BRAIDED CORDS IN FLEXIBLE COMPOSITES FOR …

BRAIDED CORDS IN FLEXIBLE COMPOSITES

FOR AEROSPACE AND AUTOMOTIVE APPLICATIONS

A thesis submitted to The University of Manchester for the degree of

Doctor of Philosophy

In the Faculty of Engineering and Physical Sciences

2013

Sabahat Nawaz

Textile Composites Group

School of Materials

The University of Manchester

Table of Contents

2

Table of Contents

LIST OF FIGURES ........................................................................................................... 6

LIST OF TABLES ........................................................................................................... 11

ABSTRACT .................................................................................................................. 12

DECLARATION............................................................................................................. 13

ACKNOWLEDGMENTS ................................................................................................. 14

COPYRIGHT STATEMENT ............................................................................................. 15

1 INTRODUCTION ................................................................................................... 16

1.1 BACKGROUND............................................................................................................... 16

1.2 PROBLEM DEFINITION ..................................................................................................... 17

1.3 RESEARCH OBJECTIVES ................................................................................................... 18

1.4 THESIS OUTLINE ............................................................................................................ 18

2 MORPHING SKINS AND BRAID TECHNOLOGY ....................................................... 20

2.1 MORPHING AIRCRAFT STRUCTURES ................................................................................... 20

2.2 HYBRID CORDS REINFORCED TIMING BELTS .......................................................................... 30

2.2.1 Glass fibre Cord Production .............................................................................. 32

2.2.2 Carbon Cord Production ................................................................................... 33

2.2.3 Carbon-Glass fibre Cord Production ................................................................. 33

2.3 HYBRID HYPER-ELASTIC CORD MANUFACTURING .................................................................. 33

2.3.1 Types of over-wrapping .................................................................................... 33

2.3.2 X-Wrapping ...................................................................................................... 34

2.3.3 The Saurer Elastotwist...................................................................................... 37

2.4 BRAIDING .................................................................................................................... 38

2.4.1 Maypole dance ................................................................................................. 39

2.4.2 Maypole braiding ............................................................................................. 40

2.5 CLASSIFICATION OF BRAIDS .............................................................................................. 43

2.5.1 2D braid structures ........................................................................................... 44

2.5.2 Braided structures with different interlacement patterns ............................... 45

2.5.3 Hybrid Braids .................................................................................................... 45

2.6 GEOMETRY OF THE BRAIDED STRUCTURE ............................................................................ 45

Table of Contents

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2.7 APPLICATIONS FOR BRAIDED CORDS ................................................................................... 51

2.8 SUMMARY ................................................................................................................... 51

3 DEVELOPMENT OF BRAIDED CORDS .................................................................... 52

3.1 ELASTOMERIC WRAPPED CORDS ........................................................................................ 52

3.1.1 Cord Production and Observations .................................................................. 53

3.1.2 Analysis of the over-wrap machine and method ............................................. 55

3.2 BIAXIAL AND TRIAXIAL ELASTOMERIC BRAID STRUCTURES ...................................................... 56

3.2.1 Biaxially Braided Elastomeric Cord................................................................... 56

3.2.2 Triaxially Braided Elastomeric Cord ................................................................. 58

3.3 BRAIDING MACHINE SET-UP FOR ELASTOMERIC CORDS .......................................................... 59

3.3.1 Controlling the Elastomeric Yarn ...................................................................... 60

3.3.2 Elastane properties .......................................................................................... 61

3.3.3 Precision elastomeric tension control .............................................................. 61

3.3.4 The machine/braid head speed ........................................................................ 63

3.3.5 Take-up machine and speed control ................................................................ 64

3.4 DEVELOPMENT AND MANUFACTURING OF HYPER-ELASTIC CORDS ............................................ 65

3.4.1 Braiding with Kevlar ......................................................................................... 65

3.4.2 Braiding with Glass fibre .................................................................................. 67

3.5 DEVELOPMENT OF THE COMPOSITE MESH SKIN .................................................................... 68

3.6 COATING THE FABRIC SAMPLE .......................................................................................... 69

3.7 DEVELOPMENT OF THE COMPOSITE LAYERED SKIN ................................................................ 69

3.8 LAMINATING THE SAMPLE ............................................................................................... 71

3.9 GEOMETRICAL ANALYSIS ................................................................................................. 72

3.9.1 Cold Mounting and Polishing for Scanning Electron Microscope) ................... 72

3.9.2 Optical Microscopy ........................................................................................... 73

3.10 ELASTOMERIC CORD TESTING ....................................................................................... 73

3.10.1 Tensile Properties ......................................................................................... 73

3.10.2 Apparatus for Tensile Testing ...................................................................... 74

3.11 RIGID CORD DEVELOPMENT ......................................................................................... 76

3.11.1 Preparing the machine components ............................................................ 77

Table of Contents

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3.12 SUMMARY ............................................................................................................... 79

4 RESULTS AND ANALYSIS ...................................................................................... 81

4.1 BRAIDING WITH KEVLAR.................................................................................................. 81

4.1.1 Kevlar + Elastane Braided Hybrid Cords ........................................................... 82

4.1.2 Testing the Cords .............................................................................................. 85

4.2 BRAIDING WITH GLASS FIBRE ............................................................................................ 92

4.2.1 Testing the glass fibre elastomeric cords ......................................................... 98

4.3 GEOMETRICAL ANALYSIS OF HYPER-ELASTIC CORDS .............................................................102

4.4 GEOMETRICAL ANALYSIS OF RIGID CORDS..........................................................................105

4.5 TENSILE TESTING OF THE CARBON-GLASS HYBRID CORDS ......................................................110

4.6 SUMMARY .................................................................................................................111

5 MODELLING OF BRAIDED CORDS ....................................................................... 113

5.1 MODELLING THE LOAD-ELONGATION BEHAVIOUR OF HYPER-ELASTIC BRAIDED CORDS ................113

5.1.1 Modelling the load-elongation behaviour of hyper-elastic yarns ..................114

5.2 GEOMETRICAL MODELLING OF BRAIDED CORDS USING CAD SOFTWARE ..................................118

5.2.1 Plotting of yarn paths .....................................................................................123

5.3 SUMMARY .................................................................................................................128

6 A BRAID TOPOLOGY SYSTEM ............................................................................. 129

6.1 INTRODUCTION TO BRAID TOPOLOGY ...............................................................................129

6.2 BRAID GEOMETRY AND BRAID DESIGN ..............................................................................132

6.3 PREVIOUS STUDIES INTO BRAID TOPOLOGY ........................................................................132

6.4 BRAID PATTERN DIAGRAM .............................................................................................133

6.5 BRAID COLOUR EFFECT DIAGRAM ....................................................................................136

6.6 BRAID TOPOLOGY MATRICES ..........................................................................................140

6.6.1 Example 1: Applying two different colours to a braid matrix ........................140

6.6.2 Example 2: Removal of every other braid bobbin in the anti-clockwise

direction .....................................................................................................................141

6.6.3 Example 3: Using two different braid yarn colours, alternative

arrangement…… .........................................................................................................143

Table of Contents

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6.7 TOPOLOGY PROGRAMMING IN MATLAB .........................................................................145

6.8 THEORETICAL TOPOLOGY SIMULATION VS. ACTUAL SAMPLES .................................................150

6.9 SUMMARY .................................................................................................................151

7 CONCLUSIONS AND RECOMMENDATIONS ......................................................... 155

7.1 SUMMARY OF FINDINGS AND ACHIEVEMENTS ....................................................................155

7.1.1 Development of hyper-elastic braided cords for morphing wing skins ..........155

7.1.2 Elastomeric yarn tension control ...................................................................156

7.1.3 Development of elastomeric cords with varying knee points ........................157

7.1.4 Development of morphing skins.....................................................................157

7.1.5 Behaviour and geometrical modelling of hyper-elastic cords ........................157

7.1.6 Development of rigid braided cords and structure analysis ..........................158

7.1.7 Creating a braid topology system ..................................................................158

7.2 RECOMMENDATIONS FOR FURTHER RESEARCH ...................................................................159

REFERENCES ............................................................................................................. 161

List of Figures

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List of Figures

Figure 2-1: Directions of flexibility for flexible composites ................................................. 20

Figure 2-2: Boeing 40A [2] .................................................................................................... 22

Figure 2-3: A classification for shape morphing of wing[3] ................................................. 22

Figure 2-4: Planform alternation shape morphing; span change, chord length change and

sweep change [3] ................................................................................................................. 23

Figure 2-5: a) Honeycomb core with face-sheets[8]; b) Honeycomb structure with Carbon

Rod reinforcement [9]; c) Objet PolyJet rapid-prototyped honeycomb [9]; d) PAM

actuator [10] ........................................................................................................................ 24

Figure 2-6: Morphing skin sample in-plane testing: (a) skin #1 on MTS; (b) data from

morphing skin in-plane testing [9] ....................................................................................... 24

Figure 2-7: Overview of carbon fibre reinforced honeycomb morphing wing design

concept[9] ............................................................................................................................ 25

Figure 2-8: Deployment of NASA Drydens I2000 inflatable wing [11] ................................. 25

Figure 2-9: Morphing wing configurations for high-lift, climb, cruise, loiter, and maneuver

.............................................................................................................................................. 26

Figure 2-10: a) Airfoil profile change with minimal change in mean camber line b) Airfoil

morphing of AAI Shadow from NACA 23015 to FX60-126 profile [21]. ............................... 27

Figure 2-11: Out-of-plane wing morphing; chord-wise bending, span-wise bending and

wing twisting [3]. .................................................................................................................. 27

Figure 2-12: a) Morphing through local change of the wing shape [25] b) Corrugated skin

for morphing wings [26] ....................................................................................................... 28

Figure 2-13: Lockheed Martin's z-wing morphing concept.[45] .......................................... 29

Figure 2-14: Time lapse photograph of the Lockheed folding wing model under different

configurations [40] ............................................................................................................... 29

Figure 2-15: Diagram of Gate's Racing belt [50] .................................................................. 30

Figure 2-16: The construction of the toothed belt .............................................................. 30

Figure 2-17: The cord layout in the belt............................................................................... 32

Figure 2-18: Diagrammatic representation of the carbon-glass cord ................................. 33

Figure 2-19: Illustration of different over-wrap methods ................................................... 34

List of Figures

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Figure 2-20: S-Wrap; Z-Wrap; Double-wrap ........................................................................ 35

Figure 2-21: X-Wrap machine set-up ................................................................................... 36

Figure 2-22: The Saurer Elastotwist machine and point of cord formation [55] ................. 37

Figure 2-23: Maypole dancing.............................................................................................. 39

Figure 2-24: Maypole braiding machine [4] ......................................................................... 40

Figure 2-25: Arrangement of circular maypole braiding ..................................................... 41

Figure 2-26: Arrangement of a yarn carrier ......................................................................... 42

Figure 2-27: Change in yarn length in relation to position on the track.............................. 43

Figure 2-28: biaxial and triaxial braid construction ............................................................. 44

Figure 2-29: Braided structures ........................................................................................... 45

Figure 2-30: a) braid angle b) a lay ................................................................................. 46

Figure 2-31: unit cell for cover factor calculation [72] ........................................................ 47

Figure 2-32: Effect of braid angle orientation on effective yarn cross-section [68] ............ 48

Figure 2-33: Jammed state in a) tension and b) compression [75] ..................................... 49

Figure 2-34: Braid geometry in an extended state .............................................................. 50

Figure 3-1: Image of the DirecTwist wrap-yarn machine .................................................... 54

Figure 3-2: Z-wrap on core after cord formation ................................................................. 55

Figure 3-3: a) Z-wrap; b) X-wrap; c) Faulty wrapping .......................................................... 55

Figure 3-4: The construction of biaxial braid with core yarns ............................................. 57

Figure 3-5: The braiding machine set up for the biaxial braid cord .................................... 57

Figure 3-6: The construction of a triaxial braid with warp yarns ......................................... 58

Figure 3-7: The braiding machine set up for the triaxial braid cord .................................... 58

Figure 3-8: Typical set-up for a biaxial braid with core yarn ............................................... 59

Figure 3-9: Cord during braiding in tensioned state vs. Cord in the relaxed state .............. 60

Figure 3-10: Load vs. Strain curve for manually testing the elastane yarn ......................... 61

Figure 3-11: BSTR ultrafeeder device ................................................................................... 62

Figure 3-12: Elastane tension control nip roller set-up ....................................................... 63

Figure 3-13: Diagram of the take-up mechanism ................................................................ 65

Figure 3-14: Frame for hand-weaving of fabric ................................................................... 68

Figure 3-16: Kevlar triaxial cord fabric, before and after coating ........................................ 69

Figure 3-15: Fabric coating set-up ....................................................................................... 69

List of Figures

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Figure 3-17. Composite skin construction ........................................................................... 70

Figure 3-18. Binding of the cord layers (a) binder stitch every other cross-over (b) binder

stitch every 6/7 rows/columns. ........................................................................................... 70

Figure 3-19: Heat Transfer Press .......................................................................................... 71

Figure 3-20: Sample preparation for SEM............................................................................ 72

Figure 3-21: The load-strain curve ....................................................................................... 73

Figure 3-22: Picture of the Instron testing machine and the Zwick testing machine .......... 75

Figure 3-23: Picture of the carbon cord stand ..................................................................... 78

Figure 4-1: The change in Elastane length throughout the braiding process ...................... 82

Figure 4-2: The Load vs. Strain curve for the Kevlar yarn samples ...................................... 82

Figure 4-3: Microscope images of the Kevlar biaxial cord in relaxed and extended state .. 83

Figure 4-4: Microscope images of the Kevlar triaxial cord in relaxed and extended state . 84

Figure 4-5: Tensile behaviour comparison of Kevlar biaxial and triaxial cords ................... 85

Figure 4-6: Stress-Strain curve for Kevlar biaxial coated fabric samples ............................. 86

Figure 4-7: Stress-Strain curve for Kevlar triaxial coated fabric samples ............................ 86

Figure 4-8: Load-Strain curve for Kevlar biaxial single cord, before and after fabric

construction ......................................................................................................................... 87

Figure 4-9: Load-Strain curve for Kevlar triaxial single cord, before and after fabric

construction ......................................................................................................................... 88

Figure 4-10: Kevlar triaxial cord coated fabric bias specimen, before and during tensile

testing ................................................................................................................................... 89

Figure 4-11: Kevlar triaxial cord coated fabric specimen, 2.5cm sample before and during

tensile testing; and longer 10cm sample ............................................................................. 90

Figure 4-12: Diagrammatical representation of cord break on the outer edge of the

sample during testing ........................................................................................................... 90

Figure 4-13: Warp yarns wrapped around a bar and clamped to prevent slippage during

testing ................................................................................................................................... 91

Figure 4-14: Stress-Strain curve for 10cm Kevlar triaxial coated fabric sample .................. 91

Figure 4-15: Comparison load-strain curve for a single Kevlar triaxial cord, before and

after fabric construction ...................................................................................................... 92

Figure 4-16: The Load vs. Strain curves for the glass fibre yarn samples ............................ 92

List of Figures

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Figure 4-17: Cross-section SEM image of the glass fibre biaxial cord ................................. 93

Figure 4-18: Cross-section SEM image of the glass fibre triaxial cord and dimensions ...... 94

Figure 4-19: Cross-sectional SEM image of the glass fibre biaxial braid structure .............. 94

Figure 4-20: SEM images showing the glass fibre triaxial braid cord structure .................. 95

Figure 4-21: Microscope images of glass fibre biaxial cord in relaxed and extended state 96

Figure 4-22: Microscope images of glass fibre triaxial cord in relaxed and extended state

.............................................................................................................................................. 97

Figure 4-23: Glass fibre cords coated with silicone ............................................................. 98

Figure 4-25: Stress-Strain curve for glass fibre triaxial coated fabric samples .................... 99

Figure 4-26: Load-strain curve for glass fibre biaxial cord, before and after fabric

construction .......................................................................................................................100

Figure 4-27: Load-strain curve for a glass fibre triaxial cord, before and after fabric

construction .......................................................................................................................100

Figure 4-28: Optical microscope images of hyper-elastic braided cords with different pre-

tensions in their relaxed and extended states ...................................................................104

Figure 4-29: Typical load-strain graphs for hyper-elastic cords with varying elastane pre-

tensions ..............................................................................................................................105

Figure 4-30. The effect of the number of braid bobbins on the braid angle .....................107

Figure 4-31. The effect of the number of braid bobbins on the cord diameter ................108

Figure 4-32: The effect of the number of braid bobbins on the yarn width .....................108

Figure 4-33. Various number of glass fibre bobbins used for over-braid of carbon cord .109

Figure 4-34. Static belt tensile strength .............................................................................110

Figure 4-35: Theoretical vs. actual results of strength of rigid cords ................................111

Figure 5-1: Load-strain relationship of braids with different braid angles ........................114

Figure 5-2: Geometry of filaments in a yarn ......................................................................115

Figure 5-3: Computed load-strain curves for hyper-elastic cords .....................................118

Figure 5-4: The shift angle of the braid yarns moving in the same direction ....................120

Figure 5-5: The braid yarn crimp path/undulation ............................................................121

Figure 5-6: The relationship between the helical braid yarn path and wrapping angle ...121

Figure 5-7: Example of Excel file coordinates for a 50 degree braid path .........................124

Figure 5-8: Braid path splines imported into AutoDesk Inventor from Excel files ............124

List of Figures

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Figure 5-9: A core inserted into the braid structure in AutoDesk Inventor .......................125

Figure 5-10: A complete 50 degrees braided structure created in AutoDesk Inventor ....125

Figure 5-11: Simulated braid geometries in AutoDesk Inventor vs. Actual braided samples

............................................................................................................................................126

Figure 5-12: Simulated 12 braid yarn sample in AutoDesk vs. Actual sample ..................127

Figure 6-1: Six-slot horngear set-up for a hercules braid. .................................................131

Figure 6-2: Developing a braid pattern for a 12 horngear machine (a) numbering braid

bobbins; (b) braid pattern. .................................................................................................134

Figure 6-3: Illustration of the bobbin movement steps .....................................................135

Figure 6-4: Predicting braid pattern by removing braid yarns. .........................................136

Figure 6-5: Colour effect diagram using two colours. ........................................................138

Figure 6-6: Colour effect diagram using 3 colours. ............................................................138

Figure 6-7: Producing sample weave effect without making physical samples (a) bobbin

set-up; (b) braid pattern; (c) braid colour effect diagram. ................................................139

Figure 6-8: A 2/2 regular braid pattern in binary matrix form ..........................................140

Figure 6-9: Creating a braid colour effect using matrices ..................................................142

Figure 6-10: The removal of rows and columns in a braid pattern matrix and resultant

colour effect diagram .........................................................................................................143

Figure 6-11: The coloured braid pattern equivalent of the braid colour matrix ...............144

Figure 6-12: Regular braid pattern simulation in MatLab .................................................148

Figure 6-13: Diamond braid pattern simulation in MatLab ...............................................150

Figure 6-14. The interlacement patterns of various numbers of braid bobbins ...............151

Figure 6-15: Theoretical braid pattern vs. actual braided samples ...................................154

List of Tables

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List of Tables

Table 3-1: Machine setting for different elastane pre-tension ........................................... 66

Table 3-2: Predicted elastane extension vs. extension ........................................................ 67

Table 3-3: Summary of rigid cord samples ........................................................................... 77

Table 3-4: Rigid cords, take-up speed vs. turns per metre .................................................. 79

Table 4-1: Knee angle and knee strain for elastomeric Kevlar cords................................... 85

Table 4-2: Summary of the stress-strain values for Kevlar fabric sample results................ 86

Table 4-3: Summary of Kevlar fabric sample results ........................................................... 87

Table 4-4: Comparison of the change in tensile properties after braiding and fabric sample

production ............................................................................................................................ 88

Table 4-5: Knee angle and knee strain for elastomeric glass fibre cords ............................ 95

Table 4-6: Summary of the stress-strain values for Glass fibre fabric sample results ......... 98

Table 4-7: Summary of glass fibre fabric sample results ...................................................100

Table 4-8: Comparison of the change in tensile properties after braiding and fabric sample

production ..........................................................................................................................101

Table 4-9: Machine settings for different braid angle .......................................................102

Table 4-10: Summary of the braid angle vs. the knee angle and maximum strain ...........105

Table 4-11: Machine settings for rigid braided cord production .......................................106

Table 4-12: Geometrical parameters of rigid braided cords with different number of braid

yarns ...................................................................................................................................106

Table 4-13: Predicted cover factor vs. actual cover factor for different number of braid

yarns ...................................................................................................................................107

Table 4-14: Theoretical calculations of maximum stress of rigid cords............................111

Table 4-15: Actual tensile results of rigid cords .................................................................111

Table 5-1: Relation between initial braid angle and maximum strain ...............................113

Abstract

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Abstract

A morphing aircraft can be defined as an aircraft that changes configuration to maximise

its performance at radically different flight conditions. Morphing structures require a

large aspect ratio and area change during flight in order to optimise operational

performance. Morphing wings are being developed to mimic bird’s wing movements.

