FINITE ELEMENT METHOD FOR POLYMER COMPOSITES …€¦ · NOTES : * If the thesis is CONFIDENTAL or...
Transcript of FINITE ELEMENT METHOD FOR POLYMER COMPOSITES …€¦ · NOTES : * If the thesis is CONFIDENTAL or...
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FINITE ELEMENT METHOD FOR POLYMER COMPOSITES BICYCLE
FRAME DESIGN
MOHAMAD TAUFIK SHAZMIR BIN MD YUSOF
UNIVERSITI TEKNOLOGI MALAYSIA
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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.
Certified by:
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.
UNIVERSITI TEKNOLOGI MALAYSIA
CONFIDENTIAL (Contains confidential information under the Official Secret Act 1972) *
RESTRICTED (Contains restricted information as specified by the
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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PSZ 19:16 (Pind. 1/07)
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.
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“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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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
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project objective. In addition, the recommendations of the project were
discussed for further studies.
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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].
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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
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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’
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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
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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
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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.
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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
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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
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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
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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
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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
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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.
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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.
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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.
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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
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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
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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
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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,
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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.
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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.
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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
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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
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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:
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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.
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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
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Figure 3.7: Model for simulation tests (Isometric view)
Figure 3.8: Model for simulation tests (Side view)
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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
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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,
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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;
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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.
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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].
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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
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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).
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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
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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.
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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
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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.
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Figure 4.8: Total deformation of buckling tube (GFRP-Isometric view)
Figure 4.9: Y-axis deformation of buckling tube (GFRP-Side View)
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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
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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.
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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.
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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)
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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
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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.
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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.
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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.
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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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REFERENCES
1. Sharp, A., Bicycle and Tricycles. The MIT Press, 1977: p. 198-199, 243-247,
303-336.
2. Sharp, A., Bicycles and Tricycles. 1896, London: Longmans.
3. Clayton, N., Early Bicycles. 1998, Princes Risborough.
4. Berto, F. and R. Van Der Plas, The Birth of Dirt: The Origins of Mountain
Biking. 2014: Midpoint Trade Books Incorporated.
5. Tony Hadland, H.-E.L., Bicycle design an Illustrated History, in Bicycle
design an Illustrated History. 2014. p. 433.
6. Australia, M., Bicycles materials, Materials Australia. 2013.
7. Ukoba Kingsley, I., Patrick Ehi1 and D. Adgidzi, Finite Element Analysis of
Bamboo Bicycle Frame. British Journal of Mathematics & Computer Science,
2015.
8. P.K, M., Fibre Reinforced Composites. Second Edition ed. 1993, New York.
9. Bing Wang, J.X., Xiaojun Wang, Li Ma, Guo-Qi Zhang, Lin-Zhi Wu, Ji-Cai
Feng, Energy absorption efficiency of carbon fiber reinforced polymer
laminates under high velocity impact. Materials and Design, 2013. 50: p. 140-
148.
10. Pultrusions, L. Pultrusion Products. [cited 2017 10 April 2017]; Available
from: http://www.libertypultrusions.com/pultrusion-products/.
11. Campbell, F.C., Introduction to composites materials. Structural Composites
Materials, 2010: p. 1-30.
12. UK, C. Introduction to Composites. 2016 [cited 2016 December 20];
Available from: https://compositesuk.co.uk/composite-materials/introduction.
13. Masuelli, M.A., Introduction of Fibre-Reinforced Polymers − Polymers and
Composites: Concepts, Properties and Processes. 2013, InTech.
14. J.Walsh, P., Carbon Fibres. 2001. 21.
15. Kaw, A.K., Mechanics of composite materials. 1997: p. 1-455.
16. Yail J.Kim, K.Z.Q., Effect of geometric discontinuities on failure of pultruded
GFRP columns in axial compression. Composite Structures, 2016. 136: p.
171-181.
![Page 81: FINITE ELEMENT METHOD FOR POLYMER COMPOSITES …€¦ · NOTES : * If the thesis is CONFIDENTAL or RESTRICTED, please attach with the letter from the organization with period and](https://reader033.fdocuments.us/reader033/viewer/2022052101/603b3e50df34bd4fcb479950/html5/thumbnails/81.jpg)
64
17. About, C. Understanding Bicycle Frame Geometry. 2013 4 October 2013
[cited 2016 20 December ]; Available from:
http://www.cyclingabout.com/understanding-bicycle-frame-geometry/.
18. Gür, Y., A new bicycle frame design via stress and structural weight analysis
with finite element method. Technics Technologies Education Management,
2014. 9: p. 25-29.
19. Peng Feng, P.Q.L.Y., Analysis of global buckling of FRP pipes under axial
compression, in Fourth International Conference on FRP composites in Civil
ENgineering (CICE2008) 22-24July. 2008: Zurich, Switzerland.
20. Hibbeler, R.C., Mechanics of Materials. 9 ed. 2013: Pearson Prentice Hall.
879.