Dynamic and Thermal Models for ECOSat-III - ULisboa · Dynamic and Thermal Models for ECOSat-III...

Dynamic and Thermal Models for ECOSat-III

Sofia de Fátima Caeiro Aboobakar

Thesis to obtain the Master of Science Degree in

Aerospace Engineering

Supervisor: Prof. Afzal Suleman

Examination Committee

Chairperson: Prof. Fernando José Parracho LauSupervisor: Prof. Afzal Suleman

Member of the Committee: Prof. Edgar Caetano Fernandes

November 2016

Dedicated to my family who always supported me during this long journey.

iii

Acknowledgments

I would like to thank my supervisor Dr. Afzal Suleman for providing me the opportunity to develop

such an interesting work in Centre for Aerospace Research in University of Victoria and for the financial

support during my stay in Canada. I would like to thank the ECOSat team for providing me informa-

tion and for helping me whenever I needed. I would like to give a special thanks to two ECOSat team

members: Cass Hussmann for all the orientation he provided during the development of my work and to

Abdul Fourteia who was always available and showed himself very helpful at all times. I would also like

to thank Stephen Warwick and Peter Sherk from Centre for Aerospace Research in Victoria International

Airport who managed to provide me a work station at the airport with all the resources I needed and for

clarifying me on some subjects of my work. I want to thank all the members of the Centre for Aerospace

Research, in both University of Victoria and Victoria International Airport, and of the ECOSat team for

the good times and amazing experience in Canada.

I would like to thank all my colleagues and professors I met during this Aerospace Engineering course

who helped me surpass my limits when I thought I couldn’t make it. I also thank my Taekwondo profes-

sor, colleagues and students. Training days always helped me to refresh my mind in times of hard work.

Last but not least, I would like to thank my mother, grandmother and brother for the unconditional

support during all my life. Your everyday support and the sacrifices made were essential to make this

dream come true.

v

Resumo

Lancar satelites para orbita e uma tarefa exigente do ponto de vista da manutencao da integridade

estrutural da carga transportada pelo lancador e do ponto de vista financeiro. Quando e decidido lancar

um satelite para orbita, o seu comportamento dinamico e o seu perfil termico durante a orbita tem de

ser mantidos dentro de um limite especıfico para garantir que nao ha falhas causadas por um projecto

estrutural e termico inadequado. Modelos de elementos finitos sao usados para prever o comporta-

mento da estrutura. Contudo, esses modelos devem ser validados por testes experimentais. Modelos

validados podem ser usados com confianca para conduzir mais simulacoes que permitam avaliar o

comportamento do satelite e corrigi-lo se necessario. Esta tarefa e mais difıcil quando se lida com pe-

quenos satelites como o caso do ECOSat-III, um CubeSat de unidade tripla. Este trabalho descreve o

processo de avaliacao do comportamento do satelite e de actualizacao do seu modelo de elementos

finitos utilizando dados experimentais, sempre que possıvel. Os requisitos a ser satisfeitos e discutidos

neste trabalho estao relacionados com a frequencia fundamental do satelite e a sua distribuicao de

temperaturas. O objectivo desta tese e aumentar a frequencia fundamental do nanosatelite e permitir

que os seus componentes operem dentro da sua margem de temperaturas de seguranca atraves do

desenvolvimento de um sistema de controlo termico. A avaliacao das consequencias de cada mudanca

de projecto foi feita e mostra que com as solucoes propostas, o ECOSat-III esta pronto para ser lancado

e sobreviver as condicoes de ambiente espacial em seguranca, do ponto de vista estrutural e termico.

Palavras-chave: Modelo de elementos finitos, Actualizacao do modelo de elementos finitos,

Frequencia fundamental, Sistema de controlo termico, CubeSat

vii

Abstract

Launching a satellite into orbit is a demanding task from the point of view of maintaining the launcher’s

payload structural integrity and from the financial point of view. When it is decided to launch a satellite

into orbit, its dynamic behaviour and its thermal profile during its orbit have to be maintained within

specified levels to guarantee that no failure is caused by an inadequate structural and thermal design.

Finite element models are used to predict the structure’s behaviour. However, these models need to

be validated by experimental tests. Validated models can be used with reliability to perform further

simulations that allow to properly evaluate the satellite’s behaviour and to correct it if needed. This task

is harder when dealing with small satellites, the case of the ECOSat-III, a triple-unit CubeSat. This work

describes the process of evaluating the behaviour of the satellite and performing its finite element model

update using experimental data, whenever possible. The requirements to be satisfied and discussed

in this work are related to the fundamental frequency of the satellite and its temperature distribution.

The objective of this thesis is to increase the fundamental frequency of the nanosatellite and to make

all its components operate in their safe temperature range by developing a thermal control system. The

evaluation of the consequences of each design change has been performed and shows that with the

proposed solutions, the ECOSat-III is ready to be launched and survive space environment conditions

safely, from the structural and thermal point of views.

Keywords: Finite element model, Finite element model update, Fundamental frequency, Ther-

mal control system, CubeSat

ix

Contents

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

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

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

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 General Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2.1 The ECOSat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2.2 Nanosatellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2.3 CubeSats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.4 The Canadian Satellite Design Challenge . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.5 Mission Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Theoretical Background 9

2.1 Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Numerical Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.2 Experimental Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.3 Finite Element Model Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.1 Heat Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.2 Heat Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.3 Transient Thermal Analysis Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 The ECOSat-III Satellite 21

3.1 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Structure Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

xi

3.3 Electronic Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4 Payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4 Dynamic Analysis 29

4.1 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.1.1 Parts Idealization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.1.2 Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1.3 Boundary Conditions and Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2 Experimental Modal Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3 Finite Element Model Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.4 New Configuration Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.5 Solution Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5 Thermal Analysis 53

5.1 Initial Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.1.1 Parts Idealization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.1.2 Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.1.3 Boundary Conditions and Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.2 Thermal Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.3 Additional Thermal Control System Improvement . . . . . . . . . . . . . . . . . . . . . . . 67

5.4 Fundamental Frequency Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6 Conclusions 75

6.1 Recommendations and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Bibliography 79

A 3U CubeSat Configuration 83

B Results from Thermal Simulations 84

C Solver Performance Optimization 93

C.1 NX NASTRAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

C.2 NX SPACE SYSTEMS THERMAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

xii

List of Tables

1.1 Satellite classification according to its mass and respective cost . . . . . . . . . . . . . . . 2

2.1 Bond albedo of different materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1 Mechanical and thermal optical properties of aluminum 6061 T6 . . . . . . . . . . . . . . 22

3.2 Mechanical and thermal properties of FR-4 . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3 Dimensions and thermal properties of each battery . . . . . . . . . . . . . . . . . . . . . . 25

3.4 Dimensions and thermal and optical properties of each solar cell . . . . . . . . . . . . . . 26

3.5 ADCS components with respective dimensions, mass and operating temperature range . 27

3.6 Properties of the hyperspectral camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.1 Idealization results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2 1D meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3 2D meshes in the vibrations FEM models . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.4 3D meshes used in the vibrations FEM models . . . . . . . . . . . . . . . . . . . . . . . . 34

4.5 Measured mass, FEM model components mass and change in density value to match

both results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.6 First natural frequencies of each FEM Model . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.7 List of parameters and responses used in the final sensitivity analysis . . . . . . . . . . . 45

4.8 Parameters with highest sensitivity coefficients in relation to the fundamental frequency . 46

4.9 Changes in the parameters with highest sensitivity coefficients in relation to the funda-

mental frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.10 Difference between the FEA and EMA responses in the end of the FEM model update . . 47

4.11 FEM Model update results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.12 Meshes used in the components added in FEM Model 5 . . . . . . . . . . . . . . . . . . . 48

4.13 Fundamental frequencies of the new configurations and its deviation from the previous

model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.14 Increase of the fundamental frequency by using stiffeners in FEM Model 5 . . . . . . . . . 50

4.15 Final configuration characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.1 Hot Case and Cold Case characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.2 2D meshes used in the thermal FEM model . . . . . . . . . . . . . . . . . . . . . . . . . . 55

xiii

5.3 3D meshes used in the thermal FEM model . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.4 Thermo-optical properties of the external surfaces . . . . . . . . . . . . . . . . . . . . . . 57

5.5 Maximum and minimum temperatures in each simulated case . . . . . . . . . . . . . . . . 62

5.6 Density, thermal conductivity and final mass of the central camera mounting plate for

different materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.7 Thermal diffusivity of different materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.8 Temperature changes when using all mounting plates with stainless steel and when using

all aluminum except for the central camera mounting plate . . . . . . . . . . . . . . . . . . 73

5.9 Fundamental frequency and solid properties after developing the TCS with all the mount-

ing plates in stainless steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.10 Fundamental frequency and solid properties after developing the TCS with only the central

camera mounting plate in stainless steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.11 Fundamental frequency and solid properties after developing the TCS without the pro-

posed additional improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

B.1 Simulated orbits and corresponding thermal loads . . . . . . . . . . . . . . . . . . . . . . 85

B.2 Operating ranges, minimum and maximum temperatures and temperature variation in

each component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86


each component when black dye is applied . . . . . . . . . . . . . . . . . . . . . . . . . . 87


each component when black dye is applied and a camera mounting plate is changed from

aluminum to stainless steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

B.5 Maximum temperature (in◦C) distribution on the PCB stack when attaching to it plates to

increase the thermal inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

B.6 Temperature delta distribution (in ◦C) on the PCB stack when attaching to it plates to

increase the thermal inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

B.7 Mass (in kg) of the attached plates to increase the thermal inertia . . . . . . . . . . . . . . 91


each component in th end of the thermal control system development process . . . . . . 92

C.1 Solver parameters to optimize their performance . . . . . . . . . . . . . . . . . . . . . . . 97

xiv

List of Figures

1.1 Nanosatellite launch market evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 CubeSat configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Existing CubeSat configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Current P-POD configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 Hyperspectral imaging process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.6 Spread-Spectrum communication system scheme . . . . . . . . . . . . . . . . . . . . . . 7

1.7 Flowchart that represents the work to be developed . . . . . . . . . . . . . . . . . . . . . 8

2.1 Solar flux during the year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 View factor calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1 External structure of the satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Configurations before and after concluding subsystems design . . . . . . . . . . . . . . . 24

3.3 30% Triple Junction Solar Cell 3G30C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4 ADCS components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.5 Momentum Wheels in pyramid configuration . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.1 Momentum wheel mounting plate idealization . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Convergence of the fundamental frequency of the momentum wheels mounting plate . . . 32

4.3 PCB idealization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.4 Convergence of the fundamental frequency of the momentum wheels mounting plate . . . 33

4.5 Different FEM models with coarse meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.6 Different FEM models with refined meshes . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.7 P-POD interior configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.8 Convergence of the fundamental frequency for different FEM Models and boundary con-

ditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.9 First mode of vibrations of each FEM model . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.10 Accelerometers locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.11 Fundamental frequency taken from the measurement of the accelerometer in the back

plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.12 Sensitivity coefficients of each parameter relative to each response . . . . . . . . . . . . . 44

4.13 Changes in the selected parameters and responses . . . . . . . . . . . . . . . . . . . . . 46

xv

4.14 FEM Models with refined meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.15 Convergence study of FEM Model 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.16 Aluminum stiffeners mounting and effect in the first mode of vibration of the satellite . . . 50

5.1 Thermal FEM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.2 Different satellite orbits as viewed from the Sun . . . . . . . . . . . . . . . . . . . . . . . . 59

5.3 Thermal analysis convergence study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.4 Thermal behaviour of the camera and its mounting plates . . . . . . . . . . . . . . . . . . 65

5.5 Thermal cycling in initial conditions, after applying black dye and after using stainless steel

in the camera mount . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.6 Proposed configurations to reduce maximum temperatures and temperature deltas . . . . 68

5.7 Thermal cycling in initial conditions, after applying black dye and after using stainless steel

in the mounting plates and as a means to increase thermal inertia . . . . . . . . . . . . . 70

5.8 Thermal cycling after developing the thermal control system . . . . . . . . . . . . . . . . . 72

5.9 First mode shape after applying the thermal control system . . . . . . . . . . . . . . . . . 74

A.1 Typical external configuration of a 3U CubeSat . . . . . . . . . . . . . . . . . . . . . . . . 83

C.1 Influence of the allocated RAM memory to NX NASTRAN solver in the simulation times . 95

C.2 Influence of the number of CPUs used in the simulation times . . . . . . . . . . . . . . . . 96

xvi

Nomenclature

Scalar entities are represented in lightface lowercase or uppercase. Vector entities are represented

in boldface lowercase. Matrix entities are represented in boldface uppercase.

Greek symbols

α Thermal diffusivity

α′ Absorptivity

ε Convergence margin

ε Emissivity

ζ Damping ratio

θ Polar angle

µ Mean value

ν Poisson’s ratio

ρ Density

ρ′ Reflectivity

σ Stefan-Boltzmann constant

τ ′ Transmissivity

φ Mode shape vector

ϕ Phase angle

χ Finite element dimensions

ω Angular frequency

ωd Damped angular frequency

Roman symbols

0 Null vector

A Area

BA Bond albedo

C Damping matrix

c Damping

CC Correlation coefficient

Cp Heat capacity matrix

cp Specific heat capacity

CTE Coefficient of thermal expansion

xvii

e Unit vector

e Euler’s number

E Young’s modulus

Er Error function

f Force vector

f Frequency

Fij View factor from surface i to surface j

G Gain matrix

G Shear modulus

h Thickness

I Identity matrix

I Electric current intensity

k Thermal conductivity

Ke Stiffness matrix

Kt Heat conduction matrix

L Distance between two entities

M Mass matrix

m Mass

P Electric power

P′ Parameter matrix

pa Parameter state vector

P1 Applied heat loads dependent on temperature vector

P2 Applied heat loads not dependent on temperature vector

pu Updated parameter vector

q Heat flux vector

q Heat flux

q Heat transfer rate

R Radiation exchange matrix

R′ Response matrix

ra Predicted response vector

ra Distance between the Sun and Earth in aphelion

Rcontact Thermal contact resistance between two surfaces

re Experimental response vector

rp Distance between the Sun and Earth in perihelion

rs Radius of the Sun

s Standard deviation

S Absolute sensitivity matrix

Sn Normalized relative sensitivity matrix

Sr Relative sensitivity matrix

xviii

T Temperature vector

T Temperature

t Time

T Temperature change with time vector

T Temperature change with time

Ts Temperature of the Sun

U Electric potential difference

V Volume

WP Parameter weighting matrix

WR Response weighting matrix

WR Response weights sum

x Displacement vector

x Velocity vector

x Acceleration vector

Subscripts

1,2,3 Local reference frame components

i, j Computational indexes / Frequency and mode shape order

n Normalized

t Iteration number

x, y, z Global reference frame components

Superscripts

T Transpose

xix

Glossary

1D One Dimensional

2D Two Dimensional

3D Three Dimensional

3U Triple-CubeSat

ACS Attitude Control System

ADCS Attitude Determination and Control System

CAD Computer Aided Design

CPU Central Processing Unit

CSA Canadian Space Agency

CSDC Canadian Satellite Design Challenge

CfAR Centre for Aerospace Research

DCMP Matrix Decomposition Module

DFL David Florida Laboratory

DMP Distributed Memory Parallel

ECOSat Enhanced Communications Satellite

EMA Experimental Modal Analysis

FEA Finite Element Analysis

FEM Finite Element Method

FFT Fast Fourier Transform

FRF Frequency Response Function

FRRD1 Modal Frequency Response Module

GPU Graphics Processing Unit

xx

HDD Hard Disk Drive

IC Integrated Circuit

ISS International Space Station

LEO Low Earth Orbit

MW Momentum Wheel

NASA National Aeronautics and Space Administration

NASTRAN NASA Structure Analysis

P-POD Poly-Picosatellite Orbital Deployer

PCB Printed Circuit Board

RAM Random Access Memory

RDMODES Recursive Domain Normal Modes Analysis

Rx Receiver

SMP Shared Memory Parallel

SSD Solid State Drive

TCS Thermal Control System

Tx Transmitter

UVic University of Victoria

xxi

Chapter 1

Introduction

1.1 Motivation

The space industry plays an important role in society and the trend is to grow even further. The

benefits of developing the space sector are not only for the advancement of science. The technology

also improves the quality of life. Therefore, it is necessary to increase the awareness of these benefits,

to motivate younger people to pursue a path in space industry and to develop the expertise to search

for innovative solutions for complex problems. Since it is difficult to test space technologies in operating

conditions, a careful modelling and analysis of all technical and design issues is necessary to increase

the likelihood of success. This thesis focuses on the development of dynamic and thermal models of a

nanosatellite. It presents some of the technical challenges encountered and presents solutions so that

the nanosatellite performs its mission successfully.

1.2 General Context

1.2.1 The ECOSat

The ECOSat, the Enhanced Communications Satellite, is a nanosatellite, or ”NanoSat”, designed by

students from different backgrounds at the University of Victoria (UVic) as a response to the Canadian

Satellite Design Challenge (CSDC). This challenge is intended to involve all the design process and

technical aspects related to the design of the satellite, but also aims to attract students to the space

engineering field. The satellite is a three-unit-CubeSat configuration, also known as 3U. Since a Cube-

Sat unit has dimensions of 10×10×11.35 cm and a maximum mass of 1.33 kg, a triple-CubeSat is

10×10×34 cm with maximum mass of 4.0 kg [1].

1.2.2 Nanosatellites

NanoSats are artificial satellites with dimensions and mass that are very small when compared to

conventional satellites. Small satellites have typical masses between 100 and 500 kg, while NanoSats

1

have 1 to 10 kg of mass [2]. The first successful nanosatellite was the Vanguard 1, with a mass of

1.47 kg. It was launched in March of 1958 by the USA while the USSR was launching larger and more

complex satellites (Sputnik 1 was launched in October of 1957 and had a mass of 83.6 kg). At the time,

the main focus was the size and reliability to support human space flight. There was a general belief that

”bigger is better” [3]. Nowadays the trend is different. From historical data it can be concluded that, in

2013, the interest in delivering NanoSats has increased by a significant amount (from 25 to 87 satellites,

approximately) and in 2016 it is expected a new significant increase (from 127 to 472, approximately),

which shows the growing launch market related to these satellites [4]. This trend is represented in

Figure 1.1.

Figure 1.1: Nanosatellite launch market evolution [4]

The increase in the interest for this particular type of satellite and also other smaller satellites is

the shorter time period of development from order to orbit (typically 10 to 12 months [5]) and low cost

of launching, since these satellites may be launched as a secondary payload, as piggy-back payload

attached to the primary and heavier payloads. Even if these satellites are the primary payload, due to

their low mass, they can be put into orbit using smaller and cheaper launch vehicles. With the emergence

of technological advances of miniaturization, a variety of small payload Nanosatellite Launch Vehicles

have been under development.

Satellite Class Mass (kg) Cost (US Million $)

Large Satellite > 500 > 50

Small Satellite 100 - 500 10 - 30

Microsatellite 10 - 100 3 - 6

Nanosatellite 1 - 10 0.3 - 1.5

Picosatellite < 1 < 0.3

Table 1.1: Satellite classification according to its mass [2] and respective cost [5]

2

To summarize, this trend can be viewed as a result of the pressure on space agency financial bud-

gets and the rapid advancement of micro-electronics, leading to the design of these smaller and more

computationally capable satellites as a ”faster, cheaper, better” means of implementing space missions

as a complement to larger satellites [5].

There is also a wide variety of applications for NanoSats. They can be used for Earth science (sup-

port understanding and monitoring of Earth processes), space science (support the understanding of

the Solar System and the Universe, for example, by monitoring the space radiation environment), to

serve as technology demonstrators (reduce risk before implementing new technologies or new design

concepts in a funded science campaign, for example, by demonstrating formation flight, aero-capture

technologies and so on) or as a know-how transfer and training (provide means and hands-on experi-

ence of technical and managerial aspects, from design, construction, test, launch and orbital operations)

[3].

Besides all the benefits, there are problems that arise when using such small satellites. The major

technical challenges that can be encountered are related to radiation, micrometeoroids, dust and ther-

mal control. A typical satellite relies on a few millimetres of shield made of structural aluminum and

accommodate electronics deep within the structure to provide radiation protection, but nanosatellites do

not have this type of protection or the room to protect electronics far from the spacecraft’s surface. It is

necessary to use local shielding of radiation sensitive elements rather than shielding the whole space-

craft. Due to the reduced dimensions and lack of shielding, the satellites will also be more vulnerable to

damage by dust or micrometeoroids. Because of the small surface area of all the components and the

satellite itself, thermal control of dissipative components may require the use of miniature active cooling

loops, thermoelectric cooling devices, micro heat pipes, among other solutions [6].

1.2.3 CubeSats

To create a standard model of small and inexpensive satellites to support demonstration applications

and to shorten the development cycle by integrating it in the academic learning cycle, the CubeSat was

developed at California Polytechnic State University and Stanford University in 1999. Since then, the

CubeSat development and use has been widespread and accepted throughout the world and satellites

composed by multiples of CubeSat units have been developed and launched.

