Planetary Gear

AIM: To design a planetary gear system and perform the MBD analysis.

DESIGN INPUTS:

• Ring Gear
• Module = 2.5 (Metric system)
• Number of teeth = 46
• Sun Gear
• Number of teeth = 14
• Input Speed of the Gear = 200 rpm.
• Number of planet gears = 4

CASES:

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

OBJECTIVE: Obtain angular velocity of the output component in each case

THEORY:

An epicyclic gear train/ planetary gear train consists of two or more gears mounted so that the centre of one gear revolves around the centre of the other. A carrier connects the centres of the outer gears and rotates to carry one gear, called the planet gear or planet pinion, around the other, called the sun gear or sun wheel. The planet and sun gears mesh so that their pitch circles roll without slip. A point on the pitch circle of the planet gear traces an epicycloid curve. In this simplified case, the sun gear is fixed and the planetary gear(s) roll around the sun gear.

For a gear, the following relation holds true:

Where: M- Module, D- Diametrical pitch, T- Number of teeth

In order to facilitate proper meshing, the module of the teeth must be same.

We do not have entire dimension data of the gears, hence have to calculate them.

1. Ring Gear
   2. M= 2.5mm
   3. T= 46
   4. D= (M*T) = 115mm
2. Sun gear
   2. m= 2.5 mm
   3. t= 14
   4. d= (m*t) = 35mm
3. Planetary gears
   2. m’= 2.5mm
   3. d’, t’ unknown

Writing an equation:

D=2d’+d [2 planetary gears and 1 sun gear fit in the ring gear]

Solving for the above equation, we get d’= 40 and t’=16

PROCEDURE:

• Open an assembly document
• From the design library, import spur gears and the ring gears by providing correct values for teeth, module and inner diameter/outer diameter
• Assemble the gears such that there exists no translation for the assembly
• Open a new part file
• Draw the carrier
• Import the carrier into the assembly and provide necessary mates
• Fix the component based on the case to be simulated and provide motor to the correct component
• Provide contact to bodies
• Calculate solution for all cases

GEOMETRY:

1. Gear assembly

2. Sketch to provide mates to the gears

3. Carrier

3. Mates provided
   
4. Final assembly
   

RESULTS AND DISCUSSION:

1. Case 1: Input to sun gear and fixed ring gear
   
   
   An average angular velocity of 270m/s is noted in this configuration.

2. Case 2: Input to ring gear and fixed sun gear
   
   
   An average angular velocity of 900m/s is noted in this configuration.
   
   
3. Case 3: Input to sun gear and fixed carrier
   
   An average angular velocity of 370m/s is noted in this configuration.

It is observed that the angular velocity of the output starts from 0 and reaches the described average value and displays slight fluctuation from it. These observed fluctuation(s) maybe due to the sudden force that acts on the gear when the teeth mesh with each other.

Please find the CAD model(s) at: https://drive.google.com/drive/folders/1pDw6ED1lCTsM7jhacVTaQ-uc_BH_D0Qh?usp=sharing