<p>It seems that when filament throughput is increased (by increasing movement speed or extrusion width/height), printing temperature also has to be increased to compensate, because the filament will have less time to spend in the melting zone. That much seems clear from practical experience. But I have two questions (or to be more precise, one question on two levels):</p>

<ol>
<li><p>Is there a good rule of thumb for this, to help people calibrate their settings?</p></li>
<li><p>How much do we know about the formula governing this behavior? Can we calculate the required hotend temperature <em>precisely</em> based on the increased throughput?</p></li>
</ol>

<p>For anyone who has studied physics / thermodynamics, this is probably simple stuff. But has the work been done for 3D printing specifically, in a way that is practically applicable?</p>

<p>I share the following train of thought to start off with. Let me know if I make any errors in reasoning.</p>

<ul>
<li><p>Presumably, every material has an optimal printing temperature just above its melting point.</p></li>
<li><p>But the thermistor doesn't read filament temperature. It reads the heat block temperature.</p></li>
<li><p>Below a certain throughput, the temperature of the filament will have time to equalize with the temperature of the heat block before it leaves the nozzle.</p>

<ul>
<li>For those slow speeds, heat block temperature should be set exactly to the material's optimal printing temperature.</li>
</ul></li>
<li><p>For greater speeds, however, heat block temperature will always have to be higher than the mark, because the filament doesn't have time to equalize.</p>

<ul>
<li>At that point, it becomes a balancing act. Find the best heat block temperature (°C) given a rate of throughput (mm³/s), the optimal printing temperature for a given material (°C), the volume of the melting zone (mm³) and <em>&lt; some other property of the material ></em>, which determines how fast it heats up. I don't know what that last property is, nor can I come up with the proper unit. The material probably approaches the temperature of the environment asymptotically. This is where thermodynamics comes in, I guess.</li>
</ul></li>
<li><p>Theoretically, running filament also cools down the heat block, but we can ignore this. If this effect is significant at all (is it?), this is already compensated for by the PID controller.</p></li>
</ul>

<p>I'm almost certainly missing some key insights. I'm curious to know what work has been done.</p>

[{'answer_id': 3352, 'author': 'StarWind0', 'author_id': 2146, 'author_profile': 'https://3dprinting.stackexchange.com/users/2146', 'pm_score': 0, 'selected': False, 'text': "<p>I see an answer not a question. It's a balancing act and there is no predefined formula. Trial and error. Keep a spread sheet. I'll dwell on this a bit.. but as someone who did speed sprinting there's really nothing else to be said other than buy an e3d and the volcano upgrade. </p>\n\n<p>You will calibrate one at a time. Thin wall. Then find solid infill is the true thermal barrier. Then sparse. You will tweak with layerheights. Get thicker nozzles 0.8+. It's a game of spinning plates. Each change will wack out another. </p>\n\n<p>Last you will get to where I did. You move so fast 5 layers down your print is still molten and moving. Especially on small parts. </p>\n"}, {'answer_id': 3453, 'author': 'Randy Steck', 'author_id': 4627, 'author_profile': 'https://3dprinting.stackexchange.com/users/4627', 'pm_score': 2, 'selected': False, 'text': "<p>I think I see what you're asking, but I think you may be thinking about it incorrectly.  It's really all about heat being added to the system at the same rate that it's leaving.  The heat block is there as a heat reservoir from which the filament draws heat for the glass transition.  The heat in that reservoir is maintained by cycling the heating coil to add energy (more heat) to the systems as it's lost.</p>\n\n<p>In the very local vicinity of the nozzle, the temperature will decrease slightly as it's being transferred to the filament, but because the heat block is massive in comparison to that drain, and because the heat block is a good thermal conductor that temperature reduction is very small.  </p>\n\n<p>I do not know what tolerance and hysteresis are built into the temp controller, but think the variation is likely small.  The difference in additional heat required (more energy into the system) for any practical difference in feed rates (40 instead of 60) is thus likely to be very small compared to the filament cooling experienced immediately after it leaves the nozzle.</p>\n\n<p>Bottom line: the adjustment you would want to make is not to increase the temp, but increase the duty cycle of the heating element to maintain the desired temperature.</p>\n"}, {'answer_id': 15585, 'author': 'FarO', 'author_id': 2338, 'author_profile': 'https://3dprinting.stackexchange.com/users/2338', 'pm_score': 1, 'selected': False, 'text': '<p>No there is no rule of thumb as far as I know and no, it\'s not obvious for someone with skills in thermodynamics.</p>\n<p>I know that if you want extreme speeds you need extreme overtemperatures, for example Annex Engineering uses ABS at 290 °C (about 50-60 °C overtemperature) with a Mosquito Magnum (rated at about 40 mm^3/s) to reach 60 mm^3/s:</p>\n<p><div class="youtube-embed"><div>\r\n                <iframe width="640px" height="395px" src="https://www.youtube.com/embed/tHI9v4wh4aA?start=0"></iframe>\r\n            </div></div></p>\n<p>Still, you need to find the optimal value based on your hotend, your extruder, your nozzle size and target flow rate. You may do static tests as explained here:</p>\n<p><div class="youtube-embed"><div>\r\n                <iframe width="640px" height="395px" src="https://www.youtube.com/embed/0xRtypDjNvI?start=0"></iframe>\r\n            </div></div></p>\n<p>There cannot be a rule for such a complex behaviour.</p>\n<p>Also, be aware that Annex Engineering uses 23 000 mm/s^2 (not a typo, really 23 thousand) as acceleration, therefore their printing head moves at basically constant speed. Also, they set the slicer with the same speed for inner/outer perimeters, infill, and so on. If you have more common accelerations like 1500-2000 mm/s^2 and different printing speeds for different features, somewhere the filament will be pushed super fast through the nozzle and everything is good, somewhere else it will slow down and it will overcook.</p>\n'}]
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