Final report Conception of nano-satellites in a …fueglist/pdfs/AndreasFueglistaler_MSc.pdf · 3. Contents I Record of ... [R4]Werner Koehldorfer, Finite-Elemente-Methoden mit CATIA

Date: July 31, 2009Issue: 1 Rev: 2Page: 1 of 123

Prepared by:

Andreas Fuglistaler

Checked by:

Dr. Maurice BorgeaudDr. Anton Ivanov

Approved by:

EPFLLausanne

July 31, 2009

Final report

Conception of nano-satellitesin a concurrent

design environment

Abstract

This master thesis project was performed at the Spacer Center EPFL during the 2009 springsemester. A structure subsystem for nano and microsatellites was established and six satelliteswere designed: one 1UCubeSat, three 3UCubeSats, one cubic and one octagonal microsatellite.Based on SwissCube, a parametrized 1UCubeSat model was designed using CATIA and imple-mented in Concurrent Design Facility (CDF). This subsystem was extended to three 3UCubeSatmodels and two microsatellite models. The CATIA models were simplified using monoblockframes and one part representations of the battery and the payload.

The structure subsystem for each satellite design consists in a CDF interface, where the pa-rameters are defined, and two CATIA assemblies. The first CATIA assembly is a 3D represen-tation of the satellite - including mechanical representation of the structure elements and theother subsystems. It is used to calculate the satellite’s main properties: its mass, volume, centerof gravity and matrix of inertia. The second CATIA assembly is used for FEM analyses, sev-eral 3D parts have been replaced by 2D or 1D parts. Four types of FEM analyses were done:static loads, modal analysis, harmonic dynamic response and transient dynamic response. TheFEM results were verified by varying mesh sizes and comparing the 1UCubeSat’s results withSwissCube. The calculations reproduce the SwissCube results. All other satellite designs arecompatible with existing launch vehicles.

Chapter I

Record of revisions

ISS/REV Date Modifications Created/modified by1/0 May 30, 2009 Initial Issue Andreas Fuglistaler1/1 July 22, 2009 Everything Andreas Fuglistaler1/2 July 31, 2009 Finalizing Andreas Fuglistaler

3

Contents

I Record of revisions 3

II References 8II.1 Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8II.2 Informative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

III Terms, definitions and abbreviated terms 9

1 Master thesis project description 10

2 Introduction 122.1 CDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Small Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 CubeSat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.2 Microsatellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.3 Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Approach 163.1 CDF interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 CAD model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.1 Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2.2 Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3 FEM Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3.1 FEM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3.2 Standard tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3.3 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 CDF interface design 194.1 Structure interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.1.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.1.2 Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.1.3 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.1.4 Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.1.5 Launch vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2 Data Exchange Macro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2.1 Exchange structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.2.2 Parameter creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2.3 Parameter synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4


5 Structure design 275.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2 Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.2.1 Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.2.2 Panesl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.2.3 Spacers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.2.4 Payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.2.5 PCB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.2.6 Motherboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.2.7 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.2.8 Inertial wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.3 Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.3.1 Part placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.3.2 1UCubeSat, SwissCube design . . . . . . . . . . . . . . . . . . . . . . . . . 325.3.3 Stretched 3UCubeSat design . . . . . . . . . . . . . . . . . . . . . . . . . . 365.3.4 Circular 3UCubeSat design . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.3.5 Layer 3UCubeSat design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.3.6 Cubic microsatellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.3.7 Octagonal microsatellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.3.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6 FEM Analysis 546.1 Launch vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.1.1 VEGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.1.2 PSLV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.1.3 SOYUZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.1.4 DNEPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.2 FEM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.2.1 Shell and Beam elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586.2.2 Meshing decision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.2.3 Additional mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.2.4 Design selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.3 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.3.1 Tedrahedral compared to 2D / 1D . . . . . . . . . . . . . . . . . . . . . . . 626.3.2 Independence of mesh size . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.3.3 Comparison with SwissCube results . . . . . . . . . . . . . . . . . . . . . . 63

6.4 Static load analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.4.1 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.5 Modal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.5.1 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.6 Harmonic dynamic response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.7 Transient dynamic response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

7 Summary 797.1 CDF interface design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.2 Structure design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.3 FEM analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

8 Conclusions 82


A User Manual 83A.1 Using an existing design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

A.1.1 Interface description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83A.1.2 Changing parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84A.1.3 Changing parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

A.2 Creating a new satellite design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

B Technical details 90B.1 1UCubeSat, SwissCube design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

B.1.1 Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90B.1.2 Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91B.1.3 Spacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94B.1.4 Payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94B.1.5 PCB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95B.1.6 Motherboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96B.1.7 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

B.2 3UCubeSat, stretched SwissCube design . . . . . . . . . . . . . . . . . . . . . . . . 98B.2.1 Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98B.2.2 Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101B.2.3 Spacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101B.2.4 Payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101B.2.5 PCB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101B.2.6 Motherboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102B.2.7 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

B.3 3UCubeSat, circular SwissCube design . . . . . . . . . . . . . . . . . . . . . . . . . 102B.3.1 Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102B.3.2 Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105B.3.3 Spacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105B.3.4 Payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105B.3.5 PCB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105B.3.6 Motherboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106B.3.7 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

B.4 3UCubeSat, layer PCB design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106B.4.1 Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106B.4.2 Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107B.4.3 Spacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109B.4.4 Payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109B.4.5 PCB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109B.4.6 Motherboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109B.4.7 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

B.5 Microsatellite, cubic design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110B.5.1 Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110B.5.2 Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111B.5.3 Spacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111B.5.4 Payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112B.5.5 PCB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112B.5.6 Motherboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113B.5.7 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113B.5.8 Wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

B.6 Microsatellite, octagonal design, Frame Parameters . . . . . . . . . . . . . . . . . 114B.6.1 Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114B.6.2 Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117


B.6.3 Spacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117B.6.4 Payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117B.6.5 PCB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117B.6.6 Motherboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118B.6.7 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118B.6.8 Wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

C Dynamic response 120C.1 Harmonic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120C.2 Transient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Chapter II

References

II.1 Normative references

[N1] A.Diana, J.Benjamin, G.Rothlisberger, [Swisscube]Phase A, Structure and ConfigurationEPFL, 2006

[N2] G.Rothlisberger, Phase B, SwissCube structural design and flight sysetm configurationEPFL, 2007

[N3] B. Bratschi, Phase B, SwissCube Satellite FEAETHZ, 2007

II.2 Informative references

[R1] Johannes Gogolok, VBA-Programmierung mit ExcelFernUniversitat Hagen , 1999

[R2] Jens Hansen, Kochbuch CATIA V5 automatisierenHANSER, 2009

[R3] Hans-Bernhard Woyand, FEM mit CATIA V5,J.Schlembach Fachverlag, 2005

[R4] Werner Koehldorfer, Finite-Elemente-Methoden mit CATIA V5HANSER, 2005

[R5] J.Wijker, Spacecraft StructuresSpringer, 2008

[R6] Wiley J. Larson & James R.Wertz, Space Mission analysis and designSTL, 2005

[R7] Launch Vehicle CatalogueESA, Revision 15, 2004

8

Chapter III

Terms, definitions and abbreviatedterms

Term ExplicationEPFL Ecole Polytechnique Federale de LausanneCDF Concurrent Design FacilityEPS Electrical Power SubsystemCOM Telecom subsystemADCS Attitude Determination and Control SubsystemDB DatabaseESTEC European Space Research and Technology CentreP-POD Poly Picosatellite Orbital DeployerXML Extensible Markup LanguageSTK Satellite Tool KitCATIA Computer aided three-dimensional interactive applicationCAD Computer Aided DesignVBA Visual Basic for ApplicationsRMS Root mean squarePCB Printed Circuit BoardFEM Finite element methodMOS Margin of safetyFOS Factor of safety

Table III.1: Abbreviated terms

9

Chapter 1

Master thesis project description

Description of the project

Concurrent design facility (CDF) is an environment where engineers of different specialtiescome together to perform systems engineering study for a project. Key elements for a CDF areteam, process, environment (including A/V and software) and knowledge management. Thegoal of this project is to develop further the “process” element of the CDF in the context of nanoand microsatellites. This work is important for designing future satellite projects.

In particular this Master Thesis shall start with establishing a Structures subsystem for nanoand microsatellites. The first step shall be to capture information from the Swiss Cube design(10x10x10 cm) and then extend designs to microsatellites with characteristic size of approxi-mately 25-30 cm. Particular attention will be given to modelling necessary physical environ-ment and test designed structures to be compatible with mission requirements. It is suggestedthat design will be carried in CATIA or Adobe Inventor packages. First order structural analysiscan be carried out in CATIA and then can be taken further in other systems.

This design and testing shall be integrated with the CDF infrastructure. In addition, thiswork will touch on some aspects of systems engineering and satellite project organization. Theoutput of this project shall be at least 3 different platforms of different sizes. A final report shallsummarise the major findings obtained in the project and an oral presentation shall be held atEPFL. The work will be performed at the Space Center EPFL.

More specifically, it is proposed to split the project in the following activities:

• Review of existing documentation and resources relating to SwissCube project

• Definition of subsystems and their interfaces

• Implementation of Structures subsystem, including integration with CDF

• First order structural analysis

• Support for internal and external reviews

• Delivery of the final report on model output and documentation.

Reference documents and source of data

The following documents and references are available at the beginning of the project:

• Swiss Cube documentation.

10


Project type

Project in the form of the “Master Thesis”, 30 credits ETCS

Deliverables

The following items should be derived during the course of the project:

• Weekly short email (half a page) describing the status of the project

• Monthly reports including an updated Gantt chart

• Draft final report, due on 17 July 2009

• Final report, due on 31 July 2009

• All software (including the source code and detailed comments) developed in this activity

Schedule1

Start of the activity: 16 February 2009Final report due: 31 July 2009Oral presentation: Between 17 and 29 August 2009 in Lausanne (TBD)

Location

The work will be performed at the Space Center EPFL during the 2009 Spring Semester.

