Conceptual Design of a Polymer Based Joint between Tether and Foundation in Tidal Energy Power Plant: Concept generation and development of a polymer based joint

Conceptual Design of a Polymer Based Joint between Tether and Foundation in Tidal Energy Power Plant

Concept generation and development of a polymer based joint

Konceptuell design av polymerbaserad joint mellan tether och fundament i tidvattenkraftverk

Konceptgenerering och utveckling av polymerbaserad joint Jonas Elisson

Faculty of Health, Science and Technology

Degree Project for Master of Science in Engineering, Mechanical Engineering 30 hp

Supervisor: Mikael Grehk Examiner: Jens Bergström 2020-07-01

Abstract

This master thesis treats the development of a new component in a tidal energy power plant. The technology that the component should be used in extracts energy from tidal an low velocity currents. This is done by that a turbine is placed on a kite which is pushed forward in the water due to the lifting force acting on the wing.

A tether connects the kite with a bottom joint that is placed on a foundation at the seabed. The bottom joint used today is heavy and expensive, which was the main reason to that this thesis was initiated. In this work, the possibility of using a polymer based design for the connection between the tether and foundation was investigated. The optimal outcome of the project was that the polymer solution should provide a spring function to the power plant.

A lot of conventional product development methods have been used in the project.

The project was divided into five parts: planning, product specification, concept generation, concept choice and conceptual design.

In order to understand what was required of the solution in terms of the spring function, a model that aimed to represent what effect a spring function would have on the power plant was developed. According to the model, a spring function in the tether direction could increase the velocity of the kite in its trajectory. The model is based on some simplifications which is assessed to need further investigation. The spring function was translated to that the component should be able to elongate as a response to the force acting in the tether direction.

In the concept choice phase it was chosen to proceed with a design similar to that of a bend stiffener. It was decided that a spring function was not required of the component, though desirable. A material selection was performed and the most optimal material for a single part that should be able withstand the tension, allow rotation, and provide a spring function was concluded to be TPU(ester, aromatic, Shore 50D). In the attempt to understand what was needed to be considered if the spring function should be solved by a material response in a polymer component, relevant theory was collected. A numerical analysis in Abaqus was performed which indicated that such a solution was unreasonable. It was then decided to proceed with the development of a bend stiffener, where the tether should be connected di- rectly to the foundation.

The thesis finally concludes with a conceptual design of a bend stiffener. The most

suitable material for a bend stiffener was concluded to be TPU(ether, aliphatic,

Shore 60D). The initial dimensions were determined by the maximum angle and

tension combination that the tether would be exposed to. A static analysis was

performed in Abaqus to illustrate the function of the product. The analysis indicated

that a bend stiffener could provide the required function. However, the stress in the

component became high, which indicated that the bend stiffener material might fail

due to the applied load. In order to fully evaluate this, it was concluded that a more

accurate material model was required.

Sammanfattning

Det här examensarbetet behandlar framtagandet av en ny komponent i ett tid- vattenkraftverk. Tekniken där komponenten ska användas utvinner energi från tidvatten- och låghastighetsströmmar. Detta görs genom att en turbin är plac- erad på en drake som trycks framåt i vattnet av lyftkraften som verkar på vingen.

En tether kopplar samman draken och en "bottom joint" som är placerad på ett fundament på havsbotten. Dagens lösning för denna bottom joint är tung och dyr, vilket var den främsta anledningen till att detta examensarbetet initierades.

I detta examensarbete utreds möjligheten att använda en polymerbaserad lösning i kopplingen mellan fundamentet i tethern. Det optimala utfallet av projektet var att den polymerbaserade lösningen skulle åstadkomma en fjäderfunktion till tidvat- tenkraftverket.

Många konventionella produktutvecklingsmetoder har använts i projektet. Projek- tet delades in i de fem delarna: planering, produktspecifikation, konceptgenerering, konceptval och konceptdesign.

För att förstå vad som krävdes av lösningen vad gäller fjäderfunktionen skapades en modell som syftade till att beskriva fjäderfunktionens effekt på kraftverket. En- ligt modellen skulle en fjäderfunktion i tetherns riktning kunna öka hastigheten på draken. Modellen är baserad på vissa antaganden som bedöms behöva vidare utred- ning. Fjäderfunktionen översattes till att lösningen skulle förlängas som ett svar på kraften som verkar i tetherns riktning.

I konceptvalsfasen valdes ett koncept som var inspirerat av böjstyvare. Det beslu- tades att det var önskvärt med en fjäderfunktion, men det var inte ett krav. Ett materialval utfördes med målet att tillåta rotation, klara maximal last och kunna förlängas. Materialvalet resulterade i att TPU(ester, aromatic, Shore 50D) var det bästa materialet för en sådan produkt. Relevant teori samlades in för att få en förståelse för vad som var nödvändigt i fallet att fjäderfunktionen skulle lösas genom förlängning av en polymerkomponent. En analys i Abaqus gjordes vilken indikerade att lösningen var orimlig. Det valdes då att gå vidare med att utveckla en konven- tionell böjstyvare, där tethern var tänkt att kopplas direkt till fundamentet.

Slutligen presenteras en konceptuell design av en böjstyvare. Det bästa materialet

för denna lösningen bedömdes vara TPU(ether, aliphatic, Shore 60D). De initiala

dimensionerna bestämdes av den mest kritiska kombinationen av kraft och vinkel

som tethern skulle vara utsatt för. En statisk analys genomfördes i Abaqus vilken in-

dikerade att en böjstyvare skulle kunna åstadkomma den krävda funktionen. Vidare

konstaterades det att spänningarna i komponenten blev höga, vilket indikerade att

materialet eventuellt skulle gå sönder på grund av den pålagda kraften. För kunna

göra en fullständig utredning av detta drogs slutsatsen att en bättre materialmodell

behöver skapas.

Acknowledgements

I would like to thank Christian Norinder and Caroline Jonsson from Minesto who have guided me through the process and for providing useful information regarding their product and technology. I would also like to send my gratitude to my supervisor Mikael Grehk at Karlstad University, who has provided valuable thoughts and inputs regarding the methodology used in the project.

