The above picture is solution to the diffusion equation 
English Translation: If you imagine a metal bar heated up on one side, as time progresses the temperature will even out. This is a plot of the temperature with one side being the length of the rod and the other being time.
But that’s probably not too interesting to most people reading this post. The interesting things is how I got the multi-colour object.
It was made by feeding one short piece of filament into the printer after another, during the print job. It was surprising to see how nicely one colour faded into the next.
Unfortunately, this broke the hacklab.to Break-R-Bot Maker Bot. The problem was that there was a sharp point on one filament that deflected the next one to the side. It was easy enough to fix (thanks to Rob for helping me!), but it seems like a bad idea to test it again oh the hacklab printer. I’m building my own, so the experiments should continue in a few weeks, anyway.
It seems like the problem should be possible to avoid as long as one makes sure that the filaments have flat ends. I am also planning to experiment with using a hot air gun to fuse pieces of filament.
(Thanks to Stefan for taking the picture of the models for me!)
Tags: 3d printing, hacklab.to, math, multi-colour printing, PDEs
December 8, 2010 at 20:49 |
Huh, pretty neat. Good old initial value problem for the heat equation. Most of the time the solution is an equation on paper, or the data stored inside the computer, or a 3d-picture on the screen, must be fun to have it turned into something fully material. But it doesn’t actually start at time=0, does it? – the far side of the model looks pretty smooth, and your initial value function has a jump in it.
December 9, 2010 at 17:51 |
Well, I have rather limited resolution when I print them, so it doesn’t come through very clearly. But the models clearly have a discontinuity, it’s just that when they get cut into layers and filled, that detail is lost.
It’s more visible on larger prints.
December 16, 2010 at 22:15 |
Keep in mind that slight changes in diameter of the filament are actually huge in terms of the flow rate changes. Since it’s not easy to adjust for this during printing, this is recommended for artistic purposes, but the objects themselves cannot be as reliable as a well-tuned single color print.
December 18, 2010 at 05:42 |
That’s a very good point. Thank you.
The ideal solution is, of course, multiple extruders and then implementing CMYK or something, but this is a good hack until then, even if it puts substantial limitations on the quality of printing that can be done…