Supervisor

Dr. Maurice Borgeaud, Director of the Space Center EPFL Co-Supervisor, Dr. Anton B. Ivanov,Space Center EPFL

Student

Mr. Andreas Fuglistaler , EPFL Mechanical Engineering Section, STI/SGM

1The normal Master spring schedule was updated to take into account Mr. Fuglistaler sickness leave duringMarch/April 2009

Chapter 2

Introduction

During the last four years, the Ecole Polytechnique Federale de Lausanne (EPFL) has been de-veloping a small satellite, which complies to the CubeSat standards, called SwissCube. Thissatellite is now fully functional and will be launched this year. The development has led to alarge knowledge base.

Figure 2.1: SwissCube satellite

At the same time, a Concurrent Design Facility (CDF) has been developed at the Space Cen-ter. The key idea of CDF is that engineers of different specialties come together and work in aparallel way on a project. This is done using a common database.

The knowledge base gained by the SwissCube project is gathered and implemented by aCDF database. Work has been done for the electrical power subsystem (EPS), the telecom sub-system (COM) and the attitude determination and control subsystem (ADCS). The main objec-tive of this work is to establish the structure subsystem, which gathers the structural knowledgeof SwissCube and is based on a new design of satellite structure systems.

2.1 CDF

In order to work in a concurrent design environment, a team of engineers of different specialtiesand a facility (CDF) is needed. The CDF consists in a workstation with the newest softwareinstalled for each subsystem and a global database (DB), enabling the team to gain access to thesame parameters (cf figure 2.2).

12


Figure 2.2: Concurrent Design Facility, interaction between the subsystems using a centraldatabase (DB)

The name CDF derives from the concurrent design facility located at the European SpaceResearch and Technology Centre (ESTEC). Other companies using concurrent engineering in-clude

• NASA JPL

• CNES

• ASI

• Boeing

• EADS Astrium.

The CDF of the Space Center has been successfully employed for designing a hybrid motor-cycle and setting up the mission design of a suborbital spacecraft.

2.2 Small Satellites

When Sputnik, the first satellite, was launched in 1957, miniaturization technologies were notvery advanced, computers especially were still very slow and very voluminous. For this reason,the first satellites were large and heavy. But, during the past 50 years, technologies have beenminiaturized, which enabled the development of much smaller satellites.

Small satellites ca be categorized in four types according to wikipedia:

• Minisatellites, 100− 500[kg]

• Microsatellites, 10− 100[kg]

• Nanosatellites, 1− 10[kg]

• Picosatellites, 0, 1− 1[kg]


2.2.1 CubeSat

CubeSat is a satellite standard developed by the California Polytechnic State University and theStanford University. There are three standards: 1UCubeSat, 2UCubeSat and 3UCubeSat. Thebase of all those satellites is a square of 10 × 10[mm]2. The height of the satellites are 100[mm],200[mm] and 300[mm] respectively.

The main reason for these standards is the use of a standard deployment system, the PolyPicosatellite Orbital Deployer (P-POD). It can either contain three 1UCubeSats, one 1UCubeSatand one 2UCubeSat or one 3UCubeSat. SwissCube was developed using the 1UCubeSat stan-dards. This project presents one 1UCubeSat design based on SwissCube and three 3UCubeSatdesigns.

2.2.2 Microsatellites

Additionally to the four satellite designs following the CubeSat standards, two Microsatelliteshave been developed, a 400 × 400 × 400[mm]3 cube and a octagonal satellite which has a mainradius of 200[mm] and a height of 400[mm].

2.2.3 Subsystems

Although the size of the satellite is very reduced, the number of subsystems remains the same.The following paragraphs give a short summary of the subsystems of a satellite.

Structure

The structure subsystem is holding together the satellite. It consists in a frame, side panels andspacers.

Payload

The payload is the whole purpose of the satellite. Therefore, all the dimensions are adjusted toit. Different payloads include cameras, photon counters or relay antennas.

Power

The electrical power subsystem (EPS) supplies the satellite with electrical power. There are twodifferent sources: solar cells and batteries. The batteries are used when the satellite is on thedark side and they are charged by the solar cells when the satellite is on the light side. A PCBcontrols the EPS.

Thermal

In smaller satellites, there are no active thermal controls. A thermal subsystem is neverthelessneeded to calculate the heat transfers and chosing the right isolation materials.

Attitude Control and Determination

The ADCS determines and controls the attitude of the satellite. For controlling, sensors areneeded, normally magnetometers and sun sensors. The determination is done using magnetotorques and inertial wheels. A PCB is needed to control the ADCS.


Control and Data Management

The CDMS supplies computing services for the satellite and provides communication betweenthe satellite and the ground station. This subsystem also needs a PCB.

Telecom

The telecom subsystem provides up- and downlink communication.two PCBs are used: COMand BEACON.

Chapter 3

Approach

The SwissCube satellite was a well defined, unique spacecraft. For that reason, not many pa-rameters had to be variable during its development. The reason for implementing the Swiss-Cube structure in the CDF, was to make it very flexible in terms of changing dimensions, mate-rials or subsystems.

3.1 CDF interface

Figure 3.1: CDF interface design

The CDF DB is the cornerstone of any CDF. All the parameters used to design a satellite needto be up to date and quickly accessible. The CDF database uses Extensible Markup Language(XML) files to store the date and MS Excel combined with VBA as its interface.

Each subsystem contains one Excel interface (cf figure 3.1) for carrying out calculations anddefining its output parameters, which can be used by all the other subsystems. The interface

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can be linked to other software, such as the satellite tool kit (STK), Matlab or computer aidedthree-dimensional interactive application (CATIA).

For the structure subsystem, the CDF database includes the following parameters of thesatellite:

• Dimensions

• Material properties

• Launch vehicle properties

• Mechanical properties

• Mass Budget

The interface contains all the dimensions and mechanical properties of every part and of thesatellite, as well as the properties of the materials used and a list of the launch vehicles.

3.2 CAD model

All the Computer Aided Design (CAD) models are designed with CATIA V5. A data exchangemacro was developed in Visual Baisc for Applications (VBA) in order to synchronize the CADmodel parameters with the values of the CDF database, thus uploading the dimensions fromthe CDF DB to the model and downloading the mechanical properties from the model to theCDF DB.

A material database, figuring the most common space materials, is also designed in CATIAand linked to the CDF database using the VBA macro.

3.2.1 Parts

The structure subsystem consists in the following parts:

• A frame, which is the skeleton of the satellite, it is designed as a monoblock structure

• Several panels, which cover each side of the satellite

• Several spacers, which connect different parts

The following parts are not actual parts of the structure subsystem but belong to other sub-systems. A mechanical representation is needed nevertheless:

• Payload

• Printed Circuit Board (PCB)

• Motherboard

• Battery

• Inertial wheel

3.2.2 Assemblies

The assembly designs consist in a unique frame assembled together, with the other parts whichdo not change in shape, but only in dimension. Assemblies have been designed for one 1UCube-Sat, three 3UCubeSat and two microsatellites.


3.3 FEM Analysis

In order to prove the reliability of the designs, three standard finite element method (FEM)analyses are done:

• Static loads

• Modal analysis

• Random vibration tests

3.3.1 FEM model

The analyses are done using the integrated FEM solver in CATIA. This is advantageous as achange of dimension or material done in the CDF database will also directly change the FEMmodel. The FEM models are not the same as the CAD models used to determine the mechanicalproperties. The latter are too complex and would slow down considerably the calculationswithout any improvement to the solution.

The key point of the FEM models is the use of as many shell and beam elements as possibleinstead of 3D elements. This speeds up considerably the calculation time and also increases theprecision of the solution. Also, the frame is considered being a monoblock, which avoids thecalculation of welded or screwed connections.

3.3.2 Standard tests

A set of standard tests is done for every satellite design. The highest external influence fora satellite are during the flight in the rocket and especially during take-off. Therefore, thesestandard tests simulate the launching environment:

• static load: in the case of a 1UCubeSat, there is the possibility of two other 1UCubeSatsbeing placed on top of it, which means a weight of 2kg. This can mean a considerableload during launching when the acceleration is of several gs. Even without any weight ontop of the satellite, it must overcome an acceleration of several gs.

• modal analysis: it is important to know which are the eigenfrequencies of the satellite andmore precisely which part of the satellite will respond to which frequency.

• random vibration test: during launching, there are many vibrations. The manufactures givethe range of frequencies and amplitudes. These vibrations are simulated on the model.

3.3.3 Verification

In order to justify the coherence of the FEM analysis results, the following verification methodshave been used:

• Independence of mesh: In order to prove this, the same calculation are performed on mesheswith different resolution.

• Compare with known results: The best comparison results are those of SwissCube, butknown results of other satellites can also be used.

Chapter 4

CDF interface design

The CDF consists in a global DB containing parameters which can be accessed by all subsys-tems. The DB is accessed by an MS Excel interface, each subsystem does have one.

Figure 4.1: Subsystem interface for 1UCubeSat design, Input sheet

Figure 4.2: Subsystem interface for 1UCubeSat design, Output sheet

All subsystem interfaces include three worksheets called Inputs (cf figure 4.1), Outputs (cffigure 4.2) and Calculations (cf figure 4.3). Out of these three, only Calculations is of any impor-tance to the user, the other two being used by the system and filled automatically by macros.

In Calculations, the user can define new global parameters which are written in the Outputworksheet and can then be used by all subsystems using the Button “Add Input”. By using thebutton “Refresh data”, the XML file is read and the Input and Output worksheets are refreshed.

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Figure 4.3: Subsystem interface for 1UCubeSat design, Calculations sheet

4.1 Structure interface

Figure 4.4: Structure subsystem, dim1,2,N being the dimensional parameters

Table 4.1 lists all the global parameters of the structure subsystem, defined in the Calculationssheet (cf figure 4.4).

Additionally to the three sheets mentioned in the previous section, the structure interfaceconsists in the following sheets:

• CATIA

• Materials

• Budget

• Structure

• Frame

• Spacer

• Payload


Parameter ExplicationTotal Mass Total mass of satellite (structure plus subsystems)Structure Mass Mass of frame, panels and spacersVolume Volume of the satelliteSurface Surface of the satelliteCenter of gravity Vector of the center of gravity of the satelliteInertia matrix Ixx, Iyy, Izz , Ixy , Ixz and Iyz

Table 4.1: Global structure parameters

• PCB

• MB

• Battery

• Wheel (depending on the satellite)

• Launch Vehicles

The CATIA sheet is needed for the data exchange (cf section 4.2).

