Dynamic Analysis of Sinusoidal, Random and Shock Vibration according to Launch Environment for Small Spacecraft Development to Asteroid 2016-HO3

IN

DEGREE PROJECT

ENGINEERING PHYSICS,

SECOND CYCLE, 30 CREDITS

,

STOCKHOLM SWEDEN 2019

Dynamic Analysis of Sinusoidal,

Random and Shock Vibration

according to Launch Environment

for Small Spacecraft Development

to Asteroid 2016-H03

AKHSANTO ANANDITO

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ENGINEERING SCIENCES

TRITA -SCI-GRU 2019:002

i

Master Thesis

Dynamic Analysis of Sinusoidal, Random and Shock

Vibration according to Launch Environment for Small

Spacecraft Development to Asteroid 2016-HO3

Author:

Supervisor

Akhsanto Anandito

Mats Åbom

Industry Supervisor

Peter Rathsman

Examiner

Stefan Hällström

A thesis submitted in fulfillment of the requirements

for the degree of Master of Science

in the

Department of Aeronautical and Vehicle Engineering

School of Engineering Sciences

TRITA-SCI-GRU 2019:002

ISSN 1651-7660

ii

Abstract

The investment of space commerce is skyrocketing and it is predicted to be a nascent business in the future. The spacecraft demand has been growing not only for NASA and other space agency’s mission but also collaboration business between small space industries, academia, and scientific community. This glimpse brought an interest to a new investor, government, military, and manufacturing company to deliver their objectives efficiently. Nowadays, many startups compete embracing innovation and pioneering the novelty of space project beyond prodigious vision in an unprecedented way. Many players foresee that decreasing size of the rocket is an important key to survive and succeed in the space business. One of the efficient acts is lowering the launch cost. This can be achieved by designing a small size, lightweight and affordable spacecraft. Within this context, a Beyond Atlas Spacecraft which will be sent to Asteroid 2016-HO3, has achieved a wet mass of 20.85 kg with the size of 24.7 x 42.2 x 40.8 cm in stowed mode and 84 x 399 x 40.8 cm in unstowed mode. However, the drawback being light and small may lead to catastrophic failure due to resonance frequency events. According to past experience, the gyro of the Swedish national satellite was damaged during ground testing and it was suspected due to high amplification when the natural frequency coincides to the main structure resonance. Therefore, this work is focusing on a spacecraft development and a non-destructive structural analysis. The coupled-load analysis of a preliminary spacecraft design including sinusoidal, random vibration and shock analysis are calculated using FEM. This effort can reduce the risk of component destruction before laboratory testing as well as understand better the dynamic behavior of the spacecraft. The critical frequency in each orthogonal axis with base input from launch environment of the LM-3A Launch Vehicle was devised. The maximum stress, amplitude, and acceleration in accordance of qualification test criteria were evaluated and discussed.

iii

Sammanfattning

Investeringen av rymdhandeln är skyrocketing och det förväntas bli en växande verksamhet i framtiden. Efterfrågan på rymdfarkoster har ökat inte bara för NASA och andra rymdorganisationens uppdrag utan även samarbete mellan små rymdindustrier, akademin och det vetenskapliga samfundet. Denna glimt väckte intresse för en ny investerare, regering, militär och tillverkningsföretag för att effektivt kunna leverera sina mål. Idag konkurrerar många startups om att omfatta innovation och banbrytande rymdprojektets nyhet bortom en fördärvad vision på ett aldrig tidigare skådat sätt. Många spelare förutser att minskad storlek på raketen är en viktig nyckel för att överleva och lyckas i rymdverksamheten. En av de effektiva handlingarna sänker lanseringskostnaden. Detta kan uppnås genom att utforma en liten storlek, lätt och prisvärd rymdfarkost. Inom detta sammanhang har en Beyond Atlas Spacecraft som skickas till Asteroid 2016-HO3, uppnått en våt massa på 20,85 kg med storleken 24,7 x 42,2 x 40,8 cm i stuvningsläge och 84 x 399 x 40,8 cm i ostoppat läge. Nackdelen som är ljus och liten kan emellertid leda till katastrofalt fel på grund av resonansfrekvenshändelser. Enligt tidigare erfarenhet skadades gyroen i den svenska nationella satelliten under marktestning och det misstänktes på grund av hög förstärkning när den naturliga frekvensen sammanföll med huvudstrukturen resonans. Därför fokuserar detta arbete på rymdskeppsutveckling och en icke-destruktiv strukturanalys. Den kombinerade belastningsanalysen av en preliminär rymdfarkostkonstruktion inklusive sinusformad, slumpvibration och chockanalys beräknas med användning av FEM. Denna insats kan minska risken för komponent förstörelse före laboratorietestning samt förstå bättre rymdskeppets dynamiska beteende. Den kritiska frekvensen i varje ortogonal axel med basinmatning från startmiljön för LM-3A-startkärlet utformades. Den maximala spänningen, amplituden och accelerationen i enlighet med kvalifikationstestkriterierna utvärderades och diskuterades.

iv

Acknowledgement

I would like to thank Beyond Atlas AB and OHB Sweden for allowing me to take a big leap towards my passion by giving an opportunity to work on a degree project. The atmosphere of concurrent engineering work has been amazing and giving me an insight on how to overcome a problem efficiently in a multidisciplinary project with senior engineers of OHB Sweden and Swedish Space Corporation (SSC). Besides experiencing the dynamics of space industry, I have also treasured a valuable lesson about the forward driven attitude to escalate the career in the space industry and academic research. The project has never been started without a short discussion with Project Manager of MIST satellite, Sven Grahn and supervision from CTO OHB Sweden, Peter Rathsman. An important key to the success of this work is learning the space career of each individual who involved in this project, especially from the inspirational Swedish Astronaut, Christer Fuglesang. I also want to thank Professor of Sounds Vibration, Mats Åbom for managing access of high-speed computer for the simulation, assessing my degree’s project work and suggestion of tailoring this writing within business perspectives accordingly. The dream team as well as supportive colleagues, Per-Erik Atterwall (Chairman), Robin Lilja (Satellite Engineer), Krister Sjölander (System Engineer), Robin Larsson (Attitude Orbit Control System), Petrus Hyvönen (System Communication) and Milan Battelino (Mission Analysis), thank you for involving me as the mechanical engineer in this adventurous journey of Swedish Space industry.

This works could have never been done without partner an international collaboration in European Space Industries: OHB Sweden, Swedish Space Corporation, KTH, Swedish Institute of Space Physics (IRF), AÅC Microtec, ENPULSION, and DHV Technology.

Last but not least, thank you for everyone out there who always been my inspiration to pursue career in space technology and beyond. This project has left a great motivation to not afraid facing more difficult challenge and to write more scientific writing for a greater purpose.

Stockholm, 2019 Akhsanto Anandito

v

Table of Contents

Abstract ... ii

Table of Contents ... v

List of Figures ... vii

List of Tables ... viii

List of Abreviations ... ix

Introduction ... 1

1.1

New Space Age ... 1

1.2

Literature review and history of spacecraft for Asteroid Mission ... 2

1.3

Beyond Atlas to 2016-HO3 ... 2

1.4

Load in Launch Vehicle ... 3

1.5

The objective of thesis work ... 3

Theory and Method... 4

2.1

Spacecraft Development ... 4

2.2

Structural Verification ... 4

2.3

Launch Requirement ... 5

2.4

Static and Dynamic Loads ... 5

2.4.1

Static ... 6

2.4.2

Modal ... 6

2.4.3

Sinusoidal ... 7

2.4.4

Random vibration ... 8

2.4.5

Shock level ... 11

Model and Idealization ... 12

3.1

Spacecraft design ... 12

3.1.1

Platform solid aluminum panel ... 14

3.1.2

Spacecraft Component ... 14

Calculation Setup ... 17

4.1

Static ... 17

4.2

Modal ... 17

4.3

Sinusoidal ... 17

4.4

Random vibration ... 18

4.5

Shock ... 19

vi

Simulation Results ... 20

5.1

Static Analysis ... 20

5.2

Dynamic Analysis ... 21

5.2.1

Modal ... 21

5.2.2

Sinusoidal ... 22

5.2.3

Random Vibration ... 26

5.2.4

Shock ... 31

Conclusion ... 32

Appended Material ... 34

Bibliography ... 41

vii

List of Figures

Figure 1.1 Asteroid 2016-HO3 orbit [Credit: NASA JPL] (left) and mission analysis (right) .... 2

Figure 1.2 Illustration inside the fairing ... 3

Figure 2.1 Structural design cycle ... 5

Figure 3.1 Spacecraft design... 12

Figure 3.2 Spacecraft orientation (0,0,0) ... 12

Figure 3.3 Simplified FE setup (left) and component accommodation (right) ... 14

Figure 4.1 Fixed location 1-6 DOF ... 17

Figure 4.2 Sinusoidal vibration test specification with safety factor ... 18

Figure 4.3 Random vibration test specification ... 19

Figure 4.4 Shock spectrum (Q=10) ... 19

Figure 5.1 Maximum Von-Mises (left) and static deformation (right) in bottom panel ... 20

Figure 5.2 Effective mass & cumulative effective mass ratio directional (left) and rotational

