Planetary Gear
AIM -Constructing a Planetary gear system with four planet gears and analyzing the angular velocities for different cases.
Theory:-A 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 (yellow), and transmits torque to the planet gears (blue) which are typically mounted on a moveable carrier (green). The planet gears orbit around the sun gear and mesh with an outer ring gear (pink). Planetary gear systems can vary in complexity from very simple to intricate compound systems, depending on the 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.
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, in the load is more evenly distributed and therefore the gears are more resistant to damage.
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
SUN GEAR
PLANETARY GEAR
RING GEAR
COMPLETE ASSEMBLY
Case 1: Fixing the Ring Gear, giving input to the sun gear and receiving output at the carrier
Case 2: Fixing the Sun gear, giving input to the Ring gear and receiving output at the carrier
Case 3: Fixing the carrier, giving input to the sun gear and receiving output at the ring gear
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=rwv=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 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=rwv=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 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.