Birds have different wing profiles at different points in their flight, where swept wings

reduce the drag at higher speeds at flight lift-off and long straight wing profile is better

for performance at low loitering speed. Hyper-extensible braided cords have been

developed to be used within morphing ‘skin’ materials.

The cords use a low-modulus elastomeric core braided around with high-modulus yarns.

These cords can be produced with various braid angles, which influence the extensibility

of the cords. The higher the braid angle, the greater the extension. The braid angle is

controlled by the precision pre-tension of the elastomeric component. A computational

model for predicting the load-strain behaviour of these hyper-extensible cords has been

developed.

In contrast to hyper-extensible cords are virtually inextensible cord reinforcement

composites, such as toothed timing belts used in car engines, which utilise a combination

of reinforcement techniques to guarantee a high quality high strength product. Braiding is

an alternate technology for producing cords with potentially superior performance in

terms of improved ability to resist unravelling as well as superior interface due to the

‘Chinese finger-trap effect.’ Carbon core with varying glass fibre braid have been

developed. This led to various braid patterns being formed.

A system for mapping braid pattern/topology has been developed. As well as the braid

pattern, the braid colour patterns can also be produced. This mathematical model

involves basic matrix manipulations, which have been proved using the MatLab program.

The predicted braid patterns have been compared with actual samples. Being able to

model braid patterns is time and cost effective compared to previous trial and error

methods.

Declaration

13

Declaration

This thesis is a presentation of my original research work. Wherever contributions of

others are involved, every effort is made to indicate this clearly, with reference to the

literature.

The work was done under the guidance of Dr Prasad Potluri, at The University of

Manchester, United Kingdom.

Acknowledgements

14

Acknowledgments

I would like to show appreciation for my family and friends for their continuous help and

support.

My Sincere thanks to my supervisor Dr Prasad Potluri for his valuable guidance, advice

and encouragement in my work throughout this period.

I would also like to thank Mr Tom Kerr and Ms Alison Harvey from the department of

Textiles and Paper, and Dr Christopher Wilkins from the School of Materials for their

assistance in experimental work. Also many thanks to the Textile Composites Group for

their consistent support.

Copyright Statement

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Copyright statement

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Taught Masters’ Dissertations August 2010 Page 7 of 14and tables

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relevant Thesis restriction declarations deposited in the University Library, The

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us/regulations) and in The University’s Guidance for the Presentation of Theses.

Chapter 1 Introduction

16

Chapter One:

1 Introduction

1.1 Background

Flexible fibre reinforced composites have seen a significant increase in applications over

the past few decades, with major focus on the aerospace and automotive industries.

Flexible composites have an advantage over the conventional rigid composites,

particularly when the application requires the material to exhibit movement in bending,

shear/torsion and in some cases extension directions. Flexible composites such as tyres

and belts are typically reinforced by cords rather than yarns or tows. These cords are

traditionally manufactured by twisting number of yarns together on twisting and doubling

machines. Braiding is an alternate technology for producing cords with potentially

superior performance in terms of improved ability to resist unravelling as well as superior

interface due to the ‘Chinese finger-trap effect.’

Considering the large number of application areas, braiding is a relatively less explored

subject area. Braids can be constructed with a wide range of yarn orientation (angles)

from 15o to 80o and with fibre continuity to produce a continuous sleeve, cord or flat

ribbon. Due to their specific properties, braided structures have many advantages over


17

other conventional composite textile preforms. Braiding technology can be used to

produce large structures such as wind turbine blades; this has been able to be achieved

by the continuous increase in braiding machine size. However, small components such as

braided cords as little as 0.5mm in diameter can be produced depending on the braiding

machine used. Braided cords have several advantages over conventional cord

reinforcement; this has been a main focus in this research.

1.2 Problem definition

This thesis focuses on the development of braided cords for applications involving

inextensible as well as hyper-extensible laminates.

Hyper-extensible laminates: as part of the development of morphing aircraft structures

such as wings there is a distinct need to develop hyper-elastic skins for covering the

skeleton morphing structure as the morphing structure needs to have good aerodynamic

profile. While there have been several research programs on morphing structures, there

has been relatively little progress made on morphing skin materials.

Cords for inextensible timing belts: cords for reinforcing timing belts need to be stiff and

relatively inextensive in order to maintain the timing of the drive train. Carbon fibre is

used for high performance cords for timing belts. However, as the carbon fibres have a

weak interface with rubber, they are often covered with glass fibres that have a superior

interface with the rubber. Currently, carbon fibre yarns are wrapped with fine s-glass

yarn with the help of a twisting machine. However, the pullout performance of these

twisted cords is poor. Where the carbon yarn is over-braided, then during pull-out, the

over-braid would have a tightening effect on the carbon cord, making it more difficult to

pull out as the pull-out force increases.

Braid topology is the pattern of the interlacement of yarns in the braided structures.

Advances in the size of the circular braiding machine, sees a continuous increase in the

number of yarn carriers the machine holds. This makes it even more important to be able


18

to analyse the braid topology prior to braiding the material, hence reducing the trial-and-

error practice. There has previously been little progress towards producing a generic

braid pattern definition and simulation, which can be applied to any braiding machine.

This is especially important when using the same braiding machine to produce a variety of

braid structures. A range of braid diameters could be produced by changing the number

of bobbins on the machine.

1.3 Research Objectives

This research has been carried out to develop high-performance braided cords for

reinforcing flexible composites and to create a generic modelling system for braided cords.

I. Development of hybrid braided cords.

a. Develop hyper-elastic biaxial and triaxial braided cords using elastane and

Kevlar/glass fibre.

b. Modelling of the load-elongation behaviour of the braided cords

c. Development of rigid cords using carbon and glass fibre yarns

II. Braid Topology

a. Analyse the braid topology and create a mathematical model to predict

braid patterns

b. Implement the model using a suitable programming tool

III. Geometrical modelling and analysis of braided cords

1.4 Thesis Outline

An in-depth literature review is carried out in Chapter 2 of the braiding techniques and

explanation of the braid geometries. It is important to have a comprehensive


19

understanding of braiding in order to utilise the braiding technology to its optimum. In

addition this section analyses current research on morphing wing structures and skins.

The development of high performance braided cords is the subject of Chapter 3. Both

rigid and elastomeric cords are developed, starting with the concept of hyper-elastic

cords for morphing wing structures, which use a low-modulus elastomeric core braided

around with high-modulus Kevlar and glass fibres. The braid parameters have been

modified to achieve a range of extensions and strengths. The rigid cords are developed

using a high-modulus carbon fibre core and high-modulus Glass fibre braid yarns, with

particular focus on using a different number of over-braid yarns and their change in

geometrical properties and the effect on the cords behaviour and strength. The

geometrical properties of the developed braided cords has been analysed, and have also

undergone tensile testing. These results are shown and analysed in Chapter 4.

A thorough analysis of the braid yarn path has been discussed in Chapter 5, with

reference to previous work. This chapter aims to standardise yarn path mappings for

circular, constant diameter braids. These structures are produced on CAD AutoDesk

Inventor software, which can easily be imported into FEA software, more specifically

ABAQUS.

Due to the number of bobbins available and the method of interlacement, braiding has a

limitation to the number of braiding patterns, compared to the vast array of available

weave patterns. Chapter 6 analyses the bobbin set-up on the braiding machine. By

reducing the number of bobbins, this changes the interlacement pattern of the braid

yarns so this section of the research concentrates on developing a mathematical model

for braid patterning. This method has been developed based on circular horngear

machines, which have a 1:2 horngear to bobbin ratio, in particular a 12 horngear machine.

The proposed methods are to generate braid patterns and colour effects with the

removal of any bobbins and/or adding a variety of coloured yarns to the braiding machine.

These methods form an analysis system which is used to generate braid patterns and

colour effects prior to producing the actual braided material.

Chapter 2 Literature Review

20

Chapter Two:

2 Morphing Skins and Braid Technology

Flexible textile composites are different from the conventional rigid composites, as they

consist of a textile reinforcement but an elastomeric matrix. This gives the composite

flexibility in bending and extension, and in some cases in the shear direction as displayed

in Figure 2-1. The reinforcement gives strength to the composite and the matrix acts to

protect the reinforcing fibres and gives body to the composite, along with contributing

significantly to the toughness and shear strength.

Figure 2-1: Directions of flexibility for flexible composites

2.1 Morphing aircraft structures

Elastomeric braids have been developed to be used within morphing ‘skin’ materials.

These morphing skins can be used in applications such as aircraft wings; therefore


21

alongside having extension and retraction properties, the cord needs to be high

performance. A morphing aircraft can be defined as an aircraft that changes configuration

to maximise its performance at radically different flight conditions. These configuration

changes can take place in any part of the aircraft, e.g. fuselage, wing, engine, and tail.

Wing morphing is naturally the most important aspect of aircraft morphing as it dictates

the aircraft performance in a given flight condition, and has been of interest to aircraft

designers since the beginning of flight, progressing from the design of control surfaces to

the variable-sweep wing.

Morphing structures require a large aspect ratio and area change during flight in order to

optimise operational performance. The following are key elements of a morphing wing

concept.

Skeleton: a spatial kinematic linkage for achieving desired wing

configurations by folding, telescoping, expanding or contracting

Actuators for configuration change

Skin: To provide an aerodynamic surface free from wrinkles by

accommodate large surface area changes.

Means of rigidising the skin

Using flexible composites for wings is not a new concept and morphing wing structures

have existed throughout the history of flight [1]. The initial airplane’s wings were made

from a woven canvas which was filled with cellulose dope (thick liquid) to make the wings

airtight. This is a flexible composite, where the canvas is the reinforcement material and

the dope is the matrix. An example is the Boeing Model 40A shown in Figure 2-2 (first

model built in the mid-1920s), which had a steel tubing for the nose, curved wood-veneer

laminate for the middle of the fuselage, and wings which were made out of wood and

fabric composite.


22

Figure 2-2: Boeing 40A [2]

Over the past few years, several researchers have presented a comprehensive review of a

classification system of the types of shape morphing wings in UAVs, a summary is shown

in Figure 2-3 [3-5]. The first category is the planform alternation; types of planform

alternation are shown in Figure 2-4. The span change occurs longitudinally along the

aircraft wing, the chord length change is the resizing of the wing along its width and the

sweep angle variation involves pivoting the wing to change their orientation angle [6, 7] .

Figure 2-3: A classification for shape morphing of wing[3]


23

Figure 2-4: Planform alternation shape morphing; span change, chord length change and sweep change [3]

A multilayer honeycomb composite has been proposed by Olympio et al., the honeycomb

structure shown in Figure 2-5a is made from aluminium and elastomeric matrix face

sheets, which could be rubber/silicone [8]. This honeycomb structure allows span change

and has been a key point in several researches. This has been further developed by

Bubert et al. using thin silicone elastomeric sheet reinforced with carbon fibre, which are

then attached to a modified honeycomb structure made from a photocure polymer [9].

These structures are shown in Figure 2-5b&c. In the research they conducted in-plane

testing of this structure; the results are shown in Figure 2-6. This structure is an ideal

candidate for span-wise wing change, where the carbon reinforcement properties are

dominant across the wing and the elastomeric matrix along the wing for span change

(Figure 2-7). This honeycomb skin can be actuated using the pneumatic arm muscle

(PAM) developed by Kothera & Wereley [10]. This concept uses a scissoring motion to

extend and contract the honeycomb structure. This is shown in Figure 2-5d.

Other research in span change wing structures has been based on inflatable structures for

morphing airfoils. These use high performance fibres such as Vectran and Kevlar for

reinforcement, which contain urethane bladders within the structure. A UV-curing resin is

used so the structure becomes rigid when exposed to UV light. The deployment of the

inflatable structure is shown in Figure 2-8 [11].


24

(a) (b)

(c) (d)

Figure 2-5: a) Honeycomb core with face-sheets[8]; b) Honeycomb structure with Carbon Rod

reinforcement [9]; c) Objet PolyJet rapid-prototyped honeycomb [9]; d) PAM actuator [10]

Figure 2-6: Morphing skin sample in-plane testing: (a) skin #1 on MTS; (b) data from morphing skin in-plane

testing [9]


25

Figure 2-7: Overview of carbon fibre reinforced honeycomb morphing wing design concept[9]

--

Figure 2-8: Deployment of NASA Drydens I2000 inflatable wing [11]

Skins for Chord change wings have been investigated using Cornerstone Research Group

Inc’s SMP VeriflexTM, dynamic modulus composites (DMC) VerifaxTM and also using

dynamic modulus foams (DMF) VerilyteTM [12].

Morphing wings are being developed to mimic bird’s wing movements [13]. Birds have

different wing profiles at different points in their flight, where swept wings reduce the

drag at higher speeds at flight lift-off and long straight wing profile is better for


26

performance at low loitering speed. Research conducted by Lentink et al. [14] studies the

morphing wings of swift birds and the effect on their glide performance. A DARPA

sponsored program in NextGen aeronautics has incorporated this wing movement into

their Batwing concept [15-18]. Their first generation model achieved 40% planform area

morphing, 30% wingspan morphing and 20o sweep angle morphing [17]. The different

architectures are shown in Figure 2-9. These wings face large geometrical changes, which

include 200% change in aspect ratio, 40% in span and 70% in wing area. Therefore it is of

the upmost importance to be able to optimise the control the wings morphing, which has

been researched by Johnson et al. [19] and Gandhi et al. [20].

Figure 2-9: Morphing wing configurations for high-lift, climb, cruise, loiter, and maneuver

The second category is the airfoil profile adjustment, an example is depicted in Figure

2-10, where the airfoil profile is varied with minimal change in the mean chamber line.

The example of the AAI Shadow was discussed by Wang & Rosen [21]. As the UAV is in-

flight, the fuel is burnt subsequently reducing the total weight of the aircraft. Initially the

airfoil is bulky to store the fuel; as the fuel is used the airfoil cross-section morphs and

adopts a more slender profile. These profile where referred to as NACA 23015 and FX60-

126 respectively. Another concept along these lines are the inflatable wings studied by

Jacob et al. [22]

The third category is the out-of-plane transformation of the wing. The different types of

out-of-plane transformation are chord-wise bending, wing-twisting and span-wise

bending shown in Figure 2-11.


27

(a) (b)

Figure 2-10: a) Airfoil profile change with minimal change in mean camber line b) Airfoil morphing of AAI

Shadow from NACA 23015 to FX60-126 profile [21].

Figure 2-11: Out-of-plane wing morphing; chord-wise bending, span-wise bending and wing twisting [3].

Chord-wise bending involves a change in the airfoil camber curvature. Such a concept has

been investigated by Diaconu et al. [23, 24] along with looking at the effects of chord

length change. Lannucci et al. [25] studied the chord-wise bending concept but in a

localised position on the wing. This area is shown in Figure 2-12a. Ge et al. [26]

researched corrugated skin as an option for morphing a wing in chord-wise bending,

which is shown in Figure 2-12b. In other material developments for chord-wise bending,

shape memory alloys (SMAs) have been used. These have wires which have unique

thermal and mechanical properties which allow them to bend and deform when heated

and cooled to specified degrees [27-29]. This SMA technology has been an area of

interest for several researchers over the past decade [30-37].


28

(a) (b)

Figure 2-12: a) Morphing through local change of the wing shape [25] b) Corrugated skin for morphing

wings [26]

In wing-twisting the airfoil profile remains the same but undergoes an out-of-plane shape

change. The span-wise bending is also referred to in literature as the lateral bending,

where the most innovative design is the folding wings by Lockheed Martin [38, 39]. This z-

wing morphing concept is shown in Figure 2-13, which is locked into position after folding

to keep the wing shape rigid. Tests show that the wing can morph and hold the desired

shape [40, 41]. The configurations during actual testing are shown in Figure 2-14. The

folding of the wings leads to a significant change in the wing area and shape, therefore

resulting in considerable changes in not just its structural but also aerodynamic features.

Several researches have been carried out on the effect of folding wings upon the aircraft

performance [42]. It is important that the wing structure remains stable in all the

different folded states. Research regarding this was carried out by Zhao & Hu [43, 44] on

folding wings and their ‘flutter frequency’, which is affected by the folding angle.


29

Figure 2-13: Lockheed Martin's z-wing morphing concept.[45]

Figure 2-14: Time lapse photograph of the Lockheed folding wing model under different configurations [40]

With a vast array of possible morphing wing structures, they all need individual skin

materials to compliment their deformability. The areas of research being pursued for

these flexible skins are compliant structures, shape memory polymers (SMP), and

anisotropic elastomeric skins [46]. The current research aims to develop hyper-elastic

cords, which are used to manufacture skins for morphing batwing structures.


30

2.2 Hybrid cords reinforced timing belts

The toothed timing belts used in car engines, utilise a combination of reinforcement

techniques to guarantee a high quality high strength product. An example is belts

manufactured by Gates Rubber ® such as Gates Racing Performance Timing Belts, which

are 300% stronger than stock belts and deliver up to three times the heat resistance over

standard rubber belts under high-load. Gates have several patents of their racing belt

technology but are continuously looking to improve their performance [47-49].

Figure 2-15: Diagram of Gate's Racing belt [50]

Figure 2-15 and Figure 2-16 are graphical representations of Gate’s racing belt, the 3 main

aspects of the belt are:

1) wear Resistant Teeth. High saturation hydrogenated nitrile butadiene rubber (HNBR)

electrometric composites contribute to the exceptional durability and heat resistance

with Aramid reinforcement;

2) robust Reinforced Tooth Jacket; durable nylon fibre provides extra wear resistance,

doubling tooth strength;

3) super Strong Tensile Cord.; added strength comes from premium, high-strength glass

cords.

Figure 2-16: The construction of the toothed belt

RUBBER

CORD

FABRIC


31

By using a carbon cord it reinforces and gives the strength to the belt however it does not

adhere directly with the rubber belt matrix, therefore a glass fibre over-coat is used,

which acts as an interface between the carbon cord and the rubber matrix. Currently a

glass fibre over-wrap is used; this produces a non-stretch flexible cord. However when

carrying out pull-out tests on the belt; the carbon is easily pulled out. What was found is

that the glass fibre stayed adhered to the rubber but the carbon came apart from the

glass fibre.

For improved pull-out properties over-braiding is a potential solution. Tubular braid is

what is used in Chinese finger traps; this concept can be applied on the carbon cord.

Where the carbon cord is over-braided, then during pull-out, the over-braid would have a

tightening effect on the carbon cord, making it more difficult to pull out as the pull-out

force increases. Over-braiding on-top of a core yarn instead of a mandrel is not a new

concept. It has previously been adopted for rope structures[51], however this method has

not been adopted for such yarn-like applications

Carbon has excellent strength along the cord axis; however it has very poor strength to

sideways impacts. So by using a glass over-wrap, this protects the carbon cord core from

any side-impact forces but equates for over 50% of the total cord diameter. If the amount

of glass fibre coverage needed can be reduced, then more carbon can be used in the cord,

subsequently increasing its strength.

In order to give better stability to the carbon filaments within the cord, twists are applied.

The number of twists affects the cord’s properties and consequently alters the properties

of the belt. A carbon cord with a higher number of twists/turns per centimetre (t/cm) will

be more flexible; subsequently the flexibility/movement of the belt increases which

promotes heat production and therefore decreasing the belt strength. It is of the utmost

importance to get the correct balance between all the parameters [52].


32

Example:

0.3 t/cm reduced flexibility reduced heat production increased strength

0.8 t/cm increased flexibility increased heat production reduced strength

Carbon cords are not the only reinforcement cords which are used for toothed belt. Cords

are also made which use only glass fibres.

2.2.1 Glass fibre Cord Production

Glass fibre cords use S2 glass fibre strands where each strand has 200 filaments. The

method of making a cord is as follows:

1) 3 strands are dipped into RFL (Resorcinal-Formaldehyde-Latex).

2) The strands are twisted clockwise (to give an S-twist) at 80 turns per metre

(tpm) to make an ‘end’.

3) 15 ends are twisted in a Z-direction at 80 tpm, this makes a cord (the cord is

1.1 mm in diameter).

4) 2 sets of cords are made, one set have a Z-twist by using the method above,

and the 2nd set have a S-twist (where the ends have a Z-twist and the cord has

an S-twist).

5) The cord is given an adhesive overcoat (which is not the most suitable because

the adhesive which is used is actually for metal-to-rubber bonding).

6) When the cords are placed in the belt, they are laid alternately as illustrated in

Figure 2-17.

When using a braided cord, 2 different types of cord are not needed, because a braid is

neutral, the strands are both in S-direction and Z-direction.

S S S Z Z Z

Figure 2-17: The cord layout in the belt


33

2.2.2 Carbon Cord Production

1) 12K carbon tow is opened and dipped in RFL.

2) The tow is twisted at 60 tpm.

3) Then an adhesive overcoat is given.

2.2.3 Carbon-Glass fibre Cord Production

1) A 6K carbon tow is twisted at 60 tpm and each glass end has a twist of 80tpm.

