Planetary Gear

Motion analysis of planetary gear train

Aim

To design a planetary gear train system with four planetary gears and obtains the angular velocity for different cases.

Introduction

A gear is a mechanical component that is used to transfer power from one shaft to another. This fundamental old machine component serves as a base to all the modern day technologies and systems like lathes, automobiles, 3D printers and robots. A gear train is a mechanical system formed by mounting gears on a frame so the teeth of the gears engage

Planetary gear train

An epicyclic train consists of two gears mounted so that the centre of one gear revolves around the centre another.The combination of epicyclic gear trains with a planet gear engaging both sun and ring gear is knows as planetary gear train.

An outer gear with inward facing teeth which meshes with the planet gears is known as the ring gear. The central gear around which the planet gears rotate and revolve is knows as sun gear. A carrier is a part which holds one or more planet gears.

Applications

• Automatic transmissions in automobiles.
• Transmission of helicopters, aircraft engines.
• Marine gearboxes and wind mills.

Animation

Pre-design hand calculations

D_r=2D_p+D_s

As we know that,

D=m*t

m*t_r=2mt_p+mt_s

2t_p=t_r-t_s = 46-14

t_p=16.

Now,

D_p=m*t_r=2.5*16

D_p=40mm.

Note: Module and pressure angle of all gears are 2.5 and 20 deg respectively

Here,

D_r=Diameter of ring gear

D_p=Diameter of planet gear

D_s=Diameter of sun gear

m= module

t_r=no of teeth of ring gear

t_p=no of teeth of planet gear

t_s=no of teeth of sun gear

3D CAD Models

Ring gear

Sun gear

Planetary gear

Carrier

Assembled model

Material used

Ring gear-Steel dry

Sun gear-Steel dry

Planetary gear-Steel dry

Motion analysis results (Input speed=200RPM)

Case 1: Providing input at sun gear and obtaining output at carrier with fixed ring gear

Average angular velocity=286 deg/s

Case 2: Providing input at ring gear and obtaining output at carrier with fixed sun gear

Average velocity= 925.25 deg/s

Case 3: Providing input at sun gear and obtaining output at ring gear with fixed carrier

Average angular velocity=367 deg/s

Observations and results

• The maximum angular velocity is obtained when the sun gear is fixed and input is given to the ring gear because the input gear is smaller than the output gear.
• The minimum angular velocity is obtained when the ring gear is fixed and input is given to the sun gear because the input gear is bigger than output gear.
• Gear ratio is inversely proportional to the diameter of the gear and the number of teeth.