Stability of LIDAR measurement buoys for registration of ......de beperkingen van het auteursrecht, in het bijzonder met betrekking met de verplichting de bron uitdrukkelijk te vermelden

Fen Van Liefferinge, Dennis Van Eecke

of offshore wind velocity profilesStability of LIDAR measurement buoys for registration

Academiejaar 2011-2012Faculteit Ingenieurswetenschappen en ArchitectuurVoorzitter: prof. dr. ir. Joris DegrieckVakgroep Toegepaste Materiaalwetenschappen

Master in de ingenieurswetenschappen: werktuigkunde-elektrotechniekMasterproef ingediend tot het behalen van de academische graad van

Begeleider: Kameswara VepaPromotoren: prof. dr. ir. Wim Van Paepegem, prof. dr. ir. Joris Degrieck

Stability of LIDAR measuring buoy for

offshore wind profile registration

Students

Fen Van Liefferinge

Dennis Van Eecke

Promotors:

Prof. Dr. Ir. Wim Van Paepegem

Prof. Dr. Ir. Joris Degrieck

Stability of LIDAR measuring buoy for offshore wind profile registration Master thesis

Master thesis – Mechanical Engineering - Permission for use of content Page a

Permission for use of content

The authors give the permission to use this thesis for consultation and to copy parts of it

for personal use. Every other use is subject to copyright law, more specifically the source

must be extensively specified when using this thesis.

Dennis Van Eecke,

Fen Van Liefferinge

June 2012


Master thesis – Mechanical Engineering - Toelating tot bruikleen Page b

Toelating tot bruikleen

De auteurs geven de toelating deze scriptie voor consultatie beschikbaar te stellen en

delen van de scriptie te kopiëren voor persoonlijk gebruik. Elk ander gebruik valt onder

de beperkingen van het auteursrecht, in het bijzonder met betrekking met de

verplichting de bron uitdrukkelijk te vermelden bij het aanhalen uit deze scriptie.

Dennis Van Eecke,

Fen Van Liefferinge

Juni 2012


Master thesis – Mechanical Engineering - Foreword Page c

Foreword

For any Engineering student, the graduating year is an exciting chapter in life. The

thesis is an important part of this. Especially this thesis where we get an

opportunity to assist in the development of a new and interesting engineering

application. We had the opportunity to put a lot of our own ideas and our own

reasoning into this document. Instead of citing dozens of references we could

spend a lot of time finding out new things for ourselves. Although we did read

books there were still a lot of questions unanswered afterwards. Especially

concerning the practical implementation of the SPH models. Even getting simple

wave tank simulations to work was a big challenge. Every stride forward we took,

was the result of a lot of thought and effort.

Happily we could count on great support of the staff of the Mechanics of Materials

and Structures dept. of the University of Ghent. Especially our thesis coordinator

Kameswara Sridhar Vepa and our thesis promotor Prof. Dr. Ir. Wim Van Paepegem.

Without the perseverance and insights of K. Vepa and the good advice of W. Van

Paepegem we would have had a much tougher time. We would like to express our

most sincere gratitude to them and to the other helpful people at MMC: Joren

Pelfrene, Ives De Baere, and everyone we forgot to mention.

Of course this work was commissioned by 3E environmental consultancy. We

collaborated with their representative Ir. Thomas Duffey. We would like to thank

him as well for the continued support, the opportunity to visit the workshop and

his constructive and helpful attitude towards us and the thesis.

Last but not least, we would like to thank our parents and family as well for

providing the support we needed to devote so much of our time on our education

in general and this document in particular. They cared for our every need and bore

the considerable financial strain students impose upon parents all for our

happiness and for a fruitful ending of our education.

Sincerely,

The authors,

Fen Van Liefferinge

Dennis Van Eecke

Stability of LIDAR measuring buoy for offshore wind profile registration Master thesis abstract

Master thesis – Mechanical Engineering –Introduction Page A

Stability of LIDAR measuring buoy for

offshore wind profile registration

By

Fen Van Liefferinge

Dennis Van Eecke

Masterproef ingediend tot het behalen van de academische graad Master in de

ingenieurswetenschappen: Werktuigkunde - Elektrotechniek

Promotoren: Prof. Dr. Ir. Wim Van Paepegem, Prof. Dr. Ir. Joris Degrieck

Scriptie begeleiders: Kameswara Sridhar Vepa

Vakgroep toegepaste materiaalwetenschappen

Voorzitter: Prof. Dr. Ir. Joris Degrieck

Faculteit Ingenieurswetenschappen en architectuur

Universiteit Gent

Academiejaar 2011-2012

Abstract

The goal of this thesis is to assist in the development of a stabilisation mechanism for

offshore meteorological measuring equipment (Lidar) and propose an optimal buoy design

to mount this upon. For this purpose, an extensive study on water wave mechanics, as well

as a study on Smoothed Particle Hydrodynamics (SPH), used to model the sea, was

conducted. The thesis consists of two parts. The first part is the modelling of the sea state

using SPH with LS-Dyna software, followed by an analysis of buoy performance. The

second part was a kinematic study in Universal Mechanism (UM) software of the

stabilization mechanism to understand its behaviour and optimize its performance. Both

studies were combined to formulate a final conclusion on the performance of the buoy and

stabilization mechanism combined. More specifically the maximum inclination of the Lidar

module. The stabilisation mechanism decreases the Lidar inclination up to 90%, increasing

accuracy of the measurements.

Keywords

SPH, water wave mechanics, Watercraft stability, stabilisation mechanism, gyroscope


Master thesis – Mechanical Engineering –Introduction Page B

Stability of LIDAR measuring buoy for offshore

wind profile registration

Fen Van Liefferinge, Dennis Van Eecke Supervisors: Kamerwara Sridhar Vepa, Prof. Dr. Ir. Wim Van Paepegem

Abstract — The goal of this thesis is to assist in the development of a stabilisation mechanism for offshore meteorological measuring equipment (Lidar) and propose an optimal buoy design to mount this upon. For this purpose, an extensive study on water wave mechanics, as well as a study on Smoothed Particle Hydrodynamics (SPH), used to model the sea, was conducted. The thesis consists of two parts. The first part is the modelling of the sea state using SPH with LS-Dyna software, followed by an analysis of buoy performance. The second part was a kinematic study in Universal Mechanism (UM) software of the stabilization mechanism to understand its behaviour and optimize its performance. Both studies were combined to formulate a final conclusion on the performance of the buoy and stabilization mechanism combined. More specifically the maximum inclination of the Lidar module. The stabilisation mechanism decreases the Lidar inclination up to 90%, increasing accuracy of the measurements. Keywords — SPH, water wave mechanics, Watercraft stability, stabilisation mechanism, gyroscope

I. INTRODUCTION

This thesis is commissioned by 3E environmental consultancy. 3E is developing a product for measuring offshore wind profiles to assess the profitability of prospective wind farm locations. A first buoy prototype has already been designed with the Lidar measuring module on top.

The quality of the Lidar measurements is inversely proportional to the misalignment of its laser from vertical. The original stabilization mechanism was built as a pendulum and the buoy consisted of two conventional steel buoys. This article researches different options on the choice of buoys and a new stabilization mechanism to increase the quality of the measurements.

II. BUOY CHOICE

A downside of the first prototype was the fact that it was very heavy and difficult to handle. The end product has to be more cost-effective. Manageability, transportability and costs are key elements. The PEM58 buoy by RESINEX meets these requirements best. The use of composite materials makes it lighter and more manageable, while its modular design leads to easier transport. The PEM58 is produced in series, most likely resulting in a lower price than the custom built prototype.

Figure 1: PEM58 [1]

III. MODELLING OF DEEP WATER WAVES

In simulations, the grid based methods are most popular. However, their applications are limited for many complex problems. These limitations become apparent when modelling free surfaces, deformable boundaries and extremely large deformations. All common in wave simulations. To be able to deal with these problems, meshfree particle methods are used. In particular the SPH-method. Unlike conventional techniques, the SPH-particles do not have a fixed connectivity, resulting in the capability to model water waves. Downsides are the increased calculation time and the possibility of clustering. [2]

Similar to real experiments, the model consists of a wave tank, a wave generator and water. This is comparable to the work of [3], only on a larger scale and in three dimensions. The model was tuned to produce waves with similar characteristics as the waves at the Thornton bank. It was calibrated using sea state data provided by GeoSea and mathematical models [4]. The results are pictured in table 1.


Master thesis – Mechanical Engineering –Introduction Page C

Sea state by GeoSea

Sea state in model

Wave period [s] 5.594 5.6

Wave height HM1 [cm] 224.46 244.6

Highest wave [cm] 275.69 276.8

Wavelength [m] 48.27 48.47

Table 1- comparison of sea state data

IV. MODELLING OF THE BUOYS

Rigid finite element models of the chosen buoys were produced. Specifications of the 3E prototype were provided by 3E themselves. Therefore this model was the most accurate. Unlike the PEM58 which was modelled only using the information available from the product catalogue. A SPAR buoy was modelled as well to serve as a reference for optimal stability. Each buoy was fitted with a platform, based on the current prototype, and simplified installations such as solar panels, battery box and Lidar.

Figure 2- 3E prototype model

Each buoy model was equipped with a mooring cable as well to prevent it from drifting away. Several options were explored to impose the effect of an undercurrent on the behaviour of the model. The most feasible option was to apply forces on the mooring cable itself. Unfortunately this was abandoned for reasons of calculation time.

V. BUOY PERFORMANCE

Buoy performance was determined by subjecting the buoy models to the modelled sea waves. The translational and rotational deviation measured relative to the starting position are tracked, but far more important is the rotational speed. The faster the buoy pitches, the less time the stabilisation mechanism has to counteract the movement. The results for the current 3E prototype (pictured in green) and the suggested alternative, the PEM58 (pictured in red), are visualised in figure 3.

Figure 3-Rotational speed versus time

Despite the fact that the PEM58 rotates 53% faster than the 3E buoy, the recommendation is still valid. The PEM58 is lighter, easier to transport, has a flat top to mount the installations on and will probably be cheaper.

VI. KINEMATIC STUDY

Figure 4: Model of stabilisation mechanism

To stabilise the Lidar, a system using a flywheel was preferred instead of an actively controlled system because of its simplicity. It only relies on a gyroscope to function. An extensive empirical study with many simulations has shown that the flywheel radius is best chosen as large as possible within practical limits. Making the flywheel thicker increases accuracy, but to a lesser extent. An excessively heavy flywheel should be avoided because of practical issues. A separate study with a differently shaped mechanism has shown that a ring shaped flywheel can yield better accuracy for a similar weight.

Any change resulting in higher flywheel capacity does increase accuracy in an ideal situation, but deteriorates the mechanism’s tolerance for disturbances. These cause a precession motion of which the amplitude is dominant compared to the amplitude excited by the buoy movement itself. The flywheel capacity should be high enough to yield sufficient accuracy, but making it too high can make precession motion too hard to damp out.

Jerking, both in rotation and translation, does not cause too big of a disturbance. Sudden acceleration or deceleration of the flywheel is most damaging.


Master thesis – Mechanical Engineering –Introduction Page D

VII. COMBINED RESULTS

Data extracted from Dyna wave simulations has been used as input to generate corresponding frame movement in UM. This way the Lidar inclination can be measured as before, but with the frame moving like the buoy would. The average and maximum absolute value of the Lidar rotation vector resulting from the UM simulations is an indicator of the accuracy of an actual mechanism on an actual buoy. The tested buoys were the 3E prototype and the PEM 58.

Figure 5: Maximum Lidar inclination for varying flywheel settings.

It is obvious the flywheel is of great benefit to accuracy. Although the 3E prototype buoy performs better in damping out wave movement, the difference in accuracy is negligible when using the gyroscope. It seems that increasing the flywheel speed from 3000 to 6000 rpm is not worth the effort, despite the theoretical conclusions of the kinematic study.

The final recommendation is that the PEM buoy in combination with the flywheel is a more manageable and cost effective solution compared to 3E’s original design. The flywheel has increased the accuracy with approximately 90% for the 3E design.

VIII. REFERENCES

[1] Resinex, Resinex, March 2012. [Online]. Available: http://www.resinextrad.com/

[2] M. B. L. G. R. Liu, Smoothed particle hydrodynamics, World Scientific Publishing Co. Pte. Ltd., 2003.

[3] J. Pelfrene, Study of the SPH method for simulation of regular and breaking waves, Gent: Universiteit Gent, 2011

[4] R. A. D. Robert G. Dean, Water wave mechanics, World scientific publishing Co. Pte. Ltd., 1992.

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Ghent University Master Thesis abstract

Master thesis – Mechanical Engineering – Table of contents Page E

Stability of LIDAR measuring buoy for offshore

wind profile registration

Fen Van Liefferinge, Dennis Van Eecke Begeleiders: Kamerwara Sridhar Vepa, Prof. Dr. Ir. Wim Van Paepegem

Samenvatting — Het onderzoek in deze thesis dient als hulp bij de ontwikkeling van een stabiliserend mechanisme voor een offshore meteorologisch meetinstrument (Lidar) en het voorstellen van een optimaal boei ontwerp om dit instrument te dragen. Ter voorbereiding werd eerst het golfgedrag bestudeerd alsook de ‘Smoothed Particle Hydrodymanics” (SPH) techniek. Deze laatste werd uiteindelijk gebruikt om de zee te modeleren. De thesis bestaat uit twee grote delen. Het eerste deel handelt over het modelleren van de zee gebruikmakend van SPH en LS-Dyna software, gevolgd door een analyse van de prestaties van de boeien. Het tweede deel is een kinematische studie in Universal Mechanism software (UM) van het stabiliserende mechanisme. Dit om zijn gedrag te doorgronden en zijn prestaties te optimaliseren. Tot slot werden beide delen gecombineerd om een besluit te trekken over de prestaties van het gecombineerde geheel van boei en stabilisatie mechanisme. Meer specifiek de maximale inclinatie van de Lidar module. Het stabiliserende mechanisme verkleint de maximale inclinatie met 90%, resulterend in een betere accuraatheid van de metingen. Trefwoorden — SPH, golftheorie, vaartuig stabiliteit, stabiliserend mechanisme, gyroscoop

I. INLEIDING

Deze thesis is geschreven in opdracht van 3E environmental constaltancy. 3E ontwikkeld een product om offshore wind profielen op te meten. Dit om de opbrengst van toekomstige windmolenparken te voorspellen. Een eerste prototype van de boei die het Lidar meettoestel draagt, is reeds gemaakt.

De kwaliteit van de metingen is omgekeerd evenredig met de afwijking die de laser van de Lidar heeft ten opzichte van de verticale richting. Het origineel bevat daarom ook een stabiliserend mechanisme dat uitgevoerd is als een pendulum. De boei zelf is opgebouwd uit twee conventionele stalen boeien. Dit artikel onderzoekt verschillende mogelijke keuzes van de boeien en het ontwerp van een nieuw stabiliserend systeem om de kwaliteit van de metingen op te drijven.

II. KEUZE VAN DE BOEI

Een groot nadeel verbonden aan het eerste prototype is zijn grote massa en het feit dat hij moeilijk handelbaar is. Het eindproduct meer kosteneffectief, handel- en transporteerbaar maken, is het voornaamste doel. De PEM58 boei van RESINEX voldoet het beste aan deze gestelde eisen. Het gebruik van composiet materialen maakt hem lichter en als gevolg ook beter handelbaar. Het modulaire design leidt tot een betere transporteerbaarheid. De PEM58 wordt tevens in serie geproduceerd. Dit resulteert hoogstwaarschijnlijk in een lagere prijs dan het op maat gemaakte prototype.

Figuur 1: PEM58 [1]

III. MODELLEREN VAN DIEP WATER GOLVEN

Methodes gebruikmakend van een rooster zijn zeer populair bij numerieke simulaties. Toch zijn hun toepassingen beperkt voor vele complexe problemen. Deze beperkingen zijn zeer duidelijk bij het modeleren van vrije oppervlakken, vervormbare grenzen en zeer grote vervormingen in het algemeen. Deze zijn allen vaak voorkomend bij het simuleren van zeegolven. Om dit toch te kunnen modelleren, wordt gebruik gemaakt van de SPH-techniek. In tegenstelling tot conventionele methodes, zijn de SPH-partikels niet vast verbonden, wat resulteert in de mogelijkheid om golven te kunnen simuleren. Er zijn echter ook nadelen aan verbonden, waaronder een sterk toegenomen rekentijd en de mogelijkheid tot clusteren. [2].


Master thesis – Mechanical Engineering –Introduction Page F

Net zoals bij praktische experimenten bestaat het model uit een golftank, een golfgenerator en water. Dit is vergelijkbaar met het werk van [3], maar dan opgeschaald en in drie dimensies. Het model is zodanig afgesteld dat de gegenereerde golven gelijkaardige karakteristieken hebben aan de golven bij de Thornton bank. Het model is gekalibreerd op basis van data over de zeegolven gemeten door GeoSea en wiskundige modellen [4]. De resultaten zijn weergegeven in tabel 1.

Sea state by GeoSea

Sea state in model

Wave period [s] 5.594 5.6

Wave height HM1 [cm] 224.46 244.6

Highest wave [cm] 275.69 276.8

Wavelength [m] 48.27 48.47

Tabel 1- vergelijking van data over de zeegolven

IV. MODELLEREN VAN DE BOEIEN

Vervolgens werden starre, eindige elementen modellen gemaakt van de geselecteerde boeien. Van de huidige boei van 3E werd voldoende data verschaft om een zeer representatief model te ontwerpen. De PEM58 daarentegen werd uitsluitend gemodelleerd op basis van informatie afgeleid uit de product catalogus. Ook werd een SPAR boei gemodelleerd die zou dienen als referentie voor optimale stabiliteit. Elke boei werd uitgerust met een platform, gebaseerd op hetgeen momenteel gebruikt door 3E, en een vereenvoudigde set van installaties zoals zonnepanelen, batterijen en de Lidar.

Figuur 2- Model van het 3E prototype

Daarbovenop werd elke boei voorzien van een kabel om te verhinderen dat deze zou afdrijven. Om de effecten van een onderstroom te incorporeren in het model werden verschillende denkpistes onderzocht. De meest haalbare optie was om de resulterende krachten te laten inwerken op de verankeringskabel. Spijtig genoeg is dit niet uitgevoerd vanwege de grote rekentijd die dit met zich zou meebrengen.

V. PRESTATIES VAN DE BOEIEN

De prestaties van de boeien werden begroot door ze te onderwerpen aan de gemodelleerde zeegolven. Zowel de translationele als de rotationele afwijking ten opzichte van de startpositie werd onderzocht. Veel belangrijker is echter de rotatiesnelheid van de boei om een as in het horizontale vlak. Hoe sneller de boei roteert, hoe minder tijd het stabiliserende mechanisme heeft om deze beweging te corrigeren. De resultaten van het huidige 3E prototype (in het groen) vergeleken met deze van de PEM58 (in het rood) zijn voorgesteld door figuur 3.

Figuur 3-Rotatiesnelheid in functie van de tijd

Ondanks het feit dat de PEM58 53% sneller roteert in vergelijking met de 3E boei, blijft deze aangeraden. De PEM58 is lichter, gemakkelijker te transporteren, heeft een vlak oppervlak waar de installaties kunnen gemonteerd worden en zal waarschijnlijk goedkoper uitkomen. Ook dient er nog op gewezen te worden dat de werkelijke PEM beter zal presteren dan het model. Dit laatste is namelijk enkel gebaseerd op informatie beschikbaar in de catalogus.

VI. KINEMATISCHE STUDIE

Figuur 4: Model van het stabiliserende mechanisme


Master thesis – Mechanical Engineering –Introduction Page G

Om de Lidar te stabiliseren werd een systeem gekozen dat gebruik maakt van een vliegwiel. Dit kreeg de voorkeur ten opzichte van een actief gestuurd systeem vanwege zijn eenvoud. Een uitgebreide empirische studie met vele simulaties wees uit dat de straal van het vliegwiel best zo groot mogelijk gekozen wordt, binnen praktische grenzen. Het dikker maken van het vliegwiel resulteert eveneens in een verhoogde nauwkeurigheid, maar dan minder uitgesproken. Een zeer zwaar vliegwiel dient vermeden te worden om praktische redenen. Een aparte studie met een vliegwiel van een andere vorm heeft aangetoond dat een ringvormig vliegwiel de metingen nog nauwkeuriger kan maken voor gelijkaardig vliegwielgewicht.

Elke verandering resulterend in betere prestaties van het vliegwiel, verbetert de accuraatheid van het systeem in ideale situaties. Het verlaagt echter de tolerantie van het mechanisme voor storingen. Deze veroorzaken een precessiebeweging met een amplitude die dominant is ten opzichte van deze van de Lidar-beweging geëxciteerd door de beweging van de boei. De capaciteit van het vliegwiel dient hoog genoeg te zijn om voor voldoende nauwkeurige metingen te zorgen, maar een te hoge capaciteit zorgt ervoor dat de precessiebeweging moeilijk is om uit te dempen.

Hevige bewegingen, zowel rotationele als translationele, veroorzaken geen sterke verstoringen. Plotse versnelling of afremming van het vliegwiel is schadelijker voor de accuraatheid.

VII. GECOMBINEERDE RESULTATEN

Data uit de Dyna golf simulaties werd gebruikt als input om corresponderende frame bewegingen te genereren in UM. Op deze wijze kan de hoekafwijking van de Lidar ten opzichte van de verticale gemeten worden, maar nu met de echte bewegingen die het op zee zou ondervinden. De gemiddelde en de absolute waarde van de rotatievector van de Lidar uit de UM simulaties dient als een indicator voor de nauwkeurigheid die het mechanisme en de gekozen boei kunnen bereiken. De geteste boeien waren het huidige prototype van 3E en de PEM 58.

Figuur 5: Maximale uitwijking van de Lidar voor verschillende vliegwiel

paramters.

Het is duidelijk dat het vliegwiel de nauwkeurigheid sterk verbetert. Ondanks het feit dat het 3E prototype beter presteert als het op uitdemping van de zee beweging aankomt, is het verschil in nauwkeurigheid klein als er gebruik gemaakt wordt van de gyroscoop. Het vliegwiel versnellen van 3000 tpm tot 6000 tpm levert niet veel meer voordeel op. Dit in tegenstelling tot de conclusies gemaakt in de kinematische studie.

Het uiteindelijke voorstel voor 3E is de PEM 58 in combinatie met het vliegwiel. Dit geheel is beter handelbaar en kosteneffectief vergeleken met het huidige ontwerp. Daarbovenop heeft het vliegwiel de nauwkeurigheid verhoogd met zo’n 90% ten opzichte van een identiek systeem met het vliegwiel uitgeschakeld.

VIII. REFERENTIES

[1] Resinex, Resinex, Maart 2012. [Online]. Available: http://www.resinextrad.com/

[2] M. B. L. G. R. Liu, Smoothed particle hydrodynamics, World Scientific Publishing Co. Pte. Ltd., 2003.

[3] J. Pelfrene, Study of the SPH method for simulation of regular and breaking waves, Gent: Universiteit Gent, 2011

[4] R. A. D. Robert G. Dean, Water wave mechanics, World scientific publishing Co. Pte. Ltd., 1992.

