harmonic planetary gear fem

Department of Mechanical and Indutrial Engineering Technology

Project 1

MODELLING OF SUN GEAR AND SHAFT

OF A HAMONIC PLANETARY GEAR By

Sandile Shembe (Student No - 201503655)

A mini-project report submitted

in partial fulfilment of the requirements for the module

STRESS ANALYSIS IV (ESA411)

FOR THE DEGREE OF BACHELOR OF

MECHANICAL ENGINEERING TECHNOLOGY

Submitted to

Supervisor - Dr. Daramy Kallon

DEPARTMENT OF MECHANICAL AND INDUSTRIAL ENGINEERING

TECHNOLOGY

FACULTY OF ENGINEERING AND THE BUILT ENVIRONEMNT

UNIVERSITY OF JOHANNESBURG

Modelling of Sun Gear and Shaft of a Harmonic Planetary Gear – ESA411

Page | 1

Submitted: Thursday 17th September, 2015

Marking plan

Chapter Section Description Sum-

mark

Maximum

Marks

1 I Abstract 5 15

II Introduction 5

III Problem formulation 5

2 I Approach 5 20

II Literature review 10

III Methodology 5

3 I Design 8 20

II Simulation (at all four sections) 10

III Results (tabular, graphical) 2

4 I Discussion (interpretation of graphs) 12 15

II List of assumptions 3

5 I Conclusion (location of critical zones) 6 10

II Recommendations 4

References 6 10

Appendices 4

Report layout 4 10

Neatness 3

Presentation 3

Total Marks 100 100

Name: ………………………..……………Student No: ………………………. ………….

Signature: ..................................................Date: …………………………………………...


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DECLARATION

I ……………………………………….. Hereby declare that this mini-project report is

wholly my own work and has not been submitted anywhere else for academic credit, either

by myself or another person.

I understand what plagiarism implies and declare that this report embodies my own ideas,

words, phrases, arguments, graphics, figures, results and organization except where reference

is explicitly made to another work.

I understand further that any unethical academic behaviour, which includes plagiarism, is

seen in a serious light by the University of Johannesburg and is punishable by disciplinary

action as stipulated by the university rules and regulations.

Name: ………………………..……………

Student No: ………………………. …….

Signature: ..................................................

Date: ………..............................................


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ACKNOWLEDGEMENTS

I would like to express my gratitude to my Lecture Dr Kallon for his guidance and assistance

which helped me to be able to conduct this Project Report appropriately.

He made it clear for me what is required from the readings taken during the lab and also what

is expected in terms of the ELO’s on the discussion.

I would also like to thank my classmates for taking their time assisting me in inventor CAD.


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ABSTRACT

This document reports the stress analysis of the Sun Gear and a shaft of a harmonic planetary

gear design assemble. Both Gear and Shaft are manufactured from mild steel. The Material

was chosen taking to considerations the mechanical properties, manufacturability and cost

study. The analysis is done so that critical stress concentrations can be identified and design

changes can be done to minimise chances of failure. Other motives for the analysis is that it is

critical to design transmission components as they possess high risk to passengers of the

motor vehicles.

The shaft and gear must withstand static and dynamic loads exacted on it. The sun gear is

locked on the shaft by a key. Loads varying from 15kN to 25kN directly on the

circumference of the gear. The assembly model is created on Inventor professional as well as

the simulation, then the stress concentration deflection is analysed and discussed in this

document.

The stress analysis of the gear and shaft is clearly illustrated graphically for the interpretation

and design decision. The graph indicates the force on the x-axis and the stress on the y-axis.

Theoretically the graph should be linear and increase proportionally.

The first graph on the table is section A-A, it indicating a true relationship between the load

applied and the stress induced. The stress is increases with the increase in load and the graph

is linear. However on the graph for B-B vs load, the stress increases with the load but it

reaches a point where it is constant.

In conclusion section A-A proved to be the only graph repreasenting true results for stress vs

load analysis.The minimum avarage principal stress is 84.45MPa and the maximum avarage

principal stress is 565.5MPa.The relationship is directly proportional because the as the force

increases the stress also increases.As it was stated on the assumptions the graph for this

material obeys Hookes law of stresses as the relationship is propotional.


