Motion analysis of Planetary Gear using SolidWorks
AIM
To perform motion analysis of planetary gear in SolidWorks
PLANETARY GEAR
A planetary gear is also known as epicyclic gear train. It contains and input and an output shaft in a co-axial arrangement. It consists of a sun gear, a ring gear, planetary gears and a carrier carrying the planet
gear or gears,all of the same size, to transmit the torque produced to the desired component. Usually, the sun gear and the planet gears are the regular spur gears whereas the ring gear is an internal spur gear. The sun and the ring gear are concentric to each other.
There are 3 shafts, each associated to sun gear, planet carrier and ring gear respectively. Often, the motion of the shaft is restricted, thus, giving input and output to the remaning two shafts. However, in some cases, 3 shaft operation is used in which two of them may be driver shaft and the remaining be driven shaft or vice-versa.
In this study, we would be considering the three cases, with the motion of each one of the three shaft being arrested respectively. In order to design the assembly, we would first need to determine the pitch diameter and the number of teeth of the planet gear with the information provided.
Given,
module of each gear, m = 2.5
Number of teeth in the sun gear, `N_s`= 14
Number ofteeth in ring gear, `N_r` = 46
Now, we have a relation between module, pitch diameter and the number of teeths given as;
`m = D/N`
Using the above relation, we can determine the pitch diameter of the sun and the ring gear.
Diameter of sun gear, `D_s` = `m*N_s`
= 2.5*14 = 35 mm
Diameter of ring gear, `D_r` = `m*N_r`
= 2.5*46 = 115 mm
Now, for perfect meshing of the teeth, the pitch diameter of planet gear should be tangential to the pitch diameter of the sun and the ring gear.
`implies` `D_s + 2*D_p = D_r` , where `D_p` is the diameter of the planet gear.
`therefore`, 35 + `2*D_p` = 115
thus, we get `D_p` = 40 mm
Once we get the diameter of the planet gear, we can determine the number of teeths using the relation described above.
Number of teeth on planet gear, `N_p` = 40/2.5 = 16
Having obtained all the necessary information, the necessary gears could be obtained for the assembly from the SolidWorks library. For the assembly, we would be using ANSI Metric system.
SUN GEAR
PLANET GEAR
PLANET CARRIER
RING GEAR
OUTPUT
Case 1: Ring gear is fixed
In this case, the ring gear is made fixed and the motor is applied to the sun gear, which acts as the input. The sun gear transmits torque to the carrier, carrying the planet gears. The planet gears are in contact with both the sun gear and the ring gear and are free the carrier is free to rotate about the central axis of the planetary gear. The motion obtained and the angular value of the carrier, provided te angular velocity of the sun gear, that is 200 RPM is shown below;
Angular velocity of carrier
Let `omega_s` = angular velocity of sun gear = `200*360/60` deg/sec
`omega_c` = angular velocity of carrier
Then, `omega_s/omega_c=1+N_r/N_s`
`therefore omega_c = omega_s/(1 + N_r/N_s)`
Theoritically, the angular velocity of the carrier comes out to be 280 deg/sec which is about same as that shown by the graph. Hence, the graph is pretty accurate.
Simulation of planetary gear
https://drive.google.com/file/d/1leF5lyPJpCm2GLtLbbOFpxVHRf1QXSTO/view?usp=sharing
Case 2: Sun gear is fixed
In this case, the sun gear is restrained to rotate and the ring gear is given a rotation of 200 RPM. Therefore, the ring gear shaft acts as input and the carrier acts as the output. The motion of the planetary gear obtained and the angular velocity of the carrier is given below;
Angular velocity of carrier
Again,
Let `omega_r` = angular velocity of the ring gear = `200*360/60` deg/sec
`omega_c` = angular velocity of the carrier
then, `omega_r/omega_c=1+N_s/N_r`
`therefore omega_c=omega_r/ (1+N_s/N_r)`
Theoritically, angular velocity of the carriercomes out to be 919 deg/sec
According to graph, the angular velocity of carrier is about 920 RPM. Hence, the graph is pretty accurate.
Simulation of planetary gear
https://drive.google.com/file/d/1PndB_ZBjTFKFTa7-R-yaOuJMsv9VEXin/view?usp=sharing
Case 3: Carrier is fixed
In this case, the carrier is held fix. The sun gear shaft is made the input shaft and the ring gear shaft is made the output shaft. Here, the planet gears act as idle gears. The sun gear is given a rotation of 200 RPM. The angular velocity of the ring gear and the simulation of the planetary gear is given below;
Angular velocity of the ring gear
Again,
let `omega_s` = angular velocity of the sun gear = `200*360/60` deg/sec
`omega_r` = angular velocity of the ring gear
then, `omega_s/omega_r = -N_r/N_s`
Here, the negative sign is due to the opposite direction of rotation of the sun and the ring gear due to the presence of the idle gear (planet gear).
Ignoring the negative sign
`omega_r = omega_s/(N_r/N_s)`
Theoritically, angular velocity of the ring gear comes out to be about 365 deg/sec. The graph also shows about the same value which proves that the graph is pretty accurate.
Simulation of planetary gear
https://drive.google.com/file/d/1qBWzKm0bVLhwR9RjQakmauCidXIXjmHJ/view?usp=sharing
CONCLUSION
Planetary gears are known for their high efficiency and high power density in comparison to other types of gears due to their contact construction. This means, they are able to transmit higher torque with smaller size, thus helping in size reduction of the component in which they are used. As the torque is distributed over several gear wheels, the tooth forces are smaller, increasing the gear life. As all the gears are continuously in esh with each other, it leads to lesser noise.
The disadvantages with the planetary gear is that it has a complex construction and complex bearings are used. Also, power dissipation is higher in case of the planetary gear than in spur gear.
REFERENCES
https://en.wikipedia.org/wiki/Epicyclic_gearing