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Stability of LIDAR measuring buoy for offshore wind profile registration Master Thesis

Master thesis – Mechanical Engineering –Introduction Page I

Table of contents

1 Introduction ............................................................................................................................... 1

2 Study of commercially available hull designs ................................................................ 4

2.1 General considerations ................................................................................................................................ 4

2.2 Stability .............................................................................................................................................................. 4

2.3 Commercial solutions ................................................................................................................................... 5

2.3.1 Catamaran ................................................................................................................................................................... 5

2.3.2 Resinex PEM 58 Catamaran buoy [2] ............................................................................................................. 8

2.3.3 Resinex PEM 58 buoy [2] ................................................................................................................................... 12

2.3.4 Spar buoy .................................................................................................................................................................. 12

2.4 Conclusion ....................................................................................................................................................... 13

3 Numerical study ...................................................................................................................... 14

3.1 Preface [3] ....................................................................................................................................................... 14

3.2 Numerical simulations in general [3] .................................................................................................. 14

3.2.1 SPH: a meshfree particle method ................................................................................................................... 14

3.2.2 Clustering .................................................................................................................................................................. 17

3.3 LS-Dyna and LS-PrePost ............................................................................................................................ 18

3.4 Water wave mechanics [6] ....................................................................................................................... 24

3.5 Wave tank design and dimensions ....................................................................................................... 26

3.5.1 Basic wave tank dimensions ............................................................................................................................. 26

3.5.2 Boundary conditions of the paddle ............................................................................................................... 29

3.5.3 Boundary conditions of the wave tank ........................................................................................................ 32

3.5.4 Summary: Basic wave tank ............................................................................................................................... 35

3.5.5 Friction interface ................................................................................................................................................... 36 3.5.5.1 Undercurrent modelling with linear water duct and pistons ............................................................................. 36 3.5.5.2 Undercurrent modelling by closed loop water circuit ........................................................................................... 37 3.5.5.3 Friction interface with moving plate .............................................................................................................................. 37 3.5.5.4 Simulating undercurrent by applying resultant forces on the mooring cable ........................................... 39

3.5.6 Additional cards ..................................................................................................................................................... 40 3.5.6.1 INITIAL_STRESS_DEPTH ...................................................................................................................................................... 40 3.5.6.2 LOAD cards .................................................................................................................................................................................. 40

3.6 Model verification ........................................................................................................................................ 41

3.6.1 Mesh convergence ................................................................................................................................................. 41 3.6.1.1 1000 kg particles ...................................................................................................................................................................... 42 3.6.1.2 Conclusions ................................................................................................................................................................................. 43

3.6.3 Further model checks .......................................................................................................................................... 48 3.6.3.1 Buoyancy check ........................................................................................................................................................................ 48 3.6.3.2 Breaking wave check .............................................................................................................................................................. 49 3.6.3.3 Dam break check ...................................................................................................................................................................... 50

3.7 Modelling the buoys for LS-Dyna .......................................................................................................... 51

3.8 Calculation time ............................................................................................................................................ 56

3.8.3 SPH particle mass versus calculation time ................................................................................................. 59

3.8.4 Mooring cable versus calculation time ........................................................................................................ 60

3.9 Simulation results on buoy performance ........................................................................................... 61

3.9.1 General information on displacement of the buoys ............................................................................... 62


Master thesis – Mechanical Engineering –Introduction Page II

3.9.2 Performance of the different buoys in terms of rotation .................................................................... 63 3.9.2.1 3E prototype buoy ................................................................................................................................................................... 63 3.9.2.2 PEM58 buoy ................................................................................................................................................................................ 65 3.9.2.3 Spar buoy ..................................................................................................................................................................................... 67 3.9.2.4 3.9.2.4 Conclusion .................................................................................................................................................................... 70

4 Study of Lidar stabilization mechanism ......................................................................... 72

4.1 Introduction ................................................................................................................................................... 72

4.2 Model overview ............................................................................................................................................ 72

4.3 Model parts, joints and parameters...................................................................................................... 76

4.3.1 Part: Frame ............................................................................................................................................................... 76

4.3.2 Part: Outer gimbal ................................................................................................................................................. 76

4.3.3 Part: Inner gimbal.................................................................................................................................................. 76

4.3.4 Part: Lidar ................................................................................................................................................................. 76

4.3.5 Part: Flywheel ......................................................................................................................................................... 77

4.3.6 Gimbal joints ............................................................................................................................................................ 77

4.3.7 Overview and reference situation .................................................................................................................. 78

4.4 Measuring performance ............................................................................................................................ 80

4.5 Parameter influence .................................................................................................................................... 83

4.5.1 Flywheel speed ....................................................................................................................................................... 83

4.5.2 Amplitude.................................................................................................................................................................. 86

4.5.3 Flywheel dimensions ........................................................................................................................................... 88

4.5.4 Flywheel weight ..................................................................................................................................................... 95

4.5.5 Flywheel offset ........................................................................................................................................................ 96

4.5.6 Lidar offset ................................................................................................................................................................ 98

4.5.7 Conclusion of mechanism geometry design: ‘super mechanism’ .................................................. 102

4.5.8 Damping .................................................................................................................................................................. 107 4.5.8.1 Effect of damping in the reference mechanism ...................................................................................................... 107 4.5.8.2 Beware of precession .......................................................................................................................................................... 111

4.6 Reaction of the mechanism to irregularities ................................................................................. 112

4.6.1 Sudden deceleration of flywheel ................................................................................................................. 112

4.6.2 Sudden changes in buoy frame movement ............................................................................................. 122 4.6.2.1 Functions ................................................................................................................................................................................... 122 4.6.2.2 Rotational jerking ................................................................................................................................................................. 123 4.6.2.3 Translational jerking ........................................................................................................................................................... 126 4.6.2.4 Change of amplitude ............................................................................................................................................................ 127 4.6.2.5 Conclusion ................................................................................................................................................................................ 128

4.6.3 Restarts during operation ............................................................................................................................... 128

4.6.4 Influence of friction ........................................................................................................................................... 130

4.7 Frequency response ................................................................................................................................. 133

4.7.1 About UM and the reference model ............................................................................................................ 134

4.7.2 Excitation of frame for typical wave periods ......................................................................................... 134

4.7.3 Resonance .............................................................................................................................................................. 137

4.8 Motor requirements ................................................................................................................................. 140

4.8.1 Motor power in steady state .......................................................................................................................... 140

4.8.2 Flywheel start-up................................................................................................................................................ 142

4.9 Conclusion .................................................................................................................................................... 146

5 Combined results ................................................................................................................ 147

5.1 3E prototype ............................................................................................................................................... 149


Master thesis – Mechanical Engineering –Introduction Page III

5.2 PEM 58 ........................................................................................................................................................... 151

5.3 Comparison ................................................................................................................................................. 152

6 Conclusion ............................................................................................................................. 154

7 References ............................................................................................................................. 156

8 Figures, graphs and tables ............................................................................................... 157

8.1 List of figures .............................................................................................................................................. 157

8.2 List of Graphs .............................................................................................................................................. 163

8.3 List of tables ................................................................................................................................................ 165


Master thesis – Mechanical Engineering –Introduction Page 1

1 Introduction

In recent times wind power is becoming increasingly important as a renewable energy

source and the subsequent demand for offshore wind farms has created a need to

accurately measure the wind profile on a particular location. A wind profile is a wind

velocity and direction distribution on a particular location in relation to the height above

the sea level. The knowledge of wind profile(s) is vital to determine the profitability and

feasibility of prospective offshore wind farm locations.

The wind profile can be measured with laser guided measuring devices such as the

‘Lidar’. A device similar to a radar, but it uses laser light instead of radio waves.

Figure 1: Lidar measuring equipment

To make a correct measurement the Lidar must remain stationary for an extended

period of time during which the unit must remain as level as possible. This is necessary

because the Lidar must take a great deal of measurements to determine the average

wind distribution and the scatter of wind velocity and direction. Typically, the device

must remain in place for several weeks.



Figure 2: Schematic overview of measuring device operating conditions

To provide these operating conditions on open ocean the measuring device must be

installed on a stable platform or a pontoon of sorts. The goal of this master thesis is to

determine the requirements and geometry of such a vessel. In order of importance, it

must be able to fulfil the following demands:

The Lidar must remain as upright as possible during normal sea conditions in

which wind turbines can still operate so that the Lidar can take measurements.

The efforts and costs to relocate the vessel must be minimized as much as

possible. Typically it must be light and/or easy to tow through the water for cost

effective transportation. Autonomous propulsion is not necessary but can be

considered. When the vessel is made to fit in a standard shipping container, it

would be a big advantage.



The vessel must be able to operate autonomously for an extended period of time.

It must have an independent, reliable and redundant on board power supply for

the Lidar and any additional equipment.

The vessel must be able to stay in the same position as much as possible despite

wind or ocean currents. There must be a means of anchoring the vessel to the

bottom reliably.

The vessel must be able to resist storm conditions within reasonable limits while

keeping the Lidar module and support system undamaged. Since wind turbines

do not operate during these conditions the Lidar inclination is no longer

important.

This thesis will consist of multiple studies.

The first study will focus on existing and/or commercially available vessels (buoys,

platforms, watercrafts,…). This study will summarize the possible solutions for the

vessel design. Later on it will be determined which design is the most stable and suitable

for our application.

In later stages there will be a study in which the selected vessels are tested and

compared to one another. This will be determined using a numerical model of a wave

tank simulating ocean waves and a CAD model of the buoys. The motion of several buoys

with different geometries will be tested and compared using this model. This study will

point out the best possible solution in terms of stability within practical limitations.

After a suitable buoy has been chosen an additional study must be made to optimally

design a system that keeps the LIDAR level given the theoretical motion of the craft

resulting from the numerical simulation. A theoretical study of a stabilising mechanism

will provide insights and should enable the reader to design a similar mechanism.

Finally the sea simulations as well as the mechanical simulations are combined to

quantify performance in actual working conditions. At that point an optimal design will

have been attained.

For easy reading, the whole Lidar stabilizing watercraft with all its peripheral

installations will be referred to as ‘the vessel’.


Master thesis – Mechanical Engineering –Study of commercially available hull designs Page 4

2 Study of commercially available hull designs

2.1 General considerations

Despite the specific nature of the vessel it is unfeasible and impractical to create a

custom made hull from the ground up. A commercially available hull, such as the hull

from a watercraft, pontoon or buoy, must be chosen and adapted to its intended purpose

afterwards. Considering there are many commercial watercrafts and installations where

stability is also a primary design feature, because of passenger comfort or necessary

stable operating conditions, there were lots of options to explore.

2.2 Stability

To be able to evaluate a good design and to not be deceived by the manufacturer’s

advertisement, a literature study was done on vessel stability. A short overview is given

in the next paragraphs.

Stability is a measure for the tendency a ship has to return to its upright position when

brought out of balance. If the ship is considered to be in rest or the disturbing forces act

very slowly, it is the static stability that tries to bring the vessel back to its equilibrium

point. The dynamic stability has to be taken into account if the vessel is subject to

sudden changes of the occurring forces. As an example, these can be due to wind or

waves. Both types of stability are very important, but mainly performance in terms of

dynamic stability will tested in the this thesis. Because, for 3E’s applications, the buoy

has to remain very stable when subject to wave forces.

An important concept in ship stability is the metacentre. The metacentre of a vessel is

the intersecting point of the work lines of the upward forces (Archimedes force) in two

different situations where the ship has a slightly different inclination. The centre of

gravity (COG) and the centre of buoyancy (COB) are visualized by the red dots in figure

3. The COB is the geometrical centre of the submerged volume and changes position due

to the different inclination. Wide but shallow or slender but deep hull shapes result in a

high metacentre. Figure 3 is a simple sketch on the construction of the metacentre. The

distance between the COG and the metacentre is known as the metacentric height and is

seen as a measure for initial static stability. In other words, a ship with a larger

metacentric height offers more resistance against overturning. The metacentric height

can be increased by a change in form, resulting in a higher metacentre, or the use of

well-placed ballast, lowering the COG. However, the larger the metacentric height, the

shorter the natural period of hull rolling, the more uncomfortable for the passengers.

Since no passengers will be present on the buoy, this causes no limitations.



Figure 3: Location of metacentre

Previous sections point out that good watercraft stability is obtained by good choice of

the relative position of the COG and the COB and the resulting metacentric height. As

state before, there are different ways to obtain this and they can be divided in a ‘weight

manner’ and a ‘form manner’. The first is due to the correct placement of ballast,

ballasting, while the latter is known as form stability. Both can be combined.

Another distinction is made between stability for the main axis of the vessel. One speaks

of transverse and long stability. However, since ocean waves are not unidirectional, the

writers of this thesis have a preference for axisymmetrical hull shapes.

In the next paragraphs the most promising commercial designs will be described and

discussed.

2.3 Commercial solutions

2.3.1 Catamaran

The well-known catamaran design is used for high speed ferries like the ‘seacat’. This

vessel was specifically designed to cross the channel at high speed with maximum

passenger comfort despite the high currents and rough seas. A lot of stability is achieved

due to the forward movement of the craft because of its hydrodynamic shape. The Lidar

vessel, however, will be stationary so this effect cannot be beneficial.

Metacentre

Waterline

COG

COB



If a catamaran was considered, the so called SWATH type would be better still. This type

of catamaran is pictured in figure 4 and performs better in violent sea conditions.

Because of this, the old fleet of pilot ships in port of Zeebrugge, Belgium, has been

replaced by more versatile SWATH type catamarans which can still operate in wind

conditions up to 10 beaufort because of their stability. Unlike the old ones who could

only operate up to 7 beaufort. One of these new ships can be seen in figure 5.

Figure 4: Conventional catamaran versus SWATH type catamaran

Figure 5: New SWATH type catamaran pilot ship for the port of Zeebrugge [1]



When the catamaran is stationary, it gets its stability due to form stability and almost

none due to ballasting. The catamaran is very performing in terms of static stability. As

stated before, dynamic stability is what will be tested and this is not that great at all for a

catamaran design. Unfortunately it pitches and rolls easily in waves, making it less

attractive.

However, the reason that the catamaran is included in this thesis, is because of its

practicality. Especially in calm seas or lakes. It could be beneficial to retrofit a small

catamaran hull and build a platform upon it to house the measuring equipment. There

have been similar endeavours in the past. Like this scientific research craft: figure 6.

Figure 6: Small catamaran research vessel

Additionally, the catamaran design offers lots of space for the equipment. Not to forget it

would be very light and, since it is designed to be a moving watercraft, very easy to

manoeuvre around. If desired, an outboard motor could be installed and make the vessel

self-propelling when necessary.

The motion of the Lidar is minimised by placing the sources of the movement, the

vessel’s hulls, further apart. The amplitude of the motion is smaller in between the hulls.

For example: A similar phenomenon can be observed in a passenger train. The

passengers sitting in the middle of a wagon experience less movement than the ones

sitting on either side. This is because the middle passengers sit as far from the motion

sources, being the train bogies, as possible. The amplitude of the motion is much smaller

in the middle of the train. This works the same for catamarans as the amplitude of the

motions is much smaller in between the hulls.



Beside bad dynamic stability, there are some more downsides. The catamaran hull will

have to be prepared and retrofitted with metal frames to be able to receive the

necessary installations for the LIDAR such as its on-board power supply and any

mooring hooks or cable attachments. This means that holes will have to be drilled in the

composite hull and metal parts will have to be fastened to it. Fastening metals to

composites is a delicate operation and will require specialized workmanship and

processes. If the fastening is not done properly, the composite could delaminate or

matrix cracks could occur. Eventually the fasteners could shear out because of fatigue

and the frame could detach from the hull and the installation could be lost.

2.3.2 Resinex PEM 58 Catamaran buoy [2]

Since our vessel is not really a moving watercraft, other vessels such as buoys or

mooring pontoons can be considered too as long as they have a stable design.

Figure 7: Stable floating plastic modular buoy for mooring applications [2]



Specifications: PEM43 – PEM58

Manufacturer Resinex

Dimensions 4300x2200mm – 5800x3000mm

Mass 8.85 tonnes – 20 tonnes

Table 1: Specification of Resinex Buoys

“The exceptional stability of the buoy is due to a particular mooring

stabilizing system which Resinex has studied to guarantee the

maintenance of a constant structure even during a 75 – ton mooring

traction.” [2]

“This particular modular system can also be transported and

positioned at a very low cost” [2]

“These ‘monsters’ with the capacity to face the most adverse meteo-

marine conditions without any difficulty” [2]

As pointed out above a catamaran definitely has some benefits. The Italian manufacturer

Resinex implemented these benefits into their buoy design thereby making a new type

of buoy. The manufacturer names these vessels a ‘catamaran’ type buoy. They are

constructed using a metal frame filled with plastic floaters. These floaters do not fill the

entire radius of the buoy, leaving a hollow area in the middle and keeping the cross

section, intersecting with the waterline, smaller than the diameter would suggest.

A great advantage the Resinex buoys offer, is that they are made from modular

components and can be (dis)assembled easily. As a consequence, handling and

transporting them is very practical.

They provide a useful platform to build upon and are purpose built to be anchored to the

seabed. The buoys are designed to remain as stable as possible since they are designed

to let passengers have access to offshore installations if needed. They can be used in

deep ocean water up to 6 km of depth. Which is more than sufficient considering the

depth limitations for windmills.

These buoys are used for mooring ships, but there was at least one case where the buoys

were successfully used to place radio transmitters at sea. Lots of preparations have

already been made to make it easier to install equipment such a micro windmills, solar

panels and perhaps measuring equipment. Also a towing hook is preinstalled. In other

words, this product has already covered a lot of practical issues.



The manufacturer produces two types. The PEM 43 (figure 8) and the PEM 58 (figure 9)

with respective diameters of approximately 4.3 and 5.8 meters. Taking into account the

dimensions of the solar panels and other installations 3E implements on the buoy, the

PEM 58 is most suitable.



Figure 8: Resinex PEM 43 Catamaran buoy. Diameter approximately 4.3m

Figure 9: Resinex PEM 58 catamaran buoy. Diameter approximately 5.8 m



2.3.3 Resinex PEM 58 buoy [2]

In a consultation with 3E, a decision was made to contact the manufacturer of the PEM

buoys, Resinex. Without going in detail the required specifications for a buoy were

clarified to the Resinex engineers. In response a suggestion was made to use their

normal PEM58 Buoy instead of the catamaran model. The buoy offers all the benefits

noted in previous paragraph, but should be even more suitable for 3E’s application.

It looks exactly the same as the buoys displayed in figure 9, but there is a steel

centrepiece instead of the centre being hollow.

2.3.4 Spar buoy

The spar buoy is mentioned because its design is a classical solution of a stable floating

buoy for installing radio equipment.

It is a slender buoy, but with a large mass located deep under the waterline, at the

bottom. Its slenderness makes the cross-section intersecting the water small. Therefore

the response to wave forces is minimized. The mass, on the other hand, acts as a

counterbalance to keep the buoy upright. Both these features combined ensure that this

buoy does not follow the wave movement and make the spar buoy superior in terms of

dynamic stability.

Despite being very stable it also has multiple drawbacks. To be able to provide enough

space for all measuring equipment etcetera, the dimensions would have to be very big.

This and the fact that it was never designed to be transported, make it very unpractical.

Towing a spar buoy is difficult, so it could only reasonably be moved over a long

distance if it was lifted out of the water onto a ship. This means only larger and more

equipped ships could transport the vessel.



Figure 10: Schematic of a typical spar buoy design.

2.4 Conclusion

The conclusion of the hull study is that there is no such thing as ‘the perfect buoy’. For

every practical use a trade-off will have to be made between dynamic stability and

practicality.

The buoy mostly meeting the needs of 3E (section 2.3.3) is the PEM 58 buoy. Not only it

has a proven stability, but due to the modular design it will be easy to handle and

transport. The large, flat top area offers lots of space for the installations and due to the

steel centrepiece their fixation can be realised with conventional techniques such as

welding, bolting,... All of this in combination with an enthusiastic manufacturer as

Resinex can produce great results.

Keep in mind that the Lidar will be suspended in a stabilizing unit. The extra movement

of the Lidar, due to the difference in stability between the spar buoy and the PEM 58,

will be minimised.

In next stages, a model of the current 3E prototype will be used in simulations and the

results will serve as a reference. Afterwards the PEM 58 and the spar buoy will be

subject of the test. The performance of the latter is useful as a measure for dynamic

stability.


Master thesis – Mechanical Engineering –Numerical study Page 14

3 Numerical study

3.1 Preface [3]

Computer models using numerical simulations have increasingly gained significance for

solving practical problems in engineering and science. It offers an inexpensive and fast

alternative to test multiple situations. The correctness is evaluated afterwards by

comparing the numerical results to experiments. Due to a lack of physical experiments

on ocean waves and the undercurrents, the results in this thesis will be compared to

expectations based on theories and literature.

3.2 Numerical simulations in general [3]

The models in this thesis use a combination of grid-based and meshfree numerical

methods.

The grid-based methods are very popular. However, their applications are limited for

many complex problems. These limitations become apparent when modelling free

surfaces, deformable boundaries and extremely large deformations. All common in wave

simulations.

3.2.1 SPH: a meshfree particle method

To be able to deal with these problems, meshfree particle methods (MPM’s) are used. In

particular the smoothed particle hydrodynamics (SPH) method. This technique is

capable of dealing with all previously mentioned challenges. On top, the SPH method is

also the oldest MPM, thus numerous improvements have been implemented. This results

in an accuracy and stability that have reached an acceptable level for practical

engineering applications.

The grid based methods consist of two fundamental frames for describing the physical

governing equations. These are conservation laws for mass, momentum and energy.

The Eulerian description is a first frame and is a spatial description, typically

represented by the finite difference method (FDM). Eulerian grid-based methods are

widely used in computational fluid dynamics (CFD).



The second fundamental frame is a material description named the Lagrangian

description. Mostly represented by the finite element method (FEM). The Lagrangian

methods are very popular for computational solid mechanics (CSM). All the modelling

done in this thesis is based on Lagrangian methods. A Lagrangian grid is fixed to the part

throughout the entire computation and therefore moves with the part as it deforms.

Because of this, the entire time history of all the field variables at a fixed point on the

part can easily be tracked and obtained. For this reason, a Lagrangian method is used for

all parts. The seawater in particular is modelled using a Lagrangian MPM.

This is excluded because the accuracy would be severely affected due to the earlier

mentioned limitations grid based methods impose. A possible option is to rezone the

mesh or re-mesh the problem domain. The rezoning techniques are quite popular for

simulations for impact, penetration, explosion, turbulence flow and fluid-structure

interaction problems. On the other hand, the rezoning techniques can be very time

consuming and material history can be lost.

As mentioned before, the MPM’s can offer an alternative solution. Here the problem

domain is discretized in particles without a fixed connectivity. That is why, in this thesis,

water is modelled using SPH-particles, a meshfree Lagrangian method. Treatment of

large deformations is relatively easy. The most significant advantage SPH especially has

over traditional grid-based numerical methods is its adaptive nature. This adaptability

of SPH is implemented at the very early stage of the field variable approximation. The

latter is performed at each time step based on a current local set of arbitrarily

distributed particles. It is, in fact, due to this adaptive nature, that SPH formulations are

not affected by the randomness of the particle distribution. More on this can be found in

following paragraphs.

Each SPH particle represents a part of the problem domain, with attributes such as mass,

position, momentum and energy concentrated on the mass or geometric centre of this

sub-domain. The key idea of mesh free methods is to provide accurate and stable

numerical solutions for integral equations or partial differential equations (PDE’s) with

all kinds of possible boundary conditions with a set of arbitrarily distributed nodes, the

particles, without using any mesh that provides the connectivity of these nodes.

The SPH method itself was invented originally for the modelling of astrophysical

phenomena. In essence the interaction of stars. It uses an integral representation

method for field function approximation. In the SPH method, this is defined as kernel

approximation and is shown underneath.



This integral is then approximated using particles. This is called particle approximation.

It is done by replacing the integration in the integral representation, of the field function

and its derivatives, with summations over all the corresponding values at the

neighbouring particles in a local domain. This area called the support domain. In this

domain the smoothing function has a non-zero value.

Figure 11: Support domain

Another important concept is the influence domain. The difference between both is

that the latter is the area in which a particle influences others, while the support domain

is an area around a field point. The use of support or influence domain leads to different

approximations: respectively the gather and scatter model. Since the smoothing length

of two particles may not necessarily be the same, a violation may occur as pictured in

figure 12. It may happen that the red particle falling within the influence domain of the

blue particle does not influence the blue particle. Therefore it is possible for the blue

particle to exert a force on the red particle, without the red particle exerting one on the

blue particle. This is an obvious violation of Newton’s Third Law. This fault is overcome

by the use of a mean value of the smoothing length for the two interacting particles. This

mean value becomes the radius of both domains. Therefore the support domain and the

influence domains for an SPH particle are practically the same.



Figure 12: 2D representation of support and influence domains for illustrating possible problems when using

different smoothing lengths.

The particle approximation is performed at every time step and depends on the current

local distribution of the particles. This mechanism grants SPH its adaptive nature. It was

initially developed as a probabilistic MPM, but was modified later on as a deterministic

MPM. This use of particle summations to approximate the integral is, in fact, a key

approximation that makes the SPH method simple without using a background mesh for

numerical integration. In this particle approximation mass and density of the particles

are introduced into the equations and therefore is attractive for hydrodynamic

simulations in which the density is a field variable in the system equations.

In mesh free particle methods each particle can be either directly associated with one

discrete physical object or be generated to represent a part of the continuum problem

domain. The latter applies to the water wave simulations.

3.2.2 Clustering

A common flaw when using SPH for numerical simulation is the occurrence of ‘clustering’. The paragraph explains the clustering phenomenon in a few sentences, since the term will be used in section 3.5.3, 3.5.5.3 and 3.6.3.

1

1

Blue influence domain Red influence domain

Force by blue on red

Support domain of (1,1)



The clustering of SPH particles is the result of a tensile instability. Parts that have an EOS are particularly sensitive to this effect. When compressed, the SPH particles repel each other. This is comparable to repulsive forces between atoms in reality. If the pressure on the SPH particle is negative, however, this can result in an unphysical clumping of the SPH particles due to an instability in the exerted attracting forces. This clumping is defined as ‘clustering’. According to [4], there is a relation between the said instability and the sign of the second derivatives of the SPH interpolating kernel when the particles are under negative pressure. A clear image of the clustering phenomenon can be observed in figure 38.

3.3 LS-Dyna and LS-PrePost

The modelling and simulating of the ocean waves and the subsequent movement of the

buoys is achieved using the LS-Dyna software. LS-Dyna is a software package developed

by Livermore Software Technology Corporation (LSTC). The software is used for

advanced multiphysics simulations by numerous industries such as automotive (figure

13), aerospace and so on.

Figure 13: Crash test [5]

One way to create, import and adjust models is with help of LS-PrePost. In LS-PrePost

the code used by the LS-Dyna Program can be created in a more user friendly way. One

can also type the code manually, however this is only recommended for the more

experienced user.



The specifications (materials, boundary conditions, …) of a model are defined in LS-Dyna

with the use of cards. For example, a material can be defined by the use of the MAT-card.

The MAT-card itself has subtypes such as MAT_ELASTIC, MAT_RIGID,… which represent

material models. When a complete model is generated it can be saved as a file with a ‘.k’

file extension or more simple a ‘k-file’. This k-file, a text file with code containing all the

defined cards, is the input for the LS-Dyna Program. The latter can interpret the cards

and their coherence and run the simulation. Afterwards, the results can be viewed and

interpreted by using the post-processing tools offered in LS-PrePost.

To create a model one usually starts with creating the geometry of the parts that have to

be included in the model. The geometry itself can be generated using the associated

tools in LS-PrePost, but they can also be imported in a STEP or IGES file format. This last

option gives the user the opportunity to make the geometries with CAD-software.

A geometry is made up out of points, edges and planes. When meshing the geometry one

creates a part, represented by a PART card. A part consists of elements (ELEMENT)

while the elements themselves are defined by a group of nodes. This hierarchy is shown

in figure 14. Different types of elements exist. For example, one node can represent an

SPH-element, while four nodes can make up a shell element or eight nodes could define

a solid element. Please remember, almost every object in Dyna is represented by a card.

Figure 14: From geometry to useable LS-Dyna code by meshing

Geometry

Points

Edges

Planes

Part

Elements

Nodes

Created in LS-PrePost or imported out of CAD software

Useable code for LS-Dyna



The PART card needs a reference to at least a material card (MAT) and a section card

(SECTION). The former specifies all the material specifications such as density, Young’s

modulus, Poisson coefficient and so on. While the latter offers the ability to define the

part as a solid, a shell, an SPH particle or a beam. There are more section definitions, but

only those used in this thesis are mentioned. When defining an SPH-part, an equation of

state card (EOS) might also be necessary. For clarity, the structure for a rigid shell part

is given in figure 15 while the corresponding extract of the k-file can be seen in figure 16.

Figure 15: Hierarchical structure used in the LS-Dyna code for a rigid shell part.