Jonas Elisson, 2020-06-02

Contents

List of Figures xiii

List of Tables xv

1 Introduction 1

1.1 Background . . . . 1

1.2 Problem Description . . . . 2

1.3 Purpose of the Study . . . . 2

1.4 Aim . . . . 2

1.5 Thesis Initiative . . . . 3

1.6 Delimitations . . . . 3

2 Pre Study 5 2.1 Technical Review . . . . 5

2.1.1 Kite Trajectory . . . . 5

2.1.2 Energy Generation . . . . 6

2.1.3 Forces Acting on the Kite . . . . 6

2.1.4 Tether Tension . . . . 7

2.1.5 Tether Characteristics . . . . 7

2.1.6 Solution of Today . . . . 7

2.1.7 Cable Management . . . . 8

2.2 Market Analysis . . . . 9

2.2.1 Competitor Analysis . . . . 9

2.2.2 Patent Search . . . 10

2.3 Literature Study . . . 11

2.3.1 Environment 100 m Below Water Surface . . . 11

2.3.2 Classification of Polymers . . . 11

2.3.3 Viscoelasticity . . . 12

2.3.4 Influence of Hydrostatic Pressure . . . 12

2.3.5 Large Strain Theory . . . 12

2.3.6 Polymer Degradation . . . 13

2.3.7 Effects of Strain Rate and Temperature . . . 14

2.3.8 Fatigue in Polymers . . . 14

2.3.8.1 The Role of Self Heating . . . 14

2.3.9 Creep . . . 14

2.3.10 Spring Function as a Material Response . . . 15

Contents

3 Theory 17

3.1 Beam Theory for Beams with Low Stiffness . . . 17

3.2 Bend Stiffeners . . . 17

3.2.1 Thermoplastic Polyurethane Elastomers . . . 18

3.2.1.1 Hydrolysis . . . 18

3.2.2 Manufacturing of Bend Stiffeners . . . 19

3.2.3 Optimized Dimensions of Bend Stiffener . . . 19

3.2.4 Design Considerations for Bend Stiffeners . . . 23

4 Methods 25 4.1 Planning . . . 25

4.1.1 Project Plan . . . 25

4.2 Product Specification . . . 26

4.2.1 Pre Study . . . 26

4.2.1.1 Technical Review . . . 26

4.2.1.2 Market Analysis . . . 26

4.2.1.3 Literature Study . . . 26

4.2.2 Delimitations . . . 27

4.2.3 Stakeholder Analysis . . . 27

4.2.4 FMEA . . . 27

4.2.5 Product Criteria . . . 27

4.2.5.1 Spring Function Model . . . 28

4.2.6 QFD . . . 29

4.3 Concept Generation . . . 30

4.4 Concept Choice . . . 30

4.4.1 Concept Evaluation . . . 30

4.4.2 Concept Development . . . 31

4.4.2.1 Material Selection Elongating Bend Stiffener . . . 32

4.4.3 Concept Validation . . . 33

4.5 Conceptual Design Bend Stiffener . . . 33

4.5.1 Material Selection . . . 33

4.5.2 Initial Dimensions . . . 34

4.5.3 3D-model . . . 35

4.5.4 Numerical Analysis . . . 35

5 Results 37 5.1 Product Specification . . . 37

5.1.1 Theoretical Model of Spring Function . . . 37

5.1.2 Product Criteria . . . 38

5.2 Concept Generation . . . 38

5.2.0.1 Full Bend+ Spring . . . 40

5.2.0.2 Beta Bend+ Spring . . . 41

5.2.0.3 Elongating Bend Stiffener . . . 41

5.3 Concept Choice . . . 43

5.3.1 Concept Evaluation . . . 43

5.3.2 Concept Development Elongating bend stiffener . . . 43

5.4 Conceptual Design Bend Stiffener . . . 44

Contents

5.4.1 Product Layout . . . 44

5.4.2 Supporting Functions . . . 44

5.4.3 Description of Concept . . . 44

5.4.4 Material Selection . . . 45

5.4.5 Manufacturing . . . 47

5.4.6 Initial Dimensions . . . 47

5.4.7 Numerical Analysis . . . 47

6 Analysis 51 6.1 Limitations . . . 51

6.2 Discussion . . . 52

6.2.1 Spring Function . . . 52

6.2.2 Spring Function and Joint in Same Part . . . 52

6.2.3 Final Concept . . . 54

7 Conclusion 57 8 Future Work 59 8.1 Spring Model . . . 59

8.2 Final Concept . . . 59

A Modelling in Abaqus I

B Tether bending characteristics III

C Stakeholder analysis V

D QFD VII

E FMEA product IX

F Script spring function XIII

G Morphological matrix XXI

H Development of concept "elongating bend stiffener" XXIII

H.1 Material selection for elongating bend stiffener . . . XXVIII

H.2 Initial dimensions elongating bend stiffener . . . XXIX

H.3 FEM- analysis for the elongating bend stiffener . . . XXXI

I Initial dimensions bend stiffener calculations XXXV

Contents

List of Figures

1.1 Component declaration of the upper part of the power plant. . . . 1

1.2 Schematic illustration of the component that the project aims to de- velop. . . . . 3

2.1 Illustration of trajectory. Drawn with inspiration from Dadd et al. . . 5

2.2 Tether tension as a function of time in the eight-shaped trajectory . . 7

2.3 Visualization of universal joint . . . . 8

3.1 A schematic illustration of a bend stiffener. . . 18

3.2 Dimension declaration for a bend stiffner. Created with inspiration from Tanaka et al. . . . 20

3.3 Illustration of parameters used by Drobyshevski. . . . 21

5.1 The kite’s absolute velocity without a spring (left) and with a spring (right), according to the model. . . 37

5.2 Functional structure diagram. . . 39

5.3 Morphological matrix combining subsolutions into complete product solutions. . . . 39

5.4 Simple sketch of concept "full bend+ spring". . . 41

5.5 Simple sketch of concept "beta bend+ spring". . . 41

5.6 Simple sketch of "Elongating bend stiffener". . . 42

5.7 Preliminary concept layout of the bend stiffener. The figure shows the bend stiffener with the tether passing through it. . . 44

5.8 Material selection chart for bend stiffener material . . . 46

5.9 The stress in the component when maximum loading case is applied. 48 5.10 The strain when maximum loading case is applied. . . . 48

