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INTERNATIONAL JOURNAL OF PROFESSIONAL ENGINEERING STUDIES Volume 9 /Issue 2 / OCT 2017 IJPRES SPUR GEAR DEVELOPMENT & ANALYSIS USING RAPID PROTOTYPING BY REVERSE ENGINEERING 1 B.PRAVEEN KUMAR, 2 MOHAMMED ISRAN SHAREEF 1 Associate professor , Dept of MECH, Talla Padmavathi College of Engineering, Kazipet, Warangal,T.S, India Email: [email protected] 2 PG Scholar, Dept of MECH, Talla Padmavathi College of Engineering, Kazipet, Warangal, T.S, India Email: [email protected] ABSTRACT This project is about application of reverse engineering. Reverse engineering helps in obtaining the geometry of part or product which is not available otherwise. Its application makes it possible to reconstruct the original component with its drawing and manufacturing process. In this project we are going to produce spur gear used in automobile by Reverse Engineering. The procedure includes various stages which will help understand the different phases of reverse engineering. The process starts with understanding the reverse engineering procedure. The part geometry is first obtained with the help of scanning technology. Then with the use of different software’s, the three- dimensional model of the spur gear is obtained. Once the CAD model is obtained the part is analyzed using SOLIDWORKS simulation tool. After the optimized geometry is obtained, the pattern of the part is obtained using Rapid prototyping machine. This can be used for casting of the original part. INTRODUCTION TO REVERSE ENGINEERING In today’s intensely competitive global market, product enterprises are constantly seeking new ways to shorten lead times for new product developments that meet all customer expectations. In general, product enterprise has invested in CAD/CAM, rapid prototyping, and a range of new technologies that provide business benefits. Reverse engineering (RE) is now considered one of the technologies that provide business benefits in shortening the product development cycle. Figure 1.1 below depicts how RE allows the possibilities of closing the loop between what is “as designed” and what is “actually manufactured Figure: product development life cycle What Is Reverse Engineering? Engineering is the process of designing, , assembling, manufacturing and maintaining products and systems. There are two types of engineering, forward engineering and reverse engineering. Forward engineering is the traditional process of moving from high-level abstractions and logical designs to the physical implementation of a system. In some situations, there may be a physical part/ product without any technical details, such as drawings, bills- of-material, or without engineering data. The process of duplicating an existing part, subassembly, or product, without drawings, documentation, or a computer model is known as reverse engineering.

Transcript of SPUR GEAR DEVELOPMENT & ANALYSIS USING …ijpres.com/pdf35/36.pdfSPUR GEAR DEVELOPMENT & ANALYSIS...

INTERNATIONAL JOURNAL OF PROFESSIONAL ENGINEERING STUDIES Volume 9 /Issue 2 / OCT 2017

IJPRES

SPUR GEAR DEVELOPMENT & ANALYSIS USING RAPID PROTOTYPING BY

REVERSE ENGINEERING 1 B.PRAVEEN KUMAR, 2 MOHAMMED ISRAN SHAREEF

1 Associate professor , Dept of MECH, Talla Padmavathi College of Engineering, Kazipet, Warangal,T.S, India

Email: [email protected] 2 PG Scholar, Dept of MECH, Talla Padmavathi College of Engineering, Kazipet, Warangal, T.S, India

Email: [email protected]

ABSTRACT

This project is about application of reverse

engineering. Reverse engineering helps in obtaining

the geometry of part or product which is not available

otherwise. Its application makes it possible to

reconstruct the original component with its drawing

and manufacturing process. In this project we are

going to produce spur gear used in automobile by

Reverse Engineering. The procedure includes various

stages which will help understand the different

phases of reverse engineering.

The process starts with understanding the

reverse engineering procedure. The part geometry is

first obtained with the help of scanning technology.

Then with the use of different software’s, the three-

dimensional model of the spur gear is obtained. Once

the CAD model is obtained the part is analyzed using

SOLIDWORKS simulation tool. After the optimized

geometry is obtained, the pattern of the part is

obtained using Rapid prototyping machine. This can

be used for casting of the original part.

