Planetary Gear
AIM: To do Motion Analysis of Planetary Gear Mechanism.
Given Data: Dimensions of the Sun Gear & Ring Gear is provided by skill-lync.
Introduction:
- Planetary Gear Mechanism is also known as 'Epicyclic gear Mechanism'
- Planetary Gear Mechanism is a gear mechanism which consists of 4 components namely; planetary gears, sun gear, ring gear & carrier.
- 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.
Applications:
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Planetary gears are often used when space and weight are an issue, but a large amount of speed reduction and torque are needed.
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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.
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Other places you will find planetary gear sets include turbine engines, automatic transmissions, and even electric screwdrivers.
- Planetary gear system also used in varies applications such as, clocks, lunar calendar, car mirror, toys, gearhead motor, etc.
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Planetary gear systems are able to produce a lot of torque because the load is shared among multiple planet gears.
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This arrangement also creates more contact surfaces and a larger contact area between the gears than a traditional parallel axis gear system. Because of this, in the load is more evenly distributed and therefore the gears are more resistant to damage.
Subtypes of Planetary Gear Mechanism:
There are subtypes of mechanism in Panetary Gear Mechanism based on the component fixed in Mechanism. They are as follow:
| Types of Mechanism |
Fixed Member |
Input | Output | Gear Ratio Formula: | Ratio Range |
| Types of Planetary | Ring Gear | Sun Gear | Carrier/ Planet Gear |
1`divide`[(zC/zA)+1] |
1/3 -1/12 |
| Types of Sun | Sun Gear | Ring Gear | Carrier/ Planet Gear | 1`divide`[(zC/zA)+1] | 1/1.2 -1/1.7 |
| Types of Star | Carrier | Sun Gear | Ring Gear | -1`divide`[zC/zA] | 1/2 -1/11 |
Advantages:
- Planetary gear is found in many variation and arrangements to meet a broad range of speed-ratio in the deign requirements.
Gear Terminologies:
- Pitch: The Circular Pitch defines the width of one tooth and one gap measured on an arc on the pitch circle.
- Pitch Circle: A pitch circle is the curve of intersection of a pitch surface of revolution and a plane of rotation.
- Pitch circle Diameter: It is the diameter of the pitch circle.
- Outside Diameter: It is the external diameter of the internal spur gear.
- Inside Diameter: It is the internal diameter of the external spur gear.
- Module: It is the ratio of the pitch circle diameter to the number of the teeths.
- Face Width: It is the length of the teeth in axial direction.
- Pressure Angle: It is the angle between the tooth face and the gear wheel tangent.
Design Criteria:
- Planetary gear system will no assemble unless the number of teeth in each gear is selected properly.
- The Pitch circle Diameter of the gears in meshing are tangent to each other.
- The Module of the gears in mesh should be equal to have a proper transmission.
- If you have any of the two parameters from the module, pitch circle diameter & Number of teeth, than you can easily find out the third paramters.
Given Data:
The dimension of the Sun-Gear are:
- No. of teeths = 14
- Module = 2.5
- Therefore, Pitch circle Diameter =115
The dimension of Ring-Gear are:
- No. of teeths = 46
- Module = 2.5
- Therefore, Pitch circle Diameter = 35
Calculation of PCD of Planet gears:
The Dimension of Planetary-Gear can be founded as following:
- Initially, we have to create two concentric circles of diamter 115 mm & 35 mm, which represents sun-gear & ring gear, respectively.
- To calculate pitch circle diameter, we have to make a circle in between the sun gear & ring gear
- Then we have to provide a tangent to that circle with the sun gear & ring gear both one by one respectively.
- Then by measuring the circle diameter, we would get the pitch circle diameter of the planet gears.
- As we know that for the gear in mesh, the module should be equal for all the gears, therefore Module of Planetary gears = 2.5
- Now after calculating pitch circle diameter diameter of planet gear, now we will calculate the no of teeth of planet gears by the formula of module.
- We found that the number of teeth for the planet gears is 16.
Modelling of gears:
- Now, as we have all the required data, we will model the different gears in different assemblies.
- Before that we will assume some of the data which are required:
- Face Width = 12
- Pressure Angle = 20
- Outside Diameter of Ring Gear = 130 mm
- Inside diameter of sun gear & planet gear = 20 mm
The above diagram shown is of Sun gear, It is shown by green colour.
- The link for the Sun Gear : Sun gear
The above diagram is of Ring Gear, It is shown by Red Colour.
- The link for the Ring Gear : Ring gear
The above diagram is of Planet Gear, It is shown by Yellow Colour.
- The link for the Planet Gear : Planet gear
The above diagram is of Carrier, It is shown by Pink Colour.
The carrier is model based on the inside diameter of the Planet gear.
- The link for the Carrier : Carrier
Assembling of the Planetary Gear Mechanism:
- For assembling all the components, i have created a new assembly.
- Then I have inserted Carrier first, after that i assign Float properties to the Carrier, so that it can move freely.
- Then i have coincide the face of the carrier with the right plane & then in have provide the coincident property to the axis of the carrier with the top plane & front plane respectively.
- Then i have imported the planet gears & then coincide the one of the face of the shaft of carrier with the internal face of the planet gear.
- Then i have provided the coincide property with the face of the gear & the right plane.
- Similarly, i have done this for 4 times for all the 4 shafts of the gear.
- Then, I have inserted the sun gear & coincide the axis of the sungear with the axis of the carrier.
- i have provided the coincident with face of the sungear to the right plane.
- Similarly, i have done this for the ring gear also.
- After completing the assembly, it looks like something:
- The link for the Assembly of the Planetary Gear Mechanism : Assembly of Planetary Gear Mechanism
Motion Analysis:
- For motion analysis the input speed of motor is given = 200 RPM.
- The Motion Anakysis is carried out with using gear mates.
- I have provided the contacts between the adjacent gears touching to each other.
- Now, the motion analysis is carried out in three different cases:
Case(1):
When the input speed is given to Sun gear & the Ring gear is fixed
Here, the Angular velocity is to be found out for the Carrier.
Result for the Case 1:
The Angular Velocity is found out to be approximately 363 deg/sec.
The Planet gear revolves around it's own axis & also rotates around the axis of sun gear.
Case(2):
When the input speed is given to Ring gear & the Sun gear is fixed
Here, the Angular velocity is to be found out for the Carrier.
Result for the Case 2:
The Angular Velocity is found out to be approximately 1004.6 deg/sec.
The Planet gear revolves around it's own axis & also rotates around the axis of sun gear.
Case(3):
When the input speed is given to Sun gear & the Carrier is fixed
Here, the Angular velocity is to be found out for the Ring gear.
Result for the Case 2:
The Angular Velocity is found out to be approximately 393 deg/sec.
The Planet gear revolves around it's own axis only.
- The link for the Motion Analysis/Results of the Planetary Gear Mechanism : Motion Analysis/Results
Conclusion:
- The Angular velocity of the Carrier when ring gear is fixed is found to be 363 deg/sec.
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The Angular velocity of the Carrier when sun gear is fixed is found to be 1004.9 deg/sec.
- The Angular velocity of the Carrier when carrier is fixed is found to be 393 deg/sec.
Video Link for the Motion Analysis :
Planetary Gear Mechanism (when carrier is fixed)
Planetary Gear Mechanism (when ring gear is fixed)
Planetary Gear Mechanism (when sun gear is fixed)