mechanical design and analysis of a deployment mechanism ... · mechanical design and analysis of a...

Mechanical design and analysis of a deploymentmechanism for low frequency dipole antenna

Mara Solange Choças Rosado

Thesis to obtain the Master of Science Degree in

Aerospace Engineering

Supervisors: Prof. Miguel António Lopes de Matos Neves

Eng. João Daniel Ramos Ricardo

Examination Committee

Chairperson: Prof. Fernando José Parracho Lau

Supervisor: Prof. Miguel António Lopes de Matos Neves

Member of the Committee: Prof. Filipe Szolnoky Ramos Pinto Cunha

November 2015

This page has been intentionally left blank.

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To the ones who have greater faith in me than myself.

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Acknowledgments

This thesis is an important goal in my academic career, leading to my master degree. I want to thank my

supervisors, Professor Miguel de Matos Neves and Professor Joao Dias for all the guidance during the

project and document review. I also take this opportunity to thank my supervisors and other Professors

from Instituto Superior Tecnico for all the wisdom they conveyed to me through time.

A great acknowledgement goes to my supervisors from Active Space Technologies, Joao Ricardo and

Fernando Simoes for their guidance, knowledge, document review and friendship during my internship.

I also thank the internship opportunity provided by Active Space Technologies and thank the people who

have helped me in this project, directly or indirectly.

I also thank my friends for all the support, motivation, companionship, adventures, relaxing and stressful

moments and for help they have given t me during my degree. Without them, my continuous good mood

and positive thinking would have been affected for sure.

For last not the least, the greater acknowledgement goes to my family, without whose support I could not

have reached this goal. They have more faith in me than myself and they are my inspiration. A special

booyah to my little sister.

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Resumo

Este trabalho visa a concepcao preliminar do projecto mecanico e analise de um mecanismo extensıvel

para uma antena dipolar de baixa frequencia. O mastro da antena e projectado de modo a cumprir os

requisitos estruturais desejados, visando obter a massa mais baixa possıvel.

Uma antena dipolar e usada em aplicacoes espaciais para executar medidas do campo electrico, in-

cluindo medidas da gama de ultra-baixas frequencias associadas com importantes fenomenos ionosfericos

e troposfericos, por exemplo ressonancia de Schumann e ondas de Alfven.

Para realizar o projecto preliminar do mastro da antena, realizou-se um estudo de conceitos dos dis-

positivos de mecanismos extensıveis disponıveis em literatura e um conceito foi escolhido para ser

desenvolvido atraves de um analytical hierarchy process simplificado. Uma abordagem inovadora foi

concebida para o conceito e um prototipo de impressora 3D foi produzido para a validar.

Uma matriz com materiais aprovados para espaco foi criada, sendo a seleccao do material baseada em

criterios que permitiram alcancar um material de baixa densidade e alta rigidez.

Um modelo de elementos finitos foi desenvolvido com o intuito de executar analises estatica, harmonica

e modal para avaliar os requisitos e escolher as dimensoes secundarias, dado que o comprimento do

mastro era um requisito. Estas analises foram realizadas tendo em conta o ambiente de lancamento e a

necessidade do desacoplamento entre as frequencias naturais do mastro e as frequencias associadas

com os fenomenos a estudar.

Dois modelos foram criados: o mais inovador nao cumpriu os requisitos, o mais seguro foi considerado

parcialmente compatıvel com estes.

Palavras-chave: antena dipolar, estrutura extensıvel, mastro telescopico, antena de baixa frequencia,

analise de elementos finitos.

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viii

Abstract

This work aims to perform the preliminary mechanical design and analysis of a deployment mechanism

for a low frequency dipole antenna. The antenna boom is designed in order to fulfil the desired structural

requirements, aiming to achieve mass as low as possible.

A dipole antenna is used in space applications to perform electric field measurements, which include

readings of ultra-low frequencies associated with important ionospheric and tropospheric phenomena,

such as Schumann resonance and Alfven wave signatures.

To perform the preliminary antenna boom design, a trade-off of concepts of deployment mechanism

devices available in literature was conducted and a concept to be developed was chosen, through a

simplified analytical hierarchy process. An innovative approach to the chosen concept was conceived

and a 3D-printer prototype was made to validate it.

A matrix of space approved materials was created and the material selection was based in criteria that

allowed achievement of a low density and highly stiff material.

A finite element model was developed in order to execute static, harmonic and modal analyses to assess

the requirements and choose boom secondary dimensions, since the boom length was among the prin-

cipal requirements. These analyses were performed taking into account the launch environment and the

need for decoupling between boom eigenfrequencies and frequencies associated with the phenomena

to be studied.

Two designs were created: the most innovative did not fulfil the requirements established, but the more

conservative approach was able to comply with most of them.

Keywords: dipole antenna, deployable structure, telescopic boom, low frequency antenna, finite

elements analysis.

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Contents

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Resumo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Environment Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Flight Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3.1 Relevant Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3.2 Deployment Mechanisms Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4 Thesis Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Design Requirements 13

3 Technologies Selection 15

3.1 Analytical Hierarchy Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2 Material Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Fundamentals 24

4.1 Beam Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2 Von Mises Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.3 Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

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5 Methodologies and Procedures 29

5.1 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.2 Modelling and Meshing Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.2.1 Computer Aided Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.2.2 Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.3 Concept Validation: 3D-printer Preliminary Prototype . . . . . . . . . . . . . . . . . . . . . 34

5.3.1 Assembling Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.3.2 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

6 Results 40

6.1 Concept 1-A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6.1.1 Static Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6.1.2 Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6.1.3 Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

6.1.4 Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.2 Concept 1-B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.2.1 Static Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.2.2 Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.2.3 Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.2.4 Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

7 Conclusions 50

7.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

References 53

A Confidential Data 58

A.1 Deployment Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

A.2 Materials Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

A.2.1 Composite Materials Equivalent Properties Calculation Matlab Code . . . . . . . . 64

A.3 3-D printer Preliminary Prototype Deployment . . . . . . . . . . . . . . . . . . . . . . . . . 68

A.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

A.4.1 Concept 1-A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

A.4.2 Concept 1-B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

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A.5 APDL Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

A.6 3D-boom2 Drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

A.7 CAD Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

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List of Tables

1.1 Sine-equivalent dynamics for Vega and Ariane 5 launchers [9, 10]. . . . . . . . . . . . . . 4

1.2 Selected boom configurations advantages and disadvantages. . . . . . . . . . . . . . . . 11

2.1 General requirements of the AST dipole antenna project [19]. . . . . . . . . . . . . . . . . 13

3.1 Analytical Hierarchy Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.1 Used software. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.2 Verification of finite element model: natural frequencies comparison. . . . . . . . . . . . . 33

5.3 Prototype 3D printed parts dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

A.1 General materials properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

A.1 General materials properties (continued). . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A.2 Composite materials properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A.2 Composite materials properties (continued). . . . . . . . . . . . . . . . . . . . . . . . . . . 62

A.3 Second stage of material selection process summary. . . . . . . . . . . . . . . . . . . . . 63

A.4 Composite materials chosen to be implemented. . . . . . . . . . . . . . . . . . . . . . . . 63

A.5 Chosen composite materials equivalent mechanical properties. . . . . . . . . . . . . . . . 64

A.6 Static analysis: values of Von Mises maximum equivalent stresses for each stowed con-

figuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

A.7 Modal analysis: first five frequencies for stowed and deployed configurations. . . . . . . . 74

A.8 Static analysis: values of Von Mises maximum equivalent stresses for each stowed con-

figuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

A.9 Modal analysis: first five frequencies for stowed and first ten for deployed configurations. . 80

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List of Figures

1.1 Longitudinal accelerations for Vega and Ariane 5. . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Mars Express mission booms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Themis mission booms configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Hinged Deployment Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5 Linear Deployment Devices [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1 Wave frequencies associated with tropospheric-ionospheric coupling on Earth. . . . . . . 14

3.1 Long mast deployment concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1 Long mast deployment concepts (continued). . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1 Common boundary conditions for the transverse vibration of a beam [34]. . . . . . . . . . 26

4.2 Kinematics of the Euler-Bernoulli beam theory (on the left) and kinematics of the Timo-

shenko beam theory (on the right) [36]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.3 Element type BEAM188 configuration [37]. . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.4 Element type SOLSH190 configuration [37]. . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.1 Boom elements striates angle configuration. . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.2 Mesh independence study: natural frequencies. . . . . . . . . . . . . . . . . . . . . . . . . 32

5.3 Mesh independence study for 10 boom elements model of solid-shell elements. . . . . . . 33

5.4 Mesh chosen to apply in finite element model. . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.5 Stowed configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.6 3D-printer preliminary prototype assembled. . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.7 Ring and linker repair parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.8 3D-linker2-4 vertical beams deformed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.9 Prototype deployment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

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6.1 Von Mises equivalent stresses: nodal solution representation. . . . . . . . . . . . . . . . . 41

6.2 Von Mises equivalent stress per frequency on selected nodes: stowed-1 configuration. . . 42


6.4 Post-processing Matlab tool display. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.5 Post-processing Matlab tool resulting graphic. . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.6 Von Mises equivalent stresses: nodal solution representation. . . . . . . . . . . . . . . . . 46

6.7 Von Mises equivalent stresses per frequency on selected nodes: stowed-1 configuration. 47


6.9 Comparison between deployed configuration eigenfrequencies and frequencies to be

avoided. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

A.1 Horizontal deployment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

A.2 Diagonal deployment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

A.3 Vertical deployment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A.4 Von Mises equivalent stresses: nodal solution representation. . . . . . . . . . . . . . . . . 72

A.5 Von Mises equivalent stress per frequency on selected nodes: stowed-1 configuration. . . 72


A.7 Post-processing Matlab tool display. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

A.8 Modal shapes corresponding to the first five eigenfrequencies for deployed configuration. 75

A.9 Von Mises equivalent stresses: nodal solution representation. . . . . . . . . . . . . . . . . 76

A.10 Von Mises equivalent stresses per frequency on selected nodes: stowed-1 configuration. 77


A.12 Eigenfrequencies comparison for boom deployed configuration of different thickness. . . . 79

A.13 Modal shapes corresponding to the first ten eigenfrequencies for deployed configuration. 81

A.13 Modal shapes corresponding to the first ten eigenfrequencies for deployed configuration

(continued). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

A.14 Concept 1-A: four first booms with linkers on the inside. . . . . . . . . . . . . . . . . . . . 99

A.15 Concept 1-A: stowed configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

xviii

Nomenclature

Greek symbols

γ Shear strain.

ν Poisson’s ratio.

ω Angular frequency.

ρ Density.

σ Stress.

τ Shear.

ε Strain.

Roman symbols

A Cross section area.