5.11 The stress at the step-time when the stresses equals compressive strength. . . 49

5.12 The strain at the step time when the stress in the component equals the compressive strength. . . 49

5.13 The step-time when the stress in the component reaches the fatigue

strength of the material. . . 50

D.1 QFD . . . VII

G.1 Polygons creating solutions . . . XXI

H.1 Preliminary concept layout . . . XXIII

List of Figures

H.2 Criteria translation for the concept . . . XXIV

H.3 Illustration of angle that should be maximized. Simplified case. . . . XXV

H.4 Material chart for material selection . . . XXVIII

H.5 Dimension illustration for elongating bend stiffener . . . XXX

H.6 The stress distribution for the elongating bend stiffener. . . XXXII

H.7 The strains for the elongating bend stiffener. . . XXXII

List of Tables

2.1 Ocean data from Folgers deep(depth 96.1 m) in Canada . . . 11 3.1 Critical angle pairs from case which the ratios presented above were

determined . . . 20 3.2 Optimized dimensions responding to the critical angle pairs presented

above. From report by Tanaka et al . . . 21 4.1 Olsson matrix . . . 27 4.2 Input values to spring model . . . 28 4.3 Elimination matrix used to determine which concepts that should be

eliminated or proceeded . . . 31 5.1 Product criteria . . . 38 5.2 Elimination matrix . . . 43 5.3 Motivation to why the final concept was made with respect to product

criteria . . . 45 5.4 Relevant mechanical properties of TPU(ether, aliphatic, Shore 60D) . 46 5.5 Input and resulting dimensions for bend stiffeners for case 1: R

=2

m, case 2: R

= 4 m and case 3: R

=6 m . . . 47

C.1 Stakeholder analysis . . . . V

H.1 Material properties used as material parameters in Abaqus . . . XXIX

H.2 Dimensions for elongating bend stiffener . . . XXXI

List of Tables

1

Introduction

This chapter gives an introduction to the project. The background, problem description and the delimitations are presented.

1.1 Background

This study aims to develop a component in a power plant used to extract energy from tidal and low-velocity ocean currents. The purpose of the power plant is to generate renewable energy from the ocean. The power plant uses a technology where a turbine is placed on a kite which, when the current goes over the wing, is pushed forward in the water by the lifting force. The result of this is that the kite obtains a velocity many times that of the current. The technology enables a large operative area where it is possible to cost effectively extract energy, since it does not require high velocity currents. An illustration of the power plant is presented in Figure 1.1.

Figure 1.1: Component declaration of the upper part of the power plant [1].

A tether is responsible for keeping the kite to its trajectory as well as protecting

the wires and control cables between the kite and the foundation. The tether is

connected to the seabed foundation via a bottom joint which allows the tether to

move in a specified range of angles that the trajectory of the kite requires.

1. Introduction

1.2 Problem Description

The bottom joint that is used today mainly consists of metal parts, which results in a heavy construction and corrosion problems. This puts high demands on the used materials, causing the solution to become expensive. The solution does not have a good way of handling the cables which causes chafing and fatigue of the cables. The current solution also results in high fatigue loads in the system.

1.3 Purpose of the Study

To solve the problem explained above, the purpose of this study is to improve the connection between the tether and the foundation. A solution that does not corrode, contains fewer parts, is less expensive and can lower the fatigue loads is investigated.

Another purpose of the study is to investigate the influence of introducing a spring function to the power plant. One hypothesis of introducing a spring function is, besides lowering the fatigue loads, that it could potentially increase the energy pro- duction of the power plant. Another hypothesis is that by accumulating energy in the spring, the difference between the maximum and minimum velocity of the kite in its trajectory could be reduced.

1.4 Aim

The aim of the thesis is to provide a conceptual design of a polymer-based solution for the connection between the tether and the foundation.

Also, the aim is to provide a theoretical model for a spring function’s influence on

the power plant. Furthermore, to investigate the possibility to integrate a spring

function in the conceptual design. The optimal outcome is that the two functions,

joint and spring function, is catered for by one component. If the two functions can

not be catered for by one component, a solution not including a spring function is

accepted. A principal image of the component that this project aims to deliver is

presented in Figure 1.2.

1. Introduction

Figure 1.2: Schematic illustration of the component that the project aims to develop.

The key questions that this project aims to answer are:

• Which polymer based concept is the best candidate to fulfill the requirements of the product?

• What effects does a spring function have on the energy output of the power plant?

• Is it possible to provide a spring and joint function in the same component?

1.5 Thesis Initiative

The project is an initiative by Minesto AB - the company that owns the patent for this technology.

1.6 Delimitations

• The thesis does not propose any new solutions for the tether or the foundation.

These parameters are viewed as fixed.

• No physical models are created or tested.

• The shape of the kite-trajectory is assumed to be the same as today.

• The tether is assumed to be infinitely stiff in tether direction, i.e no energy accumulation/energy losses occurs in the tether.

• No dynamic analyzes are performed in the project.

• The proposed design does not consider drag.

• Influence from animal life on the construction is not considered.

• Installation/detachment is not considered.

• Transportation of the product is not considered. Minesto already manufactur- ers wings that are larger than normal containers.

• No total cost estimates of the product are performed.

1. Introduction

2

Pre Study

In this chapter, the technical review, the market analysis and the literature study is presented. The technical review was used in order to create an accurate product specification. The market analysis served as a source of inspiration as well as to collect information about existing patents. In the literature study, the theory that was assessed necessary to understand the problems and mechanisms is introduced.

2.1 Technical Review

The technical review aims to give an understanding of how the product works. An overview of the main principles of the power plant is presented. The focus is on the bottom joint since that is what this thesis aims to find a new solution for.

2.1.1 Kite Trajectory

The movement of the kite can, from the bottom joint’s perspective, be defined by the angle α between the foundation and the tether, and the angle β according to Figure 2.1. The kite travels in the direction of the arrows i.e a center- down trajectory.

Figure 2.1: Illustration of trajectory. Drawn with inspiration from Dadd et al [2].

The eight trajectory that a kite with fixed tether length flies in can according to

2. Pre Study

Dadd et al [2] be defined as comprising two small circle sweeps at the ends and two large circle sweeps connecting the small circular ends. They further explain that the two great circle sweeps lays on planes that intersects with the origin. The tether can be expressed as a vector defined by the angles β and α according to Equation 2.1.

r = [cos α cos β, cos α sin β, sin α] (2.1) In their article, which deals with kites flying in air, they define the wind as a vector according to Equation 2.2.

v = [1, 0, 0] (2.2)

2.1.2 Energy Generation

The power generated from a turbine can be expressed according to Equation 2.3.

