bending there is between the applied pressure points.
(At least that's the way I initially see it w/o actually writing the free body diagram...)
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wrote:

Assuming the intent is to apply uniform pressure over the length of the caul, use the deflection curve of a uniform beam, simply supported, and uniformly loaded along the length. Since the beam equations are linear - or at least approximated by linear equations - the deflection curve would be a good approximation of the shape of the caul that would give a uniform clamping pressure.
The assumptions aren't rigorously met since the caul doesn't have a uniform cross section if one side is straight and the other is curved, nor is it likely that the material's modulus of elasticity will be perfectly consistent at every cross section along the length of the caul.
Haven't run any numbers but I'd guess the difference in results from using a circular or parabolic arc and the results of the beam deflection equations wouldn't be worth worrying about.
Tom Veatch Wichita, KS USA
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Jay Pique wrote:

I've made clamping cauls with a fair curve on my jointer by raising the outfeed slightly above the cutter height and keeping pressure on the infeed table as I pass the stock over the blades. Having the outfeed table slightly higher than the blades causes the stock to ride up causing the curve.
The trick is then getting the table back to the proper height to produce straight cuts. To do this I mark the table at the ways before changing the height adjustment.
--
Jack Novak
Buffalo, NY - USA
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If you're not sure of the outfeed table height there is one sure-fire way to adjust it dead-on.
Take about a three foot piece of stock that is known to be flat. Joint about an inch or two and stop. Turn the piece around and start from the other end and joint the entire piece. If you can still see the cut from the first end the outfeed table is too high. If you have totally cut off the cut from the first end the outfeed table is too low. If you can barely see evidence of the first cut the outfeed table is, as Goldilocks said, "just right."
G.S.
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Gordon Shumway wrote:

Nice! I'll add this one to my bag of tricks.
Thanks.
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Jack Novak
Buffalo, NY - USA
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Screw a 1 x 2 to the edge of a straight board at the ends. Push the middle of the 1 x 2 toward the board and secure it with a third screw. Run the whole stack through a tablesaw, ripping the bowed edge straight. Unscrew the 1 x 2, watch it pop into a long curved caul.
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