Evaluation of the dynamic behaviour of composite racing bicycles through outdoor field testing

Evaluation of the dynamic behaviour of composite racing bicycles through outdoor field testing Frederik Mortier

Promotoren: prof. dr. ir. Wim Van Paepegem, prof. dr. ir. Mia Loccufier Begeleiders: ir. Joachim Vanwalleghem, dr. ir. Ives De Baere Masterproef ingediend tot het behalen van de academische graad van Master in de ingenieurswetenschappen: werktuigkunde-elektrotechniek Vakgroep Toegepaste Materiaalwetenschappen Voorzitter: prof. dr. ir. Joris DEGRIECK Vakgroep Elektrische energie, Systemen en Automatisering Voorzitter: prof. dr. ir. Jan MELKEBEEK Faculteit Ingenieurswetenschappen en Architectuur Academiejaar 2010-2011

Evaluation of the dynamic behaviour of composite racing bicycles through outdoor field testing Frederik Mortier

Promotoren: prof. dr. ir. Wim Van Paepegem, prof. dr. ir. Mia Loccufier Begeleiders: ir. Joachim Vanwalleghem, dr. ir. Ives De Baere Masterproef ingediend tot het behalen van de academische graad van Master in de ingenieurswetenschappen: werktuigkunde-elektrotechniek Vakgroep Toegepaste Materiaalwetenschappen Voorzitter: prof. dr. ir. Joris DEGRIECK Vakgroep Elektrische energie, Systemen en Automatisering Voorzitter: prof. dr. ir. Jan MELKEBEEK Faculteit Ingenieurswetenschappen en Architectuur Academiejaar 2010-2011

Preface Nu ik op het punt sta mijn studies te beëindigen wil ik enkele personen bedanken die dit mogelijk maakten. Zij verdienen een woord van dank na deze twee jaren. Mijn vader in het bijzonder heeft mij de financiële hulp geboden om na mijn vorige opleiding tot industrieel ingenieur verder te studeren om het diploma van burgerlijk ingenieur te kunnen behalen. Prof. dr. ir. Wim Van Paepegem en prof. dr. ir. Mia Loccufier hebben mij een unieke kans gegeven met dit masterproefvoorstel, waarin een hoge mate van innovatie, ontwerp en onderzoek centraal stonden. Daarnaast hebben alle professoren hun steentje bijgedragen aan deze opleiding. Zonder hen was het maken van deze masterproef nooit mogelijk geweest. Zij brachten mij de nodige kennis bij om deze scriptie tot een goed einde te brengen. Ik wil mijn oprechte dank betuigen aan ir. Joachim Vanwalleghem en dr. ir. Ives De Baere, mijn begeleiders van de Universiteit Gent, die mij zeer goed ondersteunden en veel ervaring en kennis hebben overgedragen. Verder wens ik Luc Van Den Broecke te danken voor zijn hulp bij allerhande problemen. Deze ervaring heeft mij veel bijgebracht, zowel op onderzoeks- en ontwikkelingsvlak, als het communiceren en omgaan met anderen. Het belang hechten aan precisie en het kritisch beoordelen van eigen geleverde prestaties zorgde ervoor dat er tijdens het hele jaar telkens vooruitgang geboekt werd, wat ik ervoer als een grote motivatie. Ook vrienden, familie en medestudenten zijn een grote steun geweest de voorbije jaren. Dit dankwoord wil ik sluiten door hen te bedanken. Hoogachtend, Frederik Mortier

Permission for Use of Content “The author gives permission to make this master dissertation available for consultation and to copy parts of this master dissertation for personal use. In the case of any other use, the limitations of the copyright have to be respected, in particular with regard to the obligation to state expressly the source when quoting results from this master dissertation.” De auteur geeft de toelating deze masterproef voor consultatie beschikbaar te stellen en delen van de masterproef te kopiëren voor persoonlijk gebruik. Elk ander gebruik valt onder de beperkingen van het auteursrecht, in het bijzonder met betrekking tot de verplichting de bron uitdrukkelijk te vermelden bij het aanhalen van resultaten uit deze masterproef."

Frederik Mortier, May 2011

Evaluation of the dynamic behaviour of composite racing bicycles through outdoor field testing by Frederik MORTIER Masterproef ingediend tot het behalen van de academische graad van MASTER IN DE INGENIEURSWETENSCHAPPEN: WERKTUIGKUNDE - ELEKTROTECHNIEK Promotoren: prof. dr. ir. Wim VAN PAEPEGEM, prof. dr. ir. Mia LOCCUFIER begeleiders: dr. ir. Ives DE BAERE, ir. Joachim VANWALLEGHEM Vakgroep Toegepaste Materiaalswetenschappen Voorzitter: prof. dr. ir. Joris DEGRIECK Vakgroep Elektrische energie, Systemen en Automatisering Voorzitter: prof. dr. ir. Jan MELKEBEEK Faculteit Ingenieurswetenschappen en Architectuur Universiteit Gent Academiejaar 2010-2011

Summary This thesis describes the research of the dynamic behaviour of racing bicycles, in order to eventually determine the effects of the use of flax-carbon as a constructional frame material. The influence of the bicycle dynamics on the comfort of the cyclist is one of the key issues. Comfort is assessed through measuring force and accelerations at the contact points between man and bicycle. This requires the design, fabrication and calibration of several force gauges. By means of field tests, the acceleration and force data is recorded and investigated to look for the influence of parameters such as tyre pressure and road surface on the cyclist’s comfort. Next to these comfort measurements, the force distributions at the saddle, handlebar and the pedal will be examined as well as the power delivery from the cyclist.

Keywords flax fibre, composites, bicycle, dynamic behaviour, comfort, field test

Evaluation of the dynamic behaviour of composite racing bicycles through outdoor field testing F. Mortier Supervisor(s): Ives De Baere, Joachim Vanwalleghem, Wim Van Paepegem, Mia Loccufier Abstract-- This paper describes the research of the dynamic behaviour of racing bicycles, in order to eventually determine the effects of the use of hybrid flax-carbon reinforced composite as a constructional frame material. The influence on the comfort of the cyclist is one of the key variables, which is determined by measuring force and accelerations at the contact points between the human body and bicycle by means of field testing. This requires the design, fabrication and calibration of several force gauges. Field tests can then be conducted in order to examine the influence of several parameters such as tire pressure and road surface on the riders comfort. The measured force distributions at the saddle, handlebar and pedal can be used when designing bicycle frames or parts. The pedal force distributions can be used to assess the cycling efficiency Keywords-- flax fibre, composites, bicycle, dynamic behaviour, comfort, field test, absorbed power

I. INTRODUCTION

T

HE bicycle has evolved from a simple means of transportation to a high performance machine, capable of letting the cyclist achieve higher top speeds with less effort whilst still granting a proper handling. One of the key components of a bicycle is the frame. A lot of research has been done concerning reducing the overall weight by using more exotic materials and production processes. A commonly used material nowadays for both professional as amateur racing bicycle frames is carbon fibre reinforced plastic (CFRP). The use of these materials has lead to an increase in frame stiffness while the weight has been reduced drastically. This stiffness has led to a decrease in cyclist comfort due to the increased vibrations transmitted from the wheel to the human body. Museeuw Bikes, a Flemish company which designs and produces bicycle frames, tries to correct this problem by using flax fibres instead of carbon. It is claimed that the vibration damping properties of this material exceeds that of carbon composite and leads to a better cyclist comfort.

evaluation, a single scalar is computed for each acceleration, such as the r.m.s. value. A problem with this approach with regard to driving a bicycle is the fact that a commonly used technique for improving the ride quality on a rough surface is to clamp the handlebar less and let the handlebar move more freely. This in turn increases the accelerations of the handlebar since no restraining forces are exerted. This could possible lead to false conclusions in terms of cyclist comfort. A third possible method is the absorbed power approach, which takes the contact force into account [3]. The amount of power which is absorbed by the cyclist is calculated by measuring the contact force and vibration velocity at each contact point. The level of absorbed power is an indication for the comfort level [4]. The average absorbed power for the entire test duration at one contact point can be calculated as followed: ����� 𝑃𝐴𝑏𝑠 =

1 𝑇 � 𝐹(𝑡). 𝑣(𝑡)𝑑𝑡 𝑇 0

III. INSTRUMENTATION OF THE BICYCLE The implementation of the ISO or British Standard requires the placement of accelerometers. The absorbed power method however requires the measurement of both velocity and force. This velocity can be calculated by integrating the acceleration signal in time. Custom designed gauges are build to measure the forces at the saddle, pedal and handlebar. These forces are measured by mounting strain gauges in a Wheatstone bridge configuration, which enables the measurement of the force independent of the point of application. Figure 1 shows the saddle force gauge, which decouples the horizontal and vertical forces with the help of a U-shaped aluminium piece.

This article describes the method of measuring and assessing the level of comfort and the force distributions on the saddle, handlebar and pedal on a scientific basis. II. ASSESSMENT OF THE CYCLIST RIDE COMFORT Two methods are commonly used to investigate the level of comfort for human beings with regard to vibrations: the ISO2631 or the BS6841 standard [1, 2]. These are both based on the principle that an increase in accelerations, measured at the contact point between the human body and the vibrating object, leads to a decrease in comfort. Since the human body is more sensitive to low frequencies between 2 and 12Hz, the acceleration signal is first filtered with a filter which represents this frequency-dependency. As a form of

Figure 1: Saddle force gauge

The handlebar (Figure 2) and pedal spindle (Figure 3) are instrumented with strain gauges in a similar way to decouple the vertical and horizontal force components. Not only the pedal force, but also the pedal position was measured, using a

self-made encoder. All of these sensors were calibrated before use.

the leg exerts a counteracting force, which reduces the cycling efficiency. Figure 5 demonstrates the absorbed power level when cycling across mild cobblestones. It can be seen that the absorbed power decreases when the tire pressure is lowered. For these test, the absorbed power is around 12-16W, whilst the body only absorbs around 1W when cycling along a smooth surface for all tire pressures.

Figure 2: Instrumented handlebar

Figure 5: Comfort assessment according to absorbed power

When the BS6841 is used, a large decrease in comfort level is detected for cycling without loading the handlebar, as shown in the last columns of Figure 6, which is inconsistent with the actual comfort level of the cyclist. Figure 3: Instrumented pedal

IV. FIELD TESTS During field tests, the cyclist carried a backpack holding all data-acquisition equipment. One of the field tests includes measuring the force distribution at the pedal whilst cycling at a constant speed. The second test consisted of measuring the comfort level by the absorbed power method and the BS6841 method. This was performed by cycling along a smooth asphalted road and along a road paved with mild cobblestones at different tire pressures. The goal was to investigate the possibility of detecting minor and major changes in the comfort level of the cyclist and to determine whether the absorbed power method or the more conventional BS6841 method proves to be more successful.

Figure 6: Comfort assessment according to BS6841

These plots show that the alternative method of determining comfort by the absorbed power can be successfully used to assess comfort during field testing.

V. RESULTS Figure 4 shows the pedal distribution along the crank angle when cycling in regime.

VI. CONCLUSIONS The tests reveal that small differences in comfort level can be detected using the absorbed power method, whereas the BS6841 may overrate the lack of comfort when a poor contact exists between the human body and the vibrating object. The test setup can be used to investigate the influence of several parameters on the cyclist comfort or how an altered pedalling style may influence the cycling efficiency. REFERENCES

Figure 4: Pedal force distribution

The largest tangential, propellant forces take place when the pedal is almost horizontal. In the second half of the rotation,

[1] NEN-ISO 2631:1 1997 Mechanische trillingen en schokken Beoordeling van de invloed van trillingen op het menselijk lichaam. [2] BS 6841:1987 Guide to measurement and evaluation of human exposure to whole-body mechanical vibration and repeated shock. [3] Pradko, F., R. Lee, and V. Kaluza, Theory of Human Vibration Response. Mechanical Engineering, 1967. 89(2): p. 71-&. [4] Lundstrom, R., P. Holmlund, and L. Lindberg, Absorption of energy during vertical whole-body vibration exposure. Journal of Biomechanics, 1998. 31(4): p. 317-326.

Evaluatie van het dynamisch gedrag van composiet koersfietsen door middel van veldtesten F. Mortier Begeleider(s): Ives De Baere, Joachim Vanwalleghem, Wim Van Paepegem, Mia Loccufier Abstract—Deze paper beschrijft het onderzoek naar het dynamisch gedrag van koersfietsen, zodat uiteindelijk de effecten van het gebruik van hybride vlas-carbon vezel versterkte kunsstof als constructiemateriaal kan bepaald worden. De invloed op het comfort van de renner is één van de hoofdpunten, die bepaald wordt door het meten van de krachten en acceleraties aan de contactpunten tussen het menselijk lichaam en de fiets door het uitvoeren van veldtesten. Dit vereist het ontwerp, fabricatie en kalibratie van verschillende krachtsensoren. Veldtesten kunnen daarna uitgevoerd worden om de invloed van verschillende parameters zoals bandendruk en wegdekruwheid op het comfort van de renner na te gaan. De gemeten krachtdistributies aan het zadel, stuur en pedaal kunnen worden gebruikt bij het ontwerp van het frame of onderdelen. De pedaalkracht- en distributie kan worden gebruikt om de trapefficiëntie na te gaan. Kernwoorden—vlasvezel, composiet, fiets, dynamisch gedrag, comfort, veldtest, geabsorbeerd vermogen

I. INTRODUCTIE

D

E fiets is geëvolueerd van een eenvoudige vorm van transport naar een gesofisticeerde machine die de renner toelaat hogere topsnelheden te halen, met een goed stuurgedrag. Eén van de belangrijkste onderdelen van een fiets is het frame. Veel onderzoek is reeds uitgevoerd wat betreft het reduceren van het totaalgewicht door gebruik te maken van exotische materialen en productieprocessen. Een vaak gebruikt materiaal heden ten dage, in zowel professionele als amateur raceframes, is carbonvezel versterkte kunststof. Het gebruik van deze materialen heeft geleid tot een toename in de stijfheid van het frame terwijl het gewicht drastisch daalde. Deze toename in stijfheid zorgt voor een lager comfortgehalte van de renner omwille van de toegenomen vibraties die doorgegeven worden van het wiel naar het lichaam. Museeuw Bikes, een Vlaams bedrijf dat koersfietsen ontwerpt en bouwt, probeert dit probleem op te lossen door gebruik te maken van vlasvezels in plaats van carbonvezel. Dit materiaal zou betere dempingseigenschappen bezitten dan carbonvezel, welke zou leiden tot minder vibraties en dus een verhoogd comfort.

gemeten acceleratiesignaal eerst gefilterd worden met een filter die deze frequentieafhankelijkheid van de mens nabootst. Deze trilling wordt geëvalueerd door bijvoorbeeld het bepalen van de r.m.s. waarde van de trilling. Een probleem met deze aanpak bij het fietsen is het feit dat een geoefend renner vaak het stuur slechts zwak zal vastklemmen op een slecht wegdek om zo het stuur meer toe te laten te bewegen. Deze afname in klemkracht leidt dan weer tot verhoogde acceleraties van het stuur. Dit kan mogelijks leiden tot verkeerde conclusies bij het beoordelen van het comfortgehalte. Een derde mogelijk methode is het meten van het geabsorbeerd vermogen, welke de contactkracht ook in rekening brengt [3]. Het vermogen dat door de renner geabsorbeerd wordt kan berekend worden door de contactkracht en de vibratiesnelheid aan elk contactpunt te meten. Dit geabsorbeerd vermogen is een indicatie voor het comfortgehalte [4]. Het gemiddelde geabsorbeerd vermogen aan één contactpunt voor een testrit kan als volgt bepaald worden: ����� 𝑃𝐴𝑏𝑠 =

1 𝑇 � 𝐹(𝑡). 𝑣(𝑡)𝑑𝑡 𝑇 0

III. INSTRUMENTATIE VAN DE FIETS Het gebruik van de ISO standaard of de Britse Standaard vereist het plaatsen van accelerometers. De geabsorbeerd vermogen methode daarentegen vergt het meten van zowel kracht als snelheid. De snelheid kan berekend worden door het integreren van het acceleratiesignaal. Zelfgemaakte krachtcellen zijn gebouwd om de krachten te meten aan het stuur, zadel en pedaal. Deze krachten worden gemeten door het plaatsen van rekstrookjes in een Wheatstonebrugconfiguratie die toelaat de kracht te meten onafhankelijk van waar deze kracht ingrijpt. Figuur 1 toont de zadelkrachtsensor, welke de horizontale en verticale krachten ontkoppelt door gebruik te maken van een U-vormig aluminium stuk.

Dit artikel beschrijft de meet- en beoordelingsmethode van het comfortgehalte en de krachtendistributies op het zadel, stuur en de pedaal op een wetenschappelijke manier. II. BEOORDELING VAN HET COMFORT VAN DE RENNER Bij het onderzoeken van het comfort wordt vaak gebruik gemaakt van twee methoden: de ISO2631 of de BS6841 standaard [1, 2]. Deze baseren zich beide op het principe dat een toename van acceleraties, gemeten tussen het menselijk lichaam en het vibrerende oppervlak, leidt tot een afname van het comfort. De mens is het gevoeligst aan trillingen met een lage frequentie van ongeveer 2 tot 12Hz. Daarom moet het

Figuur 1: Zadelkrachtsensor

Het stuur (Figuur 2) en de pedaal (Figuur 3) zijn geïnstrumenteerd met rekstrookjes op een soortgelijke manier waardoor de verticale en horizontale krachtcomponenten ontkoppeld zijn. Niet alleen de pedaalkracht, maar ook de pedaalpositie wordt gemeten door gebruik te maken van een zelfgemaakte encoder. Deze sensoren werden gekalibreerd alvorens gebruik.

De grootste tangentiële krachten grijpen in wanneer de pedaal bijna horizontaal is. Tijdens de tweede helft van de rotatie oefent het been een tegenwerkende kracht uit, welke de trapefficiëntie vermindert. Figuur 5 geeft het geabsorbeerd vermogen weer wanneer er op een ruw wegdek gefietst wordt. Het is duidelijk dat dit vermogen daalt bij lagere bandendrukken. Voor deze tests ligt het geabsorbeerd vermogen rond 12-16W, terwijl het lichaam slechts rond 1W absorbeert bij alle bandendrukken wanneer er gefietst wordt op een vlak wegdek.

Figuur 2: Geïnstrumenteerd stuur Figuur 5: Comfortbeoordeling van het geabsorbeerd vermogen

Wanneer de Britse Standaard wordt gebruikt zal het fietsen zonder het stuur vast te nemen leiden tot laag comfortgehalte vanwege de grote gemeten acceleraties, zoals te zien is in de laatste twee kolommen van Figuur 6. Dit is inconsistent met het werkelijke comfort van de renner.

Figuur 3: Geïnstrumenteerde pedaal

IV. VELDTESTEN De testrenner droeg tijdens de veldtesten een rugzak met daarin alle data acquisitie apparatuur. Eén van de veldtesten bestond eruit de pedaalkrachtdistributie te meten terwijl de renner een constante snelheid aanhield. De tweede test bestond eruit het comfortgehalte te meten volgens de Britse Standaard en het geabsorbeerd vermogen. Dit was uitgevoerd door het fietsen op zowel een ruw als een vlak wegdek bij verschillende bandendrukken. Het doel was na te gaan of het mogelijk is kleine en grote verschillen in comfortgehalte te meten en na te gaan of de geabsorbeerde vermogen methode meer geschikt blijkt te zijn dan de conventionele Britse Standaard. V. RESULTATEN Figuur 4 toont de pedaalkrachtdistributie volgens de crankhoek wanneer er in regime gefietst wordt.

Figuur 6: Comfortbeoordeling volgens BS6841

Deze figuren geven weer dat het mogelijk is met de geabsorbeerd vermogen methode het comfortgehalte te bepalen tijdens veldtesten. VI. CONCLUSIE De testen maken duidelijk dat kleine wijzigingen in het comfortgehalte kunnen gemeten worden met de geabsorbeerd vermogen methode, terwijl de Britse Standaard het comfort mogelijks onderschat wanneer er een slecht contact bestaat tussen het menselijk lichaam en het trillend object. De opstelling kan gebruikt worden om de invloed van verschillende parameters op het comfort te bepalen of om na te gaan hoe een gewijzigde trapmethode de trapefficiëntie kan beïnvloeden. REFERENTIES [1]

Figuur 4: Pedaalkrachtdistributie

[1] NEN-ISO 2631:1 1997 Mechanische trillingen en schokken Beoordeling van de invloed van trillingen op het menselijk lichaam. [2] [2] BS 6841:1987 Guide to measurement and evaluation of human exposure to whole-body mechanical vibration and repeated shock. [3] [3] Pradko, F., R. Lee, and V. Kaluza, Theory of Human Vibration Response. Mechanical Engineering, 1967. 89(2): p. 71-&. [4] Lundstrom, R., P. Holmlund, and L. Lindberg, Absorption of energy during vertical whole-body vibration exposure. Journal of Biomechanics, 1998. 31(4): p. 317-326.

Contents Preface .............................................................................................................................................. 4 Permission for Use of Content ......................................................................................................... 5 Survey ............................................................................................................................................... 6 Contents........................................................................................................................................... 11 Samenvatting ................................................................................................................................... 14 Chapter 1:

Research request ...................................................................................................... 33

1.1

Company presentation............................................................................................................................. 33

1.2

Requested research ................................................................................................................................... 33

1.3

Description of the research .................................................................................................................... 34

Chapter 2:

Introduction to bicycle racing frames ...................................................................... 36

2.1

Introduction to composite materials ..................................................................................................... 36

2.2

Use of composites in structural design ................................................................................................. 37

2.3

Damping effect in composites ............................................................................................................... 42

2.4

Use of flax-carbon reinforcement fibres in composite frames ......................................................... 43

2.5

Bicycle structure........................................................................................................................................ 45

2.5.1

Terminology ......................................................................................................................................... 45

2.5.2

Frame design ........................................................................................................................................ 46

2.5.3

Production process .............................................................................................................................. 47

Chapter 3:

Ride comfort ............................................................................................................. 49

3.1

Introduction .............................................................................................................................................. 49

3.2

Influence of vibrations on the human body ........................................................................................ 49

3.3

Vibration due to road excitation and bicycle dynamics ..................................................................... 52

3.4

Assessment of vibrations ........................................................................................................................ 54

3.4.1

British Standard BS 6841: Whole body vibration ........................................................................... 56

3.4.2

International Standard ISO 2631:1: Whole body vibration .......................................................... 59

3.4.3

Absorbed power .................................................................................................................................. 62 11

3.4.4 3.5

International Standard ISO 5349: hand-arm vibration .................................................................. 67 Discussion of the four different proposed assessment methods ..................................................... 69

Chapter 4: 4.1

Proof of concepts ...................................................................................................... 71

Measurement of contact forces .............................................................................................................. 71

4.1.1

Introduction .......................................................................................................................................... 71

4.1.2

Force measurements using strain gauges ......................................................................................... 74

4.1.3

Proof of concept .................................................................................................................................. 77

4.1.4

Application: force gauges ................................................................................................................... 79

4.1.4.1

Measuring forces at the pedal ................................................................................................... 79

4.1.4.2

Measuring forces at the handlebar ........................................................................................... 90

4.1.4.3

Measuring forces at the saddle ................................................................................................. 96

4.2

Measuring vibration velocity................................................................................................................. 100

4.2.1

Introduction ........................................................................................................................................ 100

4.2.2

Verification of calculation method ................................................................................................. 100

4.2.3

Application.......................................................................................................................................... 102

4.3

Pedal position and cadence measurement .......................................................................................... 103

4.3.1

Introduction ........................................................................................................................................ 103

4.3.2

Theoretical background encoder ..................................................................................................... 103

4.3.3

Application.......................................................................................................................................... 104

Chapter 5:

Data Acquisition ..................................................................................................... 107

5.1

Requirements .......................................................................................................................................... 107

5.2

Data acquisition devices ........................................................................................................................ 107

5.2.1

Wired DAQ ........................................................................................................................................ 107

5.2.2

Wireless DAQ .................................................................................................................................... 109

5.3

Communication ...................................................................................................................................... 110

5.3.1

Wired communication....................................................................................................................... 110

5.3.2

Wireless communication................................................................................................................... 111

5.4

Storing data.............................................................................................................................................. 111

5.5

Field test setup ........................................................................................................................................ 111

Chapter 6:

Calibration of sensors ............................................................................................. 113 12

6.1

Introduction ............................................................................................................................................ 113

6.2

Data acquisition during calibration ...................................................................................................... 113

6.3

Calibration of force gauges ................................................................................................................... 114

6.3.1

Calibration of the pedal .................................................................................................................... 114

6.3.2

Calibration of the saddle ................................................................................................................... 116

6.3.3

Calibration of the handlebar ............................................................................................................ 121

Chapter 7:

Field testing method............................................................................................... 124

7.1

Introduction ............................................................................................................................................ 124

7.2

Instrumentation of the bicycle ............................................................................................................. 126

7.3

Post processing of acquired data ......................................................................................................... 128

Chapter 8:

Field testing results ................................................................................................ 129

8.1

Force measurements and distributions ............................................................................................... 129

8.2

Pedal force measurements .................................................................................................................... 131

8.3

Short-term: Bump test ........................................................................................................................... 134

8.4

Mid-term: Comfort level ....................................................................................................................... 138

8.4.1

Absorbed power method.................................................................................................................. 138

8.4.2

BS6841 method .................................................................................................................................. 140

8.4.3

Comparison between BS6841 and Absorbed power ................................................................... 142

Chapter 9:

Conclusion .............................................................................................................. 144

9.1

Measuring and quantifying comfort during field tests...................................................................... 144

9.2

Bicycle instrumentation ......................................................................................................................... 144

9.3

Force distribution and comfort measurements ................................................................................. 145

9.4

Further research ...................................................................................................................................... 145

Appendix A .................................................................................................................................... 147 Bibliography .................................................................................................................................. 162 List of figures ................................................................................................................................. 164 List of tables .................................................................................................................................. 168

13

Samenvatting

Samenvatting Inleiding De fiets zoals wij die nu kennen heeft de voorbije eeuw een grote evolutie doorgemaakt. Niet alleen is het concept verandert van een loopfiets naar een pedaalaangedreven tweewieler, ook de onderdelen zelf zijn in de loop der tijd sterk verbeterd. Deze evolutie wordt gesteund door de vraag naar steeds lichtere, sterkere en stijvere frames met een verhoogde esthetische waarde. Veel ontwikkelingen verbeteren de prestaties van de renners. Het frame van een fiets is één van de belangrijkste onderdelen, en de keuze van het constructiemateriaal is dan ook van groot belang. Waar voorheen hout, gesmeed ijzer en uiteindelijk stalen buizen gebruikt werden om de typische diamantvorm te maken zoals we die heden ten dage kennen, worden tegenwoordig veel exotische materialen gebruikt om de eigenschappen van de fiets nog verder te verbeteren. Een veel gebruikt materiaal is aluminium, dat vanwege zijn hoge specifieke sterkte en vormgevingsgemak kan leiden tot een lichte maar tevens sterke fiets. Bij racefietsen is echter niet alleen het gewicht van de fiets van belang, ook de stijfheid staat centraal. De specifieke stijfheid van aluminium verschilt maar weinig van dat van staal waardoor verbeteringen nog steeds mogelijk waren. Pas sinds de jaren ’70 werden composieten gebruikt als structureel materiaal om een fietsframe te ontwerpen. Dit materiaal heeft naast een hoge specifieke sterkte ook een zeer hoge specifieke stijfheid, wat toelaat een zeer stijf en sterk maar toch lichtgewicht frame te bouwen. De vrijheid in manipuleren van dit materiaal geeft de designers de mogelijkheid om de eigenschappen van het materiaal optimaal te benutten in de meest belaste plaatsen van het frame. Tevens zijn meer aerodynamische vormen van frame, voorvork en onderdelen mogelijk, wat de performantie van de fiets ten goede komt. Het doel van deze masterproef bestaat erin om het dynamisch gedrag van composiet raceframes te onderzoeken door middel van veldtesten. Met het dynamisch gedrag wordt bedoeld hoe het frame reageert op excitaties van buitenaf. Deze excitaties bestaan onder de vorm van trillingen veroorzaakt door enerzijds de ruwheid van de baan en anderzijds de trillingen die ontstaan door de trappende beweging van de renner. Het trillingsgedrag wordt afgetoetst door verschillende parameters te wijzigen: de bandendruk, de ruwheid van de weg om uiteindelijk over te gaan tot het vergelijken van verschillende framematerialen en geometrieën.