P = 1

2 ρ A U

γ (2.3)

Where ρ is the water density, A is the area swept by the turbine, U the velocity of the fluid and γ is an efficiency coefficient [3]. U is in the case of a turbine on a flying kite the relative velocity between the kite and the medium that it flies in.

2.1.3 Forces Acting on the Kite

There are four different forces acting on a flying kite: lift, weight, drag and thrust.

Lift acts perpendicular to the motion. Drag acts in the direction opposed to the motion. Thrust is the force that acts in the direction of motion. Minesto states that there are two more forces, inertia and buoyancy, acting on the kite. However the weight, inertia, and buoyancy forces were neglected in this project due to their relative small size.

Assuming that the weight, inertia and buoyancy forces can be neglected, and that an underwater kite obeys the same laws as a kite in air, the tension in the tether from the drag and the lift force acting on the wing can according to Dadd et al [2]

be expressed as in Equation 2.4.

F = √

D

+ L

(2.4)

They further explain that the drag D

and lift L

that act on the wing can be expressed according to Equations 2.5 and 2.6, respectively.

D

= 1

2 ρA

C

U

(2.5)

L

= 1

2 ρ A

C

U

(2.6)

Where A

is the projected kite area (m

), ρ is the density of the medium that the

kite flies in, U is the relative velocity between the current and the kite and C

and

2. Pre Study

C

is the drag and lift coefficient of the wing, respectively [2].

The forces acting on the kite are led via a top joint to the tether. The tether is connected to the foundation with a bottom joint. At the connection at the bottom, the cables pass through a flange and the force from the tether is led via the flange down to the bottom joint. Finally the force is led into the foundation [4].

2.1.4 Tether Tension

The tether experiences two force cycles during one eight-shaped trajectory. One cycle is defined as the period between two maxima. The simulated tension char- acteristics that the tether experience is shown in Figure 2.2, where the tension is plotted as a function of time at a constant current velocity.

Figure 2.2: Tether tension as a function of time in the eight-shaped trajectory [4].

From Figure 2.2 it can be seen that the frequency with which the load oscillates is approximately f= 0.36 Hz. The relation between the maximum and minimum force is approximately F

/F

=0.68. The maximum tether force is observed at the lowest y-position, and the minimum force at the highest y-position. The kite operates approximately 6 hours at a time, and then switch side. The switch of side means that the kite moves to the negative z-axis, according to Figure 2.1.

2.1.5 Tether Characteristics

The diameter of the tether used in this project was assumed to be 232 mm, from a discussion held with Minesto. Hence, the second area moment of inertia for the tether is 0.00227532 m

.

2.1.6 Solution of Today

The universal joint that is used today to connect the tether and foundation is ar-

ticulated in two axes, which allows the kite to travel in the trajectory [5]. The

structural elements of the system is made of metal components [6]. An illustration

of the universal joint is presented in Figure 2.3. The lower axis allows α- rotation

2. Pre Study

and the upper axis allows β-rotation, where α and β are defined as in Figure 2.1.

The lower axis also allows the kite to switch side when the tidal changes direction.

Figure 2.3: Visualization of universal joint [7].

In some cases this construction can get stuck in certain positions. This situation can occur if the U-profile placed on the upper axis has rotated maximally (trying to point to positive y-axis in Figure 2.3), and the U-profile on the lower axis aims to switch from pointing at the negative y-axis to the positive. The problem occurs since the metallic parts have a driving force of sinking due to their high density. So, if the tether has been slack and then gets in a position where the force resultant is not enough upwards, the joint will be stuck.

2.1.7 Cable Management

The cables that come from the kite via the tether needs to be connected to the

foundation in order to deliver the generated electricity to the shore as well as in-

and outgoing signals. This can be solved in different ways. Either the universal

joint can allow the cables to be led through it, or the cables need to be led around

the universal joint.

2. Pre Study

2.2 Market Analysis

The market analysis was performed in order to get inspiration as well as to investi- gate possible patents that solutions in this project could intrude on.

2.2.1 Competitor Analysis

This section presents some solutions that is already on the market but in other products or applications. The analysis focuses on products that include joints/con- nections under water.

Makani

The Makani energy kites operate by the same principle as Minesto’s kite, with the main difference that Makani’s kite operates in air and is collecting energy from the wind [8]. According to Makani’s website, the kite flies in a circle and the tether that they are using is flexible. The electricity that is generated when the rotors on the kite spin is sent down a tether to the grid [9].

Corpower

Corpower is a company that has a tethered connection to the seabed in order for their technology to work. They extract energy from waves by capturing the energy from the oscillating movement of the waves. A pre-tension is applied to pull the buoy downwards. To maximize the energy output, there is a "wavespring" in the buoy that causes a resonance response [10].

Seaflex Mooring System

Seaflex offer elastic mooring solutions for applications from single-hawser models to up to ten-hawser units for heavier applications. According to their website, one single rubber hawser can withstand more than 10 kN in tension, elongate over 100 % and then retract back to its original length. The system is putting constant tension and giving stability to the moored application. They have ropes connecting the end parts for safety reasons i.e if the system gets overloaded [11].

Seaflex Spring

Seaflex also offers a rubber spring which has the purpose of holding pontoons firmly in a fixed position. The Seaflex spring can elongate up to 50 % when it is loaded [12].

Marine Flex

Another company that develops an elastic mooring system is Marine flex [13]. The technology seems quite similar to the Seaflex mooring system since the load bearing components consist of rubber structures.

TFI Marine

TFI marine delivers compression polymer springs that is fitted in the mooring line.

2. Pre Study

According to their website [14], their solution reduces cost due to that it enables shorter mooring line length. They also explain that the peak loads decreases with up to 70% when introducing the spring to the mooring system, compared to having a mooring line without the spring.

2.2.2 Patent Search

The patent search was performed due to two reasons: to collect inspiration and to see if any concept developed in this work potentially intrudes on any existing patent.

In this section, relevant existing patents are presented.

Polymer Spring US2014217662A1

This patent claims intellectual property for a hollow tubular polymer body that functions as a compression spring [15].

Polymer Compression Spring GB2511127A

This patent applies to a polymer compression spring. The polymer compression spring is made from a plastic material that exhibits high chain resistance under compression [16].