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Table of Contents

DECLARATION ............................................................................................................................ 2

ACKNOWLEDGEMENTS ............................................................................................................ 3

ABSTRACT .................................................................................................................................... 4

CHAPTER 1 ................................................................................................................................... 9

INTRODUCTION .......................................................................................................................... 9

1.1. Project Background ..................................................................................................... 9

1.2. Problem Formulation................................................................................................... 9

1.2.1 Problem Statement ................................................................................................... 9

1.2.2 Scope of Project ..................................................................................................... 10

1.2.3 Limitations ............................................................................................................. 10

2.1 Introduction [Note: Give a one paragraph summary of this chapter] ....................... 11

2.2 Approach ................................................................................................................... 11

2.3 Literature review ....................................................................................................... 11

2.3.1 The Sun Gear and Shaft of a Harmonic Planetary Gear ........................................ 11

2.3.2 Design and Application of the Sun Gear of a Harmonic Planetary Gear .............. 13

2.3.3 Fatigue and failure of the Sun Gear and Shaft of a Harmonic Planetary Gear

Error! Bookmark not defined.

2.3.4 Engineering Stress Analysis Procedure (Steps in FEM) ....................................... 17

2.3.5 Stress Analysis of the Sun Gear and Shaft of a Harmonic Planetary Gear ........... 18


3.2 Design........................................................................................................................ 19

3.3 Simulation (at all four sections) ................................................................................ 21

3.4 Results (tabular and graphical) .................................................................................. 33


4.2 Discussions ................................................................................................................ 34

4.3 Assumptions .............................................................................................................. 35


5.2 Conclusions ............................................................................................................... 36

5.3 Recommendations ..................................................................................................... 36

REFERENCES ............................................................................................................................. 38


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LIST OF FIGURES

Figure 1.1 Planetary gear system illustration……………………………………….9

Figure 2.3.1 Mild steel Stress Vs Strain Curve…………………………………12

Figure 2.3.2.2 (a). Gantry Milling Machine………………………………………..14

Figure 2.3.2.2 (b). Gantry Milling Machine ………………………………………14

Figure 2.3.2.2(c) Other Applications of Planetary gears…………………………14

Figure 2.3.3 (b) fatigue crack……………………………………………………...15

Figure 3.2a Harmonic gear and Shaft 2 D…………………………………….….19

Figure 3.2b Sun Gear 2 D…………………………………………………………19

Figure 3.2.2 Assembly 2 D………………………………………………………..20

Figure 3.4 Stress Vs Force Graph’s……………………………………………….33

Figure 5.2.1 Stress Vs Force (A-A) graphical Representation…………………….36


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LIST OF TABLES

Table 3.1 Assemble Bill of Material

Table 3.3.1 Table of Result - 15kN






Table 3.4 Sectional Planes


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LIST OF SYMBOLS or NOMENCLATURE

Symbol Description

P Point Load

x Varying distance

y Displacement

d^2y/dx^2 Moment Integral

dy/dx Slope Integral

Mmax Maximum Moment

Ixx Moment of Inertia

D Diameter

E Modulus of Elasticity

C Integration Constants


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CHAPTER 1

INTRODUCTION

----------------------------------------------------------------------------------------------------------------

1.1. Project Background

Figure 1.1 Planetary gear system illustration

The purpose for this project is to identify critical location where the beam is likely to failure.

The analysis is done based on stresses induced by varying the load acting on the gear. The

material for the whole assemble is mild steel. Investigate the material selected satisfy the four

main properties or criteria namely High tensile and endurance strength allowing the material

to withstand static and dynamic loads respectively.

This sun gear and shaft to be design is for an automatic transmission of a Bell Front End

Loader. Then using Autodesk Inventor Professional 2015 both the sun gear and shaft is

designed, and simulate is run to identify stress concentration as well as deflection. The results

will be inspected, conclusion and recommendations are pointed out.

1.2. Problem Formulation

1.2.1 Problem Statement

A shaft of an automatic transmission planetary gear system carries a sun gear linked to three

gears orbiting around the planetary ring gear.

The assembly components are made up of mild steel. The loading on the shaft need to be

analysed for failure stress analysis. The aim is to find the location of the Fatigue and direct

stresses induced on assemble that may result in to mechanical failure. The load applied is

varied for different stress values.

The shaft geometry and material selected must be able to allow it to withstand the load of

gear and the point load varying from 15kN to 25kN acting on top of the gear and the beam is

fixed on the left-hand.