Composieten In de algemene zin van het woord kunnen composieten beschouwd worden als een vast materiaal, bestaande uit meer dan één component. Deze componenten dienen wel aanwezig te zijn in verschillende fasen, met andere woorden, er moet een duidelijk onderscheid kunnen worden gemaakt tussen de 14

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verschillende componenten. Door het samenvoegen van twee of meer materialen op een dergelijke manier, kunnen materialen vervaardigd worden met eigenschappen die sterk verschillen van de eigenschappen van de twee aparte materialen. Een composietmateriaal bestaat doorgaans uit een matrix en vezels, waar de matrix het materiaal is die de vezels met elkaar verbindt en voor de structurele integriteit zorgt. Een gekend voorbeeld zijn de zogenaamde vezelversterke kunststoffen (fibre reinforced plastics of FRP’s). Enkele courant gebruikte vezels zijn glas-, carbon- en aramidevezels. Naast deze synthetische vezels wordt ook gebruik gemaakt van natuurlijke vezels zoals jute of vlas. Deze materialen vinden hun oorsprong bij hoogtechnologische toepassingen zoals lucht- en ruimtevaart waar zeer hoge eisen worden gesteld aan het materiaal. Het is duidelijk dat de kostprijs voor composietmaterialen hoger is dan voor conventionele constructiematerialen zoals staal, beton of aluminium. Het grootste voordeel aan het gebruik van deze materialen is het lage soortelijk gewicht gecombineerd met een uitzonderlijk hoge sterkte en stijfheid die in sommige toepassingen een grootteorde hoger kan zijn dan die van de conventionele materialen. Bij composiet fietsframes wordt meestal gebruik gemaakt van carbonvezels. De reeds vermelde voordelen laten toe een frame te ontwerpen die tegemoet komt aan de eisen van de moderne renner, namelijk een laag gewicht gecombineerd met een hoge stijfheid en sterkte. Het grootste nadeel bij het gebruik van carboncomposietmaterialen is de geringe taaiheid van het materiaal. De taaiheid is een maat voor de mogelijkheid van een materiaal om energie te absorberen en plastisch te vervormen alvorens te breken. Bij een overbelasting kan dit leiden tot plotse breuken in het frame zonder voorafgaande waarschuwing. Fietsframes kunnen in essentie op twee verschillende wijzen gefabriceerd worden: door het maken van een monocoque frame of door het frame op te bouwen uit verschillende componenten, tubes en lugs genaamd.

b)

a)

Figuur 1: a) Frame design d.m.v. lugs en tubes b) Monocoque frame design

Een monocoque design frame is gemaakt uit één gedeelte, vandaar dat er voor elke model en framegrootte een aparte mal moet gebouwd worden. Het composietmateriaal wordt in deze mal aangebracht onder de 15

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vorm van prepreg. Dit zijn geweven vezelmatten die reeds geïnjecteerd zijn met kunststof maar nog niet uitgehard zijn. Om een dergelijk materiaal correct te laten uitharden zodat de gewenste sterkte bereikt wordt, moet een nauwkeurige druk- en temperatuurcyclus gevolgd worden. Dit vindt plaats in wat men noemt een autoclaaf. Om er zeker van te zijn dat de holle gedeeltes van het frame de correcte vorm krijgen en op een correcte druk belast worden tijdens dit proces, wordt een blaas in het frame geplaatst en onder druk gezet. Vervolgens worden twee malhelften op elkaar geplaatst met een zekere kracht en kan het uithardingsproces beginnen binnenin de autoclaaf. Het tweede procedé bestaat uit het afzonderlijk vervaardigen van de onderlinge buizen uit het frame (tubes) en de verbindingsstukken (lugs). Hierdoor is het mogelijk dezelfde buizen te gebruiken voor verschillende framegroottes door ze na het uitharden op de gewenste maat te zagen. Wanneer zowel de verbindingsstukken en de buizen uitgehard zijn, worden zij verlijmd om een fietskader te vormen.

Onderzoeksopdracht Deze masterproef wordt uitgevoerd in opdracht van het bedrijf Museeuw Bikes, een Vlaams bedrijf dat zich sinds 2007 richt op de semi-prof wielrennersmarkt. De onderneming produceert composiet raceframes en assembleert de fietsen in Lokeren. Museeuw Bik:es tracht zich te diversifiëren door gebruik te maken van vlasvezels in combinatie met carbonvezels, flax-carbon genoemd. Aan dit materiaal worden naast goede constructie-eigenschappen zoals sterkte en stijfheid ook betere dempingeigenschappen toegekend. Een gekend probleem bij de stijve composiet renfietsen is de grote transmissie van vibraties afkomstig van het contact tussen de band en het wegdek ten gevolge van de grote stijfheid en lage demping. Dit kan gewijzigd worden door enerzijds de geometrie en anderzijds het framemateriaal te wijzigen. Sinds 2009 werkt de onderneming samen met de Gentse Universiteit om het dynamisch gedrag van zowel het hybride vlas-carbon materiaal als de fietsframes te onderzoeken. Deze masterproef zal het dynamisch gedrag van de fietsframes testen door gebruik te maken van een geïnstrumenteerde fiets bij het uitvoeren van veldtesten. Onder dynamisch gedrag van een renfiets wordt verstaan: -

Krachten uitgeoefend op de contactpunten tussen mens en fiets

-

Pedaalkracht- en vermogenmetingen mogelijk maken

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Meten van het comfort volgens de ISO en/of BS standaard

-

Meten van het comfort volgens de absorbed power methode

Deze comfortmetingen zullen uitgevoerd worden bij gewijzigde parameters. De bandendruk en wegdek worden uit ervaring verondersteld de grootste invloed te hebben op de perceptie van comfort. In eerste instantie worden deze metingen uitgevoerd alsook de verwerking van de data, zodat het mogelijk is wijzigingen in het comfortgehalte wetenschappelijk aan te tonen. In een later stadium zal dit mogelijk maken om de invloed van het framemateriaal op het comfortgehalte te bepalen. 16

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Comfort Een vaak over het hoofd gezien aspect van het wielrennen is het comfort van de renner. De grote stijfheid van composietmaterialen en wielen en hoge bandendrukken hebben ertoe geleid dat trillingsexcitaties door het wegdek sterk worden doorgegeven aan de rijder, wat de prestaties op lange termijn negatief kan beïnvloeden [1]. Elk frame heeft namelijk bepaalde eigenfrequenties, frequenties waarop trillingen meer versterkt worden. Deze frequenties kunnen zowel experimenteel als met behulp van eindige elementen modellen bepaald worden. Wanneer de excitatie door het contact met de weg deze frequenties aanspreekt, zal de renner dit ervaren als een sterke trilling in het frame. De excitatiefrequenties afkomstig van het contact tussen band en wegdek zijn afhankelijk van de bandendruk en van de snelheid waarmee gefietst wordt. Algemeen kan gesteld worden dat bij een hogere snelheid de excitatiefrequenties zullen toenemen. De mens daarenboven is ook gevoeliger aan bepaalde frequenties van trillingen. Deze gevoeligheid is reeds intensief onderzocht en beschreven in de ISO2631 en BS6841 standaard. Deze gevoeligheid hangt af van de plaats waar het menselijk lichaam contact maakt met het trillend object. In het geval van een renner is dit het zitvlak, de handen en de voeten. Algemeen kan worden gesteld dat de mens het meest gevoelig is aan vibraties tussen 1 en 12Hz. Er bestaan meerdere mogelijkheden om het comfort ten opzichte van trillingen van een persoon te meten. De meest gekende en vaak gebruikte methoden baseren zich op de ISO2631 en BS6841 standaard [2, 3]. Hier worden de acceleraties gemeten in meerdere orthogonale assen op de plaatsen het lichaam contact maakt met het trillend object. Zoals hierboven aangehaald is de gevoeligheid van de mens ten opzichte van trillingen afhankelijk van de frequentie van de trilling. Het is bovendien vaak zo dat een trilling een heel complex gegeven is, waarin meerdere frequenties voorkomen. Om te vermijden dat onbelangrijke frequenties, waaraan de mens niet of minder gevoelig aan is, een grote invloed zouden hebben op de uiteindelijke comfortmeting, worden de acceleratiesignalen gefilterd vóór de analyse. Deze zogenaamde weegfilters simuleren de gevoeligheid van de mens aan vibraties in functie van de trillingsfrequentie. Een voorbeeld van de methode van meten is weergegeven in Figuur 2.

Figuur 2: Meten en wegen van acceleraties

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Deze gefilterde signalen kunnen op verschillende manieren verwerkt worden. De meest gekende is het bepalen van de r.m.s. waarde van het acceleratiesignaal. Deze waarden worden gebruikt om verschillende trillingsomgevingen te vergelijken met elkaar en een beoordeling te maken over het effect op het comfort en de gezondheid van de personen die deze trilling ondergaan. Naast deze conventionele methode bestaat er eveneens een niet genormeerde methode die naast het meten van de acceleraties van de trilling, ook de contactkracht meet tussen de persoon en het trillend object. Bij de toepassing van de fiets is het zo dat het beter vastgrijpen van het stuur leidt tot een betere koppeling tussen persoon en de trillende fiets. Deze betere koppeling kan ervoor zorgen dat de magnitudes van de acceleraties aan het stuur dalen. Volgens de conventionele meetwijzen zou dit moeten leiden tot een verbeterd comfort daar de acceleraties gedaald zijn. Het is echter mogelijk dat de verhoogde contactkracht leidt tot eenzelfde of zelfs slechter comfortgevoel voor de renner. Dit wordt niet gemeten volgens de ISO2631 en BS6841 methode. De Absorbed Power methode is ontwikkeld op het einde van de jaren ’60 in opdracht van het Amerikaanse leger [4]. Zoals de naam doet vermoeden wordt het vermogen gemeten dat door de persoon wordt geabsorbeerd. Er wordt aangenomen dat het comfortgehalte en het gezondheidsrisico rechtstreeks verbonden is aan dit vermogen dat gedissipeerd wordt in het lichaam. Om dit vermogen te kunnen meten moet de vibratiesnelheid en de contactkracht simultaan en in eenzelfde richting gemeten worden voor elk contactpunt. De vibratiesnelheid wordt bekomen door de acceleraties te meten met conventionele accelerometers en vervolgens dit signaal te integreren in de tijd. Uit dit vermogenssignaal in de tijd kan de piekwaarde en gemiddelde waarde berekend worden. Het is bekend dat slechts een deel van het vermogen dat constant uitgewisseld wordt van rijder naar fiets geabsorbeerd wordt door het menselijk lichaam. Het vermogen dat niet opgenomen wordt, heet het elastische vermogen, het geabsorbeerde gedeelte heet het geabsorbeerd vermogen. Indien enkel het geabsorbeerd vermogen in rekening wordt gebracht bij de comfortbepaling, wordt verondersteld dat de continue uitwisseling van elastisch vermogen geen effect heeft op de perceptie van de mens [5], iets wat betwistbaar is en nog dient verder te worden onderzocht.

Instrumentatie van de fiets Zoals eerder vermeld moeten de krachten, versnellingen en snelheden worden gemeten om het comfortgehalte te kunnen bepalen. De krachten op elk contactpunt dienen in twee richtingen te worden gemeten, in de horizontale en verticale richting. Er wordt uitgegaan dat de horizontale krachten die loodrecht op de fiets worden uitgeoefend verwaarloosbaar klein zijn. Zoals blijkt uit Figuur 3 worden er krachten op zowel stuur, zadel als pedalen uitgeoefend. Om deze krachten te meten dienen er sensoren te worden gemaakt. Nader onderzoek maakte al gauw duidelijk dat het aangrijpingspunt van de krachten op deze drie contactpunten vaak enorm kan wijzigen. Er was dus een meetprincipe nodig die de kracht kon meten ongeacht de positie waar deze kracht ingrijpt. 18

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Figuur 3: Orthogonale contactkrachten

De krachten worden gemeten met behulp van rekstrookjes. Dit zijn sensoren die de rek kunnen meten volgens het principe van elektrische weerstandsverandering ten gevolge van uitrekking. Door vier van zulke rekstrookjes te plaatsen op elke krachtsensor volgens een bepaald principe, kan een krachtmeting uitgevoerd worden die onafhankelijk is van de positie van de kracht. Dit principe werd vooraf uitgetest en werd nadien toegepast voor alle krachtmetingen. Kracht uitgeoefend op de pedaal Om de krachten op de pedaal te meten is ervoor geopteerd om een standaard klikpedaal te voorzien van rekstrookjes, wat zorgt voor een zeer compacte en accurate meetpedaal. De pedaal in kwestie heeft een zeer lange vrije spindel waar het mogelijk is om de acht rekstrookjes te plaatsen. Figuur 4 maakt de kleinschaligheid van de sensoren duidelijk. Daar deze pedaal continu meedraait met de crank, werd gekozen om de uitlezing van deze meetpedaal draadloos te laten geschieden. Met behulp van een Bluetooth module die gemonteerd is aan de binnenzijde van de crank worden zowel de tangentiële als radiale krachten gemeten en doorgezonden naar een notebook.

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Figuur 4: Volledig geïnstrumenteerde pedal

De plaatsing van de Bluetooth module is gevisualiseerd op Figuur 5. Het lage gewicht zorgt voor een minimale invloed op de metingen.

Figuur 5: Plaatsing van de Bluetooth module en batterij

Kracht uitgeoefend op het zadel De krachten op het zadel dienen eveneens in beide richtingen te worden gemeten. Hiervoor is een krachtsensor ontworpen die tussen het zadel en de zadelpen geplaatst wordt (Figuur 6). Door opnieuw gebruik te maken van de gewijzigde Wheatstonebrug configuratie kunnen de krachten op het zadel worden gemeten ongeacht waar de renner zit op het zadel. Door gebruik te maken van een U-vormig stuk kunnen de horizontale krachten en de verticale krachten afzonderlijk worden gemeten. Dit principe steunt eveneens op de eigenschappen van de gewijzigde Wheatstonebrug en werd geverifieerd door het uitvoeren van een eindige elementensimulatie. 20

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Figuur 6: Zadelkrachtsensor

Deze zadelkrachtsensor is ontworpen zodat de veiligheid van de gebruiker niet in het gedrang komt. Door het aanbrengen van de seat post clamp (zie Figuur 6) is het mogelijk om deze sensor onder eender welk conventioneel zadel te plaatsen. Kracht uitgeoefend op het stuur Als laatste contactpunt worden ook de krachten op het stuur aan linker- en rechterzijde gemeten in zowel verticale als horizontale richting. Opnieuw wordt gebruik gemaakt van de gewijzigde Wheatstonebrug configuratie om de krachten te kunnen meten. Er werd geopteerd om een bestaand stuur te instrumenteren met rekstrookjes. Echter, de eerste testen wezen op sterk foutieve uitlezingen ten gevolge van de inklemming van het holle stuur, dat voor grote vervormingen zorgde die de meetwaarden drastisch verstoorden. Ook werd er een sterke kruis-gevoeligheid gedetecteerd tussen linker- en rechterzijde, zodat een belasting aan de linkerkant een krachtmeting aan de rechterkant veroorzaakte. Daarbovenop trad er na belasting een grote offset op bij de uitlezing ten gevolge van slip van het stuur binnen de klemming. Dit probleem werd uiteindelijk verholpen door het stuur in twee delen te zagen, een rechter- en een linkerkant. Deze twee delen werden vervolgens opnieuw verbonden door het lijmen van een stalen insert in de twee stuurhelften, zoals te zien is op Figuur 7. De stuurklem grijpt in op deze insert waardoor de klemkracht, reactiekrachten en slip geen verdere invloed hebben op de metingen.

a)

b)

Figuur 7: a) Geïnstrumenteerd stuur zonder insert b) Geïnstrumenteerd stuur met insert

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Echter, de boring in de rechterhelft van het stuur is niet perfect gecentreerd, wat ervoor zorgt dat de meetassen, bepaald door de plaatsing van de rekstrookjes, niet langer orthogonaal zijn. Dit zorgt voor een grote bijkomstige moeilijkheid in de verwerking van de meetgegevens. Na veel pogingen tot kalibratie werd geopteerd om enkel de linkerzijde van het stuur te gebruiken tijdens de veldtesten, daar het comfortgedrag op deze manier ook nog steeds kan bepaald worden. Crankpositie Het is gewenst naast de pedaalkracht ook de bijhorende pedaalpositie te kunnen meten. Dit laat toe de krachten te bestuderen zowel in functie van de tijd als in functie van de crankpositie. Dankzij deze gegevens is het ook mogelijk om het instantaan en gemiddeld trapvermogen te berekenen. Dit biedt de mogelijkheid om na te gaan welke trapstijlen het meest efficiënt zijn en wat de maximaal optredende krachten zijn. Dit gemiddeld vermogen kan dan vergeleken worden met het geabsorbeerd vermogen dat berekend wordt bij de comfortmetingen. Het meten van een hoekpositie wordt doorgaans gemeten met behulp van een encoder. Deze encoder zet de rotatiepositie van een as om in een digitaal signaal. Dit digitaal signaal kan door middel van gepaste data acquisitiekaarten omgezet worden in een hoekpositie. Daar het maken van een mechanische verbinding tussen een dergelijke encoder en de trapas vrij moeilijk te realiseren is en bovendien veel gewicht zou toevoegen aan de fiets, werd gekozen om zelf een encoder te vervaardigen. Twee inductieve sensoren (A en B op Figuur 8) worden over de tanden van het grote tandwiel vooraan geplaatst. Indien het aantal tanden van het tandwiel gekend is, kan de omwentelingssnelheid of –positie berekend worden door het aantal elektrische pulsen te tellen. Door deze sensoren ruimtelijk gezien een halve tandsteek te verplaatsen ten opzichte van elkaar, zullen de signalen afkomstig van deze sensoren elektrisch gezien 90° uit fase zijn. Door de na- of voorijling te bestuderen kan dan ook de rotatiezin bepaald worden. Door als laatste ook een derde sensor C te voorzien is het mogelijk een absoluut nulpuntpositie te bepalen.

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b)

a)

Figuur 8: a) plaatsing van de twee inductieve sensoren A en B en de absolute nulpunt sensor C b) Close up van sensor A en B

Na het debuggen blijkt deze setup heel betrouwbaar en tevens heel licht te zijn. Ondanks de zeer beperkte ruimte tussen de sensoren A en B en het tandwiel werd er tijdens het veldtesten nooit contact gemaakt tussen beide. Meten van de vibratiesnelheid Wanneer het comfort bepaald wordt door gebruik te maken van de ISO en BS normen, dienen enkel acceleraties te worden gemeten. Hiervoor wordt doorgaans gebruik gemaakt van accelerometers. Deze kleine sensoren meten de acceleraties volgens een bepaalde as en zijn eenvoudig in plaatsing en gebruik. Wanneer echter het geabsorbeerd vermogen wordt bepaald, moeten naast de contactkracht ook de vibratiesnelheid gemeten worden. Compacte sensoren die de snelheid meten zijn niet beschikbaar op de markt. De snelheid kan echter bepaald worden door de gemeten acceleratie te integreren in de tijd. Dit kan zowel real-time als bij het nabewerken van de data. Om de goede werking van deze twee methodes te verifiëren werd een testopstelling bedacht waarbij een elektrische shaker een bepaalde trilling werd opgedragen. Deze trilling werd gemeten door zowel een accelerometer als een laser vibrometer, zoals geïllustreerd in Figuur 9. Een laser vibrometer is een toestel dat heel accurate snelheidsmetingen kan verrichten die kunnen dienen als ijkingspunt.

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Figuur 9: Testopstelling

Uit de metingen bleek dat bij lagere frequenties tussen 1 en 10 Hz er een faseverschuiving optreed tussen de berekende en de gemeten snelheid wanneer gebruikt wordt gemaakt van de realtime methode. Dit is te wijten aan interne hoogdoorlaatfilters. De nauwkeurigheid van de achteraf berekende snelheden is lager dan die van de real-time berekende snelheden en voldoet niet om gebruikt te worden voor de testen. Tijdens het veldtesten zal dus zowel het acceleratie- als snelheidssignaal worden opgeslagen.

Data acquisitie tijdens het veldtesten Daar deze testen niet afgenomen worden in een labo maar tijdens veldtesten op de baan, dient alle dataacquisitieapparatuur meegenomen te worden tijdens het rijden. De testrijder zal een rugzak dragen met daarin alle benodigde onderdelen (Figuur 10): een connectorbox waar alle aansluitingen, afkomstig van de fiets, aangesloten worden; de data-acquisitiekaarten; een voedingsbatterij voor deze kaarten en als laatste een notebook die instaat voor de verwerking en opslag van de data.

Figuur 10: Opstelling tijdens het veldtesten

De krachten worden gemeten door gebruik te maken van de reeds besproken krachtsensoren. Het is echter zo dat ten gevolge van externe factoren zoals temperatuur etc. een offset in de meting kan optreden na verloop van tijd. Dit wil zeggen dat alvorens de aanvang van een test deze offset op 0 moet worden gesteld. Deze offsetcorrigering wordt uitgevoerd door het indrukken van een knop nabij het stuur 24

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wanneer de fiets in onbelaste toestand verkeert. Een tweede knop is voorzien waarmee commando wordt gegeven om data op te slaan. Dit vereenvoudigt het testen en vermijdt onnodig grote bestandsgroottes.

Figuur 11: Volledige data-acquisitie opstelling

Kalibratie van krachtsensoren De sensoren om de uitgeoefende krachten te meten op zowel stuur, zadel als pedaal dienen uiteraard te worden gekalibreerd zodat de gevoeligheid van de sensoren gekend zou zijn. Hiervoor werden meerdere werkstukken gefabriceerd die het mogelijk maakten de sensoren te plaatsen in een elektromechanische trekbank. Niet enkel de gevoeligheid werd gecontroleerd, ook de stijfheid en gevoeligheid bij transversale belasting werd nagegaan. Uit deze metingen bleek dat de gevoeligheid voor de zadelkrachtsensor en de geïnstrumenteerde pedaal heel goed was. De rechterhelft van het geïnstrumenteerde bleek echter niet te voldoen en werd bijgevolg niet gebruikt tijdens de veldtesten.

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Uitvoeren van veldtesten Voor deze thesis zijn, naast de vele tests om alle subsystemen uit te testen, drie testprogramma’s opgesteld om verschillende aspecten van het fietsen te bestuderen. Als eerste test werd de geleverde pedaalkracht onderzocht zodat de distributie van radiale en tangentiële krachten op de pedaal kon worden voorgesteld in functie van de tijd en in functie van de crank hoek. Vervolgens werd het dynamisch gedrag van de fiets onderzocht bij het rijden over een hobbel, zodat een groter inzicht in het gedrag tussen mens en fiets verkregen werd. Hier wordt het fenomeen van uitgewisseld en geabsorbeerd vermogen in detail uitgelegd. Als laatste werden een serie ritten uitgevoerd op zowel een heel vlakke weg als op een lichte kasseiweg. Tijdens deze testen werd de bandendruk systematisch opgevoerd. De data werd gebruikt om de distributie van de krachten na te gaan op zowel het zadel als op het stuur. Daarnaast werd ook het comfortgehalte berekend door gebruik te maken van de British Standard en de Absorbed Power methode. De invloed van de bandendruk en de ruwheid van het wegdek werd hiermee bepaald. Deze test hebben als doen na te gaan hoe goed bepaalde kleinere invloedsfactoren te meten zijn tijdens veldtesten, zodat later een uitgebreider testprogramma kan worden opgesteld bij het onderzoeken van de invloed van het framemateriaal of –geometrie.

Resultaten Krachtendistributies Uit de veldtesten op het vlakke wegdek en de kasseiweg kunnen de krachtendistributies opgesteld worden. Deze geven aan wat de kans is dat een bepaalde kracht zich voordoet. Deze gegevens kunnen gebruikt worden bij het ontwerp van fietsen of bij het testen van frames of onderdelen in laboratoria tijdens statische of dynamische vermoeiingsproeven. Figuur 12 tot en met Figuur 15 geven de krachtdistributies weer op de verschillende contactpunten tussen de mens en de fiets bij een vlak wegdek en bij een kasseiweg aan een snelheid van 30km/h. Opvallend zijn de normale verdelingen van de krachten. Verder is de spreiding op de krachten veel groter bij een ruwe ondergrond.

26

Samenvatting

b)

a)

Figuur 12: Distributie van de horizontale zadelkrachten voor a) vlak wegdek b) kasseiweg

b)

a)

Figuur 13: Distributie van de verticale zadelkrachten voor a) vlak wegdek b) kasseiweg

De piekwaarden van deze krachten bij een vlak wegdek zijn een veelvoud van deze bij een kasseiweg. Iets wat zeker van belang is bij het bepalen van de sterkte van onderdelen.

a)

b)

Figuur 14: Distributie van de horizontale stuurkrachten voor a) vlak wegdek b) kasseiweg

a)

b)

Figuur 15: Distributie van de verticale stuurkrachten voor a) vlak wegdek b) kasseiweg

27

Samenvatting

Pedaalkracht- en vermogendistributie De pedaalkracht en –positie werden opgeslagen tijdens een rit met een constante snelheid van 38km/h. Een gedeelte van deze data werd geanalyseerd om te demonstreren wat de mogelijkheden van deze meetopstelling zijn. Figuur 16 geeft weer hoe de krachten verlopen tijdens het fietsen in regime. Meest opvallend is de tegenwerkende kracht dat het been uitoefent tussen 195° en 345°, wat voor een verminderde efficiëntie zorgt. Het verloop van de tangentiële en radiale krachten voor meerdere omwentelingen is weergegeven in Figuur 17, waarin de spreiding op de data duidelijk gevisualiseerd wordt. Doorheen alle metingen werd een piekkracht van 1500N geregistreerd. Het spreekt voor zich dat deze eigenschappen gebonden zijn aan de renner.

Figuur 16: Oriëntatie en amplitude van de pedaalkracht onder verschillende crankhoeken

28

Samenvatting

Figuur 17: Verloop van de tangentiële en radiale krachten in functie van de crankhoek

Met behulp van deze metingen kan ook het verloop van het trapvermogen berekend worden. De omtreksnelheid van de pedaal, die voor deze berekeningen nodig zijn, kan immers bepaald worden uit de metingen van de crankhoek. De eerder vermelde tegenwerkende krachten zorgen voor een aanzienlijk negatief trapvermogen, wat wil zeggen dat wanneer het ene been voor een aandrijvende kracht zorgt, niet alleen de fiets en fietser voortstuwt maar tevens het andere been deels opheft. Het vermogenverloop is cyclisch met een piekvermogen van ongeveer 450W terwijl het gemiddelde vermogen 105W bedraagt. Dit is uiteraard een meting op één pedaal, waardoor het totale gemiddelde vermogen op 210W mag geschat worden indien beide benen voor een gelijke bijdrage leveren. Het negatieve vermogen loopt op tot ongeveer 100W.

Figuur 18: Trapvermogen

29

Samenvatting

Dynamisch gedrag bij het rijden over een hobbel De data die werden opgeslagen bij het rijden over een zelfgemaakte hobbel, werden geanalyseerd om beter inzicht te verkrijgen in de uitwisseling van vermogen en energie. Hiermee kon een vereenvoudigd model van de fiets, waarmee de herkomst van het geabsorbeerd vermogen word gedemonstreerd, worden geverifieerd. Dit model gaf aan dat de fietser een deel kinetische energie opneemt bij het oprijden van de hobbel en slechts een deel terug afgeeft bij het afrijden van deze hobbel. Het verloren gedeelte energie is opgenomen door de rijder ten gevolge van dempingen in het menselijk lichaam. Figuur 19 geeft de vermogenswisseling weer tussen mens en fiets. Op 1.7s wordt de hobbel opgereden en stelt het negatieve vermogen het vermogen voor dat door de rijder wordt opgenomen. Dit wordt rond 1.75s gedeeltelijk terug afgestaan aan de fiets, zoals blijkt uit de grafiek.

