Planetary Gear
AIM: Run a motion analysis with different input and output condition.
OBJECTIVES:
- Calculate the pitch circle diameter and the number of teeth for the planet gear.
- Motion analysis for a different condition.
PLANETARY GEAR
A planetary gear (also known as epicyclic gear train) consists of two gears mounted so that the center of one gear revolves around the center of the other. A carrier connects the centers of the two gears and rotates to carry one gear, called the planet gear or planet pinion, around the other, called the sun gear or sun wheel.
INPUTS
DIFFERENT CONDITION
|
Sr. No |
Input |
Output |
Fixed |
|
1 |
Sun Gear |
Carrier |
Ring Gear |
|
2 |
Ring Gear |
Carrier |
Sun Gear |
|
3 |
Sun Gear |
Ring Gear |
Carrier |
STEP-WISE PROCEDURE:
- First, we have to create a gear with help of design library for the given number of teeth and pitch circle diameter and save as a separate part.
- Now we have to assemble all the gear with help of appropriate constrain.
- Then go to motion analysis and give the contact between all the gears.
- Give the motor to the input as different condition and set the speed 200 rpm.
- Due to high input speed we have to increase the frames per second to capture every degree of rotation.
- Then calculate the motion data and plot the graph for the angular velocity of input and output component.
OUTPUT PLOTS
Case 1: Ring gear is fixed; Sun gear is input gear and the carrier is output
Input angular velocity
Output angular velocity
ANIMATION
https://drive.google.com/file/d/1XTEJ-B_ds9JxxpAbCyK_RQv3_-NaSqxi/view?usp=sharing
Case 2: Sun Gear is fixed; Ring gear is input gear and the carrier is output
Input angular velocity
Output angular velocity
ANIMATION
https://drive.google.com/file/d/1yKL2xA9URT9CYZpnE2x6CFUgamonjchP/view?usp=sharing
Case 3: Carrier is fixed, Sun gear is input gear and the Ring gear is output
Input angular velocity
Output angular velocity
ANIMATION
https://drive.google.com/file/d/1IY1nt9FaRTHXxwT5iLToYvo7KbR2Y159/view?usp=sharing
CONCLUSION
In the case of a simple planetary gear train formed by a carrier supporting a planet gear engaged with a sun and ring gear, the fixed carrier train ratio is computed as the speed ratio of the gear train formed by the sun, planet and ring gears on the fixed carrier. This is given by
`R=ω_s/ω_r =-Z_r/Z_s`
The fundamental formula of the planetary gear train with a rotating carrier is obtained by recognizing that this formula remains true if the angular velocities of the sun, planet and ring gears are computed relative to the carrier angular velocity. This becomes,
`R=(ω_s-ω_c)/(ω_r-ω_c )=-Z_r/Z_s`
Case 1:
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.
As the ring gear is fixed
From this we get
`ω_c≈280` deg/sec
Which we get in the plot as output.
Case 2:
When the sun gear is fixed and input is given to ring gear , 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.
As the sun gear is fixed
From this we get
`ω_c≈920` deg/sec
Which we get in the plot as output.
Case 3:
When the carrier is fixed and input is given to sun gear, the sun gear will rotate the planet gear but planet gear is only rotate about is axis and planet gear rotate the ring gear. In this ring gear rotate in the opposite direction of sun gear.
As the carrier is fixed
From this we get
`ω_r≈-365` deg/sec
Which we get in the plot as output.
I also conclude that when we use solid contact between the gears, we get the small deviation in the angular velocity plot which is not smooth. So, when we give the gear mate in assembly and try to get the motion analysis and plot the graph for angular velocity.it is smooth one we get. I try this for the case 3 and I get plot like this and value of angular velocity is also same which is derive by formula.
PART AND ASSEMBLY LINK
https://drive.google.com/drive/folders/1q67WNut02trlhG_o_Gm95fPOSbdFUAht?usp=sharing
REFERENCE
https://en.wikipedia.org/wiki/Epicyclic_gearing#Gear_ratio_of_standard_epicyclic_gearing