(right) in 100 modes ... 21

Figure 5.3 Natural frequency on 1

st

_{- 4}

th

_{mode ... 22}

Figure 5.4 Sin response X-direction (0-100 Hz) ... 23

Figure 5.5 Sin response Y-direction (0-100 Hz) ... 23

Figure 5.6 Sin response Z-direction (0-100 Hz) ... 23

Figure 5.7 Random response X-direction (0-2000 Hz) ... 27

Figure 5.8 Random response Y-direction (0-2000 Hz) ... 27

Figure 5.9 Random response Z-direction (0-2000 Hz) ... 27

Figure 5.10 Maximum stress on shock simulation ... 31

Figure 5.11 Maximum displacement on shock simulation ... 31

Figure A-1 Logarithmic sin response X-direction ... 35

Figure A-2 Logarithmic sin response Y-direction ... 36

Figure A-3 Logarithmic sin response Z-direction ... 37

Figure A-4 Logarithmic random response X-direction ... 38

Figure A-5 Logarithmic random response Y-direction ... 39

viii

List of Tables

Table 2.1 Deliverable project plan ... 4

Table 2.2 Sine excitation at spacecraft base (Limit Loads) ... 8

Table 2.3 LM-3 qualification level ... 9

Table 2.4 C-100 Clamp band shock level ... 11

Table 3.1 Mass, coordinate and moment inertia of spacecraft component ... 13

Table 3.2 Structure and screw properties ... 14

Table 4.1 Sin input ... 17

Table 4.2 PSD input ... 18

Table 4.3 Shock input ... 19

Table 5.1 Static deformation, shear, principal and normal stress ... 20

Table 5.2 Participation factor and effective mass ... 21

Table 5.3 Equivalent stress on 1

st

_{- 4}

th

_{mode ... 22}

Table 5.4 Principle stress on 1

st

_{- 4}

th

_{mode ... 22}

Table 5.5 Shear stress on 1

st

_{- 4}

th

_{mode ... 22}

Table 5.6 Sin response in natural frequency X-direction ... 24

Table 5.7 Sine response in natural frequency Y-direction ... 25

Table 5.8 Sin response in natural frequency Z-direction ... 26

Table 5.9 PSD response of resonant frequency in X-direction ... 28

Table 5.10 PSD response of resonant frequency in Y-direction ... 29

Table 5.11 PSD response of resonant frequency in Z-direction ... 30

ix

List of Abreviations

ANTXN Antennae X Negative ANTXP Antennae X Positive

ASD Amplification Spectral Density B.LS Bracket Laser Range Finder B.RW Bracket Reaction Wheel B.ST1 Bracket Star Tracker 1 B.ST2 Bracket Star Tracker 2 BAT Battery package

CLA Coupled Load Analysis CNSA Chinese Space Agency EoM Equation of Motion EPS Electrical Power System ESA European Space Agency ISRU In-situ Resource Utilization IRF Institutet för Rymdfysik

JAXA Japanese Space Exploration Agency JEM Japanese Experiment Module J-SSOD JEM Small Satellite Orbital Deployer KTH Kungliga Tekniska Högskolan LEO Low Earth Orbit

LS Laser Range Finder MEO Middle Earth Orbit MTRPY Motor Positive Y MTRNY Motor Negative Y

NASA National Aeronautics Space Administration NEO Near Earth Orbit

OBC On Board Computer

TCM Telecommunication Combined Memory PA Payload

x

PDR Preliminary Design Review PPU Propulsion Unit

PSD Power Spectral Density SA Solar Array

SBIR Small Business Innovation Research SSC Swedish Space Corporation

ST1 Star Tracker 1 ST2 Star Tracker 2

STTR Small Business Technology Transfer SANY Solar Array Negative Y

SAPY Solar Array Positive Y SSPA Solid State Power Amplifier THS Thruster

TRANS Transponder RW Reaction Wheel

xi

Nomenclature

𝐷

Displacement spectrum in each of global cartesian directions and rotation

𝐸

Young’s modulus

𝑓

𝑚𝑎𝑥 Frequency maximum

𝑓

𝑚𝑖𝑛 Frequency minimum

𝐹𝑎 _{Applied load vector / enforced excitation}

𝐹𝑟 Reaction load vector

𝐺

Shear modulus (input

𝐺

𝑥𝑦)

𝐺

𝑗 Modal loads

𝑀

𝑒𝑓𝑓 Mass effective

𝑁 Number of element

𝑆

Slope

𝑆

𝑑𝑖 Response PSD dynamic part

𝑆

𝑠𝑖 Response PSD Pseudo-Static part

𝑆

𝑠𝑑𝑖 Response PSD Covariance part

𝑆

𝑝𝑖 Power spectral density for ith

𝑡 time

𝑢

𝑓 Free displacement

𝑢

𝑑 Dynamic displacement

𝑢

𝑠 Pseudo-static displacement

Q Amplification factor

𝜔

𝑖 Natural circular frequency at ith

𝛾

𝑖 Participation factor

𝜓

𝑖 the i Mode shape

𝜌 Density

Ω Input (imposed) circular frequency ω Output (natural) circular frequency 𝜃 Angle of displacement

xii

𝜁

Damping ratio [𝐴] Spectral acceleration [𝐶] Structural damping matrix

[

𝐶

𝑓𝑓 ] Structural damping fully correlated

[

𝐶

𝑓𝑟 ] Structural damping partially correlated

[

𝐶

𝑟𝑓 ] Structural damping partially correlated

[

𝐶

𝑟𝑟 ] Structural damping uncorrelated

{𝐹𝑎_{} Applied load vector / enforced excitation}

{𝐹𝑟_{} Reaction load vector}

[𝐾] Structural stiffness matrix [

𝐾

𝑓𝑓 ] Stiffness fully correlated

[

𝐾

𝑓𝑟 ] Stiffness partially correlated

[

𝐾

𝑟𝑓 ] Stiffness partially correlated

[

𝐾

𝑒] Element stiffness matrix

[𝑀] Structural mass matrix [

𝑀

𝑓𝑓 ] Mass fully correlated

[

𝑀

𝑓𝑟 ] Mass partially correlated

[

𝑀

𝑟𝑓 ] Mass partially correlated

[

𝑀

𝑟𝑟 ] Mass uncorrelated

{𝑢̈} Nodal acceleration vector {𝑢̇} Nodal velocity vector {𝑢} Nodal displacement vector {

𝜙

}𝑖 Eigenvectors

{Γ} Modal participation factor {

𝑢

𝑓} Free displacement

{

𝑢

𝑠} pseudo-static displacement

1

Chapter I

Introduction

1.1 New Space Age

The space age is an era encompassing the activities of space exploration influenced by different contemporary events. In late of 1950, the cold war between Russia and USA marked the rising of space technology. The space age is thought to have officially begun on October 4th, 1957, with the launch of Sputnik 1 by the Soviet Union – the first artificial satellite to be launched into orbit [25]. The sign of Space 1.0 is symbolized by an attempt of human into outer space and the first trial is achieved by Yuri Gagarin [26]. Afterward, a huge success of first landing to lunar surface Apollo 11 triggered an incredible growth in space activity. Another successful work followed by a collaboration of International Space Station inspires an interest towards space to the world. Started in the 21st _{century, the democratization of Space 2.0 arose when a few big private and small}

companies appeared on the space market for telecommunication and military business.

The space component requires an advanced technology. Its research and development are leveraged by an enormous budget and seemed impossible to achieve without involving governmental support. However, after the successful launch and automatic landing of reusable rocket Falcon 9 from a private company, SpaceX, the space business is becoming more optimistic followed by appearance of many startups. This event marks a revolution as Space 3.0. Several initiatives to bring space into business has been expanding globally, for instance, a program from ESA Business Incubator Centre [13], NASA solicitation proposal and SBIR/STTR (Small Business Innovation Research/Small Business Technology Transfer) [14-15]. As Space 3.0 remains, the giant business such as Mitsubishi enters a space business by giving a fund for lunar exploration [34]. These events may influence the interest of investors shifting into space technology.One of the most popular missions, the definite goal of sending human to Mars is a cornerstone to drive a new breakthrough technology and may become an investment market, such as creating a settlement on Mars, In-Situ resource utilization (ISRU), robotics, biotechnology, radiation protection and physiological studies of human who lived in other than Earth [8-9]. These ventures require innovation from broad scientific disciplines and indisputably enables a collaboration of multi-nations to work on space projects [10-11]. Then, the dawn of Space 4.0 is just begun. However, the industry has an obstacle to overcome because launch cost beyond LEO is still relatively expensive.

To generate high affordability, the mass of the spacecraft which proportional to the production cost, and launch budget, becomes an import key at the beginning of new space age. Nowadays, many businesses offer small spacecraft launch in different ways. Such as, JAXA offers a relatively affordable price or collaboration for a small scientific payload less than 50 kg from JEM Small Satellite Orbital Deployer (J-SSOD) “Kibo” Module in International Space Station [12]. A private company, Zero to Infinity, is targeting commercialization of cheap launch from helium balloon [16]. A sounding rocket company, Rocket Lab stated that “Rockets are shrinking because satellites are shrinking” [20]. These events infer that any object which sent to space is getting smaller within a time. So, a major transformation of space business is near to this age and it will be promising for a small spacecraft. Besides lowering the cost, a lighter spacecraft requires less energy for detumbling which is more efficient to perform a complex mission such as docking to refuel a satellite. Therefore,

2

for future space endeavor, the justification and critical thinking skill of an engineer in lowering weight and size of the robust small spacecraft are essential.

1.2 Literature review and history of spacecraft for Asteroid Mission

The asteroid mission is nowadays seen as an ordinary planetary exploration in near-Earth orbit. Within fast growing technology and mature spacecraft development approach, it may enable asteroid mining which eventually could transform into a space economy. The benefit of understanding its origin also helps an early stage protection initiative against asteroid strike.

The first spacecraft which made a comprehensive scientific measurement of asteroid composition was NEAR Shoemaker with wet-mass 805 kg (170 x 150 x 170 cm). The spacecraft was designed by John Hopkins University Applied Physics Laboratory (APL) NASA to study near-Earth asteroid Eros [2]. The only spacecraft orbiting to the asteroid belt, Dawn with 1,217 kg (164 x 1970 x 177 cm) studied the surface of Asteroid Vesta and Ceres [35]. Hayabusa 2 with 590 kg (160 x 200 x 125 cm) has landed in Asteroid Ryugu in June 2018 and will send the first sample return of C-type Asteroid in 2020 [36]. OSIRIS-REx with 2,110 kg (244 x 315 x 244 cm) arrived in Asteroid Bennu in December 2018 and detected the chemical signature of water [37]. The cooperation between NASA and JAXA for Hayabusa 2 and OSIRIS REx spacecraft is to reveal an evolution of materials of solar system. The record of heaviest spacecraft held by the ESA’s Rosetta with 3,000 kg to study Lutetia and 2867 Steins [38]. The lightest spacecraft record so far is PROCYON with 65 kg (150 x 150 x 55 cm) to investigate asteroid (185851) 2000-DP2017 [39-40]. Unfortunately, in the middle of mission, malfunction of the ion thruster occurred, and the contact with spacecraft lost after Earth flyby [17]. This event illustrates that the small spacecraft needs to be accounted with extra attention in the future mission.

