Epicyclic gear train motion analysis

Objective: To obtain angular velocity plot for different parts of the planetary gear with different input parts.

Epyicyclic gear train:

In epicyclic gear train,the axis of the shaft on which the gears are mounted may move relatively toa fixed axis. A simple gear train is a train in which a gear A and the arm C have a common axis at O1 about which they can rotate. The gear B meshes with gear A and has its axis on the arm at O2, about which gear B can rotate. If the arm is fixed and arm is rotated about the axis of gear A, then the gear B rotates around gear A. Such a motion is called epicyclic and the gear train arrangment is known as epicyclic gear train. The gear train are useful for transmitting high velocity ratios with gears of moderate size in a comparatively lesser space. The epicyclic gear train is used in the back gear lathe, differential gears of automobiles, wristwatches etc.

A compound epicyclic gear train(internal type) consists of two co-axial shafts. One sun gear, four planetary gear and an annular gear arrange internally.

Design Input:

Ring gear

• Module = 2.5
• Number of teeth = 46
• Diameter = Module*number of teeth = 115 mm

Sun gear

• Number of teeth = 14
• Diameter = Module*number of teeth = 35 mm

Planetary gear

• Diameter = Radius of ring - radius of sun = 57.5-17.5 = 40mm
• Number of teeth = Diameter/module = 40/2.5 = 16

Motion analysis are done on following cases:

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

Motor input is 200 rpm.

Procedure:

1. The 3D model is created with above design inputs.
2. Motor speed is set to 200 rpm
3. For each cases motor is set to input gear, gears are fixed and result is taken from the output gear when analysis is caculated.

Observations:

1. Case I:

Angular velocity graph.

Average angular velocity = 279.49 rpm

2. Case II:

Angular velocity graph.

Average angular velocity = 918.67 rpm

3. Case III:

Angular velocity graph.

Average angular velocity = 364.38 rpm

Results:

1. For case I, output is 279.49 rpm.
2. For case II, output is 918.67 rpm.
3. For case III, output is 364.38 rpm.

Conclusion.

1. When input is given through sun gear, while ring gear is fixed output is 1.4 times more than input.
2. When input is given through ring gear, while sun gear is fixed output is 4.6 times more than input.
3. When input is given through sun gear, while planetary gear is fixed output is 1.7 times more than input.
4. Thus variable ouput speed can be obtained through this simple gear train just by changing the input gear.

Google drive file containing 3D model and motion analysis data: https://drive.google.com/drive/folders/13PkKSlrZEZA9nDwEXnQOHc0QOGIAw2ql?usp=sharing