Challenge

Planetary Gear

AAditya Kumar Jha15 Jul 2020

AIM:

To model and study the motion analysis of Planetary Gear by using SOLIDWORKS.

THEORY:

A planetary gear set is made up of three types of gears: a sun gear, planet gear and a ring gear. The sun gear is located at the center and transmits torque to the planet gear which are typically mounted on a movable carrier. The planet gear orbit around the sun gear and mesh with an outer ring gear. Planet gear systems can vary in complexity from very simple to intricate compound systems, depending on the application.

Terminology for Spur Gears

Figure shows some of the terms for gears.

Figure :-Spur Gear

In the following section, we define many of the terms used in the analysis of spur gears. Some of the terminology has been defined previously but we include them here for completeness.

Pitch surface : The surface of the imaginary rolling cylinder (cone, etc.) that the toothed gear may be considered to replace.
Pitch circle: A right section of the pitch surface.
Addendum circle: A circle bounding the ends of the teeth, in a right section of the gear.
Root (or dedendum) circle: The circle bounding the spaces between the teeth, in a right section of the gear.
Addendum: The radial distance between the pitch circle and the addendum circle.
Dedendum: The radial distance between the pitch circle and the root circle.
Clearance: The difference between the dedendum of one gear and the addendum of the mating gear.
Face of a tooth: That part of the tooth surface lying outside the pitch surface.
Flank of a tooth: The part of the tooth surface lying inside the pitch surface.
Circular thickness (also called the tooth thickness) : The thickness of the tooth measured on the pitch circle. It is the length of an arc and not the length of a straight line.
Tooth space: The distance between adjacent teeth measured on the pitch circle.
Backlash: The difference between the circle thickness of one gear and the tooth space of the mating gear.
Circular pitch p: The width of a tooth and a space, measured on the pitch circle.
Diametral pitch P: The number of teeth of a gear per inch of its pitch diameter. A toothed gear must have an integral number of teeth. The circular pitch, therefore, equals the pitch circumference divided by the number of teeth. The diametral pitch is, by definition, the number of teeth divided by the pitch diameter. That is,

where

`p=(pi*D)/N`

`P=N/D`

Hence,

`p*P=pi`

p = circular pitch

P = diametral pitch

N = number of teeth

D = pitch diameter

That is, the product of the diametral pitch and the circular pitch equals .

Module m: Pitch diameter divided by number of teeth. The pitch diameter is usually specified in inches or millimeters; in the former case the module is the inverse of diametral pitch.
Fillet : The small radius that connects the profile of a tooth to the root circle.
Pinion: The smaller of any pair of mating gears. The larger of the pair is called simply the gear.
Velocity ratio: The ratio of the number of revolutions of the driving (or input) gear to the number of revolutions of the driven (or output) gear, in a unit of time.
Pitch point: The point of tangency of the pitch circles of a pair of mating gears.
Common tangent: The line tangent to the pitch circle at the pitch point.
Line of action: A line normal to a pair of mating tooth profiles at their point of contact.
Path of contact: The path traced by the contact point of a pair of tooth profiles.
Pressure angle : The angle between the common normal at the point of tooth contact and the common tangent to the pitch circles. It is also the angle between the line of action and the common tangent.
Base circle :An imaginary circle used in involute gearing to generate the involutes that form the tooth profiles.

INPUTS FOR GEAR DESINING

The following inputs for designing the Planetary Gear are

Ring Gear

Module = 2.5 (we 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:

For Ring Gear-

Module (m) =2.5

No. of teeth (T) =46

We know that

`m= D_R/T`

`∴ D_R=m×T=2.5×46=115mm`

For Sun Gear-

Module (m) =2.5

No. of teeth (T) =14

We know that

`m= D_S/T`

`∴ D_S=m×T=2.5×14=35mm`

For Planet Gear-

_{`D_R/2=D_S/2+D_P`}

`115/2=35/2+D_P`

`∴ D_P=((115-35))/2=80/2=40`

`m= D_P/T`

`∴T=D_P/m=40/2.5=16`

Where,

D_R is the pitch circle diameter of Ring gear

D_S is the pitch circle diameter of Sun gear

D_P is the pitch circle diameter of Planet gear

m is the module

T is the number of teeth

We are going to run a simulation on the following cases,

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

OBJECTIVES:

To calculate the pitch circle diameter and the number of teeth for the planet gear.
To perform the motion analysis on Planetary gear system.
To obtain plots of angular velocity for different output position in different cases.

PROCEDURE:

First we go to assembly

Then to import gear we go to to the design library

And after that click on toolbox, click on Add in now

Then select the ANSI Metric system.

Then go to power transmission option.

Select gear and now select internal spur gear drag and drop on window.

Now we set the module, pitch circle dia, face width,external dia etc and finally click ok to complete the import of gear.

Similarly import sun gear

Similarly import Planet gear

Now we are going to design the carrier as per the shaft dia of gear.

Assembly

We create a new assembly and import the carrier first, followed by the required gears from the design library.
We give the constraints for the gear with respect to the edges and faces of the carrier.
Various mates used in the assembly are coincident mate and distance mate with axis and face of the carrier.

Now we go to perform the the motion analysis.

Before starting the motion study, we have to make sure that there should not be any interference between the gear teeths.

We have checked the motion of the assembly by enabling the physical dynamics option in the move/rotate components, before starting the motion study.

We performed motion study by applying various conditions(3-cases) given in the challenge and get the output plots.

PLOTS:

case-1

Input	Output	Fixed
Sun Gear	Carrier	Ring Gear

INPUT PLOT

Since the we give constant speed of 200 RPM hence,we get the constant angular velocity.

OUTPUT PLOT

Here we see the variation is high (approax between 200 to 415 degree/sec)

CASE-2

Input	Output	Fixed
Ring Gear	Carrier	Sun Gear

INPUT PLOT:-

Since the we give constant speed of 200 RPM hence,we get the constant angular velocity.

OUTPUT PLOT:

Here Variation is slightly less than previous case.

SOLID WORKS PART FOLDER:

Here we have attached the google drive link for SOLIDWORKS part file

Solid works part file

ANIMATION

Case-1

Input	Output	Fixed
Sun Gear	Carrier	Ring Gear

CASE-2

Input	Output	Fixed
Ring Gear	Carrier	Sun Gear

CONCLUSION:

The motion study helpful in simulating the performance of the Planetary gear system and also gives outline of the model for better output.

REFRENCES:

Planetary Gear

Terminology for Spur Gears

Figure shows some of the terms for gears.

Figure :-Spur Gear

Ship work like this
in your own course.

Talk to a career counsellor

Terminology for Spur Gears

Figure shows some of the terms for gears.

Figure :-Spur Gear

Ship work like thisin your own course.

Talk to a career counsellor

Ship work like this
in your own course.