Part

Mat

Rigid

Density

Young’s modulus

…

Section

Shell

ElForm

Thickness

…



Figure 16: Extract of k-file

Just as in an experimental wave study the performance of the buoys will be tested in a

wave tank. A wave generator, named ‘the paddle’, will produce the waves. More over the

exact design and dimensions can be found in sections 3.4 and 3.5.

As an example, the working method of wave tank creation is explained brief and to the

point. For parts with a simple geometry it is easier to define the nodes and elements

directly instead of creating a geometry and meshing it. To create the paddle, two planar

elements are constructed. Both elements together can be interpreted as the centre plane

of the paddle. It seems impossible to make a paddle with a rotational axis at the bottom

edge. The software does not allow to select an axis, but places it at the centreline of the

part. For this reason two elements are used instead of one.



Figure 17: Paddle

When adding the SECTION_SHELL card to the part ‘paddle’ a shell thickness has to be

defined. A value of 0.2 means the shell thickness is 20 centimetres. One can think of it as

10 centimetres added to each side of the centre plane. This can be seen in figure 18. Here

the centre plane of the paddle can be seen in top view, represented by the green line.

Finally the MAT_RIGID card is added.

Figure 18: Spacing between the parts and particles

Node

Element

Rotation axis



As discussed in section 3.2, SPH-particles are used to model the water. One way to create

an SPH part in LS-PrePost is by defining a box that contains all SPH-particles. The outer

dimensions of this box have to be specified. Once this is done, the spacing of the

particles, named pitch length, between neighbouring particles in all major directions has

to be determined. It was decided to take the same pitch length in each direction.

Together with the initial, user definable, density this pitch length determines the

particle mass. This mass is fixed during the entire simulation. This in contrast to the

volume and the density of the particles.

The SPH-particles all together can represent a piece of glass, a human being or in this

case seawater. The physical behaviour of the SPH-part is also derived from a material-

and a SECTION-card. When using NULL_MATERIAL, as in this thesis, an EOS_card is

needed as well. In this case EOS_GRUNEISEN. It is very important to fine-tune the

parameters in these card to make sure the modelled water acts and reacts just as real

water. The used values can be found in table 2.

Material card

Density ρ 1000 kg/m3

Viscosity 0.001 m/s2

Section card

CSLH 1.3

Table 2: Material and section card parameters for SPH

Due to the salinity of the seawater the real density is around 1020 kg/m³. Instead of this

value a density of 1000 kg/m3 was chosen, as seen in table 2, to be able to easily

calculate the SPH-particle mass. Smaller particle masses generally give more stable and

more realistic simulation. However, as said before, calculation time is a limiting factor. In

section 3.6.1 a mesh convergence test is done to determine and optimum in calculation

time and representativeness.

A very important card to implement is the CONTACT-card. This makes sure the water

stays in the wave tank, reacts to the paddle movement and keeps buoy afloat. The

particular contact card used is CONTACT_AUTOMATIC_NODES_TO_SURFACE in

combination with CONTROL_CONTACT. The contact gives repelling forces between

nodes of the parts where contact is defined. These forces increase when the nodal

distances decrease.



To avoid very large contact forces at the start of a simulation, one should avoid nodes

penetrating into other parts. This would result in an unphysical behaviour. However, the

SPH-particles do have to be closely packed. The correct method to do so is shown in

figure 18. In this figure the green line is the top view of the centre plane of the paddle

while the red box is the SPH-box. The blue circles in the box represent the SPH-particles.

When using this method in combination with small SPH-particle weights, say 8 kg or

less, contact will not fail. The use of heavier particles will most likely result in a contact

failure. One can use the thickness override options, but this does not guarantee a

satisfying result.

3.4 Water wave mechanics [6]

To be able to develop representative models of realistic sea states an extra study was

done on water wave mechanics. Multiple books and articles ( [7] [6] [3] [8] [9]) have

been studied, but also sea state data on the Thornton Bank provided by 3E and Geo Sea

was inspected thoroughly. An extract of this study can be found in following paragraphs.

Gravity and surface tension tend to maintain a level water surface. Due to forces acting

on the fluid, and counteracting gravity and surface tension, waves are formed. These are

so called wind generated waves and will be simulated in the models. Another category,

the tides, which are the longest known water waves, are the result of the gravitational

attraction of the moon and the sun.

The most important parameters to describe a wave are its wavelength λ0, wave height H

and the wave period T. Other parameters can be determined theoretically from these

quantities. Using figure 19, the wavelength can be defined as the horizontal distance

between two successive wave crests. However, in this thesis, wavelength is represented

by λ0 instead of L. The period T is the time required for two successive crests to pass a

particular point. The speed of the wave, called the celerity C, is defined as C= λ0/T. The

wave amplitude a is H/2. The wave tank dimensions, the boundary conditions of the

paddle will be deduced, and the correctness of the simulations will be checked using

these parameters.

Figure 19: Wave characteristics [6]



A real sea wave is a superposition of a large number of sinusoids moving in different

directions. The use of this linear wave theory makes it possible to simulate the sea in a

number of different simulations followed by a superposition of the results. This has been

shown to be reasonably accurate for some purposes. At first this method was preferred

to simulate the sea in a representative manner. However, due to factors as calculation

time, multiple simulations with changing orientation of the buoys would be very time

consuming. For this reason only one simulation per buoy, and thus no superposition,

will be made. Because only the movement of the buoy in the water is of interest and

waves in deeper water appear to be rather random, this has no effect on the reliability of

the results.

In table 3 one can find an extract of the sea state data as provided by GeoSea.

Measurements of every hour of every day in September, October and November in the

year of 2011 were given. These were taken at the Thornton bank, which is a sandbank in

the North Sea and the location of a wind farm. It goes without saying that this is a very

representative to the working environment of the 3E buoy. To subject the buoys to a

tough test, a selection of only the roughest sea states over the three months was made. It

is this selection that is displayed in table 3. The wave height HM1 gives the mean of the 1

% highest waves measured in a time span of one hour. The last row gives the mean

values of all selected measurements.



Date and time Wave height HM1 Highest wave Wave period

(highest energy)

[cm] [cm] [s]

11.09.2011 (21u00) 253.53 311.40 6.67

11.09.2011 (22u00) 307.17 377.29 6.67

21.09.2011 (18u00) 242.33 297.64 5.88

21.09.2011 (19u00) 262.64 322.59 5.88

07.10.2011 (02u00) 483.01 593.26 7.69

07.10.2011 (03u00) 457.87 562.39 7.69

17.10.2011 (22u00) 191.80 235.59 6.67

17.10.2011 (23u00) 212.48 260.98 6.25

01.11.2011 (03u00) 106.66 131.00 3.57

01.11.2011 (04u00) 111.98 137.54 3.57

01.11.2011 (11u00) 106.74 131.11 4.55

03.11.2011 (16u00) 110.11 135.24 3.85

03.11.2011 (17u00) 110.25 135.42 3.85

04.11.2011 (08u00) 164.08 201.53 4.17

04.11.2011 (09u00) 172.55 211.94 4.35

06.11.2011 (17u00) 265.11 325.63 7.14

06.11.2011 (18u00) 257.45 316.22 6.67

Mean values 224.46 275.69 5.59

Table 3: Sea state date on the Thornton bank

3.5 Wave tank design and dimensions

3.5.1 Basic wave tank dimensions

This wave tank was designed for testing purposes after the example of Joren Pelfrene.

The wave tank dimensions are chosen to model a so called ‘deep water’ wave.

As stated before, the dimensions of the wave tank will also be determined based on the

values of table 1 and relations found in [6].



The authors of this thesis had a meeting with someone from the department of maritime

technologies at the University of Ghent. It was said that 25 metres is a common

wavelength in the North Sea at Zeebrugge. This value will serve to determine the length

of the wave tank. This length has a linear relation with the wavelength. More concretely,

wave tank length should be equal to three times the wave length. The dimensions of the

wave tank will be determined based on a wavelength of 25 metres, although the

wavelength derived from GeoSea will be longer. The wave tank will be 75 meters long in

total. This is done to limit the amount of SPH-particles needed to fill the tank and

consequently reduce calculation time. A more detailed overview follows in the next

paragraphs.

The buoy will be placed in deep water, so the simulations should be representative for

deep water conditions. ‘Deep water’ is a relative concept. In [6], a relation between the

tank depth h and the wave length λ0 is found for deep water waves. Here it was

proposed that the wavelength of a deep water wave expressed relatively to the tank

depth is:

λ0: Wavelength of wave

h: Tank depth

When using 25 metres for λ0, a lower value to limit tank dimensions, it becomes:

When substituting twenty five meters for λ0 the tank depth h of the wave tank becomes

16 meters. Again, the only reason the value of 25 metres is used for λ0 to make sure the

wave tank is not excessively large.



To extract the real wavelength out of the sea state data by GeoSea a relation between

wave period and wavelength is needed. This was found on the website of the Flemish

Hydrography [9] and can be written as follows.

There is a large dispersion for the occurring wave periods and also the water depth at

the Thornton bank varies between 12 and 27 meters. For this reason there will also be a

large variation in discernible wavelengths. When substituting the mean value of 5.59

seconds, as found with the GeoSea data, as the wave period and taking h as the average

depth at the Thornton bank, which mathematically is 19.5 meters, in the formula above,

the wavelength is 48.27 meters.

The generated waves in the simulations should have this value for the wavelength. The

boundary conditions for the paddle will be set to do so.

Otherwise, when using a value of 25 metres for the wavelength and the tank depth h

of 16 a value of the wave period T of 4.003 seconds was calculated. This value fits right

in the wave data provided by GeoSea. This proves once more that the chosen value to

determine the depth and length of the tank is also pretty accurate.



As a summary table 4 gives some of the design parameters.

Wavelength to determine tank dimensions 25 m

Wave tank depth 16 m

Wave tank length 75 m

Target wavelength of the generated waves 48.27 m

Target wave period 5.594 s

Target average wave height 224.46 m

Target largest wave height 275.69 m

Table 4: Summary the design parameters for basic wave tank

3.5.2 Boundary conditions of the paddle

In the book [6], it is said that the flap type wave maker is the more efficient for deep

water waves. This power efficiency is the main reason the flap type wave generator is so

popular in experimental wave studies. A picture of a real wave tank can be seen in figure

20, while a schematic representation of a flap type wave maker can be seen in figure 21.

The displacement S of the wave generator, which can be seen in figure 21, is known as

the stroke.

Figure 20: Wave Tank CSI Chicago [10]



Figure 21: Flap type wave maker

The water displaced by the wave maker should be equal to the crest volume of the

propagating wave form. The volume of a wave crest can be calculated like this:

‘k’, in the formula above, is known as the wave number. This is calculated as λ0/(2∙π).

The volume displaced by the paddle, with h the water depth and S the stroke of the

paddle, is:

Which makes, for a flap type wave generator:

h

S

S: Paddle stroke

h: tank depth

Flap type wave maker

or paddle



This simple correlation for the ratio of wave height to stroke is accurate only for low

values of .

When extracting some values out of the GeoSea measurements the stroke of the wave

generator S can be calculated. As previously mentioned 48.47 meters will be used as a

typical wavelength λ0 in the North Sea and 2.757 meters as target maximum wave

height. The depth of the wave tank h was chosen to be 16 meters in section 3.4.

However for values of greater than two, this simple correlation is not that accurate.

In this case equals 2.07408. So another correlation will be used for reasons of

accuracy. The correlation suggested for k∙h greater than 2 becomes, with wave height H

and stroke S, according to [6] is:

When substituting the mentioned values the stroke S can be calculated and becomes

S=2.573m

This value will initially be used as the stroke of the wave maker. This is done by setting

an appropriate value for the amplitude of the sinusoidal function used as a boundary

condition in LS-Dyna. Further fine-tuning will be done using the output of the simulation

as feedback.

The sinusoidal curve is defined in DEFINE_CURVE and is used as load curve (LC) in the

PRESCRIBED_MOTION_RIGID card.



The used sine function is:

The value of 1.123 for the angular speed ω is a characteristic value for North Sea waves.

This value is attained with the use of the GeoSea data. The mean value for the period at

rougher sea conditions, extracted out of table 3 is 5.594 seconds.

The amplitude A is set to 0.1, but will be fine-tuned using the scale factor SF in the

PRESCRIBED_MOTION_RIGID card. In the final model this value is set to 0.895. The

amplitude A itself yields no displacement in meters, but the maximum deflection angle

in radians. With the rotational axis set at the level of the seabed the used stroke S’ is

As can be seen the value of S’ is somewhat larger than the theoretical stroke S of 2.573

metres, found with the theoretical formulations. However, the used stroke S’ gives

waves in best agreement to the sea state data. In addition, a more violent sea is even

better to test the performance of the buoys.

3.5.3 Boundary conditions of the wave tank

A big problem when simulating ocean waves, are the limited dimensions of the wave

tank. In practice, the sea can be regarded as an infinitely big domain, but due to our

restricted computer calculation power the dimensions in the numerical simulation are

very small in the relative sense. Because of this, waves will ‘see’ boundaries and interact

with them. The result is that the waves will reflect on the boundaries. The interest of the

simulations lies only in the movement of the buoys so the reflections themselves would

not be dramatic. However, because the reflections might cause a standing wave instead

of a travelling wave, they should be minimized.

An infinite domain can be simulated by taking special measures to absorb wave energy

at the boundaries. There are different ways to implement a wave energy absorber. Some

suggestions found in literature and some personal ideas of the writers of this thesis are

discussed below.



One of them, as discussed by Milgram [7], is based on the flap type wave generator. The

idea is that the paddle moves in such a way that it is invisible to the incident wave. So to

generate a wave, the fluid is pushed forward by the paddle and thus making a crest. In

this case, an absorbing paddle moves backwards when the wave arrives, making it

appear as if the wave has passed through. To make it an efficient absorber, the paddle

motion has to be just right, making it insufficiently robust for our purposes.

Another technique, used in Boussinesq wave modelling [7], is the use of a sponge layer.

This is a more user friendly manner to prevent reflection and prevent a standing wave.

The sponge layer is an extra layer of SPH particles at the boundary opposite to the wave

maker, but with added artificial damping. The damping is applied using the card

*DAMPING_PART_MASS. The damping coefficient has to be determined by trial and

error and will differ from case to case. It has been proven that the values of the damping

coefficients increase with increasing depth. The sponge layer is an extra part of SPH

particles with the same particle spacing as for the particles representing the water. A

sponge layer that is one wavelength λ0 long in the wave direction should be sufficient.

Just as for the sea water NULL-material is used in combination with the GRUNEISEN

equation of state (EOS). In the EOS, the value for the speed of sound c is set to 100 m/s.

This is done to reduce the calculation time. The sponge layer is visualized with a red

colour in figure 22. A Dyna model can be observed in figure 23.

Figure 22: Wave tank design with sponge layer from [7]

Figure 23: Model with 3E prototype, cable and sponge layer

Sponge layer



Due to the large dimensions of the wave tank, the use of a sponge layer would increase

the amount of nodes with about 33%. The consequence is an even longer calculation

time. Which is unsurpassable considering the limited calculation power.

For this reason an SPH_SYMMERTY_PLANE is used. If this is implemented, the model

behaves as though there is an imaginary mirror image of the wave tank against the right

side. LS-Dyna does not mirror the entire wave tank, but only the three rows of SPH

closest to the SPH symmetry plane. At the symmetry plane it seems as if two waves with

the same amplitude, but different propagation directions meet. Reflection is not fully

eliminated, but calculation time is greatly reduced in comparison to the use of a sponge

layer.

As a proof of the performance of the SPH_SYMMETRY_PLANE a sequence of screenshots

is shown in figure 24, visualizing the travelling wave. In other words, the use of an

SPH_SYMMETRIE_PLANE was successful.

Figure 24: Travelling wave in Dyna model

However, for longer simulations it can be seen that a travelling wave evolves into a

standing wave. This phenomenon has only been observed for a 37.5 m long wave tank,

though. For the termination times set, no standing wave is formed for the 75 m long

wave tank.

An SPH symmetry plane was also chosen at the bottom of the wave tank instead of a

rigid wall, which is used at the sides of the tank. Clustering is reduced heavily because of

this. In LS-Dyna symmetry planes are used to model a continuous domain, so a

symmetry plane on the bottom makes the water behave like it would in a deeper tank.



3.5.4 Summary: Basic wave tank

A schematic representation of the modelled basic wave tank is shown as a summary in

figure 25:

Figure 25: Boundaries and dimensions

The final model of the wave tank has:

Flap type wave generator, known as the paddle, on the left side

Representative domain with a length of three wavelengths where wave

behaviour can be observed

At the side opposite to the wave generator an SPH-symmetry plane is used to

prevent the generation of a standing wave.

The water is modelled with SPH. This technique and the materials were discussed

earlier.

The tank width is chosen to be 10 meters. This is more than sufficient to make sure the

buoy will not hit the walls.

SPH-symmetry plane (Back)

SPH- symmetry plane

(Bottom)

Rigid wall (Sides)

3∙λ0 = 75m

10m Water depth = 16m

Wave generator

(Moving)



3.5.5 Friction interface

3.5.5.1 Undercurrent modelling with linear water duct and pistons

Now that the tank and the wave generator have been created, the model can be

expanded to incorporate the effects of the undercurrents typically encountered in

oceans. The speed of this undercurrent can rise op to 2,5 meters per second [8]. A

current speed of 1,5 meters per second is believed to be representative.

This undercurrent could be modelled using a moving stream of SPH particles. However,

LS-Dyna supports neither particle generators nor destructors. However, a flow of

particles could be generated by using a pseudo generator and a pseudo destructor. How

this system was implemented, is explained below.

Figure 26: Scheme of undercurrent duct

The wave tank sits on top of a narrow water duct. The water in this duct is forced to flow

by pistons pushing it along. The translational speed of the pistons determine the speed

of the undercurrent. The duct is much longer than the wave tank because the duct

volume before and after the wave tank serves as a particle buffer . The minimal buffer

length is easily calculated:

Minimal buffer length = termination time ∙ current speed

This setup understandably succeeds in creating an underwater flow and creating a

friction interface with the bottom particles of the wave tank. Obvious disadvantages are

that a lot more particles are needed and the geometry is more complicated.

Accumulation of outflowing particles, unable to enter the outflux buffer, was also an

issue.



3.5.5.2 Undercurrent modelling by closed loop water circuit

To escape the limitations of the buffer size on the termination time a closed loop SPH

particle circuit was considered. A geometry with a closed loop circuit was modelled and

is pictured in figure 27.

Figure 27: Undercurrent circuit model

The current circulates in the water duct on the bottom of the wave tank (red part). The

undercurrent is propelled by a rotor (grey part) that keeps the water circulating. This

model has indeed the advantage that very long buffers are no longer needed but the

geometry and contact definitions are so complex that this idea was abandoned.

3.5.5.3 Friction interface with moving plate

One could think that modelling of the undercurrent is not about the undercurrent itself,

but about the friction interface between the upper body of water, moving under

influence of the wind and exhibiting the wave motion, and the lower layer of water

flowing at the undercurrent speed. Even more important is the effect of the

undercurrent on the mooring cable . A very efficient way to model this is the use of a

moving plate which slides against the bottom particles. The translation itself was done

with the use of the PRESCRIBED_MOTION_RIGID card combined with a unity vector as

LC and VAD set to tree.



The first model that was made to realize this friction effect used protrusions. A

screenshot can be seen in figure 28. Due to the compression of particles between the

paddle and the closest lump, very strange phenomena could be observed.

Figure 28: Lumped plate friction model

Another attempt to avoid these phenomena was to use a plate with friction. This is

pictured in figure 29. The friction was set using the DEFINE_FRICTION card and making

small changes for the associated parameters in the contact definitions. The plate would

represent the interference of an undercurrent layer and a top layer moving at a different

speed. Friction added to this plate is in agreement with the relative speed of the

undercurrent that is desired to be modelled. The plate had the desired effect, but due to

rapid clustering (section 3.2) it was inappropriate to use in longer simulations.

Figure 29: Friction plate model



3.5.5.4 Simulating undercurrent by applying resultant forces on the mooring

cable

Eventually a concept was thought out to impose the effect of the undercurrent without

disturbing the SPH particles. Instead of trying to model the undercurrent itself, the

resulting forces on the mooring cable could be applied. This can be done using the

LOAD_BEAM_ELEMENT card since there is only one beam element used to represent the

mooring cable. This option is the most feasible, but due to a lack of time it will not be

implemented. The implementation itself is not the problem tough. A practiced Dyna user

can incorporate the needed card in a few minutes and so it has been done. Again the

calculation time was the killjoy. The final model has a buoy anchored with a mooring

cable, without resultant undercurrent forces. With the use of a supercomputer owned by

the University of Ghent it still takes about a thousand hours to run the simulation. For

some unexplainable reason the cable has an immense effect on calculation time. Adding

forces to the cable would only worsen the this influence.

Figure 30: Buoy model with mooring cable and two forces: downwards and sideways

Buoy



3.5.6 Additional cards

3.5.6.1 INITIAL_STRESS_DEPTH

Another card that was tried is the INITIAL_STRESS_DEPTH card. This card initializes

solid element stresses where stress is a function of depth. The card was added hoping it

would not only work on solids, but also set the hydrostatic pressure before the

simulation starts.

For heavy particles, in the early stages of the research, strange effects were observed

due to the settling of hydrostatic pressure and the effects on the particle spacing

between the bottom SPH-particles. In essence, it was a transient phenomenon.

Initially all SPH-particles are arranged in a grid with equal spacing in all major

directions. This can be seen in figure 31. At the start of the simulation the hydrostatic

pressure is set and the particle spacing changes, while particle mass is fixed. Therefore

volumes and, as a consequence, the reaction forces of the contact change. Because of the

large mass of the SPH particles in early simulations this entailed unphysical effects.

Later on, this transient phenomenon was minimized as detailed models were used with

heavily reduced particle weights. In retrospect this card had no or just a minimal effect.

Figure 31: Initial grid of the SPH-particles

3.5.6.2 LOAD cards

An absolute necessity is the inclusion of gravity in the simulation. Gravity is not present

as standard, but with the use of LOAD_BODY_Z and the correct LC this can easily be

solved. This card affects every part in the model.



To simulate the launch of the buoy in the water as if executed with a crane an additional

card is used. This is LOAD_BODY_GENERALIZED_SET_PART en works only on the buoy.

The load curve is defined as piecewise function and yields the following features.

The first 2 seconds of the simulation, the buoy hovers above the water. This to make

sure the buoy does not interact with the water when the transient phenomenon of the

SPH is still in progress. Gravity is completely counteracted.

In the next stage the buoy is lowered slowly into the water. This is implemented to make

sure the buoy does not slam too hard into the water and the SPH particles do not get

compressed too much. Gravity is counteracted up to 75%. More on this in section 3.8.3.

After 7 seconds from the start, the upward forces defined by the

LOAD_BODY_GENERALIZED_SET_PART card are all cancelled.

3.6 Model verification

3.6.1 Mesh convergence

It is important that the modelled water has a steady behaviour and behaves just as

actual water. Apart from using the correct values in the MAT- and SECTION-card and

implementing the appropriate EOS, as mentioned before, the convergence of the mesh

should also be checked.

As explained before, large pitch lengths result in high particle masses. In turn this can

result in unphysical behaviour. The behaviour of the SPH-water in terms of stability,

contact, wave period, wave height and wavelength are checked for increasingly smaller

pitch lengths until convergence occurs and a stable simulation is guaranteed.

The pitch lengths were chosen in a way the associated particle masses were 1000 kg,

500 kg, 250 kg, 100 kg, 50 kg, 25 kg, 12 kg ,10 kg and 8 kg. Even smaller particle mass

simulations were executed, up to 1 kg. However, the long simulation times made this

very unpractical.

The measurements are made using the post processing tools in LS-PrePost. Nodal time

history of the z-displacement is used to check the wave height and the wave period. The

selected nodes are all in the vicinity of where the buoy would be placed. The latter is not

yet included in these simulations. Wavelength is measured by selecting two nodes at the

crest of two consecutive waves. All measurements were done seven times to be able to

average them out.



3.6.1.1 1000 kg particles

A huge benefit of working with heavy particles is that the required computation power

and calculation time are very small. A ninety second simulation of the sea can run in

under ten minutes. Nevertheless, this is also the only benefit. Due to the immense mass

of the ‘water droplets’ contact failure is inevitable. In figure 32 failing contact is pictured.

The water goes through the paddle and splashes up a rigid wall, left to the paddle. The,

non-visible, rigid wall is included in the model to ensure the SPH-particles stay enclosed

in a relatively small volume. As can be seen in following subsections, this contact

problem fades when particle mass decreases while contact definitions remain

unchanged.

Figure 32: Failing contact

Rigid wall

Contact failure



Measurement [#] Period Wave height Wavelength

[-] [s] [m] [m]

1 5.89 1.47 46.07

2 6.42 2.44 56.56

3 5.40 1.57 41.74

4 5.30 1.64 55.77

5 6.10 0.92 47.03

6 5.59 2.33 22.85

7 5.71 1.59 50.23

average 5.77 1.71 45.75

max 2.44 56.56

Standard deviation 0.40 0.52 11.40

Table 5: Table of wave measurements in Dyna models for 1000 kg particles

3.6.1.2 Conclusions

It would be a waste of paper to include all tables, for all listed particle masses, in this

thesis. Only relevant conclusions have been documented.

It can be concluded that simulations run more stable when particle weight is decreased.

The amount of particles leaking out of the wave tank decreased and for 25 kg particles,

this was negligible compared to the 1000kg simulations. This can be seen in figure 33.

Figure 33: Wave tanks with 25kg (upper) and 1000kg(lower) particles.



This leakage and the settling of the hydrostatic pressure at time step 0 have a great

effect on the water level. For the 1000 kg particles, the sea level was 2 metres lower than

intended. This poses a problem, because the buoys would be lowered into the water as if

performed by a crane. The first two seconds of the simulation the buoy hangs steady

above the water. Between two and seven seconds the buoy drops slowly into the water.

This is achieved by adding an extra force on the part set ‘buoy’, which counteracts

gravity. If the sea level is lower than intended, the buoy will not be in place when the

extra force is no longer present and the buoy falls in at full speed.

As the pitch length decreased this effect on the sea level decreased as well, as can be

seen in figure 34. The sea level is appointed with the red line.