Figuur 19: Vermogensuitwisseling

Comfortmetingen De data afkomstig van de testritten op een vlakke weg en een kasseiweg werden gebruikt om vast te stellen of de methode van het geabsorbeerd vermogen al dan niet bruikbaar is en al dan niet beter geschikt voor deze veldtesten dan de ISO of BS standaard. Figuur 20 illustreert het opgenomen vermogen bij het rijden over een lichte kasseiweg bij verschillende bandendrukken. Een tweede doel van deze tests was om te demonstreren of de verschillen in comfort al dan niet meetbaar waren. Daarom werden twee parameters gewijzigd waarvan de invloed op het comfort bekend is: de bandendruk en het wegdek.

30

Samenvatting

Figuur 20: Geabsorbeerd vermogen op een kasseiweg bij verschillende bandendrukken en/of fietsposities

Het geabsorbeerd vermogen is beduidend lager wanneer een vlak wegdek gekozen wordt, zoals te zien is op Figuur 21.

Figuur 21: Geabsorbeerd vermogen op een vlakke weg bij verschillende bandendrukken en/of fietsposities

Deze metingen geven aan dat comfortmetingen tijdens veldtesten mogelijk zijn met deze opstelling. Wanneer dezelfde data gebruikt wordt bij de methode volgens de Britse Standaard, waarin enkel de acceleraties van belang zijn, kan gezien worden dat wanneer de fietser het stuur slechts zwak vasthoudt, het gemeten comfortgehalte drastisch verslechterd lijkt te zijn. Dit is te wijten aan de verhoogde acceleraties bij deze lagere krachten. De methode volgens het geabsorbeerd vermogen houdt rekening met deze krachten en biedt dus een zeker voordeel.

31

Samenvatting

Verdere meetprogramma’s moeten worden opgesteld om de invloed van meerdere parameters na te gaan. Zo kan duidelijk gemaakt worden welke parameter de grootste invloed heeft op het comfortgedrag en uiteindelijk ook wat de invloed is van het framemateriaal of de framegeometrie. Met het beëindigen van deze masterproef is een volledig geïnstrumenteerde fiets beschikbaar met bijhorende data-acquisitie. Ook de software, nodig voor de real-time verwerking en opslag alsook de nabewerking van data is reeds geschreven. Uit de metingen blijkt dat de methode van het geabsorbeerd vermogen waardevol is bij het bepalen van het comfortgehalte in situaties waarin het mogelijk is dat het lichaam contact verliest met het vibrerende object, zoals een fiets.

32

Chapter 1: Research request

Chapter 1:

Research request

1.1 Company presentation Johan Museeuw is a Belgian rider who has won many races, including many classic races as well as a world championship. By 2004, Johan Museeuw and Joris Van Raemdonck sat together to discuss the development of an entire new collection of racing bicycles. Van Raemdonck, an engineer at IPA, a company which designs structures in composites for as well automotive as aeronautic applications, had recently developed the hybrid composite flax-carbon material. The design process was handed out to Roberto Billato, head designer at Billato Linea Telai with great expertise involving the design of light weight bicycles. By 2006, Fangio Reybrouck joined Museeuw and Van Raemdonck. Together, they founded Museeuw Bikes. Carpentier Holdings joined the group in mid 2007 as an investor. IPA subsequently withdrew, so the flax-carbon weave production patent and the flax fibre treatment process patent were transferred to Libeco Belgium and Museeuw Bikes for the production of bicycles and related parts and accessories. Libeco Belgium produces the flax-carbon fabric in Meulebeke, Belgium. In 2007, the first prototypes were made and tested. Later on, the first actual production bikes were presented to the press. Museeuw Bikes claims that the use of flax-carbon fibre composite as a substitute for carbon fibre composite enhances the damping properties of the frame, so that the comfort level of the rider improves. This should lead towards better performance of the rider involved.

1.2 Requested research As mentioned above, Museeuw Bikes manufactures racing bicycle frames using the hybrid composite flaxcarbon as construction material. As this material is only recently developed, many parameters are still unknown. In order to fully understand the properties and advantages of this flax-carbon composite, research has to be conducted. By 2009, Museeuw Bikes is working in association with the Ghent University in order to fully investigate all properties of this material, on the macroscopic level as well as on the structural level. This involves following projects: -

Full material characterization of natural hybrid materials for computational structural analysis.

-

Optimization of a bicycle road frame for weight, stiffness and comfort by using innovative lay-up designs and production processes. 33

Chapter 1: Research request

-

Computational (FEA) analysis of new frame concepts.

-

Determination of the influence of the use of flax-carbon on the comfort level of the rider by means of field testing with fully equipped bicycles frames.

This research started in 2009 and involved the determination of basic parameters of the flax-carbon material, especially the damping behaviour of various types of composite materials. These experiments were conducted by Joachim Vanwalleghem [6] and Joeri De Thaeye [7]. These theses led to the conclusion that experimental verification of numerical analysis was needed when considering damping of a fully equipped bicycle with rider. Also, the correct lay-up scheme of the composite frame is needed to develop a good analytical model. It also proved to be rather difficult to measure the damping properties of composite materials on small samples. Much work has been done concerning the use of equipment and software, making a solid base for further investigation.

1.3 Description of the research Bicycles have evolved much throughout the years, especially the frames. These frames not only ensure the structural integrity of the bicycle, but also have a great influence on the cyclist’s perception of comfort whilst cycling. A main goal of bicycle frame manufacturers is to produce the lightest, strongest and stiffest frame possible, making use of new, exotic materials and production processes. These innovations have led to professional frames with weights well under 1kg. A downside to these positive evolutions is the decrease in the cyclist’s comfort level, since a stiffer frame leads to an increased transmission of road roughness vibrations towards the cyclist. When designing bicycles with this drawback in mind, it would be useful to know what parameters have the largest influence on this perception. Within this thesis, experiments will be conducted in order to determine the comfort level of the cyclist under several conditions. When conducting experiments in a laboratory environment, multiple parameters can be better controlled in comparison to field testing, for example temperature, wind, humidity etc.. However, a downside of this approach is the lack of some very important influences, such as the position of the rider, the translational movement of the entire bike plus rider, influence of the rider when anticipating rough surfaces etc.. This leads to believe that field testing of these composite racing bicycles will result in more realistic data, needed to compare different materials and setups. The collected data will not only be used to extract information about the cyclist’s comfort, but will give more knowledge about force distributions at the contact points between the cyclist and the cycle. The research starts with an introduction of the used materials and production processes commonly used by frame manufacturers. An insight is given into the properties of the flax fibre and their damping characteristics. Secondly, common methods for assessing human comfort level with regard to vibrations is explained. The benefits and drawbacks of several methods are discussed as well as the use of a non standardized method called absorbed power. In order to measure this comfort in a scientific way, several 34

Chapter 1: Research request

sensors are required. Some of these sensors are self-made and based on certain concepts. These concepts are first proved before the actual building and designing of the components. After a brief summary of the used data-acquisition setup, the calibration of the self-made sensors is given. Once the entire bicycle is equipped with the needed sensors, a test program is put together so that the influence of parameters such as the tyre pressure and the road surface roughness on the cyclist’s comfort can be examined. Next to these results concerning comfort, force distributions on the saddle, handlebar and pedal is given for different road surface roughnesses. It can be concluded that this thesis is twofold: first of all the bicycle will be equipped and secondly, a test program will be carried out.

35

Chapter 2: Introduction to bicycle racing frames

Chapter 2:

Introduction to bicycle racing frames

2.1 Introduction to composite materials In the broad sense, all solid materials composed of more than one component can be referred to as composite materials. These different components are present in separate phases. The composites discussed here are fibre reinforced plastics (FRP). Generally speaking, fibre reinforced composites consist of two components: a binder or matrix and reinforcement fibres. These two materials usually have complementary properties. This results in a material having properties which are noticeably different from the properties of the two constituents. The matrices of most importance currently available are polymeric. As a generalization, polymers have low strengths and stiffness. These polymers can either be thermoplastic or thermoset. Thermoplastic polymers can be moulded and then melted again, whereas the thermoset plastics are cured after moulding, which results in a strong bond between the molecules. Thermoset plastics cannot be melted after being cured. The heating of these materials results in decomposing and thus destroying of the polymer. Polyester resin is often used in general projects. Because of its UV sensitivity, this polymer tends to degrade over time and therefore has to be coated. Another thermoset plastic is vinylester resin, which has a lower viscosity then polyester resin. Epoxy resin produces a stronger and more temperature-resistant material, however it is also more expensive. In contrast to these thermoset plastics there are also shape memory polymer (SMP) resins. These have the property of being able to deform plastically when heated above their glass transition temperature, the temperature at which the viscosity suddenly drops . The fibres used in FRP can be divided into two main categories according to the fibre length: short fibres and continuous fibres. The composites made with continuous fibres will often constitute a layered or laminated structure. The fibres arrangement can be woven, unidirectional (UD) or random oriented. The short fibres are used when the parts are manufactured by means of injection moulding. The fibres used can either be synthetic or organic. Glass, carbon, metal and ceramic fibres are the most common synthetic materials. Jute, flax and wood are examples of natural materials which can be used to extract fibres from. Due to the difference in properties of the two constituents in a composite, the mechanical properties of the composite depends on the direction of the fibres within it. This dependency of the properties towards fibre direction gives composites an anisotropic character and an orthotropic character in the case of

36

Chapter 2: Introduction to bicycle racing frames

laminated composite at angles of 90°. Other materials such as steel or aluminium have mechanical properties which are not depended on direction. These are called isotropic materials. The most important advantage of composites [8] towards commonly used materials such as steel or aluminium is the reduction of weight, without the loss of strength or stiffness, which results in a high stiffness to weight ratio (specific stiffness) and a high strength to weight ratio (specific strength). The layers of the composite can be arranged to make use of the anisotropic behaviour to strengthen a part in certain areas in certain directions. This gives tremendous freedom in designing and engineering a composite part. The materials used in composites are usually corrosion resistant, which lead to longer service life. Due to a high viscoelastic loss, the damping properties of composites are considered to be superior to those of metals. Important drawbacks [9] to the use of composite materials are the high cost. The fibres are quite expensive compared to ordinary construction materials. Also, the production process involves a lot of labour-intensive handling in order to become the layered structure by means of stacking multiple layers of woven fibres on top of each other in an expensive mould. These layers can either be impregnated before the actual stacking, these are called pre-impregnated (prepreg) or the binder can be injected afterwards (wet impregnation). The laminated structure then needs to be cured under pressure, this is done inside an autoclave. This heating and pressurizing process requires a time consuming and expensive autoclave process, in which the pressure and heat is controlled over time. These properties make composites attractive for specific applications where high performance materials are required. The aeronautic industry makes use of composites in various areas such as aeroplanes and satellites. High performance vehicles also often make use of composites for the fabrication of the panels and/or chassis. Another important sector is the sport article industry such as tennis rackets, bicycle frames, etc..

2.2 Use of composites in structural design Over the years, the type of materials used for the fabrication of bicycles frames have become more and more important. Whereas the earliest bicycle frames where manufactured of wood and wrought iron, modern frames make use of more exotic materials such as [10] high grade steel, aluminium alloy, titanium, magnesium and composites. The use of these materials, combined with better design, led to higher performance vehicles. In bicycle frame design, composite material is often used because of its high degree of formability and strength. Next to carbon fibres, glass fibres and aramid fibres are often used, which goes by the name Kevlar™ and Spectra™. These fibres are not as strong as carbon fibres, but are tougher. This toughness indicates the amount of energy the material can absorb when impacted. Epoxy is usually used as the 37

Chapter 2: Introduction to bicycle racing frames

matrix constituent. As mentioned before, the layout of the textile layers in composites can influence the strength and stiffness in a certain direction. Manufacturers make use of this property to strengthen and stiffen heavily loaded areas of the frame. A major advantage of composite racing frames compared to aluminium frames are the higher stiffness and higher strength whilst being less heavy. This results in a very responsive bicycle, as the frame almost does not flex whilst steering. The ease of manufacturing complex frame and tube shapes gives way to very aerodynamic designs of the fork and frame, again leading to higher possible top speeds at the same power input of the cyclist. In bicycle design, carbon fibre reinforced plastics (CFRP) are commonly used for high end frames. In essence, there are two possible ways of manufacturing a frame using composites: making a monocoque frame or a lugged composite frame. The lugged method is similar to the method used for the manufacturing of steel or aluminium frames. The diamond shape of the frame is realised by connecting tubes to each other by gluing them into lugs (Figure 1), as opposed to welding of aluminium or steel. This is a relative cheap way of producing a composite frame since the moulds used for making the tubes can even be used for every frame size in the case straight tubes are used. These tubes are simply cut to length prior to gluing.

Figure 1: Museeuw MF5 lugged frame [11]

The monocoque frame on the other hand, is made as a single piece as can be seen in Figure 2. This means there is no extra weight due to the presence of the lugs and glue, and no severe stress concentrations are present when designed correctly. The major disadvantage is the use of a very expensive mould, for every frame size. As can be seen in Figure 2, the monocoque design allows for more complex shapes.

38

Chapter 2: Introduction to bicycle racing frames

Figure 2: Museeuw MC6 monocoque frame [11]

Unlike steel or aluminium, carbon fibre frames are very sensitive to overload or damage. This can be explained by looking at the parameters which define the material. When a tensile stress test is performed, a stress-strain curve can be plotted as can be seen in Figure 3. This curve is unique for each material and defines how it behaves under stress, elastically and plastic. Linear elastic behaviour states that the strain in the material is proportional with the imposed stress. When the stress is removed, the piece returns to its original state without any plastic deformation. This proportionality is defined by the Young’s modulus (Emodulus). The higher this E-modulus is, the stiffer the material is considered to be. When the stress is raised above the yield strength, plastic deformation can occur. Brittle materials do not plastically deform but fail above a certain stress level, whilst ductile materials are capable of yielding. This yielding causes strain hardening of the material, increasing its ultimate tensile strength. This property makes it possible to have a long elongation of the material before failure. It should be noted that when plastic deformation has taken place, the Young’s modulus remains the same, so no stiffness is lost.

39

Chapter 2: Introduction to bicycle racing frames

Figure 3: Stress-strain diagram of a material capable of strain hardening

Aluminium alloys are commonly used for the fabrication of bicycle frames. Figure 4 shows that this material has a relatively high yield strength and is capable of plastically deforming. The strain before failure can be up to 12%, which means that the frame will not immediately break when an overload takes place. Due to the high strain before failure, this deformation can be visible to the naked eye, making it possible to detect when an overload has occurred.

Figure 4: Stress-strain plots for different aluminium alloys [12]

Carbon, aramid and glass fibres are considered to be brittle. As can be seen in Figure 5, no yielding occurs when a tensile stress test is performed on these materials. These materials are not capable of plastically deforming under load, but will fail immediately when an overload takes place. Hence, the strain before failure, which is about 2% is much lower than for steel or aluminium alloy. When a bicycle frame is 40

Chapter 2: Introduction to bicycle racing frames

subjected to too high loads, this will lead to failure of the frame, often resulting in drastic breakage. Due to the low strain before failure, damage to the frame after an overload can sometimes not be easily detected and can cause safety issues.

Figure 5: Stress-strain plots for different brittle fibres [13]

The ultimate tensile strength of these fibres is very high compared to those of steel or aluminium alloy, in the order of GPa rather than MPa. The toughness of a material is the ability to absorb energy before rupturing. The area under the stressstrain curve is an important parameter for the toughness of a material. By looking at the two stress-strain curves above, it is obvious that ductile materials have greater toughness than brittle materials. Table 1: Properties of some materials used in bicycle construction [10]

Material

Modulus of

Ultimate

Elongation

Density

Specific

specific

elasticity,

tensile

at failure

(kg/dm³)

UTS

E

E (GPa)

strength,

(%)

(MPa.dm³/kg)

(MPa.dm³/kg)

UTS (MPa) Steel Reynolds 325 (CrMo)

200

700-900

>10

7.85

90-115

25.5

193-214

515-758

40-60

8.03

64-94

24-26.6

6061-T6

68.9

310

12

2.8

110

24.6

7075-T6

71.7

570

11

2.8

203.6

25.6

90

1500

3.5

2.63

570

34.2

200-300

+-2000

1.25

1.75

1142

114-171

301 stainless steel Aluminium alloy

Composites Glass-epoxy CFRP-UD (0 °)

41

Chapter 2: Introduction to bicycle racing frames

Table 1 sums up often used materials in bicycle construction. Steel is the heaviest of all construction materials, whilst composites and aluminium alloys are clearly lighter. An important fact is the high elasticity modulus and ultimate tensile strength of CFRP-UD (UD for unidirectional, meaning the fibres are all aligned along one axis). Combined with the low density, this results in a very low weight and very stiff bicycle frame. As mentioned above, the elongation before failure is drastically smaller for composites compared to conventional construction materials. A good way of comparing material properties is by examining their specific Young’s modulus and specific UTS. The table shows clearly that the composite fibres have significantly better properties in correlation with their weight.

2.3 Damping effect in composites When structures are subjected to vibrational stresses, energy is being dissipated into heat due to the damping effect of the material. This vibration absorption capability of a material can be expressed by the damping factor. With increasing damping factor, the rate of energy absorption increases. The energy loss can either be due to passive damping or to active damping. The first takes place when energy is dissipated in added damping devices, joint or the actual structural material damping, the latter occurs when energy is dissipated in controlled actuators. It is obvious that no active damping takes place when a bicycle frame is subjected to vibrations. Damping occurs in both the composite material as in the added devices and structures such as wheels, bearings, handlebar tape and saddle cushioning. Compared to metals and alloys, the damping mechanism in composite materials are very complicated. There are many different sources of energy dissipation [14]: a) The major contribution to composite damping is due to the matrix. However, the fibre damping must be included in the analysis as carbon fibres have high damping compared to other types of fibre. b) Damping due to interphase includes the region adjacent to the fibre surface all along the fibre length. c) Damping due to damage can consist of either frictional damping due to slip in the unbound regions between the fibre and matrix interface or due to energy dissipation in the area of matrix cracks, broken fibres etc.. d) Viscoplastic damping at large amplitudes of vibration or high stress levels due to the stress concentrations between the fibres, especially in thermoplastic composite materials. e) Thermoplastic damping due to cyclic heat flow from the region of compressive stress to the region of tensile stress in the composite.

42

Chapter 2: Introduction to bicycle racing frames

The actual damping factor of composites cannot easily be determined [6]. Literature shows that composites usually have good damping capabilities [15]. Damped vibrations show an exponential decay. A system with a single degree of freedom (SDOF) can be under-damped, meaning that even though damping is present, the system will still oscillate but with attenuating amplitude (Figure 6).

Figure 6: Impulse response of an under-damped system (red), exponential decay (green)

The mathematical solution for a dampened SDOF structure, submitted to a shock impulse is [16]: 𝑞𝑖𝑛 = 𝑎. exp(−𝜁𝜔𝑛 𝑡) sin (𝜔𝑝 𝑡 + 𝛷)

Where ζ stands for the damping factor, ωn is the undamped natural frequency of the system and ωp is the damped natural frequency of the system. Φ stands for the phase shift, while a is the initial amplitude. This equation clearly shows that the response decays exponentially in time. In an under-damped system, ζ lays between 0 and 1. The damping factor for steel and aluminium is respectively around 0.001 and 0.002. Apart from the material, this damping factor for more complex structures is also dependent on the boundaries and bearings, which contribute to the overall damping [17]. Hence, it is difficult to determine an exact value for the damping factor of a material. The damping factor of composite materials is found to be usually higher than those of steel or aluminium alloy.

2.4 Use of flax-carbon reinforcement fibres in composite frames Carbon and aramid fibres are reinforcing fibres which offer premium performance at premium cost. These are made from synthetic polymers. As a substitute for these synthetic fibres, natural fibres can be 43

Chapter 2: Introduction to bicycle racing frames

used. The advantages of natural fibres, such as sisal or flax, for example, are their relatively high stiffness, relatively low cost and possibly better recyclability [18]. Possible disadvantages can be their high moisture sensitivity and variability in diameter and length. Flax fibre composites, for example, have already been implemented by car manufacturers. Flax fibre’s mechanical properties are mainly influenced by the crystalline and amorphous elements, the degree of polymerization, the porosity content and the size of the lumen (hollow core) [19]. Flax fibres present a polygonal shape with 5 to 7 sides. The longitudinal view of a fibre (Figure 7) reveals a nonconstant transverse dimension. The fibres are thicker nearer the root and become thinner nearer the tip. On average, a fibre is 19 μm in width and 33 mm in length. It is, however, important to note the variation of the geometric dimensions, i.e., the transverse and longitudinal dimensions lie in the range of 5 to 76 μm and 4 to 77 mm, respectively. The flax fibre consists of highly crystalline cellulose fibrils spirally wound in a matrix of amorphous hemicellulose and lignin. The fibrils are oriented with a tilt angle of 10–11° with respect to the axis of the fibre and hence display a unidirectional structure.

Figure 7: Composition of flax fibre and stem

Flax fibres, extracted from the stem of a flax plant are called technical fibres. Each stem contains approximately 700-1400 technical fibres with a length of 0.5 – 1m. The physical properties are listed in Table 2 [20]: Table 2: Physical properties of flax fibre

Material

Modulus of

Ultimate

Elongation at

Density

Specific

specific

elasticity,

tensile

failure

(kg/dm³)

UTS

E

E (GPa)

strength,

(%)

(MPa.dm³/kg)

(MPa.dm³/kg)

414-759

31-69

UTS (MPa) Flax fibre

45-100

600-1100

1.5-2.4

1.4-1.5

As can be seen in the table above, flax fibres have a relatively high ultimate tensile strength, making them the strongest natural fibre. The elongation at failure is about the same as for carbon fibre as well as the same coefficient of thermal expansion. This makes it possible to produce what is called a hybrid composite, composed of flax and carbon fibres [21]. This enhances the properties of the natural fibre even 44

Chapter 2: Introduction to bicycle racing frames

further. It has been stated that natural fibre composites, especially flax fibre, have improved mechanical damping properties compared to carbon fibre composites. These good damping qualities are due to the nature of the matrix and fibres, due to energy dissipation in the area of matrix cracks and broken fibres which naturally occur [22] and due to poorly bonded fibres through the promotion of extensive interfacial slippage in the case of untreated fibres [23]. It can be seen that these damping properties are highly dependent of environment temperature and vibration frequency. With increasing temperature, the damping factor tends to rise. This can explained by the changing molecular properties of the matrix within the usable temperature range. The damping factor decreases with increasing excitation frequency, primarily due to the lower amplitudes at higher frequencies, leading to less energy loss due to slippage between the fibres. The major limitations of using these fibres as reinforcements in such matrices include poor interfacial adhesion between polar-hydrophilic fibres and non polar-hydrophobic matrix, and difficulties in mixing due to poor wetting of the fibres with the matrix. Therefore, it is imperative that natural fibres should be subjected to chemical modification to increase the compatibility and adhesion between fibres and matrix [22]. These possible beneficial properties of flax combined with carbon (flax/carbon) used as a hybrid composite, led a Flemish company Museeuw Bikes to believe that using this material would improve the shock and vibration absorbing properties of a bicycle frame. Flax UD (unidirectional) and carbon are woven together and applied layer by layer in the main tubes of a lugged frame. Three frame types are built: MF1 (Mueeuw Flax 1) in which the main tubes of the frame consist of 50/50 carbon/flax mix in fibres, the MF3 in which a 65/35 carbon/flax mix in fibres is used and the MF5 in which a 20/80 carbon/flax mix is applied. Since there has not been much research conducted in the field of damping properties of natural fibres, it is likely that the hybrid composite flax-carbon is not used at its maximum potential beneficial properties. Flax fibre reinforced composites have a similar density and a lower strength than carbon fibre reinforced composites. In flax-carbon reinforced composites, this leads to the use of higher wall thickness and thus making the frame slightly heavier.

2.5 Bicycle structure 2.5.1 Terminology As with every machine, some terminology goes along with bicycles and bicycle parts. Throughout this thesis, most of the terms will be used to aid explanations. Figure 8 gives most relevant parts and their names. The diamond shaped frame in essence consists of nine different tubes: the seat post, the head tube, the top tube, the down tube, two chainstays, two rearstays and the seat tube. As mentioned before, 45

Chapter 2: Introduction to bicycle racing frames

these can either be separate pieces glued together or built together as one piece, making a monocoque frame. The drivetrain contains the pedal, the crank arm, the chain rings, the chain, two derailleurs and a sprocket on the rear wheel. The saddle is mounted on the seat post, which can either be a part of the frame in a monocoque design, or can be adjustable in height in a lugged frame. The seat can usually be adjusted laterally by sliding on the seat rails. The handlebar is mounted on the stem which is in turn mounted on the top of the fork.

Figure 8: Labelling of different parts of a racing bicycle

2.5.2 Frame design Throughout the years, bicycle frame design has gone through a process which involved, next to engineering skills, a lot of trial and error. Wooden frames had multiple drawbacks, one of them being that the stresses in the bottom bracket due to the pedalling forces are far too high for any wood to handle. Wrought iron replaced wooden frames since the 1860s. These frames were still solid and thus very heavy. In the height of the industrial revolution, frames were built from steel tubing, which offered a very light weight, stiff frame. By 1885 there was a first successful rear-drive safety bike by J.K. Starley [24] and only five years later a cycling boom was in progress. This bicycle was the first to have a diamond shape frame as it is today. In all this time, the basic design of a bicycle frame has not been altered, but rather improved and optimized. Although many other designs have been proposed, it seems that the traditional diamond shape is a very good concept, since it consist of two triangles and thus being very stiff. In the 1980s, a 46

Chapter 2: Introduction to bicycle racing frames

more radical design involved the use of a cast magnesium alloy frame [25]. Problems with reliability and manufacturing ended the production. Another very often used material is aluminium since its weight/strength ratio exceeds that of steel. It was not until the mid 1970s that Exxon made use of advanced composites to construct bicycle frames. In this design, the lugged frame consisted of aluminium lugs and carbon fibre-reinforced composite tubes. This design eventually led to the development of the monocoque frame, which excludes lugs. Working with composites enables the designer to optimize the aerodynamic performance of the bicycles, since it is possible to realize complex geometrical shapes. This advantage also led to the redesigning of other components e.g. seat posts, handlebar, rims and cranks. Steel inserts are still used inside a composite fibre frame in areas such as fork ends, bottom bracket shells, headsets. These are weak spots which can be weakened by corrosion over time, eventually leading to failure [26]. In 2009, over 13 million bicycles were sold in the United States [27] and in 2007 1.32 million in the Netherlands [28], making the bicycle market a multimillion dollar industry.

2.5.3 Production process FRP racing bicycle frame structures are mainly produced form prepreg laminates which are laid up in an open mould as can be seen in Figure 9:

Figure 9: One half of the mould used to produce a composite bicycle frame

While stacking the laminates, a bladder is inserted inside the frame tubing. Once the two mould halves are placed on top of each other, the prepreg is heated [29]. As the correct temperature is reached, the bladder is blown up by air, which results in the pressing of the laminates against the inner mould surface. This heating causes a chemical reaction known as curing which solidifies the matrix binder. After this curing, the cured part is removed from the mould (Figure 10). This technique creates an outer surface with a rather good quality. Due to possible misalignments between the two moulds, which creates burrs at the places where the two moulds meet, sanding of the frame is often needed. Another production process is 47

Chapter 2: Introduction to bicycle racing frames

called differential design [29] in which pre-manufactured tubes and lugs are fixed in a bonding rig, wrapped with prepreg material in the joining areas and cured in a second step. The advantage of this method compared to integral design is that a relatively small number of moulds are necessary to produce the tube set. The tubes can be cut to size according to the frame size in which they will be used. This is only feasible in case straight tubes are used, since the cross section has to remain the same after cutting the tubes. Furthermore, the precise positioning of the prepregs is easier in straight structures. Unfortunately, this double curing procedure adds up to the production time and increases the chance of a poor surface quality in the tube-to-tube joining area. In both processes, the pressure and heat distribution over time are critical to achieve a good bond between matrix and fibres and between different prepreg laminates.

