Spur Gear Differential

I saw a Torsen differential recently and thought it was an interesting concept. Something about the symmetry appealed to me. Anyway, I was thinking about how it could be improved upon for the purposes of 3D printability.

Firstly, we can do away with the right angled gears so all axes can be parallel. This orientation will lend itself to print-in-place methods. Obtuse is probably too strong a word, but I'm not buying the worm/wheel explanation. With a 45 degree helix angle, it's ambiguous which is which. The reason it's harder to backdrive is due to the size difference and we have size differential at home.

Herringbone gears, because why not? Eliminate axial loads, make it smoother. Shouldn't even need bearings for the planet gears as the normal operation is for these to lock up. Maybe I misunderstand. Helical gears start behaving a lot like worm gears when the tooth count is low and the angle is steep enough. Perhaps it is precisely the nature of the axial loading that makes them so difficult to backdrive. Not to worry, sans bearings ours offers plenty of resistance.

Turns out this is a well established arrangement not too dissimilar to Type II Torsen or just plain old Spur Gear Differentials, but we'll make sure we have good rotational symmetry and mesh the gears all the way around. More planet gears in contact also helps distribute load.

In terms of finding an actual application, I've kept pretty close to a form factor (thing:2805059) I came across that was intended for the 1:10 scale OpenRC Truggy (thing:42198), although this could use a little polish.

Although it is mostly print-in-place, I decided to leave it able to be disassembled for maintenance and lubrication via the press fit lid. Also saves worrying about the overhang.
It could benefit from a single bearing to keep the main drive gear true, but I was also aiming for minimal to no required hardware for this iteration.

The planet gears can also be reinforced by pins, skewers or nails for high load applications as they are the weakest across the grain. We could probably extend the meshing surface of the main drive gear the full height of the case or use belt drive, too. There is also room for carrier bearings, if required.

This is based off a previous planetary gear system, but the ring gears have been omitted. We are required to use a carrier driven input, so the ring gears are redundant and take up space.
It might be worthwhile to include them for their stabilizing effect in lieu of carrier bearings and the additional friction might actually help in limiting slip.

Random Z-Seam alignment recommended, as well as 0.2mm layer height. It did prove to be a little difficult to free up as we simply don't have a lot of mechanical advantage on those planet gears by design. I ended up using a bolt to punch out individual planets from below to get everything moving before applying lube. Print-in-place still saves the packing puzzle of assembly but you could still print parts individually if you were so inclined.

Results

Not quite ready for practical application, but could be with some minor improvements.

All the drive force is borne by the planet gears and the carrier interface. Even if there is minimal differential action, there is still a lot of grinding force here and the carrier will quickly wear, despite the large number of contact points. The planet gears themselves are also quite fragile, but reinforcement pins solve this. We still require some kind of bearing or bushing to prevent the carrier getting chewed out.

It is also quite difficult to back drive, but this is the intention (kind of like steering without rolling). Still, lubrication is required for smooth action.

In the interests of not requiring specialized hardware (bearings or bushings). One suggestion is to use steel washers and nails. A small recess to seat a washer and some glue should make an adequate bearing surface for a nail axle. Alternatively, use a larger washer to cover the entire carrier plate and drill holes for the pins.