INTRODUCTION TO REVERSE ENGINEERING In today’s intensely competitive global market,

product enterprises are constantly seeking new ways

to shorten lead times for new product developments

that meet all customer expectations. In general,

product enterprise has invested in CAD/CAM, rapid

prototyping, and a range of new technologies that

provide business benefits. Reverse engineering (RE)

is now considered one of the technologies that

provide business benefits in shortening the product

development cycle. Figure 1.1 below depicts how RE

allows the possibilities of closing the loop between

what is “as designed” and what is “actually

manufactured

Figure: product development life cycle

What Is Reverse Engineering?

Engineering is the process of designing, , assembling,

manufacturing and maintaining products and

systems. There are two types of engineering, forward

engineering and reverse engineering. Forward

engineering is the traditional process of moving from

high-level abstractions and logical designs to the

physical implementation of a system. In some

situations, there may be a physical part/ product

without any technical details, such as drawings, bills-

of-material, or without engineering data. The process

of duplicating an existing part, subassembly, or

product, without drawings, documentation, or a

computer model is known as reverse engineering.

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Reverse engineering is also defined as the process of

obtaining a geometric CAD model from 3-D points

acquired by scanning/ digitizing existing

parts/products.

Figure: Physical-to-digital process

USE OF REVERSE ENGINEERING

Following are some of the reasons for using reverse

engineering:

• The original manufacturer no longer exists, but a

customer needs the product, e.g., aircraft spares

required typically after an aircraft has been in service

for several years.

• The original manufacturer of a product no longer

produces the product, e.g., the original product has

become obsolete.

• The original product design documentation has been

lost or never existed.

• Creating data to refurbish or manufacture a part for

which there are no CAD data, or for which the data

have become obsolete or lost.

• Inspection and/or Quality Control–Comparing a

fabricated part to its CAD description or to a standard

item.

• Some bad features of a product need to be

eliminated e.g., excessive wear might indicate where

a product should be improved.

• Strengthening the good features of a product based

on long-term usage.

• Analyzing the good and bad features of

competitors’ products.

• Exploring new avenues to improve product

performance and features.

• Creating 3-D data from a model or sculpture for

animation in games and movies.

• Creating 3-D data from an individual, model or

sculpture to create, scale, or reproduce artwork.

• Architectural and construction documentation and

measurement.

• Fitting clothing or footwear to individuals and

determining the anthropometry of a population.

• Generating data to create dental or surgical

prosthetics, tissue engineered body parts, or for

surgical planning.

• Documentation and reproduction of crime scenes.

The above list is not exhaustive and there

are many more reasons for using reverse engineering,

than documented above.

REVERSE ENGINEERING –THE GENERIC

PROCESS

The generic process of reverse engineering is a three-

phase process as depicted in Figure below. The three

phases are scanning, point processing, and

application specific geometric model development.

Figure: Reverse engineering – the generic process

Reverse engineering strategy must consider the

following:

• Reason for reverse engineering a part

• Number of parts to be scanned–single or multiple

• Part size–large or small

• Part complexity–simple or complex

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• Part material–hard or soft

• Part finish–shiny or dull

• Part geometry–organic or prismatic and internal or

external

• Accuracy required–linear or volumetric

Phase 1– Scanning

This phase is involved with the scanning strategy–

selecting the correct scanning technique, preparing

the part to be scanned, and performing the actual

scanning to capture information that describes all

geometric features of the part such as steps, slots,

pockets, and holes. Three-dimensional scanners are

employed to scan the part geometry, producing

clouds of points, which define the surface geometry.

These scanning devices are available as dedicated

tools or as add-ons to the existing computer

numerically controlled (CNC) machine tools. There

are two distinct types of scanners, contact and

noncontact.

a. Contact Scanners

These devices employ contact probes that

automatically follow the contours of a physical

surface .In the current market place, contact probe.

Figure: Contact scanning touch probe.

b. Noncontact Scanners

Figure: Optical scanning device.

A variety of noncontact scanning technologies

available on the market capture data with no physical

part contact. Noncontact devices use lasers, optics,

and charge-coupled device (CCD) sensors to capture

point data, as shown in Figure

Figure: Vertical faces–touch probe versus a laser.

Phase 2–Point Processing

This phase involves importing the point cloud data,

reducing the noise in the data collected, and reducing

the number of points. These tasks are performed

using a range of predefined filters. It is extremely

important that the users have very good

understanding of the filter algorithms so that they

know which filter is the most appropriate for each

task. This phase also allows us to merge multiple

scan data sets. Sometimes, it is necessary to take

multiple scans of the part to ensure that all required

features have been scanned. This involves rotating

the part; hence each scan datum becomes very

crucial. Multiple scan planning has direct impact on

the point processing phase. Good datum planning for

multiple scanning will reduce the effort required in

the point processing phase and also avoid

introduction of errors from merging multiple scan

data.

