Extruder design 1: (Printable ?) 100:1 Hypocycloidal gearbox
Here’s a quick preview of some of the extruder design work I’m doing.
I’ll do a write up of the results when I’ve tested the prototype, but here’s the gist of the design:
The bearings are omitted from the images below. There will be a 624ZZ at each dimple around the edge, and 608ZZs around the drive shaft. I’ll machine the prototypes from nylon and 6082T6 Aluminium alloy, but this design should be printable.
100:1 Hypocycloidal reducer (exploded, view 2)
Here’s one that someone else made (using some printed and some machined parts as best I can see):
Here’s how it works, in short: the cranked drive shaft causes the lobed rotor to move eccentrically, such that the lobes on only one side at a time engage with the rollers around the edge of the casing. There is one more roller than there are lobes, so when the crank has rotated by one revolution the roller has counter-rotated by one roller. The second set of rollers on the output flange have a similar interaction, so for each full revolution of the rotor, the output flange rotates by one roller.
If you’d like more information on these gearboxes, I recommend the page I started with as a jumping off point: http://www.zincland.com/hypocycloid/
Hypocycloidal gearboxes are interesting here because they offer high torque and high ratio in a small package with large features, and so may be printable.
Why we want a better gearbox
Our extruders, even the geared ones, are torque limited: they could easily extrude faster except for the fact that the drive doesn’t have enough torque. Typically the extruder drive stepper motor will run below 10rpm. We are a long way from reaching the peak mechanical power in our drive motors, let alone the maximum step rate. The obvious improvement is to use a higher ratio gearbox.
Stepper motors have an S shaped torque/rpm curve: high torque at low rpm, rapidly falls off at medium rpm, and tails away gradually to nothing a very high rpm. Mechanical power = torque * speed. For any stepper there is an rpm that gives the most possible power, where torque is still high, but speed (rpm) is high too. If we can operate the motor at around that speed, we get the most out of it.
Consider a typical NEMA17 stepper: the Zapp Automation SY42STH47-1684B. PPM on stepper data sheets mean “pulses per minute” and that’s the same as “steps per minute”. From the data sheet we see that it has a torque of 0.32 Nm @ 1000 ppm (= 5 rpm) and 0.20 Nm @ 7k ppm (= 35 rpm).
0.32*5/60 = ~27mW mechanical power at 5 rpm
0.2*20/60 = ~70mW mechanical power at 35 rpm
ie: at the fastest speed that the datasheet provides a spec for, the mechanical power is still increasing. For the sake of argument, assume that our target motor speed is 80 rpm.
Suppose that we wanted the extruder to extrude at 32mm/s, and we decide on a 30mm diameter feed wheel, and we have a 0.3mm tip orifice.
The feedstock has a cross sectional area of 3*3 = 9mm^2
The extrusion has a cross sectional area (ignoring die swell, etc) of 0.3.*0.3 = 0.09mm^2
This means that for each mm we feed in, we get 9/0.09 = 100mm out.
So for an output rate of 32mm/s we input feedstock at 0.32mm/s
Which implies that we turn the feed wheel at:
60*0.32/(pi*30) = ~0.2 rpm
Since we want to get 0.2 rpm at the gearbox output with 80 rpm at the input, we need an 80/0.2 = 400:1 reducing gearbox.
Under no load, the stepper can probably do something like 1000 rpm, so with that ratio we will still have a good speed headroom for ooze prevention and other similar uses.
Why do we want a larger feed wheel? Two reasons:
Larger diameter should improve the grip on the filament (more contact area).
Larger diameter should increase the sytematic accuracy in the feed rate. As nophead commented, it’s hard to know what the effective diameter of a pinch wheel is, because it’s hard to know how far the filament is pressed into the ridges on the wheel. Since you don’t know the diameter, you can’t be sure exactly how much filament you’re feeding per rev of the wheel. As the wheel becomes larger this effect becomes less severe, since a given absolute diameter variation would be a smaller proportional variation, and so a smaller variation in the amount of filament feed per rev.
Ideally, I’d like a 400:1 reduction, but I’m starting with 100:1, and we can take it from there.
100:1 Hypocycloidal reducer (exploded, view 1)
This is a work in progress. I’ll post design files at some point. Comment if you have an urgent desire to work on them.
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Thanks again. That’s the page I started with, and I had a link to it in an earlier draft, but it looks like I cut but didn’t paste it. :-/
Now fixed.
Looks sweet – I’ve seen a few designs like this, but I’ve been curious what the friction losses would be. Any idea on what the efficiency of a good hypcocycloid gear is? Nophead was a little surprised with the losses in his worm gear design.
It sounds like you are planning on using bearings as the outer teeth – that could really help with the friction. I’m away from my repraps until August 5th, but I might try printing one of these when I get back – could increase the Z travel on my extruder.
Wade
Why could the diameter not be measured?
One could use one or more “rolling pinch forks” or some other device to better know the exact diameter and correct the extruder stepper speed appropriately, if necessary.
Thank you. Video is often much clearer than words, and I’ve now embedded that near the top.
I agree that the rotor and output face look printed (on a commercial machine) but the main casing and drive shaft look machined to me. I think the drive shaft will become a challenging vitamin in much the same way that the heater hot side parts are.
Perhaps we can make in from three parts and bolt it together, but I’m concerned that it would be hard to make in sufficiently rigid.