E Young’s modulus/Modulus of elasticity.

f Frequency.

G Modulus of rigidity.

g G-force.

I Area moment of inertia.

r Radius.

V Volume.

Subscripts

c Composite.

e External.

f Fibre.

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i Internal.

L Longitudinal.

m Matrix.

T Transverse.

t Time component.

x, y, z Cartesian components.

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Glossary

AHP Analytical Hierarchy Process

ANSYS Software from ANSYS Inc.

AST Active Space Technologies

BC Boundary Condition

CAD Computer Aided Design

CATIA Software from Dassault Systemes

CoG Centre of Gravity

DoF Degree of Freedom

ECSS European Cooperation for Space Standardiza-

tion

ELF Extremely Low Frequency

FE Finite Element

FEA Finite Element Analysis

FEM Finite Element Method

IST Instituto Superior Tecnico

LEO Low Earth Orbit

MATLAB Programming language and interactive envi-

ronment from The MathWorks, Inc.

MLI MultiLayer Insulation

SLF Super Low Frequency

TRL Technology Readiness Level

ULF Ultra Low Frequency

UV Ultraviolet Radiation

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Disclaimer

The author states that she does not officially represent Active Space Technologies in any way although

she has been an intern at Active Space Technologies. All that is stated is the result of research or

learning by the author, regardless of whether or not acquired through Active Space Technologies.

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Chapter 1

Introduction

This work consists in the preliminary mechanical design of a deployment mechanism for a low frequency

dipole antenna, regarding structural requirements presented in chapter 2.

A dipole antenna is an instrument used in several space missions that allows for studying of aerody-

namics and electrodynamics phenomena in the higher layers of the atmosphere, characterizing space

weather patterns, studying the surface and subsurface phenomena in planetary bodies. However, uti-

lization of dipole antennas has been frequently discarded due to mass and deployment issues.

A dipole antenna is composed by a set of two monopole antennas that are usually incorporated in the

satellite opposite walls. From a strictly mechanical point of view, a monopole antenna is mostly a long

boom (mast) of a, preferably, low-conductive material with a spherical shell of a high-conductive material

on its tip. In terms of antenna science, we should bear in mind that instrument sensitivity is directly

proportional to the distance between the two spherical shells, meaning the longer the boom the better

for antenna sensitivity, providing the possibility of readings in the lower frequency ranges: extremely low

frequency (ELF) - 3 to 30 Hz; super low frequency (SLF) - 30 to 300 Hz; ultra low frequency (ULF) - 300

to 3000 Hz.

A structural challenge nowadays is to reduce the boom mass of these antennas and improve their

deployment mechanisms, taking into account the effects (e.g., interference) of vibration modes of the

structure in instrument sensitivity.

In this work the preliminary mechanical design of the antenna boom is presented, in which static and

harmonic analysis were performed for a simplified finite element model of the boom, in order to ascertain

if the chosen materials and design criteria are suitable for the launch environment. Modal analyses were

also performed for the stowed and deployed configurations with the main purpose of optimizing boom

mass without placing frequencies in the undesired range, where they can affect instrument readings.

1

1.1 Motivation

As stated before, the use of this instrument has been neglected. If deployment mechanism improve-

ments and mainly mass reduction could be achieved, dipole antennas would be employed more fre-

quently in space missions, in order to provide more sensitive frequency readings, since some phenom-

ena have signatures in the low frequency range.

Dipole antenna allows for electric field measurements and, according to Simoes et al. [1], has a major

importance in the study of some phenomena, briefly listed below:

• Troposphere-ionosphere coupling: aerodynamics and electrodynamics phenomena;

• Atmospheric electricity: global electric circuit, lightning, transient luminous events;

• Aeronomy, space plasma physics, magnetohydrodynamics, magnetosphere processes;

• Electromagnetic wave propagation: Alfven waves, Schumann resonance frequencies, geomag-

netic pulsations, whistlers, tweeks, Trimpi effect, lower and higher hybrid oscillations;

• Equatorial and auroral ionospheric phenomena: using both AC and DC electric fields;

• Ionospheric patterns: daily, seasonal, annual, and biennial periodicities;

• Tropospheric and space weather patterns: el nino, la nina and solar cycle variability;

• Surface and subsurface phenomena in planetary bodies: soil stratification, water/ice features,

buried oceans.

Within these phenomena, the major scientific interest of Active Space Technologies in the dipole antenna

project is the study of electromagnetic wave propagation, namely Schumann resonance signatures.

Besides mass concern, according to Puig et al. [2], designs based on large rigid and non-deployable

structures are constrained in size by the fairings’ dimensions. With this in mind and given the difficulty in

developing launchers capable of sending larger payloads, long masts need to be deployable structures,

with a high stowed-to-deployed-length ratio.

In order to increase the usability of dipole antenna, we must design a reliable deployment mechanism

lighter than the existing ones, fulfilling the design requirements.

1.2 Environment Characterization

A brief clarification of the space environment in which the antenna will operate is presented in this

section.

Regarding the altitude at which the antenna will operate, according to Simoes et al. [3], although Schu-

mann resonances (electromagnetic oscillations in the Earth-ionospheric cavity, generated by lightning

2

activity ) only happen up to an altitude of 100 kilometres, there has been Schumann resonances sig-

natures detected at 400 to 850 kilometres of altitude, indicating that the spacecraft where the dipole

antenna could be implemented may orbit in a Low Earth Orbit (LEO), which altitude goes from 200 km

to 700 km [4].

According to Milkovich et al. [5], the environment for LEO is mainly subjected to ultraviolet radiation (UV),

vacuum and thermal gradients. The solar power density in the Earth vicinity is about 1.4 kWm−2. In

addition, UV radiation (0.1 - 0.4 µm) is not absorbed by the atmosphere and is usually responsible for

coatings and organic molecules degradation. The vacuum characterization, which pressure varies be-

tween 10−19 - 10−11 Pa, has a major importance in the dimensional and materials mechanical properties

changes, due to vacuum outgassing that results in loss of moisture and solvents. Finally, temperature

cycling can lead to microcracking, thermal warping and deterioration of critical surfaces.

Also according to Milkovich et al. [5], the expectable lifetime for a structure in a LEO is about 10 years.

Unlike the conductivity in the atmosphere that is very low (2x10−14 Sm−1), plasma ionization in the

ionosphere is very high and the electrical conductivity is in the order of mSm−1 or larger.

According to Fraser et al. [6], in LEO, high energy, neutral atomic oxygen atoms (ATOX) and ionizing

radiation can severely degrade polymeric materials by reacting with their organic molecules.

When discussing space qualified systems, temperature is one of the most important parameters to

be assessed. Literature does not show a clear consensus about temperature in space. According to

Santiago-Prowald and Drioli [7], antenna elements usually experience a thermal environment from 173K

to 423K (-100◦C to 150◦C). However, in higher orbits this can reach extreme temperatures, typically in

the range between 83 and 433K (-190◦C to 160◦C), due to the Sun’s direct radiation, deep space sink

and the absence of convection in space. According with Milkovich et al. [5], for LEO, the temperature

usually varies between 173K and 313K (-100◦C and 40◦C). In fact, the temperature range is a function

of many parameters, namely altitude, daytime and nighttime conditions, type of illumination, solar ac-

tivity, and reflection from the Earth (albedo). On the other hand, some characteristics of the materials

employed also play an important role, e.g., emissivity and reflectivity of the surface, shape of the walls.

Since there is no atmosphere protection, changing from sunlight to shadow and vice versa implies an

abrupt change in temperature designated thermal shock that causes an impulsive excitation, resulting

in free oscillations of the boom-satellite system [8]. This excitation is caused by the object expansion by

different amounts due to its thermal gradients. Furthermore, thermal gradients generate thermoelectric

effects that affect instrument sensitivity.

Thermal shock prevention involves thermal gradient reduction by increasing material thermal conductiv-

ity and strength and reducing its coefficient of thermal expansion [8].

Finally, according with Santiago-Prowald and Drioli [7], antennas must be protected by thermal hardware

to limit the temperature range and gradients, and to control the heat exchange with the platform, as well

as thermoelastic distortions. Passive thermal control devices consist of multilayer insulation (MLI), sun-

shields, coatings and paints. The choice of outer-layer material is driven by thermo-optical properties,

glint prevention, electrical grounding, atomic oxygen and protection from micrometeoroid impacts. Usu-

3

ally aluminized Kapton, black Kapton, white paint or Beta cloth are emplpoyed. These possible shields

and coatings should also be appropriate to reduce radiation effects on structural materials. It is prefer-

able to have coatings degradation, as long as its particles effects do not compromise instrumentation,

i.e., outgassing from coatings degradation should not be sufficient to implicate for example optical in-

struments damages.

1.2.1 Flight Environment

During flight stage, the spacecraft is subjected to diverse static and dynamic loads.

Regarding two widely used launchers (Vega and Ariane 5) user’s manuals ([9, 10] respectively), the

typical longitudinal acceleration does not exceed a load factor of 7 g for Vega and 4.55 g for Ariane 5.

The typical longitudinal load factors for these two launcher vehicles are shown in Figure 1.1 and the sine-

equivalent dynamics that affect the launch vehicle during powered flight for the considered launchers are

summed up in Table 1.1.

Launcher Frequency Band (Hz)Sine Amplitude (g)

Longitudinal Lateral

Vega

1 - 5 0.4 0.4

5 - 45 0.8 0.5

45 - 110 1.0 0.5

110 - 125 0.2 0.2

Ariane 52 - 50 1.0 0.8

50 - 100 0.8 0.6

Table 1.1: Sine-equivalent dynamics for Vega and Ariane 5 launchers [9, 10].

4

(a) Vega: Typical longitudinal acceleration for SSO mission [9].

(b) Ariane 5: Typical longitudinal acceleration [10].

Figure 1.1: Longitudinal accelerations for Vega and Ariane 5.

5

1.3 Background

With the ability of measuring electric signatures of phenomena occurring in the atmosphere, dipole

antennas have sometimes been used in space missions for investigating atmospheric patterns of not

only planets but also a few moons.

In this Section is summarized the review of available scientific publications about the principal missions

with dipole antennas and associated technologies, as well as a review of the existing deployment de-

vices.

1.3.1 Relevant Missions

Dipole antennas were implemented in space missions like Mars Express, Cassini, Themis, Van Allen

probes (former RBSP), with different technologies and purposes.

The principal missions available in scientific literature, listed above, that used dipole antennas were

reviewed and their relevant aspects are summarized below:

1. Mars Express

With the main purpose of detecting water ice deposits in the subsurface of Mars, an instrument

comprising a dipole and a monopole antennas was incorporated in the spacecraft.

Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) is a low-frequency

(0.1-5.5 MHz) nadir-looking pulse limited radar sounder and altimeter with ground penetration ca-

pabilities, Picardi et al. [11].

Its structure is composed of foldable composite tubes, shown in Figure 1.2(a), that are a combina-

tion of flattenable tubes foldable by the hinges made in the tubes by removal of material. This type

of hinges resemble to tape springs.

(a) Flattenable Foldable Tubes [12]. (b) Instrument MARSIS deployed [13].

Figure 1.2: Mars Express mission booms.

6

In this mission, the dipole antenna is 40 m tip-to-tip long and the monopole is 7 m long and the

total mass is 7.5 kg, accordingly with [12].

2. Cassini

In this mission, to investigate radio wave emission of the Kronian system, the instrument Radio

Plasma Wave Science (RPWS) could be adapted presenting three monopole antennas or one

dipole and one monopole antennas.

According to Gurnett et al. [14], each monopole antenna is 10 m long and when adapting a set

of two monopoles in a dipole antenna this becomes 18.5 m tip-to-tip long. Their structure is

composed of conducting cylinders of 28.6 mm of diameter.

3. Themis

With the scientific objectives of this mission related to the nature of magnetic sub-storm instabilities,

according to Auslander et al. [15], each of the five identical synchronized probes needed to perform

these studies has three orthogonal dipoles. Only one dipole, the one coaxial with the spacecraft

Z-axis has a stiff structure, being the other two spin-plane wire-booms.

The spacecraft has a spinning movement about their Z-axis, allowing the deployment of wire-

booms. These booms achieve a length of 40 and 50 m tip-to-tip.

The dipole stiff axial boom is a 6.4 m long Stacer boom. Its boom configuration is displayed in

Figure 1.3(b).

(a) Themis on orbit deployed booms configuration [15]. (b) Themis stiff axial Stacer boom configuration [15].

Figure 1.3: Themis mission booms configuration.

4. Van Allen probes (former RBSP)

According to Wygant et al. [16], the goal of the Electric Field and Waves (EFW) Investigation on

the Radiation Belt Storm Probe (RBSP) mission is to understand the role of electric fields in driving

energetic particle acceleration, transport, and loss in the inner magnetosphere of the Earth.

Identically to the Themis mission, the Van Allen probes EFW comprise two orthogonal pairs of

7

centrifugally deployed spin-plane booms with a 100 m tip-to-tip length and a pair of spin-axis

Stacer booms, 12 to 14 m long, length adjustable by adding a wire.

1.3.2 Deployment Mechanisms Review

According to Conley [17] and Fortescue and Stark [18], there are mainly four groups of deployment

devices, listed below:

1. Hinged Deployment Devices

These deployment mechanisms (see Figure 1.4) allow for operation of systems simply by rotating

or translating a hinge or linkage. They allow for multiple degrees of freedom and they can work

cooperatively to deploy a system.

The hinges can be rigid of flexible, the latter being the simplest method for connecting two com-

ponents that have motion relative to each other during deployment. An example of a rigid hinge is

the Galileo mission whip antenna hinge.

Hinged Deployment Devices will not be considered in the design of the boom. Nevertheless, it is

worth considering this type of deployment devices in the design of a positioning mechanism, which

will place the folded antenna from a position parallel to the satellite wall where the antenna is fixed

to a perpendicular position, in order to enable deployment.

(a) Hinge of a whip antenna: hingecoupled with torsional spring [18].

(b) Rosetta lander landing gear [18].

Figure 1.4: Hinged Deployment Devices.

2. Linear Deployment Devices

There are five main categories of linear deployment devices:

2.1. Wire Deployers

All conventional wire deployers operate on one very important principle: The spacecraft must

be spinning during and after deployment for the mechanism to work properly, Conley [17].

8

A wire deployer deploys due to the centrifugal force caused by the satellite spinning. This

force also induces tension in the wire, directly related with the mechanism stiffness.

2.2. Tubular Booms

A tubular boom is an one-part extendible boom. In its stowed position it is a flat geometry

stored on reels and when its deployment occurs transforms from a flat to a curved geometry,

as displayed in Figure 1.5(a), gaining stiffness from this transition.

The most attractive characteristics of this type of boom is the low stowage volume per de-

ployed length ratio and its low mass.

Amongst the least attractive characteristics it can be listed a low stiffness and boom strength

limited by buckling at the root and the possibility of boom uncouple in the centre due to long

length.

2.3. Telescopic Booms

Telescopic tubes are most often used to obtain a fair amount of stiffness during deployment,

high stiffness and strength when deployed, and a small storage diameter when fully stowed,

Conley [17].

Telescopic booms, shown in Figure 1.5(b), cannot provide a length as long as tubular booms,

but they present more strength and they have a less risky deployment. Frequently, a deploy-

ment powered actuator provides the deployment with the necessary force in the centre of the

nested tubes. This leading tube sequentially picks up rollers on the inside of each tube until

full length is achieved.

In order to preserve the required stiffness characteristics, a telescopic boom must be design

with tight tolerances.

2.4. Coilable Masts

A coilable mast, displayed in Figure 1.5(c), is a deployable structure composed of longerons

(continuous components), battens and diagonals. Longerons run the full length of the mast,

battens are structural elements lying in a plane perpendicular to the longerons and diagonals,

as the name suggests, criss-cross every square face of each side of the mast.

In a stowed configuration, the longerons are bent and twisted into a helix pattern. During

stowage, strain energy is stored to be employed in a self-deployment.

This light weight mechanism has a minimum stowed-to-deployed height ratio. However, its

stiffness is only guaranteed by the battens buckling, that serve as compression springs push-

ing longerons away from each other, and the diagonals tension connecting the longerons.

Other disadvantaged is the uncontrolled deployment that may affect the spacecraft attitude.

2.5. Articulated Masts

An articulated mast, presented in Figure 1.5(d), is simply a pinned truss structure that can be

stowed by folding the primary structural members (longerons) at pivot joints (articulations).

Identically to Coilable Masts, the structure stiffness results from the pivot joints.

This type of device needs a powered deployment actuator.

9

(a) Tubular boom. (b) Telescopic boom.

(c) Coilable mast. (d) Articulated mast.

Figure 1.5: Linear Deployment Devices [17].

3. Surface Deployment Devices

This type of mechanisms is appropriate to deploy systems where the surface area is the primary

parameter of interest. They are usually applied in high-gain antennas (rigid surfaces) and solar

arrays (flexible surfaces) systems.

4. Volume Deployment Devices

Volume deployment devices are suitable for inflatable structures. They have not been widely ap-

plied in space, but there is a large body of literature that studies the possibilities of this type of

deployment mechanism. One of the most interesting studies rely on the possibility of a post-

10

deploying self-regidizing structure that would allow to harden the system after the deployment.

Adding to the Linear Deployment Devices listed above the Mars Express MARSIS boom concept, re-

named as Hinge Integrated Mast, four concepts were chosen for further research. Their main advan-

tages and disadvantages are summarized in Table 1.2.

Concept Advantages Disadvantages

Tubular Boom• Low stowage volume per deployed

length;

• Self-deployment: it uses the strain

energy stored during coiling to de-

ploy;

• Low mass;

• Uncontrolled deployment - possible

failure;

• Strength limited by buckling at the

root;

• Long booms may uncouple in the

centre;

Telescopic Boom• Fair amount of stiffness during de-

ployment;

• High stiffness and strength when de-

ployed;

• Small stowage diameter when fully

stowed;

• High mass;

• Powered deployment actuator

needed;

• Locking mechanisms between

booms needed;

Coilable Mast• Can be stowed in 2 % of its deployed

height;


energy stored during stowage to de-

ploy;

• Low mass;

• Low stiffness;

• Uncontrolled deployment - deploy-

ment must be constrained to prevent

side effects in the satellite attitude;

Hinge Integrated

Mast • Hinges are part of the longerons, af-

ter removal of material;


energy stored in hinges to deploy;

• Low mass;

• Uncontrolled deployment;

• Low stiffness;

Table 1.2: Selected boom configurations advantages and disadvantages.

1.4 Thesis Layout

This thesis offers a preliminary design for a project under development in Active Space Technologies,

consisting in the development of a triaxial dipole antenna. Therefore, there is confidential content that

will only be available in appendix and will be public after termination of the confidential contract, five

years after the thesis publishing.

11

In Chapter 1 it is presented the motivation to design and analyse the deployment mechanism of a dipole

antenna, with the main objective of increasing its missions’ applicability. A brief background is also

presented, in Section 1.3, which consists of a review of available scientific publications about missions

that employed dipole antennas and already implemented deployment mechanisms.

In Chapter 2, the design requirements of the project are introduced and, in more detail, the general

structural requirements that directly shape the contents of this thesis.

Chapter 3 presents the assessment of technologies and the chosen solution to be developed.

Chapter 4 presents a brief explanation of the concepts considered relevant to understanding thesis

results.

In Chapter 5 are presented the adopted software and methodologies to implement the chosen solution

and subsequent analysis. With this chapter as reference, the reader should be capable of reproducing

the results obtained, which are presented in Chapter 6.

After presenting and discussing the results, the conclusions of this work are presented in Chapter 7

followed by future work that should be developed to conclude the design and analysis of this instrument,

listed in section 7.1.

This thesis concludes with the list of references used for the whole work, and also includes appendices

where confidential data is shown.

12

Chapter 2

Design Requirements

In this chapter the list of requirements used in the project are shown in Table 2.1, where those in bold

are directly related to the present thesis.

Type Description Value Criticality

Structural Deployment mechanism length (folded) ≤ 2 m HighStructural Boom mass (incl. auxiliary mechanisms) ≤ 2 kg HighStructural Boom length (deployed) ≥ 10 m MediumStructural Critical range of vibration modes 0.1 - 100 Hz MediumStructural Boom length variability ≤ 1 mm (10m reference) MediumStructural Boom composition (material) Preferentially dielectric LowStructural 3-axial (3 dipoles) 6 booms Low

Thermal/Radiation Plastic membrane sensitivity to UV radiation High

Thermal/Radiation Boom envelope sensitivity to UV radiation High

Thermal/Radiation Electronics response to UV radiation High

Thermal/Radiation Electronics drift over temperature High

Thermal/Radiation Boom thermal expansion Medium

Thermal/Radiation Boom length variability ≤ 1 mm (10m reference) Medium

Electrical Electromagnetic compatibility High

Electrical Wiring unfolding High

Electrical Vibration-induced electric noise High

Electrical Electronics sensitivity High

Electrical Data acquisition Waveform vs spectra High

Electrical Wiring capacitance Medium

Electrical Electrode capacitance Medium

Electrical Fluttering-induced electric noise Medium

Electrical Space charge effects Medium

Electrical Booms materials Low

Software Data compression algorithms efficiency High

Software Frequency domain analysis FFT and other methods High

Software Algorithm validation and calibration High

Software Burst mode data memory storage Medium

Software Time domain analysis (burst mode) Medium

Software Telemetry constrains Low

Table 2.1: General requirements of the AST dipole antenna project [19].

