School of EngineeringBEng(Hons) Project in Mechanical Engineering

Final Project Report

The Testing and Development of Cardboard Tubes as a Structural Material with the

Intended Application being the Construction of a Bicycle

James Goddings

2015/16

Project Supervisor: Dr. Geoff GossMechanical Engineering BEng(Hons)

Project (ENG_6_424_1516)Part Time

School of EngineeringBEng(Hons) Project in Mechanical Engineering

The Testing and Development of Cardboard Tubes as a Structural Material with the

Intended Application being the Construction of a Bicycle

James GoddingsStudent No: 3131147

Submission Date: 30/04/16Project Supervisor: Dr. Geoff GossModule: Project (ENG_6_424_1516)

Part Time

This report has been submitted for assessment towards a Bachelor of Engineering Degree in Mechanical Engineering in the Department of Engineering and Design, London South Bank University. The report is written in the author’s own words and all sources have been properly cited.

Author’s Signature:

Date:

Table of Contents

Abstract............................................................................................................. iGlossary............................................................................................................ ii1. Introduction................................................................................................1

1.1 The History of the Cardboard Bicycle......................................................11.2 Cardboard Forms.....................................................................................21.3 The Bicycle as an Mechanical Engineering Application...........................3

2. Project Aim.................................................................................................43. Objectives..................................................................................................44. Deliverables...............................................................................................65. Technical Background................................................................................6

5.1 Bicycle Frame Materials..........................................................................65.2 The Advantage of Larger Diameter Tubes...............................................85.3 Why Build a Bicycle from Cardboard?...................................................105.4 Is Cardboard Suited to Building A Bicycle?...........................................11

Printable...................................................................................................11Reusable and Recyclable.........................................................................11Inexpensive to Manufacture.....................................................................11Mechanical Strength................................................................................12Low Density..............................................................................................13

5.5 Cardboard’s Limitations........................................................................13Moisture...................................................................................................13Fatigue.....................................................................................................13Manufacturing Defects.............................................................................13

6. Technical Approach..................................................................................146.1 Laboratory Testing of Cardboard Tubes................................................14

Apparatus.................................................................................................14Experimental Procedure...........................................................................14Results.....................................................................................................16Discussion................................................................................................16

6.2 Frame Design........................................................................................18

Existing Frame Designs............................................................................18Geometry.................................................................................................19

6.3 Finite Element Analysis.........................................................................206.4 Tube Development...............................................................................226.5 Joint Development................................................................................256.6 Construction of the Front Triangle........................................................266.7 Re-Design and Construction of Rear Triangle.......................................276.8 Construction of Forks and Prototype Front Wheel..............................286.9 Waterproofing....................................................................................286.10 Prototype Testing...............................................................................28

7. Results and Discussion.............................................................................287.1 Evaluation of the Project......................................................................287.2 Evaluation of the materials developed.................................................297.3 Evaluation of the design process..........................................................307.4 Evaluation of the project management process...................................317.5 Evaluation of the final product...........................................................31

Conclusions....................................................................................................32APPENDIX A....................................................................................................A1

Laboratory Testing Results and Charts.......................................................A1APPENDIX B Finite Element Analysis..............................................................B1

Analysis 1 Static Study - Seated Whilst Pedalling Right Pedal....................B1Analysis 2 Static Study - Seated Whilst Pedalling Left Pedal......................B2Analysis 3 Static Study – Standing Whilst Pedalling Left Pedal.................B3Analysis 4 Static Study – Standing Whilst Pedalling Right Pedal...............B4Analysis 5 Static Study – “Hitting a Pothole” while Seated........................B5Analysis 6 Static Study – Braking while Standing......................................B6Analysis 7 Static Study – Falling Mass.......................................................B8Analysis 8 Static Study – Falling Frame.....................................................B9

APPENDIX C Models and Build Photos............................................................C1APPENDIX D....................................................................................................D1

Product Design Specification for a Cardboard Bicycle Frame and Forks. .D1Prototype Bicycle Frame and Forks Costing for Project............................D1Table of Bicycle Ancillary Donor Parts Used for Build..............................D2Dimensional Analysis of Prototype Frame and Forks...............................D2

APPENDIX E Gantt Chart.................................................................................E1

References......................................................................................................... IFigure References....................................................................................... IReferences.................................................................................................. IBicycle Industry Testing Standards............................................................VOther Standards.........................................................................................V

Abstract

This project examines the mechanical properties of cardboard, focussing on cardboard tubes and their development as a viable structural material. Few studies have been made on the properties of cardboard tubes; however they are an abundant resource and provide an inexpensive, sustainable alternative to current materials. Axial compression tests are carried out on cardboard tubes to establish their mechanical properties. This data is used in the development of enhanced forms with the application being the design and manufacture of a prototype cardboard bicycle frame and forks. Through the achievement of this objective, the project seeks to prove the materials developed, and provide insight into the feasibility of the cardboard bicycle as a product.

i

Glossary I=SecondMoment of Area /Moment of Inertia

ro=Outer /External Diameter

ri=Inner / Internal Diameter

δ=Displacement /Deflection

L=Length

E=Youn g' sModulus/ElasticModulus

θ=Angular Displacement / Angular Deflection

T=Torque

A=Area

V=Volume

γ=StiffnessCoefficient , see Equation5.2.8

φ=Wall Ratio, seeEquation5.2 .9

λ=Wall Ratio, see Equation5.2 .9

R=Radius of Gyration

m'=Mass per unit length(metre)

ii

Top Tube

Down Tube

Seat TubeHead Tube

Seat Stays

Chain Stays

Front Forks

Rear Dropouts

Handlebars

Stem

Front Dropouts

Fork Legs

Fork Crown

Bottom BracketCranks

Bicycle Frame

1.IntroductionThe original title of this project was “Eco-bicycle”, the challenge being to design and build a cardboard bicycle. After reassignment from the project’s proponent supervisor/assessor, and discussion with the new supervisor/assessor, a decision was taken to change to the project title to its current form.

The Testing and Development of Cardboard Tubes as a Structural Material with the Intended Application being the Construction of a Bicycle

It is agreed that this presents more opportunity to approach the project from an analytical engineering angle. The most important question to arise from this discussion is, “Why build a cardboard bicycle?”

This project seeks to answer this question, and in the process establish, whether cardboard is a viable structural material and if so, how to build a bicycle from it to prove this.

1.1 The History of the Cardboard BicycleThere is precedent for the manufacture of a functional cardboard bicycle. Two well-publicised attempts have been made previously:

Figure 1.1.1 Left - Phil Bridge’s honeycomb panel cardboard bicycle 2008, Right - Izhar Gafni’s cardboard bicycle 2012

Whilst pursuing a Product Design degree from Sheffield Hallam University in 2008, Phil Bridge built a cardboard bicycle from honeycomb cardboard panels produced for advertising hoardings and the building industry. The final product is elegantly designed and received publicity from local and national media; however it was a downscaled model that could not be pedalled, and could only support 75kg statically. This demonstrates the concept, but does not prove the mechanical viability of building a functional bicycle from cardboard.

In 2012 Izhar Gafni was successful in building a mechanically sound functional bicycle from cardboard and launched a crowd-funding scheme on Indiegogo to raise $2 million to fund the setup of Cardboard Technologies, a company for producing his cardboard bicycle. The fundraiser fell short only raising $40,000, the schemes failure is attributed to the “lucky owners” of the first bicycles being asked to pay in excess of $500 for a bicycle with a claimed retail price of $20 to the third world. (www.Indiegogo.com, 2012)

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Both Phil Bridge and Izhar Gafni cite the low cost and recyclability of cardboard as their reasons for choosing cardboard as a material to build a bicycle. They also both claim they

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could supply a $20 retail product to the market, a claim discussed in Section 7.5.

1.2 Cardboard Forms

Figure 1.2.1 from Top Left to Bottom Right, Plain Card Stock, Corrugated Cardboard, Honeycomb Cardboard and Cardboard Tube

Cardboard is manufactured in different forms, illustrated by Figure 1.2.1, and is currently used in the building industry for the manufacture of honeycomb cored doors, stud wall panels and lightweight countertops. The architect Shigeru Ban, who specialises in designing buildings from sustainable materials has even designed and built large architectural structures from cardboard tubes with metal joints.

Figure 1.2.2 Both Shigeru Ban designs - Left - The Japanese Pavilion Expo 2000 Hannover, Germany, Right - Cardboard Tube Bridge with the Pont du Gard, France in

background (A 2000-year-old Roman aqueduct)

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Cardboard tubes are a widely available form of cardboard used as packing and packaging products for transport and sale. They have a number of characteristics that make them well suited to this:

Printable Reusable and recyclable Inexpensive to manufacture Mechanically strong Low in density

This project will investigate the mechanical properties of cardboard tubes (see Section 6.1 and APPENDIX A) and their development as a feasible structural material for the design and manufacture of a functional bicycle (see Sections 6.2-6.10 and APPENDICES C and D).

1.3 The Bicycle as an Mechanical Engineering ApplicationThe modern bicycle experiences all modes of mechanical forces, both static and dynamic, see Figures 1.3.1 and 1.3.2. As a result, the frame of a bicycle experiences all modes of structural stresses at some point during its use; this makes it an excellent application for examining a structural material.

Figure 1.3.1 and 1.3.2 show a model of a conventional double triangle truss frame and critical force bearing components (see Section 6.2). The model has been developed for Finite Element Analysis (see Section 6.3 and APPENDIX B), and is used in Figures 1.3.2-1.3.3 to illustrate the modes of forces that a bicycle experiences during normal seated use.

When seated but exerting no propulsive pedalling force, the rider’s acceleration under gravity causes their mass to exert a static downward force on the saddle, handlebars and pedals. As a result, an equal upward force is generated from the ground on the tyre contact patch that is translated through the bicycle. This places the truss members in either compression or tension according to their position in the frame.

Figure 1.3.1Forces experienced by a bicycle when in a situation analogous to Newton’s First Law with the rider seated

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Compression

Tension

Normal Reaction Force

Force Exerted by

Rider

The forces illustrated in Figure 1.3.1 are always experienced when the rider is mounted (unless airborne), and vary in their ratios between the components depending on the riding situation and gradient. They have been excluded unless essential from Figure 1.3.2 for clarity.

Figure 1.3.2 demonstrates pedalling considered statically at the point where the rider places an unequal force on one pedal. A bending moment results about the bottom bracket. The rider anchors this application of force by pulling upwards on the handle bar on the same side whilst also pulling on both handlebars towards the saddle; this creates a torsion couple about an axis through the frame. The force also creates tension in the chain (or belt) which compresses the seat stay on the drive side of the rear of the bicycle and creates a bending moment about the seat tube.

Figure 1.3.2 Forces, moments and couples experienced by a bicycle when the rider applies a propulsive pedal force to the left pedal resulting in forward acceleration

The action of pedalling is cyclic, placing unequal forces on the pedals alternating from one side to the other, this creates dynamic forces, bending moments and torsion couples within the frame. These presents a considerable challenge for a bicycle designer as the stresses generated can cause fatigue in the bicycle frame and components, leading to failures.

This analysis forms the basis of the design of the reinforced cardboard forms and their construction into a prototype bicycle frame and forks (see Section 6.2-6.10 and APPENDICES B and C), the ultimate goal of this project.

2.Project AimThe aim of this project is to investigate an existing form of cardboard available on the consumer market, by testing and developing it as a structural material; the intended application being the construction of a prototype bicycle frame and forks.

