Planetary Gear

MOTION ANALYSIS OF “PLANETARY GEAR MECHANISM” USING SolidWorks

1.AIM: To analyse the motion study of Planetary Gear Mechanism using SolidWorks.

2.OBJECTIVE:

• To create 3D models of all the parts used in Planetary Gear mechanism,
  1. Ring Gear
  2. Sun Gear
  3. Planetary Gear
  4. Carrier

• To perform motion analysis by rotating the input gear at a constant speed of 200 rpm.
• To calculate the pitch circle diameter and the number of teeth for the planet gear.
• To run a simulation on the following three cases,

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

• To plot graph for Angular Velocity of the output part.

3. INTRODUCTION:

3.1 Gear :- Gear is a transmission element, where it transfers power, torque from one point to another in the transmission line. Gears are commonly used in for transmitting torque, power from engine in all types of automobiles (but some uses belt drives) industries e.t.c. These are used when power input system and the power output system are close to each other. Gears transmit the power, torque at constant speed ratio when it meshes with another gear. This constant speed ratio depends on ratios of the radius of the gears.

fig.1: Some various types of gear

fig.2: Gear Terminology

3.2 PLANETARY GEAR:- Planetary gears are also referred to as epicyclic gear trains. They contain an input and an output shaft in a coaxial arrangement. They consist of a number of gear wheels arranged around a central gear. Since this arrangement is reminiscent of planets orbiting the sun, the central wheel is also referred to as the sun gear, while the surrounding ones are called planet gears. They are located within an external gear ring (i.e. ring gear). The sun gear is driven by a motor and transmits its motion to the surrounding planet gears, which roll against the surrounding gear ring and thus orbit the sun gear evenly. The planet gears are mounted on a joint carrier that is connected to the output shaft. The rotational speed of the output is lower than that of the drive, and the torque of the output is higher in reverse proportion. The more gear wheels mesh with each other, the higher the torque. In general, one planetary gear system contains three to four planet gears.

A Carrier is also a part of planetary gear, on which all the planet gears are mounted.

Planetary gears commonly comprise a combination of several gear wheels toggled within and behind each other, on the basis of this simple basic form. Several simple planet gear sets can be merged into a multiple gear unit. This enables a hub gear changer in a bicycle to have in excess of the three speeds usually achieved with a simple gear set.

fig.3: Planetary Gear nomenclature

3.2.1 Advantages of planetary gears:-

1. High efficiency
2. Compact construction
3. High power density

Planetary gears are characterized by their high level of efficiency; they also display a high power density in comparison to other types of gears, due to their compact construction. The use of the external ring gear in particular reduces both the volume and mass of this type of gear. It also enables high torque transmission in a small construction space thanks to the use of multiple parallel tooth combinations with several orbiting wheels. As the torque is distributed over several gear wheels, the tooth forces are smaller than in other types of gear. Moreover, no synchronization is necessary, which means that it is possible to change gear without interrupting the traction. As all gear wheels constantly mesh with each other, the planetary gear operates at a low noise level.

3.2.2 Disadvantages of planetary gears:-

1. Complex construction
2. Higher power dissipation than with spur gears
3. Complex bearings

The disadvantages of planetary gears are their complex construction and higher power loss compared to spur gears. As the power is transmitted through at least two meshed teeth, the power dissipation is double that of a simple spur gear. Moreover, this type of gear requires complex bearings, especially if it is to be used as a three-shaft gear.

fig.4: Animation showing a Planetary Gear in operation

4. CALCULATION:

Formulae -

`"Module""=""Pitch circle diameter" /"Number of teeth"`

`"Diameter Pitch""="1/"Module"`

Where, denotation of terms as-

Module `→` m

Pitch circle diameter `→` d

Number of teeth `→` T

Ring Gear :

Module (m) = 2.5 (given)

Number of teeth (T) = 46 (given)

Pressure angle = 20

Face width = 6 mm

As we know that,

`"Module""=""Pitch circle diameter" /"Number of teeth"`

So, Pitch circle diameter (d) `=` m`xx`T `=` 2.5`xx`46 `=` 115 mm

Outside diameter = 130 mm (assumed) [should always be greater than Pitch circle diameter]

Sun Gear :

Module (m) = 2.5 (given)

Number of teeth (T) = 14 (given)

Pressure angle = 20

Face width = 6 mm

So, pitch circle diameter (d) `=` m`xx`T `=` 2.5`xx`14 `=` 35 mm

Nominal shaft diameter = 16 mm (assumed here)

Planet Gear :

Module (m) = 2.5 (given)