This satellite is a type of nanosatellite, it takes advantage of all the benefits associated with that class

of satellites. As an additional advantage, California Polytechnic State University and Stanford University

also developed a standard and inexpensive deployment system: the Poly-Picosatellite Orbital Deployer,

known as the P-POD [9]. Currently there are other deployment designs available to accommodate

CubeSats like the T-POD (Tokyo Picosatellite Orbital Deployer) from Tokyo University, the X-POD (Exper-

imental Push Put Deployer) from the University of Toronto Institute for Aerospace Studies/Space Flight

Laboratory, the J-POD (JAXA-Picosatellite Orbital Deployer) from JAXA, the NPSCuL (Naval Postgradu-

ate School CubeSat Launcher) from Naval Postgraduate School and the NRCSD (NanoRacks CubeSat

Deployer) from NanoRacks, among other systems. The mechanisms inherent to each deployer are very

3

(a) CubeSat with a mug for scale [7] (b) Multiple unit CubeSats [8]

Figure 1.2: CubeSat configurations

Figure 1.3: Existing CubeSat configurations [4]

similar, but the maximum satellite dimensions they can accommodate differ from each other. Some of

the deployment systems allow to launch CubeSats with dimensions different from the standard.

The deployment system is the interface between the launch vehicle and the satellite it is carrying.

It is designed to have minimum mass and high adaptability to different launch vehicles. It is capable

of guaranteeing that in the event of a CubeSat failure, the launch vehicle and other payloads remain

protected against mechanical, electrical and electromagnetic interference, and that during deployment,

the CubeSats are released with minimum spin and low probability of collision with the launch vehicle

or other spacecraft. The latest version of the P-POD deployment mechanism is shown in Figure 1.4.

Its tubular design allows to predict a linear trajectory for the payload and low spin after deployment, by

means of a spring and rails for the satellite to glide as it exits the P-POD [10]. The configuration post

deployment is also shown in Figure 1.4.

1.2.4 The Canadian Satellite Design Challenge

The CSDC is hosted by Geocentrix Technologies and is supported by companies such as Boeing,

MDA, Magellan Aerospace, TRIUMF, Mitacs, DRDC (Defence Research and Development Canada),

Analytical Graphics Inc., SED Systems, MAYA, Appspace, UrtheCast and the CSS (Canadian Space

Society). CSDC invited universities across Canada to design a fully operational CubeSat and its science

4

(a) Closed P-POD with respective reference frame (b) Open P-POD

Figure 1.4: Current P-POD configuration [10]

mission. With this purpose, it allows to put the technical knowledge of nanosatellite technologies into

practice and to develop new research and expertise. In this competition, the CSDC acts like a space

mission costumer like the CSA (Canadian Space Agency) and NASA (National Aeronautics and Space

Administration) and each team acts like a prime contractor. It began its initial offering in January of

2011. While in the first edition of the competition the ECOSat team reached the third place, in the

second edition the ECOSat team won the first place with the nanosatellite ECOSat-II and secured its

launch into orbit. The third edition started in September of 2014 and ended in June of 2016. ECOSat-III

did not qualify in the top three places but was able to test a configuration different from the previous

ECOSat designs. Some of the general requirements which are directly related to the current thesis are:

• Teams should design their mission to be able to operate in LEO (Low Earth Orbit) between 400

km and 800 km and in both sun-synchronous orbit (at different Equator Crossing Times) and in the

orbit of the ISS (International Space Station).

• The spacecraft shall be designed to accomplish its mission purpose and to maintain spacecraft

health during the design lifetime of the mission.

The complete list of rules and requirements to be met can be checked in [11]. As for design, interface

and environmental testing requirements, those that are directly related to the present thesis are:

• The spacecraft configuration and dimensions shall be of a ”3U”, a triple-CubeSat, as defined in

Appendix A (10×10×34 cm), in the launch configuration.

• Aluminum 7075, 6061, 5005, and/or 5052 shall be used for both the main spacecraft structure and

the corner rails.

• The spacecraft shall have 4 rails, one per corner, along the Z axis.

• The edges of the spacecraft corner rails shall be rounded to a radius of at least 1.0 mm.

• All parts shall remain attached to the spacecraft during launch, ejection and operation.

5

• The spacecraft mass shall not exceed 4.0 kg.

• The spacecraft centre of mass shall be located within no more than 2.0 cm from the spacecraft’s

geometric centre in the X and Y axes, and not more than 7.0 cm from the spacecraft’s centre in

the Z axis, in the launch configuration.

• The spacecraft shall have a fundamental frequency of at least 90 Hz in each axis.

The complete list of design, interface, and environmental testing requirements to be met can be

checked in [12].

1.2.5 Mission Overview

The ECOSat-III has two primary missions: hyperspectral imaging of Canada and implement a below-

the-noise-floor communications system. As a consequence of fulfilling these missions, UVic’s knowl-

edge of Communications and Attitude Determination and Control System (ADCS) will be expanded.

The gained know-how benefits the University itself, its students, and allows to spread the knowledge

to younger students by arranging faculty tours to high school students and workshops to engineering

students, which ultimately increases the interest in engineering and space.

Hyperspectral imaging, or imaging spectroscopy, makes use of spectroscopy to produce digital imag-

ing. The hyperspectral camera captures the light radiance for several spectral bands of the electromag-

netic spectrum for each pixel. The final image is obtained by a set of images layered on top of one

another, forming the hyperspectral image cube, or the ”hypercube”. Each image that forms the ”hyper-

cube” represents one particular wavelength band [13]. This allows to achieve great precision and detail

to characterize objects, much greater than the obtained through a normal colour camera, which only

captures three spectral channels: red, green and blue. Its applications include satellite remote sensing,

military target precision, industrial quality control, laboratory measurements, clinical instruments, pre-

cision agriculture, biotechnology, environmental monitoring, forensics, counterfeiting detection and so

on. By comparing the spectral signature of unknown objects to that of known substances, its chemical

composition can be identified.

The noise floor can be defined as the measure of the signal created from the sum of all noise

sources and unwanted signals within a system. In order to detect signals below the noise floor, different

techniques of spread spectrum communications must be used. Those techniques spread the bandwidth

of a signal in the frequency domain. The signal to be transmitted must be processed by a spread-

spectrum code, which diffuses the information in a larger bandwidth, before the transmission antenna,

and after the receiving antenna, the signal must be processed by another spread-spectrum code, in

order to reconstitute the information into its original bandwidth [14]. This theory is based in Shannon’s

formula for channel capacity, which can be consulted in [15].

6

Figure 1.5: Hyperspectral imaging process [13]

Figure 1.6: Spread-Spectrum communication system scheme [14]

1.3 Objectives

The main purpose of this thesis is to improve the mechanical design of the ECOSat-III satellite and

to validate the safety and integrity of structural and electrical components by means of dynamic and

thermal analyses. To this end, a Finite Element Method model (FEM model) has been created based on

the CAD model of the satellite. Modal analyses of the structure were performed in order to determine

the lowest natural frequencies and the corresponding mode shapes of the satellite. Experimental and

numerical results are compared to improve the FEM model. If the obtained results do not comply with

the requirements specified by the CSDC, a solution must be proposed.

Thermal analyses are conducted by simulating the satellite’s orbit to analyse the thermal cycling of

the electronics stack and structural components. If needed, a thermal control system is developed to

maintain the satellite’s temperatures controlled within specified limits.

7

Figure 1.7: Flowchart that represents the work to be developed (the red box represents work developedby others which results are used in this work)

1.4 Thesis Outline

This thesis is organized as follows:

Chapter 2: presentation of the theoretical background related to the work to be developed. It includes

the theory that supports the modal analyses and thermal analyses contained in this work.

Chapter 3: overview of the current ECOSat-III mechanical design and configuration. The reader is

familiarized with the satellite design and subsystems.

Chapter 4: development of the FEM model and simulations used to compute the fundamental fre-

quency of the satellite. The results of modal analyses are presented and compared with experimental

results. The FEM model is improved and a solution to increase the fundamental frequency is proposed.

Chapter 5: development of the FEM model and simulations used to obtain the temperature distribu-

tion in the satellite. The results of thermal analyses are presented and solutions are proposed to develop

a thermal control system that allows the satellite to operate in a safe temperature range.

Chapter 6: presentation of the conclusions, contributions, design recommendations and future work

suggestions.

8

Chapter 2

Theoretical Background

In this chapter, the historical and theoretical background and state of the art of the techniques used

to model the vibration and thermal performance of the NanoSat structure and to perform experimental

testing will be presented. The decisions taken and documented in subsequent chapters are based in

the theoretical background presented in this chapter.

2.1 Dynamic Analysis

2.1.1 Numerical Modal Analysis

Modal analysis of a structure allows to evaluate its linear dynamic characteristics. A natural mode of

vibration is characterized by a harmonic motion of every point of the structure around a point of equilib-

rium which is passed by at the same instant for all the points. The frequency of this harmonic motion

is called the natural frequency. The first of the natural frequencies of a structure is called fundamental

frequency. The physical parameters that most influence the natural vibration modal data of a structure

are the magnitude and distribution of masses and inertia, the elastic properties and the boundary con-

ditions. Improper modal analysis and testing may lead to failures or near failures. Some documented

examples are: expensive modification of design due to minimum frequency specification not satisfied,

low frequency vibrations interference in on-board experiments due to coupling with the control system

and orbital environment effects and failure due to fatigue caused by excessive vibration testing that

caused resonance in the structure [16]. According to [17], the equations of motion of a multi-degree of

freedom system can be represented in matrix form as follows:

Mx + Cx + Kex = f (2.1)

Since one wants to compute the natural frequencies and modes of vibration, there is no force applied

to the structure. Then, f = 0. Because natural frequencies correspond to the undamped case, C will

9

not have influence in the calculation. Therefore, the equation of motion can be simplified to:

Mx + Kex = 0 (2.2)

Which corresponds to the undamped free vibration of the system. Assuming a harmonic solution:

x = φ sin(ωt+ ϕ) (2.3)

Substituting it in the equation of motion, the eigenequation is obtained:

(Ke − ω2M)φ = 0 (2.4)

The eigenvalues are the values ω2 and the eigenvectors are φ. From the eigenvalues and eigenvec-

tors, it is possible to obtain the natural frequencies and natural mode shapes, respectively. A non-trivial

solution of the mode shapes is obtained for:

det(Ke − ω2M) = 0 (2.5)

Expanding the equation above, one obtains the characteristic equation. Solving it for ω, the natural

frequencies in Hz may be calculated from:

fi =ωi

2π(2.6)

Substituting the natural frequencies in rad/s, ω, in the eigenequation and choosing an arbitrary value

for one of the components of the corresponding mode shape, all the other components of the mode

shape are computed. This can be done because the mode shape is intended to give information only

about the shape of the vibration in each natural frequency, not the amplitude of that vibration. Normally,

the mode shapes are normalized relative to the mass matrix by using the expression:

φTinMφin = I (2.7)

The number of natural frequencies and corresponding mode shapes are equal to the number of

degrees of freedom of the system. Still according to the same reference ([17]), when a linear elastic

structure is in free or forced vibration, its vibration shape can be given by a linear combination of all its

natural mode shapes.

If M and Ke are symmetric and real, the mode shapes are orthogonal, which means that each

mode shape is unique and cannot be obtained by linear combination of the other modes. Formally, that

property is represented by:

φTi Mφj = 0, i 6= j (2.8a)

φTj Keφi = 0, i 6= j (2.8b)

10

Taking into account the relationship between mass and stiffness, one obtains Rayleigh’s equation

which describes that the natural frequencies will be higher for a stiffer and lighter structure:

ω2i =

φTi Keφi

φTi Mφi

(2.9)

If the structure presents damping, each frequency of damped vibration can be calculated by consid-

ering the following solution in each equation represented by Equation 2.1:

xi = Ciesit (2.10)

C and s in the previous equation represent constants. Substituting the solution in each equation of the

system, which represents each degree of freedom of the system, the frequency of damped vibration can

be obtained from:

ωdi =√

1− ζ2i ωi (2.11)

where ζ is the modal damping ratio and is given by:

ζi =ci

2miωi(2.12)

ci and mi represent the damping and mass terms of the correspondent equation. An oscillatory motion

only results if ζ < 1, which corresponds to the underdamped case. In that situation, the frequency of

damped vibration is always lower than the natural frequency.

According to [18], NX NASTRAN has several numerical methods to obtain the natural frequencies

and corresponding mode shapes. There are two main methods for extracting real eigenvalues: transfor-

mation and tracking methods. With transformation methods, the eigenequation is transformed in a form

from which the eigenvalues are easily extracted. With tracking methods, the eigenvalues are extracted

by an iterative procedure. When the modal analysis simulation is selected, the user may choose be-

tween Lanczos method and Householder method. The Householder method is a transformation method

and is better applied to small matrices, having a low cost in computing such modes but high cost if

the matrices are large. The Lanczos method is a combination of the advantages of transformation and

tracking methods and is better applied to medium and large matrices but maintains a medium cost in

computing modes in both small and large matrices. For that reason, the recommended eigenvalue

extraction method is the Lanczos method and therefore, it will be the method used in the modal analysis.

2.1.2 Experimental Modal Analysis

It is possible to obtain the natural frequencies and modes of vibration of a structure using experimen-

tal techniques. For that, the structure must be subjected to a certain input force and the output displace-

ment, velocity or acceleration must be measured by the corresponding sensors in different points of the

structure. Two types of tests can be performed: impact testing or shaker testing.

11

The impact testing is the most popular method. In order to perform this test an impact hammer to

input the force in the structure is used. A cell load is attached to the hammer’s head to measure the

applied force. The sensors measure the output in fixed directions and points of the structure. The input

frequency range that is excited is controlled by the hardness of the hammer’s head. The harder its

tip, the wider the frequency range. It is advised to choose several different impact locations in order to

reduce the possibility of not exciting a particular mode of vibration. However, the impact location must

also take into account the local flexibility of the structure and the possibility of a double impact. The

shaker testing consists of attaching a shaker to the structure and input a force in the desired frequency

range. The shakers are also provided with loads cells to control the input force and sensors are used

to measure the output in the desired directions and points of the structure [19]. The shaker testing is

usually chosen when the structure is large and heavier or when low frequencies are desired. In the first

case, the hammer’s impact in the structure may not be able to excite it uniformly and in the second case,

the time duration must be long enough to be able to excite the structure at low frequencies, which is

harder using the hammer’s impact on the structure.

The obtained results from the modal tests are Frequency Response Functions (FRFs). These func-

tions consist of the ratio of the output response of the structure due to the applied force, transformed

from the time domain to the frequency domain using Fast Fourier Transform (FFT) algorithms. The fre-

quency response is a complex number. The resonance frequencies of the structure are the peaks of

its amplitude diagram. When those peaks are hard to identify, the phase diagram may be used to help

identify the resonance frequencies. The resonance frequencies are characterized by a shift in the phase

angle. From displacement or acceleration outputs, the mode shape components are the peak values of

the imaginary part, while for velocity outputs, they are the peak values of the real part. The modal damp-

ing is the width of the resonance peaks measured at the half power point [20] of the amplitude diagram.

It must be noted that the resonance frequency is different from the natural frequency if the structure

presents damping. In that case, the resonance frequency will be lower than the natural frequency, as

seen before. It must be noted that from the FRF amplitude and phase diagrams and from the FRF real

and imaginary parts, different information is obtained.

Because the experimental testing was not performed by the author, further details about Experimen-

tal Modal Analysis (EMA) theoretical background will not be provided in this work. More information on

this subject may be consulted in the references [19] and [20].

2.1.3 Finite Element Model Update

Analytical models such as the FEM models provide predictions of the behaviour of a structure through

Finite Element Analysis (FEA) and allow to conduct parametric studies if there are characteristics of the

structure that are unknown or unavailable. It is common to find incompatibility between the experimental

and numerical modal data sets. This can happen for numerous reasons that can range from modelling

errors, lack of information about the materials and boundary conditions, accuracy problems or misinter-

pretation of the results. Thus, it is very important to compare numerical data to experimental data in

12

order to properly correct and validate the analytical model and obtain a more reliable and realistic FEM

model, which can be used to perform more simulations or to evaluate configuration changes of the struc-

ture, instead of preparing more experimental tests. This is known as Finite Element Model Updating and

it can be accomplished by using proper software. The software used to perform FEM model updating

was FEMtools. This software was provided by CfAR located in Victoria International Airport.

To perform FEM model update, the user has to specify what kind of responses the FEM model is in-

tended to present and what kind of parameters can be changed to achieve those responses. Responses

can be resonance frequencies and the mass of components. Parameters can be material or geometrical

properties, spring stiffness, boundary conditions and lumped mass properties. To select the parameters

that have a significant effect in the target responses, a sensitivity analysis must be performed. Sensitivity

analysis quantifies the rate of change of a response with respect to a change in a parameter. The result-

ing quantities are called sensitivity coefficients and form the sensitivity matrix S. They can be computed

using differential analysis.

Sij =∂R′ii∂P′jj

(2.13)

where i = 1, 2, ..., N and j = 1, 2, ...,M . N and M represent the total number of responses and param-

eters considered in the sensitivity analysis, respectively.

It can be shown that for the case of the natural frequency as a response, the sensitivity coefficients

can be calculated by solving Equation 2.14 [21].

∂fi∂P′jj

=

φTi (

∂Ke

∂P′jj− 4π2f2

i

∂M

∂P′jj)φi

8π2fi(φTi M)φi

(2.14)

where f is the natural frequency, φ is the corresponding mode shape and Ke and M are the stiffness

and mass matrix of the structure, respectively. For the case where the mass is chosen as a response,

the sensitivity coefficients are given Equation 2.15.

∂m

∂P′jj=

∂mj

∂P′jj=

(ρjVj)

∂P′jj(2.15)

where ρ is the density and V is the volume of element j. With the calculations above, the sensitivity

coefficients obtained are absolute sensitivities and use the units of the response and parameters con-

sidered. To compare the sensitivities of different parameters with respect to the same response, relative

sensitivities must be computed by using:

Sr =∂R′ii∂P′jj

P′jj (2.16)

where Sr is the relative sensitivity matrix. The sensitivities can also be normalized with respect to the

response value:

Sn = SrR′−1ii (2.17)

where Sn is the normalized relative sensitivity matrix.

13

The model updating process adjusts the parameter values with the objective of obtaining the desired

values of the responses, taking into account the confidence and parameter bounds. The relationship

between the responses and the parameters can be expressed as a Taylor series expansion truncated

after the first term:

r′e = r′a + S(p′u − p′0)⇔ ∆r′ = S∆p′ (2.18)

where r′e is the vector containing the reference response (experimental data), r′a is the vector containing

the predicted response for a state p′0 of the parameter values and p′u is the vector containing the up-

dated parameter values. Iterations are required to solve the equation, using a pseudo-inverse technique

(least squares) or Bayesian technique (weighted least squares). To include the confidence in the initial

parameter values and in the reference responses, the Bayesian parameter estimation must be used. It

consists of minimizing the error between the model predictions and the test data. The error function is

given by:

Er = ∆r′TWR∆r′ + ∆p′

TWP∆p′ (2.19)

where WR is the diagonal weighting matrix that represents the confidence in the experimental data

and WP is the diagonal weighting matrix that represents the confidence in the model parameters. In

FEMtools the confidence is defined by means of the statistical scatter, which is normalized with respect

to the mean value of the response or parameter:

Scatter =s

µ(2.20)

where s is the standard deviation and µ is the mean value. To minimize the error, the following algorithm

is used:

p′u = p′0 + G(−∆r′) (2.21)

G = WP−1ST (WR

−1 + SWP−1ST )−1 (2.22)

where G is the gain matrix. To improve the stability of the iterative method, i.e. to avoid the error growth,

the normalized sensitivity matrix is used.

Since the model updating process is an iterative method, convergence and stop criteria must be

defined. The convergence and stopping criteria used in FEMtools are:

1. The value of the reference correlation coefficient CCt is less than a selected convergence margin

ε1: CCt < ε1. When using natural frequencies as response, CC is defined as the weighted

absolute relative difference between the frequencies:

CC =1

WR

N∑i=1

WRii

∆fifi

(2.23)

WR =

N∑i=1

WRii (2.24)

2. Two consecutive values of the reference correlation coefficient are within a selected convergence

14

margin ε2: |CCt+1 − CCt| < ε2.

3. The number of iterations exceeds the maximum number allowed.

2.2 Thermal Analysis

In satellites, multiple modes of heat transfer are combined and the boundary conditions are time

varying which require transient analysis to correctly predict the structures response. In this section the

heat sources will be listed accordingly to the type of heat transfer they are included in.

2.2.1 Heat Sources

Radiation

This mode of heat transfer does not require matter to propagate. It results from the loss of internal

energy in order to achieve thermal equilibrium with the surroundings. There are three main sources of

radiation that reach the spacecraft: solar radiation, albedo and Earth radiation. Additionally, considering

only one component of the satellite, it will receive radiation from the surrounding components and it will

radiate to the surroundings.

Solar Radiation To calculate the solar flux that reaches a satellite orbiting Earth, first, one needs

to calculate the total emissive power of the Sun. Stefan-Boltzmann Law relates the total emissive power

of a black body with its temperature. The total emissive power represents the total heat flux emitted by

a body [22]. Assuming the Sun behaves as a black body, it is possible to apply that law to the present

case:

qsolar = σT 4s (2.25)

where Ts represents the Sun’s effective temperature. The effective temperature of a body is the temper-

ature of a black body that would allow to emit the same total amount of electromagnetic radiation. To

compute the total heat transfer rate emitted by the Sun, the heat flux emitted is multiplied by the Sun’s

surface area:

Qsolar = qsolar × 4πr2s (2.26)

The heat flux that reaches a satellite orbiting Earth is not constant. Because the heat is spread over

a wider area as the distance to the Sun increases, the rate of heat flux that reaches a satellite during

Earth’s perihelion and aphelion is different. Dividing the heat rate emitted by the Sun by the surface

area of a sphere which radius is equal to the distance from the Sun to the satellite in those positions,

the maximum and minimum heat fluxes that reach the satellite can be computed. The approximate heat

flux that reaches Earth during its orbit is presented in Figure 2.1. The altitude of the satellite can be

neglected since it is not significant when compared with the distance between the Sun and the Earth.