Figure 34: Sea level for 1000 kg(upper) and 25 kg(lower) particles

Sea level at -2m

Sea level at -0.5m



The average wavelength, period and wave height however do not really change for

decreasing particle weights. One thing that can be seen is that the deviation between the

different measurements decreases and for small particle masses each wave is similar.

This can be seen in table 6, included underneath, by noting the decrease of standard

deviation (stdev) for smaller particle weights.

1000 kg

Measurement period wave height wavelength

[s] [m] [m]

1 5.89 1.47 46.07

2 6.42 2.44 56.56

3 5.40 1.57 41.74

4 5.30 1.64 55.77

5 6.10 0.92 47.03

6 5.59 2.33 22.85

7 5.71 1.59 50.23

average 5.77 1.71 45.75

max 2.44 56.56

stdev 0.40 0.52 11.40

100 kg

Measurement period wave height wavelength

[s] [m] [m]

1 5.50 3.93 47.68

2 5.70 4.30 48.81

3 5.50 4.43 48.80

4 5.70 4.50 47.08

5 5.60 4.21 48.59

6 5.80 4.70 47.81

7 5.70 4.69 46.41

average 5.64 4.39 47.88

max 4.70 48.81

stdev 0.11 0.27 0.92

Table 6: wave measurements in Dyna models for 1000 kg and 100kg particles



Finally, the chosen pitch length was a trade of between detail and calculation time. An

optimum was found for 8 kg particles. As said before, simulations with 1 kg particles had

very promising results, but were very unpractical as well for file size as for calculation

time.

3.6.2 Sea state accuracy

Now a stable model has been established and particle mass is set to 8 kg, it is important

to check whether or not our SPH-modelled sea is representative for a real sea state.

In section 3.4 sea state data provided by GeoSea was combined with theoretical

relations extracted out of [6]to quantify what would be a common sea state to simulate.

For the reader’s convenience the conclusion is summarised in table 7.

Wave period T 5.594 s

Wave height HM1 224.46 cm

Maximum wave height 275.69 cm

Wavelength λ0 48.27 m

Table 7: Experimental wave data by GeoSea

The accuracy of the sea model will be verified by comparing these theoretical values to

the measured values. This is achieved using the post processing tools in LS-PrePost.

Using the nodal time history of the z-displacement, the graphs of figure 35 and figure 36

were made. The graphs are included with additional information in the following

paragraphs. Only the first 25 seconds of a 90 second simulation are pictured to clarify

the graphs. However, the transient phenomenon has already damped out, so these

results are representative for the entire simulation.

The first parameter that was checked is the wave period T. The calculated average value

was 5.594 seconds. The mathematical average of the pictured wave periods is 5.6

seconds and thus in very good agreement with the theoretical value.



Figure 35: Wave period; Z-displacement (in meters) versus time (in seconds)

Another very important parameter is wave height. The measurements were done using

the trace function in LS-PrePost. The wave height was measured as in figure 36.

Figure 36: Wave height; Z-displacement (in metres) versus the time (in seconds)

According to the wave data provided by GeoSea a mean value of the top 1 % highest

waves is 224.46 centimetres while mean value of the recorded highest waves is 275.69

centimetres. The average wave height in the simulation is 244.6 centimetres, while the

highest is 276.8 centimetres. In section 3.5 the paddle stroke S was determined using

theoretical formulations out of [6]. The stroke S was said to be 2.573 metres. As said, in

the simulations a higher value was used and this is also the one used for the wave

generation represented by figure 36.

Wave height

5.9 s 5.3 s



The desired wavelength λ0 to simulate was 48.27 metres, as seen in figure 37. As said

before the wave tank itself is 75 metres long now but if the ‘rule of thumb’ (length is tree

wavelengths) was followed it had to be twice as long. This would result in a tank of

about 150 metres in length and an extremely high amount of SPH particles. To limit the

calculation time a length of 75 metres was chosen. However the wave generator should

still produce waves with a wavelength of 48.27 metres. This was checked by subtracting

the x-position of two selected nodes at the crest of two adjacent waves. This is pictured

in figure 37. The average wavelength that was measured was 48.4746 metres.

Figure 37: Measured wavelength

3.6.3 Further model checks

3.6.3.1 Buoyancy check

Another very important property to check, is the buoyancy. This is done by adding a

solid buoy with simple geometry to the simulations. By varying the density of this solid

buoy and visually checking whether or not it floats, sinks or, with a density equal to this

of the water, stays at a giving depth the model was approved. A screenshot of a

simulation can be seen in figure 38. Please note that in order to be able to repeatedly do

these tests a smaller wave tank was used. This to suppress calculation time. This subject

will be handled later on in detail.

≈48.4746 metres



Figure 38: Buoyancy check

3.6.3.2 Breaking wave check

Another way to check if our SPH-modelled water behaves as real water is to simulate

breaking waves. In order to do so the motion of the wave generating paddle is enlarged.

By raising the scale factor in the card BOUNDARY_PRESCRIBED_MOTION_RIGID the

paddle will have a larger amplitude and the generated waves will become increasingly

violent. As can be seen in figure 39 LS-Dyna can handle simulation of breaking waves.

Also a splash-up can be seen in the screenshot at the right.

Figure 39: Screenshots of breaking waves

Clustering



3.6.3.3 Dam break check

As a final verification of the model, a dam break test was performed. The results will not

be discussed in depth, since a great deal on this topic can be found in [7].

In figure 40 the evolution of the water level is visualised for the dam break tests. The

results on the left are those extracted from the performed dam break test. The volume of

the water held by the dam before breaking was 6000m3, about 12000 times larger than

the one in the test on the right. This explains the difference of one order of magnitude on

the vertical axes. Please note the similarity of the curve on the left with the experimental

data, visualised by the red dashed line on the right in figure 40. This again confirms the

accuracy of the model.

Figure 40:- Z-coordinate of water level for LS-Dyna Dam Break test (left) and experimental and Joren’s data (right).

Right picture from [7]

Screen shots of the test are pictured in figure 41. The huge volume of water in the dam at

t=0 explains the violent reaction and thus the huge splash against the left wall.



1 2

3 4

5 6

7 8

Figure 41: Series of screenshots of the executed dam break test

3.7 Modelling the buoys for LS-Dyna

From the initial phase of the thesis three buoys were selected for testing. As a reference,

the first working prototype by 3E would be tested. The others were the PEM-58 buoy by

RESINEX and an a spar buoy. The last one because of its proven stability and the PEM

because of its modular design which makes it perfect for transportation. The final choice

will be a trade-off between the performance in terms of dynamic stability in the wave

tank and practicality. Keep in mind that not the entire movement of the buoy will be

transferred onto the LIDAR because of the extra stabilizing system which will come on

top of the buoy. The latter will be discussed in chapter 4.



In a first step detailed drawings were made in CAD-software. Materials, shell

thicknesses, etc. were defined to be able to locate the centre of gravity and the exact

mass of the different parts. 3E has also provided CAD-drawings of their current design.

Based on this, platforms for the buoys were drawn. These detailed 3D-drawings could be

imported in LS-Dyna.

However, to reduce calculation time and to be able to run multiple simulations, a

simplified design was made. A visual representation of this design can be seen in figure

42. This simplified design is used to debug and fine-tune the models further. Special

consideration was given to make sure these simplified models would be good

representatives for the real buoys. The LIDAR and its stabilizing structure are

represented by one part. This part has the combined weight, and the centre of gravity

was chosen to be at approximate the same location, as the combination LIDAR and

frame. The battery box has remained unchanged in terms of dimensions and weight.

Figure 42: Detailed CAD drawing (left) and simplified mesh (right) for the PEM58 buoy

Of course, when buoy-water interaction was brought to an appropriate level, more

detailed versions of the buoys were created. This to be able to simulate the movement of

the whole more accurately. The gimbals are now introduced as well as the solar panels.

The frames and platforms are built using I-beams. The platform where all installations

are fixed upon is based on the current design by 3E, but its base is now a square instead

of the original rectangular form. This fits the axisymmetrical shape of the spar buoy and,

in some ways, of the PEM58, better. A CAD-drawing can be seen in figure 43.



Figure 43: Platform drawn with CAD

The more detailed and meshed designs for the 3E buoy, PEM 58 and spar buoy

respectively, can be seen in the figures below. The design is made based on a

combination of CAD-files provided by 3E, photographs taken on a visit to the

construction area of the 3E buoy and data of weights of the different parts. Some

photographs are shown in figure 44.

Figure 44: Detailed 3E buoy Dyna model



Figure 45: Detailed PEM58 buoy Dyna model

Figure 46: Detailed spar buoy Dyna model



Figure 47: 3E working prototype

The buoyancy of the modelled buoys has been checked in a wave tank of 10 deep, 10

meters wide and 10 meters long. Fine-tuning was necessary because information on

shell thicknesses of the buoy and inner structures were not available on the internet and

manufacturers keep this information classified. Standard a shell thickness of two

centimetres was chosen as standard and good buoyancy was guaranteed with small

changes in the density of the used materials.

Figure 48: Buoyancy check



3.8 Calculation time

LS-Dyna and its PrePost are undoubtedly very powerful programs. The ability to model

a real sea-situation as truthful as possible and the accuracy of the simulations are not

limited by the program itself, but by the computer used to run it. When using more

detailed models, calculation time easily rises up to unfeasible values. If changes were

made to the model, a part in it or a value in one of the cards, it literally takes hours or

even days to see which effect the changes had and whether or not it was a good idea to

make them in the first place. This makes the optimisation a lengthy and frustrating task.

Again, this explains why in some of the model checks above smaller wave tanks and

simplified buoy-designs were used.

To limit the calculation time to a practical value a trade-off was made between the

calculation time itself and the model detail. To give an example, the simulation of most of

the models discussed in this thesis cannot be done on a ‘normal’ laptop (Intel i7

processor and 8GB RAM), where the RAM is the limiting factor. When a more detailed

simulation is run, LS-Dyna demands up to 70 GB of RAM. The calculation times noted in

the following paragraphs are these when using a high performance workstation owned

by University Of Ghent (Intel Xeon processor and 24GB RAM).

3.8.1 Material choice versus calculation time

An easy way to reduce calculation time is to use Null-material in combination with a

Gruneisen-equation of state instead of using the fluid-elastic-fluid-material. The latter

does not require an equation of state. To reduce calculation time the speed of sound,

which has to be specified in the Gruneisen-EOS, is set to a lower value than normal. It

was said, as a rule of thumb, speed of sound can be reduced up to 10% of the actual

value. Even though a value of 100m/s is even less, it works great and its accuracy has

been proven in earlier sections and in [7]. In this way the simulations run significantly

faster while staying representative. The fluid-elastic-fluid material also offers the

opportunity to change the value for the speed of sound, although in a more impractical

way. Null-material offers multiple other advantages too. One of them being a better

behaviour for compressibility. Other ideas to reduce calculation time are discussed

below.

The parts of the buoys are all modelled as rigid. This means that mass and mass

distribution is equal to reality, but the parts cannot deform. This rigidness offers a huge

benefit in calculation time over deformable materials.



3.8.2 Wave tank design versus calculation time

A first idea was to make a water tank with the following dimensions (see table 8)

Knowing that the use of a small pitch length for the SPH-particles for the whole domain

would result in an insanely high amount of nodes it was chosen to split the domain in

two. One section would be a fine top layer with a more coarse layer underneath, named

the depth layer. This can be seen in figure 49. Because of the difference in weight the

more heavy depth layer would always stay on the bottom and intermixing between the

two layers would be negligible. Or so it was assumed.

Dimensions of original model

Width 20 m

Length 75 m

Depth 66 m

Pitch length between SPH

Top layer 0.25 m

Depth layer 1 m

Table 8: Original dimensions (deep sea)

Figure 49: Two layer model

Top layer

Depth layer



Multiple approaches were tested. One of them was to implement the top and depth layer

as two different parts as seen in figure 50. The two parts would have the same material-

and section-card and the same equation of state. The only difference, besides the part

number of course would be the spacing (pitch length) between the SPH-particles which

make up the part. Many models and a thorough inspection of the resulting simulations

later the conclusion could be made that this was not possible. Due to the difference in

pitch length and weight of the particles very unphysical behaviour was observed.

Contact, even though this does not have to be defined explicitly between two SPH-parts,

kept on failing.

Another problem was a transient phenomenon due to the hydrostatic pressure which is

set on time equals 0+ seconds. The bottom particles will be pushed closer together

under influence of the weight of the other particles resting on top of them. The result is a

drop of the water level, as discussed earlier. When one keeps in mind that the depth

layer had a pitch length of one meter in every direction it is easily found that for each

cubic meter there is exactly one SPH-particle. With the density of water, being

, this means that every ‘droplet of water’ weighs one ton. The result is that

the transient phenomenon is actually very violent. After the drop the particles are more

closely packed than they should be. Therefore there are great repulsing forces due to the

contact launching the top layer multiple meters above water level. A card called

INITIAL_STRESS_DEPTH was used, hoping it would set the hydrostatic pressure before

the first time step. However, the effect of this card is negligible as discussed earlier.

Figure 50: Dyna two layer model: Two layers, two parts

Instead of implementing the two layers as two different parts they could also be placed

under the same part number. A screenshot of such a model is demonstrated in figure 51.

Contact between paddle and SPH or wave tank and SPH is defined by using node sets

representing the distinctive layers. The results were unsatisfying and roughly the same

as those of previous paragraph.



Figure 51: Dyna two layer model: Two layers, one part

A smaller wave tank was designed because it is apparently impossible to work with a

fine top layer and a coarse bottom layer and because filling the whole tank with the

small SPH-droplets would result in millions and millions of nodes. To be able to run a

stable simulation the weight of the SPH-particles should be fairly low. In section 3.6.1, 8

kg was chosen as an optimum. Even the powerful desktop could not run this simulation,

but the UGent clustered super computer (cluster) provided the necessary computational

power. Eventually it was chosen to set the dimensions of the wave tank to be

representative for a sea state at the Thornthon bank. The work method in order to

determine the wave tank dimensions was already been shown in paragraph 3.5.1. The

90 second simulations for the final model takes an estimated 1000 hours to complete on

the cluster. In this model the buoy and the mooring cable is, of course, included.

3.8.3 SPH particle mass versus calculation time

To be able to check the effect of different cards or values in the LS Dyna input files it is

necessary to run multiple simulations. A normal reflex is to make a simple file, in this

case a file with a coarse sea, so the simulation does not take long.

At a first attempt the pitch length for the SPH particles was set to be one metre. As

mentioned before these results in modelled water droplets with a fixed weight of one

tonne. The whole simulation can run in under 5 minutes. Nevertheless, it has already

been mentioned before that the benefit of low calculation time is heavily tempered by

the instabilities in the models.



It has been shown that particle weight has to be decreased to assure a stable situation.

When adjusting the pitch length with a quarter, up to 0.25 metres, the particle weight

decreases to 15.625 kg. On the other hand, simulation time rises from a couple of

minutes to an approximate 16 hours. Contact can be fine-tuned relatively easy when

using the slave surface thickness override (SST) in the contact card. Leakage is

eliminated and the hoped-for waves are attained. The transient phenomenon due to the

setting of the hydrostatic pressure is reduced to an acceptable level, tough still present.

To deal with this, the buoy hovers above the water level until the sea has reached its

steady state condition. This is done by adding a upward force to the buoy, which

counteracts gravity for the first two seconds. However, when the buoy slowly drops in

after two second, another unwanted phenomenon presents itself. The density of the SPH

particles decreases significantly. Due to this drop, and keeping in mind the constant

mass of the particles, the individual SPH volume increases. The particles are too closely

packed in the wave tank and the repulsing forces of the contact become very high. The

effect is that particles get launched out of the tank, again.

The only solution is to decrease the particle weight once more. When using a particle

mass of one kg the wave tank contains seven and a half million particles and the memory

demand is too high to run on an ordinary desktop (octacore with 24 GB of ram) and use

of the UGent cluster is needed. The simulations with one kg particles were set on hold,

because of the immense demand for RAM. Even the supercomputer could not handle

these files. For the small period these simulation have ran, it was noted they were very

stable and the interaction with the buoy was just as hoped. This explains the settlement

for the use of 8 kg particles that was made in paragraph 3.6.1. It offers great detail for

reasonable calculation time.

3.8.4 Mooring cable versus calculation time

The buoy should be moored to the seabed. In theory two nodes are enough to be able to

define the cable. However, as explained before, to simulate the effects of an

undercurrent we defined more beam elements to model the cable behaviour with more

detail and to be able to impose ‘undercurrent forces’ on these beam elements. Two

effects will be taken into account. The first is a constant force, representing a drag force.

The second will be a sudden pull to represent cable snagging.

The cable material is CABLE_DISCRETE_BEAM and also a BEAM-section is used. Using

these a steel cable is modelled with a diameter of 0.01 m.

To investigate the influence of adding a cable to our model on the calculation time tree

easy models were created. A first model only had a wave tank and a coarse sea. In the

second one an solid cubical buoy was added. This buoy was moored by a two-node cable

in the third model. A screenshot of these models can be seen in figure 52.



Figure 52:Wave tank (left), wave tank and buoy (centre), wave tank and moored buoy (right)

Remarkably the cable was very heavy to process by LS-Dyna. The simulation of the first

two models took only 4 minutes to run. By adding the cable only three extra nodes were

incorporated, but calculation time rose up to 10 hours. In other words a factor of 150

more. A comparable result was found when the same procedure was repeated in more

detailed simulations and the calculation time went up to a 1000 hours. This represents

an increase with a factor 5.

3.9 Simulation results on buoy performance

At this time, good operation of the wave tank and its wave generator has been achieved.

The wave generator’s boundary conditions are calculated and set to create a sea state

comparable to where the buoys will actually operate. Meanwhile, the selected buoys are

modelled and tested in smaller wave tanks and cable behaviour is optimised. In other

words, everything is done to be able to check buoy behaviour in realistic circumstances.

In this section the performance of the buoys at sea is discussed and compared. To be

able to do so, ‘nodout’-data is used in LS-Dyna. This option makes it possible to retrieve

information on the position, velocity, acceleration and rotation of selected nodes. In this

case, only one node had to be selected since the whole structure is defined as rigid. The

cable‘s attachment point to the buoy has been especially chosen for every buoy. The

reason for this is that special care was taken to place the attachment point exactly

underneath the COG of the entire buoy.

Due to problems regarding computational time, only a very limited amount of data has

been obtained from the simulations. The termination time of the simulations is set to be

90 seconds. However, the simulations have only ran for a maximum of 30 seconds.



3.9.1 General information on displacement of the buoys

The translation of the buoy does not really affect the Lidar vessel’s performance. For the

accuracy of the Lidar’s measurements, it is only important that it stays as level as

possible. The position will vary of course, within reasonable limits. The cable will

prevent the buoy from drifting away. The displacement of the 3E buoy is only included

to clarify some statements made earlier. The graphs showing the displacement of other

buoys are very similar and for that reason they are not included in this thesis.

In figure 53, the displacement in all major directions is shown for the current prototype

of the 3E buoy. It is chosen to work in a right-handed coordinate system using:

X-axis in the length direction of the wave tank, pointing away from the paddle

Y-axis in the width direction of the wave tank

Z-direction in the ‘upward’ sense

Figure 53: Displacement in x- (red), y- (green) and z-direction (blue) for the 3E buoy

The x-displacement, pictured in red, shows the back and forth motion in the direction of

the waves the buoy exhibits when subject to the wave forces. The buoy is moored and

thus this motion is limited.

The y-displacement is shown in green. As can be seen, the buoy drifts a maximum of

20cm in the y-direction from its starting position. This is mentioned to prove that the

suggested 10m tank width is indeed sufficient, as stated in 3.5.4.

X direction Y direction Z direction Translation [m] Time [s]



The z-displacement is shown in blue. For the first 2 seconds the displacement is zero

followed by a slow lowering of the buoy, because of the used LOAD-cards as mentioned

in 3.5.6.2. Afterwards, the buoy follows the wave motion. It can be seen that the wave

height is not exactly the same as the z-displacement of the buoy. This is due to the

rotation of the buoy itself and the fact that the selected node is at the lowest point of the

buoy (greatest effect of the rotation).

3.9.2 Performance of the different buoys in terms of rotation

As discussed in previous paragraphs, calculation time is a serious issue. Because of this,

a smaller wave tank was designed to be able to interpret the results on buoy

performance. This wave tank has a length of only 35 m. Other dimensions were kept the

same.

Even though the dimensions were smaller, the simulation still took a long time to run. So

long in fact, that the simulation of the PEM58 could only run for 17 seconds and this

already took it 94 hours, 28 minutes and 45 seconds. While LS Dyna’s projected run time

was 10 hours.

3.9.2.1 3E prototype buoy

Figure 54 displays the rotation of the buoy around all mayor axes. Since the waves are

unidirectional, only the rotation around the y-axis, perpendicular to the wave direction,

is noteworthy. This is why in following graphs only the this rotation will be pictured.

The maximum inclination is observed at 13.33 seconds and is 0.24 radians (13.75°). A

screenshot of the simulation at the moment of maximum inclination is shown in figure

55.

Figure 54: rotation around x- (red), y- (green) and z-axis (blue) for the 3E buoy

around X axis around Y axis around Z axis Rotation [rad] Time [s]



Figure 55: side view of 3-buoy model at 13.33 seconds showing the maximum inclination

Limitation of the maximum inclination is important, but far more important is the

rotational speed. This is pictured in Figure 56. The slower the buoy tilts, the more time

the Lidar stabilisation mechanism has to counteract this movement. Detailed

information on this topic in found in 4.6.2. The maximal rotational speed for the 3E buoy

is 0.183 rad/s (10°/s) at 19.95 seconds. This is so slow that for the first two waves in the

simulation, will not follow the wave motion entirely, but stays tilted with a positive

inclination.

Figure 56: rotational speed around y-axis for the 3E buoy

13.75°

Rotation speed[rad/s] Time [s]



It can be seen there is a peak at the end (after 26 seconds). This has nothing to do with

an error in the simulation or a strange movement of the buoy, but is merely a

consequence of an imperfection in LS-Dyna itself. If one terminates the simulations or

extracts date from it before it has ran completely, strange effect are noticeable for the

final seconds.

3.9.2.2 PEM58 buoy

Same discussion of the results can be made for the PEM58 buoy.

The maximum inclination, seen figure 57, is found at 16 seconds and is 0.25 rad (14.32°). This is

visualised in figure 58. It can be seen that the PEM58 follows the wave motion more than the 3E

buoy.

Figure 57: rotation around the y-axis for the PEM58

Rotation [rad] Time [s]



Figure 58: side view of PEM58 model at 16 seconds showing the maximum inclination

The maximal rotational speed is 0.2639 rad/s ( 15.12°/s) at t equals 8.9 seconds.

Figure 59: rotational speed around y-axis for the PEM58 buoy

14.32°

Rotation speed [rad/s] Time [s]



3.9.2.3 Spar buoy

Many problems have occurred during the spar buoy tests. Even though the total mass

divided by the volume that should be submerged in the water is equal to the density of

the water, the spar buoy does not stay afloat. A possible solution would be to decrease

the densities of the used materials of the spar buoy up to the point where the buoyancy

of the spar buoy is acceptable. However, this only led to two extreme scenarios: or the

spar buoy sinks or the spar buoy is barely submerged (figure 60).

Figure 60: Barely submerged, but floating SPAR buoy

Some possibilities for the reason the spar buoy sinks are listed below.

First of all, some parts of the SPAR Buoy shown in figure 60 will be defined. The pink

part will be described as ‘the cylinder’, while the blue part is named ‘the buoy’ and the

entire construction is named ‘the spar buoy’. This will make the following explanation

more readable. The dotted red line denotes to where the buoy should be submerged.

Just as the 3E buoy and the PEM58, the spar buoy would be lowered into the water as if

lowered by a crane. When the buoy contacts the water, it pushes it away. However,

when the buoy is totally submerged, a suction effect is present at the time the cylinder

enters the water. This creates vortices pushing the buoy down, making it sink even

deeper. This theory is visualized in Figure 61.

Desired location of the water level

Buoy

Cilinder



Despite the fact that the SPH water model behaves well for wave modeling, it cannot be

denied that the particle size is immense in comparison to real water droplets. Because of

their size and mass, the particles do not surround the spar buoy as completely as real

droplets would. Their size makes the particles react slower as well. Consequently the

submerged volume of the spar buoy is not always equal to the displaced water volume.

This has an obvious effect on buoyancy according to the law of Archimedes. This

imperfection would be less apparent when using smaller sized particles.

Both effects push the spar buoy deeper into the water than expected. Because the

buoyancy tests are executed in smaller wave tank (10m deep), due to the calculation

time (see 3.8), it quickly reaches the bottom and interacts with the SPH-symmetry plane.

However, since both mechanisms can be regarded as transient phenomena, the buoy

might reach a representative steady state motion if the simulations were longer and the

tank was deeper. This could not be tested, due to a lack of time.



Figure 61: sketch showing vortices when placing the spar buoy

Because the performance of the Spar Buoy would be a great benchmark, a lot of effort

was made to find another solution. The following model enhancements or changes have

been tried:

Cili

nd

er

Buoy

Cili

nd

er

Buoy

L L

Large water particles react slower

than they should. Impulse laden jets

of water rush to the low pressure

zones. Too much and too late.

The subsequent vortices push the

buoy down. The Spar buoy moves

further downward than it is

supposed to. It takes some time for

this phenomenon to disappear.

Cili

nd

er

Buoy



A boundary condition was used that moved the buoy into place, left it there for 3

seconds in order for the transient phenomena to damp out. After this, the

boundary condition was eliminated.

Using the fill algorithm of the SPH-particles to fill the wave tank with SPH water

surrounding the buoy, when the buoy was held into its correct position.

Filling the wave tank with SPH water, placing the spar buoy in its correct place

(before the start of the simulation) and deleting all intersecting nodes.

Unfortunately all of the proposed solutions above did not have the desired outcome.

3.9.2.4 Conclusion

In figure 62 and figure 63, a combination of the results for the 3E buoy and the PEM58 buoy is

made.