2) 11 glass ends are wrapped around a carbon core as illustrated in Figure 2-18.

3) 2 different cords are made, one set has the glass end twisted in an S-direction,

and the other set in a Z-direction.

2.3 Hybrid hyper-elastic cord manufacturing

2.3.1 Types of over-wrapping

An over-wrap of yarns on a core yarn/product can be in several different manners, which

are shown in Figure 2-19:

i. Single Covering a single yarn strand is wound in one direction onto a core

ii. Double Covering two strands of yarn are wound onto a core in opposite

directions

iii. Birolex this uses a combining proves where the cover is simultaneously textured

and combined with the core

iv. Air Intermingling the core and multi-filament yarns pass through a pressurised

air jet, this causes the filaments of the covering yarn to separate, and therefore

partially intermingle around the core.

1.1mm

Figure 2-18: Diagrammatic representation of the carbon-glass cord


34

Figure 2-19: Illustration of different over-wrap methods [53]

Bilorex and air intermingling are not suitable options to produce a structurally stable cord,

single covering and double covering are over-wrap options which can be considered to

produce high performance cords.

2.3.2 X-Wrapping

Over-wrapping can be in two directions, clockwise (which is referred to as an S-wrap) and

anticlockwise (which is a Z-wrap). It is possible to over wrap in one direction, and then

pass the cord through the machine again but changing the orientation of the wrapping so

it over-wraps in the other direction to give a double covering shown in Figure 2-20. With

using both wrap yarn orientation it produces a cross over X-wrap [54]. If the X-wrap cord

is extended then the criss-cross orientation of the yarns cause them to tighten around the

core yarn. These types of cords display greater strength than cord with a wrap-yarn in a

single direction.


35

Figure 2-20: S-Wrap; Z-Wrap; Double-wrap

Ideally the set up of the machine should be a two-in-one style where with one pass of the

core yarn through the machine, there is stage one where a S-wrap is applied to the cord

and then stage 2 where a Z-wrap is applied to the cord, this will produce a double-

wrapped cord (also referred to as a X-wrapped cord). This would save 50% of the time

that it would take to insert the S and Z wrap individually. The X-wrap machine set-up as

discussed by Louis et al. [55] is shown in Figure 2-21.


36

Figure 2-21: X-Wrap machine set-up


37

2.3.3 The Saurer Elastotwist

Another method to wrap a yarn around a core is using a hollow spindle. Where the wrap

yarn bobbin is mounted on a hollow spindle and the core yarn is supplied through the

centre of the spindle. The wrap yarn meets the core yarn at the top of the spindle, the

core yarn covering point. At the covering point, the twisting occurs and the core yarn is

covered.

The Saurer Elastotwist is shown in Figure 2-22 [56]. It has a patented hollow spindle and

has a rotating spindle pot with a lid. The wrap yarn is mounted on a flanged supply bobbin

and the yarn doesn’t move in a balloon-like manner, but instead it is driven off the

flanged bobbin by centrifugal forces. Because there is no ballooning motion, it means that

the wrap yarn is under a uniform, low tension; and also means that the core yarn is

straight, so has exceptional retraction capacity in the elastomeric end product.

Figure 2-22: The Saurer Elastotwist machine and point of cord formation [56]


38

The behaviour of elastomeric wrapped yarns have been studied by Dent [57] and Abbott

[58]. Instead of making elastomeric wrap yarns, elastomeric braided yarns/ cords can also

be produced. This allowed s and z orientated fibres to be places simultaneously. Braiding

creates interlacements between the braid yarns so create a more stable and uniform

structure. Not much research has been conducted on elastomeric braided yarns. However

one such research programme was conducted by Rodionov and Manukyan using

polyamide yarns as the braid and lycra as the elastomeric component [59].

2.4 Braiding

Braiding is the formation of comparatively narrow fabrics or rope-like structures by

diagonally interlacing three or more strands of material. In conventional braiders, yarn

carriers rotate along a circular track; with half the carriers in a clock-wise direction while

the remaining carriers in counter clockwise direction, similar to a maypole arrangement

[60]. As a result, the two sets of yarns interlace with each other at a bias angle to the

machine axis. In order to contrast with lace-making, braiding may also be defined as the

production of ribbon-like or rope-like textures by interlacing of one set of threads in such

a manner that no two adjacent threads make complete turns about each other [1].

Braiding has traditionally been used for producing textile structures such as shoelaces and

ropes. However, in recent years, technical application areas such as fibre reinforced

composites and medical implants are becoming popular. By using 3-dimensional

mandrels, one can produce 3D textile preforms for applications such as aircraft rotor

blades. Braided structures are similar to woven structures in terms of the topology of

yarn interlacement. For example, Diamond, Regular and Hercules braids are similar to

Plain, 2/2 Twill and 3/3 Twill weaves respectively. Braids are commonly produced in a

tubular form, only a few centimetres in diameter due to a limited number of yarns used,

whereas woven fabrics are often produced as a broad cloth, several-metres wide.


39

2.4.1 Maypole dance

Braiding resembles a traditional maypole dance in which people dance around a pole

holding ribbons tied to the pole at the centre as shown in Figure 2-23. Dancers are

divided into two groups (typically men in one group and women in the second group)

with half travelling around the pole in clock-wise direction while the other half travelling

in an anti-clockwise direction. Dancers move from the inner circle to outer circle or from

the outer circle to inner circle, after passing each dancer moving in the opposite direction.

As a result, each dancer is constantly moving between inner and outer circles causing the

ribbons to interlace with each other. The resulting ribbon structure is identical to a braid.

A similar concept has been replicated in maypole braiding machines [61].

Figure 2-23: Maypole dancing


40

2.4.2 Maypole braiding

The traditional maypole braider can either be vertical or horizontal and is a relatively

simple mechanism to control. Examples of vertical and horizontal braiding machines are

shown in Figure 2-24. The maypole braiding machine has two sets of yarn carriers rotating

on a circular track, one set rotating in the clockwise direction and the other set rotating in

the counter clockwise direction; during this process, they interlace with each other to

form a tubular braided structure. The braided structure is created either as a continuous

sleeve or gets deposited on a solid mandrel [62]. The resulting braid is continuously

moved forward using a take-up mechanism.

Figure 2-24: Maypole braiding machine [4]


41

Figure 2-25: Arrangement of circular maypole braiding

The maypole braiding machine consists of a track plate with two sinusoidal tracks criss-

crossing each other as shown in Figure 2-25. Each yarn carrier is located in a slot of a

horndog and hence propelled either in clockwise or anti-clockwise direction [63]. The

horndogs are driven by horngears, which are shown in Figure 2-26. Since adjacent

horngears mesh with each other, they rotate in opposite directions and hence driving

adjacent horndogs in opposite directions. Yarn carriers get transferred from one horndog

to the next when the slots are aligned. For example in Figure 2-25, yarn carriers shaded

black continue to travel in the anti-clockwise direction and yarn carriers shaded white

continue to travel in the clockwise direction.


42

Figure 2-26: Arrangement of a yarn carrier

Since the yarn carriers move continuously from an inner circle to an outer circle, the

change in yarn length (difference in length between l1 , l2 or R1, R2 ) must be compensated

, which is shown in Figure 2-27. As shown in Figure 2-26, yarn passes around a roller

mounted on a dancing arm. The dancing arm, tensioned by a spring, can retract the yarn

when the yarn carrier is closer to the centre and release extra length when the yarn

carrier is farther from the centre. Yarn tension can be adjusted by the dancing arm

tension.


43

Figure 2-27: Change in yarn length in relation to position on the track

2.5 Classification of Braids

The braid structures can be classified into two main groups:

two-dimensional (2D) braids;

three-dimensional (3D) braids.

Two-dimensional (2D) braids refer to single layer structures whereas 3D braids refer to

multi-layer inter-connected structures [64-67].


44

2.5.1 2D braid structures

2D braided structures are either biaxial or triaxial in configuration as seen in Figure 2-28.

The biaxial construction is the most commonly used and has two sets of yarns in opposite

directions, where yarns in one direction are passing under and over the other. This is a

popular structure because the construction is predictable, it has consistency in lay-up and

the braid can match any shape. A biaxial braided sleeve can be draped over a mandrel

with varying cross-sections without creating wrinkles.

Figure 2-28: biaxial and triaxial braid construction

The triaxial braid consists of a third set of longitudinal yarns in addition to the biaxial

interlacing yarns and which contribute to the overall braid performance [68]. They are

supplied from a stationary creel and fed through the centre of horngears/horndogs.

These longitudinal yarns are often referred to as axial/warp yarns. These warp yarns are

not necessary for the braid formation, but provide the braid with its essential

characteristics, such as tensile and compression strength in addition to an improved

modulus in applications such as fibre-reinforced composites. However, the use of these

warp yarns can lock the diameter of the braid and prevent its natural tendency to expand

and contract; but if elastomeric yarns are used then this limitation can be overcome.


45

Smart fibres can also be incorporated into the triaxial braid as the warp threads, to give a

smart braid which can be used, for example, as an actuator/sensor.

2.5.2 Braided structures with different interlacement patterns

The braid interlacement patterns are very similar to woven structures. Diamond braids

are similar to plain weave with 1/1 configuration. Regular braids have 2/2 twill weave

repeat whereas Hercules braids have 3/3 twill weave repeat as seen in Figure 2-29 [69,

70].

Figure 2-29: Braided structures

2.5.3 Hybrid Braids

A mix of different yarns can be used which is referred to as a hybrid braid, this consists of

two or more distinctly different types of yarns being used to produce the braid. It is

advantageous for applications where the fabric requires the properties of various

materials and also produces braids with an assortment of aesthetic properties.

2.6 Geometry of the braided structure

The braid output is usually measured in stitches/picks per cm for both flat braid and

tubular braids. The output can also be measured by the lay distance; this is the length the


46

braid has travelled during a complete cycle of any one yarn carrier (one rotation), to

create a complete helix in the braid. The way to measure this is to, at the beginning of the

braid, mark one of the yarns to act as a reference (this fault on the yarn will not matter if

it is at the beginning of the braid, because it can just be discarded). Then run the machine

for a few centimetres, the marked yarn will be visible, and the lay distance can be

measured, this is shown in Figure 2-30. The lay distance can be calculated by using the

braid-head speed, which is the number of rotations of a bobbin around the machine (Vr)

and the take-up speed (Vt) such that L = Vt/Vr. [69, 71]

The braid angle () is the orientation angle of the interlacing yarns with respect to the

braid axis as shown in Figure 2-30. The braid angle depends on the lay (L) and the

circumference of the braid. The braid angle can be calculated using the following formula:

(2-1)

(a) (b)

Figure 2-30: a) braid angle, b) a lay

If the braid is being used to cover a core yarn or a product (e.g. metal wire for electrical

purposes) then the area of the core which the braid covers is referred to as the braid

cover factor. This is determined by the diameter of the core/mandrel (which is being

covered), the braid angle, the number of yarn carriers and the width of the yarn (which

depends both on the linear density and the twist of the yarn). This is another important


47

geometrical parameter especially in applications where 100% cover is required. The cover

factor can be predicted based on a single unit cell as shown in Figure 2-31 [72].

Figure 2-31: Unit cell for cover factor calculation [73]

The braided structure forms a number of parallelograms in the circumferential direction

equal to Nc/2 where Nc is number of yarn carriers. ABCD represents the unit cell for

analyzing the braid geometry. Cover factor may be calculated using the following formula

[5]:

(2-2)

W=yarn width (or diameter if it is a round yarn)

Nc =number of yarn carriers

R= effective mandrel/ braid radius

=braid angle

Biaxial braided fabrics behave like a trellis during tensile or compressive deformation and

offer very little resistance until a state of jamming is reached. The jamming state is


48

important for both elastic and rigid structures. In elastic structures it is desirable that the

jammed state in extension is reached at the desirable maximum elongation so that the

structure is stable. For rigid structures the yarns are required to lie comfortably against

the mandrel or the core, if the yarns are jamming during braiding then it is possible that

there are gaps between the mandrel/core and the over-braided sleeve. It is important to

get the correct jamming state with respect to the required braid geometry.

When a circular yarn is introduced into a braided structure its cross-section is

substantially changed and adopts an elliptical shape [74]. The amount that the cross-

section changes, is dependent on the position within the braid with respect to the

interlacements. Since the yarns are at an angle to the braid axis, effective yarn width is

as shown in Figure 2-32.

Figure 2-32: Effect of braid angle orientation on effective yarn cross-section [69]

Geometrically, a braided structure is considered to be jammed if half the yarns are in

contact with each other as shown in Figure 2-33. This jamming angle along with cover

factor was a key point in research conducted by Zhang et al [75]

()


49

Figure 2-33: Jammed state in a) tension and b) compression [76]

The jammed state in tension can be calculated using Equation 2-4:

(2-4)

In fact, half the yarns form a circle in a tensile jammed state while all the yarns form a

circle in a compression jammed state. In order to consider both the states, a yarn

compaction factor has been introduced into Equation 2-5 [6]

(2-5)

where,

Rj = jammed braid radius

=yarn compaction factor ranging from 1 (in case of compression) to 2 (in case of tension)


50

Figure 2-34: Braid geometry in an extended state

When a braid is stretch the braid angle decreases from 1 to 2 while the unit cell height

increases from l1 to l2, this is shown in Figure 2-34. Initially, the force required to extend

the braid is relatively small in order to overcome frictional resistance at the interlacement

points. Once the braid is jammed, load-extension behaviour is dominated by de-crimping

and yarn transverse compaction. Tensile strain in a braid may be calculated using the

following formula:

(2-6)

The tensile force versus strain relationship of biaxial braids has been studied by several

authors including Phoenix [77] and subsequently Hopper et al. [78] studied mechanics of

biaxial braids with an elastic core. Hopper et al identified four modes of deformation

depending on the relative diameters of the core and the braided sleeve. Subsequently,

Hristov et al. [60] modelled a biaxial sleeve without a core. Potluri et al. [79] modelled

stress-strain behaviour of a braided cored for knee ligament prostheses. These

mechanical models are useful in predicting the braid behaviour in a number of products

including ropes, cords and medical prosthesis.

1

2

1

2


51

2.7 Applications for braided cords

Braided fabrics were traditionally used as shoe laces, candle wicks, parachute cords, sash

cords, fishing lines and dress trimmings. Industrial products such as hydraulic hoses,

electrical cables, wiring harnesses have been developed through the 20th century.

However, since the 1970s, the main focus has been on fibre reinforced composites due to

the phenomenal growth in space technologies.

Recreational composites include sports bike frames, hockey sticks, baseball bats, tennis

racquets and fishing rods. Ropes and cord structures make their use as bungee cords and

archery string. Braided socks have been used in the manufacture of medical prosthetic

devices such as artificial limbs, especially in the socket area due to the highly conformable

nature of braids [11]. Smaller cord structures have been used in the medical profession in

the use of artificial ligaments [79], sutures and dental implants [80].

2.8 Summary

Flexible composite applications in morphing aircraft wing structures have been identified.

For morphing wings the skin material needs to be able to extend to a certain degree

whilst maintaining its structural stability and then contract back to the original shape.

Another flexible composite application that has been identified are timing belts, which

currently use glass fibre over-wrapped carbon cord as their primary reinforcement. It is

identified by the timing belt manufacturers that the carbon cord exhibits poor pull-out

properties due to its inability to adhere to glass or rubber. Although these two

applications are completely diverse they can both be improved using a similar technology,

that being braided cords. The maypole braiding technique has been analysed in detail

including braided structures and braid geometry.

Chapter 3 Development of Braided Cords

52

Chapter Three:

3 Development of Braided Cords

This chapter talks about the development of elastomeric braided cords and rigid braided

cords. As described in the previous chapter, currently over-wrapping is being used to

make rigid cords developed by Gates Inc., so that they can be used as a comparison to the

braided alternative. However because hyper-elastic cords for use in morphing wings is a

new concept, this research initially looks at the development of wrapped hyper-elastic

cords and the limitations of using such a method.

3.1 Elastomeric wrapped cords

To develop the hyper-elastic over-wrapped cord a wrapping machine was used, this was

the DirecTwist machine shown in Figure 3-1. The DirecTwist machine consists of a core

yarn which is threaded vertically into the machine and a wrap-yarn which is threaded

through the eyelet of a rotating plate, then through the same guide eye as the core yarn

(this is the cord formation point). When the machine runs, the rotating plate turns

causing the wrap yarn to have a balloon formation. The wrap yarn circles around the core

yarn, therefore winding around the core yarn. The cord passes a series of tensioning

devices and is wound onto the bobbin; this is what pulls the cord through the machine.


53

The number of wraps per metre can be altered, so the amount of wrap coverage and the

wrapping angle can be altered. The machine settings can be altered to give an S-wrap or a

Z-wrap, but the sample has to be given a wrap in one direction, and then be passed

through the machine a second time, giving the cord wrapping in the other direction. The

number of core yarns, and the number of wrap yarns (fed into the machine) can be varied.

There is also a specifically designed let-off mechanism for elastomeric wrap yarns, but it is

only designed to control the elastane if it is used as a wrap yarn.

3.1.1 Cord Production and Observations

The yarns used to produce the wrapped cord are Kevlar and elastane. Four elastane yarns

were used as the core, and a single Kevlar yarn was used as the wrap-yarn. The elastane

yarn is fed through the machine as a core yarn, there are several yarn guides/contact

points which it passes, this adds to the tension of the yarn, with elastane this is a problem

because it will be hard to control the tension of the yarn and it will be under a great

amount of tension. However the machine was run by using as few yarn guides as possible

and a set of tensioning plates was used to control the tension/extension of the elastane.

Initially a Z-wrap was applied to the wrap cord at the highest workable speed, which is

6000 turns/min. This speed refers to the rotations of the wrapping plate; this determines

the number of wraps of the wrap-yarn. If a faster speed was applied then the entire

DirecTwist machine vibrated loudly.

Figure 3-2 shows the cord passing through the machine after the initial wrap has been

applied; the cord is under tension, and is wound onto the bobbin under this same tension.

At this point there is not a high level of wrap-yarn coverage on the core yarn, however

when the cord is taken off the bobbin, the elastomeric yarn contracts so there is better

coverage as shown in Figure 3-3a.


54

Figure 3-1: Image of the DirecTwist wrap-yarn machine

CORE YARN

WRAP YARN

FEED EYELET

WRAP YARN

CORD


55

Figure 3-2: Z-wrap on core after cord formation

This cord was then passed through the machine again as a core yarn, but this time an S-

wrap was applied to it as shown in Figure 3-3b. However the cord extends again during

this and the core yarn is harder to control using tensioning plates as previously used with

the elastane yarn. Due to the addition of a yarn on the outside of the core, and the pull-

through of the machine, the core slips through, causing a coagulation of core and wrap

yarn at the cord formation point, therefore inserting faults into the cord, which is shown

in Figure 3-3c.

Figure 3-3: a) Z-wrap; b) X-wrap; c) Faulty wrapping

3.1.2 Analysis of the over-wrap machine and method

The main problem is the control of the core yarn, due to the position and set up of

the machine it is difficult to make the required changes to the machine; adding

tensioning devices to control the core yarn.


56

The cord take-up is in the extended state and not in the relaxed state. Due to

machine set-up limitations, no alterations can be made to the take-up mechanism.

The rotating plate which the wrap-yarn passed through revolves at high speed and

the yarn is in constant contact with the eyelet, this promotes fibre fibrillation.

As the wraps are inserted around the core yarn, due to the rotation of the plate, a

twist is also applied to the wrap yarn. This will decreases the strength of the cord

because Kevlar performs at its optimum when the fibres in the yarn tow are

straight.

3.2 Biaxial and Triaxial Elastomeric Braid Structures

The braiding machine is a Cobra 450, which has 24 yarn carriers as shown in Figure 3-5. At

the fastest speed it runs at 27 revolutions per minute (one revolution is a complete

rotation of a single yarn carrier).

3.2.1 Biaxially Braided Elastomeric Cord

The biaxial elastomeric braid consists of:

4 braid yarns

4 elastane core yarns

Only 4 braid yarns were used in the initial developments because the aim was to make a

yarn-like braid so they were required to be of minimal diameter. 4 braid yarns is the

lowest number of yarns to braid needed to make a uniform structure. However, two

other samples have also been made with the Kevlar yarns, which used 8 braid bobbins

and 12 braid bobbins respectively.

To create the biaxial braid the elastane yarns are passed horizontally through the centre of

the braiding machine and the braid yarns intertwine around them, creating an overwrap

of the braid yarns over the elastane, placing the elastane in the centre of the cord. Figure

3-5 shows the braiding machine set-up for a biaxial cord and Figure 3-4 shows a

representation of the biaxial braid structure, where there are 4 core yarns, and an over-

braid.