4.1.1 Materials

Figure 4.5: Subsystem interface for 1UCubeSat design, Materials sheet

The Materials sheet (cf figure 4.5) lists all the used materials: the name, the Young Modulus,the Poission ration, the density, the yield strength and the thermal expansion. The latter two areof informational use only and can be left empty if not available.

4.1.2 Budget

The Budget sheet (cf figure 4.6) lists the budgets for the mass, the volume, the surface, the centerof gravity as well as the matrix of inertia for all parts. It also lists the number of occurrencesfor each part and sums up the total mass, volume and surface of the structure subsystem, (TotalStructure) as well as for the whole satellite (Total).


Figure 4.6: Subsystem interface for 1UCubeSat design, Budget sheet

4.1.3 Structure

Figure 4.7: Subsystem interface for 1UCubeSat design, Structure sheet

The Structure sheet (cf figure 4.7) lists the mechanical properties of the satellite, includingstructure parts and the other subsystem parts. These values should be the same as the ones ofthe Budget worksheet, but they are calculated differently, in the Budget sheet, the values are cal-culated by summing up the values of the different parts, in this sheet, the values are calculatedby CATIA.


Figure 4.8: Subsystem interface for 1UCubeSat design, Frame sheet

4.1.4 Parts

The dimensions of the parts are defined in the Frame (cf figure 4.8), Panel, Spacer, Payload, PCB,MB, Battery and eventually the Wheel (depending whether ADCS is done using inertial wheelsor not) worksheets. More details on those parts are given in section 5.2.

Each parameter has a description, a name, a value and a unit. The description is not obliga-tory for the data exchange to work (but it is definitely a good idea to put one in order to remem-ber), the name, value and unit are all three needed as they are used for the synchronization (cfsection 4.2).

4.1.5 Launch vehicles

Figure 4.9: Subsystem interface for 1UCubeSat design, Launch vehicles sheet

The Launch vehicles sheet (cf figure 4.9) gives an overview of the launch vehicles which aremost probably being used. The values are only for informational purposes and are not linkedto any other worksheet.

4.2 Data Exchange Macro

The CATIA sheet organizes the date exchange between the database and CATIA. It was exam-ined first if the design table of CATIA could be used for this task. The answer is yes, but notrecommended at all, for the following reasons:


• CATIA does not register names, but only numbers. This means CATIA does not know thename of the sheet where the parameters are defined; it only knows whether it is the firstsheet or the second sheet. As MS Excel sheets can be easily shuffled around, this is a bigdrawback

• There is no control on when CATIA synchronizes the parameters. Sometimes it takes afew seconds, sometimes a few minutes until CATIA starts synchronizing

• Once the link between the MS Excel file and CATIA is broken, it is often impossible toreestablish it

• Restrictions due to using the student version of CATIA makes the use of design tables forassemblies almost impossible

For these reasons, it has been decided to develop a VBA macro to synchronize the parameters.

4.2.1 Exchange structure

Figure 4.10: Direct data exchange

Figure 4.11: Indirect data exchange

There are two possibilities for synchronizing the parameters:


• Synchronize the parameters directly with the part parameters (cf figure 4.10)

• Create a list of user defined parameters in the assembly design, which are linked to thepart parameters and are only synchronized with the parameters (cf figure 4.11)

On first view, the direct data exchange seems to be the natural choice, for being much sim-pler. But there are indeed several important drawbacks:

• The exchange macro needs to know the exact file name of every part

• The parameters are not stored globally in the CAD model

• Exchanging parts in the assemblies (for example a different payload) demands a lot ofwork from the user

Considering this, the indirect data exchange strategy has been favored. It requires additionaldevelopment, however in the end the interface between CATIA and MS Excel is more stable.

4.2.2 Parameter creation

Figure 4.12: Subsystem interface for 1UCubeSat design, CATIA sheet

Each parameter defined in Frame, Spacer, Payload, PCB, MB, Battery and eventually Wheel hasa counterpart in the assembly called “Sheetname Parametername” which is linked to a part.One parameter can be linked to several parts, For example the PCB parameters are linked to allthe different PCB (EPS, COM, CDMS, ADCS and BEACON). By pushing the button “Make Out-put List” in the CATIA sheet, a list of all these variables is created under “Output Variables” (cffigure 4.12). The values and units are referenced to the parameter values in the correspondingworksheets.

Similarly, all the parameters used in the Budget worksheet have counterparts in the assembly,called “Partname” ”property”, for example Frame Mass or Battery Volume. By pushing thebutton “Make Input List” in the CATIA sheet, a list of all these variables is created under “InputVariables”. The values in the Budget sheet are referenced to the values in the “Input Variables”list. All the variables defined in the Structure sheet are as well referenced to this list.

4.2.3 Parameter synchronization

In order to synchronize the parameters, the user has to push the button “Synchronize”. Thereis no need to push the buttons “Make Output List” and “Make Input List” as these macros arecalled first using the synchronizing macro in order to make sure they are up to date.


The synchronizing macro is described in figure 4.13: it first creates the two lists, then opensthe CATIA assembly file defined in “CATIA File Name: “ and uploads all the output variables.As a next step, the assembly must be updated within CATIA, an order which is given by themacro. Once the update is finished, all the input variables are downloaded, which automaticallyfills the Budget and Structure worksheets with the correct values. Finally, the FEM assembly filedefined in “FEM File Name” is opened, the output variables are uploaded to it and the FEMassembly is updated.

The button “Clear all” is used only for testing purposes. The lists are cleared first anywayby pushing any other button.

Figure 4.13: Flow diagram of parameter synchronization

Chapter 5

Structure design

All the structure designs are made using CATIA V5. The structure design consists in the ma-terial database, the parts which have a link to the material database and the assemblies whichare constructed using the parts. These assemblies are referred to as mechanical assemblies, as theyallow the calculation of the satellites mechanical properties, the mass, the volume, the surface,the center of gravity and the inertial matrix.

A second, different type of assembly, is created for the FEM calculations, these will be de-scribed in chapter 6 and referred to as FEM assemblies.

5.1 Materials

The materials used are all defined in a CATIA material database. This database can be comple-mented if a wanted material is missing. The materials currently in the database are summarizedin table 5.1.

Material Young Modulus[GPa] Poisson Ratio[−] Density[

kgm3

]Al-7075 71.6 0.33 2810Al-6061-T6 69 0.33 2700Certal 72 0.33 2750Ti-6Al-4V 114 0.342 4430Stell 420 200 0.24 7800FR-4 30 0.33 1900

Table 5.1: Material properties

All those materials are supposed to be isometric. It is possible to create anisometric materialsin the CATIA material database, but has not been done in this project.

5.2 Parts

There are three main structure parts: the frame, the panels and the spacers. Minor parts suchas screws are not considered. These assemblies are used to get a rough first estimation of themechanical properties of the satellite. For this purpose, screws are not needed.

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(a) Panel (b) Spacer (c) Payload

(d) PCB (e) Motherboard (f) Battery

(g) Inertial wheel

Figure 5.1: Parts

Mechanical representations of the following subsystems have been made:

• Payload

• PCBs

• Motherboard

• Battery

• Inertial wheel

Beside the frame, all the parts have the same shape in all assemblies, except for very fewdetails. The figures shown in this section are the parts for the 1UCubeSat, but they are repre-sentative for all satellite designs, the parameter names are the same, only the values change.

The relations between the parameters change for each assembly. The latter are described inannex B.

5.2.1 Frame

The frame is the most complicated piece of all, and also the only one which differs in everysatellite design. The task of the frame is to offer a stable but light skeleton, which holds thesatellite together. Some features of the frame, such as the sidebars, are of mechanical purpose


only. They help to strengthen the structure. Other features, such as the payload attachmentbars, have a defined task in enabling attaching subsystems in the satellite.

The material selection for SwissCube is aluminum, this is a requirement of the CubeSat spec-ifications. In order to fulfill those requirements, the 1UCubeSat and 3UCubeSat frames must bemade of aluminium. For the microsatellites, using titan is an important alternative; its densityis higher, but at the same time, its Young modulus is also much higher, which strengthens thestructure.

The SwissCube structure has been designed as a monoblock structure, cut out out of a singleblock. The monoblock technology can be used for 1UCubeSats and also for 3UCubeSats, but forthe two microsatellites, this is not possible anymore.

In this work it was decided to design all satellite frames (including the microsatellites) asmonoblocks. This allows to shorten design and analysis time. First order analysis will exposeweak design points, which will serve as a basis for more detailed analysis. Also design tradeoffs can be performed very quickly during Phase A activities.

As the frame design depends highly on the spacecraft design used, these parts are describedin the Assembly section (section 5.3).

5.2.2 Panesl

The panels (cf figure 5.2) are used to cover the satellite and provide the surface for mountingsolar cells, sensors and other components. There are several possibilities for the material: hon-eycomb composites, carbon fibers or metals.

For the cubic satellite designs, there are six panels, four side panels and two top panels. Thetop panels differ from the side panels, as they need to have space for the rails. For the octagonaldesign, there are ten panels: eight side panels and two top panels.

5.2.3 Spacers

The spacers (cf figure 5.2) are used in order to fix the PCBs to the frame and connect the PCBstogether. They are also used as thermal connectors between the PCBs and the frame. Thematerial selection for the spacers in SwissCube is Certal aluminium, and there is no reason tochange this for the new satellite designs.

5.2.4 Payload

The payload (cf figure 5.2) is the reason why the satellite exists. For SwissCube, the payload isa small camera; for the larger satellites, the payload was also supposed to be a camera, only alittle bigger. A camera is a very complex construction, with many parts of its own. In this first-step study, the payload is simplified as a single part, having the same mass as the real payloadwould have.

5.2.5 PCB

Most subsystems need some electrical circuits, which are printed on a PCB (cf figure 5.2). Themechanical representation of a PCB is rather simple - it is just a flat shell. The material for PCBsis FR-4. There are four to six PCBs for the different satellite designs, depending whether theCMDS is integrated on the motherboard or is a separate PCB and whether the payload needsan own PCB or not.