Since the purpose of this work is the preliminary design and analysis of the antenna boom, all the

13

requirements labelled with Electronics or Software will not be discussed because their understanding

is not necessary to proposed solution of the problem, and some of the presented requirements directly

related with the boom design will only be slightly discussed because with a project progress there will

be the need for design update.

Regarding the 3-axial dipole antenna requirement, it can be obtained with three sets of two monopole

antennas. In order to simplify the hereafter analysis upon the spacecraft assembly and to facilitate

the satellite attitude control, dipoles should be orthogonal among themselves and each pair should be

coaxial. This requirement will not be taken into consideration in this work.

A boom length equal or superior to 10 m implies a highly splitted total structure, because the folded

length is required to be equal to or lower than 2 m. At least five sections are needed.

The objective of achieving a boom mass of 2 kg (for each dipole) is highly ambitious. This has been

already achieved in other missions, but not for a maximum length variability requirement of 0.01 % of the

deployed boom length. To fulfil this target, the boom must have a great stiffness, which led to materials

selection: materials should be highly stiff to withstand loading conditions without compromising the

length variation requirement and it should be a low density material as well.

Less critical but also important are the vibration modes of the boom, because they can directly interfere

with the frequencies associated to signatures of some phenomena to be studied. The objective is to

avoid as far as possible a match between these and the boom eigenfrequencies.

Regarding the planet Earth, the wave frequencies associated with the tropospheric-ionospheric environ-

ment are listed below, according to Simoes et al. [1]:

• Schumann resonance (first five peaks):

– 7.9 ± 0.25 Hz;

– 14.1 ± 0.5 Hz;

– 20.6 ± 0.5 Hz;

– 26.8 ± 0.5 Hz;

– 32.9 ± 0.5 Hz

• Ionospheric Alfven resonator: 0.1-4 Hz (∼0.2 Hz between consecutive peaks);

• Sferics and tweeks: first transverse mode - 2 kHz;

• Whistlers: ∼2n ± 0.1 kHz, n=1,2,...;

Figure 2.1: Wave frequencies associated with tropospheric-ionospheric coupling on Earth.

Apart all project requirements, it was also discussed that we should avoid spin-plane configurations,

because the a priori intention is to implement this instrument in a non-spinning spacecraft. Therefore,

the boom configurations like wire-boom for example will not be considered.

14

Chapter 3

Technologies Selection

After selecting the deployment mechanisms to study in Chapter 1.3, four concepts were created and

then qualitatively evaluated in Section 3.1. These concepts and their properties are listed below:

• Concept 1 - Telescopic Boom

This concept adapts the widely used telescopic boom concept with an innovative solution: an en-

gineless actuator to assist the boom deployment.

As stated in Chapter 2, the mass requirement of 2 kg is of great ambition. References of a tele-

scopic boom mass are Bourrec et al. [20], where a minimum of 0.79 kgm−1 is achieved and Mo-

brem and Spier [21], with a minimum of 1.47 kgm−1. This last example in its deployed configuration

is shown in Figure 3.1(a).

– Technology Readiness Level (TRL) - 9;

– Opening:

* Concept 1-A: Clock and counter-clockwise spinning booms 1

· Needs linking between two-by-two boom elements;

· Significant friction;

· Only needs deployment aid until the second boom element (from the root).

* Concept 1-B: Straight or spin concordant opening

· Lower friction;

· Needs deployment aid until the last boom element (from the root);

– Deployment mechanism complexity:

* Booms to fulfil the deployed and stowed length;

* Pre-deployment positioning mechanism;

* Locking mechanism before deployment;

* Locking mechanism after deployment;

1The original idea of this concept is from Active Space Technologies Engineer Frederico Teixeira.

15

* Links between two-by-two boom elements in the first scenario (Concept 1-A);

* Deployment actuator, described in section A.1.

• Concept 2 - Coilable Mast

This concept has the best deployed-stowed length ratio and uses its deformation storage strain

energy to deploy.

An example of existing applications are shown in Figure 3.1(b). Although masts mass is usually

about 0.25 kgm−1, the deployment mechanism achieve about 1.3 kgm−1 [22].

– TRL - 9;

– Opening:

* Uncontrolled deployment: needs constraint for control;

· Solution already implemented: an electric spool to force slowly deployment;

* Needs to increase stiffness for long length;


* Longerons, battens and diagonals sufficient to fulfil the deployed and stowed length re-

quirements;


* Locking mechanism after deployment provided by battens;

* A deployment constraint: electric spool;

· Needs electric power;

(a) Deployed telescopic boom [21]. (b) Coilable mast: Self-Deployed AstroMast [22].

Figure 3.1: Long mast deployment concepts.

• Concept 3 - Hinge Integrated Mast

Like the previous one, concept 3 also uses its deformation storage strain energy to deploy. The

16

mass reference for this concept is about 0.180 kgm−1, in the Mars Express mission [12], Figure

3.1(c).

– TRL - 9;

– Opening:

* Uncontrolled deployment: needs constraint for control;

* Self-locking after deployment;

* Needs to increase stiffness for long length;


* Sufficient longerons to fulfil the deployed and stowed length requirements;


* A deployment constraint: possible solution - Shape Memory Alloy integrated in hinges in

the material that will allow deployment after activation by electric power.

• Concept 4 - Tubular Membrane Mast

A particular case of tubular masts is considered: an omega-shape tubular mast, fabricated in its

deployed position and deformed afterwards in a flat position that is coiled in a reel. Although with

this mast a mass of 0.100 kgm−1 was already achieved, it has not been yet implementer in space

missions [23, 24]. Its representation is shown in Figure 3.1(d).

– TRL - 6;

– Opening:

* Uses storage strain energy during deformation to deploy;

* Uncontrolled deployment - needs constraint to control:

· Solution already tested: an inflatable (with gas) thick polymer hose inside the boom

and velcro stripes along the boom;

* Possibility of buckling in the root;

* Needs to increase stiffness;


* Omega-shape boom flatted and coiled on reel;


* Velcro to slow the deployment;

* Membrane to inflate and induce deployment.

17

(c) Hinge integrated mast: Flattenable Foldable Tube (FFT)[12].

(d) Tubular membrane mast [23].

Figure 3.1: Long mast deployment concepts (continued).

3.1 Analytical Hierarchy Process

The analytical hierarchy process (AHP) is a systematic method for comparing a list of objectives or

alternatives. In engineering problems/challenges, it can be a powerful tool for comparing alternative

design concepts [25].

AHP is based in a decision by objectives, which are compared among them by an established normalized

set of weight previously defined. In this case, it was made a simplified matrix, where criteria were defined

to assist in the choice of the deployment mechanism. Each criterion was evaluated from 1 to 5, where

5 is the best case scenario, for each concept, and each had an attributed weight of 1 to 5, sorted by

design requirements criticality (Chapter 2), being 5 the highest one:

• Mass

• Length

• Integration

• Stowage Volume

• Auxiliary Mechanisms

• Controlled Deployment

• Strength

• Fail-Safe

• Technology Readiness Level (TRL) [26]

• Reliability

• Ageing Reliability

• Risk

18

Criterion Weight Concept 1 Concept 2 Concept 3 Concept 4

Mass 5 2 2 3 5

Length 5 4 2 5 4

Integration 3 3 4 3 3

Stowage Volume 2 4 5 4 5

Auxiliary Mechanisms 2 4 4 4 4

Controlled Deployment 5 5 4 3 4

Strength 4 4 2 3 3

Fail-Safe 4 4 4 3 4

TRL 3 5 5 5 3

Reliability 3 4 5 5 *2

Ageing Reliability 3 5 3 5 3

Risk 5 4 3 1 1

Total 4.0 3.4 3.5 3.5 3

Table 3.1: Analytical Hierarchy Process.

The two concepts with highest average marks are the telescopic boom and the tubular membrane mast.

Even though hinge integrated mast concept got the same result as tubular mast concept, the last one

presents a greater hypothesis of innovation.

Although mass plays a major role is this decision, the uncontrolled deployment and the lack of reliability

in the system have cut out the tubular membrane mast concept.

The telescopic boom concept, with the above presented variations has proven to be the right amount

of innovation and safety, both in terms of space application and in terms of modelling and performing

structural analysis.

For the telescopic boom concept are presented two options: case A and case B, being the most in-

novative solution the first one. Option B will only be taken in account if option A does not fulfil the

requirements. As a preliminary design, system modelling for analysis will be basic, fitting both options.

3.2 Material Selection

The material selection for the preliminary design of the antenna boom requires a trade-off of an inter-

section between multiple material related disciplines and the project requirements.

As stated in section 1.2, the boom material should have a high thermal conductivity and strength and

a low thermal expansion coefficient in order to prevent thermal shock that would possibly lead to non-

desirable mechanical deformations.

During launch stage the material should not pass its yield strength in order to not compromise the

subsequent deployment of the stowed boom.

In chapter 2 a call of attention is made to the required material high stiffness and its low density need.

The material selection was performed in mainly three stages. In the first one, it was made an extensive

data collection for some pre-selected materials for aerospace applications. This data is available in Ta-

2This value was not attributed due to lack of information.3This value was calculated with all criteria weights except the Reliability one.

19

ble A.1 and takes into account data about outgassing, ionizing radiation and UV effects, when found in

literature.

Afterwards, it became necessary to relate the material properties with boom frequencies location. As-

suming that all the low mass and small dimensions elements in relation with boom length and radius

are neglected in the preliminary design of a telescopic boom, this can be approximately modelled by

stepped beams of hollow circular sections.

According to Silva and Maia [27], the eigenfrequencies of a free vibration beam (Euler-Bernoulli beam

theory) is given by:

ω = β2

√

EI

ρA, (3.1)

where β is a particular solution of the motion equation applying boundary conditions that leads to this

expression, E is the material Young’s modulus, I represents the area moment of inertia of the beam, ρ

the density and A the beam cross section area.

For a beam eigenfrequencies calculus, the only material properties dependence is given by Young’s

modulus and density, E and ρ, respectively. Therefore, the second stage of material selection was

performed based on the square-root of Young’s modulus by density ratio and density itself, to minimize

mass. These values are summed up in Table A.3.