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Figure 3-4: The construction of biaxial braid with core yarns

Figure 3-5: The braiding machine set up for the biaxial braid cord

CORE YARNS

OVER BRAID

BRAIDED

CORD


58

3.2.2 Triaxially Braided Elastomeric Cord

The triaxial elastomeric braid consists of:

4 braid yarns

4 elastane warp yarns

The elastane yarns are passed through the centre of the horngears (which the braid yarn

carriers oscillate around); the braid yarns intertwine in between and around the elastane

warp yarns and are incorporated inside the braid.

Figure 3-6: The construction of a triaxial braid with warp yarns

Figure 3-7: The braiding machine set up for the triaxial braid cord


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Figure 3-6 shows a representation of the interlacements between the warp and braid

yarns in a triaxial braid and Figure 3-7 shows the machine set-up to produce the triaxial

braid. Due to the structural restrictions in the interlacements, there will always be a slight

gap between the braid yarns when they cross over, revealing some warp yarn. So there

will not be 100% coverage of the elastomeric yarns.

3.3 Braiding machine set-up for elastomeric cords

The elastomeric yarn passes through a tensioning device to stretch the yarn before

passing through the braiding machine. Tension is also applied to the braid yarns to keep

their let-off as smooth as possible. The yarns are pulled through the braiding machine by

the take-up device. The elastomeric yarn and the braid yarn meet at the braid formation

point (the point where the cord is formed), the cord is kept under tension until it passes

through the take-up device; here the cord relaxes to give the completed cord structure.

This set-up is illustrated in Figure 3-8.

The braiding machine which has been used can carry a total of 24 yarn carriers (for the

braid yarn). The minimum number of yarns to make a braid is four, this would be ideal to

produce a thin light weight cord, so only four braid yarns have been used.

Figure 3-8: Typical set-up for a biaxial braid with core yarn

When braiding with an elastomeric core, in order to optimise the extension percentage

with the most efficient production timing and product quality, it is essential to obtain the


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right balance between the elastomeric yarn delivery tension, the machine/yarn carrier

speed and the take up speed.

3.3.1 Controlling the Elastomeric Yarn

Elastomeric yarns, can reach great lengths of extension. The one which has been used in

this research has around 825% maximum extension. When braiding, the braid yarns are

kept under a tension, so during braiding there is a pulling action on the elastomeric yarn.

For a smooth braid, the elastomeric yarn also needs to be kept under tension during the

braiding process. The tension needs to be controlled in such a way so that there is an

even pull-through of the yarn. So a tensioning device is used to tension/stretch the

elastomeric yarn prior to the braiding.

Pre-tensioning the elastomeric yarn influences the braid angle of the cord in the relaxed

state because after the cord passes through the take-up rollers, the elastomeric yarn

relaxes and the braid structure contracts. Therefore the cord in the relaxed state has a

higher braid angle to the cord in the tensioned state and is illustrated in Figure 3-9.

Figure 3-9: Cord during braiding in tensioned state vs. Cord in the relaxed state

Ideally, the yarn should be extended/ drawn to what the maximum extension of the cord

is required. This will give the cord the correct amount of extension, which is needed in its

final use; without any unnecessary tension in the cord. If the elastomeric yarn is extended

100% and then goes through braiding, when the cord retracts, it will go back to the

original length.


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3.3.2 Elastane properties

The key element for the elastomeric behaviour of the cords is to use an elastomeric yarn;

in this research a 124tex elastane has been used, which has a diameter of 0.5mm. The

strain which this project looks at is between 0-300% and in the required application of the

cord the elastane will not be tested to failure. In order to get an idea of the initial

behaviour of the elastane, the elastane was tested manually using a set of weights. Two

marks were drawn on an elastane sample 5cm apart; specified weights were hung from

the sample and the new distance between the two marks was measured. The strain

percentages were calculated.

Figure 3-10: Load vs. Strain curve for manually testing the elastane yarn

The results have been plotted in Figure 3-10 which shows a significantly different

behaviour to when tested with tensile testing apparatus. For example, if 150% strain is

considered, this is achieved using 0.5N load with the manual method, whereas the results

from the machine tests show that 150% strain is achieved at an approximate load of 2N.

3.3.3 Precision elastomeric tension control

The elastomeric yarn tension can be controlled by several methods.

a) Initially the elastane tension was controlled by using a set of tensioning discs. This set-

up was used for the original samples. It was observed that when the discs were tightened


62

to increase tension on the elastane yarn, the yarn feed stopped but then due to a build up

of tension there was a sudden feed of elastane yarn. This created an inconsistency of yarn

feed, therefore this set-up is not suitable for variable tension controls.

b) Tension control device are another option. These devices have a yarn storage unit

which keeps a specific amount of yarn stored on the dial, as the yarn is pulled through,

the tension changes, causing the dial to rotate and keep a constant amount of yarn on the

dial and a consistent tension on the yarn. They have electronic controls so the yarn

tension can easily be controlled by changing its settings. Examples of tension control

devices are the LGL Electronics’ spin feed device and Best Technologies Study and

Research (BSTR) ultrafeeder device shown in Figure 3-11.

These devices keep the yarn at a constant tension if the machine speed changes or/and

when the yarn packages gradually get empty. There are several features of the devices,

all for the benefit of controlling the yarn tension, such as a high grip wheel and high

precision tension measuring sensor. To get at least 100% extension in the elastomeric

yarn it requires a load of 0.4 Newton, which is equivalent to 40 grams. The ideal tension

control device would be the BSTR ultrafeeder, this gives up to 100 grams of tension, so

provides a wide range of tensions.

Figure 3-11: BSTR ultrafeeder device


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c) The third option is using a set of feed rollers. This method is one that has been

previously used for in making elastomeric wrap yarns. The feed rollers will run at a

different speed from the braid take-up rollers, therefore creating a constant extension of

the elastane yarn. The effects of the draw ratio on an elastic core yarn have previously

been investigated by Kakvan et al. [81] but this was on core-spun yarns, however it does

show the effects of elastane pre-tensioning/drawing. The current set-up was developed

and consists of a set of nip rollers which is controlled by a gear; the speed of the gear is

controlled by a voltage control system. The set up is shown in Figure 3-12.

Figure 3-12: Elastane tension control nip roller set-up

3.3.4 The machine/braid head speed

The machine speed is the number of rotations a yarn carrier makes, this can be varied.

The maximum rotation speed of one yarn carrier in the machine is 27 rpm. In order to

obtain the maximum amount of production it is ideal that the machine is run at a high


64

speed. However, when using glass fibre it was found that because glass fibre is so brittle

that when the machine speed is too high then the friction between the fibres/filaments

may cause them to cut each other, leading to yarn failure. In addition, if there is too much

fibrillation of the fibres (commonly seen in Kevlar) then this may lead to reduced strength

in the end product and also to it being visually unacceptable.

The optimum speed for glass fibre was 17 rpm, if it is any higher than this, then because

of the steep angle of braid formation, the glass fibres start to cut each other, leading to

yarn failure. Kevlar however does not have this problem, so the machine was set to the

highest speed of 27rpm. With Kevlar, there is a problem of fibrillation. This can be

overcome by changing the tension in the yarn carrier tension control device.

As mentioned in the previous chapter the machine speed/braid head speed and the take-

up speed can be used to predict the braid angle. However, this can only predict the braid

angle during braiding. After the braid has passed the take-up device, the braid contracts

due to the pre-tensioning of the elastane yarn. Therefore the braid angle of the cord is

not a straightforward prediction.

3.3.5 Take-up machine and speed control

The take-up mechanism, which was used is shown in Figure 3-13. The take-up speed

determines two things, the braid angle and the production amount. If the machine speed

is kept constant and the take-up speed is increased, then this will increase the braid angle

during braiding. However, this angle is not the actual angle on the final cord; because the

core yarn is under tension; at the end when the braid is relaxed, the structure will

contract to give the actual braid angle. In addition, the faster the speed of the take-up

rollers, the higher the amount of final cord that is produced; provided that the core yarn

is kept under the same amount of tension throughout braiding, so that the end product

will relax/contract the same amount.


65

Figure 3-13: Diagram of the take-up mechanism

Initially the ideal braid parameters were derived from trial and error in order to get full

cover of the braid whilst keeping the elastomeric tension constant and changing the take-

up speed and the braid head speed. The amount of cover can be predicted using the

cover factor equation stated in Chapter 2, however it is tricky to use this equation for

elastomeric braided cords, therefore the trial and error method was adopted.

3.4 Development and manufacturing of hyper-elastic cords

Kevlar and glass fibre yarns were used to produce the braided cords, in addition to

elastane which provided the elastic properties. Kevlar was the ideal candidate for such

application as it is a high-performance fibre, which is popular in morphing wing

applications alongside Vectran, which unfortunately was not available to use for this

research. Glass fibre was another option, again because it is a high-performance fibre and

was available during this research.

3.4.1 Braiding with Kevlar

The Kevlar used was a fine tow, so resembles a yarn; therefore it will be referred to as a

yarn. It is a 22tex yarn. Kevlar is prone to fibrillation, and with the incorrect machine

settings it may cause yarn failure. After trial and error, the ideal machine settings were

established, with only minor fibrillation. In addition the yarn tension control on the yarn


66

carriers plays a very important role controlling the amount of fibrillation of the Kevlar

yarns during braiding. As mentioned in the previous chapter in Figure 2-7, the length of

the braid yarn changes as the bobbin moves from the inner and outer positions of the

braid track. As this length change is accommodated by the tension control device in the

bobbin carrier [82], this causes a forwards and backwards movement of the yarn and

friction between the yarn and the pulleys, aiding fibrillation. A high tension is preferred,

so a tension of 150 grams force (gf) was used.

The initial braid settings used for the biaxial and triaxial braids were the following:

Machine speed: full speed, 27revolutions/minute

Take-up speed: 6metres/hour

Actual cord production: Biaxial – 2m/hr

Triaxial – 1m/hr

As previously discussed, the amount of cord extension is dependent upon the braid angle

and the jamming position of the braid when extended. If there is a higher braid angle

there is a greater degree for extension. One method of creating such braids is by varying

the pre-tension of the elastane yarns. After the nip roller elastane feed device was

developed, it was used in the braid set-up to produce braids with varying elastane pre-

tension. Four different pre-tension settings were used. The braid head speed was kept

constant at 27rpm and the take-up speed was kept constant too at 75mm/min. The

machine settings used are shown in Table 3-1:

Number of braid

yarns

Pretension

Number

Pretension

Speed

Braid head

speed

Take-up

Speed

4 #2 22mm/min 27rpm 75mm/min




Table 3-1: Machine setting for different elastane pre-tension


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During braiding, the actual extension of the elastane before braid formation was

measured, and then the amount of contraction of the braid after passing through the

take-up rollers was also measured. This was carried out by marking on the elastane/cord

and measuring the length using a ruler. These actual results were compared to the

predicted results using the machine parameters as shown in Table 3-2.

Elastane

pretension

Let-off speed

(mm/min)

Take-up speed

(mm/min)

Predicted

extension (%)

Actual Extension

(%)

#2 22 75 240 232

#3 32 75 134 110

#4 41 75 83 60

#5 72 75 4.1 15

Table 3-2: Predicted elastane extension vs. extension

3.4.2 Braiding with Glass fibre

The glass fibre specifications are EC722/1/3 150S

Because glass fibre is so brittle and sharp, if the braiding machine is run at high speeds,

then the yarns just act as a slicer and cut into the other yarns at the braid formation point.

So the glass fibre cannot be processed at high speeds, after trial and error with the

machine speed, elastomeric yarn tension and the take-up speed, the ideal machine

settings which cause the least amount of damage to the yarns whilst producing the most

efficient quantity of braid are:

Machine speed: 17 revolutions/minute

Take-up speed: 4 metres/hour

Actual cord production: Biaxial – 2m/hr

Triaxial – 1m/hr

The actual cord production is the length of cord in the relaxed state. There is a large

difference in the actual amount of cord produced for the triaxial cord and the biaxial cord,

this could be because the yarns in the triaxial cord take a different path to the biaxial

cords and have a greater degree of freedom to retract.


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3.5 Development of the composite mesh skin

The braided cords were woven to make a fabric sample. However due to the diameter

and stretch of the cords it was difficult to produce a closely woven sample whilst

maintaining a consistent tension of the cords. Therefore, a mesh fabric was produced.

The fabric sample has a 1/1 plain weave, and is hand woven using a frame shown in

Figure 3-14 with removable bars to aid the removal of the samples from the frame. The

vertical warp yarns are wrapped around the bars at intervals to give 2.5 ends/cm of fabric.

The horizontal weft yarns are woven in and out of the warp yarns and around the wire

rods to keep the structure of the fabric; the wefts are also inserted to give 2.5 picks/cm.

This gives even mesh fabric samples.

As the samples are a mesh structure, they need to be reinforced with a matrix material,

so that it maintains its shape during fabric handling and sampling. The fabric needs to be

stretchy so the matrix also needs be elastomeric to such a degree that it will allow the

fabric to be extended to the failure point (for the sake of testing, the actual application

will not be extended the fabric to failure). A silicone based matrix is ideal; it can be

stretched and will contract back to the original length.

Figure 3-14: Frame for hand-weaving of fabric

Rod to wrap weft cords around

Frame

Bar to wrap weft cords around


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3.6 Coating the Fabric Sample

The silicone matrix that is used is a multipurpose silicone which is wet to start with to

allow it to be applied easily and is self-curing. Initially a thin layer of silicone in spread on

a non-stick sheet, then the fabric mesh sample (still inside the frame) is placed on it.

Another layer of silicone is applied on top of the fabric, ensuring that the air gaps

between the cords are filled. An additional non-stick sheet is placed to cover the sample.

The assembly is placed in a press which has metal plates both on the bottom and top

shown in Figure 3-15. The sample is kept under constant pressure between these two

plates until the silicone is fully cured. The sample is removed, and is easier to handle than

the fabric without the matrix.

Figure 3-16 shows the Kevlar triaxial cord sample before and after coating.

Figure 3-16: Kevlar triaxial cord fabric, before and after coating

3.7 Development of the composite layered skin

During the weaving of the mesh, it was difficult to control the tension of the elastomeric

cord. This produced unevenness within the sample. It was therefore suggested that

Non-stick sheet

Frame with sample

Metal plate

Figure 3-15: Fabric coating set-up

1 cm 1 cm


70

instead of weaving the cord, the cords were layered up in 0o and 90o directions. The

layers were bound together using an elastomeric binder yarn as shown in Figure 3-17.

Figure 3-17. Composite skin construction

If the cord layers are bound at every other cross-over point as visible in Figure 3-18a then

this is a very long and tedious process as they are manually done. The subsequent sample

was produced by missing 6/7 cords and applying a line of binding in both the 0o and 90o

directions of the skin as seen in Figure 3-18b.

Figure 3-18. Binding of the cord layers (a) binder stitch every other cross-over (b) binder stitch every 6/7

rows/columns.

(a) (b) 1 cm 1 cm


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3.8 Laminating the sample

A thermoplastic elastomeric laminate was used to stabilise the fabric structure. There are

numerous methods to apply a laminate to a fabric, one of the simplest methods is to use

a Heat Transfer Press, similar to the one displayed in Figure 3-19. The laminate has an

adhesive face which is placed facing the fabric; the laminate is applied to both sides of the

fabric. The sample is placed in the press inbetween the two hot plates. The heat, pressure

and length of time the sample is in the press for can be specified. In the correct condition,

the adhesive melts and bonds the matrix laminate to the fabric. Even though these

samples were not tested, this method of producing the fabric samples is well-suited to

maintaining uniformity of the cord tension.

Figure 3-19: Heat Transfer Press


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3.9 Geometrical analysis

3.9.1 Cold Mounting and Polishing for Scanning Electron Microscope

Cold mounting is a process where samples are mounted in a pot and then submerged in

resin. An araldite resin is used which requires a hardener and cures at room temperature.

Because the elastomeric cords are very flexible, the samples were initially coated with a

thin layer of resin, once the resin cured, the samples were mounted inside the pot and

the resin poured in. The mounted sample is then sanded to reveal the sample and then

undergoes a series of polishing processes to get a clear surface for the best images. After

cold mounting and polishing a sample, it then undergoes a carbon coating process. A thin

layer of carbon is added to the sample, this gives a better surface image. After carbon

coating, the sample is attached to a stub using a double sided sticky copper tape. Lines of

paint containing silver are applied to the sample, around the area which is going to be

analysed (i.e. the cord) and connecting it to the metal stub as shown in Figure 3-20; this

improves the conductivity and focuses as many electrons as possible on this area.

The Scanning Electron Microscope (SEM) was used to capture magnified images of the

cross-sections of the elastomeric cords. By using the SEM it gives high resolution images

at high magnification, so the structural analysis of the cords can be made. Interlacements

of yarns can be viewed and the dimensions of the cords can be measured.

Figure 3-20: Sample preparation for SEM

Sample mounted in a resin block

Metal Stand

Silver paint

Copper Tape


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3.9.2 Optical Microscopy

When the cord is stretched by hand, there’s a point at which the cord cannot be

stretched any more, at this point the angle of the braid can be referred to as the knee

angle. If the cord is stretched beyond this point then there will be permanent

deformation of the cord structure. The knee angle can be measured by taking a

microscope image of the cord in the stretched state and using image analysing software

to measure the angle.

3.10 Elastomeric cord testing

3.10.1 Tensile Properties

The tensile properties of a material can be classified in different ways. For the tensile

property analysis of the yarns used and the cords produced, the load-strain curve shown

Figure 3-21 is ideal because it is difficult to define a cross-sectional area for the yarns and

cord. Therefore, the breaking force is generalised in terms of the maximum load applied

(Newtons) and the degree of extension is defined as strain percentage. In addition to

these parameters, the gradients 1 and 2 show the relationship between the load and

strain; and the knee point marks the optimum performance of the materials, after this

point the deformations which occur within the fabric are permanent. In a braided

structure, the knee point indicates the locking/jamming position of the braid structure

when under extension.

Figure 3-21: The load-strain curve


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3.10.2 Apparatus for Tensile Testing

Braided elastomeric cords are a new concept, so there are no standards for testing these

cords. Standards have been devised to test these samples. The test method and

equipment have been kept consistent throughout the research, so the results can be

generalised and are comparable.

3.10.2.1 Cord sample preparation

To test the yarn and cord samples, the Instron tensile testing machine was used with

round clamps shown in Figure 3-22.

Samples

Length of specimens, 20cm

Number of specimens, 5

Procedure

Gauge length of 10cm

Sample was placed around the top jaw and clamp, then around the bottom jaw

and clamp.

The readings for the force applied, length of extension and strain percentage were taken.

3.10.2.2 Fabric sample preparation

To test the coated fabric samples, the Zwick tensile testing machine was used with flat

clamps covered in sandpaper, which are shown in Figure 3-22. The strip test was used

which is where the full width of the test specimen is gripped in between the jaws.

Samples

20mm by 50mm

Number of specimens, 5

Procedure

Jaws are set 20mm apart


75

The sample is clamped in the stationary jaws so it passes longitudinally through

the centre of the front jaws

Because of the mesh structure and the silicone matrix, when the clamps close

there is a slackness in the sample, to remove this slackness the gauge is changed

to a length of 25mm whilst the sample is still inside the clamps.

A pre-tension of 0.5N was added because the fabric is elastomeric

The readings for the force applied, length of extension and strain percentage were taken.

Figure 3-22: Picture of the Instron testing machine and the Zwick testing machine


76

3.11 Rigid cord development

The rigid cords were developed with a specific application of timing belts; however the

material can be applied more widely as rubber reinforcement. The aim of glass fibre over-

braided carbon core cords was to improve the adherence of the carbon with the rubber

of the timing belts. In order to give better stability to the carbon filaments within the cord,

twists are applied. The number of twists affects the cord’s properties and consequently

altering the properties of the belt. A carbon cord with a higher number of twists/turns per

centimetre (t/cm) will be more flexible; subsequently the flexibility/movement of the belt

increases which promotes heat production and therefore decreasing the belt strength. A

review of braided composites for stiffness critical applications was conducted by Ayranci

and Carey [68].

0.3 t/cm reduced flexibility reduced heat production increased strength

0.8 t/cm increased flexibility increased heat production reduced strength

Four different samples were produced and Table 3-3 shows a summary of their

specifications. Cords with a low glass fibre coverage and full fibre coverage (samples 1

and 2) were developed using four braid bobbins and 24 braid bobbin respectively.

However, it was found that after the development of sample 2, when it was used to

construct the timing belt, the belt developed a bumpy surface. The subsequent over-

braiding of sample 4 was carried out using 12 braid bobbins instead of 24. This suggests

that a compression jamming position of the over-braid had been reached but the jam

diameter was greater than the carbon core diameter.

Wrap cord diameter 1.1 mm

Sample 1 braided cord diameter 1.065 mm

Sample 2 braided cord diameter 1.252 mm


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Carbon cord twist

level

Glass fibre over-braid

coverage

Number of braid

bobbins

SAMPLE 1 0.3 t/cm Minimum Coverage 4

SAMPLE 2 0.3 t/cm Maximum Coverage 24

SAMPLE 3 0.8 t/cm Minimum Coverage 4

SAMPLE 4 0.8 t/cm Maximum Coverage 12

Table 3-3: Summary of rigid cord samples

The materials were provided by Gates and are as follows:

Specifications of the carbon cord:

TORAY T700 12K 31E HSN04

Specifications of the glass fibre yarn:

AGY 'S2' GLASS FIBRE WITH A GLYCIDOXY SILANE COATING

The carbon cord has been treated with a RFL coating. It is used as a core for the glass fibre

over-braid.

