Planetary Gear

OBJECTIVE:

To design a Planetary Gear and carry out its Multibody Dynamics simulation

Ring Gear: Module = 2.5, Number of teeth = 46

Sun Gear: Number of teeth = 14

Input Speed of the Gear = 200 rpm. Design a carrier such that the number of planetary gear is 4. The simulation is to be carried out for 3 different cases:

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

Input - Rotary Motion given to that part as input.

Output - Angular Velocity of that part is to be plotted as a graph.

Fixed - Make that particular component as a fixed part.

Gear mates are not to be used, while carrying out the simulations

SOLUTION:

A planetary gear, also known as epicyclic gear train, is a gear assembly consisting of two gears (atleast) such that one of the gears revolves around the centre of the other. The gears are held together by a member called carrier. The gear held at the centre is called as the sun gear and the gear revolving around the sun gear is called the planetary gear. Common applications of the mechanism can be seen in turbine engines and 3d printers.

The current assembly consists of 7 bodies; 1 ring gear, 1 sun gear, 4 planetary gears and 1 carrier. The ring gear is an internal spur gear with teeth on the inside surface. The gears are arranged in such a way that, the sun gears and planetary gears are inside the ring gear and in the same plane. The carrier consists of four pins, which are used to hold the planetary gears.

1. Ring gear

2. Sun gear

3. Planetary gear

4. Carrier

5. Assembly

Gear calculations:

Given,

m = 2.5, RG_t = 46, SG_t = 14

Planetary gear relation: RG_t = 2 x PG_t + SG_t

From the above relation, PG_t = (46 – 14)/2 = 16

For proper meshing of the teeth between the gears, the module should be equal.

Hence, m_rg = m_sg = m_pg = 2.5

Module = Diameter of gear/ number of teeth in the gear

Therefore, D_pg = 40mm, D_rg = 115mm and D_sg = 35mm, where ‘D’ is the pitch circle diameter.

The shaft hole diameter, in the ring gears, was taken given as 20mm and the carrier was designed accordingly.

Motion Analysis and Results

The motion analysis was carried out for three different cases. Solid contacts were defined between all adjoining contacts and the results were recorded at 600 fps and with precise contacts enabled.

Case 1: Sun gear – Input, Carrier – Output and Ring gear – Fixed

Here, the input rotary motion at a constant speed of 200 rpm is given to the Sun gear and the angular velocity of the carrier was measured, while holding the ring gear stationary.

Case 2: Ring gear – Input, Carrier – Output and Sun gear – Fixed

Here, the input rotary motion at a constant speed of 200 rpm is given to the Ring gear and the angular velocity of the carrier was measured, while holding the sun gear stationary.

Case 3: Sun gear – Input, Ring gear – Output and Carrier – Fixed

Here, the input rotary motion at a constant speed of 200 rpm is given to the sun gear and the angular velocity of the ring gear was measured, while holding the carrier stationary.

From the plots, it can be observed that the angular velocity remains almost constant. This is consistent considering the input rotary motion is given at a constant speed.