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Physics page 2


The 3d printer is a complex machine with many different variations, but the heart of machine is always the mechanism or process that is moved by the x, y, and z axis. In the case of the Extrusion printer, the heart is the extrusion head. It moves solid plastic through a heated chamber to its melting point and squirts out the hot plastic as the extrusion head is moved around; Thus creating each layer.

The two main parts of an "extruder" are the "Hot End" and the "Cold End"

nozzle.jpg                        extruder.jpeg
https://www.hotends.com/image/cache/data/standard/jhn_mk5b-500x500.jpg                http://reprap.org/mediawiki/images/thumb/2/27/M8_2gears.jpg/500px-M8_2gears.jpg

Displayed above are two commonly used hot and cold ends in the most baseline extruding 3d printer, again, the Reprap. A "J-Head" and "Wade's Geared Extruder". (An interesting note: Wade's Geared Extruder is made mostly by another 3d printer.)

The part we are going to focus on is Wade's Geared Extruder.

Below is the materials list copied from reprap.org
not my work
"

Materials

Printed Parts

Quantity Description Type Comments Diagram
1 extruder block RP File:M8 Extruder 3.zip M8-extruder-block-3.jpg
1 extruder idler block RP File:M8 Extruder 3.zip M8-extruder-idler-block-2.jpg
1 11 tooth drive gear RP File:M8 Gears.zip 11t17p.jpg
1 39 tooth M8 hub driven gear RP File:M8 Gears.zip 39t17p.jpg
" -end quote

The important information we must take from this table is the number of "teeth" in each of the gears: "11 tooth drive gear" and "39 tooth M8 hub driven gear"

Because the gear teeth must fit together, we can assume they are the same size. This is useful because we won't have to take the diameter or circumference of gears, rather we can compare the number of gears to find out mechanical advantage of the system.

Output # of gears
___________________________________________
Input # of gears

39
__________
11

which is approximately 3.55

An average stepper motor has about 40 N·cm of holding torque
(
http://reprap.org/wiki/NEMA_17_Stepper_motor)

For the sake of Physics 211, we will convert to SI Units:

40N/1cm
· 100cm/1m = 4000 N·m

So if the stepper motor exerts 4000 N
·m to the small gear, how much force is put out (what is the output force)?

4000 N·m  · 3.55 = 14200 N·m

The force of the stepper motor is exerted over a larger distance, thus creating a larger output force.
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I am soooo fake pre-loading this image
      so the navigation doesn't skip while loading the over state. I
      know I could use the sliding doors technique to avoid this fate,
      but I am too lazy.