3.11.1 Preparing the machine components

The components of the braiding machine need to be as refined as possible. The main

concern is yarn breakage because glass fibres are brittle; the glass fibre yarn is prone to

fibrillation and breakages. Care needs to be taken when winding the glass fibre onto the

braiding bobbins, the yarn should be kept under enough tension so it is tight against the

bobbin but not too tight or the yarn will break during winding. The optimum tension is

15g, this was measured using a running yarn tension measuring device to make sure that

this tension is always consistent when winding the bobbins. Also glass fibre is slippery so

the bobbins need to be handled carefully or else the glass yarns may slip over each other

causing fibre breakages.

Additionally the glass fibre yarn let-off tension from the braid carrier during braiding

needs to be controlled. This again should be at the minimum level so as to not put

unnecessary tension on the yarn. The minimum tension is measured using a spring

mailto:[email protected]


78

balance which is a stationary yarn tension measuring device; this tension is measured at

100g.

The carbon cord was passed through the centre of the braiding machine. The carbon was

freely let-off with a slight back-tension by placing a rubber tube on the bobbin stand on

which the carbon cord bobbin was mounted as shown in Figure 3-23.

Figure 3-23: Picture of the carbon cord stand

As a comparison to the currently used cords which have 80 turns/metre of glass fibre

over-wrap on carbon cord, the braided cord was also developed to have 80 turns/metre

of braided yarn. In order to get the maximum production, the braid head speed was kept

at its highest (27 turns/min) and the optimum take-up speed was calculated. This can be

calculated using the following formula:

Take-up speed (cm/min) = turns per cm/ braid head speed (turns/min)

In this case the ideal take-up speed is 33.75 cm/min. with the current take-up device it is

difficult to get such precision hence a round figure of 35 cm/min was used. Prior to

braiding one of the braid yarns was marked; this ensured that the actual number of turns

could be measured. When using these machine parameters, it resulted in 90 turns/metre

and only 30 cm of actual production. In order to decrease the number of turns/metre the

take-up speed was increased to 40 cm/min, but this gave 75 turns/metre; hence a


79

compromise take-up speed of 37.5 cm/min was used, this gave 84 turns/metre. It is

difficult to exactly get 80 turns/metre, but this is the closest possible. The difference in

the predicted versus the actual production could be due to the actual take-up of the cord.

Even though the take-up rollers were set as a certain speed, the actual production speed

was different, a summary is shown in Table 3-4. This could be due to slight slippage of the

cord. It is not ideal to apply more tension onto the cord during take-up in case of any

damage occurring to the braided cord. This shows that although braid parameters can be

predicted, there is still the need for some trial and error methods.

Machine Speed Take-up Speed Actual Production Turns per Metre

27 turns/min 35cm/min 30cm/min 90

27 turns/min 37.5cm/min 33cm/min 84

27 turns/min 40cm/min 38cm/min 75

Table 3-4: Rigid cords, take-up speed vs. turns per metre

The initial 4 cord samples were tested by Gates Inc. This included the tensile testing.

Further analysis of using different numbers of bobbins and the effect on the braid

geometry was carried out. Samples with varying braid yarns of 4, 8, 12, 16, 20, and 24

were made. These sample structures were analysed under optical microscopy and their

geometries were compared with their predicted geometries. The cords were also tested

for their tensile properties.

3.12 Summary

The over-wrapping technique has been conducted using the DirecTwist machine to create

an elastomeric cord with an x-wrap. It was observed that the elastomeric core component

of the cord requires a great amount of tension control, which was not available in the

machine. This caused faults to appear in the resultant cord. In addition, due to several

yarn contact point in the manufacturing process, the Kevlar yarn exhibited extensive

fibrillation.


80

A braiding machine set-up has been developed to produce rigid hybrid cords. In addition

the braiding machine has been used to produce braided elastomeric cords. Triaxial and

biaxial braided cords have been produced using glass fibre, Kevlar and elastane. Several

elastane yarn tension control devices have been investigated. A tension control

mechanism has been developed, which can precisely control the elastane yarn tension at

various tension settings. Biaxial Kevlar-elastane cords have been developed using

different elastane yarn pre-tension.

Flexible composite skins have been developed using the braided cord. Initially the cords

were woven, which created a mesh structure. The woven mesh structure was coated

using silicone. This created an extensible and contractible structure; however a closed

structure is desirable, so a second skin was developed. This skin was producing by

layering of the cords and binding them using an elastomeric thread. This fabric was

laminated with a thermoplastic film.

A full analysis and testing results of all of the samples is given in chapter 4.

Chapter 4 Results and Analysis

81

Chapter Four:

4 Results and Analysis

As stated earlier it is assumed that if an elastomeric material, in this case elastane, is

extended to a certain degree then it will come back to its original state once relaxed,

however this is not the case. Once the elastomeric yarn is extended, it actually doesn’t

retract back to its original length. During cord production the change in the length of the

elastomeric yarn was observed, after tension has been applied, during braiding, and after

the cord retracts. Figure 4-1 shows that if a 5cm length of elastane is tensioned, braided

over and is then relaxed, then the cord will only return to a length of 6.15cm.

4.1 Braiding with Kevlar

The Kevlar used was a fine tow, so resembles a yarn; therefore it will be referred to as a

yarn. It is a 22 tex yarn. The Kevlar yarn’s tensile properties were tested; these values can

be used to compare the effect of braiding on the yarn strength and the product

extension. The behaviour of the yarn is shown in Figure 4-2. The tensile test results of a

single Kevlar yarn are:

AVERAGE MAXIMUM LOAD: 37 N AVERAGE STRAIN TO FAILURE: 2.39 %


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Figure 4-1: The change in Elastane length throughout the braiding process

Figure 4-2: The Load vs. Strain curve for the Kevlar yarn samples

4.1.1 Kevlar + Elastane Braided Hybrid Cords

The diameters for the Kevlar braided cords are:

1 Biaxial cord

Triaxial Cord

Diameter 1.20 mm Diameter 1 1.30 mm

Diameter 2 1.58 mm


83

(a) Relaxed state

(b) Extended state

Figure 4-3: Microscope images of the Kevlar biaxial cord in relaxed and extended state


84

(a) Relaxed state

(b) Extended state

Figure 4-4: Microscope images of the Kevlar triaxial cord in relaxed and extended state

Table 4-1 gives a summary of the braid angles in relaxed and extended states. The biaxial

braid is shown in Figure 4-3, where in the relaxed state the braid angle is 66o and in the

extended state it is 26o. The triaxial braid is shown in Figure 4-4, where the braid angle in

the relaxed state is 60o and in the extended state its 22.5o.


85

Biaxial Cord Triaxial Cord

Knee Angle 26o 22.5o

Knee Strain 160 % 168 %

Table 4-1: Knee angle and knee strain for elastomeric Kevlar cords

4.1.2 Testing the Cords

The biaxial and triaxial cords were tested; the comparison of their tensile behaviour is

displayed in Figure 4-5.

Figure 4-5: Tensile behaviour comparison of Kevlar biaxial and triaxial cords

The fabrics were tested in the warp, weft and bias directions. Because the behaviour of

fabric in the warp and weft directions is similar, they can be used to create an average of

the fabric test results. The stress strain values have been summarised in Table 4-2 and the

behaviour of the samples are in Figure 4-6 and Figure 4-7.


86

Kevlar Biaxial Kevlar Triaxial

Warp Weft Average Bias Warp Weft Average Bias

Maximum

Stress (MPa) 2.23 2.43 2.33 0.31 1.79 1.88 1.84 0.41

Strain to

Failure 1.86 2.01 1.94 1.55 4.28 4.26 4.27 2.57

Table 4-2: Summary of the stress-strain values for Kevlar fabric sample results

Figure 4-6: Stress-Strain curve for Kevlar biaxial coated fabric samples

Figure 4-7: Stress-Strain curve for Kevlar triaxial coated fabric samples


87

The summary of the maximum load and strain to failure is shown in Table 4-3, and their

behaviour has been compared with a corresponding single cord sample and is shown in

Figure 4-8 and Figure 4-9.

Kevlar Biaxial Kevlar Triaxial

Warp Weft Average Bias Warp Weft Average Bias

Maximum

Load (N) 111 122 117 16 98 107 103 22

Strain to

Failure (%) 186 201 194 155 428 426 427 257

Table 4-3: Summary of Kevlar fabric sample results

Figure 4-8: Load-Strain curve for Kevlar biaxial single cord, before and after fabric construction


88

Figure 4-9: Load-Strain curve for Kevlar triaxial single cord, before and after fabric construction

Tensile results comparison for the equivalent of single biaxial and triaxial cords are given

in Table 4-4.

Biaxial 4 glass fibre

strands

Single cord

One cord from fabric

Maximum Load (N) 148 73.37 19.44

Maximum Strain (%) 2.39 183.42 193.69

Triaxial 4 glass fibre

strands Single cord

One cord from fabric

Maximum Load (N) 148 84.67 16.46

Maximum Strain (%) 2.39 349.9 421.53

Table 4-4: Comparison of the change in tensile properties after braiding and fabric sample production

The behaviour of the bias fabric samples at a consistant rate, and the failure of the

sample is recorded to be under a low load. By observations as shown in Figure 4-10 it was

seen that the cords in the samples were being pulled out from the matrix as opposed to

being broken. This is because not even a single cord has been clamped by both the top

and bottom clamps. If extensive amounts of cords were available then bigger samples

would be better suited to being tested.


89

Figure 4-10: Kevlar triaxial cord coated fabric bias specimen, before and during tensile testing

The behaviour of the fabric in the warp and the weft direction is similar; this is expected

because the same cord was used in both directions. However the shape of the load-strain

curve does not imitate the shape of the load-strain curve for a single cord.

This is because the woven fabric sample is an open mesh-like weave and has a stretchy

silicone matrix; when the specimen is clamped inside the testing jaws, the cord on the

inside of the fabric tries to migrate out, causing an hour-glass shape. Figure 4-11 shows

the 2.5cm samples which when clamped in the testing jaws, have concaved edges; and

during testing as the fabric sample extends,the load is not evenly distributed. The stress is

focused on the cords on the outside edge of the fabric. Therefore, when the specimen

fails, it is usually one cord on the outer edge as seen in Figure 4-12, which fails and

effectively causes the failure of the total specimen. In order to counteract this effect, a

longer sample was used. With using a longer sample of 10cm as seen in Figure 4-11 the

load is distributed more evenly amongst all of the cords, the stress-strain curve for the

10cm fabric sample is shown in Figure 4-14.


90

Figure 4-11: Kevlar triaxial cord coated fabric specimen, 2.5cm sample before and during tensile testing; and

longer 10cm sample

Higher extensions were seen from the specimens due to slippage of the cords from the

coated fabric samples within the clamping jaws. This is due to factors such as the length

of the specimen, the matrix used, and the placement of the specimen in the clamping

Figure 4-12: Diagrammatical representation of cord break on

the outer edge of the sample during testing


91

jaws. The solution is to have a longer specimen which extends through both jaws, not to

apply the silicone matrix to the specimen where the jaws will grip the sample, and use a

continuous warp cord, with the ends wrapped around a metal bar as shown in Figure

4-13.

Figure 4-13: Warp yarns wrapped around a bar and clamped to prevent slippage during testing

Figure 4-14 shows the stress-strain behaviour of the 10cm slippage preventive sample.

This sample exhibited a more similar behaviour to the single cord sample. These have

been compared in Figure 4-15.

Figure 4-14: Stress-Strain curve for 10cm Kevlar triaxial coated fabric sample


92

0

Figure 4-15: Comparison load-strain curve for a single Kevlar triaxial cord, before and after fabric

construction

4.2 Braiding with glass fibre

The glass fibre used for this study has a strain percentage of 1.88% which is most likely

influenced by the twist in the yarn. The maximum load strength of a single yarn is on

average 27N. The typical load-strain behaviour of the glass fibre yarn is shown in Figure

4-16

Figure 4-16: The Load vs. Strain curves for the glass fibre yarn samples


93

Both the biaxial and the traixal glass fibre braid were produced at the same machine

settings as each other, so that the results are comparable. Figure 4-17 shows the cross-

sectional structure of the biaxial cord, it has an oval shape and the diameter varies but

has an average of diameter of 1.4mm. The 4 elastane core yarns seem to have merged in

the centre of the braid; however in the triaxial braided cords the elastane yarns are

distinctly separate as can be seen in Figure 4-18.

The diameter of the triaxial braid compared to the biaxial braid is considerably more. This

is due to the cross-section shape where the biaxial braid adopts an oval shape and the

triaxial braid has a cross-like formation. This is more visible in Figure 4-18 which shows

the triaxial braid at different orientations.

The diameters for the glass fibre braided cords are:

Biaxial cord

Triaxial Cord

Diameter 1.40 mm Diameter 1 1.50 mm

Diameter 2 1.72 mm

Figure 4-17: Cross-section SEM image of the glass fibre biaxial cord


94

Figure 4-18: Cross-section SEM image of the glass fibre triaxial cord and dimensions

Figure 4-19 is a clear illustration of the orientation of glass fibre filaments in a biaxial

braid. Half of the filaments are facing in the clock wise direction and half the yarns in the

counter-clockwise direction. The direction of the filament is the braid angle.

Figure 4-19: Cross-sectional SEM image of the glass fibre biaxial braid structure


95

Figure 4-20: SEM images showing the glass fibre triaxial braid cord structure

Glass fibre has very brittle fibre filaments, and if the fibre orientation changes then the

fibres can break easily; this can be seen in Figure 4-20. On the edges where the glass yarn

bends, there is breaking of glass filaments. The cords were observed under a microscope

and were extended to examine the change of the braid angle and also the amount of

extension which is possible by hand as in Figure 4-21 and Figure 4-22. The reason is that

in application the cord will not be used at the load to break, but is the extension of the

cord where it can be easily extended prior to permanent deformation. These positions are

referred to as the knee angle and the knee strain.

Biaxial Cord Triaxial Cord

Knee Angle 32o 22.5o

Knee Strain 111.66 % 200 %

Table 4-5: Knee angle and knee strain for elastomeric glass fibre cords


96

0

Figure 4-21: Microscope images of glass fibre biaxial cord in relaxed and extended state


97

Figure 4-22: Microscope images of glass fibre triaxial cord in relaxed and extended state

In the relaxed state the biaxial braid angle is 57o and in the extended state its 32o; and the

triaxial cord the braid angle in the relaxed state is 60o and in the extended state its 22.5o.

In addition, by examining the change in the length of the sample, the knee extension can


98

be calculated. This is 112% for the biaxial cord and 200% for the triaxial cord as given in

Table 4-5.

4.2.1 Testing the glass fibre elastomeric cords

When testing the cord samples, at the point where the cord is clamped, there was

considerable filament breakage, because the clamp had a crushing effect on the brittle

Glass fibre causing the cord to keep failing at the clamp. To counteract this, the cords

were coated with a layer of silicone around the areas which would be subjected to

clamping as shown in Figure 4-23.

Figure 4-23: Glass fibre cords coated with silicone

After weaving the cord samples into fabric samples and coating them, three tests were

carried out for each sample in the warp direction. The stress-strain behaviour of the fabric

samples is displayed in Figure 4-24 and Figure 4-25. These graphs plot the Stress in MPa

against the strain values, which have been summarised in Table 4-6. (NB, the Warp3

values for the triaxial fabric have been discounted because they are anomalous).

Glass fibre Biaxial Glass fibre Triaxial

Warp1 Warp2 Warp3 Average Warp1 Warp2 Warp3 Average

Maximum

Stress (MPa) 1.35 1.05 1.13 1.18 1.43 0.86 0.46 1.65

Strain to

Failure 1.65 1.13 1.47 1.42 3.32 3.05 1.86 3.19

Table 4-6: Summary of the stress-strain values for Glass fibre fabric sample results


99

Figure 4-24: Stress-Strain curve for glass fibre biaxial coated fabric samples

Figure 4-25: Stress-Strain curve for glass fibre triaxial coated fabric samples

A summary of the tensile results is displayed in Table 4-7. This summarises the results in

terms of maximum load (N) and the strain to failure as a percentage; so the results can be

compared with the results for the glass fibre yarn and cords. The tensile behaviour of a

single biaxially braided cord compared with the typical behaviour of the fabric sample is

shown in Figure 4-26. The tensile behaviour of a single triaxially braided cord and the

typical behaviour of the corresponding fabric sample is shown in Figure 4-27.


100

Glass fibre Biaxial Glass fibre Triaxial

Warp1 Warp2 Warp3 Average Warp1 Warp2 Warp3 Average

Maximum

Load (N) 67 53 56 59 100 60 32 80

Strain to

Failure (%) 165 113 147 142 332 305 186 319

Table 4-7: Summary of glass fibre fabric sample results

Figure 4-26: Load-strain curve for glass fibre biaxial cord, before and after fabric construction

Figure 4-27: Load-strain curve for a glass fibre triaxial cord, before and after fabric construction


101

Table 4-8 shows the comparison of the properties of 4 straight glass fibre yarns, against

the braided cord equivalent and the fabric sample equivalent.

Tensile results for a single cord:

Biaxial 4 glass fibre

strands

Single

cord

One cord from

fabric

Maximum Load (N) 108 28 9.79

Maximum Strain (%) 1.88 174.03 141.95

Triaxial 4 glass fibre

strands

Single

cord

One cord from

fabric

Maximum Load (N) 108 30.3 10.69

Maximum Strain (%) 1.88 211.08 289.84

Table 4-8: Comparison of the change in tensile properties after braiding and fabric sample production

By using braiding, it allows the extension of yarns which previously have little or no

extension. In this instance a single glass fibre yarn has an extension of only 1.88%, but

when braided biaxially has an extension of 174% and triaxially 211%. By triaxially braiding

the cord, there is a higher strain percentage. This could be because the glass fibre yarn

takes a longer path, so there is a greater length of yarn which is involved in the elongation.

A single cord consists of four glass fibre ends; therefore the braided cord should have four

times as much tensile strength as one single yarn. However the average tensile strength

of a biaxial cord is 28N and the strength of four glass fibre yarns is 108N collectively. This

means that after biaxially braiding glass fibre, it has lost 75% of its strength. When the

cord is made into a fabric sample and tested, the strength per single cord was concluded

to be on average 9.79N, this is a 91% loss of strength.


102

When using the triaxial method of braiding, the average load to failure for a single cord is

30.3N which is a 72% strength loss. When made into a fabric the strength of a cord is

calculated at 10.69, which gives an overall strength loss of 90%.

4.3 Geometrical analysis of hyper-elastic cords

Using the developed nip roller set-up to precisely control the elastane let-off, four

samples were produced. Four samples using four braid bobbins with different elastane

setting. The machine settings are given in Table 4-9.

Number of braid

yarns

Pretension

Number

Pretension

Speed

Braid head

speed

Take-up

Speed





Table 4-9: Machine settings for different braid angle

The braid angles of the cords were measured by taking their image under the optical

microscope and analysed using the ImageJ software. The cords were extended by hand

until the braid jam was reached. Again an optical microscope image was taken and

analysed for the braid angle. These optical images for each of the samples are shown in

Figure 4-28. The samples were tested to failure. The maximum strain to failure was

obtained. A summary and comparison of the braid angles, the knee angle and the

maximum strain of the cords are given in Table 4-10.

A comparison of the load-strain behaviour of the samples with different braid angles are

shown in Figure 4-29. The graph shows a shift in the knee strain with a change in the

elastane pre-tension which ultimately determines the braid angle. As the braid angle

increases, this results in greater extension.


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(a) Elastane pre-tension #2, relaxed state

(b) Elastane pre-tension #2, extended state

(c) Elastane pre-tension #3, relaxed state

(d) Elastane pre-tension #3, extended state


104

(e) Elastane pre-tension #4, relaxed state

(f) Elastane pre-tension #4, extended state

(g) Elastane pre-tension #5, relaxed state

(h) Elastane pre-tension #5, extended state

Figure 4-28: Optical microscope images of hyper-elastic braided cords with different pre-tensions in their relaxed and extended states


105

Elastane

pretension

Braid

angle

Braid angle at

knee Max strain %

#2 67 29.63 402

#3 58 30.88 264

#4 50 30.81 144

#5 53 31.31 63

Table 4-10: Summary of the braid angle vs. the knee angle and maximum strain

Figure 4-29: Typical load-strain graphs for hyper-elastic cords with varying elastane pre-tensions

4.4 Geometrical analysis of rigid cords

The carbon cord was over-braided with various numbers of glass fibre yarns/bobbins.

These were 4, 8, 12, 16, 20 and 24 bobbins, which is the maximum the machine can hold.

