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FINITE ELEMENT METHOD FOR POLYMER COMPOSITES BICYCLE

FRAME DESIGN

MOHAMAD TAUFIK SHAZMIR BIN MD YUSOF

UNIVERSITI TEKNOLOGI MALAYSIA

  

 

 

 

DECLARATION OF THESIS / UNDERGRADUATE PROJECT PAPER AND COPYRIGHT

Author’s full name : MOHAMAD TAUFIK SHAZMIR BIN MD YUSOF

Date of birth : 6TH DECEMBER 1994

Title : FINITE ELEMENT METHOD FOR POLYMER COMPOSITES BICYCLE FRAME DESIGN Academic Session : 2016/2017-2

I declare that this thesis is classified as:

I acknowledged that Universiti Teknologi Malaysia reserves the right as follows:

1. The thesis is the property of Universiti Teknologi Malaysia. 2. The Library of Universiti Teknologi Malaysia has the right to make copies for the

purpose of research only. 3. The Library has the right to make copies of the thesis for academic exchange.

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941206-10-5081 DR. SHUKUR BIN HJ. ABU HASSAN (NEW IC NO. /PASSPORT NO.)  NAME OF SUPERVISOR

Date: 22 JUNE 2017 Date: 22 JUNE 2017

NOTES : * If the thesis is CONFIDENTAL or RESTRICTED, please attach with the letter from the organization with period and reasons for confidentiality or restriction.

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organization where research was done) * OPEN ACCESS I agree that my thesis to be published as online open

access (full text) √ 

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UTM(FKM)-1/02

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

VALIDATION OF E-THESIS PREPARATION Title of the thesis: FINITE ELEMENT METHOD FOR POLYMER COMPOSITES

BICYCLE FRAME DESIGN Degree: BACHELOR OF ENGINEERING (MECHANICAL) Faculty: FACULTY OF MECHANICAL ENGINEERING Year: 2016/2017 I MOHAMAD TAUFIK SHAZMIR BIN MD YUSOF declare and verify that the copy of e-thesis submitted is in accordance to the Electronic Thesis and Dissertation’s Manual, Faculty of Mechanical Engineering, UTM _____________________ ______________________

(Signature of the student) (Signature of supervisor as a witness)

Permanent address: Name of Supervisor: DR. SHUKUR BIN HJ.

BLOK C 112 PANGSAPURI PDRM, ABU HASSAN

TAMAN SRI ANDALAS,

41200 KLANG, SELANGOR. Faculty: MECHANICAL ENGINEERING Note: This form must be submitted to FKM, UTM together with the CD.

  

“I hereby declare that I have read this thesis and in my

opinion this thesis is sufficient in term of the scope and quality for the

award of the degree of Bachelor of Engineering (Mechanical)”

Signature : …………………………………………………...

Name of Supervisor : Dr. Shukur Bin Hj. Abu Hassan

Date : 22 JUNE 2017 

.

FINITE ELEMENT METHOD FOR POLYMER COMPOSITES BICYCLE

FRAME DESIGN

JUNE 2017

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

A thesis submitted in fulfillment of the

requirements for the award of the degree of

Bachelor of Engineering (Mechanical)

MOHAMAD TAUFIK SHAZMIR BIN MD YUSOF

ii

DECLARATION

I declare that this thesis entitled “Finite Element Method for Polymer

Composites Bicycle Frame Design” is the result of my own research except as cited

in the references. The thesis has not been accepted for any degree and is not

concurrently submitted in candidature of any other degree.

Signature

:

………………………………..

Name

:

MOHAMAD TAUFIK SHAZMIR

BIN MD YUSOF

Date

:

22 June 2017

iii

To my lovely father and mother, who always give me endless love, trust,

constant encouragement over the years, and especially for their prayers.

To all my family members and friends, for their patience, support, love,

and for enduring the ups and downs during the completion of this thesis.

This thesis is dedicated to them.

DEDICATION

iv

I wish to express my deepest appreciation to all those who helped me either

directly or indirectly to complete this project. First and foremost I would like to thank

God almighty who provided me with strength, direction and purpose throughout the

project.

Special thanks to my final year project supervisor, Dr. Shukur bin Hj. Abu

Hassan for all his patience, guidance and support during the completion of this project.

Through his expert guidance in mechanical engineering field, I was able to overcome

all the obstacles and tackle all the problems that I encountered in these two semesters

of my project. In fact, he always gave me immense hope every time I consulted with

him over problems relating to my project.

In addition, I would like to thank all my lecturers and friends who helped me

either directly or indirectly upon completing this project.

I would like to give a very special thanks and love to my mother, Mrs.

Norazlina and my father, Mr. Md Yusof for their endless support and dedication.

Last but not least, I would like to thanks everyone for their encouragement and

constructive advice

ACKNOWLEDGEMENT

v

Bicycle is the main transportation which has been used from a long time ago.

There are many bicycle frame designs that have been created by the passage of time

and technological development. Polymer composites is the material of modern

technology that is used in building a bicycle frame and it is relatively new to the bicycle

frame market. Polymer matrix composites offer a lot of benefits such as light in weight,

can configure the properties according to the design and higher strength to weight and

stiffness to weight ratios. However, the fibre direction of pultruded polymer

composites usually in one direction and thus buckling could occur when subjected to

axial compressive load. The buckling test must be conducted as part of design and

quality control process before go through formed into complete bicycle frame. Tube

geometry is determined as referred to the standard bicycle frame. Tubes were tested

using the same diameter but with different lengths to study the buckling load behaviour

respective to each tube configuration. Then, the diameters of each tube were changed

in order to investigate the relationship between the buckling load and different

diameters with the same thickness of the tube. The tube is then subjected to computer-

aided simulations to predict the buckling load. The results of modelling indicate that

buckling load could be improved by changing the thickness of the tube without

changing the original diameter. The buckling loads of the tube significantly decrease

beyond a slenderness ratio of 100. The comparison between two materials was carried

out to examine differences in the buckling load of the tube. In conclusion, the buckling

load of each tube can be examined by analysing it according to the changes of

geometry of the tube.

ABSTRACT

vi

Basikal adalah merupakan pengangkutan utama yang telah digunakan dari

zaman dahulu. Banyak reka bentuk kerangka basikal yang telah dicipta mengikut

peredaran zaman dan perkembangan teknologi. Polimer komposit adalah merupakan

bahan teknologi moden yang digunakan dalam membina rangka basikal dan ia juga

agak baru dalam pasaran rangka basikal. Polimer matriks komposit menawarkan

banyak manfaat seperti ringan, boleh menyelaraskan sifat mengikut reka bentuk dan

kekuatan yang lebih tinggi kepada berat dan kekerasan kepada penurunan berat nisbah.

Walau bagaimanapun, arah gentian polimer Pultruded komposit biasanya dalam satu

arah dan dengan itu lengkokan boleh berlaku apabila beban dikenakan pada arah paksi

mampatan. Ujian lengkokan perlu dijalankan sebagai sebahagian daripada proses reka

bentuk dan pengawalan kualiti sebelum ia dibentuk menjadi rangka basikal yang

lengkap. Geometri setiap tiub ini telah dipilih berdasarkan geometri basikal yang

berada dipasaran. Tiub diuji dengan menggunakan diameter yang sama dan panjang

yang berbeza untuk mengkaji beban lengkokan setiap tiub. Kemudian, diameter setiap

tiub diubah untuk mengkaji hubungan antara beban lengkokan dan diameter yang

berbeza dengan ketebalan tiub yang sama. Tiub kemudian diuji dengan menggunakan

simulasi komputer untuk meramal nilai beban lengkokan. Keputusan simulasi

menunjukkan bahawa beban lengkokan boleh diperbaiki dengan menambah ketebalan

dinding tiub tanpa mengubah diameter asal. Beban lengkokan tiub menurun dengan

ketara melibihi nisbah kelangsingan 100. Perbandingan antara dua bahan telah

dijalankan untuk mengkaji perbezaan dalam lengkokan beban tiub. Secara kesimpulan,

beban lengkokan setiap tiub boleh diperiksa dengan menganalisis ia mengikut

perubahan geometri setiap tiub.

