Argthtjtr

One thing I never understood is the so-called "Extrusion Multiplier" (EM) or "Flow Rate", which is e.g. in Simplify3D set to 0.9 for PLA and 1.0 for ABS.

I always thought that this parameter is just a way to fix an underlying miscalculation or misconfiguration?
I mean, it feels like if you are doing a calculation, getting the wrong solution and simply "correct" it by a multiplier - isn't that cheating?

But on the other hand, S3D suggests two different values for the EM, depending on the type of plastics used. This would lead me to think that there is maybe a physical property which justifies the EM.

No, the Flow rate or Extrusion multiplier is to compensate for different materials and temperature ranges.

Where does the factor come from?

Let's say we calibrated our nozzle for work at 200°C with PLA, so 100 mm extrusion are correct and want to print ABS. ABS behaves differently and we get bad prints. What is wrong? Well, they do behave differently in the heat, and print at different temperatures. One easily noticeable difference between the two is the heat expansion coefficient.

Now, I had to scrounge through research papers and Material/Technical Data Sheets for PLA, so take that one with a grain of salt. But we can clearly compare the various plastics heat expansion coefficients:

• PLA: $41 frac{text{µm}}{text{m K}}$ ^{a TDS}
  


• ABS: $72 to 108 frac{text{µm}}{text{m K}}$
  


• Polycarbonate: $65 to 70 frac{text{µm}}{text{m K}}$
  


• Polyamides (Nylons): $80 to 110 frac{text{µm}}{text{m K}}$

Those are just three randomly picked plastics that clearly are printable. If we heat one meter of them by one Kelvin, they'd expand by that length (a couple micrometer). We heat the later three printing materials to about 200-240 K over the room temperature (~220-260 °C), so we'd expect these the materials to expand by the following ranges:

• PLA: 6.97 to 7.79 mm ⁽¹⁾
  


• ABS: 14.4 to 25.92 mm ⁽²⁾
  


• Polycarbonate: 13 to 16.8 mm ⁽²⁾
  


• Polyamides (Nylons): 16 to 26.4 mm ⁽²⁾
  

^{1 - using 170 K and 190 K temperature difference for its normal print temperature range of ca 190 to 200 °C
2 - first: low expansion at 200 K increase, then high expansion at 240 K}

You have calibrated your printer for one of these values somewhere in there. And now you get a different filament that has a different color and a different blend or even you swap from PLA to ABS or switch from one brand to another - the result is: you get a different heat expansion coefficient somewhere in that range and you have almost no chance to know it. The heat expansion coefficient, in the end, has an effect on the pressure in the nozzle and this the speed the material leaves the nozzle, which impacts die swell and so the overall printing behavior.

Remember that heat expansion is not the only thing that is happening in the nozzle. Other big factors are for example the viscosity of the polymer at its printing temperature, its compressibility (which depends for example on chain length or embedded fillers), the geometry of the nozzle, the length of the melt zone... they all play a role in how exactly the print gets to come out.

We can sum all those up under a general "behavior in the nozzle" tag, and as a result one gets vastly different flow/extrusion multipliers, like the 0.9 for PLA/1 for ABS in Simplify3D.

gaining the factors

Most of these are determined by trial and error using a factor of 1 and dialing up manually until proper printing is achieved on the machine, then putting that factor back into the software.

As a side note: Ultimaker Cura has (in its filament database) the ability to save flow rates into each different filament, but does initialize all with 100 % default.

TL;DR

It is a way to adjust to the relative difference between the behavior of filaments (using one of your filaments as the calibration) and not cheating.

That's one way to look at it, I guess. I think a more accurate way is to consider it an "ad-hoc calibration" where one realizes that their printer isn't extruding enough/too much and the EM adjusts the flow to extrude the correct amount.

The underlying calculation, at least the main one, would be the steps/mm set in the firmware. If it's off, one fix is to figure out how much it is off by and change the EM to that. The better solution is to determine the actual steps/mm and flash the firmware so that the EM can be set to 1.