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Heating the print surface: doing the numbersThursday, November 27. 2008
Scaling up Metalab's heated printing surface...
Recently, Marius, at Metalab in Austria, reported that printing onto a heated surface solved the problem of getting plastic to stick AND greatly reduced warping of the printed object. As you might imagine this report drew a considerable amount of interest, since warping has been one of the most serious technical challenges faced by the Reprap project.  Metalab simply placed a layer of what appears to be mineral fiber cloth on top of their particle board working surface, placed what appears to be heavy gage nichrome wire on top of that and then placed a single sided raw printed circuit board, copper side up, on top of that. From the placement of the power clips it appears that they attempted to heat the whole surface. My first problem was to determine the area that they were trying to heat. The configuration looked familiar, and in this picture from Marius' blog he was attempting to print a standard old-style Mk II filament guide. I prototype my controller boards, as a rule on Euroboard scaled stripboards, those being easy to acquire where I live. I pulled a spare Euroboard and a filament guide from my stocks and quickly determined that Metalab was also using a Euroboard scaled printed circuit board.  What that means is that Metalab was heating a 10x16 cm surface. At the end of Marius' blog entry he demonstrates a second pass at the design problem. 
Here you can see that they've simply sandwiched the nichrome between the
fiberglass sides of two Euroboards. It's an elegant solution at that scale if
not particularly energy efficient or scalable. What is important, however, was
that for this design they gave parameters for the nichrome heating element that
they used successfully. Doing a quick scaling of that load to Tommelise 2.0's working surface, 12x12 inches or ~930 cm^2, the scaling factor works out to... 930/(10x16) = 5.8 That means that to heat Tommelise's full print surface I am looking at... (25 Watts)(5.8) = 145 Watts. Given that Tommelise 2.0 only draws about 20 Watts max while operating, that is a rather huge additional amount of energy to use. Because of that, I decided to do some quick calculations to see if I could see a way clear to get a better handle on this problem. To begin with, Metalab is radiating off of a clean copper surface. That gives you an emmisivity of about 0.1. Assuming an ambient temperature of about 20 C, a heated surface of 120 C and applying that information into an expression of a formula for radiant exchange which assumes an ambient emissivity of 1.0, you plug numbers into an expression like this...
At a similar temperature differential one would expect natural convection losses in a still air environment  M. Yazdanian and J. H. Klems, Measurement of the Exterior Convective Film Coefficient for Windows in Low-Rise Buildings, ASHRAE transactions, v100, Pt. 1, pp 1087-1096, 1994. to be running something on the order of 2-4 Watts K/m^2. For our work surface this would be on the order of 10-20 Watts/side. That would mean that we would be looking at a total energy demand of around 30-50 Watts for a Metalab configuration in a still air situation. Kick the convection level up to, say 4 meters/second as we do when we direct an air stream at the top of the printed surface and your convection contribution would increase by a factor of five on the top side of the heated surface. With such a configuration you'd be looking at... 9 Watts (radiation) + 10-20 watts (bottom side convection) + 50-100 Watts (top side convection) = ~70-130 Watts Metalab chose copper as their print surface. Providentially copper has a
very low emissivity (~0.1). If they had used anodized aluminum instead, they
would have been looking at a radiation fraction for a single side of around 70
Watts. Similarly, if they had printed a raft across the whole top side they
could expect to be an effective emissivity of the top of the raft of 0.95 which
would have raised the radiation contribution of that side to just over 80
Watts.
Obviously, we can greatly improve on the performance of the Metalab design,
which was purely exploratory in nature. Insulating the bottom half of the
printing surface would effectively reduce the energy demand by a bit less than
half.
With respect to materials, while the printed circuit boards have the
rigidity to handle surface deflection on a Euroboard scale, I doubt that they
can be reasonably expected to do so at wider spans given the depth of the
boards. Cross-bracing under the printed surface assembly should, however, put
that right. Another question remains as to how the fiberglass printed circuit
boards would handle 100 degree heating and cooling cycles over a long
period.
The one thing to remember is that while the heated printing surface offers
us a technical fix to the warping problem that is unlike anything developed
heretofore, it has substantial energy requirements. Taking such an option would
pretty much put paid to the notion of Reprap machines operating off batteries in
a third-world environment.
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This was my first reaction for warping, heat it for longer.
Heating can reduce warping because shrinking occurs later. This is obviously a way to improve quality. I wonder what will happen when heating the TOP layer would, but not the whole object would work better. So a radiating hot nichrome wire around the head where you're printing. The problem is not to get things too hot, that's why we're cooling anyway. Otherwise you get another level of warping: melting during printing.
After the first few layers have been printed you should be able to start reducing the current to heater for subsequent layers until eventually you can shut the heater off altogether.
That won't change the system's peak power requirement but it should substantially reduce the total power requirements for building a part.
As far as energy requirements for heating go, one could always design a combustion based heater for the battery version.
While less convenient then electric heating it would be fairly easily available world wide. One might even get it for "free" off the waste heat of an electric generator powering the rest of the RepRap.
Awesome work!
I just wanted to add some more bits of info.
it does not relly improve the sticking unless its really hot (at least not with copper). You can get it to stick but only with a raft (because thats so regular that it sticks easier). But if you do a raft the raft fuses with the object (because of the heating) So you would really like to skip the raft. Other materials than bare copper could solve this problem.
I should also write this to the wiki...
Thanks for the clarification on sticking! That's valuable information. I appreciate your sharing it with us. You really need to do an extended entry on your work on the main Reprap blog so that the whole developer community can benefit from your breakthrough. :-)
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