All other braiding machine parameters were kept constant and are given in Table 4-11.

The different braid structures are shown in Figure 4-33. Not only changes to the number

of braid yarns affect the way the cord looks, but it also affects the cord geometries. These

cord structures were analysed under a microscope to determine their braid angle, the

0

10

20

30

40

50

60

70

0 50 100 150 200 250 300 350 400 450

Load

(N

/co

rd)

Strain %

Load-strain behaviour of cords with different elastane pretension

#2

#3

#4

#5


106

cord thickness (diameter) and a single yarn width. A summary of the cord geometries are

given in Table 4-12 are also presented in Figure 4-30 and Figure 4-31. As the number of

braid yarns increases so does the diameter of the braided cord, and so does the braid

angle. It can be seen that as the number of braid bobbins/yarn increases, so does the

level of coverage over the carbon core and because there is a higher number of yarns, the

over-braid is gradually approaching a jamming state. As the jamming state is reached, this

is indicated by the jamming angle, which is indicated by little change in the braid angle.

Core diameter

(mm)

Take-up speed

(mm/min)

Braid-head speed

(turns/min)

Predicted Braid

Angle (degrees)

0.98 375 27 12.5

Table 4-11: Machine settings for rigid braided cord production

No. of braid

bobbins

Yarn Width

(mm)

Cord Diameter

(mm)

Braid angle

(degrees)

4 0.47 1.05 11.48

8 0.45 1.21 13.62

12 0.43 1.26 15.80

16 0.41 1.32 16.60

20 0.39 1.37 17.21

24 0.30 1.40 17.34

Table 4-12: Geometrical parameters of rigid braided cords with different number of braid yarns

The cover factor can be predicted, a comparison between the predicted cover factor and

the actual cover factor are given in Table 4-13. The predicted cover factor takes into

account the core diameter and the dimensions of single glass fibre yarn and the predicted

braid angle (calculated from the machine parameters). The actual cover factor is

calculated by taking optical microscope images of the braided cords (Figure 4-33) and

using the image analysis software (ImageJ) to measure the yarn width and the braid angle,


107

from which the cover factor was calculated. There was minimal difference between the

predicted and the actual measured values.

Number of

braid yarns

Predicted

cover factor

Actual cover

factor

4 0.56 0.53

8 0.89 0.84

12 0.99 0.98

16 1 1

20 1 1

24 1 1

Table 4-13: Predicted cover factor vs. actual cover factor for different number of braid yarns

Figure 4-30. The effect of the number of braid bobbins on the braid angle


108

Figure 4-31: The effect of the number of braid bobbins on the cord diameter

Figure 4-32: The effect of the number of braid bobbins on the yarn width

Number of braid bobbin


109

(a) 4 braid yarns

(b) 8 braid yarns

(c) 12 braid yarns

(d) 16 braid yarns

(e) 20 braid yarns

(f) 24 braid yarns

Figure 4-33: Various number of glass fibre bobbins used for over-braid of carbon cord


110

4.5 Tensile testing of the carbon-glass hybrid cords

Rigid cord samples 1, 2, 3, and 4 were used in the manufacturing of timing belts and

underwent static belt testing. The results of the tensile test results are shown in Figure

4-34. The tensile strength of sample 1 and 2 using a carbon cord of 0.3 t/cm were greater

than those for samples 3 and 4 where the carbon cord was 0.8 t/cm. The samples with

the maximum glass fibre over-braid coverage, samples 2 and 4, showed higher tensile

strength than their minimum coverage counterparts, sample 1 and 3 respectively.

Figure 4-34: Static belt tensile strength

By taking the strength of a single carbon core yarn and adding the strength of the glass

fibre yarns, this gives a theoretical strength of the all yarns collectively, which are given in

Table 4-14. The actual strength of the cords are given in Table 4-15. The theoretical and

actual values are compared in Figure 4-35.

Up until 8 braid yarns the actual results match the theoretical results. As the number of

braid yarns increase after this, there is lower actual strength than the predicted strength.

This suggested that not all the braid yarns are contributing towards the cords ultimate

strength. A reason for this could be because the braid has surpassed its jamming limit,

instead of being in the tension jammed state; it is in the compression jammed state.


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Number of

glass fibres

Max load of Glass

fibres (kN)

Max load of Glass

fibres + Carbon (kN)

Cross-sectional

area (mm2) Stress (GPa)

4 0.0825 1.0597 3.2987 3.4957

8 0.1650 1.1422 3.8013 4.3419 12 0.2474 1.2247 3.9584 4.8478

16 0.3299 1.3072 4.1469 5.4207 20 0.4124 1.3896 4.3040 5.9810 24 0.4949 1.4721 4.4061 6.4863

Table 4-14: Theoretical calculations of maximum stress of rigid cords

Number of

Bobbins Load (kN) Stress (GPa)

Displacement

(mm) Strain Strain %

4 1.0943 3.6096 11.4475 0.0458 4.5790

8 1.1770 4.4741 11.3867 0.0455 4.5547 12 1.1519 4.5599 11.6984 0.0468 4.6793

16 1.2279 5.0920 11.4492 0.0458 4.5797 20 1.2321 5.3028 10.9726 0.0439 4.3890 24 1.2654 5.5753 11.5309 0.0461 4.6124

Table 4-15: Actual tensile results of rigid cords

Figure 4-35: Theoretical vs. actual results of strength of rigid cords

4.6 Summary

The biaxial and triaxial hyper-extensible Kevlar and glass fibre cords were tested.

Although the machine parameters were kept the same when producing the biaxial and


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triaxial braids, it was observed that there was a significant difference in the maximum

strain for the two different structures in both cases for Kevlar cords and glass fibre cords.

The cords were used to produce mesh fabrics, which were tested. Comparisons were

made between individual yarn strength, cord strength and equivalent mesh fabric

strength. It was observed that after braiding the yarns experienced significant reduction

in the maximum load where this reduction is even greater in the glass fibre samples

compared with the Kevlar samples and further more reduction in strength when the cords

were made into the mesh fabric.

Hyper-elastic cord samples with four varying braid angles were produced. It was observed

that when different pre-tensions are applied to the elastane yarn (prior to braiding), then

the braided cords have varying angles in their relaxed state. Greater elastane pre-tension

resulted in higher braid angles in the cords. The cords with the higher braid angles were

observed to have higher maximum strain percentage; however the jamming angle was

similar for all the samples.

Rigid cords with varying number of braid yarns were developed. It was observed that as

the number of braid yarns increased, so did the cover factor of the braid yarn over the

core. In addition as the number of braid yarns increased so did the diameter of the

braided cords and the braid angle. An increased number of braid yarns created a jamming

state of the yarns where the yarns started to clump together, this is observed by the

reduction of yarn width within the braid.

In addition, the maximum strength of the rigid cords was compared to theoretical values.

The theoretical and actual were initially similar but as the number of braid yarns

increased, this in turn reduced the actual maximum load values of the cord. This is

because as the increase in the number of braid yarns passed the initial jamming state, this

eventually resulted in a loose over-braid on the core yarn and therefore causing the over-

braid to become less effective as a contributor to the overall cord strength.

Chapter 5 Modelling of Braided Cords

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Chapter Five:

5 Modelling of Braided Cords

5.1 Modelling the load-elongation behaviour of hyper-elastic braided

cords

The mechanics of a hybrid braid with an elastic core have previously been researched by

Hopper et al. [78] alongside that of Rodinov and Manukyan [59]. However subsequently

there has not been much research on elastomeric braids and the modelling of such

products. This research looked at the development of four various cords, which had

different braid angles. This was achieved by changing the pre-tension on the elastane

yarn. The initial braid angle, the knee braid angle and the maximum strain of the samples

are compared in Table 5-1.

Braid Initial braid angle

(degrees)

Braid angle at knee

(degrees) Max strain %

Braid 1 29 27 22

Braid2 38 27 49

Braid 3 52 27 89

Braid 4 73 27 254

Table 5-1: Relation between initial braid angle and maximum strain


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It can be seen from Figure 5-1 that the knee point on the graph can be shifted by

changing the braid angle. Hence it is possible to design a yarn with the required load-

strain relationship for a given state of deployment (of the morphing structure).

Figure 5-1: Load-strain relationship of braids with different braid angles

5.1.1 Modelling the load-elongation behaviour of hyper-elastic yarns

A computational model for predicting the load-strain behaviour of hyper-elastic yarns has

been developed. The model is based on the principle of virtual work. The inputs to the

model are:

Stress-strain behaviour of elastane yarn

Stress-strain behaviour of Kevlar yarn

Yarn twist angle calculated from braid angle and core diameter


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Load-elongation characteristics of the filaments

Poisson’s ratio of the yarns

The load-strain behaviour of hyper-elastic yarns may be divided into two stages.

Stage 1: the low-modulus stage; this is dominated by the elastane yarns. The Kevlar yarns

are subjected to a kinematic rotation up to the knee point without significant

contribution to the load/stress.

Yarn strain at the knee point can be computed using the following equation based on

kinematic rotations:

(5-1)

The force generated in the yarn is a function of the elastane stress-strain curve.

Stage 2: from the knee point; the load-deformation is dominated by complex interaction

between the core and braided yarns. The mechanics of this stage were originally derived

for spun yarns, which is shown in Figure 5-2; and subsequently modified for braided cords.

Figure 5-2: Geometry of filaments in a yarn

Strain Analysis

The relationship between the strain in a filament, i, when the yarn is subjected to a strain

is given in equation (5-2) where s is length measured along the yarn axis and u is

the extension.


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(5-2)

where,

= yarn Poisson’s ratio

= helix angle (which is a representation of the braid angle)

This relationship is valid for small strain values but more specifically it assumes that the

helical angle of the filaments do not change with yarn deformation.

Energy Considerations: Virtual Work

Using the principle of virtual work the relationships between external forces and strains

for the yarn are derived in the following analysis.

The incremental strain energy of a single filament is:

(5-3)

where

(5-4)

(Note: n is the filament layer number within a yarn; i is the filament number within a layer;

and L is an arbitrary length of yarn, generally one twist)

Substituting equation (5-1) into equation (5-4):

(5-5)

Summing up for the filaments in the yarn:

(5-6)

where,

N = number of layers in yarn

K = number of filaments in a given layer n


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Principle of stationary potential energy

δ δ δ

where,

= sum of the elastic strain energy stored in the deformed body

= potential energy of the applied forces

At equilibrium

The variation of potential energy of external torque is:

Hence the axial tensile contribution of each filament is obtained by combining equation (4)

& (5):

(5-7)

The tensile contribution for each filament has to be added to obtain the tension/strain

relationship for the whole yarn.

Figure 5-3 presents the computed load-strain behaviour of four braided yarns (which

have been used to produce braids with four different braid angles). These curves compare

favourably with the experimental curves presented in Figure 5-1.


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Figure 5-3: Computed load-strain curves for hyper-elastic cords

5.2 Geometrical modelling of braided cords using CAD software

Previous work has been conducted on looking at the relationship between the braid

parameters and the effect of the braid geometry. Other work conducted by Rawal et al.

modelled the geometrical path of a helix, not only cylindrical but on a conical shape [83].

This model however assumes that the yarn is taking a straight helical path, where in

actual fact there are interlacements between the braid yarns so there is a degree of

crimping which needs to be taken into account when modelling braid. Other yarn paths


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apart from a regular circular braid path were investigated by Rawal et al. [84] alongside

other researchers [85, 86]. Walker et al. [87] also conducted a brief study on the braid

geometry and the interaction point of the braid yarns. Several other bits of research have

been conducted in predicting and modelling braid geometry [88-91] and Alpyildiz [92].

These models are based on 2D circular braiding, other research has also looked

specifically at 3D braiding too [93-96].

The profile shape which the yarn takes after braiding was researched by Byun [97],

however this study was more concentrated on triaxial braided structures. This shape

change is also a factor in nesting which was studied by Birkefeld et al. [98]. These are

more in-depth studies of the yarn cross-sectional shape, whereas Lyons et al. [74]

predicted a simple elliptical shape; this will be used in this study for ease of modelling.

This section aims to collectively analyse the braid geometries investigated in previous

research and apply the theories to braided cord modelling.

Rawal et al. studied the geometrical modelling of yarn paths and suggested equations to

map the helical path of braid yarns along a constant circular diameter [83]. The path

rotates around a circle of x,y coordinates and traverses along the z axis. The path

coordinates can be calculated as:

(5-8)

(5-9)

(5-10)

where,

r = radius of the tubular braid

= braid angle

= wrapping angle on the mandrel, where 0<<2

In the equations, the positive values are for yarns in the anti-clockwise direction, and the

negative values are for yarns moving in the clockwise direction. Several braid yarns can be


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plotted depending on how many braid yarns are being used, where is the shift angle

between two yarns moving in the same direction as shown in Figure 5-4 and n is the

number of braid yarns moving in the same direction then

the helical points of all

the braid yarns can be calculated by:

(5-11)

(5-12)

(5-13)

where i = 1,2,3...n

Figure 5-4: The shift angle of the braid yarns moving in the same direction

However, by using the above equations to maps the helices, this will create splines which

intersect with each other. The calculations do not take into account the yarn crimp

(undulations). Figure 5-5 shows typical undulation geometries of a regular 1/1 braid,

where p is an undulation length between two braid yarns rotating in the same direction

and a is minor diameter of the braid yarn (thickness of braid tow). Alpyildiz [92] proposed

a method to define the crimp in terms of a sine wave. By combining the sine wave and

the helical path this creates undulations in the braid yarn path.


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Figure 5-5: The braid yarn crimp path/undulation

Figure 5-6: The relationship between the helical braid yarn path and wrapping angle

Using the relationship between the helical braid yarn path and the wrapping angle, as

shown in Figure 5-6, the length of an undulation (p) can be calculated as:

(5-14)

By rearranging this equation, the radius can also be represented as:

(5-15)


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Where a is minor diameter of the braid yarn (thickness of braid tow), a/2 is the

amplitude. The period of 2/q=2p. Considering the sine wave, the undulation path can be

written as:

(5-16)

The undulation/crimp in the braid yarns has an effect on the actual radius of the braid.

The crimp path can be written on the x,y axis as a sine wave in terms of the wrapping

angle (). This has been defined in detail by Alpyldiz (2011) and can be calculated by the

following:

(5-17)

where r = radius of braid

The x, y, and z coordinates of the braid paths moving in the anti-clockwise direction can

be calculated by the following equations:

(5-18)

(5-19)

(5-20)

where i = 1,2,3...n

Braid yarns moving in the clockwise direction also follow a sine wave path, however, the

braiding yarns in the clockwise direction pass over the braiding yarns in the anti-clockwise

direction. This is accounted for by adding a shift in the braid crimp path r(), which for the

clockwise yarns is calculated as:

(5-21)


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Because the clockwise paths are in the opposite direction to the anti-clockwise yarn

paths, the x, y coordinates are also reversed. The x, y, z coordinates can be calculated

using the following equations:

(5-22)

(5-23)

(5-24)

where i = 1,2,3...n

5.2.1 Plotting of yarn paths

The point for mapping the yarn path can be calculated using an Excel file. This file can be

imported into AutoDesk Inventor to create a spline/yarn path. The x, y, z coordinates of

each single yarn path are saved in individual files and all the yarn paths can be imported

into the same AutoDesk Inventor file to give the full profile of the braid yarn paths. The

splines need to be assigned a cross-section, which will ‘sweep’ around the core. First the

core is created; this is achieved by creating a circle and extruding the shape to the

required length.

Models of the elastomeric Kevlar braids have been created. The models have been

created with different braid angles to compare with the actual samples. The models have

been created for the braid with braid angles of 67o, 58o and 50o. The full example given is

for 50o braid angle. The model represents 4 Kevlar yarns which are interlaced with a

diamond (1/1) braid pattern.

Figure 5-7 shows a snippet of an Excel file for a braid yarn path. All four of the imported

braid path splines are shown in Figure 5-8. The core of the braid is a collective of four

elastane yarns. The elastane core is represented as a single cylindrical shape in Figure 5-9

because the four elastane yarns combine with each other after braiding as shown in

Figure 4-17.


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Figure 5-7: Example of Excel file coordinates for a 50 degree braid path

Figure 5-8: Braid path splines imported into AutoDesk Inventor from Excel files


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Figure 5-9: A core inserted into the braid structure in AutoDesk Inventor

Figure 5-10: A complete 50 degrees braided structure created in AutoDesk Inventor

To assign a cross-section shape to the spline, create a plane normal to the spline at the

point initial point of the spline. Create a shape centred on the spline, and specify the

dimensions. In this case, the Kevlar yarn dimensions were measured to be 0.4mm x

0.13mm. Sweep this profile along the spline path and around the core as a guide surface.


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The cross-sections need to assign to each spline individually to give the final braid profile.

Figure 5-11 shows comparisons of braid simulations for angles 67o 58o and 50o compared

to the actual braided samples.

(a) Braid simulation for 67o

(b) Actual 67o

braid

(c) Braid simulation for 58o

(d) Actual 58o

braid

(e) Braid simulation for 50o

(f) Actual 50o

braid

Figure 5-11: Simulated braid geometries in AutoDesk Inventor vs. Actual braided samples


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(a) Simulation of a 12 strand braid

(b) Actual 12 strand braid

Figure 5-12: Simulated 12 braid yarn sample in AutoDesk vs. Actual sample

Braids with higher numbers of braid yarns can also be simulated using the above

mentioned equations. However these are for producing a diamond (1/1) braid structure.

This is applicable for the elastomeric cords developed in this study which use four braid

yarns. 12 braid yarns placed at regular intervals on a 1:2 horngear to yarn carrier


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machine, this also produces a diamond structure. A geometrical simulation was produced

for this and is shown in Figure 5-12 in comparison to the actual 12 braid yarn sample.

5.3 Summary

A computational model for predicting the load-elongation behaviour of hyper-elastic

braided cords has been developed. The model is shown to agree well with experimental

results.

In additional a geometrical model has been developed for modelling braided cords using

CAD software. The model has been applied successfully to model 1/1 diamond braid

structures with various braid angles. These simulations have been compared with actual

braid samples. The simulated models agree well with the structure of the actual braided

cord samples.

Chapter 6 A Braid Topology System

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Chapter Six:

6 A Braid Topology System

6.1 Introduction to braid topology

Braiding was originally used for rope structures but its versatility and the development of

braid machinery means that braiding can be used in diverse applications. The pattern

which is created by the interlacement of the yarns is called the “braid pattern”. The braid

pattern corresponds to the positioning of yarn bobbins on the braiding machine [99]. A

variety of designs can be produced by removing and repositioning bobbins. Patterns with

colour effects can be given to the braid by changing the colour and positions of the yarn

bobbins. Very little work has been carried out by researchers in this field of predicting

braid topology. A paper by Ravenhorst et al. [100] discusses spool pattern tools and braid

topology, and a study by Bicking [101] research in bobbin placement and yarn colour

effect.

There is a need for predicting the braid pattern to reduce time preparation for braiding by

reducing trial and error methods of producing different braid patterns and colour effects.

By going one step further and adding the braid colour effects to this program, one can

also predict the colour effects alongside the choice of braid topology. This will


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considerably cut down the preparation time. This provides a good reason for creating

computer generated braid topology. A computerised system, BraidCADTM would work by

selecting the bobbins, bobbin placement, yarn type and colour, which will prompt the

program to automatically draw a visual braid topology diagram. CAD software has been

used previously to simulate 3D braided structures [102] and similar software has been

designed previously for woven fabrics, such as ScotWeave [103].

Before analysing the braid pattern it is necessary to understand the braiding machine and

yarn carrier configuration [63]. The circular braiding machine also known as the maypole

braiding machine, is named after the maypole dance as it adopts the intertwining motions

of the people and ribbons during the dance. The traditional maypole braider is a relatively

simple mechanism to control. It has two sets of yarn carriers rotating on a circular track,

one set rotating in the clockwise direction and the other set rotating in the anticlockwise

direction. During this process, the yarns moving in the opposite directions interlace with

each other to form a tubular braided structure. The braided structure is either created as

a continuous sleeve or is deposited on a solid mandrel [62]. The resulting braid is

continuously moved forward using a take-up mechanism. As illustrated in Figure 6-1 the

white bobbins move around the machine in a clockwise direction and the black bobbins

move in an anticlockwise direction. In a conventional circular horngear machine the ratio

of horngears to yarn carriers is 1:2, so for every horngear there are two yarn carriers.

Therefore, for a 12 horngear machine there are a total of 24 yarn carriers where 12 will

be moving clockwise and 12 anticlockwise. Likewise for a 24 horngear machine there are

48 bobbins. Figure 6-1 is a systematic diagram of a 12 horngear/24yarn carrier machine.