1.3 Beyond Atlas to 2016-HO3

The aim of Beyond Atlas Project is to build a spacecraft to explore an asteroid 2016-HO3. This asteroid is suspected as a small near-Earth object (NEO) with no more than diameter of 100 meters. The unique fact of this asteroid is known as Earth's companion or quasi-satellite within 38 to 100 lunar distances from Earth as depicted in Figure 1.1

Figure 1.1 Asteroid 2016-HO3 orbit [Credit: NASA JPL] (left) and mission analysis (right) The spacecraft is expected to launch into MEO (Medium Earth Orbit) using electric propulsion in 2020. MEO is chosen because it is suited for a radiation perspective. The spectrometer inside the spacecraft will identify a mineral in the asteroid. However, the hard landing plan to the asteroid is not yet considered. The system and mission analysis were initiated by the individual space enthusiast from OHB Sweden, KTH, SSC and IRF.

3

1.4 Load in Launch Vehicle

Figure 1.2 Illustration inside the fairing

The spacecraft is sent as a payload in rocket vehicle of LM-3A. Illustrated in Figure 1.2, it is suspected that eight spacecrafts with the different mission will be aboard with Beyond Atlas Spacecraft. As many types of loads occur randomly during the launch phase, a resonance frequency each spacecraft must be addressed. In general, the load is divided into three types: Static/quasi-static loads, dynamic loads and mechanical vibration loads [3,21]. The primary issue is often difficult to predict due to the dynamic behavior of the excitation and structural response occurring in wide frequency range [3-4]. If the base excitation aggregates to system’s natural frequency when the external force from arbitrary direction connected to structure or base plane, it will lead to component overloading. During resonant vibration, the stress response may increase until the structure suffers buckling, yielding, fatigue, crack propagation and failure.

The vibration load can cause major or minor damage. The major damage is a highly catastrophic problem which can lead to mission failure during the launch phase. The minor is an undetected small breakage of the component but deteriorating. Therefore, all load circumstances in a series of the event should be investigated intensively to deliver the mission successfully.

In rocket flight, there are a series of events that must be considered. The flight environments that generate static and dynamic loads are specified as follows:

• The static acceleration generated by the different stages of the launch vehicle (quasi-static acceleration event)

• The low-frequency dynamic response (0-100 HZ)

• The high-frequency random vibration environment, impingement from Launch Vehicle to spacecraft/satellite/payload system in transient flight events (20-2000 Hz).

• The high-frequency acoustic pressure environment (20-8000 Hz) • Shock events (100 -10KHz)

1.5 The objective of thesis work

The aim of this project work is to assess and evaluate the spacecraft design compliance and give brief information by presenting in a single document with all relevant information about the dynamic load analysis. The expected output of this work: proper justification of all equipment and structure safety according to launch environment. Therefore, the mathematical calculation of coupled load analysis (CLA) document can be presented to launch contractor.

4

Chapter II

Theory and Method

2.1 Spacecraft Development

The structural design, analysis, and verification process are in accordance with the procedure given by OHB Sweden as well as referred to ESA ECSS E-32 "Structure". In this case, Beyond Atlas Spacecraft has reached in Phase B based on deliverable project scope in Table 2.1.

Table 2.1 Deliverable project plan

2.2 Structural Verification

The Preliminary Design Review (PDR) starts from spacecraft structure analysis. A flowchart of the methodology used to verify the structural design and analysis is depicted in Figure 2.1. In the space industry, the load analysis is known as Coupled Load Analysis (CLA). The limit load includes mass and size estimation. The mathematical analysis and proper justification of CLA shall be presented to launch provider before laboratory test.

5

Figure 2.1 Structural design cycle

2.3 Launch Requirement

The requirement is provided in launch vehicle user's manual [1]. During the PDR phase, the qualification and requirement were studied in accordance with the launch environment. The critical series of events which could lead to catastrophic failure shall be considered particularly in static and dynamic loads with the non-destructive method. The instances of possible failure include component going astray, engine failure and explosion during ignition.

The primary condition which shall be fulfilled to prevent the spacecraft dynamic coupling with corresponding the launch vehicle (LM-3A) includes:

• The recommended safety factor: 1.25.

• The structural natural frequency of the first-third mode > 20 Hz

2.4 Static and Dynamic Loads

The formula approach and its derivative are in accordance with ANSYS Documentation [33]. To model the condition from fundamental approach, the equation of motion for the linear structure as follows

[𝑀] {𝑢̈} + [𝐶] {𝑢̇} + [𝐾]{𝑢} = {𝐹𝑎_}

(2.1) where mass matrix [M], damping matrix [C], stiffness matrix [K], nodal acceleration vector {𝑢̈}, nodal velocity vector {𝑢̇}, nodal displacement vector {𝑢}, total applied load vector {𝐹𝑎}

6

2.4.1 Static

The static structural analysis is main requirement for all degrees of freedom (DOFs) and fixed constraints 1-6 DOF were set in separation interface. The equilibrium equation starts in form

[𝐾]{𝑢} = {𝐹𝑎_{} + {𝐹}𝑟_}

(2.2) where reaction load vector {𝐹𝑟}, and displacement {𝑢}. In this case, the load vectors are modeled in form of component weight or applied gravity.

For finite element, the equation becomes

[𝐾] = ∑ [𝐾𝑒] 𝑁

𝑚=1

(2.3)

where number of elements N and element stiffness matrix [𝐾𝑒].

2.4.2 Modal

Modal analysis is used to determine a structure's vibration characteristics. A component of the spacecraft can suffer a high amplification when its natural frequency coincides to another part in one boundary condition. To avoid this phenomenon, mapping the frequency envelope numerically can be a tool to account the dynamic behavior.

Eigenvalues and vectors

The structure stiffness matrix includes pre-stress effects from earth gravity force. To extract eigenvalue and eigenvector, the formulation of mode-frequency and buckling are

[𝑀]{𝑢̈} + [𝐾]{𝑢} = 0 (2.4) Assume harmonic motion

{𝑢} = {𝜙}𝑖sin(𝜔𝑖𝑡 + 𝜃𝑖) (2.5)

{𝑢̇} = 𝜔𝑖{𝜙}𝑖cos(𝜔𝑖𝑡 + 𝜃𝑖) (2.6)

{𝑢̈} = −𝜔𝑖2{𝜙}𝑖sin(𝜔𝑖𝑡 + 𝜃𝑖) (2.7)

where an angle of displacement 𝜃𝑖 , eigenvectors {𝜙}𝑖 and natural circular frequency at ith 𝜔𝑖.

(−𝜔𝑖2[𝑀] + [𝐾] {𝜙}𝑖) = {0} (2.8)

This equality is satisfied if either n eigenvectors {φ}i = {0} or if det ([K] - ω2 _{[M]) is zero. The}

first option is the trivial one and, therefore, is not of interest. The second one gives

|−𝜔𝑖2[𝑀] + det[𝐾]| = {0} (2.9)

Equation 2.9 is an eigenvalue problem which may be solved for up to n eigenvalues 𝜔𝑖2, and n

eigenvectors, {𝜙}𝑖, which satisfies Equation 2.8, where n is the number of DOF.

Mode Shape

7

{𝜙𝑖𝑇}[𝑀]{𝜙}𝑖= 1 (2.10)

Natural Frequency

Natural frequencies fi then can be calculated in (cycles/s) as

𝑓𝑖=

𝜔𝑖

2𝜋 (2.11)

Participation Factor

The participation factors for base excitation are calculated by

𝛾𝑖 = {𝜙}𝑖𝑇 [𝑀] {𝐷} (2.12)

where D is assumed unit displacement spectrum in each of global cartesian directions and rotation about each of these axes. This measures the amount of mass contributing in each direction for each mode. The ratio is simply another list of participation and normalized to the largest.

Effective Mass

The effective mass can be written as 𝑀𝑒𝑓𝑓= 𝛾2 [𝜙]_𝑖𝑇_[𝑀]{𝜙} 𝑖= 𝛾𝑖 2 if {𝜙}𝑖𝑇[𝑀]{𝜙}𝑖= 1 (2.13)

Ideally, the sum of the effective masses in each direction should equal the total of structure’s mass and this depends on the number of modes extracted [29]. The ratio of effective mass to total mass can be useful for determining an adequate number of modes extracted.

2.4.3 Sinusoidal

Sinusoidal (harmonic) or sine vibration usually occurs during the ignition, shutdown, transonic flight and stage separation [1]. To withstand loads that vary sinusoidally (harmonically) at different cycle and phase, detecting resonant response and avoid it are necessary.

