Planetary Gear (SOLIDWORKS)

1. OBJECTIVES - Constructing a Planetary gear system with four planet gears and analyzing the angular velocities for different cases

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

2. GIVEN-

• Ring Gear
  • Module = 2.5 (You 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

3. THEORY-

An epicyclic gear train (also known as planetary gear) consists of two gears mounted so that the center of one gear revolves around the center of the other. A carrier connects the centers of the two gears and rotates to carry one gear, called the planet gear or planet pinion, around the other, called the sun gear or sun wheel. The planet and sun gears mesh so that their pitch circles roll without slip. A point on the pitch circle of the planet gear traces an epicycloid curve. In this simplified case, the sun gear is fixed and the planetary gear(s) roll around the sun gear.

An epicyclic gear train can be assembled so the planet gear rolls on the inside of the pitch circle of a fixed, outer gear ring, or ring gear, sometimes called an annular gear. In this case, the curve traced by a point on the pitch circle of the planet is a hypocycloid.

The combination of epicycle gear trains with a planet engaging both a sun gear and a ring gear is called a planetary gear train.In this case, the ring gear is usually fixed and the sun gear is driven.

Epicyclic gears get their name from their earliest application, which was the modelling of the movements of the planets in the heavens. Believing the planets, as everything in the heavens, to be perfect, they could only travel in perfect circles, but their motions as viewed from Earth could not be reconciled with circular motion

4. CALCULATIONS-

• PCD of the Ring gear & Sun gear :

Ring gear PCD = 46*2.5 = 115

Sun Gear PCD = 14*2.5 = 35

• PCD of the Planet gear :

Radius of Ring gear= Diameter of the Planet gear + radius of sun gear

Rr = Dp + Rs

Therfore,

Dp =Rr - Rs

Dp=115/2 - 35/2 = 40mm

• Number of teeths of Planet gear:

Pitch diameter, D=m*T

where m=module

T= Number of teeth

therefore, T=D/m = 40/2.5 = 16

5. Creating the 3D model-

For creating gear go to

Design library --> Toolbox --> ANSI metric --> Power transmission --> gears for sun and planet gears choose Spur gear, for Ring gear choose Internal Spur Gear

The created models are as shown.

Pressure angle = 20 degree

Face Width = 20 mm

• Ring gear (Internal spur gear)

• Sun gear (spur gear)

• Planet gear (spur gear)

• Carrier model

• Final assembly

6. MOTION ANALYSIS-

In the motion study, make contacts between the followings.

• Carrier and the Planet gears
• Sun gear and the Planet gears
• Ring gear and the Planet gears

The material for each contact is Steel (Dry).

• Case 1: Fixing the Ring Gear, giving input to the sun gear and receiving output at the carrier

Animation:

Angular Velocity vs Time plot for Carrier:

• Case 2: Fixing the Sun gear, giving input to the Ring gear and receiving output at the carrier

Animation:

Angular Velocity vs Time plot for Carrier:

• Case 3: Fixing the carrier, giving input to the sun gear and receiving output at the ring gear

Animation:

Angular Velocity vs Time plot for Ring Gear:

Google Drive Link - https://drive.google.com/drive/folders/1tFq3x3ZzAv_SXfi-ZoMNFboqrpuA5dTy?usp=sharing

7. 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

• 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">v=r*w is the velocity at the mating 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.
• 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 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 as r in v=rw">v=r*w is greater for ring gear and hence output obtained will be more than the case 1, as can be seen from the plot.
• 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

8. Conclusions-

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