Motion Study Analysis of Epicyclic/Planetary Gears using Solidworks

Aim:- Motion Study Analysis of Epicyclic/Planetary Gears using Solidworks

Objective:-

1. To design a carrier for an assembly of sun and planetary gears.
2. To study motion analysis for 3 cases that are:

• Study1- Input of 200RPM to the Sun gear and study output at the Carrier keeping the Ring gear fixed.
• Study2- Input of 200RPM to the Ring gear and study output at the Carrier keeping the Sun gear fixed.
• Study3- Input of 200RPM to the Sun gear and study output at the Ring gear keeping the Carrier fixed.

Introduction:-

An epicyclic gear train (also known as planetary gear) 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. The planet and sun gears mesh so that their pitch circles roll without slip. A point on the pitch circle of the planet gear traces an epicycloid curve. In this simplified case, the sun gear is fixed and the planetary gear(s) roll around the sun gear.

Advantages of a planetary gear system

The planetary gear system has lots of advantages as compared to traditional gearboxes which are given below:

1. A planetary gear system could be used to secure a higher gear ratio in compact space. Therefore we prefer to use planetary gearing arrangements where we need to reduce the speed in compact space.
2. For a similar gear ratio, the planetary gear system will have lightweight as compared to the traditional gearbox.
3. Power transmission efficiency will be quite good as compared to traditional gearboxes i.e. higher proportion of input energy will be delivered with the help of such gearing arrangement.
4. The planetary gear system will have higher torque transmission capability and will have lower inertia.
5. The load that is being transmitted will be shared between multiple planet gears, hence load distribution will be quite good and torque transmission will also be increased by using planetary gearing arrangement.

Disadvantages of a planetary gear system

There are several disadvantages of the planetary gear system also as mentioned below:

1. The cost of a planetary gear system is high as compared to a traditional gearbox.

2. Designing and manufacturing of planetary gear system are quite complex.

3. Constant lubrication is required.

4. The epicyclic gear system has high bearing loads.

Applications of Epicyclic Gears

The applications of the Epicyclic Gear train are as follows:

1. They are used in running the armature of a wind turbine.
2. Used in various automobiles running under Automatic Transmission.
3. It is also used in tractors and bicycles.

Data Required for Designing:-

Given data:

Module of Ring gear = 2.5(Metric system)

Number of teeth of Ring gear = 46

Number of teeth of Sun gear = 14

Input speed of the gear = 200RPM

Number of Planet gears = 4

Note:- We have not used Gear Mates in assembly.

Calculations:

Pitch circle diameter (PCD) = Number of teeth * Module

PCD ring gear = 46*2.5 = 115mm

PCD sun gear = 14*2.5 = 35mm

To calculate PCD of planet gear, we need number of teeth which can be obtained as given below:

Number of teeth(Ring gear) = 2*Number of teeth(Planet) + Number of teeth(Sun)

Therefore, 46 = 2P + 14        >>  2P =32

P = 16, Hence, Number of teeth for Planetary gear is 16

PCD planet gear = 16*2.5 = 40mm

3D Models and 2D Drawings:-

Carrier: It will hold the sun and planet gears in position and restrict them from falling.

Sun Gear: It is located at the center of the Gearbox and was in mesh with the Planet Gears. More than one sun gear is also attached to achieve different outputs.

Planet Gear: The Planet Gears can rotate around their axis and also under the axis of the Sun Gear and Ring Gear. The Planet Gears are under constant mesh with Sun Gear and the Ring Gear for transmitting the torque.

Ring Gear: It is the outermost Gear which was in the form of a ring whose inner side has angular cut teeth such that they will be in mesh with the outer teeth of the planet gears. When the Ring Gear is under motion, it will achieve higher speeds than others.

Assembly:

Motion Analysis:-

Study 1-  Input of 200RPM to the Sun gear and study output at the Carrier keeping the Ring gear fixed.

 In this case, the Planet gear should have to “Spin as well as Turn“, because it is in contact with the sun and the ring gear but the ring gear is stationary. As the carrier is attached to the planet gear, it will turn along with the planet gears. Thereby, we can get a lesser speed.

The speed of the Planetary Gearbox is calculated by the below formula i.e.

 V = (radius) of Sun Gear * ω(angular velocity)

Observations:

• Ring Gear is fixed
• Sun Gear rotates in Counter-clockwise (CCW) direction
• Planet Gear rotates in Clockwise (CW) direction.
• The shaft rotates in Counter-clockwise (CCW) direction

Plots/Graphs:-

Angular velocity of carrier ranges between 27.3 deg/sec to 28.7 deg/sec.

Simulation:-

Study 2-  Input of 200RPM to the Ring gear and study output at the Carrier keeping the Sun gear fixed.

This is the opposite case as of the previous one. In this case, the planetary gear reverses its direction to satisfy the condition of speeds.

The speed at the contact of the planet and ring gear will be higher than the speed at the contact of the planet and the sun gear (compared to the previous case). This is because the radius of the Ring gear is larger than the radius of the Sun gear.

This will make the Planet gear "Spin and Turn" at a higher speed and this will make the Planet Carrier rotate at a higher speed.

Observations:

• Sun Gear is Fixed
• Planet Gear rotates in counter-clockwise (CCW) direction
• Ring Gear rotates in counter-clockwise (CCW) direction

Plots/Graphs:-

Angular velocity of carrier ranges between 903 deg/sec to 935 deg/sec which is quite greater than the study1.

Simulation:-

Study 3-  Input of 200RPM to the Sun gear and study output at the Ring gear keeping the Carrier fixed.

In this case, the planet gears are not allowed to turn, but they can spin and this spin will be opposite to the rotation of the Sun gear.

The Spinning Planet Gear will make the Ring Gear rotate in the opposite direction I.e. the direction of rotation of the Ring Gear will be opposite to that of Sun Gear. Thus we will get the reverse gear in this case.

Observations:

• Planet Carrier is Fixed
• Sun Gear rotates in counter-clockwise (CCW) direction
• Planet Gear rotates in clockwise (CW) direction
• Ring Gear rotates in clockwise (CW) direction

Plots/Graphs:-

Angular velocity of Ring gear ranges between 358 deg/sec to 381 deg/sec.

Simulation:-

Conclusion:-

1. In study 1, the Angular velocity of carrier ranges between 27.3 deg/sec to 28.7 deg/sec.

2. In study 2, the Angular velocity of carrier ranges between 903 deg/sec to 935 deg/sec which is quite greater than the study1.

3. In study 3, the Angular velocity of Ring gear ranges between 358 deg/sec to 381 deg/sec.

Link to the google drive - https://drive.google.com/drive/folders/1aVCIvFyR2C75k6MD0qao6Nt-sf-K3B8S?usp=sharing

Reference:-

https://en.wikipedia.org/wiki/Epicyclic_gearing