Considering the equation of motion, assume [F] and {u} are harmonic with input (imposed) circular frequency Ω {𝐷} = {𝐹𝑚𝑎𝑥 𝑒𝑖𝜓}𝑒𝑖Ω𝑡 (2.14) = {𝐹𝑚𝑎𝑥(cos 𝜓 + 𝑖 sin 𝜓)}𝑒𝑖Ω𝑡 = {{𝐹1} + 𝑖{𝐹2}}𝑒𝑖𝜓𝑡 {𝑢} = {𝑢𝑚𝑎𝑥 𝑒𝑖𝜓}𝑒𝑖Ω𝑡 (2.15) = {𝑢𝑚𝑎𝑥(cos 𝜓 + 𝑖 sin 𝜓)}𝑒𝑖Ω𝑡 = {{𝑢1} + 𝑖{𝑢2}}𝑒𝑖Ω𝑡

where mode shape 𝜓, take two-time derivatives

{𝑢} = ({𝑢1} + 𝑖{𝑢2})𝑒𝑖Ω𝑡 (2.16)

{𝑢̇} = 𝑖Ω({𝑢1} + 𝑖{𝑢2})𝑒𝑖Ω𝑡 (2.17)

{𝑢̈} = −Ω2_({𝑢

1} + 𝑖{𝑢2})𝑒𝑖Ω𝑡 (2.18)

8

(−Ω2_{[𝑀] + 𝑖Ω[𝐶] + [𝐾])({𝑢}

1} + 𝑖{𝑢2}) = ({𝐹1} + 𝑖{𝐹2}) (2.19)

Sinusoidal Level

Table 2.2 Sine excitation at spacecraft base (Limit Loads)

Frequency [Hz]

Test Load

Acceptance

Qualification

Longitudinal

5-8

3.11 mm

4.66 mm

8-20

0.8 g

1.2 g

20-100

3.0 g

4.5 g

Lateral

5-8

2.33 mm

3.50 mm

8-20

0.6 g

0.9 g

20-100

2.0 g

3.0 g

Sweep Rate

4 oct/min

2 oct/min

The limit load is shown in Table 2.2. To determine the sinusoidal input within frequency 0-100Hz, the acceleration excitation is modeled as

𝑎𝑓𝑟𝑒𝑓= 𝛿𝑞𝑢𝑎𝑙𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 1000 × (2𝜋 × 𝑓𝑟𝑒𝑓)2 𝑔 (2.20) where g standard is 9.82 m/s2_{, 𝑓}

𝑟𝑒𝑓 (upper and lower bound frequency) is obtained from limit

loads Table 2.2 (for this case only 5 Hz and 8 Hz).

2.4.4 Random vibration

The random vibration is transmitted internally into the rocket, mechanically causing everything on board to vibrate. It may be dangerous for the thin section and a light component such as solar arrays [19]. Random vibration is highly repetitive and non-periodic complex vibration caused by an imbalance situation [18]. Random vibration can be represented in the frequency domain with a Fourier transform or power spectral density function [18].

Power Spectral Density

Power spectral density (PSD) is a statistical measure defined as the limiting mean-square value of a random variable. It is used in random vibration analyses in which the instantaneous magnitudes of the response can be specified only by probability distribution functions that show the probability of the magnitude taking a value. This analysis technique calculates only the steady-state forced vibrations of a structure. By inputting PSD value, each mode is calculated from eigenvector results by using the term of "Mode coefficient" [27] that can be written as 𝐴𝑖= 𝛾𝑖 𝜔𝑖2 (𝑆𝑝𝑖𝜔 ( 𝜋 4𝜁− 1) + ∫ 𝑆𝑝𝑑𝜔 𝜔_𝑖 0 ) 1 2 (2.21)

Where damping ratio 𝜁, participation factor 𝛾𝑖 (Equation 2.12), Power Spectral density for ith

9

PSD Input

The random vibration specification LM-3 for the PSD input is described in Table 2.3. Table 2.3 LM-3 qualification level

Frequency [Hz] 150 800 ASD / PSD [g2_{/Hz] 0.11 0.11}

The xoctaves band from frequencies fupper and flower at 20 Hz and 2000 Hz is given by

𝑥 in octave = 2_{log (}𝑓𝑢𝑝𝑝𝑒𝑟 𝑓𝑙𝑜𝑤𝑒𝑟)

(2.22) The PSD at 20 Hz and 2000 Hz are given by

𝑃𝑆𝐷20 𝐻𝑧=

𝑃𝑆𝐷𝑢𝑝𝑝𝑒𝑟

10𝑥g/10

(2.23) 𝑃𝑆𝐷2000 𝐻𝑧= 𝑃𝑆𝐷𝑙𝑜𝑤𝑒𝑟 10𝑥g/10 (2.24)

where gain

g is the ratio of the amplitude of the system response to the input signal.

The N in dB at 20 Hz and 2000 Hz can be written as

𝑁 in dB = 10 log (𝑃𝑆𝐷𝑢𝑝𝑝𝑒𝑟

𝑃𝑆𝐷_{𝑙𝑜𝑤𝑒𝑟}) (2.25)

The Slope is given by

S in dB/octave = 𝑁

𝑥 (2.26)

The area for 20-150Hz, 150-800 Hz and 800-2000 Hz are calculated by A𝑟𝑒𝑎 = 10 log (2) (𝑃𝑆𝐷𝑢𝑝𝑝𝑒𝑟 10 log(2)+𝑆)(𝑓𝑢𝑝𝑝𝑒𝑟 - 𝑓𝑙𝑜𝑤𝑒𝑟 𝑓𝑢𝑝𝑝𝑒𝑟 𝑓_{𝑙𝑜𝑤𝑒𝑟} 𝑆 10 log (2)) (2.27) 𝑔𝑅𝑀𝑆 for qualification = √∑ 𝐴𝑟𝑒𝑎 (2.28)

Random input

The random inputs can be full correlated, uncorrelated or partially correlated. The procedure of calculation is based on computing statistic approach response and combining between them. So, the complete equation of motions is segregated into free and DOF as

[[𝑀𝑓𝑓] [𝑀𝑓𝑟] [𝑀𝑟𝑓] [𝑀𝑟𝑟]] { {𝑢̈𝑓} {𝑢̈𝑟} } + [[𝐶𝑓𝑓] [𝐶𝑓𝑟] [𝐶𝑟𝑓] [𝐶𝑟𝑟]] { {𝑢̇𝑓} {𝑢̇𝑟} } + [[𝐾𝑓𝑓] [𝐾𝑓𝑟] [𝐾𝑟𝑓] [𝐾𝑟𝑟]] { {𝑢𝑓} {𝑢𝑟} } = {{𝐹} {0}} (2.29) Where 𝑢𝑓 (free DOF), 𝑢𝑟 (restrained) and {𝐹} is nodal force excitation activated by a non-zero

value. The free displacements can be devised into pseudo-static and dynamic as

{𝑢𝑓} = {𝑢𝑠} + {𝑢𝑑} (2.30)

10

{𝑢𝑠} = −[𝐾𝑓𝑓] −1 [𝐾𝑓𝑟]{𝑢𝑟} = [𝐴]{𝑢𝑟} (2.31) for [𝐴] = −[𝐾𝑓𝑓] −1

[𝐾𝑓𝑟] where spectral acceleration [𝐴]. Substituting those Equations with

assumption light damping into EoM

[𝑀𝑓𝑓]{𝑢̈𝑑} + [𝐶𝑓𝑓]{𝑢̇𝑑} + [𝐾𝑓𝑓]{𝑢𝑑} = {𝐹} + ([𝑀𝑓𝑓][𝐴] + [𝑀𝑓𝑟]){𝑢̈𝑟} (2.32)

The term on the right-hand side represents the equivalent forces due to excitations. Then, the modal loads 𝐺𝑗 (j=1,2,3...n) are defined by

𝐺𝑗 = {Γ𝑗}𝑇 {𝑢̈𝑟} + 𝛾𝑗 (2.33)

Further theory and reference can be found at Manual ANSYS Documentation set Chapter 17.7.10: Random Vibration Method [33].

Mean Square Response

The mean square response of the 𝑖𝑡ℎfree displacement is 𝜎𝑓𝑖2 = _{∫ 𝑆} 𝑑𝑖(𝜔)𝑑𝜔 + ∞ 0 ∫ 𝑆𝑠𝑖(𝜔)𝑑𝜔 + ∞ 0 2| ∫ 𝑆𝑠𝑑𝑖(𝜔)𝑑𝜔| ∞ 0 (2.34) 𝜎𝑑𝑖2 + 𝜎𝑠𝑖2+ 2𝐶𝑣(𝑈𝑠𝑖 𝑈𝑑𝑖)

where the closed-form solutions for linear PSD in log scale are utilized each integration [23,24] as 𝜎𝑑𝑖2 = ∑ ∑ 𝜙𝑖𝑗𝜙𝑗𝑘𝑄𝑗𝑘 𝑛 𝑘=1 𝑛 𝑗=1 (2.35) 𝜎𝑠𝑖2 = ∑ ∑ 𝐴𝑖𝜚𝐴𝑖𝑚𝑄̅𝜚𝑚 𝑟2 𝑚=1 𝑟2 𝜚=1 (2.36) 𝜎𝑠𝑑𝑖2 = ∑ ∑ 𝜙𝑖𝑗𝐴𝑗𝜚𝑄̇𝑗𝜚 𝑟2 𝜚=1 𝑛 𝑗=1 (2.37)

Finally, the equivalent stress mean-square response [22] can be computed as 𝜎̇𝑑𝑖2 = ∑ ∑ 𝜓𝑜𝑗𝐴𝜓𝑖𝑘𝑄𝑗𝑘 𝑛 𝑘=1 𝑛 𝑗=1 (2.38)

The GRMS can be computed as

𝐺𝑅𝑀𝑆= √ 1 𝑁∑ 𝑥𝑖 2 𝑁 𝑖=1 (2.39)

11

2.4.5 Shock level

The idea is inputting the shock level in boundary condition then review the maximum displacement and equivalent stress. To determine the shock input, N is given by

𝑁 in dB = 𝑆𝑅𝑆(Q=10)𝑥 (2.40)

Where Q is dynamic amplification factor which has been assumed for the generation of the SRS and 𝑆𝑅𝑆(Q=10) (dB/octave) is obtained from clamp band (separation system) shock level in

Table 2.3. The xoctaves band from frequencies fupper and flower can be calculated by Equation

2.22.