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Torsion

Bending Moment

Acceleration

Friction

3.Objectives3.1. Quantify the mechanical properties of cardboard tubes through laboratory testing and attempt to classify their modes of failure in order to qualify their suitability for development as bicycle frame and forks construction materials.

Progress: Unconfined compressive strength tests have been performed on cardboard tubes, results are shown in Section 6.1 and APPENDIX A.

3.2. Using structural reinforcing elements, improve the mechanical properties of cardboard tubes in order to improve their suitability as a structural material for constructing a prototype bicycle frame and forks.

• Design, Construction and Testing of Composite materials incorporating combinations of cardboard forms, with cardboard tubes as the principal component

Progress: Reinforced cardboard forms have been designed and produced with improved mechanical properties (see Section 6.4), tested (see Section 6.1 and APPENDIX A) and applied to the construction of a prototype bicycle frame and forks (see Section 6.6-6.9 and APPENDIX C).

3.3 Develop joints to connect the developed composite cardboard forms with sufficient structural integrity to construct a prototype bicycle frame and forks.

Progress: Joints have been designed and manufactured, optimising their mechanical properties for application being the construction of a prototype bicycle frame and forks (see Section 6.5).

3.4 Design a prototype bicycle frame and forks using the materials and construction techniques developed.

• Product Design Specification (P.D.S.) for a cardboard bicycle frame and forks.

• Finite Element Analysis (F.E.A.) of a bicycle model using generic data and BS EN ISO 4210-6:2015 test requirements, to highlight areas exposed to higher stresses.

Progress: A P.D.S. has been produced, see APPENDIX D along with an F.E. model of a bicycle frame with geometry matching that of the intended design, this has had Analysis performed on it in line with generic data, and BS EN ISO 4210-6:2015 (see Section 6.3). From these analyses a prototype bicycle frame and forks have been designed and manufactured.

3.5 Construct a prototype bicycle frame and forks using the materials and construction techniques developed, in order that it may be tested to assess the frame’s integrity and the suitability of cardboard as a bicycle frame material.

• Development of construction techniques specific the developed cardboard forms.

• Manufacture of a jig for construction, to control and evaluate the dimensions and angles of the constructed frame.

• Health and Safety Risk Assessment for all construction processes and methods.

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Progress: Construction techniques specific to using the developed cardboard forms have been developed (see Section 6.4-6.9 and APPENDIX C).

A jig has been constructed, allowing the dimensions and angles of the frame to be controlled during construction (see Section 6.6).

A prototype bicycle frame and forks have been manufactured using the materials and construction techniques developed (see Section 6.4-6.9 and APPENDIX C).

3.6 Analyse and test the completed prototype bicycle frame, and demonstrate its performance in comparison to existing bicycle frames.

• Quality Assurance and Quality Control (Q.A.Q.C.) in the form of a dimensional analysis of the final bicycle frame and an evaluation of the uniformity and applicability of the final materials.

• Laboratory testing of the final bicycle frame in line with the industry standards.

• Final proof test to ride the bicycle.

Progress: The bicycle frame and forks have been dimensionally analysed (see APPENDIX D)and the uniformity and applicability of the final materials evaluated.

Laboratory testing of the prototype bicycle frame has not been possible, discussed in Section 6.10 and Section 7.

The prototype bicycle has not been ridden due to schedule overruns, however it will be ready prior to the presentation of this project on 13 th June 2016, and providing it passes elementary safety evaluation it will be ridden in a demonstration.

3.7 Evaluation of the project

• Evaluation of the materials developed their applicability to building a bicycle frame and the possibility of use as structural products suitable for other parts and applications.

• Evaluation of the design process.

• Evaluation of the project management process.

• Evaluation of the final product

Progress: The project has been evaluated and the results are discussed in Section 7. and 8.

4.DeliverablesThe deliverables for this project will be demonstrated at the presentation on 13thJune 2016 or submitted prior in accordance with predetermined deadlines, they consist of the following

Final Project Report Supervisor Meeting Record Health and Safety Risk Assessment Bicycle Frame Construction Jig

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Laboratory Testing Samples Cardboard Development Examples Prototype Bicycle Frame and Forks

5.Technical Background5.1 Bicycle Frame MaterialsSince the invention of the “Rover Safety Bicycle” by John Kemp Starley in 1885 metals have been the optimum material choice of the bicycle frame designer. Metals have many advantageous characteristics for building a bicycle frame: High Tensile Strength, High Young’s Modulus, High Malleability and Ductility, and the ability to be Brazed or Welded.

Bicycle frames and components undergo considerable forces, most significantly in the forms of torsion and bending moments, which impart high stresses to localised areas of those components (Dwyer F. et al. 2012). A material with a high tensile strength allows a safe, strong structure to be realised capable of withstanding those stresses without failing.

Figure 5.1.1 Left, The Rover Safety Bicycle - Right, The Lu-Mi-Num

A high Young’s Modulus permits a stiff frame to be constructed that does not deform excessively from loads the rider places on it, effecting efficient transfer of the rider input forces and giving predictable handling traits.

Malleability, ductility and the ability of metals to be brazed or welded all facilitate the manufacture of bicycle frames and components. Malleability and ductility enable metals to be formed into useful shapes, especially the drawing or extrusion of tubing, which has been the staple of bicycle manufacture since the 1880’s. Brazing and welding are exceptionally efficient means by which to joint materials, and if realised properly can be as strong as the principal material itself.

Today steel accounts for 85-90% (David Lundy, 1994) of bicycle frames, other materials include titanium, carbon fibre and predominantly aluminium. Despite the first aluminium bicycle frame being built in 1896, the Lu-Mi-Num, aluminium bicycle frame production did not become more widespread until the 1980’s.

Prior to the 1980’s manufacturers who had tried to use the material had merely tried to imitate the design of steel frames leading to overly compliant frames, which tended to fail under the principle forces experienced due to fatigue. Aluminium is far less fatigue resistant than steel as discussed by Dwyer F et al. (2012), having a proportionally lower fatigue strength relative to other strength characteristics.

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Aluminium alloys generally harden with age, a characteristic that is exploited by solution heat treatment. Solution heat treatment improves the materials tensile strength, however it can also make the material more brittle and prone to stress fracturing through fatigue. When exposed to the environmental elements of variable temperature and humidity whilst being dynamically stressed, aluminium can naturally age and harden.

During the late 1970’s Gary Klein an American chemical engineer developed a number of techniques allowing aluminium to be applied proficiently as a bicycle frame material, one of the most significant of which was making frames from larger diameter tubes.

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5.2 The Advantage of Larger Diameter TubesThe Second Moment of Area or Moment of Inertia for a Tube:

Equation 5.2.1

I=π r o

4

4−π r i

4

4

When applied to the Bending of a Beam: Equation 5.2.2

δ=−P L3

48EI

The Polar Moment of Inertia: Equation 5.2.3

J=π ro

4

2−π r i

4

2

When applied to the Torsional Deflection of a Shaft:Equation 5.2.4

θ=TLJ

The Area for a tube: Equation 5.2.5

A=π r o2−π r i

2

When applied to the Compression or Extension of a Member:Equation 5.2.6

δ=−PLEA

The Volume of a Tube Wall: Equation 5.2.7

V=( π r o2−π r i2 )L

These formulae show that doubling the radius of a tube with constant length, whilst maintaining the same volume of material in the wall will have no effect on the weight or compressive strength of the tube, it will however quadruple the tubes ability to resist torsion or bending moments. In a truss structure such as a bicycle frame, this increases the overall stiffness of the structure, improving its resistance to displacement and deformation under load.

Chart 5.2.10 uses Equations 5.2.1 to 5.2.8 to demonstrate a matched increase in stiffness of 6061 T6 aluminium and 4130 Cromoly steel tubes, with increasing tube outer diameter between 25 and 38 mm.

Stiffness Coefficient used in Chart 5.2.10: Equation 5.2.8

StiffnessCoefficient (γ )=48 EI

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This data is normalised relative to the mass per unit length of 4130 Cromoly steel, with a resulting mass per unit length for 6061 T6 aluminium until a wall ratio of 60:1 is reached for steel.

Wall Ratio and Slenderness Ratio Equation 5.2.9

Wall Ratio¿(φ)=Tube DiameterWallThickness

= dt=

2 ro(r o−r i)

¿TermedWall Ratio ¿avoid confusionwith Slenderness Ratio

Slenderness Ratio ( λ )= Tube LengthRadius of Gyration

= LR

= L√I / A

A 60:1 wall ratio is considered critical in bicycle manufacture (Nichols S, 2015) and other tubular structures. For example, El-Reedy M. (2012) in his textbook “Offshore Structures: Design, Construction and Maintenance” cites 60:1 as the threshold design safety limit for fixed tubular steel structures. Whereas, BS EN ISO 19902:2007 - Petroleum and natural gas industries - Fixed steel offshore structures, 80:1 is considered the maximum safe limit; however through experiment in “Uncertainty quantification and risk assessment of offshore structures,” Obisesan A. (2012) showed that 50:1 is a more practical limit.

This 60:1 ratio appears to be independent of material properties (assuming material homogeneity), as the finite element simulations of Pled F. et Al. (2007), and work carried out by National Advisory Committee For Aeronautics (1947) and National Aeronautics and Space Administration (1970) on Aluminium tubes demonstrates. Homogeneous materials appear to converge at this ratio as the mode of buckling transitions from an axisymmetric concertina mode for ratios <40:1 through a transitional 40:1>60:1 where mixed modes can occur, to >60:1 beyond which Euler and Multi-nodal Shell, or Diamond buckling occur. Singer J. et Al. (2012) confirm this experimentally.

Referring back to Chart 5.2.10 ,the trend for aluminium is continued beyond 38mm matching the ultimate stiffness and maintaining tensile tube strength greater than or equal to that of 4130 steel at 38mm until the same 60:1 ratio is reached for aluminium. This shows that aluminium tubes with larger diameters are capable of matching and even exceeding the strength and stiffness of steel tubes, whilst saving considerable weight. To illustrate these trends visually, scale models of aluminium and steel tubes, generated in SolidWorks, are superimposed over the chart

This demonstration and Equations 5.2.1-5.2.7 have significance in the development of cardboard as a structural material in Sections 6.4-6.9:

Tensile and Compressive Strength of a structural member can only be increased by increasing the axial surface area of the member.

Resistance to Bending Moments and Torsion can be increased by increasing the moment of inertia of a member.

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Chart 5.2.10 the relationship between Stiffness and Mass per Unit Length for 4130 Steel and 6061 T6 Aluminium Tubes with increasing outer diameters. All data sourced from Aerospace Specification Metals Inc

A2

20 25 30 35 40 45 50 550

20,000

40,000

60,000

80,000

100,000

120,000

140,000

0

100

200

300

400

500

600

700

800

900

1,000

Steel Stiffness Coefficient [Pam^4]Aluminium Stiffness Coefficient [Pam^4]Steel Mass per Unit Length [g/m]

Tube Outer Diameter [mm]

Stiffn

ess C

oefic

ient

[Pam

4]

Mas

s Per

Uni

t Len

gth

[kg/

m]

6061 T6Alu-minium

4130 Cro-moly Steel

5.3 Why Build a Bicycle from Cardboard?Cycling is a non-pollutant transport means that “offers people a route out of poverty and a means to improve their lives, giving them opportunities to travel to work and school, giving small scale farmers and traders the opportunity to reach customers further afield, or take more produce to market” (Alexei Sayle, circa 2000).