Then, one obtains Equations 2.27. This fact must be taken into account when evaluating the thermal

behaviour of a satellite.

15

Figure 2.1: Solar flux during the year [23]

qsolar maxin Earth

=Qsolar

4πr2p

(2.27a)

qsolar minin Earth

=Qsolar

4πr2a

(2.27b)

According to [24] and [25], Ts = 5772 K, rs = 6.957 × 108m, rp = 147.09× 109 m, ra = 152.10× 109 m.

The power absorbed, transmitted and reflected by each component of the spacecraft depend on the

materials’ absorptivity, transmissivity and reflectivity and depend on the area of the components viewed

by the Sun. The solar radiation absorbed by the satellite can be written as:

Q solarabsorbed

= α′solarFSun−componentASunqsolar (2.28)

α′solar represents the component’s absorptivity of solar radiation. The view factor between a surface

i and a surface j, Fi−j is given by:

Fi−j =1

Ai

∫Ai

∫Aj

cos θi cos θjπL2

dAidAj (2.29)

The polar angles θi and θj are the angles between the line that connects surface i and j and the

normal vector to the surface i and j respectively, as shown in Figure 2.2.

Because the Sun’s dimensions are much larger than the satellite’s dimensions and because solar

radiation is direct (it’s not diffuse), the view factor FSun−component is simplified to:

FSun−component =

∫Acomponent

cos θcomponent

πL2dAcomponent (2.30)

For the same material and for the same wavelength:

α′ + τ ′ + ρ′ = 1 (2.31)

16

Figure 2.2: View factor calculation [22]

And for an opaque material, τ ′ = 0.

Albedo Albedo is the part of the solar radiation that reaches Earth and is reflected back to space.

It is related to reflectivity, which measures the amount of radiation a surface can reflect, but reflectivity

is a spectral property, since it is a function of the wavelength of the incident radiation. Albedo, in the

other hand, is the integrated product of incident solar radiation spectral composition and the spectral

reflectivity of the object [26]. It is difficult to estimate how much sunlight is reflected back since each

material reflects different amounts of incident radiation. The atmosphere itself plays an important role in

reflecting the radiation. The weather is also very important, since clouds can have different densities and

formations which affect the albedo [27]. Some values of the albedo for different materials are presented

in Table 2.1.

Material Concrete Water Ice Gravel Sand Forests

Bond Albedo 0.30 0.05 0.69 0.72 0.24 0.10

Table 2.1: Bond albedo of different materials [28]

According to [25], Earth’s bond albedo may be taken as BA = 0.306. This value includes the fraction

of solar radiation reflected by particles of the atmosphere (scattering), reflected by clouds and reflected

by Earth’s surface. Thus, the radiation that reaches the satellite by reflection of Sun’s emitted flux on

Earth may be calculated. The heat flux that reaches Earth and is reflected back to space is given by

Equation 2.28 where the absorptivity and the component subscript are substituted by the albedo factor

and Earth subscript, respectively:

Q solarreflected by Earth

= BAFSun−EarthASunqsolar (2.32)

The heat flux that reaches a satellite’s component after the radiation from the Sun has been reflected

by the sunlit side of Earth is then given by:

Q albedoabsorbed

= α′solarFEarth sunlit−componentQ solarreflected by Earth

(2.33)

17

This can be written as:

Q albedoabsorbed

= α′solarFEarth sunlit−componentAEarthqalbedo (2.34)

where:

qalbedo = BAFEarth−Sunqsolar (2.35)

And the reciprocity relation of view factors was used:

FSun−EarthASun = FEarth−SunAEarth (2.36)

In this case, the view factor calculation can’t be simplified, since the reflected solar radiation is diffuse.

The reflected solar radiation incident on the component can have any direction.

Earth Infrared Radiation Like the Sun, Earth also emits radiation that reaches the spacecraft.

Because Earth’s temperature is much lower than the Sun’s, the radiation emitted by the Earth is primarily

located in the infrared zone of the electromagnetic spectrum. If one assumes Earth as a black body, then

the same set of equations presented to the solar radiation calculation may be applied. This assumption

is valid if the effective temperature of the Earth is used, correcting the consideration of ε = 1. First,

the heat rate emitted by the Sun and absorbed by Earth is calculated, taking into account Earth’s bond

albedo and the solar radiative flux that reaches it [29]. In this calculation it is assumed Earth is opaque:

the heat flux that reaches Earth is either reflected back to space or absorbed.

Qsolar absorbedby Earth

= α′solarFSun−EarthASunqsolar (2.37)

where α′solar = 1−BA, since Earth is considered opaque. Assuming Earth is in thermal equilibrium, the

heat rate emitted by the Sun and absorbed by Earth must be equal to the infrared heat rate emitted by

Earth:

Qinfrared = Qsolar absorbedby Earth

(2.38)

Working on both sides of Equation 2.38, the following expression is obtained:

qinfrared = α′solarFEarth−Sunqsolar (2.39)

and:

Q infraredabsorbed

= α′infraredFEarth−componentAEarthqinfrared (2.40)

where α′infrared represents the component’s absorptivity of infrared radiation. Since Earth is provided

with a significant atmosphere, it is considered that this infrared radiation is uniform for the whole Earth

area, i.e. the sunlit and dark sides of the Earth are considered to emit the same infrared radiation. If the

satellite orbited the Moon or Mercury, this approximation wouldn’t be valid.

18

Radiation to Space The heat flux lost by the satellite’s different components to the environment

is given by Stefan-Boltzmann Law, modified to take into account the materials’ emissivity, since the

components cannot be approximated to a black body:

Qemitted = AcomponentεcomponentσT4component (2.41)

Radiation from the Surroundings The surrounding components will radiate to each component

being analysed. Due to the low temperatures of the components, it can be considered that the radiation

emitted by the surrounding components is in the infrared zone of the electromagnetic spectrum. Then:

Qsurroundingsabsorbed

= α′infrared

∑i

Fi−componentAiεiσT4i (2.42)

where i refers to a surrounding body.

Conduction

In this mode, heat can be transferred through solids, liquids or gases from a high energy source to

lower energy sources, by atomic and molecular activity. Therefore, the direction of heat conduction is

the direction of temperature gradients, and is opposed to positive temperature gradients: conduction

transfers heat from high temperatures to lower temperatures. It can be concluded that the heat flux

resultant of heat conduction is a vector quantity and follows Fourier’s Law [22]:

qconduction = −(kx∂T

∂xex + ky

∂T

∂yey + kz

∂T

∂zez) (2.43)

This mode of heat transfer is present in the satellite, where heat will is spread from high temperature

components to low temperature components. Taking the scalar value and considering that the two

components can be made of different materials, the heat rate is:

Qconduction = −∑i

Tcomponent − TiLi

kiA+Rcontact +

Lcomponent

kcomponentA

(2.44)

where Qconduction is positive if heat is being transferred from a surrounding component to the component

being analysed and is negative if it is being transferred in the opposite sense. The term Rcontact is the

contact resistance which is a consequence of the imperfect contact between two surfaces. Its value

must be determined empirically and tables with measured values are available in the literature.

Convection

This mode of heat transfer is present whenever there is energy transfer between a surface and a

moving fluid over the surface [22]. Due to the atmosphere rarefaction with altitude, this mode of heat

transfer can be neglected when dealing with satellites.

19

Internal Heat Generation

The satellite itself is a heat source since its electrical components dissipate energy, transforming

electric energy in thermal energy. This happens because the components aren’t perfect electric current

conductors, having internal electric resistance. Thus, each electric component will contribute to heat

generation, Qgeneration, in the following way:

Qgeneration = Pe = UI (2.45)

2.2.2 Heat Balance

For each component, the net heat rate is given by:

Qnet = Qin − Qout + Qgeneration (2.46)

mcpT = Q solarabsorbed

+ Q albedoabsorbed

+ Q infraredabsorbed

− Qemitted + Qsurroundingsabsorbed

+ Qconduction + Qgeneration (2.47)

2.2.3 Transient Thermal Analysis Simulation

According to [30], using NX Siemens, the general equation to be solved in transient thermal analysis

is:

CpT + KtT + RT4 = P1 + P2 (2.48)

The equation is solved by implementing Newmark’s method with adaptive time stepping. This method

can be consulted in the same reference mentioned before. Although the time steps across iterations are

automatically adjusted by an adaptive time stepping scheme, a conservative initial time step is estimated

by:

∆t =χ2

min

10αmax(2.49)

α =k

ρcp(2.50)

where ∆t represents the initial time step, χ represents the finite elements dimensions, α represents the

thermal diffusivity, k represents the thermal conductivity and cp represents the specific heat capacity.

The next time steps are calculated taking into account the relation between the maximum variations

of temperature with time verified in the current time step and the previous one. If the ratio between

the maximum temperature variations with time in the current and previous time step is smaller than a

tolerance value (predefined as 0.1), then the time step is doubled. If that ratio is larger than the tolerance

value, a proper time step is predicted. The procedure to obtain the new time step is described in [30].

It is noted that if temperature boundary conditions are imposed, the initial temperature in those points

must be equal to the temperature specified by the boundary conditions.

20

Chapter 3

The ECOSat-III Satellite

This chapter introduces the configuration and design of the external structure of the satellite and

internal accommodation of its components, subsystems and payloads. Since the static, dynamic and

thermal behaviour of the structure can not be determined before an initial decision of the internal layout

of the components, there is the possibility that some of the requirements are not satisfied with the

configuration presented in this chapter, which would then lead to changes in the way the components

are mounted in the nanosatellite. Then, this initial arrangement of components is based in past satellite

designs and the restrictions related to the payload.

The mechanical design described in this chapter was not developed by the author but must be

mentioned, since throughout this work, some components of the satellite will be referred. Then, this

chapter may be seen as a reference point to the location of each component and subsystem of the

satellite.

In the next sections of this chapter, the requirements, the external structure and the electronic sub-

systems of the satellite will be described.

3.1 Requirements

There are several constraints which condition configuration of the satellite: the constraints specified

in the CSDC [12], in the CubeSat requirements [1] and by the payload to carry. The full list of the

requirements can be consulted in the given references. Summarizing the most important requirements

in terms of configuration and solid properties:

• The spacecraft configuration and dimensions shall be of a ”3U”, a triple-CubeSat, as defined in

Appendix A (10×10×34 cm), in the launch configuration.

• Aluminum 7075, 6061, 5005, and/or 5052 shall be used for both the main spacecraft structure and

the corner rails.

• The spacecraft shall have 4 rails, one per corner, along the Z axis, with edges rounded to a radius

of at least 1.0 mm, minimum width of 8.5 mm and ends with a minimum surface area of 6.5×6.5

mm2 contact area.

21

• The spacecraft mass shall not exceed 4.0 kg.

• The spacecraft centre of mass shall be located within no more than 2.0 cm from the spacecraft’s

geometric centre in the X and Y axes, and not more than 7.0 cm from the spacecraft’s centre in

the Z axis, in the launch configuration.

Related to the scientific mission designed for the ECOSat-III there is also the requirement that the hy-

perspectral camera lens must be pointing in the Nadir direction while in orbit, and must not be obstructed

by any other component. Adding to these requisites, there are also dynamic and thermal requirements

that must be satisfied, but can only be verified after the first design of the ECOSat-III has been decided.

It is crucial that the decisions made in terms of arrangement and accommodation in the satellite take

into account that the manufacturing, assembly and wiring harness are possible, facilitated and logical.

Furthermore, one must keep in mind that the decisions made will then affect static, dynamic and thermal

performance.

3.2 Structure Subsystem

The general function of the external structure of the satellite is to accommodate the needed sub-

systems and payloads to correctly operate the satellite and perform the proposed scientific missions. It

unites all the components and provides rigidity to the satellite. According to the requirements listed in

the previous section, there is some flexibility in terms of the configuration of the external structure. One

can choose the type of aluminum used for the structure and although the dimensions of this structure

are specified, one can choose if the structure is obtained from a single block of material or if the faces

are made from panels which are then assembled together.

Aluminum 6061 was chosen since it combines good mechanical and thermal properties with low

density. Although it is not the aluminum with the highest strength, it is the least expensive and still

presents good mechanical properties. The material should be black anodized in order to facilitate the

thermal control of the structure. By that process, passive thermal control is assured. Another benefit of

black anodizing the external surfaces is that stray light that interferes with the hyperspectral camera will

be reduced, i.e. the black surface and high absorptivity allow to reduce the amount of light reflected by

the surface of the satellite, reducing the interference with the camera lens [31]. However, the decision to

use a black paint in the aluminum or not will be taken after the first thermal simulations, to determine if

it is indeed necessary. Some properties of anodized aluminum 6061 are presented in Table 3.1.

Density, ρ (kg/m3) 2711

Young’s Modulus, E (GPa) 68.9

Thermal Conductivity, k (W/(mK)) 166.9

Specific Heat Capacity, cp (J/(kgK)) 986

Table 3.1: Mechanical and thermal properties of aluminum 6061 T6

As for the way the primary structure is built, it was decided to assemble the structure from multiple

aluminum panels, since they are easily machined, their price is lower and produce less waste material.

22

However, the final body can be heavier and have areas of high stress concentrations due to the need

of using fasteners, when compared with the case of using a unique block of aluminum. The external

structure of the satellite is presented in Figure 3.1.

Figure 3.1: External structure of the satellite

3.3 Electronic Subsystems

There are several electronic subsystems that guarantee the satellite remains operational during its

mission. An electronic stack with the majority of the subsystems was designed and mounted in the lower

section of the satellite. This stack consists of a series of printed circuit boards (PCBs) connected to a

single one, perpendicular to the others. Each PCB has a specific function, according to the integrated

circuits (ICs) and components mounted in each one. The distance between each board is kept by

aluminum standoffs which are mounted in each corner of each board.

Each PCB has a thickness of 1.6 mm. The material used in these boards is a layered laminate of FR-

4 and copper. The number of copper layers can be 2, 4 or 8 and each has typically a thickness of 18-35

µm. FR-4 is a composite material made of fibreglass with epoxy resin. FR stands for Flame Retardant

and 4 indicates woven glass reinforces epoxy resin. It can be considered an orthotropic material with

the properties presented in Table 3.2. The presented mechanical properties were not provided by the

PCBs manufacturer. They were the result of research of these properties for this material. However,

other different values for these properties were found, which increases the uncertainty of the properties

of the PCBs used in the real model of the satellite.

The number of PCBs needed to accommodate all the subsystems was initially assumed to be 10.

Since the distribution and the conclusion of the design of the subsystems accommodated in the elec-

tronics stack was only concluded after the experimental testing took place, the number of boards needed

23

Young’s Modulus, E11 (GPa) 22.4 Poisson’s Ratio, ν12 0.1425



Shear Modulus, G12 (GPa) 11.0 Specific Heat Capacity, cp (J/(kgK)) 1250

Shear Modulus, G13 (GPa) 11.0 Coefficient of Thermal Expansion, CTE11 (K−1) 20×10−6

Shear Modulus, G23 (GPa) 0.70 Coefficient of Thermal Expansion, CTE22 (K−1) 20×10−6

Density, ρ (kg/m3) 1850 Coefficient of Thermal Expansion, CTE33 (K−1) 86.5×10−6

Table 3.2: Mechanical and thermal properties of FR-4 [32]

differs from the initial assumption. After concluding the subsystems design, it was concluded that only 8

PCBs were needed. Because the experimental testing took place with the initial design, but the correct

number of boards is different, both configurations must be presented since both will be analysed in this

work. It must be noted that the subsystems distribution is only determined for the final configuration,

since the initial one was only temporary and an initial estimative. Both configurations are presented in

Figure 3.2. In the next paragraphs, the most important components are described.

(a) Initial configuration (b) Final configuration

Figure 3.2: Configurations before and after concluding subsystems design

Connector board: provides physical support to connect the solar cells, deployment switches and

other components.

Battery boards: support the batteries that store the power generated by the solar panels, regulate

and distribute it by the rest of the subsystems that require electric energy, making use of the adequate

integrated circuits (ICs) for that purpose. To store the energy generated,a total of 8 Lithium Ion ICR18650

C2 2800mAh batteries provided by LG Chem was chosen in the initial design and was reduced to 6 in

the final design. Each battery has the properties presented in Table 3.3.

24

Mass, m (g) 50

Height (mm) 65.05

Diameter (mm) 18.29±0.11

Thermal Conductivity, k (W/(mK)) 12

Specific Heat Capacity, cp (J/(kgK)) 795

Operating Temperature Range (◦C) 0 to 45

Table 3.3: Dimensions and thermal properties of each battery [33], [34]

Magnetorquers board: supports the magnetorquers which are auxiliary ADCS actuators. They pre-

vent saturation and de-saturate the momentum wheels (MWs), the primary ADCS actuators. 3 magne-

torquers are used, one for each axis. Each magnetorquer consists of a coil around an iron core through

which electric current passes, producing a rotational torque.

GPS board: supports the GPS, essential to identify the position of the satellite during its orbit.

On-Board Computer board: supports the electronics necessary to provide the satellite with process-

ing capabilities.

Receiver (Rx) board: supports the electronics necessary to receive information sent from the ground

station. It includes one of the scientific payloads, the Below-Noise-Floor Communication System.

Transmitter (Tx) board: supports the electronics necessary to transmit information from the satellite

to the ground station. It also includes the Below-Noise-Floor Communication System.

Back plane: Physically connects all the PCBs to an easier mounting and dismounting of the electron-

ics stack.

For the electronic stack to be able to operate, it is necessary to generate electric power that can be

used. For that purpose there is a total of 21 solar cells distributed in 3 PCBs, each fixed on the satellite’s

lateral faces, except the face pointing in nadir direction. The chosen solar cells are the 30% Triple

Junction Solar Cell 3G30C – Advanced (80 µm) provided by AZUR SPACE Solar Power. The dimensions

of each solar cell and the real model can be consulted in Figure 3.3 (left and right, respectively). The

dimensions are in millimetres.

For a solar cell with similar semiconductor materials, some of the mechanical and thermal properties

are presented in Table 3.4.

Above the electronics stack, in the middle section of the satellite, an aluminum plate is mounted,

attached to the external structure, and with momentum wheels mounted on it. This section is part of the

ADCS which is responsible for determining the satellite orientation and position and for maintaining it

with the desirable orientation, even if external disturbances are applied. The ADCS consists of sensors,

25

Figure 3.3: 30% Triple Junction Solar Cell 3G30C [35]

Surface Area, A (cm2) 30.18

Thickness, h (µm) 80±20


Mass (of all 21 cells), m (g) 31.69

Thermal Conductivity, k (W/(mK)) 45.5

Specific Heat Capacity, cp (J/(kgK)) 327.0

Coefficient of Thermal Expansion, CTE (K−1) 6.03×10−6

Emissivity, ε 0.85

Absorptivity, α 0.91

Table 3.4: Mechanical, thermal and optical properties of each solar cell [35]

actuators and ICs mounted in a PCB similar to the ones described for the electronic stack. Some of

the required sensors and actuators are a GPS, magnetometers, gyroscopes, sun sensors, an Inertial

Measuring Unit (IMU) and momentum wheels and magnetorquers. Most of the sensors and actuators

are located in the electronics stack. The momentum wheels are located in this central section of the

satellite and the sun sensors in the solar panels. Although the specific parts for each system were not

decided to the date, some of the considered possibilities by the ECOSat team have the properties listed

in Table 3.5 and they are represented in Figure 3.4. It is important to know the operating temperature

range of similar components so that the thermal control system to be developed can maintain each

component within its safe temperature range.

In the ECOSat-III, 4 momentum wheels in a pyramid configuration are used, although 3 would be

enough to control the attitude of the satellite. This enables to reduce the perturbations caused by each

motor, enables to make a null space vector of the torque during the stabilization of the momentum

wheels around the nominal speed, and it provides redundancy and flexibility in the distribution of wheel

angular momentum [41].

In the final design, concluded after the experimental testing, a PCB board to connect the momentum

wheel motors (the ACS board) is added and located below the mounting plate, in contact with it.

26

Component Model Quantity Size(mm)

Mass(g)

OperatingTemperatureRange (◦C)

GPS [36]Novatel OEM615Dual-FrequencyGNSS Receiver

1 46×71×11 24 -40 to 85

Magnetometer [37] Freescale MAG3110 1 2×2×0.85 - -40 to 85

Gyroscope [38] Freescale FXA21002 1 4×4×1 - -40 to 85

Sun Sensor [39] NSS CubeSat SunSensor 6 33×11×6 5 -25 to 50

MomentumWheels Motor [40]

MICROMO1202H004BH 4

ViewRefer-ence

1.1 -30 to 85

Magnetorquer - 3 - - -20 to 165

Table 3.5: ADCS components with respective dimensions, mass and operating temperature range

(a) GPS [36] (b) Magnetometer [37] (c) Gyroscope [38]

(d) Sun Sensor [39] (e) Momentum Wheel Motor [40]

Figure 3.4: ADCS components

3.4 Payload

The Below-Noise-Floor Communication System is integrated in the communications system, in the

receiver and transmitter board. The hyperspectral camera is located in the upper section of the satellite.