Phase 3–Application Geometric Model

Development

In the same way that developments in rapid

prototyping and tooling technologies are helping to

shorten dramatically the time taken to generate

physical representations from CAD models, current

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RE technologies are helping to reduce the time to

create electronic CAD models from existing physical

representations. The need to generate CAD

information from physical components will arise

frequently throughout any product introduction

process. The generation of CAD models from point

data is probably the most complex activity within RE

because potent surface fitting algorithms are required

to generate surfaces that accurately represent the

three-dimensional information described within the

point cloud data sets. Most CAD systems are not

designed to display and process large amounts of

point data; as a result new RE modules or discrete

software packages are generally needed for point

processing.

INTRODUCTION TO POWER

TRANSMISSION

Power transmission states that speed and torque

conversions from rotating power source to other

device. Here in our project we design and analysis

the intermediate shaft for stress and deflection, it is

necessary to know the applied forces. If the forces are

transmitted through gears, it is necessary to know the

gear specifications in order to determine the forces

that will be transmitted to the shaft. But stock gears

come with certain bore sizes, requiring knowledge of

the necessary shaft diameter.

Figure: compound reverted gear train.

This project will focus on an overview of a power

transmission system design, demonstrating how to

incorporate the details of each component into an

overall design process.

TYPES OF POWER TRANSMISSION

SYSTEMS

Transmissions types include

Manual Transmission

Automatic Transmission

Semi-automatic transmission

Power Transmission Devices

Mechanical power can be transmitted across large

distances in a variety of ways. Shafts transfer motion

from point to point along their axis of motion. Shafts

can be connected to each other by the following ways

Gear Drive

Chain Drive

Belt Drive

Gear Drive

Gear drive is a mechanism consisting of toothed

wheels that engage and transmit rotary motion,

usually transforming angular velocity and torques.

Gear drives are the most practical and wide spread

type of mechanical transmission. They are used to

transmit power— from negligibly small values to

tens of thousands of kilowatts-and to transmit

circumferential forces of fractions of a gram to 10

mega Newton’s (1,000 tons force).

Figure: gear drive

Gear drive with spur gears: (a) straight cut,

(b)helical,(c)herring bone,

(d) bevel,(e) with spiral teeth, (f) with internal

gearing.

The main advantages of gear drives are their

significantly smaller dimensions, high efficiency

(losses in precision-made, well-lubricated drives are

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1-2 percent, and, under especially favorable

conditions, 0.5 percent), longer life and greater

dependability, lack of slippage, and small shaft loads.

The disadvantages of gear drives include noisy

operation and the need for precision manufacture.

Gear drives are classified according to the

relationship of the axes to the drives.

Gears

Gear is a part, as a disk, wheel, or section of a shaft,

having cut teeth of such form, size and spacing that

they mesh with teeth in another part to transmit or

receive force and motion

The gears in a transmission are analogous to the

wheels in a pulley. An advantage of gears is that the

teeth of a gear prevent slipping.

Gears are the most common means used for power

transmission

They can be applied between two shafts which are

Parallel Collinear

Perpendicular and intersecting

Perpendicular and nonintersecting

Inclined at any arbitrary angle

Classification of gears

Figure: classification of gears

Spur Gears

General: Spur gears are the most commonly used

gear type. They are characterized by teeth which are

perpendicular to the face of the gear. Spur gears are

by far the most commonly available, and are

generally the least expensive. The basic descriptive

geometry for a spur gear is shown in the figure

below.

Limitations: Spur gears generally cannot be used

when a direction change between the two shafts is

required.

Advantages: Spur gears are easy to find, inexpensive,

and efficient.

Figure: spur gear

METHODOLOGY USED FOR CASE STUDY

OF GEAR

A case study of Gear is done for the purpose of

obtaining point cloud data which was exported into

associate nursing .stl format of the CAD program.

The best method to approximate a 3D geometrical

model is by approximating it with lots of triangular

aspects.

A. THE TYPICAL REVERSE ENGINEERING

PROCESS CAN BE SUMMARIZED IN

FOLLOWING STEPS

1. Physical model which needs to be redesigned or to

be used as the base for new product.