Figure 62: rotation around y-axis. Red for the PEM58 and green for the 3E buoy

Figure 63: rotational speed [rad/s] versus time [s] for the 3E and the PEM58 buoy

PEM 58 3E prototype Rotation [rad] Time [s]

PEM 58 3E prototype Rotation speed[rad/s] Time [s]



A summary of the data can be found in table 9. Especially the relative numbers are easy

to interpret.

The PEM58 model has been constructed based on plans and pictures. However,

materials used, were not specified, neither was the mass distribution nor information on

the inside structure of the buoy. The actual buoy will be quite different and will most

likely perform better than the model used in these simulations.

3E buoy PEM58

Inclination

Maximum [°] 13.75 14.32

Relative [3E buoy = 1] 1 1.04

Amplitude [°] 18.91 25.21


Rotational speed

Maximum [°/s] 9.74 14.89


Amplitude [°/s] 19.48 26.36

Relative [3E buoy =1] 1 1.35

Table 9: Summary of the simulation results for 3E and PEM58 buoy

It can be seen that the PEM58 buoy scores worse on every performance parameter.

However, as stated in section 2, the PEM58 buoy is by far the most practical. Mostly due

to its lighter weight and the modular design. On top of this, the stabilization mechanism,

discussed in chapter 5, will damp out most of the movement and keep the Lidar level. It

remains to be seen how the vessel, buoy plus stabilizing unit, performs.


Master thesis – Mechanical Engineering –Study of Lidar stabilization mechanism Page 72

4 Study of Lidar stabilization mechanism

4.1 Introduction

One of the main parts of this thesis is the design of a system that keeps the Lidar module

facing upwards despite the motion imposed by the sea. Looking at existing sea craft, one

could get inspiration for such a mechanism. Travelling by sea has been the only method

to cross the Atlantic Ocean for a very long time. Since a ‘smooth passing’ was vital for

passenger comfort and profits; systems were thought out to stabilise the ocean going

ships despite rough sea conditions. Two of the most important solutions engineers came

up with were gyroscopic stabilisers down in the ship’s lower decks and hydrodynamic

stabilising ‘wings’ on the ship’s hull under the waterline. Since the latter can only be

used for moving vessels it’s the former that might provide a solution for the stationary

Lidar buoy. Sources on the internet reveal that wealthy yacht owners can buy gyroscope

‘modules’ which can be bolted down to the ship’s frame to reduce rolling and pitching of

the ship with surprising results. Although today the hydrodynamic wing option is the

most popular, some ocean liners have successfully relied on gyroscopes since the 1930’s.

So a solution based on a gyroscope was chosen to stabilise the Lidar.

4.2 Model overview

Unlike the yachts, passenger comfort is not an issue for the Lidar vessel. To reduce the

necessary size and power requirements of the gyro mechanism and to increase its

performance, a dual gimbal linkage system was thought out, similar to the gyroscopes

one could have seen in a physics lesson. The movement of an inner Lidar supporting

module is made independent of the motion of the sea craft using two rotating joints. The

inner frame or gimbal, holding the Lidar, rotates in an outer frame or gimbal which

rotates again in an external subframe fixed to the buoy. Both axes are perpendicular to

each other.

The shape and construction of the mechanism as well as the position of the parts was

inspired on a prototype mechanism. Later on it shall be explained that some aspects of

this are not necessarily ideal.

The inner, and independently moving, frame with the Lidar is stabilised by a gyroscope

much smaller than the one that would be needed to stabilise the entire craft. CAD

drawings of such a linkage system are shown in figure 64 with artificial colouring to

distinguish the separate components.



Figure 64: CAD drawing of linkage system to make the Lidar move independently

Rotation axis: Inner gimbal – outer gimbal

Rotation axis: Outer gimbal – Frame

Lidar module

Inner gimbal

Outer gimbal

Frame; fixed to buoy

Fixed



The dimensions of the components in the CAD drawing are based on visual clues of the

first Lidar prototype. This model however is made only for simulations and empirical

research. But the actual dimensions may differ slightly. Also, for simplicity, physical axes

are not modelled. Motion is described with mathematically formulated joint definitions.

This is why the components appear to be floating while, in fact, they have been fixed in

space with a mathematical formulation. Please note that both rotation axes are not in

the same plane for this design. This is not advantageous since the position of the

point around which the Lidar rotates – designated as ‘the rotation point’ – is

dependent on both axis’ rotational coordinate. This will be discussed later on.

The software used to simulate this mechanism is ‘Universal Mechanism’ by Universal

mechanism Lab. For readability the software will be referred to as ‘UM’. The CAD

components were imported in UM as ‘images’ and their mechanical relations were

carefully defined. What this looks like in the software animation window is shown in

figure 65.

Figure 65: UM animation window: representation of Lidar stabilizing mechanism model

Please take careful notice of the fact that the Y-axis is upwards instead of the Z-

axis. All components from the CAD drawing can be recognized. The flywheel, shown in

red, was added in UM with parameterized dimensions. This means that the flywheel is

modelled as a simple disc and its height, density and radius can be changed easily to

allow for quick optimization of flywheel dimensions.

Z-axis X-axis

Y-axis



All components shown are considered to be made of steel with a density of 7800kg/m³

for most simulations. Except for the Lidar box which has a weight imposed by a weight

parameter. For this study, that weight is assumed to be 45kg, which is the current

weight of the actual system.

An important reference point is the centre point of the inner gimbal’s rotation axis with

the outer gimbal. Both the position of the Lidar module and the flywheel can be set with

parameters in relation to this point.

Figure 66: Offset parameters of mechanism model in UM and reference points.

The frame will also rotate relative to a stationary reference frame in UM just like the

buoy moves because of the waves relative to a stationary reference in real life. The

centre of rotation is also a reference point and it is located 1.18 meters downward

relative to the first reference point. The real buoy will rotate around its centre of gravity

which will be lower than the upper reference point. This implies that buoy rotations also

involve translations and translational accelerations for the Lidar. The offset between

said points might be important to mechanism performance. If the Lidar-flywheel

subsystem is suspended like a pendulum, then the fact that the ‘centre of rotation of

frame movement’ (figure 66) is below the Lidar will have more effect.

Lidar offset

Flywheel offset

Reference point for offset parameters

Center of rotation of frame movement



4.3 Model parts, joints and parameters

4.3.1 Part: Frame

As mentioned before the frame moves with respect to an inertial reference frame. It’s

rotation around the rotation reference point is expressed in radians and has a sinusoidal

expression for the X and Z axis. The time variable is ‘t’.

So the frame has four parameters concerning its movement.

ax Amplitude of x-axis rotation [rad]

az Amplitude of z-axis rotation [rad]

Tx Period of x-axis excitation [s]

Tz Period of z-axis excitation [s]

Table 10: Parameters of Frame movement.

Amplitude values of 0.1 rad have been chosen for most of the simulations because it is a

representative value for measurement conditions of the Lidar. The excitation periods

(inversely proportional to angular frequencies) are studied more intensively and its

relation to the maximum inclination of the Lidar will be carefully looked at later on.

4.3.2 Part: Outer gimbal

No parameters. Weight: 49.53 kg.

4.3.3 Part: Inner gimbal

No parameters. Weight: 35.73 kg.

4.3.4 Part: Lidar

Box shaped part. It represents the Lidar module. Its offset in relation to the central

reference point is also a parameter.



oLidar Offset of Lidar module [m]

Table 11: Lidar offset parameter

The mass of the Lidar is considered 45kg for most simulations. The offset is typically

zero but can be changed to tune performance.

4.3.5 Part: Flywheel

The flywheel image is, unlike the CAD imported images of other parts, a simple cylinder

determined by parameters. Its rotational speed is a parameter as well.

Rflywheel Radius of flywheel [m]

hflywheel Height of flywheel [m]

Ωflywheel Flywheel angular speed [rad/s]

[rpm]

oflywheel Flywheel offset [m]

Table 12: Flywheel geometry and movement parameters

R and h are parameters that must be optimized. The best values within practical limits

are 1cm height and 0.5m radius. The flywheel angular speed is taken to be 3000 rpm or

6000 rpm. These speeds are achievable with invertor fed induction motors. Its offset is

also a parameter. These parameters will be discussed further. Naturally, the flywheel

weight can be calculated:

4.3.6 Gimbal joints

The rotational joints between the gimbals are very simple 1 degree of freedom

rotational joints. However, an expression was implemented defining a restoring

moment:



Figure 67: Relative movement and restoring moment.

A damping and stiffness coefficient is added to create the restoring force as a function of

the relative speed and position of the joint. The zero position reference is the position

when all parts’ Y-axis are perfectly aligned. These coefficients are relevant because a

spring or a damper could be installed if necessary to tune performance. Friction will not

be taken into account for this research because it is unclear what type of bearings and

lubricants will be used. Friction is considered as a disturbance and will be studied

separately later on in section 4.6.4.

Cstiff Stiffness coefficient [N.m/rad]

Cdiss Damping coefficient [kg.m/rad/s]

Table 13: Joint restoring force parameters

Of course one could define axis specific coefficients for each axis. But research has

shown that the effort of tuning each axis separately is really not worth the time because

both axis behave so similar. The units for these values will be identical throughout this

thesis and they will not always be mentioned. When stated ‘a damping value of 20’ one

should interpret this as ‘a damping value of 20 kg.m/rad/s’.

4.3.7 Overview and reference situation

The reference situation will now be defined. It is a set of parameters that has been

optimized given specific input. The reference values are given in the right column. This

set of parameters shall be referred to as the ‘reference mechanism’ and is very

important.

Part 1

Relative position: x

Restoring moment: M

Part 2

Relative speed: v



Excitation parameters

ax Amplitude of x-axis rotation 0.1 rad

az Amplitude of z-axis rotation 0.1 rad

Tx Period of x-axis excitation 5 s

Tz Period of y-axis excitation 5 s

Optimization parameters

Ωflywheel Flywheel angular speed 3000 rpm

6000 rpm

Rflywheel Radius of flywheel 0.5 m

hflywheel Height of flywheel 0.01 m

oflywheel Flywheel offset 0.2 m

oLidar Offset of Lidar module 0 m

Cstiff Stiffness coefficient 0 N.m/rad

Cdiss Damping coefficient 20 kg.m/rad/s

Table 14: Summation of reference mechanism model parameters

This reference mechanism is quite optimized. So any change made to the optimization

parameters for the given environment parameters should lead to a decrease of

performance or to an impractical or unfeasible geometry. In almost all of the simulations

the values Tx and Tz will be chosen equal as well as the ax and az values. This makes it

look like the frame rotates around the bisector of the axes. This is the ‘worst case’ since

both gimbals will have to rotate and the restoring force of both pairs of bearings is

exerted. The next paragraph will discuss the influence of parameters on the model.



4.4 Measuring performance

The mechanism performance is inversely proportional to the maximum Lidar inclination

angle. The smaller the maximum inclination angle, the better the system is doing its job.

For illustration purposes, a graph showing the X and Z inclination angles of the Lidar

part is shown below for the reference mechanism (flywheel speed is 6000 rpm) in a 120

second simulation of the mechanism with a sinusoidal moving frame as described

earlier. It shows the satisfying performance of the system with maximum inclination

values as low as 0.07 degrees for 6000 rpm, which can barely be seen with the naked eye

in the graphical representation. It looks like the reference mechanism performs very

well.

Figure 68: Result of 120 sec simulation of the reference mechanism. X and Z inclination is shown with max. inclination

value of 0.07 degrees. Speed: 6000 rpm

Z axis X axis Inclination [rad] Time [s]

6000 rpm



Figure 69: Sine function of angular movement definition of frame.

The difference in amplitudes for the rotation of X and Z axis is caused by the difference

in rotational inertia for the outer and inner gimbal respectively. It does not matter which

axis is observed for system optimization. For further research the Z-axis was chosen

since this axis shows the largest inclinations.

The inclination functions look like a superposition of two sinusoids: one with a high

frequency equal to the excitation frequency (f=2∙π/T) and one with a lower frequency of

40 mHz (with a flywheel speed of 6000 rpm). The lower frequency sinusoid is caused by

a so called precession motion. This motion is exhibited by all gyroscopes if its initial

position differs slightly from vertical or if it is disturbed. Unlike the excitation

component it damps out over time. The precession motion should not be present in a

theoretically ideal situation yet it still is. This is due to the fact that the frame joint

definition function has a discontinuity in the derivative at t equals zero as shown in

figure 66.

The calculations are made with a numerical iterative solver and values preceding the

time origin are zero. This error will not affect the conclusions made in this theoretical

study because any detrimental or beneficial influence of parameter changes will still be

clear in the increase or decline of the max amplitude and in the excitation component,

despite any precession. Yet is it still worthwhile to keep track of both the output signal’s

components. From now on they will be defined as the precession component and

the excitation component for the higher frequency and the lower frequency

component respectively.

Non-physical discontinuity of angular speed at t=0 is the cause of the high frequency oscillations in the Lidar inclination angles



Figure 70: Inclination signal component definition

If the gyroscope was aligned exactly vertical and the Lidar and flywheel were perfectly

held steady during flywheel acceleration there should not be any precession motion. The

precession decreases over time due to the damping in the bearings but only very slowly.

A simulation result of the reference mechanism for the Lidar Z-axis inclination angle is

shown below with a termination time of 10 minutes. Precession becomes much more

important in physical situations and shall be looked at very extensively later on.

Figure 71: 600 sec simulation of reference mechanism highlighting the slow decline in precession

For further analysis the absolute maximum of the Lidar inclination will be measured.

The graph above shows that representative maximum values can be measured with only

60 seconds of simulation time.

Excitation component

Excitation frequency

Precession component

Low frequency

Total inclination

Z inclination [rad] Time [s]

First representative maximum.

Precession motion decreases over time

6000 rpm



4.5 Parameter influence

Now that the mechanism’s performance can be evaluated, the influence of the

mechanism’s parameters on its performance can be made.

4.5.1 Flywheel speed

The easiest parameter is discussed first. To put it simply: a high flywheel speed yields

lower maximum amplitudes. The reference mechanism has a flywheel angular speed of

3000 or 6000 rpm. These speeds are achievable with an invertor fed induction motor. A

fast DC motor could also serve well but would impose more demanding maintenance.

Figure 72: Simulation of Lidar inclination for varying flywheel speeds. Lower amplitude curves represent higher

speeds and vice versa.

Relevant numbers from figure 72 are summarized in another graph below. As shown, a

power function fits the empirically generated graph quite conveniently. It could be

concluded that it is worthwhile to increase the speed to 6000 rpm.

But it looks like beyond that point it is no longer desirable to increase speeds further

since it will not change the results that much for the better. Very high speeds, such as

9000 rpm may give rise to practical issues. Speeds lower than 3000 rpm are really not

desirable for the mechanism performance.

Please observe that both amplitudes decline with decreasing speed; both the sine with

the excitation frequency and the precession motion.

1500 rpm 3000 rpm 4500 rpm 6000 rpm 7500 rpm 9000 rpm Z inclination [rad] Time [s]

1500 - 9000 rpm



Graph 1: Maximum Lidar inclination versus flywheel speed and the interpolating power function.

Speed Maximum inclination Relative to 0 rpm Relative to 3000 rpm

Rpm Radians Degrees % %

0 0.02108 1.208

602.67%

1500 0.00613 0.351 -70.92% 104.33%

3000 0.00300 0.172 -85.77%

4500 0.00188 0.108 -91.08% -37.33%

6000 0.00143 0.082 -93.22% -52.33%

7500 0.00124 0.071 -94.14% -58.83%

9000 0.00101 0.058 -95.21% -66.37%

Table 15: Results of simulation series for varying speeds

In order to gain more insight, longer simulations were carried out for 3000, 6000 and

9000 rpm. The results show a shift in the amplitudes of both sine components:

excitation component and precession component. The period of the precession motion

changes as well.

y = 0.3437x-1.008

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

1500 3000 4500 6000 7500 9000

Max

imu

m in

clin

atio

n [

°]

Flywheel speed [rpm]

Practical:

Using an invertor to feed the motor is very interesting for this application. It can be powered directly from the batteries and it makes high speeds possible. The most important is its ability to let the induction motor start the flywheel without draining excessive current. Since overcoming the inertia at startup requires the most power; a less powerful motor can be chosen because maximum torque is also available at the lowest speeds.



Figure 73: 20 minute simulations of Lidar inclination for varying flywheel speeds. Lower amplitude curves represent

higher speeds and vice versa.

Graph 2: Lidar inclination components versus flywheel speed (primary vertical axis) and precession period versus

flywheel speed (secondary vertical axis).

The results in graph 2 show that the decline in maximum amplitude observed earlier

was mostly due to a decline in precession amplitude. In the simulations, the sine

functions component’s heights were measured. This is the amplitude multiplied by two.

The ‘excitation amplitude’ (the amplitude of the sine component with the same

frequency as the excitation functions) does not change much. The fact that the increase

in precession period versus the flywheel speed seems to be a perfectly linear relation is

noteworthy as well.

0

50

100

150

200

250

0

0.001

0.002

0.003

0.004

0.005

0.006

3000 6000 9000

Pre

cess

ion

pe

rio

d [

s]

Am

plit

ud

e [

rad

]

Flywheel speed [rpm]

Ex. ampl.

Prec. ampl.

Prec. per.

3000 rpm 6000 rpm 9000 rpm Z inclination [rad] Time [s]



At this point it is instructive to remind the reader that the precession motion is the

result of the relatively violent starting discontinuity and should not be present. The

maximum Lidar inclination graphs could be lower if only the excitation component were

present, such as in a theoretically ideal situation. The authors have decided to keep track

of the influence of changes on the precession motion because, later on, it will be

established that the precession motion is the biggest cause of mechanism inaccuracy and

will be common with practical applications. The starting discontinuity is of benefit to the

research.

Although it seems that one should always strive for ultra-high rpm’s it is not always a

wise choice. A fast flywheel increases the gyroscopes capacity to fight inertia but it also

makes it increasingly difficult to damp out the precession motion. Precession with a long

period is tougher to damp out than precession with a lower period.

4.5.2 Amplitude

How will the components of Lidar inclination, precession and excitation, react if the

excitation amplitude changes? Obviously an increase in amplitude means a decrease in

performance.

Please remember that the Lidar inclination function is composed of two components: an

excitation component with the same period as the frame movement and the precession

period with a much larger period. The components are called excitation and precession

component respectively. (See 4.4)

A series of simulations with the reference mechanism were carried out with the

following amplitudes: 0.025, 0.05, 0.1, 0.2 rad.



Figure 74: Simulation of reference mechanism with changing amplitudes Smaller amplitudes yield lower maxima.

The simulation’s result in graph 3 shows clearly that changing the amplitude does not

affect the period of precession. The maximum inclination rises linearly as expected.

Graph 3: Lidar inclination versus excitation amplitude.

It looks like the rise of maximum amplitude is linear as well as the increase in both of its

components. The excitation amplitude rises the quickest and the precession rises

somewhat slower. This behaviour was to be expected since the excitation period

remains the same.

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 0.05 0.1 0.15 0.2 0.25

Lid

ar in

clin

atio

n [

rad

]

Excitation amplitude [rad]

Max ampl

Exc ampl

0.025 rad 0.05 rad 0.1 rad 0.2 rad Z inclination [rad] Time [s] 6000 rpm



4.5.3 Flywheel dimensions

What dimensions should the flywheel have to make the mechanism perform at its best?

This paragraph will look into this problem.

Figure 75: Scheme of flywheel dimensions and offset.

(Flywheel)

x

y

o

R

h

Lidar pivot point, Reference point, Simulation origin

Global reference system

Cartesian

Flywheel reference system

Cylindrical

ζ

θ

ρ

Iζζ: Inertia of rotation axis Iρρ: Inertia of radial axis



Figure 76: Reference mechanism. Observe the thin flywheel with a large diameter.

In this paragraph the influence and the optimization of the flywheel geometry and its

offset will be discussed. The flywheel material is steel with a density of 7800 kg/m³.

Other relevant parameters can be calculated using these expressions.

R: Flywheel radius

h: Flywheel height

mflywheel: Flywheel mass

Iζζ: Inertia around rotation axis

Iρρ: Inertia around radial axis

During the research of the influence of the flywheel radius it became clear very quickly

that it should be as large as possible. This is why the reference mechanism has

approximately the largest possible flywheel radius within practical limits: a radius of

0.5m. The reference mechanism shows a flywheel thickness of just 1 cm to keep the

weight down to a practical value. The question is: how much will the performance suffer

if the flywheel is given a smaller diameter when the height is kept constant? This would

also mean that the weight decreases as well. Perhaps a lighter mechanism would be

more convenient?



Figure 77: Simulation of Lidar inclination for changing flywheel radius with constant height. Speed is 6000rpm.

From figure 77 can be deduced that the performance suffers greatly when the flywheel

radius decreases. The precession component amplitude does not change much. The

excitation component amplitude seems very dependent on the flywheel diameter. If one

looks carefully at the red curve (0.2 m) it can be seen that the precession motion is still

noticeable but only in the beginning. It damps out very quickly. This is to be expected

because with a radius of 0.2 the flywheel is very small and its capacity to fight the

restoring force of the dampers and inertia is reduced. (More on precession: see section

4.5.8 on damping.) Looking at the table 16 it seems that both inertia’s rise with

increasing radius and decreasing inclinations.

Var Radius Height Weight Iζζ Iρρ Iζζ ∙ Iρρ Max.incl Exc. Incl Relative

Unit m m kg kg∙m² kg∙m² kg²∙m4 rad rad %

0.20 0.01 9.80 0.20 0.10 0.02 0.039840 0.030715 2929.66%

0.30 0.01 22.05 0.99 0.50 0.49 0.006630 0.005625 404.18%

0.40 0.01 39.21 3.14 1.57 4.92 0.002535 0.001949 92.78%

0.50 0.01 61.26 7.66 3.83 29.32 0.001315 0.000960 0.00%

Table 16: Results and calculated values of simulation with changing radius and constant thickness

0.5 m 0.4 m 0.3 m 0.2 m Z inclination [rad] Time [s] 6000 rpm



Graph 4: Lidar inclinations (primary axis) and flywheel weight (secondary axis) versus changing radius

It looks as though the graph exhibits exponential behaviour for the inclination values.

The excitation component is also shown above. (Please remember: The difference

between the maximum inclination and the excitation component is the precession

component.) It seems that precession becomes slightly worse for lower radii, but as

mentioned before, it damps out quicker. For this flywheel geometry optimisation

research the excitation amplitude is most relevant. A good flywheel will keep this value

down. Still, it is good to keep an eye on precession. A flywheel can perform really well in

theory but can be useless in practice if it responds very bad to precession induced

disturbances.

To try and understand how important other parameters such as weight and height

matter more simulations will be undertaken. Flywheel capacity has a lot to do with

inertias. This will be the focal point of the oncoming simulations.

The flywheel thickness’ effect on performance is next. The flywheel thickness is changed

while keeping its radius at the reference value. Please read the results below.

0

10

20

30

40

50

60

70

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.2 0.3 0.4 0.5

Fly

wh

ee

l we

igh

t [k

g]

Max

imu

m in

clin

atio

n [

rad

]

Flywheel radius [m]

Max. incl.

Exc. Incl.

Weight



Figure 78: Simulation of Lidar inclinations of Z axis for varying flywheel thickness. Lower radii yield higher maxima.

Performance can still be increased by making the flywheel heavier, it seems, with

minimal influence on precession period.

Var Radius Height Weight Iζζ Iρρ Iζζ ∙ Iρρ Max. incl Exc. Incl Relative


0.50 0.005 30.63 3.83 1.91 7.33 0.001066 0.000659 32.02%

0.50 0.010 61.26 7.66 3.83 29.32 0.001116 0.000736 0.00%

0.50 0.020 122.52 15.32 7.66 117.34 0.001315 0.000960 -15.13%

0.50 0.040 245.04 30.63 15.35 470.12 0.001736 0.001787 -18.94%

Table 17: Results and calculated values of simulations with changing thickness and constant radius

Relevant measurements are visualised below.




Graph 5: Maximum Lidar inclination versus flywheel thickness for a constant radius.

It looks as if more accuracy can be achieved by making the flywheel heavier, but the

performance increase comes at a high price. A flywheel of almost 250 kg is not exactly

practical. A much bigger motor would be needed as well which is unfeasible because of

the Lidar buoy’s limited power supply. The tables show that the parameter ‘Iζζ ∙ Iρρ’ has a

strong correlation with performance. This is because a high inertia around the rotation

axis increases flywheel performance and because a high inertia around the radial axis

increases the force needed to tilt the flywheel from vertical. So the mechanism’s

performance is expected to be proportional to the value of ‘Iζζ ∙ Iρρ’. This hypothesis is

tested by making more graphs.

If all the results so far in this paragraph were rearranged and an XY-plot was made in

which the product of inertias was plotted on the x-axis and the maximum Lidar

inclination was plotted on the y-axis, then a monotonously descending curve would

appear if the hypothesis were true.

Graph 6: XY-plot of the product of inertias and the maximum Lidar inclination.

0

50

100

150

200

250

300

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0 0.01 0.02 0.03 0.04 0.05

We

igh

t [k

g]

Incl

inat

ion

[ra

d]

Flywheel height [m]

Exc. Incl.

Exc. Incl.

Weight

0.000000

0.010000

0.020000

0.030000

0.040000

0.050000

0.00 100.00 200.00 300.00 400.00 500.00

Max

imu

m in

clin

atio

n

Product of inertias [kg^2*m^4]

Reference

flywheel



Not exactly what one would expect. Looking at graph 6 it seems that, for lower values,

the performance increases drastically (the Lidar inclination decreases). But for very high

values the performance remains constant. So there is a point where additional increase

in inertia is of no benefit anymore. It looks as if the hypothesis is wrong. A final series of

simulations was made each with a constant product of inertia equal to the value

calculated for the reference mechanism. If the hypothesis were true the mechanism

performance would be more or less constant. It is not.

Var Radius Height Weight Iζζ Iρρ Iζζ ∙ Iρρ Max. incl Exc. Incl Relative


0.2000 0.2967 290.82 5.82 5.04 29.32 0.009380 0.005470 613.31%

0.3000 0.0763 168.37 7.58 3.87 29.32 0.003940 0.002090 199.62%

0.4000 0.0244 95.67 7.65 3.83 29.32 0.001918 0.001242 45.86%

0.5000 0.0100 61.26 7.66 3.83 29.32 0.001315 0.000960 0.00%

Table 18: Results and calculated values of simulations with constant product of inertias.

