Planetary Gear
Planetary Gear Set :
The planetary gear set or the epicyclic gear train is an important component of an automatic gearbox. In this study, we have done an analysis of various cases of the planetary gear set. Input and output angular velocities are calculated for all the cases.
The planetary gear set is a set of gears including sun spur gear, planet gears, and internal ring gear. Carrier is attached to the planet gears which is taken as output in some cases. It's of simple gear mechanism where linear velocity remains the same for two gears at the place of contact.
Calculations for planet gear:
module for all the gears = 2.5
module = (diameter)/(no of teeth)
for sun gear, no of teeth = 14
diameter (pitch circle) = 14*2.5 = 35 mm
for internal spur ring gear, no of teeth = 46
diameter = 46*2.5
= 115 mm
thus, the pitch circle diameter of planet gear will be = (115-35)/2
= 40 mm
no of teeth in planet gear = 40/2.5
= 16
* Internal ring gear outer diameter, sun gear internal diameter and planet gear inner diameters are selected accordingly. Carrier shaft daimeter is equals to the plant inner diameter.
Angular Velocity and Some Specifications :
Input rpm = 200
input angular velocity = 2*3.14*N/60
= 20.93 rad/sec
Some specifications: I have used-
No of frames per second = 250
Precise contact = On
All the parts, assemblies, and animations are attached along with this report.
Case 01 :
In this case, the input is given to sun gear and output is achieved at carrier while keeping ring gear fixed.
Sun gear angular velocity graph is given below-
This is almost constant throughout which is obvious as we are giving input as constant rpm.
Output or carrier angular velocity varies as follows-
Explanation: The highest value of carrier angular velocity is around 326 deg/sec which is almost one-third of the input velocity (20.933 rad/sec or ~1200 deg/sec). The variation in the values is due to the non-continuous and improper contact between teeth or backlash phenomenon. This condition is of the very first gear in an automatic gearbox vehicle.
The below figure shows two points A & B. A is the contact point of sun and planet gear and B is the contact point of planet and ring gear. At point A, motion is transferred to the planet gear in the reverse direction. But as the ring gear is stationary, total linear velocity should be zero at the point B, thus the planet gears rotate in the clockwise direction about the axis of the ring gear. Which results in the rotation of the carrier. The output angular velocity decreases firstly due to the fact that the size of planet gear is greater than the sun gear, secondly point B is far from A and it requires a less angular velocity of the carrier to maintain the zero velocity at B.
Case 02 :
In this case, the sun gear is kept fixed and input is provided to the ring gear. The output is achieved at the carrier. Various graphs are plotted for the case. Following graph is of input or ring gear angular velocity-
The graph remains almost constant which is an again obvious result of constant input rpm.
Output angular velocity graph is shown below (carrier)-
Explanation:- In this case, the highest angular velocity is around two-third of the input velocity which results in a higher gear position. Again some fluctuation in the values is due to the improper connection of gears or backlash phenomenon.
The output velocity, in this case, is higher than the previous case because - the planet gear is transferred motion by ring gear which rotates the planet gear in the same direction with higher velocity (due to small size). As the angular velocity of planet gear is high about its own axis, it needs high angular velocity about sun gear axis to maintain the total zero velocity at point A (sun gear is fixed).
Case 03 :
In this case, the input is given to the sun gear and output is achieved at ring gear keeping carrier fixed. Sun gear angular velocity remains constant as shown below-
Following results are achieved for the output from ring gear-
Explanation:- In this case, the output velocity again reduces to one-third of the input. But this time there will be one major difference from the previous cases in the sense that the output is in the reverse direction this time. This is the case of reverse gear.
Summary:-
In this report, I've included various cases of a planetary gear set. All the input and output velocities are explained with graphs. First case, where the input was provided to the sun gear and output was achieved at the carrier, it was the condition for the initial gear position in the automatic gearbox. The second was of some high velocity and the third case was of reverse gear.
Assembly file and part files are attached to this report.