SIMULATION AND ANALYSIS OF PLANETARY GEARS.

1. Objective:-

1.1 Design planetary gear with the following parameters: 

• Ring Gear:
  • Module = 2.5 (use the metric system in design modeller)
  • Number of teeth = 46
• Sun Gear:
  • Number of teeth = 14

• Input Speed of the Gear = 200 rpm.
• Number of planet gears = 4

1.2 Simulation & Analysis of a planetary gear system with the following conditions:

2. Basic:-

2.1 What is gear:

A Gear May be defined as any tooth member designed to transmit (or) Receive motion from another member by successively engaging the tooth. the function of gear is to work smoothly while transmitting motion or torque. for this, the angular velocity ratio at all times should remain constant. 

2.2 Gear Terminology:

Generally, gear is identified by the pitch circle diameter, Module and Number of teeth. if we have any two-parameter between the module, pitch of circle and number of teeth we can find the third one. 

Note:- The Gear terminology has many terms but for our analysis, we are taken limited terminology, which is explained in the calculation section of the procedure. the common terminology is shown below.

In order to mate gear properly and correct power transmission, the pitch circle of both mating gears are should be tangent to each other. Also, the module of the two gear should be the same.

for our problem, we need to understand ring gear and spur gear. The ring gear is also called as an internal spur gear. So, the spur gear is the simplest form of gear having teeth parallel to the gear axis. the contact of two teeth takes place over the entire width along with a line parallel to axes of rotation.

2.3 Planetary Gears:

The Planetary gears are also called as an epicyclic gear train, it is a combination of the ring gear and spur gear. the planetary gears consist of four parts the sun gear, which is rotated about its own axis. the second gear is ring gear which is act as a housing for gear assembly. the third one is planet gear which is mounted between Sun and ring gear.

In addition to this, we have a carrier. A carrier is a component on which the whole planetary gear assembly is mounted. with the help of carrier by fixing different component of the Assembly we can get different output.  we can find this type of gear set up in Automotive transmission and also in mechanical lathe machine.

3. Procedure:-

Before proceeding further we need to calculate the unknown parameters of the gear which is as follows.

3.1 Gear Parameters Calculation:-

i. Formula Used:

In our problem, we have three parameters i.e pitch circle diameter, module and number of teeth. As we know, if we have any two-parameter between the module, pitch of circle and number of teeth, we can find the third one. Hence, to calculate the required parameters we are using the following formula.

 `[m = d/T]`

Where:-

m = module

[The module is also known as Addendum which is the ratio of reference diameter (or) Pitch diameter to the number of teeth. a module is the unit of size that indicates how big or small a gear is.]

d = pitch diameter

[Pitch diameter is a diameter of the pitch circle.]

T = number of teeth

ii. Calculating Parameters: 

a. for Ring gear:

m = 2.5 

T = 46

d = ?

therefore, `d= m*T` ;      `d = 2.5 * 46` ;       

`d = 115`

b. for Sun gear:

Similarly, As we did the above calculation, we can find out the pitch diameter for sun gear also.

i.e   `d = 35`

c. for Planet gear:

In planet gear, we need to find out pitch diameter and number of teeth also. so here we cannot directly apply the formula as above. here we need to first find out the value of pitch diameter. as we know,

[ Radius of Ring Gear = Radius of Sun gear + Diameter of planet gear ]  

[ 115/2 = 35/2  +  Diameter of planet gear ]

therefore, Diameter of planet gear   

i.e  `d= 40`

Now by using the main formula we can find out the number of teeth.

i.e    `m = d/T`        hence,        `T = 16`

Note:- Module is same for all the gears.

After calculating all unknown parameters the final result table is as follows.

3.2 Designing Parts:-

To design Planetary gear we are going to use Solidworks software. the Solidworks provides design library of gear where we can select the appropriate gear and directly by providing parameter we can draw it. the ring gear is internal spur gear whereas other two are normal spur gear all external spur gear.