5.2.6 Motherboard

In order to avoid cable spaghetti, the connections between the PCBs is done using a mother-board (cf figure 5.2). Technically speaking, the motherboard is also a PCB, but its mechanicalrepresentation has a different form. That is why, from a mechanical point of view, the mother-board is a different part.

5.2.7 Battery

As for the payload, the battery (cf figure 5.2) is not one single part, but an assembly of its own,consisting in the battery, the battery box and connection wires. Since in this project, only themechanical properties are of importance, the battery is designed as one piece having the realweight. The dimensions depend on the selected batteries, the dimensions used in this projectare the SwissCube values.

5.2.8 Inertial wheel

The attitude control can be made with inertial wheels (cf figure 5.2) or with magneto torques.Magneto torques are not designed in this project, since they do not influence the mechanicalproperties of the satellite. SwissCube does not use inertial wheels, but only three magnetotorques. The 3UCubeSats are designed without inertial wheels, but it is very possible to simplyinclude one if needed.

The microsatellites on the other hand are too heavy for magneto torque control only and aretherefore designed with three inertial wheels. The selection of the material is rather open, but itmust be a heavy material and should not be too much influenced by thermal changes.

5.3 Assemblies

Six different satellite designs have been done: one 1UCubeSat, three 3UCubeSat, one cubic mi-crosatellite and one octagonal microsatellite (cf figure 5.2). In this chapter, every satellite designis described, where the parts are placed and which are their advantages and disadvantages.


(a) 1UCubeSat (b) stretched 3UCubeSat de-sign

(c) 3UCubeSat, circular de-sign

(d) 3UCubeSat, layer design

(e) Cubic microsatellite (f) Octagonal microsatellite

Figure 5.2: Satellite designs


5.3.1 Part placement

Once the main dimensions of the satellite are fixed, the placement of all the subsystems insidethe satellite needs to be considered. The placement of the panels is of course on the six (respec-tively ten for the octagonal design) sides of the satellite.

The highest priority must be the placement of the payload, without it, the satellite wouldnot have any purpose to exist. In all six satellites, the payload is centrally placed, along one ofthe main axes. Being one of the heaviest pieces of the satellite, this helps maintain the centerof gravity close to the geometrical center of the satellite, which is a requirement of the CubeSatstandards, but also is important for all satellite designs to improve their attitude control system.

The placement of the attitude control devices is of great importance as well, they are placedorthogonal to each other, and their main axe should go as close as possible through the centerof gravity (cf figure 5.3), this way, the ADCS can be the most efficient.

Figure 5.3: Satellite design, placement of attitude control devices

The placement of the battery is best close to the payload as this device is probably the mostdemanding in electrical power. If possible, it should also be close to the EPS PCB.

Once the placement of the payload, the ADCS and the batteries are decided, there needs tobe space for the PCBs and the motherboard. Naturally, all the PCBs need to be in contact withthe motherboard. For all six satellite designs, the PCBs are fixed to the frame (and sometimesonto each other) using spacers.

5.3.2 1UCubeSat, SwissCube design

The 1UCubeSat design is directly derived from the SwissCube project. The same placement ofthe parts is used - the only thing that differs is that the dimensions are not fixed, but can beparametrized. This model is of importance also for comparing its FEM analysis results withthose found for SwissCube, as those results have been verified experimentally.


Design description

Figure 5.4: 1UCubeSat, SwissCube design, front view

The 1UCubeSat design is a 100×100×100[mm]3 cubic picosatellite, figures 5.4 and 5.5 showthe basic placement of the parts. In its geometrical center, along the X axis, the payload (pink)is placed. It is attached to the front side of the frame (grey). There is a hole of the size of thepayload on the front panel (blue) in order to give the payload, which in the case of SwissCubeis a camera, free view. Directly attached to the payload is the battery (green). The battery isattached to the frame using two attachment bars.

Five PCBs (different colors) are placed in the remaining free space to the left and right of thepayload. Spacers are used to keep distance between the PCBs and to attach them to the framein each corner of the PCBs. The PCBs are connected to the motherboard (red), which is placedon the top side of the satellite. The subassembly for the PCBs is shown in figure 5.6.


Figure 5.5: 1UCubeSat, SwissCube design , top view

Figure 5.6: 1UCubeSat, SwissCube design, PCB subassembly


Frame

Figure 5.7: 1UCubeSat frame

The basic structure of the frame is based on four rails, which are interconnected using thin-ner sidebars. Additionally to those, there is an attachment block for the payload (figure 5.8) andattachment bars for the battery and the PCBs (figure 5.9.

Figure 5.8: 1UCubeSat, SwissCube design, payload attachment block

Figure 5.9: 1UCubeSat, SwissCube design, battery / PCB attachment block

Advantages and Disadvantages

The SwissCube design for 1UCubeSats is a very good one. It uses all the space available, andthe frame is extremely light. The ability to quickly and easily assemble the satellite makes theexperimental testing of the satellite very easy.

The biggest drawback of this design is of course its size, but this is no real drawback sincethe idea was to create a 1UCubeSat and therefore, the size is a requirement.


If a small payload is enough and the goal is to create a cheap but functional satellite, theSwissCube design is definitely a good solution.

5.3.3 Stretched 3UCubeSat design

The first 3UCubeSat is a stretched version of the SwissCube design. Most of the parts are juststretched by a factor 3 in the z direction. This of course is not exactly the case for the frame,even though there is a big resemblance between the 1UCubeSat frame design and the presentframe design. Some additional side bars had to be added in order to strengthen the structure.

It has also to be supposed that the payload not only increases in length but also in diameter,which as a result leaves less space between the payload and the frame. This slightly changesthe arrangement of the PCBs.

Design description

Figure 5.10: Stretched 3UCubeSat design, front view

Since this design is directly derived from the SwissCube design, only few arrangementschange. One major change is the main direction. For SwissCube, the payload is perpendicularto the rails. For changing from 100× 100× 100[mm]3 to 300× 100× 100[mm]3, the length of therails is changed, not the length of the sidebars. This implies that the payload is parallel to therails in order to use the whole length of the satellite. For that reason, the attitude of most partshas changed by 90◦.

Figures 5.10 and 5.11 show the arrangement of the parts. The payload (pink) is placed par-allel to the rails in the center of the satellite and is attached to the frame (grey) on the top side.The top panel (blue) does have a hole in it to enable the view of the payload. The battery (green)is placed just below the payload and attached to the frame using two sidebars.

It has to be assumed that the payload is not only longer but also wider than the payload usedfor SwissCube. As the 3UCubeSat only differs in length to the 1UCubeSat, this seriously reduces


Figure 5.11: Stretched 3UCubeSat design, top view

the space left between the payload and the frame. Therefore, depending on the diameter of thepayload, there is only space for one PCB each left and right of the payload. On the other side,there is 300[mm] of length as disposition contrary to only 100[mm].

Therefore, only half of the length of the satellite is used for the PCB length. This enablesthe placement of two PCBs on each side of the payload, one on top of the other. The PCBs areattached to the frame using spacers (orange) in each corner.

The main requirement of the placement of the motherboard is its connection to all PCBs.Having fixed the placement of these, there is only one possible placement for the motherboardavailable, in the middle of the satellite, orthogonal to the PCBs. This means that the mother-board is also orthogonal to the payload. Therefore the motherboard must have a hole in themiddle. The PCB subassembly is shown in figure 5.12.

Figure 5.12: Stretched 3UCubeSat design, PCB subassembly


Frame

Figure 5.13: Stretched 3UCubeSat design, frame

As for the 1UCubeSat design, the present frame is based on four rails, connected by sidebars.There are five sidebars to guarantee the stiffness of the satellite. An attachment block stands ontop for the payload and bars are available to attach the PCBs.

Figure 5.14: Stretched 3UCubeSat design, motherboard attachment

The frame is not completely symmetrical: the motherboard is attached on the middle side-bars and therefore, these sidebars are situated below the geometrical center (cf figure 5.14).

Advantages and disadvantages

The 3UCubeSat designs offer a volume which is three times bigger. Most of the volume isneeded for the payload, and since a longer payload is probably also wider, the actual space leftis rather smaller than bigger compared to the 1UCubeSat.

In the present design, the remaining space is not effectively used, as only two of the foursides are used for the PCBs. The design being very simple, this can be seen as an advantage,but the disadvantages outweighs this advantage.

The present design is only to be recommended when a very thin payload is used, in orderto be able to use two layers of PCBs on each side. If the payload is wider, the circular design(section 5.3.4) has to be favored.


5.3.4 Circular 3UCubeSat design

The second 3UCubeSat is an improved version of the stretched 3UCubeSat design. As has beenseen, the biggest problem of the stretched version is the lack of space left for the PCB placementwith increasing payload diameter.

Hence the idea to use all four sides of the frame instead of only two sides as in the formerdesign. The circular arrangement of the PCBs in this design conducted to some minor problemsconcerning how to attach them on the frame, but a satisfactory solution was found.

Design description

Figure 5.15: Circular 3UCubeSat design, front view

This design is directly derived from the former design and they are therefore very similar.Figures 5.15 and 5.16 show the placement of the different parts.

The placement of the payload (pink), the battery (green) and the motherboard (red) remainthe same. The placement of the PCBs (different colors) is done using all four sides of the satellite,which uses the remaining space more efficiently. As the attachment bars for the X side PCBs arein the way of the Y side PCBs and vice versa, they do not have the same shape, as can be seenin the PCB subassembly (cf figure 5.17).


Figure 5.16: Circular 3UCubeSat design, top view

Figure 5.17: Circular 3UCubeSat design, PCB subassembly


Frame

Figure 5.18: Circular 3UCubeSat design, frame

The only difference of this frame compared to the former satellite design is the attachmentbars, which have a more complex form to allow the attachment of two PCBs which are orthog-onal to each other (cf figure 5.19).

Figure 5.19: Circular 3UCubeSat design, attachment bar


The present design is an improved version of the former 3UCubeSat design. It uses efficientlythe whole volume within the standards requirements. As a slight disadvantage, the complexityof the design can be named, but there should be no difficulties in assembling the satellite. Onlythe complexity is a factor for manufacturing the frame, but nowadays manufacturing technolo-gies are well enough advanced to enable such a construction.