Figure 10: Placing the frame inside the mould for forming and curing

48

Chapter 3: Ride comfort

Chapter 3:

Ride comfort

3.1 Introduction Comfort is a term used to describe how an environment is felt by a human being. The sense of comfort can be influenced by several parameters: space, sound, light, climate (temperature, humidity, heat radiation), air quality, vibrations etc.. Comfort on its own is not sensed by the human body, but rather the lack of comfort, i.e. discomfort. This discomfort is felt when parameters like temperature or noise exceed a certain threshold. As a consequence of the great variety amongst human beings, the determination of these thresholds and sensitivity of the human body to these parameters is very subjective. Usually, a statistical research is conducted so that the thresholds and sensitivities measured and calculated, are applicable to the population mean. The International Association for the Study of Pain (IASP) has developed a classification in which it describes pain or discomfort according to five categories [30]: -

Duration and severity

-

Anatomical location

-

Body system involved

-

Cause

-

Temporal characteristics

In most cases, discomfort is only transitory, lasting until the noxious stimulus is removed, such as discomfort. Long lasting pain is called chronic. Certain parts of the human body are more sensitive to pain than others, so that the anatomical location is of importance when evaluating the comfort level. Not only the neuropathic (caused by damage to the somatosensory system) system, but also the vascular (blood vessels), the myofascial (skeletal muscles or the fibrous sheath surrounding them) and rheumatic (joint and surrounding tissues) systems can be overstimulated. Since the actual perception of pain takes place in the brain, the cause of the pain can either be somatogenic (as a consequence of a perturbation of the body) or psychogenic (as a consequence of a perturbation of the mind). Finally, a classification in pattern of occurrence can be established. This includes the reoccurrence of the pain and the fluctuation of the severity in time.

3.2 Influence of vibrations on the human body Next to climate parameters, vibrations are a very important factor in determining the level of comfort experienced by the rider of a bicycle. All of the studies below assume that the rider is positioned correctly 49

Chapter 3: Ride comfort

in regard to frame size and settings considering saddle position and handlebar position, which can be expected for (semi-)professional cyclists. Few studies have been conducted on vibrations on road bicycles. In the automotive world, the abbreviation NVH (Noise, Vibration and Harshness) is typically used to refer to the study of acoustic and mechanical oscillations in vehicles and their subjective perception by humans [31]. It should be stated that the frequency ranges of vibrations in Figure 11 are not clearly separated. The difficulty is compounded by the fact that the perception of noise and vibration is different depending on the person. Harshness is a term used to describe oscillations between 20 and 100 Hz which can both be heard and felt by the rider. Vibrations under 20 Hz, together with harshness, are of most importance when riding a bicycle.

Figure 11: Oscillation frequency ranges associated with the terms noise, vibration and harshness [31]

These vibrations will have several effects on the human body, one of them is the resonance vibration of body parts. The human body consist of several parts connected to each other at the joints by muscles and tendons. Many attempts have been undertaken in order to develop a functional model of the human body. The model shown in Figure 12 represents the human body as several rigid body elements connected to each other by dashpots and springs [32]. This lumped parameter model will only be able to simulate the human response to longitudinal vibration. Nevertheless, this visco-elastic concept consisting of damped mass-spring systems makes it clear that resonance frequencies will be present when the human body is excited at certain frequencies.

50

Chapter 3: Ride comfort

Figure 12: Lumped parameter model of the human body

The following table gives the range of frequencies at which body parts vibrate [31]: Table 3: Natural frequencies of human body parts

Body part

Head (axial) Shoulders Chest

Spine

Stomach

Forearms

Palms

Legs

Hz

appr. 25

10-12

4-8

16-30

50-200

appr. 2

4-5

appr. 60

The resonance of the abdominal part with resonance frequency of 4-8 Hz seems to be the most important with regard to the perception of comfort. The eyeballs are also susceptible to resonance at frequencies between 20-90 Hz [33], which can cause a blurry sight, resulting in a lack of vision and eventually in a lack of control when riding a bicycle. These frequencies all lay within the frequency range that can be expected from road surface roughness excitation. It can be concluded that human vibration leads to resonance of certain pieces the body, increasing the sense of discomfort. Not only resonance phenomenons have an influence, mechanical reactions of the human body, manifested as a deformation and bending of parts of the body, can also take place with the following effects [34]: -

Changes and possible disruptions of the normal core processes both in individual organs of the body and in molecular or cellular structures.

-

Pinching of the tissues, blood and lymph vessels.

-

Resonance and standing waves in blood vessels.

-

Extension and compression of nerve tissue.

-

Heating resulting from friction.

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Chapter 3: Ride comfort

Next to these more local effects, the vibration imposes a dynamic load on the skeleton and can result in damage to the tissues as a result of counteracting forces from supports. Research has shown that the arterial pressure and pulse frequency changes under influence of vibration. All of these effects and the sense of discomfort also depend on the duration of the vibrations. There have been few attempts to obtain quantitative relationships between discomfort and exposure time. Many of them suggested limits for vibration environments, offering lower limits for long durations. As a rule of thumb, the sensitivity of the human body to vibrations is directly proportional to the duration time and directly proportional to the square of the intensity of the vibration. Research has shown that whole-body vibration generally concerns frequencies between about 0.5 and 100 Hz and acceleration magnitudes between about 0.01 and 10 m/s² [35]. Several norms and standards are published regarding the quantitative determination of human comfort. These all include the measuring of the accelerations at the contact point between the human body and the vibrating object. These acceleration signals can then be assessed in order to quantify the level of discomfort. The most common methods are the ISO2631 [3] and the BS6841 [2] standards.

3.3 Vibration due to road excitation and bicycle dynamics The contact between the tyres and the road is the main source of vibrations and oscillations experienced by the rider. When cycling over uneven road surfaces, the wheels follow the topography of the roadway. This topography can be classified to standardized measurements of the surface power spectral density (PSD) over the wave number, as can be seen in Figure 13. It is possible to represent a vibration by the sum of a finite or infinite number of harmonic components: 𝑢(𝑡) = � 𝑢𝑖 . cos(𝜔𝑖 . 𝑡 + 𝛼𝑖 ) 𝑖=𝑙

Every frequency component ωi has its own amplitude ui and phase αi. This explains the presence of multiple vibration frequencies.

Figure 13: Example of road roughness PSD plot

52

Chapter 3: Ride comfort

The abscissa of this PSD plot is expressed in cycles per metre. This clearly shows the dependency of the experienced road roughness to the velocity of the cyclist. As the rider speeds up, the excitation values shift into higher frequency regions. The first damper of these vibrations with regard to the comfort of the human being is the tyre and rim itself. In fact, on racing bicycles, these are very important aspects when considering the comfort level. Secondly, the frame passes through the vibrations from the wheels to the pedal, handlebar and saddle. These points of contact act as the last dampers of vibration between the cyclist and the cycle. When considering the bicycle as a system, the road roughness can be seen as an input and the vibrations at the contact points as the output. In real life, measuring the input as the vibration caused by the road surface roughness is a daunting task. It is more feasible to measure the vibrations at the rear and front dropout. Next to the road surface roughness, the forces generated by the cyclist applied to the contact points (saddle, handlebar and pedals) also induce vibrations throughout the frame. As with all structures, the frame also possesses natural frequencies, i.e. the resonance frequencies at which the frame absorbs less energy. This leads to a high amplification of the input vibrations, causing the frame to oscillate in a specific way, called a mode. The amplification of vibrations at natural frequencies is very dependent on the present damping. In heavily damped structures, the oscillation will not only decay faster as explained above, but will also provide less amplification of frame oscillations at natural frequencies. Figure 14 shows the first four modal shapes of the MF1 frame, calculated by Joachim Vanwalleghem.

Figure 14: Numerical calculation of the modal shapes of the MF5 Frame

53

Chapter 3: Ride comfort

To verify these results, a modal analysis is performed on the same frame, which resulted in a good comparison between the model and the actual frame. The first seven natural frequencies lay between 24 Hz and 67.5 Hz. The damping ratio of these modes are about 2% [6]. These measurements were performed on a freely suspended unassembled frame without rider. It is obvious that the presence of the cyclist affects the dynamic behaviour of the assembled bicycle greatly. Researchers have shown that the natural frequencies of the frame shifted in a higher frequency region when a rider is present [36]. Also, and even more important, the damping factor increased significantly, up to 4-5%. When subjected to vibrations when riding, the bicycle itself will absorb vibration energy. However, not all energy can be absorbed, so the cyclist will have to absorb some of the energy. As mentioned above, the amplitude of the vibrations felt by the rider are smaller and decay faster with an increased overall damping factor of the frame. However, if the frame is too stiff, most of the vibrations will be passed through to the cyclist. This phenomenon is counteracted by most bicycle designer by ensuring less stiff areas on the bike, especially the front fork. A more comfortable bike will usually be more flexible and provide a better suspension of the cyclist than a racing bike. It is common believe that too much comfort leads to more energy dissipation within the frame, resulting in a lower performance of rider and bicycle. Recent studies on the other hand have shown that the power loss by suspension systems is negligible when cycling on a smooth surface. In fact, the increased comfort level may lead to better performance since muscle fatigue due to vibration sets in later. It can be concluded that a higher degree in comfort level, without confessing too much stiffness of the bicycle frame, may lead to a higher performance of the rider engaged in long distance events [1].

3.4 Assessment of vibrations Since the 1960’s, different standards have been developed in order to quantify the severity of the vibration level to which the human body may be exposed. The vibrating of the entire human being is called wholebody vibration, while the vibration of the hand and arm is called hand-arm vibration. All of these standards are based upon measurements of the acceleration of the contact zone between the human body and the vibrating object. The development and verification of most of these techniques is an ongoing process, as the quantification of the human sense is not straightforward. The most tested and used standards up to this moment are the International Standard ISO 2631 (1997) [3], the British standard BS 6841 (1987)[2] for whole-body vibration and the International Standard ISO 5349 (2002) [37] for hand-arm vibration. The basic concept of these standards lays in the measurement of the acceleration signal, which is assumed to be a good parameter for the comfort level. This acceleration signal is taken from the most meaningful contact points between the human body and the vibrating surface. Since the perception of comfort is a subjective matter, all of these standards are essentially based upon the correlation between the subjective human perception and the calculated comfort level based on acceleration measurements. Research has shown that the human sensitivity to vibration is dependent of the frequencies at which the contact point 54

Chapter 3: Ride comfort

vibrates. In order to cope with this sensitivity, all the acceleration signals are filtered before processing with a filter that represents this sensitivity, as illustrated in Figure 15. This reduces or enforces the amplitude of certain frequencies in the measured acceleration signal. These weighting curves are determined for the population mean, so different persons will experience vibrations slightly differently.

Figure 15: Whole body vibration test method [11]

Studies also concluded that a change in posture (sitting, laying down, standing) changes the needed filter. The direction in which the acceleration is measured with respect to the human body also alters this dependency. Once the measurements are taken and appropriately filtered, different analysis methods are available. Since many vibration patterns can occur in real life, a different approach is used according to each circumstance. The following patterns are most common (Figure 16): harmonic (one single frequency), periodic, random and transient or shock. In case of cycling across rough terrain, the signal will be random with a possible degree of periodic vibration (for example cobblestones every 15cm) and shock impulses.

Figure 16: Different vibration patterns [38]

In the late 1960’s, Pradko, Lee and Kaluza [4] developed another assessment method based on the acceleration level and contact force, instead of only accelerations, which is called the absorbed power method. In order to calculate the power that is transmitted from the vibrating object to the human body, the 55

Chapter 3: Ride comfort

vibration velocity and the contact force is measured. Multiplying these two time signals for every contact point gives the absorbed power in time. When averaging this signal, one scalar quantity may be described by magnitude only. This number is additive so that the absorbed power of multiple contact point may be summed in multi-degree-of-freedom environments. This method has been compared to the other, more conventional standards, and has been proven to be successful in determining the comfort level of the human being [39]. This absorbed power method produces a scalar quantity which has relevance in the measuring of the comfort level when cycling, since it calculates the power loss due to vibrations. It is believed that a light person riding a bicycle will experience more severe accelerations than a more heavy person. The ISO and BS norm would then asses the ride of the lighter person to be more uncomfortable. The absorbed power method however, takes into account the increased contact forces for the more heavy person by multiplying the measured contact force with the vibration velocity (which is derived from the acceleration). The attenuation effect of more heavy persons on the acceleration level is hereby overcome when assessing the comfort level. Following is a discussion concerning the different standards and methods [40].

3.4.1 British Standard BS 6841: Whole body vibration This standard is released in 1987 and defines, next to a measurement and evaluation procedure, an action level that can be used to asses vibration severity an shock. This method is used within the frequency range of 0.5 – 80 Hz. Where the vibration has a low crest factor (the ratio of the peak acceleration to the r.m.s. value of the frequency-weighted signal), evaluation may be based on root-mean-square (r.m.s.) measures. For vibrations with high crest factor, the vibration dose value (VDV) must be used. This last methods incorporates a fourth power calculation, which amplifies the effect of larger shocks, which correlates to the increased sensitivity for large amplitude vibrations or shocks. When vibrations have lower crest factors, the use of eVDV (estimated VDV) can be considered but is not recommended. The calculation of the r.m.s., crest factor and VDV value is explained below. Figure 17 shows the action tree used in the British Standard.

56

Chapter 3: Ride comfort

Figure 17: Method of evaluation and assessment defined in BS 6841[2]

axes of vibration Twelve axes are defined for evaluation of vibration for the seated person: three translational and three rotational between the seat and the ischial tuberosities, three translational axes between the back and the backrest and three translational axes beneath the feet. For each of these axes, a certain weighting filter and multiplying factor is used.

Figure 18: Axes of vibration for BS 6841 (1987) [2]

57

Chapter 3: Ride comfort

Frequency of vibration As mentioned above, this standard defines weighting of the vibration signal as the procedure for obtaining a single value from multiple frequency or random vibration in order to assess the severity of the vibration. Four frequency weighting filters are defined: Wb, Wc, Wd and Wd. Wb is used for the assessment of vertical vibration on the supporting surface, Wd is used for the assessment of horizontal vibrations on the supporting surface and Wc is used for the for-and-aft vibration of a backrest for seated persons. Wd, Wb and Wc are the most often used filters. As can be seen for these filters in Figure 19, the sensitivity of the human body towards vibrations is highest for the frequency range 1 – 12 Hz. These curves are made by conducting experiments on a large group of humans, according to the different postures. These filters only represent the transmissibility of vibrations from a vibrating object through the human body, but does not withhold any information concerning health issues, caused by intensive exposure to vibrations.

Figure 19: Different weighting filters for ISO 2631, BS 6841 and ISO 5394

Magnitude and duration of vibration The primary quantity for expressing vibration magnitude is the weighted root-mean-square acceleration. The r.m.s. value is defined as followed: 1

2 1 𝑇 2 (𝑡)𝑑𝑡� 𝑎𝑤 = � � 𝑎𝑤 𝑇 0

58

Chapter 3: Ride comfort

With aw the weighted acceleration signal. However, when motions are intermittent or contain occasional high peak values, the r.m.s. magnitude will underestimate the severity of the vibration. In order to determine a limit for the use of the r.m.s. value, a maximum crest factor of 6 is defined. This crest factor is calculated as followed: 𝑐𝑟𝑒𝑠𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 =

𝑝𝑒𝑎𝑘 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑙𝑢𝑒 𝑟. 𝑚. 𝑠. 𝑣𝑎𝑙𝑢𝑒

Above this limit, a different method, the vibration dose value (VDV) will be used. The method for calculating this vibration dose value is defined as

𝑉𝐷𝑉 = ��

𝑡=𝑇

𝑡=0

1 4

𝑎4 (𝑡)𝑑𝑡� (𝑚𝑠 −1.75 )

where a(t) is the frequency weighted acceleration and T is the total period in which the vibration may occur. This method has the advantage that the value is not divided by the total time, so that periods in which no severe vibrations occur will not significantly change the obtained value. This means that this method can be used for assessing shocks and transients. Another method makes use of an estimated vibration dose value, defined as 1

𝑒𝑉𝐷𝑉 = [(1.4 . 𝑎𝑟𝑚𝑠 )4 . 𝑏]4

in which b is the duration time in seconds. This method will underestimate the true vibration dose value when the crest factor exceeds 6. Even more, the factor 1.4 is not explained by this standard and makes this method inferior to the VDV or r.m.s. method.

3.4.2 International Standard ISO 2631:1: Whole body vibration This standard was first released in 1974 and has been improved in 1997. The basic principle is the same for this ISO standard as for the British Standard. A measured acceleration is first frequency weighted and then assessed by making use of r.m.s. values. This standard incorporates two different weighting filters. The frequency range in which it is usable remains 1 – 80Hz. The action tree for ISO 2631 can be seen in Figure 20:

59

Chapter 3: Ride comfort

Figure 20:Method of evaluation and assessment defined in ISO 2631 [3]

Axes of vibration In the first version of this standard, only the vibration in the three translational axes centred in the body at the heart were considered. The standard was republished in 1997 and has changed measurement axes as shown in Figure 21:

Figure 21: Axes of vibration for ISO 2631 [3]

60

Chapter 3: Ride comfort

In this standard, the coordinate system moves with the body as it changes orientation with respect to gravity. It also assumes that rotational vibration could be adequately assessed by the translational components away from the centre of rotation. The overall weighted vibration values can be obtained by the following formula, also called the vector sum: 𝑎 = �(1.4. 𝑎𝑥𝑤 )² + �1.4. 𝑎𝑦𝑤 �² + 𝑎𝑧𝑤 ²

The use of the factor 1.4 is not referred to in the standard. Vibration in x and y direction are considered to be more hazardous than in the z direction. In the later renewed version of 1997, the procedure was to use the highest frequency-weighted acceleration in any axis. However, when two or more axes are comparable, the vector sum formula can be used to assess the vibration. The uncertain use of this multiplication factor 1.4 may lead to a 40% error if the wrong assumption is made. Frequency of vibration As can be seen in Figure 19 on p58, vibration frequencies between 4 - 8 Hz have the most influence on the human sensitivity to vibration acceleration. The weighting curves Wd, We and Wk are primarily used to asses vibrations in a seated position. Wk is used in the z direction for seated persons at the seat surface, whereas Wd is used in the x and y direction. The third curve We is used for the rotational vibrations at the seat surface. Magnitude and duration of vibration The basic evaluation method is based on the calculation of the r.m.s. value of the vibration acceleration as followed: 1

2 1 𝑇 2 (𝑡)𝑑𝑡� 𝑎 𝑤 = � � 𝑎𝑤 𝑇 0

where aw(t) is the weighted acceleration in time. This method will only be used when the crest factor of this signal is below or equal to 9. A large disadvantage of this method when examining vibrations, consisting of both large peaks and periods with low vibrations, is that the averaging procedure by dividing by the measuring time smoothens out these peaks, which may lead to wrong conclusions. When the crest factor is above 9, the standard suggests other methods. One of them is the running r.m.s. method, which is defined by the following formula: 1

2 1 𝑡0 𝑎𝑤 (𝑡0 ) = � � [𝑎𝑤 (𝑡)]²𝑑𝑡� 𝜏 𝑡0 −𝜏

61

Chapter 3: Ride comfort

where aw(t) is the instantaneous frequency weighted acceleration, τ is the integration time for the running average, t is the time and t0 is the instantaneous time. ISO 2361 recommends an integration time of 1s. Another suggestion is to make use of the VDV method as described in BS 6841.

3.4.3 Absorbed power This method of analyzing vibration hazards has not been implemented in standards. ISO en BS methods defines analyzing methods making use of the weighted acceleration signals at the contact surface. Only the acceleration level and not the contact force is taken into account and therefore it can be argued that it presents a poor description about the extent of vibration actually transmitted to the body. The developers of this theory, Pradko, Lee and Kaluza [4], claimed that the amount of vibration energy, either absorbed or exchanged between the vibrating surface and the body may be a better measure of the physical stress on the body since it takes into consideration the interplay between the vibrating structure and the body in contact with it [5]. Energy as a scalar quantity is considered easier as it is possible to simply add up every contribution of every direction and of every contact point. The instantaneous power transmitted to the body is: 𝑃𝑇𝑟 = 𝐹(𝑇). 𝑣(𝑡) ≡ 𝑃𝐴𝑏𝑠 (𝑡) + 𝑃𝐸𝑙 (𝑡)

where PAbs(t) is the absorbed part of the power. This power is absorbed by dissipation in the body due to internal damping. PEl(t) is the elastic part of the power which is constantly delivered and removed. This means that the time average of this elastic portion of the power is zero. The time averaged absorbed power ������ 𝑃𝐴𝑏𝑠 equals the absorbed power:

������ 𝐹(𝑡). 𝑣(𝑡) = 𝑃𝐴𝑏𝑠 = ������������

1 𝑇 � 𝐹(𝑡). 𝑣(𝑡)𝑑𝑡 𝑇 0

This method of vibration effect analysis on the human body requires the measurement of not only the vibration velocity instead of vibration acceleration, but also the contact force at every point of contact. The product of vibration velocity and contact force is a scalar product, meaning that the angle between the direction of the contact force and the vibration velocity needs to be determined. A more convenient method is to measure the contact force and vibration velocity in time at a certain contact point in two or three different orthogonal directions. By doing so, the product can easily be calculated for every direction and the different values for the different directions can be summed in order to determine the total absorbed power at a certain contact point. Since power is a well known scalar quantity, it can be more easily interpreted when analyzing different circumstances. Only the absorbed power is taken into consideration, although it can be discussed whether the elastic power may have an influence on the perception of comfort. 62

Chapter 3: Ride comfort

The basic principle of this method is that a certain amount of absorbed power is equally harmful or causes an equal feeling of discomfort for the human being, regardless of the frequency. Axes of vibration Since this method requires the measurement of contact force and vibration velocity, the axes of vibration can be chosen by the user. However, when measuring in two or more directions at a certain contact point, it is recommended to measure in orthogonal directions. This reduces the possible chance of errors in calculations. There is no difference in measuring method or measuring position with changing posture of the body. Research has shown that the posture of the sitting person, either relaxed or erected, has little influence when determining the absorbed power in correlation with the comfort experienced by the human [41]. Frequency of vibration As mentioned above, the basic principle assumes that the total amount of absorbed power is a value by which the comfort level can be determined. In this assumption, no distinction is made between different frequencies. This lack of frequency-weighing makes the implementation of this method easier [5]. Magnitude and duration of vibration The transferred power for a certain contact point can be calculated as followed: 𝑃𝐴𝑏𝑠 (𝑡) = 𝐹(𝑡). 𝑣(𝑡)

where F(t) and v(t) are the instantaneous force and vibration velocity, respectively. The average of PAbs(t) can be calculated over the test duration: ������ 𝑃𝐴𝑏𝑠 =

1 𝑇 � 𝐹(𝑡). 𝑣(𝑡)𝑑𝑡 𝑇 0

In order to fully understand the phenomenon of absorbed power, the energy exchange between cyclist and bicycle is examined when cycling over a bump. A simplified model is used, where the bicycle can be regarded as a unicycle as can be seen in Figure 22.

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Figure 22: Simplified bicycle model

If the bump is assumed to be sinusoidal of shape, the speed at which this bump is taken is low enough and the wheel diameter is small compared to the bump, it can be assumed that the tyre will stay in contact with the surface at all times, thus following the sinusoidal shape of the bump. Figure 22 also depicts the chosen positive axes for the contact force between the mass m and the saddle as well as the velocity v in the vertical direction. Following graphs do not have axis labels since this conceptual study does not depend on the actual values of the investigated velocities, forces, accelerations or absorbed power. The up and down movement is determined by the sinusoidal shaped bump as illustrated in Figure 23.

Figure 23: Sinusoidal bump with amplitude 2

The vertical velocity v of the mass m can easily be calculated by deriving the displacement. This velocity v is plotted in Figure 24.

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Figure 24: Vertical velocity v

The acceleration of the mass is calculated by deriving the velocity v as can be seen in Figure 25.

Figure 25: Vertical acceleration a

As mentioned above, the absorbed power is calculated by multiplying the vertical force F with the vertical velocity v. Keeping the chosen coordinate system in mind, the contact force F between the mass and the saddle can be calculated as 𝐹 = 𝑚. (𝑔 − 𝑎)

This will only be true if the connection between the saddle and the mass m is stiff. In reality, the saddle cushion and muscle and fat tissue of the human body will undergo deformations due to the sudden increase in contact force between saddle and human body. This deformation will dissipate energy under the form of heat. This means that the contact force when cycling down the bump will be less in amplitude then when cycling up the bump. This decay in amplitude is simulated by an exponential function 𝐹 = 𝑚. 𝑔 − 𝑚. 𝑎. 𝑒 −0.1𝑡

Figure 26 a) shows the ideal force distribution in time when no energy is lost by dissipation whilst Figure 26 b) shows a decaying contact force, the mass is chosen to be 1, the gravity is 9.81.

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Chapter 3: Ride comfort

a)

b)

Figure 26: a) Contact force without absorption b) contact force with absorption

The absorbed power is calculated by multiplying the velocity with the contact force. This is shown in Figure 27.

b)

a)

Figure 27: a) Instantaneous power exchange when no energy is dissipated b) instantaneous power exchange when energy is dissipated

This plot shows the power exchange between saddle and the human body for the ideal situation and the situation in which energy is dissipated. When the power is negative, power is delivered towards the human body. This is the case when the cyclist is pushed upwards when cycling up the bump. In fact, kinetic energy from the forward movement of the bicycle is being converted into potential energy and kinetic energy for the upward velocity of the cyclist. Once the cycle reaches the top of the bump, no power or energy is exchanged. When cycling down the bump, the cyclist loses its potential energy and kinetic energy from the downward movement. In the case of energy dissipation, not all consumed energy is transferred back into the bicycle as in Figure 27a. Since the plots do not show a clear difference, it is clear that the amount of absorbed energy is low compared to the exchanged energy. The absorbed energy can be better visualised by integrating these two plots, as illustrated in Figure 28.

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Chapter 3: Ride comfort

a)

b)

Figure 28: a) Total absorbed energy without dissipation b) total absorbed energy with dissipation

Figure 28 a) clearly shows that at the end of the bump an equal amount of energy is transferred back into the bicycle, leaving no energy absorbed by the human body. Figure 28 b) shows that at the end of the bump a small amount of energy is lost by dissipation. As explained above, negative power is power absorbed by the human body when these sign conventions for positive velocity and force are taken into account. This proves the theory behind the concept of absorbed power. As mentioned above, the absorbed power theory applied to the determination of the comfort level of a human being only takes the absorbed power level into account, whilst the theory shows that only a fraction of the exchanged energy is absorbed. The energy that is absorbed by the human body, but later exchanged back into the vibrating object is not taken into account which has been questioned by some researchers [5].

3.4.4 International Standard ISO 5349: hand-arm vibration This standard can be compared to the ISO2631:1 standard as it assesses the vibration to which the hands are subjected. The main principle is the same as the accelerations near the hand are measured in two or three axes. This acceleration signal is filtered by a weighting curve before determining the severity of the vibration. Axes of vibration As with the whole-body vibration evaluation, a basicentric coordinate system for the hand is given, shown in Figure 29.

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Figure 29: Basicentric coordinate system for the assessment of hand-arm vibration [37]

The total vibration level is determined by taking the root of sum of squares of the filtered acceleration signals in the three directions: 𝑎 = �𝑎𝑥𝑤 ² + 𝑎𝑦𝑤 ² + 𝑎𝑧𝑤 ²

Frequency of vibration

Figure 30 shows an increased sensitivity of the hand and arms to vibrations of higher frequency, compared to the assessment of whole-body vibration. The accelerations measured near the hand will be filtered with a filter representing this shape for x, y and z direction vibrations.

Figure 30: Frequency weighting curve Wh for hand arm vibration [37]

Magnitude and duration of vibration The basic evaluation method is based on the calculation of the r.m.s. value of the vibration acceleration as followed: 1

2 1 𝑇 2 (𝑡)𝑑𝑡� 𝑎 𝑤 = � � 𝑎𝑤 𝑇 0

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where aw(t) is the weighted acceleration in time. The magnitude of the vibration determines the maximum duration of exposure. Limits of exposure are given by this standard.