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1.2.2 Scope of Project

Designing a sun gear and shaft of harmonic planetary gears, and then selecting mild steel as a

base material that will provide acceptable yield strength, cost effective and that has good

manufacturability.

The design assemble needs to simulated for stress analysis results and conclusion need to be

drawn based on the results. CAD simulation is done to investigate the degree of failure of the

selected material; this is achieved by data inputting material properties on the design model.

Deflection and slope is calculated for the designed assembly at maximum point load of 25KN

applied at 42mm from the fixed end.

The following is guideline or scope of the project.

1. Literature review on material selection for planetary gears.

2. Select mild steel as a material for the shaft, gear and key of the planetary system.

3. Determine the slope and deflection at maximum loading.

4. Model the design and do stress analysis on inventor.

1.2.3 Limitations

Since material is assigned based on the procedure stated on this report and can only be

proved by calculations and stress analysis on Inventor Auto Cad.The limitations are practical

testing of the material selected, because selection was done by investigating the material used

in industry then selected on the standard tables.

To ensure proper selection of material, hardness test must be done on the material then a

prototype must be manufactured to do precise test


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CHAPTER 2

Approach, Literature Review and Methodology

----------------------------------------------------------------------------------------------

2.1 Introduction

The engine drives the transmission, and then the transmission will transmit the drive through

the propeller shaft to the axle for wheel drive. In the system there must be a sun gear and

shaft of a planetary gear system, this system or mechanism convert the reciprocating motion

to rotational motion. Therefore the harmonic shaft is induced with mechanical stresses and

then material selection becomes a critical or import factor in the design so as to try and

minimise those stresses. The literature covers the theory behind material selection,

application and methodology of designing effective structures.

2.2 Approach

In this design the history and applications of a sun gear and a harmonic shaft is investigated.

The sun gear and shaft being designed is used on the automatic transmission. In this design

the shaft and the gear are mild steel and assemble is simulate on CAD for stress analysis and

deformation, results are documented on chapter three.

The material to be selected must also have the shaft diameter as a standard size so that the

design can be cost effective. Results will be illustrated by the drawing programme so that it

can be concluded about the impact of the applied force on the shaft of selected material.

2.3 Literature review

2.3.1 The Sun Gear and Shaft of a Harmonic Planetary Gear

The sun gear is located at the centre of the planetary gears traveling on the ring gear. The sun

gear is transmitting torque from the shaft to the planet gears.

Therefore the material of the sun gear must be able to withstand bending and torsional

stresses induced by the motor driving the harmonic shaft. When the sun and planetary gear

system was invented the aim was to convert reciprocation motion to rotary motion. In trying

to convert the reciprocating motion to rotary motion the planetary gears are exposed to

mechanical stress in different planes.


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The following performance material indices are considered for the material selection of

transmission gears.

surface fatigue limit

root bending fatigue limit

wear resistance of tooth’s flank and

Machinability.

The material used for the gear and shaft design is mild steel.

Mild Steel

Mild steel composition consist of iron alloy containing 0.3 % carbon ,but the range is

normally between 0.1-0.25 %.It main characteristics are its ductility and malleability.

Those characteristics are important and therefore mild steels are used to manufacture

fasteners and also used in railings and decorative gates.

The property of malleability allows mild steels to be bent, twisted without fracture and

fatigue.

Figure 2.3.1 Mild steel Stress Vs Strain Curve (Design of Steel Structures at Indian Institute

of Technology Madras)


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Low Carbon steels

Low carbon steels has less composition of carbon, ranging from 0.05% to 0.3%.Generally in

vehicle body panels, pipes chains, rivets and fasteners the composition of carbon is between 0

.05 And 0.2 while on gears, shafts it ranges from 0.2 – 0.3 % of C.

Low carbon steels are normally used where high strength is not a requirement.

2.3.2 Design and Application of the Sun Gear of a Harmonic Planetary Gear

2.3.2.1 Design of the Sun Gear of a Harmonic Planetary Gear

Transmissions of this century are becoming more based on high speeds and precision which

then require gear systems with special design.

Therefore planetary gears are mostly used in machines that are required to transfer

information, energy and materials. The design is in such a way that there are no internal

backlash or minimal if complex to ignore totally. The design of harmonic gears have

advantages of high output capacity on the bearing.

The other advantages of modern design of harmonic gears high torque capacity, precise

positioning geometry, compact design, single stage high ratios and high effectiveness.