Since it was not selected at the time of the development of this work, the initial design and the model

assembled for testing do not include it. However, the final computational model includes a typical hyper-

spectral camera for similar applications and has the properties presented in Table 3.6. These properties

were provided by the ECOSat team.

The only components in Figure 3.2 that were not mentioned in this chapter are the deployment pins,

the deployment switches and the antenna PBC. The deployment pins and the deployment switches are

responsible for the deployment of the satellite from its deployer when the desired altitude is reached.

The antenna PCB accommodates the means to establish communication between the ground station

27

Figure 3.5: Momentum Wheels in pyramid configuration [42]


Young’s Modulus, E (GPa) 68.98

Poisson Ratio, ν 0.33

Thermal Conductivity, k (W/(m·K)) 154.3

Specific Heat Capacity, cp (J/(kg·K)) 896

Coefficient of Thermal Expansion, CTE (K−1) 22.38×10−6

Operating Temperature Range (◦C) 0 to 50

Table 3.6: Properties of the hyperspectral camera

and the receiver and transmitter PCBs.

28

Chapter 4

Dynamic Analysis

It is fundamental to assure that the satellite will be able to withstand external disturbances that result

in unwanted vibrations. In orbit, the satellite may also be subjected to vibrations that result from the

operation of some of its systems. For example, rotor imbalance due to manufacturing tolerances, me-

chanical bearing friction and irregularities, and lubrication degradation are the most common sources of

vibrations in momentum wheels [43]. Other sources of vibrations are thermal snaps, which occur when

thermally induced stress is released [44], and the bending of solar arrays due to thermal gradients, which

induce torques on the satellite [45]. These type of vibrations are known as micro-vibrations because they

are low amplitude vibrations and occur at frequencies up to 1 kHz [46]. They can be amplified by struc-

tural resonances. During launch to orbit, the launch vehicle will also induce vibrations on its payload, but

these type of vibrations have higher amplitude, being structurally more demanding. The corresponding

sources of vibration occur between lift-off and the separation of the payload from the launch vehicle,

and can be wind gusts at the beginning of the launch phase, launcher engines thrust and extinction,

stage separation, sound pressure due to the engines and aerodynamic flows, among other sources.

Even during the payload transportation to the launch site, the spacecraft is subjected to vibration loads

[47]. The resulting vibrations can lead to damage or failure of sensitive payload components. To prevent

such from happening, as specified in the CSDC requirements, the satellite must have a fundamental

frequency of at least 90 Hz in each axis, as specified before in this thesis. This requirement is directly

related to the vibration environment to which the satellite is subjected while it is being transported into

orbit inside the launch vehicle and is also related to the lowest natural frequencies of the launch vehicle

itself. This way, resonance originated from the coupling between the nanosatellite and the launch ve-

hicle may be prevented. In this work it will be assumed that venting of all of the satellite’s components

is already guaranteed, so that the pressure difference between any component and the environment is

minimal.

In order to verify the fundamental frequency, modal analyses will be performed using Siemens NX

9.0 to evaluate the lowest natural frequencies and modes of the satellite. The confidence in this soft-

ware is high, since it is possible to obtain natural frequencies and modes of vibration of beams and

plates according to the corresponding analytical solution, which guarantees the validation of the method

29

used. After obtaining the results from the modal analyses, the results will be compared with the results

from experimental tests from David Florida Laboratory (DFL), located in Ottawa. Then, using both the

numerical and experimental results, the FEM model will be updated using FEMtools. The FEM model

update will allow to obtain a more reliable model. The most recent configuration of the satellite will also

be analysed to conclude if both configurations have similar behaviour. If the results between the two

configurations are comparable, the results of the FEM model update will be applied to the new configu-

ration and the study of the first one will be discontinued, since it will not be used in the future. With the

updated model, if the satellite doesn’t satisfy the requirements, a solution will be proposed. In the end of

this chapter, a reliable FEM model should be obtained and must indicate that the fundamental frequency

of the satellite is above 90 Hz.

4.1 Finite Element Analysis

To perform the simulations necessary to evaluate the structure’s dynamic behaviour, it is necessary

to create the FEM model of the structure. Since the model of the satellite is very detailed, it must be

simplified to be less time consuming to perform simulations. The dynamic behaviour of some of the

simplified components will be compared with the original one, to prove that the idealization process

does not affect significantly the dynamic behaviour. A bottom-up approach was chosen to produce the

final FEM model. A simplified model is simulated and it will progress to a more complex structure until

the final model is reached. In this section, the idealization process, the mesh types, the different FEM

models and the results obtained are described.

4.1.1 Parts Idealization

Structure idealization is necessary to remove unnecessary details in the geometry. This way, the

mesh generation process is simplified because it reduces the need of using large number of elements to

properly mesh the small details and it also avoids abrupt transitions in mesh size near the small feature

zones. In the case of modal analysis, since the study of stress concentrations will not be taken into

account, small holes and blends can be removed. In the case of the ECOSat-III the idealization process

consisted in eliminating round edges and small features and transforming some bodies in 2D surfaces

and 1D beams:

• Side panels, rails and PCBs: round edges eliminated.

• Momentum wheel mounting plate: round edges and small holes eliminated.

• Bottom and top plates, electronics stack PCBs, back plane, solar panel PCBs, antenna PCB,

camera protection panel, battery clips: transformation to 2D surfaces by using their midplane as

its equivalent and attributing its respective thickness. It is possible to do so because the thickness

of these parts is small when compared to its other dimensions.

• Batteries: removal of small design features.

30

• Standoffs and screws: substitution by 1D beams. It is possible to do so, because their length is

much larger than their other dimensions.

Some of the idealized parts were individually considered and were simulated in similar conditions

as the ones present in the assembly to verify that their dynamic behaviour did not change significantly.

Since the amount of results to show is too extensive, only some of the comparisons between the original

and idealized parts are shown in Table 4.1. The calculated frequencies are up to 10 corresponding

modes of vibration or up to the first frequency higher than 2000 Hz. As shown in the table, the error

in estimating the first frequencies is always lower than 5%. Therefore, the idealized parts are accepted

as good representatives in estimating the natural frequencies of the original parts. In Figure 4.1 one

of the meshes obtained for the momentum wheel mounting plate in both ideal and non-ideal cases is

presented. Analysing that figure, the increase in elements density near the small holes proposed to

be analysed is clear, as well as the difference in the number of nodes in both cases, when the same

element size is proposed for both meshes. The corresponding convergence study is shown in Figure

4.2. In Figure 4.3 and 4.4 the case of the PCBs is also presented.

PartSide Panels Rails Camera Panel

freal fideal Error freal fideal Error freal fideal Error

(Hz) (Hz) (%) (Hz) (Hz) (%) (Hz) (Hz) (%)

Mode 1 1507.9 1469.6 -2.54 337.4 352.0 4.33 495.8 505.3 1.91

Mode 2 1704.1 1663.1 -2.40 361.9 370.1 2.26 622.6 634.3 1.87

Mode 3 1919.3 1859.9 -3.09 978.8 1017.1 3.92 779.4 789.1 1.24

Mode 4 1987.1 1922.1 -3.27 1014.8 1036.5 2.14 1022.6 1036.5 1.36

Mode 5 2507.8 2393.5 -4.56 1914.0 1984.2 3.67 1142.8 1156.7 1.22

Mode 6 - - - 1981.0 2008.2 1.37 1171.3 1187.7 1.40

Mode 7 - - - 2618.9 2675.4 2.16 1595.7 1607.2 0.73

Mode 8 - - - - - - 1831.8 1842.4 0.58

Mode 9 - - - - - - 1903.2 1924.7 1.13

Mode 10 - - - - - - 2214.0 2232.6 0.84

PartBottom/Top Plate MW Mount PCB

freal fideal Error freal fideal Error freal fideal Error

(Hz) (Hz) (%) (Hz) (Hz) (%) (Hz) (Hz) (%)

Mode 1 2310.5 2341.1 1.32 9211.5 9188.5 -0.25 629.3 625.9 -0.54

Mode 2 - - - - - - 817.7 812.2 -0.68

Mode 3 - - - - - - 1050.1 1043.0 -0.68

Mode 4 - - - - - - 1311.8 1309.3 -0.19

Mode 5 - - - - - - 2066.3 2054.9 -0.55

Table 4.1: Idealization results

31

(a) Non-Idealized (18549 nodes) (b) Idealized (9574 nodes)

Figure 4.1: Momentum wheel mounting plate idealization

Figure 4.2: Convergence of the fundamental frequency of the momentum wheels mounting plate

4.1.2 Finite Element Model

As mentioned previously, a bottom-up approach was followed in order to progress from simple to

complex FEM models of the satellite. It was necessary to do so, since the satellite consists of a large

number of parts assembled together. This way, the connections and contacts between components can

be correctly defined in an easier way. The different FEM models obtained are the following:

FEM Model 1: The first model consists only of the external structure of the satellite.

FEM Model 2: The second model includes the PCB stack without electronics mounted.

FEM Model 3: The third model includes the solar panels PCBs, the camera panel, the antenna PCB,

the batteries and corresponding clips and the bases where each momentum wheel is mounted. This

32

(a) Non-Idealized (393280 nodes)

(b) Idealized (76386 nodes)

Figure 4.3: PCB idealization

Figure 4.4: Convergence of the fundamental frequency of the momentum wheels mounting plate

FEM model represents the actual satellite tested.

The FEM models include 1D, 2D and 3D meshes:

• 1D meshes are used to represent the standoffs, screws and the connections between different

parts, for example, between screws and the parts they connect, and between the PCBs in the

electronics stack and the back plane. Some properties of the 1D meshes are presented in Table

33

4.2.

• 2D meshes are used to represent the parts which were idealized as 2D surfaces. The PCBs were

modeled with only FR-4 since the thickness of the copper layers doesn’t affect the significantly its

dynamic behaviour. Some properties of the 2D meshes are presented in Table 4.3.

• 3D meshes are used to represent the other parts. Some properties of the 3D meshes are pre-

sented in Table 4.4.

Part Element Type Material

Standoffs CBEAM Aluminum 6061

Screws CBEAM Steel

Connections RBE3 -

Table 4.2: 1D meshes

Part Element Type Thickness (mm) Material

Bottom and TopPlates

CQUAD8 4.8 Aluminum 6061

PCBs (electronicsstack, backplane,

solar panels, antenna)CQUAD8 1.6 FR-4

Camera panel CQUAD8 1 Aluminum 6061

Battery Clips CQUAD8 0.56 Aluminum 6061

Table 4.3: 2D meshes in the vibrations FEM models


Side Panels CTETRA10 Aluminum 6061

Rails CTETRA10 Aluminum 6061

Momentum Wheels Mounting Plate CTETRA10 Aluminum 6061

Momentum Wheels Base CTETRA10 Aluminum 6061

Batteries CHEXA20 -

Table 4.4: 3D meshes used in the vibrations FEM models

To correctly evaluate the results from each FEM model, different element sizes must be used to verify

if the results change significantly with each used mesh, i.e., to analyse the convergence. In Figure 4.5

and Figure 4.6, the three models are presented with coarse meshes and refined meshes, respectively.

To avoid unnecessary discrepancies between the FEA and the EMA results, the mass of the real

satellite and some of its components was measured in order to correct the density of the material used

in the FEM model. It is important to have the correct mass in the FEM model, since it affects greatly

the natural frequencies of the structure. Since the measuring weighting process was accomplished

by the author after the experimental testing took place, the only time when the satellite’s real model

was available, some of the components could not be disassembled without damaging the structure.

This introduces a certain level of uncertainty in the model. In Table 4.5, the measured masses and

34

(a) FEM Model 1 (b) FEM Model 2 (c) FEM Model 3

Figure 4.5: Different FEM models with coarse meshes

(a) FEM Model 1 (b) FEM Model 2 (c) FEM Model 3

Figure 4.6: Different FEM models with refined meshes

the corresponding masses of the initial FEM model components are presented. The initial density of

the modelled components and the density required to obtain the same mass as the real components

are also presented in Table 4.5. Some of the components did not need a mass correction, since the

measured value and the value obtained from the FEM model are close. In the case of the electronics

stack, which included the ten PCBs, the back plane, the batteries, the battery clips, the standoffs, the

35

ComponentReal Model FEM Model

Mass Mass Initial Density Correct Density

Antenna PCB 48.5 g 48.5 g 1850 kg/m3 -

Solar Panel PCB 78 g 78.5 g 1850 kg/m3 -

Camera Panel 24.3 g 24.5 g 2711 kg/m3 -

Top Plate 91.3 g 94.0 g 2711 kg/m3 2633.1 kg/m3

Side Panel 77 g 78.6 g 2711 kg/m3 2655.8 kg/m3

Rail 63 g 63.1 g 2711 kg/m3 -

MW MountingPlate + MW Stands

129 g 129.3 g 2711 kg/m3 -

Electronics Stack 802.5 g 747.0 g - -

Table 4.5: Measured mass, FEM model components mass and change in density value to match bothresults

bottom plate and some connector elements between the PCBs and the back plane, it was not possible

to disassemble the different components. Because of this, even with the difference in the obtained

masses, no correction was made, because it was not known which component needed the correction.

These components will then have a higher uncertainty in their mass than the others. As a first estimate, it

can be considered that the mass of the batteries is about 50 g (as referred in Chapter 3), the battery clips

and used glue have a mass of 10.5 g, the bottom plate’s mass is 92 g (based on the top plate’s mass),

the shorter standoffs’ mass is 1 g, the bigger standoffs’ mass is 1.6 g, and the remaining connectors’

mass is about 45 g. With this considerations, the PCBs and the back plane would weight about 206.2 g.

As mentioned before, these values have higher uncertainty than the other values in Table 4.5.

4.1.3 Boundary Conditions and Loading

The most significant source of vibrations among all the sources described before is the launch ve-

hicle. Therefore, to predict the structure’s behaviour, it must be analysed in its launch configuration. In

this configuration, the satellite is accommodated in the deployment system. According to the P-POD

deployment system and other similar systems, the only parts of the satellite that are in contact with the

P-POD are the four rails [10]. Then, those components will be constrained. The interior of the P-POD

with the main spring extended is shown in the Figure 4.7.

The P-POD’s rails, in each of its corners, are the surfaces where the satellite rails will glide during

deployment. Those rails guarantee that the satellite is deployed with minimal rotation rate because of

the contact between them and the satellite rails. Therefore, the satellite rails should not be allowed to

present lateral motion. However, due to clearance between the satellite and the P-POD, it is possible

that the rails present lateral displacement during launch.

To clarify about the real boundary conditions, the current version of the P-POD fully constrains the

satellite rails in the Z direction, but it is allowed to move in X and Y directions due to clearance. These are

the boundary conditions adopted in this study. However, if the Z direction is constrained tightly enough,

the friction force created in X and Y directions is enough to surpass the force generated by the induced

36

Figure 4.7: P-POD interior configuration [1]

acceleration. In other words, it is possible to obtain X and Y directions fixed at the bottom and top of the

rails, using the P-POD deployer, if the slip load generated is greater than the vibration load. Because the

CSDC does not specify if the deployer to be used is the P-POD or other similar system, both boundary

conditions sets will be analysed:

• Boundary conditions set 1: rails fixed along their length.

• Boundary conditions set 2: rails fixed in their base.

Since one needs to know the natural frequencies and corresponding modes of vibration, i.e. in free

vibration conditions, no loading is applied.

Because the model to analyse is an assembly of different components mounted together, it was

necessary to define surface contacts between components with faces in contact. Otherwise, the com-

ponents would penetrate in each other, giving incorrect results for the natural frequencies and mode

shapes. For these constraints to be taken into account, it was also necessary to crate a Statics subcase

before the Eigenvalue Method subcase of Solution 103 Real Eigenvalues. These constraints were the

more difficult to apply and consumed hundreds of hours of simulations, since the contacts definition is

not straightforward and leads to a long process of trial and error, and in each trial it is necessary to

wait for an iterative method to resolve the contacts between the components before proceeding to the

eigenvalue problem.

4.1.4 Results

To perform the modal analysis Solution 103 Real Eigenvalues and the solver NX NASTRAN (NASA

Structure Analysis) were used. The results obtained in terms of natural frequencies for each FEM model

is presented in Table 4.6. The convergence of the results with the number of elements in the mesh is

presented in Figure 4.8.

Because the two different boundary conditions generated similar results in FEM Model 2 and because

the first mode of vibration is similar in this model and in FEM Model 3, it was decided to use only fixed

37

(a) FEM Model 1 with fixed rail bases only (b) FEM Model 1 with fixed rails

(c) FEM Model 2 (d) FEM Model with fixed rail bases only 3

Figure 4.8: Convergence of the fundamental frequency for different FEM Models and boundary condi-tions.

rail bases as boundary conditions in FEM Model 3. As shown in the convergence graphs, convergence

isn’t fully achieved due to computational resources limitations. Further mesh refinements were not viable

since the last meshes used already needed tens of hours to be solved. Although convergence is not

achieved, a trend is noticeable, since the slope of the natural frequencies decreases with the increase

of the number of elements used in the FEM models used. A small study on the hardware resources

allocation to NX NASTRAN solver is presented in Appendix C.1. The first mode of vibration of each of

the FEM models is shown in Figure 4.9. The modes of vibration do not provide information about the

amplitude of vibration. The shown deformation was chosen for an easy visualization of each mode.

According to the results, the ECOSat-III meets the requirement of having a fundamental frequency

higher than 90 Hz. Since the results are not fully converged and there may be errors in the modelling

process, this result can’t be accepted as proof that the satellite actually satisfies the requirement. To

verify that, the satellite must be assembled and tested in Experimental Modal Analysis to validate the

numerical results.

38

FEM Model 1 FEM Model 2 FEM Model 3

Number of nodes 605906 888790 943007

Boundary Conditions Fixed rails Fixed bases Fixed rails Fixed bases Fixed bases

f1 (Hz) 1091.2 516.1 195.1 193.3 100.6

f2 (Hz) 1132.6 556.0 216.5 216.2 110.2

f3 (Hz) 1146.2 684.3 346.2 346.0 123.3

Table 4.6: First natural frequencies of each FEM Model

(a) FEM Model 1 with fixed rails (left) and with fixedrail bases only (right)

(b) FEM Model 2 (c) FEM Model 3

Figure 4.9: First mode of vibrations of each FEM model

4.2 Experimental Modal Analysis Results

Experimental testing of the satellite was performed in DFL in Ottawa, by some of the elements of the

ECOSat team with the Canadian Space Agency, as part of the CSDC competition. The experimental

testing consisted in performing a sine sweep from 5 Hz to 2200 Hz, followed by a random vibration test

and followed by another sine sweep. The first sine sweep is used to identify the resonance frequencies

of the satellite. The random vibrations simulate launch conditions. The last sine sweep is used to verify

if the resonance frequencies change or if they remain the same. If they change, then there was a

failure in a component or a connection was broken, altering the dynamic behaviour of the satellite. In

the case of the ECOSat-III, it was verified there were changes in the resonance frequencies after the

random vibration test. It was later verified that this change was caused by some screws that got loose,

making the structure less stiff, decreasing the natural frequencies. These three tests were performed for

each of the satellite axis. Since the objective is to compare the resonance frequencies with the natural

frequencies obtained with FEA, only the results from the first sine sweep are going to be analysed.

Six points were used as measuring points and accelerometers were mounted in the chosen locations.

Those points can be seen in Figure 4.10. The acceleration is measured in the direction normal to

the surface they are located in. It was chosen to use two accelerometers for each direction. Two

39

accelerometers measure the acceleration in the x direction: one in one of the side panels of the structure

(Point 1) and other in one of the solar panels PCB (Point 2); two measure the acceleration in the y

direction: one in one of the bases where the MWs will be mounted (Point 3) and other in the back plane

of the PCB stack (Point 5); two measure the acceleration in the z direction: one in the first PCB (Point

4) and other in the seventh PCB (from top to bottom) (Point 6). The mentioned x, y and z directions

are correspondent to the reference frame used in the FEM model, which is visible in the mentioned

figure. Each accelerometer allows to obtain a frequency response for each of the tests. Considering

only the sine sweep before random testing, there is a total of 18 measurements of the acceleration with

the frequency. Due to the large amount of data, only the needed part of the results will be shown in this

work.

Figure 4.10: Accelerometers locations

As mentioned in the previous section, the expected result for the fundamental frequency was about

100.6 Hz. However, the results from the experimental testing showed that the fundamental frequency

is around 85 Hz, instead of the predicted 100.6 Hz. This result is shown in Figure 4.11. Considering

the real fundamental frequency as 85 Hz, the corresponding error in the estimation of the fundamental

frequency by the computational model is about 18.4%. This result shows that the computational model

must be corrected using a process of FEM model updating. Furthermore, because the first natural

frequency is below 90 Hz, a design change is necessary to increase that frequency.

The difference between the computational model and the real model results can have many sources.

One of the reasons is that the boundary conditions during the experimental testing may be different

from the ones simulated in the computational model because of the interaction between the testing

hardware and sensors mounted and the satellite itself. Another reason is that the structure may present

damping, which decreases the resonance frequencies to a value lower than the natural frequencies.

Furthermore, the lack of computational resources to obtain a mesh which shows convergence of the

40

Figure 4.11: Fundamental frequency taken from the measurement of the accelerometer in the backplane

results also contributes to increase the error between the two values. As shown before, the results

obtained did not fully converge. The last simulation performed still showed a trend in the decrease of

the fundamental frequency of the satellite. Therefore, it can be concluded that with a finer mesh, the

difference between both results would decrease. For last, another reason why the results differ is that the

mechanical properties of FR-4 material were not provided by the PCBs manufacturer and as mentioned

in Chapter 3, the properties that can be found in different sources are very different from each other.

