Planetary Gear

Aim: Design a planetary gear system and analyze the body dynamics using Solidworks.

Objective: 1. Based on the given condition below, calculate the pitch circle dia. and no. of teeth for each gear.

• Ring Gear

• Module = 2.5
• Number of teeth = 46

• Sun Gear

• Number of teeth = 14

• Input Speed of the Gear = 200 rpm.
• Number of planet gears = 4

2. Generate plots for angular velocity output with some initial conditions.

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

Introduction: A planetary gear system also referred to as an epicyclic gear train is used to transmit power and using the gear ratio it can be varied. This whole system consists of majorly 4 components Ring gear, Sun gear, planetary gear, and a carrier. Like in the picture shown below.

The planetary gears and sun gear are connected to a carrier and this system is in mesh with the ring gear that is an outer one. Moreover, a carrier is also called a cage arm where output is obtained. Moreover, the input is given to one of the gear either ring or sun gear and sun gear, ring, or carrier is fixed and output is obtained from one of the following. The major advantage of this system is that it can be used where heavy torque transmission is required. In this system, if torque is transmitted than the load is evenly distributed among all the gear as they’ve good surface contact which makes the system more reliable and less prone to damage.

Components Used:

1. Ring gear: It is a kind of internal spur gear with module 2.5, 46 teeth here.

2. Planetary Gear: It is a normal spur gear with shaft die, a module of 2.5, and 16 teeth count.

3. Sun gear: It is also a kind of spur gear with module 2.5, 14 teeth, and nominal shaft die.

Design: Import the gear from the design library using the ANSI metric and give the input conditions based on calculation.

Design library > Toolbox > ANSI metric > Power transmission > Internal Spur gear for ring gear ,Spur gear as Sun, planetary gear.

Calculations:

Formula Used: M = d/T

Where M is my module of the gear.

d is pitch diameter of the gear.

T is no, of teeth of the gear.

Ring gear:

Given, M = 2.5 and T= 46.

So Pitch diameter = 46* 2.5 = 115mm

Sun Gear:

M= 2.5 and T= 14

So, Pitch dia. = 2.5*14 = 35 mm

Planetary Gear :

We know that,

PCD Planetary gear + PCD Sun gear/2 = PCD Ring gear/2

From this, we get Pitch Dia Planetary gear = 40mm

Since M= 2.5

So teeth = 40 /2.5 = 16

S. No	Gear Type	Module	Pitch Dia (mm)	No. of Teeth
1	Ring gear	2.5	115	46
2	Planetary gear	2.5	40	16
3	Sun gear	2.5	35	14

Plots: Case 1: Ring Gear is Fixed.

The output is on Carrier.

Motor input is given to the sun gear.

Case 2: Sun gear fixed

The output is on Carrier.

Motor input is given to the ring gear.

Case 3: Carrier is fixed.

The output is on the ring gear.

Motor input is given to the sun gear.

Observation & Conclusion: In the first case we fix the ring gear, motor input was given to the sun gear and output was recorded on the carrier. The above plot for case 1 shows the variation of angular velocity w.r.t time. It ranges from 0-296 deg/sec.

In 2nd case, we fix the sun gear and motor input was given to the ring gear and output was measured on the carrier. The above plot for case 2 shows the variation of angular velocity w.r.t time which ranges from 0-934 deg/sec. It can be observed that the obtained angular velocity is highest among all three cases because as planetary gears are small and in mesh with ring gear which is larger gear so for smaller gear i.e. planetary gear velocity ratio will be higher.

Similarly, in 3rd case, we fix the carrier, input was given to sun gear and output was measured on sun gear which is shown in the above plot for case 3. The angular velocity varies from 0-385 deg/sec.

Animation Links: Case 1 Ring gear is fixed

https://drive.google.com/file/d/11DCU9rg0LloZTXzZXbAbjmo-Q7tnNfhM/view?usp=sharing

Case 2 Sun gear is fixed

https://drive.google.com/file/d/1yHtyg6b4KcGoqaeLLaRFpqbI7GdFrQhp/view?usp=sharing

Case 3 Carrier is fixed

https://drive.google.com/file/d/13kA4BIguBwTSjyzp3kD9fDQOyg-us-W-/view?usp=sharing