2. Scanning the physical model to get the point

cloud. The scanning can be done using various

scanners available in the market.

3. Processing the points cloud includes merging of

points cloud if the part is scanned in several settings.

The outlines and noise is eliminated. If too many

points are collected then sampling of the points

should be possible.

4. To create the polygon model and prepare .stl files

for rapid prototyping.

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5. To prepare the surface model to be sent to

CAD/CAM packages for analysis.

6. Tool path generation with CAM package for

suitable CNC machine manufacturing of final part on

the CNC machine.

In this thesis we are producing the Gear C of shaft 2nd

of Hero bike.The below shown figures are the Gear C

of 29 teeth.

Figure: front view of Gear which has to be produced

Figure: side view of Gear which has to be produced

Figure: Back view of Gear which has to be produced

Figure: Isometric view of Gear

The Gear has been scanned in a Roland Model lpx-

600 laser scanner.

The Roland Model lpx-600 laser scanner is a medium

sized scanner used to scan object of maximum height

of around 150 mm and diameter of 120 mm. It

operates with interface of computer with software Dr.

Picza which helps in setting up the scanning

parameters and also shows the scanning process. It

stores the scanned file in .stl format. The scanner is

shown in fig.

Figure: Roland Model LPX-600 Laser Scanner

Once the scanned image of object is obtained using

scanner it is exported into .stl format shown in fig..

The parameter set in the above software decides the

quality of scanned image. As the time for scanning

increases the quality of scanned image improves.

Figure: Stl Image File of Scanned Component

B. OBTAINING THE SOLID GEOMETRY

FROM THE POINT CLOUD DATA

The original .stl data is scattered and contains some

noise around the boundary of model. The noise

creates a problem while generating a solid model so it

has to be cleaned from the data. Solidworks software

has Scan to 3D option which help to point out the

noise from the data and with the help of noise

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reduction tool the noise is reduced. Then we get a

clean .stl data which can be used for further

processing

INTRODUCTION TO SOLIDWORKS

Solid works mechanical design automation software

is a feature-based, parametric solid modeling design

tool which advantage of the easy to learn windows TM

graphical user interface. We can create fully associate

3-D solid models with or without while utilizing

automatic or user defined relations to capture design

intent.

SOLIDWORKS SCAN TO 3D

Using the SolidWorks software’s ScanTo3D

functionality, you can open scan data from any

scanner (mesh or point cloud files) or curve data from

mathematics software, prepare the data, then convert

it into a surface or solid model.

ScanTo3D significantly reduces the time required to

build complex 3D models from non-digital data.

Designers can use ScanTo3D for various purposes:

Medical designers - Create anatomical

objects for reference.

Figure: Example of a solid created from scanned data

of a hand, using the Surface Wizard's Automatic

creation.

Consumer product designers - Create quick

representations of physical components

made from clay, foam, etc.

Machine designers - Create quick references

to OEM parts.

Figure: Scan to 3D overview

Two Methods for Converting Scan Data to a

Solid Model.

Semi-manual Creation: Direct Mesh

Referencing

Direct mesh referencing is useful for very

complex surfaces, such as consumer products.

Semi-automated Creation Using Wizards

The Mesh Prep and Surface Wizards guide you

through the ScanTo3D process

Exporting files:

After you import a mesh or cloud point file into a

SolidWorks document using ScanTo3D, We export

the document as another file type that contains the

mesh or cloud point data.

1. Click File > Save As.

2. Select a file format in Save as type:

ScanTo3D (*.xyz)

ScanTo3D (*.wrl).

ScanTo3D (*.stl).

ScanTo3D (*.3ds)

ScanTo3D (*.iges)

The scanned file is imported in solidworks software

which helps to extract geometry from the .stl file or

point cloud data shown in figure below to Solid

geometry.

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Figure: .Stl file imported to solidworks Scan to 3D

By using Mesh preparation wizard meshing of the

.Stl file is done.

Increasing the global smoothness then entering into

surface wizard manager for adjusting surface

resolution.

Figure: surface failure areas

Figure: individual sub meshes are identified

Now all the surface are extracted as shown below

Figure: surfaces extraction

Figure: model is completed with extra surfaces

Finally the base model is complete by using Trim,

knit, fillets and chamfer options for generating solid

model. The file is saved in .STL format.