3.5 Discussion of the four different proposed assessment methods In order to compare the different methods of analyzing vibration and consequently the comfort level experienced by the human body, experiments have been conducted to compare the subjective comfort level with the calculated comfort level. The method with the best correlation between the subjective and the calculated comfort level is considered to be the best. The average absorbed power (AAP) and vibration dose value (VDV) methods turned out to be the most promising methods for assessing transients, random signals and shocks. The ISO 2361 method proved to be adequate for assessing small amplitude harmonic signals using the r.m.s. method [39]. With increasing body weight of the human body subjected to vibration, the total absorbed power increased. With the intention of reducing the influence of this parameter, the absorbed power can be normalized against the individual static sitting weight, i.e. in units of Wkg-1. Thresholds for the absorbed power have been defined for male and female bodies, 5.4 . 10-3 Wkg-1 and 4.5 . 10-3 Wkg-1 respectively. The absorbed power method seems to be promising to incorporate into the examination of the different bicycle frame materials and bicycle setups. This requires the measurement of either force and velocity at every contact point in every direction. The measuring of force also provides useful information about the forces in play when riding a bicycle. Based on this literature, the BS 6841 and AAP methods will be used. Acceleration measurements will be necessary to determine the crest factor and consequently the correct analysing method to use within the BS 6841. In order to be able to use these different techniques, following parameters need to be measured: -

contact force at each contact point in every useful orthogonal direction

-

vibration velocity at each contact point in every useful orthogonal direction

-

vibration acceleration at each contact point in every useful orthogonal direction

The ISO standard provides practical information on measuring accelerations. The sensitivity axes of the transducers (accelerometers) should not deviate more from the preferred orthogonal axes than 15°. If feasible, the transducers should be mounted orthogonally. The accelerometers should be mounted as close as possible to the contact surface between the body and vibrating object. The signals should first be conditioned by passing them through a low pass filter having a cutoff (-3dB) frequency of approximately 1.5 times the highest frequency of interest in order to maximize the signal to 69

Chapter 3: Ride comfort

noise ratio. A sample frequency of at least 3 times the minimal expected vibration frequency is recommended. A sample rate of 400Hz satisfies. As many information as possible should be noted when conducting an experiment, for example how conditions change over time, vibration axes etc..

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Chapter 4:

Proof of concepts

4.1 Measurement of contact forces 4.1.1 Introduction The absorbed power method requires the measurement of the contact force between the human body and the vibrating object at every contact point in every useful direction (mostly two orthogonal directions). The human body makes contact with a conventional bicycle at five points: the two feet at the pedals, the two hands at the handlebar and the bottom at the seat as can be seen in Figure 31.

Figure 31: Orthogonal contact forces

Only forces in the proposed x and y directions will be measured, as the influence of forces in the transversal direction z is assumed to have a negligible effect on the perception of comfort for the rider. This assumption is supported by the fact that the excitation by the road roughness is primarily in the y direction. Several force gauges will be made so that these contact forces can be measured accurately. In order to decide an appropriate measuring range for the forces at these points of contact, standards and literature are used to give an idea about the forces in play when riding a bicycle. The European Standard EN 14781 [42] is developed in order to ensure the safety of racing bicycles. Lower fatigue strength limits and static strength requirements are given for every part of the bicycle. 71

Chapter 4: Proof of concepts

The minimum static strength of the handlebar is checked by conducting the following tests:

Figure 32: Lateral bending test handlebar and stem assembly

This maximum expected loading from this standard reveals that a range of 1000N (Figure 32) for either side of the handlebar is sufficient. This parameter can be used to design the correct force gauge.

Figure 33: Fatigue test handlebar and stem assembly out-of-phase-loading (a), in-phase loading (b)

Not every force gauge can withstand fatigue loading, so the maximum expected fatigue loading as can be seen in Figure 33 should be taken into account when ordering or designing force gauges. The maximum expected static loading of the pedal spindle can be defined as 1500N at the centre of the pedal spindle as can be seen in Figure 34:

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Chapter 4: Proof of concepts

Figure 34: Fatigue test for pedal spindle

The fatigue loading consists of a constant load of 65kg at the centre of the pedal while rotating at 100rpm. As last contact point, the maximum expected forces on the saddle can also be extracted out of the standard.

Figure 35: Static strength test saddle clamp

Figure 35 shows that the maximum expected force on the saddle is 1000N at 25mm of the front of the saddle, while Figure 36 gives an indication of the required fatigue strength, also being 1000N but at the rear of the saddle:

Figure 36: Fatigue strength test at maximum 4Hz for 200000 cycles

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Chapter 4: Proof of concepts

4.1.2 Force measurements using strain gauges Several methods are possible for measuring forces. The one used in the scope of this thesis is by making use of strain gauges. Whenever a force is exerted onto a piece with a certain elasticity, the material will strain. This strain is an elongation due to tensile stress, or shrinkage due to compression. This strain can be measured by making use of a strain gauge, for example Figure 37.

Figure 37: Typical strain gauge with dimension of 2.5 x 5.8 mm to 45 x 5 mm

This small device consists of an insulating flexible backing which supports a metallic foil pattern. The gauge is mounted onto the place where the strain needs to be measured by means of a suitable adhesive. As the object strains, the metallic foil is deformed, causing its electrical resistance to change, which is related to the strain by the quantity know as the gauge factor (GF), which is dependent of the material of the strain gauge. This very small change in resistance can be measured, usually by making use of what is called a Wheatstone bridge as can be seen in Figure 38. Typical resistance values of undeformed strain gauges are 120, 350 or 1000Ω.

Figure 38: Wheatstone bridge configuration

The basic principle is a quarter bridge in which one of the four resistors above is the strain gauge and the other three are stable resistors of the same resistance. A stable DC voltage VEX is applied between the 74

Chapter 4: Proof of concepts

ground and Vex. The change in resistance of the strain gauge will change the voltage reading V of the centre voltage gauge. This voltage is related to the ΔR from the strain gauge due to straining. This relation can be calculated as followed (assuming R2 to be the strain gauge): 𝑅4 𝑅2 𝑉 = 𝑉𝑒𝑥 . ( − ) 𝑅4 + 𝑅3 𝑅2 + 𝑅1

If the following relation between relative resistance change, strain and gage factor (GF) is known 𝐺𝐹. 𝜀 =

𝛥𝑅 𝑅

then the first formula can be reformulated for a quarter bridge: 𝐺𝐹. 𝜀 𝑉 1 = .� 𝜀� 4 𝑉𝑒𝑥 1 + 𝐺𝐹. 2

The second term in the right indicates the nonlinearity of this type of bridge. A quarter bridge is also sensitive to temperature changes, which causes the resistance to change. A better alternative is to use four strain gauges instead of one. This is called a full bridge circuit, in which all of the resistors are active strain gauges (Figure 39), and is four times more sensitive than the quarter bridge and is linear with respect to the strain. In this configuration, strain gauge R1 and R4 are placed on one side of the part which undergoes compressive strain due to the bending force. This results in a decrease in resistance for these strain gauges. On the other side of the part, the two other strain gauges R2 and R3 are mounted. The elongation strain results in an increase in resistance for these strain gauges.

Figure 39: Placement of strain gauges in a typical full bridge configuration

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Chapter 4: Proof of concepts

The relation between the voltage ratio can be formulated as followed: 𝑉 = 𝐺𝐹 ∗ 𝜀 𝑉𝑒𝑥

This typical full bridge placement of strain gauges has numerous advantages: the influence of temperature changes is negligible since all strain gauges change in resistance equally and thus leaving the resistance ratio unaltered, the sensitivity is increased and the voltage output is linear according to the exerted strain. When measuring the forces that the rider exerts on the handlebar, pedals and saddle, the chance exists that the contact forces will not act on the same position while cycling, for example when the cyclist moves his hands further away from the stem. When the distance between the strain gauges and the force increases in Figure 39, the bending moment will increase causing the strain to increase. This will lead to an output voltage which is linear to the magnitude of the force F and to the distance at which this force acts. This renders the use of the typical full bridge configuration in order to measure these forces impossible. Fortunately, a change in this full bridge configuration makes the bridge insensitive to the actual position of the force [43]. An example of this bridge configuration and the placement of the strain gauges is shown in Figure 40:

Figure 40: Force position independent full strain gauge bridge

The strain gauges at position 1 will equally but oppositely change in resistance as so will the strain gauges at position 2. The strain at position 1 and position 2, respectively, is: 𝜀1 =

𝜎1 𝑀1 = 𝐸 𝑊1 . 𝐸 76

Chapter 4: Proof of concepts

𝜀2 =

𝜎2 𝑀2 = 𝐸 𝑊2 . 𝐸

With σ being the stress at the surface of the beam, E the young’s modulus, M the bending moment at position 1 or 2 and W the section modulus at position 1 or 2. When comparing a beam with a constant cross section, W1 is equal to W2. The formula for the conventional full bridge can be rewritten as: 𝑉 = 𝑉𝑒𝑥 . �

𝑉𝑒𝑥 𝛥𝑅1 𝛥𝑅2 𝑉𝑒𝑥 . 𝐺𝐹 𝑅 − 𝛥𝑅1 𝑅 − 𝛥𝑅2 �= � �= − − . (𝜀1 − 𝜀2 ) 𝑅 − 𝛥𝑅2 + 𝑅 + 𝛥𝑅2 𝑅 − 𝛥𝑅1 + 𝑅 + 𝛥𝑅1 2 𝑅 𝑅 2

If the strain is substituted by the formulas above, the output-excitation voltage ratio can be expressed by 𝐺𝐹 𝑉 = . (𝑀1 − 𝑀2 ) 𝑉𝑒𝑥 2. 𝑊. 𝐸

which reveals the main principle of this configuration: the difference in bending moment is measured and not the force itself. Following proves this statement: 𝐺𝐹 𝐺𝐹 𝐺𝐹 𝑉 = . (𝑀1 − 𝑀2 ) = . 𝐹. �(𝑐 + 𝑏) − 𝑐� = . 𝐹. 𝑏 2. 𝑊. 𝐸 2. 𝑊. 𝐸 𝑉𝑒𝑥 2. 𝑊. 𝐸

which clearly shows that the output voltage is only dependent on the force F, the gauge factor G, the dimension of the beam W, the material of the beam E and the distance b between the two strain gauges at one side. There is no dependency of the distance c nor a. To enhance the sensitivity of this configuration, the following can be done (when considering a constant cross section): -

increasing the distance b as much as possible

-

use strain gauges with high gauge factor GF (is usually around 2)

-

use a material with low young’s modulus E

-

use a cross section with a low section modulus W

The last two options clearly weaken the beam and is usually not an option. When considering irregular beam shapes, the strain gauges should be placed at positions with the most difference in strain possible. These positions can be determined using Finite Elements Analysis (FEA).

4.1.3 Proof of concept In order to examine the correct functioning of the proposed altered Wheatstone bridge strain gauge configuration, a proof of concept is built. This concept consists of a round steel bar with a diameter of 12mm. Four strain gauges are mounted on this bar, two in line at one side (which can be seen in Figure 41) and two in line diametrically opposed to the first two.

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Chapter 4: Proof of concepts

Figure 41: Proof of concept steel bar equipped with four strain gauges

This concept was needed in order to determine whether or not it was possible and feasible to attach strain gauges to a surface with such a low curvature radius. This turned out to be no problem. The strain gauges were protected against damage and insulated by coating them with an epoxy layer. Secondly, the main working principle of the concept needed to be verified, which is the position independence of the applied force on the output signal. This was done by clamping the test bar at one end and suspending a previously weighted mass at the other end at various distances from the clamping end. Figure 42 proves the main working principle, since the voltage reading from the bridge is practically the same for each different position of the suspended mass.

Figure 42: A suspended mass of 670g at three different locations gives the same voltage output The output voltage was connected to a DAQ system of National Instruments, consisting of a NI9949 full bridge connector, a NI9172 CompactDAQ chassis equipped with a NI9237 bridge module. After the signal was sampled at 1650 Hz, the signal was filtered using a low pass filter at 2.5 Hz in order to achieve a stable reading. If a suspended mass of 1449.6g was used, an average error of 2 g in five samples was recorded, resulting in an error percentage of only 0.138%. The sensitivity of the Wheatstone bridge was

78

Chapter 4: Proof of concepts

calculated to be 0.232.10-4 mV/(V.g), while the measured sensitivity was 0.234.10-4 mV/(V.g) when an excitation voltage of 5 VDC was used, which resulted in a very sensitive and precise reading. Due to the inevitable misalignment of the strain gauges and the known Poisson effect, which causes strains in the transversal direction of the load, an output voltage may be detected when the bridge configuration is loaded in the transverse direction. Ideally, in this type of loading, the reading of the bridge should remain zero. This phenomenon is known as cross-sensitivity and is visualised in Figure 43. The high degree of cross-sensitivity for this concept is most probably due to the misalignment of the strain gauges. Closer inspection after attaching the strain gauges concluded that the two strain gauge pairs are not perfectly diametrically opposed. This cross-sensitivity will have to be taken into account when calibrating the force gauges and when measuring during field testing. A more precise placement of the strain gauges onto these force gauges will be needed in order to further reduce the amount of cross-sensitivity.

Figure 43: Visualisation of the cross-sensitivity of the Wheatstone bridge to transversal loads

4.1.4 Application: force gauges 4.1.4.1 Measuring forces at the pedal The forces which the rider exerts on the pedals when pedalling are useful data when developing a bicycle frame, since the greatest forces and stresses appear in the bottom bracket, near the pedals. The direction and size of the pedalling force is not constant during one revolution as can be seen in Figure 44. As mentioned above, the maximum expected force according to EN 14781 is 1500N. The rotating speed of the pedal is equal to the cadence, which is usually between 80 and 120rpm.

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Chapter 4: Proof of concepts

Figure 44: Pedalling force amplitudes and direction

The forces on the pedal will be measured making use of the altered Wheatstone full bridge configuration as discussed above. The forces in radial and tangential direction will be measured in order to determine the magnitude and direction. This means that two separate Wheatstone bridges will be placed on one single spindle, one bridge 90° rotated against the other as can be seen in Figure 45.

Figure 45: Placement of strain gauges in altered full bridge configuration onto the spindle

In order to measure the forces on the pedals while cycling, a system needs to be developed which can accurately measure the force magnitude and direction. This system ideally is as small and lightweight as possible in order not to have a large influence on the dynamics of the bicycle or cyclist. It is opted to design a pedal/system which can be mounted onto every possible crank-arm with the regular 9/16 x 20tpi thread. Figure 46 shows the different components of a bicycle pedal.

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Chapter 4: Proof of concepts

Figure 46: Terminology of the parts of a pedal

There are two possible ways of measuring both amplitude and direction of the forces acting on the pedal. The first design makes use of a spindle which can turn freely in the crank-arm (Figure 47) instead of the conventional threaded pedal (Figure 48). The pedal body will then be connected to the spindle without the possibility of rotation. This design has the advantage that the spindle does not rotate relative to the foot. The strain gauge bridge is connected with wires to the data acquisition equipment. The rotating of the spindle would cause these wires to wrap around the spindle if this spindle was to be fixed to the crank-arm as in a conventional pedal.

Figure 47: Fixed spindle-pedal body design

Figure 48: Pedal design with spindle connected to the crank-arm (conventional)

This design makes it possible to run the wires along the leg of the cyclist. Since the placement of the strain gauges on the spindle determines which bridge measures which force in a certain direction, the angular position of the pedal body relative to the crank-arm needs to be measured in order to obtain the tangential 81

Chapter 4: Proof of concepts

and radial forces when cycling. Therefore, an encoder has to be mounted on the pedal, which is a disadvantage. Several fixed spindle-pedal body designs are possible. A first design is one which uses two ball bearings on each side of the crank to support the spindle as can be seen in Figure 49. The forces acting on each individual bearing can easily be calculated. Research conducted by Coleman [44] revealed that the maximum exerted force in regime cycling in practice almost never reaches above 1000N. This load value can be used to determine the durability of concept designs.

Figure 49: Sketch of the bicycle pedal design using two ball bearings

The radial load of the right bearing R2 is 4296N and the radial left bearing load R1 is 3296N. Bearings that can cope with these kinds of loads are relatively large. Better inspection of the crank-arm in position next to the chain stay revealed that the clearance between both is too small to fit a bearing, rendering this design unfeasible. A second design consist of a sliding bearing instead of ball bearings in order to reduce the required space. Bronze is often used as slide bearing material because of its excellent anti-friction and anti-wear properties. Unfortunately, the maximum allowed surface pressure of these bushings is 7MPa [45]. A simple calculation reveals that if no bending moment due to the force is taken into account, the maximum surface pressure for a bearing surface of 8 x 27mm is: 𝑝=

1000𝑁 𝐹 = = 4.6𝑀𝑃𝑎 𝐴 8.27𝑚𝑚² 82

Chapter 4: Proof of concepts

It is obvious that the large forces due to the bending moment will drastically increase this pressure at the left and right side of the bushing. This design does not satisfy.

Figure 50: Sketch of the bicycle pedal design using a slide bearing

A third way of supporting the spindle is by using only one bearing at one side of the crank which has to withstand both the forces and bending moments as shown in Figure 51. Typically, a double row angular contact ball bearing is used in such applications. Even though these bending moments and radial forces can easily be calculated, it is difficult to take the bending moments into account when determining the correct bearing. The maximum radial force is 1000N and the bending moment is: 𝑀 = 𝐹. 𝑎 = 1000𝑁. 85𝑚𝑚 = 85𝑁𝑚

Figure 51: Sketch of the bicycle pedal design using one double row angular contact ball bearing

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Chapter 4: Proof of concepts

The selected bearing should remain rather small and lightweight. A wide bearing will increase the bending moment on the thread in the crank-arm, which is not allowed for safety reasons. The bearing 3201 is a double row angular contact ball bearing with an inner diameter of 12 mm, outer diameter of 32 mm and is 15.9mm wide, which is considered to be the outer dimension limits for a practical design. The dynamic and static load ratings Cr and C0r, are 10600N and 5850N, respectively. These dimensions and the previously calculated bending moments can be used to determine the axial load of the bearing: 𝐹𝑎 = 𝑀.

2 85000𝑁𝑚𝑚 = = 7727𝑁 𝑑 11𝑚𝑚

It should be noted that this calculated axial force only applies to the top and bottom of the bearing, which in turn results in drastically higher local loading of the balls in the bearing at these places. The equivalent dynamic load is: 𝑃 = 0.67. 𝐹𝑟 + 1.41. 𝐹𝑎 = 0.67.1000𝑁 + 1.41 .7727𝑁 = 11565𝑁

The basic lifetime in 106 cycles can be calculated as followed: 𝐿10

𝐶𝑟 𝑝 10600 3 � = 0.77.106 𝑐𝑦𝑐𝑙𝑒𝑠 =� � =� 𝑃 11565

At a rotation speed of 100rpm this bearing should survive for 128h, which is sufficient for field testing. These large forces usually occur at the start, when the rotating speed is very low. In this case, the equivalent load should be compared to the static load rating. It is obvious that the equivalent load of 11565N is larger than the static load rating of 5850N, which may result in plastic deformation of the raceways and rolling elements. Together with possible weight and safety issues, this design does not fully satisfy the demand. Finally, it seemed more feasible to make use of a standard pedal. This means that a conventional pedal design, at which the spindle is screwed into the crank-arm, will be used. As mentioned above, this would cause the wires from the strain gauges to the DAQ to wrap around the spindle when the crank-arm rotates. This means that the connection between the strain gauges and DAQ should be achieved either by placing a slip ring between the frame and the crank-arm or by wireless communication. The narrow space between the crank-arm and the frame requires a pancake design slip ring, which consists of multiple concentric rings, rather than rings placed next to each other as with a conventional design slip ring. The slip ring could be placed between the crank-arm on the left hand side and the frame as shown in Figure 52. There are not many manufacturers which produce these kind of slip rings. After a thorough search there was no slip ring available that could meet the specifications. Either the width was too large or the diameter of the slip ring caused ground clearance issues. The large rings could also induce too much electrical noise by the sliding of the brushes as well as they would function as antennas. 84

Chapter 4: Proof of concepts

Figure 52: Wired connection between strain gauges and DAQ using a slip ring

Since the wired communication did not seem feasible, a wireless solution or a wireless data logger system was assessed. Data loggers that were capable of feeding two Wheatstone bridges, reading in two bridge output voltages, sampling these voltages at a high enough rate (above 200 Hz) and storing enough data for field testing were not found. Wireless strain gauge bridge amplifiers/transmitters make use of Wi-Fi or Bluetooth in order to communicate with a computer, which in turn processes the incoming data and stores it onto its hard disk drive. ME-Meßsysteme GmbH is a manufacturer of these kind of systems. The module GSV-4BT has the following properties: -

Bluetooth connection

-

4 16bit Wheatstone bridge channels: full, half or quarter (120, 350 or 1000Ω)

-

range 2mV/V or 10mV/V

-

sampling rate max 250Hz

-

lithium-polymer battery 3.7V power supply

-

dimensions: 60mm x 33mm x 10mm

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Chapter 4: Proof of concepts

Figure 53: Bluetooth bridge amplifier GSV-4BT, Bluetooth adapter USB-stick and battery The battery and Bluetooth module can be placed on the inside of the crank-arm as a result of the small dimensions as illustrated in Figure 54. By doing so, the module is also protected against damage that may be caused by accidently striking it with the feet.

Figure 54: Wireless solution for amplifying and transmitting signals by Bluetooth

This solution is feasible and will be implemented in the final design. Because of the small dimensions of both battery and Bluetooth module, the weight is kept low. This design also allows for the use of a standard pedal, which can in turn be mounted on any crank-arm with the same thread dimensions. The Speedplay Zero Stainless clipless pedal is chosen as a standard pedal. The manufacturer provides the possibility of ordering these pedals with spindles up to 13 mm longer than regular (Figure 55). Two full strain gauge bridges consist of eight strain gauges. These need to be attached to the spindle of the pedal, so the request for such a long spindle is obvious. Speedplay Zero pedals differ from others in that a long section of the spindle is free. This enables the attachment of the eight strain gauges in this region.

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Chapter 4: Proof of concepts

Figure 55: Speedplay Zero Stainless clipless pedal

In order to fully benefit the working principle of the altered Wheatstone bridge configuration with the intention of increasing the sensitivity as discussed above, the loading of the spindle is simulated using the Finite Elements Analysis program ABAQUS™. This enables the visualisation of the strain of the pedal under load, so that the ideal positioning of the strain gauges can be determined. Figure 56 shows the meshed spindle and a section view, revealing the hollow inside.

Figure 56: Section view of the spindle and meshed spindle The maximum expected strain which the strain gauges will have to undergo, can be calculated using 1000N as a load value placed in the middle of the pedal body. This implies that a load of 500N is placed on each of the two sections on the spindle where the bearings fit that support the pedal body. The Von Mises stress for this situation is plotted in Figure 57. The maximum stress is 350MPa, well below the yield strength of the material, stainless steel 17- 4, which may be well beyond 1000MPa, depending on the heat treatment.

Figure 57: Von Mises stresses in the spindle at a load of 1000N

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Chapter 4: Proof of concepts

The maximum expected axial strain is displayed in Figure 58 and is around 1780µε (microstrain). Since the fatigue limit of most strain gauges is around 1500µε and these high loads will only occur on very rare occasions, the use of normal strain gauges is allowed. The axial strain is plotted against the axial distance which reveals the linear decrease in strain for areas closer to the applied force.

Figure 58: Axial strain plotted against axial distance at the top of the spindle at a load of 1000N

The ideal positioning can be determined on basis of this plot. From what is proven above, the difference in strain between two strain gauges at one side should be maximized in order to obtain the best sensitivity of the Wheatstone bridge. This can be done by placing one strain gauge as close as possible to the crank side of the cylindrical part of the spindle and one as close as possible to the side of the pedal body. The correct strain gauge is chosen on basis of the specifications and requirements provided by the manufacturer, Vishay. The use of strain gauges with a gauge length longer than 3mm is recommended for stability reasons. The diameter of the cylindrical part of the spindle is 11 mm and thus the circumference is about 34.5 mm which means that the gauge width needs to be as small as possible so that the crosssensitivity is kept to a minimum. Another important property is the self-temperature-compensation (S-TC) number. This number indicates for what type of substrate material the strain gauge should be used in order to reduce the thermal output, i.e. change in output voltage solely due to a change in temperature. 88

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The use of full bridge configurations with all the strain gauges mounted onto the same specimen ensures the least temperature influence since all the strain gauges alter equally in resistance due to changing temperature. The S-T-C number for stainless steel 17 – 4 is 06. The strain gauge L2A 06 125 LW - 350 is chosen for this application. This strain gauge has preattached ribbon lead wires.

Figure 59: Strain gauge L2A 06 125 LW -350

The lines on which the strain gauges are aligned to are applied with great care on a lathe, as an attempt to minimize the chance of cross-sensitivity. Figure 60 shows the finished pedal spindle next to a regular pedal.

Figure 60: Unprotected finished pedal and a regular pedal

This finished pedal needs to be protected against damage caused by incidental striking with the shoe or other. A heat shrink tube is placed over the spindle to protect the whole from water or debris. To ensure no mechanical damage will destroy the strain gauges, a steel tube is shoved over the spindle as can be seen in Figure 61. The presence of this protection has no influence on the correct functioning of the pedal. 89

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Figure 61: Protected finished pedal

Every connection between battery, charger, Bluetooth module and pedal is realized with connectors, so the whole setup can easily be disassembled and placed onto another other crank-arm. Figure 62 shows the compact design of the whole setup.

Figure 62: Bluetooth module, battery and pedal mounted on the crank-arm

4.1.4.2 Measuring forces at the handlebar The forces at the handlebar will be measured by the same principle as the pedal forces. It is opted to adapt a standard aluminium alloy handlebar. This ensures a lightweight system which has nearly no influence on the rider or on the measurements itself. The forces will be measured by attaching strain gauges in the altered Wheatstone bridge configuration to each side of the handlebar in the vertical and horizontal direction as illustrated in Figure 63. A total of sixteen strain gauges are required for this application, two times four at each side of the stem.

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Figure 63: Placement of the strain gauges on the handlebar

Such a handlebar is usually manufactured by bending and hydroforming a thin-walled tube. Since the bending theory of beams is not fully applicable to the bending of short, thin-walled hollow tubes, the maximum expected strains in the areas of interest need to be determined using Finite Elements Analysis. Plane stress elements with a thickness of 2.05 mm are used to model the handlebar. Only half the handlebar needs to be modelled as a result of the symmetry, which drastically reduces the calculation time. Since this is a commercially available handlebar, no strength analysis needs to be conducted. A horizontal forward load of 500 N is applied at the left hand side of the handlebar in the simulation to investigate the strain gradient near the stem as can be seen in Figure 64.

Figure 64: Visualisation of the Von Mises stresses in the handlebar at a horizontal load of 500N

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The strain gauges will be attached to the cylindrical part of the handlebar with the largest diameter, so there is still enough place to grip the handlebar. It is obvious that the largest strains will occur here as the bending moment is largest. Since only this particular region of the handlebar is of interest, the legend in Figure 65 is scaled down to maximize the visualisation of the strain gradient. This figure also shows the strain gradient in function of the axial distance, starting from the beginning of the cylindrical part of the handlebar at the left. It reveals a nonlinear strain distribution. The strain gauges will not be placed directly next to the stem so that the change of possible damage when mounting the stem is reduced.

Figure 65: Visualisation of the strain gradient near the stem at a horizontal load of 500N

As the diameter of this handlebar is 31.8 mm, the strain gauges may be larger than the ones used on the spindle, to increase the convenience of attaching them. Different tools are made so the alignment lines for the gauges can be applied correctly, since the handlebar cannot be mounted in a lathe. Figure 66 demonstrates the compact dimensions of the fully instrumented handlebar on which the hands can still be placed next to the strain gauges. This setup almost does not add weight to the entire bicycle.

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Figure 66: Fully instrumented FSA handlebar with close up image of the strain gauges

Unfortunately, when experimenting with the handlebar with various magnitudes and variations of loads, a large amount of offset was detected between the voltage output before and after the loading for every output channel. This voltage offset was in the range of 30 to 40% of the loading, which results in an unacceptable error for field testing. The only reason for this phenomenon is that the strain at the places of the strain gauges is altered after loading and does not return to its original strain state. Due to microscopic slip at the edge of the connection between stem and handlebar, residual tensile or compressive stresses can build up after loading, resulting in different stresses at the strain gauges before and after loading, inherently changing the strain state [10]. The result of this slippage is visualised in Figure 67, where the edges of the stem clamp are worn by fretting as a result of the slip and an impression can be seen on the handlebar.

