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Assuming heat transfer to melt the filament is not an issue, what’s the bottleneck in pushing more filament through the nozzle? Is extrusion volume per time proportional to applied extruder torque?

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  • $\begingroup$ What is your end goal? If you push a ton of material thru, then you need equivalent speed control on the X-Y drives to place the material properly. See, for example, modified setups which allow extruding soft clay (5 mm nozzle or bigger) $\endgroup$ – Carl Witthoft Jun 3 '19 at 17:52
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The molten plastic in the extruder becomes a hydraulic fluid effectively when it gets melted. You're pushing on a fat piston (1.75 mm or 2.85 mm, depending on filament type), and shoving fluid out through a 0.4 mm or so hole. There's a limit to flow rate at a given pressure, but the bigger issue actually tends to be friction. Molten plastic really loves to grab on to metal, and the ratio of surface area to volume is fairly high in the long, skinny tube that is the inside of an extruder. To make matters worse, the not-quite-molten section of the melt zone up at the top normally doesn't make a lot of contact with the walls due to lower pressures not deforming the plastic all that much, but at higher pressures you get much more deformation, increasing the linear distance that the plastic is dragging against the tube walls, and the pressure with which the two surfaces are bonding together. Especially in cheapo clone extruders you'll find roughly bored inner surfaces with many circumferential grooves which exacerbate this issue - this is why most extruders have a PTFE lining as far down as they can go. I had this issue in my $3 "all-steel" extruder barrel, where even printing PLA was an issue because of how readily the plastic formed huge plugs and grabbed the inside of the extruder.

So what you end up with, is that increased torque mostly linearly translates to increased pressure, which results in linearly increased friction inside the barrel, plus a little bit extra due to extra deformation in the top of the melt zone. You can polish the inside of the barrel (heatbreak? seen both terms) to help alleviate internal friction somewhat.

To make things even more fun, there's obviously a limit with how much force you can exert through the mating surface of a single hobbed bolt and the side of the filament. Too much force and the teeth will simply rip off the side of the filament and then you'll have no feeding torque whatsoever. To get much higher torque you'd need to design an extruder that both supports the filament much better than modern designs do, and spreads the force out over a larger surface area, either by using a much larger diameter feed gear, or multiple tightly-coupled feed gears.

I went into some degree of detail on the feed mechanism in this answer that another user asked about using a commercial extruder for plastic injection molding, which overlaps somewhat with your question here.

I know the original question assumed perfect heat transfer that was not a limiting factor to the process, but how that actually works is relevant to the question as well. E3D took one approach with their Volcano design, simply by making the melt zone much longer to increase heat transfer; the downside is there's obviously substantially more friction when you've got 4x the linear distance of molten plastic against metal, assuming you're not using a PTFE liner. This does have the advantage of letting the plastic take its time to reach the target temperature, decreasing how far over your target plastic temperature you need to have the heating element. One thing not often discussed in 3d printers is the fact that the plastic asymptotically approaches the temperature registered on your thermistor. If you're printing very, very slowly, your plastic will nearly be exactly at the target temperature. If you print very quickly with very high volumes, you'll tend to have slightly cooler plastic than intended because it simply wasn't in contact with the heater long enough to come up to temperature. The solution for very small designs might be higher temperatures, but the drawback there is that if you slow down even for a moment, say moving to thinner line widths or picking up and moving the extruder, you'll overheat the plastic. So there's practicality questions that need to be answered to determine how you'll actually heat that much plastic to the right temperature. Increased distance improves reliability at the cost of increased friction (and therefore extruder torque required), and increased temperature mostly bypasses that question at the cost of reliability.

TL;DR Increased extrusion speed requires increased pressure, which increases friction dramatically and in a non-linear fashion and results in stripped filament.

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  • $\begingroup$ Could you theoretically do an "all PTFE" hotend? Something like nonstick cookware, all the way through the nozzle. $\endgroup$ – R.. GitHub STOP HELPING ICE Jun 1 '19 at 5:10
  • $\begingroup$ This is a super useful answer, thank you very much! Most interesting bit is "increased torque mostly linearly translates to increased pressure, which results in linearly increased friction inside the barrel". I think flow rate is about proportional to delta-pressure, but how does it relate to friction? So optimally we'd probably want a metal hotend with a very,very thin PTFE lining all the way down? $\endgroup$ – user1282931 Jun 1 '19 at 12:50
  • $\begingroup$ All PTFE would reduce friction to be sure, at the expense of limiting how hot you can get the entire assembly. PTFE starts breaking down not far past ABS printing temperatures. As far as friction vs flow rate, I'm honestly not 100% sure how they correlate, because I'm not well versed in hydraulic fluid physics, but I can tell you that hydraulic friction through tubes is well documented and you could probably do some reading on Wikipedia to get a decent idea. $\endgroup$ – Nach0z Jun 1 '19 at 14:31
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    $\begingroup$ "shoving fluid out through a 0.4 mm or so hole" Larger hole diameter nozzles are also available. One would have to determine if the heater could keep the plastic molten if more plastic was being pushed thru a larger hole. A search on Amazon shows nozzles with up to 1.0mm hole (vs the more commonly supplied 0.4mm nozzle). If one had a printer that used 3mm filament (vs the smaller 1.75mm), that printer might have a larger diamater nozzle hole as well. $\endgroup$ – CrossRoads Jun 3 '19 at 17:02
  • $\begingroup$ I think your analysis is too pessimistic - consider a design that takes 10-mm diameter input filament, with appropriately sized drive gears. $\endgroup$ – Carl Witthoft Jun 3 '19 at 17:54

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