Multihelical Composite Spring US2002158392A1

This patent is for a multi-helical composite spring. The patent is for a helical spring comprising one or more layers of material in a first helical coiled configuration and one or more layers of material in a second helical coiled configuration. Furthermore, each layer of the first helical coiled configuration lays over one layer of the second helical coiled configuration at several intersections, to form a single spring unit [17].

Composite Coil Spring WO2014014481A1

The patent include a composite coil spring comprising a coil body extending along a coil axis. The body includes a core and a plurality of fiber material impregnated with a polymer material [18].

Bend Stiffener US2008295912A1

This patent is related to bend stiffeners for underwater use. One example where it is used is for wave powered energy generation. The innovation’s purpose is to resist excessive bending of cables in underwater applications. The preferred material for the bend stiffener is neutral in water or denser [19].

Bend Stiffener US10472900B2

This patent applies to a bend stiffener comprising an elongate stiffener body that

is made of polymer material. It further has a root end and a free end. There is a

passage trough the bend stiffener embracing a flexible member. The stiffener body

consists of at least two stiffener body parts which define the passage. Furthermore,

this patent claims that each of the stiffener parts are provided with an interface

2. Pre Study

member that includes materials that are stiffer than the polymer material [20].

2.3 Literature Study

This section presents a description of the environment that the product should operate in. An introduction is given to polymers in general. Furthermore, the material mechanics theory that was assessed necessary in order to evaluate a polymer solution in the present application is presented.

2.3.1 Environment 100 m Below Water Surface

The light range that is able to travel down to a depth of 100 m in coastal ocean waters is within the span of 510-550 nm [21]. For a location where the depth is ap- proximately 100 m, the amount of dissolved oxygen in the water is almost constant at 3 ml/l from a depth of 20 meters and down [22].

What distinguish seawater from other water bodies on earth is the salinity. The Ocean Network Canada [22] explain that the chemical compounds of the dissolved components in seawater contain nearly all the elements in the periodic table. The key elements are chlorine ions (55% by weight) Sodium(30.6% by weight) and Sul- phate ions (7.7% by weight) [22].

Furthermore, Ocean Network Canada [23] present data from Folgers passage in Canada where the depth is 96.1 m. The data is presented as curves over time, and the approximate span in Table 2.1 represents the maximum and minimum values from 2019. Folgers deep is located in British Columbia [23] where the surface water temperature range from 6° to 20° [22].

Table 2.1: Ocean data from Folgers deep(depth 96.1 m) in Canada [23]

Measure Value

Oxygen concentration 1-6 (ml/L) Practical salinity 31-33.5 (psu)

Temperature 8-10 °C

2.3.2 Classification of Polymers

The three major polymer categories are Thermoplastics, Thermosetting and Elas- tomers.

Thermoplastic polymers are built up by long chains by joining monomers. The struc-

ture of these types of polymers are in general flexible linear chains. These polymers

soften and are formed by viscous flow when heated above certain temperatures. In

typical thermoplastic polymers, the bonding within the chain is covalent, and the

chains are held together by weak secondary bonds [24].

2. Pre Study

Thermosetting polymers are defined by a high amount of cross linkage between long chains of molecules, which form three-dimensional network structures. These types of polymers are generally stronger, more rigid but more brittle than thermoplastics, due to that the chains cannot rotate or slide. Thermosets has low ductility and in a tensile test, these type of polymers show similar behavior as brittle metals and ceramics. Thermosets have relatively high glass transition temperature. One type of thermosettings are epoxies, which are thermosetting polymers with a tight C-O- C ring. Epoxy are commonly used in high performance fiber reinforced polymers (FRP) [24].

Elastomers have an intermediate structure where some cross linkage between the molecular chains occur. This type of polymers have the ability to elastically deform to a large extent, without having a permanent change in shape. In elastomers, vis- cous plastic deformation is avoided and large elastic deformation is made possible by cross-linking the chains. Elastomers show a non-linear elastic behavior which can be explained by that in the beginning, the elastic modulus decreases due to that the chain uncoils. After the chains have been extended, the elastic deformation occurs by stretching of the bonds, causing the elastic modulus to increase. The elasticity of the rubber is determined by the amount of cross-links. Furthermore, elastomers are used above their glass transition temperature [24].

The mechanical properties of solid polymers are a consequence of the chemical com- position as well as the polymers structure at the molecular and supermulecular levels [25].

2.3.3 Viscoelasticity

Polymer materials are in general viscoelastic, which means that the strain or stress in the material varies over time. A given polymer can, depending on the temperature and loading time, show all the intermediate range of properties between an elastic solid and a viscous liquid. The response of a material that combines both liquid-like and solid-like features is termed viscoelasticity [25].

2.3.4 Influence of Hydrostatic Pressure

The shear yield strength of a polymer material increases substantially up to a hy- drostatic pressure of about 300 MPa. The strain at witch yield occurs also increases with increasing pressure [25].

2.3.5 Large Strain Theory

Ward and Sweeney [25] writes that the most noticeable feature of natural rubber

and other elastomers is their ability to undergo large elastic deformation. They

provide information regarding the fact that the driving force of the elastic recovery

is the entropy, and concludes with the equation presented in Equation 2.7.

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( δ U

δ l )

= 0 (2.7)

They state that this demonstrates that the elasticity occurs only from the change in entropy. This expression comes from assuming constant volume and temperature during uniaxial tension [25].

They continue by considering simple elongation λ along one principle axis. By assuming incompressibility of the elastomer, they obtain an expression for the stress according to Equation 2.8.

σ = N kT (λ − 1

λ

) = G(λ − 1

λ

) (2.8)

They conclude that NkT equals the shear modulus of the rubber, G, and λ is the extension ratio. They further explain that a general definition of strain that is not limited to small strains can be expressed according to Equation 2.9.



= 1

2 (λ

− 1), 

= 1

2 (λ

− 1), 

= 1

2 (λ

− 1) (2.9)

2.3.6 Polymer Degradation

Guoa et al [26] states that amorphous polymers suffers from a time dependent pro- cess known as physical ageing or structural relaxation. This is due to that amorphous polymers are in an non-equilibrium state below the glass transition temperature, meaning that it continuously evolves to a stable state. They state that the effect from ageing in a polymer significantly can influence the thermomechanical proper- ties and hence also the macroscopic behavior of the polymer [26]. White [27] also states this fact, and further explain that for semi-crystalline materials the ageing behavior is more complex than for amorphous. He further mentions that the crystal phase is relatively inert with respect to ageing, but emphasises that the the ageing then is restricted to the adjacent amorphous phase [27].

