Analysis of a Planetary Gear System

Objective

Constructing a planetary gear system with four planet gears fixed to a carrier and analyzing the angular velocities of the input and output gears.

Introduction

A planetary transmission system (or Epicyclic system as it is also known), consists normally of a centrally pivoted sun gear, a ring gear and several planet gears which rotate between these. This assembly concept explains the term planetary transmission, as the planet gears rotate around the sun gear as in the astronomical sense the planets rotate around our sun.
The advantage of a planetary transmission is determined by load distribution over multiple planet gears. It is thereby possible to transfer high torques utilizing a compact design.

In the model created here, the gears are all spur gears.

Individual Gears

Sun Gear

Planet Gear

Internal Gear

Carrier

Dimensions & Conditions

Module = 2.5 for all the gears.

Internal Gear(Ring gear), Number of teeth = 46

Sun Gear, Number of teeth = 14

Number of planetary gears = 4

Speed of Input gear = 200rpm

From Calculations,

Diameter of Internal gear = 115mm

Diameter of Sun gear = 35mm

Diameter of Planet gear = 40

Conditions for Analysis

Sl.No	Input	Output	Fixed
1	Sun Gear	Carrier	Ring Gear
2	Ring Gear	Carrier	Sun Gear
3	Sun Gear	Ring Gear	Carrier

The link to the Parts and the assembly: https://drive.google.com/open?id=19wRNDyvsehY4_NQFTRpEAwerDhp7Bdra

Results

1) Internal Gear(Ring gear) is fixed, Sun gear is input gear and the carrier is output.

Input

Output

Link to the animation:https://youtu.be/lPOcNirM6MA

2) Sun Gear is fixed, Internal gear(Ring gear) is input gear and the carrier is output.

Input

Output

Link to the animation: https://youtu.be/FRf3rEFYVn8

3) Carrier is fixed, Sun gear is input gear and the Internal gear(Ring gear) is output.

Input

Output

Link to the animation:https://youtu.be/nOr0QrMRzWA

Conclusions

• The output speed is lower than the input speed in all cases.
• When Sun gear is input gear, the required speed is achieved within a short duration of time. But when ring gear is input gear, the required speed is achieved linearly with time.
• The output speed has small disturbances due to collisions between the gear tooth.