Planetary Gear

Topic:

Planetary Gear

Introduction:

Planetary Gear

An epicyclic gear train (also known as planetary gear) consists of two gears mounted so that the centre of one gear revolves around the centre of the other. A carrier connects the centres of the two gears and rotates to carry one gear, called the planet gear, around the other, called the sun gear. 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.

Given:

Use the following inputs for designing the Planetary Gear

Ring Gear

• Module = 2.5 (You must use the metric system in design modeler)

• Number of teeth = 46

Sun Gear

• Number of teeth = 14

Input Speed of the Gear = 200 rpm.

Number of planet gears = 4

Calculation:

• Diameter of the Planet gear :

Radius of Ring gear= Diameter of the Planet gear + radius of sun gear

Rr = Dp + RsTherfore,

Dp =Rr - Rs

Dp=115/2 - 35/2 = 40mm

D = 40 mm

• Number of teeths of Planet gear:

Pitch diameter, D=m*Twhere m=module

T= Number of teeththerefore,

T=D/m = 40/2.5 = 16

T = 16 teeths

Creating the geometry and the assembly

For creating gear from Toolbox > go to design library > Toolbox > ANSI metric > Power transmission > Gears

1. For sun and planetary gears choose Spur gear

2. For Ring gear to choose Internal Spur Gear

3. Pressure angle = 20

4. Face Width = 20 mm

i. Ring gear (Internal spur gear)

ii. Sun gear

iii. Planet gear

iv. Carrier model

v. Final Assembly

Motion Analysis

In the motion study make contacts between the followings.

• Carrier and the Planet Gears

• Sun gear and the Planet Gears

• Ring gear and the Planet Gears

TheMaterial for each contact is Steel (Dry)

The input speed to the motor in each case is 200 RPM

There are 3 cases,

1. Case 1: Ring gear fixed

Motor - sun gear.

The plot of an angular velocity of the carrier against time.

2. Case 2: Sun Gear Fixed

The plot of an angular velocity of the carrier against time.

3. Case 3: Carrier Fixed

The plot of an angular velocity of the carrier against time.

Conclusion:

1. In the first case, when the input is given to the sun gear and output is obtained at the carrier keeping the ring gear fixed, the planet gear not only rotates about their axis but are also forced to roll on the inside of the ring gear along with the carrier as the Ring gear is fixed. The angular velocity obtained for this case is 279.999deg/sec and varies in a very small fraction.

2. In the second case, when the input is given to the ring gear and output is obtained from the carrier keeping the sun gear fixed. The angular velocity achieved is maximum since the internal gear is big and planet gears are small comparatively so when a large gear meshes with a small gear the velocity achieved from the small gear is high because the velocity ratio is high. The angular velocity obtained for this case is 920.00005deg/sec and varies in a very small fraction.

3. In the third case, the carrier is fixed and output is to be obtained from the ring gear with the input given to Sun gear, all the gears rotate about their axis. The planet gears rotate only about their axis and transmit motion from sun to the ring and since the ring gear is big in diameter the angular velocity achieved is less. The deviations that are visible in the graphs show that there are points where sliding is occurring between the gears. For making the graph more smoother we can use precise contact. The angular velocity obtained for this case is around 365.217 deg/sec and varies in a very small fraction.