This design is recommended when a 3UCubeSat design is requested.


5.3.5 Layer 3UCubeSat design

The last design of the 3UCubeSats is a different approach, instead of using the sides of the framefor the PCB placements, the PCBs are placed in layers, having a hole in the middle for givingspace for the payload. That way, the PCBs do have a secondary function in strengthening thesatellite.

Design description

Figure 5.20: Layer 3UCubeSat design, front view

Figures 5.20 and 5.21 show the arrangement of the parts. Again, the placement of the pay-load (pink)) and the battery (green) remains the same. But the arrangement of the motherboard(red) and the PCBs is quite different. Instead of using the sides of the satellite for the PCBs andplacing the motherboard orthogonally to the payload, the roles are this time reversed: the moth-erboard is on one side of the satellite, attached by spacers (orange), and the PCBs are orthogonalto the payload, having a hole in the middle and using the sidebars as support.

The PCB subassembly is shown in figure 5.22. The motherboard is very long (300[mm]), it istherefore attached on each corner and in the middle. The two PCBs placed in the middle are ofslightly different form in order not to interfere with the spacers.


Figure 5.21: Layer 3UCubeSat design, top view

Figure 5.22: Layer 3UCubeSat design, PCB subassembly


Frame

Figure 5.23: Layer 3UCubeSat design, frame

Out of the three 3UCubeSat designs, this frame is the simplest. There is only one attachmentblock for the payload on top, attachment bars only on one side of the frame for the motherboardand attachment bars on the bottom for the battery.


There is one big disadvantage using the present design, the surface available for the PCBs de-pends directly on the diameter of the payload. The big advantage is it being very simple toassemble and a very simple frame design.

This design can only be used for very thin payloads and even then, the surface of the PCBsis very restricted. Therefore, this design is not recommended.

5.3.6 Cubic microsatellite

The first microsatellite is a further development of the SwissCube design, this time to a 400 ×400 × 400mm3 volume. This satellite has a 64 times bigger volume and requires therefore adifferent design. Most notably, the frame has to be strengthened with crossbars and thickerbars and a special placement for the inertial wheels has to be taken into consideration. On theother hand, the placement of the PCBs is a minor problem because the little space needed bythe PCBs is no big worry in larger satellites.

Design description

At first sight, this design looks like an inflated version of the 1UCubeSat, due to its cubic form,but the inside changes quite considerably. Figures 5.24 and 5.25 show the arrangement of theparts.

Again, in order to keep the center of gravity as close to the geometrical center of the satelliteas possible, the payload is placed in the middle. It is attached to the frame on the front sideand in the middle of the satellite. Directly attached to the payload is the battery, which is itselfattached to the frame.


Figure 5.24: Cubic microsatellite, front view

The inertial wheels are orthogonal to each other on three sides of the frame: the bottom, theback side and the left side. Their axis is attached to the frame through holes.

The PCBs are placed on the right side of the payload using half the width as well as thewhole length of the satellite. They are attached to the frame and onto each other using spacersin each corner and in the middle. The motherboard is on top of the payload and the PCBs,connected to all of them and attached directly to the frame. The PCB subassembly is shown infigure 5.26.


Figure 5.25: Cubic microsatellite, top view

Figure 5.26: Cubic microsatellite, PCB subassembly


Frame

Figure 5.27: Cubic microsatellite, frame

As this satellite design is considerably bigger and therefore heavier than the 1UCubeSatsand the 3UCubeSats, the frame needs to be much stronger. In order to fulfill this requirement,the design is no more based on four rails, but on eight rails, defining all the side edges of thesatellite.

There are slightly thinner sidebars going through the middle of each side. In order to avoidshearing strains, cross bars going from corner to corner have been added.

The attachment block not only consists in the front side attachment bars, but is a wholestructure, forming a secondary frame within the frame. This helps attaching the payload andalso diminishes thermal influences from other elements such as the battery on those parts of theframe, therefore improving the precision of the payload. As in the other designs, the PCBs areattached using special attachment blocks.


This microsatellite design is a simple construction, enabling quick assembly of all the subsys-tems. The production of the frame needs to be reviewed. As a monoblock construction is notvery probable, solutions could include a monoblock payload sub frame, where the remainingparts are welded or differently fixed or consists in constructing each rail separately before weld-ing the frame together that way.

One advantage of this design is its relative independence of dimensions, this design can beused in the range from 200 × 200 × 200[mm]3 up to 600 × 600 × 600[mm]3, the only thing thatneeds to be changed is the size of the rails, the side bars and the cross bars, which can be easilydone using the CDF interface. These changes need of course be determined for each case takinginto account the weight of the satellite and the outer influences, mostly during launch.

A small disadvantage is the slightly inefficient use of the given volume, there are many“empty holes” inside the satellite which are of no use at all.


5.3.7 Octagonal microsatellite

A different frame design was wanted for the last microsatellite. The main goal was to use moreefficiently the satellites volume. Several shapes were taken into consideration, mostly a circular,a hexagonal and a octagonal shape.

The problem with a circular design is that there is a serious loss of volume due to the changebetween round and rectangular parts, as is described in figure 5.28 (a)). A good use of all thevolume in a circular satellite can only be obtained by either using round PCBs (cf figure 5.28(b))or placing the PCBs below the payload (cf figure 5.28(c))). Both possibilities differ too muchfrom the precedent designs and would need a redesign of every part of the satellite design.

Figure 5.28: Satellite design, circular form

The problem with the hexagonal form is the placement of the inertial wheels. Two wheelscan be comfortably be placed, one on the bottom and one on the side, but the placement of thethird wheel on the other hand is not easily done, as a hexagonal form does not have a third sidewhich is rectangular to the other two (cf figure 5.29).

Figure 5.29: Satellite design, hexagonal form

For that reason, and especially with the problems encountered with the hexagonal form, aoctagonal form has been chosen, where the placement of the three inertial wheels is no problem.


Design description

Figure 5.30: Octagonal microsatellite, front view

Figures 5.30 and 5.31 show the placement of the parts. This design is very different to theother designs, as there are more sides (ten instead of six) and much fewer orthogonal angles.The panels are either of rectangular (the side panels) or of octagonal shape (the top panels). Thepayload is placed in the middle, attached to the frame on the top and in the middle. The batteryis placed below the payload and attached to the frame.

One inertial wheel is placed on the bottom and the other two are placed on two sides, or-thogonal to each other. The size of those two wheels is restricted by the side length of theoctagon, this is why they are smaller than the bottom wheel.

The PCBs are placed on the sides except on the two sides used for the inertial wheels. Theyare much higher than wide and are therefore not only attached using spacers to the frame on allfour corners but also in the middle. The motherboard is placed on the bottom of the satellite,below the payload and battery, and is of octagonal form. Figure 5.32 shows PCB subassembly.


Figure 5.31: Octagonal microsatellite, top view

Figure 5.32: Octagonal microsatellite, PCB subassembly


Frame

Figure 5.33: Octagonal microsatellite, frame

The base of the frame is a regular octagon. In each corner stands an octagonal rail. Theoctagonal form of the satellite avoids most of the shearing stresses, which is of an advantage,but, there is a much bigger tendency to torsion stresses, therefore, there are sidebars in themiddle of the satellite. Again, as for the cubic microsatellite design, there is a payload blockinside the frame, with an opening on top. This payload block consists in eight thinner railsand ends in a cross on the bottom. No attachment bars are needed for the spacers as these aredirectly attached to the sidebars on top, in the middle and on the bottom.


The octagonal microsatellite design is a slightly more complex construction than the cubic mi-crosatellite design, which means that the construction of the frame is more difficult, using sev-eral octagonal parts. The procedure of assembly is not trivial, and the construction of the frame,which in the present case is only designed as a monoblock, plays a crucial role on the way ofassembling the satellite.

As an advantage over the cubic satellite, it can be noted that it uses far more efficientlythe satellite volume. Also, as for the cubic design, this design is mostly independent of thedimensions, as long as the dimensions of the rails and the sidebars is adapted. If the length ofthe satellite is much reduced or increased, the number of sidebars needs to be changed. A veryshort satellite does not need sidebars in the middle whereas a much longer satellite needs morethan only one set of sidebars in the middle.


5.3.8 Discussion

The 1UCubeSat design is a parametrized version of the SwissCube design. The other satellitesare derived from this design. Of course, it is not possible to simply inflate the 1UCubeSat designto get the desired dimensions. The frame would not be rigid enough and the arrangement ofthe subsystems would not be efficient.

The first 3UCubeSat design that was developed was the stretched SwissCube design. Itresembles most closely the 1UCubeSat design. It is in fact the inflation of the 1UCubeSat frameto 300[mm] height with additional sidebars. The arrangement of the PCBs remains the same: leftand right to the payload. Only half of the height is used for one PCB, enabling the placementof two PCBs, one on top of the other. This design has one big drawback: the space available forthe PCBs is very limited due to the increased payload radius.

The second 3UCubeSat design, the circular SwissCube design, is an improvement over thestretched SwissCube design. It uses the available space more efficiently, all four sides aroundthe payload are used for the PCBs instead of only two. Given the same satellite volume asfor the stretched SwissCube design which only allows the placement of four PCBs, this designallows the placement of up to six PCBs.

The third 3UCubeSat design was the test of a different idea. The PCBs are placed orthogonalto the payload, therefore strengthening the structure. But this design has a very big drawback:the surface of the PCBs decreases with increasing payload diameter. Because of this disadvan-tage, this design cannot be recommended.

The two microsatellite designs have much more volume available. For this reason, the place-ment of the PCBs is a minor issue. The most important placement factor in this case are theinertial wheels. For efficient use, they need to be orthogonal to each other and their axes shouldgo through the center of gravity.

The first microsatellite design is a further extension of the SwissCube design. The frameis strengthened using large rails at all edges of the cube. It uses not only sidebars but alsocrossbars in order to strengthen the design even more. As the design is cubic, the use of spaceis not ideal, there is a lot of unused volume in this design.

The second design is aimed at using the available volume more efficiently. An octagonalshape was chosen which allows to use six of eight sides for the placement of PCBs. The last twosides are used for the inertial wheel placement.

Table 5.2 gives an overview of the satellite designs.