Like the mechanical properties of FR-4, other material properties and modelling errors contribute to the

increase of the error. Even if each source of error has a small contribution, the sum of all the sources

can increase the error to the obtained value of 18.4%.

As for the modes of vibration, the information provided was incomplete, as the FRF phase diagrams

were not delivered to the ECOSat team. This represents a drawback, since one has to assume that

the mode shape correspondent to the fundamental frequency is similar in both the computational model

and the real model. However, there are strong evidences that point that the first mode of vibration is

the one obtained using NX NASTRAN solver. The first evidence is the acceleration readings from the

different accelerometers locations. The FRF amplitude diagram of the back plane is the one with a higher

response between 80 and 90 Hz, which complies with the first mode of vibration being characterized

by the significant deformation of the back plane. The second evidence is that the following natural

frequencies and the corresponding mode shapes of the satellite are also characterized by a deformation

of the back plane. Although this data is not validated, it still shows that the PCB stack is the less stiff zone

of the satellite, by a fair amount. Because of these evidences, it was accepted that the computational

mode shape and the experimental one are the same, or at least, similar.

41

4.3 Finite Element Model Update

To obtain a computational model which can simulate the dynamic behaviour of the satellite with more

precision, a FEM model update must be performed. However, three major limitations were encountered

and may compromise the results obtained.

The first limitation is the type and quality of the experimental results. The testing results delivered

were the FRF amplitude diagrams, in paper, without the associated electronic files generated by the

used software. That way, it was not possible to use signal processing to obtain accurate values for the

resonance frequencies (peaks of the FRF amplitude diagram) or information about damping (amplitude

and width of the FRF peaks). Furthermore, the information about the modes of vibration was incomplete

(FRF phase diagrams were not delivered). This way, it was necessary to assume that the modes of

vibration during testing had the same shape as the ones obtained with NX NASTRAN and that they

appeared in the same order. As mentioned before, there is evidence that the shape of the modes of

vibration is similar in both numerical and experimental results, so this assumptions have experimental

evidence as support.

The second limitation is the number of accelerometers used during testing. Only 6 sensors were

used, each measuring one degree of freedom. Although the information about their location is useful to

obtain information about the mode shapes, it is not enough to correctly identify each mode. There may

be local differences between the numerical and experimental mode shapes and there may even exist

modes of vibration that were not detected. This last situation can occur if the location of the sensors are

close to nodal points in the corresponding mode of vibration.

The third limitation is related to the license used in FEMtools. The available license limited the FEM

models used up to 50000 nodes. In the convergence study of FEM model 3, the most refined mesh has

943007 nodes while the coarsest mesh has 133529 nodes. This means that in order to be able to per-

form a FEM model update, the computational model must be even more simplified, which will increase

the difference between the natural frequencies of the computational and real models. To mitigate this

limitation it was decided to perform the FEM model update in a model that satisfies the size limit imposed

by the available license and apply the results manually in the FEM model with the finest mesh.

To reduce the model to 50000 nodes or less, it was necessary to idealize:

• The momentum wheels mounting plate and the side panels to 2D surfaces meshed with CQUAD8

elements;

• The batteries to 1D elements of the type CBEAM;

• Remove the battery clips from the model and connect directly the batteries to the corresponding

PCB with RBE3 elements;

• Suppress the holes used to bolt the solar panels, camera panel and antenna PCB to the side

panels, creating a node where their centre was located, to ensure the bolts are connected to those

points. The resulting mesh is more uniform, since the small elements near those holes are no

longer needed.

42

The simplified FEM model has 20326 elements and 49809 nodes. Its fundamental frequency is 110.3

Hz, representing an error of 29.8% when compared with the experimental fundamental frequency. To

update the obtained FEM model the following procedure was followed:

1. Import the FEA model file to obtain the geometry, mesh and boundary conditions;

2. Import the FEA results file to obtain the natural frequencies and mode shapes;

3. Define the measuring points used in the experimental testing;

4. Define the resonance frequencies obtained in testing;

5. Pair the measuring points with the closer nodes to those points;

6. Since there is no information about the mode shapes of experimental testing, use enforced pairing

to pair the measured experimental frequencies with the numerical ones. It was chosen to pair

the frequencies by order of appearance: the first experimental with the first numerical, the second

experimental with the second numerical and so on. Due to the lack of information about the mode

shapes, only the fundamental frequency of both models was paired;

7. Define the experimental resonance frequency and known component masses as the target re-

sponses of the model update;

8. Compute stiffness and mass matrices of the FEA model;

9. Select the parameters to change during the model update, define the upper and lower limits and

the level of confidence in their current values. The parameters that can be selected can be geo-

metric properties, material properties or boundary conditions. Geometric properties can be shell

thickness or cross section area. Material properties can be density, Young’s modulus, shear mod-

ulus, Poisson’s ratio and others. Boundary conditions are the stiffness of springs which substitute

fixed boundary conditions.

10. Perform sensitivity analysis to confirm if the target response is sensitive to changes of the selected

parameters. Delete the parameters to which the target response shows low sensitivity.

11. Perform a correlation analysis between the experimental and numerical frequencies to determine

the error functions between the numerical results and the experimental results;

12. Start the model updating to minimize the error functions;

13. Accept changes in the parameters and select new parameters to a new update if necessary or

reject changes in the parameters and select different parameters.

The target responses were chosen to be the fundamental frequency and the mass of the PCBs of the

electronics stack including the back plane, the standoffs, and batteries, the momentum wheel mounting

plate, the top and bottom plates, the solar panels and antenna, the camera panel, the side panels and

the rails and momentum wheel stands, since these values were measured, although some of them with

more precision than others because the mass of the components was measured after the assembly of

the satellite, and some of the components could not be disassembled without damaging the structure.

Some of the masses had already been manually corrected in the FEM models used before, but it was

43

chosen to allow small changes in those values, in order to obtain better results in obtaining a FEM model

with a fundamental frequency closer to the experimental one.

When boundary conditions are selected as parameters, the fixed nodes of the structure are converted

to springs and their stiffness must be specified. Setting the lower and upper bound of the stiffness it

was verified that the sensitivity analysis returned null sensitivity coefficients, which means that the first

mode of vibration is not affected by the stiffness of those springs. Therefore, boundary conditions were

excluded as parameters. Geometry and material properties were selected as parameters. In terms

of geometry, the thickness of the PCBs, solar panels, antenna panel, momentum wheel mount and

bottom and top plates were selected. The confidence in these values was high and a low range of

variation to these parameters was chosen. For material properties, Young’s modulus, density, shear

modulus and Poisson’s ratio were selected for the different materials. While the confidence in aluminum

and steel properties was set high, the confidence in the properties of FR-4 material were set to low.

This is justified by the fact that the manufacturer did not provide that information and the documented

values found through research are very different from one another. Therefore, the lower and upper

bound for FR-4 material were chosen to match the minimum and maximum values found for those

properties in literature. In total, 55 parameters were selected. Performing a sensitivity analysis, some

of the parameters revealed very low sensitivity coefficients to all the responses. The parameters with

coefficients lower than 10−3 were excluded, resulting a total of 30 parameters. Performing again the new

sensitivity analysis, although some sensitivity coefficients are much lower than others, it was preferred

not to simplify the process any further. The sensitivity coefficients obtained for each parameter in relation

to each response is presented in Figure 4.12, not only for the final sensitivity analysis but also for the

first one. The list of parameters and responses used in the final sensitivity analysis is presented in Table

4.7.

(a) First sensitivity analysis (b) Final sensitivity analysis

Figure 4.12: Sensitivity coefficients of each parameter (material and geometric properties) relative toeach response (fundamental frequency and masses)

44

Parameters Responses

1

E

Standoffs Fundamental Frequency

2 MW Mounting Plate PCBs in Electronics Stack and Back Plane

3 Bottom and Top Plates MW Mounting Plate

4 Side Panels (Central Section) Bottom and Top Plates

5 Rails and MW Stands Solar Panels and Antenna

6

ρ

MW Mounting Plate Camera Panel

7 Bottom and Top Plates Side Panels (Tabs)

8 Solar Panels and Antenna Side Panels (Central Section)

9 Camera Panel Rails and MW Stands

10 Side Panels (Tabs) Batteries

11 Side Panels (Central Section)

12 Rails and MW Stands

13 Batteries

14

h

PCBs in Electronics Stack and Back Plane

15 MW Mounting Plate

16 Bottom and Top Plates

17 Solar Panels and Antenna

18 Camera Panel

19 Side Panels (Tabs)


21G

MW Mounting Plate

22 Bottom and Top Plates


24Ex



26Ey



28 Gxy PCBs in Electronics Stack and Back Plane

29 Gxz PCBs in Electronics Stack and Back Plane

30 Gyz PCBs in Electronics Stack and Back Plane

Table 4.7: List of parameters and responses used in the final sensitivity analysis

45

The parameters with higher sensitivity coefficients in relation to the fundamental frequency response

are presented in Table 4.8. In this table, the lower and upper bounds for these parameters and the

confidence in their initial value is also presented. Using the 30 parameters that resulted from the second

sensitivity analysis, the FEM model update process took 7 iterations to decrease the natural frequency

error from 29.8% to 14.4%, by reducing the fundamental frequency from 110.3 Hz to 97.2 Hz. The

changes in the parameters and in the responses in each iteration are shown in Figure 4.13. The changes

in the parameters mentioned in Table 4.8 are presented in Table 4.9 and the obtained responses in the

final iteration are presented in Table 4.10.

Component Parameter Confidence Lower Bound Upper Bound

PCBs inElectronics Stackand Back Plane

h 85% -5% 5%

Ex 75% -35% 15%

Ey 75% -35% 15%

Gxz 75% -5% 100%

Gyz 75% -5% 100%

Batteries ρ 95% -5% 5%

Standoffs E 90% -5% 5%

Table 4.8: Parameters with highest sensitivity coefficients in relation to the fundamental frequency

(a) Parameter changes (b) Response changes

Figure 4.13: Changes in the selected parameters and responses in each iteration of the updating pro-cess

It can be verified that although some of the parameters changed the maximum value allowed, and

some of the components masses ended with a deviation of 5% in relation to the experimental value,

the error obtained in the fundamental frequency is still high. The reduction in the error is not enough to

consider that the simplified model is reliable. Therefore, the changes in the parameters obtained from

the FEM model update were manually applied in NX Siemens to the finest mesh used. Introducing the

updated geometry and material properties, the error decreased from 18.4% to 2.5%, with a frequency

46

Component Parameter Initial Value Final Value Change

PCBs inElectronics Stackand Back Plane

h 1.6 1.52 -5%

Ex 22.4 GPa 14.6 GPa -35%

Ey 22.4 GPa 14.6 GPa -35%

Gxz 630 MPa 598.5 MPa -5%

Gyz 199 MPa 189.1 MPa -5%

Batteries ρ 3100 kg/m3 3255 kg/m3 5%

Standoffs E 68.98 GPa 65.53 GPa 5%

Table 4.9: Changes in the parameters with highest sensitivity coefficients in relation to the fundamentalfrequency

Response FEA EMA Difference

Fundamental Frequency 97.2 Hz 85.0 Hz 14.4%

PCBs and Back Plane 195.9 g 206.2 g -5.0%

MW Mounting Plate 76.0 g 76.3 g -0.4%

Bottom and Top Plates 188.0 g 188.5 g -0.3%

Solar Panels and Antenna 285.5 g 285.6 g -0.005%

Camera Panel 24.6 g 24.6 g -0.0003%

Side Panels (Tabs) 142.9 g 143.0 g -0.08%

Side Panels (Central Section) 159.2 g 159.4 g -0.1%

Rails and MW Stands 315.0 g 315.0 g 0.003%

Batteries 431.0 g 410.5 g 5.0%

Table 4.10: Difference between the FEA and EMA responses in the end of the FEM model update

drop from 100.6 Hz to 87.1 Hz. This result is acceptable, ending the FEM model update process. In

Table 4.11, the results of interest obtained from the FEM model update are summarized.

ftesting

(Hz)

Simplified FEM Model Refined FEM Model

Before Update After Update Before Update After Update

f (Hz) Error (%) f (Hz) Error (%) f (Hz) Error (%) f (Hz) Error (%)

85 110.3 29.8 97.2 14.4 100.6 18.4 87.1 2.5

Table 4.11: FEM Model update results

4.4 New Configuration Modal Analysis

As previously mentioned in Chapter 3, after the experimental testing in Ottawa, it was decided to

make some design changes, since the subsystems design was only concluded after the testing. There-

fore, new simulations and testing are needed, in order to verify what effects it will have in the natural

frequencies of the satellite. In this work, the FEA using NX Siemens and NX NASTRAN solver will be

performed. Then, the results will be compared with the previous FEA results. In the future, experimen-

tal testing will allow to validate the computational model and perform a new FEM update if necessary.

47

Because it was not possible to perform new experimental testing, it was decided that if the new con-

figuration FEA provides similar results to the previous ones already shown in this work, then the FEM

model update results will also be implemented in this new configuration to obtain more reliable results.

However, it is essential to validate the model with experimental testing in the future. It is important to

study the behaviour of this new configuration because it may be used in future designs, for instance, the

ECOSat-IV, when a new CSDC begins.

In this new configuration, the PCB stack is changed and a PCB is added below the momentum wheel

mounting plate. The number of batteries changes from eight to six, distributed in two PCB, three in each

one. Finally, a hyperspectral camera, the momentum wheels, the solar cells, the deployment pins and

switches and a battery holder will be mounted in the structure in order to verify what are the effects in

the fundamental frequency of the satellite. The model with the modified PCB stack will be referred as

FEM Model 4 and the model with the camera, momentum wheels, solar cells and deployment pins and

switches mounted on the satellite as FEM Model 5. Some properties of the meshes used in the added

components in FEM Model 5 can be checked in Table 4.12.

Camera Mounting Plates CTETRA10 Aluminum

Camera CTETRA10 -

Momentum Wheels CTETRA10 Aluminum

Battery Holder CTETRA10 Steel

Deployment Switches CHEXA20 Steel

Deployment Pins CTETRA10 Ultem

Solar Cells CQUAD8 -

Momentum Wheels PCBs CQUAD8 FR-4

Table 4.12: Meshes used in the components added in FEM Model 5

To evaluate the fundamental frequency in FEM Model 4, a mesh with element size equal to the cho-

sen mesh in FEM Model 3 was used. To evaluate the fundamental frequency in FEM Model 5, a new

convergence study was performed, since there is a significant quantity of new components and connec-

tions in the model. The used meshes for both models is presented in Figure 4.14. The convergence

study for FEM Model 5 is presented in Figure 4.15 and the obtained results for both models is shown in

Table 4.13 which also presents the results from FEM Model 3 and the deviation of the new results from

that model.

FEM Model 3 FEM Model 4 FEM Model 5

f1 (Hz) f1 (Hz) Deviation (%) f1 (Hz) Deviation (%)

Before Update 100.6 99.8 -0.8 97.1 -3.5

After Update 87.1 86.0 -1.3 83.4 -4.2

Table 4.13: Fundamental frequencies of the new configurations and its deviation from the previous model

From the results, it is concluded that the changes in the configuration are not significant enough to

make the fundamental frequency to change by a significant amount, for both the model before updating

and after updating. For that reason and since the fundamental frequency decreases with the changes

48

(a) FEM Model 4 (b) FEM Model 5

Figure 4.14: FEM Models with refined meshes

Figure 4.15: Convergence study of FEM Model 5

made in the last FEM models, it was decided to use the last FEM model, FEM Model 5 with updated

properties, to develop a solution to increase the fundamental frequency to above 90 Hz. This way, if this

FEM Model presents a fundamental frequency higher than 90 Hz, the other FEM models will also verify

that condition.

Although the updated FEM Model 3 was validated by experimental data and the following FEM mod-

els seemed to present the same behaviour as the previous one, this consideration must be validated by

49

new experimental data in the future.

4.5 Solution Development

As concluded from the results of the experimental modal analysis, the fundamental frequency does

not comply with the requirement of being higher than 90 Hz. A solution must be found to increase the

fundamental frequency. To avoid going through a process of a major design change that would signif-

icantly modify the configuration of the satellite, it was decided to constrain the first mode of vibration.

This way, the stiffness of this mode of vibration increases and so does the first natural frequency. The

solution found was to add two small aluminum pieces, attach them to the side panel in the direction of

the first mode of vibration and fix one of the PCBs with highest displacement: the magnetorquers board.

The location of the aluminum pieces is shown in Figure 4.16. In the same figure and in Table 4.14, the

difference between the original mode of vibration and the modified mode of vibration and the increase

in the fundamental frequency are presented.

(a) Aluminum stiffeners mounted on the side panel and magne-torquers PCB

(b) First mode of vibration of the structure without(left) and with (right) stiffeners

Figure 4.16: Aluminum stiffeners mounting and effect in the first mode of vibration of the satellite

Without stiffeners With stiffeners

f1 (Hz) 83.4 130.6

Table 4.14: Increase of the fundamental frequency by using stiffeners in FEM Model 5

According to the results shown, it can be concluded that the fundamental frequency increased by

a significant amount, meeting the requirement of being higher than 90 Hz. While the original mode

shape is characterized by a symmetric deformation of the back plane, by using the aluminum stiffeners

the PCB stack deforms in a similar shape only in the portion above the stiffeners. The lower portion

presents lower displacement relative to the maximum displacement, reflecting the increase in the stiff-

50

ness of the structure. Although the fundamental frequency obtained can be considered close to 90 Hz,

the requirement of presenting a fundamental frequency of at least 90 Hz already takes into account a

safety margin considering the lowest natural frequencies of the launch vehicle and the dominant fre-

quencies excited during launch.

With the suggestion to increase the fundamental frequency of the satellite, no major design changes

were needed and the weight of the satellite was not increased significantly. The only drawback is that

the experimental testing did not provide the mode shapes of the satellite and if the first mode of vibration

differs from the obtained with the computational model, then the addition of the stiffeners may be less

effective than presented in this work. However, due to the evidences presented in the end of the Ex-

perimental Modal Analysis section, it is acceptable to assume the computational mode shape is at least

similar to the real one.

The final configuration obtained with the stiffeners mounted has the following properties, which all

comply with the CSDC requirements:

Total mass 2.278 kg

Center of mass in relation to geometric centre (0.19, 0.03, 0.45) mm

Fundamental frequency 130.6 Hz

Table 4.15: Final configuration characteristics

During the dynamic analysis, all the simulations were performed considering an environment temper-

ature of 20◦C, since the fundamental frequency imposed was relative to launch conditions. Therefore,

the coupling between dynamic and thermal analysis along the satellite’s orbit was not considered. In a

more advanced stage of the dynamic analysis of the satellite, this coupling may be performed, in order

to evaluate the effect of the temperature distribution of the satellite in the natural frequencies. This would

help to quantify the perturbations on the ADCS.

51

Chapter 5

Thermal Analysis

To prevent failure, thermal analysis must be taken into consideration. A structure can experience

thermal stresses under uniform temperature if it is made of different materials and the differences in the

materials coefficients of thermal expansion produce strain discontinuities. If the thermal loads reach a

point where the material of a component begins to buckle or if it is subjected to many cycles of thermal

loading such that it can fail due to fatigue, the whole structure is compromised [47]. This simple fact is

an example of how important it is to carry on a proper thermal design of a structure. Regarding thermal

aspects and specifically for space applications, some of the risks that can lead to the mission failure are:

• High temperature peaks: produce high thermal stresses reducing components safe life and pro-

duce high thermal deflections that lead to attitude and pointing errors;

• High temperature deltas: produce on-orbit cyclic thermal stresses that may lead to failure due to

fatigue;

• Inadequate temperature for the normal operation of a system.

The two worst cases regarding the spacecraft’s temperature must be analysed. These two cases

are opposite to one another: in one case it is considered the systems are all operating at full power and

with maximum solar flux and in the other case an idle power consumption is considered with minimum

solar flux. These two cases are known as the Hot Case and the Cold Case, respectively, and are

characterized in Table 5.1.

Hot Case Cold Case

Solar Flux 1411.00 W/m2 1323.64 W/m2

Camera Worst Case Consumption Off

Image Compression On Off

OBCDH Normal Power Mode Low Power Mode

Downlink On Off

Uplink Processing Waiting

Table 5.1: Hot Case and Cold Case characteristics

53

If the thermal analysis reveals the existence of systems in poor thermal condition for its normal

operation, or if the temperature peaks and deltas need further improvement, the thermal design will

be re-addressed to find solutions for the detected problems. The thermal control subsystem will then

ensure that each subsystem will operate in its safe operating temperature range.

To perform the simulations necessary to evaluate the structure’s thermal performance, it is necessary

to create a new FEM model of the structure. This FEM model is different from the model used in modal

analysis since there are components which are relevant for thermal analysis but were simplified for

modal analysis. In the following sections, the idealization process, the used meshes and FEM model,

and the results obtained are described.

5.1 Initial Finite Element Analysis

5.1.1 Parts Idealization

As in the case of vibration simulations, it is necessary to idealize some of the parts to obtain more

uniform meshes and obtain results faster. In this case, the idealizations made are:

• Side panels and rails: round edges eliminated.

• Momentum wheel mounting plate: round edges and small holes eliminated.

• Batteries: removal of small design features.