White [27] also brings up some information regarding the ageing effect at elevated temperatures. He states that if a polymer is subjected to an elevated temperature in the presence of a aggressive chemical agent (such as oxygen), chemical reactions may occur. The many changes that become present during these conditions are known as thermal degradation. He further mentions that this is important even if the polymer is not designed to operate in such an environment, since the manu- facturing often involves elevated temperatures. Stabilizers are therefore often used in moulding compounds due to this, if only to protect the polymer from chemical degradation in the forming of the product [27].

Most polymers will, according to Polymer properties database [28], change suffi-

ciently when exposed to heat, light and oxygen. On their website they state that

this will have a dramatic effect on the products service life and properties, and that

one way of slowing down this is to add UV-stabilizers and antioxidants. They further

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states that stress have an accelerating effect on the negative effects related to oxida- tion and heat. The resistance to degradation depends on the chemical composition of the polymer and the resulting effect differs between different polymers i.e they can e.g suffer from embrittlement (chain hardening) or softening (chain scission) [28].

2.3.7 Effects of Strain Rate and Temperature

Ward and Sweeney [25] explain that strain rate and temperature has an impact on the tensile strength and ultimate strain in polymers. They mention that, except for when the molucelular chains have complete mobility, such as in the case of very low strain rates and high temperatures, viscoelastic effects dominates the fracture pro- cess. They further provide data showing that as the strain rate decreases, the tensile strength also decreases. The ultimate strain show more temperature dependency, and increases with decreasing strain rate at low temperatures, and decreases with decreasing strain rate at higher temperatures. The tests were they have obtained this were performed on a rubber [25].

2.3.8 Fatigue in Polymers

The effect of a cyclic stress is to initiate microscopic cracks in the material or at the surface, followed by crack propagation and then leading to eventual failure [25].

Bierögel and Grellmann [29] states that a cyclic loading can cause component fail- ure at lower stresses than in the case of a static loading. They further explain that the typical stress- strain behavior of a polymeric structure essentially are what de- termines the specific fatigue behavior of the plastic. They further mention that as the load increases, the absorbed energy by the material damages grows, resulting in an increase in temperature in the polymer. At high frequencies, this may result in thermal failure due to the low thermal conductivity of polymers [29].

2.3.8.1 The Role of Self Heating

Shojaei and Volgers [30] have investigated the fatigue behavior of unfilled polymers with focus on the self heating effect. They state that to develop a tool for the prediction of the fatigue life for polymers and PMC is challenging and requires information about time and temperature dependent damage mechanisms. They further explain that one also needs to take into account environmental effects, ageing, load frequency, surface finish and the fraction between maximum and minimum stress. They explain that when the self heating phenomenon overcomes the rate dependent mechanisms introduced above, the material will get a lower lifetime due to heat softening effects. Self heating is directly corresponding to the stress level and the cyclic frequency [30].

2.3.9 Creep

Creep in polymers at low strains, unlike creep in metals, is essentially recoverable

when unloaded. For the general case of a linear viscoelastic solid, the total strain e

is the sum of the immediate elastic deformation e

, the delayed elastic deformation

2. Pre Study

e

and the Newtonian flow e

. The Newtonian flow is identical with the deformation of a viscous liquid that obeys Newton’s law of viscosity [25].

2.3.10 Spring Function as a Material Response

Mechanical springs can be defined as elastic bodies that have the function of de- flecting or distorting under load, and that then recovers when unloaded [31]. Chiu et al. [32] states that the main factor to consider when designing a spring is the specific strain energy of the used material which can be expressed according to Equation 2.10.

U = σ

Eρ (2.10)

where σ is the stress, E is the Young’s modulus and ρ is the density.

Furthermore, the potential energy stored in the spring could then be expressed according to Equation 2.11.

E

= 1

2 k δ

(2.11)

And the force needed to extend a spring δ is given by Hooke’s law presented in Equation 2.12.

F = k δ (2.12)

Where k is the spring constant.

Ward and Sweeney [25] have on the matter of linear viscoelasticity stated that the maximum stored elastic energy in a polymer material can be expressed according to Equation 2.13.

E = 1

2 G

e

(2.13)

Where G

is called the storage modulus and defines the energy stored in the ma- terial due to the applied strain. They define a complex modulus as presented in Equation 2.14.

G

= G

+ i G

(2.14)

where G

is the storage modulus as described above, and G

defines the dissipa- tion of energy and is called the loss modulus. G

can be expressed according to Equation 2.15.

G

= ∆ E

π e

(2.15)

Ward and Sweeney [25] have further described that the loss factor tan δ of the material is given by Equation 2.16.

tan δ = G

G

(2.16)

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The behavior of this factor is that it is almost zero when the material is in the

rubbery and glassy state, that is, for low and high frequencies, respectively. The

loss factor reaches its maximum in the intermediate region, where the viscoelastic

behavior is dominant [25].

3

Theory

Two concepts were developed in the concept choice phase. Both concepts were based on the shape of a bend stiffener. One concept on a solid body in the shape of a bend

stiffener which aimed to provide a spring function. The other concept was a conventional bend stiffener. The theory in this chapter was used to develop and

evaluate both concepts.

3.1 Beam Theory for Beams with Low Stiffness

Barten [33] has developed an expression for the deflection of beams with low stiff- ness. He states that any point on the beam can be described by four independent quantities. These quantities are the coordinates x and y, the angle θ and the arc length s from the origin of coordinates, which he sets to be in the clamped end. The conclusion from his work that describes the angle at the free end with respect to the neutral axis of a clamped beam is presented in Equation 3.1 [33].

sin θ

= tanh( P L

2EI ) (3.1)

He further states that the length of the moment arm, that is needed to calculate the maximum bending stress in the clamped end, can be expressed according to Equation 3.2.

x

= 2EI

P tanh( P L

2EI ) (3.2)

3.2 Bend Stiffeners

A bend stiffener is often used as an ancillary component to protect submerged cables in floating units. The main purpose of the bend stiffener is to avoid large bending stresses and fatigue of the cables. A bend stiffener often contains two parts, where the attachment to the foundation is metallic, and bend stiffener body is a polymer.

