Planetary Gear

Modelling and Analysis of Planetary Gear using Solidworks

Aim

To model and analyse planetary gear system in Solidworks.

Objectives

1. Model a Ring Gear with Module = 2.5 , Number of teeth = 46
2. Model a Sun Gear with number of teeth = 14
3. Calculate pitch diameter and number of teeth for planet gear and model them
4. Design a carrier for four planetary gear
5. Motion analysis of different cases by fixing different gears and changing input gears.

a) Case 1 : Input- Sun gear, Output- Carrier arm, Fixed- Ring gear

b) Case 2: Input- Ring gear, Output- Carrier arm, Fixed- Sun gear

c) Case 3: Input- Sun gear, Output- Ring gear, Fixed- Carrier arm

Introduction

A planetary gearbox is a gearbox with the input shaft and the output shaft aligned. A planetary gear set is made up of three types of gears; a sun gear, planet gears, and a ring gear. Epicyclic gears get their name from their earliest application, which was the modelling of the movements of the planets. The sun gear is located at the center, and transmits torque to the planet gears which are typically mounted on a moveable carrier. The planet gears orbit around the sun gear and mesh with an outer ring gear. A planetary gearbox is used to transfer the largest torque in the most compact form. This requirement applies to a variety of industries, including tractors and construction equipment where a large amount of torque is needed to drive the wheels.

Calculations of the pitch circle diameter and the number of teeth for the planet gear

Module = Pitch diameter/ No of teeth

`m = d/Z`

The module of all gears will be same as they are meshing each other.

`d_"ring" = d_"sun" + 2d_"planet"`

So `d_"planet" = (( d_"ring" - d_"sun")/2)`

	No of teeth	Pitch Diameter
Ring	46	115
Sun	14	35
Planet	16	40

CAD Geometry

The modelling of standard gears are easy with the help of design library of solidworks. Follow the below options to model any standrad gears.

Design Library > Toolbox > ANSI Metric > Power Transmission > Gears

Ring gear

Sun gear

Planet gear

Carrier

Assembly

Motion study setup

The motion features of the software can assist with a wide range of motion study depending on how complicated your requirements are, and they can be divided into three categories:

• Animation: If you simply wish to create some nice visuals for presentation or marketing without consideration of mass and gravity effects, then animation is for you.
• Basic Motion: For an extra layer of complexity that takes into consideration the effects of mass, springs, gravity and physical collision detection, then a Basic Motion study is more suited for your requirements.
• Motion Analysis: This is the top tier of motion study and takes into account a wider range of physical interactions such as impact effects, damping, force, momentum, etc.

Steps for motion analysis

1. Activate the motiton analysis plugin of solidwokrs in add-ins tab.
2. Select the motion analysis from the left drop down menu where there are other option including animation and basic motion. Animation will be selected as default so we need to select motiton analysis from the list.
3. In case 1 and 3 the sun gear is given as input and hence motor is given to sun gear and an rpm of 200 is set from the menu. For case 2 the ring gear is input and motor is given to ring gear. The gears can be fixed and made free by using the option of fix/float option. For this right click the part to find this option.
4. As the gears should mesh and move during the motion analysis we should give information to solidwworks that these are solid contact bodies. For this we use 'Contact' option from motion analysis options.
5. Motiton study properties can be selected to input necessary accuracy details and also to enable precision contact.
6. After including all settings to analyse the motion click the calculate button.
7. Using 'Results and plots' option we can plot different graphs and get results. Angular velcoity can be selected from dropdown menu Displacement/Velocity/Acceleration > Angular velocity > Magnitude and select the surface of the output.

Example: Motor input for case 1 and case 3

Example: Setting solid body contact.

Animation

Case 1: Input- Sun gear, Output- Carrier arm, Fixed- Ring gear

Case 2: Input- Ring gear, Output- Carrier arm, Fixed- Sun gear

Case 3: Input- Sun gear, Output- Ring gear, Fixed- Carrier arm

Results, Observation and Explanation

Using one of the method of solving the epicyclic gear theoretically (referred from standard textbooks), for the current gear setup if the carrier moves in Y rpm and sun will rotate independelty in X rpm, then the planet will move with `-14/16X + Y` rpm and Ring will rotate with `-14/46X + Y` rpm . Negative sign notates the rotation direction. These equations are got considering the gear ratios. A link is attached in the reference section for further reading.

Case 1 plot : Input- Sun gear, Output- Carrier arm, Fixed- Ring gear

The torque is provided to sun gear. The angular velocity of carrier increases rapidly and a small drop is witnessed due to gear sliding and mesh gripping. After that the angular velocity remians constant with minor jerks in motion. The angular velocity is lowest in this case compared to all other cases. The planet gears not only rotate about their axis but are also rotate on the inside of the ring gear. This extra support results in high torque transmitting capacity.

Solving it theoretically using above given equation derived using standard methods we get output of carrier as 280 deg/sec which is almost accurate from the plot result.

Case 2 plot: Input- Ring gear, Output- Carrier arm, Fixed- Sun gear

The torque is provided to ring gear. The angular velocity of carrier increases rapidly. After that it's almost constant with minor jerks in motion. But a minor drop as in the first case is not visible as toque transmitting is low. The angular velocity of carrier is more compared to other cases because of large gear ratios of planet gears and ring gear. This results in high speed and low torque transmitting capacity.

Solving it theoretically using above given equation derived using standard methods we get output of carrier as 920 deg/sec which is almost accurate from the plot result.

Case 3 plot: Input- Sun gear, Output- Ring gear, Fixed- Carrier arm

As the carrier gets fixed it becomes like a simple gear train. The sun gears rotate only about their axis and transmit motion to the planet and the planet to the ring. Since `V prop 1/"No of Teeth"` Velocity of Sun is greater than Ring. This results in low speed of output.

Solving it theoretically using above given equation derived using standard methods we get output of carrier as 365.21 deg/sec which is almost accurate from the plot result.

From all the three cases the highest angular velocity is obtained in case 2 and the lowest angular velocity output is for case 1.

CAD FILE

The 3D model files : Link

https://drive.google.com/drive/folders/1fTqbytuUumqS_H6j59h5YZiZqa8tLj7j?usp=sharing

Conclusions

Modelling and analysis of a planetary gear was performed successfully.

Reference

https://www.youtube.com/watch?v=QVzPr-RRA8c