Table 5.3.1 shows 3 environmental factors associated with the production of raw materials. Steel and Aluminium production are extremely energy intensive and polluting compared to Cardboard production. The water consumption figures include water usage figures in brackets, these show metal production has become more efficient at treating and reusing water than the paper and pulp industry.

It is notable that these figures are for the production of virgin material from its naturally occurring state, and not recycled material. The gains in using recycled materials are similar across the board, saving approximately 60% of the energy and CO2 production, as extracting the raw material from its naturally occurring state accounts for much of these figures.

Global Steel Production

Global Aluminium Production

Global Paper and Board Production

Energy Consumption [kWh/tonne] 4500 14000 12

Water Consumption [m3/tonne] 3 (28) 1 (26) 10(25)

CO2 and Equivalents Production

[tonne/tonne]0.9 9.2 0.4

Table 5.3.1 Environmental Impact of Primary Cardboard versus Primary Metal Production

Bicycles are produced using higher-grade alloys from virgin material. Cardboard is currently produced using an average of 60% recycled material, and it is possible to create products with up to 100% recycled material, although it is optimal to use approximately 15% virgin material in order to maintain strength characteristics (IEA, 2007).

Table 5.3.1 does not tell the whole story of modern high-end bicycle frame production, where the environmental impact of raw material production is compounded significantly using further energy intensive manufacturing processes including welding and heat treatments. Table 5.3.2 presents a manufacturer’s figures for the production of two high-end bicycle frames. It is notable that these are figures per kilogram of frame production, with typical frame mass of approximately 1 kilogram. The figures take into account the entire process from raw materials in their naturally occurring state to final product.

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Specialized Roubaix

Carbon Fibre

Specialized Allez

Aluminium

Energy Consumption [kWh/kg] 420 1600

Water Consumption [m3/kg] 2.2 1.5

CO2 and Equivalents Production [kg/kg] 65 170

Table 5.3.2 Environmental Impact of Production of 2 High End Bicycle Frames

Assuming all 430 million bicycle owners in China (Brown, L., 2009) decided to upgrade to an aluminium bike similar to the Specialized Allez it would consume 688 [TWh] of energy, 22 times China’s total annual electricity output for 2012 (IEA, 2013). The CO2 emissions for each individual would be equivalent to driving a new car 1360 [km], 10% of the average Chinese driver’s annual mileage (Huong Huo et Al. 2012).

Cardboard, or paperboard as it is more correctly termed, is a widely used consumer product mainly used in the packing and shipping industry. It is widely available in all regions, can be manufactured from a sustainable resource, trees, and is 100% recyclable. It is also biodegradable, and can be burnt to create energy at the end of its lifecycle; in fact many cardboard production facilities in Canada are now net Energy producers (IEA, 2007).

Producing bicycles from cardboard will utilise an existing inexpensive recycled product and re-appropriate it for use in the construction of a new product that can then be implemented as a non-pollutant transport means.

5.4 Is Cardboard Suited to Building A Bicycle?As mentioned in Section 1, cardboard has a number of characteristics that make it well suited to use as a packing and packaging material.

Printable Whilst not a structural advantage, it may be a desirable attribute for the production of a bicycle, enabling graphics and possibly advertising to be applied to a bicycle quickly and inexpensively with existing equipment. An end user may even be able to customise their bicycle at no extra cost.

Reusable and Recyclable These are considered sustainability advantages, which make them desirable but non-critical attributes for a structural material; however in many industries regulations governing certain regions dictate that materials must achieve an certain level of sustainability.

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Inexpensive to Manufacture Cardboard is mass produced from Pine trees, an inexpensive, sustainable raw material, renewable through replanting, that is produced on equivalent scales to steel and aluminium.. Trees are felled and processed in a pulping mill into wood pulp, a fibrous material. The pulp is processed in a rolling mill into Kraft paper rolls and further processes by various methods into the different types of cardboard (see Figure 1.2.1)

Corrugated Cardboard is made by passing Kraft paper through a corrugating machine which folds the paper into its rounded wave, or fluted form. Corrugated paper layers are then layered up with flat liner layers and glued together with a corn starch adhesive (Kline J. 1991). This process is facilitated by high pressure steam.

Honeycomb Cardboard is made in a similar way to corrugated cardboard, Kraft paper is passed through a continuous honeycomb core machine which cuts adheres and folds the paper into an expandable hexagonal form. This honeycomb core layer is then laminated up with flat liner layers on both sides, and glued together in a laminating machine.

Cardboard Tubes are produced in a continuous process using a tube laminating machine. Multiple Kraft paper strips are passed through an adhesive bath and over tensioning rollers before being wrapped under pressure by a Mobius belt over a mandrel. The continuous tube passes through a series of cutters that move longitudinally along the tube as it is cut to the required lengths without interrupting the process.

Mechanical StrengthMechanical strength is an essential structural characteristic and vital in the manufacture of a bicycle.

Equations 5.2.1-5.2.7 show Young’s Modulus E, to be a critical value for structural materials, denoting its ability to resist stress whilst exhibiting elastic behaviour. A high Young’s Modulus, high Ultimate Tensile Strength and high Yield Strength are all essential characteristics of a good structural material.

Two groups, one based in Sweden and the other France have made a number of investigations into the mechanical properties of Corrugated Cardboard. The French studies of Allaoui S. and Aboura Z. (with collaborators in 2004, 2008 and 2009) result in data for Young’s Modulus of Kraft paper of 8.5 [GPa] in the fibre biased direction, a feature introduced by the rolling practice during manufacture with 3.5 [GPa] in the lateral direction. The Ultimate Tensile Strength in the fibre biased direction is 40 [MPa], with a Yield at 28 [MPa]. The data agree with the Swedish studies of Nordstrand T. and Nyman U. (with collaborators in 1997, 2000 and 2004), although they achieved Ultimate Tensile Strength as high as 85 [MPa]. This makes raw Kraft paper approximately 25 times less stiff than 4130 Cromoly steel and 15 times weaker (10 times less stiff than 6061-T6 aluminium and 8 times weaker).

Allaoui S. and Aboura Z. (with collaborators in 2004, 2008 and 2009) give values of 630 -850 [Mpa] for the Young’s Modulus of a single “C” fluted constructed board in the Machine Direction (running along the flutes), and 430 – 550 [MPa] in the Cross Direction (across the flutes). Tensile Strength results were obtained of 5 [MPa] and a Yield of 2.5 [MPa] of a single “C” fluted constructed board in the Machine Direction, and a Tensile Strength of 2.9 [MPa] and a Yield of 1.8 [MPa] in the Cross Direction.

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There is very little data available on the mechanical properties of cardboard tubes, therefore part of this project has been dedicated to investigating these properties, see Section 6.1. These tests are limited in scope to obtain data for completing the objectives of this project, however they could form the basis of further research.

Low DensityKraft Paper’s density according to the Scandinavian Pulp, Paper and Board Testing Committee 2001 is 790 [kg/m3] making it approximately 10 times less dense than 4130 Cromoly steel and 3.5 times less dense than 6061-T6 aluminium.

A high grade Kraft paper single “C” fluted constructed board has a quoted mass per unit area of 300 [g/m2] (Teakcroft, 2016), with a thickness of 4.1mm (Allaoui S. et al., 2009) this equates to a density of 73 [kg/m3] equating to 107 times less dense than 4130 Cromoly steel and 37 less dense than 6061-T6 aluminium. Taking the data above, corrugated cardboard has a strength to weight ratio on a par with steel 4130 Cromoly steel and 6061-T6 aluminium.

Given the favourable strength to weight ratio data, it should be possible to use cardboard to create a structural material capable of making a bicycle frame and forks.

5.5 Cardboard’s LimitationsIt is worth considering cardboard’s limitations that affect its suitability as a structural material. These are all considerable issues when considering the manufacture of a prototype bicycle frame and forks.

MoistureCardboard is susceptible to water (see Section 6.8), being a composite of fibres and a bonding agent, starch. Untreated it will degrade and eventually dissolve if immersed in water. Exposed to high humidity cardboards structural characteristics degrade. Allaoui S. et al. (2009).

FatigueAs non-homogeneous composites, cardboard forms are susceptible to anisotropic fatigue and cyclic hysteresis where accumulative strain can cause degradation of the composites structure, causing premature failure at a much lower stress than anticipated. (Chawla, Krishan K. 2012 and Singer J. 2002)

Manufacturing Defects Cardboard is an inexpensive mass produced material used in non-critical applications such as packing boxes, with redundancy built into their structure. Whilst standards for QAQC procedures and mechanical properties tolerances are implemented, they are not as stringent as those employed during the manufacture of critical structural materials. Structural materials undergo strict QAQC procedures, even to the point of CT scanning the materials for defects at the molecular level.

Manufacturing defects could cause unexpected or premature failures despite good design practices.

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6.Technical Approach6.1 Laboratory Testing of Cardboard Tubes

Figure 6.1.1 GDS Instruments 50 [kN] compressive load frame setup for a test with cardboard tube aligned and checked.

Laboratory Testing Results and ChartsApparatusA 50 [kN] capacity, servo actuated ball screw, compressive load frame with spherical seat and 10 [kN] S-beam type load cell are used to apply axial loads to the cardboard samples. A GDS logging interface and a PC equipped with GDS Lab software are used to control and record the tests.

A calibrated steel ruler and Mitotoyu digital callipers are used to measure the sample dimensions, and align the samples.

A calibrated engineer’s spirit level is used to check the load frame is level.

Experimental ProcedureThe test window of the load frame is first adjusted to a suitable height for the samples under test. The load frame is then aligned, levelled, and connected to the logging interface.

The load cell is attached with a spherical seat, a flat ground Perspex loading plate is attached, and the cell wired up to the logging interface.

The logging interface is connected to the computer, and the correct calibration factors entered into the control/logging software.

A test plan is prepared for each type of test:

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For the initial test on each sample type, a series of 3 stress cycles within the elastic region and then a ramp to failure are programmed as 7 separate ramp stages:

1. Ramp up within elastic region at 0.5 [kN/minute] and hold for 1 [minute] (normally accounts for bedding in of the sample)

2. Ramp down 0.5 [kN/minute] and hold for 1 [minute]3. Repeat 1. and 2.5. Repeat 1. and 2.7. Ramp to failure at 1 [kN/minute] (limited by load cell to 10 [kN]

Further repeat tests on each sample type, are ramped to failure in a single stage:

1. Ramp to failure at 1 [kN/minute] (limited by load cell to 10 [kN])

The tests are ended before total failure of the samples due to the angular deviation exceeding a practicable limit of approximately 5°.

Notes:

Sample types A and E through F were all sourced from a single supplier (CT).

Sample types B through D are recycled architectural bond paper roll cores from another supplier (HP).

Sample types C and D have been modified as outlined in Section 6.4 Tube Development, with ribs and stringers. Both have four 5.2 [mm] thick stringers, C†

has 5.2 [mm] thick radial ribs at 20 [mm] spacing, whereas D†† has 5.2 [mm] thick ribs at 10 [mm] spacing. Table 5.1 forms a summary of unconfined compression tests on cardboard tubes, charts can be found in APPENDIX A relating to these results.

Sample types A and E through F were all sourced from a single supplier, Cores and Tubes (CT), Croydon.