Planetary gears sizes and configuration vary widely depending on desired speed ratios and

design requirements. That is an advantage that allows them to be used in various applications

for example in clocks, car mirrors, toys, automobile transmissions and turbine engines.

2.3.2.2 Application of the Sun Gear of a Harmonic Planetary Gear

An example of application of sun gear of harmonic planetary gear mechanism is a gantry

milling machine of large turbine components. This machine has high cutting forces going up

to 30KN.

The harmonic planetary gear system design is able to handle the pre-load torque that can be

varied which the machine operating mode. In this application there are very high

accelerations in torque and precision is also important as this is governed by a co-ordinate

system. When one actuator of the milling machine acts as a brake it increases the pre-load

which remove the backlash in the pinion ring and the torsional stiffness is increased as well.

And the advantages of this system arrangement are high performance without comprising

accuracy. Below the machine is illustrated.


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Figure 2.3.2.2 (a). Gantry Milling Machine

Figure 2.3.2.2 (b). Gantry Milling Machine

Figure 2.3.2.2(c) Other Applications of Planetary gears


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2.3.3 Fatigue and failure of the Sun Gear and Shaft of a Harmonic Planetary Gear

Figure 2.3.3(a) Failure due to heavy static loads induced.

Figure 2.3.3 (b) According to the research done by the K S Rangasamy College of

Technology, the failure that was observed here was caused by rust then the gear failed

because of fatigue crack.


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2.3.4 Engineering Materials

Materials selected for gear application are expected to provide a combination of

characteristics without comprising cost in trying to satisfy the requirements. Physical

properties that are significant for gear material are fatigue, shear, static strength, wear

resistance, toughness and strength at high temperatures.

Engineering materials properties vary because they depend on a wide range of factors, such

as chemical composition, processes of manufacture, molecular defects, heat treatment and

temperature.

Usually on ATSM tables and charts, the common properties that are specified are the

ultimate, yield strength, compressive strength, Modulus of elasticity normally when looking

in tension and torsion, then Brinell hardness and finally fatigue stress factors.

Constrains in selecting the gear material are the component geometry, manufacturability and

cost effectiveness.

For the purpose of this project the materials that are being investigated are Plain carbon

steels, medium carbon steels and low alloy ASTM High strength steel.

Plain carbon steels

.

2.3.5 Engineering Materials Selection Procedure

Gears can be made from variety of material depending on application needs, for example they

can be manufactured from Steel, Cast Iron, nylon, acetal etc.

Normally the first step in selecting the material is to gather information about the

performance requirements of the system where the gear will be used. Thus assist on choosing

the material with sufficient physical and chemical properties, then processing requirements.

According NSI-AGMA 2004-B89 Gear Material Manual, there seven guidelines used in this

project for material selection for sun gear and shaft they are listed below:-

1. Physical Mechanical Properties

2. Grade and Heat Treatment

3. Manufacturability

4. Availability and Cost

5. Hardenability and Size Effects

6. Cleanliness

7. Dimensional Stability


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Other requirements for material selection during design stage are, design requirements such

as knowing what the application of the component to be designed, essential requirements that

need to be met e.g. strength and stiffness etc. The material life is mostly affected by corrosion

and fatigue.

The geometric and material properties also are a requirements and these assist in determining

equations for constrains such as yield, fracture, buckling etc.

2.3.6 Engineering Stress Analysis Procedure (Steps in FEM)

Essential steps to be followed for stress analysis are as follows:-

Discretization

In this step it where the nodes are selected and the element mesh is formed either in

2d or 3D.The mesh is a formation of shapes such as triangles, quadrilaterals,

tetrahedral, prismatic etc.

Selection of element to be analysed

Selection of displacement function

Displacement function can any polynomial, that function will produce an approximate

result and it will also satisfy basic requirements for the analysis.

Defining the stress verses strain relationship

Derive the element stiffness matrix

To derive the element stiffness matrix, nodal forces are used because they are related

to the stiffness. In this step the material is also specified.

The function consist of force, stiffness and displacement.

Derivation of overall matrices and equations

In this step the matrices for each nodal points is assembled to form a global.

Solving for nodal displacements

Specify the boundary conditions

Solving for element forces applied at nodes

Interpretation of the results


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2.3.7 Stress Analysis of the Sun Gear and Shaft of a Harmonic Planetary Gear

Due to the mechanical movements in the transmission, the sun gear and harmonic planetary

gears become under mechanical stresses. These stresses results into catastrophic failures if

unidentified.