To proceed further, click on design library > click on toolbox > click on add-in now. after that, we required to select unit system therefore we are Selecting 'ANSAI inch' standard as a unit system. we can see multiple components out of which we are selecting power transmission. we can see various power transmission parts but we need gear so we are selecting gear here. in gears, we can see there are seven types of gears out of which we are first selecting a ring gear. after selecting the gear type we can substitute the value of each gear and get the desired output. the parameters taken for each gear is given step by step below.

3.2.1 Designing Ring Gear:-

Parameters taken:

module = 2.5 ; diametral pitch = 0.5 ; number of teeth = 46 ; Pressure angle  = 20 degree; face width = 20 ; outside diameter = 115.

3.2.2 Designing Sun Gear:-

Parameters taken:

module = 2.5 ; diametral pitch = 0.5 ; number of teeth = 14 ; Pressure angle  = 20 degree; face width = 20  ; Nominal shaft diameter = 11.

3.2.3 Designing Planet Gear:-

Parameters taken:

module = 2.5 ; diametral pitch = 0.5 ; number of teeth = 16 ; Pressure angle  = 20 degree; face width = 20  ; Nominal shaft diameter = 11.

The planet Gear surrounded around the sun gear is as shown below.

3.2.4 Designing Carrier:-

Parameters taken:

parameters taken from gears size.

3.3 Assembling All the Component:-

By assembling we can do simulation and analysis. the proper assembly is most important to do simulation and analysis else we get an error in our result.

To simplify the Assembly we are starting our assembly with a carrier part. because with the help of this we can define all the dimension and constraints for gear assembly. first, we are importing carrier in assembly, we can see here our carrier is fixed by default Hence by right click on a carrier we can make it to float. After that, with the help of mates, we assembled all the components in the planetary gear system. 

The Selection Of mates is as shown in the below figure

The final Assembly after applying mates is as follows.

Note:- Here we are taken solid body mates, not Gear mates.

4. Simulation:-

By fixing, providing input to a different component of the planetary gear assembly we get different outputs as follows.

4.1 First Case:

4.2 Second Case:

4.3 Third Case:

5. Result and Conclusion:-

5.1 First Case:- Plot for Angular velocity of Carrier with the following conditions.

Here we can see that the initial angular velocity is zero and when the rotor starts rotating the angular velocity increases drastically and Decreases. we also see that there is fluctuation in the angular velocity which is caused due to the Inertia of a Gears. As our gear assembly gets momentum the fluctuation in the angular velocity reduces and it maintains a constant speed. 

5.2 Second Case:- Plot for Angular velocity of Carrier with the following conditions.

As plot defines the angular velocity is zero at the initial stage and rotor start rotating the angular velocity increases drastically but the decrement in the angular velocity caused due to inertia is less as compared to the first case. The input is provided to the ring gear and the sun gear is fixed which causes the reaction force to move the planet gears along with the carrier. Further, the fluctuation induced is decreased with time and maintain a constant rate.

5.3 Third Case:-  Plot for Angular velocity of Ring Gear with the following conditions.

Detailed View:

From the plot, the angular velocity is not zero at the initial stage as compared to the other cases. This is caused due to sudden change in the inertia of the gear and the contact between the gear is not maintained initially. when each gear attached properly and transfer the momentum the fluctuations get reduced and maintains constant angular velocity with the respect to time.

5.2 Conclusion:- 

In the first case where input in sun gear and output is a carrier with the 200 rpm but the carrier velocity is lower as compared to other cases. This caused due to the gearing ratio. Hence we can conclude that from the Simulation of the Epicyclic Gear train, by fixing the different parts of the assembly we can use it in a different application. Also, Epicyclic Gear train has the following Advantages.

i. This system could be used to secure a higher gear ratio in compact space.

ii. It has a higher torque transmission capability and will have lower inertia.

iii. It gives higher Power transmission efficiency as compared to traditional gearboxes.

iv. Service life will also be quite good if we compare it with traditional gearboxes service life for a similar load.

References:-

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

The flow of Report:

1. Objective.

2. Basic.

3. Procedure.

4. Simulation.

5. Result and Conclusion.