Periodic Tabe of GearBearings

caution: The code needs to be updated to use the new library: 
https://www.printables.com/model/430614-cycloid-gear-library
( http://www.thingiverse.com/thing:777936 )
 
In future advanced nanotech context: 
http://apm.bplaced.net/w/index.php?title=Periodic_table_of_gearbearings

See section instructions (further down) for some practical info.

A bit about some hidden logic in planetary gears:

Not every combination of tooth numbers allows to distribute the planets equally around the circumference. If the combination allows equal (equiangular) distribution it can be that the planets are a multiple of the minimal mounting distance away from one another (they are not maximally closely packed) making the assembly weaker than it could be.

To allow more tooth number combinations and have the planets as closely/tightly packed as possible the planets can be organised in groups (which is done here). For this the greatest common divisor of the gear teeth numbers defines the number of planet groups (starting points for filling). The number of sun and planet teeth is then defined by multiplicators to that common divisor.

The cycloidical shape of the teeth allows (and requires for small prints) toothnumbers smaller than in involute gears. The compatible tooth number combinations thus become more sparse. Groupling planets by the gcd value and distributing then in patches around the circumference allows more options.

Cycloidical profile pros and cons:
★ smaller toothnumber possible - more compact design possible
★ stronger for same pitch - less fragile teeth than involute profile

(+) it has less parameters than "normal" gears (simpler)
(+) wider contact area (concave on convex) -> less wear & friction
? more efficient than involute profile ?

(++) better for additive FFF manufacturing because smooth profiles allows for higher printing speeds.
(-) harder for subtractive manufacturing (because of tool challenges)

(++) gears can (and want to be) pressed together, no deed to enforce gear distance by bearings rather the gear contact itself can act as one of the bearings.
(-) distance between gears is not continuously variable like with involute teeth (irrelevent for a gearbearing like here)

(-) Pressure angle can't be adjusted, it is varying max-zero-max -> potential vibration -> more wear & friction BUT herringebone profiles can highly fully alleviate that.

Instructions

If you print splitted parts you need their mirrored versions too.
The grooves on the outside of the ring are for blocking rotation with pieces of 3mm filament (That by now almost no one uses anymore - oops).
The cylinder where the bearing goes in needs to have matching grooves.

Set your slicer to distribute the seam at random positions.

Printing parts separately for post assembly makes stringing impossible and may allow for tighter tolerances. But keep the minimum time per layer high enough for the small planets to not deform.

Perhaps use nylon/PA if you have such filament at hand. Delrin/POM if you dare.

The 45° bevel cutoffs help preventing fusion of planets with sun and ring when the part is in place printed in assembled state and the first layer is squished.

The bevels (cut off edges) also can aid in slide-in-assembly when the part is printed in separate pieces.

They bevels look nice too but also weaken the bearings strength a bit and make it harder to judge the chosen clearance by eye.

Known issues:

Spur gear-bearings are very hard to get pretty much backlash free and smooth running at the same time. Especially when in place printed.

This one is far on the loose side ATM.
Adding more bearing thickness may be advisable too.

Teaser:
Expect tapered gear-beraings that can pre-tension all backlash down to virtually zero.

Category: Parts