Figure 67: Fretting wear as a result of microscopic slip at the edges of the stem

Another encountered problem was the cross-sensitivity not only between x and y direction at one side of the handlebar, but also between the left and right side of the handlebar in the same direction. 93

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As an attempt to reduce the residual stresses after loading, various stem types were mounted (Figure 68). The offset problem was reduced by mounting different stem types although the cross-sensitivity between the left and right side was still clearly present.

Figure 68: Various stem types

The cross-sensitivity between left and right can be eliminated by decoupling the two sides by cutting the handlebar in half and connecting them with an insert by gluing as shown in Figure 69. The used glue was an industrial two component adhesive developed for structural connections with the capability of filling gaps. The insert was made out of aluminium in order to achieve the same thermal expansion coefficient.

Figure 69: Cut view of the glued insert in one half of the handlebar

Testing revealed that the problem of cross-sensitivity between either side was not eliminated, so that could be concluded that both sides are not fully decoupled. Figure 70 shows the reaction forces in the stem as the result of an applied force on the handlebar. The reaction force on the other side of the handlebar from 94

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where the force is applied ensures that the strain at that side will also change. This problem is inherently linked with the use of a stem between right and left side of the handlebar.

Figure 70: Visualisation of the reaction forces in the stem

As a final attempt to fully decouple the two sides and eliminate the cross-sensitivity, the handlebar was yet again cut in half, leaving the right and left side of the handlebar with half the previously glued insert. Total decoupling can only be achieved when the two sides are no longer clamped in the stem so the reaction forces do not have an influence on the measurement. A second insert was fabricated and was glued into the first insert, which was first drilled and then reamed to the correct size.

Figure 71: Half handlebar with glued insert, drilled and reamed

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This second insert will be clamped in the stem and so it will have to endure al the bending forces of the handlebar, so the use of aluminium was not feasible. Instead, a high strength steel alloy, 42CrMo4V was used. The edges of the insert are rounded in order to reduce stress concentrations. The connection between the first and the second insert was realized by gluing.

Figure 72: view of the second glued insert in the handlebar

Testing revealed that there is a total decoupling of the left and right hand side in this configuration, drastically simplifying the processing of the signals. As the strength may be compromised by inserting this piece and no longer clamping the actual handlebar tube, the calibration of the handlebar is performed by loading up to 500N to be sure no fracture will occur during field testing.

4.1.4.3 Measuring forces at the saddle As final point of contact between the cyclist and the bicycle, the forces exerted on the saddle also need to be measured in both x and y direction. A force gauge between the saddle and the seat post will be instrumented with strain gauges in a way similar to the manner of the pedal spindle and handlebar. The goal is to develop the gauge so that it can be fitted on any type of seat post or saddle clamp. As most of the weight of the cyclist is often carried by the saddle, a strength analysis of this gauge is a necessity. Forces of about 1000 N vertical and up to 400 N horizontal can be expected. For safety reasons, this limit will be extended towards 1200 N and 900 N for the vertical and horizontal direction, respectively. The main difficulty in the design is the decoupling between x and y direction. There is no obvious bicycle part available to attach two strain gauge bridges as with the pedal spindle and handlebar. Mounting the strain gauges onto the seat post would only enable the measurement forces in x and z direction instead of x and y direction. A separate gauge is fabricated which can be fitted between the saddle and the seat post clamp. Champoux et al. have already developed such a device and were able to decouple the forces by placing a U-shaped gauge between the saddle and the seat post [46]. When mounting two altered Wheatstone strain gauge bridges onto this U-shaped gauge, the measured forces are not only fully decoupled, they are also independent of the point of application of this force on the saddle. It can be expected that cyclist does not remain seated at the exact same point throughout all test cycles, which 96

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justifies the need for such a system. According to the designs studies in literature, a final design of this gauge is presented in Figure 73.

Figure 73: Saddle force gauge instrumented with two altered Wheatstone strain gauge bridges

This piece is placed right beneath the saddle as the seat rails of the saddle fit in the two slots at the top side. At the bottom side, two steel rods with the same diameter of the seat rails are inserted in order to simulate a saddle (Figure 74). This ensures the possibility to use this gauge on every standard seat post and saddle.

Figure 74: Mounted saddle force gauge

As explained above, the altered Wheatstone strain gauge bridge works on the principle of measuring a difference in bending moments, instead of force, to create an output voltage. This means that when the bending moment on one of the arms of the U-shaped gauge is constant throughout its entire length, the strain gauges will all strain an equal amount and thus the bridge remains stable. To investigate this working 97

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principle of this system, and to conduct a strength analysis and weight optimization, a Finite Elements Analysis is necessary. Figure 75 represents an illustration of the forces by which the gauge will be analysed. Several different load cases will be solved in order to investigate the influence of the magnitudes of the forces and position dependency of the vertical force on the strain gradient in both arms.

Figure 75: Illustration of the forces on the meshed part

When a vertical force is applied, the strains in the vertical arm of the gauge are constant, whilst the strains in the horizontal arm increase away from the applied force as can be seen in Figure 76. Simulations revealed that when the vertical force was applied further away from the saddle clamp, simulating a driver sitting on the front of the saddle, the strain increases. However, the strain gradient remains the same, verifying the working principle of the gauge. Figure 76 also shows the strain gradient of the top side of the horizontal arm at different loads and different point of application. It reveals that the strain gradient doubles when the load is doubled and that, even though the absolute strain is larger, the strain gradient remains the same for equal loads, even if the point of application differs. This model confirms the linearity of this force gauge.

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Figure 76: Visualisation of the strain gradient (linear on the horizontal arm and constant in the vertical arm) in the horizontal arm at different vertical loads F at different distances a

The dimensions were tuned in order to reduce the overall weight of the sensor. The material chosen is AlMgSi, a high grade aluminium which has a tensile strength of 275-300MPa and a yield strength of 240255MPa. The worst case scenario loading consist of a vertical force of 1200 N at a distance of 120 mm from the centre of the saddle clamp and a horizontal force of 900 N in the centre of the saddle clamp, at which the maximum stresses may not exceed the yield strength divided by a safety factor of 2. Initial testing revealed a correct and precise functioning of the gauge. Placement of the gauge on the bicycle was no problem and no obstruction for the cyclist was observed as a result of the presence beneath the saddle.

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4.2 Measuring vibration velocity 4.2.1 Introduction The determination of the comfort level of the cyclist by the absorbed power method requires the measurement of not only the forces as described above, but also the measurement of the vibration velocity in the same direction at the point where the force is measured. The absorbed power is calculated by the following formula: ������ 𝑃𝐴𝑏𝑠 =

1 𝑇 � 𝐹(𝑡). 𝑣(𝑡)𝑑𝑡 𝑇 0

This vibration velocity usually has a small amplitude. The ISO 2631 standard considers an acceleration level of 2m/s² to be uncomfortable. In order to given an idea about the velocity amplitudes, an example is worked out: When investigating a vibration frequency of 12Hz, a maximum velocity of 26.5mm/s and a maximum amplitude of 0.35mm can be expected. At a frequency of 3Hz, the maximum velocity and amplitude are 106mm/s and 5mm, respectively. It can be stated that these small values at higher frequencies are difficult to measure. Even more so, at every contact point, the velocity needs to be measured in x and y direction. The ISO Standard and the British Standard require the measurement of accelerations at the contact points. This means that accelerometers will be fitted on the bicycle. The vibration velocity can be calculated by integrating this acceleration signal. LabView, a platform and development environment for a visual programming language from National Instruments, has the capability to integrate acceleration signals to velocity signals in real-time or by post processing. If an acceleration signal with a DC component is integrated in time, it will have a drift effect on the velocity signal. The module that integrates the acceleration takes this into account by filtering with a high pass filter at a very low frequency. Since such a filter has a transfer function which causes some frequencies to have a larger time delay than others, it can be assumed that the calculated vibration velocity signal differs from the actual vibration velocity.

4.2.2 Verification of calculation method In order to determine the difference between both calculated and actual velocity a test setup is built. An electric shaker (LDSV 406/8 – PA100E, Appendix A) will be ordered to vibrate at a random vibration pattern, with a frequency range of 5 to 800Hz at an acceleration amplitude of 0.01g. On top of the vibrating surface of this shaker a relative accelerometer (PCB 325C65, Appendix A) is placed as can be seen in Figure 77. Such a device measures relative accelerations, which means that the earth’s gravity is not measured. This signal is then processed with a National Instruments chassis NI9072 and an acceleration module NI9234, to be able to read in the signal in the programming environment of LabView in which 100

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the data will be integrated into velocity. The actual velocity of the vibrating surface will be measured by a laser Doppler vibrometre, a scientific instrument which can very accurately measure vibration velocity making use of the Doppler effect when a laser is directed towards the moving surface.

Figure 77: Test setup measuring velocity vs. calculated velocity

The first test revealed that, although the signals appeared to be the same, a phase shift between both is present. Figure 78 show the phase shift between the measured and the calculated frequency at a vibration of 37Hz. The tests showed that there is no drift in time for the integrated signal, as a result of the low pass filtering of the acceleration signal.

Figure 78: Visualisation of the phase shift between the measured velocity and the calculated velocity at 37Hz

A different phase shift is present for different frequencies, as can be seen in Figure 79, where the difference in amplitude between both signals is not constant.

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Figure 79: Visualisation of the phase shift between the measured velocity and the calculated velocity for a random signal

This frequency dependent phase shift may cause a large difference in amplitude compared to the actual velocity, resulting in a wrong reading at any given time. An average error of up to 4.5% for a random signal was detected as a consequence of this shift. This frequency dependent phase shift is investigated and can be seen in Figure 80. The phase shift is largest for the low frequencies in the range of interest.

Figure 80: Phase shift between actual velocity and calculated velocity

A method to overcome this problem is to filter the actual velocity measured by the laser vibrometre with a high pass filter with the same characteristics as the integration module, so that both signals are shifted to an equal amount. Unfortunately, this filter could not easily be found, so further experimental research was needed in order to determine this filter. As a result of many tests, a high pass 11th order Butterworth filter with a high pass frequency of 0.5 Hz gave the best results, leading to an error of maximum 1.4% for a random signal with a frequency range of 5 – 800 Hz, which is acceptable.

4.2.3 Application The concept behind this idea is to measure the vibration velocity by integrating the acceleration signal and filter the measured force signal with this 11th order Butterworth filter so an equal phase shift would be introduced. A downside to this solution is that the dc-component is removed from the force signal, which is unacceptable since this would alter the calculations tremendously. After all, it is opted to use the 102

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integrated acceleration signal as velocity signal and not to filter the force signal. Since no literature mentions this phase shift even though similar high pass filters are used in the integration process, the results will be comparable to other.

4.3 Pedal position and cadence measurement 4.3.1 Introduction As concluded in 4.1.4.1, the pedal will be designed so that the spindle does not rotate relative to the crankarm. As a result of this decision, the radial and tangential forces can easily be determined no matter at what angle the crank-arm might be. A downside is that the horizontal and vertical forces cannot be directly measured, as a consequence of the constantly turning coordinate system as shown in Figure 81.

Figure 81: Visualisation of the rotating measurement coordinate system

It is requested to be able to measure the power input of the cyclist at any given time, and determine the force distribution of the tangential and radial forces not only in time but also with respect to the crank angle. Therefore, a simultaneous reading of both forces via the Bluetooth module and the crank angle are needed. The pedal position in time will be measured, making it possible to determine the rotation velocity of the pedal or cadence. This can be used to determine the instantaneous and average power input of the cyclist as the formula for power is 𝑃𝑎𝑣𝑔

1 𝑡=𝑇 = � 𝐹𝑡𝑎𝑛𝑔 . 𝑣𝑡𝑎𝑛𝑔 . 𝑑𝑡 𝑇 𝑡=0

where Ftang and vtang are the tangential force and tangential velocity, respectively.

4.3.2 Theoretical background encoder In typical rotational velocity or position measurements, a rotary encoder is used. Two kinds of encoders exist: incremental or absolute encoders. An incremental encoder measures the change in position relative 103

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to the previous one, whereas an absolute encoder measures the absolute rotational position. An incremental encoder consist of two sensors placed along a rotating disc or cylinder, which has gaps or teeth. Every time a gap or teeth passes a sensor, the sensor changes its output from high to low or vice versa and so creates a square wave. The second sensor is placed at a slightly different angle so the square wave from this sensor is 90° out of phase with the square wave of the first sensor. If the number of teeth is known, the rotational velocity can easily be determined by measuring the time between a rising and falling edge of one of the square waves. The angular position between a rising and falling edge is also dependent on the number of teeth. The position is calculated by counting the number of falling edges, however, the sense of rotation is of importance, since the angular position increases in one direction and decreases in the other rotational direction. The sense of direction is defined by the phase shift between both square waves. Figure 82 shows two square wave forms of both sense of directions, revealing the different phase difference.

Figure 82: Two square wave forms for right en left sense of direction

One disadvantage of an incremental encoder is that the absolute position itself cannot be determined, so a third sensor is needed to indicate the absolute zero point. This sensor is only activated once every rotation when the crank-arm is in a certain position.

4.3.3 Application Absolute encoders are usually larger and heavier than incremental encoders although the overall weight of encoders is often small. A connection between the chainset and this encoder is needed, which can be achieved by running a small belt or chain from the chain rings. Unfortunately, this leaves one chain ring and thus one gear unusable and may cause the setup to be destroyed in case this gear is selected. Therefore, it is opted to design an incremental encoder which makes use of the teeth of the largest front chain ring as illustrated in Figure 83. The two yellow sensors A and B sense the teeth of the sprocket and 104

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produce two square waves, shifted in time. The green sensor C is the absolute zero point sensor, which is activated once every turn.

Figure 83: Placement of the three sensors along the chain ring

Two types of sensor may be chosen for this task: optical or inductive. Optical sensors have the advantage to be very light weight, fast switching and do not depend on the type of material. Unfortunately, the presence of the chain may lead debris to be deposited on the sensors, disabling the system. Therefore, inductive sensors are chosen as the chain ring itself is made of a steel alloy. Since the only position where the two sensors can be placed without disturbing the front derailleur or chain is at the rear side of the front sprocket, the dimensions of the sensors will have to be small. Two Turck inductive U-slot sensors, which fit over the chain ring, are placed together on a aluminium rail, which eases the tuning of the position of the sensors as shown in Figure 84.

Figure 84: Placement of the two inductive sensors on the chain ring

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The small dimensions of the sensors allow a snug fit on the chain stay and ensure the crank-arm to rotate freely and allow the cyclist to select every gear. The position of the sensors is tuned with the aid of an oscilloscope. The duty cycle of each square wave is determined by the depth position over the chain ring inside the sensor. An ideal square waveform has a 50% duty cycle. To optimize the encoder and reduce the chance of misreading, the two square waveforms should ideally be 90° out of phase. This can be adjusted by sliding one of the two sensors along the aluminium rail. The third sensor, needed for the absolute zero position detection, cannot be mounted on this side due to clearance issues. Therefore, this inductive sensor is placed on the other side of the frame (Figure 85) and detects a small pin, mounted on the back of the crank-arm, ensuring a precise measurement.

Figure 85: Placement of the third absolute zero position inductive sensor

The absolute zero sensor is enabled if the user wants to measure an angle that is reset every time the crank passes the sensor, or can be disabled when the total angular change in position compared to the initial starting angle is wanted. Although this setup worked perfectly in lab conditions, field tests revealed that the absolute zero sensor did not work in certain circumstances. In order to increase the reliability of the system, the inductive switch was replaced by a reed contact switch which switched state when in the presence of a magnetic field. A magnet was attached to the rear of the crank arm. Further field tests showed that this setup makes for a reliable angular position measurement.

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Chapter 5:

Data Acquisition

5.1 Requirements Whenever accurate data reading is required, a good data acquisition setup is needed. The quality of such devices can be expressed for instance in bit depth and in maximum sampling rate. If one module offers more than one input channel, it is recommended that in high demanding applications, the reading of all the channels takes place simultaneous. Some cheaper modules read in data over multiple channels by multiplexing, which causes a time delay between the channels. In the case of the integration of the acceleration signal to calculate the velocity signal, together with the reading of strain gauge bridges, this may lead to incorrect reading and results. Another factor in this mobile application is the maximum weight of the complete acquisition setup. Since extra weight will inevitably influence the results, the weight must be kept to a minimum. The battery, which feeds the data acquisition cards in this mobile application, will have a large impact on the overall weight and so it is wise to select a rechargeable battery of a smaller size. The communication between the sensors and the cards will pick up noise by induction of electric and magnetic fields. Choosing the right cable and connectors will reduce the amount of noise pick-up and will also reduce the chance of wrong connections when sensors are constantly plugged in or out. Care has to be taken so that the maximum input voltage of acquisition cards is not exceeded, which can lead to the destruction of both card and chassis, the device in which the card is plugged in. According to the Nyquist theorem, the sample rate should be at least twice maximum frequency of interest. The ISO-2631 standard even suggests a sample rate of three times the maximum frequency of interest. As seen in Figure 19 which illustrates the weighting curves for the human body, the sensitivity for vibrations above 125Hz is -30dB, so the sensitivity is only one thousands of that at lower frequencies between roughly 4 – 12 Hz. Using the ISO standard as a guide, the maximum needed sample frequency is 375 Hz.

5.2 Data acquisition devices 5.2.1 Wired DAQ The devices used are from National Instruments which ensure an easy to establish communication with the measurement software LabVIEW. In order to determine the correct DAQ modules, the different input signals have to be defined. 107

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First of all, each measurement of force in one single direction requires an input channel. The cards used are the NI9237 modules which have a total of four inputs per card. Since force has to be measured in x and y direction on the saddle, the left side of handlebar and the right side of the handlebar, six input channels are needed, requiring two NI9237 modules. Second, the measurement of acceleration is required at each point in the same direction as the measured forces as well as at the rear and front dropout of the bicycle in vertical direction. The NI9234 is a highaccuracy frequency measurement card with four input channels per card. As described above, eight input channels are needed, requiring two NI9234 modules. Third, the measurement of the cadence and position of the pedal requires an I/O module with an optional counter. The NI9401 card is used for this task, which has two counters. When conducting experiments without the use of the cadence measurements, this card is used as an I/O module on which two switches are connected, one to set the force readings at each force sensor to zero (in case any offset should be present when the bicycle is not loaded) and one for the starting and stopping of measurements. These switches are located on the stem for easy access (Figure 86).

Figure 86: Calibration and save data switch attached to the stem

The inputs of this card are high when the voltage at a pin exceeds 2V with a maximum of 5.25V. This DC current is attained from the battery pack, which has a voltage of 12V. This requires the placement of a 5V voltage regulator so that the voltage switched towards the cards is a stable 5V signal. All of these modules are mounted on a chassis, which reads in the required channels and transmits this information through an USB cable to the computer. The chassis NI9172 is used considering it has 8 slots in which modules can be mounted. The chassis itself also performs measurements and analysis tasks, as the signals from the angular encoder are processed by the chassis and not the computer, reducing the calculation time. As a summary, following devices are used: -

2 NI9234 frequency measurement modules

-

2 NI9237 bridge modules 108

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-

1 NI9401 I/O and counter module

-

1 NI9172 chassis

Figure 87: Data-acquisition cards, chassis and battery power supply

Since this is a mobile application, all of these modules are fed by the chassis which in turn is fed by a battery. The maximum required current is determined for the worst case scenario, in which all the slots of the chassis are used. The producer of this chassis claims a maximum power consumption of 15W at 11 30V input voltage. As a result, a 12V lead-acid battery with a capacity of 2.2Ah is chosen as it is easy to recharge and has a limited weight.

5.2.2 Wireless DAQ As mentioned in 4.1.4.1, the strain gauge bridges on the pedal spindle are connected to a Bluetooth module which feeds and reads in the bridge in a ratiometric fashion. This data is then transmitted by Bluetooth to a Bluetooth USB adapter, which enables the user to read in data in LabVIEW. This GSV4BT module of MeSysteme reads in all four channels simultaneous with a bit depth of 16 bit, and then transmits it to the Bluetooth adapter on the computer. Tests revealed that a good connection has to be established and a high performance computer is needed in order to let the delivered program work reliable at the highest sample rate of 250Hz. The communication between the module and the computer is a one way direction communication when the actual reading has begun. In case the program is not executed fast enough, the input buffer at the computer floods and stops the program. This buffering process also causes a non-constant sample rate to be noticed when storing the data, especially at the highest sample rate. A high performance laptop is thus needed to avoid these problems. The module is fed by a 3.7V lithium-polymer battery, which can easily be charged by applying a 7V voltage on another port on the Bluetooth module. In order to ease the dismantling of the system, all components are connected to each other by connectors. 109

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Test revealed that the presence of a mobile phone nearby the module can disturb the Bluetooth signal. This kind of interference is due to the strong electric fields which influence the amplifier inside the module, not the interference with the Bluetooth signal.

5.3 Communication 5.3.1 Wired communication Since the DAQ devices described above are used by several persons throughout the year, an easy dismantling of the whole acquisition setup is required. The cables connected to the Wheatstone strain gauge bridges are first separately connected to an adapter, which is in turn connected to the NI9237 bridge module with a STP (Shielded Twisted Pair) cable. As mentioned before, the maximum input voltage at the ports of the NI9401 I/O module is limited to 5.25V. Since only one 12V battery is used, this voltage needs to be reduced to 5V using a voltage regulator. The inductive switches, which are also connected to the NI9401 module, need a voltage supply of 10-30V and have an output that switches between 0 and 8.5V. In this case, the voltage regulator is placed behind the inductive switch and reduces the 8.5V to 5V. All of these components are best placed inside a protective box, so accidental damage is avoided. This box (Figure 88) also enables a quick disconnection of the sensors on the bicycle and the data acquisition setup and strongly reduces the change of a wrong connection. Figure 88a shows the connectors on the front side. The inductive switches, the switches on the handlebar and the strain gauge bridges on saddle and handlebar are connected with DIN-connectors whilst the accelerometers are connected using BNCconnectors. Four voltage regulators are mounted on the inside on the sides of the box as can be seen in Figure 88c. Every cable, except the coax cables from the accelerometers, is shielded from the sensor trough the box and to the acquisition modules. This shielding is only effective when connected to ground. Off course, when conducting field tests, a ground is not available, so this shielding will only be beneficial when conducting experiments in the lab where a ground connection is available.

a)

b)

c)

Figure 88: Connector box a) from sensors b) to data acquisition c) inside

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5.3.2 Wireless communication The Bluetooth module connects wirelessly with an adapter on the notebook. This adapter is connected to an USB extension cable, so it can be placed outside the backpack, ensuring a better connection with the module. Test revealed that the presence of a mobile phone nearby the module can disturb the Bluetooth signal. This kind of interference is due to the strong electric fields which influence the amplifier inside the module, not the interference with the Bluetooth signal. Many other possible wireless bridge amplifiers have been examined. The module needed to be capable of reading in two full strain gauge bridges at a sample rate of at least 250 Hz with sufficient bit depth and small dimensions. Only a few option are available on market of which most are too expensive. Combining two separate one bridge amplifiers was not an option as the data coming in by two Bluetooth channels cannot be guaranteed to be synchronised.

5.4 Storing data All data is stored in .txt files, including a header which holds information about date and time of measurement and the names of the different channels. All raw data is stored and later processed using MatLab, a program used for the analysis and manipulation of arrays and matrices. All described NI modules have a minimum sample rate of 1650Hz, which results in an excessive amount of data. Whenever possible, the data will be resampled in real-time to 400 Hz before storing, which reduces the amount of data by about a factor 4. This sample rate is higher than the required sample rate of 375Hz according to the ISO2631 standard.

5.5 Field test setup The cyclist conducting a field test will carry a backpack which holds the data acquisition setup. This includes first and foremost a notebook which processes the data and stores it on to its hard disk. The weight of this component is responsible of most of the overall added weight and so a small 14” notebook (Dell Latitude E4310) with high performance is chosen. The complete chassis with mounted NI modules is also fitted inside the rucksack and connected to the notebook by USB. The lead-acid battery is placed next to the chassis which it feeds. All the cables coming from the NI modules are connected to the connector box, which hangs outside the backpack. As a last step, the cables, coming from the sensors on the bicycle, are connected to the other side of the connector box. An illustration of this setup can be seen in Figure 89. The total added weight of the full setup is around 9.6kg.

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Figure 89: Field testing setup

Care has to be taken not to accidently shortcut the battery, which could lead to hazardous situations. The cooling of the notebook needs to be ensured as it is confined in a small space. Foam parts are cut to improve the cooling of the notebook by leaving room for ventilation. The full test setup is shown in Figure 90.

Figure 90: Actual field testing setup

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Chapter 6:

Calibration of sensors

6.1 Introduction The force gauge sensors built for this thesis (instrumented pedal spindle, instrumented handlebar and saddle force gauge) are assumed to produce an output voltage linear to the applied force. Calibration of these sensors is needed to determine this linearity and the sensitivity of each sensor. A calibration load cell is used to accurately determine the actual applied force. This force is then plotted against the output of the sensor so that a sensitivity can be determined. The output of strain gauge bridges is expressed in mV/V, since these measurements are ratiometric, meaning that the output voltage is divided by the input voltage of the bridge, which drastically improves the accuracy and signal to noise ratio. When conducting these tests, it is absolutely crucial that the force is correctly applied in the right direction. Various parts are manufactured so that the saddle force gauge, the handlebar and the pedal can be mounted and correctly positioned inside an electromechanical tensile testing machine. Every rig is perfectly aligned horizontally and vertically using a laser line level. Next to the linearity and sensitivity of each sensor in each sensing direction, the independence of the point of application of the force is investigated by applying a same amount of force at various locations. The output voltage of the unloaded strain gauge bridge will also be measured so that the cross-sensitivity can be determined. As a last parameter, the force measurement of the calibration load cell will also be saved. These data are analysed in MatLab, which makes it easy to visualise and to fit a curve to determine the sensitivity. When calibrating the saddle force gauge, the displacement caused by the applied force will be measured in order to quantify the spring rate. This spring rate is then used to assess the influence of the gauge on the transmitted vibrations.

6.2 Data acquisition during calibration During the calibration process, the setup remains the same as when conducting field testing so that the influence of a changed acquisition setup is minimized. Since a tensile testing machine only has one direction of movement (up or down), a pulley rig is manufactured so that this vertical movement can be translated to a horizontal movement with the use of a steel cable. This pulley system causes friction, so that the applied force should be measured by the calibration load cell (Sensy 5930, Appendix A) as close as possible to the gauge that will be tested. This load cell has a maximum load capacity of 1000 N, which is 113

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sufficient to test all parts. All data is visualised and stored by LabView at a sample rate of 10Hz. The velocity of the tensile testing machine is set to 2mm/min. The pedal spindle forces are acquired by a wired test setup instead of the Bluetooth module, in order to increase the reliability and the ease of the measurements. Figure 91 illustrates the pedal spindle calibration setup.

Figure 91: Pedal calibration setup

6.3 Calibration of force gauges 6.3.1 Calibration of the pedal The pedal spindle is screwed into a specially built mount which can be positioned into place so that the pulling force is perfectly vertical, as can be seen in Figure 92. Before the actual calibration takes place, the spindle is slightly loaded and then rotated in the mount so that only one strain gauge bridge has a change in output voltage. By doing so, one measurement axis of the spindle is perfectly vertical aligned. If the spindle is then again rotated over exactly 90° with the use of an angle gauge, the output voltage of the unloaded strain gauge bridge indicates that no force is measured in that transverse direction. This suggests a perfect decoupling of the forces in x and y direction, thanks to the good alignment of the strain gauges and the precise dimensions and tolerances of the spindle. This indicates that only the sensitivity in both directions need to be determined and no cross-sensitivity is present, which was verified during the actual calibration.