It is worth noting that although beryllium presents properties as good as composite materials, it will not

be considered for this design because its machining results in toxic particles and derivatives and has a

limited supply chain [7].

The composite materials were selected based on an ECSS standard [28] and the principal suppliers

lists of space approved prepregs4: Hexcel [29], Cytec and TenCate. A complete list of these materials

properties is available in Table A.2.

Based on Table A.3, it was decided to choose a composite material that would allow for a better com-

promise between low density and high stiffness. This decision completes the third stage of material

selection.

Three carbon-fibre composite prepregs were chosen: the one with the higher value of the square-root

of Young’s modulus to density ratio, the one with the lowest density and an intermediate.

Not being the aim of this work the material optimization, with AST and a supplier of composite materials

assistance, it was chosen a common plies orientation for maximizing bending and torsional stiffness:

[0◦ , 0◦ , 0◦ ,±45◦

]s, which means that the composite material will have eight plies: three at 0◦ , one at

45◦ , one at −45◦ and other three at 0◦ . The laminate setup is supported by Sickinger et al. [24], where

it states that the choice of a stacking sequence made up of a combination of 0◦ and ±45◦ is essentially

based on the requirement to minimize bending.

With a typical 60 % fibre volume and the material properties available in Table A.2, the materials equiv-

alent properties were calculated with expressions for orthotropic materials, according with [30, 31].

To find the material equivalent properties for a global reference frame (x, y), it is first necessary to

4Prepreg - fabric reinforcement that has been pre-impregnated with a resin system.

20

calculate the local longitudinal (L) and transverse (T) properties, corresponding to 0◦ and 90◦ of the

unidirectional prepregs, respectively:

ρc = ρmVm + ρfVf , (3.2)

EL = EmVm + EfVf , (3.3)

ET =1

Vf

Ef+ Vm

Em

, (3.4)

Gf =Ef

2(1 + νf ), (3.5)

Gm =Em

2(1 + νm), (3.6)

GLT =1

Vf

Gf+ Vm

Gm

, (3.7)

νLT = Vfνf + Vmνm, (3.8)

νTL =ET

EL

νLT , (3.9)

where m is the subscript for matrix, f for fibre, c for composite, L for longitudinal and T for transverse, G

represents the modulus of rigidity, Vi the volume fraction of subscript i, and ν the Poisson’s ratio.

After estimating the mechanical properties shown above, the stress-strain relations for each ply are

given by:

ε = [Q]−1σ ⇔

εL

εT

γLT

=

1EL

−νTL

ET0

−νLT

EL

1ET

0

0 0 1GLT

σL

σT

τLT

, (3.10)

from which we can obtain the local Q matrix:

[Q] =

EL

1−νLT νTL

ELνTL

1−νLT νTL0

ET νLT

1−νLT νTL

ET

1−νLT νTL0

0 0 GLT

, (3.11)

being σL the longitudinal stress, σT the transverse stress, τLT the shear, εL the longitudinal strain, εT

the transverse strain and γLT the shear strain.

For transform the local reference frame into the global one, it is necessary to calculate the [Q] matrix. It

is worth noting that, according to Kirchhoff hypothesis from the Laminate Plate Theory, it is admitted a

plane stress state, which means that the plies are homogeneous and orthotropic and their perpendicular

sections in relation to the neutral fibre remain perpendicular after deformation.

[Q] = [T ]−1σ [Q]−1[T ]ε, (3.12)

21

where [T ]−1σ e [T ]ε are given by:

[T ]−1σ =

cos2θ sin2θ −2cosθsinθ

sin2θ cos2θ 2cosθsinθ

−cosθsinθ cosθsinθ cos2θ − sin2θ

, (3.13)

[T ]ε =

cos2θ sin2θ cosθsinθ

sin2θ cos2θ −2cosθsinθ

−2cosθsinθ 2cosθsinθ cos2θ − sin2θ

, (3.14)

being θ defined as the angle between the global longitudinal axis (x) and the longitudinal fibre direction

(L), measured in the counter-clockwise direction.

For each ply angle, it is calculated its elastic properties in the global reference frame:

σL

σT

τLT

= [T ]σ

σx

σy

τxy

, (3.15)

εL

εT

γLT

= [T ]ε

εx

εy

γxy

. (3.16)

With Equations (3.15) and (3.16), the [Q] is found for each angle and it is possible to calculate the matrix

[A], needed to estimate the material equivalent properties:

Aij =n∑

k=1

[Q](k)ij (zk − zk−1), (3.17)

where (zk − zk−1) represents each ply thickness.

Finally, we have:

Ex =1

A−111 H

, (3.18)

Ey =1

A−122 H

, (3.19)

Gxy =1

A−133 H

, (3.20)

νxy =A−1

21

A−111

, (3.21)

νyx =A−1

12

A−122

, (3.22)

being H the laminate thickness.

The MATLAB code used for these calculations is available in section A.2.1.

As materials data sheets did not specified the Poisson’s ratio, a typical value for carbon fibre/epoxy

composites of high-modulus is used [32, 33]: νLT = 0.3, νm = 0.34, νf = 0.28.

22

The calculus of material equivalent properties with the chosen stacking sequence allows modelling of the

material as orthotropic without properties and orientations for each ply. This is a preliminary approach

and later in the project, after material optimization, each ply information should be inserted in the finite

element model.

The chosen composite materials equivalent properties are displayed in the Table A.5.

23

Chapter 4

Fundamentals

In the current chapter is resumed the information gathered on available scientific literature to explain the

basic concepts considered relevant to the comprehension of the thesis.

A brief theoretical formulation is presented to support the preliminary design and analysis performed.

4.1 Beam Vibration

As stated in section 3.2, the antenna boom is better described by beam elements.

A detailed formulation of systems mechanical vibrations is available in Rao [34], from which the pre-

sented formulation is taken.

From the Euler-Bernoulli beam theory, the equation of motion for forced lateral vibration of a uniform

beam can be written as:

EI∂4w

∂x4(x, t) + ρA

∂2w

∂t2(x, t) = f(x, t). (4.1)

For free vibration, f(x, t) = 0 and the equation of motion becomes

c2∂4w

∂x4(x, t) +

∂2w

∂t2(x, t) = 0, (4.2)

where

c =

√

EI

ρA. (4.3)

Two initial conditions and four boundary conditions are needed for finding a unique solution for w(x, t),

because equation of motion involves a fourth-order derivative with respect to x and a second-order

derivative with respect to t.

The free-vibration solution can be found using the separation of variables method

w(x, t) = W (x)T (t), (4.4)

24

where W (x) is known as the normal mode or characteristic function of the beam.

Substituting in Equation (4.2) leads to

c2

W (x)

d4W (x)

dx4= −

1

T (t)

d2T (t)

dt2= ω2, (4.5)

where ω represents the natural frequency of vibration.

Equation (4.5) can now be rewritten as two equations:

d4W (x)

dx4− β4W (x) = 0 (4.6)

andd2T (t)

dt2+ ω2T (t) = 0, (4.7)

where

β4 =ω2

c2=

ρAω2

EI. (4.8)

From equation 4.8, the natural frequencies of the beam are computed as:

ω = β2

√

EI

ρA= (βl)2

√

EI

ρAl4, (4.9)

where l represents the beam length.

The solutions for equations 4.6 and 4.7 can be found from boundary conditions and initial conditions,

respectively. These solutions are detailed in Rao [34].

In Figure 4.1 is presented the common boundary conditions for the transverse vibration of a beam, with

established values of βl for the first four natural frequencies.

The natural frequency ω is given in radians per second. For the frequency to be given in Hertz it is

necessary to divide it per 2π radians:

f =ω

2π. (4.10)

Finally, for a annulus cross section, the second moment of area is given by:

I =π

4

(

r4e − r4i)

, (4.11)

where re and ri and the external and internal radius, respectively.

25

Figure 4.1: Common boundary conditions for the transverse vibration of a beam [34].

26

4.2 Von Mises Criterion

According to Beer et al. [35], Von Mises criterion defines that a given structural component is safe as

long as the maximum value of the distortion energy per unit volume in that material remains smaller

than the distortion energy per unit volume required to cause yield in a tensile-test specimen of the same

material. This means that as long as the maximum equivalent stress obtained, due to the applied forces,

for the structure in study does not exceed the material tensile strength, plastic deformation does not

occur.

Being deformation defined by any change in size or shape of the object by applying force on it or due to

temperature changes, plastic deformation is the irreversible process of deformation, i.e, once removed

the applied force, if the structure does not return to its original size and shape, it has suffered plastic

deformation.

Formulation and a more detailed description of this criterion is available in Beer et al. [35].

4.3 Finite Element Method

In this section are described the basic principles of Finite Element Method (FEM).

FEM is a numerical method which allows the discretization of a complex continuous domain into a group

of simplest sub-domains. Because of this discretization, the solution of FEM is given in discrete values

at chosen nodes, denominated degrees of freedom (DoF). For a beam, each node has six degrees of

freedom: displacement in the three cartesian axis (x, y and z) and rotation about them.

Euler-Bernoulli Beam Theory

In the Euler-Bernoulli beam theory, is it assumed that plane cross sections perpendicular to the axis of

the beam remain plane and perpendicular to the axis after deformation, Reddy [36]. This means that

transverse shear strain is not considered.

Timoshenko Beam Theory

In the Timoshenko beam theory, the normality assumption is not used, i.e., plane sections remain plane

but not necessarily normal to the longitudinal axis after deformation, the transverse shear strain is not

zero, Reddy [36].

In Figure 4.2 are shown the kinematics of the Euler-Bernoulli beam theory (on the left) and kinematics

of the Timoshenko beam theory (on the right).

It is worth noting that when a beam is considered to be slender, i.e., when one dimension is at least

10 times superior than the others, the results obtained with Timoshenko beam theory are similar to the

ones obtained with Euler-Bernoulli beam theory.

27

Figure 4.2: Kinematics of the Euler-Bernoulli beam theory (on the left) and kinematics of the Timoshenko

beam theory (on the right) [36].

Formulation and a more detailed description of this method and theories is available in Reddy [36].

ANSYS Elements Type

The beam element used,BEAM188, is a two-node beam element in 3D indicated for slender to moder-

ately thick structures and it is based in the Timoshenko beam theory, which includes shear-deformation

effects [37]. It has six degrees of freedom (DoF) in each node: ux, uy, uz, ROTx, ROTy and ROTz,

correspondents to displacement in x, y and z and rotation about x, y and z axis, respectively.

The solid-shell element considered for the model is SOLSH190, which is used for simulating shell struc-

tures from thin to moderately thick. This element is similar to a 3D solid element with shell properties,

based on Mindlin-Reissner shell theory, which is equivalent to the Timoshenko beam theory for plates.