Graph 7: Lidar inclination versus flywheel radius. Product of inertias is constant at the reference value.

Although the product of inertias has remained constant, performance still increases

rapidly with increasing radius. It is all about the radius, it seems. Finally a couple of

design rules for a cylindrical flywheel can be formulated:

1. Increase radius as much as possible considering space limitations.

Large performance gain. Consider changing design for additional space.

0.000000

0.001000

0.002000

0.003000

0.004000

0.005000

0.006000

0.007000

0.008000

0.009000

0.010000

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55

Lid

ar in

clin

atio

n [

rad

]

Flywheel radius [m]

Max. incl.

Exc. Incl.



2. Increase thickness as much as possible considering weight and power limitations.

Smaller performance gain. Changing weight/power limitations should not

require much more resources or it is not worth it.

4.5.4 Flywheel weight

The flywheel could be manufactured out of a lighter or a heaver material if needed.

Looking at the formulae in section 4.5.3, it is obvious that changing the density ρ will

have a similar effect to changing the thickness h. Nevertheless the flywheel material

should be looked at. A series of simulations was undertaken with a flywheel made of

aluminium (2700 kg/m³), steel (7800 kg/m³ (ref)) and lead (11340 kg/m³).

Figure 79: 90 second simulation of reference mechanism with a flywheel made from varying materials. Heavier

materials yield lower maximum inclinations.

The relevant measurements are summarized in Graph 8:

Aluminium Steel Lead Z inclination [rad] Time [s] 6000 rpm



Graph 8: Inclination for varying flywheel density

The weight of the flywheel only seems to affect the amplitude of the excitation

component. It is very clear it is beneficial to make the flywheel heavy, just as expected.

The performance gained from an increase in density of 45.38% (steel to lead) only leads

to a performance gain of about 10%. (Table 19) This is not great considering the fact

that both the extra weight and the soft lead can cause additional practical issues. It can

be concluded that that steel is best kept as the material of choice for the flywheel.

Var Radius Height Weight Iζζ Iρρ Iζζ ∙ Iρρ

Max.

incl Exc. Incl Relative


(Aluminum) 0.50 0.01 21.21 5.30 1.33 7.03 0.00222 0.00192 71.17%

(Steel) 0.50 0.01 61.26 15.32 3.83 58.69 0.00129 0.00095

(Lead) 0.50 0.01 89.06 22.27 5.57 124.04 0.00117 0.00081 -9.97%

Table 19: Results of simulation series with different flywheel materials.

4.5.5 Flywheel offset

Another very important parameter to consider is the flywheel position. More specifically

the distance of the flywheel to the Lidar.

0.00000

0.00050

0.00100

0.00150

0.00200

0.00250

0 2000 4000 6000 8000 10000 12000

Lid

ar in

clin

atio

n [

rad

]

Density [kg/m³]

Max. incl.

Exc. Incl.



Figure 80: Simulation of Lidar inclinaton for varying flywheel offset. Smaller amplitudes represent smaller offset and

vice versa.

Var Radius Max. Incl Exc. Incl Relative

Unit m rad rad %

0.20 0.001315 0.000960 0.00%

0.25 0.001452 0.001043 10.42%

0.30 0.001599 0.001147 21.60%

0.35 0.001726 0.001236 31.25%

Table 20: Results and calculated values of simulations with changing offset

Relevant results are summarized below.




Graph 9: Maximum Lidar inclination versus flywheel offset for the reference mechanism.

Mounting the flywheel lower down worsens the precession motion and deteriorates

performance. This can be seen by looking at the graph of the simulation results. (Graph

9) Precession amplitude remains constant, its period shortens. Excitation amplitude

rises. The decrease in performance is linear and predictable. So if the flywheel must be

positioned slightly lower for some reason it is not very bad.

From a practical point of view a large offset is definitely not desirable. Larger offsets

limit the available space for installations under the Lidar module. Typically a Lidar and

flywheel assembly is easier to build with a smaller offset. Since smaller offset values

perform better as well, it can be concluded that is wise to put the flywheel as close as

possible to the Lidar within practical limits. However, no special measures should be

undertaken to mount it especially close.

The flywheel offset is only part of the more extensive research of the optimal positioning

of components. Much more conclusions will be made in the next paragraph.

4.5.6 Lidar offset

The position of the Lidar module in the reference mechanism is inspired on its position

in the prototype of the actual mechanism. This doesn’t mean that performance can’t be

enhanced by changing that position. Two experiments will be undertaken: one with the

Lidar positioned higher and one with the Lidar positioned lower. Just as in figure 81.

0.000000

0.000200

0.000400

0.000600

0.000800

0.001000

0.001200

0.001400

0.001600

0.001800

0.002000

0.15 0.20 0.25 0.30 0.35 0.40

Lin

dar

incl

inat

ion

[ra

d]

Offset [m]

Max. incl.

Exc. Incl.



Figure 81: Mechanism configurations respectively with the Lidar moved downwards and upwards.

Figure 82: Comparison of the reference mechanism and a mechanism with the Lidar positioned lower.

It looks like moving the Lidar down has had a detrimental effect on performance. The

excitation component amplitude and the precession component amplitude increase.

Because the Lidar was moved down, the flywheel has moved down as well to keep it

from intersecting the Lidar. So the change of flywheel offset can account for some of the

loss in performance, especially for excitation amplitude gain, but not all of it. Actually,

comparing the earlier conclusions and these can be confusing. One would think that

moving the Lidar down would create a pendulum of sorts of which the mass distribution

would be helpful to achieve an upright position of the system.

Reference Lidar down Z inclination [rad] Time [s]

6000 rpm



In practice, moving the mass that needs stabilizing further from the rotation point

increases precession dramatically. The increase in excitation component amplitude can

be explained by pointing out that the buoy’s centre of gravity lies way below the offset

reference point (and centre of gimbal rotation). (See 4.2) So a rotation of the buoy’s

frame implies a significant translation of the Lidar. This translation means translational

acceleration. If the Lidar subsystem is suspended as a pendulum, this acceleration

means that it will start swaying and, despite the efforts of the flywheel, lead to an

increase in Lidar inclination angle of the excitation component. The same reasoning

could be done for the flywheel, since it has also a mass.

Figure 83: Illustration of Lidar subsystem swaying.

It can be concluded that the whole ‘pendulum’ idea is misleading. To make a system

work without a flywheel while suspended as a pendulum it could only work with

carefully tuned active dampers.

Subsystem COG in rotation point.

OPTIMAL

Subsystem COG below rotation point.

PENDULUM



Figure 84: Comparison of the reference mechanism and a mechanism with the Lidar positioned higher. The reference

position yields higher excitation amplitude.

The simulation above was undertaken with the Lidar moved upwards. Because the

flywheel would intersect the gimbals if it were moved up with the Lidar, it was kept in

the same position. As shown in the previous mechanism pictures. This means that the 45

kg Lidar is 200mm above and the 61 kg flywheel 200mm below the offset reference

point. The COG of the Lidar-flywheel subsystem is not far from the offset reference point

and the current rotation point. If the theory explained in the previous paragraph is true

this configuration should lead to better performance and it does. The simulation results

shown in figure 84 prove that both the precession component and excitation component

have decreased in amplitude. The precession period has increased, though. This is

caused by the fact that the pendulum, harmful as it may be for mechanism performance,

does help damp out precession a little (very little in fact) because its mass distribution

opposes the precession misalignment.

The Lidar position was not the only aspect of the research mechanism inspired by the

prototype. The shape of the gimbals was as well. This shape means that the outer

gimbals’ X rotation axis is 40mm above the inner gimbals Z rotation axis. This makes the

position of the inner subsystem’s rotation point dependent on the rotation. (The inner

subsystem consists of Lidar, inner gimbal and flywheel) During the previous discussion,

the offset reference point was always regarded as the rotation point while this was not

completely true. The real rotation point was not far away but its actual position was

unknown (See 4.2) If a new mechanism was to be designed it would definitely be worth

the trouble to make sure that said gimbal axes are in the same plane and that the centre

of rotation was independent of the movement.

Lidar up Reference Z inclination [rad] Time [s] 6000 rpm



4.5.7 Conclusion of mechanism geometry design: ‘super mechanism’

The previous parts contained lots of numbers and simulation results. The most

important things to remember are:

It is good to strive for a high rotational speed for the flywheel. The higher the

better. From 6000 rpm onwards the performance gain becomes very little. When

disturbances are expected, it’s better to choose lower rpm to reduce settling time.

(See section 4.5.8.2)

A flywheel must have a large inertia around the rotation axis for its weight,

within practical limits. The inertia is calculated in a local coordinate system with

the flywheel COG as origin.

The entire subsystem that must be kept upright, consisting of Lidar, flywheel and

inner gimbal, must have its centre of gravity as close as possible to the point

around which the gimbals and outer frame rotate to prevent swaying.

It is good to emphasise the fact that the gimbals are a no more than an unfortunate

necessity to make the mechanism physically possible. Their inertia should be kept as

low as possible for good mechanism performance because then their influence (more

specific: inertia) becomes less of a nuisance.

To prove all this, a ‘super mechanism’ was made in CAD design software and imported

into UM. Figure 85 shows what it looks like.

Figure 85: Screenshot of ‘Super mechanism’ in UM. Would be difficult to build. Physical axes not drawn. Frame and

Lidar module drawn in wireframe.



Figure 86: ‘Super mechanism’. From below. The flywheel is a ring around the Lidar itself with a hub at the bottom.

Figure 87: Side view of ‘super mechanism’. Look at the Lidar module’s orientation which is, as far as the eye can see,

perfectly upright while the mechanism is moving.

The gimbals are hollow box-sectioned steel tubes. The flywheel is no longer a disc, but a

ring. (The construction of a parameterized ring in UM would be very difficult.) The

flywheel weight is approximately the same as the reference mechanism’s flywheel:

about 61kg. All other specifications and parts are exactly the same as for the reference

mechanism, such as frame and Lidar.



Figure 88: Flywheel of the ‘super mechanism’. A ring instead of a disc. A central hub was added to make it possible to

attach a motor.

So the ‘super mechanism’ has:

Rotation speed of 3000 or 6000 rpm. Unchanged.

Flywheel with high rotational inertia Iζζ

Stabilized subsystem COG exactly coincident with rotation centre.

Lighter gimbals with coplanar rotation axes

It can be expected that this mechanism performs much better than the reference

mechanism. And it does. As shown in the simulations at 6000 rpm.



Figure 89: Simulations of Lidar inclination comparing the super mechanism to the reference mechanism

It seems that the super mechanism’s excitation component amplitude is much smaller

than the reference mechanism. The maximum inclination is 56% smaller, the excitation

component is 67% smaller. However the precession period of the super mechanism

seems very long. And it is.

Figure 90: Simulations of Lidar inclination comparing the super mechanism to the reference mechanism. Simulation

time is 1200 seconds or 20 minutes.

Super mechanism Ref. mechanism Z inclination [rad] Time [s] 6000 rpm

Super mechanism Ref. mechanism Z inclination [rad] Time [s] 6000 rpm



In the 1200 second, or 20 minutes, simulation the precession amplitude becomes

apparent as well as the scale of the performance increase. Relevant numbers are

compared below.

Graph 10: Comparison of the reference mechanism to the hypothetical ‘super mechanism’.

The development of the ‘super mechanism’ has verified the conclusions made. But, and

there is a big but, the mechanisms performance comes at a high price. The gyroscopes

capacity is now so big precession motion becomes much harder to damp out. Especially

at 6000 rpm. Good performance means nothing if a slight disturbance induces a

precession motion that goes on for hours. On the other hand, if the mechanism was well

protected, it could deliver similar accuracy to an actively controlled system with none of

the worries and costs that active components (pistons, active dampers, electronics …)

would bring.

For the remainder of the thesis the old reference mechanism will be used, since it is

more representative.

0

10

20

30

40

50

60

Inner weight Outer weight

Ref

Super

0

2

4

6

8

10

12

Inertia ofrotation axis

Inertia of radialaxis

Ref

Super

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

Excitation inclination Maximum inclination

Ref

Super

(Gimbals)



4.5.8 Damping

4.5.8.1 Effect of damping in the reference mechanism

The reference mechanism has some damping to control precession. The next study

covers the mechanisms behaviour when the damping is changed. Speed is now 3000

rpm to make damping more obvious.

Figure 91: Simulation of Lidar inclination for changing damping. Higher amplitudes mean higher damping values.

Flywheel speed is 3000 rpm.

Graph 11: Lidar inclination versus damping for the reference mechanism.

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

0.005

0 20 40 60 80 100

Incl

inat

ion

an

gle

[ra

d]

Damping [kg*m/rad/s]

Total Incl

Exc Inclin

20 kg.m/rad/s 40 kg.m/rad/s 80 kg.m/rad/s Z inclination [rad] Time [s]

3000 rpm



cdiss Total Incl Exc Inclin Relative

kg.m/rad/s rad rad %

20 0.002598 0.001913 0.00%

40 0.00315 0.002412 21.25%

80 0.004605 0.003774 77.25%

Table 21: Results and calculated values of simulations with changing offset.

It looks as though the damping decreases performance and it does so seemingly in a

linear fashion. So why does the supposedly optimized reference situation have a

damping value of 20? Because, if there were no damping, precession would not diminish

at all (from a purely theoretical point of view). This is unacceptable since precession is

destined to occur at some point. Almost anything that can go wrong has precession as a

result. This is discussed in section 4.6.

To quantify how fast the precession is damped out. It is deliberately excited by starting

the simulation with no frame movement and an initial mechanism inclination value of

0.1 rad for both rotation axes. As shown in figure 92:

Figure 92: Mechanism with misaligned start-up position. Frame is fixed.



Figure 93: Simulation results for verying damping with misaligned startup of 0.1 rad and stationary frame. 1200 sec

simulation. 3000 rpm

The simulation results seem to show that the intersection of the curves and the half life

line consistently seem to coincide with local maxima. This is due to the fact that the

chosen damping coefficients are multiples of each other. Half-life times are multiples of

the precession period. It is also obvious that the precession period remains constant

when damping is changed. The period is about 82 seconds. Half-life values are plotted in

graph 11.

Graph 12: Half-life of precession motion.

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80 100

Hal

f Li

fe [

s]


Half-life line

20 kg.m/rad/s 40 kg.m/rad/s 60 kg.m/rad/s 80 kg.m/rad/s Z inclination [rad] Time [s] 3000 rpm



The half-life diminishes with increasing damping. This is a good thing, but it comes at

the cost of an increase in excitation amplitude which should be kept as low as possible.

Especially if absolute accuracy is important. If this is the case, one could opt for a

flywheel speed of 6000 rpm. But how will the precession behaviour fare?

Figure 94: Simulation results for changing damping with misaligned startup of 0.1 rad and stationary frame.

Graph 13: Results of 6000 rpm simulation series compared to 3000 rpm.

~16 min

~8min ~5.5min ~4min

~1hour 3min

~32min

~21min 16min

0

500

1000

1500

2000

2500

3000

3500

4000

0 20 40 60 80 100

Hal

f Li

fe [

s]


3000 rpm

6000 rpm

20 kg.m/rad/s 40 kg.m/rad/s 60 kg.m/rad/s 80 kg.m/rad/s Z inclination [rad] Time [s]

6000 rpm



It was already mentioned that increasing the flywheel’s capacity means it becomes more

difficult to damp out precession motion and this shows in graph 13. Half-life results for

6000 rpm are much higher. If the mechanism builder opts for 6000 rpm it might be

worthwhile to use more damping to increase robustness and sacrifice some accuracy in

ideal situations because the increase in excitation component in relation to damping is

less severe than the decrease in half life.

It may be worthwhile considering that actual bearings dissipate energy and damp

motions due to viscous shearing of its lubricants. So arguably a reference situation with

damping present is more representative for a physical situation. If the naturally

occurring damping is enough to fight precession remains to be seen, but it is not to be

expected. Additional damping can be effectuated by adding rotational dampers in any

case.

4.5.8.2 Beware of precession

From the previous paragraph one can deduce that precession motion, whatever the

cause, can be the most dominant effect for Lidar misalignment. So perhaps sometimes

more effort should be put into fighting the precession motion than into getting the,

already very small, maximum amplitude down in a theoretical and ideal situation. Nit

picking in the ideal situation provided insight in flywheel optimization, but in a real

situation, with a semi optimal flywheel, it is the precession motion that should be

reduced as much as possible.

Prone to disturbances

• Lower speed

• Higher damping

Free of disturbances

• Higher speed

• Lower damping

Practical:

Damping can be effectuated by installing rotational dampers on the axes, like in the prototype. This thesis is a ‘pioneering’ research in the sense that its aim is to gain a thorough insight into the basics of the behavior of this mechanism. When designers become more experienced in the design of such a mechanism though it might be worthwhile to use computer controlled dampers with variable damping coefficient. When the computer detects precession motion, the dampers could be adjusted accordingly. When the system is stable, the dampers needn’t be switched on.



4.6 Reaction of the mechanism to irregularities

Since the mechanism will be used in a hostile environment and has to operate

autonomously it is important to check the response of the theoretical model to

disturbances. If the theoretical model shows no important decline in performance for a

certain disturbance, no special measures have to be undertaken in the design of an

actual mechanism. If the model responds violently, countermeasures for the specific

disturbance should be built in to the actual mechanism.

In the following paragraphs certain disturbances will be described and the mechanism

model will be extended to allow for parameterized definition of the more complex

disturbance movements.

4.6.1 Sudden deceleration of flywheel

If something were to happen to the motor or if the flywheel was struck by an object it

would decelerate abruptly. The reference mechanism is simulated like before but the

flywheel speed has a sudden dip. This requires a more complex position description in

the flywheel-Lidar joint. Although it is quite difficult to slow down a 61 kg flywheel

spinning at high speed this must be looked into because the flywheel angular

momentum is one of the key elements for the mechanism behaviour. The mechanism is

expected to react very badly to this.

The flywheel angular speed is described by figure 95:

Figure 95: Flywheel angular speed function with parameters composed of constants and cosines

a

d

b

ω

t

c

spee

d



ω Normal speed rpm

d Speed dip height rpm

a Dip start time s

b Dip duration s

c Spring back duration s

b + c Total dip duration s

Table 22: Parameters of flywheel speed function

The function is smooth, the derivative (angular acceleration) has no discontinuities. It is

actually composed of constants and cosine functions. The position function, which is

implemented in UM, is the integral of the speed function. To see the detrimental effect of

this phenomenon, simulations were configured with the following parameters and

executed. Since the disturbance is expected to cause precession motion the flywheel

speed is set at 3000 rpm. The first series is representative for small changes while a

second series is representative for ‘disasters’. Simulation results are printed for the most

spectacular changes. Please note that for the first ‘a’ seconds the situation is ‘normal’ and

is exactly like the reference situation at 3000 rpm.

ω 3000 rpm

d

50 100 200

rpm

400 800 1600

a 120 s

b 1 s

c 10 s

Table 23: Table with parameters for testing of detrimental speed dip: changing speed difference



Figure 96: Detail of flywheel angular speed for the parameters described above for the ‘disastrous’ speed dips.

Figure 97: Simulation of Lidar inclination for large speed dips of 200, 400 and 800 rpm. Before t equals 120 the

situation is the reference situation. Total duration is 240 sec.

400 rpm dip 800 rpm dip 1600 rpm dip Z inclination [rad] Time [s]

3000 rpm

400 rpm dip 800 rpm dip 1600 rpm dip Angular speed [rad/s] Time [s]



Graph 14: Lidar inclination for simulation with different speed dips.

A few pointers:

The proposed disastrous speed drops are very high and unlikely to occur. This is

fortunate because the induced precession motions are 313%, 671% and 1781%

worse than the reference situation at 3000 rpm for a speed dip 400, 800 and

1600 rpm respectively.

It looks as if the maximum inclination has an almost linear correlation with

height of the speed dip for reasonable values. One could conclude that the

induced precession motion will be approximately doubled in amplitude when the

speed drop is twice as severe for a quick drop in speed.

The half-life of the exponential decay is the same for all simulations above

because the damping was not changed.

In general: Slowing down the flywheel abruptly causes precession motion and

should be avoided.

Next up is the investigation of the influence of the speed dip duration. Simulate with the

following parameters:

0

0.01

0.02

0.03

0.04

0.05

0.06

0 500 1000 1500 2000

Lid

ar in

clin

atio

n [

rad

]

Speed dip height [rad/s]

Excitaton ampl.

Max ampl.

Ref max.



ω 3000 rpm

d 200 rpm

a 120 s

b 1 2 4 s

c 10 s

Table 24: Table with parameters for testing of detrimental speed dip: changing dip time.

Figure 98: Simulation of Lidar inclination with a dip in the speed at 120 seconds. Varying speed dip duration.

1 sec dip 2 sec dip 4 sec dip Z inclination [rad] Time [s] 3000 rpm



Graph 15: Lidar inclination for a constant spring back and changing dip duration.

1 sec dip 2 sec dip 4 sec dip Time [s] 3000 rpm

Left: Flywheel speed [rad/s] Right: Flywheel acceleration [rad/s²]

Figure 99: Flywheel angular speed and acceleration for said simulations.

It seems mechanism performance decreases first with increasing dip duration and then

increases again. The results above may seem surprising. One would think that less

abrupt speed dips would be less detrimental, but the opposite is true when dip time

rises from 1 to 2 seconds. What if the dip time was changed like in the last simulations,

but the total period with a speed difference remained constant (or b+c=10) for every

value of b?

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0 1 2 3 4 5 6

Lid

ar in

clin

atio

n [

rad

]

Dip duration b [s]

Excitaton ampl.

Max ampl.



ω 3000 rpm

d 84 Rad/s

a 120 s

b 1 2 3 4 5 6 7 8 9 s

c 9 8 7 6 5 4 3 2 1 s

Table 25:Table with parameters for testing of detrimental speed dip: changing dip time with constant total dip period.

For brevity, the simulation result graphs will be omitted because they look similar to the

last ones. Only the acceleration graph will be shown. The relevant results are

summarized below and compared to the previous graph.

Figure 100: Flywheel angular acceleration for speed dip simulations for constant dip time.

Flywheel acceleration [rad/s^2] Time [s]

3000 rpm



Graph 16: Lidar inclination versus dip duration for simulation series with constant speed dip time.

It seems that the mechanism’s performance is influenced by the shape of the speed dip.

If the speed dip period of the speed dip function is mirrored the mechanism reacts

similarly. It can certainly be said there are differences in the negative effects depending

on the speed dip characteristics.

A small and quick speed dip is not very bad. (Figure 101) An example of a physical

phenomenon that could cause this is an object impacting the flywheel. The mechanism

parts’ inertia makes sure the mechanism is unflustered.

A large but very gradual change in speed is not so bad either. (Figure 103) This could

happen when an invertor fed motor’s input frequency is gradually changed.

Changes of which the integral of the acceleration function for the dip period is large and

of which the speed is under 8 seconds are the worst, it seems. These could only happen

because of a severe motor or invertor failure of some other sort of mechanical failure.

Acceleration is just as bad as deceleration.

The first two theories are tested first. (The last one was deduced from the previous

experiment) The simulation below is configured with parameters representing a very

small and fast dip similar to the one the flywheel would experience if it was struck by a

small object. It can be observed that the precession motion is not very noteworthy.

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0 2 4 6 8 10

Lid

ar in

clin

atio

n [

rad

]

Dip duration [s]

Max. ampl.

Excitaton ampl.



ω 3000 rpm

d 50 rpm

a 120 s

b 0.1 s

c 3 s

Table 26: Parameterset for fast speed dip simulation

Figure 101: Simulation of Lidar inclination with very fast but small speed dip at t equals 120 seconds.

The simulation below is held with parameters representing a gradual change of speed

form 3000 to 6000 rpm as shown in figure 102. Like an invertor output frequency being

changed from 50 to 100Hz for a fast induction motor. The speed change causes nothing

more than a minor transition effect. After the flywheel speed is stable at 6000 rpm, the

Lidar inclination quickly settles to the regime seen earlier at the constant speed

simulation for 6000 rpm.

Dip

Z inclination [rad] Time [s] 3000 rpm



ω 3000 Rad/s

d -3000 Rad/s

a 120 s

b 120 s

c 10000 s

Table 27: Parameterset for gradual speed change.

Figure 102: Flywheel speed for experiment of gradual variation in flywheel speed.

Practical:

As mentioned before, increased flywheel capacity means increased performance, but makes the mechanism less forgiving for disturbances. This is why it is worthwhile to protect the flywheel and motor assembly both mechanically and electrically. A casing around the flywheel and motor can protect it from disturbances. Well protected power electronics and cables minimize the chance for electrical issues. Motor bearings would be protected against the corrosive environment as well, eliminating the need for special bearings and lubricants with lower friction coefficient and motor requirements as a result. Any protective covers should be kept as light as possible for mechanism performance and must possess no large flat surfaces since it might be subject to wave slamming. One must keep in mind to create the protection in such way that it does not affect the motor cooling capabilities negatively.



Figure 103: Simulation result for Lidar inclination with gradually changing flywheel speed. Transition from 3000 to

6000 rpm. Transition time is 120 seconds.

One can conclude that small mishaps and gradual changes may happen without

compromising performance. If a remote operator wished to change the flywheel

speed/capacity he or she may do so without harming accuracy much as long as the

change of speed is very gradual.

4.6.2 Sudden changes in buoy frame movement

A floating buoy attached to a cable is subject to jerking when the current or waves act to

move the buoy. How will the mechanism react to this? First, the jerking motion is split

up into two components: a pitching and a translational component. The first will be

modelled by suddenly changing the amplitude of the sinusoidal motion. The second can

be modelled by translating the entire mechanism in a representative way.