ABSTRAK

vii

TABLE OF CONTENTS

CHAPTER

TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF SYMBOLS xiii

1 INTRODUCTION 1

1.1 Background of Research 1

1.2 Problem Statement 2

1.3 Objective 2

1.4 Scope of Study 2

1.5 Thesis writing framework 3

2 LITERATURE REVIEW 5

2.1 Review of Bicycle History 5

2.2 Mountain Bike Review 8

viii

2.2.1 Bicycle frame geometry 10

2.3 Review of Frame Building Materials 12

2.3.1 Wood 12

2.3.2 Composites 13

2.4 Composites materials 16

2.4.1 Fibre Reinforced Polymer 18

2.5 Manufacturing Process 20

2.5.1 Pultrusion Process 20

2.6 Buckling 23

2.7 Summary 27

3 METHODOLOGY 28

3.1 Overall Research Process 28

3.2 Structural Analysis 29

3.2.1 Tube Separation 30

3.3 Computer-Aided Modelling and Simulation 31

3.3.1 Limits and Assumptions 32

3.3.2 Preliminary Modelling. 33

3.3.3 Modelling and Finite element analysis for Test Simulation

35

3.4 Theoretical calculation 37

3.5 Comparison between Simulation and Theoretical Data 37

3.6 Summary 38

4 RESULTS AND DISCUSSIONS 39

4.1 Analytical Analysis 39

4.2 Buckling Load Test on Constant Tube Diameter. 44

ix

4.2.1 Computer-Aided Simulation 44

4.2.2 Results Discussion 46

4.2.3 Comparison between Simulation and Calculation Critical

Buckling Load 48

4.3 Buckling load for Different Diameter of Tube. 49

4.3.1 Computer-Aided simulation 49

4.3.2 Results Discussion 51

4.4 Buckling test for Different wall thickness. 53

4.4.1 Computer-Aided Simulation. 53

4.4.2 Results and Discussion 55

4.5 Buckling load test for different composites materials 56

4.6 Summary 58

5 CONCLUSION AND RECOMMENDATION 60

5.1 Conclusion 60

5.2 Recommendations for Future Research 62

REFERENCES 63

x

LIST OF TABLES

TABLE NO.

TITLE PAGE

2.1 The mechanical properties of T700/Carbon [9] 15

2.2 Comparison of Properties of E-Glass and S-Glass [15] 19

2.3 The mechanical properties of E-glass fibre Reinforced

Polyester [16] 20

3.1 Type of load exists in each tube during static structural

analysis 31

3.2 New diameter referred from standard bicycle tube

geometry 36

4.1 Length of tube with 42 mm diameter 44

4.2 The data of buckling load for E-glass fibre reinforced

Polyester 47

4.3 A new diameters for tubes having a same thickness about

1.5mm 49

4.4 The buckling load of a Bicycle Frame Tubes with

different diameter 51

4.5 Effects of tube wall thickness 55

xi

LIST OF FIGURES

FIGURE NO.

TITLE PAGE

2.1 (a) Draisienne bicycle, drawn from Drais's plan by

Joachim Lessing; the cloak and side panniers are

reconstructed [1] and (b) Gompertz's hand drive

sketched by Dave Wilson [1] 6

2.2 (a) The first comercial Michaux velocipede and (b) High-

wheeler or the ordinary [2, 3] 7

2.3 Rigid fork mostly used in cross country bikes 9

2.4 Full suspension usually used in Enduro type of mountain

bike 9

2.5 Basic dimensions of traditional frames 10

2.6 The bamboo bicycle frame build for test [7] 13

2.7 Continuous fibres 17

2.8 Random orientation of fibres 17

2.9 The pultrusion system 22

2.10 (a) Fiberglass Pultruded Rod (b) Fiberglass Grating (c)

Pultruded fiberglass Electrical shape (d) Structural

fiberglass pultrusion [10] 23

2.11 The bars displaced when load is applied at the top of one

bars 24

2.12 Pinned-Pinned supported 25

2.13 Columns deflect under various type of supports 26

3.1 Overall research flowchart 29

3.2 Analytical analysis flow chart 29

xii

3.3 Free body diagram for static structural analysis 30

3.4 Label of main tube member in the bicycle frame [17] 31

3.5 Modelling and simulation flow chart 32

3.6 A line body technique was applied in modelling tube 33

3.7 Model for simulation tests (Isometric view) 34

3.8 Model for simulation tests (Side view) 34

3.9 Theoretical calculation flow chart 37

3.10 Comparison between simulation and theoretical data

flowchart 38

4.1 Free body diagram of Mountain Bike Frame 40

4.2 Solving Using method of sections 41

4.3 Analysis on point B 42

4.4 Analysis on point C 42

4.5 Total deformation of buckling tube (GFRP- Isometric). 45

4.6 Y-axis deformation of buckling tube (GFRP- Side View). 45

4.7 Buckling load versus length of E-GFRP tube 47

4.8 Total deformation of buckling tube (GFRP-Isometric

view) 50

4.9 Y-axis deformation of buckling tube (GFRP-Side View) 50

4.10 Graph of Buckling Load versus Bicycle Frame Tubes 52

4.11 Simulation results on E-glass fibre Reinforced Polyester

(a) thickness = 2 mm (b) thickness = 2.5 mm (c)

thickness = 3 mm (d) thickness = 3.5 mm (e) thickness

= 4 mm 54

4.12 Graph of buckling load versus wall thickness for tube

having several of thickness range from 2mm to 4mm 56

4.13 Graph of Buckling Load versus Slenderness Ratio for

different composites system 57

xiii

LIST OF SYMBOLS

E - Young’s Modulus

I - Moment of Inertia

K - Effective length factor

L - Length of column

Pcr - Buckling load

Le - Effective length

r - Radius of gyration

P - Load applied

k - Spring stiffness

∆ - Displacement of pin from original position

F - Restoring force

INTRODUCTION

1.1 Background of Research

This research is carried out to analysed buckling load of a polymer composites

tube just before it assembled becomes a bicycle frame. Bicycle is a transportation that

had been used from a long time ago. Germany was invented the first bicycle in 1817

which was called as “running machine” [1]. Structure of the bicycle is an important

part in producing a bicycle because there are several factors that gives impact on the

bicycle frame such as road-induced load and rider-induced load. Usually bicycles were

made up from steel material. The technology has been rapidly improving and getting

renewed in paralleled with the development of design and calculation techniques in

computer. In order to reduce the weight of the bicycle and increase the toughness of

the bicycle frame, a polymer composite was been introduced as another material to

replace steel. To achieve the best performance on both events track events and road

events, weight and stiffness of the pole plays an important role. However, most of

composites bicycle frames were made through closed mold processes and rarely using

pultruded composites. Through this research the data of buckling behaviour should be

obtained.

2

1.2 Problem Statement

The polymer composites can be very high strength, stiffness and very light in

weight. In advanced of technology nowadays, polymer composites materials were used

in manufacturing bicycle frame due to high performance and durability. However,

buckling is critical in the bicycle frame due to load-induced on the structure member

which some of the members will be subjected to compression load. Hence by using

finite element method, analysis on the structure member can be carried out in order to

study the critical buckling load.

1.3 Objective

The objective of this research is to study the buckling behaviour of Pultruded

Fibre Reinforced Polymer composites tubes using Finite Element Method.

