What determines minimum layer height?

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Sublime
To start with the width needs to be at least as big as the nozzle hole for
positional accuracy. If not the walls will end up being uneven since the extrusion
can be to either side of the exit hole.

The max width we can print at is the free air extrusion width which is often
around 0.2mm larger than the drilled hole (this will vary with material, orifice
length and temperature). To find your specific size extrude into free air at a
constant speed (speed that appears to turn the hobbed bolt the same rate as
printing would turn it) and then measure the resulting filament with calipers.

Then we should say that the max height of any extrusion should not exceed 66% of
the width (width = 150% of height) this is to ensure the extruded filament is
making good contact with the layer below. For best strength we want the height
50% of the width or less (width = 200% of height or more).

The key I have found to good extrusion is a certain pressure inside the nozzle.
If it is too high we get blobs at the end of of paths. If too low we are printing
with ooze and not really forcing out the plastic under pressure. This means to
maintain the same pressure inside the nozzle at all heights we should narrow the
extrusion width as we go lower. I do this by dividing the difference between nozzle
diameter and free air diameter (die swell) between the max height (free air * 0.66)
and a theoretical minimum height (nozzle diameter * 0.1666) to get the ideal width
for any height. This gives us free air extrusion width at max height and nozzle
diameter at minimum height and a linear division between them.

There is more to take into account though. We can look at the volume of plastic that
is extruded on each step of a 5D extruder.
This is ((Filament_Radius^2)*3.14159)*(1/steps_per_mm_E) = volume per step. If you
take this into account you will see that if we want to print a single dot the diameter
of our extrusion we have a minimum height we can do that without over extruding. Or we
have a minimum diameter we can extrude at at any height. This results in the extrusion
diameter getting larger as we go down below a certain point. But to maintain that
magical extrusion pressure that gives use the best prints we then need to slow down
because the larger extrusion width at the lower height would require more force at the
same speed.

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cat.farmer
Thanks sublime. It will take me about 3 more times reading through that to take it all in.
With all that math ..is this considered the end all equations to good prints or just a starting point to find what works best? I ask because i have been slowly trying to tune my printer, and i'm tring to understand what makes a good print, i can get a good looking peice of plastic off the bed, but that doesn't mean it is a quality print. Sorry derailing this thread..

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NewKidOnTheBlock
Sublime: Thank you for the detailed explaination and even more thanks for your calculator lol

As a follow up question, how would one go about making sure everything is set up properly to ensure quality prints if the printer has multiple print-heads with different diameters?

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Sublime

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NewKidOnTheBlock
Sublime: Thank you for the detailed explaination and even more thanks for your calculator lol

As a follow up question, how would one go about making sure everything is set up properly to ensure quality prints if the printer has multiple print-heads with different diameters?

Currently this is a little bit of a problem. The firmware does not allow different steps per mm for each extruder so you have to do it all in the slicer of your choice. I recommend Kisslicer or Cura.