"unfolding" ellipsoidal surface sections

[Audacity]

I recently joined a firm that creates domed ceiling systems as a systems and manufacturing engineer.

One of the projects I have been assigned is to redevelop an existing method for ellipsoidal shaped surfacing. Currently, paper developments are made until the best fit is made by eye. I have been charged with taking CAD data and either making plotted patterns or sending them to the CNC router for production that way.


Here is where I run into my problem. I have no issues with modeling the specific piece of the ellipsoid surface (remember these are domed ceilings), but I cannot flatten it as to make the pattern for the CNC machine/pattern. I know that these are not true triangular shaped pieces (imagine sectioning the ellipse plan view into 8 pieces just for example).

What is the best way to flatten these? I have tried using a couple other packages (SW, 3DS Max, Mesh Unfold, etc) and programs with varied (but poor) results but want to stay in Inventor if possible. I found a few old threads on conical sections that sounded like they related but didn't seem to work for me (v5 vs v11 I guess) Any ideas? (thanks!)

 

[BOPman]

I personally haven't tried to do what you're asking about, but I can tell you that you're seriously limited to what R5 can do versus even R9.

Point being, don't be surprised to learn that you won't have the capabilities to perform the task at hand. Although, I stand to be corrected.

 

[Audacity]

Perhaps I was unclear with my wording.

I have 11 professional. Most of the threads on unfolding have been from previous releases.

I am aware of the engine change from 10 to 11 and have done the registry switch to revert, but then I get an error instead of the model simply turning. It was a glimmer of hope as if maybe my method of modeling was bad, but no luck so far (been trying various formats and methods).

I fear I'm going to have to use a very inaccurate method from a program like 3DS Max with a flattening script (like a skinning script for character painting) or keep on making the paper patterns and developments until it works.

If it helps anyone, I have SolidWorks 2k7 as well and Alias Studio 13.

Thanks BOPman

 

[BOPman]

OK, I understand now...Sorry.

Do you have a model or picture you can upload? It'd be nothing to at least look at and see if I can't give you some kind of answer.

BTW, have you checked mCADforums.com??

 

[Audacity]

I have scanned mCAD, but haen't posted there or anything. That's where I found out about the engine change actually.

Here is a picture of the finished product and a screen grab from AutoCad as far as current methods of drafting for the products...

http://xs216.xs.to/xs216/07243/Ellipse.PNG

(picture of previously done ellipse)

http://xs216.xs.to/xs216/07243/ellipse2.PNG

(plans showing veneer patterns)


You can see in the model that was previously done that the edges are raised on each panel. The goal of this is that the edges line up properly and it can be ground smooth. Without being able to develop the proper curve on the edge, they remain raised (because there is a small iris shaped gap that develops)


Any help is greatly appreciated!

 

[btrueblood]

Wow. Just to get it right - that is a doubly-elliptical ellipsoid (not sure of the terminology but anyway, elliptical in two axes)? Do you press the veneer strips around the outside of a male mold, or into a female mold?

The problem, as you know, is that ellipsoids are not ruled surfaces, so you find a set of facets to make an approximate shape that is "good enough". In math language, you are finding the surface of an elliptical cone that intersects along the ruled lines in your plan view pattern. See wikipedia, "ruled surfaces".

So, the solution is: you find the equations of the edges of the surfaces (this are just sections of ellipses), and then find the equation for the elliptical cones that joins (passes thru) adjacent edges, then solve for the flattened shape of the elliptical cone. That last step is the tricky one.

 

[Audacity]

Yes, the general way to draw the shapes is to draw an ellipse, cut in half along major axis, then revolve around the major axis. The shape is just plain hard to deal with, haha.


As for applying the veneers, they are pressed into a female mold (just purchased a new vacuum pump system to bag these).


I'm thinking that maybe the mesh unfolders for 3DS are the way to go. The calculus on it is nasty for even the arc lengths on each section. It would be incredibly hard to calculate the side drafts to create flat joints too (we're talking about incredibly thick veneers to be ground smooth).


I'm playing in Matlab, Maple, and Mathematica to see if one of them will generate the arc length equations for all of the surfaces and then generate them to just an xy pattern

 

[btrueblood]

Sounds like fun...for a given value of fun!

Seriously, I am tinged with a bit of envy, that's a neat geometrical puzzle to work on. You KNOW there is a solution, but how to grind it out repeatably?

I can probably puzzle out how to generate the arc lengths of the elliptic conic sections once they are defined (step 2, above). But do you have a routine for "flattening" an elliptical cone? (Just tried to get the "sheet metal" modeller in Inventor to flatten an elliptical bend, it chokes. Ha ha, take that Autodesk!).

And oy, getting edges of thick veneer to line up straight?
Hmm. I think I could find that too, but only approximately, by solving the same problem twice (once for the inner surface, once for the outer surface). The problem is that the real wood will distort, but the method assumes no distortion.

What would the customer say if you "cheated" and just vacuum-formed a wood-grained poly sheet? Better yet, don't tell him, just form two or three, cut the ellipsoids up on a bandsaw and glue various pieces from different parents back together!

 

[Audacity]

Haha, I like the plastic idea. We have a thermo-forming vacuum table with the capacity for this... hmmm.

I also considered a massive chunk of veneer and having it milled out with a ball mill =D . Turns out the $50,000 chunk of veneer quality lumber is a problem for my budget.


I'm not thinking Inventor will help me on this one though. I've tried it on 5, 9 pro, 11 pro, and 2008 pro with no dice for any of them.

Thanks for the help and encouragement guys, haha.

 

[btrueblood]

How about doing it as triangular facets (a-la geodesic dome, Buckminster Fuller)? The facets would not need to be distorted, so the math gets quite a bit easier.

 

[Audacity]

Well, in my search for a way to unfold this, I had a great deal of success with converting it to a polygon mesh with 3DS Max (import as an IPT then convert to various mesh styles and resolutions). The end result was very geodesic, unfortunately, the end result of what I'm looking for as a finish on the inside of the dome is "glass."

Perhaps if I could find a way to grind the inside smooth with a gantry system or something to eliminate the interior facets, but that's just more headache I think.

 

[jlcochran1]

You mentioned you also had SW, you might look at Logopress3 for unfolding double curved surfaces

http://www.logopress3.com/en/

Also possibly exporting from Inventor into a trial version of Rhino and trying the "smash" command, although may not be accurate enough.

http://rhino3d.com/