1.4 Scope of Study

The scope of study covers understanding the overall project needs through

literature review. The parametric study on current bicycle frame design is to get the

information about the geometry of the bicycle frame and to calculate the force that

possibly involve on each tube of the frame. There are three types of FRP composites

materials has been established such as Epoxy Carbon UD pre-preg, E-Glass Fibre

reinforced polyester and unidirectional T700/Epoxy composites. The buckling load

has been analysed in the form of a circular tube using ANSYS software. The Euler

buckling theoretical equation has been used to verify the FEA outcomes.

3

1.5 Thesis writing framework

The thesis is consisted of five chapters, in which each chapter will describe the

project detail. The short explanation of each chapter is planned as follows:

a) Chapter One is an introduction of the whole research by identifying

the parameters requirement. The background of project was talked

about overall studies that would be carried out, which included the

objective of the study, significant of the study and scope of the study.

b) Chapter Two is discussed on literature review of related studies. The

topic that would be discussed in the literature review more on theory

and field studies. Applied theories included Euler’s buckling formula

and buckling behaviour when free-ends constrained was applied. For

field studies, it is related to analysis of composites tube under

compression axial loading. Besides that, the linear buckling analysis is

performed using ANSYS software.

c) Chapter Three is dealing with project research method which

describes a project overall process, computer-aided modelling and

simulation and theoretical calculations.

d) Chapter Four describes about the result obtained through simulation.

The basic theory of buckling that had been discussed in chapter 2 was

applied to engineering application follows by analytical and numerical

analyses.

e) Chapter Five is the conclusion and recommendations of the project.

This part would discussed the outcomes of the project parallel to the

4

project objective. In addition, the recommendations of the project were

discussed for further studies.

LITERATURE REVIEW

To achieved research objective, literature review of previous research is made

to gain more information, technique and as a guideline for this research. The contents

reviewed include composite materials, history of bicycle, mountain bike bicycle,

mechanics of composite materials and various tests on mechanical properties of

materials.

2.1 Review of Bicycle History

Bicycles were introduced from early 1800’s made from the wood and typically

whatever was found in the local area. The first bicycle has been invented by Baron

Karl von Drais who is resident of Mannheim that studied mathematics and mechanics.

His bicycle was named Draisienne and some people call it two-wheeled “running

machine” with front-wheel steering from outset as shown in the Figure 2.1(a). He start

to develop this “running machine” when horses were killed because lack of fodder.

However he had no preconception that the steering would enable him to balance but

simply thought that it would be a convenience [1].

6

Bicycle during that time take a lot of people attention until they imitate Von

Drais bicycle. One was the London coachmaker Denis Johnson, who made a seemingly

more elegant conveyance having a mainly iron instead of a wooden frame but it a little

bit heavier. He called it “dandy-horse”. The used of bicycle have spread to clergymen,

tradesman and mailmen. However, it only the rich people can afford it because the cost

was too high. Figure 2.1(b) shows the bicycle that was made by Lewis Gompertz in

1821 which the front wheel was fitted a swinging-arc ratchet drive so that the rider

could pull on the steering handles to assist his feet.

Figure 2.1: (a) Draisienne bicycle, drawn from Drais's plan by Joachim Lessing; the

cloak and side panniers are reconstructed [1] and (b) Gompertz's hand drive sketched

by Dave Wilson [1]

Later on, the second step of the bicycle development continues in 1860s after

development died down substantially by 1821. During this phase, developments of

bicycles start with adding pedals and cranks to the front wheel of a Draisienne. This

type of bicycle as shown in Figure 2.2 (a) was invented by Pierre Michaux who arrived

in Brooklyn in 1865 possibly with a crude bicycle with cranks and pedals. He

7

successfully produced pedals velocipedes in increasing no in 1867-1869. He also

amazed James Carroll, who provided funds for U.S. patent no. 59,915, the first for

such a machine [1].

However, most of the bicycle during that time having a problem with balancing

the bicycles while riding and practically are not safe due to the design itself.

Significantly can see the high wheeler or ordinary bicycle which having two-wheel

and the driving wheel having 60 inches about 1.5m in diameter as illustrated in Figure

2.2(b). In the third step of bicycle development, they more focussing on building the

modern “safety” bicycle which to have the rider sitting between two wheels moderate

size. Many attempts were made for producing a safety bicycles is not only considering

the design also include type of tires, free-wheels, variable gears, tubular frames, sprung

wheels and brakes. In 1885, Rover Safety Bicycle had been produced by John Kemp

Starley and William Sutton, had direct steering and the shape of the frame something

very close to diamond frame used in most bicycles today.

Figure 2.2: (a) The first comercial Michaux velocipede and (b) High-wheeler or the

ordinary [2, 3]

In the United States, the enthusiasm for lightweight road bikes was increasing,

a few enthusiasts in Marin Country, California, began experimenting with old Schwinn

clunkers for downhill off-rad racing [4]. The sales of bicycle in America and Europe

are outstanding; many buyers switched from road bikes to all-terrain or ‘mountain’

8

bikes. Component of bicycle also change from skinny tires to fat, and style of riding

from a crouched position on dropped handlebars to a more erect position on flat

handlebars. In addition, they reached extraordinary levels of sophistication, many

having front and rear suspension, hydraulic disk brakes, wide- range twenty-seven-

speed gears and frame made from titanium, aluminium steel (chromoly) or carbon

fibre.

2.2 Mountain Bike Review

After road bicycle was invented in early 1800s, mountain bikes take place in

the middle of 1970s which had reach extraordinary levels of sophistication. The early

builders of mountain bikes were principally concerned with strengthening diamond

frame and making suitable provision for evolving componentry [5]. Mountain bike or

some people call all-terrain is a bicycle designed for off-road cycling. Mountain biking

is one of an extreme sports, riding through different type of terrain, mountain on trails

and dirt roads. Most of the mountain bikes can do both on road and also off-road but

it speciality more on off-road during climbing hill and downhill.

Mountain bikes share similarities with other bikes, but incorporate features

designed to enhance durability and performance in rough terrain. These typically

include suspension on the frame and fork, large knobby tires, more durable heavy duty

wheels, more powerful brakes, and lower gear ratios needed for steep grades with poor

traction. Typically mountain bikes are ridden on mountain trails, single tracks, logging

road and other unpaved environment. All types of terrain include washouts, rocks, ruts

and roots.

Moreover Mountain bikes have many subtypes include cross country, free-ride

biking, downhill mountain biking, all-day endurance biking, and a variety of track and

slalom competition. Basically, mountain bike are made in the different design

9

according to the style of riding and type of terrain in order to get an optimum

performance. Mountain bike design are not fully depending on the material stiffness

only, it’s geometry of the frame also give an impact on the performance of bicycle [6].

Mountain bikes can be classified based on suspension configuration such as rigid, full

suspension, hard tail and soft tail. Rigid bikes or rigid forks as shown in Figure 2.3

means there is a bicycle without suspension either front or rear. Hard tail bicycle means

bicycle equipped with a suspension fork while soft tail bicycle having neither front nor

rear suspension nor most of road bike are designed for having this type of suspension

than mountain bike. Full suspension means a bicycle having both rear and front

suspension as shown in the Figure 2.4.

Figure 2.3: Rigid fork mostly used in cross country bikes

Figure 2.4: Full suspension usually used in Enduro type of mountain bike

10

2.2.1 Bicycle frame geometry

Mostly bicycle frames were builds in various types of design and geometry. It

is because, the bicycle were built according to the size of users and according to their

specification. The tube size of the frame also has many variables of diameter and wall

thickness. In addition, the bike frame involves many sub structure as shown the Figure

2.5.

Figure 2.5: Basic dimensions of traditional frames

The head tube angle in the picture is the angle at which the head tube is to the

ground. The head tube angle can be adjust according to the style of riding and tracks,

the steeper head angle, there is less effort required to steer it which means the bike has

faster steering. Whereas, the slacker head angle will need more effort to steer it and

the bike has slower steering. For instance for example, Touring bikes are slacker in

head angle compared to their road/CX relatives because they carry weight, and a

slower steering speed helps with the bike’s stability. For comparison of head tube angle

for different bikes as example Touring bikes about 71-72 degrees, Road bikes about

73-74 degrees and Cyclocross or CX about 72-73 degrees.

