Planetary Gear

Aim of The Project:

Motion analysis of a Planetary Gear System.

Objectives:

1. To calculate the 'Pitch Circle Diameter' and the 'Number of Teeth' for the Planet Gear.
2. Performing Motion Analysis of the Planetary Gear System.
3. Obtaining plots of Angular Velocity for different outputs.

Introduction:

Epicyclic gearing or planetary gearing is a gear system consisting of one or more outer, or planet, gears or pinions, revolving about a central sun gear or sun wheel. Typically, the planet gears are mounted on a movable arm or carrier, which itself may rotate relative to the sun gear. Epicyclic gearing systems also incorporate the use of an outer ring gear or annulus, which meshes with the planet gears. Planetary gears (or epicyclic gears) are typically classified as simple or compound planetary gears. Simple planetary gears have one sun, one ring, one carrier, and one planet set. Compound planetary gears involve one or more of the following three types of structures: meshed-planet (there are at least two more planets in mesh with each other in each planet train), stepped-planet (there exists a shaft connection between two planets in each planet train), and multi-stage structures (the system contains two or more planet sets). Compared to simple planetary gears, compound planetary gears have the advantages of larger reduction ratio, higher torque-to-weight ratio, and more flexible configurations.

Simulation Cases:

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

Given Input Parameters:

1. Ring Gear
   • Module = 2.5
   • Number of teeth = 46
2. Sun Gear
   • Number of teeth = 14
3. Input Speed of the Gear = 200 rpm.
4. Number of planet gears = 4

Planetary Gear Specifications:

Module(m) = 2.5

Pitch Circle Diameter = p

No.of teeth = N

`m=p/N`

`p_((r))` = 115 mm

`p_((s))` = 35 mm

Calculation:

`(p_((r)) )/2 = (p_((s)))/2 + p_((p))`

`p_((p)) = 40 mm`

`N_((p)) = 40 /2.5 =16`

Screenshots of Parts and Assembly:

Ring Gear:

Sun Gear:

Planet Gear:

Carrier:

Whole Assembly:

OUTPUTS AND PLOTS:

1st Case Study:

Fixing Ring gear and giving input to the Sun gear and getting output at the Carrier.

Input Plot (Angular Velocity vs Time):

Output Plot (Angular Velocity vs Time):

Animation link: Ring gear fixed

2nd Case Study:

Fixing Sun gear and giving input to the Ring gear and getting output at the Carrier.

Input Plot (Angular Velocity vs Time):

Output Plot (Angular Velocity vs Time):

Animation Link: Sun Gear Fixed

3rd Case Study:

Fixing Carrier and giving input to the Sun gear and getting output at the Ring Gear.

Input Plot (Angular Velocity vs Time):

Output Plot (Angular Velocity vs Time):

Animation Link: Carrier Fixed

RESULTS

As we can see from the above plots we are getting different output angular velocity for the same input angular velocity by mere changing the input gears

1. In case 1, that is when the ring gear is fixed and the input is given to the sun gear, at the point of contact between the sun and the planet gear the velocity will be same, but at a point where the planetary gear is in contact with the ring gear, the velocity should be zero. So to satisfy this, the planet gear should spin as well as turn simultaneously to satisfy both these conditions.v = rw is the velocity at the meeting point of sun and planet gear and input is given to the sun gear hence speed depends on the radius of the sun gear for this case.
2. In Case 2, the input is ring gear and the sun gear is fixed, the ring gear will rotate the planet gear and the point of contact between the planet and ring gear should have the same velocity and also the velocity of the mating point of sun and planet gear should be zero, so to satisfy this, the planet gear will spin as well as turn. but the output obtained will be more asr in v=rw is greater for ring gear and hence output obtained will be more than the case 1, as can be seen from the plot.
3. In case 3, the carrier is fixed, so the planet gears will only spin and will not revolve around the sun gear, and the output will be obtained at the ring gear which will spin in an opposite direction to the sun gear and hence a reverse gear will be obtained

Conclusions:

1. The angular velocity obtained is maximum in Case 2.
2. Small disturbances are produced in the output due to the mating of gears.
3. The output angular velocity is lower than the input angular velocity in each case.

Google Drive link of my Parts and Assembly Solidworks files:

Solidworks files of Parts and Assembly of The Planetary Gear Train

References:

https://en.wikipedia.org/wiki/Epicyclic_gearing