Due to the specific number of bobbins on each braiding machine and the method of

interlacement, braiding has a limitation of the braiding patterns that can be produced,

compared to the vast array of available weave patterns. In weaving, a weave pattern can

be designed which is then incorporated into the weaving machine to produce the

required fabric design. Braided structures are similar to woven structures in terms of the

topology of yarn interlacement. For example, Diamond, Regular and Hercules braid

patterns are similar to Plain 1/1, 2/2 Twill and 3/3 Twill weaves respectively (Figure 6-1)


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[69, 70]. Braids are commonly produced in a tubular form and only a few centimetres in

diameter due to a limited number of yarn carriers available/used, whereas woven fabrics

are often produced as a broad cloth, several-metres wide. In a 24 yarn carrier machine

when all 24 bobbins are in use, the structure of the braid is a regular construction, this is a

2/2 twill weave but in the bias direction. The braid pattern equivalent of a 3/3 twill weave

is called the Hercules braid. This braid cannot be produced on the conventional horngear

machines which have a horngear to yarn carrier ratio of 1:2. With these conventional

machines, the largest symmetrical repeat is a 2up 2down, step1 pattern (regular braid).

In order to produce a Hercules braid, a 1:3 horngear to bobbin carrier ratio is required.

This means that there will be a larger number of bobbins which the braiding machine and

horngears need to accommodate. Previously, for a 1:2 horngear machine, each horngear

consisted of four slots to allow the movement of bobbins without them coming into

contact with any adjacent bobbins, however, these horngears will not be sufficient to

house all of the bobbins for a 1:3 braiding machine. Therefore, additional slots are

required to house the extra bobbins; every horngear has six slots instead of the usual four.

These different horngears are also discussed in Brunnschweiler’s paper Braids and

Braiding [104]. Figure 6-1 shows a diagrammatic representation of a section of a 1:3

horngear to bobbin carrier machine set-up. In the diagram, the circles represent the

bobbin carriers, where the white carriers have a leftwards motion and the black carriers

have a rightwards motion. Each horngear has six slots and every bobbin carrier is

accommodated for throughout the horngear rotations and carrier movements.

Figure 6-1: Six-slot horngear set-up for a hercules braid.


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6.2 Braid geometry and braid design

The interlacements of the yarns in a braid are similar to those of weaving. However, in

weaving, the warp and weft yarns are facing in the 0o and 90o directions, whereas in

braiding the direction of the yarns are in bias directions. The bias directions usually refer

to ± 45o but in braiding this angle varies. The braid angle () is varied by changing the

machine parameters (braid-head speed and take-up speed), hence changing the

appearance of the braid [71, 105, 106]. For the ease of explanation and diagrammatic

visualisations, the methods mentioned henceforth assume that the yarns are in ± 45o

directions. This method was also adopted by Bicking for a project on fancy braids.

6.3 Previous studies into braid topology

Not much concentration has been given in researching the appearance of the braided

structure with regard to the braid yarn pattern mapping. Bicking [104] conducted a

project on the production of fancy braids, where the positioning of different coloured

bobbins in various positions on the braiding machine created an assortment of fancy

braid colour patterns. The study proposed a method of using point paper designs to plan

the various colour strategies which would produce certain patterns. Bicking also proposed

a bobbin/spool set-up diagram which correlated with the point paper designs and used a

key to explain the set-up of the bobbins. The spool set-up diagram gives a base in case the

same braid pattern needs to be reproduced.

Ravenhorst and Akkerman [105] proposed a method for relating the braid pattern to the

spool patterns. The braid pattern is used to determine the set-up of the spools prior to

braid manufacturing. The two sets of braid yarns used are referred to as warp (X) and

weft (O), where each set is circling in opposite directions. Ravenhorst et al. use the canvas

method for visualisation of the braid pattern; this uses a set of lines to represent the yarn,

which depict the direction of these surface yarns. The removal of every alternate spool,

subsequently removes the corresponding row/column on the braid pattern diagram.


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Previous studies provide a good base for the explanation of braid topology; however the

work is very narrow. The braid topology needs to be generalised so that the methods may

not only be used in braids formed by circular braiding machines but also for braids

produced with any braiding methods. This is simply achieved by using a universal system

of mapping the yarn behaviour as discussed in this paper.

6.4 Braid pattern diagram

In a braiding machine each bobbin has a set path and movement, which will always stay

the same throughout the machine cycle. A braid pattern can be designed by first

numbering each of the bobbins as shown in Figure 6-2a. By studying these movements

and by taking into account the bobbin arrangements, the braid pattern can be composed

as seen in Figure 6-2b. A weave pattern consists of columns and rows and because a braid

is similar to a weave but in the bias direction, the braid pattern makes sense to be in the

bias1 and bias2 diagonal directions. Every diagonal row represents the interlacements of

a different yarn. Each row has been numbered to correspond with its bobbin’s position on

the braiding machine. A shaded square represents a top yarn float of the bias1 yarn (and

bottom float of a bias2 yarn) and a blank square represents a top float of a bias2 yarn

(and a bottom float of bias1 yarn). This braid pattern produced is the regular braid.

Figure 6-3 shows the yarn carrier/bobbin movements for four yarns moving in the

clockwise and anti-clockwise directions. As the horngears rotate through the machine

cycles, the yarn carriers move in a continuous path in-between one another. In the

example, the anti-clockwise rotating bobbins are in the bias1 (B1) direction, and clockwise

rotating bobbins are bias2 (B2). The bobbins in each direction have been labelled in

ascending numerical order. In the example B1 bobbin 1 will always go over B2 bobbin 1

and 2; B1 bobbin 2 will always go under B2 bobbin 1 and 2, and so on. For the ease of

explanation Figure 6-3 shows the movement of four B1 yarns and four B2 yarns; however

all the yarn carriers would be moving at the same time.


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Figure 6-2: Developing a braid pattern for a 12 horngear machine (a) numbering braid bobbins; (b) braid

pattern.


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Figure 6-3: Illustration of the bobbin movement steps


136

It is not necessary to use all 24 bobbins but it is chosen because it gives the braid the

maximum yarn placement possible. However, fewer yarns can be utilised for different

product specifications, this gives the braid a different structure. By using the braid pattern

in Figure 6-4a, a braid pattern for any arrangement using any number of bobbins can be

produced. If a bobbin is removed then those yarn interlacements are removed from the

braid pattern. On the braid pattern diagram this is equivalent to removing a diagonal line

from the braid pattern. For example if every alternate bias1 and bias2 bobbin is removed

(bobbin 2,4,6,8,10,12), this results in the removal of these 6 diagonal lines in each

direction from the braid pattern diagram (Figure 6-4b). Figure 6-4c shows the resulting

braid pattern diagram; this creates a diamond braid structure.

Figure 6-4: Predicting braid pattern by removing braid yarns.

6.5 Braid colour effect diagram

Different types and combinations of yarns and colours of yarns can be used to produce

braids, which give varying textures and colour patterns. This can produce a hybrid braid

and also make the braid more visually appealing. In addition it may suit the purpose of a

certain application, such as if a conductive wire or LED need to be introduced into the

braid, then the braid colour effect diagram would indicate the positions within the braid

where the components would be visible.


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The colour effect diagram can be produced using the same method that is used to

produce a weave colour effect diagram. The weave colour effect is produced by using the

weave pattern diagram and assigning colours to each warp and weft yarn [107-110].

These principles can also be applied to the braid pattern diagram to create a braid colour

effect diagram.

Figure 6-5 illustrates the stages to create a braid colour effect diagram. Two yarn colours

have been used in the example, colour1 and colour2. The arrangements of the colours are

indicated along the bottom sides of the diagram where each bias1 and bias2 bobbin is

assigned a yarn colour. The colour effect is based on a regular braid pattern, which is

produced using a complete set of bobbins on a 12 horngear machine. The stages of

producing a colour effect are as follows.

(a) The braid pattern is inserted in the form of dots where the dots indicate the float

of bias1 yarns.

(b) The bias1 bobbins are followed diagonally in a consecutive order, where there is a

braid mark (where bias1 is a float), those squares are filled with a solid colour to

show a yarn that colour will be visible at those points. For the bobbins which have

been assigned colour1, the dotted squares have been filled with colour1, and for

the bobbins which are assigned colour2, the dotted squares have been shaded

with colour2.

(c) The bias2 bobbins are followed diagonally in a consecutive order, where there is a

blank square (where there is a bias2 float), those are filled with a solid colour. For

the colour1 bobbins the squares are filled with colour1 and for the colour2

bobbins, the blank squares are shaded with colour2,

(d) Shows (b) and (c) collectively.

(e) Shows the complete colour effect with the braid markers removed.

This colour effect produces a zig-zag pattern.


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Figure 6-5: Colour effect diagram using two colours.

By introducing new colours or a new arrangement of different coloured yarns, this will

change the colour effect of the braid. Figure 6-6 shows the colour effect of a regular braid

when there are three colours introduced in a regular manner, which produced Z-like

shapes:

(a) shows the application of the colour effects of bias1 yarns on the braid pattern,

(b) shows the addition of the colour effects of the bias2 yarns

(c) shows the complete colour effect with the removal of the braid pattern dots.

Figure 6-6: Colour effect diagram using 3 colours.


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The regular braid patterns which are used in both Figure 6-5 and Figure 6-6 have

significantly different colour effects, just by the organisation of colour choice.

The greater the number of bobbins which the machine can carry, the greater the number

of colour arrangements that can be made and therefore a greater variety of designs.

Colour effects can be incorporated into any braid pattern. Figure 6-7 shows an example

where a selection of braid bobbins has been removed. The figure shows the bobbin

arrangements and the method used to establish the braid pattern diagram:

(a) shows the positions of the bobbins, where the bobbins which are to be removed

have a line through them;

(b) shows the actual braid diagram and the colours that each bobbin has been

assigned;

(c) shows the simplified braid pattern and colour effect diagram. This diagram clearly

shows the stripy diagonal pattern of the braid due to the yarn interlacements and

the arrangement of different coloured yarns.

Figure 6-7: Producing sample weave effect without making physical samples (a) bobbin set-up; (b) braid

pattern; (c) braid colour effect diagram.


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6.6 Braid topology matrices

Braid topology can be mathematically modelled by using matrices where each row and

column of the braid relates to every row and column (mn) of the binary matrix. Where a

shaded block in the braid topology indicates the anti-clockwise yarn being on the surface

of the braid, this is represented in the matrix as a 1. Where there is a blank block in the

braid pattern (where the clockwise braid yarns are on the surface), this is represented in

the matrix as a 0. A regular braid matrix is shown in Figure 6-8. Different colour or types

of yarns can be used in one braid. The braid matrix needs to be manipulated to show the

different colours.

Figure 6-8: A 2/2 regular braid pattern in binary matrix form

6.6.1 Example 1: Applying two different colours to a braid matrix

Figure 6-9 shows an example of using matrices to derive a braid colour effect diagram

using a regular braid binary matrix and two different yarn colours represented by ‘a’ and

‘b’. For the anti-clockwise yarns colour 'a' is used and for the clockwise rotating bobbins

colour 'b' is used. When a 12x12 identity matrix which includes the 'a' is multiplied by the

original binary matrix; then for every position where there is a 1, it will be replaced by the

colour notation 'a'. This indicates that colour 'a' will be in those positions in Figure 6-9a.

For every 0 notation on the matrix needs to assigned colour 'b'. In order to do this, the


141

original matrix needs to be converted so that the 0s become 1s and the 1s become 0s.

This can be achieved by creating what is known in matrices terms as a not matrix where in

the matrix where there are zero value elements these are set to 1, otherwise all other

elements in the matrix are set to zero [111], this is shown in Figure 6-9b. Using this not

matrix, it can be multiplied by an identity matrix which includes colour 'b' to represent

the clockwise bobbins. The resultant matrix shows that where there were 1s in the

original matrix, have been replaced by ‘b's as seen in Figure 6-9c. Both of the

implemented colour matrices can be added together to give the complete colour matrix

of a 12x12 coloured braid topology as seen in Figure 6-9d.

6.6.2 Example 2: Removal of every other braid bobbin in the anti-clockwise

direction

If braid bobbins are removed from the braiding machine, this affects the braid topology.

This can be implemented in the braid matrix, by multiplying by an identity matrix. In the

case of removing an anticlockwise bobbin from the braid pattern, this will translate to the

removal of a column in the matrix, and the removal of a clockwise bobbin will translate to

the removal of a row in the matrix. Both the column and the rows cannot be removed in

one instance; they have to be performed separately.

The 12x12 matrix is Am n, where 'n' represents the number of columns, if k is the number

of bobbins are removed, then the original matrix needs to be multiplied by identity matrix

Im n-k. In this example k=6 and the identity matrix is 12x6. This gives the new matrix Am n-k,

which is 12x6 as shown in Figure 6-10.In order to remove the rows from the 12x6 Am n-k

matrix, it needs to be multiplied by an identity matrix which has m-k (6) number of rows,

Im-k n, this would be a 6x12 matrix. The resultant matrix would be a 6x6 matrix

represented as the algorithm Am-k n-k (Figure 6-10b).Letter a and b represent two different

colours; if the corresponding colours are placed in that manner then this represents the

new braid colour pattern (Figure 6-10c).


142

12 b 0 0 1 1 0 0 1 1 0 0 1 1 a 0 0 0 0 0 0 0 0 0 0 0 0 0 a a 0 0 a a 0 0 a a

11 b 0 1 1 0 0 1 1 0 0 1 1 0 0 a 0 0 0 0 0 0 0 0 0 0 0 a a 0 0 a a 0 0 a a 0

10 b 1 1 0 0 1 1 0 0 1 1 0 0 0 0 a 0 0 0 0 0 0 0 0 0 a a 0 0 a a 0 0 a a 0 0

9 b 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 a 0 0 0 0 0 0 0 0 a 0 0 a a 0 0 a a 0 0 a

8 b 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 a 0 0 0 0 0 0 0 0 0 a a 0 0 a a 0 0 a a

7 b 0 1 1 0 0 1 1 0 0 1 1 0 x 0 0 0 0 0 a 0 0 0 0 0 0 = 0 a a 0 0 a a 0 0 a a 0

6 b 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 a 0 0 0 0 0 a a 0 0 a a 0 0 a a 0 0

(a) 5 b 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 a 0 0 0 0 a 0 0 a a 0 0 a a 0 0 a

4 b 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 a 0 0 0 0 0 a a 0 0 a a 0 0 a a

3 b 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 a 0 0 0 a a 0 0 a a 0 0 a a 0

2 b 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 a 0 a a 0 0 a a 0 0 a a 0 0

1 b 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 a a 0 0 a a 0 0 a a 0 0 a

a a a a a a a a a a a a

1 2 3 4 5 6 7 8 9 10 11 12

Amn x Imn

Bobbin #

Colour

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

0 0 1 1 0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

0 0 1 1 0 0 1 1 0 0 1 1

(b) 0 1 1 0 0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

0 0 1 1 0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0 0 1 1 0

b 0 0 0 0 0 0 0 0 0 0 0 12 b 1 1 0 0 1 1 0 0 1 1 0 0 b b 0 0 b b 0 0 b b 0 0

0 b 0 0 0 0 0 0 0 0 0 0 11 b 1 0 0 1 1 0 0 1 1 0 0 1 b 0 0 b b 0 0 b b 0 0 b

0 0 b 0 0 0 0 0 0 0 0 0 10 b 0 0 1 1 0 0 1 1 0 0 1 1 0 0 b b 0 0 b b 0 0 b b

0 0 0 b 0 0 0 0 0 0 0 0 9 b 0 1 1 0 0 1 1 0 0 1 1 0 0 b b 0 0 b b 0 0 b b 0

0 0 0 0 b 0 0 0 0 0 0 0 8 b 1 1 0 0 1 1 0 0 1 1 0 0 b b 0 0 b b 0 0 b b 0 0

0 0 0 0 0 b 0 0 0 0 0 0 x 7 b 1 0 0 1 1 0 0 1 1 0 0 1 = b 0 0 b b 0 0 b b 0 0 b

0 0 0 0 0 0 b 0 0 0 0 0 6 b 0 0 1 1 0 0 1 1 0 0 1 1 0 0 b b 0 0 b b 0 0 b b

(c) 0 0 0 0 0 0 0 b 0 0 0 0 5 b 0 1 1 0 0 1 1 0 0 1 1 0 0 b b 0 0 b b 0 0 b b 0

0 0 0 0 0 0 0 0 b 0 0 0 4 b 1 1 0 0 1 1 0 0 1 1 0 0 b b 0 0 b b 0 0 b b 0 0

0 0 0 0 0 0 0 0 0 b 0 0 3 b 1 0 0 1 1 0 0 1 1 0 0 1 b 0 0 b b 0 0 b b 0 0 b

0 0 0 0 0 0 0 0 0 0 b 0 2 b 0 0 1 1 0 0 1 1 0 0 1 1 0 0 b b 0 0 b b 0 0 b b

0 0 0 0 0 0 0 0 0 0 0 b 1 b 0 1 1 0 0 1 1 0 0 1 1 0 0 b b 0 0 b b 0 0 b b 0

a a a a a a a a a a a a

1 2 3 4 5 6 7 8 9 10 11 12

Amn x Imn

0 0 a a 0 0 a a 0 0 a a b b 0 0 b b 0 0 b b 0 0 b b a a b b a a b b a a

0 a a 0 0 a a 0 0 a a 0 b 0 0 b b 0 0 b b 0 0 b b a a b b a a b b a a b

a a 0 0 a a 0 0 a a 0 0 0 0 b b 0 0 b b 0 0 b b a a b b a a b b a a b b

a 0 0 a a 0 0 a a 0 0 a 0 b b 0 0 b b 0 0 b b 0 a b b a a b b a a b b a


0 a a 0 0 a a 0 0 a a 0 + b 0 0 b b 0 0 b b 0 0 b = b a a b b a a b b a a b


(d) a 0 0 a a 0 0 a a 0 0 a 0 b b 0 0 b b 0 0 b b 0 a b b a a b b a a b b a


0 a a 0 0 a a 0 0 a a 0 b 0 0 b b 0 0 b b 0 0 b b a a b b a a b b a a b


a 0 0 a a 0 0 a a 0 0 a 0 b b 0 0 b b 0 0 b b 0 a b b a a b b a a b b a

Amn + Imn

Figure 6-9: Creating a braid colour effect using matrices


143

12 b b a a b b a a b b a a 1 0 0 0 0 0 12 b a b a b a

11 b a a b b a a b b a a b 0 0 0 0 0 0 11 b a b a b a

10 a a b b a a b b a a b b 0 1 0 0 0 0 10 a b a b a b

9 a b b a a b b a a b b a 0 0 0 0 0 0 9 a b a b a b


7 b a a b b a a b b a a b x 0 0 0 0 0 0 = 7 b a b a b a

(a) 6 a a b b a a b b a a b b 0 0 0 1 0 0 6 a b a b a b



3 b a a b b a a b b a a b 0 0 0 0 0 0 3 b a b a b a

2 a a b b a a b b a a b b 0 0 0 0 0 1 2 a b a b a b


1 2 3 4 5 6 7 8 9 10 11 12 1 3 5 7 9 11

Am n x Im n-k = Am n-k

12 b a b a b a

11 b a b a b a

10 a b a b a b

0 1 0 0 0 0 0 0 0 0 0 0 9 a b a b a b 11 b a b a b a

0 0 0 1 0 0 0 0 0 0 0 0 8 b a b a b a 9 a b a b a b

0 0 0 0 0 1 0 0 0 0 0 0 x 7 b a b a b a = 7 b a b a b a

(b) 0 0 0 0 0 0 0 1 0 0 0 0 6 a b a b a b 5 a b a b a b

0 0 0 0 0 0 0 0 0 1 0 0 5 a b a b a b 3 b a b a b a

0 0 0 0 0 0 0 0 0 0 0 1 4 b a b a b a 1 a b a b a b

3 b a b a b a

2 a b a b a b 1 3 5 7 9 11

1 a b a b a b

1 3 5 7 9 11

Im-k n x Amn-k = Am-k n-k

(c)

Figure 6-10: The removal of rows and columns in a braid pattern matrix and resultant colour effect diagram

6.6.3 Example 3: Using two different braid yarn colours, alternative

arrangement

Another example is to use two different yarn colours in an alternate arrangement in both

the clockwise and anti-clockwise directions. In a similar manner as previously done, the

colour matrix for the anti-clockwise colour bobbins (matrix columns) is derived as shown

in Figure 6-11a. Then the clockwise bobbin colour matrix (matrix rows) is derived by using

the not matrix as shown in Figure 6-11b. The two colour matrices are added together to

give the overall colour matrix as shown in Figure 6-11c. The different matrices letters are

equivalent to the different yarn colours; therefore the braid colour pattern can be derived

as shown in Figure 6-11d.

b a b a b a b a b a b a

a b a b a b a b a b a b






144

12 b 0 0 1 1 0 0 1 1 0 0 1 1 a 0 0 0 0 0 0 0 0 0 0 0 0 0 a b 0 0 a b 0 0 a b

11 a 0 1 1 0 0 1 1 0 0 1 1 0 0 b 0 0 0 0 0 0 0 0 0 0 0 b a 0 0 b a 0 0 b a 0

10 b 1 1 0 0 1 1 0 0 1 1 0 0 0 0 a 0 0 0 0 0 0 0 0 0 a b 0 0 a b 0 0 a b 0 0

9 a 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 b 0 0 0 0 0 0 0 0 a 0 0 b a 0 0 b a 0 0 b