Name Description Advantages(+) andDisadvantage(-)

1UCubeSat100× 100× 100

[mm3

]+ Light frame

SwissCube design + Efficient use of volumePCBs placed on 2 sides of the payload - Small

Stretched 3UCubeSat100× 100× 300

[mm3

]+ Simple design

Directly derived from 1UCubeSat - Inefficient use of volumePCBs placed on 2 sides of the payload - Only 4 PCBs

Circular 3UCubeSat100× 100× 300

[mm3

]+ Efficient use of volume

Improvement of stretched 3UCubeSat + Up to 6 PCBsPCBs placed on 4 sides of the payload - Difficult to assemble

Layer 3UCubeSat 100× 100× 300[mm3

]+ Stiff structure

PCBs used to strengthen structure - Small PCB surfacePCBs have a hole in the middle

Cubic microsatellite

400× 400× 400[mm3

]+ Large volume

Derived from 1UCubeSat + Easy to assembleSeveral sidebars and crossbars - Inefficient use of volumePCBs placed on one side - Rather big deformations3 Inertial wheels

Octagonal microsatellite

400×�400[mm3

]+ Stiff structure

octagonal base shape + Large volumePCBs placed on six sides + Efficient use of volume3 Inertial wheels - Complicated to assemble

Table 5.2: Overview of satellite designs

Chapter 6

FEM Analysis

A satellite model is not worth a great deal as long as there is no indication on its behavior toexternal influences. This behavior can be calculated using FEM analysis. It has to be noted thatFEM analysis are always assumptions, they never represent the real values. The significanceof the results increases by increasing the number of details. On the other hand, the calculationtime is also significantly increases by the number of details.

FEM calculations can be done using CATIA to calculate static loads, eigenfrequencies anddynamic response analyses. In this project, tests are included for all three analysis cases. Thesetests and are not meant to be complete, additional test scenarios are certainly be needed in orderto completely qualify the satellite models. These tests are supposed to give an overview of whatare the possibilities of the FEM models.

As all satellite models are parametrized, the test results given in this section are not the lastword to be said. The results change when one alters a parameter. The results given in thissection prove the soundness of the models as all the values are in a good range.

6.1 Launch vehicles

The strongest influences to the satellite are during the launch. Detailed launch information onall launch vehicles are therefore needed. Four launch vehicles are discussed in this section, theVEGA launcher of ESA, The PSLV launcher of India and the Soyus and DNEPR launchers ofRussia.

6.1.1 VEGA

The VEGA launch vehicle was supposed to launch SwissCube. Unfortunately, its development,which should have been finished in 2007, is still delayed. Nevertheless, once the developmentis finished, this is the most probable launcher to be used as Switzerland is part of the ESA.

The VEGA launcher is supposed to have the following properties:

• Payload capability of 1500[kg] at 700× 700[km] (cf figure 6.1)

• 6± 1g maximum acceleration

• 5g root mean square (RMS) at a range of 20− 2000[Hz] (cf figure 6.2)

54


Figure 6.1: Payload capacity of VEGA launcher

Figure 6.2: Random vibration level of VEGA launcher

6.1.2 PSLV

The PSLV is an Indian launch vehicle and is used to launch SwissCube. It has the followingproperties:

• Payload capability of 1600[kg] for LEO and 1000[kg] for GEO (cf figure 6.3)

• 7g maximum acceleration

• 4.47g RMS at a range of 20− 2000[Hz]


Figure 6.3: Payload capacity of PSLV launcher

6.1.3 SOYUZ

The SOYUZ launcher is Russian and is one of the most successful launchers ever to be devel-oped. It has the following properties:

• Payload capability of 7100[kg] at 200[km] (cf figure 6.4)

• 4.3g maximum acceleration

• 5g RMS at a range of 20− 2000[Hz] (cf figure 6.5)

Figure 6.4: Payload capacity of SOYUZ launcher


Figure 6.5: Random vibration level of SOYUZ launcher

6.1.4 DNEPR

DNEPR is a Russian launcher with the following properties:

• Payoad capability of 3700[kg] at 300[km] (cf figure 6.6)

• 7.8g maximum acceleration

• 3g RMS at a range of 20− 2000[Hz]

Figure 6.6: Payload capacity of DNEPR launcher

6.2 FEM Model

Before creating a FEM Model, we tried to use the mechanical model for the FEM analysis, butthis was quickly discarded for the following reasons:


• constraints: when creating a “normal” CAD model, one goal is to minimize the numberof constraints, for example, if a surface of a part touches another part on several surfaces,a contact constraint is only generated at one location - the other contacts are automatic.This is not anymore possible for FEM calculations. Each contact between two parts needsto be declared and specified.

• 3D elements vs. shell and beam elements: In the mechanical model, all parts are 3D elements,even very thin parts like the panels and PCBs have a thickness. For FEM analysis, it isuseful to use shell (2D) or even beam (1D) elements if possible, which reduces the numberof nodes and also increases the accuracy of the result.

6.2.1 Shell and Beam elements

The normal way to mesh three dimensional structures is to use tetrahedron or cubic 3D ele-ments. The latter are mostly used for simple geometries and are not used in this project, asrectangular 3D elements would be rather inflexible with changing parameters.

Tetrahedron 3D element meshes give good results if their shape is close to a regular tetra-hedron, but the accuracy of the result diminishes with increasing irregularity. For this reason,very flat 3D structures are very badly calculated using tetrahedron element meshes, unless theside length of those tetrahedrons is equal or smaller to the thickness of the structure, which isnormally impossible because this would lead to a far too high number of elements.

Figure 6.7: shell element

For this reason, triangular 2D element meshes, called shell meshes, were introduced (cf fig-ure 6.7). The main idea is to interpret the 3D structure as a 2D structure for the meshing process.The calculation of the shells still lead to 3D results. As in the case of the tetrahedron 3D elementmeshes, the triangular 2D element meshes generate good results if the triangles are close tobeing regular but decrease in accuracy if the triangle becomes very irregular.

If the width of a shell structure diminishes considerably, the triangles of a shell mesh becomeirregular unless the side length is very much reduced. For those cases, 1D element meshes,called beam meshes, are used (cf figure 6.8). For the mesh, the structure is interpreted being 1D,but the results are still 3D.


Figure 6.8: beam element

In addition to the increase of accuracy, the use of as many shell and beam elements as possi-ble also decreases considerably the calculation time. This is due to the following reasons:

• By using 2D or 1D elements, the number of nodes decreases as there is one dimension lessto mesh.

• For 3D elements, the reduction of a side length by a factor of n leads to a increase of nodesby a factor of n3, for 2D elements, only to a increase of n2 and for 1D elements even onlyto a increase of n

As the calculation time directly depends on the number of nodes, reducing the numberof nodes is very crucial for reducing the calculation time. It is possible to connect shell andbeam elements to tetrahedron elements using specific connection elements. These elementsare directly included by CATIA if a connection between two elements of different meshes isdefined.

6.2.2 Meshing decision

As indicated in the former section, the use of shell and beam meshes instead of tetrahedronmeshes is of importance not only to increase the speed of calculation but also to increase theaccuracy of the results. The meshing of the different part has been selected as followed (thesame for all six assemblies):

• Tetrahedron 3D mesh: Frame, Payload and Battery

• Triangular shell (2D) mesh: Panels, PCBs and motherboard

• Beam (1D) mesh: Spacers

The frame structure resembles a combination of several beam elements. Therefore, a testassembly using beams has been done for the 1UCubeSat frame, but the eigenfrequency resultsare 20% different to the tetrahedron solutions. The several details of the frame (payload andbattery attachment blocks) have too much influence on the eigenfrequency, which cannot besimulated by beams.

Figure 6.9 shows the 1UCubeSat, SwissCube design FEM assembly. The red circles indicatethe beam elements for the Spacers, the 0, 8mm indicate the thickness of the panels and thePCBs. The green triangles indicate the mesh, the size of the triangle is proportional to the mesh


Figure 6.9: 1UCubeSat, SwissCube design, FEM model

size. The blue symbol below the satellite indicates that it is framed below. The black symbolresembling a screw indicates a fastened connection.

6.2.3 Additional mass

It is possible to add distributed or punctual masses to a CATIA FEM model. distributed masseswere added for the PCBs and the Panels. For the PCBs, this mass represents the electroniccomponents and was defined to be equal to 15[g]. For the Panels, this mass represents thesolar panels, and is equal to 4.5[g]. Both mass selections were done according to the SwissCubevalues.


6.2.4 Design selection

Dimensions

All the tests are done with the standard dimensional settings which are summarized in table6.1.

Model Dimension Value [mm]1UCubeSat x and y 100

z 100rails 9× 9sidebars 3× 4

3UCubeSat x and y 100z 300rails 9× 9sidebars 3× 4

Cubic microsatellite x, y and z 400edge bars 10× 10side bars 5× 5

Octagonal microsatellite payload radius 150z 400bar width 10

Table 6.1: Dimensional parameters

Materials

The materials selected are described in table 6.2.

Part MaterialFrame Al-7075Panels FR-4Spacers CertealPCBs FR-4Motherboard FR-4Wheels Steel 420

Table 6.2: Materials

6.3 Verification

The verifications are mostly done using the eigenfrequency calculation as these are numberswhich are easy to compare. Several verifications are done, both internal and external. The inter-nal verifications include the comparison between shell/beam elements to tetrahedral elementsand the independence of the mesh size of the models.

For external verification, the results of the 1UCubeSat SwissCube model are compared tothe SwissCube results.


6.3.1 Tedrahedral compared to 2D / 1D

The first five eigenfrequencies of a beam and a shell mesh are compared to its tetrahedral coun-terpart.

Beam element

Figure 6.10: Spacer, tetrahedral (left) and beam (right) mesh

The comparison part is a spacer (cf figure 6.10), the results can be seen in table 6.3.

Number Tetrahedral[Hz] Beam[Hz] Difference[%]#1 76499 67088 12, 3#2 76504 67088 12, 3#3 112047 112105 0, 518#4 185713 135008 27, 3#5 203412 135008 33, 6

Table 6.3: Eigenfrequency comparison between tetrahedral and beam mesh

The first three eigenfrequencies are reasonably alike, but the last two eigenfrequencies differquite a lot. A reason for this is the very high value of the eigenfrequencies, which is more proneto errors.