11

The fork rake as in the figure above is the offset of the fork dropout center from

the straight line of the steering axis (centerline of the fork’s steerer tube). The steering

can be faster when the fork rake is increased, whereas, the steering becomes slower

when the fork rake is decreased. It is clearly shows that the head tube angle and the

fork rake as the measurement of the speed of steering. The Touring bikes have more

rake than road and Cyclocross bikes to increase their wheelbase length, provide more

toe clearance and to increase the forks comfort. The wheelbase length is the distance

from the center of front tire to the center of rear tire. A touring bike’s geometry is

optimised so that it is stable carrying front and rear loads. This is evident through a

slacker head angle and a higher fork ‘trail’ than both road and Cyclocross bikes. Road

bike steering is tuned to be fast with a low trail front end. This makes sense in a racing

situation where you may need to change direction in a split second. A Cyclocross

bike’s geometry almost always falls somewhere in the middle between touring and

road bikes.

One of the more important measurements on a frame bike is the chainstay

length. A longer chainstay length is desirable to increase the wheelbase (making the

bike more stable) and to provide ample heel clearance from the panniers. Heel

clearance is especially important for riders with large feet. Chainstay more accurately

known as the rear centre. This is the horizontal measurement between the centre of the

rear wheel and the centre of the Bottom Bracket (BB). Short back ends are not

necessarily a good thing because they make a bike loop out more easily on climbs and,

contrary to popular belief, do not help it to corner. It is a complicated issue, but together

with the front centre, the chainstay length determines where you are on the bike

(central, further back, further forward). There is no right or wrong here, but greater

length can help a bike to feel more stable descending, and also help keep the front end

down when climbing. As a rough guide, 450mm is the norm on most 29ers, 435mm

on 650b bikes.

Top tube is also the main geometry in the bicycle frame. Top tube can be

divided into two category which is Top Tube length (TT) and Effective Top Tube

length (ETT). The Top Tube length or Effective Top Tube length usually provide on

12

manufacturer’s bike geometry info. Most top tubes are not perfectly horizontal, so

effective top tube length is not the length of the tube, but the horizontal distance

spanned from the head tube to the seat post. What is describes is how stretched out

you will be on the bike. Comfort-oriented bikes feature a shorter top tube combined

with a slacker head angle. Performance-oriented bikes often combine a longer effective

top tube length with a steeper head tube angle.

2.3 Review of Frame Building Materials

Throughout the years frame building materials have evolved from what we

now think as very primitive materials to space age materials which were unknown to

our society only 30 years ago. It is this improvement in materials which allowed to the

greatest extent the evolution in bicycle frame design. This section will review most of

the frame building materials which have been used in the past. It will show the

advantages and disadvantages of the different materials and explain the apparition and

disappearance of some of them. This analysis will help to rationalize the use of

polymer composites material for use in this project.

2.3.1 Wood

Wood was used in the very first bicycle frames produced. Von Drais'

Draisienne and most other hobby horses in the 1800's were made of wood [1]. Since a

minimum stiffness was required in order to prevent enormous bending and potential

collapse, heavy wood was often used resulting in very heavy structures. This combined

with the tremendous work required to shape the wood made designers and builders

quickly realize that this material was not the solution, even though some good wood

frames were successfully built. Around the 1870’s, metal construction became

13

dominant, but wood continued to be used sporadically in the construction of frames,

rims and mudguards even until the 1930’s. A bamboo was used in the construction of

frames. Figure 2.6 shows a bamboo frame from the research paper, the analysis of

Bamboo bicycle frame using Finite Element Analysis [7]. However, because of the

scarcity of this wood in the cities and the increasing use and understanding of steel,

wood and bamboo frames have completely disappeared.

Figure 2.6: The bamboo bicycle frame build for test [7]

2.3.2 Composites

Fibre reinforced polymeric composites are relatively new to the bicycle frame

market. Since many composites offer higher strength-to-weight and stiffness-to-

weight ratios than most metallic materials used in frame construction, it is logical that

designers have turned to these materials in order to fabricate lighter, stronger and

stiffer frames. The anisotropic nature of composites is very beneficial for improving

the weight of frames as reinforcement can be placed along the structural load paths

rather than other regions where low loads exist. The number of possible fibre and

matrix combinations allows the choice of exactly the desired property in a certain

frame region. Different fibres may be chosen such as E-glass, carbon, Kevlar and

boron, and these fibres may be used in combination in the same material. In this case

14

each fibre's specific properties could be used in an optimized way in order to give the

structure desired properties. In the past, fibre materials used for bicycle construction

have included carbon, aramid, boron and glass fibres. These fibres were incorporated

with either epoxy, polyester or vinylester thermosetting resins. As example the

properties of T700/Epoxy is shown in the Table 2.1. T700/Epoxy is trade names of

carbon composite materials developed under TORAY Company. The numbers in the

designation is not indicates the stiffness of the material which is primarily determined

by the way the carbon tubes are arranged and placed in the material.

Epoxy Carbon UD pre-preg is a composites which can be used in all

applications where excellent mechanical and physical properties are required. The

carbon fibre has been pre-impregnated with resin system which includes the proper

curing agent. The surface is slightly oxidized either with a gas treatment or an

electrolytic bath to roughen it and improve its stability to bond to the resin. However,

not all frame builders choose this type of composites to make a bicycle frame due to

pre-pregs are pricey even the cost of the resin fabric and cure is added up. By

comparing both composites it was found that the carbon strength are difference which

Epoxy Carbon UD has greater Young’s Modulus compared to the T700/Epoxy. Due

to the contemporary carbon fibre production, the Young’ Modulus increase as the

strength of carbon fibre increase. But in terms of cost T700/Epoxy would probably be

a better bet. It is requires special tooling to produce thus is significantly more

expensive than T700/Epoxy.

New fibres and matrix materials appear on the market each year with new and

improved properties. The matrix material in all frame constructions in the past has

been thermosetting (heat-cured) resin whereas no documentation on the use of

thermoplastic (heat melting) matrix material could be found in the literature.

Thermoplastic matrices allow easy molding with excellent material properties

especially related to the increase in fracture toughness in the order of 50-100 times

with respect to thermosetting matrices [8]. Thermoplastic composites have found their

way into some new bike handlebars, and may revolutionize the frame building market

in the years to come. Also when the price of ceramic and Vectran fibres and metal

15

matrix composites will have come down to reasonable levels, they could be used

successfully for frame building.

Composite tubes can be manufactured using the filament winding process, by

rolling woven material over a mandrel to make a tube, or by using dry woven braid

with a resin infusion process such as resin transfer moulding (RTM). In addition, tube

also can be manufactured using a pultuded process, by pulled the material through the

dies. The basic pultrusion process is discussed in the manufacturing process section.

Finished tubes are then assembled in the traditional diamond shape structure using lugs

which are made out of steel, aluminium, titanium, or composite materials. However,

this tube and lug approach does not use one of the advantages of composites over

metals which is their formability. The tube and lug design is less than optimum and

has created many problems in the past which have given composite frames a very bad

reputation. However, this research is only focussing on the buckling behaviour of the

tube just before it assembled become one complete structure.

