MOTION ANALYSIS OF PLANETARY GEAR SYSTEM

AIM: MOTION ANALYSIS OF PLANETARY GEAR SYSTEM

THEORY:

A planetary gear mechanism also is known as Epicyclic Gear Train, is a gear mechanism consisting of 4 components, namely, sun gear A, several planet gears B, internal gear(ring gear) C and carrier D that connects planet gears as seen in the image below. It has a very complex structure rendering its design or production most difficult; it can realize the high reduction ratio through gears, however, it is a mechanism suited to a reduction mechanism that requires both small size and high performance such as transmission for automobiles.

A planetary gearbox is a gearbox with the input shaft and the output shaft aligned. A planetary gearbox is used to transfer the largest torque in the most compact form (known as torque density). The rotation speed of an automobile’s engine in the general state of driving amounts to 1,000 – 4,000 rotations per minute (17 – 67 per second). Since it is impossible to rotate tires with the same rotation speed to run, it is necessary to lower the rotation speed utilizing the ratio of the number of gear teeth. Such a role is called deceleration; the ratio of the rotation speed of the engine and that of tires is called the reduction ratio.

Planetary gear mechanisms have a characteristic of being able to change the reduction ratio by choosing which of the components is to be fixed.
For example, suppose internal gear C is fixed, the input axis is connected to sun gear A, and the output axis carrier D.

Where is the planetary gearbox usually used (in the transmission):

• In a robot to increase the torque
• In a printing press to reduce the speed of the rollers
• For precise positioning
• In a packaging machine for reproducible products

OBJECTIVE:

• To perform the motion analysis of the planetary gear mechanism with the following cases and plot angular velocity of the output gear.

GIVEN:

1. Ring Gear
1. Module = 2.5 (You must use the metric system in design modeller)
2. Number of teeth = 46
2. Sun Gear
1. Number of teeth = 14
3. Input Speed of the Gear = 200 rpm.
4. Number of planet gears = 4
5. Nominal shaft diameter of planet gear = 12 mm

CALCULATION:

To calculate the design parameters of the planetary gear, we first calculate the pitch circle diameters of the ring gear and planet gear. Then, by matching pitch circles of mating gears we can get the pitch circle diameter and no. of teeth of the planetary gear.

We know that, m (module) = (pitch circle diameter)/(no.of teeth) = D/T
Dsun = m*T = 2.5*14 = 35 mm
Dring = m*T = 2.5*46 = 115 mm
Dplanet = (Dring - Dsun)/2 = 40 mm
Nplanet = 40/2.5 = 16

Now we have design parameters of all gear, therefore we can create a CAD model of the planetary gear mechanism.

CAD MODEL AND ASSEMBLY

Using the design toolbox in SolidWorks, the CAD model of internal spur gear(ring gear) and spur gears(1 sun and 4 planetary ) were imported by providing the design parameters i.e. module and no. of teeth. Using the nominal shaft diameter of planet gear, the carrier is modelled. In the assembly, proper mates are given so as to perform the desired motion study.

MOTION ANALYSIS:

To perform the motion study for the three cases, we set up a motor with rpm of 200 to the input gear and provide all contacts. In each case, we fix the gear which is required to be fixed. Then after running the simulation, we get results of the angular velocity of the output.

CASE1: Sun Gear: input (200 RPM), Ring Gear: Fixed, Carrier: Output

https://youtu.be/5ETnmKIU4_M

CASE2: Sun Gear: Fixed, Ring Gear: input (200 RPM), Carrier: Output

https://youtu.be/cKv5ZdeG3wI

CASE3: Sun Gear: input (200 RPM), Ring Gear: Output, Carrier: Fixed

https://youtu.be/1eFrCyhw8zA

OBSERVATION:

CASE	ANGULAR VELOCITY OF OUTPUT (Deg/sec)
Case1	300
Case2	951
Case3	384

EXPLANATION OF PLOTS:

• Case1: When the input is given to sun gear and the ring gear is fixed, we get output in the carrier. In this case, the velocity of planetary gear at the junction where it meets with ring gear has to be constant because ring gear is fixed. Therefore, it spins as well as rotates. The velocity of planetary gear at the junction where it meets sun gear adds up because of rotation and spin in one direction. As all the planet gears rotate, we get output in the carrier as rotation. One thing to note is that the velocity at the junction of planet and sun gear is not large as the radius of sun gear is not much large, it is rather small. Therefore, we get slow angular speed as output in the carrier.
• Case2: When the input is given to ring gear and the sun gear is fixed, we get output in the carrier. In this case, the velocity of planet gear at the junction of sun gear is zero as spin and rotation are in the opposite direction. Also, the velocity of planet gear adds up at junction where it meets ring gear. One thing to note is that, in this case, the velocity of at this junction is more as the radius of the ring gear is more than the sun gear in the previous case. Therefore, the carrier rotates at larger angular velocity than the previous case. Hence, we get large angular speed as output in the carrier.
• Case3: When the input is given to sun gear and the carrier is fixed, we get output in-ring gear. In this case, the planet gear acts intermediate between sun and ring gear. But in this case, the output i.e. ring gear rotates in the opposite direction. Therefore, we get output that is revered.

CAD MODEL FILE: https://drive.google.com/drive/folders/1amJ88Il0B6q8lVUA5WIwgrQ6fSd05dbN?usp=sharing

CONCLUSION:

From the project, we can say that planetary gear mechanism is very useful for transmission application in automobiles where there is a requirement of both to reduce and to amplify the large angular velocity that is coming directly from the engine. Hence, the planetary gear system gives us controlled output which depends on the condition that which gear component is fixed and where the input is given. Therefore, by choosing the requirement we get a different range of output (low speed, high speed, reverse) from the planetary gear mechanism.