Sample types B through D are recycled Hewlett Packard (HP) architectural bond paper roll cores.

Sample types C and D have been modified as outlined in Frame Construction with ribs and stringers. Both have four 5.2 mm stringers, C† has 5.2mm ribs at 20mm spacing, whereas D†† has 5.2mm ribs at 10mm spacing.

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Results

Sample Number

Tube O.D.

[mm]*

Tube I.D.

[mm]*

Young’s

Modulus [GPa]

0.02% Yield Stress [MPa]

Ultimate Compressive Stress [MPa]

A1 34 26 1.18 4.2 6.32

A2 34 26 NA 5.28 6.25

A 34 26 1.18 4.74 6.29

B1 55 51 1.56 5.90 8.46

B2 55 51 NA 6.80 9.27

B3 55 51 NA 4.15 5.50

B4 55 51 NA 7.30 10.63

B 55 51 1.56 6.04 8.47

C1† 55 51 1.54 5.96 9.88

D1†† 55 51 1.28 9.55 10.32

E1 50 45 1.38 4.72 6.22

E2 50 45 NA 4.65 6.50

E 50 45 1.38 4.69 6.36

F1 34 26 1.04 2.36 5.35

F2 34 26 NA 3.37 6.18

F 34 26 1.04 2.87 5.77

Table 6.1.2 Summary of results from unconfined compression tests on cardboard tubes

Table 6.1.2 forms a summary of unconfined compression tests on cardboard tubes. A complete set of charts can also be found in APPENDIX A relating to these results, along with photos of tested samples.

DiscussionChart 6.1.3 illustrates the combination of modes of failure by which cardboard tubes fail under axial compression throughout a 1 [kN/min] load ramp. All tested samples of types A-E failed in the sequence indicated:

1. Yield caused by lateral delamination of the paper layers creating a larger effective surface area, and stabilising the structure temporarily as load increases.

2. The sample shears at an embedded seam like spiral manufacturing flaw between the helical windings.

16

3. The sheared section causes the tube to destabilise and the load deviates from acting axially causing the tube to buckle inelastically, kneeling to one side.

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0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

2

4

6

8

10

12

B20.2% Line

Strain ԑ

Stre

ss σ

[MPa

]

Chart with Figure 6.1.3 Typical Stress – Strain response of a spiral wound cardboard tube to 1kN/min load ramp to failure

A3

1

2

312

3

0 0.0005 0.001 0.0015 0.0020

200000

400000

600000

800000

1000000

1200000

f(x) = 1192005217.14453 x − 730086.664210364R² = 0.999949195202444

f(x) = 1184031803.82497 x − 686937.8921011R² = 0.999946556759759f(x) = 1172857758.37626 x − 627995.553799508

R² = 0.999969371466131

Stress V Strain

Strain ԑ

Stre

ss σ

[MPa

] "Bedding in of sample"

3 "Elastic" rampsto ensure repeat-

ableYoung's Modulus

Trendline Equations

Hysteresis

A1

Chart 6.1.4 Typical Stress – Strain response of a spiral wound cardboard tube to 0.5kN/min elastic load ramp cycles on sample A1.

0 0.005 0.01 0.015 0.02 0.0250

2

4

6

8

10

12

B20.2% LineC10.2% LineD10.2% Line

Strain ԑ

Stre

ss σ

[MPa

]

Chart 6.1.5 Comparison of Stress – Strain response of spiral wound cardboard tubes with differing levels of reinforcement to 1kN/min load ramp

A4

The only exception to this sequence were the type F samples which had a slenderness ratio ( λ ) of approximately 10:1, double any of the other tubes which all had a slenderness ratio ( λ )of approximately 5:1, and a wall ratio (φ) of 6:1 versus 9:1 respectively. It was noted during the F sample tests that the tubes began kneeling outward before yielding by local delamination of the paper layer construction. This occured on the side of the end face toward which the tube was kneeling as it came under increasingly bias load. There was very little spiral winding seam shear.

Chart 6.1.4 demonstrates the typical response of a spiral wound cardboard tube to the initial 0.5kN/min load cycles. The first cycle forms a “bedding in” phase, where any irregularities in the cardboard tubes cut edges at both ends are loaded and the surfaces flattened. When the sample is then unloaded and reloaded in the second cycle it behaves in a more conventional elastic manner forming a straight line Stress versus Strain response. This process is repeated to enable a repeatable mean value for Young’s Modulus to be obtained. A small hysteresis and a slight hardening of the sample is produced between cycles, evident from the progressively increasing gradient of trendlines; however this is an limited effect of less than 1%.

Figure 6.1.6

Tested cardboard samples; Left to Right - B2, C1, D1

A notable result is that not all cardboard tubes are made equal, the HP tubes have superior mechanical properties to the CT tubes; they are approximately 50% stiffer and stronger. The tubes intended for use in the construction of a bicycle frame and forks are the CT tubes, CT is very kindly supplying the tubes free of charge (FOC) in production line lengths, which are longer than cut down commercially available lengths.

The CT tubes result in the following mechanical properties, which are used to develop the bicycle frame and forks in Sections 6.2-6.7:

Young’s Modulus = 1.2 [GPa]

Yield Strength = 4.7 [MPa]

Ultimate Compressive Strength =6.3 [MPa]

Chart 6.1.5 compares the Stress versus Strain response of tube types B, C and D. Types C and D have been modified as outlined in Section 6.4. As predicted, the small amount of axial surface area added to the tubes cross section in samples C1 and D1 has increased the axial mechanical properties. The Young’s Modulus has not changed significantly as the material composition has not been altered; however a 60% increase in Yield Strength and a 20% increase in Ultimate Compressive Strength

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have been achieved in the most reinforced D1 sample. Most interesting is the nature by which this appears to have occurred.

Studying the samples in Figure 6.1.6 it is evident that the less reinforced sample C1 failed in the same manner as B2 delaminating and buckling at one end through an embedded spiral flaw; D1 however failed by spirally delaminating along the entire length of the tube at every seam. It can be concluded that rib and stringer reinforcements have stabilised the tube along its length, preventing failure at an isolated weak point, most likely a manufacturing defect. This allowed the full potential strength of the tube to be realised.

6.2 Frame DesignExisting Frame Designs

The earliest bicycle frames were of the simple beam design, which has become more popular recently with the uptake of foldable bicycles for commuters. The Lotus bicycle that Chris Boardman won an Olympic Gold Medal and broke many world records on is a Z or S-beam variation of this design.

Ever since its perfection in the late 1880’s the double triangle or diamond truss design has been the design of choice for bicycle manufacturers. This is due mostly to the sound engineering of a triangle truss, where forces are transmitted in “straight lines” along the tubes, which reinforce each other, spreading the load through the “incompressible” triangular structure efficiently.

These 2 predominant design types are quite often combined, with a beam bridging the head tube and seat tube, and a triangle truss connecting the rear wheel to the seat tube. The other significant category in terms of numbers is the Monocoque. Most

monocoques could be classed as a variation on a beam structure; however they are normally formed as a complex single element designed in its entirety with radically varying material thicknesses throughout.

Another interesting design, the Moulton Space Frame, which formed the basis of one of the fastest bikes to have been designed; and is now outlawed in competitive cycling along with Z or S-beam designs.

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Figure 6.2.1 Moulton Speed

Emphasis in this project is placed on designing a double triangle truss frame with cardboard tubes. There are many reasons why the double triangle truss has been the staple of bicycle designs for 140 years, including the fact that it is forced upon the designers of competitive bicycles by the UCI, cycling’s governing body, however it remains a design classic and lends itself well for static and dynamic analyses.

GeometryThere are a number of different factors to take into account when designing a bicycle. For example, there are at least six different commercially available wheel sizes, 650c, 700c, 26”, 27.5”, 29”, not including folding or children’s bicycles. Due to budget constraints on this project a selection of donor parts will be used, constraining the frame design. These are listed in APPENDIX D.

There are a number of dimensions and angles formed by a bicycle frame and forks that directly affect the handling and comfort of a bicycle, typical values are summarised in Table 6.2.3.

Figure 6.2.2 Critical frame dimensions affecting bicycle handling with the proposed values for a cardboard frame.

1. Seat Tube Angle – A steeper seat tube angle shortens the top tube and opens the rider’s hip angle. When incorporated with dropped handlebars, this places the rider in a more forward position laid over the bicycle favoured by road and track cyclists. Conversely, a shallower angle lengthens the top tube and closes the rider’s hip angle. This forces the rider into an upright position favoured by mountain bikers and leisure cyclists, often encouraged by a shorter stem and upward swept handlebars. Another effect of a shallower seat tube angle is the shortening of the seat stays, this makes for a stiffer more responsive rear end when pedalling and steering

2. Head Tube Angle – A steeper head tube angle creates more responsive steering that requires a smaller input force to change the front wheel angle; racing road bikes often have a very steep head tube angle, to make them feel light, agile and responsive. Conversely, a shallower angle creates a heavier, slower, less edgy steering response favoured by mountain bikers and leisure cyclists.

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Head Tube Angle

Seat Tube Angle

Trail

BB drop

3. Trail – Has a more significant effect on steering response than head tube angle. A bicycle can be leaned into a turn, moving mass over to one side of, and creating a radius between the front and rear tyre contact patches. The bicycle will naturally follow this radius.Trail is the term used for the offset between the tyre to ground contact patch and a line projected along the head tube and forks to the ground. Less trail creates a lighter, more nervous feel, whereas increased trail creates a more stable, but heavier feel that will tend to self-centre the steering angle when the bicycle is upright and moving forward.

4. Bottom Bracket Drop –A lower bottom bracket places mass below the wheel axles creating a more stable, “on rails” feeling when the bicycle is leant over while cornering. It takes less effort to lean the bicycle creating a more agile, responsive feel. A higher bottom bracket raises the overall centre of gravity, when cornering this requires more effort to lean the bicycle into a corner, and creates a less stable feel.Too low a bottom bracket restricts pedalling when cornering and the irregularity of terrain over which the bicycle can be ridden.

Bicycle Type Seat Tube Angle [°]

Head Tube Angle [°]

Trail [mm] Bottom Bracket Drop

[mm]Road Racing 72-76 70-74 40-70 50-70City/Touring 70-74 70-72 60-80 50-80

Mountain Bike 70-74 66-72 60-100 10-50Downhill

Mountain Bike66-70 64-68 75-150 (-50)-25

Table 6.2.3 Typical ranges of critical bicycle geometry values

Ergonomics are the most important consideration in bicycle geometry, as the rider may have to be seated and pedalling for prolonged periods. A number of different bicycle types have been mentioned, all with different objectives. The riding position of any bicycle should be as comfortable as possible taking into account these objectives. People range in a number of metrics that effect bicycle design, height, leg length and arm length and foot size being among the most important.Before carrying out any structural analysis, a generic bicycle double triangle truss frame to establish the geometry of the proposed design has been modelled in SolidWorks. (see Figure 6.2.4 APPENDIX C). The proposed geometry suits a rider 175 cm to 185 cm and places the rider in a neutral position typical of that of a city hybrid bicycle or mountain bicycle.

6.3 Finite Element AnalysisA generic frame and forks assembly have been modelled in SolidWorks (see Figure 6.2.4 APPENDIX C). These form the basis of an FEA investigation involving a number of simulations using input data from “Bicycle frame optimization by means of an advanced gradient method algorithm” (L.Maestrelli, A. Falsini, 2008), data which is believed to originate from “Forces applied to a bicycle during normal cycling”. Journal of Biomechanics 12, 527-541 (Soden, P. Adeyefa, B. 1979), although it is not clearly cited.