Table 2.1: The mechanical properties of T700/Carbon [9]

Property Value

Young’s Modulus X (GPa) 132

Young’s Modulus Y (GPa) 10.3

Young’s Modulus Z (GPa) 10.3

Poisson’s Ratio XY 0.25

Poisson’s Ratio YZ 0.38

Poisson’s Ratio XZ 0.25

Shear Modulus XY (GPa) 6.5

Shear Modulus YZ (GPa) 3.91

Shear Modulus XZ (GPa) 6.5

Tensile Stress X (MPa) 2100

Tensile Stress Y (MPa) 24

Tensile Stress Z (MPa) 65

Compression Stress X (MPa) 1050

Compression Stress Y (MPa) 132

Compression Stress Z (MPa) 132

Shear Stress XY (MPa) 75

Shear Stress YZ (MPa) 75

Shear Stress XZ (MPa) 75

16

2.4 Composites materials

The combination of two or more material to produce better properties is known

as composite materials [11]. The two constituents are a matrix and reinforcement. The

reinforcing phase material could be in the form of particles, flakes or fibres. Mostly,

the reinforcement is stronger, harder, and stiffer than the matrix. The matrix phase

materials are generally continuous. Examples, of composites system include epoxy

reinforced with graphite fibres and concrete reinforced with steel, etc. A particulate

composites may be platelets, any irregular or regular geometry, or spherical. They are

much weaker and less stiff than continuous fibre composites, but they are much

cheaper. The reinforcement inside particulate reinforced composites usually less which

up to 40 to 50 volume percent due to difficulties in processing and brittleness [11].

A fibre can be divided into two type continuous fibre and discontinuous fibre.

Continuous fibre usually have long aspect ratio which the length-to-diameter (l/d) and

vary greatly while discontinuous fibre have short aspect ratios. This shows that fibre

has a greater length than its diameter. Normally, continuous-fibre composites have a

choice of orientation while discontinuous-fibres composites are not. Examples of

continuous reinforcement are unidirectional, helical winding and woven cloth in

Figure 2.7, while discontinuous reinforcement as shown in Figure 2.8, random mat

and chopped fibres.

17

Figure 2.7: Continuous fibres

Figure 2.8: Random orientation of fibres

Different orientation of continuous fibres could offers desired strength and

stiffness properties with fibre volumes as high as 60 to 70 percent [11]. Strength of

fibre depends on its diameter because of small amount of surface defects compared to

the material produced in bulk. In addition, the cost of fibre increases due to decreasing

in diameter. Typical fibres include aramid, carbon and glass which may be

discontinuous or continuous.

18

Composite materials are not complete without matrix to binding the fibres

together. The matrix such as polymer, ceramic or metal is in continuous phase. The

matrix also protecting the fibres from the environment, distributing the load to fibres

and shield the fibres from damage due to handling. The primary reason composite

materials become highly demand in industry is because the composite can be very

strong and stiff, very light in weight and ratios stiffness-to-weight and strength-to-

weight are several times greater than aluminium or steel. In addition, fatigue properties

are generally better than for common engineering metals and high corrosion resistance.

For example, carbon-fibre reinforced composite can be five times stronger than 1020

grade steel while having only one fifth of the weight [12].

However, composite are not totally excellent in all application, it also have

weaknesses. In term of cost composite materials are very expensive if strength and

stiffness are required. This is because the diameters of the fibre are small and

manufacturing process for shaping composites material consume much time and cost.

Composite can be classified into three categories, Metal Matrix Composites (MMC),

Ceramic Matrix Composites (CMC) and Polymer Matrix Composites (PMC).

2.4.1 Fibre Reinforced Polymer

Fibres reinforced polymer is a composite material made from combination of

polymer matrix with fibres [13]. The polymer is a matrix that used to bind the fibres

together usually uses epoxy, polyester or vinylester. Fibres can be arranged in two-

dimensional or even three-dimensional arrays. The arrangement of the fibre direction

could give different mechanical properties. The strength of the fibre also could be

determine by the transverse and axial orientation and by the number and size of flaws

[14]. Fibre reinforced polymer are composites that widely used in advanced

engineering, with their usage ranging from aircraft, cars, helicopters, sports goods,

buildings and ships.

19

The most common fibre used in engineering materials includes glass, Carbon,

graphite and Kevlar. The fibre used in the making of bicycle frame is E-glass. Glass

offer a better properties include low cost, high strength, good insulating properties and

high chemical resistance. Glass fibre can be divided into two types of glass which are

name as E-glass and S-glass. The letter “E” in E-glass stands for electrical because it

was design for electrical applications while “S” letter stands for higher content of silica

[15]. The used of glass fibre reinforced polymer is still new in bicycle industries. The

comparison of properties of E-glass and S-glass and mechanical properties of

pultruded GFRP and is as shown in Table 2.2 and Table 2.3 respectively.

Fibre composite materials are characterized prominently by anisotropic, which

is related to the designing of performance. The mechanical and physical properties of

fibre composite materials could be determined by the direction of fibre arrangement,

ply stacking sequence and layer number, however, resin and fibre type and relative

volume fraction also play a role in the determination of mechanical and physical

properties. Therefore, in designing engineering structure that having different of load

distributions and application, the corresponding material and ply designing is needed

to meet the established requirements. Taking advantage of this feature, the optimal

design of parts, reliable, to be safe, reasonable and economical could be obtained.

Table 2.2: Comparison of Properties of E-Glass and S-Glass [15]

Property Units E-Glass S-Glass

Specific Gravity - 2.54 2.49

Young’s Modulus GPa 72.4 85.50

Ultimate tensile

strength MPa 3447 4585

20

Table 2.3: The mechanical properties of E-glass fibre Reinforced Polyester [16]

Property Value

Tensile stress (longitudinal) 207 MPa

Tensile stress (transverse) 48 MPa

Tensile modulus (longitudinal) 17 GPa

Tensile modulus (transverse) 6 GPa

Compressive stress (longitudinal) 207 MPa

Compressive stress (transverse) 17 GPa

Compressive modulus (longitudinal) 17 GPa

Compressive modulus (transverse) 7 GPa

Shear modulus 3 GPa

Poisson’s ratio 0.33

Density 1800 kg/m3

2.5 Manufacturing Process

Many methods can be employed to manufacture a composite structure. For

manufactured bicycle frame more than one process exists. Each method has its

advantages and disadvantages. Hence, for a certain application, it is important to know

which method to use. The process that will be used in producing the E-glass fibre

reinforced Polyester is pultruded process.

2.5.1 Pultrusion Process

Pultrusion is a type of continuous automated closed moulding, composite

processing method. The basic mechanism of putrusion system is same as that of the

metal extrusion process. The only difference is that in extrusion process, material is

pushed through the dies whereas in pultrusion, material is pulled through the dies.

Reinforcement in terms of continuous rovings or fibre mats is unrolled from creel

holding rolls and passes through a resin tank. In resin tank, fibres are dipped

thoroughly to get completely wetted fibres. Now, these resin saturated fibres are

21

guided to the hot die where the desired profile is given to these resin impregnated fibres

with the help of dies. Curing of the composite also takes place in this section due to

heating. Now, the cured composite profile is pulled with the help of gripper coming

from the hot dies. Finally, putruded profiles are cut with the help of a cutter which is

inbuilt after the pulling mechanism in the pultrusion system. The schematic of

pultrusion system is shown in Figure 2.9. Sometimes, in the resin tank, some filler

materials are added which also go with the fibre roving. Though, excess resin is

removed in the hot die portion due to pressure, but in some pultrusion systems, a pre

former is used in between the resin tank and hot die. In the pre-former, excess polymer

is squeezed out and uncured composite is generated which is then passed through hot

die section. The pultrusion process is generally used and is suitable for thermoset

polymer composites and a constant cross section profile of the composite product is

produced on a continuous basis. As the cross section of product is uniform, the fibre

distribution and alignment and resin impregnation is good in this process. Though rate

of production is high but a large variation in area of cross section is difficult to achieve.

The expenditure requirement to start pultrusion process is low as compared to other

costly and complex moulding processes.

There is mainly having six important components of pultrusion system which

govern the processing of composites. These components include fibre creels,

preformer, resin impregnation system, hot dies, pulling mechanisms and cut off saws.

All these components are working together to produce one pultruded composites

having a same cross sectional. The components are as illustrated in the Figure 2.9.