• Momentum wheel PCBs, battery clips and solar cells: transformation to 2D surfaces due to their

thickness.

In this case it was not appropriate to use 2D surfaces to represent the PCBs and the bottom and top

plates because the out of plane thermal behaviour must be correctly simulated, and because it is not

possible to define a thermal contact between a surface and a perpendicular surface meshed with 2D

elements. The standoffs cannot be substituted by 1D elements because the thermal coupling between

the parts they connect is better modelled with the 3D model of the standoffs. An alternative to the use

of the 3D model of the standoffs would be using thermal couplings between the holes of consecutive

PCBs, but it was chosen not to use that option because the simulation time did not improve and because

the standoffs do not have an uniform geometry, which would complicate the definition of the thermal

coupling.

5.1.2 Finite Element Model

Like the FEM model used in modal analysis, the thermal FEM model also has different components

meshed with different element types:

• The components meshed with 2D elements are the momentum wheel PCBs, the battery clips and

the solar cells. Some of the properties of the 2D meshes used is presented in Table 5.2.

54

• The components meshed with 3D elements are the external structure, the batteries, the battery

holder, the camera and its mounting plates, the momentum wheels and their bases and mounting

plate, the standoffs the PCBs from the electronics stack, solar panels and antenna, the back plane

and the stiffeners. These components cannot be simplified since the temperature distribution

in each of the components is very important to represent their cyclic thermal behaviour during

consecutive orbits. The use of 3D elements is essential to identify the critical components from the

thermal point of view. Some of the properties of the 3D meshes used is presented in Table 5.3.

• No 1D elements were used.

Part Element Type Thickness (mm) Material

Momentum WheelPCBs

CQUAD8 0.56 FR-4 and Copper laminateequivalent

Battery Clips CQUAD8 0.5 Aluminum

Solar Cells CQUAD8 0.18 -

Table 5.2: 2D meshes used in the thermal FEM model


Side Panels CTETRA10 Aluminum

Rails CTETRA10 Aluminum

Camera and MWs MountingPlate

CTETRA10 Aluminum

Momentum Wheels Base CTETRA10 Aluminum

Momentum Wheels CTETRA10 Aluminum

Bottom and Top Plates CHEXA20 Aluminum

Camera CTETRA10 -

Batteries CHEXA20 -

Battery Holder CTETRA10 Steel

PCBs (Stack, SP, Antenna,Back Plane)

CTETRA10 FR-4 and Copper laminateequivalent

Standoffs CTETRA10 Aluminum

Stiffeners CTETRA10 Aluminum

Table 5.3: 3D meshes used in the thermal FEM model

Although it would be important to model each of the integrated circuits mounted in the PCBs, it was

not possible to do so because the choice of which ICs to use was not taken at the start of the thermal

analysis, therefore their dimensions, properties and operating temperature ranges are not known. For

this reason, the ICs were not mounted in the PCBs but the operating temperature ranges presented in

Table 3.5 were considered.

In the thermal model, it is necessary to add surface-to-surface contacts between the components that

are in contact with each other, just like in the vibrations model. These thermal contacts will be located

55

where the surface contact was defined in that model. In bolt connections, thermal couplings must be

defined, so that the thermal conductivity of bolts is taken into account. These thermal couplings should

be defined where the bolt connections using RBE elements were in the vibrations model. Because of

that, it is easier to understand what type of constraints will be necessary to add, and therefore, only one

FEM model was used, instead of using the bottom-up approach.

Unlike in the vibrations model, the copper layers of the PCBs must be taken into account, since they

are the portion of the PCBs that allow the thermal connection between the PCBs and the standoffs

because of its higher thermal conductivity. The overall thermal conductivity of the PCBs will be different

in the in-plane direction and in the through-plane direction. If those values of thermal conductivity are

determined then it will not be necessary to define the laminate structure, reducing the simulation times.

A model to estimate those two values is available in [48], based in experimental measurements, and the

expressions to estimate the in-plane and through-plane thermal conductivities, respectively, are:

kin−plane = 385hCu

h+ 0.87 (5.1a)

kthrough−plane = [3.23(1− hCu

h) + 0.0026

hCu

h]−1 (5.1b)

where hCu is the total thickness of the copper layers and h is the total thickness of the PCB. The result

of the thermal conductivities has units of W/(mK). In this work it will be considered that each PCB has

two copper layers, each with 35 µm, which corresponds to 1 ounce of copper spread over 1 square

feet, a common configuration. Because each board has a thickness of 1.6 mm, the resulting thermal

conductivities are: kin−plane = 17.71W/(mK) and kthrough−plane = 0.32W/(mK).

To define the thermal couplings at the bolt locations, the total thermal conductance between the two

connected holes must be defined. The total thermal conductance is defined as the heat rate that passes

through a certain area and length, when the temperature difference between each end is 1◦C or 1K. The

SI units are W/K. The thermal conductance is derived from Fourier’s Law. Rearranging Equation 2.50,

the thermal conductance can be derived:

Conductance =Qconduction

∆T=kA

L(5.2)

The thermal conductivity, area and length are relative to the material and geometry of the bolt.

To account for radiation exchange, it is necessary to define the thermo-optical properties of the

components. Since those properties depend not only of the material but also on the surface finishing,

they are simulated creating Modeling Objects and assigning them to the corresponding meshes. As a

simplification, it was considered that only the external surfaces received solar radiation. The components

with surfaces that participate in this radiation exchange are the rails, the solar panels, the antenna, the

camera panel the camera lens and the bottom and top plates. As a first study of the thermal behaviour,

56

it was considered that none of the components is treated with paint or surface coatings. If necessary,

the effect of adding such features will be analysed after the worst case conditions are established. In the

conditions described, the thermal-optical properties defined for the external surfaces of each component

are presented in Table 5.4.

α ε

Rails [22] 0.15 0.85

Bottom and Top Plates [22] 0.15 0.85

Camera Panel [22] 0.15 0.85

Camera Lens [22] 0.05 0.90

Antenna Panel [49] 0.85 0.56

Solar Panels PCBs [49] 0.85 0.56

Solar Cells [35] 0.91 0.85

Table 5.4: Thermo-optical properties of the external surfaces

The obtained FEM Model is similar to FEM Model 5 from vibration simulations, with the differences

described in this section. The mesh used is coarser than the mesh used in FEM Model 5 and is pre-

sented in Figure 5.1.

Figure 5.1: Thermal FEM Model

5.1.3 Boundary Conditions and Loading

The solver to be used is NX SPACE SYSTEMS THERMAL and the solution is Space Systems Ther-

mal, which allows to simulate the heat loading while the satellite is in orbit. Instead of applying thermal

loads and constraints for each component of the satellite, Simulation Objects, Constraints and Ther-

mal Loads are created. The solar flux, Earth’s infrared radiation and albedo are modelled by the Orbital

57

Heating Simulation Object, the radiation exchange with the environment is modelled with Radiation Con-

straint and the heat generated by the electronics stack and other electric components is modelled with

the Heat Load Thermal Load.

To correctly model the radiation exchange with the environment, the external surfaces are selected in

the Radiation Simulation Object. The radiative environment temperature is then set to −273.15◦C (0 K).

The Orbital Heating Simulation Object requires the orbit characteristics to correctly account for the

solar, infrared and albedo heat fluxes. Since the orbit isn’t fully defined, some possible orbits were con-

sidered, taking into account the requirements of the CSDC and the payload itself. The CSDC requires

that the satellite must be able to operate in sun-synchronous orbits between 400 and 800 km of altitude,

or equal to the ISS orbit (which is just above 400 km). However, due to the mission of hyperspectral

imaging of Canada, the ECOSat team determined that below 600 km of altitude, the mission would not

be viable. Even in orbits between 600 and 800 km of altitude, the mission would only be successful if the

launch time of the satellite lied between 9 am and noon. Therefore, it was decided to simulate two differ-

ent orbits, at two different launch times and in two different Earth positions relative to the Sun (aphelion

and perihelion) and power consumption conditions (full power and minimum power consumption). This

means that eight different simulations were prepared to determine which two orbits presented the worst

case conditions. If the satellite is able to operate in these conditions, then it will be able to operate in

intermediate conditions as well. The two orbit altitudes and launch times affect the final orbit around

Earth. Those orbits are presented in Figure 5.2.

To compute the solar heat fluxes that reach the satellite, the software makes use of Equations 2.27.

The results are automatically computed and are q solarperihelion

= 1412.73W/m2 and q solaraphelion

= 1322.47W/m2

for the perihelion and aphelion, respectively.

The predefined value for the bond albedo by Siemens NX is the same mentioned in Chapter 2:

BA = 0.306.

To account for the infrared radiation, the software uses the flux that leaves Earth instead of the flux

that reaches the satellite. The predefined value of 237.04W/m2 is used.

To define the Heat Loads, it is necessary to know the power consumed by the electronics. Some

systems will have different operational configurations depending if full power or minimum consumption

is being considered. Because the ICs to be used are not determined yet, neither their location in each

PCB, it was chosen to simplify the thermal model and consider the thermal loads correspondent to each

of ICs is not applied to the corresponding IC but to all of the upper area of the corresponding PCB where

it should be mounted. This may result in a loss of accuracy of the model, leading to lower temperature

peaks, since the same thermal load is being spread over a wider area than the area of the IC. It is advised

that in a future work the thermal analyses are improved by mounting the ICs in the computational model

and applying the heat loads directly to those components for more accurate results.

To determine the power dissipated by each component, a spreadsheet developed by the ECOSat

58

(a) Altitude = 600 km, Launch time = 9 am (b) Altitude = 800 km, Launch time = 9 am

(c) Altitude = 600 km, Launch time = 12 pm (d) Altitude = 800 km, Launch time = 12 pm

Figure 5.2: Different satellite orbits as viewed from the Sun

team was used. This spreadsheet takes into account the satellite’s orbit and computes in multiple time

increments whether the satellite is receiving sunlight or not, to determine the power generation by the

solar panels. When the solar panels are receiving sunlight, the batteries are charging. When they are

not receiving sunlight, the batteries start discharging. The hyperspectral camera will only be working in

case the satellite is mapping the desired zone while receiving sunlight. Although there is this difference

in the operating times of some of the components, another simplification was made: it was considered

that those components are always operating, dissipating the same energy during the whole orbit as the

energy dissipated only during sunlight. The majority of the electronics operate during sunlight as well as

in the shadow zone. However, for the ones that are not always operating, this is another simplification

that may lead to errors. In worst case conditions, some of the components may have special consump-

59

tion conditions, as presented in Table 5.1.

The thermal simulations start with the assumption that the satellite is at a uniform temperature of

20◦C. This value does not affect the final results but may influence the elapsed time in each simulation.

If it is a bad initial guess of the satellite’s temperature, it will increase the simulation times, because

more iterations will be needed to achieve the final result. The convergence criterion was chosen to be a

temperature change less than 0.1◦C between two consecutive orbits.

In Table B.1, the different eight cases mentioned are characterized in terms of orbit altitude, launch

time and heat dissipation in each major electronic component.

5.1.4 Results

Before presenting the results, it is important to verify if the used mesh is adequate and if the num-

ber of positions along the satellite’s orbit where the temperatures are computed is enough to obtain a

converged solution. However, it was verified that these simulations take a much larger time period to

generate the results than the vibration simulations. For that reason, it was not possible to increase the

number of nodes in the mesh and the number of orbital positions simultaneously. Instead, it was decided

to use a coarse mesh and increase the number of orbital positions. Then, a time instant and three node

locations were chosen to register the verified temperatures. The chosen node locations are in the top

plate, in the OBC board and in one battery clip. The same procedure was followed while maintaining a

minimum number of orbital positions and increasing the number of nodes in the mesh. This way, two

different convergences could be analysed. The results of these convergence studies allowed to con-

clude that the results do not fully converge but the temperatures do not change by a significant amount.

This situation is more critical in the case of the mesh convergence. The case of the number of orbital

positions can be considered fully converged. The convergence study described is shown in Figure 5.3.

When solving one simulation with the finest mesh and highest number of orbital positions, it was

verified that the simulation times were not adequate, since they were very high (close to 60 hours of

continuous processing) and it was probable that a thermal control system had to be developed, which

would require many simulations to evaluate possible solutions. For this reason, it was decided to use

a coarser mesh and less orbital positions to calculate the temperatures in the satellite. This decision

was accepted because although the solution does not reflect the converged case of the mesh and the

number of orbital positions, the deviation from it is not high. In the case of the number of orbital positions,

the chosen value of 12 can be considered converged. In the case of the number of nodes, although the

chosen value of 201002 is not in the zone where the trend of convergence is clearer, the results do

not differ very much from the finest mesh used. A small study on hardware resources allocation to NX

SPACE SYSTEMS THERMAL is presented in Appendix C.2.

The orbits and thermal loads presented in Table B.1 were simulated. To determine which of the eight

cases correspond to the hot case and to the cold case worst conditions, the maximum and minimum

60

(a) Temperature convergence with number of orbital positions where the heatbalance is performed

(b) Temperature convergence with number of nodes

Figure 5.3: Thermal analysis convergence study considering an orbit with 600 km of altitude with thesatellite launched at 12 pm, with maximum power consumption and in the perihelion. Node 1: Top plate;Node 2: OBC board; Node 3: Battery clip.

temperatures achieved in each case were verified. The results are presented in Table 5.5, where the

Hot and Cold cases are highlighted in red and blue colours, respectively.

According to the results obtained, the two worst case conditions are:

• Hot Case: Altitude of 600 km, Earth in the perihelion and satellite launched at 12 pm;

• Cold Case: Altitude of 800 km, Earth in the aphelion and satellite launched at 9 am.

If the satellite is able to safely operate in these two extreme cases, then it will also safely operate in

61

Altitude Launch Time Earth Position Tmax (◦C) Tmin (◦C)

600 km

9 amAphelion 12.72 -17.41

Perihelion 45.8 -9.07

12 pmAphelion 29.33 -12.50


800 km

9 amAphelion 11.84 -17.44


12 pmAphelion 28.27 -13.70


Table 5.5: Maximum and minimum temperatures in each simulated case

any altitude between 600 and 800 km, in any other Earth’s position relative to the Sun, and in any other

time of launch between 9 am and 12 pm. To evaluate the thermal cycling of the components to verify

the temperature peaks and temperature deltas, the two worst cases were selected and the average

nodal temperature of each component was plotted against time. This allowed to obtain the maximum

and minimum temperatures and temperature deltas of each component along a full orbit of the satellite.

The results are presented in Table B.2. In the same table, the operating temperature ranges for the

components is also presented. If the registered minimum and maximum temperatures comply with the

operating range, their status is assumed to be ”OK”. If this does not happen, their status is ”NOT OK”.

According to the results, the hyperspectral camera and the batteries have a minimum average tem-

perature that falls below their minimum operating temperature, in the Cold Case. Because of this, it is

necessary to develop a Thermal Control System. From the results it can also be verified that the hottest

component in the Hot Case is the OBC board which reaches a maximum average temperature of 51.5◦C.

The coldest components in the Cold Case are the external structure and the solar panels which reach

a minimum average temperature of about -15◦C. It can also be verified that in the electronics stack, the

temperature deltas are higher in the Hot Case than in the Cold Case. In the Hot Case the temperature

deltas reach 28.2◦C and in the Cold Case reach 17.7◦C.

5.2 Thermal Control System

Having noted that the temperatures of some subsystems fall outside of the safe temperature range,

a thermal control system (TCS) must be implemented. It is preferred to implement a TCS instead of

changing the satellite’s configuration, since that could lead to difficulties in other systems operations,

would affect the structural integrity of the satellite and would require starting a new modal analysis from

scratch. Implementing a TCS in smaller satellites poses a higher challenge than in larger satellites.

While small satellites may suffer high temperature changes in a small time period, larger satellites tend

to decrease or increase their temperature in a much slower rate due to their higher mass and consequent

higher thermal inertia. A common cause of mission failure is the failure of the TCS due to unforeseen

factors or lack of human and financial resources for its proper development. The TCS must be able

to control the temperature of all the components within an acceptable range without interfering in any

62

operations of the satellite. There are two types of thermal control systems: passive or active.

Passive systems have no moving parts or electric power input. They include multi-layer insulation

surfaces to absorb or reflect internal or external radiation, thermal blankets which shade the satellite from

excessive heating and retain internal heat to prevent too much cooling, coatings or paints to increase

the emissivity or absorptivity of the surfaces, reflectors to dissipate heat to space, heat spreaders which

conduct heat from a small spot to larger heat sinks, which experience lower temperature deltas, and

other similar techniques. Active systems are typically used when sudden changes of temperature or high

temperature deltas may occur. These systems include heat pipes and heaters controlled by sensors.

Heat pipes are effective in transferring heat from one location to another one. The pipe is a sealed tube

through which a fluid passes. In the hot end of the tube, the fluid boils. The vapour expands into the pipe,

carrying the heat, and when reaches the cold end, it condenses, releasing the heat and returning to the

initial point, the hot end, to initiate this cycle again. Heaters consist of electrical resistance elements that

generate heat by Joule effect [50].

While passive systems are simple, highly reliable, lighter, cheaper and simple to implement, they

have lower heat transfer capacity than active systems. Since the constraint of low mass, cost and limited

power is an issue in NanoSats, passive thermal control systems are preferred. For this reason, a passive

TCS will be implemented. If this system does not put the temperatures of the components within their

operating range, an active thermal control system will be implemented.

The first option consists in using black dye in the external surfaces to increase the absorptivity.

This way, a bigger portion of radiation is absorbed by the satellite, and less is reflected, increasing the

temperature of the components. This corresponds to the use of black anodized aluminum and black

PCBs for the solar panels and antenna panel. The values of the absorptivity and emissivity of these

surfaces was considered to be 0.95 and 0.90 respectively [51]. The obtained results for the minimum

and maximum temperatures and for the temperature deltas in worst case conditions are presented in

Table B.3.

It can be verified that applying this procedure, the batteries are now within its temperature operating

range. As for the hyperspectral camera, its minimum temperature is still below its limits. Verifying that

the minimum temperature of the camera is very close to the minimum operating temperature, it was

decided to change the material of one of its mounting plates. Inspecting the thermal behaviour of the

camera, it was verified that heat was being transferred to the external structure which is at a lower

temperature when the camera reaches its minimum temperature. For that reason, it was decided to

change the material of one of the camera’s mounting plates. The current design uses aluminum for

the three mounting plates. Using a material with a lower thermal conductivity in one of the mounting

plates, there would be a lower heat conduction from the camera to the external structure. However, that

material must be able to keep the stiffness of the structure, in order to keep the fundamental frequency

higher than 90 Hz, and it should not increase the weight of the satellite by a significant amount. Different

materials and their thermal conductivity and density are presented in Table 5.6.

Analysing the different possibilities and comparing them with the currently chosen material for the

camera plate, stainless steel was considered the most adequate option. Although titanium is much

63

Material Density (kg/m3) Thermal Conductivity (W/(mK)) Plate Mass (g)

Aluminum 2711 166.9 27.2

Titanium 4500 21.9 45.3

Stainless Steel 8000 14.9 80.5

Iron 7870 80.2 79.2

Zinc 7140 116.0 71.9

Table 5.6: Density, thermal conductivity and final mass of the central camera mounting plate for differentmaterials

lighter than stainless steel and the thermal conductivity is similar, this material is much more expensive

than stainless steel, and for that reason, that option was excluded. Since the volume of the plate is

low, choosing stainless steel for the camera mounting plate won’t have a significant effect in the final

mass of the structure. Therefore, stainless steel was chosen as the camera thermal insulator. Applying

the change of material to the camera mounting plate, the total weight of the satellite increased from

2.278 kg to 2.330 kg and the minimum temperature of the hyperspectral camera increased from -0.98◦C

to 5.51◦C. The change in temperature distribution in the camera and camera mounting plates when

aluminum and stainless steel is used is represented in Figure 5.4.

The results obtained after applying this change can be consulted in Table B.4. In Figure 5.5 the

thermal cycling of the camera and the batteries in cold case conditions after using stainless steel in

one of the camera mounts is plotted along the thermal cycling obtained in the initial conditions and after

applying the black dye in external surfaces. The maximum and minimum operating temperatures are

represented by a red and blue line, respectively.

64

(a) Temperature distribution with central camera mounting plate in aluminum

(b) Temperature distribution with central camera mounting plate in stainless steel

Figure 5.4: Thermal behaviour of the camera and its mounting plates

65

(a) Camera Cold Thermal Cycling

(b) Batteries Cold Thermal Cycling

Figure 5.5: Thermal cycling in initial conditions, after applying black dye and after using stainless steelin the camera mount

66

5.3 Additional Thermal Control System Improvement

With the all the components operating within their specified limits, one may look at the temperature

peaks and temperature deltas and decide if they can be improved in the sense of increasing minimum

temperatures, decreasing maximum temperatures and reducing the temperature deltas. With the pas-

sive TCS implemented so far, some of the maximum temperatures and temperature deltas increased.

For example, in the case of the OBC board in Hot Case conditions, the maximum temperature increased

from 51.49◦C to 62.14◦C, and its temperature delta from 25.44◦C to 32.66◦C. Since some of the temper-

atures in the electronics stack are below 40◦C and some of the temperature deltas slightly above 10◦C,

it was decided to study how to reduce the maximum temperatures and temperature deltas by making

those parameters more uniform across the electronics stack. The following study and solution found is

a suggestion only, since the satellite could operate safely without further improvements. However, it was

decided to perform this study to increase the satellite’s reliability and useful life.

