Planetary Gear

AIM:

Constructing a planetary gear system with four planet gears fixed to a carrier and analyzing the angular velocities of the input and output gears.

INTRODUCTION:

planetary gear set is made up of three types of gears; a sun gear, planet gears, and a ring gear. The sun gear is located at the center and transmits torque to the planet gears, which are typically mounted on a moveable carrier. The planet gears orbit around the sun gear and mesh with an outer ring gear. Planetary gear systems can vary in complexity from very simple to intricate compound systems, depending on the application. Planetary gear systems are able to produce a lot of torque because the load is shared among multiple planet gears. This arrangement also creates more contact surfaces and a larger contact area between the gears than a traditional parallel axis gear system. Because of this, the load is more evenly distributed, and therefore the gears are more resistant to damage.

Application:

Planetary gears are often used when space and weight are an issue, but a large amount of speed reduction and torque are needed. This requirement applies to a variety of industries, including tractors and construction equipment where a large amount of torque is needed to drive the wheels. Other places you will find planetary gear sets include turbine engines, automatic transmissions, and even electric screwdrivers.

Input Parameters:

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

Planetary Gear

• Number of teeth in Planetary Gear = 40/2.5 = 16

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

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

Calculation:

The module(m) is the ratio of reference diameter (or) Pitch diameter to the number of teeth.

`m=d/T`

here,

`m` = module

`d` = pitch circle diameter

`T` = number of teeth

For Ring gear:

Module(`m`) = 2.5

Number of teeth(`T`) = 46

So, Pitch circle diameter, `d=m*T`= 2.5*46 = 115

For Sun gear:

Module(m) = 2.5

Number of teeth(T) = 14

So, Pitch circle diameter, `d=m*T` = 2.5*14 = 35

For Planet gear:

Module(m) = 2.5

Number of teeth(T) =?

Radius of Ring Gear = Radius of Sun gear + Diameter of planet gear

(m*T/2)Ring = (m*T/2)Sun + (m*T)Planet

No. of teeth of Ring gear = No. of teeth of Sun gear + 2 × No. of teeth of Planet gear

46 = 14+2*Tplanet

Tplanet = 16

So, Pitch circle diameter(d) = m*T = 2.5*16 = 40

Sl.No	Type of Gear	Module	Pitch Circle Diameter(mm)	No. to Teeth
1	Ring Gear	2.5	115	46
2	Sun Gear	2.5	35	14
3	Planet Gear	2.5	40	16

Gear Design:

i. RING GEAR:

ii. SUN GEAR

iii. PLANET GEAR

iv. CARRIER MODEL

v. FINAL ASSEMBLY

ANALYSIS:

Case 1:

Fixing the Ring Gear, giving input to the sun gear and receiving output at the carrier

Contact Force B/W Planetry gear and Ring gear

Case 2:

Fixing the Sun gear, giving input to the Ring gear and receiving output at the carrier

Contact Force B/W Planetry gear and Ring gear

Case 3:

Fixing the carrier gear, giving input to the sun gear and receiving output at the ring

Contact Force B/W Planetry gear and Ring gear.

Conclusions

• In 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 103.9999 deg/sec and varies in a very small fraction.

• In 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 92.0005 deg/sec and varies in a very small fraction

• In third case,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. 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 36.5217 deg/sec and varies in a very small fraction