The polymeric part is usually made of polyurethane and has a conical shape [34]. A

schematic image of the cross section of a bend stiffener is presented in Figure 3.1.

3. Theory

Figure 3.1: A schematic illustration of a bend stiffener.

The introduction of a bend stiffener results in a gradually increase in bend stiffness from the small value at the compliant structure to a higher value at the connection to the rigid structure. Usually, the polymeric part of a bend stiffener does not provide any tension carrying effect, more than the friction between the cable and the bend stiffener [35].

3.2.1 Thermoplastic Polyurethane Elastomers

Themorplastic polyurethane elastomers (TPU’s) are built up by alternative cova- lently bounded hard segments and soft segments. One brand name for different types of thermoplastic polyurethane elastomers (TPU) is Elastollan, provided by the company BASF. They describe TPU’s as advantageous due to that they have high wear and abrasion resistance, high tensile strength, outstanding resistance to propagation, excellent damping characteristics, very good low-temperature flexibil- ity and high resistance to oils, greases, oxygen and ozone. They further describes that the material can be used to produce products by extrusion, molding and injec- tion molding techniques [36].

BASF produces both polyester-based and polyether-based Elastollan, where they mention that what characterizes polyester-based products are high mechanical prop- erties, heat resistance and resistance to mineral oils. They also describes that what characterizes polyether based TPU’s are excellent hydrolysis resistance, high cold flexibility and resistance to microorganisms. They mention that besides the three basic components, additives are added in many of the Elastollan products. It is also possible to add other additives such as mold release agents and plasticizers to modify specific properties. Glass fibers can also be added to increase rigidity [36]. The soft segments in a polyester based TPU comes from polyester, which Bardin et al [37]

describes have an order of magnitude lower hydrolysis resistance than urethane.

3.2.1.1 Hydrolysis

According to Lima de Oliveira [38] the most common degradation mechanism for

polyurethanes operating in seawater is hydrolysis. They explain that the chemical

3. Theory

reaction with water molecules causes a decrease in network density, which causes a decrease of mechanical properties [38].

Bardin et al [37] have investigated the effect of water on TPU-ester mechanical properties and structure. In their article, they show that the water absorption is low at low temperatures, and increases at higher temperatures. They further provide a graph where they show the scissions as a function of time, at different temperatures.

The lowest temperature they investigated was at 40°C and they showed that with a stabilizer, the predicted scissoring effect by hydrolysis was almost at a constant level 0. They have also performed uniaxial tensile tests on the specimens, showing that with stabilizers, the elongation at break of the material at 40°C was almost unaffected up to 900 days (no data points shown thereafter). The anti-hydrolysis agent used in the study was amonomeric carbodiimide which they mentioned is commercialized as Stabaxol [37].

3.2.2 Manufacturing of Bend Stiffeners

Plastiprene [39], which is a company that have developed and manufactured bend stiffeners for more than 20 years, manufactures bend stiffeners by following steps:

• Build a mold tool

• Create a steel insert component that is used for the attachment to the rigid surface

• Assemble mold tool and insert pre-heat tooling

• Inject the polyurethane into mold

• Cure cycle

• Demold and finish

They also states that, in order to transfer the loads from the bend stiffener to the rigid attachment, a steel interface structure is molded into the base of the conical bend stiffener [39].

According to Ashby [40], one of the manufacturing methods for polymers that en- ables the largest thickness is polymer casting. The maximum thickness for this method is approximately 100 mm. The main issue with a too thick section is that shrinkage of the material becomes a problem [40].

3.2.3 Optimized Dimensions of Bend Stiffener

Tanaka et al. [34] have applied an optimization algorithm on the design process of

a bend stiffener. In their model, they only consider the polymer part which the

cable passes trough, since the metallic foundation attachment part is significantly

more rigid than the rest of the bend stiffener. They also mentions that a bend

stiffener typically has a much greater bend stiffness than the pipe that passes trough

it [34]. The dimensions that they have investigated and optimized are presented in

3. Theory

Figure 3.2.

Figure 3.2: Dimension declaration for a bend stiffner. Created with inspiration from Tanaka et al [34].

In their optimization process they have used following constraints to their problem formulation:

• Maximum allowable curvature of the cable

• The maximum allowable strain in the polymeric part

• Maximum bending moment at the base of the bend stiffener

They investigated a bend stiffener at 100 m depth, where the critical force and angle pairs that they used in their report is presented in Table 3.1.

Table 3.1: Critical angle pairs from case which the ratios presented above were determined [34]

Tension (kN) Angle (Degrees)

33.7 48.5

30.7 50.8

26.4 52.2

16.4 54.7

19.2 56.8

In their work, they set a limiting value of strain in the material of 5 % and a

maximum curvature of 0,25. The values on the dimensions for this case in the op-

timization performed by Tanaka et al [34] were according to Table 3.2.

3. Theory

Table 3.2: Optimized dimensions responding to the critical angle pairs presented above. From report by Tanaka et al [34]

Dimension Value (m)

L

2.7

L

0.25

D

0.38

D

0.177

Drobyshevski [41] has developed expressions for determination of initial design pa- rameters for "ideal" bend stiffeners, by obtaining a constant curvature over its entire length. The objective of his analysis was to determine the length l and the shape of the diameter along the length, given a target value of the curvature. He further explains that it is convenient to use the ideal bend stiffener formulation for initial sizing in the design process of a bend stiffener [41]. He has presented equations for the angle (at the tip of the bend stiffener) and length of the "ideal" bend stiffener.

These equations are presented here in Equation 3.3 and Equation 3.4, respectively.

θ

= δ − 2 arcsin[ k0 2

s

EI

T ] (3.3)

l = δ k

− 2

k

arcsin[ k0 2

s

EI

T ] (3.4)

EI

is the bending stiffness of the pipe and k

is the target curvature value. The other parameters are illustrated in Figure 3.3.

Figure 3.3: Illustration of parameters used by Drobyshevski. Used with permission

from Drobyshevski [41].

3. Theory

Drobyshevski [41] also states that the equations presented above is only valid when the condition presented in Equation 3.5 is fullfilled.

k

< 2

s

EI

T sin[ δ

2 ] (3.5)

He continue by defining the non-dimensional length as presented in Equation 3.6.

˜ l = l

s

T EI

= 1

u [δ − 2 arcsin[ u

2 ]] (3.6)

where u is the non dimensional curvature, which is expressed according to Equa- tion 3.7.

u = k

s

EI

T (3.7)

He has also developed an expression for the non-dimensional outer diameter, ac- cording to Equation 3.8.

