When I began playing with 3d printers back in 2009, there was woefully little documentation on how any of this stuff worked or why. It was basically blind faith on my part that the people designing these things even thought about the technical details at all. This phenomenon is no more apparent than in hot ends. Hot end/extruder design has until recently been borderline mysticism. I've seen a staggering number of metals, motors, nozzles, part counts, and heat sinks. Really, it's been everything.
We are really proud of the simplicity of our hot ends, and we fully intend to discuss the whole design at length one day, but for now, I'm going to focus on some thermal analysis to help all the hot end designers and tinkers out there in the world.
Anyone who's used an early desktop 3d printer knows the frustration of waiting minutes and minutes for the hot end to heat up. To eliminate that frustration we designed our hot end to use a low-thermal-mass needle so there is less to heat up, a 24v system so we can get twice the power of traditional systems, and a 40 watt heater so the hot end can reach most extrusion temperatures in well under a minute.
Of course, once you get to the edge of the map, there be monsters. See, in a hot end the mass of the hot end itself acts as what's called an integrator, or in less technical terms, it's the hot water tank in your house. We've essentially made our hot end the 3d printing equivalent of a tankless water heater. As we soon learned, Marlin (the open source control software we currently use) is incapable of sampling at a satisfactory interval to form a really stable control loop. Either from hardware limitations of the chip and board, or software limitations of the code, by the time it looks back at the thermistor, the temperature has changed too much because there is so little material to heat. Most printers have much beefier hot end (bigger hot water tank) meaning they get much more stability, but far less responsive temperature control. And, as an added side effect, we see a much larger difference between our observed temperature and the actual temperature of the part melting the plastic, and as we print more exotic materials these temperatures diverge even more.
The assumption of a uniform temperature hot end works at one specific temperature and a steady-state system, but what about printing with two different materials with very different melting points? It's not all so cut and dry. The hot end's thermal system has many elements, but one really convenient way to analyze them is with what's called the "hydraulic analogy." Since thermal, electrical, mechanical, and hydraulic systems all are solved by similar differential equations they are analogous in many ways. We can take advantage of the substantial literature available on circuit analysis, and simply translate our not very well understood thermal system to an electrical one. Heat doesn't transfer through different elements of a system perfectly, and that resistance to heat transfer is exactly analogous to electrical resistance, so the hot end at near steady-state conditions can be pretty well modeled as a resistor network. Having done this only briefly in school, I wrote down the process as I went through it for our hot end. I'm posting it here (http://goo.gl/es70uc), and to spare everyone from having to discern my handwriting, it's done with LaTex. Coming soon, more detailed modeling, and even more exciting math.
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