simple planetary gear set how to work and calculate

In this post I will explain simple planetary gear set. How does it work and calculate? A planetary gear set has four main items : sun gear,  ring gear, carrier, planetary gears. Sun gear and planetary gears are outer gear assembly. Ring gear and planetary gears are

1. How does simple planetary gear set work?

+ Case 1: We will fix carrier, planet gear rotate around their axis.  Sun gear is input power. Sun gear and planet gear are external gear and therefore rotation transmission is reversed. Ring gear and planet gear are internal gear and therefore rotation transmission is same.

+ Case 2. We will fix ring gear. When carrier rotates around it-self, planet gear will have two transmission, rotate around it-self  and center axis of carrier.

+ Case 3: We will fix sun gear. When carrier rotates around it-self, planet gear will have two transmission, rotate around it-self and center axis of carrier.Ring gear will rotate following the planet gear.

2. How to calculate planetary gear set ratio transmission?

The first, all gears in the planetary gear set have same module.  Sun gear has A teeth, planetary gears have B teeth, ring gear has C teeth. Because they will assemble together so we have C=A+2B

We have 6 working status

+ We will fix carrier.

If sun gear is input power -> Output is ring gear. We can calculate ratio transmission by formula: i = -A/C -> reduce speed system

If ring gear is input power -> Output is sun gear. : i = -C/A -> increase speed system

+ We will fix sun gear, planet gear can rotate around their axis.

If carrier is input power -> Output is ring gear. i = 1/(1+A/C)

If ring is input power -> Output is carrier. i = 1/(1+C/A)

+ We will fix ring gear, planet gear can rotate around their axis.

If sun is input power -> Output is carrier .  i = 1+C/A

If carrier is input power -> Output is sun gear.  i =1+A/C

 

You can see this video below for more detail.