D = ˜ D(0)

d

= (1 + γ f (u))

(3.8)

where d

is the diameter of the pipe. He has further provided the equation presented in Equation 3.9 which is needed in order to proceed with the initial sizing.

f (u) = 1

u

[cos([2 arcsin[ u

2 ]] − cos[δ]] (3.9)

The parameter γ describes how close the elastic modulus of the pipe is that of the bend stiffener material. He has expressed this parameter according to Equation 3.10.

γ = 64 EI

π d

E

(3.10) Here E

is the elastic modulus of the bend stiffener material. He has further pro- vided an expression for the maximum strain in the bend stiffener, which he explains can be used to determine the target curvature value k

. He states that the maxi- mum strain of the bend stiffener is at the foundation, where the largest diameter is found. The expression for the largest strain that he has provided is presented here in Equation 3.11.



= 

+ 

(3.11)

The strain component ε

comes from the strain due to bending. The other strain component ε

comes from the strain due to the axial tension [41]. These components are presented in Equation 3.12 and Equation 3.13.



(0) = κ

D(0)

2 = d

u 2

s

T

EIp [1 + γ f (u)]

(3.12)



(0) = − 4 T E

π d

u

f (u)

(1 + γ f (u))

− 1 (3.13)

3. Theory

3.2.4 Design Considerations for Bend Stiffeners

Bai et al [42] states that for inspectable polymetric parts used in a subsea environ-

ment, a fatigue safety factor of 3 is needed. For uninspectable parts, this factor

increases to 10. They further explain that the design of a conical bend stiffener is

performed by looking at the most severe tension and angle combination that satisfies

the minimum bending radius given by the cable. The main design parameters are

the material, the length and the maximum external diameter [42].

3. Theory

4

Methods

This chapter presents the methods that have been used in the project. The four phases planning, product specification, concept choice and conceptual design are

explained.

This project aimed to deliver a new component and in such cases, the develop- ment process is characterized by a high level of creativity, large contribution of not previously known solutions, uncertainties and risks [43]. Design and construction processes are often to complex for anyone to solve them solely through intuition, and hence a more systematic approach is required. One strategy that is mentioned by Johannesson et al [43] is to start analyzing the required functions that the solution should provide. After the required functions have been identified, the focus should be to find solutions to the sub-functions, and then combining them into complete product solutions.

4.1 Planning

A product development process is often divided into seven steps: product specifi- cation, concept generation, concept choice, conceptual design, detail construction, prototype testing and final construction [43]. The goal and expectations of this work was however to provide a conceptual design. Thus, the activities included in the planning were limited to the four first steps of the product development process.

4.1.1 Project Plan

The aim of the project plan was to obtain a guiding document to simplify the struc- ture of the work. The project plan was handled as a living document since new activities came up, as well as that some activities were assessed unnecessary and thus removed. The project plan was created by first writing a background explain- ing why the project was initiated as well as defining the problem description. A work breakdown structure diagram was created in order identify activities that needed to be performed. A Gannt-chart was created to give information about when each activity should start and be completed.

A project model was also created stating what the different phases in the project

contained of and how the phases were connected. The project model contained of

the six work packages: planning, product specification, concept generation, concept

4. Methods

choice, conceptual design and presentation.

To prevent possible errors in the project, a risk assessment was performed in the Failure Modes and Effects Analysis (FMEA)- format. Different parts of the project were thought of and possible risks were observed and evaluated. By working with subjective and coarse estimates, FMEA can be used early in the process [43].

4.2 Product Specification

The aim of the product specification was to get a deeper understanding of the task as well as to collect complementary information to the problem description. The product specification answered the question of what should be accomplished by the work. The result of this work functioned as the basis for the concept generation phase, as well as a reference when the concepts were evaluated [43].

4.2.1 Pre Study

The pre study was performed in order to obtain the required knowledge about the product and the present problems. This was necessary in order to set up a correct product specification. The pre study was divided into three parts: technical review, market analysis and literature study [44].

4.2.1.1 Technical Review

The technical review was performed by reading articles dealing with the motion of kites. Furthermore, internal documents provided by Minesto were read in order to obtain a deeper understanding of the current solution and problems. The technical review was documented and served as the basis when formulating the problem de- scription of the project. The spring function was analysed and the required input to create a theoretical model for this function was found.

4.2.1.2 Market Analysis

The competitor analysis was made with the purpose of collecting inspiration in prod- ucts that already exist on the market. The analysis was confined to products with a similar function as the one presented in the technical review.

The patent search was used in order to obtain information about competing solutions to the component that this project aimed to develop. Also to find well known technical solutions. It was also used to provide ideas that could be used later in the development process [43].

4.2.1.3 Literature Study

The literature study was performed by finding information related to the problem

description. Information that could potentially be useful to answer the questions

4. Methods

stated in the introduction, was collected and documented [45]. Several potential risks were detected in the FMEA during the project, and therefore the literature study became an iterative tool in the project. This was done with the aim of finding information that could serve as evidence which could either prove or decline different hypothesises that came up during the project.

4.2.2 Delimitations

The delimitations were discussed and determined together with Minesto, to assure that their expectations on the project would be fulfilled. The purpose of the delim- itations was to make the project goals achievable in the time frame of the project, as well as to steer the work in the right direction without performing unnecessary activities.

4.2.3 Stakeholder Analysis

The different stakeholders of the project were identified. The stakeholder analysis was performed in order to identify anyone that would be affected by the product.

The purpose of the analysis was to collect requirements and requests from each stakeholder [43].

4.2.4 FMEA

In order to localize potential things that could go wrong with the product, and to come up with product criteria that could prohibit these errors from happening, FMEA was used [43].

4.2.5 Product Criteria

The product criteria came from three different sources:

• Given by project description

• Appeared when performing analysis and clarification of task

• Followed as a result of a construction decision

The criteria were collected by using the Olsson matrix presented in Table 4.1 [43].

Table 4.1: Olsson matrix

Process Environment Human Economy

Generation 1.1 1.2 1.3 1.4

Production 2.1 2.2 2.3 2.4

Disposal 3.1 3.2 3.3 3.4

Use 4.1 4.2 4.3 4.4

Elimination 5.1 5.2 5.3 5.4