This means this theory also takes into account transverse shear strains through the thickness of the

structure. It has three degrees of freedom: ux, uy, uz.

The BEAM188 and SOLSH190 elements geometry are displayed in Figures 4.3 and 4.4, respectively.

More information about these elements can be found in [37, 38].

Figure 4.3: Element type BEAM188 configuration

[37].Figure 4.4: Element type SOLSH190 configura-

tion [37].

28

Chapter 5

Methodologies and Procedures

5.1 Software

The software used during the preliminary mechanical design and analysis of the antenna boom is re-

sumed in the Table 5.1.

Software type Software Version/Release Analysis type

CAD CATIA V5R20 Design

FEA ANSYS Mechanical APDL 15.0 Static

FEA ANSYS Mechanical APDL 15.0 Harmonic

FEA ANSYS Mechanical APDL 15.0 Modal

Numerical computing programming Matlab R2013a Programming

Table 5.1: Used software.

5.2 Modelling and Meshing Generation

Computed Aided Design (CAD) modelling and Finite Element Analysis (FEA) modelling and meshing

are presented in this section.

5.2.1 Computer Aided Design

The boom modelling was perform using CATIA parameters. This means that for executing any dimen-

sional change it is only necessary to change the parameter and rather than design itself. Design modifi-

cations are only required when geometric changes are desired or parameter alterations lead to modelling

errors.

In order to develop the telescopic with clockwise and counter-clockwise design, it was decided that each

boom should have three striates of high-relief and their slot in the previous boom to allow rotation be-

29

tween them. Each boom should spin about 90◦ in total. The space between these features is to be

fulfilled with straight striates where the linkers between boom elements are going to slide. A represen-

tation is shown in Figure 5.1.

(a) Boom elements striates angle configuration. (b) Boom striates example.

Figure 5.1: Boom elements striates angle configuration.

Each boom design was performed in CATIA Wireframe and Surface Design and Part Design, completing

the following steps:

• Wireframe and Surface Design

1. Sketching a rectangle;

2. Revolving the rectangle;

3. Creating inner and outer helices;

4. Helix extrapolation and normal plane to he-

lix creation for both cases;

• Part Design

1. Closed surface;

2. External and internal helix striate sketch;

3. Rib and slot helix sketches, respectively;

4. Circular pattern of helix striates: 3 inci-

dences equally distributed by 360◦;

5. Pocket at bottom and top of the boom to re-

move excesses from helix external striates;

6. Internal linkers straight striates sketch;

7. Pocket of linkers straight striates;

8. Circular pattern of linkers striates: 3 in-

cidences equally distributed by 360◦ be-

tween helix striates.

As shown in Figure 5.1, there is a need of four straight striates for linkers to prevent their overlap during

the boom elements rotation movement. 10 elements were designed, completing a total of 9.9 m.

For linkers design, a telescopic structure was also necessary, because each linker must have at least a

boom length plus the linkers parts that slide (sliders) in the boom elements striates lengths.

Each linker has 17 parts, being two of them the sliders and other two circular connections between

30

the three linkers of each two boom elements, with the goal of helping preventing linkers torsion. The

remaining 13 parts constitute the linker telescopic main structure. Each part has a hollow squared cross

section and two stops so they stay engaged when deployed.

The linker parts design was performed through the use of CATIA’s Part Design pad features.

5.2.2 Finite Element Model

Before CAD design was perform, a simple initial finite element model was created with the aim of validate

the finite element model design. This model consists of one hollow cylinder of 10 meters long, with

external and internal diameters of 50 and 48 mm, respectively.

Before selecting the boom material, titanium was chosen as a reference to validate the finite element

model. The titanium properties used were:

• Density: ρ = 4460 kgm−3;

• Young’s modulus: E = 114 GPa;

• Poisson’s ratio: ν = 0.34

In a first stage, four models were created with beam, shell, solid-shell and solid elements; a modal

analysis was then run. All the four models have presented similar results for natural frequencies, with a

maximum relative deviation of 0.6 % among them.

It was decided that only beam and solid-shell elements would be considered in the finite element mod-

elling. Beam elements are suitable for the preliminary analysis of the structure. Solid-shell elements are

suitable when design detailed elements are needed to perform a more realistic modelling and analysis,

because solid-shell combines the three-dimensional properties of solid elements, allowing to analyse

what happens in thickness for example, with the characteristics of shell elements, ideal for models that

have two dimensions much larger than the third one.

For preliminary modelling and analysis, it was considered that the structure had one extremity con-

strained in space, i.e. fixed, and the other end was free, i.e. unconstrained, due to the expected mass

of the antenna boom being at least 100 times lower than the satellite where it will be mounted on. It

was also considered that design details such as helix striates and linkers straight striates would have a

minimal impact in the computations, because of their small dimensions; hence they were neglected.

The modelling procedures adopted were also successfully validated by performing some ANSYS Me-

chanical APDL Verification Manual [39] examples: VM59 for beam188 type of element modelling, VM6

and VM82 for solsh190 type of element modelling.

Mesh Independence Study

Before validating these simple models, a mesh independence study was performed for beam and solid-

shell models. The purpose o this study is to achieve a model whose results are as independent as

31

possible from the number of elements used. It is worth noting that increasing the number of elements

will extend the computational memory and time needed for meshing and analysis.

Is is defined as convergence criterion the relative deviation from the subsequent mesh refinement be

lower than 1 %:

Deviation(%) = 100×

∣

∣

∣

∣

valueN − valueN+1

valueN+1

∣

∣

∣

∣

≤ 1%, (5.1)

where N represents the mesh refinement to be evaluated and N + 1 represents the subsequent refine-

ment.

In a first stage, a mesh with 2 elements in thickness and 20 elements per 360◦ arc was performed and

the number of elements per one meter length was varied: 10, 20, 50, 100. This study is displayed in

Figure 5.2. Although no relative deviation superior to 1 % was registered to the first and second meshes,

it was chosen the third one, with 50 elements per meter, in order to respect a reasonable element aspect

ratio. Afterwards, elements in thickness were varied from 1 to 3 and no significant deviation in frequency

values was seen, remaining the mesh with 2 elements in thickness. Finally, a variation in the number

of elements per circle was performed from 20 to 100 with intervals of 20 and the maximum relative

deviation achieved was about 0.6 %, inferior to the 1 % criterion. However, it was noticed that the larger

the number of element in a circle, the nearest the frequency values achieved were from the theoretical

ones. For this reason, it was chosen to use 40 elements per circle.

With 50 elements per meter, 40 per circle and 2 per thickness, it is guaranteed that there is no aspect

ratio superior to 1:30.

(a) Beam element model. (b) Solid-shell element model.

Figure 5.2: Mesh independence study: natural frequencies.

Model Verification

In Table 5.2 are presented the first frequencies obtained from finite element models, including a relative

deviation from the theoretical values, which were calculated from Equations (4.9) and (4.11) for a fixed-

free beam (see Table 5.2).

As shown in Table 5.2, the frequency values obtained with FEM have a maximum relative deviation of

0.73 % (model with beam elements). This means that the structure is slender, being the results obtained

32

Natural frequencies, f (Hz)

Theoretical beam188 Relative deviation (%) solsh190 Relative deviation (%)

0.9805 0.9784 0.21 0.9787 0.18

6.1444 6.1249 0.32 6.1277 0.27

17.205 17.121 0.49 17.131 0.43

33.714 33.469 0.73 33.495 0.65

Table 5.2: Verification of finite element model: natural frequencies comparison.

with Timoshenko beam theory in FE similar to the ones obtained with Euler-Bernoulli beam theory. This

results verifies the modelling and meshing procedures. The relative deviation from theoretical values is

given by:

Relative Deviation(%) = 100×

∣

∣

∣

∣

valueFEM − valueTheory

valueTheory

∣

∣

∣

∣

(5.2)

After verifying the modelling for one-part boom, a solid-shell elements model with 11 boom elements was

created and its values were compared with another software using solid elements; similar results were

obtained, straightening the validity of the approach. The deviation of the eigenfrequencies computed

with both software was lower than 1 % for at least the lowest 10 eigenmodes. This model had a total

boom length of 10 m.

Afterwards, a 10 boom elements model was designed, fulfilling a length of 9.9 m. A mesh independence

study for the number of elements per meter was performed for both models, being the last one displayed

in Figure 5.3. As these models are a consecutive replication of the first one, the mesh of 2 elements in

thickness and 40 per circle was held.

Figure 5.3: Mesh independence study for 10 boom elements model of solid-shell elements.

As for one-part models, the calculations converged to the first mesh with 10 elements per meter, with

a maximum relative error of 0.3 %, but it was decided to employ the third mesh, with 50 elements per

meter, in order to respect a maximum aspect ratio of 1:20. This mesh is displayed in Figure 5.4.

Finally, regarding the stowed configuration, two finite element models were assembled, both with solid-

shell elements and the previous chosen mesh to the deployed model. For these models, 10 boom ele-

33

Figure 5.4: Mesh chosen to apply in finite element model.

ments were modelled, being the longitudinal coordinate of the extremities defined by the space needed

for linkers structures stowage. This means that each boom element will have a longitudinal advance

equal to linkers stowage size in relation to the previous boom element. After modelling, the first model,

hereafter referred as stowed-1 configuration, shown in Figure 5.5(a), would have all the coincident nodes

coupled to simulate a mono-block structure, and the second, hereafter referred as stowed-2 configura-

tion and presented in Figure 5.5(b), would only have the coincident nodes in boom elements extremities

coupled, to simulate locking in extremities.

These two constrained configurations were considered because the final stowed structure would be

something in between. It will not be as rigid as a mono-block (stowed-1) and it will not be as free as the

stowed-2 solution because there will be a safety element during launching, like a brace for example, that

adds rigidity to the model and allows for an adjust in the structure frequencies.

(a) Stowed-1. (b) Stowed-2.

Figure 5.5: Stowed configurations.

Modelling, analysis and post-processing were performed based in specific software guides [37, 40, 41].

5.3 Concept Validation: 3D-printer Preliminary Prototype

In order to validate the chosen concept of deployment mechanism, concept 1-A, it was produced a 3D-

printer preliminary prototype in a thermoplastic polymer (acrylonitrile butadiene styrene), as shown in

34

Figure 5.6.

(a) Deployed. (b) Stowed.

Figure 5.6: 3D-printer preliminary prototype assembled.

It is worth mentioning that measures of this prototype are not to scale with respect to the intended

antenna, because it had to fulfil the 3D-printer requirements.

The 3D-printer used is a Leapfrog Creatr [42] that has an extruder size of 0.35 mm and it was used a

overlapping of 35 %. A 1 mm tolerance between contact surfaces is required.