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Further input data is calculated from the test parameters for evaluating bicycle frames and forks in “BS EN ISO 4210-6:2015 Cycles — Safety requirements for bicycles - Part 6: Frame and fork test methods”. The principle of conservation of energy has been applied, and the Work-Energy method has been applied to the drop test requirements in the “Falling Mass Test” and the “Falling Frame Test” to calculate forces for static analyses. A 25% rebound has been assumed, based upon videos available online of a selection of these tests.

This section forms a summary of the findings, and has been used as a tool for highlighting the areas of most concern in the design of a cardboard bicycle frame and forks. Loading details and results for each test can be found in APPENDIX B. These analyses have been important in understanding the nature of stresses placed on a bicycle.

Figure 6.3.5 Resultant Von Mises Stress - Generic Frame and Forks Assembly- 6061 T6 Aluminium -Analysis 1 - Static Study - Seated Whilst Pedalling Right

Pedal

From the analyses six main areas of concern have been identified, these are illustrated in Figure 6.3.5 and numbered in order of severity:

1. Downtube - In every simulation, the area at the top of the downtube, just behind the head tube encounters high stresses. This is a well-documented (Dwyer F et al. 2012) area for fatigue failures in aluminium bicycle frames. The downtube is frequently made a larger diameter and wall thickness to compensate for these stresses and is often reinforced by means of a welded, shaped metal plate called a Gusset.

2. Bottom Bracket - In all pedalling simulations the bottom bracket area confronts high stresses. This is another well-documented (Callens A., Bignonnet A., 2012) area for fatigue failures in aluminium bicycle frames. The area behind the chain stays is often reinforced with a CNC machined yolk to increase strength and stiffness.

21

1

2

34

56

3. Handlebars – Due to their nature to act as a lever, the handlebars endure high stresses at their base; this is a serious concern in this project, as handlebar failures can cause serious accidents, with severe consequences to the rider. There is a separate section of BS EN ISO 4210 specifically for handlebars that is more commonly enforced by governments than other sections

4. Seat Stays and Top Tube– When the rider is seated, the top of the seat stays and the top tube encounter high instantaneous stresses when bumps or drops are negotiated by the rider.

5. Fork Crown – The fork crown forms a junction between the members supporting the front wheel and the frame, therefore it must communicate any load transfer between the front wheel and the rest of the bicycle. This places high stresses on this area, even during simulations where the principle forces are pedalling.

6. Chain Stays- The chain stay area around the rear dropout experiences high stresses during static pedalling simulations due to the chain tension from the transfer of power to the rear wheel.

There is an obvious commonality between these areas of high stress, they all occur near junctions between members. This places extra emphasis on the design of joints in Section 6.5, as they will be essential to the success of a prototype frame and forks.

Figure 6.3.20 shows an early simulation performed as an experiment, using the mechanical properties to make a preliminary assessment of cardboard as a bicycle frame material. The image shows three identical frames, except they are made of different materials

4130 Cromoly Steel 6061-T6 Aluminium CT-Cardboard Tube

Figure 6.3.20 Displacement [mm] of a generic bicycle frame under an asymmetrical pedalling load of 1000N, simulating a static the BS EN ISO 4210-6:2015 Pedal Spindle

Fatigue Test for 3 materials.

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6.4 Tube DevelopmentThrough the literature review and cardboard tube testing, the mechanical properties established show cardboard to be comparable to metals in yield strength and ultimate tensile/compressive strength on strength to weight ratio basis. Therefore adding more material, by increasing the wall thickness of tubes it is possible to make cardboard tubes strong enough to build a bicycle frame. The Young’s Modulus of cardboard is proportionally inferior to metals on a strength to weight ratio basis, so the resulting frame would suffer from being too compliant.

Referring back to Equations 5.2.1-5.2.8 it is evident that there are two properties of a tube that effect its resistance to both bending and twisting, these are Young’s Modulus (E) and the Moment of Inertia (I or J). Young’s Modulus is a property inherent to the material itself, and in this case remains fixed, so a method must be found to increase the Moment of Inertia of the tubes.

One method, as shown in Chart 5.2.10 (see APPENDIX A) is to increase the tubes outer diameter. Another method is to increase the distance between the inner diameter and the outer diameter. The simplest way to do this is adding material is to make the wall thickness greater. For a bicycle, this becomes impractical with the thicknesses required, as the mass becomes too great: Calculation 6.4.1 compares the bending of a typical Aluminium 6061-T6 tube with a stiffness matched cardboard tube. The following assumptions have been made:

Aluminium 6061-T6 has a Young’s Modulus of 68.9 [GPa], 57 times stiffer than Cardboard at 1.2 [MPa] see Section 6.1.

An typical Aluminium tube wall thickness for a 38 [mm] down tube can be as thin as 1.0 [mm] between butts (most of its length) (Columbus, 2014).

For an equal displacement (δ ) from two different materials, the stiffness coefficient( γ )=48 EI must be equal.

Equation 5.2.1 → Calculation 6.4.1

I aluminium=π19 [mm ]4

4−

π18 [mm ]4

4=1.99×104[mm4]

Equation 5.2.2, assuming (P) and (L) remain constant →

∴ γaluminium=48×68.9 [GPa ]×1.99×104 [mm4 ]=6.58×104 [N m2 ]

∴ I cardboard=6.58×104 [N m2 ]48×1.2 [GPa ] =1.14×106 [mm4 ]

Increasing the cardboard tube outer diameter to a reasonable size of 70 [mm], considering it must fit between the rider’s legs:

ri={4π ( π 35[mm]4

4−1.14×106[mm4 ])}

14=14.6[mm]

Therefore, a cardboard tube with a 70 [mm] outer diameter and a 29.2 [mm] inner diameter would have the same stiffness coefficient ( γ ) as a typical aluminium bicycle downtube.

23

The mass per metre of these tubes for comparison would be:

μaluminium=ρaluminiumV=2700 [kg /m3 ] (π (19×10−3 )2 [m ]−π (19×10−3 )2 [m ])×1m

¿0.314 [kg ]

μcardboard=ρcardboardV=790 [ kg/m3 ] (π (35×10−3 )2 [m ]−π (14.6×10−3 )2 [m ] )×1m

¿2.51 [kg ]

This would make the cardboard bicycle frame very heavy. The solution is to borrow principles implemented on existing structural members to increase the moment of inertia whilst minimising weight from other structures. A good example is an I-beam, which places the majority of the material in the flanges, as far from the centroid of the cross-section as possible, whilst remaining joined by as narrow a web so the beam may act as a single member. Consideration was made of a number of ideas:

Figure 6.4.2 Early Development Ideas

Different shaped tubes are fashionable in modern bicycles. Often they gain moment of inertia benefits in one plane however; they will always make a compromise in another plane.

The chosen objective is to develop circular profile cardboard tubes, increasing their moment of inertia by joining a tube within a tube using a honeycomb structure between the two tubes.

Honeycomb structures are already used in cardboard products (see Section 1), and have been used in the development of spacecraft and racing car chassis to create strong, stiff, lightweight structures. The assembly will have the effect of creating a tube with a small inner diameter and a large outer diameter with a fraction of the mass, and allow optimisation of the corrugated cardboard reinforcements flute and Kraft paper machine direction orientations.

Figure 6.4.3 (see APPENDIX C) illustrates the design and manufacturing process of the reinforced cardboard tubes for use in the bicycle frame:

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1. From development sketches, profile drawings were created in AutoCAD, these were transferred to the laser cutter.

2. After developing a custom laser cutting profile for cutting corrugated cardboard, ribs and stringers were laser cut.

3. A working prototype reinforced tube was constructed, shown with a cutaway to demonstrate the internal structure.

4. The prototype was evaluated, and deemed too heavy, so a model was developed in SolidWorks for lightweight reinforced tubes for laboratory testing. The model was broken down into rib and stringer profiles and laser cut using the methods learnt in steps 1. To 3.

5. The method developed for assembly of the tubes in step 3. was improved, a method that is carried through the project:

.

Figure 6.4.4 Final Bicycle Frame Down Tube, before shaping of reinforcement core.

Laser cut ribs and stringers are assembled, bonded together, then the inner tube is slid in and bonded into the assembly, and finally the outer tube is slid over and bonded to the inner assembly.

The final image in Figure 6.4.3(see APPENDIX C) demonstrates the component parts of the test compound tubes at different stages of construction, from right to left, Inner Tube, Inner Tube inside Reinforcement Assembly, Reinforcement Assembly, Outer Tube, Fully Assembled Reinforced Tube.

The final reinforced tube is better illustrated by Figure 6.4.4which shows the end one of the final bicycle tubes constructed before final shaping of the reinforcement core to match the coped outer tube (see Section 6.5).

6.5 Joint DevelopmentOne of the major obstacles to the design and construction of a circular profile tubular double triangle truss frame is the joining of the component tubes. Two methods are used to joint metal bicycle frames, welded butt joints and brazed tubes into lugs.

Welding is an excellent method for joining circular profile metal tubes, where effective penetration and well formed fillet profile can be attained, however many materials, including composites, cannot be welded.

Brazing tubes into lugs was the primary method of manufacture of bicycles until the 1970’s, when welding techniques and material improvements enabled welding to become the predominant method. Lugged jointing lends itself well to materials that

25

cannot be welded and has had a renaisance with the advent and proliferation of carbon fibre bicycles.

The lug forms an oversized junction of sleeves, that the main tubes are bonded into. The main benefit of lugged construction for composite materials is the maximisation of bonding area. There are a number of factors affecting the strength of a bonded joint as discussed in Section 3 of “Design Requirements for Bonded and Bolted Composite Structures” (Broughton et al. 2002), the most important factor being the maximisation of bonding area.

For this project, lugs formed by an oversized tube have been developed. The oversized tube is pierced by the main frame tubes (top tube, down tube and seat tube) which are in turn pierced by the bearing housing tube for the moving part (steerer tube, bottom bracket axle or seat post). The assembly is filled with an integral matrix of bonded corrugated cardboard which has a number of intended benefits versus a bonded or welded butt joint:

1. The inter-piercing of tubes provides a mechanical pin joint fixing. Once assembled and bonded this increases the stiffness of the joint and prevents the main frame tubes from being pulled out of the junction.

2. By combining both an internal butt joint and a long sleeve joint the bonding area is maximised.

3. The corrugated cadboard matrix increases the contact surface area of the lug sleeves, and also provides a support structure to spread static loads and dampen dynamic loads, in the same manner as a spoked wheel.

In designing the lugs a number of challenges have been overcome; including designing coping patterns for internally butted pierced tube joints, and creating complex, joined matrices of laser cut cardboard profiles, see Figure 6.5.2.

Coping the tubes involved modelling the tubes in Solidworks and using the Sheet Metal function to unroll the tubes into flat patterns. The patterns were precisely adhesive taped to each tube, and the tubes cut with a sharp craft knife.

26

Tube Bonded to Matrix

Tube Butt Jointed

and Bonded to Head Tube

Bearing Housing Tube Inserted and Bonded to Matrix

Main Frame Tube Inserted

Tube Bonded to MatrixTube Bonded to MatrixTube Bonded to MatrixTube Bonded to Matrix

Tube Butt Jointed

and Bonded to Head Tube

Tube Butt Jointed

and Bonded to Head Tube

Tube Butt Jointed

and Bonded to Head Tube

Tube Butt Jointed

and Bonded to Head Tube

Figure 6.5.2 Final Head Tube Joint under construction, illustrating the principles of the jointing system developed for this project.