4.6.2.1 Functions

To test the effect of an excitation amplitude change the original model is extended, just

like in the last paragraph. This time however, it is not the flywheel position function that

is extended but the excitation functions that make the frame move in a sinusoidal

fashion. The functions used to be simple sinusoids, but have been extended with a

parameterized and more complex envelope function as shown figure 104:

Z inclination [rad] Time [s]

3000/6000 rpm

3000 rpm Transition 6000 rpm



Figure 104: Excitation function with envelope and its parameters.

The same envelope function can also be used as a single input function without the sinus

movement to keep the frame steady and impose a single and sudden rotation at time a. It

is similar to the flywheel speed dip function, but imposed on the frame as a rotation. The

amplitude function could look like the red line shown figure 104 without the sine.

4.6.2.2 Rotational jerking

a1 First amplitude value Rad

a2 Second amplitude value Rad

a3 Third amplitude value Rad

a Start time s

b First transition time s

c Second transition time s

sin_on Control parameter:

=0: Only envelope

=1: Sine with envelope

-

Table 28: Parameters of amplitude function of sudden change model

a1

a3

a2

a b c



At first a simple test will be carried out. Imagine the mechanism upright when suddenly

it is jerked to one side and back again. The Lidar would start swaying (if the COG of the

Lidar subsystem has offset to the rotation point. See 4.5.6 Some offset will typically be

present.) but the gyroscope will counteract this motion. It is expected that the

mechanism will exhibit precession motion after the disturbance. Several simulations will

be made according to the following table:

a1 0 Rad

a2 0.05 0.10 0.15 0.20 Rad

a3 0 Rad

a 2 s

b 2 s

c 2 s

sin_on 0 -

Table 29: Rotational jerking simulation parameters: amplitude of impulse

Figure 105: Plots of frame movement functions for amplitudes 0.05, 0.10, 0.15, 0.20

0.05 rad 0.10 rad 0.15 rad 0.20 rad Frame inclination [rad] Time [s]



Figure 106: Simulation results for Lidar inclination for a disturbance amplitude of 0.05 , 0.1, 0.15, 0.2 rad.

Graph 17: Results for simulation of mechanism reaction to sudden rotational jerking with the set of parameters

described above. The depicted values are the amplitude of the precession motion in steady state and not of the violent

transition maxima. The same experiment was carried out of 6000rpm.

The rotational jerking for the given duration does not disturb the mechanism too much.

Only a very violent rotational ‘tug’ can cause a noteworthy precession. An unlikely event

considering the buoy weighs several tonnes.

It is possible to include more results, but that would be a waste of time. More

simulations were undertaken but they all pointed out that rotational jerking is nothing

to worry about.

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 0.05 0.1 0.15 0.2 0.25

Lid

ar in

clin

atio

n [

rad

]

Max frame deviation [rad]

Max ampl 3000

Ref 3000

Max ampl 6000

Ref 6000

0.05 rad 0.10 rad 0.15 rad 0.20 rad Z inclination [rad] Time [s] 3000 rpm



4.6.2.3 Translational jerking

Now research analogous to the previous paragraph will be undertaken with similar

functions, only for translation instead of rotation. The translation movement is parallel

to direction (1,4,1). This is to create a representative cable snagging motion on one hand

and a worst case scenario on the other hand. Pulling directions aligned with one of the

axes or perpendicular creates less of a disturbance.

Figure 107: Direction of translational motion (1,4,1)

The following parametersets represent a normal situation where, suddenly, the frame is

tugged down.

a1 0 m

a2 -0.05 -0.125 -0.25 -0.5 m

a3 0 m

a 120 s

b 2 s

c 2 s

(Normal frame movement with amplitude 0.1 and

period of 5 seconds. Similar to the reference situation)

Table 30: Translational jerking simulation parameters



Figure 108: Simulations of Lidar inclination. Sudden translation at t equals 120 seconds.

The results above show that translational jerking is nothing to worry about. The only

effect of the translation is a slight transition phase. Whet it has passed, the movement is

exactly the same as seen in the theoretically ideal reference mechanism simulations.

Further analysis is not needed. When the dip duration is varied the results are similar: a

calm transition phenomenon and a steady state identical to the theoretically ideal

situation.

4.6.2.4 Change of amplitude

As mentioned earlier; the functions can also be sinusiodal with the step like function as

an envelope. This can simulate a change in amplitude. The simulation (figure 109) shows

the results (Lidar z-angle) of the reference mechanism starting with an excitation

amplitude of 0.1 rad and switching to 0.2 in two different time intervals: 120 seconds

and 15 seconds:

Z inclination [rad] Time [s] 3000 rpm



Figure 109: Simulation of Lidar inclination for gradually changing amplitude from 0.1 to 0.2 rad.

There is absolutely no transition phenomenon nor dynamic effect visible in the results.

Even when testing with very sudden envelope functions. This means that all changes can

be regarded as quasi instantaneous. All maximum Lidar angles correspond with the

amplitude at the same time. Changes in amplitudes don’t cause problems as well. A

sudden tug inducing a pitch motion such as a cable snag was more detrimental, but still

not a real threat. Especially at a realistic transition time.

4.6.2.5 Conclusion

It can be concluded that jerking is not a threat to the accuracy of the measurements the

Lidar will take. Only when the mechanism is pitched very violently, the effect is

noticeable. Very sudden pitch movements are, considering the buoy’s bulkiness, very

unlikely.

4.6.3 Restarts during operation

If a problem occurs the flywheel may stop spinning. How bad will the performance be if

this happens? And what happens if the flywheel is restarted? To find out, simulations

will be carried out in which the flywheel is stationary for 120 seconds and is then

accelerated to 6000 rpm in a specified time.

15 sec transition 120 sec transition Z inclination [rad] Time [s] 6000 rpm 0.1 - 0.2 rad



Figure 110: Simulations of Lidar inclination at start-up for varying start-up durations.

First things first. The mechanism’s performance with the flywheel inactive is 1868%

worse than the reference mechanism at 6000 rpm. An inactive flywheel means a

maximum inclination of 1.61°. When the flywheel is accelerated a violent transition

phenomenon is observed followed by a new steady state regime with an induced

precession motion. The transition regime is not really important. However, the newly

induced precession motion is. Its relationship with the transition time is shown graph

18.

Graph 18: Maximum Lidar inclination in steady state after flywheel acceleration from 0 to 6000 rpm.

2min

4 min

6min

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 50 100 150 200 250 300 350 400

Ste

ady

stat

e m

axim

um

incl

inat

ioo

n

afte

r ac

cele

rati

on

[ra

d]

Flywheel acceleration time [s]

Max SS inclination

0 - 6000 rpm

120 sec transition 240 sec transition 10 sec transition Z inclination [rad] Time [s]

Steady state Steady state



It looks like it is worthwhile to restart the flywheel as gently as possible. In case the

flywheel drive’s power electronics were incapable of achieving this, the effect could be

very bad as shown in the simulation results. If the motor spins up the flywheel in 10

seconds, the resultant maximum inclination is 6.4° and it will take very long to damp

out.

Changing flywheel speed without compromising performance too much is possible if the

changes are very gradual.

4.6.4 Influence of friction

Of course friction should be reduced as much as possible but it is inevitable. To quantify

the detrimental effect of friction, the force function of the joints were changed to include

friction force:

A constant restoring moment was added working in the opposite direction of rotation.

The force is determined by the friction coefficient μ, the load on the bearings [kg], the

gravitational constant g [m/s²] and the radius of the axis [m] rotating in the bearing.

The bearings used are roller bearings. The friction coefficient of these bearings is around

0.001 for oil lubricated bearings. For greased and sealed bearings however friction is

expected to be higher and because the working conditions for these bearings will be

especially bad. The friction coefficient is estimated at 0.01. The axis diameter is

estimated to be 6 cm.

To check how much it would pay off to decrease friction to 0.001 and to see how bad it

would be if the friction coefficient rose to 0.03 a series of simulations will be

undertaken:



μ 0 0.001 0.003 0.01 0.03 -

mload X 200 kg

mload Z 150 kg

g 9.81 m/s^2

raxis 6 cm

(Normal frame movement with amplitude 0.1 and

period of 5 seconds. Like in the reference situation)

Table 31: Parameters for friction research

Figure 111: Simulation of Lidar Z axis inclination for varying friction coefficient. Simulation time is 90 seconds.

The simulations show an increase in amplitude as expected. It can be seen that only the

excitation component increases and not the precession. The precession period remains

the same. The shape of the graphs seem to change for higher friction due to the force

discontinuity caused by the discontinuous ‘signum’ function.

6000 rpm

0.001 0.003 0.01 0.03 Z inclination [rad] Time [s]



Graph 19: Graphs of friction coefficient research for both Lidar axes.

For the first three data points the relation between performance and friction coefficient

seems completely linear. Only for the highest value the linear relation is somewhat

broken, but only by a small margin. The graphs above show that the performance

decrease is entirely due to the excitation component. It may also be noted that the slope

of the graphs is steeper for the X axis than for the Z axis. This is because the X axis’

bearings carry more load and produce more friction moment. Let see how much

performance declines in the relative sense.

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0 0.01 0.02 0.03

Lid

ar in

clin

atio

n [

rad

]

Friction coefficient [-]

Max ampl Z Exc ampl Z

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 0.01 0.02 0.03

Lid

ar in

clin

atio

n [

rad

]


Max ampl X Exc ampl X

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Lid

ar in

clin

atio

n [

rad

]


Max ampl X

Exc ampl X

Max ampl Z

Exc ampl Z



Mu Max ampl Z Exc ampl Z Relative Max ampl X Exc ampl X Relative

- rad rad % rad rad %

0 0.00129 0.000964 0.000838 0.000596

0.001 0.00132 0.000974 1.73% 0.000856 0.000609 2.15%

0.003 0.00135 0.000994 4.23% 0.000892 0.000636 6.42%

0.01 0.00148 0.00108 14.02% 0.00103 0.000744 23.09%

0.03 0.00190 0.00142 46.49% 0.00151 0.00116 80.07%

Table 32: Friction simulation results. Absolute numbers.

All together the mechanism responds well to the friction. It does not really affect

performance too badly. That said, it is still worthwhile to reduce friction as much as

possible. For example: the Z axis inclination is 14% worse for a friction coefficient of

0.01 but only 4.2% for a friction coefficient of 0.003.

4.7 Frequency response

Previously optimal flywheel geometry and component arrangement was discussed. The

reaction of the mechanism to disturbances has been covered as well. Now it is time to

check how the mechanism reacts to changes in excitation period by changing frequency.

This research is conducted with the flywheel speed set at 3000 rpm. At which

frequencies will the mechanism resonate? Are those frequencies in a relevant range?

Can the joint dampers and/or springs be tuned to improve performance in certain

frequency ranges?

Expectations from a theoretical standpoint:

Excitation amplitude should not affect resonance behaviour/frequencies.

Damping should not shift resonance peaks or only very slightly. Resonance peak

amplitudes should lower with increasing damping.



4.7.1 About UM and the reference model

Please take careful consideration of the fact that the mechanism parts in UM are

infinitely strong and stiff. Deformability, which would give an extra damping effect, is

not simulated. When the mechanism resonates, UM may show extremely violent results.

The reaction forces for such a movement would have to be impossibly high, high enough

to deform any physical component. Any violent amplitudes or movements shown in

simulation results, when the mechanism resonates, must be interpreted wisely.

Typically the results will show whether or not the mechanism resonates. However, the

numbers will be useless to determine the actual movement if the mechanism were real,

since deformation would occur.

The axes connecting the bearings are not modelled. Of course these points would

represent an elastic point in the mechanism. They are not present in the model so

resonance frequencies can change compared to an actual mechanism.

At this point it is unclear what an actual mechanism will look like. The current reference

mechanism’s dimensions were inspired by the 3E’s prototype but even this mechanism

looks quite different. Its sole purpose was to provide insights to help develop such a

mechanism. It is unclear what decisions shall be made in the future. Will an entire new

mechanism be developed or will the older mechanism continue to serve but with a

flywheel added?

Despite the fact that some of the results are not representative in the absolute sense,

behaviour should still be similar to an actual mechanism and frequencies should be

within the same order of magnitude.

4.7.2 Excitation of frame for typical wave periods

Simulations were carried out in a period range of 2.5 seconds to 10 seconds. The most

relevant range lies between 4 and 7 seconds. 5 seconds has always been the reference

value up until now which is approximately the most common value.

The depicted values are maximum Lidar inclinations. This is enough information since

the most important factors are the global performance and the possible danger of

resonance.

The reference mechanism was tested in two configurations:

1. The standard reference mechanism with changing excitation period.

2. The standard reference mechanism with changing excitation period and a

stiffness coefficient of 50 N.m/rad for both axes.



…And two amplitudes for excitation: 0.1 and 0.2 rad. Just to verify the theoretical

expectations.

Graph 20: Comparison of the results for both versions of the reference mechanism for both amplitudes. This confirms

the proposition that a change of amplitudes doesn’t cause a shift in the frequency behavior.

The results above show that the amplitude doesn’t change the behaviour of the system

in the measured period range. It looks like very high values, meaning resonance, are not

present in the relevant range. This is good news. This means that the reference

mechanism is in no danger of resonating for reasonable excitation periods. It becomes

really interesting when the graphs are rearranged to compare the normal version versus

the version with extra stiffness.

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

2 3 4 5 6 7 8 9 10

Max

imu

m L

idar

incl

inat

ion

[ra

d]

Excitation period [s]

Ampl 0.2 + spring

Ampl 0.1 + spring

0

0.002

0.004

0.006

0.008

0.01

0.012

2 3 4 5 6 7 8 9 10

Max

imu

m L

idar

incl

inat

ion

[ra

d]


Ampl 0.2

Ampl 0.1



Graph 21: Same as the previous graphs but rearranged to show the different behaviour caused by the extra stiffness.

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

2 3 4 5 6 7 8 9 10 11

Max

imu

m L

idar

incl

inat

ion

[ra

d]


Ampl 0.1 + spring

Ampl 0.1

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

2 3 4 5 6 7 8 9 10 11

Max

imu

m L

idar

incl

inat

ion

[ra

d]


Ampl 0.2 + spring

Ampl 0.2



The results above point out the interesting changes the extra restoring force has caused.

It seems that the added spring in the joints helps overcome inertia for high

frequency/low period excitations producing higher accuracy in the low period range.

The spring’s stiffness counteracts the flywheel at low frequency/high period excitations

producing bad results in the high period range. Since high periods are far more common

than low periods, the system without spring looks the most promising and it is less

complex (no spring needed). Also, exceptional periods outside the normal range are far

more likely to occur on the high period side than on the low period side thanks to the

buoy’s inertia. It looks like the stiffness coefficient shifts the point where the mechanism

is most accurate on the excitation period axis. One could impose a stiffness to put the

optimum exactly at 5 seconds. There would not be much difference compared to the

performance without spring and is not worth risking bad performance for large period

movements and even the cost of the spring. For the reference mechanism, this is the

safest option since the lowest excitation periods have the most accuracy.

It can be concluded that the mechanism cannot be brought into resonance because of the

motion imposed by the waves. Another source of movement is the vibration of the

motor. The motor’s frequency can be any value between 0-100Hz because of the

invertor. So it is worthwhile to discover the frequencies at which the mechanism does

resonate. From this point on only the reference mechanism without spring will be used

for testing.

4.7.3 Resonance

The resonance peaks are not discovered yet. So where do they lie? For the unsprung

reference mechanism one would think that the mechanism will not resonate at low

frequencies but at high frequencies and it does of course. The sinusoidal excitations

functions served nicely to research the mechanism’s reactions but they can also serve to

impose high frequency low amplitude oscillations. Amplitude for frame excitation is set

at about 0.5° or 0.009 rad.



Simulation for 1000Hz:

Figure 112: Simulation of the reference mechanism excited with 25 ms of excitation period or 40Hz of excitation

frequency. Excitation amplitude is about 0.5°. Duration: 18 seconds.

While the excitation is barely noticeable the Lidar inclination has an order of magnitude

of 100° and rising. Clearly resonance. The graph may not show a realistic result. It just

indicates that the mechanism reacts very violently.

Subsequent research shows that mild resonance starts at an excitation frequency of the

frame of around 300 Hz for the reference model. The damping, as expected, makes the

mechanism respond to a broader range of frequencies. More specifically between 300

Hz to 1500 Hz (approximately). A precise measurement is unnecessary since absolute

numbers are not really significant here. It sufficient to conclude that wave excitation will

not bring the system into resonance.

The motor however, with its higher invertor frequency, just might be the problem. To

check this, the flywheel position function was expanded to incorporate a vibration term.

v: Vibration amplitude: set at about 0.5 degrees

f: Vibration frequency

If the system responds badly for frequencies between 50 and 100 Hz it would be bad.

Simulation results are shown for Lidar x axis inclination and z axis inclination.

3000 rpm

1000 Hz excited Z inclination [rad] Time [s]



Graph 22: Simulation of Lidar z inclination for varying vibration frequencies.

Lidar z angle inclinations show that the inner gimbal does not come into resonance for

the measured frequencies. If that were the case the excitation amplitude would increase.

The max amplitude did increase however but only because of an increase in precession

component. This component damps out like previously described, so the precession is

not enforced. It seems to be caused by a start-up phenomenon that intensifies when the

vibration frequency rises.

Graph 23: Simulation of Lidar x inclination for varying vibration frequencies.

0

0.005

0.01

0.015

0.02

0.025

0 200 400 600 800 1000 1200

Lid

ar z

incl

inat

ion

[ra

d]

Vibration frequency [Hz]

Max ampl

Exc ampl

0

0.1

0.2

0.3

0.4

0.5

0.6

0 500 1000 1500 2000

Lid

ar x

incl

inat

ion

[ra

d]

Vibration frequency [Hz]

Max ampl

Exc ampl

Difference is maximum precession amplitude.



The x angle shows that there is nothing to worry about. It can be seen that the outer

gimbal responds to frequencies starting from 400Hz. But these frequencies will not be

attained by the motor drive. One can see that, because of the damping, the system

responds to a broad range of frequencies. The increase in maximum amplitude is now

caused by both the increasing precession phenomenon and resonance responsible for

the rise in precession and excitation component respectively. The actual peak values of

the resonance amplitudes in the graphs above could not be uncovered because from

2000Hz onwards it becomes very difficult to measure the excitation amplitude reliably.

Please note that when the outer gimbal rotates around its axis more mass is displaced

than when the inner gimbal rotates. The outer gimbal holds the inner gimbal and the

Lidar-flywheel subsystem. The inner gimbal only holds the Lidar-flywheel subsystem.

Because of the extra mass the resonance frequency for the outer gimbal is lower than for

the inner gimbal. In any case both of the gimbals’ resonance frequencies lie way above

100Hz.

4.8 Motor requirements

Since the buoy’s power sources will consist of solar panels and small windmills, it is

important to know the motor power requirements and more specifically if these

requirements are sufficiently low for the available power source.

Please keep in mind that all the following calculations have been made for the

unchanged reference mechanism.

4.8.1 Motor power in steady state

How much power will the motor need if the mechanism is spinning and the buoy is

moving? It is expected to be a very low figure. Bear in mind that in a system such as a

bicycle, the gyroscopic forces exerted by the wheels are quite low and yet they still

succeed in keeping the bike stable. This is because these forces act to keep the system

from tilting and try to keep it as level as possible. When the system is level this means

that it does not rotate (except for the spinning axis) and, as a consequence, no inertia

needs to be overcome. The forces are small, but they act as if controlled by an ultra-fast

feedback controlled system. Because the system reacts immediately, the correction force

needn’t be large. This means that a bicycle with wheels weighing as low as 1kg each can

keep itself and a 75kg rider up without difficulty.

In case of the reference mechanism, the most important forces to fight will be the

damping and the tilting force exerted by the Lidar subsystem’s inertia if it’s COG is not in

the rotation point. (See 4.5.6) The further the Lidar subsystem’s COG is from the centre

of rotation, the more torque the flywheel has to counteract.



In UM, the speed is fixed with an expression at 3000 rpm. A certain torque is needed to

keep the speed at this rate. The reaction torque in the joint will be indicative of the

torque a motor would have to apply to keep the speed at 3000 rpm. In reality, a motor

will not react as fast as the infinitely fast responding theoretical simulation in UM. Still, it

should be quite representative. Because the flywheel is accelerated infinitely fast, a non

physical transition phenomenon was encountered. This is why only values between 10

and 20 seconds are analysed because this represents two oscillation periods in the

reference situation (2 times 5 seconds).

This was tested for the reference mechanism and for the reference mechanism with

changed flywheel offset. The latter will have a Lidar flywheel subsystem with changed

COG and this should need more torque to work. Results are shown in figure 113.

Figure 113: Reaction torque in Lidar-flywheel joint in UM model of reference mechanism and the reference

mechanism with doubled flywheel offset. Time window is 10 to 20 seconds in the simulation.

It looks like changing the Lidar-flywheel subsystem’s COG indeed increases the work the

motor, just as predicted. The transition phenomenon takes longer too for the changed

offset simulation, but that is not really important. The focus is on the torque for the

reference mechanism.

3000 rpm

Reference Double offset Torque [Nm] Time [s]



Graph 24: Reaction torque in Lidar-flywheel joint in UM model of reference mechanism. Time window is 10 to 20

seconds in the simulation.

Torque Power

Average 5.28E-06 Nm 1.66 mW

Maximum 3.92E-03 Nm 1.23 W

Table 33: Statistics of torque shown in Graph 24

It looks like the torque needed to keep the flywheel turning is really low. A physical

mechanism will have more disturbances and drag, but the required power should still be

very low compared to the power needed to accelerate the flywheel. (See 4.8.2) Even if

the steady state requirements was a two digit number, it would still be acceptable.

4.8.2 Flywheel start-up

Accelerating the heavy flywheel is a far bigger challenge for the small motor than

keeping it up to speed once it is running. At this point it is not clear what type of motor

drive will be used so an energy equation will have to do.

The model’s flywheel is a simple disc with certain inertia. All the motor has to do is

overcome the inertial torque of the flywheel during a predefined start-up time.

Variables

ωend: Final speed of flywheel

Tfinish: Time span during which the flywheel must accelerate

t: Time variable

-0.00500

-0.00400

-0.00300

-0.00200

-0.00100

0.00000

0.00100

0.00200

0.00300

0.00400

0.00500

Torque [Nm]



Calculated values

Izz: Flywheel inertia

ω(t): Instantaneous speed

α(t): Instantaneous flywheel acceleration

M(t): Instantaneous torque

P(t): Instantaneous power

Mmax: Max torque Mavg: Average torque

Pmax: Max power Pavg: Average power

Equations

The following values were substituted: 3000 rpm (~314 rad/s) for an acceleration time

of 240 sec (4 min). Figure 114 shows what the functions look like.



Acceleration: α [1/s²] Speed: ω [1/s]

Torque: M [Nm] Power: P [Watt]

Figure 114: Function visualisation of motor start-up model

The main statistics are:

Torque [Nm] Power [W]

Average 10.02 1574.5

Max 15.75 3212.9

Table 34: Statistics of evaluated functions for flywheel start-up model.

It can be noted that quite a lot of power is needed for an acceleration time of 4 minutes.

3.2 kiloWatt to be precise. Please bear in mind that this power is only needed for a small

duration and not continuously.

Although the capacity of the vessel’s power generating systems is far below the

maximum power listed above, this is not a problem because of the battery. The motor

will run off the battery and, since it will be quite large, it can easily provide the power

needed for a short period of time. When the flywheel is accelerated, the power

requirements become very low and the battery can recharge.



If the maximum power or maximum torque is imposed by specifications one can deduce

the approximate acceleration time using the model above.

These formulae can help determine the acceleration time when the motor is the limiting

factor. These functions are visualised in figure 115 and figure 116 for 3000 rpm.

Figure 115: Maximum torque for a final speed of 3000 rpm for varying acceleration time.




4.9 Conclusion

It can be concluded that the motor must be able to generate a peak power up to several

kilowatt depending on the desired acceleration time. Remember, in case the flywheel

has to be restarted at sea, it is beneficial to do so as gently as possible like discussed in

4.6.3. Once the flywheel has been accelerated the motor power requirements are very

low.


Master thesis – Mechanical Engineering –Combined results Page 147

5 Combined results

Now it is time to put all the preceding research together in a coupled simulation.

The process of the creation of LS-Dyna models in LS-Prepost was already discussed in

chapter 3. The Dyna model contains a wave tank with a body of water, agitated by a

paddle to create sea waves with a controlled period, wavelength and wave height. The

model is specifically tuned to represent a sea sate where a wind turbine will operate.

This sea sate can be regarded as violent, but not so that breaking waves occur. Of course

the model contains a buoy that floats in the body of water and is moored to the seabed

with a cable. How each of the three buoys performs is discussed in 3.9.

After the numerical simulation study, a kinematic study of the Lidar stabilisation

mechanism was carried out using Universal Mechanism software (UM). The Lidar

mechanism’s holding frame was agitated with a prescribed sinusoidal motion with a

specified period and amplitude. These and other input parameters, such as flywheel

speed, were varied to test the model and to help tune its performance. The result is a

stabilisation mechanism model with a supposedly optimal size and placement within

practical limits.

Now the moment has come to make the holding frame move as if its movement was

caused by the buoy attached to it while it is floating in the sea. This way the performance

of the mechanism can be assessed when it moves in a realistic way. Finally it will be

possible to determine how accurately the Lidar will be stabilised.

Please note that the following UM simulation is not a true coupled simulation. Both

programmes will not be running at the same time and will therefore not interact. This

means that the inertial forces exerted by the mechanism on the buoy frame do not affect

the buoy in the Dyna simulation in any way. This induces a small error because the buoy

movement is simulated as if the mechanism was completely rigid, which it is not. This

error is completely negligible because of the small ratio of the mechanism’s weight to

the buoys. Any force the mechanism might exert on the buoy will not change its

movement significantly. The extremely slight gain of accuracy a true coupled simulation

might provide does not justify the extra difficulties. The actual procedure is pictured in

figure 117.