The creel should be located in such a way that it should provide uniform and controlled

tension to roving while transferring to the pultrusion system. For continuous and

uninterrupted supply of the roving strand, a second back-up roving package is also

provided besides running package. The shape and size of creel is decided on the basis

of number of roving packages to be handled and its dimension and the distance to be

maintained in between the strands. Preform plates are critical component of pultrusion

system as it properly aligns and feeds the reinforcement to the heated die. If pre-

forming system is not properly functioning, it may lead to bad quality output and

failure of pultrusion system. Resin impregnation system has a resin bath tank. The size

of the tank depends upon the volume of resin to be handled. Resin impregnation system

22

may have a heating arrangement for the resin to enhance fibre wetting but the working

life of bath is decreased due to heating system.

Figure 2.9: The pultrusion system

A wide variety of reinforcement and resin systems are used to fabricate

composite materials with exceptional properties. The reinforcing materials used are:

glass (E-glass and S-glass), carbon, aramid fibres in the form of roving strands, mat

(continuous filament mat, chopped strand mat) and fabrics. Specific properties can be

achieved by altering the design of the fabric reinforcement. Sometimes veils are also

used in pultrusion system to achieve high quality surface layer of the pultruded

component. These veils may have pre-printed designs and logos that appear in the final

product. Generally, unsaturated polyester, epoxy, vinyl ester resin and phenolic resins

are used as matrix materials. The fillers and additives are also incorporated during

composite fabrication as per the design requirement. There are more type and shape of

pultruded products that can be manufactured such as C-shape, H-shape and rod as

shown in the Figure 2.10,

23

Figure 2.10: (a) Fiberglass Pultruded Rod (b) Fiberglass Grating (c) Pultruded

fiberglass Electrical shape (d) Structural fiberglass pultrusion [10]

2.6 Buckling

A structure may fail to support its load when a connection snaps, or it bends

until it is useless, or a member in tension either pulls apart or a crack forms that divides

it, or a member in compression crushes and crumbles, or, finally, if a member in

compression buckles, that is, moves laterally and shortens under a load it can no longer

support. Of all of these modes of failure, buckling is probably the most common and

most catastrophic.

There is a critical load for buckling of a slender column. A column is a simple

common case of a compression member. With any smaller load, the column would

remain straight and support it. With any larger load, the least disturbance would cause

the column to bend sideways with an indefinitely large displacement; that is, it would

buckle. Calculating the critical buckling load is crucial for determining the adequacy

of columns.

METHODOLOGY

This chapter present the methodology of the research of buckling load on tube.

A procedure for research or research methodology is planned and carried out. The

methodology includes an overall plan, methodology of simulation tests and extraction

and analysis of data.

3.1 Overall Research Process

The research is initiated by studying the previous research related to the topic

to gained information adequately addressed that required for this research. Then, the

next step is to obtain the appropriate materials for use as a polymer composites tube.

After that, computer-aided modelling and simulation is carried out based on the

materials selected. Theoretical calculations are then done for every test simulated as

a verification tool. Lastly, the results of both methods are compared and analysis of

result is done. The overall research process is shown in the Figure 3.1.

29

Figure 3.1: Overall research flowchart

3.2 Structural Analysis

Analytical analysis is carried out to calculate the forces involved in the bicycle

structure. The 2D analysis is then done using basic of statics knowledge. The geometry

of the bicycle frame is shown in the Figure 3.2:

Figure 3.2: Analytical analysis flow chart

30

The geometry of the bicycle frame was obtained from a standard bicycle frame.

Then, before start the calculation the length and angle of the bicycle frames must be

drawn. The loads and constraint were imposed on the structure about 3000N static load

on the seat tube and the pin constrained was applied on a rear tire. To perform the static

analysis the free body diagram of the structure must be drawn to observe the direction

of the load as shown in the Figure 3.3. The basic truss theory was implemented during

the analysis. The type of load involved in each tube and the length of tube referred

from the standard bicycle was tabulated in Table 3.1.

Figure 3.3: Free body diagram for static structural analysis

3.2.1 Tube Separation

However, this research is going to analysis on single tubes member of the

structure just before it becomes one structure and the tubes were divided into five

tubes. The analysis on single tube was made to analyse the buckling load capacity of

each tube. Based on the analytical analysis the major type of loads involved were

compression load as tabulated in Table 3.1. To do a buckling analysis due to

31

compression load, assumption should be made by assuming the tube will experienced

compression load only. The tubes member has been given a name as shown in the

Figure 3.4:

Table 3.1: Type of load exists in each tube during static structural analysis

Tube Names Type of force Length (mm)

Top Tube (TT) Compression 590

Down Tube (DT) Tension 660

Seat tube (ST) Compression 432

Chain stay (CS) Tension 420

Seat Stay (ST) Compression 475

Figure 3.4: Label of main tube member in the bicycle frame [17]

3.3 Computer-Aided Modelling and Simulation

The computer-aided modelling and simulation is carried out using

ANSYS workbench 16.0 software, for more specific ANSYS Static Structural

and ANSYS Linear buckling analysis. The flow chart for this process has been

made and it is shown in Figure 3.5:

32

Figure 3.5: Modelling and simulation flow chart

3.3.1 Limits and Assumptions

The modelling is done by follow to a few assumptions. The assumptions made

for this research;

i The tubes are buckle due to compression force.

ii The bond between matrix and fibre is perfect.

iii The matrix and fibre obey Hooke’s Law.

iv The composite is assumed to be isotropic

v The fibres possess uniform strength.

vi The fibres are continuous and parallel.

vii The space between fibres and modulus of elasticity are uniform.

33

3.3.2 Preliminary Modelling.

The purpose of doing preliminary is to test the accuracy of the model by

assigning the structural steel to the tube as a benchmark material. The model was

design using the line body techniques as in Figure 3.6. In addition, the material

properties of E-glass fibre reinforced polyester, T700/epoxy added into the software

material library while the Epoxy Carbon UD was simply used from the ANSYS

library. To obtain the optimum elements used for the model, the convergence test must

be done. The different views for model of the tube in ANSYS software are as in

Figures (3.6-3.8). The fixed parameters of the model for simulation tests are as

follows;

i Dimensions

Length : 590 mm

Diameter : 42 mm

Thickness : 1.5 mm

ii Mesh

Element size : 10 mm

No. of Elements : 119

No. of Nodes : 59

Figure 3.6: A line body technique was applied in modelling tube

34

Figure 3.7: Model for simulation tests (Isometric view)

Figure 3.8: Model for simulation tests (Side view)

35

3.3.3 Modelling and Finite element analysis for Test Simulation

After the preliminary modelling was done and the accuracy was obtained, the

simulation for the model is modified by adding the constraint and loading as required

by the chosen test. The test is start with assigned structural steel as the benchmark

material and analysed to determine the accuracy of the model. The test and their

parameters are as below;

a. Buckling test for same diameter.

This test is run to determine the vertical displacement and load multiplier of the

tube by fixing the diameter and thickness of the tube. The parameters of the model are:

i Fixed-free constraint

ii A point load applied on the free end starting with 1000N until 10000N

iii The vertical displacement is determined

iv The load multiplier is determined

v Using the length as shown in the Table 3.1

b. Buckling test for different diameter.

This test is run to determine the vertical displacement and load multiplier of

the tube by fixing the thickness and diversifying diameter of the tube. The parameters

of the model are:

i Fixed-free constraint

ii A point load applied on the free end starting with 1000N until 10000N

iii The load multiplier to be determined

iv Using the length as shown in the Table 3.1

v The diameter of tube range from 2mm to 4mm

36

The diameter of the tube was changed to see effect on the buckling load. The

new diameter of the tube is referred from the standard bicycle frame as in Table 3.2.