6.6 Construction of the Front TriangleThroughout the processes described in Section 6 a CAD model was being developed and refined, culminating the final model displayed in Figure 6.6.1 (see APPENDIX C) was realised. In addition to generating the production drawings, sections for laser-cutting and coping patterns for the frame and fork components, this model was used to produce the jig required to assemble them, see Figure 6.6.2.

A jig is an essential tool in achieving accurate and precise construction of a frame. The jig holds the components in the correct position whilst the components are joined. In this instance, the jig also aided construction by providing a guide for sanding the lug tubes to achieve the correct angles and separation required for a well-bonded joint. This is critical stage in construction, any sizing or alignment problems will cause excessive flexing and could result in point loads at the joints, leading to fatigue and failure.

The frame was first assembled dry within the jig to check angles and dimensions, and to fine-tune the fit within lugs. Then the tubes were disassembled, adhesive applied to the lugs and tubes, reassembled, and finally clamped in the jig and left to dry for 24 hrs.

Figure 6.6.2 Left, Section through model developed in SolidWorks of front triangle – Right, Frame components in the process of assembly in the frame jig, more photos of

construction are included in APPENDIX C.

6.7 Re-Design and Construction of Rear Triangle Initially the intention was to use cardboard tubes for the rear triangle of the bicycle, however whilst modelling the design in CAD a number of problems were encountered and a different solution had to be developed.

The first issue with using cardboard tubes for the rear triangle is that the diameter of tube required to support the loads predicted would have to be so large that where they are jointed to the front triangle, the joints would interfere with the rider’s legs when pedalling.

The other main issue is packaging the moving parts necessary to drive the rear wheel around the tubes is not possible.

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During research of cardboard forms and the search for material suppliers, contact was established with a supplier willing to supply Tri-Wall cardboard at no cost. Tri-Wall is a triple layered corrugated cardboard made of 3 C fluted layers interleafed with 5 paper liner layers. It is claimed to be incredibly strong, a single layer can support 680 [kg/m2] during transport (ULine 2016).

This led to the design of a tri-wall cardboard rear triangle incorporating a number of features illustrated by Figure 6.7.1 (see APPENDIX C)

A folded junction under the downtube running along the flute direction to maximise the bonding area of the interface between the front and rear frame triangles

Introduction of a third triangle to optimise the directionality of the Tri-Wall cardboard rear triangle in the flute direction, maximising strength and stiffness

Use of the existing front triangle lug joint tubes at the bottom bracket and top of the seat tube to act as pins; spreading the load over as large an area as possible and acting as a mechanical joint to prevent reliance on adhesive joints.

Multiple layers of cardboard to increase strength and stiffness of the rear triangle, one of which is removable to allow access to the drivetrain and brake parts for setup and maintenance

6.8 Construction of Forks and Prototype Front WheelUsing the lessons learnt, and methods developed in designing, manufacturing and constructing the cardboard bicycle frame explained in Sections 6.2-6.7, forks and a prototype front wheel have been produced. Models and photographs of the final products can be viewed in APPENDIX C.

6.9 WaterproofingSection 5.5 highlights the sensitivity of moisture to cardboard. This is a major limitation of cardboard as a structural material. Cardboard tubes are produced in a waxed coated form, which are claimed to be waterproof for shipping crucial architectural drawings and similar items.

Through research a number of methods of waterproofing were explored. Most of the methods encountered involved volatile organic chemicals and unsustainably produced resins. An interesting Epoxy resin called Poly-Soy was discovered, a resin produced from 100% Soya protein, a natural renewable resource, and the supplier was willing to supply a sample at no cost, however there are shipping restrictions as they only manufacture the product in the U.S.A.

The prototype frame and forks have been coated in two coats of diluted Polyvinyl Acetate followed by two coats of Polyurethane Varnish. Similar to fatigue, waterproof coatings require long-term evaluation, and could form the basis of further research work.

6.10Prototype TestingPrototype testing is an area of the project that has been neglected up to this juncture. The ambition at the outset of the project was to test the prototype frame and forks using some or all of the BS EN ISO 4210-6:2015 tests.

28

These tests are not a legal requirement in any state or country yet, but form the basis of good practice for safety assurance in the bicycle industry. The standard for frames and forks contains 14 tests.

Two quotes were obtained from a German testing centres for these tests one had a breakdown of tests ranging from €150-€500 per test, the other quoted a discounted rate of €5000 for a full suite of tests. These costs are beyond this projects budget; however the development of testing apparatus would form a very good basis for future work. There is currently only one recognised provider of these tests in the U.K., Bureau Veritas, this may leave a gap in the market which forms an opportunity for an institution such as a University to develop and offer such testing.

7.Results and Discussion7.1 Evaluation of the ProjectThis project was ambitious from the outset; in essence it constitutes the marriage of two projects in one; “The Testing and Development of Cardboard Tubes as a Structural Material”, and “The Design and Construction of a Cardboard Bicycle.”

Through the testing and development of cardboard tubes as a structural material, interesting insights have been made in an area where very little prior work exists. If engineers and architects are to develop the use of cardboard as a structural material, this provides a solid building block for future work. This work could be expanded and developed in a great many directions:

Testing of more samples from a variety of manufacturers, in differing dimension ratios, both slenderness (λ) and wall thickness ()

Development of a means for analysing the material density and homogeneity for cardboard tubes

Bending moment and torsion testing Dynamic and long term fatigue testing Investigating environmental effects, such as humidity/moisture effects and

ambient temperature

Section 6.1 and APPENDIX A demonstrate a strong correlation of the nature by which spiral wound cardboard tubes fail under axial compression. This could give insight to the manufacturers of cardboard tubes as to the methods by which they could produce stronger tubes and eliminate manufacturing defects.

Spiral wound structures are employed in ventilation ducts, pipelines and drill pipe. The study of spiral-welded pipes is a well-documented field that has major implications in the Oil and Gas Industry (Winston Revie R. 2015). Spiral wound pipes are inexpensive to produce and can be made in a continuous process like cardboard tubes, however there are structural consequences to this method of manufacture that in certain situations make them inferior to drawn, extruded or straight seamed pipe.

The design and construction of a cardboard bicycle frame has been a much larger undertaking than anticipated, (see Sections 6.2-6.9 and APPENDIX C). Ordinarily a small team of engineers and designers would be employed to design and construct a bicycle frame and forks from conventional materials. Compounding this with attempting to design and build a frame using a novel composite material, whose properties are virtually undocumented has been a considerable challenge for an

29

individual. It has been a great achievement to produce a prototype bicycle frame and forks from materials researched, tested and developed in the course of this project.

The workload and underestimation of task duration has led to overruns on some of the later scheduled tasks critical to evaluating the final product. This will not be overlooked and the project remains ongoing until the presentation and submission of the hardware on the 13th June 2016. Before this date, the outstanding tasks will be completed, and the author will attempt to prove the bicycle during the presentation.

7.2 Evaluation of the materials developed The reinforced cardboard tubes developed during the project proved to be stronger and stiffer than their constituent parts during the compression testing completed in Section 6.1. Combined with the further development made after this testing and improved construction techniques a substantially stronger and stiffer material has been produced capable of supporting more than the 1 [tonne] on a single 56 [mm] outer diameter tube, that the testing samples sustained, see Chart 6.1.5.

These tubes are manufactured from a material that in this instance is made from at least 85% (potentially 100%) recycled raw material, and remains 100% recyclable at the end of its lifespan. This could have implications for the use of cardboard tubes in structural situations as a sustainable alternative to existing materials.

Low cost sustainable buildings – i.e. temporary housing in disaster areas, temporary classrooms for schools, temporary repair/support kits for structures awaiting final repair

Low cost structural medical aids, temporary wheelchairs, crutches and prosthetic limbs, or permanent ones for those who cannot afford current offerings

Manufacturing techniques would have to be improved and altered for scalability. The 56 [mm] outer diameter, 22 [mm] inner diameter tubes 800 [mm] long took 1 [hr] to laser cut and 6 [hrs] of labour to construct, followed by 12 [hrs] adhesive curing time and waterproof coat curing time. The laser cutting time could be slashed to a few seconds with investment in the production of a single cutting die, such as those used to cut cardboard boxes from sheets of corrugated cardboard, however labour time would still be considerable.

The best solution would be to develop a structural medium that could be produced in a continuous process, similar to the fluted/corrugated layers used in corrugated cardboard sheets, or the honeycomb filler used in honeycomb panels. This structural spacer could be integrated into the production of tubes with the benefits gained from an increased moment of inertia.

It remains to be evaluated whether the materials developed are truly suitable for constructing bicycles. The real tests are long term, nearly all bicycle failures are due to accumulated fatigue. It is well documented that composite materials, especially laminated materials, often suffer from separation of the structural material and matrix material when fatigued. No information is available on the ability of spiral wound cardboard tubes to resist fatigue, so this project produce ongoing insights should the bicycle frame and forks last for any duration, as the author intends to fatigue test it through use.

30

7.3 Evaluation of the design processTo maintain relevance to the pursuit of a BEng in Mechanical Engineering a theory and FEA based design process has been emphasised. A fundamental Product Design Specification has been included see APPENDIX D. Further use of design tools like Functional Decomposition, SWOT Analysis and a Scoring Table would have been useful, however when only considering an individual’s views these types of analyses can be biased and result in a constrained outcome, even when the individual sets out to be objective. Consultation with other engineers and designers or collaboration in a team would be a huge advantage in this type of project, leading to a greater diversity of ideas and solutions.

The Finite Element Analysis represents a considerable amount of valuable work. Whilst researching this project and requesting rudimentary data as a starting point for analysis, it was discovered that mainstream companies are very protective over the data produced by this type of work. An excellent academic exercise would be to use sensors and strain gauges attached to a modern bicycle frame and perform tests to gather empirical data, and then use that data as a basis for an FEA model. This type of analysis would have been very valuable as the existing data in the public domain is dated.

For a thorough, more diverse design process, it would be advisable to have performed a survey of potential customers. It may be that Izhar Gafni, see Section 1. has already provided an answer to the customer appeal aspect of a cardboard bicycle in his products failure to raise capital. This may be the restriction on the viability of a cardboard bicycle as a consumer product, the lack of a market.

7.4 Evaluation of the project management processOverall the project planning has been well executed, the Gantt Chart produced (see APPENDIX E) has been very useful in guiding the project, and has allowed a good balance of work progress and production quality. Unfortunately, some of the later tasks, which through the design have become critical to the final product, were underestimated in complexity and duration. Their complexity has led to the requirement of advice and assistance from technicians, which has required alterations to the schedule and schedule synchronisation considerations.

It has been exceptionally useful to develop a working relationship with most of the Engineering Department technicians, all of whom have provided excellent guidance in the use of the Universities engineering facilities; this has expedited the progress of the project.

