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Machine Calibrating

In this blog post we try to answer the question, what should be the layer height if the head speed is 16mm/s and the motor speed is 40rpm. So calibrating the extruder theoretically, rather than trial and error.

Since I had my printing machine I always had some sort of printing deficiency. I always suspected,
that I made my settings wrongly or didn't adjusted it right.

I asked on the forum how am I supposed to set my machine/skeinforge settings right, and I was told that I should follow this walkthrough blog post.
I tried it, but I lacked the proper tool to do it right. I only have an "analogue" caliper, where the accuracy in theory 0.05mm, but Im only able to read it reliably 0.1mm:

Following the above tutorial requires a digital caliper with 1 ┬Ám (0.001mm) measuring accuracy.

The idea, that a measuring is required, when we know every details of the machine, is rather strange. So I asked nophead, what is his method to adjust the settings right. He said, he calculates the layer height and does not need to do any "trial and error", like the above mentioned blog post. We exchanged some emails, and here it goes the explication (at least what I grok from it):

So we are trying to determine the layer height. Before we start, I think I should clear up the terminology and the known/unknown variables.

d: diameter
d_i: input diameter
d_o: output diameter
V: Volume
V_i: Input Volume
V_o: Output Volume
v: velocity (speed)
v_i: Input velocity
v_o: Output velocity (head speed)
L: length of filament
L_i: Input filament length
L_o: Output filament length
Gr: Gear ratio
Known values:
d_i=3 delim{[}mm{]} (filament diameter)
v_o=16 [mm/s] (head movement speed)
rpm=40 [1/min] (motors revolutions per minute)
head speed=16 mm/s
Unknown values:
d_o=? (output diameter, the extruded filament diameter)
layer width=0.8*d_o
deposited filament width=1.2*d_o

Calculating the output diameter

Assumption: What is going into the extruder is coming out too.*

So the input volume is equal to the extruded volume:
*: Ignoring the thermal expansion.

The volume of a cylinder:

So: V=r^2*pi*L

The cross-section of the input filament and the output filament is a circle (the deposited output filament has an oval shape, but when it comes out from the extruder nozzle, it is round).

So the input and output Volume is:

We know, that V_i=V_o, so:
After much simplification:

Where L_i = v_i*T and L_o=v_o*T respectively.
We can simplify with T:

Where v_o=16mm/s=960mm/min. And v_i is:
v_i=(rpm*Gr)*(thread pitch*cos alpha)

Where Gr=14/17:

And alpha is 20 degree:

Thread pitch is 1 mm and rpm is 40.

So finally the equation:
v_i=40*(1/min)*{14/17}*1*(mm)*cos 20
d_o=3*mm*sqrt{(40*(1/min)*{14/17}*1*(mm)*cos 20)/(960*(mm/min))}
d_o=0.5387 mm

From this:
layer width = 0.8 * d_o = 0.431 mm
deposited filament width = 1.2 * d_o = 0.6464 mm

Hope it was useful.

Some additional thoughts:

  • The nozzle size does not come into the equation.
  • it sets practical limits on d_o. Must be less than the die swell
  • The die swell depends on the plastic and the v_o

Note: Also I didnt tried out in practice. So I will update the post once I tried it out.
Note 2: The Mendel building is progressed quite well, just Im a bit behind with blogging.

Filed under: theory Comments Off
Comments (3) Trackbacks (1)
  1. Very nice write-up and diagrams. I tend to work the other way, so I start with 0.5mm filament giving 0.4mm layers and let the software work out the correct RPM from that.

  2. Yeah, seems more logical. However I was always wondering what should be the correct layer height for 40rpm. So I was already playing with layer heights, just never liked the result. 40 rpm is such a round number;-)

  3. Interesting details and drwaings I may need to look at these again before too long if my basic Mendel extruder fails to work as expected will be building it this weekend.. so great timing too on your posting with this and Nopheads I cant go wrong if I need to make some gearing for my extruder Thank you.