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Figure 92: Calibration setup for the pedal spindle

Since the load limit of the calibration load cell is 1000N and the pedal is designed to withstand much larger forces, no safety hazard occurs when testing up to 500N, so the tie-wrap does not break. Before measuring commences, the output voltage of a bridge in unloaded situation is softwarematically set to zero, which corresponds with a load of 0N. Figure 93 and Figure 94 show a perfect linear relation between the output voltage of a bridge and the applied load in the direction of that bridge. The sensitivity is the reciprocal of the constants shown in the plots. The output voltage is given in V/V, since the bridges are acquisitioned ratiometric.

Figure 93: Plot of the output voltage of bridge 1 against the applied load in direction 1

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The sensitivity for direction 1 is: 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 1 =

1 𝑁 = 1432.0288 −7 𝑚𝑉 6.9831𝑒 𝑉

Figure 94: Plot of the output voltage of bridge 2 against the applied load in direction 2

The sensitivity for direction 2 is: 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 2 =

1 𝑁 = 1448.6875 𝑚𝑉 6.9028𝑒 −7 𝑉

These factors will be used to calculate the forces exerted onto the pedal in both radial and tangential direction. Tests have shown that the noise level of this pedal with the use of the Bluetooth module is around 0.8N, which results in a very precise measurement. The pedal is even capable of detecting its own weight when the crank is turned. The position independence of the applied force is checked manually, by comparing the output voltages of the loaded bridge when the applied force takes place at various distances from the pedal mount. No change in voltage output is detected when applying the force within a reasonable range at the end of the spindle.

6.3.2 Calibration of the saddle The saddle force gauge is fixed on a mount that allows positioning inside the tensile testing machine. First, the position independence of the applied load is inspected by applying the same load at different distances. Figure 95 shows a compressive test in which a blunt tip is pushed into the saddle at various distances from the front of the saddle. 116

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Figure 95: Vertical compressive loading of the saddle force gauge at various distances from the front of the saddle

An LVDT (linear variable differential transformer), which precisely measures the deflection of the saddle force gauge at load, is placed beneath the seat and will give an indication about the stiffness of the gauge. Table 4 shows the independence of the vertical output with regard to the application point of the force. The horizontal output rises when the force is applied at the front. As the bending moment around the vertical arm of the gauge rises, which in turn causes a larger elastic deformation of the whole setup, the saddle force gauge is tilted ever so slightly and so a horizontal force is detected. The deflection is dependent on the distance at which the force takes place. The stiffness in the vertical direction lays between 2200 and 250N/mm, even though this last low value is only reached when the load takes place at the absolute front of the saddle, which is not realistic. Table 4: Measurements at vertical load at various distances

distance (mm)

Force (N)

Output horizontal

Output vertical

(mV/V)

(mV/V)

deflection (mm)

245

100

0.000337

0.0250

0.045

195

100

0.000365

0.0245

0.060

145

100

0.000295

0.0252

0.175

95

100

0.000085

0.0255

0.290

45

100

0.000056

0.0256

0.400

Figure 96 shows a more rigid setup that is chosen for the actual calibration of the vertical loading. An LVDT is placed on the top of the gage and the calibrated load cell is placed close to the gauge to 117

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determine the applied load. The steel cable to which the load cell is connected is aligned vertically with a laser line level.

Figure 96: Vertical tensile loading of the saddle force gauge

Figure 97 clearly represents the linear relation between the applied vertical load and the vertical voltage output. The output changes linearly with the applied load and is negative since a tensile load in the suggested direction is defined to be negative.

Figure 97: The output voltage of the horizontal and vertical bridge plotted against the applied vertical load

The horizontal loading setup is demonstrated in Figure 98. The pulley redirects the vertical pulling force of the tensile testing machine to a horizontal force. To determine the independence of the point of application of the force, the calibration load cell is placed at various distances from the top of the saddle force gauge. The pulley wheel is adjusted in height accordingly. 118

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Figure 98: Horizontal tensile loading of the saddle force gauge at various distances

Table 5 shows the output voltages at these various distances. As with the vertical loading, a deflection of the whole gauge under load results in an increasing measurement of force in the vertical direction, even though they are very small. In real life situations, it is not expected that the point of application of horizontal load on the saddle will fluctuate much. The measurements in horizontal direction remain stable, which means the measurement of the force is independent of the point of application. Table 5: Measurements at horizontal load at various distances

distance (mm)

Force (N)

Output

horizontal Output vertical

(mV/V)

(mV/V)

deflection (mm)

25

100

0.02174

0.00078

0.087

35

100

0.02171

0.00081

0.102

45

100

0.02184

0.00093

0.103

55

100

0.02200

0.00097

0.112

65

100

0.02188

0.00114

0.110

A good decoupling between the vertical and horizontal output at a horizontal load can be seen in Figure 99. Again, the gauge is loaded in a direction defined as negative. The calibration load cell is placed at a distance of 25mm for this calibration.

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Figure 99: The output voltage of the horizontal and vertical bridge plotted against the applied horizontal load

Given these two sets of calibration data for both the vertical loading and horizontal loading of the saddle, a relation between each voltage output and the applied vertical and horizontal force can be described. At a vertical load, considering the load to be negative, the following relations exist: 𝑉 𝑉𝑣𝑒𝑟𝑡 = 2.4716 . 10−7 . 𝐹𝑣𝑒𝑟𝑡 [ ] 𝑉

𝑉 𝑉ℎ𝑜𝑟 = −1.3142 . 10−9 . 𝐹𝑣𝑒𝑟𝑡 [ ] 𝑉

At a horizontal load, considering the load to be negative, the following relations exist: 𝑉 𝑉𝑣𝑒𝑟𝑡 = 1.2431. 10−9 . 𝐹ℎ𝑜𝑟 [ ] 𝑉 𝑉 𝑉ℎ𝑜𝑟 = 2.3666. 10−7 . 𝐹ℎ𝑜𝑟 [ ] 𝑉

A combination of the above creates the following linear system:

𝑉 𝑉𝑣𝑒𝑟𝑡 = 2.4716 . 10−7 . 𝐹𝑣𝑒𝑟𝑡 + 1.2431. 10−9 . 𝐹ℎ𝑜𝑟 [ ] 𝑉 𝑉 𝑉ℎ𝑜𝑟 = 2.3666 . 10−7 . 𝐹ℎ𝑜𝑟 − 1.3142 . 10−9 . 𝐹𝑣𝑒𝑟𝑡 [ ] 𝑉

Solving this system for Fvert and Fhor gives following relations for the horizontal force and vertical force: 𝐹ℎ𝑜𝑟 = 4225.353 . 𝑉ℎ𝑜𝑟 + 22.463 . 𝑉𝑣𝑒𝑟𝑡 (

120

𝑁 ) 𝑚𝑉 𝑉

Chapter 6: Calibration of sensors

𝐹𝑣𝑒𝑟𝑡 = 4045.733 . 𝑉𝑣𝑒𝑟𝑡 − 21.278 . 𝑉ℎ𝑜𝑟 (

𝑁 ) 𝑚𝑉 𝑉

These equations are used to calculate the actual vertical and horizontal force. The parameters of the formulae above clearly show the good decoupling between horizontal and vertical measurements. Testing revealed that play in the clamping results in a higher degree of cross-sensitivity due to the tilting of the saddle force gauge. As a result of this tilt, the bridge that should not be excited by the force, gives an output voltage. Therefore, the clamping parts need to be stiff and the clamping bolt between seat post and saddle force gauge has to be adequately tightened.

6.3.3 Calibration of the handlebar As mentioned in 4.1.4.2, The handlebar has been tested manually for several times in order to investigate the cross-sensitivity from one side of the handlebar to the other. At first, several issues had to be resolved in order to reduce the severe cross-sensitivity and influence of the clamping force on the measurements. This involved cutting the handlebar in two and fitting two inserts. It was not until the last adjustment of the handlebar that it worked as indented and so a proper calibration could be conducted. The last alterations of the handlebar eliminated the influence of the clamping, so that no cross-sensitivity from one side of the handlebar to the other was detected. The tightening torque of the bolt which clamp the handlebar to the stem, has no effect on the measurements. The hole in one of the handlebar halves, in which the insert was fitted, was not perfectly centred. The results of these first tests showed that the axes in which the forces are measured differ from the intended axes. The strain gauges are attached in a way that the forces on the handlebar should normally be measured at an angle of

90°, horizontally and vertically. Calibration revealed that the axes of

measurement differ significantly from the ideal at the right hand side of the handlebar. On this side, the drilled hole in which the second insert is glued, is not perfectly centred, which may explain this difference. The directions of the axis of measurement are needed in order to correctly calculate the horizontal and vertical forces. Figure 100 shows the orientation of the measurement axes on the handlebar. These axis directions clearly illustrate the large deviation in comparison with an ideal orthogonal setup for the right side. Calculating the force components in an orthogonal system (X,Y) from the measurements in a non-orthogonal system (U,V) proves to be difficult.

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Figure 100: Orientation of the measurement axes of the handlebar

Figure 101 shows the projection of the actual force F onto an orthogonal coordinate system (FX and FY) and onto a non-orthogonal coordinate system (FU and FV). In case of the right hand side of the handlebar, a non-orthogonal measurement coordinate system is present. The idea is to recalculate the measured values of FU and FV to their respectively orthogonal components FX and FY.

Figure 101: Projection of the force F onto the orthogonal axes X and Y and non-orthogonal axes U and V

Following equation can be used to calculate the angle δ:

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tan 𝛿 = −

cos 𝛽 1 𝐹𝑈 + sin 𝛽 sin 𝛽 𝐹𝑉

from here, the orthogonal components FX and FY can be calculated: 𝐹𝑋 = 𝐹𝑈

𝐹𝑌 = 𝐹. cos(𝛿 + 90° − 𝛽)

= 𝐹𝑉 . sin 𝛽 − 𝐹𝑉 . tan 𝛿 cos 𝛽

Extended tests showed that the implementation of the equation above does not fully satisfy, since the applied force is not accurately measured and can switch from negative to positive due to the tangent in the equation. This difficult calculation in combination with non-linearities in the measurements as a result of the non-symmetric dimensions of the off-centre drilled hole make it difficult to reliably measure the forces at this side of the handlebar. It is decided that the measurements of the right side of the handlebar will be stored but not processed as the reliability of the reading is compromised.

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Chapter 7:

Field testing method

7.1 Introduction In order to determine the effects of certain parameters on the comfort level of the cyclist, a field testing program is put together. The effect can be assessed by examining the vibrations and forces exerted on the bicycle by the cyclist in short-term, mid-term or long-term measurements. It is chosen to perform short term and mid-term tests as a start of the measurements, since the influences of other parameters such as temperature, wind speed, wind direction etc. are best controlled in a short period of time. A form of a short-term test is the assessment of the transient response when cycling over a bump or from a ridge. This is called a bump test. The small amount of acquired data from these tests makes it possible to examine the vibration in the frequency domain as well as in the time domain. This kind of test is preferred over other types of tests when assessing the absorbed power level, since a single, large excitation (peak in accelerations due to small bump in the road for example) can cause large absorbed power measurements which would be smoothed out in time when performing longer tests. Nevertheless, a bump test does not give real-life information about the absorbed power level. A mid-term test is performed multiple times over the same route which has a length of a few hundred metres. These experiments can be used to examine the frequency spectrum of the excitation vibrations as well as the transmissibility towards the contact points where the cyclist touches the frame. These transmissibility plots give information on how the frame responds to certain frequencies and can be used to determine the level of damping caused by the frame. Comfort levels can be assessed by either the absorbed power method as well as the conventional ISO en BS methods. Long-term test are performed by cycling a whole event in the order of tens or hundreds of kilometres. These test might give a more clear view of the difference in comfort levels in real-life conditions. A disadvantage of these kinds of test is the large amount of acquired data and increased rider influence, which makes post-processing rather difficult and time consuming. The main objective of this thesis is twofold: first, determining the comfort level and the influence of several parameters on this comfort and secondly determining force distributions at the saddle, handlebar and pedal. Several parameters can be altered in order to determine a difference in comfort level. The first test will involve changing parameters of which it is expected to have the largest influence. Experience learns that both tyre pressure and road surface roughness play a significant role in the comfort level. In a later stage,

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it is possible to change the frame to investigate the influence of the used frame material or frame geometry. The type of wheel rim, handlebar tape and saddle can also have a certain effect. Since many variables come into play when conducting tests outside the laboratory, such as wind speed, temperature, etc., multiple runs are required at each chosen parameter change. The time signals are then assessed for each run. The comfort values obtained for all runs at one certain parameter setup are then averaged. Laboratory tests revealed that it is not possible to measure the pedal force and position simultaneous with the forces and accelerations at the saddle and handlebar due to the complex programming of the communication with the Bluetooth module, which transmits the force data coming from the pedal. Pedal force test will thus be conducted separate from the comfort tests. The pedal force and crank position data can be used to assess the force distributions in radial, tangential, horizontal and vertical direction in either function of time or in function of the crank position. Further calculation makes it possible to determine the instantaneous and averaged power input from the cyclist. Different cycling techniques and bicycle setups (such as rider position and gear ratios) can be examined by comparing these values and distributions. Total force amplitude distribution can be used to further develop pedals and pedal spindles for strength and fatigue. The main goal of the conducted experiments is to demonstrate the ability to accurately measure forces and accelerations which are then post-processed into useful data. Many test runs are made to make sure all subsystems work properly before experimenting. Following experiments have been conducted: 1) Investigation of the pedal force distribution when cycling in regime conditions: A constant speed of 38km/h will be maintained on a flat an smooth asphalted road over a considerable length. Pedal force distributions and instantaneous and average power input in time or with respect to crank-arm angle will be analyzed for these data. 2) Investigation of the absorbed power when cycling over a small bump: Cycling over a small bump in order to verify the analytical modal explained in 3.4.3. Conclusions about the absorbed power level will be made. 3) Investigation of the influence of tyre pressure and road surface when cycling in regime conditions: The tyre pressure is changed from 5 to 9bar in steps of 1bar, for both an evenly asphalted road as a road consisting of light cobblestones as can be seen in Figure 102. This test is used to investigate the influence of the road surface and tyre pressure on both the comfort level and force distributions at the saddle and handlebar. For every condition, three runs are taken so that an average value can be extracted. 125

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a)

b)

Figure 102: a) Smooth asphalted road b) mild cobblestones

7.2 Instrumentation of the bicycle When examining the comfort level during field testing, the bicycle is equipped with accelerometers on the following places: -

front wheel dropout, vertical direction

-

rear wheel dropout, vertical direction

-

saddle force gauge, vertical direction

-

saddle force gauge, horizontal direction

-

left side of handlebar, vertical direction

-

left side of handlebar, horizontal direction

The data of all six accelerometers is stored as well as the real time calculated velocity derived from the last four accelerometers listed above, which is used for the calculation of the absorbed power level. The accelerometers at the saddle and handlebar are placed as close as possible to the contact point between the human body and bicycle. Contact forces between the human body and the bicycle are measured at the following places: -

saddle force gauge, vertical direction

-

saddle force gauge, horizontal direction

-

left side of handlebar, vertical direction 126

Chapter 8: Field testing results

-

left side of handlebar, horizontal direction

A switch is placed near the handlebar (Figure 86, p108) which controls the calibration process at the start of the measurement to eliminate possible offset errors of the force measurements and another one which controls the saving of data, so the user can decide whenever data is saved. All cables coming from the bicycle are placed along each other to form an umbilical cord which is connected to a connector box, which ensure fast connection en disconnection of the cables without having to disconnect the data acquisition modules. This box is attached to the outside of a backpack which will be carried by the cyclist. These data acquisition modules, together with the chassis they are mounted in, is placed inside the backpack. A 12V battery is used as a power supply for this chassis. An USB cable connects the chassis with a laptop, which is also placed inside the backpack. When examining only the pedal force, no accelerometers need to be attached to the bicycle. Only the two inductive switches and the absolute zero switch from the encoder will be attached to the connector box (Figure 84, p105). Since only one digital data acquisition module is necessary for these measurements, a smaller and lighter chassis can be used. The Bluetooth connection between the laptop and the Bluetooth module at the crank requires the use of a Bluetooth USB dongle. The bicycle used for these tests is the MF5, which has the most percentage of flax of all Museeuw Bikes models, and is equipped with the following parts: -

Saddle

: Prologo EVO TR

-

Wheels

: Campagnolo Khasmin

-

Tyres

: Vredestein Fortezza Tricomp

-

Groupset

: Campagnolo Athena 4S

The weight of every item in the total setup is given in Table 6. Table 6: Weight of all items during testing

Item

Weight (kg)

Test person

86.0

MF5 bicycle without instrumentation

8.8

MF5 bicycle with instrumentation

11.0

Backpack filled with laptop, battery, connectorbox

7.4

and data-acquisition cards and chassis

These weights show that a total of 2.2kg is added to the bicycle. The saddle force gauge and instrumented handlebar are responsible for most of this weight. It is expected that the weight of the handlebar can be reduced by approximately 1kg when redesigned. The weight of the data-acquisition cards and chassis is fixed and cannot be reduced. A high performance 14” notebook was used for these tests as the weight 127

Chapter 8: Field testing results

was of the lowest available on the market. A good autonomy is also of importance when conducting field tests. Figure 103 shows the entire data-acquisition setup used while cycling.

Figure 103: Full field testing setup

7.3 Post processing of acquired data All of the acquired data will be analyzed making use of MatLab, a numerical computing environment and programming language. This program is designed to work with large amounts of data and has several modules used for signal processing. By simulating known signals (a sine wave as acceleration signal for example) of which r.m.s. values for instance are known, the calculation methods can be verified. Certain data will be processed by Excel, for example pedal force distributions in function of time or in function of crank angle.

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Chapter 8:

Field testing results

8.1 Force measurements and distributions Developing racing bicycle frames requires the use of accurate expected peak forces and force distributions. Obviously, these peak forces and force distributions depend greatly on several parameters such as cycling style, cyclist weight, bicycle setup and external influences such as the slope of the road, wind direction and magnitude and so forth. A goal of this thesis is to demonstrate the ability to measure and visualise these peak and average values and distributions. Further tests will be needed to examine the influence of all parameters involved. Data is extracted from two field tests, one which involves cycling a 180m course on a very even asphalted road and one which involves cycling across a 160m course on light cobblestones. Figure 104 shows the sign conventions for the forces, accelerations and velocities at the handlebar and saddle, which has been chosen for these experiments.

Figure 104: Sign conventions for expected forces

Figure 105 to Figure 108 illustrate the distribution of an exerted force on either the saddle or handlebar in horizontal or vertical direction. Pedal force distributions are more complex and will be handled separately. The plots clearly show a natural distribution around a certain average force. It is obvious that the force distribution is spread more widely when cycling across rough terrain, nevertheless, the mean values remain roughly the same for both surface roughnesses. Figure 105 shows a predominantly negative horizontal saddle force, which means that this force is exerted from the front to the back of the bicycle. The mean value lays around -50N. 129

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b)

a)

Figure 105: Horizontal saddle force distribution when cycling across a) evenly asphalted road b) light cobblestones

Figure 106 shows the large difference in vertical saddle force between both surface roughnesses. As can be expected, the direction of these forces is positive. A maximum peak force of 1400N is detected for light cobblestones whilst the mean force is around 500N. The mean vertical saddle force on an even road is slightly higher, around 550N, probably due to the more permanent contact between buttocks and saddle.

b)

a)

Figure 106: Vertical saddle force distribution when cycling across a) evenly asphalted road b) light cobblestones

The horizontal handlebar force distribution illustrated in Figure 107 shows a mean force of around 2025N. Roughly taken, this horizontal force on one side of the handlebar is about half the measured horizontal saddle force in counter direction. The vertical handlebar force distribution is illustrated in Figure 108 and shows a similar distribution.

a)

b)

Figure 107: Horizontal handlebar force distribution when cycling across a) evenly asphalted road b) light cobblestones

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b)

a)

Figure 108: Vertical handlebar force distribution when cycling across a) evenly asphalted road b) light cobblestones

8.2 Pedal force measurements For these measurements only the pedal force and crank arm angle is measured. A constant speed of 38km/h is maintained on a very smooth asphalted road. The wheels have a circumference of 2.10m and the used gear ratio is 50/13. A tailwind of about 10 to 15km/h was present at the time of testing. The tyres were inflated to a pressure of 9bar, the maximum allowed by the manufacturer. The crank length is 175mm. Figure 109 shows the sign conventions and reference axes for these measurements. It should be noted that the coordinate system in which the tangential and radial force is measured constantly rotates along with the rotating crank. A propelling pedal force results in an increasing crank angle.

Figure 109: Sign conventions for crank angle, tangential and radial force

A portion of all the acquired data is selected to demonstrate the ability to extract useful information about the pedalling dynamics. Figure 110 shows the time signal of both radial and tangential forces. 131

Chapter 8: Field testing results

Figure 110: Radial and tangential pedal forces in function of time

Both these forces can be plotted with respect to the crank angle to give better understanding of the distribution of these forces as shown in Figure 111. It clearly shows that the tangential component is largest when the crank angle reaches 90°, so roughly when the downwards pushing force of the leg is perpendicular to moment arm, resulting in an almost optimum efficiency. Once the pedal reaches the lowest point (at 180°), the leg rest on the pedal for the second half of the revolution, resulting in a negative tangential force of around 70N, which counteracts the cycling force exerted from the other leg. The radial component has no effect on the efficiency of the pedalling motion. It can be seen that this component is largest right before the pedal reaches the bottom position. When the crank angle is around 75°, the tangential force is almost maximal whilst the radial force is around zero, which indicates that the force exerted by the cyclist at that point is perfectly tangential and fully contributes to the propelling of the bicycle.

Figure 111: Radial and tangential pedal forces with respect to the crank angle

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These forces can be better interpreted when visualised as in Figure 112. This plot shows the total exerted force at every 15° for an entire revolution. It clearly depicts the large pedalling forces when the leg is pushing down but also the counteracting tangential forces when the foot is moving upward.

Figure 112: Visualisation of the total force distribution

This visualisation can be used to further increase efficiency of certain pedalling styles, as the total force should be maintained as high as possible in a tangential direction in order to increase input power. The counteracting forces, which the leg exerts when it is moving upwards, should be avoided. Some people even develop a cycling style were the leg pushes down the first half of the revolution and pulls up the second half, even though these styles are discussed: Aerobic muscle tissue fibres, responsible for delivering a continuous power for endurance exercises, rely on blood flow to replenish the chemicals they use, which does not flow when a muscle is contracted. It is suggested that when the muscles do not have enough time to relax and thus ‘refuel’, these pedalling styles could even lower the cyclist’s performance instead of enhancing [10]. Another important concept commonly used in cycling sports is the input power delivered by the cyclist. This can be extracted from these data by calculating the pedals circumferential velocity and multiplying it with the tangential force. This circumferential speed can be obtained by examining the crank angle in function of time, as shown in Figure 113. As it turns out, cycling at this specific load leads to a very constant crank rotation, as the plot shows a near perfect linear relation between the crank angle and time. The speed of pedalling or cadence for this test is 1.22rps or 73.2 rpm. 133

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Figure 113: Cumulated crank angle in time

This in turns makes it possible to calculate the instantaneous and average input power in function of time, as illustrated in Figure 114. The graph shows that the input power is very cyclic with peaks up to 500W and an average input power of 105W. This results in an average input power of 210W when assuming the working action of both legs to be equal. It is striking that even though these data were extracted from cycling in regime at medium to high speed (38km/h), a considerable amount of negative power is delivered. This means the one leg is pushing down not only to propel the cyclist en bicycle, but also to lift the other leg. This plot consequently shows how an inappropriate cycling style may reduce efficiency and thus overall performance.

Figure 114: Visualisation of the instantaneous and average input power

8.3 Short-term: Bump test As described in 3.4.3, the theoretical one-wheeled model illustrates how energy is absorbed by the cyclist when cycling over up a bump and partially transferred back to the bicycle when cycling down the bump. A 134

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way of verifying the principle idea of this model is by cycling over a bump with a fully equipped bicycle and analyzing accelerations, forces and energy transfers. One measurement is described in detail in order to explain the dynamic behaviour of both bicycle and human body when cycling over a bump. A self made bump (Figure 115) was placed on a smooth asphalted road. The edges of the bump are chamfered so the impact on the wheel is more gradual.

Figure 115: Bump

This bump is taken at a speed of around 10km/h as an attempt to maintain contact between the tyre and the road or bump at all times. The accelerations measured at the front and rear dropout are shown in Figure 116. A negative acceleration is an upward acceleration. The front wheel hits the bump at 1.37s, the rear wheel at 1.69s

Figure 116: Front and rear wheel acceleration

The vertical acceleration of the saddle is nearly identical to that of the rear wheel. It can be noticed that the rear wheel acceleration levels out between 1.7 and 1.8 seconds, something that can only be explained by assuming the rear wheel does not stay in contact with the road/bump at all times. Figure 117 gives a possible wheel trajectory which can explain the values of the vertical acceleration. The constant downward acceleration takes place as a consequence of the falling of the wheel until it hits the road, which causes a large upward acceleration peak. The double integration of the acceleration signal confirms this trajectory.

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Figure 117: Possible wheel trajectory

Figure 118 shows the vertical saddle force in time. The peak at 1.4s shows that the body is put out of balance by the shock of the front wheel. The cyclist attempts to correct this movement and so the saddle force decreases until around 1.7s. The rear wheel then hits the bump which throws the cyclist slightly off the saddle, resulting in a vertical saddle force which suddenly decreases to 0N. At 1.8s, the rear wheel hits the road. A force of around 100N is then measured, coming from the inertia of the unloaded saddle. It is not until 1.95s, until the buttocks touch the saddle again.

Figure 118: Vertical saddle force

Using these data, the power can be visualised, as shown in Figure 119. When the sign of the transmitted power is negative, the power is transmitted from the bicycle to the body, and vice versa. It clearly shows that when the rear wheel hits the bump, the human body absorbs power and then partly transmits it back to the bicycle as the bicycle drops down again. The curve between 1.7 and 1.8s shows a good resemblance with the simplified model.

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Figure 119: Power transfer between cyclist and bicycle

The absorbed power, as it is used for determining the comfort level, averages this curve and sometimes uses the peak values for a comparative study. When this power plot is integrated in time, the amount of absorbed energy can be calculated. A negative energy level means that energy is absorbed by the cyclist. The large negative peak at 1.73s in Figure 120 shows the amount of energy that is transmitted to the body as the rear wheel hits the bump. Most of this energy is transmitted back to the bicycle 0.05s later. As the increased potential energy of the cyclist is converted into kinetic energy of the bicycle as it falls down. A total energy of around 4J is absorbed by the cyclist, which is a realistic value.

Figure 120: Total absorbed energy

In order to further verify the simplified model, a bump with a perfect sinusoidal shape should be build so the wheel stays in full contact at all times. A method of validating this model is by examining the velocity decrease as a rider drives over several bumps. This velocity decrease can be used to determine the energy loss due to cycling over the bumps. The energy loss calculated with the absorbed power should then be less than the energy loss by decrease in velocity, since more energy dissipation mechanisms take place when cycling over a bump, such as friction.

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8.4 Mid-term: Comfort level A main goal of this thesis was to instrument the bicycle so that the comfort level of the cyclist in field testing conditions could be measured. The accuracy and reproducibility can only be examined by conducting multiple runs on a known course with the same bicycle setup. In the comparisons below, two courses are used: a 180m long smooth asphalted road and a 160m long course paved with mild cobblestones. The cyclist is ordered to maintain a constant speed of 30km/h for all runs. The main objective is to quantify the comfort level for these two courses with the tyre pressure as a parameter, so the numeric difference can be investigated. These tests will give an idea whether or not it is possible to detect minor changes in comfort level. Different comfort assessment methods will be compared: the BS6841 standard and the absorbed power method.

8.4.1 Absorbed power method The absorbed power levels are calculated without filtering the velocity or force signals. A total of three runs per tyre pressure has been taken. For every run, the absorbed power is calculated at the saddle and handlebar, in both the vertical as the horizontal direction. The total absorbed power for each run is calculated by taking the sum of these four values. The average and standard deviation is then calculated for each tyre pressure which enables the visualisation of the spread in these values. It should be pointed out that in all cases the absorbed power level at the handlebar is low compared to that at the saddle, even when keeping in mind only one side of the handlebar is measured for these tests. Smooth asphalted road Figure 121 shows the average absorbed power per three runs at different test conditions. The standard deviation is plotted above and below the average value is respectively a green and a red bar. The average absorbed power level is also measured when cycling with unloaded handlebar and when cycling without loading the saddle. Most of the power is absorbed at the saddle, due to the high forces present. By looking at the plots of both rear wheel dropout acceleration and the vertical saddle acceleration, it is clear that most of the vibrations experienced at the saddle are coming from the rear wheel.