Table 2.4 C-100 Clamp band shock level

Frequency [Hz]

SRS (Q=10)

100-1000

9.0 dB/octave

1000-5000

4000 g

To determine shock input into shock simulation, an acceleration input at 100 Hz is calculated by

𝑎100 𝐻𝑧=

𝑎𝑢𝑝𝑝𝑒𝑟

10𝑥/20 (2.41)

The equation for displacement response for each mode shape ith _{𝜙}

𝑖 can be computed by

{𝑅}𝑖= 𝐴𝑖{𝜙}𝑖 (2.42)

12

Chapter III

Model and Idealization

3.1 Spacecraft design

In the early stages, the project begins with a component/instrument identification. The suitable components and scientific payload are decided based on objectives. The main instrument includes propulsion module, solar array, reaction wheel, gyro, star trackers, laser range finder, EPS, battery, TCM, OBC, EPXs, SSPA, and transponder. The components which constitute stiffness and mass inside the spacecraft are depicted as follows in Figure 3.1 and listed in Table 3.3.

Figure 3.1 Spacecraft design

The considered origin axis [0,0,0] of spacecraft aligning to solar panel axis is depicted in Figure 3.5. The spacecraft was drawn by a parametric function depending on the location of all components and its connection. Once whole parts are attached to the structure with an appropriate integration in assembly process, the size minimization is considered and can be adjusted based on requirement.

13

Table 3.1 Mass, coordinate and moment inertia of spacecraft component

No Equipment Mass (kg)

Center of Gravity (mm) Principal Mass Moment Intertia from CoG (Kg.mm2) X Y Z I_xx Iyy Izz 1 Panel XP 0.311 114.349 2.113 -24.534 3960.667 2252.939 1711.413 2 Panel XN 0.32 -114.208 1.313 -21.94 4012.93 2243.017 1773.579 3 Panel YP 0.298 0 114.248 -22.037 2217.109 3699.018 1485.415 4 Panel YN 0.316 0.784 -114.381 -25.841 2325.521 3879.971 1558.277 5 Panel ZN 0.389 -2.823 2.503 -159.847 1858.648 1920.05 3770.755 6 Reaction Wheel 1.1 66.2 -45 40 1267.789 1365.65 269.813 7 Star Tracker 1 0.1 60.094 79.073 43.389 71.706 29.037 71.542 8 Star Tracker 2 0.1 -66.573 -45.911 -108.094 71.706 29.037 71.542 9 EPS 0.5 -92 0 39 8.333 8.333 8.333 10 Laser Range 0.033 -95.338 70.51 -50.696 4.233 6.894 9.063 11 OBC 0.13 -49.91 -103.99 -93.61 124.019 258.155 144.831 12 TCM 0.13 -49.91 -86.76 -93.61 124.09 258.507 145.124 13 Payload 0.95 -37.675 53.716 -108.819 2356.266 2368.939 2214.016 14 Battery 1.068 -49.5 0 21.5 2922.362 680.55 2602.103 15 Transponder 1.3 49.141 17.315 -89.805 4477.067 2402.526 3013.315 16 SSPA 1.1 97.006 17.001 -90.747 3724.792 1653.635 2236.687 17 Propulsion unit 8 0 0 171.3 47835.194 47835.194 76791.214 18 EPX 1 0.035 87.42 -92.19 -62.43 4.012 7.151 4.125 19 EPX 2 0.035 87.42 -105.4 -62.43 4.013 7.152 4.126 20 EPX 3 0.035 87.42 -92.19 -102.05 4.014 7.153 4.127 21 EPX 4 0.035 87.42 -105.4 -102.05 4.015 7.154 4.128 22 Motor PY 0.395 0 51.05 0 254.472 29.24 254.547 23 Motor NY 0.395 0 -51.05 0 254.472 29.24 254.547 24 Bracket RW 0.018 109.85 -44.333 40.529 51.842 26.054 25.843 25 Bracket ST1 0.029 85.349 79.309 43.298 31.485 26.347 25.958 26 Bracket ST2 0.028 -66.5 -46 -132.016 22.995 23.511 30 27 Bracket Ls 0.062 -84.017 69.629 -40.556 19.595 24.561 28.945 28 SA YP 1.519 -1.866 165.613 1.442 12289.923 16585.926 5835.704 29 SA YN 1.519 -1.866 -165.613 1.442 12289.923 16585.926 5835.704 30 AnT Xp 0.3 121.75 0 -38 3250 2250.625 1000.625 31 AnT Xn 0.3 -121.75 0 -38 3250 2250.625 1000.625 Total 20.85 4.361 0.648 47.171

14

3.1.1 Platform solid aluminum panel

The structure platform side panels (MX, MY, PX, PY) and bottom panel (MZ) 24 x 24 x 42.4 cm are assigned with the material of machined Aluminium 6082-T6 - the thickness of 1 mm and with rib thickness of 2 mmThe structure and screw properties are shown in Table 3.2.

Table 3.2 Structure and screw properties

Material AA-7075-T6 SS-304 Screw Unit

Density 2800 9640 Kg/m3

Modulus Elasticity E1 71.7 193 GPa

Shear Modulus in plane G12 26.9 81 GPa

Poisson’s ratio, v 0.33 0.28

-Yield Strength 380 262 MPa

Ultimate tensile strength 460 505 MPa

Allowed stress 328 - MPa

Safety factor desired 1.4 -

-3.1.2 Spacecraft Component

For simplification, all components were modeled as a cube connected to concentrated mass. To simulate parts of the structure not explicitly modeled, the components are represented as a concentrated mass in Figure 3.3. The inertia values and center gravity of masses used in the analysis can be found in Table 3.1. Considering the boundary condition, the panels were connected by beam Rigid Body Element (RBE2) represented as screw M4 ranging length from 10-26 mm and all contact regions were assumed as frictionless.

Figure 3.3 Simplified FE setup (left) and component accommodation (right)

Reaction Wheel

The three-axis integrated micro flywheel generates the reaction torque by adding and decelerating the wheel body to control satellite posture precisely. Micro flywheel components

15

include digital control circuit, drive motor, wheel, and cable (100 x 116 x 115 mm). It has design life for more than 1 year. The maximum level of sine vibration is 10g and random is 14.33grms.

Star Tracker

The star tracker consists of a sensor with refractive optic, focal length 25 mm and baffle (32 x 32 x 90 mm). Star tracker 1 is pointing in X+ direction and Star tracker 2 is pointing to Z-. The exclusive angle is 35 deg towards the sun and 250 _{towards Earth. It supports an}

autonomous attitude determination, nominal attitude tracking, and photographic function. It has a design life of 3 years, environmental tolerance 13g for sine and 13.5 grms for random vibration.

Laser Range Finder

The Laser range finder consists of apertures, mounting and electrical data interface (44 x 33.5 x 50 mm). It operates at the “eye-safe” wavelength of 1.55 μm and is not visible to night vision equipment. It has environmental tolerance of 1500g for shock vibration.

OBC and TCM

The OBC and TCM consist of PCB and aluminium casing (each 90 x 95 x 17 mm). These have environmental tolerance sin 15g (21-60 Hz), sin 6g (65-100 Hz), 0.05 g2/Hz (100-300 Hz) 5.3 grms and 200g for a shock. These have sensitivity against resonant frequency below 100 Hz.

Payload

The payload consists of spectral imager, regular camera and spectrometers (100 x 100 x 110 mm). It performs asteroid capture imaging with wavelength range 500-900 nm and spectral resolution 5-15 nm.

Battery

The battery box is a Li-ion cell for electrical power storage (165 x 75 x 45 mm). It supplies an amount of electric power to instruments. It consists of a graphite-based anode and lithium cobalt oxide-based cathode.

Transponder and SSPA

Transponder (Transceiver) consists of a band-limiting, communication device, oscillator and power amplifier (180 x 130 x 66 mm). It converts the frequency of the signal received and transmitted through antenna. SSPA (Solid State Power Amplifier) is attached in the transponder. These two devices have acceptance of environmental tolerance sine 10g (15-100Hz), 10.13 grms, 1.25 g2/Hz (100-600 Hz) and 1200g for shock test.

Propulsion Unit

The propulsion unit is using Field Emission Electric Propulsion (FEEP) and chemical thruster containing indium (240 x 240 x 119 mm). It propels to perform orbit changes and provides highly accurate thrust ranging from 10 – 1500 μN.

16

EPX

EPX is antenna switch device which capable of handling low to medium radio frequency power (41 x 34 x 13.2 mm). There are four EPX attached and one component consists of solder terminals and female connectors. It has acceptance criteria sine tolerance of 10g, 10 grms for random vibration and 500 g for shock vibration.

Motor

The Motor (stepper motor) is an actuator device to activate the releasing system for solar panel (102 x 26 x 26 mm). The nominal power consumption has been calculated taking into consideration a rotated angle of 180 degrees and a rotational speed of 1.333 rpm.

Antennae

The antenna (X-Band patch array) consists of rectangular transmission and reception patch (200 x 300 x 3.5 mm). The patch array antenna has a high gain of 24 dBi for X-band.

EPS (Electrical Power System)

The EPS consists of a PCB power board and casing (210 x 110 x 40 mm). It supports power management system for all electrical equipment in the spacecraft, which includes the electrical propulsion unit, solar deployer mechanism, reaction wheel, payload, TTC and star tracker.

Solar Panel

The one panel for one side has a dimension of 0.33 x 0.214 x 0.0011 m. The solar array has eight panels connected between two kinds of hinges and the deployment mechanism is activated by motor stepper rotation. With deployed solar panel and antennae, the dimension of the spacecraft becomes 24 × 400 × 42.4 cm.

17

Chapter IV

Calculation Setup

4.1 Static

For static loads conditions, the applied forces are defined by standard gravity parameter (9.82 m/s2_{) to each solid element and concentrated mass. The constraint X, Y, and Z}

direction were defined at triangular separation interface where located at the edge of the bottom panel towards Z- the direction in Figure 4.1.

