Planetary Gear
Planetary Gear Mechanism
A gear train that consists of gears similar to the solar system i.e. it has a sun gear, planetary gear and also ring gear(outermost gear). Gears has a tendency to rotate about its own axis and also the central axis of the arrangement.
Here the mechanism is obseverd in 3 different cases at 200 rpm and also the variation of the angular velocity of the output gear as mentioned with respect to the time.
Initially the SUN,PLANETARY and RING gear are designed using the solidworks toolbox in ANSI METRIC as per the given module.
The number of teeth and the pitch circle diameter(PCD) of the planetary gears was found fromt he geometrical approach using the solidworks sketch. In the sketch, as the PCD of sun and ring gear were known, so the circle of the gicen dimensions were made concentrically. Then the planetary gear PCD cirlce was made in such a way that the randomly made circle was given the contraints of being tangent to the cirls of the sun and ring gear respectively. This lead us to find the PCD of the planetary gears there by the number of the teeth on it as the module was given. It was made tangent as the meshing of gears are done in a smooth manner when the PCD's of each gear in mesh are tangent to each other.
Formula used: `m=(PCD)/n`
where m= module of the gears,
PCD= Pitch Circle Diameter
n= Number of teeth on the gear.
So by using the above relation, as the module given was 2.5 and the PCD of planetary gears form the solidworks sketch was found to be 40mm, so the number of teeth on using the formula resulted as 16.
The assmebly was made using the mate options like concentric and coincident. No Gear mate was used.
Also a Carrier was designed based on the dimensions of the planetary gears and their arrangement.
Case 1:
Input - Sun gear; Output - Carrier; Fixed - Ring Gear.
The motor feature was given to the sun gear with respect to its central axis and also the contact bodies to all bodies as steel and then on the calculation and then from the resulted plot of the angular velocity of the carrier(output) it was observed that the angular velocity gradually increase with respect to the time and then becomes constant throughout.
The mates like concentric and coincident were used but the ring gear was fixed and also the concentric mates for the 4 planetary gears were suppressed so that those move around the sun gear.
The following shows the plot for angular velocity and the time.
Case 2:
Input - Ring Gear; Output - Carrier; Fixed - Sun Gear.
The motor feature was given to the ring gear with respect to its central axis and also the contact bodies to all bodies as steel and then on the calculation and then from the resulted plot of the angular velocity of the carrier(output) it was observed that the angular velocity suddenly jumps from 0 to a high value of 470 deg/sec and then gradually increses to the maximum with respect to time and from there it becomes constant at that maximum value.
The mates like coincident anad concentric were used and the sun gear was fixed and also the concentric mates for the 4 planetary gears was suppressed in order to freely move the gears around the sun gear with having the mesh with sun and the ring respectively.
Case 3:
Input - Sun gear; Output - Ring Gear; Fixed- Carrier.
The motor feature was given to the sun gear with respect to its central axis and also the contact bodies to all bodies as steel and then on the calculation and then form the resulted plot of the angular velocity of the ring gear(output) it was observed that the angular velocity gradually increases with time and then becomes constant throughout.
The mates like coincident anad concentric were used and though the carrier was fixed, it got fixed by default when the 4 planetary gears were fixed in location by using the concentric mates.
The following shows the plot for angular velocity and the time.