Planetary Gear
Aim:-Study of Planetary gear tarin System.
Theory:-
Gears are mechanical components used to transfer motion between two shaft.The most wonderful thing about Gears are their ability to maintain constant angular velocity ratio.Also known as gear ratio
`Gear Ratio = (omega1)/(omega2)`
Where
`omega1`=Angular velocity of Drive or pinion
`omega2`=Angular velocity of driven or Gear.
Thus for a gear system the driven as well as the drive has only one dof i.e. rotation about any one common axis
In this picture the smaller gear is called the pinion while the bigger is known as Gear.
Depending on the arrangment of gear they are called Gear train.The various type of gear train include
- Simple Gear Train
- Compound Gear Train
- Epicyclic Gear Train
Each have their owm advantage and specific use in the world.
Simple Gear Train
The video below shows simple gear train.As well as their gear ratio.
This Software was developed by IITians and surely is good to understand the kinematics of Mechanism. Gears are higher contact pairs which transmit constant angular velocity ratio between two shaft.
The shafts however could be of any orientation, like parallel,intersecting,non-intersecting,or inclined shafts. Each type of problem resulted in creating various types of gears.They Include Bevel,Spur,worm and many more
The Simulation is of simple Spur Gear Train.As you can see Blue is the input Gear while the Yellow is the output Gear.And the variation in Gear ratio is clearly seen.This Change in gear ratio causes the change in input speed.
This Variation is controlled by no of Teeths.However the Red and Green gear are only for show because it doesn't modifies the output velocity they are only for connecting distant gears where sprocket or belt cant br opt for .Or when we need input velocity for various purpose .
`(Nblue)/(Nyellow)=(Tblue)/(Tred)*(Tred)/(Tgreen)*(Tgreen)/(Tyellow)`
Thus
`(Nblue)/(Nyellow)=(Tblue)/(Tyellow)`
Compound Gear Train
Compound Gear are used when we have restriction in space or we need multiple output from a single output.
Compound Gears are commonly used in Gears where hour,minute,second hands are driven by a single motor.
`(Nblue)/(Nyellow)=(Tblue)/(Tred)*(Tgreen)/(Tyellow)`
Epicyclic Gear Train
Epicyclic Gear Train apart from other arrangement has two degree of freedom.
It is also called Planetary Gear beacuse of the Sun Planet configuration.The central Gear is know as Sun while the outer gear are Planets.
The internal Gear is known as Ring Gear and the arm is also called as carrier.
Planetary Gears have 2 degree of freedom.
Analytical Study of the given Problem.
The given problem
- Ring Gear
- Module = 2.5 (You must use the metric system in design modeler)
- Number of teeth = 46
- Sun Gear
- Number of teeth = 14
- Input Speed of the Gear = 200 rpm.
- Number of planet gears = 4
For Kinematic Study we are requred to calculate the outpur at three cases
| Sl.No | Input | Output | Fixed |
| 1 | Sun Gear | Carrier | Ring Gear |
| 2 | Ring Gear | Carrier | Sun Gear |
| 3 | Sun Gear | Ring Gear | Carrier |
Tplanet =16
Solving the problem uisng tabular method
| Angular Velocity of Arm | Angular Velocity of Sun | Angular Velocity of Planet | Angular Velocity of Ring |
| 0 | 1 | `-(Ts)/(Tp)` | `-(Ts)/(Tr)` |
| 0 | `x` | `-(Ts)/(Tp)*x` | `-(Ts)/(Tr)*x` |
| `y` | `y+x` | `y-(Ts)/(Tp)*x` | `y-(Ts)/(Tr)*x` |
| `y` | `y+x` | `y-(7)/(8)*x` | `y-(7)/(23)*x` |
Case1.
Simulation showing the motion of the entire assembly
Ring Gear is fixed
Sun Gear is given input.
Carrier is the output
Thus,
`y+x=200`
`y-(7)/(23)*x=0`
Solving then gives
x=153.33rpm
y=46.67rpm
Solidworks gives the ouput in terms of degree/s thus
y=280.02 degree/s
After Simulating in Solidworks,Output graph for Carrier
The Average of all the values give y=279.79 degree/s
Case2
Simulation showing the motion when Sun Gear is fixed
Sun Gear is Fixed
Ring is given input
Carrier is the Output
Thus
`y-(7)/(23)=200`
`x+y=0`
`y=153.33`rpm
x=-153.33 rpm
In terms of degree/s y=919.98 degrees/s
The graph shows the output from Solidworks
The mean of the Output is 917.46 degrees/s(Simulation)
In terms of degree/s y=919.98 degrees/s (Analytical)
Case 3
Simulation showing the motion of the case
Carrier Fixed
Sun Gear as Input
Ring as Output
Thus
`x+y=200`
`y=0`
x=200 rpm
Output:-`y-(7)/(23)*x`
Output:-60.87rpm
or 365 degrees/s
Plot shows the output angular velocity of carrier
The average of the output is 364.44 degrees/s(Simulation)
Output:- 365 degrees/s(Analytically)
Conclusion:Thus the simuation is verified analtically.