In the planetary gears the stresses increases as the torque increases. The vibrations that occur

during rotation in the system courses fatigue in critical areas where the shafts are fixed. In

design of planetary gears, finite element analysis is applied to a single tooth so that results are

accurate. The material strength is the key factor in major consideration for the operational

loading. CAD software’s are used to analyse the structures programmes such as Pro

Engineer, PTC creo, solid works and Inventor.

2.4 Methodology

The design methodology followed could be summarized as follows;

Step 1: Modelling assemble consisting of a gear, shaft and key.

Step 2: Select Mild steel as base material.

Step 3: Apply different loads ranging from 15 kN to 25kN with increments of 2 kN

Step 4: Create a simulation and run.

Step5: Assemble is then analysed for weight, stress and displacement.

Step6: The results are then compared to the commercial figures and observed if they

are still within mechanical operational requirement, and if not then iterations from

step 3 are necessary.

Design constraints

The dimensions must not be altered.

The load position and increments must be kept constant throughout.


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CHAPTER 3

Modelling of Sun Gear and Shaft

----------------------------------------------------------------------------------------------

3.1 Introduction

The design consist of assemble of a gear, shaft and key. The structure forms a cantilever

beam fixed on the left-hand of the beam. The position of the load is 44mm from the fixed

wall. The magnitude of the load applied is varied from 15kN to 25kN and simulation is done

to identify the location of critical failure points.

3.2 Design

Below there are 2 dimensional drawings for the assemble and its parts

Figure 3.2a.Gear and shaft assemble.

Figure 3.2b.Gear.


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Figure 3.2c. shaft

Figure 3.2d.Gear and shaft assemble with dimensions (Illustration)

Table 3.1 Assemble Bill of Material

Bill of Material

Parts List Material Quantity

Gear Steel, Mild 1

Shaft Steel, Mild 1

Key Steel, Mild 1


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3.3 Simulation (at all four sections)


Name Minimum Maximum

Volume 45817.5 mm^3

Mass 0.359668 kg

Von Mises Stress 0.0856843 MPa 678.622 MPa

1st Principal Stress -224.781 MPa 806.017 MPa

3rd Principal Stress -815.195 MPa 247.271 MPa

Displacement 0 mm 0.194262 mm

Safety Factor 0.30503 ul 15 ul

Von Mises Stress


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1st Principal Stress

3rd Principal Stress


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Table 3.3.2Table of Result - 17kN


Volume 45817.5 mm^3

Mass 0.359668 kg






Von Mises Stress


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Volume 45817.5 mm^3

Mass 0.359668 kg






Von Mises Stress


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Volume 45817.5 mm^3

Mass 0.359668 kg






Von Mises Stresses


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1st Principal Stresses

3rd Principal Stresses


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Table 3.3.5Table of Result – 23 kN


Volume 45817.5 mm^3

Mass 0.359668 kg






Von Mises Stresses


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Table 3.3.6 Table of Result – 25 kN


Volume 45817.5 mm^3

Mass 0.359668 kg






Von Mises Stresses


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3.4 Results (tabular and graphical)

Table 3.4 Sectional Planes

F (kN) A-A B-B C-C D-D

15 84,45 -18,65 -121,7 -121,7

17 151,25 -27 -207 -207

19 238,5 -30 -298,5 -567

21 338 -30 -398 -766

23 447 -30 -507 -984

25 565,5 -30 -625,5 -1221

Graphical Representation

Figure 3.4 Stress Vs Force Graph’s


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CHAPTER 4

Discussion of Results - Stress Analysis of the Sun Gear and Shaft

----------------------------------------------------------------------------------------------

4.1 Introduction

This chapter discusses the results of the stress analysis report generated from Inventor

simulation. The stresses that were developed in the analysis were, then tabulated and used to

derive graphs that represent the relationship between the stress and the force. The readings

are separated by sectional planes namely A-A, B-B, C-C & D-D. These graphs are clearly

explained in this chapter and it can be seen that only the graph of section A-A is on the

positive axis thus shows the where there is high concentration of stresses. Assumptions are

also stated in this chapter for the design.

4.2 Discussions

4.2.1 Interpretation of the first four graphs

The stress analysis of the gear and shaft is clearly illustrated graphically for the interpretation

and design decision. The graph indicates the force on the x-axis and the stress on the y-

axis.Theoritically the graph should be linear and increase proportionally.

