# How to calculate the output torque on a split ring gear?

I have a nema 17 motor and I'm trying to lift 5 pounds of weight at a distance of 16 inches.

Correct me if I'm wrong, but it comes out to roughly 9 newton meters of torque required.

On my digital scale, the motor can apply 260 grams of force at a distance of 56 millimeters.

aka 14560 g/mm aka 14.56 kg/mm aka 0.14 nm

9nm / 0.14 nm = 64 times weaker that needed

So I created a split ring planetary gearbox that has a 92:1 reduction ratio using this site:

Pastable I O B: 15 30 31

Input Teeth: 15

Base Teeth: 31

Output Teeth: 30

Then I created and 3d printed the gearbox:

When I test the gearbox against the digital scale. It is only able to apply 1000 grams of force with an arm 57 mm long before stalling out.

57000 g/mm aka 57kg/mm aka 0.56 nm

Which is only a strength multiplication of about 4.

It was my understanding that the reduction ratio correlates directly to the torque and speed.

The output shaft would rotate 92 times slower, but have 92 times more torque.

Where did I go wrong in my understanding of this?

• Friction, alignment error. Gears always have some losses to friction. Alignment issues cause you to expend energy in bending your components (and then don't do useful things on unbending). I suggest laser cut sheet metal over 3d printed plastic and grease if you want to waste less energy.
– Abel
Jan 22 at 12:45
• Can also try adding a solid plate connecting shafts going through the three little gears to help maintain their alignment.
– Abel
Jan 22 at 21:18
• @Abel you're absolutely certain that over 90% of the torque is being lost due to an alignment issue and nothing else?
– John
Jan 23 at 5:10
• As you are the one with the physical hardware, you are the one in a position to verify. What stands out to me in your design is that it requires the gears to be constrained in a certain way but lacks low friction items to make that happen. What makes your 3 little gears stay upright when being forced in shear? It's that they are jammed between the upper and lower sections and that jamming takes force which in turn makes friction.
– Abel
Jan 24 at 9:24
• Also considering it over 90% is like counting your chickens before they're hatched. You aren't using a conventional planetary gearbox to begin with since you are missing a good carrier.
– Abel
Jan 24 at 9:33