Table 3.2: New diameter referred from standard bicycle tube geometry

Tube Names Diameter (mm) Length (mm)

Top Tube (TT) 33 590

Down Tube (DT) 48 660

Seat tube (ST) 30 432

Chain stay (CS) 28 420

Seat Stay (ST) 24 475

c. Buckling test for different thickness.

This test is run to determine the critical buckling load of the tube respect to

the wall thickness of the tube. The parameters of the model are:

i Fixed-free constraint

ii A point load applied on the free end starting with 1000N until 10000N

iii The load multiplier to be determined

iv Using the length as shown in the Table 3.1

v The range of wall thickness from 2 mm to 4 mm.

d. Buckling test for Different Slenderness Ratio

This test is run to determine the buckling load of the tube when subjected to

the different slenderness ratio. The parameters of the model are:

i Fixed-free constraint

ii A point load applied on the free end starting with 1000N until 10000N

iii The load multiplier to be determined

iv Using the length as shown in the Table 3.1

v A wide variety of the slenderness ratios from 60 to 140

Each test is run using the structural steel as the bench marks and followed by

the E-glass fibre reinforced Polyester, T700/Epoxy and Epoxy Carbon UD. Then,

37

finite element analysis is carried out on the simulation model. The data and information

from the tests are extracted and tabulated accordingly.

3.4 Theoretical calculation

Theoretical calculations for each test are done to verify the accuracy of the

computer-aided model and simulation. The process flowchart of this step is shown in

Figure 3.9;

Figure 3.9: Theoretical calculation flow chart

The formulae and equation required for the theoretical calculations are

obtained through literature study. Then, the constants and required parameters for each

test is applied into the theoretical equation to obtain a theoretical value. This value is

then exported for comparison and verification of the computer-aided model values.

3.5 Comparison between Simulation and Theoretical Data

Comparison of simulation and theoretical data is done to verify the accuracy

of the constructed model. The comparison is done by determining the percentage error

when simulation data is compared to theoretical data. The process flowchart for this

step is displayed in Figure 3.10;

38

Figure 3.10: Comparison between simulation and theoretical data flowchart

The comparison purpose is to calculate the percentage of error between

simulation and theoretical to evaluate the accuracy for both data. The theoretical data

used as a reference.

3.6 Summary

The research will follow this methodology as to obtain results before a

discussion made. Methodology is important to determine the whole research process

was in the correct path. This methodology is also able to make this research more

structured and organized. It also describes the steps of the research and simulation. At

the end, research focused on discussion and report preparation. Raw data that were

generated from numerical and analytical analysis were interpreted. As the last stage of

the research, future directions and recommendations of the research were identified,

so that improvement can be done in the future.

RESULTS AND DISCUSSIONS

In this chapter, the analysis of the tube was discussed. The buckling theory was

implemented as discussed in Chapter 2. The buckling theory was used to determine

the buckling load for each tube and when the tube will start to buckle. The geometry

configuration and materials properties as parameters to study the buckling load on each

tube. The results obtained are discussed further in this chapter.

4.1 Analytical Analysis

As stated on the previous chapter, this study was to find the buckling load on

each tube. However, the analytical analysis for the whole structure must be done to

determine the direction of the force either compression or tension on each tube. The

analytical was made using 2D truss analysis which involve the section and point load

analysis. As in the Figure 4.1, the whole structure has been drawn in form of free body

diagram using the geometry obtain from the Chapter 2. The load was applied on the

seat tube is about 3000 N and pin constraint was applied on the rear tire which refer

from work by Yilmaz Gur, Ilker Eren and Ziya Aksoy [18].

42

tube BD or Top Tube (TT), BC or Seat Tube (ST) and CD or Downtube (DT), the free

body diagram of point load is shown in the Figure (4.3&4.4).

Figure 4.3: Analysis on point B

Figure 4.4: Analysis on point C

The analysis on the point B was to determine the magnitude of FBC and FBD.

Based on this magnitude we would know the type of load induced in each tube either

compression or tension. The calculation is still the same, by solving x-component and

44

4.2 Buckling Load Test on Constant Tube Diameter.

The purpose of conducting this test is to determine the loading that causes the

tube to buckle during real life application. The diameter of the tube is constant at

42mm, while the length of the tube is different according to the length of standard

bicycle frame. The length of the tube as represent in the Table 4.1.

Table 4.1: Length of tube with 42 mm diameter

Tube Names Length (mm)

Top Tube (TT) 590

Down Tube (DT) 660

Seat tube (ST) 432

Chain stay (CS) 420

Seat Stay (ST) 475

4.2.1 Computer-Aided Simulation

The linear buckling analysis was carried out using ANSYS software. The

buckling load of the tube due to compressive loading on its free end is determined. A

load of 1000N is set as the initiation of compressive loading for the tube and continues

until 10000N. The results of the simulations are as displayed in Figure (4.5&4.6).

45

Figure 4.5: Total deformation of buckling tube (GFRP- Isometric).

Figure 4.6: Y-axis deformation of buckling tube (GFRP- Side View).

Based Figures 4.5 and 4.6 it can be observed that the compressive load on the

free end, which is a simulation of the compressive load imposed at top of the tube

46

causes the tube to deflect at the free end when the tube buckles. The deformation of

the pole can also be observed by the colour contour of the tube, with the maximum

deformation observed to be at the tube free end.

By using Linear Buckling analysis, the load multiplier is calculated and

displayed on the interface. By using the load multiplier, the load that causes the pole

to buckle can be determined. For the GFRP or E-glass fibre reinforced Polyester tube,

the buckling load based on simulation is as follows;

Buckling load = Load Applied x Load multiplier

= 1000N x 4.6357

Critical Buckling Load = 4635.7 N

4.2.2 Results Discussion

The data of the all simulation of E-glass fibre reinforced Polyester is determine

and tabulated in Table 4.2. From the data obtained, the graph of buckling load versus

length of tube was plotted as in Figure 4.7 to do an analysis on the buckling respect to

length of tube.

47

Table 4.2: The data of buckling load for E-glass fibre reinforced Polyester

Tube Names Buckling load (N) Length of tube (mm)

Top Tube (TT) 4635.7 590

Down Tube (DT) 3716.6 660

Seat tube (ST) 8527.2 432

Chain stay (CS) 9005.9 420

Seat Stay (ST) 7089.7 475

Figure 4.7: Buckling load versus length of E-GFRP tube

As shown in the graph above, the longest tube has the lowest buckling load

compared to shortest tube. Pattern graph shows that the buckling loads decreasing

linearly respect to length of the tube. This also could be explained by using Euler’s

formula in which the length of the column is inversely proportional to the critical load.

. In the previous research, they have discussed on the stability of FRP pipes under axial

compression which is by testing pultruded GFRP pipes made from E-glass fiber and

vinyl resin with circle section with outer diameter of 41.2mm and thickness of 3.6mm,

they have found that pipes with smaller slenderness ratio can be compressed to fracture

at the ultimate compressive strain caused by lateral deformation after buckling,

whereas, the pipes with larger slenderness ratio buckle in elastic and fail in oversize

deformation [19]. The slenderness ratio of the tube has been calculated for the longest

49

For this test, there is only a meagre 1.83% error between the two critical

buckling loads. Therefore, it is acceptable to state the simulation is verified and valid

to be used.

4.3 Buckling load for Different Diameter of Tube.

The purpose of this test is to compare the previous buckling load of tube having

a same diameter with the tube having different diameter. The comparison was made to

study the effect of buckling load due to changes in diameter of tube. The new diameter

of tube was referred from a standard bicycle frame as shown in the Table 4.3.

Table 4.3: A new diameters for tubes having a same thickness about 1.5mm

Tube Names Length of tube

(mm)

Outer diameter

(mm) Inner Diameter (mm)

Top Tube (TT) 590 33 30

Down Tube (DT) 660 48 45

Seat tube (ST) 432 30 27

Chain stay (CS) 420 28 25

Seat Stay (ST) 475 24 21

4.3.1 Computer-Aided simulation

The linear buckling analysis was carried out using ANSYS software. The

buckling load of the tube due to compressive loading on its free end is determined. A

load of 1000N is set as the initiation of compressive loading for the tube and continues

until 10000N. The diameters of the tubes were changed to a new diameter. The results

of the simulations are as displayed in Figure 4.8&4.9.