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Figure 121: Absorbed power level at different test conditions for a smooth road surface

Figure 121 shows an absorbed power level of around 1W for all test conditions except the unloaded saddle run. As expected, a lower tyre pressure does not alter the comfort level drastically when cycling over a smooth surface. It can be expected that for these tests, the input power of the cyclist is between 90150W, which gives an idea about the percentage of power loss due to absorbed power. The plot also shows a fairly good reproducibility at every test conditions, even though more runs per test condition are necessary to give an exact view over the spread in these values. Mild cobblestones The results from these tests give a more clear view of the tyre pressure influence on the comfort level. Figure 122 shows an increase in absorbed power, and thus a decrease in comfort, for higher tyre pressures. The absorbed power for these test conditions lays between 6 and 18W, which is a relative high value compared to the input power of the cyclist.

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Figure 122: Absorbed power level at different test conditions for mild cobblestones

The difference between different road surfaces can thus easily be detected, since the values between a smooth surface and mild cobblestones differ by about 12-15W .

8.4.2 BS6841 method The BS6841 standard is based only on accelerations and first requires the calculation of the crest factor (which is the peak acceleration value divided by the r.m.s. value, after the acceleration signal has been filtered with the appropriate weighting filter). When the crest factor exceeds 6.0, the vibration dose value (VDV) should be used. Since the accelerations are measured in horizontal direction at the saddle and handlebar and in vertical direction at saddle and handlebar, the crest factor is calculated for each signal. The highest of these values determines whether or not the VDV or r.m.s. method is used. Almost all crest factors in each run exceed 6.0 and thus it is decided that all runs will be analyzed using the VDV method, since r.m.s. and VDV values cannot be compared with one another. The VDV value for the vibrations at the saddle and handlebar is calculated for both vertical and horizontal direction. These values cannot simply be added as with the absorbed power level. The VDV values in horizontal and vertical direction at one contact point can be assessed together by calculating the vector sum: 2 2 + 𝑉𝐷𝑉ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 ) 𝑉𝐷𝑉𝑡𝑜𝑡𝑎𝑙 = �(𝑉𝐷𝑉𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙+

Data from the same test runs as for the absorbed power calculations is used for this method.

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Smooth asphalted road The crest factor exceeds the value of 6 for almost all runs, since the r.m.s. values are very low, while occasional peaks are still present. It is decided that the VDV method will be used to assess the comfort level, as instructed by the standard. The VDV values for the handlebar and saddle are plotted in respectively Figure 123 and Figure 124. No direct relation between the tyre pressure and VDV values can be derived from these graphs.

Figure 123: Vibration dose value at the handlebar at different test conditions for a smooth road surface

Figure 124: Vibration dose value at the saddle at different test conditions for a smooth road surface

A large spread in data is seen for tyre pressure 8 and 6bar. So again, more test runs are necessary in order to determine this spread. 141

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Mild cobblestones A more rough surface gives a more distinct relation between VDV values at different tyre pressure. The spread is much smaller than for the test runs on a smooth surface.

Figure 125: Vibration dose value at the handlebar at different test conditions for mild cobblestones

As expected, the VDV values decrease with decreasing tyre pressures, leading to a better comfort.

Figure 126: Vibration dose value at the saddle at different test conditions for mild cobblestones

8.4.3 Comparison between BS6841 and Absorbed power A big advantage of the absorbed power method over the BS6841 method is that contact forces between the human body and the vibrating object are taken into account. It is reasonable to assume that when cycling over rough terrain, the buttocks or hands do not continuously make contact with respectively the 142

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saddle or handlebar. This can either be intentional or due to severe shocks. Either way, when the body does not make contact with the bicycle at a certain contact point, no forces or accelerations are transmitted toward the body, so no discomfort can be felt at that stage. Figure 123 to Figure 126 show very large VDV values when cycling without loading the handlebar or saddle, which should indicate a very low comfort level. This is not realistic since professional cyclists and mountain bike riders lift themselves out of the saddle when passing very rough terrain. This demonstrates the ability of the absorbed power method to evaluate the comfort level even when no full contact is made. These plots also prove that when the contact force between the human body and vibrating object is lowered, the acceleration amplitudes will increase, something the absorbed power method takes into account and the BS6841 method does not. A second advantage of the absorbed power method is the ability to simply sum all values. This value is expressed in Watt, which can be related to the input power of the cyclist and makes it more easy to interpret. A r.m.s. or VDV value can only be interpreted when compared with other tests or charts. The need for force gauges and the increased bicycle weight is a disadvantage of the absorbed power method, since these sensors will influence the dynamic behaviour of the bicycle. The goal is thus to restrict the added weight to a bare minimum. The BS6841 method shows a significantly lower comfort level at the handlebar than at the saddle, whilst the absorbed power data show significantly higher absorbed power levels at the saddle instead of the handlebar.

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Conclusion

Three main goals are achieved within this master thesis. First, a thorough literature study about the dynamics of a bicycle, frame materials and comfort assessment methods has been performed. Secondly, many components and gauges have been made in order to fully instrument the bicycle for field testing. As last, field tests are conducted with the purpose of examining the capabilities of the instrumentation and analyzing results such as force distributions and comfort levels.

9.1 Measuring and quantifying comfort during field tests The ISO2631 or the BS6841 standards are usually used to assess the comfort level of a human subjected to vibrations. These standards analyse the accelerations at which the human body of arms and hands are subjected. The contact forces between the body and the vibrating object are not taken into account, even though it can be expected that when riding a bicycle, an increased contact force, due to higher body weight or different cycling style, decreases the acceleration magnitudes. This could lead to wrong conclusions when determining the comfort level using one of these standards. The absorbed power method takes this into account, as can be seen by the results. The absorbed power level is around 1W for a smooth road at all tyre pressures and between 13 and 17W for a road paved with mild cobblestones, increasing with increasing tyre pressure. The absorbed power method rates the discomfort at the handlebar much lower than the British Standard does, so the question can be asked whether or not the hands and arms are more sensitive to absorbed power than the whole body, since the BS6841 uses different weighting filters for whole body vibration and hand-arm vibration.

9.2 Bicycle instrumentation The majority of time is spent on the design and fabrication of numerous parts and gauges which enable the real-time measurement of forces. The saddle force gauge and the instrumented pedal fully live up to the expectations in that they produces a stable, offset-free and linear signal. The decoupling of the horizontal and vertical forces is near to perfect.

The instrumented handlebar is susceptible to

improvements, as the weight can possible be reduced by 0.5-1kg. The encoder, used for the measurement of the crank angle, provides a good reading and adds little weight to the entire bicycle. A full setup is available which lets the researcher conduct outdoor field tests, including a button to zero out any offsets and a button which enables the recording of data.

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9.3 Force distribution and comfort measurements Many interesting results have come from the experiments, such as the force distributions on saddle and handlebar for different road roughnesses. These forces can be used in the design of bicycle components as well as for the static and fatigue testing of bicycle frames or components in laboratory conditions. Pedal forces can be very accurately measured together with the crank angle. This enables the visualisation of the forces in time or in function of the crank angle, as well as the power input. These measurements can be used to assess the influence of the body posture on the efficiency as well as the pedalling style. The force amplitudes can be used to develop pedals for fatigue and strength. One major objective of this thesis was to be able to measure the comfort level of the cyclist during field tests. The results reveal that it is possible to measure minute influences on the comfort level, such as tyre pressure. All the software was written so real-time measurement en post processing is possible. The tests show that an increase in tyre pressure leads to a decrease in cyclist’s comfort. The absorbed power has many advantages over the two more commonly used standards and it is recommended that this method should be used in further research when there is a possibility that the body looses contact with the vibrating object.

9.4 Further research First of all, the instrumentation should be improved by redesigning the instrumented handlebar. The used design has been altered several times, leading to an increased weight. The new design should incorporate a solid aluminium bar with drilled out ends, so the weight is kept to a minimum while still remaining a good strain response. Since these bicycles have hollow bottom brackets and the Bluetooth module has two extra channels, a second pedal could be instrumented with strain gauges so that the forces on both pedals can be examined. The connection between the notebook and this Bluetooth module and the LabView program can be further improved so that a more stable sample rate can be achieved. If possible, a selfmade wireless strain gauge bridge amplifier can be built. The overall weight of the data-acquisition setup cannot be reduced much further, although the placement of all the components inside the backpack may be altered to improve the comfort for the cyclist while testing. Secondly, a more intensive test program should be put together to fully investigate the influence of several parameters on the force distribution and pedalling efficiency. following parameters can be investigated: -

Effect of posture on the cycling efficiency

-

Effect of pedalling style on cycling efficiency

Even more important is the study of the influence of several parameters on the comfort level of the cyclist. These may include: 145

-

Effect of the tyre pressure

-

Effect of the road surface

-

Effect of the frame material

-

Effect of the frame geometry

-

Effect of velocity

-

Effect of posture of the human body

A further investigation regarding the transmissibility of vibrations from the rear and front dropout toward the contact points between the cyclist en cycle may give more information about the most significant frequencies which cause the most discomfort. The effects of eigenfrequencies can also be examined. Again, the influence of all the parameters above can be investigated. Since, keeping the suggested changes aside, the bicycle is fully instrumented and software has been written for the real-time acquisition and post processing, these test can be conducted without any major changes. Investigating many parameters is necessary since it will point out the difference in effect between those parameters. This may put the use of certain frame materials in perspective with respect to cyclist comfort and can give bicycle designers a method of verifying the choices they make with regard to improving the cyclist’s comfort.

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Appendix A Data sheets and drawings A.1 Accelerometers 1. Calibration certificate PCB Accelerometer, type:352C64, SN: 99055 2. Calibration certificate PCB Accelerometer, type:352C64, SN: 110062 3. Calibration certificate Brüel & Kjaer , type:4507, SN: 30858 A.2 Shaker and Power amplifier 4. Data sheet shaker LDSV406 5. Data sheet Power Amplifier PA100E-CE A.3 Force sensor A.4 Fabricated parts 6. Saddle force gauge 7. Spindle mount 8. Spindle dummy 9. Stem mount 10. Saddle and spindle mount 11. base plate 12. rod saddle force gauge 13. pulley mount 14. stem mount for shaker

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Bibliography [1] Nielens, H. and T. Lejeune, Bicycle shock absorption systems and energy expended by the cyclist. Sports Medicine, 2004. 34(2): p. 71-80. [2] BS 6841:1987 Guide to measurement and evaluation of human exposure to whole-body mechanical vibration and repeated shock. [3] NEN-ISO 2631:1 1997 Mechanische trillingen en schokken - Beoordeling van de invloed van trillingen op het menselijk lichaam. [4] Pradko, F., R. Lee, and V. Kaluza, Theory of Human Vibration Response. Mechanical Engineering, 1967. 89(2): p. 71-&. [5] Lundstrom, R., P. Holmlund, and L. Lindberg, Absorption of energy during vertical whole-body vibration exposure. Journal of Biomechanics, 1998. 31(4): p. 317-326. [6] Vanwalleghem, J., Study of the damping and vibration behaviour of flax-carbon composite bicycle racing frames. 2010. [7] Thaye, J.D., Determination of the static mechanical behaviour of flax-carbon raceframes. 2010. [8] Lubin, G., Handbook of composites. 1998: Thomson Science. [9] Strong, A.B., Fundamentals of composite manufacturing: materials, methods and applications. 2008: Society of Manufacturing Engineers. [10] Burrows, M., Bicycling science. 2004: Massachusetts Institute of Technology. [11] Museeuwbikes. http://www.webking.be/museeuwbikes/. Available from: http://www.webking.be/museeuwbikes/. [12] Aluminiummatter. www.aluminium.matter.org.uk. [13] http://spacecollective.org/aumber. [14] Chandra, R., S.P. Singh, and K. Gupta, Damping studies in fiber-reinforced composites - a review. Composite Structures, 1999. 46(1): p. 41-51. [15] Bachmann, H., Vibration problems in structures: practical guidelines. 1995. [16] Loccufier, M., Cursus Mechanische Trillingen. 2010. [17] Irvine, T., Damping properties of materials. 2004. [18] Frederick T. Wallenberger, N.W., Natural fibers, plastics and composites. 2004. [19] Baley, C., Influence of kink bands on the tensile strength of flax fibers. Journal of Materials Science, 2004. 39(1): p. 331-334. [20] Wallenberger, F.T. and N.E. Weston, Natural fibers, plastics and composites. 2004, Boston [etc.]: Kluwer Academic Publishers. [21] Fakirov, S., Handbook of engineering biopolymers : homopolymers, blends and composites. 2007, Munich; Cincinnati: Hanser ; Hanser Gardner. [22] John, M.J. and R.D. Anandjiwala, Chemical modification of flax reinforced polypropylene composites. Composites Part a-Applied Science and Manufacturing, 2009. 40(4): p. 442-448. [23] Harris, B., Fatigue in composites : science and technology of the fatigue response of fibrereinforced plastics. 2003, Boca Raton, Fla. [u.a.]: CRC Press [u.a.]. [24] Herlihy, D.V., Bicycle : the history. 2004, New Haven: Yale University Press. [25] Haydn, S. http://www.haydn-automation.co.uk/Kirk-History.htm. [26] http://www.sheldonbrown.com/frame-materials.html#carbon. 2010. [27] http://nbda.com/articles/industry-overview-2009-pg34.htm. 2009. [28] http://www.fiets.nl/news.asp?newsid=1004&newscatid=2&page=5. 2007. [29] Eckehard Fozzy Moritz, S.H., The engineering of Sport 6. volume 3, ed. i.s.e. association. 2006. [30] Beltrutti, D., Handbook of chronic pain. 2006, Hauppauge, N.Y.: Nova Science. [31] Heißing, B., Chassis handbook fundamentals, driving dynamics, components, mechatronics, perspectives ; with 75 tables. 2011, Wiesbaden: Vieweg + Teubner. [32] Barbu Daniela Mariana, I.B., Cornel Druga, THEORETICAL CONSIDERATIONS CONCERNING THE HUMAN BODY BEHAVIOUR IN A VIBRATIONAL MEDIUM. 2007, Univerisity of Brasov. 162

[33] Brüel and Kjær, Human vibration. 1989, Nærum, Denmark: Brüel & Kjær. [34] International, C.-I.-W.H.O.S., et al. Man under vibration, suffering and protection : proceedings of the International CISM-IFToMM-WHO Symposium, Udine, Italy, April 3-6, 1979. Amsterdam; New York; Warsaw; New York, N.Y.: Elsevier Scientific Pub. Co. ; PWN--Polish Scientific Publishers ; distribution for the U.S.A. and Canada, Elsevier/North-Holland. [35] Griffin, M.J., Handbook of human vibration. 1990, London; San Diego: Academic Press. [36] Champoux, Y., S. Richard, and J.M. Drouet, Bicycle structural dynamics. Sound and Vibration, 2007. 41(7): p. 16-+. [37] ISO 5349-1:2002 Mechanical vibration -- Measurement and evaluation of human exposure to hand-transmitted vibration. [38] OH, J.-H. and B.-J. Park. The whole-body vibration evaluation criteria of forestry machines. 2004. [39] Mansfield, N.J., P. Holmlund, and R. Lundstrom, Comparison of subjective responses to vibration and shock with standard analysis methods and absorbed power. Journal of Sound and Vibration, 2000. 230(3): p. 477-491. [40] Griffin, M.J., A comparison of standardized methods for predicting the hazards of whole-body vibration and repeated shocks. Journal of Sound and Vibration, 1998. 215(4): p. 883-914. [41] Mansfield, N.J. and M.J. Griffin, Effect of magnitude of vertical whole-body vibration on absorbed power for the seated human body. Journal of Sound and Vibration, 1998. 215(4): p. 813-825. [42] EN 14781, 2005, Racing bicycles - Safety requirements and test methods. [43] Alvarez, G. and J. Vinyolas, A new bicycle pedal design for on-road measurements of cycling forces. Journal of Applied Biomechanics, 1996. 12(1): p. 130-142. [44] Coleman, S.G.S., THE USE OF FORCE PEDALS FOR ANALYSIS OF CYCLING SPRINT PERFORMANCE. 1998. [45] Matek, W., H. Roloff, and M. Roloff, [Theorieboek]. 2000, Schoonhoven: Acad. Service. [46] Champoux, Y., et al., Measuring the dynamic structural load of an off-road bicycle frame. Experimental Techniques, 2004. 28(3): p. 33-36.

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List of figures Figure 1: Museeuw MF5 lugged frame [11] ............................................................................................................ 38 Figure 2: Museeuw MC6 monocoque frame [11] .................................................................................................. 39 Figure 3: Stress-strain diagram of a material capable of strain hardening ......................................................... 40 Figure 4: Stress-strain plots for different aluminium alloys [12] ......................................................................... 40 Figure 5: Stress-strain plots for different brittle fibres [13] ................................................................................. 41 Figure 6: Impulse response of an under-damped system (red), exponential decay (green) ............................ 43 Figure 7: Composition of flax fibre and stem ........................................................................................................ 44 Figure 8: Labelling of different parts of a racing bicycle ...................................................................................... 46 Figure 9: One half of the mould used to produce a composite bicycle frame ................................................. 47 Figure 10: Placing the frame inside the mould for forming and curing ............................................................. 48 Figure 11: Oscillation frequency ranges associated with the terms noise, vibration and harshness [31] ..... 50 Figure 12: Lumped parameter model of the human body ................................................................................... 51 Figure 13: Example of road roughness PSD plot ................................................................................................. 52 Figure 14: Numerical calculation of the modal shapes of the MF5 Frame ....................................................... 53 Figure 15: Whole body vibration test method [11] ............................................................................................... 55 Figure 16: Different vibration patterns [38] ........................................................................................................... 55 Figure 17: Method of evaluation and assessment defined in BS 6841[2] .......................................................... 57 Figure 18: Axes of vibration for BS 6841 (1987) [2] ............................................................................................. 57 Figure 19: Different weighting filters for ISO 2631, BS 6841 and ISO 5394 ................................................... 58 Figure 20:Method of evaluation and assessment defined in ISO 2631 [3] ........................................................ 60 Figure 21: Axes of vibration for ISO 2631 [3] ....................................................................................................... 60 Figure 22: Simplified bicycle model ......................................................................................................................... 64 Figure 23: Sinusoidal bump with amplitude 2 ........................................................................................................ 64 Figure 24: Vertical velocity v .................................................................................................................................... 65 Figure 25: Vertical acceleration a ............................................................................................................................. 65 Figure 26: a) Contact force without absorption b) contact force with absorption ......................................... 66 Figure 27: a) Instantaneous power exchange when no energy is dissipated b) instantaneous power exchange when energy is dissipated ......................................................................................................................... 66 Figure 28: a) Total absorbed energy without dissipation b) total absorbed energy with dissipation ........... 67 Figure 29: Basicentric coordinate system for the assessment of hand-arm vibration [37] ............................. 68 Figure 30: Frequency weighting curve Wh for hand arm vibration [37] ............................................................ 68 Figure 31: Orthogonal contact forces ..................................................................................................................... 71 Figure 32: Lateral bending test handlebar and stem assembly ............................................................................ 72 Figure 33: Fatigue test handlebar and stem assembly out-of-phase-loading (a), in-phase loading (b).......... 72 Figure 34: Fatigue test for pedal spindle ................................................................................................................. 73 164

Figure 35: Static strength test saddle clamp ........................................................................................................... 73 Figure 36: Fatigue strength test at maximum 4Hz for 200000 cycles ................................................................ 73 Figure 37: Typical strain gauge with dimension of 2.5 x 5.8 mm to 45 x 5 mm .............................................. 74 Figure 38: Wheatstone bridge configuration .......................................................................................................... 74 Figure 39: Placement of strain gauges in a typical full bridge configuration ..................................................... 75 Figure 40: Force position independent full strain gauge bridge .......................................................................... 76 Figure 41: Proof of concept steel bar equipped with four strain gauges ........................................................... 78 Figure 42: A suspended mass of 670g at three different locations gives the same voltage output ............... 78 Figure 43: Visualisation of the cross-sensitivity of the Wheatstone bridge to transversal loads ................... 79 Figure 44: Pedalling force amplitudes and direction ............................................................................................. 80 Figure 45: Placement of strain gauges in altered full bridge configuration onto the spindle ......................... 80 Figure 46: Terminology of the parts of a pedal ..................................................................................................... 81 Figure 47: Fixed spindle-pedal body design ........................................................................................................... 81 Figure 48: Pedal design with spindle connected to the crank-arm (conventional) .......................................... 81 Figure 49: Sketch of the bicycle pedal design using two ball bearings ............................................................... 82 Figure 50: Sketch of the bicycle pedal design using a slide bearing .................................................................... 83 Figure 51: Sketch of the bicycle pedal design using one double row angular contact ball bearing ............... 83 Figure 52: Wired connection between strain gauges and DAQ using a slip ring ............................................. 85 Figure 53: Bluetooth bridge amplifier GSV-4BT, Bluetooth adapter USB-stick and battery ........................ 86 Figure 54: Wireless solution for amplifying and transmitting signals by Bluetooth ........................................ 86 Figure 55: Speedplay Zero Stainless clipless pedal ................................................................................................ 87 Figure 56: Section view of the spindle and meshed spindle ................................................................................ 87 Figure 57: Von Mises stresses in the spindle at a load of 1000N ....................................................................... 87 Figure 58: Axial strain plotted against axial distance at the top of the spindle at a load of 1000N............... 88 Figure 59: Strain gauge L2A 06 125 LW -350 ........................................................................................................ 89 Figure 60: Unprotected finished pedal and a regular pedal ................................................................................. 89 Figure 61: Protected finished pedal ......................................................................................................................... 90 Figure 62: Bluetooth module, battery and pedal mounted on the crank-arm................................................... 90 Figure 63: Placement of the strain gauges on the handlebar ............................................................................... 91 Figure 64: Visualisation of the Von Mises stresses in the handlebar at a horizontal load of 500N .............. 91 Figure 65: Visualisation of the strain gradient near the stem at a horizontal load of 500N ........................... 92 Figure 66: Fully instrumented FSA handlebar with close up image of the strain gauges ............................... 93 Figure 67: Fretting wear as a result of microscopic slip at the edges of the stem ............................................ 93 Figure 68: Various stem types................................................................................................................................... 94 Figure 69: Cut view of the glued insert in one half of the handlebar ................................................................. 94 Figure 70: Visualisation of the reaction forces in the stem .................................................................................. 95 Figure 71: Half handlebar with glued insert, drilled and reamed ........................................................................ 95 Figure 72: view of the second glued insert in the handlebar ............................................................................... 96 165

Figure 73: Saddle force gauge instrumented with two altered Wheatstone strain gauge bridges .................. 97 Figure 74: Mounted saddle force gauge .................................................................................................................. 97 Figure 75: Illustration of the forces on the meshed part ...................................................................................... 98 Figure 76: Visualisation of the strain gradient (linear on the horizontal arm and constant in the vertical arm) in the horizontal arm at different vertical loads F at different distances a............................................... 99 Figure 77: Test setup measuring velocity vs. calculated velocity ...................................................................... 101 Figure 78: Visualisation of the phase shift between the measured velocity and the calculated velocity at 37Hz............................................................................................................................................................................ 101 Figure 79: Visualisation of the phase shift between the measured velocity and the calculated velocity for a random signal ............................................................................................................................................................ 102 Figure 80: Phase shift between actual velocity and calculated velocity ............................................................ 102 Figure 81: Visualisation of the rotating measurement coordinate system ....................................................... 103 Figure 82: Two square wave forms for right en left sense of direction ........................................................... 104 Figure 83: Placement of the three sensors along the chain ring ....................................................................... 105 Figure 84: Placement of the two inductive sensors on the chain ring ............................................................. 105 Figure 85: Placement of the third absolute zero position inductive sensor .................................................... 106 Figure 86: Calibration and save data switch attached to the stem .................................................................... 108 Figure 87: Data-acquisition cards, chassis and battery power supply .............................................................. 109 Figure 88: Connector box a) from sensors b) to data acquisition c) inside..................................................... 110 Figure 89: Field testing setup .................................................................................................................................. 112 Figure 90: Actual field testing setup ...................................................................................................................... 112 Figure 91: Pedal calibration setup .......................................................................................................................... 114 Figure 92: Calibration setup for the pedal spindle .............................................................................................. 115 Figure 93: Plot of the output voltage of bridge 1 against the applied load in direction 1 ............................ 115 Figure 94: Plot of the output voltage of bridge 2 against the applied load in direction 2 ............................ 116 Figure 95: Vertical compressive loading of the saddle force gauge at various distances from the front of the saddle ................................................................................................................................................................... 117 Figure 96: Vertical tensile loading of the saddle force gauge............................................................................. 118 Figure 97: The output voltage of the horizontal and vertical bridge plotted against the applied vertical load ..................................................................................................................................................................................... 118 Figure 98: Horizontal tensile loading of the saddle force gauge at various distances ................................... 119 Figure 99: The output voltage of the horizontal and vertical bridge plotted against the applied horizontal load .............................................................................................................................................................................. 120 Figure 100: Orientation of the measurement axes of the handlebar ................................................................ 122 Figure 101: Projection of the force F onto the orthogonal axes X and Y and non-orthogonal axes U and V ..................................................................................................................................................................................... 122 Figure 102: a) Smooth asphalted road b) mild cobblestones .......................................................................... 126 Figure 103: Full field testing setup ......................................................................................................................... 128 166

Figure 104: Sign conventions for expected forces .............................................................................................. 129 Figure 105: Horizontal saddle force distribution when cycling across a) evenly asphalted road b) light cobblestones .............................................................................................................................................................. 130 Figure 106: Vertical saddle force distribution when cycling across a) evenly asphalted road b) light cobblestones .............................................................................................................................................................. 130 Figure 107: Horizontal handlebar force distribution when cycling across a) evenly asphalted road b) light cobblestones .............................................................................................................................................................. 130 Figure 108: Vertical handlebar force distribution when cycling across a) evenly asphalted road b) light cobblestones .............................................................................................................................................................. 131 Figure 109: Sign conventions for crank angle, tangential and radial force ...................................................... 131 Figure 110: Radial and tangential pedal forces in function of time .................................................................. 132 Figure 111: Radial and tangential pedal forces with respect to the crank angle ............................................. 132 Figure 112: Visualisation of the total force distribution ..................................................................................... 133 Figure 113: Cumulated crank angle in time .......................................................................................................... 134 Figure 114: Visualisation of the instantaneous and average input power........................................................ 134 Figure 115: Bump ..................................................................................................................................................... 135 Figure 116: Front and rear wheel acceleration ..................................................................................................... 135 Figure 117: Possible wheel trajectory .................................................................................................................... 136 Figure 118: Vertical saddle force ............................................................................................................................ 136 Figure 119: Power transfer between cyclist and bicycle ..................................................................................... 137 Figure 120: Total absorbed energy......................................................................................................................... 137 Figure 121: Absorbed power level at different test conditions for a smooth road surface .......................... 139 Figure 122: Absorbed power level at different test conditions for mild cobblestones ................................. 140 Figure 123: Vibration dose value at the handlebar at different test conditions for a smooth road surface ..................................................................................................................................................................................... 141 Figure 124: Vibration dose value at the saddle at different test conditions for a smooth road surface ..... 141 Figure 125: Vibration dose value at the handlebar at different test conditions for mild cobblestones ...... 142 Figure 126: Vibration dose value at the saddle at different test conditions for mild cobblestones ............ 142

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List of tables Table 1: Properties of some materials used in bicycle construction [10] ........................................................... 41 Table 2: Physical properties of flax fibre ................................................................................................................ 44 Table 3: Natural frequencies of human body parts ............................................................................................... 51 Table 4: Measurements at vertical load at various distances .............................................................................. 117 Table 5: Measurements at horizontal load at various distances ........................................................................ 119 Table 6: Weight of all items during testing ........................................................................................................... 127

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