Planetary Gear

Introduction to Gear:

Gears are mechanisms that mesh together via teeth and are used to transmit rotary motion from one shaft to another. They are typically mounted, or connected to other parts, via a shaft or base. Also defined by two important items: radius and number of teeth. They are typically mounted, or connected to other parts, via a shaft or base.

Types of Gears:

1. Spur gear
2. Helical gear
3. Bevel gear
4. Double helical or herringbone gear
5. Internal or ring gear
6. Worm and worm wheel
7. Rack and pinion

Gear Nomenclature/Terminology:

In gear nomenclature/terminology, there are four circles to keep in mind:

• Addendum circle: The outer circle touching the outermost points of the teeth.
• Pitch circle: The imaginary rolling circle produced during rotation by mating gears.
• Base circle or root circle: The circle from which the involute tooth profile is developed.
• Dedendum circle: The circle touching the bottom of the tooth profile.

Here for power transmission we have to mate the gear properly, in order to do that the pitch circle of both mating gears must be tangent to each other. Also, module of the two gears must be same.

The ring gear is also called as an internal spur gear. The planetary gear and sun gear is also called as spur gear.

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PLANETARY GEAR:

A carrier connects the centres of the two 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.

In a simple planetary setup, input power turns the sun gear at high speed. The planets, spaced around the central axis of rotation, mesh with the sun as well as the fixed ring gear, so they are forced to orbit as they roll. All the planets are mounted to a single rotating member, called a cage, arm, or carrier.

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OBJECTIVE:

Following inputs are used for designing the Planetary Gear. (using the metric system)

Ring Gear

• Module = 2.5
• Number of teeth = 46

Sun Gear

• Number of teeth = 14
• Number of planet gears = 4

Other inputs

• Input Speed of the Gear = 200 rpm.
• The dimensions of the carrier depend on the shaft diameter of the planet gear.

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With the above input parameters, you are going to run a simulation on the following cases,

Input	Output	Fixed
Sun Gear	Carrier	Ring Gear
Ring Gear	Carrier	Sun Gear
Sun Gear	Ring Gear	Carrier

Hint:

• Input- Rotary Motion given to that part as input.
• Fixed-Make that particular component as a fixed part.
• Output- After motion analysis, Angular Velocity of that part is plotted as a graph.

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PROCEDURE:

Formula used:

M = d / T

(Generally, Module is the ratio of the reference diameter of the gear divided by the number of teeth.)

Where,

M = Module

d = Pitch Diameter of the Gear

T = Number of Teeth

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Sun Gear Calculation:

From the given input data, we know that

Module, M = 2.5

Number of Teeth, T = 14

Now, we need to calculate the Pitch Diameter of Gear (d) for the Sun Gear by using the above formula. On rearranging the formula,

Pitch Diameter of gear, d = Module (M) * Number of Teeth (T)

On substituting the known values,

d = 2.5*14

d = 35

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Ring Gear Calculation:

From the given input data, we know that

Module, M = 2.5

Number of Teeth, T = 46

Now, we need to calculate the Pitch Diameter of Gear (d) for the Ring Gear by using the above formula. On rearranging the formula,

Pitch Diameter of gear, d = Module (M) * Number of Teeth (T)

On substituting the known values,

d = 2.5*46

d = 115

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Planet Gear Calculation:

In this case, we need to find both Pitch Diameter of the Planet gear (d) as well as the Number of Teeth (T). Hence we cannot apply the above formula for calculation. Instead we can use the formula given below:

Radius of ring gear = Radius of sun gear + Radius of planetary gear

Also we can calculate the pitch diameter of planetary gear by drawing the circle that is tangent to both the sun gear as well as the ring gear and if we evaluate the circle, we get the Pitch Diameter of planetary gear as 40:

i.e. d=40

Now we can use the Module Formula to calculate the Number of teeth (T) by rearranging, T = d / M

On substituting the known values, we get the Number of teeth for the planetary gear as 16.

i.e. T = 16

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As a result we have the following parameters for designing the Planetary Gear that includes Module, Number of teeth and Pitch Diameter of gear.

	MODULE	NUMBER OF TEETH	PITCH DIAMETER OF GEAR
Ring Gear	2.5	46	115
Sun Gear	2.5	14	35
Planetary Gear	2.5	16	40

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DESIGNED PARTS & ASSEMBLY FILE:

Ring Gear:

Module = 2.5

Pitch Diameter of Gear = 115

Number of teeth = 46

Pressure angle = 20 degree

Face width = 12

Outside diameter = 130

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Sun Gear:

Module = 2.5

Pitch Diameter of Gear = 35

Number of teeth = 14

Pressure angle = 20 degree

Face width = 12

Shaft diameter = 20

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Planetary Gear:

Module = 2.5

Pitch Diameter of Gear = 40

Number of teeth = 16

Pressure angle = 20 degree

Face width = 12

Shaft diameter = 10

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Assembled Planetary Gear Contains the following parts:

Sun Gear	1 no
Ring Gear	1 no
Planetary Gear	4 no
Carrier	1 no

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MOTION STUDY ANALYSIS:

Motion study 1: Plotting the Angular Velocity for the Below Condition

Input	Ø Sun Gear
Output	Ø Carrier
Fixed	Ø Ring Gear

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Motion study 2: Plotting the Angular Velocity for the Below Condition

Input	Ø Ring Gear
Output	Ø Carrier
Fixed	Ø Sun Gear

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Motion study 3: Plotting the Angular Velocity for the Below Condition

Input	Ø Sun Gear
Output	Ø Ring Gear
Fixed	Ø Carrier

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PROBLEM FACED:

The major problem faced here is to mate the gears for getting the right rotation of gars without using the gear mate. By trial and error I have rectified my error, and now I can able to produce the Planetary Gear.

RESULT:

Thus the Planetary gear is been designed and stimulated the motion analysis by using the Multibody Dynamics in Solidworks.

Drive Link for Part & Assembly Files : Planetary Gear MBD