It is also worth noting that the linkers between alternate booms are not telescopic, as in the CAD model,

in order to simplify the printing and assembly processes.

The prototype parts designed in CATIA and their critical measures are presented in Table 5.3. The same

procedures of CAD design presented in subsection 5.2.1 were followed.

After designing, the parts were printed and their surfaces were smoothed by Active Space Technologies

employees: Nuno Martins; Frederico Teixeira and Miguel Cardoso.

35

Name Product Specifications Name Product Specifications

3D-boom1

• Maxinum heigth:

100 mm

• Maximum width:

80 mm

• Minimum thickness:

2 mm

3D-boom2

• Maxinum heigth:

100 mm

• Maximum width:

74 mm


2 mm

3D-boom3

• Maxinum heigth:

103 mm

• Maximum width:

56 mm


2 mm

3D-boom4

• Maxinum heigth:

103 mm

• Maximum width:

38 mm


2 mm

3D-base1

• Maxinum heigth:

2 mm

• Maximum width:

80 mm


2 mm

3D-base2

• Maxinum heigth:

2 mm

• Maximum width:

62 mm


2 mm

3D-linker1-3

• Maxinum heigth:

102 mm

• Maximum width:

86 mm


1.5 mm

3D-linker2-4

• Maxinum heigth:

94 mm

• Maximum width:

56 mm


1.5 mm

3D-link3

• Maxinum heigth:

13 mm

• Maximum width:

86 mm


1.5 mm

3D-link4

• Maxinum heigth:

3 mm

• Maximum width:

10 mm


1.5 mm

Table 5.3: Prototype 3D printed parts dimensions.

36

A CAD error was found after printing: the height of boom2, boom3 and boom4 was 93 mm instead of

100, 103 and 103 mm respectively.

To correct this error a ring repair part of about 7 millimetres height and 3D-base2 radius was cut of

paper-board. This ring repair part was glued to 3D-base2 in order to increase 3D-boom2 height.

A second existing 3D-linker2-4 was cropped so its bottom part could be glued to the 3D-linker2-4 bottom,

owing to rise 3D-boom3 and 3D-boom4. These solutions are displayed in Figure 5.7.

Figure 5.7: Ring and linker repair parts.

5.3.1 Assembling Procedure

The necessary items to perform the prototype assembling are:

• 3D printed parts, displayed in Table 5.3;

• Glue1:

– Epoxy Structural Adhesive 2216 B/A;

• Grease/lubricant 1:

– WD401;

• Heat gun1:

– 230V - 50Hz;

– 1800 W;

– I: 75 ◦C - 400 ◦C; II: 85 ◦C - 600 ◦C;

Subsequently, there are presented the most important assembling instructions:

1. Place 3D-boom2; stops in the straight striate up;

2. Place 3D-boom3 inside 3D-boom2; stops in the straight striate down;

3. Place 3D-boom4 inside 3D-boom3; stops in the straight striate down;

1In order to repeat the assembling, the item does not need to be exactly the same as long as it can provide similar results.

37

4. Place 3D-linker2-4 from the bottom of 3D-boom4, connecting to the straight striate of 3D-boom2

in its bottom;

5. Glue 3D-link4 at the top of 3D-linker2-4 vertical beams;

6. Glue 3D-base2 at the bottom of 3D-boom2; 3D-linker2-4 stays above the base;

7. Place 3D-boom2 inside 3D-boom1; stops in the straight striate up;

8. Place 3D-linker1-3 outside 3D-boom1, connecting to its straight striate;

9. Glue 3D-link3 at the top of 3D-linker1-3 vertical beams;

10. Glue 3D-base1 at the bottom of 3D-boom1; 3D-linker1-3 stays above the base.

Each glueing step must respect the cure time of the chosen glue to prevent the glued parts from discon-

nection. A heat gun may be carefully used to accelerate this process.

A few errors occurred during the assembling process. During the glueing of 3D-link4 to 3D-linker2-4 a

deformation occurred in the vertical beams, as shown in Figure 5.8. The most probable cause of this

deformation is the heat gun incorrect use. As the glued surfaces could not be seen, the material could

have been softened by heating and, when pressure was applied, deformation could have happened. A

small breach also appeared in one beam. It was strengthen with glue.

Figure 5.8: 3D-linker2-4 vertical beams deformed.

This deformation has made the deployment difficult, due to a significant increase in friction in the straight

striate of the 3D-boom4, where the 3D-linker2-4 should slide.

5.3.2 Testing

In order to test the prototype deployment, a deployment actuator was also used. The deployment with

actuator is shown in Figures A.1, A.2 and A.3 in appendix A.

Maintaining 3D-boom1 fixed, the deployment actuator slowly pushed 3D-base2, forcing a synchronised

opening of the remaining booms.

38

For the deployment shown in Figure 5.9, no actuator was used. Only force of gravity was applied and

the assisted deployment was softened by holding the linker between boom 1 (3D-boom1) and boom 3

(3D-boom3).

Figure 5.9: Prototype deployment.

The concept was alidated, deploying all booms synchronously provided that the clockwise and counter-

clockwise rotation and the linkers between alternate booms:

• Boom 3 (3D-boom3) only shows translation movement with respect to boom 1 (3D-boom1);

• Boom 4 (3D-boom4) only shows translation movement with boom 2 (3D-boom2);

• Boom 2 (3D-boom2) presents translation and rotation movement with respect to boom 1 (3D-

boom1).

Prototype assembling and testing was performed with the assistance of Fernando Simoes, from Active

Space Technologies.

39

Chapter 6

Results

Assessment of length, width and thickness of the boom elements is very important regarding mass mini-

mization. Because of unsuccessful attempts of producing an optimization routine in ANSYS Mechanical

APDL that would provide the optimized values for thickness and radius of each boom of the model, it

was decided to use the same thickness for all boom elements and a sort of manual primary optimization

was performed.

6.1 Concept 1-A

6.1.1 Static Analysis

A static analyses was performed focused on launch environment. The antenna, in its stowed configura-

tion, was subjected to its own weight plus a static acceleration delivered by the launcher vehicle. Relying

on Israr [43], steady loading and response conditions are generally assumed during these analysis and

the loads are acted on the geometric centre of the structure. In this case, as the structure centroid is

on its hollow part due to symmetry, the resultant force was applied on the top part of the boom, in the

longitudinal position of the centroid.

Since this is a preliminary design and there are many design uncertainties, a typical engineering safety

factor of 2 was applied to the maximum static acceleration described in Section 1.2 (7 g) to test if the

structure in its stowed configuration is deformed during launch. Although parallel to the mounting plane

of the satellite loads are in general inferior to the longitudinal ones, an equal value was applied in the

three cartesian coordinates (x, y, z), in order to cover all possible future antenna booms positioning.

Summarizing, an acceleration of 14 g plus the boom weight (mass× g) was applied on one node of the

external radius of the boom, in its centroid longitudinal coordinate, in the three cartesian coordinates, in

order to obtain the maximum stress applied to the structure and compared it with the material strength.

The applied force representation is displayed in Figure 5.5, in Chapter 5.

The difference between material tensile strength for 0◦ and 90◦ is about two orders of magnitude, where

40

the composite with fibres at 0◦ is the one that has the greater strength. Although the stacking sequence

does not include fibres at 90◦ and is mainly composed of fibres at 0◦ , the value of tensile strength taken

as reference will be one order of magnitude lower than the one for 0◦ and it must not be exceeded by

the value of maximum stresses obtained in the analysis, with the aim of preventing plastic deformation

from happening.

For both stowed configurations, stowed-1 and stowed-2, the analyses were performed varying the boom

thickness and the maximum equivalent stresses obtained (Von Mises stresses) are displayed in Table

A.6.

Comparing the results with each one of the chosen carbonfibre composite materials tensile strength

multiplied by 0.1, the material with the lower density and the minimum possible thickness were chosen

to continue the boom design. Figure 6.1 shows the contour plot of nodal solution for the Von Mises

stresses in both stowed configurations (complete version: Figure A.4).


Figure 6.1: Von Mises equivalent stresses: nodal solution representation.

Stowed-2 configuration was modelled without any contact between boom elements. The only constraint

was the coupled nodes in the end of each boom in contact with the next or the previous one. This

simplified model is visible in Figure 6.1(b), where the boom elements have a non-continuous behaviour.

A best solution for this modelling would be to implement contact elements between the walls of the boom

elements, like ANSYS Mechanical APDL element conta173.

As the next stage of finite element modelling is to introduce some design details, as helix striates and

linkers straight striates, it will be necessary to ensure a minimum thickness sufficient to allow the details

modelling. This decision should be taken after consulting composite materials manufacturers, who have

a better perception of the needed machining processes and requirements.

6.1.2 Harmonic Analysis

Continuing focused on launch environment, the sine equivalent dynamics are chosen for harmonic anal-

ysis, from 0 to 150 Hz, with a resolution of 0.2 Hz, with a load intensity of 2 g (safety factor of 2) and the

boom weight, in the three directions. As performed for static analysis, this load is applied on one node

of the external radius of the boom, in its centroid longitudinal coordinate.

41

When performing harmonic analysis, the Full Method solution was applied, without damping. It uses the

full system matrices to calculate the harmonic response [41] (matrices available in [41, 38]) and is the

easiest available method for harmonic analysis, having the disadvantage of being more computational

expensive than the other available method.

Once again, the maximum value of stress obtained in the analysis must not exceed the minimum ma-

terial strength value. Graphics of equivalent stresses per frequency are displayed for the two stowed

configurations on three nodes: the one where force was applied (Figures 6.2(a) and 6.3(a)), a node on

the top of the base, boom fixed end, (Figures 6.2(b) and 6.3(b)) and a node on the top of the free end

(Figures 6.2(c) and 6.3(c)). Complete versions displayed in Figures A.5 and A.6.

Maximum equivalent stresses are three orders of magnitude lower than the reference value of tensile

strength considered for stowed-1 configuration and one order of magnitude above for the stowed-2

configuration. From Figures 6.2 and 6.3 it is possible to see that stowed-1 configuration has its first

eigenfrequency about 45 Hz, while stowed-2 configuration has its first eigenfrequency about 23 Hz.

(a) Node where force was applied. (b) Node on the top of the boom base.

(c) Node on the top of the boom free end.

Figure 6.2: Von Mises equivalent stress per frequency on selected nodes: stowed-1 configuration.

42

(a) Node where force was applied. (b) Node on the top of the boom base.



43

6.1.3 Modal Analysis

Block Lanczos was the mode-extraction method applied while performing modal analyses; it is used for

large symmetric eigenvalue problems [41]. The number of modes to extract was always superior by ten

than the number the user asks to see, to allow for better convergence of the results.