50

Figure 4.8: Total deformation of buckling tube (GFRP-Isometric view)

Figure 4.9: Y-axis deformation of buckling tube (GFRP-Side View)

51

Based on the figures above, it is clearly shows that the deformation of the tube

having 33mm diameter is large compare to the tube having 42mm diameter as shown

in the Figure 4.5&4.6. The deformation of the pole can also be observed by the colour

contour of the pole. The test is run same as the previous in ANSYS Linear Buckling

to obtain the load multiplier for each tube. The load multiplier is calculated and

displayed on the interface. The buckling load of the tube could be determined using

the load multiplier. The E-glass Fibre reinforced Polyester tube, the buckling load

based on simulation is as follows;

Buckling load = Load Applied x Load multiplier

= 1000 x 2.1971

Pcr = 2197.1 N

4.3.2 Results Discussion

The simulation is done for all the tube to determine the buckling of the tube

having a new diameter. The buckling load for each tube was tabulated in Table 4.4.

The graph of buckling load vs diameter tube is plotted as in Figure 4.10 to study the

effect of buckling load respect to the diameter of tube.

Table 4.4: The buckling load of a Bicycle Frame Tubes with different diameter

Tube Names Load multiplier for 1kN load

imposed.

Buckling load based

on simulation (N)

Top Tube (TT) 2.1971 2197.1

Down Tube (DT) 5.6002 5600.2

Seat tube (ST) 3.0211 3021.1

Chain stay (CS) 2.5738 2573.8

Seat Stay (ST) 1.2406 1240.6

52

Figure 4.10: Graph of Buckling Load versus Bicycle Frame Tubes

The graph shows that Seat Stay has the least value of buckling load this

indicates that the Seat Stay will buckle first if the load applies on the tube are greater

than their buckling load. The diameter of the Seat Stay is 24mm which is the smallest

compared with the others tubes. According to the theory explained in mechanics of

solid book, the column will buckle about principal axis of the cross section having the

least moment of inertia [20]. The moment of inertia for Seat Stay is 6739mm4 which

is the least moment of inertia compared to others such as Top Tube (18225mm4), Down

Tube (59287.3mm4), Seat Tube (13674mm4) and Chain Stay (10997.1mm4). Through

this analysis moment of inertia gives effect on the buckling load as we could see the

previous analysis which Seat Stay diameter is 42mm, the length is still same about

475mm but the buckling load produced is bigger about 7089.7N compare to the current

diameter which produced only 1240.6N and it is about 83% difference of critical

buckling load. The modification on the Seat Stay tube should be made to improve the

buckling load which will be discussed in the next analysis.

53

4.4 Buckling test for Different wall thickness.

The purpose of conducting this test is to improve the buckling load of seat stay

by modifying the thickness of the tube. Based on the previous test the buckling load

for seat stay was found to be the lowest compare to others tube. The thickness of the

tube will be increase range from 2mm to 4mm with increment of 0.5 mm.

4.4.1 Computer-Aided Simulation.

The analysis is conducted using ANSYS Linear Buckling. The constraint of

the tube is imposed by fixing the bottom of the tube and free at the top. The E-glass

fibre reinforced Polyester was assigned to the tube. A thickness of the tube is set to 2

mm until 4mm and a load of 1000N is set as the compressive load of the tube. The

deformation of the tube having different thickness is shown in the Figure 4.11.

54

Figure 4.11: Simulation results on E-glass fibre Reinforced Polyester (a)

thickness = 2 mm (b) thickness = 2.5 mm (c) thickness = 3 mm (d) thickness = 3.5

mm (e) thickness = 4 mm

Based on the figures above, it can be observed that for each tube with different

thickness will compute different load multiplier. The compressive load on the free end

causes the tube to deflect. However, the tube is still safe due to the load multiplier is

greater than one. The buckling load of each tube is calculated by using the load

multiplier compute from the ANSYS Linear Buckling analysis. The calculation of

buckling load is as follows;

Buckling load = Load Applied X Load multiplier

= 1000 X 1.5528

Pcr = 1522.8N (2mm thickness)

55

4.4.2 Results and Discussion

The analysis was made to prove that thickness of the wall could contribute in

changing the buckling load of the tube. By referring from previous analysis, it observed

that the structure that will buckle first is Seat Stay due to small value of buckling load.

The purpose of this simulation is want to observed the relation between thickness of

the wall with buckling load by maintaining the length of the tube. The buckling was

essentially a linear function with respect to the wall thickness within the simulated

range from 2mm to 4mm. The data is as shown in the Table 4.5 and the graph will be

plotted as shown in the Figure 4.12.

Table 4.5: Effects of tube wall thickness

Thickness of the

wall (mm) Buckling load (N)

Moment of Inertia (mm4)

2.00 1552.8 8432 2.50 1821.7 9889 3.00 2051.6 11133 3.50 2246.5 12186 4.50 2410.1 13069

56

Figure 4.12: Graph of buckling load versus wall thickness for tube having several of

thickness range from 2mm to 4mm

The data has been plotted and it shows that the buckling load is a linear function

with respect to the wall thickness. This can be explained by fundamental stability

theory: the global buckling load of an axially loaded member linearly increases with

its moment of inertia [16].

4.5 Buckling load test for different composites materials

The Top Tube were taken from the previous analysis as a sample to test the

buckling load for a tube having a variety of slenderness ratio and assign with different

materials. The materials properties of the materials were obtain from Chapter 2. The

effect of different materials on the buckling load of the column is depicted in the graph

as shown in the Figure 4.13.

57

Figure 4.13: Graph of Buckling Load versus Slenderness Ratio for different

composites system

The buckling load of the tube as shown in the graph, exponentially reduced

with respect to the slenderness ratio. As depicted above, the rate of buckling load drop

was relatively significant up to a 100 slenderness ratio and beyond. The percentage

difference of the tube with slenderness ratio Le/r = 60 to 80 is about 39% for Epoxy

carbon UD tube. Henceforth, for T700/Epoxy tube shows that the buckling load drop

about 41% from slenderness ratio of 60 to 80. It can be conclude that, the Epoxy

Carbon UD would gave a better buckling load as the modulus is high compared to

other materials.

59

load due to changing in moment of inertia. The moment of inertia also can be increased

by changing the diameter of the tube. In addition, the slenderness ratio of each tube

effects the buckling load. The highest slenderness ratio will produced the lowest value

of buckling load. It is also proved by test the tube by using a different composites

materials system. Moreover, the load multiplier generated from ANSYS software

could indicates when the tube will buckle. The tube is safe when the load multiplier is

greater than one and it was buckled when the load multiplier is less than one. Thus this

geometry configuration could increase and decrease the buckling load of the tube.

62

5.2 Recommendations for Future Research

i Fabrication of prototype for experimental study

It is recommended that an E-glass fibre Reinforced Polyester composite

tube is fabricated and every test that has been simulated be carried out

experimentally. By doing experimental research, the results of the simulations

can be verified in another way other than only by theoretical calculations.

ii Use different constraint

It is recommended that further research be done to study a buckling load

under different constraint. The structure of bicycle frame consist a various type of

constraint such as fixed-ends, Pinned- fixed ends and Pinned-ends. The various

constraints will produce different value of buckling load.

iii Use polymer composites materials with different multiple fibre.

It is recommended that to use polymer materials composites with

different multiple of fibres. The tube will not only buckle under one type of force

such as compressive force. It is also can buckle due to torsion and flexural. The

different orientation of fibres will produce a different value of modulus. Thus, the

materials can be assume as orthotropic.

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