7.5 Evaluation of the final productCraig Calfee, one of the foremost custom bicycle builders in the world was contacted early on when searching for FEA data in the conception of this project; his personal reply included a short but poignant 2 points:

1. Consider the real world economics of the finished product, including labor.

Both Phil Bridge and Izhar Gafni claimed they could supply a $20 (£14) retail cardboard product to the market and cited this as one of their primary reasons for designing a cardboard bicycle. There are complete steel bicycles available in the UK

31

for $120 (£84.99, sportsdirect.com,.2016) Taking into account 20% VAT, and other taxes, rates and overheads; this probably results in a cost to the retailer of $30-$40 (£20-£27) for a complete bicycle.

During this project the materials were donated free of charge. Comparison with retail sellers in Table 7.1, see APPENDIX D show the material costs to be £35 ($50), adjusting for bulk scaling could probably bring this down to $20-$30 (£14-£20), but this takes no labour into consideration and does not allow for any of the components necessary to drive and stop a bicycle. The labour and laser cutting costs, again donated free of charge on this project, amount to £2115 ($3080), assuming market costs for the laser cutting and minimal labour costs of the author at £15/hr, which when accounting for National Insurance and other business rates would approximately represent the minimum wage.

2. Have fun with it and make it something you can be seen riding without embarrassing yourself.

The project has been successful in producing a prototype cardboard bicycle frame, forks and wheel. The dimensional tolerances achieved (see APPENDIX D) and aesthetic finish (see APPENDIX C) exceed the author’s expectations.

Two questions are asked earlier in Section 5: “Why Build a Bicycle from Cardboard?”, and “Is Cardboard Suited to Building a Bicycle?” This project, the data presented and the arguments made all provide a case presenting cardboard in a favourable light, whilst addressing some of its limitations. As a project, it has been informative, challenging and an excellent test of the author’s mechanical engineering skills.

When regarding the feasibility of a cardboard bike as a consumer product the best question to ask would be, “Would anyone buy a bicycle made from Cardboard?” The evidence does not weigh heavily in favour of cardboard.

A possible means by which to successfully market a cardboard bicycle would be to develop a kit that could be assembled with no adhesive or tools in an hour or two, similar to 3D printer kits. It could be delivered in the cardboard tubes used for the build. The product could very easily and inexpensively have customised graphics printed on it. If produced at a low enough cost it may be a marketable corporate promotional/advertising product.

Conclusions This project is successful in fulfilling its aims, Section 3. Cardboard Tubes have been tested and developed as a structural material

founded on theoretical analysis and empirical testing. A prototype bicycle frame and forks have been designed and constructed.

This project has delivered on all of its deliverables, Section 4.

Evidence has been presented in Sections 5 and 6, proving cardboard is a practicable structural material that has well established sustainability benefits over existing materials.

An elementary insight into the modes of failure of spiral wound cardboard tubes under compression has been presented, in Section 6.1.

32

It has been imparted and backed-up by theory and simulation that a bicycle frame is an excellent structural exercise for comprehensive analysis of a structural material, Sections 5 and 6.

Strong evidence has been presented, and before the final submission stage of this project a definitive answer will be obtained to prove it possible to build a structurally viable bicycle frame and forks from the materials developed.

Currently there is no viable market for a cardboard bicycle; it is therefore not a saleable product, but formed an interesting mechanical engineering pursuit.

.A number of future work opportunities have been identified, some of which may form valuable research projects; others which could form a lucrative business opportunity.

33

APPENDIX A Laboratory Testing Results and Charts

Sample Number

Tube O.D.

[mm]*

Tube I.D.

[mm]*

Young’s

Modulus [GPa]

0.02% Yield Stress [MPa]

Ultimate Compressive Stress [MPa]

A1 34 26 1.18 4.2 6.32

A2 34 26 NA 5.28 6.25

A 34 26 1.18 4.74 6.29

B1 55 51 1.56 5.90 8.46

B2 55 51 NA 6.80 9.27

B3 55 51 NA 4.15 5.50

B4 55 51 NA 7.30 10.63

B 55 51 1.56 6.04 8.47

C1† 55 51 1.54 5.96 9.88

D1†† 55 51 1.28 9.55 10.32

E1 50 45 1.38 4.72 6.22

E2 50 45 NA 4.65 6.50

E 50 45 1.38 4.69 6.36

F1 34 26 1.04 2.36 5.35

F2 34 26 NA 3.37 6.18

F 34 26 1.04 2.87 5.77

Table 6.1.2 Summary of results from unconfined compression tests on cardboard tubes

Notes:

Sample types A and E through F were all sourced from a single supplier (CT).

Sample types B through D are recycled architectural bond paper roll cores from another supplier (HP).

Sample types C and D have been modified as outlined in Section 6.4 Tube Development, with ribs and stringers. Both have four 5.2 [mm] thick stringers, C† has 5.2 [mm] thick radial ribs at 20 [mm] spacing, whereas D†† has 5.2 [mm] thick ribs at 10 [mm] spacing.

A1

Chart 5.2.10 the relationship between Stiffness and Mass per Unit Length for 4130 Steel and 6061 T6 Aluminium Tubes with increasing outer diameters. All data sourced from Aerospace Specification Metals Inc.

A2

20 25 30 35 40 45 50 550

20,000

40,000

60,000

80,000

100,000

120,000

140,000

0

100

200

300

400

500

600

700

800

900

1,000

Steel Stiffness Coefficient [Pam^4] Aluminium Stiffness Coefficient [Pam^4]Steel Mass per Unit Length [g/m] Aluminium Mass per Unit Length [g/m]Steel Critical Buckling Ratio, Outer Diameter to Wall Thickness 60:1

Tube Outer Diameter [mm]

Stiffn

ess C

oefic

ient

[Pam

4]

Mas

s Per

Uni

t Len

gth

[kg/

m]

6061 T6Aluminium

4130 Cro-moly Steel

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

2

4

6

8

10

12

B20.2% Line

Strain ԑ

Stre

ss σ

[MPa

]

Chart with Figure 6.1.3 Typical Stress – Strain response of a spiral wound cardboard tube to 1kN/min load ramp to failure

A3

1

2

312

3

0 0.0005 0.001 0.0015 0.0020

200000

400000

600000

800000

1000000

1200000

f(x) = 1192005217.14453 x − 730086.664210364R² = 0.999949195202444

f(x) = 1184031803.82497 x − 686937.8921011R² = 0.999946556759759f(x) = 1172857758.37626 x − 627995.553799508

R² = 0.999969371466131

Stress V Strain

Strain ԑ

Stre

ss σ

[MPa

] "Bedding in of sample"

3 "Elastic" ramps

to ensure repeat-able

Young's Modu-lus

Trendline Equations

Hysteresis

A1

Chart 6.1.4 Typical Stress – Strain response of a spiral wound cardboard tube to 0.5kN/min elastic load ramp cycles on sample A1.

0 0.005 0.01 0.015 0.02 0.0250

2

4

6

8

10

12

B20.2% LineC10.2% LineD10.2% Line

Strain ԑ

Stre

ss σ

[MPa

]

Chart 6.1.5 Comparison of Stress – Strain response of spiral wound cardboard tubes with differing levels of reinforcement to 1kN/min load ramp

A4

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

2

4

6

8

10

12

A10.2% LineA20.2% Line

Strain ԑ

Stre

ss σ

[MPa

]

Chart 6.1.6 Comparison of Stress – Strain response of A-Type spiral wound cardboard tubes 1kN/min load ramp

0 0.0005 0.001 0.0015 0.0020

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

2000000f(x) = NaN x + NaNR² = 0

f(x) = 1596197772.41047 x − 1004624.96514635R² = 0.999863993671236f(x) = 1524676912.62878 x − 843717.308235223

R² = 0.999854193482412

B1

Strain ԑ

Stre

ss σ

[MPa

]

Trendline Equations

Chart 6.1.7 Elastic Stress – Strain response of sample B1, spiral wound cardboard tube to 0.5kN/min elastic load ramp cycles.

A5

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

1

2

3

4

5

6

7

8

9

B40.2% LineB30.2% LineB20.2% LineB10.2% Line

Strain ԑ

Stre

ss σ

[MPa

]

Chart 6.1.8 Comparison of Stress – Strain response of B-Type spiral wound cardboard tubes 1kN/min load ramp

0 0.0005 0.001 0.0015 0.002 0.0025 0.0030

500000

1000000

1500000

2000000

2500000

3000000

3500000

f(x) = 1681839190.49781 x − 2028605.18994257R² = 0.999569089483157

f(x) = 1577829926.28803 x − 1672218.70330107R² = 0.999899355194178f(x) = 1508952062.55009 x − 1291396.56887925

R² = 0.999952732085775

C1

Strain ԑ

Stre

ss σ

[MPa

]

Trendline Equations

Chart 6.1.9 Elastic Stress – Strain response of sample C1, spiral wound cardboard tube to 0.5kN/min elastic load ramp cycles

A6

0 0.0005 0.001 0.0015 0.0020

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

2000000

f(x) = 1459637687.44223 x − 124855.060183292R² = 0.999890446748551f(x) = 1218057517.62964 x + 187073.612094664

R² = 0.99977414470867f(x) = 1171982447.83298 x + 316648.304812197R² = 0.999627383462718

D1

Strain ԑ

Stre

ss σ

[MPa

]

Trendline Equations

Chart 6.1.10 Elastic Stress – Strain response of sample D1, spiral wound cardboard tube to 0.5kN/min elastic load ramp cycles

0 0.0005 0.001 0.0015 0.0020

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

2000000f(x) = 1407175090.98007 x + 121690.289307303R² = 0.999697684987763

f(x) = 1379232772.53458 x + 190987.35512073R² = 0.999841865570371

f(x) = 1364121935.61015 x + 260459.062359969R² = 0.99982754967566

E1

Strain ԑ

Stre

ss σ

[Pa]

Trendline Equations

Chart 6.1.11 Elastic Stress – Strain response of sample E1, spiral wound cardboard tube to 0.5kN/min elastic load ramp cycles

A7

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

2

4

6

8

10

12

E20.2% LineE10.2% Line

Strain ԑ

Stre

ss σ

[MPa

]

Chart 6.1.12 Comparison of Stress – Strain response of E-Type spiral wound cardboard tubes 1kN/min load ramp

0 0.0002 0.0004 0.0006 0.0008 0.0010

100000

200000

300000

400000

500000

600000

700000

800000

900000

1000000

f(x) = 1063401078.47036 x + 221459.195216235R² = 0.999234382068361f(x) = 1040415622.60265 x + 243140.290711499

R² = 0.999923038388111f(x) = 1030481268.96737 x + 264164.874809172R² = 0.99988818164477

F1

Strain ԑ

Stre

ss σ

[Pa]

Trendline Equations

Chart 6.1.13 Elastic Stress – Strain response of sample F1, spiral wound cardboard tube to 0.5kN/min elastic load ramp cycles

A8

0 0.005 0.01 0.015 0.020

2

4

6

8

10

12

F20.2% LineF10.2% Line

Strain ԑ

Stre

ss σ

[MPa

]

Chart 6.1.14 Comparison of Stress – Strain response of F-Type spiral wound cardboard tubes 1kN/min load ramp

A9

APPENDIX B Finite Element AnalysisAnalysis 1 Static Study - Seated Whilst Pedalling

Right Pedal

Figure 6.3.3 Forces Applied to Generic Frame and Forks Assembly- 6061 T6 Aluminium -Analysis 1

B1

Fixed

Fixed

490N 480N

160N

30N

360N

115N

Figure 6.3.4 Resultant Von Mises Stress Generic Frame and Forks Assembly-

6061 T6 Aluminium -Analysis 1

Analysis 2 Static Study - Seated Whilst Pedalling Left Pedal

Figure 6.3.5 Forces Applied to Generic Frame and Forks Assembly- 6061 T6 Aluminium -Analysis 2