One option is to increase the thermal inertia. To increase the thermal inertia, a material with lower

thermal diffusivity should be attached to the PCB stack. The thermal diffusivity of a material is given by

Equation 2.50 and it depends on the material’s thermal conductivity, density and specific heat capacity.

The selected solution will be a compromise between the added mass to the satellite, the decrease of

the temperature peaks and the decrease of the temperature deltas. Since the results of adding a certain

material with a certain geometry are not straightforward, it was decided to simulate different cases: at-

tach one, two or three plates with thickness of 3, 4 or 5 mm and width of 40 or 60, of aluminum, stainless

steel or titanium. These materials were selected because they are typical materials used in aerospace

applications and because stainless steel and titanium are materials with low thermal diffusivity, while

aluminum is a material with high thermal diffusivity, allowing to confirm that materials with lower thermal

diffusivity have a better performance for this objective. The thermal diffusivity of the different materials

considered is in Table 5.7, while the corresponding thermal conductivity was already presented in Table

5.6. The proposed configurations are presented in Figure 5.6.

Aluminum Stainless Steel Titanium

Thermal Diffusivity (m2/s) 97.1×10−6 3.95×10−6 9.32×10−6

Table 5.7: Thermal diffusivity of different materials [22]

The results obtained in the electronics stack in terms of maximum temperature and temperature

deltas are presented in Tables B.5 and B.6, respectively, in units of ◦C. The registered values in each

column corresponding to a certain geometry and material are in top to bottom order: Connector Board,

Battery Board 1, Upper Batteries, Battery Board 2, Lower Batteries, Magnetorquers Board, GPS Board,

OBC Board, RX Board and TX Board. The total mass of the attached plates in presented in Table B.7

in units of kg. Green colours represent lower values while red values represent higher values. For the

three cases, it is desired to obtain lower values, since they represent lower maximum temperatures,

temperature deltas and mass.

Based on the values obtained in each table, the worst results were excluded, i.e, the results with

67

(a) 1 plate with width of 40 mm (b) 2 plates with width of 40 mm (c) 3 plates with width of 40 mm

(d) 1 plate with width of 60 mm (e) 2 plate with width of 60 mm (f) 3 plate with width of 60 mm

Figure 5.6: Proposed configurations to reduce maximum temperatures and temperature deltas. Theplates added to the electronics stack are presented in grey.

higher temperature peaks, higher temperature deltas and a mass above 0.500 kg were excluded. These

excluded options appear in the three mentioned tables with text in grey colour. To select the better option

of the remaining ones, it was decided to use the following procedure:

• Select the maximum temperature, maximum temperature delta and maximum mass verified in the

remaining options (56.40◦C, 33.83◦C and 0.465 kg respectively);

• Normalize the maximum temperatures, temperature deltas and mass, according to the maximum

values from the previous step. The results are values between 0 and 1;

• Compute the average value of each solution option for each of the three tables. The results are

values between 0 and 1;

• Compute the weighted average for each solution by assigning to each one of the parameters

characterized by each table a weight that reflects their importance. Weights of 50%, 45% and

5% were assigned to the maximum temperature, temperature delta and mass, respectively. The

68

low importance given to the mass is based on the fact that the heavier solutions were already

excluded. The results are still between 0 and 1;

• Select the lowest result as the best solution.

Following this procedure, the solution selected was to attach two stainless steel plates with width of

60 mm and thickness of 3 mm, with a total mass of 0.372 kg. Because a significant mass was added to

the lower portion of the satellite, the centre of mass of the satellite must be checked to verify if it is still

within the required limits. Verifying the centre of mass, with the proposed solution, it would move in the

Z axis direction but would still be within the required limits.

With the improvement of the thermal behaviour of the electronics stack, other section that could be

thermally improved is the camera, which show high temperature deltas in hot case conditions, as can

be verified in Table B.4. Consulting that table, the corresponding temperature delta is 24.1◦C.

To attenuate that temperature delta, it was decided to use stainless steel in the remaining camera

mounting plates. Since this change in material occurs above the current centre of mass of the satellite,

to avoid a new displacement of the centre of mass in the same direction as when adding the high thermal

inertia plates, it was decided to also change the momentum wheel mounting plate material to stainless

steel. This material was chosen because it isolates the components from the external structure, which

presents one of the highest temperature deltas. Furthermore, the benefits of using stainless steel were

already demonstrated when the material of the central camera mounting plate was changed to this

material and when the plates to increase the thermal inertia of the electronics stack were attached.

It is important to point out that using aluminum instead of stainless steel in these remaining mounting

plates is not obligatory to maintain the satellite within a safe temperature range, but is beneficial. The

results of implementing the high thermal inertia plates and changing the remaining camera mounting

plates and momentum wheels mounting plates to stainless steel are presented in Table B.8. In Figure

5.7, the thermal cycling of the ACS and OBC boards in Hot Case conditions is presented. The different

curves represent the thermal cycling in the initial conditions, after applying black dye in the external

surfaces and after attaching the high thermal inertia plates and changing the mounting plates material

to stainless steel.

The conclusions that can be taken from the results in Cold Case conditions by comparing Table B.8

with the previous results are:

• All the components operate within the operating temperature ranges and the maximum and mini-

mum temperatures and the temperature deltas were reduced in absolute value;

• Using all three camera mounting plates in stainless steel improves the thermal behaviour of the

hyperspectral camera by increasing the minimum temperature by about 28◦C and decreasing the

maximum temperature by about 15◦C, resulting in a decrease of about 13◦C in the temperature

delta, when comparing with the initial results;

• All the minimum and maximum temperatures and the temperature deltas in the electronics stack

69

(a) ACS Hot Thermal Cycling

(b) OBC Hot Thermal Cycling

Figure 5.7: Thermal cycling in initial conditions, after applying black dye and after using stainless steelin the mounting plates and as a means to increase thermal inertia

increased as a consequence of applying black dye to increase some components minimum tem-

peratures. By attaching high thermal inertia plates, those effects were decreased;

• Using the momentum wheels mounting plate in stainless steel improves the thermal behaviour

of the momentum wheels and the ACS board by decreasing the maximum temperature by about

70

1◦C for both components, by increasing the minimum temperature by about 3◦C and 5◦C, respec-

tively, resulting in a decrease of about 4◦C and 6◦C, respectively, in the temperature delta, when

comparing with the results after applying black dye.

In Hot Case conditions:

• All the components operate within the operating temperature ranges and the maximum and mini-

mum temperatures and the temperature deltas were reduced in absolute value;

• Using all three camera mounting plates in stainless steel improves the thermal behaviour of the

hyperspectral camera by increasing the minimum temperature by about 24◦C and decreasing the

maximum temperature by about 2◦C, resulting in a decrease of about 22◦C in the temperature

delta, when comparing with the initial results;

• All the minimum and maximum temperatures and the temperature deltas in the electronics stack

increased as a consequence of applying black dye. By attaching high thermal inertia plates, those

effects were decreased and the temperatures were more uniform: while the batteries and battery

boards increased the temperature delta by 3-4◦C, the remaining boards decreased the tempera-

ture delta by about 5◦C;

• Using the momentum wheels mounting plate in stainless steel improves the thermal behaviour of

the momentum wheels and the ACS board in a similar way described in Cold Case conditions;

• The maximum temperature verified in the electronics stack after applying all the solutions proposed

is 52.56◦C in the OBC board, which is about 10◦C lower than the maximum temperature registered

in the same component when only black dye was applied as a TCS.

The thermal cycling of some of the components are presented in Figure 5.8, where both Hot Case

and Cold Case conditions are plotted simultaneously, along with the operating ranges correspondent to

the dotted lines. In the case of the electronics stack, the less flexible temperature range was selected

as the operating temperature range, even though some of the boards could operate at higher or lower

temperatures than the ones presented.

71

(a) Camera Thermal Cycling (b) Batteries Thermal Cycling

(c) Electronics Stack Thermal Cycling (d) External Structure Thermal Cycling

(e) Solar Panels Thermal Cycling

Figure 5.8: Thermal cycling after developing the thermal control system

In case the ECOSat team does not find appropriate to change all of the mounting plates from alu-

72

minum to stainless steel, the only essential mounting plate to change to stainless steel is the central

camera mounting plate. In that case, the hyperspectral camera, the momentum wheels and the ACS

board would decrease their minimum temperature and their temperature delta would increase. The

differences between the two solutions can be verified in Table 5.8.

Cold Case

ComponentTmin (◦C) Tmax (◦C) ∆T (◦C)

Aluminum Steel Aluminum Steel Aluminum Steel

Camera 5.51 15.17 22.85 20.96 17.34 5.79

MWs -6.15 -3.18 24.63 23.79 30.78 26.97

ACS Board -6.19 -0.97 24.63 23.24 30.82 24.21

Hot Case

ComponentTmin (◦C) Tmax (◦C) ∆T (◦C)

Aluminum Steel Aluminum Steel Aluminum Steel

Camera 14.35 26.17 38.40 33.70 24.05 7.53

Momentum Wheels 1.37 3.99 43.81 42.50 42.44 38.51

ACS Board 1.98 7.14 43.81 41.76 41.85 34.62

Table 5.8: Temperature changes when using all mounting plates with stainless steel and when using allaluminum except for the central camera mounting plate

5.4 Fundamental Frequency Check

Because there was a change of material in some components and new components were added, a

new dynamic analysis is needed to verify that the fundamental frequency is still acceptable. Applying

the changes to the last FEM Model, the new fundamental frequency was computed. The results and the

solid properties of interest are shown in Table 5.9.

Total mass 2.772 kg

Centre of mass in relation to geometric centre (0.03, -0.03, -4.35) mm


Table 5.9: Fundamental frequency and solid properties after developing the TCS with all the mountingplates in stainless steel

It can be verified that the fundamental frequency increased significantly as a consequence of adding

the stainless steel plates to the electronics stack, which constrain the first mode of vibration. The result-

ing mode of vibration is presented in Figure 5.9. With these results, a fundamental frequency higher than

90 Hz and a thermal control system that allows all the components operate within their safe temperature

range, it can be concluded that now the satellite is ready to be safely launched to orbit, survive space

environment conditions and perform its missions, from the dynamic and thermal point of view.

In case the ECOSat team does not find appropriate to change all of the mounting plates from alu-

minum to stainless steel, maintaining only the central camera mounting plate with stainless steel as

73

Figure 5.9: First mode shape after applying the thermal control system

material, the fundamental frequency, the centre of mass and the total mass would be similar to the

previous obtained values and can be checked in Table 5.10.

Total mass 2.702 kg

Centre of mass in relation to geometric centre (-0.01, -0.02, -3.57) mm


Table 5.10: Fundamental frequency and solid properties after developing the TCS with only the centralcamera mounting plate in stainless steel

In case the ECOSat team does not find appropriate to implement the additional TCS improvement

at all, implementing only the necessary TCS to make the satellite’s components operate within their

safe temperature range, the fundamental frequency, the centre of mass and the total mass would be

the ones presented in Table 5.11. It can be verified that the only changes when compared with the

results presented before implementing the TCS are the total mass and the component in Z direction of

the centre of mass.

In all the presented solutions, it can be verified that the requirements of having a total mass lower

than 4.00 kg, a fundamental frequency higher than 90 Hz and a centre of mass located within 2.0 cm

and 7.0 cm of its geometric centre in the X and Y direction and in the Z direction, respectively, are all

satisfied.

Total mass 2.330 kg

Centre of mass in relation to geometric centre (0.19, 0.03, 3.90) mm


Table 5.11: Fundamental frequency and solid properties after developing the TCS without the proposedadditional improvements

74

Chapter 6

Conclusions

This work started with a computational model of the ECOSat-III. From that model, the dynamic and

thermal behaviour had to be simulated and analysed and if necessary, improve that behaviour by propos-

ing and simulating the effect of the design changes. However, only a partial model was experimentally

tested and design changes were made by the ECOSat team after testing that partial model.

Therefore, first one had to change the computational model to correspond to the tested model and

verify if the simulated behaviour was similar to the tested one. If the results obtained by computational

simulations were similar to the results by experimental testing, then the computational model could

be considered reliable. If the results were not similar, the computational model had to be updated to

better match the experimental results, so that the model could be considered reliable. In this case, the

computational model would have to be updated to match the simulated results with the experimental

ones. These results did not comply with the required dynamic behaviour because the fundamental

frequency of the satellite was below the required value, so a design change had to be proposed. Before

proposing a solution, the effect of changing the satellite configuration to the final configuration after

the experimental tests were performed was evaluated and it was concluded that the results were close

enough to the tested ones, so that the new computational model obtained could still be considered

reliable. Since the first configuration will not be used in the future, it was then decided to abandon that

configuration and use the final configuration to obtain a solution to increase the fundamental frequency.

The proposed solution was to add two aluminum parts to constrain the first mode of vibration, increasing

the fundamental frequency to a value above the minimum allowed as a consequence.

To guarantee a good thermal performance of the satellite, the worst case conditions in terms of

minimum temperatures and maximum temperatures to be reached by the satellite were identified, the

components that reached temperatures beyond the safe range were identified and a thermal control

system had to be developed to avoid the components of reaching those non-safe temperatures. Since

the non-safe temperatures appeared in the cold case, it was suggested to use black colours in the

external surfaces of the satellite and to isolate the camera from the external structure by changing the

material of one of its mounting plates to increase the minimum temperatures of the satellite. With this

procedure, a passive thermal control system was implemented and all the components could operate

75

in their safe temperature range. An additional design change was suggested but was not essential

to the satellite’s survival in space environment conditions. It consisted in adding high thermal inertia

plates along the electronics stack and change the remaining mounting plates to stainless steel. This

changes reduced the maximum temperature and temperature deltas in hot case conditions. A new

modal analysis was also performed and confirmed that the fundamental frequency was still above the

minimum required value. In fact, due to the plates added to the electronics stack, the fundamental

frequency even increased. The mass and centre of mass were also verified and were within the required

limits.

The initial configuration of the ECOSat-III was not ready to be safely launched into orbit and survive

space environment conditions. With the developed work, both dynamic and thermal behaviour were

analysed, allowing the design of solutions to prepare the satellite to survive those conditions. The

natural frequency, the total mass, the centre of gravity and the temperature distribution are within the

allowed ranges. All the objectives initially proposed were accomplished. This work also offers bases to

future studies and analysis for the ECOSat team and for other students who choose to work in a similar

area.

6.1 Recommendations and Future Work

The next step to take in the analysis of the ECOSat-III is to choose the ICs and missing components

to use in each of the PCBs and add them to the computational model. Then, the routing and wiring

must be developed. That can be achieved by using NX mechanical and electrical routing module from

NX Siemens. That module also allows to output the details to manufacturing. With all the components

added, it is advised to detail the thermal simulations by applying the thermal loads correspondent to

the power dissipation in each of the ICs instead of spreading the thermal loads by the PCBs area. This

procedure can increase the temperature peaks in the ICs and allows to conclude if the thermal control

system is adequate or if it needs to be improved. Although the presence of the ICs in each board should

not affect significantly the fundamental frequency of the satellite, the mass of the ICs should be taken

into account in a new modal analysis to verify the results. If all of the results satisfy the requirements,

then the complete model should be manufactured and tested. Even if the ICs and the payload cannot

be added to the prototype, at least a dummy mass should be added to simulate their presence.

In a future project, it is recommended to finish the design of all of the satellite’s subsystems before

building the experimental model to avoid design changes that cannot be tested. Although the effects

of the design changes can be evaluated as presented in this work, the resulting computational model

will not have the same reliability as it would have if it had the same configuration as the tested model.

Another recommendation is to increase the computational resources available, in order to obtain more

accurate results and to guarantee that the meshes used generate solutions that are converged. This

also helps to meet critical deadlines. For example, it is important that the computational model does not

show flaws or errors before proceeding to the experimental testing. This way, one knows what to expect

from the testing results.

76

It is also recommended that to prepare the experimental testing the Pre-Test Planning tool from

Siemens NX is used. This allows to analyse each mode of vibration and determine the number of

sensors and their location to correctly identify each mode of vibration during experimental testing. This

way, one would be sure that the desired modes of vibration and corresponding resonance frequencies

would be captured during the experimental testing.

As shown in this work, the FEM model not always represents the actual model accurately. Therefore,

it is advised that the ECOSat team invest in an experimental apparatus that allows the testing of the

satellite in terms of its natural frequencies, so that more data can be extracted from the experiment and

a more reliable updating process of the FEM model can be obtained. It would be particularly important

to obtain the shapes of the experimental modes of vibration and to use a higher number of sensors to be

able to represent the experimental modes of vibration and compare with the simulated ones. This way,

if design changes are needed to satisfy the requirements, the upgraded FEM model used to perform

those changes is more reliable. If the design change involves a major change in the configuration, that

new configuration could be tested again.

77

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82

Appendix A

3U CubeSat Configuration

Figure A.1: Typical external configuration of a 3U CubeSat [1]

83

Appendix B

Results from Thermal Simulations

84

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B(W

)0.

525

0.51

50.

530

0.51

8

Mag

neto

rque

rsP

CB

(W)

0.10

2

GP

SP

BC

(W)

0.04

5

OB

CP

CB

(W)

3.02

50.

3025

2.99

00.

299

3.04

10.

304

3.00

10.

300

RX

PC

B(W

)0.

502

0.05

00.

502

0.05

00.

502

0.05

00.

502

0.05

0

TXP

CB

(W)

0.76

20.

076

0.73

90.

074

0.77

20.

077

0.74

70.

075

Tabl

eB

.1:

Sim

ulat

edor

bits

and

corr

espo

ndin

gth

erm

allo

ads

85

Operating

Range

HotC

aseC

oldC

ase

Com

ponentT

min

( ◦C)

Tm

ax

( ◦C)

Tm

in( ◦C

)T

max

( ◦C)

Status

∆T

( ◦C)

Tm

in( ◦C

)T

max

( ◦C)

Status

∆T

( ◦C)

Cam

era0

502.21

31.27O

K29.06

-12.536.20

NO

TO

K18.73

Mom

entumW

heels-30

85-1.69

31.79O

K33.48

-14.596.59

OK

21.18

AD

Sboard

-3085

-1.3931.87

OK

33.26-14.63

6.56O

K21.19

ConnectorB

oard-45

8512.67

31.74O

K19.07

-6.675.51

OK

12.18

Battery

Board

1-40

8518.23

29.03O

K10.80

-3.074.28

OK

7.35

UpperB

atteries0

4519.21

28.60O

K9.39

-2.423.98

NO

TO

K6.40

Battery

Board

2-40

8520.59

31.67O

K11.08

-1.076.43

OK

7.50

LowerB

atteries0

4521.29

30.67O

K9.38

-0.645.76

NO

TO

K6.40

Magnetorquers

Board

-2085

12.3635.82

OK

23.46-8.11

6.84O

K14.95

GP

SB

oard-40

8513.27

37.64O

K24.37

-8.796.82

OK

15.61

OB

CB

oard-40

8526.05

51.49O

K25.44

-8.238.03

OK

16.26

ReceiverB

oard-40

8513.4

40.21O

K26.81

-10.146.88

OK

17.02

TransmitterB

oard-40

8511.52

39.75O

K28.23

-10.896.83

OK

17.72

SolarP

anelY+

-2550

-2.3234.06

OK

36.38-15.22

8.17O

K23.39

SolarP

anelY--25

500.11

29.61O

K29.50

-15.795.08

OK

20.87

SolarP

anelX+

-2550

-2.4632.19

OK

34.65-15.41

6.59O

K22.00

Structure

-100100

-1.7031.81

OK

33.51-15.04

6.51O

K21.55

TableB

.2:O

peratingranges,m

inimum

andm

aximum

temperatures

andtem

peraturevariation

ineach

components

86

Ope

ratin

gR

ange

Hot

Cas

eC

old

Cas

e

Com

pone

ntT

min

(◦C

)T

max

(◦C

)T

min

(◦C

)T

max

(◦C

)S

tatu

s∆T

(◦C

)T

min

(◦C

)T

max

(◦C

)S

tatu

s∆T

(◦C

)

Cam

era

050

6.57

42.3

1O

K35

.74

-0.9

824

.02

NO

TO

K25

Mom

entu

mW

heel

s-3

085

2.62

43.1

4O

K40

.52

-4.9

224

.17

OK

29.0

9

AC

Sbo

ard

-30

853.

2043

.18

OK

39.9

8-3

.03

23.8

OK

26.8

3

Con

nect

orB

oard

-45

8518

.45

41.7

2O

K23

.27

5.91

22.3

5O

K16

.44

Bat

tery

Boa

rd1

-40

8525

.04

38.3

1O

K13

.27

11.1

820

.29

OK

9.11

Upp

erB

atte

ries

045

26.1

037

.63

OK

11.5

311

.57

20.0

8O

K8.

51

Bat

tery

Boa

rd2

-40

8527

.40

40.9

9O

K13

.59

13.0

522

.34

OK

9.29

Low

erB

atte

ries

045

28.1

839

.73

OK

11.5

513

.34

21.8

6O

K8.

52

Mag

neto

rque

rsB

oard

-20

8516

.94

46.0

1O

K29

.07

3.87

23.9

0O

K20

.03

GP

SB

oard

-40

8517

.78

47.9

0O

K30

.12

3.08

23.9

5O

K20

.87

OB

CB

oard

-40

8530

.87

62.2

1O

K31

.34

3.57

25.2

7O

K21

.7

Rec

eive

rBoa

rd-4

085

17.8

150

.70

OK

32.8

91.

