Analysis of Planetary Gear Systems

AIM

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

OBJECTIVE

• To create 3D models for all parts.
• To perform motion analysis by rotating the input gear at 200 rpm.
• To obtain a plot for Angular velocity of the output.
• To export the results to a spreadsheet.
• To create motion study for three conditions-

Study number	Input	Output	Fixed
1	Sun gear	Carrier	Ring gear
2	Ring gear	Carrier	Sun gear
3	Sun gear	Ring gear	Carrier

THOERY ON PLANETARY GEARS

The Planetary gears are also called as an epicyclic gear train, it is a combination of the ring gear and spur gear. the planetary gears consist of four parts the sun gear, which is rotated about its own axis. the second gear is ring gear which is act as a housing for gear assembly. the third one is planet gear which is mounted between Sun and ring gear.

In addition to this, we have a carrier. A carrier is a component on which the whole planetary gear assembly is mounted. with the help of carrier by fixing different component of the Assembly we can get different output.we can find this type of gear set up in Automotive transmission and also in mechanical lathe machine.

DESIGN PARAMETERS

• Ring Gear:
  • Module = 2.5 (use the metric system in design modeller)
  • Number of teeth = 46
• Sun Gear:
  • Number of teeth = 14

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

CALCULATIONS

The module(m) is the ratio of reference diameter (or) Pitch diameter to the number of teeth.

m=d/T

here, m = module

d = pitch circle diameter

T = number of teeth

For Ring gear:

Module(m) = 2.5

Number of teeth(T) = 46

So, Pitch circle diameter(d) = m*T = 2.5*46 = 115

For Sun gear:

Module(m) = 2.5

Number of teeth(T) = 14

So, Pitch circle diameter(d) = m*T = 2.5*14 = 35

For Planet gear:

Module(m) = 2.5

Number of teeth(T) =?

Radius of Ring Gear = Radius of Sun gear + Diameter of planet gear

(m*T/2)_Ring = (m*T/2)_Sun + (m*T)_Planet

No. of teeth of Ring gear = No. of teeth of Sun gear + 2 × No. of teeth of Planet gear

46 = 14+2*T_planet

T_planet = 16

So, Pitch circle diameter(d) = m*T = 2.5*16 = 40

After calculating all unknown parameters the final result table is as follows.

Sr. No.	Gear	Pitch Circle Diameter	Module	Number of Teeth
1.	Ring Gear	115	2.5	46
2.	Sun Gear	35	2.5	14
3.	Planet Gear	40	2.5	16

MODELS

Ring gear

Sun gear

Planet gear

shaft

Assembly

RESULTS

Plot for Angular velocity of Carrier with the following three conditions

First Case- Plot for Angular velocity of Carrier with the following conditions.

Input	- Sun Gear
Output	- Carrier
Fixed	- Ring Gear

Here we can see that the initial angular velocity is zero and when the rotor starts rotating the angular velocity increases drastically. we also see that there is fluctuation in the angular velocity which is caused due to the multiple components in the assembly. As our assembly gets momentum the fluctuation in the angular velocity reduces and it maintains a constant speed. Animation-utu.be/B17vW3uDLtI

Second Case- Plot for Angular velocity of Carrier with the following conditions.

Input	- Ring Gear
Output	- Carrier
Fixed	- Sun Gear

Animation-https://youtu.be/Rb1qrXvpdcs

As plot defines the angular velocity is zero at the initial stage and rotor start rotating the angular velocity increases drastically. but fluctuation induced is decreased with time and maintain a constant rate.

Third Case- Plot for Angular velocity of Ring Gear with the following conditions.

Input	- Sun Gear
Output	- Ring Gear
Fixed	- Carrier

Animation-https://youtu.be/lxdQG3j8TkI

As plot defines the angular velocity is zero at the initial stage and as input rotation increases the angular velocity increases drastically and maintain constant throughout.

CONCLUTIONS

• 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.