The first graph on the table is section A-A ,it indicating a true relationship between the load

applied and the stress induced.The stress is increases with the increase in load and the graph

is linear. However on the graph for B-B vs load ,the stress increases with the load but it

reaches a point where it is constant.

The graph for section D-D & C-C the relationship is linear but the trend is ever decreasing

which indicates that as the load increases the stress is lesser .It is then found that as you move

closer to the load location the stress tend to decrease even when the load is increased.

From the graphical interpretation it can be deduced that the stress is concentrated more on the

fixed end between the shaft and the wall.as it is shown on figure 4.2.1 the concentration is

more on the fixed wall.


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4.2.1 Stress Concentration critical points illustration

4.3 Assumptions

1. The material in the model complies with Hooke’s law and therefore stress is directly

proportional to strain.

2. The induced displacements are small enough to ignore the change in stiffness caused

by loading.

3. Boundary conditions do not vary during the application of loads. Loads must be

constant in magnitude, direction, and distribution. They should not change while the

model is deforming.

4. All loads are applied slowly and gradually until they reach their full magnitudes. After

reaching their full magnitudes, loads remain constant (time-invariant).


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CHAPTER 5

Conclusions and Recommendations

----------------------------------------------------------------------------------------------

5.1 Introduction

This chapter documents the conclusion about the stress analysis performed on assemble. The

stresses from the graphs were tabulated and grouped into sections. Plane A-A graph produced

results that shows the true relationship between stress induced and force applied.

Recommendations are also stated in this chapter, recommendations such as position of the

load and method of calculating the sectional stresses need to be investigated for accuracy.

5.2 Conclusions

5.2.1 Interpretation of final graph (Location of critical zones)

The graph that possess more appropriate results is for section A-A since the relationship of

the stress and force is proportional. Below is the graph of section AA. The minimum avarage

principal stress is 84.45MPa and the maximum avarage principal stress is 565.5MPa.

Figure 5.2.1 Stress Vs Force (A-A) graphical Representation

The minimum avarage principal stress is 84.45MPa and the maximum avarage principal

stress is 565.5MPa.The relationship is directly proportional because the as the force increases

the stress also increases.As it was stated on the assumptions the graph for this material obeys

Hookes law of stresses as the relationship is propotional.The sectional stresses indicate that as

the planes shift away from the critical stress area the stress concentration decreases and that is

clear when the assemble simulate is viewd.


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The graphical results also illustrate the material selected obeys Hooks law.The material is

alos not brittle ,that is proven by the analysis since it didn’t breck but it resisted the and

consumed the stress applied.

Recommendations

Load needs to be applied at the centre of the gear so that it can act in line with the

weight of the gear.

The gear need to be designed with the tooth for more accurate results, and remove the

holes because they affect the stress.

The method of calculating the sectional stresses need to be investigated for accuracy.


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REFERENCES

Examples of References

1. http://www.ehow.com/facts_6961115_properties-uses-mild-steel.html

2. Analysis of Stresses and Deflection of Sun Gear by Theoretical and ANSYS

Method_PDF

3. 02/05/2015,http://www.ezlok.com/TechnicalInfo/MPCarbonSteel.html

4. (Published in 1997) Strength of Materials For Technicians ;J.G Drosky

5. (Published: 2011-01-04)Mechanics of Materials 6th Edition .James Gere

6. DA6-BeamFormulas Downloaded document

7. (1 Mar. 2010) Shigley's Mechanical Engineering Design 9th Edition by Budynas,

Richard, Nisbett, Keith

8. Marks' Standard Handbook for Mechanical Engineers

Appendix_B.pdf

9. 10/05/2015,https://www.google.co.za/search?q=planetary+gear+transmission

10. 06/05/2015,https://www.google.co.za/search?q=Gantry+Milling+Machine

11. 10/05/2015,Carbon Steel Hand Book by D. Gandy; EPRI Project Manager

12. Developments In Abrasive WaterJet Technology

13. http://www.wjta.org/wjta/New_Developments_etc.asp, Accessed August 2011

14. WaterJet Technology

15. http://www.todaysconcretetechnology.com/waterjet-cutting-will-create-new-

opportunities-for-designers.html, Accessed August 2011

http://www.ehow.com/facts_6961115_properties-uses-mild-steel.html


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Appendices

harmonic planetary gear fem

Education