Stowed configuration

According to Fortescue and Stark [18], in order to avoid the dynamic coupling between spacecraft and

Ariane 5 launch vehicle that causes quasi-static loads and dynamics transients to increase, possible

apportioned requirements are 30 - 80 Hz for fixed base major spacecraft appendages and 100 Hz for

equipment, i.e., equipment should not have any eigenfrequency lower than 100 Hz. This frequency

requirement was not achieved, the first eigenfrequecy for both stowed configurations is lower than 100

Hz.

The first five frequencies values for both stowed configurations are displayed in Table A.7.

Deployed configuration

Regarding the deployed configuration, coupling between frequencies associated with natural signatures,

reported in Chapter 2, and boom eigenfrequencies should be avoided.

The first five eigenfrequencies values are displayed in Table A.7 and its correspondent modal shapes

are shown in Figure A.8.

Post-processing Matlab Tool

A Matlab post-processing tool was created in order to provide a better perception of natural frequencies

placement in the deployed configuration. This tool reads the modal results file produced by APDL code

for modal analysis and puts data in a plot that also represents Schumann resonance and Alfven wave

frequencies, allowing for a clear visual perception of them. It also allows comparison between two files

of results. A tool display is shown in Figure 6.4 and the image gotten from the tool for this case study

is presented in Figure 6.5. As shown, the first boom eigenfrequency is in the range of Alfven waves

frequencies and the measurements can be affected by it. Schumann’s resonance frequencies were

successfully avoided.

The coloured markets (square - x direction, circle - y direction and diamond - z direction) associated with

each eigenfrequency have a connecting with the modal participation factors, which are a comparison

between the effective mass of the structure that is affected by a frequency and the total mass of the

structure. Participation factors give us an indication of the portion of mass of the structure that can be

affected. When a participation factor in one direction becomes red means that its respective frequency

affects at least 50 % of the total mass, orange is associated to the range of 20 % to 50 %, yellow between

44

Figure 6.4: Post-processing Matlab tool display.

Figure 6.5: Post-processing Matlab tool resulting graphic.

10 % and 20 %, green between 5 % and 10 % and blue stands for a participation factor lower than 5 %.

The star markets become purple when a eigenfrequency of the boom matches the Alfven waves range

and red when it is coincident with a Schumann resonance, including the tolerance values.

45

6.1.4 Mass

All the previous results were performed without linker structures. These structures, as designed in CAD

modelling, represent an increase in volume of about 4 %, with respect to the boom FE model. Although

the change in volume is not much, there is a significant change in the cross section area along the boom

elements. This means that all the previous results are only valid in a qualitative way, showing that this

concept is not suitable for the desired mass design requirement. Hereupon, it was decided to repeat the

previous analysis to a boom configuration for concept 1-B.

6.2 Concept 1-B

This concept does not require linkers (neither structures or striates) or helix striates (neither ribs or slots).

It only needs guides for locking mechanisms and these are of very small dimensions in comparison with

boom parts lengths and diameters and it is considered that they do not have a significant effect in the

boom mass.

6.2.1 Static Analysis

For concept 1-B and maintaining the 10 boom elements configuration, the minimum radius is obtained

by the thickness variation. It is worth noting that the minimum radius also depends on the electric wires

thickness. For this study is assumed that the wires will in total have a maximum diameter of 10 mm.

The static analyses performed are similar to the previous ones and the primary optimization is obtained

varying thickness and, in this case, consequently the radius of the boom elements, which are a depen-

dent of thickness. The values obtained are displayed in Table A.8 and Figure 6.6 shows the contour plot

of nodal solution for the Von Mises equivalent stresses in both stowed configurations for concept 1-B

(complete version: Figure A.9) after material and thickness selection. The minimum thickness was first

selected resorting to static results and the final thickness was selected after performing modal analysis

for the deployed configuration, trying to avoid Schumann resonance and Alfven wave frequencies while

respecting the mass requirement.


Figure 6.6: Von Mises equivalent stresses: nodal solution representation.

46

6.2.2 Harmonic Analysis

The harmonic analyses performed were similar to the previous ones and the graphics of Von Mises

equivalent stresses per frequency within the range from 0 to 150 Hz are shown in Figures 6.7 and 6.8

(complete versions displayed in Figures A.10 and A.11.

For both stowed configurations, the maximum equivalent stresses obtained do not exceed the maximum

settled strength value, which means that no plastic deformation occurs for this stage of the launch. From

Figures 6.7 and 6.8 it is possible to see that stowed-1 configuration has its first eigenfrequency about 68

Hz, while stowed-2 configuration has its first eigenfrequency about 107 Hz. As stowed-2 configuration

is the less rigid of the two stowed configurations, its first eigenfrequency would be expected to be lower

than the first eigenfrequency of stowed-1 configuration.

(a) Node where force was applied. (b) Node on top of the boom base.


Figure 6.7: Von Mises equivalent stresses per frequency on selected nodes: stowed-1 configuration.

47

(a) Node where force was applied. (b) Node on top of the boom base.



6.2.3 Modal Analysis

Stowed configuration

Regarding the stowed configuration modal analysis, the boom first eigenfrequency is lower than 100 Hz,

and therefore the frequency requirement for instruments during launch environment is not respected.

Deployed configuration

After performing the primary optimization with frequencies placement while respecting the mass require-

ment, available in Figure A.12, thickness and corresponding radius were chosen. The deployed config-

uration comparison between eigenfrequencies and the frequencies to be avoided is displayed in Figure

6.9. As shown, in order to respect the mass requirement not all of the frequencies may be avoided:

the first and second eigenfrequencies of the boom matches the range of Alfven waves frequencies.

48

Schumann’s resonance frequencies were successfully avoided.

Figure 6.9: Comparison between deployed configuration eigenfrequencies and frequencies to be

avoided.

6.2.4 Mass

Although the mass requirement has been fulfilled, the structure does not respect all the requirements.

For instance, the first eigenfrequency in the stowed configuration does not respect the desired minimum

value of 100 Hz. It is also important to remember that the mass requirement of 2 kg per boom regards

all deployment mechanism systems, but the value achieved is only valid for the boom structure.

Finally, we should bear in mind that the thickness obtained must be evaluated by a composite materials

manufacturer, in order to confirm that it is possible to produce the structure with its imprinted details.

49

Chapter 7

Conclusions

This work was performed in collaboration with the company Active Space Technologies and its main

purpose was the study and development of a preliminary design of a triaxial dipole antenna for space

applications. This work was focused primarily in the structural requirements presented in Chapter 2,

with special attention to mass, length and length variability requirements, that lead to the assessment of

material properties and design dimensions in order to fulfil the project objectives. The design presented

in this work is partially compliant with those requirements.

The selection of materials was conducted in a way to reach a compromise between low density and high

stiff components, in order to respect the mass and length variability requirements of the project. Three

carbon-fibre composite materials were selected for later assessment, based on Young’s Modulus to den-

sity ratio and density. The material equivalent properties were found for a typical stacking sequence that

maximizes bending and torsional stiffness, in order to minimize boom length variation during operations.

After performing static and harmonic analyses, which simulated the in-flight environment, for a stowed

configuration, it was chosen the material with the lowest density, as long as the material could sustain

the static loads applied during launch.

Static analyses performed had the principal aim of comparing the obtained maximum Von Mises equiv-

alent stresses with the material tensile strength in order to assess whether the structure would suffer

plastic deformation during launch. Harmonic analyses performed with reference sine dynamic loads had

the same purpose of the static analyses.

It is worth mentioning that stowed-2 configuration has not produced very reliable results. It is necessary

to improve this configuration by adding contact elements between booms contact walls.

Modal analyses for the stowed configuration had the main goal of checking if the structure eigenfrequen-

cies would not interfere with satellite and launcher vehicle frequencies during launch. For the deployed

configuration, the principal objective was to characterize decoupling between antenna boom eigenfre-

quencies and natural frequencies to be measured.

The design of Concept 1-A brings an innovative approach to the telescopic boom deployment problem.

It only requires an actuator to apply force on the second boom (from the root) in order to open the whole

50

structure. This means that the actuator does not have a long distance to cover. This concept was proven

to work properly through the production of a 3D-printer model. This preliminary prototype has proven

that the clockwise and counterclockwise rotations between consecutive booms cause the synchronous

opening of the whole structure once the actuator triggers the movement. However, this design did not

fulfil all structural requirements, given the design limitations previously discussed. One possible solution

to reduce the mass of the structure is to design linker structures outside of the main boom instead of

inside, so the major external radius can be reduced. It is worth noting that this reduction has to be done

regarding the required length for linker structures perform the established rotation.

The design of Concept 1-B has fulfilled almost all of the assessed requirements with only a few ex-

ceptions: the fact that the first boom eigenfrequency in its stowed configuration does not respect the

established value for instruments, and the fact that the first and second boom eigenfrequencies in the

deployed configuration are coincident with Alfven waves frequencies range, which may introduce noise

in the antenna measurements. On the other hand, Schumann resonance frequencies were successfully

avoided.

The great disadvantage of this concept is the distance that the deployment actuator must cover because

it would be applying force at the tip boom (last from the root) which in turn would deploy the consequent

ones. A possible integrated solution between Concept 1-A and Concept 1-B could be envisioned, dimin-

ishing the length to be covered by the actuator in relation to Concept 1-B and decreasing the mass in

relation to Concept 1-A.

Summarizing, the proposed deployment mechanism idea of Concept 1-A was proved to work but the

mass requirement was not fulfilled. Mass requirement was achieved for Concept 1-B, which was also

successful in the decoupling of Schumann resonances frequencies. It was not so successful avoiding

the Alfven range frequencies where first and second eigenfrequencies of the boom were positioning.

Although more innovative, the Concept 1-A does not respect at least one of the most important require-

ments proposed. The Concept 1-B is a safer approach to the telescopic boom design but its inherent

innovation belongs exclusively to the deployment actuator system.

7.1 Future Work

The preliminary design of the antenna boom was not completed. The requirement with respect to boom

length variability was not assessed. The most relevant load that affects it, disregarding impact from

space debris, is the thermal shock due to the transition from shadow to sunlight and vice-versa.

Future work for mechanical design and analysis of the dipole antenna deployment mechanisms may

include:

• Improve stowed configuration modelling by adding contact elements (conta173) in order to obtain

reliable results from analysis;

• Perform thermal analysis to ascertain the boom length variation with thermal shock and thermal

51

cycling;

• Design chosen concept details;

• Design deployment actuator system;

• Assembly and analysis of the dipole antenna;

• Assembly and analysis of the triaxial dipole antenna;

52

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