Figure 4.1 Fixed location 1-6 DOF

4.2 Modal

For dynamic loading conditions, the material behavior must be treated as linear. The pre-stress load output from the static analysis is used to calculate natural frequencies and mode shapes. For this case, the damping is assumed zero and set of natural frequency is ranging between 1-100 modes.

4.3 Sinusoidal

The idea is to calculate the structure's response in steady state (frequency domain) with forced vibrations (sine input) of at 0-100 Hz and obtain a graph of some g response. Once "Peak" responses are identified on the graph, the acceleration (g) is then reviewed at those specific frequencies. The results of conversion from displacement into acceleration (g) were obtained after performing the calculation of Equation 2.20. Given the distance of the lowest peak to the highest peak at qualification level 4.66 mm between 5-8Hz, the acceleration input can be defined in Table 4.1 and Figure 4.2.

Table 4.1 Sin input

Frequency [Hz] 5 8 8 20 100

Acceptance Longitudinal [g] 0.313 0.800 0.8 3.0 3.0 Lateral [g] 0.234 0.599 0.6 2.0 2.0

Qualification Longitudinal [g] 0.468 1.199 1.2 4.5 4.5 Lateral [g] 0.352 0.901 0.9 3.0 3.0

18

Figure 4.2 Sinusoidal vibration test specification with a safety factor

For this project, a focus is narrowed to qualification level in longitudinal directional excitation.

4.4 Random vibration

Given the qualification criteria of PSD/ASD for 150 Hz and 800 Hz is 0.11 g2/Hz, the PSD input from Equation 2.21 is shown in Table 4.2 and Figure 4.3. The idea is reviewing acceleration in the peak response, GRMS each component and 3σ-RMS stress of the screws with the frequency domain between 0-2000 Hz. The gain

of +6 dB at 20-150 Hz and -3 dB

at 700-2000 Hz are obtained from ECSS [3].

Table 4.2 PSD input Gain [dB] 20 150 800 2000 ASD / PSD [g2/Hz] 0.002 0.11 0.11 0.05 Octaves * 2.91 2.42 1.32 dB * 17.44 0.00 -3.97 Slope [dB/Octave] * 6.00 0.00 -3.00 Area * 5.62 73.13 82.60 Total [gRMS] 12.70 0,1 1 10 1 10 100 A cc e le ration [ g] Frequency [Hz]

Acceptance Longitudinal Acceptance Lateral Qualification Longitudinal Qualification Lateral

19

Figure 4.3 Random vibration test specification

4.5 Shock

Given the separation clamp shock levels; the slope reference between 100Hz and 1000Hz is 9 dB/Oct, the shock envelope can be defined in Table 4.3 and Figure 4.4. The SRS at 100 Hz was calculated using Equation 2.40-2.41. The SRS at 1000 Hz and 5000 Hz were obtained from environmental test standard [1].

Table 4.3 Shock input

Figure 4.4 Shock spectrum (Q=10) 0.000 0.000 0.000 0.001 20 200 2000 PS D [g 2/H z] Frequency [Hz]

LM-3 Qualification level Equipment Qualification Test Level LM-3 Acceptance level Equipment Acceptance Test Level

10 100 1000 10000 100 1000 10000 SR S ( Q= 10) [g ] Frequency [Hz] Qualification Level +6 dB -6 dB Frequency [Hz] 100 1000 5000 SRS (Q=10) [g] 127.995 4000 4000

20

Chapter V

Simulation Results

The mesh geometry (618,070 elements) was modeled with tetra 2 mm and 0.5 mm in zone interest. To increase the results accuracy, the mesh was preserved in the zone interest where the maximum stress occurs. The zone interest is in the ribs around the payload connection and separation interface. The calculation was solved using ANSYS 18.0 and post-processed by MATLAB.

5.1 Static Analysis

For static analysis, the Equivalent Stress (Von-misses), Normal stress and Shear stress results were far off from criterion of yield strength, ultimate shear and compressive stress of AA-7075. These maximum/minimum values are an indicator of zone interest where the sizing or optimization may be considered.

Table 5.1 Static deformation, shear, principal and normal stress Equivalent Stress Total Deformation Deformation X Deformation Y Deformation Z Minimum 4.3e-004 MPa 0. mm -0.013 mm -0.008 mm -0.123 mm Maximum 29.356 MPa 0.182 mm 0.022 mm 0.138 mm 0.003 mm Shear Stress

Principal

Stress Normal X Normal Y Normal Z Minimum 2.4e-004 MPa -9.699 MPa -19.309 MPa -22.421 MPa -17.596 MPa Maximum 14.892 MPa 8.245 MPa 8.238 MPa 6.388 MPa 7.755 MPa The small deformation in Figure 5.1 shows that all joints and B.C were correctly defined. This condition must be fulfilled because the pre-stress load results are used as an input of dynamic response calculation. The highest stress of 29.356 MPa occurred at rib around separation interface indicates no plastic deformation.

21

5.2 Dynamic Analysis

5.2.1 Modal

Frequency domain of modal simulation results in X, Y, and Z direction were a plot in Figure 5.2-5.3 and Table 5.2 - 5.5.

Figure 5.2 Effective mass & cumulative effective mass ratio directional (left) and rotational (right) in 100 modes

Table 5.2 Participation factor and effective mass

Recalling a rule Equation 2.13, by comparing the cumulative extracted effective mass to real mass (93.3 - 99.7%) illustrates that 100 modes are adequate for this simulation. The high value in directional/rotational axis indicates the mode will be excited in that axis. From Table 5.2, the first and second highest participation factor in Y-direction is on first mode (20.291 Hz) while X-direction is on second mode (21.874 Hz). The first mode is slightly close to frequency limit requirement (>20Hz).

X Y Z RX RY RZ X Y Z RX RY RZ

1 20.291 1.21E-02 0.117 -0.0279 -16.4 1.74 0.354 1.47E-04 0.0138 7.77E-04 268 3.01 0.126 2 21.874 0.115 -1.13E-02 8.96E-04 2.02 15.4 -0.451 0.0132 1.27E-04 8.04E-07 4.06 236 0.204 3 42.990 2.38E-02 -5.51E-03 2.59E-04 -1.46 2.13 -7.98 5.69E-04 3.04E-05 6.69E-08 2.14 4.53 63.6 4 43.012 -9.76E-03 7.24E-03 8.08E-03 0.614 -2.19 4.87 9.53E-05 5.24E-05 6.53E-05 0.377 4.78 23.8 5 43.676 2.31E-03 1.33E-02 2.36E-02 0.769 -0.543 0.409 5.34E-06 1.76E-04 5.56E-04 0.591 0.295 0.167 6 47.563 5.27E-03 -6.94E-03 -1.45E-02 -6.51E-02 -1.6 1.24 2.77E-05 4.82E-05 2.10E-04 4.23E-03 2.57 1.54 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 100 1648.100 -0.0025 0.0045 0.0018 0.7260 0.2360 0.2380 6.35E-06 2.02E-05 3.12E-06 5.27E-01 5.56E-02 5.64E-02

0.01945 0.02027 0.02052 Sum Participation Factor Frequency (Hz) Mode

Effective Mass (tonne)

(to n n e) (to n n e)

22

Figure 5.3 Natural frequency on 1st _{- 4}th _mode

From Figure 5.3, the deflection is decreasing within the mode and largest one occurs in the second mode. In Table 5.3 – 5.5, the Von-mises, principal stress and shear stress from 1st _{mode to forth}

exceeded the yield limit of the material.

Table 5.3 Equivalent stress on 1st _{- 4}th _mode

Equivalent Stress Mode 1 Equivalent Stress Mode 2 Equivalent Stress Mode 3 Equivalent Stress Mode 4 Maximum 855,29 MPa 2524,3 MPa 4074 MPa 2630,9 MPa Minimum 0,030 MPa 0,015 MPa 0,096 MPa 0,041 MPa

Table 5.4 Principle stress on 1st _{- 4}th _mode

Principal Stress Mode 1 Principal Stress Mode 2 Principal Stress Mode 3 Principal Stress Mode 4 Maximum 429,32 MPa 2980,1 MPa 5008,6 MPa 3314,1 MPa Minimum -271,94 MPa -687,53 MPa -1007,2 MPa -603,21 MPa

Table 5.5 Shear stress on 1st _{- 4}th _mode

Shear Stress Mode 1 Shear Stress Mode 2 Shear Stress Mode 3 Shear Stress Mode 4 Maximum 433,92 MPa 1400,1 MPa 2264,6 MPa 1460,8 MPa Minimum 0,015 MPa 0,008 MPa 0,051 MPa 0,024 MPa

5.2.2 Sinusoidal

Frequency domain simulation results of sine vibration X, Y, and Z direction were plot in Figure 5.4 – 5.6 and Table 5.6 – 5.8.

23

Figure 5.4 Sin response X-direction (0-100 Hz)

Figure 5.5 Sin response Y-direction (0-100 Hz)

24

Table 5.6 Sin response in natural frequency X-direction

Sin response in g amplification tells which component that contribute the most to overall structural response during the high peak in resonant frequency. The sin response was reviewed to avoid high amplification event in resonant frequency.