5624

.13

OK

22.5

7

Tran

smitt

erB

oard

-40

8515

.52

50.1

0O

K34

.58

0.76

24.2

8O

K23

.52

Sol

arP

anel

Y+

-25

501.

0548

.44

OK

47.3

9-5

.71

25.6

1O

K31

.32

Sol

arP

anel

Y--2

550

4.33

41.9

4O

K37

.61

-6.4

522

.18

OK

28.6

3

Sol

arP

anel

X+

-25

500.

7144

.21

OK

43.5

-6.7

824

.57

OK

31.3

5

Str

uctu

re-1

0010

03.

1443

.12

OK

39.9

8-5

.49

24.2

6O

K29

.75

Tabl

eB

.3:

Ope

ratin

gra

nges

,min

imum

and

max

imum

tem

pera

ture

san

dte

mpe

ratu

reva

riatio

nin

each

com

pone

nts

whe

nbl

ack

dye

isap

plie

d

87

Operating

Range

HotC

aseC

oldC

ase

Com

ponentT

min

( ◦C)

Tm

ax

( ◦C)

Tm

in( ◦C

)T

max

( ◦C)

Status

∆T

( ◦C)

Tm

in( ◦C

)T

max

( ◦C)

Status

∆T

( ◦C)

Cam

era0

5014.35

38.4O

K24.05

5.5122.85

OK

17.34

Mom

entumW

heels-30

851.37

43.81O

K42.44

-6.1524.63

OK

30.78

AC

Sboard

-3085

1.9843.83

OK

41.85-6.19

24.63O

K30.82

ConnectorB

oard-45

8517.46

41.96O

K24.50

5.3222.45

OK

17.13

Battery

Board

1-40

8524.53

38.63O

K14.10

10.5320.77

OK

10.24

UpperB

atteries0

4525.65

37.88O

K12.23

11.2920.26

OK

8.97

Battery

Board

2-40

8526.87

41.30O

K14.43

12.5222.94

OK

10.42

LowerB

atteries0

4527.73

39.97O

K12.24

13.0722.04

OK

8.97

Magnetorquers

Board

-2085

16.1646.32

OK

30.163.24

24.08O

K20.84

GP

SB

oard-40

8516.87

48.23O

K31.36

2.3524.15

OK

21.80

OB

CB

oard-40

8529.48

62.14O

K32.66

2.7425.47

OK

22.73

ReceiverB

oard-40

8516.71

51.07O

K34.36

0.7224.48

OK

23.76

TransmitterB

oard-40

8514.66

50.76O

K36.10

-0.2024.63

OK

24.83

SolarP

anelY+

-2550

0.8745.95

OK

45.08-6.95

26.06O

K33.01

SolarP

anelY--25

502.09

41.01O

K38.92

-7.6822.63

OK

30.31

SolarP

anelX+

-2550

0.7644.02

OK

43.26-7.16

24.78O

K31.94

Structure

-100100

1.8443.79

OK

41.95-6.72

24.71O

K31.43

TableB

.4:O

peratingranges,

minim

umand

maxim

umtem

peraturesand

temperature

variationin

eachcom

ponentw

henblack

dyeis

appliedand

acam

eram

ountingplate

ischanged

fromalum

inumto

stainlesssteel

88

3x60

mm

3x40

mm

2x60

mm

1x60

mm

5mm

4mm

3mm

5mm

4mm

3mm

5mm

4mm

3mm

5mm

4mm

Alu

min

um

41.4

141

.71

41.9

942

.05

42.2

542

.46

41.7

042

.18

42.3

342

.46

42.4

7

40.4

840

.81

41.1

341

.13

41.3

641

.63

39.7

540

.33

40.5

239

.93

39.9

5

39.3

139

.58

39.8

339

.97

40.1

640

.37

39.3

639

.81

39.9

538

.93

38.9

3

41.3

141

.69

42.0

942

.07

42.3

642

.72

40.6

941

.32

41.5

941

.66

41.7

2

39.8

640

.19

40.5

340

.60

40.8

641

.17

40.0

840

.60

40.8

240

.22

40.2

6

42.4

842

.93

43.4

343

.35

43.7

144

.17

43.0

443

.68

44.0

644

.97

45.1

0

42.8

243

.31

43.8

743

.78

44.2

044

.74

43.5

144

.20

44.6

545

.88

46.0

5

45.7

946

.32

46.9

447

.21

47.6

648

.27

48.1

648

.88

49.4

053

.83

54.0

4

43.4

443

.96

44.5

844

.46

44.9

245

.53

44.4

345

.15

45.6

747

.37

47.5

7

43.4

243

.94

44.5

444

.36

44.8

145

.40

44.4

345

.13

45.6

247

.18

47.4

2

Sta

inle

ssS

teel

39.2

339

.65

40.0

540

.12

40.4

640

.69

39.8

440

.17

40.4

640

.98

41.1

3

38.0

238

.40

38.7

238

.85

39.1

539

.27

37.7

037

.93

38.1

338

.41

38.5

3

37.2

037

.54

37.8

237

.99

38.2

738

.37

37.4

737

.72

37.9

037

.60

37.7

0

39.3

539

.80

40.2

240

.39

40.8

041

.03

39.4

239

.72

39.9

440

.55

40.7

0

38.2

338

.61

38.9

839

.19

39.5

639

.76

38.6

939

.01

39.2

639

.28

39.3

9

42.0

442

.76

43.4

743

.45

44.1

044

.66

43.1

043

.66

44.2

044

.92

45.1

8

43.2

544

.11

45.0

144

.89

45.7

046

.48

44.5

145

.20

45.9

146

.53

46.8

9

47.2

648

.29

49.4

549

.49

50.5

151

.59

50.2

351

.09

52.0

455

.28

55.7

6

44.7

745

.71

46.7

146

.66

47.5

848

.49

46.3

347

.08

47.8

548

.70

49.1

0

44.6

545

.51

46.4

046

.47

47.3

248

.14

46.1

546

.82

47.4

848

.38

48.7

3

Tita

nium

40.0

240

.33

40.5

240

.69

40.8

340

.95

40.4

640

.65

40.8

141

.25

41.0

2

38.6

938

.93

38.9

939

.27

39.3

339

.31

38.7

638

.25

38.3

138

.60

38.2

8

37.7

838

.01

38.0

538

.37

38.4

238

.39

37.9

238

.00

38.0

537

.76

37.4

6

40.1

940

.51

40.6

541

.04

41.1

741

.23

40.5

340

.07

40.1

540

.81

40.5

2

38.9

439

.23

39.3

439

.76

39.8

739

.91

39.2

939

.42

39.5

339

.48

39.2

0

43.4

543

.96

44.3

744

.66

45.0

245

.35

44.1

844

.55

44.8

845

.43

45.2

9

44.9

845

.64

46.2

346

.48

47.0

047

.53

45.8

946

.38

46.8

747

.25

47.1

9

49.4

150

.29

51.2

051

.59

52.3

753

.29

52.4

452

.72

53.5

056

.29

56.4

0

46.6

747

.39

48.0

748

.49

49.1

149

.75

47.9

248

.37

48.9

149

.52

49.5

2

46.3

747

.00

47.5

648

.14

48.6

749

.19

47.6

247

.91

48.3

649

.13

49.1

0

Tabl

eB

.5:

Max

imum

tem

pera

ture

(in◦ C

)dis

trib

utio

non

the

PC

Bst

ack

whe

nat

tach

ing

toit

plat

esto

incr

ease

the

ther

mal

iner

tia

89

3x60mm

3x40mm

2x60mm

1x60mm

5mm

4mm

3mm

5mm

4mm

3mm

5mm

4mm

3mm

5mm

4mm

Alum

inum

26.4727.50

28.5526.85

27.6128.40

26.9027.67

28.4226.33

26.72

22.8823.65

24.3822.59

23.1423.68

20.7521.28

21.7918.37

18.61

20.1020.76

21.3819.79

20.2720.72

19.7620.10

20.5116.01

16.15

22.3923.14

23.8622.06

22.5923.10

20.2420.66

21.1518.12

18.35

19.4320.09

20.7219.07

19.5419.97

19.0619.43

19.8415.48

15.63

26.5127.49

28.4827.20

27.8828.55

27.6028.32

29.0228.24

28.62

26.5827.58

28.6027.26

27.9628.68

27.6128.38

29.1228.93

29.34

26.7527.76

28.8027.49

28.2028.94

27.8528.61

29.3929.74

30.17

27.0928.09

29.1527.95

28.6629.41

28.3529.07

29.8730.78

31.20

27.5428.54

29.5828.55

29.2529.99

29.0629.67

30.4631.09

32.36

Stainless

Steel

22.7923.80

24.8024.08

24.8225.49

23.5224.30

25.0224.12

24.58

17.4118.07

18.5917.57

17.9818.17

16.1116.45

16.6815.7

15.90

15.2616.04

16.2115.25

15.5915.74

15.2115.54

15.7413.69

13.86

16.3316.98

17.5316.17

16.6416.91

15.4315.82

16.0715.43

15.66

14.2914.84

15.3114.05

14.4614.69

14.3414.72

14.9713.14

13.33

21.2422.51

23.8521.95

23.0024.17

23.1324.11

25.1825.93

26.62

21.8323.27

24.8022.53

23.7525.17

23.8825.00

26.2727.05

27.85

22.4223.93

25.5723.23

24.6626.25

24.6025.94

27.4328.26

29.10

23.1124.86

26.8324.41

25.9027.56

25.8427.26

28.8129.74

30.59

24.3526.10

28.0725.71

27.2028.89

27.2328.64

30.1831.26

32.09

Titanium

24.8625.45

25.9125.54

25.8826.13

25.2125.45

25.7425.02

25.19

18.6418.86

18.8418.21

18.2017.99

17.9316.76

16.6316.01

16.09

16.2416.42

16.3815.78

15.7615.58

15.7815.78

15.6513.97

14.02

17.5717.84

17.8716.96

17.0316.95

17.1216.16

16.0715.82

15.93

15.3515.57

15.5814.73

14.7714.67

15.0215.06

14.9913.47

13.55

23.9224.76

25.6624.24

25.0325.90

25.3726.01

26.8127.39

27.86

24.8625.85

27.0325.24

26.2127.28

26.4727.23

28.1829.00

29.25

25.6426.92

28.2426.32

27.3828.55

27.5828.46

29.4530.00

30.59

26.8928.21

29.6027.63

28.7529.97

28.9329.86

30.9131.51

32.18

28.1329.45

30.8528.94

30.0731.31

30.2431.23

32.3033.04

33.83

TableB

.6:Tem

peraturedelta

distribution(in◦C

)onthe

PC

Bstack

when

attachingto

itplatesto

increasethe

thermalinertia

90

3x60

mm

3x40

mm

2x60

mm

1x60

mm

5mm

4mm

3mm

5mm

4mm

3mm

5mm

4mm

3mm

5mm

4mm

Alu

min

um0.

354

0.28

20.

212

0.23

50.

188

0.14

10.

236

0.18

80.

127

0.11

80.

094

Sta

inle

ssS

teel

1.03

20.

825

0.62

0.68

90.

551

0.41

30.

688

0.55

0.37

20.

344

0.27

5

Tita

nium

0.57

90.

465

0.34

80.

387

0.30

90.

232

0.38

60.

310.

209

0.19

30.

155

Tabl

eB

.7:

Mas

s(in

kg)o

fthe

atta

ched

plat

esto

incr

ease

the

ther

mal

iner

tia

91

Operating

Range

HotC

aseC

oldC

ase

Com

ponentT

min

( ◦C)

Tm

ax

( ◦C)

Tm

in( ◦C

)T

max

( ◦C)

Status

∆T

( ◦C)

Tm

in( ◦C

)T

max

( ◦C)

Status

∆T

( ◦C)

Cam

era0

5026.17

33.70O

K7.53

15.1720.96

OK

5.79

Mom

entumW

heels-30

853.99

42.50O

K38.51

-3.1823.79

OK

26.97

AC

Sboard

-3085

7.1441.76

OK

34.62-0.97

23.24O

K24.21

ConnectorB

oard-45

8516.06

40.92O

K24.86

4.3322.10

OK

17.77

Battery

Board

1-40

8521.43

38.60O

K17.17

8.1521.10

OK

12.95

UpperB

atteries0

4522.10

38.21O

K16.11

8.9120.52

OK

11.61

Battery

Board

2-40

8523.86

40.31O

K16.45

9.7222.27

OK

12.55

LowerB

atteries0

4524.28

39.53O

K15.25

10.2221.39

OK

11.17

Magnetorquers

Board

-2085

18.7644.69

OK

25.934.76

22.88O

K18.12

GP

SB

oard-40

8519.33

46.42O

K27.09

4.0123.06

OK

19.05

OB

CB

oard-40

8524.20

52.56O

K28.36

3.8123.70

OK

19.89

ReceiverB

oard-40

8518.52

48.39O

K29.87

2.5823.30

OK

20.72

TransmitterB

oard-40

8516.68

48.03O

K31.35

1.9323.34

OK

21.41

SolarP

anelY+

-2550

1.7545.58

OK

43.83-6.48

25.78O

K32.26

SolarP

anelY--25

502.62

40.39O

K37.77

-7.2622.20

OK

29.46

SolarP

anelX+

-2550

0.3644.81

OK

44.45-6.73

24.44O

K31.17

Structure

-100100

2.6843.32

OK

40.64-6.26

24.27O

K30.53

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92

Appendix C

Solver Performance Optimization

Throughout this work, the simulations performed became progressively more complex and therefore

more demanding in terms of computational and time resources. Because the process of developing

a correct FEM model can require a series of simulations and corrections due to incorrect modelling, it

was necessary to optimize NX NASTRAN and NX SPACE SYSTEMS THERMAL solvers performance

according to the available hardware resources. This way, each solver can run the simulations in the

minimum time possible.

It was found that for the available resources, the performance limiting factors for NX NASTRAN were

the RAM memory and disk I/O speed and for NX SPACE SYSTEMS THERMAL it was the number of

available CPUs. It was decided to study what could be done to reduce the simulation times of each

solver. This appendix is intended to show which parameters were taken into account to increase the

speed of the solvers and to give some context on this subject to future students who have to work with

FEM models that demand high computational resources.

C.1 NX NASTRAN

As mentioned before, the simulations using NX NASTRAN depend significantly on the available RAM

memory and I/O speed. Different analysts suggest a minimum of 64 to 128 GB of available RAM and

1 TB of SSD disk. The reason is because NASTRAN originates large amounts of data (scratch files).

If the size of the produced data is large enough, it won’t fit in RAM memory and must be written in the

hard drive, increasing the solution time since I/O operations are slower in SSD or HDD devices than in

RAM memory. When the memory is not enough for the desired analysis, SSD devices are preferable

because they are faster than HDD devices up to three times.

The next step to optimize performance would be to develop a workstation with several homogeneous

computers and make use of DMP (Distributed Memory Parallel) computing. This allows to subdivide the

problem and distribute it between the several nodes (individual computers) for faster solutions. To use

DMP it would be necessary to upgrade the NX NASTRAN license. However, the use of this functionality

is only advisable to very large FEM models. In the case of the present work, it would not be essential to

93

use this feature.

The available hardware in CfAR had 20 GB of RAM, 2 TB of HDD and 8 CPUs @ 2.93 GHz. The

author’s laptop had 16 GB of RAM, 1 TB of HDD, 25 GB of SSD and 4 CPUs @ 2.00 GHz. Because

both the available hardware had specifications below the suggested, the simulation times were very high

and did not allow to present proper convergence studies, as shown in Chapter 4.

To reduce the simulation times, it was necessary to adjust how the solver would use the available

resources. It was found that in the laptop case, dedicating about half of the RAM memory to NASTRAN

itself leads to reduced simulation times, since the other half will then be effectively used to buffer the

I/O operations by the operating system. The scratch files, which demand a high rate of I/O operations,

should be stored in memory as a fraction of the memory dedicated to NASTRAN, and in fast I/O disks.

Improved performance was obtained when using half of NASTRAN memory to scratch files, then using

the available space in the SSD disk and use the HDD disk for the rest of the scratch files. Because

the available SSD had a very limited capacity, for denser meshes, the solution time was not significantly

reduced but still presented advantages. As for the hardware in CfAR, it was found that an higher per-

centage of dedicated RAM reduced the simulation times, since the available RAM memory was higher.

Other performance parameters tested were the number of CPUs used, the NASTRAN words length

and the I/O blocks size (buffsize). Using more processors reduced the simulation times more significantly

in coarser meshes. In denser meshes it was verified that the slow I/O operations due to the use of the

HDD led to long times where the CPUs were below 10% of activity. The use of more than one processor

in one solution in a single machine is equivalent to SMP (Shared Memory Parallel) computing. Using

NASTRAN words of 4 bytes instead of 8 bytes reduced the simulation times when the same amount

of RAM was used in both cases. However, using 4 bytes only allows to allocate 8 GB of memory to

NASTRAN. In the case of the laptop which had less memory available, using 4 byte words along with

7.99 GB of dedicated memory allowed to reduce the simulation times. In the case of the computer in

CfAR, the increase of the words length to 8 bytes was compensated by the increase of dedicated RAM

memory to 16 GB which was possible due to the larger RAM available. Using the maximum value of

65537 words for the I/O blocks also reduced the simulation times. A small study on the influence of the

allocated RAM memory and words length on the simulation times is presented in Figure C.1. It can be

verified that while the laptop shows better performance with 7.99 GB of allocated RAM memory and 4

byte words, CfAR computer shows better performance with 16 GB of allocated RAM memory and 8 byte

words.

NX Siemens 10 includes the functionality of using the GPU (Graphics Processing Unit) to accelerate

the solution processes that use certain modules: DCMP and FRRD1. To obtain the natural frequencies,

only the DCMP module is used, in contact iterations. The functionality was tested and revealed that the

simulation times increased. This could be due to the fact that the DCMP module does not require a

significant time to be executed when compared to the overall simulation times and therefore, requesting

the GPU and initiating it in each iteration takes more time than the decrease in solution time. Another

plausible reason is that the GPU impact would be most significant for sparse matrices with maximum

front size larger than 30 K [52], which does not happen in the FEM models simulated in this work (this

94

(a) Laptop (b) CfAR computer

Figure C.1: Influence of the allocated RAM memory to NX NASTRAN solver in the simulation times

value can be verified in the .f04 file).

Other possibility taken into account was the use of RDMODES (Recursive Domain Normal Modes

Analysis) which allows to obtain less accurate solutions but faster by partitioning the eigenvalue problem

and distributing each segment by the different processors [53]. This method is an alternative to the

Lanczos method and is indicated to achieve good performance for very large problems. In the present

problem, it led to the increase of the solution time and therefore was not used.

C.2 NX SPACE SYSTEMS THERMAL

This solver has less flexibility than NX NASTRAN. The only parameter that was allowed to be tested

in the performance was the number of CPUs. It was concluded that the more CPUs used, the faster

the solution is, since this solver demands almost 100% of CPU activity while computing the view factors

along the satellite’s orbit. On the other hand, the memory demanded is negligible. Since only the number

of CPUs could be changed, the computer in CfAR showed a much better performance in solving these

thermal analysis.

DMP computing would bring many advantages since the number of CPUs would increase with the

increase of nodes added to the solution, but the license used did not support that functionality and would

have to be upgraded. In the case of thermal simulations, this feature would be a great improvement. As

mentioned in this work, it was not possible to show convergence of the results and the chosen mesh was

one of the coarsest meshes simulated. With the increase of the number of processors used, it would

be possible to reduce significantly the simulation times. When comparing the simulation times using 4

processors (laptop) and 8 processors (CfAR), it was verified the time needed using 4 processors was

almost the double of the needed time using 8 processors. An alternative to use DMP would be to simply

increase the number of processors in the computer. The results of the study of the influence of the

number of CPUs used in the simulation times is shown in Figure C.2. It can be seen that when more

than half of the maximum number of processors is selected, the decrease in simulation times is lower (it

95

is more noticeable in CfAR PC case). This is due to the fact that although there are n processors, the

physical cores are onlyn

2. This means that each core is capable of running two threads and the gain in

running two threads in each core is lower than using two cores to run one thread each. In Figure C.2,

Figure C.2: Influence of the number of CPUs used in the simulation times

the simulation times presented were measured at 10%, 50% and 100% of processing 1 orbital request.

To simulate a whole orbit, 17 orbital requests must be processed. This means that the decrease in

simulation times is even greater that what is represented in the figure.

One feature to take into account in the thermal simulations is that if in different simulations the mesh

used and simulated orbit is the same, the results from one of the simulations can be used as a starting

point to the other, by activating the ”Restart” option in the solution properties. For example, if different

materials, different thermo-optical properties, different thermal loads or a different solar heat flux are to

be simulated, the module that computes the view factors can use the results from a previous simulation,

decreasing significantly the simulation times, since this module is the one that takes the longer time to

be computed. However, one can’t take advantage of this feature when adding components to the mesh

or when changing the number of elements in the mesh. If the ”Restart” option is enabled, it is advised to

use a single processor, because it does not bring any advantages to use multiple processors when the

view factors are not computed.

A list of the parameters used for each solver is presented in Table C.1.

96

NX NASTRAN NX SPACE SYSTEMS THERMAL

CfAR PC Laptop CfAR PC Laptop

Memory 16 GB 7.99 GB - -

Scratch Memory 8 GB 4 GB - -

Number of CPUs 8 4 8 4

Word Size 8 4 - -

I/O Block Size 65537 65537 - -

Table C.1: Solver parameters to optimize their performance

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