The beam values are definitely more accurate than the tetrahedral values, which can benicely seen by comparing frequencies #1 and #2 and frequencies #4 and #5, which shouldhave the same value as they are the same frequencies, for a different symmetry. They are indeedthe same for the beam element, but differ very little for the first two frequencies and quite a lotfor the last two frequencies. This again is a indication that the accuracy of the frequenciescalculated by the tetrahedral element diminishes when increasing frequency.

Shell element

The comparison element is a panel (cf 6.11, the results can be seen in table 6.4.The values are very similar and therefore, the shell mesh can be used instead of the tetrahe-

dral mesh without any loss of accuracy.


Figure 6.11: Panel, tetrahedral (left) and shell (right) meshes

Number Tetrahedral[Hz] Shell[Hz] Difference[%]#1 3, 35 3, 34 0, 29#2 8, 78 8, 66 1, 4#3 21, 2 20, 8 0, 98#4 26, 9 26, 4 1, 8#5 31, 6 30, 8 2, 5

Table 6.4: Eigenfrequency comparison between tetrahedral and shell mesh

6.3.2 Independence of mesh size

This is a very important criterion, for if the solution changes with the mesh size, it cannot becorrect.

The test procedure is rather simple: once the wanted mesh size is decided, the eigenfrequen-cies are calculated and saved. The mesh is then refined and the eigenfrequencies are calculatedonce more and compared to the first results. The second calculation of the eigenfrequenciestakes much more time, as the calculation time is dependent on the mesh size.

This test has been performed with all six FEM assemblies and the solutions proved to beindependent of the mesh size in all cases.

6.3.3 Comparison with SwissCube results

The 1UCubeSat design of this project is a copy of the SwissCube project, therefore, the FEManalysis results should be equal. Two values are compared, the lowest eigenfrequency and thehighest von Mises stress at a side bar (cf [N3], pages 15 to 22). For the latter, a different testwas done than the ones described in section 6.4. An additional force of 10g · 2[kg] ≈ 200[N] wasapplied on the top side of the satellite. This is the standard test done for SwissCube.


Eigenfrequency

The lowest eigenfrequency of SwissCube calculated by Abaqus is 175[Hz] whereas the lowesteigenfrequency found in this project (cf table 6.7) is 201[Hz]. This is a difference of 12.5%. Thisdifference results from the different representation of the electronic components.

For the SwissCube FEM analysis, the PCB structure has been represented as two shell ele-ments, fastened to each other. The first one represents the PCB itself, the second one representsthe electronic components. The second shell element has a weight of 15[g] and a very low Youngmodule of only 2[MPa]. This softens the PCB structure and leads to lower eigenfrequencies.

For the FEM analysis in this project, the additional electronic elements are represented as adistributed mass on the PCB. This was considered being more accurate, the electronic parts donot influence the stiffness of the PCB part, they just add an additional mass.

Von Mises stress

The highest von Mises stress of the SwissCube frame is “about 8MPa” and the one calculatedin this project is 8, 8[MPa]. The value in the SwissCube analysis is not given precisely, however,the results can be considered to be similar.

6.4 Static load analysis

The highest static load on a satellite is during the launch. The accelerations can go up to 7.5g.Using a safety factor (FOS) of 1.25, which means a maximum acceleration of 10g. The CubeSatsatellites are inside the P-POD during launch, this means a maximum mass of two 1UCubeSats(2kg) on top of the 1UCubeSat design and no additional weight for the 3UCubeSats. For thetwo microsatellite, it is supposed that they only have to endure their own weight during thelaunch, as they do not have any additional charges on top of them.

For the standard tests, it is assumed that the satellites are “standing” in the launch vehicle.Therefore the acceleration is in the z direction. The satellite is attached to the bottom.

The static load analysis for all satellites is defined as followed:

• 10g in z direction

• attached on the bottom

• no additional charge except for 1UCubeSat (2[kg])

6.4.1 Calculations

The FEM analysis can calculate the displacement and the von Mises stresses in the structure andindicate where they are. The displacement values are of informational value mostly in order tobe able to quickly see impossible values.

The von Mises stress values indicate the stress at a given area, taking into consideration allthree directional stresses. The von Mises value needs to be below the materials yielding stress,otherwise, the material is in plastification. The von Mises stress is defined as followed:

σv =

√(σ1 − σ2)2 + (σ2 − σ3)2 + (σ1 − σ3)2

3where σ1, σ2 and σ3 are the constraints in the three main directions.The margin of safety (MOS) can be calculated using the following equation:

MOS =loadallowed

loadapplied × FOS− 1

The yield stress of aluminium is of 400[MPa] and the factor of safety (FOS) is defined as 1.25.


6.4.2 Results

The results for the static loads are given in table 6.5 for the assemblies and in table 6.6 for theframes. All the stress values are well below the yield values, and the displacement vectors arevery small (a few [µm]s).Therefore the static loads are of no danger whatsoever for the satellites.

Part Displacement[mm] von Mises stress[MPa] MOS1UCubeSat, SwissCube design 0.0002 0.285 1220stretched 3UCubeSat design 0.0003 0.387 825circular 3UCubeSat design 0.0003 0.192 1670layer 3UCubeSat design 0.0003 0.173 1850Cubic microsatellite 0.05 2.7 118Octagonal microsatellite 0.001 1.4 227

Table 6.5: FEM Analysis assembly, maximal results for static loads

Part Displacement[mm] von Mises stress[MPa] MOS1UCubeSat, SwissCube design 0.002 0.862 370stretched 3UCubeSat design 0.004 0.874 365circular 3UCubeSat design 0.005 1.5 212.3layer 3UCubeSat design 0.005 0.878 363Cubic microsatellite 0.16 5.88 53Octagonal microsatellite 0.08 3.24 98

Table 6.6: FEM Analysis frame results for static loads

1UCubeSat, SwissCube design

Figure 6.12: 1UCubeSat, SwissCube design, displacement vectors for 10g, exagerated scaling

As can been seen in figure 6.12, the highest displacements are on the top panels. This solu-tion is very intuitive as the acceleration is in the z direction and the top panels are the thinnestparts. For the frame (cf figure 6.13), it is the sidebars with PCB attachment bars on them, whichare the most influenced. The PCBs as a side effect strengthen these sidebars.


Figure 6.13: 1UCubeSat, SwissCube design, frame under 10g influence, exaggerated scaling

The parts attached in the z-direction, such as the side panels and the PCBs, encounter thesmallest displacement values.

3UCubeSat, stretched and circular SwissCube design

Figure 6.14: stretched 3UCubeSat design, displacement vectors for 10g, exaggerated scaling


Figure 6.15: stretched 3UCubeSat design, frame under 10g influence, exaggerated scaling

Figure 6.16: circular 3UCubeSat design, circular SwissCube design, displacement vectors for10g, exaggerated scaling

The stretched and circular SwissCube designs (cf figures 6.14 and 6.16) are very similar intheir configuration as to external influences on the z axis. it is therefore of no surprise that bothshow the same displacements, maximum values for the top panels and the motherboard, andminimal values for the side panels and the PCBs.

By comparing the two frames (cf figures 6.15 and 6.17), one recognizes an important defor-mation of the payload block for both frames. For the circular design, the deformation of themiddle side bars is much higher due to fact that the attachment block is heavier.


Figure 6.17: stretched 3UCubeSat design, frame under 10g influence, exaggerated scaling

layer 3UCubeSat design

Figure 6.18: layer 3UCubeSat design, displacement vectors for 10g, exaggerated scaling

The layer PCB design for the 3UCubeSat (figure 6.18) shows the highest displacement for thePCBs, which are, differently to the other designs, orthogonal to the z direction. This again is nosurprise, as the PCBs are only attached by the edges. The fact that there is a hole in the middlereduces the PCBs stiffness and increases the displacement value. Nevertheless, it cannot beforgotten that even the maximum displacement is of only 0.003[mm] and is therefore very low.

The most important deformation of the frame (cf figure 6.19) is the payload attachmentblock.


Figure 6.19: layer 3UCubeSat design, frame under 10g influence, exaggerated scaling


Figure 6.20: Cubic microsatellite, displacement vectors for 10g, exaggerated scaling

The highest deformation for the cubic microsatellite design (cf figure 6.20) are the two crosseson top and on bottom. The bottom cross is more deformed than the top one because of the ad-ditional weight of the inertial wheel attached to it.

Not surprisingly, the highest deformation of the frame (cf figure 6.21) are the two crosses,which are bending here under the influence of the 10g acceleration.


Figure 6.21: Cubic microsatellite, frame under 10g influence, exaggerated scaling


Figure 6.22: Octagonal microsatellite, displacement vectors for 10g, exaggerated scaling

The octagonal microsatellite design (cf figure 6.22) has a much lower maximal displacementvalue than the cubic design. This is due to its more compact form and the more efficient use ofspace. The highest displacements are at the frame itself at the sidebars.

The most important deformation of the frame (cf figure 6.23) is the inertial wheel attachmentcross.


Figure 6.23: Octagonal microsatellite, frame under 10g influence, exaggerated scaling

6.5 Modal analysis

The modal analysis calculates the eigenfrequencies. The frequencies are calculated using themodel attached to the bottom, this simulates best the launch environment.

6.5.1 Calculations

The most flexible parts of the satellite designs are the panels and the PCBs, as they are very thinand connected to the frame only on the edges, in the case of the panels, and on the corners, inthe case of the PCBs. A calculation of the first 20 eigenfrequencies showed that all twenty areeither the panels or the PCBs.

It is important to know that the lowest eigenfrequencies all come from the panels and PCBs,but it is also very important to know the eigenfrequencies of the frame. Therefore, eigenfre-quencies were not only calculated for the whole assembly but also for the frame alone.

A parameter to fix for the eigenfrequency calculations is the accuracy. As these values areonly used for a first indication of the eigenfrequencies, an accuracy of 1 was set. Higher accu-racies are of course possible, but they would slow down the calculations considerably withoutadding much information.

