Planetary Gear

A Planetary gear (also known as epicyclic gear train) consists of a larger Ring gear, planet gears, and a sun gear. The sun gear is mounted at the center around which the Planet gears are mounted which can revolve around them. The planet gears are meshing internally with the Ring gear which is an internal gear. A carrier is mounted to the planet gears as shown in the image. The combination of epicycle gear trains with a planet engaging both a sun gear and a ring gear is called a planetary gear train.

Here we are using the spur gears. This type of assembly is used in an automatic transmission in vehicles.

Number of components required are:

Ring gear-1

Sun gear-1

Planet gear-4

Carrier-1

Calculation:

The diameter of the Planet gear :

The radius of Ring gear= Diameter of the Planet gear + radius of the 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

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

The ring gear, planet gears, sun gear, and the carrier are assembled as shown in the below image. The assembly is done using mate option by properly aligning all the components in such a way that no component overlap on each other. Here we are not using mechanical gear mates as we have to analyze the motion for 3 cases.

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).

There are 3 cases

The input speed to the motor in each case is 200 RPM. The motion analysis is done for 5 seconds.

Case 1:

Ring gear fixed. Motor - sun gear.

The plot of an angular velocity of the carrier against time.

Case 2:

Sun gear fixed. Motor - Ring gear.

The plot of an angular velocity of the carrier against time.

Case 3 :

Carrier fixed. Motor - Sun gear.

The plot of an angular velocity of the Ring against time.

Observation and conclusion :

• In the first case when the input is given to the sun gear and output is obtained at the carrier keeping the ring gear fixed, the planet gear not only rotates about their axis but are also forced to roll on the inside of the ring gear along with the carrier as the Ring gear is fixed. The angular velocity obtained for this case is between 235-313 deg/sec.
• In the second case when the input is given to the ring gear and output is obtained from the carrier keeping the sun gear fixed. The angular velocity achieved is maximum since the internal gear is big and planet gears are small comparatively so when a large gear meshes with a small gear the velocity achieved from the small gear is high because the velocity ratio is high. The angular velocity obtained for this case is between 800-1017 deg/sec.
• In the third case, the carrier is fixed and output is to be obtained from the ring gear with the input given to Sun gear, all the gears rotate about their axis. The planet gears rotate only about their axis and transmit motion from sun to the ring and since the ring gear is big in diameter the angular velocity achieved is less. The deviations that are visible in the graphs show that there are points where sliding is occurring between the gears. For making the graph more smoother we can use precise contact. The angular velocity obtained for this case is around 340-402 deg/sec.

Animation :

The animation link for the above 3 cases is provided below.

Case 1

https://drive.google.com/file/d/12AP4bY9vzlB8EqCV66GBTVj59FUDsudS/view?usp=drivesdk

Case 2:

https://drive.google.com/file/d/128K2U5B1hKyv9etzNmm80sUIKiRQaJa0/view?usp=drivesdk

Case 3:

https://drive.google.com/file/d/125Opz1AIA7_VElVeY65fjG1PvSxeXV9L/view?usp=drivesdk