Planetary Gear

PLANETARY GEAR ANALYSIS

OBJECTIVE: To run the simulation of planetary gear having sun gear, a ring gear, carrier, and four planet gears.

Theory: The planetary gear train also known as the epicyclic gear train is one of the most important and interesting inventions in engineering. They are speed variation mechanisms and often used in automobiles as a vital part of automatic transmissions. It has the following major parts-

1. Sun gear
2. Planet gears
3. Ring gear
4. carrier

Planet gears revolve around the central gear(sun gear). Typically planet gears are mounted on a movable arm or carrier which itself may rotate relative to the sun gear. Outer ring gear meshes with the planet gears.

Problem Specification:

Inputs for designing the Planetary 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

The dimensions of the carrier depending on the shaft diameter of the planet gear.

Cases for simulation-

CALCULATION:

In order to mesh gears should have the same module ( the ratio of pitch circle diameter to the no of teeth)

Therefore Module of Ring gear=Module of Planet gears=Module of Sun gear=2.5

And, 2.5=D_R/T_R=D_P/T_P=D_S/T_S

Where D_R =Pitch circle diameter of the Ring gear

T_R =no of teeth in Ring gear

D_P =Pitch circle diameter of PLanet gear

T_P =no of teeth in Planet gear

D_S =Pitch circle diameter of Sun gear

T_S =no of teeth in Sun gear

Using the above equation

Pitch circle diameter of the Ring gear = 115 mm

Pith circle diameter of PLanet gear = 40 mm

Pitch circle diameter of Sun gear = 35 mm

no of teeth in Sun gear = 14

3D Models:

models have been made using the design library of Solidworks in the ANSI Metric system

Pressure angle = 20 degree

Ring gear

Planet Gear

Sun Gear

Carrier

Assembly: Assembly is done using suitable mates. Gear mates option is not used

Results

Case 1 Ring Gear is fixed input in sun gear output from the carrier.

Case 2 Sun Gear is fixed input in Ring gear output from the carrier.

Case 3 carrier is fixed input in Sun gear output from the Ring gear.

Assumptions:

1. Gear material is Steel dry
2. motor speed is 200 Rpm
3. gravity is in the y-direction
4. contact is solid body contact

Result Explanation:

Case1- In this case, the ring gear is fix and input is provided in the sun gear sin case of meshing between the two gears speed of point of intersection must be the same so for this case, planet gear should have

1) a certain speed at the point of contact with the sun gear and

2) the speed should be zero at the point of contact with the ring gear as it is stationary

so to satisfy both of these two conditions planet gear should spin as well as turn. As the carrier is attached to the planet gear it will turn along with the planet gears. so we get the output from the carrier.

Case2- (Sun Gear is fixed input in Ring gear output from the carrier)

It is just the opposite of the previous case as ring gear rotates planet gear must have the velocity at the point of contact of the ring gear and zero velocity at the point of contact with sun gear as it is stationary so to satisfy these conditions at the same time planet gears forced to rotate as well as spin but in opposite direction as in case 1. In this case, because the ring gear radius is higher this will make the planet gear turn and rotate at a higher speed thus carrier will turn at a higher speed.

Case 3- (the carrier is fixed input in Sun gear output from the Ring gear)

So as the carrier is fixed the planet gears are not allowed to turn and can only spin this spin is the opposite of the rotation of the sun gear. This spinning planet gear will make the ring gear rotate in the same direction therefore the direction of rotation of ring gear is opposite to the sun gear and we get reverse gear.

ANIMATION LINKS

CASE1 https://drive.google.com/file/d/19biSSE9BHuF_r12yNW9NbfhTFdFMAsoJ/view?usp=sharing

CASE2 https://drive.google.com/file/d/1kEqs3zdXEOjDFu4Ghr8Ozbw8aH7j04iT/view?usp=sharing

CASE3https://drive.google.com/file/d/1EWfYeQ_sNxu-V1AZLy9dJjTdY8Hwtl70/view?usp=sharing

File link

https://drive.google.com/drive/folders/1Miq8moTmKnuBLb8Rn1zjNJ758ia2AIiF?usp=sharing