PLANETARY GEAR MOTION ANALYSIS

Aim :
Constructing a Planetary gear system with four planet gears and analyzing the angular velocities for different cases

Objective :
Design planetary gear with the following parameters:

Ring Gear:
Module = 2.5 (use the metric system in design modeller)
Number of teeth = 46

Sun Gear:
Number of teeth = 14
Input Speed of the Gear = 200 rpm.
Number of planet gears = 4

Simulation & Analysis of planetary gear system with the following conditions:

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

create the plots of outputs

Introduction:

Planetary Gear System or an epicyclic gear train is used to set different gear ratios by using three sets of the gears sun gear, planet gear, and ring gear.
All the planet gears are mounted to a single rotating member, called a cage, arm, or carrier where the output is obtained.
A planetary gear set is comprised of an outer gear ring that's called the ring gear. As they rotate inside of the ring gear, the planetary gears create pitch circles
that can be formed into a gear train that, in turn, is hooked up to input and output shafts.
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 nd
planetary gear sets include turbine engines, automatic transmissions, and even electric screwdrivers.
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.

Calculation:
Module needs to be same for each gear for the law of gearing to satisfy.

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

Module =
For Ring gear PCD = 46*2.5 = 115
For Sun Gear PCD = 14*2.5 = 35

Now (PCD of Sun Gear)/2 + PCD of Planetary Gear = (PCD of Ring Gear)/2 which gives
PCD of Planetary Gear = 40
Number of teeth in Planetary Gear = 40/2.5 = 16

3D models

1.carrier

2.sun gear

3.ring gear

4.planetary gear

5.Assembly

output Plots:

Case 1 :

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

Annimation link:

https://www.youtube.com/watch?v=VgbcJG0YpG0

Case 2 :

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

Annimation link:

https://www.youtube.com/watch?v=VRdDEf7i4NU

Case 3:

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

Annimation link:

https://www.youtube.com/watch?v=WqyZpFrTvHk

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 xed 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 = rwis 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 xed, 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 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 xed, 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

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

Drive links of the models:

https://drive.google.com/file/d/1I4GNnhDhvAJmpCJkFByDwVPy2lwYk5rT/view?usp=sharing

https://drive.google.com/file/d/1lBq1nWS-FXrsqk-AChbAyGSihwyWHtQf/view?usp=sharing

https://drive.google.com/file/d/1kl6MijtwSFS-rTlcbXFwg6C-Ao18u3sn/view?usp=sharing

https://drive.google.com/file/d/1GstHGLorWH84_ncxx-O4OJpCS2QnaYTq/view?usp=sharing