Pressure angle = 20

Face width = 6 mm

As we know here that,

`("Pitch circle radius" )_"Ring gear" =("Pitch circle radius" )_"Sun gear" +("Pitch circle diameter" )_"Planet gear"`

`=>"d" _"ring gear" /2="d" _"sun gear" /2+"d" _"planetary gear"`

`=> 115/2=35/2+"d"_"planetary gear"`

`=> 57.5=17.5+"d"_"planetary gear"`

`=> "d"_"planetary gear" = 57.5 - 17.5`

`=> "d"_"planetary gear" = 40`

`therefore("Pitch circle diameter")_"Planetary gear"=40`

We also know that,

`=> "Module" "=" "Pitch circle diameter" /"Number of teeth"`

`=> "T" = "d"/"m"`

`therefore"T" = 40/2.5 = 16`

Nominal shaft diameter = 24 mm (assumed here)

Carrier :

For Cylindrical handle part,

Circle diameter = 26 mm

Length = 90 mm

Middle flat part of carrier head extruded = 5 mm

5. 3D MODELS :

• All the dimensions are in the unit system of MMGS (i.e. millimeter, gram, second).

Ring Gear

Sun Gear

Planet Gear

Carrier

Assembly Design :

For performing assembly, we need to import the 3D model of parts which have to be assembled; here those model parts are as follows -

Part or, Model	Quantity
Ring gear	1
Sun gear	1
Planet gear	4
Carrier	1

fig.5: Planetary Gear

Motion Study :

• Motion study can be done in SolidWorks by using ‘Motion Analysis’ under ‘SolidWorks Motion’ option from ‘SolidWorks Add-Ins’.

So, we are going to choose the ‘SolidWorks motion’ option from ‘SolidWorks Add-Ins’ and then going to ‘Motion Analysis’ option which we can find below in the SolidWorks window.

6. BODY OF CONTENT :-

6.1 Study-1 (Motion analysis for Carrier when Ring gear is fixed and input is provided to the Sun gear)

Firstly, going to set up the motor for the input (i.e. Sun Gear) at a constant speed of 200 rpm. And assigning the rotation of the motor as clockwise direction.

Setting up time frame for our motion study to 6 seconds.

After that going to assign solid body contact by selecting contact option for all the parts by selecting two parts at a time which are going to be in contact. There we can also assign material to the models. So, selecting ‘Steel (Dry)’ material for all the parts.

Now, setting up the number of frames per second equal to 25 frames per second.

After that going to make fix the Ring gear. Except Ring gear all the other parts should be selected as float.

Now we will calculate the motion study and we will get the plot as by clicking on result and plot section as -

fig.6: Angular_Velocity Vs Time plot of carrier when Ring gear is fixed

6.2 Study-2 (Motion analysis for Carrier when Sun gear is fixed and input is provided to the Ring gear)

For this we will follow the same process as performed in our above study with a few changes in that, which are as follows-

Make the Sun gear to be fixed this time. Except Sun gear all the other parts should be selected as float.

Now we will calculate the motion study and we will get the plot as by clicking on result and plot section as -

fig.7: Angular_Velocity Vs Time plot of carrier when Sun gear is fixed

6.3 Study-3 (Motion analysis for Ring gear when Carrier is fixed and input is provided to the Sun gear)

For this we will follow the same process as performed in our above study with a few changes in that, which are as follows-

Make the Carrier to be fixed this time. Except Carrier all the other parts should be selected as float.

Now we will calculate the motion study and we will get the plot as by clicking on result and plot section as -

fig.8: Angular_Velocity Vs Time plot of Ring gear when Carrier is fixed

7. RESULTS :-

Study-1 (Motion analysis for Carrier when Ring gear is fixed and input is provided to the Sun gear) :

fig.9: Angular_Velocity Vs Time plot

Animation Video

Study-2 (Motion analysis for Carrier when Sun gear is fixed and input is provided to the Ring gear) :

fig.10: Angular_Velocity Vs Time plot

Animation Video

Study-3 (Motion analysis for Ring gear when Carrier is fixed and input is provided to the Sun gear) :

fig.11: Angular_Velocity Vs Time plot

Animation Video

Link for Results, 3D models, spreadsheet, animation :-

https://drive.google.com/file/d/1K8jVAh6qp4oZH_sT4B2wtHc-s4qGK87j/view?usp=sharing

8. ERRORS :-

The most common errors occur due to the various reasons –

1. Improper contact relations between the different parts of assembly.
2. Keeping unnecessary relations between the parts as suppressed; it’s better to delete them if not necessary.
3. Wrong selection of degree of freedom for the parts.

8.1 Error while performing motion study with fixed Ring gear-

8.2 Error while performing motion study with fixed Carrier –