Figure 117: Flow of data and relation between programmes

From the output of the Dyna simulations for each buoy, representing the movement of a

specific node in both translation and rotation, is exported and converted to a text file

format. After the exporting process is completed, the part of LS-Dyna in this simulation

is completed. The definition of the frame movement in relation to UM’s inertial

coordinate system is effectuated using the text files. UM simulates the mechanism’s

movement just like it has before. Only now the frame translates and rotates the exact

same way as the buoy moves, instead of just in a sinusoidal fashion. The text files contain

a sampled record of the position of a node (X, Y, Z position) and its rotation (rotation

around X, Y, Z axes). Because the buoy model is rigid, this means that the position of all

the buoy’s points can be determined. UM interpolates the points in the position and

rotation datavectors using spline functions in order to be able to calculate the first and

second derivative. Please note that a total of six files/variables was needed.

K-file Dyna model of wavetank with buoy.

LS Dyna calculation

(Dyna output) Buoy position X-Y-Z

(Dyna output) Buoy rotation X-Y-Z

(Text file) Buoy position X-Y-Z

(Text file) Buoy rotation X-Y-Z

Conversion

Universal mechanism simulation

Frame movement definition

(Plot & data) Lidar rotation X-Y

Stabilization Performance analysis This section

Buoy movement analysis See REF



The Lidar performance was measured earlier using the Lidar inclination around the Z –

axis. This was sufficient because performance numbers were only relevant in the

relative sense. It was all about getting the inclination as low as possible and checking if

the mechanism reacts positively or negatively to certain changes. For the coupled and

realistic simulations, the absolute numbers have true meaning. That is why the

mechanisms performance will be measured using the absolute value of the total rotation

vector, which is the algebraic sum of all three rotation vectors. This inclination is

directly correlated to the quality of the Lidar’s measurements.

5.1 3E prototype

The 3E prototype was tested first. The movement of the buoy itself was visualised in

Figure 118. The simulations are repeated for different flywheel speeds: 0, 3000 and

6000 rpm. This will show how much effect the flywheel has in a realistic situation and

will reveal the extent of the benefit to increase speed to 6000 rpm. Please remember

that the inclination is now an absolute value and is always positive. The total duration is

28 seconds.

Figure 118: Simulation result for Lidar inclination on the 3E prototype buoy (absolute value of the rotation vector). No

flywheel curve is the highest.

It looks like it is definitely worthwhile to install the flywheel.

No flywheel 3000 rpm 6000 rpm Inclination [Rad] Time [s]



Figure 119: Detail of Figure 118

Flywheel

speed

Average inclination Relative Maximum inclination Relative

0 0.09449 rad 5.41° 0.23623 rad 13.54°

3000 0.01160 rad 0.66° -87.72% 0.02549 rad 1.46° -89.21%

6000 0.01029 rad 0.59° -89.11% 0.02315 rad 1.33° -90.20%

Table 35: Results of coupled simulation of 3E prototype buoy

It seems the performance increase related to a faster spinning flywheel that looked

promising during the kinematic study is not so relevant with more realistic boundary

conditions. Compared to the simulation with the flywheel present, but inactive, the

maximum inclination is about 89.91% lower for 3000 rpm and just 90.20% for 6000

rpm. It can be concluded that the flywheel increases performance dramatically, but it is

not very beneficial to increase speed to 6000 rpm.

3000 rpm 6000 rpm Inclination [Rad] Time [s]



5.2 PEM 58

Next up is the PEM 58. Only 18 seconds were simulated because of limitations in

computing power and time. Similar tests to the ones of the 3E buoy will be executed:

Figure 120: Simulation result for Lidar inclination on the PEM 58 buoy (absolute value of the rotation vector). No

flywheel curve is the highest.

The flywheel proves itself yet again.


No flywheel 3000 rpm 6000 rpm Inclination [Rad] Time [s]

3000 rpm 6000 rpm Inclination [Rad] Time [s]



Flywheel

speed

Average inclination Relative Maximum inclination Relative

0 0.10953 rad 6.28° 0.25000 rad 14.32°

3000 0.01244 rad 0.71° -88.64% 0.02542 rad 1.46° -89.83%

6000 0.01095 rad 0.63° -90.01% 0.02311 rad 1.32° -90.76%

Table 36: Results of coupled simulation of PEM buoy

Similar observations can be made to the 3E prototype. The comparison will be most

revealing.

Please remember that the SPAR buoy was not simulated (see 3.9.2.3) because of

limitations in computation power.

5.3 Comparison

All results have been put together. 3E prototype simulations were longer than the PEM

simulations respectively 28 and 17 seconds:

Figure 122: Simulation result for Lidar inclination of both buoys (absolute value of the rotation vector).

3E No flywheel 3E 3000 rpm 3E 6000 rpm PEM No flywheel PEM 3000 rpm PEM 6000 rpm Z inclination [rad] Time [s]




3E 3000 rpm 3E 6000 rpm PEM 3000 rpm PEM 6000 rpm Z inclination [rad] Time [s]


Master thesis – Mechanical Engineering –Conclusion Page 154

6 Conclusion

It is obvious that, despite the lesser dynamic performance of the PEM compared to the

3E prototype as a wave filter, the results are very similar. The stabilisation mechanism

takes the more violent movement of the PEM 58 in its stride. So if a choice had to be

made between the two buoys, cost would be the deciding factor and not performance.

This comparison would likely favour the PEM 58 (see 2.3.3).

Graph 25: Average inclination values of both buoy types compared

Graph 26: Maximum inclination values of both buoy types compared

0.00000

0.02000

0.04000

0.06000

0.08000

0.10000

0.12000


Lid

ar in

clin

atio

n [

rad

]

Average

3E

PEM

0.00000

0.05000

0.10000

0.15000

0.20000

0.25000

0.30000


Lid

ar in

clin

atio

n [

rad

]

Maximum

3E

PEM


Master thesis – Mechanical Engineering –Conclusion Page 155

The graphs showcase the flywheel performance once more. System performance

remains almost identical despite the different behavior of each buoy. The choice of buoy

should really be based on cost effectiveness rather than dynamic stability because the

stabilizing mechanism irons out most of the bad behavior the chosen buoy might have.

Just as suggested in the beginning (part 2.3.3) the PEM 58 is, according to this research,

more suited for the job than 3E’s own prototype because it more practical. As long as the

Lidar is suspended in a similar construction as the reference mechanism with a flywheel,

the Lidar accuracy can be superior to that achieved by the support mechanism currently

used by 3E.

On the practical side, lots of improvements could be made. These can be seen in figure

124. Ideally, only the laser emitting part of the Lidar should be stabilised. As a

consequence, the stabilisation mechanism could be constructed much smaller yielding

similar, of even better, accuracy with only a fraction of the costs.

Figure 124: Concept sketch with added practical improvements


Master thesis – Mechanical Engineering –References Page 156

7 References

[1] V. nieuwsdienst, “Deredactie.be,” 3 Mei 2012. [Online]. Available:

http://www.deredactie.be/cm/vrtnieuws/regio/westvlaanderen/1.1150084.

[Accessed 3 Mei 2012].

[2] Resinex, Resinex, Maart 2012. [Online]. Available: http://www.resinextrad.com/.

[3] M. B. L. G. R. Liu, Smoothed particle hydrodynamics, World Scientific Publishing Co.

Pte. Ltd., 2003.

[4] D. L. H. S. W. A. J. Swegle, “J. Computational physics,” 1995, pp. 116-123.

[5] L. S. T. Corporation, “LS Dyna,” LSTC, 2012. [Online]. Available:

http://www.lstc.com/.

[6] R. A. D. Robert G. Dean, Water wave mechanics, World scientific publishing Co. Pte.

Ltd., 1992.

[7] J. Pelfrene, Study of the SPH method for simulation of regular and breaking waves,

Gent: Universiteit Gent, 2011.

[8] P. Chapman, “Ocean currents,” Advameg, Inc, [Online]. Available:

http://www.waterencyclopedia.com/Mi-Oc/Ocean-Currents.html. [Accessed 24

April 2012].

[9] V. Hydrografie, “Golftheorie,” Vlaamse Hydrografie, 2012. [Online]. Available:

http://www.vlaamsehydrografie.be/hm_atlas_cd/www/theorie/golftheorie/golfth

eorie.htm. [Accessed 19 April 2012].

[10] M. Chicago, “Tsunami wave tank,” MSI Chicago, 2012. [Online]. Available:

http://www.msichicago.org/whats-here/exhibits/science-storms/the-

exhibit/tsunami/tsunami-wave-tank/. [Accessed 19 April 2012].


Master thesis – Mechanical Engineering –Figures, graphs and tables Page 157

8 Figures, graphs and tables

8.1 List of figures

Figure 1: Lidar measuring equipment ..................................................................................................... 1

Figure 2: Schematic overview of measuring device operating conditions ................................ 2

Figure 3: Location of metacentre .............................................................................................................. 5

Figure 4: Conventional catamaran versus SWATH type catamaran ............................................ 6

Figure 5: New SWATH type catamaran pilot ship for the port of Zeebrugge [1].................... 6

Figure 6: Small catamaran research vessel ........................................................................................... 7

Figure 7: Stable floating plastic modular buoy for mooring applications [2] .......................... 8

Figure 8: Resinex PEM 43 Catamaran buoy. Diameter approximately 4.3m ........................ 11

Figure 9: Resinex PEM 58 catamaran buoy. Diameter approximately 5.8 m ........................ 11

Figure 10: Schematic of a typical spar buoy design. ....................................................................... 13

Figure 11: Support domain ....................................................................................................................... 16

Figure 12: 2D representation of support and influence domains for illustrating possible

problems when using different smoothing lengths. ....................................................................... 17

Figure 13: Crash test [5] ............................................................................................................................ 18

Figure 14: From geometry to useable LS-Dyna code by meshing ............................................. 19

Figure 15: Hierarchical structure used in the LS-Dyna code for a rigid shell part. ............. 20

Figure 16: Extract of k-file......................................................................................................................... 21

Figure 17: Paddle .......................................................................................................................................... 22

Figure 18: Spacing between the parts and particles ....................................................................... 22

Figure 19: Wave characteristics [6] ...................................................................................................... 24

Figure 20: Wave Tank CSI Chicago [10] ............................................................................................... 29



Figure 21: Flap type wave maker ........................................................................................................... 30

Figure 22: Wave tank design with sponge layer from [7] ............................................................. 33

Figure 23: Model with 3E prototype, cable and sponge layer ..................................................... 33

Figure 24: Travelling wave in Dyna model ......................................................................................... 34

Figure 25: Boundaries and dimensions ............................................................................................... 35

Figure 26: Scheme of undercurrent duct ............................................................................................ 36

Figure 27: Undercurrent circuit model ................................................................................................ 37

Figure 28: Lumped plate friction model .............................................................................................. 38

Figure 29: Friction plate model ............................................................................................................... 38

Figure 30: Buoy model with mooring cable and two forces: downwards and sideways . 39

Figure 31: Initial grid of the SPH-particles ......................................................................................... 40

Figure 32: Failing contact .......................................................................................................................... 42

Figure 33: Wave tanks with 25kg (upper) and 1000kg(lower) particles............................... 43

Figure 34: Sea level for 1000 kg(upper) and 25 kg(lower) particles ....................................... 44

Figure 35: Wave period; Z-displacement (in meters) versus time (in seconds) ................. 47

Figure 36: Wave height; Z-displacement (in metres) versus the time (in seconds) .......... 47

Figure 37: Measured wavelength ........................................................................................................... 48

Figure 38: Buoyancy check ....................................................................................................................... 49

Figure 39: Screenshots of breaking waves ......................................................................................... 49

Figure 40:- Z-coordinate of water level for LS-Dyna Dam Break test (left) and

experimental and Joren’s data (right). Right picture from [7] .................................................... 50

Figure 41: Series of screenshots of the executed dam break test .............................................. 51

Figure 42: Detailed CAD drawing (left) and simplified mesh (right) for the PEM58 buoy

.............................................................................................................................................................................. 52

Figure 43: Platform drawn with CAD ................................................................................................... 53



Figure 44: Detailed 3E buoy Dyna model ............................................................................................ 53

Figure 45: Detailed PEM58 buoy Dyna model .................................................................................. 54

Figure 46: Detailed spar buoy Dyna model ........................................................................................ 54

Figure 47: 3E working prototype ........................................................................................................... 55

Figure 48: Buoyancy check ....................................................................................................................... 55

Figure 49: Two layer model ...................................................................................................................... 57

Figure 50: Dyna two layer model: Two layers, two parts ............................................................. 58

Figure 51: Dyna two layer model: Two layers, one part ............................................................... 59

Figure 52:Wave tank (left), wave tank and buoy (centre), wave tank and moored buoy

(right) ................................................................................................................................................................ 61

Figure 53: Displacement in x- (red), y- (green) and z-direction (blue) for the 3E buoy . 62

Figure 54: rotation around x- (red), y- (green) and z-axis (blue) for the 3E buoy ............. 63

Figure 55: side view of 3-buoy model at 13.33 seconds showing the maximum

inclination ........................................................................................................................................................ 64

Figure 56: rotational speed around y-axis for the 3E buoy ......................................................... 64

Figure 57: rotation around the y-axis for the PEM58..................................................................... 65

Figure 58: side view of PEM58 model at 16 seconds showing the maximum inclination

.............................................................................................................................................................................. 66

Figure 59: rotational speed around y-axis for the PEM58 buoy ................................................ 66

Figure 60: Barely submerged, but floating SPAR buoy .................................................................. 67

Figure 61: sketch showing vortices when placing the spar buoy .............................................. 69

Figure 62: rotation around y-axis. Red for the PEM58 and green for the 3E buoy ............. 70

Figure 63: rotational speed [rad/s] versus time [s] for the 3E and the PEM58 buoy........ 70

Figure 64: CAD drawing of linkage system to make the Lidar move independently ......... 73



Figure 65: UM animation window: representation of Lidar stabilizing mechanism model

.............................................................................................................................................................................. 74

Figure 66: Offset parameters of mechanism model in UM and reference points. ............... 75

Figure 67: Relative movement and restoring moment. ................................................................. 78

Figure 68: Result of 120 sec simulation of the reference mechanism. X and Z inclination

is shown with max. inclination value of 0.07 degrees. Speed: 6000 rpm ............................... 80

Figure 69: Sine function of angular movement definition of frame. ......................................... 81

Figure 70: Inclination signal component definition ........................................................................ 82

Figure 71: 600 sec simulation of reference mechanism highlighting the slow decline in

precession ........................................................................................................................................................ 82

Figure 72: Simulation of Lidar inclination for varying flywheel speeds. Lower amplitude

curves represent higher speeds and vice versa. ............................................................................... 83

Figure 73: 20 minute simulations of Lidar inclination for varying flywheel speeds. Lower

amplitude curves represent higher speeds and vice versa. ......................................................... 85

Figure 74: Simulation of reference mechanism with changing amplitudes Smaller

amplitudes yield lower maxima. ............................................................................................................. 87

Figure 75: Scheme of flywheel dimensions and offset. .................................................................. 88

Figure 76: Reference mechanism. Observe the thin flywheel with a large diameter. ....... 89

Figure 77: Simulation of Lidar inclination for changing flywheel radius with constant

height. Speed is 6000rpm. ......................................................................................................................... 90

Figure 78: Simulation of Lidar inclinations of Z axis for varying flywheel thickness.

Lower radii yield higher maxima. .......................................................................................................... 92

Figure 79: 90 second simulation of reference mechanism with a flywheel made from

varying materials. Heavier materials yield lower maximum inclinations. ............................ 95

Figure 80: Simulation of Lidar inclinaton for varying flywheel offset. Smaller amplitudes

represent smaller offset and vice versa. .............................................................................................. 97

Figure 81: Mechanism configurations respectively with the Lidar moved downwards and

upwards. ........................................................................................................................................................... 99



Figure 82: Comparison of the reference mechanism and a mechanism with the Lidar

positioned lower. .......................................................................................................................................... 99

Figure 83: Illustration of Lidar subsystem swaying. ................................................................... 100

Figure 84: Comparison of the reference mechanism and a mechanism with the Lidar

positioned higher. The reference position yields higher excitation amplitude. ............... 101

Figure 85: Screenshot of ‘Super mechanism’ in UM. Would be difficult to build. Physical

axes not drawn. Frame and Lidar module drawn in wireframe.............................................. 102

Figure 86: ‘Super mechanism’. From below. The flywheel is a ring around the Lidar itself

with a hub at the bottom......................................................................................................................... 103

Figure 87: Side view of ‘super mechanism’. Look at the Lidar module’s orientation which

is, as far as the eye can see, perfectly upright while the mechanism is moving. ............... 103

Figure 88: Flywheel of the ‘super mechanism’. A ring instead of a disc. A central hub was

added to make it possible to attach a motor. .................................................................................. 104

Figure 89: Simulations of Lidar inclination comparing the super mechanism to the

reference mechanism ............................................................................................................................... 105

Figure 90: Simulations of Lidar inclination comparing the super mechanism to the

reference mechanism. Simulation time is 1200 seconds or 20 minutes.............................. 105

Figure 91: Simulation of Lidar inclination for changing damping. Higher amplitudes

mean higher damping values. Flywheel speed is 3000 rpm. .................................................... 107

Figure 92: Mechanism with misaligned start-up position. Frame is fixed. ......................... 108

Figure 93: Simulation results for verying damping with misaligned startup of 0.1 rad and

stationary frame. 1200 sec simulation. 3000 rpm ........................................................................ 109

Figure 94: Simulation results for changing damping with misaligned startup of 0.1 rad

and stationary frame. ............................................................................................................................... 110

Figure 95: Flywheel angular speed function with parameters composed of constants and

cosines ........................................................................................................................................................... 112

Figure 96: Detail of flywheel angular speed for the parameters described above for the

‘disastrous’ speed dips............................................................................................................................. 114

Figure 97: Simulation of Lidar inclination for large speed dips of 200, 400 and 800 rpm.

Before t equals 120 the situation is the reference situation. Total duration is 240 sec. 114



Figure 98: Simulation of Lidar inclination with a dip in the speed at 120 seconds. Varying

speed dip duration. ................................................................................................................................... 116

Figure 99: Flywheel angular speed and acceleration for said simulations. ........................ 117

Figure 100: Flywheel angular acceleration for speed dip simulations for constant dip

time. ................................................................................................................................................................ 118

Figure 101: Simulation of Lidar inclination with very fast but small speed dip at t equals

120 seconds. ................................................................................................................................................ 120

Figure 102: Flywheel speed for experiment of gradual variation in flywheel speed. .... 121

Figure 103: Simulation result for Lidar inclination with gradually changing flywheel

speed. Transition from 3000 to 6000 rpm. Transition time is 120 seconds. ..................... 122

Figure 104: Excitation function with envelope and its parameters....................................... 123

Figure 105: Plots of frame movement functions for amplitudes 0.05, 0.10, 0.15, 0.20 . 124

Figure 106: Simulation results for Lidar inclination for a disturbance amplitude of 0.05 ,

0.1, 0.15, 0.2 rad. ........................................................................................................................................ 125

Figure 107: Direction of translational motion (1,4,1) ................................................................. 126

Figure 108: Simulations of Lidar inclination. Sudden translation at t equals 120 seconds.

........................................................................................................................................................................... 127

Figure 109: Simulation of Lidar inclination for gradually changing amplitude from 0.1 to

0.2 rad. ........................................................................................................................................................... 128

Figure 110: Simulations of Lidar inclination at start-up for varying start-up durations.

........................................................................................................................................................................... 129

Figure 111: Simulation of Lidar Z axis inclination for varying friction coefficient.

Simulation time is 90 seconds. ............................................................................................................. 131

Figure 112: Simulation of the reference mechanism excited with 25 ms of excitation

period or 40Hz of excitation frequency. Excitation amplitude is about 0.5°. Duration: 18

seconds. ......................................................................................................................................................... 138

Figure 113: Reaction torque in Lidar-flywheel joint in UM model of reference mechanism

and the reference mechanism with doubled flywheel offset. Time window is 10 to 20

seconds in the simulation. ...................................................................................................................... 141



Figure 114: Function visualisation of motor start-up model ................................................... 144


........................................................................................................................................................................... 145


........................................................................................................................................................................... 146

Figure 117: Flow of data and relation between programmes .................................................. 148

Figure 118: Simulation result for Lidar inclination on the 3E prototype buoy (absolute

value of the rotation vector). No flywheel curve is the highest. .............................................. 149

Figure 119: Detail of Figure 118 .......................................................................................................... 150

Figure 120: Simulation result for Lidar inclination on the PEM 58 buoy (absolute value

of the rotation vector). No flywheel curve is the highest. .......................................................... 151


Figure 122: Simulation result for Lidar inclination of both buoys (absolute value of the

rotation vector). ......................................................................................................................................... 152


Figure 124: Concept sketch with added practical improvements .......................................... 155

8.2 List of Graphs

Graph 1: Maximum Lidar inclination versus flywheel speed and the interpolating power

function. ............................................................................................................................................................ 84

Graph 2: Lidar inclination components versus flywheel speed (primary vertical axis) and

precession period versus flywheel speed (secondary vertical axis). ....................................... 85

Graph 3: Lidar inclination versus excitation amplitude. ............................................................... 87

Graph 4: Lidar inclinations (primary axis) and flywheel weight (secondary axis) versus

changing radius ............................................................................................................................................. 91

Graph 5: Maximum Lidar inclination versus flywheel thickness for a constant radius. ... 93

Graph 6: XY-plot of the product of inertias and the maximum Lidar inclination. ............... 93



Graph 7: Lidar inclination versus flywheel radius. Product of inertias is constant at the

reference value. ............................................................................................................................................. 94

Graph 8: Inclination for varying flywheel density ........................................................................... 96

Graph 9: Maximum Lidar inclination versus flywheel offset for the reference mechanism.

.............................................................................................................................................................................. 98

Graph 10: Comparison of the reference mechanism to the hypothetical ‘super

mechanism’. ................................................................................................................................................. 106

Graph 11: Lidar inclination versus damping for the reference mechanism. ...................... 107

Graph 12: Half-life of precession motion. ........................................................................................ 109

Graph 13: Results of 6000 rpm simulation series compared to 3000 rpm......................... 110

Graph 14: Lidar inclination for simulation with different speed dips. ................................. 115

Graph 15: Lidar inclination for a constant spring back and changing dip duration. ....... 117

Graph 16: Lidar inclination versus dip duration for simulation series with constant

speed dip time. ............................................................................................................................................ 119

Graph 17: Results for simulation of mechanism reaction to sudden rotational jerking

with the set of parameters described above. The depicted values are the amplitude of the

precession motion in steady state and not of the violent transition maxima. The same

experiment was carried out of 6000rpm. ........................................................................................ 125

Graph 18: Maximum Lidar inclination in steady state after flywheel acceleration from 0

to 6000 rpm. ................................................................................................................................................ 129

Graph 19: Graphs of friction coefficient research for both Lidar axes. ................................. 132

Graph 20: Comparison of the results for both versions of the reference mechanism for

both amplitudes. This confirms the proposition that a change of amplitudes doesn’t

cause a shift in the frequency behavior. ........................................................................................... 135

Graph 21: Same as the previous graphs but rearranged to show the different behaviour

caused by the extra stiffness. ................................................................................................................ 136

Graph 22: Simulation of Lidar z inclination for varying vibration frequencies. ............... 139

Graph 23: Simulation of Lidar x inclination for varying vibration frequencies. ............... 139



Graph 24: Reaction torque in Lidar-flywheel joint in UM model of reference mechanism.

Time window is 10 to 20 seconds in the simulation.................................................................... 142

Graph 25: Average inclination values of both buoy types compared.................................... 154

Graph 26: Maximum inclination values of both buoy types compared ................................ 154

8.3 List of tables

Table 1: Specification of Resinex Buoys .................................................................................................. 9

Table 2: Material and section card parameters for SPH ................................................................ 23

Table 3: Sea state date on the Thornton bank ................................................................................... 26

Table 4: Summary the design parameters for basic wave tank .................................................. 29

Table 5: Table of wave measurements in Dyna models for 1000 kg particles ..................... 43

Table 6: wave measurements in Dyna models for 1000 kg and 100kg particles ................ 45

Table 7: Experimental wave data by GeoSea ..................................................................................... 46

Table 8: Original dimensions (deep sea) ............................................................................................. 57

Table 9: Summary of the simulation results for 3E and PEM58 buoy ..................................... 71

Table 10: Parameters of Frame movement. ....................................................................................... 76

Table 11: Lidar offset parameter ............................................................................................................ 77

Table 12: Flywheel geometry and movement parameters .......................................................... 77

Table 13: Joint restoring force parameters ........................................................................................ 78

Table 14: Summation of reference mechanism model parameters .......................................... 79

Table 15: Results of simulation series for varying speeds ........................................................... 84

Table 16: Results and calculated values of simulation with changing radius and constant

thickness .......................................................................................................................................................... 90

Table 17: Results and calculated values of simulations with changing thickness and

constant radius .............................................................................................................................................. 92



Table 18: Results and calculated values of simulations with constant product of inertias.

.............................................................................................................................................................................. 94

Table 19: Results of simulation series with different flywheel materials. ............................. 96

Table 20: Results and calculated values of simulations with changing offset ...................... 97

Table 21: Results and calculated values of simulations with changing offset. .................. 108

Table 22: Parameters of flywheel speed function ........................................................................ 113

Table 23: Table with parameters for testing of detrimental speed dip: changing speed

difference ...................................................................................................................................................... 113

Table 24: Table with parameters for testing of detrimental speed dip: changing dip time.

........................................................................................................................................................................... 116

Table 25:Table with parameters for testing of detrimental speed dip: changing dip time

with constant total dip period. ............................................................................................................. 118

Table 26: Parameterset for fast speed dip simulation ................................................................ 120

Table 27: Parameterset for gradual speed change. ...................................................................... 121

Table 28: Parameters of amplitude function of sudden change model ................................ 123

Table 29: Rotational jerking simulation parameters: amplitude of impulse ..................... 124

Table 30: Translational jerking simulation parameters ............................................................. 126

Table 31: Parameters for friction research ..................................................................................... 131

Table 32: Friction simulation results. Absolute numbers. ........................................................ 133

Table 33: Statistics of torque shown in Graph 24 ......................................................................... 142

Table 34: Statistics of evaluated functions for flywheel start-up model. ............................ 144

Table 35: Results of coupled simulation of 3E prototype buoy ............................................... 150

Table 36: Results of coupled simulation of PEM buoy ................................................................ 152

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