8 b 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 a 0 0 0 0 0 0 0 0 0 a b 0 0 a b 0 0 a b

7 a 0 1 1 0 0 1 1 0 0 1 1 0 x 0 0 0 0 0 b 0 0 0 0 0 0 = 0 b a 0 0 b a 0 0 b a 0

(a) 6 b 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 a 0 0 0 0 0 a b 0 0 a b 0 0 a b 0 0

5 a 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 b 0 0 0 0 a 0 0 b a 0 0 b a 0 0 b

4 b 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 a 0 0 0 0 0 a b 0 0 a b 0 0 a b

3 a 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 b 0 0 0 b a 0 0 b a 0 0 b a 0

2 b 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 a 0 a b 0 0 a b 0 0 a b 0 0

1 a 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 b a 0 0 b a 0 0 b a 0 0 b


1 2 3 4 5 6 7 8 9 10 11 12

12 b 1 1 0 0 1 1 0 0 1 1 0 0 b 0 0 0 0 0 0 0 0 0 0 0 b b 0 0 b b 0 0 b b 0 0

11 a 1 0 0 1 1 0 0 1 1 0 0 1 0 a 0 0 0 0 0 0 0 0 0 0 a 0 0 a a 0 0 a a 0 0 a

10 b 0 0 1 1 0 0 1 1 0 0 1 1 0 0 b 0 0 0 0 0 0 0 0 0 0 0 b b 0 0 b b 0 0 b b

9 a 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 a 0 0 0 0 0 0 0 0 0 a a 0 0 a a 0 0 a a 0

8 b 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 b 0 0 0 0 0 0 0 b b 0 0 b b 0 0 b b 0 0

7 a 1 0 0 1 1 0 0 1 1 0 0 1 x 0 0 0 0 0 a 0 0 0 0 0 0 = a 0 0 a a 0 0 a a 0 0 a

(b) 6 b 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 b 0 0 0 0 0 0 0 b b 0 0 b b 0 0 b b

5 a 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 a 0 0 0 0 0 a a 0 0 a a a 0 a a 0

4 b 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 b 0 0 0 b b 0 0 b b 0 0 b b 0 0

3 a 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 a 0 0 a 0 0 a a 0 0 a a 0 0 a

2 b 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 b 0 0 0 b b 0 0 b b 0 0 b b

1 a 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 a 0 a a 0 0 a a 0 0 a a 0


1 2 3 4 5 6 7 8 9 10 11 12

0 0 a b 0 0 a b 0 0 a b b b 0 0 b b 0 0 b b 0 0 b b a b b b a b b b a b

0 b a 0 0 b a 0 0 b a 0 a 0 0 a a 0 0 a a 0 0 a a b a a a b a a a b a a

a b 0 0 a b 0 0 a b 0 0 0 0 b b 0 0 b b 0 0 b b a b b b a b b b a b b b

a 0 0 b a 0 0 b a 0 0 b 0 a a 0 0 a a 0 0 a a 0 a a a b a a a b a a a b


0 b a 0 0 b a 0 0 b a 0 + a 0 0 a a 0 0 a a 0 0 a = a b a a a b a a a b a a

(c) a b 0 0 a b 0 0 a b 0 0 0 0 b b 0 0 b b 0 0 b b a b b b a b b b a b b b

a 0 0 b a 0 0 b a 0 0 b 0 a a 0 0 a a a 0 a a 0 a a a b a a a b a a a b


0 b a 0 0 b a 0 0 b a 0 a 0 0 a a 0 0 a a 0 0 a a b a a a b a a a b a a

a b 0 0 a b 0 0 a b 0 0 0 0 b b 0 0 b b 0 0 b b a b b b a b b b a b b b

a 0 0 b a 0 0 b a 0 0 b 0 a a 0 0 a a 0 0 a a 0 a a a b a a a b a a a b

b b a b b b a b b b a b b b a b b b a b b b a b

a b a a a b a a a b a a a b a a a b a a a b a a

a b b b a b b b a b b b a b b b a b b b a b b b

a a a b a a a b a a a b a a a b a a a b a a a b


a b a a a b a a a b a a = a b a a a b a a a b a a

(d) a b b b a b b b a b b b a b b b a b b b a b b b



a b a a a b a a a b a a a b a a a b a a a b a a

a b b b a b b b a b b b a b b b a b b b a b b b


Figure 6-11: The coloured braid pattern equivalent of the braid colour matrix


145

6.7 Topology programming in MATLAB

MatLab stands for Matrix Laboratory and is the ideal option for producing and

manipulating braid matrices. The initial step is to start off with a single repeat, in the

regular braid case this is a 4x4 matrix. This repeats 3 times across and 3 times down.

Colours can be assigned to different yarns. Because MatLab deals solely in numbers and

not letters, in the example the two colours are ‘1’ and ‘2’, where colour 1 is assigned to

clockwise bobbins and colour 2 is assigned to the anticlockwise bobbins. The MatLab

coding for this example is given below and the resultant image/visualisation is shown in

Figure 6-12.

>> % the 2/2 regular braid 4x4 matrix

>> A = [0 0 1 1 ;0 1 1 0 ;1 1 0 0;1 0 0 1]

A =

0 0 1 1

0 1 1 0

1 1 0 0

1 0 0 1

>> % for a complete 12x12 repeat, the basic 4x4 matrix repeats 3 times across and 3 times

down

>> B=[A,A,A;A,A,A;A,A,A]

B =

0 0 1 1 0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

0 0 1 1 0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

0 0 1 1 0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

>> % to assign colour '1' to the regular braid matrix, it needs to be multiplied by a

diagonal matrix of one


146

>> eye(12)

ans =

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 1

>> B*eye(12)

ans =

0 0 1 1 0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

0 0 1 1 0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

0 0 1 1 0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

>> % the ‘not’ of the regular matrix can be produced

>> not(B)

ans =

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

0 0 1 1 0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

0 0 1 1 0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1 1 0 0 1

0 0 1 1 0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0 0 1 1 0


147

>> % to assign colour '2' to the not regular matrix, multiply eye(12) by 2 and multiply by

not(B)

>> eye(12)*2*not(B)

ans =

2 2 0 0 2 2 0 0 2 2 0 0

2 0 0 2 2 0 0 2 2 0 0 2

0 0 2 2 0 0 2 2 0 0 2 2

0 2 2 0 0 2 2 0 0 2 2 0

2 2 0 0 2 2 0 0 2 2 0 0

2 0 0 2 2 0 0 2 2 0 0 2

0 0 2 2 0 0 2 2 0 0 2 2

0 2 2 0 0 2 2 0 0 2 2 0

2 2 0 0 2 2 0 0 2 2 0 0

2 0 0 2 2 0 0 2 2 0 0 2

0 0 2 2 0 0 2 2 0 0 2 2

0 2 2 0 0 2 2 0 0 2 2 0

>> % the two colour matrices can be added to give the final colour matrix

>> C= B*eye(12)+eye(12)*2*not(B)

C =

2 2 1 1 2 2 1 1 2 2 1 1

2 1 1 2 2 1 1 2 2 1 1 2

1 1 2 2 1 1 2 2 1 1 2 2

1 2 2 1 1 2 2 1 1 2 2 1

2 2 1 1 2 2 1 1 2 2 1 1

2 1 1 2 2 1 1 2 2 1 1 2

1 1 2 2 1 1 2 2 1 1 2 2

1 2 2 1 1 2 2 1 1 2 2 1

2 2 1 1 2 2 1 1 2 2 1 1

2 1 1 2 2 1 1 2 2 1 1 2

1 1 2 2 1 1 2 2 1 1 2 2

1 2 2 1 1 2 2 1 1 2 2 1

>> % produce the image of the matrix can be produced in gray scale format

>> imagesc(C);

>> colormap(gray)


148

Figure 6-12: Regular braid pattern simulation in MatLab

The image of the matrix is similar to the braid pattern diagrams, which proves that matrix

manipulation is MatLab can produce the required results. Furthermore, in MatLab it is

possible to ‘kill’ specifically selected rows and columns in the matrix to imitate the

removal of bobbins from the braiding machine and therefore the yarn interlacements.

The colour matrix is copied under a new name prior to manipulation so that the original

matrices remain the same and can be used again. The selected columns are initially

removed and then the selected rows. From the resulting matrix image, it shows that if

every other bobbin is removed in the clockwise and anticlockwise directions i.e. every

other row and column are removed from the matrix; this produces a diamond braid

pattern, which is shown in Figure 6-13. This is what has previously been predicted during

manual braid pattern derivations.


149

>> % assign colour matrix C to new matrix D prior to manipulation, so matrix C does not

get re-written

>> D=C

D =

2 2 1 1 2 2 1 1 2 2 1 1

2 1 1 2 2 1 1 2 2 1 1 2

1 1 2 2 1 1 2 2 1 1 2 2

1 2 2 1 1 2 2 1 1 2 2 1

2 2 1 1 2 2 1 1 2 2 1 1

2 1 1 2 2 1 1 2 2 1 1 2

1 1 2 2 1 1 2 2 1 1 2 2

1 2 2 1 1 2 2 1 1 2 2 1

2 2 1 1 2 2 1 1 2 2 1 1

2 1 1 2 2 1 1 2 2 1 1 2

1 1 2 2 1 1 2 2 1 1 2 2

1 2 2 1 1 2 2 1 1 2 2 1

>> % removing every other column starting from 2 to 12

>> D(:,2:2:12)=[]

D =

2 1 2 1 2 1

2 1 2 1 2 1

1 2 1 2 1 2

1 2 1 2 1 2

2 1 2 1 2 1

2 1 2 1 2 1

1 2 1 2 1 2

1 2 1 2 1 2

2 1 2 1 2 1

2 1 2 1 2 1

1 2 1 2 1 2

1 2 1 2 1 2

>> % before removing rows, assign the new manipulated matrix D to matrix E

>> E=D;

>> % remove every other column starting from 2 to 12

>> E(2:2:12,:)=[]


150

E =

2 1 2 1 2 1

1 2 1 2 1 2

2 1 2 1 2 1

1 2 1 2 1 2

2 1 2 1 2 1

1 2 1 2 1 2

>> % view image, and view as gray scale

>> imagesc(E)

>> colormap(gray)

Figure 6-13: Diamond braid pattern simulation in MatLab

6.8 Theoretical topology simulation vs. actual samples

It is necessary to compare the theoretical topology simulation with actual samples in

order to verify the braid pattern. Figure 6-14 shows theoretical representations of the

braid pattern on a constant mandrel diameter using a varying number of braid yarns. The

numbers of bobbins are 4, 8, 12, 16, 20 and 24. Actual samples were produced using glass

fibre as the yarn moving in the clockwise direction and carbon fibre representing braid

bobbins moving in the anti-clockwise direction. These different tows have been used so

the yarn patterns and interlacements can easily be visualised.


151

Figure 6-14. The interlacement patterns of various numbers of braid bobbins

In Figure 6-15 the theoretical braid patterns have been placed upon the actual samples.

This is to show whether the theoretical and practical work both coincide with one another.

As can be seen, both the patterns match each other.

6.9 Summary

A system for the analysis and prediction of braid topology and colour effects for biaxial

braids produced on circular braiding machines has been developed. This system enables

any braid topology to be produced with regard to bobbin placement and the use of

different types and colours of yarns. It is a time saving method of visualising the

appearance of the braid material without undergoing trial-and-error processes. This

system has been applied to circular braiding machines with a 1:2 horngear to yarn carrier

ratio; however the basics of this system can also be applied to any other braiding machine.

The methods developed are a manual analysis, which is an option for analysing the braid

topology of material produced on small braiding machines.


152

A mathematical model for predicting braid topology has been developed. This model

utilises matrix manipulation and has proved successful in predicting 1/1 diamond and 2/2

regular braid topologies by using the MatLab software. This mathemcatical model makes

it is feasible to predict the braid topology for braids produced on larger braiding machines.

The development of a BraidCAD software is an ideal option for simulating virtual braid

patterns. The BraidCAD software will incorporate the methods of analysing the braid

topology alongside colour effects. There are many additional factors which determine the

braid appearance, such as yarn diameter, braid angle, and braid spacing. The BraidCAD

software will incorporate these factors into the simulation to give the best visualisation.

This research analyses the basics of braid topology, but gives a wide scope for future

research and applications.


153

Theoretical Braid Pattern Actual Braided Samples

4 Braid Yarns

8 Braid Yarns

12 Braid Yarns


154

Theoretical Braid Pattern Actual Braided Samples

16 Braid Yarns

20 Braid Yarns

24 Braid Yarns

Figure 6-15: Theoretical braid pattern vs. actual braided samples

Chapter 7 Conclusions and Recommendations

155

Chapter Seven:

7 Conclusions and Recommendations

7.1 Summary of findings and achievements

The research aimed at the development of braided cords for use in high performance

flexible composite applications. Hyper-elastic braided cords for use in morphing wing

structures have been developed. The maximum strain of these cords can be varied by

varying the braid angle. A model has been developed to predict the load-elongation

behaviour of these cords. Alongside these hyper-extensible cords, virtually inextensible

cords for reinforcements have also been developed specifically for use in timing belts.

These cords have been developed with varying braid cover factors with different numbers

of braid yarns. By selecting certain braid yarns, this alters the braid pattern. A system to

predict these braid patterns/topologies has been developed. A mathematical model has

been created to form not just braid patterns but to also incorporate braid colour patterns.

7.1.1 Development of hyper-elastic braided cords for morphing wing skins

Extensible cords have been developed using biaxial and triaxial braid structures. And

elastomeric yarn (elastane) was used as a core yarn for biaxial braids and as warp yarns


156

for triaxial braids. Kevlar and glass fibre were used as braid yarns to produce both biaxial

and triaxial braided cords. Both are high performance yarns, however when braiding with

glass it was found to be more difficult than with Kevlar. During braiding, the yarns are at

an angle to each other, if the angle is too steep then the glass fibre yarns slice each other.

Kevlar yarns also have their drawbacks; the filaments are prone to fibrillation, but

ultimately exhibit higher strength than the glass fibre yarn which was used in this

research. Due to the delicacy and brittleness of the glass fibre yarn, it is not a suitable

option to use for braiding high-performance, high-strength elastomeric cords.

The strength of a Kevlar and glass fibre yarns were compared to their cord counterparts.

Braiding these high performance yarns results in a loss in their strength. This is due to the

contact points between the yarn and several guide rollers and guide eyes. During

deployment of the morphing wing structures, they will not be extended to failure so this

is not of primary concern. The load-extension behaviour of biaxial and triaxial cords were

analysed. Triaxial yarns can achieve larger extensions in comparison to biaxial yarns.

7.1.2 Elastomeric yarn tension control

The braid angle in elastomeric cords is controlled by the pre-tension of elastane prior to

braiding. Pre-tensioning of the elastane yarn has been investigated using tensioning discs,

an ultra feed tension control device and a set of nip rollers. Initially the tensioning discs

employed, once the braid production was streamlined gave a consistent tension, however

if the tensioning plates were adjusted, then again the braid would need to be streamlined,

which is a waste of time and not ideal. The ultra feed device only houses one yarn, so to

use multiple yarns (in this research 4), then a set-up of 4 feed devices would have been

required and would have been costly. A nip-roller set-up was developed, similar to the

take-up device. The speed of the nip rollers can be precisely controlled to alter the

elastane feed into the braiding process. The elastane feed and the braid take-up

determines the pre-tension of the elastane and ultimately the extension of the elastane.

The relaxation of the elastane after braiding determines the braid angle.


157

7.1.3 Development of elastomeric cords with varying knee points

The knee strain is the strain up to the position of the jamming of the braid yarns. The

knee strain varies depending on the braid angle. The braid angle varies depending on the

amount of elastane pre-tension. Four different samples with different braid angles have

been produced. Their initial braid angles, knee braid angle and maximum strain have

been analysed. Although their initial braid angles are different, the knee angles are

similar. Cords with a higher initial braid angle have greater strain limits than those with

lower initial braid angles.

7.1.4 Development of morphing skins

An elastomeric skin structure was produced using the braided cords. Mesh structures

were produced and coated with silicone. During manufacturing of the mesh fabric it was

difficult to control the cord tension during weaving. When testing the mesh fabric

samples, the samples failed due to the failure of a single cord. This mesh coated silicone is

not the ideal fabric of a morphing skin. A new fabric structure has been developed, which

consists of two layers of cords in the 0o and 90o directions. The two layers are bound

together using a low modulus elastomeric wrap yarn. This bi-direction layered fabric is

laminated with a polyurethane film. The number of layers can be increased to create a

thicker skin. However the binding of the layers is carried out by hand stitching, which is

time consuming.

7.1.5 Behaviour and geometrical modelling of hyper-elastic cords

A computational model for predicting the load-strain behaviour of hyper-elastic cords has

been developed. The load-strain behaviour of four braided cords has been computed,

these models are based on braids with four different braid angles. These curves compare

favourably with the experimental curves.

Braided cords have been designed on AutoDesk Investor software to simulate braids with

different braid angles. For hyper elastic cords, this does not imitate the exact geometry,


158

due to the complex nature of extension and contraction of the elastane and braid

geometry during and after braiding. The restriction of the braid yarns on the elastane

core required further research. However the same equations can be used to model rigid

braids as there is no elastic behaviour. These geometrical models can easily be imported

in ABAQUS finite element analysis (FEA) software.

7.1.6 Development of rigid braided cords and structure analysis

The number of braid yarns used may affect the level of cover. The cover factor is

important especially in applications which require 100% cover, but is desired to use the

minimum number of braid yarns to save time and money. In the development of hybrid

carbon and glass fibre cords for rigid cords, the level of cover factor has been predicted

and actual cover has been calculated. There is a slight variation with the predicted cover

factor and actual cover factor, where the actual cover is less than that predicted. This

could be due to the fact that the braid yarns are guided over several tension/guide rollers

and guide eyelets, this causes the yarn to gather and therefore reducing its effective

width.

7.1.7 Creating a braid topology system

A thorough analysis of the braid topology with varying number of braid yarns has been

conducted. This research proposes a method to generate braid patterns depending on

any selection of braid carriers on the braiding machine. Physical samples been created to

confirm the predicted braid patterns. The method can be applied to circular braiding

machines of any size. The initial model has been developed for a 1:2 ratio horngear to

braid carrier machine, but the same concept can be applied to any other ratio circular

braiding machine. The model works off the braid pattern generated when using a full

machine of bobbins. Various braid colour patterns can be created, similar to techniques

used for producing weave colour patterns.


159

The braid patterns were initially created manually but then a matrix model was

developed. By using basic matrix manipulations, braid patterns as well as braid colour

patterns can be derived. The mathematical matrices model to predict the braid topology

has been verified using the MatLab software. Basic coding in the MatLab software

produces the new braid patterns. Currently the regular and diamond structures have

been produced but MatLab coding has allowed simplification in generating of any braid

pattern.

7.2 Recommendations for further research

Elastomeric braided cords – In previous studies Kevlar and Vectran were suggested as

candidates for morphing wing skins, however Vectran was unavailable for this study. For

further research it would favourable to compare the performance of Vectran braided

elastomeric cords, with Kevlar braided cords.

Fabrication of morphing skin material – A structure for morphing skins has been proposed

in this study, however further development of the skin is required. This may involve

varying the number of cord layers in the cross ply fabric. Also following on from this, skins

of various deployment is another area of study.

The cross ply layers in this study have been stitched together with an elastomeric wrap

yarn. This has been carried out by hand. This however is a time consuming method,

ideally in the future an automated stitching process would be used. In addition the laying

of the cord requires a precision tension control mechanism so all the cords are layered

with the same tensions.

Modelling braided cords – In past studies, only equations for diamond and regular braid

paths have been derived. As discussed in the braid topology chapter, braid patterns vary

depending on the arrangement of yarn bobbins on the braiding machine. Equations need

to be generated for the mapping of other interlacement patterns apart from diamond and

regular structures.


160

The geometrical models which are produced in AutoDesk Inventor can be imported into

ABAQUS to create a FEA model. Development of FEA models is the next step for in

modelling cord behaviour.

Analysis of rigid cords – Carbon core cords with different numbers of glass fibre braid

yarns have been produced and the structures have been analysed. The development of

these cords was aimed at improving the pull-out strength of the carbon core from rubber

timing belts. Future work will involve conducting these pull out tests to assess the effect

of the number of braid yarns and braid topology on the pull-out performance.

The development of a BraidCAD software – There are several CAD programs which

generate weave patterns, however there is currently no such thing for braiding. A braid

topology mapping system has been developed in this research. Further to this a BraidCAD

software can be developed to automatically produce illustrations of the braid patterns.

This research concentrates on circular braid topology however it would be beneficial to

develop a generic topology model for 3-dimensional braid structures as well.

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