Figure: Final model after trimming the surfaces

Figure: Four views of the Gear

The drawings are generated for the Gear model and

the following dimensions are obtained.

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Figure: Isometric view of the Gear model

Figure: Three views of the gear

Figure: Back view of the gear

INTRODUCTION TO SOLIDWORKS

SIMULATION

SolidWorks® Simulation is a design analysis system

fully integrated with SolidWorks. SolidWorks

Simulation provides simulation solutions for linear

and nonlinear static, frequency, buckling, thermal,

fatigue, pressure vessel, drop test, linear and

nonlinear dynamic, and optimization analyses.

Static Analysis

When loads are applied to a body, the body deforms

and the effect of loads is transmitted throughout the

body. The external loads induce internal forces and

reactions to render the body into a state of

equilibrium. Linear Static analysis calculates

displacements, strains, stresses, and reaction forces

under the effect of applied loads.

STRUCTURAL ANALYSIS OF GEAR

Gear analysis can be performed using analytical

methods which required a number of assumption and

simplifications which aim at getting the maximum

stress values only but

gear analyses are multidisciplinary including

calculations related to the tooth stresses .In this work,

an attempt will been made to analyze bending stress

to resist bending of helical gears, as both affect

transmission error. Due to the progress of computer

technology many researchers tended to use numerical

Methods to develop theoretical models to calculate

the effect of whatever is studied. numerical methods

are capable of providing more truthful solution since

they require very lessrestrictive assumptions. Finally

the results obtained by theoretical analysis, AGMA

calculations and finite element analysis are compared

to check the correctness.

This procedure is based on the principle of

differential geometry that pertains to envelopes of

curves and surfaces.

The above equation is lewis bending equation to

calculate bending stresses developed in gears.

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Where

RESULTS OF MAXIMUM BENDING STRESS

FROM LEWIS EQUATION FOR

GEAR1

Material properties

Loads and Fixtures

Mesh Information

Study Results for face width 8.5 mm

Stress

Deformation

Strain

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Factor of safety

A factor of safety less than 1 at a location indicates

that the material at that location has failed.A factor of

safety of 1 at a location indicates that the material at

that location has just started to fail. A factor of safety

greater than 1 at a location indicates that the material

at that location is safe.

So our design is safe for given loading condition.

Study Results for face width 10.5 mm

Stress

Deformation

Strain

Factor of safety

Study Results for Face Width 12.5mm Stress

Deformation

Strain

Factor of safety

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Study Results for Face Width 14.5mm Stress

Deformation

Strain

Factor of safety

RESULTS AND DISCUSSIONS

The structural stress analysis of the gear tooth model

is carry out using the FEA in Solidworks simulation.

The load applied at the tooth of the gear .by applying

the analysis over the tooth which is facing the load

we get the stress distribution in the numeric as well

as in the form of the color scheme. By varying the

face width and keeping the other parameters constant

various models of the gear are created. For

determining at any stage during the design of the gear

face width is an important parameter. The results of

the variation in face width from (8.5 mm to 14.5mm

)there is continuous decrement in the value of the

stress of the tooth of the gear stress. Results of

theoretical and static analysis are closer, therefore

the design are accepted. As it is seen clearly from all

tables and graphs the maximum bending stress values

are increase with the decrease of face width. In this

work we got on two results as follow

_ Theoretical results (from Lewis equation directly)

_ Static analysis results

And all results are closer as shown in graphs.

Effect of face width:

The effect face width on maximum bending stress is

study by varying the face width for five

Values which are (b=8.5mm, 10.5mm, 12.5mm,

14.5mm) the magnitude of the stresses obtained for

those face widths are displayed.

Comparison of theoretical stress values and solid

works values

Table: comparison of bending stresses (theoretical

and software)

INTRODUCTION TO RAPID PROTOTYPING

Rapid Prototyping (RP) can be defined as a

group of techniques used to quickly fabricate a scale

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model of a part or assembly using three-dimensional

computer aided design (CAD) data. What is

commonly considered to be the first RP technique,

Stereo-lithography, was developed by 3D Systems of

Valencia, CA, USA. The company was founded in

1986, and since then, a number of different RP

techniques have become available.

Why Rapid Prototyping?

The reasons of Rapid Prototyping are

• To increase effective communication.

• To decrease development time.

• To decrease costly mistakes.

• To minimize sustaining engineering changes

• To extend product lifetime by adding

necessary features and eliminating redundant features

early in the design.

