Planetary Gear

Aim:

To do the motion analysis on the planetary gear/epicyclic gear train.

Introduction:

A Planetary gear consists of a ring gear, sun gear and planet gears.

In an epicyclic or planetary gear train, several spur gears (planet gears) are distributed evenly around the sun gear.

The planet gears are meshing internally with the ring gear which is an internal gear.

These types of gears are found in automatic transmissions and in mechanical lathe.

Planetary gear consists of four parts:

1. Sun gear
2. Ring gear
3. Planetary gear
4. Carrier: Carrier is a gear on which all the planetary gears are mounted.

GEARS:
Gear are identified by Pitch Circle Diameter, number of teeth and module. If we have any 2 parameters, then the third parameter can be found out. Let’s say we have module and Pitch Circle Diameter then the number of teeth can be calculated.

Module is the ratio of Pitch Circle Diameter to the Number of teeth.

Diametral pitch is the inverse of module.

Given Statement of the problem:

• Ring gear
• Module = 2.5 (Must use the metric system in design modeler)
• Number of teeth = 46
• Sun Gear
• Number of teeth = 14
• Input speed of the gear = 200 rpm
• Number of planet gears = 4

The dimension of the carrier depends on the shaft diameter of the planet gear.

With the above input parameters, we are going to run a simulation on the following cases:

Calculation of parameters:

Formula: Module = PCD / No of teeth

PITCH CIRCLE DIAMETER OF RING GEAR:

PCD of ring gear = Module x No of teeth

PCD of ring gear = 2.5 x 46

PCD of ring gear = 115

PITCH CIRCLE DIAMETER OF SUN GEAR:

PCD of Sun gear = Module x No of teeth

PCD of Sun gear = 2.5 x 14

PCD of Sun gear = 35

PITCH CIRCLE DIAMETER OF PLANET GEAR:

Radius of Ring gear (Rr) = PCD of planet gear (Dp) + Radius of Sun gear (Rs)

PCD of planet gear (Dp) = Radius of Ring gear (Rr) – Radius of Sun gear (Rs)

PCD of planet gear (Dp) = (115/2) – (35/2)

PCD of planet gear (Dp) = 40

Therefore,

Number of teeth of Planet gear = PCD/ Module

Number of teeth of Planet gear = 40 / 2

Number of teeth of Planet gear = 16

DIAMETRAL PITCH OF ALL GEARS = 1 / Module

= 1 / 2.5

= 0.4

FINAL RESULTS OF UNKOWN PARAMETERS:

Sr no.	Gear	Module	Diametral pitch	Number of teeth	Pitch Circle Diameter
1.	Sun gear	2.5	0.4	14	35
2.	Planet gear	2.5	0.4	16	40
3.	Ring gear	2.5	0.4	46	115

Creating Gears from Toolbox in Assembly of SolidWorks

• Sun Gear
• 
• Planet gear
• 
• Ring gear
• 
• Carrier:
• 

The dimensions of the carrier are depending upon the shaft diameter of the planet gear.

• Final Assembly

Motion Analysis for 3 different cases:

The 3 different cases are as follows:

CASE:1

Motor input is given to Sun Gear and Ring Gear is fixed

Output: Carrier

Observation of Case1:

• In the first case, the sun gear is fixed and input is given to Sun gear and output result is obtained at carrier.
• Therefore the planet gear rotates about sun gear and also it rotates about its own axis. Also the sun gear and the carrier rotate.
• The angular velocity obtained is around 300 deg/sec

Animation link: https://youtu.be/iHFC81O9bMQ

Observation:

CASE:2

Sun gear fixed and input is given to ring gear

Output: Carrier

Observation of Case2:

• In this case the sun gear is fixed and the input gear is ring gear, output is obtained at carrier.
• As the input gear i.e. ring gear is large than other gear the angular velocity obtained is very high.
• The angular velocity obtained in this case is in between 800 deg/sec to 1000 deg/sec.

Animation link:https://youtu.be/-EQ3scax4z0

CASE:3

Carrier Fixed and input is given to Sun gear

Output: Ring Gear

Observation of case3:

• In this case the input is given to sun gear and the output is ring gear and the carrier is fixed
• The planet gear rotates around the sun gear and the ring gear. The sun gear is very small as compared to ring gear therefore the angular velocity is less in this case.
• The angular velocity in this case is around 350 deg/sec.

Animation link:https://youtu.be/rcWykpE8ChA