B2

Fixed

Fixed

490N480N

115N30N

360N

160N

Figure 6.3.6 Resultant Von Mises Stress Generic Frame and Forks Assembly-

6061 T6 Aluminium -Analysis 2

Analysis 3 Static Study – Standing Whilst Pedalling Left Pedal

Figure 6.3.7Forces Applied to Generic Frame and Forks Assembly- 6061 T6 Aluminium-Analysis 3

B3

Fixed

Fixed

1660N1200N

150N

640N

50N

50N

Figure 6.3.8 Resultant Von Mises Stress Generic Frame and Forks Assembly-

6061 T6 Aluminium -Analysis 3

Analysis 4 Static Study – Standing Whilst Pedalling Right Pedal

B4

Fixed

Fixed

1660N

1200N

640N

150N

50N50N

Figure 6.3.9 Forces Applied to Generic Frame and Forks Assembly- 6061 T6 Aluminium-Analysis 4

Figure 6.3.10 Resultant Von Mises Stress Generic Frame and Forks Assembly-

6061 T6 Aluminium -Analysis 4

Analysis 5 Static Study – “Hitting a Pothole” while Seated

B5

2400N

Figure 6.3.11 Forces Applied to Generic Frame and Forks Assembly- 6061 T6 Aluminium-Analysis 5

Figure 6.3.12 Resultant Von Mises Stress Generic Frame and Forks Assembly-

6061 T6 Aluminium -Analysis 5

B6

Figure 6.3.13 Resultant Von Mises Stress Generic Frame and Forks Assembly- 6061 T6 Aluminium -Analysis 5 - Close-up of reverse angle to equal scale as

6.3.13

Analysis 6 Static Study – Braking while Standing

Figure 6.3.14 Forces Applied to Generic Frame and Forks Assembly- 6061 T6 Aluminium-Analysis 6

B7

Slider

Fixed200N

200N

200N

200N

400N

400N

Figure 6.3.15 Resultant Von Mises Stress -Generic Frame and Forks Assembly- 6061 T6 Aluminium -Analysis 6

Figure 6.3.16 Resultant Von Mises Stress - Generic Frame and Forks Assembly- 6061 T6 Aluminium –Analysis 6- Close-up of reverse angle

Analysis 7 Static Study – Falling Mass

B8

220N220NSlider

Fixed

Figure 6.3.17 Forces Applied to Generic Frame and Forks Assembly- 6061 T6 Aluminium-Analysis 7

Figure 6.3.18 Resultant Von Mises Stress Generic Frame and Forks Assembly- 6061 T6 Aluminium -Analysis 7

Analysis 8 Static Study – Falling Frame

B9

Slider

Fixed

1260N

1400N

870N

Figure 6.3.19 Forces Applied to Generic Frame and Forks Assembly- 6061 T6 Aluminium-Analysis 8

Figure 6.3.19 Resultant Von Mises Stress Generic Frame and Forks Assembly- 6061 T6 Aluminium -Analysis 8

B10

APPENDIX C Models and Build Photos

Figure 6.2.4 Generic bicycle frame generated in SolidWorks to establish proposed geometry and dimensions for prototype cardboard bicycle frame.

C1

Figure 6.4.3 Design and manufacturing process for the compound cardboard tubes developed for laboratory testing. This process has be refined and

applied to the manufacture of the actual frame tubes of the final prototype

C2

Design Sketch

Prototype Tube

Laser Cutting Machine

Reinforced Tubes for Materials Testing, showing Constituent Parts and Final

Assembly

Drawing from Model

After Testing these Tubes were Evaluated and Redesigned for the

Final Bicycle Frame Tubes

Broken Down into Profile Drawings

1 2

34

56

Figure 6.4.5Final Bicycle Frame Down Tube, after shaping of reinforcement core to match coped outer tube

Figure 6.6.1SolidWorks Model of front triangle

C3

Figure 6.6.3 Frame jig production drawing

Figure 6.6.4 Complete front triangle jig prior to building front triangle

C4

Figure 6.6.5Front triangle assembled and bonding in jig

Figure 6.6.6 Front triangle during waterproofing and drying.

C5

Figure 6.7.1 Final render of completed bicycle model

Figure 6.7.2 1SolidWorks Model of rear triangle

C6

Figure 6.7.3 Rear triangle and front triangle mated and bonded to eachother, after waterproofing.

Figure 6.8.1 1SolidWorks Model of front forks

C7

Figure 6.2.12 Front forks part way through construction.

Figure 6.2.13 Front wheel prototype after construction.

C8

APPENDIX DProduct Design Specification for a Cardboard Bicycle Frame and Forks

A bicycle is a form of transport Function – To transport the rider (and cargo) from one location to another.

A bicycle frame and forks are the main structural elements of a bicycle

ESSENTIAL FUNCTIONS DESIGN CRITERIA DESIRABLE CRITERIA

Must Fulfil Should Fulfil

Connect the two wheels together

Constructed with as high a percentage of cardboard as

possibleCompliant enough

to provide a comfortable ride

Support the riders weightComply with BS EN ISO 4210-

6:2015 Aesthetically pleasing

Provide a stable platform to transmit propulsion forces to the driving

wheel

Stiff enough to transmit power efficiently to the driving wheel

and steering inputs to the steering wheel.

Lightweight

Provide a stable platform to transmit steering

forces to the steering wheel

Provide a suitable riding position

Provide a stable platform to transmit braking forces

to the wheel brakesOperate in all weathers

Prototype Bicycle Frame and Forks Costing for Project

Materials Quantity

Retail Cost

Per UnitProject Source

Ø56mm Cardboard Tube 2 £2.74 Cores and Tubes (FOC)

Ø 96mm Cardboard Tube 1 £4.66 Cores and Tubes (FOC)

Ø 75mm Cardboard Tube 1 £3.52 Cores and Tubes (FOC)

Ø 38mm Cardboard Tube 2 £1.32 Cores and Tubes (FOC)

Ø 22mm Cardboard Tube 4 £0.96 Cores and Tubes (FOC)

Ø 50mm Cardboard Tube 1 £1.84 Cores and Tubes (FOC)

Tri-Wall Cardboard 1 £7.80 SAL Packing(FOC)Materials Total £29.78

D1

ServicesLaser Cutting 27[hrs] £30 LSBU (FOC)Labour 87[hrs] £15 Authors timeServices Total £2115.00

Table of Bicycle Ancillary Donor Parts Used for BuildPart Description SourceFront Wheel for Testing 26” Sun Rhyno Rim on

Scott 20mm through axle Hub and Sapim Spokes

Donor from authors bicycle

Rear Wheel 26”Vuelta DH Rim on Shimano Deore LX hub and DT Swiss Spokes

Hand built from spare parts by author

Front and Rear Brakes Avid Elixir 1 Hydraulic Disc Brakes with 180mm front and 140mm rear discs

Donor old spare parts from author

Drivetrain Gates Carbon Drive Belt with 42 tooth front sprocket and 22 tooth rear sprocket.

Kindly donated by Gates free of charge (FOC).

Bottom Bracket Shimano Deore LX Donor spare parts from author

Cranks DMR Moto X 170mm Donor old spare parts from author

Pedals DMR V8 Magnesium Donor spare parts from author

Dimensional Analysis of Prototype Frame and Forks

Dimension Proposed Value [mm]

Actual Value (Error) [mm]

Top Tube 637 633 (-2)Head Tube 199 200 (+1)Down Tube 735 742 (+7)Seat Tube 415 414 (-1)Chain Stay 425 L 421 (-4) and R 420 (-5)Seat Stay 491 489 (-2)Fork Legs 490 L 485 (-5) and R 485 (-5)

Angle Proposed Value [°] Actual Value [°]Seat Tube 74 73-74Head Tube 68 68-69

D2

APPENDIX E Gantt Chart

E1

E2

Awaiting Completion

ReferencesFigure ReferencesUnless stated figures are original works produced by the author and remain Copyright of James Goddings, London South Bank University 2016

1.1.1

Left - BBC, (2008) Cardboard Bicycle http://www.bbc.co.uk/manchester/content/articles/2008/06/13/160608_cardboard_bike_feature.shtml

Right - Wired Magazine, (2013) Recycling the way we make our bicycles http://www.wired.co.uk/magazine/archive/2013/03/start/recycling-the-way-we-make-our-bicycles

1.2.1

Flat Card Stock - http://www.cutcardstock.com/collections/brown-card-stock

Honeycomb Cardboard - http://www.sciencestockphotos.com/free/engineering/slides/cardboard_strength.html

1.2.2

Left - Hiroyuki Hirai - Japanese Pavilion - http://www.archdaily.com/608506/12-things-you-didn-t-know-about-pritzker-laureate-frei-otto/55008db8e58ece81290000e5-1-jpg

Right - Compagnie MECO – Bridge, http://www.compagniemeco.com/?p=499

5.1.1

Left - Rover Safety Bicycle - http://www.imeche.org/news/news-article/coventry-s-rover-safety-bicycle-receives-prestigious-award

Right - Lu-Mi-Num - http://www.bikequarterly.com/images/LuMiNum800.jpg

6.2.1

Moulton Bicycles (2016) – Moulton Speed - http://www.moultonbicycles.co.uk/models/MoultonSPEED.html

All Accessed in April 2016

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European Commission, 2016, Reducing CO2 emissions from passenger cars, http://ec.europa.eu/clima/policies/transport/vehicles/cars/index_en.htm, accessed on 22/02/2016

Groover M.P (2010), Fundamentals Of Modern Manufacturing: Materials,Processes,and Systems, Fourth Edition, Lehigh University, USA, John Wiley & Sons, Inc., ISBN 978-0470-467002, 2010

Hong Huo, Qiang Zhang, Kebin He, Zhiliang Yao, Michael Wang, 2012, Vehicle-use intensity in China: Current status and future trend, Energy Policy 43 (2012) p.6–16

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IV

Bicycle Industry Testing StandardsBS EN ISO 4210-1:2014 Cycles — Safety requirements for bicycles Part 1: Terms and definitionsBS EN ISO 4210-2:2015 Cycles — Safety requirements for bicycles Part 2: Requirements for city and trekking, young adult, mountain and racing bicyclesBS EN ISO 4210-3:2014 Cycles — Safety requirements for bicycles Part 3: Common test methodsBS EN ISO 4210-4:2014 Cycles — Safety requirements for bicycles Part 4: Braking test methodsBS EN ISO 4210-5:2014 Cycles — Safety requirements for bicycles Part 5: Steering test methodsBS EN ISO 4210-6:2015 Cycles — Safety requirements for bicycles Part 6: Frame and fork test methodsBS EN ISO 4210-7:2014 Cycles — Safety requirements for bicycles Part 7: Wheels and rims test methodsBS EN ISO 4210-8:2014 Cycles — Safety requirements for bicycles Part 8: Pedal and drive system test methodsBS EN ISO 4210-9:2014 Cycles — Safety requirements for bicycles Part 9: Saddles and seat post test methodsBS EN ISO 8098:2014 Cycles — Safety requirements for bicycles for young children

Other StandardsBS EN ISO 19902:2007 - Petroleum and natural gas industries — Fixed steel offshore structures, January 2008, ISBN 978 0 580 58288 2

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