Extruder gearing

I'm building a second printer, and I've been looking at Extruders, most of the widely used designs (Wades etc) seem to have about 3:1 or 4:1 gearing.
Does anyone have a source where the "ideal" gearing for a particular setup is calculated.

I understand there are a number of factors nozzle size, filament diameter temperature, plastic etc.
I'm just wondering where the 3:1 or 4:1 actually came from.

I'm not sure where the actual decided on reduction came from but I'm sure it was a matter of space available had something to do with it. A couple things happen when you have a gear reduction, for example, you'll gain torque but loose speed. So if you make your driven gear too tall, you'll be limited on retraction speed and extruding speed of the filament.

Also, if you wanted to get more torque, you would have to make your driven gear taller with more teeth. The prusa design is already pretty tight with how tall the gear is. So I guess it's a game of numbers and just playing with it until it feels right.

Hope this helps

bdc
~Stay Calm out there

You could calculate the required gearing exactly if you accurately knew the force required for pushing the filament (in all conditions) and the maximum sustained torque that the motor can generate. As far as I know no-one has calculated it like this, since there's way too many variables affecting the required filament pushing force... mostly it seems to be "direct drive doesn't give enough force, let's put some gearing on it".

I'm currently using a 47:9 gearset but I modelled and printed a compatible 2.5:1 set of gears because retraction becomes too slow at the 5:1 gearing... Haven't gotten around to installing them yet. Even 2.5:1 should give more than enough torque (I have a motor with 59 Ncm torque rating)

AFAICS the are several contributing factors

Enough torque
Enough resolution for those people printing at very low layer thicknesses - though I suspect this isn't much of an issue in reality.
Physical space restrictions

I was just wondering, looking at extruder for another build, I'd seen a couple of direct drive extruders and was wondering why most of the widely used ones were in the 4/5:1 range. And whether someone had actually done the math.

It just so happens that the Wade's gear ratio is about the same as the difference in torque required for 3mm and 1.75mm. So 1.75mm can be direct drive but 3mm needs about 3:1 gearing with typical hot ends and NEMA17 motors.

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Thanks, that makes the direct drive extruders make more sense.
The funny thing being I "knew" that but it never occurred to me.

My buddy just asked me this so I thought it would be a good tip for everyone out there that didin't know.

If you want to know the gear reduction, just count the number of teeth on the gears. For example if the drive gear has 5 teeth and the driven gear (big one) has 10 teeth, you have a 2:1 reduction.

Hope this helps if anyone was reading this and wondering what was going on.

bdc
~Stay Calm Out There