How to find the maximum print speed your printer can acheive ?

There are so many variables limiting the printing speed and/or quality you can acheive with your 3D printer. Many of them are interlinked, so I'm proposing a calculator so you can find out the what could be the maximum printing speed that's acceptable for your printer.

This post is split in 3 parts: Extrusion, Displacement, Cooling. The maximum print speed is the value that satisfy all these constraints.

Extrusion

Extruding plastic implies:

  1. Pushing the (cold) filament into a heated chamber so it can become viscuous.
  2. Heat the plastic fast enough so it becomes viscuous.
  3. Pushing enough plastic so that the pressure in the heated chamber overcome the required pressure to extrude the plastic out of the nozzle.
  4. Applying the amount of plastic on a part as specified by the 3D program (G-Code).

Point 1 above means that you must have an extruder that's powerful enough to reach and sustain the extruding pressure. If the (cold) filament is not plastic, it means that any volume of filament pushed by the extruder will get out of the nozzle. If the filament is plastic (due to a too high temperature for example), then it'll start to clog in the path and the relation input = output is no more valid, since the plastic will start to compress when it soften, and decompress when retracted: a differential equation is required to model this.

Most printers are designed so that the filament is kept as solid as possible until it enters the hotend, so the simple relation above applies.

When trying to reach the maximum speed of your printer, you'll be flirting with this limit. So it's important to remember the physical process to understand we'll compute below.

In the calculator below, we'll compute the maximum extrusion speed you can perform once you've calibrated it.

Extrusion speed and flow calculator

Nozzle hole size mm
Expected print speed mm/s
Layer height mm
Flow of plastic to extrude mm3/s
Filament diameter mm
Required extrusion speed for this flow mm/s
Required extrusion speed for this flow (in mm/min) mm/min

Maximum print speed from extrusion speed calculator

Nozzle hole size mm
Layer height mm
Filament diameter mm
Extrusion speed mm/s
Computed plastic flow mm3/s
Maximum print speed mm/s

But how do you find the maximum extrusion speed for your hotend ?

The extrusion speed is the speed at which you can drive your extruder and still get consistent plastic output. Since it depends on the ability of your hotend to melt a given plastic volume, you'll need to create a 2 dimension matrix. On one axis, you'll write down the extruder speed and on the other you'll write down the hotend temperature. The value in each cell of the matrix is the amount of plastic you've extruded for the combinaison of (hotend temperature, extruder speed).

Usually, the higher the extruder speed, the more likely it'll fail to sustain the pressure required to extrude plastic out of the hotend, so it'll miss steps => extrude less plastic. By weighting the extruded plastic for each combination, you can figure out how well the extruder performed for such combination.

So:

  1. Send a M83 once to change to relative extrusion (so you don't have to accumulate your numbers)
  2. Send a M109 Rxxx (replacing xxx with the desired temperature to test). It'll only return ok when the hotend reached the temperature.
  3. Clean your bed and make sure it's cold (you'll need to remove the extruder filament often, you don't want it to stick).
  4. Select a speed to test (for example 3mm/s, and convert it in mm/min by multiplying by 60 or use the calculator above). You'll then need to set the extrusion speed with a G1 Fxxx (replacing xxx by the speed you want to test).
  5. Then you'll need to prime the nozzle by sending a G1 E30
  6. (Optionally) you can pause the extrusion with G1 F3 followed by G1 E0.1
  7. Remove the drop of filament from the nozzle now.
  8. Reset the speed if you paused the extrusion with G1 Fxxx (replacing xxx by the speed you want to test)
  9. And extrude some filament G1 E300 (depending on your firmware, the extrusion length might be limited to 250mm or less so adjust in consequence)
  10. Capture the filament and weight it. You'll need a kitchen scale that's precise enough here.

If you perform the steps above for each combination of extrusion speed and temperature (you'll need to increase the temperature when you increase the extrusion speed, but don't go above to 260°C or 270°C for PLA) and report in an spreadsheet, you'll be able to observe and compare the limitation of the flow from the hotend. Typically, at a fixed temperature of 210°C, the quantity of extruded plastic will decrease when the extrusion speed increase. But if you increase the hotend temperature at the same time, you'll recover this loss up to a tuple.

This tuple (extrusion speed, temperature) will give you the maximum extrusion speed your hotend can support. Then enter the extrusion speed in the calculator above and you'll find out the maximum print speed you can acheive.

This speed is theorical, since it's the case when the printer has finished accelerating (which needs space to perform), and the plastic has cooled enough to adhere but is not dripping on the last layer. With a 20% margin, you should be safe here.

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