Rapid Prototyping decreases development time by

allowing corrections to a product to be made early in

the process. By giving engineering, manufacturing,

marketing, and purchasing a look at the product early

in the design process, mistakes can be corrected and

changes can be made while they are still inexpensive.

The trends in manufacturing industries continue to

emphasize the following:

• Increasing number of variants of products.

• Increasing product complexity.

• Decreasing product lifetime before

obsolescence.

• Decreasing delivery time.

Methodology of Rapid Prototyping

The basic methodology for all current rapid

prototyping techniques can be summarized as

follows:

1. A CAD model is constructed, and then

converted to STL format. The resolution can

be set to minimize stair stepping.

2. The RP machine processes the .STL file by

creating sliced layers of the model.

3. The first layer of the physical model is

created. The model is then lowered by the

thickness of the next layer, and the process

is repeated until completion of the model.

4. The model and any supports are removed.

The surface of the model is then finished

and cleaned

Some of the methods of rapid prototyping are

STEREO-LITHOGRAPHY

LAMINATED OBJECT MANUFACTURING

FUSED DEPOSITION MODELING

SELECTIVE LASER SINTERING

SELECTIVE LASER SINTERING

A laser beam is traced over the surface of a tightly

compacted powder made of thermoplastic material

(A). The powder is spread by a roller (B) over the

surface of a build cylinder (C). A piston (D) moves

down one object layer thickness to accommodate the

layer of powder

The power supply system (E) is similar in function to

the build cylinder. It also comprises a cylinder and

piston. The piston moves upward incrementally to

supply powder for the process.

Heat from the laser melts the powder where it strikes

under guidance of the scanner system (F). The CO2

laser used provides a concentrated infrared heating

beam. The entire fabrication chamber is sealed and

maintained at a temperature just below the melting

point of the plastic powder. Thus, heat from the laser

need only elevate the temperature slightly to cause

sintering, greatly speeding the process. A nitrogen

atmosphere is also maintained in the fabrication

chamber which prevents the possibility of explosion

in the handling of large quantities of powder

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After the object is fully formed, the piston is raised to

elevate the object. Excess powder is simply brushed

away and final manual finishing may be carried out.

It may take a considerable time before the part cools

down enough to be removed from the machine. Large

parts with thin sections may require as much as two

days of cooling time

Figure: Selective Laser Sintering

Figure: Selective Laser Sintering Machine (RPT

Systems)

PROTOTYPING OF THE GEAR USING

SELECTIVE LASER SINTERING –

RAPIDPROTOYPING SYSTEM

FORMIGA P 100 - small, fast, efficient, e-

Manufacturing in the Compact Class Plastic laser-

sintering system for the direct manufacture of series,

spare parts and functional prototypes

The FORMIGA P 100 represents laser-sintering in

the compact class. With a build envelope of 200 mm

x 250 mm x 330 mm, the FORMIGA P 100 produces

plastic products from polyamide or polystyrene

within a few hours and directly from CAD data. The

machine is ideally suited for the economic production

of small series and individualized products with

complex geometry – requirements which apply

among others to the medical device industry as well

as for high-value consumer goods. At the same time,

it provides capacity for the quick and flexible

production of fully functional prototypes and patterns

for plaster, investment and vacuum casting. With

turnover times of less than 24 hours the FORMIGA P

100 integrates itself perfectly in a production

environment that requires the highest level of

flexibility. The system distinguishes itself also by

comparatively low investment costs.

Technical Specifications:

Technical Data

Table No – 1

Dimensions

Table No – 2

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Data preparation

Table No – 3

CONCLUSIONS

In theory of Gear, we are considering that

the load is acting at one point and the stress

is calculated. The calculation of maximum

stresses in a gear at tooth root is three

dimensional problems. The accurate

evaluation of stress state is complex task.

The contribution of this thesis work can be

summarized as follows:

The strength of gear tooth is a crucial

parameter to prevent failure. In this work, it

is shown that the effective method to

estimate the root bending stress using three

dimensional model of a gear and to verify

the accuracy of this method the results with

different face width of teeth are compared

with theoretical values.

The face width is an important geometrical

parameter in design of gear as it is

expected in this work the maximum

bending stress decreases with increasing

face width.

REFERENCES

[1]. Cheng, Y., And Tasy C.B., Stress Analysis Of

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