From Table 5.6, many amplification events occurred at 85 Hz. The response exceeded the criteria for reaction wheel, star tracker 1 at 85 Hz and 98 Hz. The response of OBC, TCM, EPXs, Motors surpassed the limit criteria at 85 Hz. Stepper motor has the highest amplification of 101.33G at frequency 85 Hz. 44 47 60 64 79 85 98 Limit Equipment Mass (kg) 1 Reaction Wheel 1.1 0.74 4.07 2.03 2.98 7.37 34.80 17.76 10 2 Star Tracker 1 0.1 0.12 1.35 0.52 2.31 0.07 37.24 11.02 13 3 Star Tracker 2 0.1 0.03 0.16 0.32 1.21 2.06 5.03 1.577 13 4 EPS 0.5 0.03 2.34 0.83 0.72 0.40 5.08 4.037 -5 Laser 0.033 0.42 1.34 0.71 1.19 1.82 25.92 2.633 -6 OBC 0.13 0.22 0.31 0.91 1.37 1.59 15.20 1.461 6 7 TCM 0.13 8.05 0.73 1.20 2.98 2.22 12.35 1.655 6 8 Payload 0.95 0.02 0.24 0.11 4.31 56.33 8.72 0.663 -9 Battery 1.068 0.02 2.05 0.65 0.53 0.30 6.27 3.993 -10 Transponder 1.3 0.14 0.94 0.11 1.16 0.85 7.39 7.758 10 11 SSPA 1.1 0.14 0.94 0.10 1.15 0.84 7.24 7.679 10 12 Thruster 8 0.43 0.39 2.16 0.54 0.86 7.15 0.68 13 SA PY 1.519 0.93 0.75 14.80 2.23 0.92 4.00 0.862 -14 SA NY 1.519 0.48 0.02 9.50 6.79 0.82 10.51 2.492 -15 EPX1 0.035 0.34 0.77 1.21 4.37 1.02 18.37 1.347 10 16 EPX2 0.035 0.28 0.20 1.17 1.11 0.77 22.55 1.735 10 17 EPX3 0.035 0.20 1.08 0.94 3.09 0.97 10.51 0.596 10 18 EPX4 0.035 0.17 0.36 0.78 0.84 0.34 13.47 0.98 10 19 Motor PY 0.395 1.33 1.50 12.96 6.12 8.21 101.33 0.478 -20 Motor NY 0.395 1.40 0.44 13.78 4.74 6.65 89.80 4.127 -21 Bracket RW 0.018 0.74 4.11 2.03 3.01 7.42 34.80 17.86 -22 Bracket ST1 0.029 0.11 1.33 0.52 2.30 0.10 37.45 10.92 -23 Bracket ST2 0.028 0.02 0.08 0.17 0.64 1.08 2.68 0.832 -24 Bracket LS 0.062 0.40 1.51 0.72 1.18 1.99 28.16 2.781 -25 ANT XP 0.3 0.69 15.92 0.27 9.10 2.16 12.24 4.243 -26 ANT XN 0.3 10.20 2.93 0.63 6.45 1.37 8.05 2.452 -10.20 15.92 14.80 9.10 56.33 101.33 17.86 13.00 0.02 0.02 0.07 0.07 0.07 0.48 0.48 6.00 G Amplification (9,8 m/s2) No Frequency Resonance (Hz) Maximum Minimum

25

Table 5.7 Sine response in natural frequency Y-direction

From Table 5, many amplification events occurred at 64, 78 and 85 Hz. The response of reaction wheel, OBC, TCM, SSPA, and Transponder exceeded the criteria at 78 and 85 Hz. The response for star tracker 1 exceeded the criteria at 98 Hz. The first and second highest response occurred in EPS and Antenna X negative directional at 85 Hz.

43 47 51 58 64 78 85 98 Limit Equipment Mass (kg) 1 Reaction Wheel 1.1 3.02 2.31 1.84 0.64 1.73 21.94 28.98 8.57 10 2 Star Tracker 1 0.1 3.13 3.46 3.38 1.28 4.26 1.64 5.51 21.02 13 3 Star Tracker 2 0.1 0.09 0.09 0.01 0.06 0.58 0.95 3.06 0.89 13 4 EPS 0.5 2.54 2.04 2.69 0.59 5.2 10.71 58.57 3.38 -5 Laser 0.033 1.63 1.27 2.17 0.35 0.07 6.97 48.27 3.51 -6 OBC 0.13 0.51 0.55 4.14 2.75 11.94 6.13 7.43 0.79 6 7 TCM 0.13 0.51 0.55 4.14 2.75 11.94 6.13 7.43 0.79 6 8 Payload 0.95 0.05 0.1 0.19 0.14 2.57 3.87 3.56 0.79 -9 Battery 1.068 2.72 2.2 2.57 0.68 5.06 14.18 35.51 4.06 -10 Transponder 1.3 1.74 0.2 1.38 0.1 1.68 13.27 23.78 9.41 10 11 SSPA 1.1 1.53 0.74 1.33 0.26 2.04 14.59 31.33 6.24 10 12 Thruster 8 0.09 1.07 1.15 0.22 4.07 9.86 22.86 1.15 13 SA PY 1.519 0 1.22 11.94 3.84 30.31 20.61 33.57 4.82 -14 SA NY 1.519 0.33 10.11 2.65 6.98 34.59 29.18 35.71 0.73 -15 EPX1 0.035 1.57 1.84 2.61 2.8 9.23 5.16 7.21 0.95 10 16 EPX2 0.035 1.57 1.84 2.61 2.8 9.23 5.16 7.21 0.95 10 17 EPX3 0.035 0.96 0.67 1.93 1.76 5.84 2.37 4.79 0.72 10 18 EPX4 0.035 0.96 0.67 1.93 1.76 5.84 2.37 4.79 0.72 10 19 Motor PY 0.395 0.09 0.75 11.33 3.59 27.65 18.27 27.35 4.15 -20 Motor NY 0.395 0.37 9.25 2.78 6.57 31.63 25.92 29.59 0.77 -21 Bracket RW 0.018 2.65 0.83 2.23 0.14 3.32 17.76 39.49 2.13 -22 Bracket ST1 0.029 2.9 1.5 2.86 0.63 3.92 7.28 16.02 12.55 -23 Bracket ST2 0.028 0.05 0.05 0.01 0.03 0.32 0.48 1.72 0.48 -24 Bracket LS 0.062 1.8 1.19 2.42 0.27 0.57 8.02 46.12 4.15 -25 ANT XP 0.3 1.92 0.96 1.73 0.2 0.05 15.61 34.8 4.55 -26 ANT XN 0.3 1.65 1.55 2.01 0.51 0.89 6.51 56.02 2.75 -3.13 10.11 11.94 6.98 34.59 29.18 58.57 21.02 13.00 0.00 0.05 0.01 0.03 0.05 0.48 1.72 0.48 6.00 Maximum Minimum G Amplification (9,8 m/s2) No Frequency Resonance (Hz)

26

Table 5.8 Sin response in natural frequency Z-direction

From Table 5, many amplification events occurred at 64, 78, 80 and 85 Hz. The response of the reaction wheel and Transponder exceeded the criteria at 64, 78, 80 and 85 Hz. The response of star tracker 1 and SSPA surpassed the criteria at 64, 78 and 85 Hz. The response of OBC and TCM have surpassed the criteria at 85 Hz. The highest amplification of 42.86G occurred in star tracker 1 at 85 Hz.

5.2.3 Random Vibration

Frequency domain simulation results of random vibration and GRMS each component X, Y, and Z direction were plot in Figure 5.7 – 5.9 and Table 5.9 - 5.12.

47 51 64 78 80 85 98 Limit Equipment Mass (kg) 1 Reaction Wheel 1.1 2.12 0.49 12.86 22.55 12.86 16.22 1.86 10 2 Star Tracker 1 0.1 1.83 1.06 18.27 15.1 8.83 42.86 1.44 13 3 Star Tracker 2 0.1 0.15 0.03 0.85 1.18 0.68 3.28 1.08 13 4 EPS 0.5 1.03 0.49 11.53 8.76 4.82 21.53 8.26 -5 Laser 0.033 0.59 1.01 15 7.09 4.91 4.82 7.83 -6 OBC 0.13 0.16 0.64 2.13 3.42 1.87 8.74 0.94 6 7 TCM 0.13 0.19 1.75 5.63 5.34 2.54 6.09 0.72 6 8 Payload 0.95 0.17 0.12 2.43 4.2 0.07 2.8 0.65 -9 Battery 1.068 1.74 0.69 11.94 9.15 5.02 24.49 8.14 -10 Transponder 1.3 1.71 0.92 15.61 18.78 10.71 38.57 9.11 10 11 SSPA 1.1 1.35 0.67 14.59 17.04 9.68 33.57 4.07 10 12 Thruster 8 0.95 0.45 11.63 10.15 5.71 19.9 3.06 13 SA PY 1.519 23.47 6.22 10.51 15.51 7.94 30.1 6.07 -14 SA NY 1.519 17.24 11.53 1.83 5.44 1.84 7.66 0.15 -15 EPX1 0.035 1.05 0.07 1.02 0.78 1.19 22.65 1.76 10 16 EPX2 0.035 0.4 0.02 0.19 2.08 1.73 22.14 1.68 10 17 EPX3 0.035 0.39 0.76 1.89 0.6 1.14 22.24 1.74 10 18 EPX4 0.035 0.17 0.27 0.13 2.05 1.72 21.84 1.67 10 19 Motor PY 0.395 21.02 8.49 33.27 14.49 9.11 25.51 7.6 -20 Motor NY 0.395 17.96 11.84 1.29 5.89 2.12 7 0.04 -21 Bracket RW 0.018 1.19 0.16 11.84 17.76 9.83 28.27 2.95 -22 Bracket ST1 0.029 1.61 1.04 17.65 15.2 8.92 38.88 1.38 -23 Bracket ST2 0.028 0.15 0.03 0.85 1.18 0.68 3.28 1.08 -24 Bracket LS 0.062 0.78 1.03 14.9 7.56 5.25 2.14 7.71 -25 ANT XP 0.3 0.05 0.66 12.86 16.22 9.19 30.1 2.83 -26 ANT XN 0.3 0.88 0.46 10.71 8.29 4.6 19.29 8.05 -23.47 11.84 33.27 22.55 12.86 42.86 9.11 13.00 0.05 0.02 0.13 0.60 0.07 2.14 0.04 6.00 Frequency Resonance (Hz) G Amplification (9,8 m/s2) Maximum Minimum No

27

Figure 5.7 Random response X-direction (0-2000 Hz)

Figure 5.8 Random response Y-direction (0-2000 Hz)

28

Table 5.9 PSD response of resonant frequency in X-direction

PSD response results illustrate what excitation frequencies contribute the most to overall structural response. The random response was reviewed to avoid high amplification event in resonant frequency.

