Planetary Gear

Aim:
To set-up the complete assembly of Planatery Gear Train Mechanism and perform the following 3 motion studies with plots for each.

S.No	Input	Output	Fixed
1	Sun Gear	Carrier	Ring Gear
2	Ring Gear	Carrier	Sun Gear
3	Sun Gear	Ring Gear	Carrier

Introduction:

Gear:
A gear is a kind of machine element in which teeth are cut around cylindrical or cone shaped surfaces with equal spacing. By meshing a pair of these elements, they are used to transmit rotations and forces from the driving shaft to the driven shaft.

Gear Drive:
A mechanism consisting of toothed wheels that engage and transmit rotary motion, usually transforming angular velocity and torques.

Planetary Gear Drive:
A planetary gear set is made up of three types of gears; a sun gear, planet gears, and a ring gear. In some cases even carriers are used. 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. Planetary gear systems can vary in complexity from very simple to intricate compound systems, depending on the application.
These set of arrangements are used in tractors, turbine engines, automatic transmissions, and even electric screwdrivers.

Given below is an representation of Planetary Gear Drive which consists of Ring,Sun,Planet gears and a carrier:

Basic terms of gears used in this project:

Pitch Circle Diameter(PCD):
It is the diameter of that circle which passes through the center of all the bolts hole or wheel bolts or wheel rim holes or stud.

Module:
It is the unit of size that indicates how big or small a gear is. It is the ratio of the reference diameter of the gear divided by the number of teeth.

Formula Used:

• PCD = No. of teeth of gear x Module
• PCD of Planet gear= PCD of Ring gear-PCD of Sun gear/2

Procedure:

1. Model Design:
Includes making the cad model of the system that is to be analyzed.

2. Assembly:
With the help of mates parts are combined to form an Assembly.

3. Applying Set-Up:
Includes setting up the motor, contacts and material.

4. Motion Analysis:
The solver is run giving out the results for plots including forces,velocities,accelerations and identifying the minimum and maximum values of those to determine the critical regions.

Case Study:

1. Model Design:

• Ring Gear:
  

First we start with modelling of Ring Gear with the following steps:

• Go to Design Library -->Toolbox -->ANSI Metric -->Power Transmission -->Gears -->Internal Spur Gear.

• Select the following parameters:

  Module	2.5
  No. of Teeth	46
  Pressure Angle	20
  Outer Diameter	130
  Face Width	20

• Given below is the result:

Fig 1: 3D Model of Ring Gear

• Sun Gear:

Now we start with modelling of Sun Gear with the following steps:

• Go to Design Library -->Toolbox -->ANSI Metric -->Power Transmission -->Gears -->Spur Gear.

• Select the following parameters:

  Module	2.5
  No. of Teeth	14
  Pressure Angle	20
  Nominal Shaft Diameter	20
  Face Width	20

• Given below is the result:

Fig 2: 3D Model of Sun Gear

• Planet Gear:

Now we start with modelling of Planet Gear with the following steps:

• Go to Design Library -->Toolbox -->ANSI Metric -->Power Transmission -->Gears -->Spur Gear.
• Now to get no. of teeth of planet gear we calculate it:

Calculation:

PCD = N x MOD

PCD Of Ring = 2.5*46
= 115 mm

PCD od Sun=2.5*14
=35 mm

PCD of planet gear= PCD of ring gear-PCD of sun gear/2
= 115-35/2
= 40mm

No. Of teeth of Planet= PCD/MOD
= 40/2.5
=16

• Select the following parameters:

  Module	2.5
  No. of Teeth	16
  Pressure Angle	20
  Nominal Shaft Diameter	20
  Face Width	20

• Given below is the result:

Fig 3: 3D Model of Planet Gear

• Carrier:

Lastly we will build the Carrier. It can be build according to our suitable dimensions.

Fig 4: 3D Model of Carrier

2. Assembly:

For the assembly we have to create a sketch and apply mates to it with the parts for creating complete assembly.

Fig 5: 2D Sketch for Assembly

Now After succesful application of mates we get the below result.

