Planetary Gear (Multibody Dynamics using Solidworks)

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

Theory- Planetary Gear System or an epicyclic gear train is used to set different gear ratios by using three sets of gear 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.
Planet gears, for their size, engage a lot of teeth as they circle the sun gear, therefore they can easily accommodate numerous turns of the driver for each output shaft revolution
With more planets gears comes an increase in load capacity and torsional rigidity; the more divided the load, the less deflection, and wear of gear teeth

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

S.No      Input                  Output           Fixed

1           Sun Gear            Carrier           Ring Gear
2           Ring Gear           Carrier           Sun Gear
3           Sun Gear            Ring Gear       Carrier

                                                               Sun Gear

                                                                       Planet Gear

                                                                      Ring Gear

Case 1: Fixing the Ring Gear, giving input to the sun gear and receiving output at the carrier

                                                                Input

                                                                  Output

Case 2: Fixing the Sun gear, giving input to the Ring gear and receiving output at the carrier                                                 

                                                                         Input

                                                                      Output

Case 3: Fixing the carrier, giving input to the sun gear and receiving output at the ring gear  

                                                                   Input

                                                                  Output

  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.$v=rw$is 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 the 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 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

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