Split Ring Planetary Gearbox

Personal

Individual

January 2023 - Present

Skills:

CAD (Fusion 360)
3D Printing/Rapid Prototyping
Gear theory

Python

Planetary Gearboxes

Planetary gearboxes are a gear-reduction system often found in transmissions containing a singular sun gear, multiple planetary gears which revolve around the sun gear, and a singular ring gear which sits around the planetary gears and meshes with the planetary gears. They offer a compact way of obtaining high-reduction ratios, as well as multiple reduction ratios depending on the input gear, output gear, and stationary gear (which gear is fixed). They boast little backlash and can also easily be coupled to create multiple-stage compound gearboxes with even higher reduction ratios, but can be difficult to backdrive at higher ratios.

The common layout of a planetary gear set

Source

Split-Ring Planetary Gearbox

One of my main goals is to eventually create a 3D printed robotic arm, and this project is the first step in that journey. First, I needed a way to increase the torque on my stepper motors through a reduction system. I was looking at cycloidal drives and harmonic drives, but both did not boast the gear reduction ratios I wanted and required a lot of non 3D printed parts, which I didn't want for my first project. While I was researching other ways, I came across a unique compound planetary gearbox called a split-ring compound planetary gearbox. It is a unique two-stage planetary gearbox which can boast an exponentially higher gear ratio than a traditional compound planetary gearbox. The main principle behind a split-ring planetary gearbox is similar to that of a harmonic drive and cycloidal drive, where the final ratio is determined by a difference in gear teeth between the input ring and the output ring. I included a picture below:

A diagram of a 48:1 gear reduction ratio I created

In a split-ring planetary gearbox, there are two stages, on, which I consider the input stage and the other the output stage. Each stage consists of its own sun, planets, and ring gear. The unique part about this gearbox is that the output gears all share the same axis of rotation as the input gears below it. The input sun turns the input planet gears, which in turn causes the input planet gears to revolve around it. However, the output planets are attached to the input sun and revolve around in the same fashion. Because the output ring gear does not have the same amount of teeth as the input ring gear, the output ring gear must shift over a certain amount of teeth, similar to the way the output shifts in a harmonic drive. For example, if there is a 4 teeth difference between the input and output ring gears, then every time the planet gears finish a full rotation, the output ring gear must shift over 4 teeth to continue meshing properly. From this, we can see where the high ratios come from. The planetary gears must finish one full rotation to cause the output ring gear to only rotate a certain amount of teeth, and there is a ratio between the input sun gear and the planets which is multiplicative with this gear tooth difference.

One thing to note is that the output sun gear does not drive the rotation of the output planet gears, but is there to help force the output planet gears into the output ring gear. It cannot rotate at the same speed as the input sun gear and should freely rotate on the input axis. The entire system can also be driven by directly rotating the planet gears through a carrier, but the sun gears should still be added to force the planet and ring gears to mesh.

Designing Your Own

There are many considerations which need to be made when designing a planetary gearbox and many equations that have to be satisfied to ensure proper meshing of the gears between every system. Unfortunately, solving the entire system of equations to target a desired gear ratio is a complicated task with multiple solutions and because you are solving for the number of gear teeth, which have to be whole numbers, the simpler solution is to test all possible solutions while maintaining a) a large enough gear module and b) gear numbers that make sense and verify that they satisfy the equations. I wrote my own Python script packaged into a Tkinter GUI to make the designing of a split-ring planetary gearbox simpler. The Github can be found here.

GUI of the script

First Prototype

To ensure everything worked, I created a small prototype gearbox with an overall gear ratio of around 48:1. I 3D printed it on my BambuLabs P1S and everything meshed together well!

Current Workings

My next step is to integrate everything into a working gearbox with a 3D printed slew bearing. I am using an ESP32 combined with an Arduino CNC shield and DRV8825 drivers to power the NEMA 17 stepper motor.