Fig 6: Front View of the Assembly

Fig 7: Final Assembly

3. Motion Analysis:

CASE 1 :– INPUT OUTPUT FIXED

SUN GEAR CARRIER RING GEAR

• Now we fix the Ring gear.
• In Motor Options, we select the axis of Sun Gear with 200 RPM in clockwise direction.
• Contact between the gears
  1. Solid contact between ring gear and all the 4 planet gear (material steel dry)
  2. Solid contact between Sun gear and all the 4 planet gear (material steel dry)
• Once the calculation is done, plot the graph for Angular Velocity of Carrier.

Result:

Fig 8: Angular Velocity plot of Carrier

Fig 9: Angular Velocity plot of Carrier in Excel

CASE 2 :– INPUT OUTPUT FIXED

RING GEAR CARRIER SUN GEAR

• Now we fix the Sun gear.
• In Motor Options, we select the axis of Ring Gear with 200 RPM in clockwise direction.
• Contact between the gears
  1. Solid contact between ring gear and all the 4 planet gear (material steel dry)
  2. Solid contact between Sun gear and all the 4 planet gear (material steel dry)
• Once the calculation is done, plot the graph for Angular Velocity of Carrier.

Result:

Fig 10: Angular Velocity plot of Carrier

Fig 11: Angular Velocity plot of Carrier in Excel

CASE 3 :– INPUT OUTPUT FIXED

SUN GEAR RING GEAR CARRIER

• Now we fix the Carrier.
• In Motor Options, we select the axis of Sun Gear with 200 RPM in clockwise direction.
• Contact between the gears
  1. Solid contact between ring gear and all the 4 planet gear (material steel dry)
  2. Solid contact between Sun gear and all the 4 planet gear (material steel dry)
• Once the calculation is done, plot the graph for Angular Velocity of Ring gear.

Result:

Fig 12: Angular Velocity plot of Ring Gear

Fig 13: Angular Velocity plot of Ring Gear in Excel

Animation:

The model parts and Assembly is given in the link below:
https://drive.google.com/file/d/132i7P-BMVRk8bL8EQsqS8EMD7TU1fYN_/view?usp=sharing

Animation of Case 1 :
https://drive.google.com/file/d/1tKV9NYlLq_lXWilv1hJ6mT3IEd7NUcTz/view?usp=sharing

Animation of Case 2 :
https://drive.google.com/file/d/1H7QDH095aOhQHrI8yRZASqioRUR7TZKA/view?usp=sharing

Animation of Case 3 :
https://drive.google.com/file/d/1_em-piGXedn1yeJXC9t5BoUz0FgtwtBm/view?usp=sharing

Conclusion:

• In Case 1 :– INPUT(200 RPM) OUTPUT FIXED

  SUN GEAR CARRIER RING GEAR

  
  By giving the input to the Sun gear it rotate about its axis thus rotating the planet gears as they are connected to the Sun gear. Since the planet gears are connected to the carrier, even it rotates. (The angular velocity lies between 260-300 deg/sec)

• In Case 2 :– INPUT(200 RPM) OUTPUT FIXED

  RING GEAR CARRIER SUN GEAR

  
  By giving the input to the Ring gear it rotate about its axis thus rotating the planet gears as they are connected to the Sun gear. Since the planet gears are connected to the carrier, even it rotates. (The angular velocity lies between 850-950 deg/sec)

• In Case 3 :– INPUT(200 RPM) OUTPUT FIXED

  SUN GEAR RING GEAR CARRIER

  
  By giving the input to the sun gear it rotate about its axis thus rotating the planet gears as they are connected to the Sun gear. Since the planet gears are connected to the carrier, it tries to rotate but since it is fixed the power is transmitted to the ring gear by rotating planet gear about its axis. (The angular velocity lies between 330-400 deg/sec)

• From all plots, we observe that the highest angular velocity will be shown in Case 2 when the input is given to the Ring gear and the output is calculated on carrier.Thos is due to the fact that Ring gear has the larger radius.