Planetary Gear

Title - Motion analysis on the planetary gear Assembly with a carrier.

This type of gear assemblies is are mostly used in automatic transmission.

Components - 1 sun gear

4 planetary gears

1 ring gear

1 carrier.

Calculation of Pitch Circle Diameter and No. of Teeth in Planet Gears:

• The module is the same for all the gears.

The relation between the pitch circle diameter and no. of teeth is as follows -

D = m * t

D = pitch diameter

m = module and t = no. of teeth

Dia of ring / 2= Dia of planetary gear + Dia of sun gear / 2

115/2 = D.P. + 35 / 2

D.P. (Dia of planetary gear) = 57.5 -17.5 = 40mm

Geometry Creation and assembly -

For creating gear from Toolbox -

go to design library - Toolbox - ANSI metric - Power transmission - gears

for sun and planetary gears choose Spur gear

for Ring gear to choose Internal Spur Gear

Pressure angle = 20 degree

Face Width = 20 mm

Carrier geometry -

Whole assembly -

We didn't apply gear mate in this assembly.

But, keeping the position of each gear such as they don't overlap on each other.

save and rebuilt the assembly model.

Motion analysis -

before going into cases add contact pairs -

There are total 8 contact pairs -

4 contact pairs - associating with a sun gear and planetary gear (material -apply dry steel)

4 contact pairs - associating with a Ring gear and planetary gear (material -apply dry steel)

There are 3 cases -

Input speed = 200 rpm

Case 1]

Ring gear fixed

motor - sun gear - 200 rpm

The plot of an angular velocity of the carrier against time

Case 2]

Sun gear fixed

motor - Ring gear - 200 rpm

The plot of an angular velocity of the carrier against time

Case 3]

Carrier fixed

motor - Sun gear - 200 rpm

The plot of an angular velocity of the Ring against time

CONCLUSION:

1. In case 1- when the input is given (200 rpm) 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 since it is fixed (rolling action is present).
2. In case 2- when the input is given to the ring gear (200 rpm) 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. A this can be seen in the plot of angular velocity.
3. In case 3- when a carrier is fixed and output is to be obtained from the ring gear the opposite happens. 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.
4. { 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.}

LINKS FOR THE SIMULATIONS:

case 1] -

Case 2]

Case 3]