In Table 5.9, the GRMS for reaction wheel, star trackers, OBC, TCM, transponder, SSPA, and EPXs exceeded the limit criteria. The highest and lowest grms did occur in EPX 3 and thruster. The response for OBC and TCM surpassed the maximum limit PSD criteria. The highest PSD response of 6.05e-1 G2_{/Hz occurred in EPX 1 at 479.9 Hz.}

78.82 335.1 479.9 513.28 657.7 706.9 Limit Equipment Mass (kg) GRMS (G) Limit (G)

1 Reaction Wheel 1.1 13.15 14.33 5.04E+00 4.45E-01 2.74E-01 1.11E+00 1.88E-04 2.14E-02 -2 Star Tracker 1 0.1 18.13 13.50 1.46E-02 3.89E-01 6.86E-01 6.25E+00 4.23E-02 8.95E-02 -3 Star Tracker 2 0.1 41.03 13.50 1.14E-01 2.65E+01 1.22E-02 1.80E+01 1.65E-01 4.35E-01 -4 EPS 0.5 8.61 - 9.29E-03 3.71E-02 2.82E-01 8.25E-01 2.63E-02 5.82E-01 -5 Laser 0.033 32.12 - 3.45E-01 4.24E-01 1.58E+01 6.28E+00 2.23E-01 5.56E-01 -6 OBC 0.13 15.76 5.30 2.68E-01 1.17E-03 1.31E-01 2.49E+00 1.25E-01 7.33E+00 5.00E-02 7 TCM 0.13 42.72 5.30 5.33E-01 9.29E-02 1.03E+00 2.95E+01 9.97E-01 5.11E+01 5.00E-02 8 Payload 0.95 9.65 - 4.70E+01 4.00E-02 3.20E-05 1.96E-04 1.21E-05 3.80E-04 -9 Battery 1.068 8.81 - 5.58E-03 2.35E-02 2.74E-01 8.86E-01 3.39E-03 3.07E-02 -10 Transponder 1.3 8.54 10.13 4.86E-02 4.45E-01 7.16E-04 5.74E-03 4.06E-05 5.70E-03 1.25E+00 11 SSPA 1.1 8.60 10.13 4.69E-02 4.33E-01 1.02E-03 1.11E-02 1.67E-05 4.05E-03 1.25E+00 12 Thruster 8 2.69 - 7.97E-02 3.13E-04 4.62E-03 8.23E-02 5.16E-04 1.08E-02 -13 SA PY 1.519 5.62 - 7.67E-02 1.42E-02 1.40E-02 1.05E-01 5.40E-04 2.13E-02 -14 SA NY 1.519 6.27 - 6.63E-02 8.78E-02 3.04E-03 3.97E-02 1.79E-02 2.11E-01 -15 EPX1 0.035 47.28 10.00 1.36E-01 5.64E-02 6.05E+01 2.64E+01 1.24E+01 9.68E+00 -16 EPX2 0.035 18.07 10.00 6.12E-02 7.62E-03 8.10E+00 2.00E+00 1.43E+00 3.18E+00 -17 EPX3 0.035 52.51 10.00 1.15E-01 4.41E-02 1.15E+01 1.28E+01 5.45E+01 3.28E+01 -18 EPX4 0.035 19.27 10.00 1.23E-02 1.15E-03 1.64E+00 9.58E-01 7.97E+00 2.87E+00 -19 Motor PY 0.395 17.11 - 7.02E+00 4.03E-02 1.65E-01 1.86E+00 5.83E-02 1.41E-01 -20 Motor NY 0.395 17.31 - 4.59E+00 4.07E-01 5.25E-03 7.99E-02 3.16E-02 1.28E+00 -21 Bracket RW 0.018 13.09 - 5.12E+00 4.35E-01 2.64E-01 1.03E+00 1.77E-04 2.07E-02 -22 Bracket ST1 0.029 18.06 - 1.65E-02 3.83E-01 6.75E-01 6.15E+00 4.22E-02 9.05E-02 -23 Bracket ST2 0.028 21.99 - 3.17E-02 7.39E+00 3.55E-03 5.16E+00 4.54E-02 1.53E-01 -24 Bracket LS 0.062 31.86 - 4.09E-01 1.99E-01 9.15E+00 5.84E+00 1.07E+00 1.54E+00 -25 ANT XP 0.3 4.47 - 3.12E-01 1.14E-02 1.13E-03 4.20E-02 5.11E-04 3.40E-02 -26 ANT XN 0.3 3.51 - 1.71E-01 6.84E-02 5.42E-04 1.94E-02 5.17E-04 2.51E-02

-52.51 14.33 4.70E+01 2.65E+01 6.05E+01 2.95E+01 5.45E+01 5.11E+01 1.25E+00 2.69 5.30 0.005584 0.000313 3.2E-05 0.000196 1.21E-05 0.00038 0.05 Frequency Resonance (Hz) Response PSD (G2/Hz) Maximum Minimum No

29

Table 5.10 PSD response of resonant frequency in Y-direction

In Table 5.10, the GRMS for star trackers, OBC, TCM, and EPXs exceeded the limit criteria. The highest and lowest did occur in EPX3-4 and thruster. The response for OBC and TCM surpassed the maximum limit PSD criteria. The highest PSD response of 4.41e+1 G2_{/Hz occurred in OBC}

and TCM at 707 Hz.

64.4 263.7 335.1 513.3 659 707 Limit Equipment Mass (kg) GRMS (G) Limit (G)

1 Reaction Wheel 1.1 12.06 14.33 1.78E-01 9.35E-02 2.33E-01 3.26E-01 3.34E-03 2.07E-02 -2 Star Tracker 1 0.1 29.43 13.50 6.40E-01 4.26E-01 2.45E+00 2.10E+01 9.84E-02 9.80E-01 -3 Star Tracker 2 0.1 27.34 13.50 9.33E-03 4.85E-02 3.56E+01 6.44E+00 2.32E-02 3.07E-01 -4 EPS 0.5 11.88 - 1.01E+00 2.34E-03 3.83E-03 7.75E-02 9.41E-02 5.55E-01 -5 Laser 0.033 20.83 - 1.36E-02 6.97E-02 6.70E+00 3.47E-01 1.07E-01 3.42E-01 -6 OBC 0.13 42.48 5.30 4.31E+00 2.14E-03 1.04E+00 3.22E+01 7.70E-01 4.41E+01 5.00E-02 7 TCM 0.13 42.48 5.30 4.31E+00 2.14E-03 1.04E+00 3.22E+01 7.70E-01 4.41E+01 5.00E-02 8 Payload 0.95 15.10 - 2.01E-01 4.91E-02 1.19E+01 9.60E-03 2.45E-03 2.80E-03 -9 Battery 1.068 11.33 - 9.53E-01 5.27E-03 5.64E-02 4.27E-01 4.63E-02 1.61E-02 -10 Transponder 1.3 10.19 10.13 6.95E-02 1.81E-02 2.64E-01 5.81E-02 2.23E-04 2.70E-02 1.25E+00 11 SSPA 1.1 9.68 10.13 1.06E-01 6.43E-03 3.27E-01 1.36E-01 3.77E-03 7.97E-03 1.25E+00 12 Thruster 8 4.68 - 6.45E-01 1.39E-04 2.42E-03 4.40E-03 4.98E-05 5.03E-05 -13 SA PY 1.519 10.42 - 2.98E+01 4.12E-04 1.04E-02 9.38E-02 4.71E-03 2.16E-01 -14 SA NY 1.519 14.01 - 3.81E+01 1.52E-02 2.18E-02 7.51E-01 4.17E-02 1.21E+00 -15 EPX1 0.035 35.06 10.00 2.77E+00 3.40E+01 1.35E+00 6.93E-01 1.44E+01 1.05E+01 -16 EPX2 0.035 35.06 10.00 2.77E+00 3.40E+01 1.35E+00 6.93E-01 1.44E+01 1.05E+01 -17 EPX3 0.035 44.03 10.00 1.10E+00 1.93E+01 8.76E-01 1.71E+01 1.92E+01 3.09E+01 -18 EPX4 0.035 44.03 10.00 1.10E+00 1.93E+01 8.76E-01 1.71E+01 1.92E+01 3.09E+01 -19 Motor PY 0.395 10.96 - 2.47E+01 2.11E-05 7.26E-05 1.10E-01 3.69E-02 9.08E-01 -20 Motor NY 0.395 14.02 - 3.18E+01 5.00E-04 1.51E-04 4.09E-01 3.81E-02 8.03E-01 -21 Bracket RW 0.018 9.04 - 4.45E-01 2.13E-03 4.04E-03 1.28E-01 4.93E-05 1.33E-03 -22 Bracket ST1 0.029 18.22 - 5.68E-01 1.40E-01 7.80E-01 7.70E+00 2.33E-02 2.19E-01 -23 Bracket ST2 0.028 14.44 - 2.89E-03 1.33E-02 9.68E+00 1.83E+00 6.99E-03 8.87E-02 -24 Bracket LS 0.062 26.76 - 3.37E-02 8.21E-02 6.83E+00 1.38E-01 1.81E-01 6.27E-01 -25 ANT XP 0.3 16.83 - 1.25E-02 5.77E-03 3.60E-01 2.60E-01 2.80E-02 5.87E+00 -26 ANT XN 0.3 19.39 - 5.85E-02 3.49E-02 3.21E+00 3.49E-01 1.49E+00 1.70E-01

-44.03 14.33 3.81E+01 3.40E+01 3.56E+01 3.22E+01 1.92E+01 4.41E+01 1.25E+00 4.68 5.30 0.002886 2.11E-05 7.26E-05 0.004401 4.93E-05 5.03E-05 0.05 Maximum

Minimum No

Frequency Resonance (Hz)