6.5.2 Results

Unfortunately, it is not possible to include video animations of the eigenfrequencies in the re-port, as those are done quite nicely by CATIA. In this section, the first ten eigenfrequencies ofthe assembly and the first five eigenfrequencies of the frame and a indication of which part isinvolved are given.

1UCubeSat, SwissCube design

As can be seen in table 6.7, the ten lowest Eigenfrequencies all come from the PCBs, whichis very logical, as the PCBs are, together with the panels, the thinnest parts. The panels arefastened all along the four edges, therefore they are much stiffer and their Eigenfrequency ismuch higher. It has to be noted that always five frequencies are similar, if not alike - this is dueto the fact that there are five PCBs in this assembly, one frequency per PCB.

Having the lowest eigenfrequency at 210[Hz] means that there are no problems with frequen-cies, the minimum Eigenfrequency for the CubeSat standards are set to 30[Hz] and all eigenfre-quencies are above this value.

The values in table 6.8 show a very high first eigenfrequency for the frame, which indicatesits good stiffness.


Number Value[Hz] Part#1 198 PCB, bending#2 200 PCB, bending#3 201 PCB, bending#4 201 PCB, bending#5 201 PCB, bending#6 336 PCB, torsion#7 338 PCB, torsion#8 339 PCB, torsion#9 339 PCB, torsion#10 339 PCB, torsion

Table 6.7: Eigenfrequencies of the 1UCubeSat, SwissCube design assembly

Number Value[Hz] Location#1 500 Rails bending x direction#2 513 Rails bending y direction#3 631 Rails torsion#4 693 Rails torsion#5 1262 Sidebars, bending

Table 6.8: Eigenfrequencies of the 1UCubeSat, SwissCube design frame

Stretched 3UCubeSat design

Number Value[Hz] Part#1 106 PCB, bending#2 106 PCB, bending#3 106 PCB, bending#4 106 PCB, bending#5 181 PCB, torsion#6 181 PCB, torsion#7 181 PCB, torsion#8 181 PCB, torsion#9 290 PCB, bending#10 290 PCB, bending

Table 6.9: Eigenfrequencies of the stretched 3UCubeSat design assembly

The values in table 6.9 show again that even the lowest eigenfrequencies are much higherthan the required 30[Hz]. Once more, all the frequencies come from the PCBs which againare the thinnest parts and the least attached to the frame. There is always a number of equaleigenfrequency, this time only four, which is logical since this designs only consists in fourPCBs.

The eigenfrequencies in table 6.10 seem at first glance very low, and it seems surprising theydo not show up in table 6.9. But, it cannot be neglected that the whole satellite structure ismuch strengthened through the side panels, the PCBs and most importantly the payload itself.Therefore, a rather low first Eigenfrequency of the frame, still very well beyond the limit, is noreason to worry at all.


Number Value[Hz] Location#1 87[Hz] Rails, bending in y direction#2 89[Hz] Rails, bending in x direction#3 160[Hz] Rails, torsion#4 470[Hz] Rails and payload attachment, “dancing”#5 518[Hz] Everything, bending

Table 6.10: Eigenfrequencies of the stretched 3UCubeSat design frame

Circular 3UCubeSat design

Number Value[Hz] Part#1 98 x side PCB, bending#2 98 x side PCB, bending#3 98 x side PCB, bending#4 98 x side PCB, bending#5 118 y side PCB, bending#6 118 y side PCB, bending#7 182 y side PCB, torsion#8 182 y side PCB, torsion#9 190 x side PCB, torsion#10 190 x side PCB, torsion

Table 6.11: Eigenfrequencies of the circular 3UCubeSat design assembly

The values in table 6.11 are very similar to those in table 6.9. This is not surprising, as thearrangement of the parts is very similar, the only difference being the addition of two PCBs.There is a slight difference between the x side PCBs (first four and last two frequencies) and they side PCBs, this is due to the fact that the y side PCBs are slightly less wide.

Number Value[Hz] Location#1 82 Rails, bending in y direction#2 85 Rails, bending in x direction#3 158 Rails, torsion#4 412 Rails and payload attachment, “dancing”#5 537 Everything, bending

Table 6.12: Eigenfrequencies of the circular 3UCubeSat design frame

The first eigenfrequencies in table 6.12 are the same as those in table 6.10, only the values areslightly different. Therefore, the same argument as in the former case can be made.

Layer 3UCubeSat design

The values in table 6.13 are very high. This is due to the fact that the PCBs are very small. Themotherboard has a bigger surface than the PCBs, therefore its eigenfrequency is lower.

The reasoning with the low frequencies in table 6.14 is the same as in the other two 3UCube-Sat cases. The higher frequency cases are more regular than in the other two cases because thisframe has a much simpler design.


Number Value[Hz] Part#1 365 satellite, bending#2 380 satellite, bending#3 506 Motherboard, bending#4 511 Motherboard, bending#5 607 Motherboard, bending#6 621 Motherboard, bending#7 669 PCB, bending#8 680 PCB, bending#9 693 PCB, bending#10 713 PCB, bending

Table 6.13: Eigenfrequencies of the layer 3UCubeSat design assembly

Number Value[Hz] Location#1 87 Rails, bending in y direction#2 89 Rails, bending in x direction#3 165 Rails, torsion#4 467 Rails, bending in x direction#5 471 Rails, torsion

Table 6.14: Eigenfrequencies of the layer 3UCubeSat design frame


Number Value[Hz] Part#1 48 PCB, bending#2 48 PCB, bending#3 48 PCB, bending#4 48 PCB, bending#5 48 PCB, bending#6 48 PCB, bending#7 52 Frame, inertial wheel attachement#8 60 Frame, inertial wheel attachement#9 61 PCB, torsion#10 61 PCB, torsion

Table 6.15: Eigenfrequencies of the Cubic microsatellite assembly

Compared to the eigenfrequencies for the 1UCubeSat and the 3UCubeSats, there are alreadyvery low eigenfrequencies for the frame in table 6.15. This is due to the high mass of the inertialwheel attached to the frame. Other than this, also the eigenfreqnecies of the PCBs is lower,because they are much longer and wider, but still have the same thickness.

The lowest eigenfrequencies are still beyond the 30[Hz], but they are getting closer. For thisreason, when choosing this satellite design, the thickness of the rails and sidebars needs to bereconsidered, the use of thicker PCBs may be needed.

The values in table 6.16 show reasonably high values. This is due to the use of wider railsand sidebars. There is the special case that the lowest eigenfrequency of the frame alone ishigher than the lowest eigenfrequency of the frame in the assembly configuration (table 6.15),but this can be explained by the fact that the low frequency in the assembly case is influencedby the weight of the inertial wheel.


Number Value[Hz] Location#1 180 inertial wheel attachment bar bending#2 215 backside cross bending#3 238 all cross sections bending#4 258 inertial wheel attachment bar bending#5 286 all cross sections bending

Table 6.16: Eigenfrequencies of the Cubic microsatellite frame


Number Value[Hz] Part#1 59 toppanel, bending#2 59 PCB, bending#3 59 PCB, bending#4 59 PCB, bending#5 59 PCB, bending#6 59 PCB, bending#7 59 PCB, bending#8 79 PCB, bending#9 79 PCB, bending#10 79 PCB, bending

Table 6.17: Eigenfrequencies of the Octagonal microsatellite assembly

All the eigenfrequencies given in table 6.17 are either in the top panel or the PCBs. The toppanel has a rather low eigenfrequency because of the big hole in the middle. If this model ischosen, the material selection for this panel needs to be reconsidered.

The remaining frequencies all come from the PCBs. In order to get higher frequencies, athickening of the PCBs can be considered.

Number Value[Hz] Location#1 77 Rails, bending#2 80 Rails, bending#3 98 Rails, torsion#4 273 Inertial wheel attachment cross#5 318 Everything, dancing

Table 6.18: Eigenfrequencies of the Octagonal microsatellite frame

6.6 Harmonic dynamic response

Harmonic dynamic response tests show how the model is influenced by an imposed oscillationwith a given frequency and amplitude. The test done in this case is a “white noise” tests, whichis a band of oscillation on all frequencies, with a amplitude equal to one (cf figure 6.24).

The calculation of the harmonic dynamic response requires the result of a modal analysis.The calculated frequencies are used to calculate the harmonic dynamic response. Therefore, theresults of section 6.5 are used. As only the first ten eigenfrequencies are calculated, the highesteigenfrequency also limits the range of the harmonic dynamic response.


Figure 6.24: white noise

Figures 6.25 hows the harmonic dynamic response of the 1UCubeSat design. The otherresults are in annex C.1.

Figure 6.25: Response of 1UCubeSat, SwissCube design to white noise; pink: top panel; green: x sidepanel; dark blue: y side panel; yellow, light blue and pink: x, y and z responses of the frame;black: PCB

6.7 Transient dynamic response

Transient dynamic response tests show how the model is influenced by a time limited appliedforce. The test chosen is a shock, modelled by a a force of 10[N] which is applied during 0.001[s],as can be seen in figure 6.26.

As in the harmonic dynamic response, the results of a modal analysis is needed. These re-sults are again taken from section 6.5. Figure 6.27 shows the response to a shock of the 1UCube-Sat design. The other results are in annex C.2.


Figure 6.26: Shock

Figure 6.27: Response of 1UCubeSat, SwissCube design to a shock; pink: top panel; green: x sidepanel; dark blue: y side panel; yellow, light blue and pink: x, y and z responses of the frame;black: PCB

6.8 Discussion

The four FEM analyses performed enable to get a rough overview of the soundness of the satel-lite designs and also indicate week points. The eigenfrequency are all above the required 30[Hz]but decrease with increasing height. The layer 3UCubeSat design has a very high lowest eigen-frequecy.

The von Mises stresses all indicate very low deformation even under the influence of anacceleration of 10g. Even the lowest MOS values are obove 100. It is interesting to note that theparts inside the satellite help to strengthen the structure, as the highest von Mises stresses forthe frame alone are higher than for the complete model.

Table 6.19 summarizes the most important results.An important aspect is to point out weak spots. Except for the 1UCubeSat design, all designs

are new and will therefore most probably be improved. Therefore, knowing the weakest partsis a good start for looking for improvement.

The stretched and the layer 3UCubeSat designs are not recommended, therefore, weak spotsare only pointed out for the other four designs. Table 6.20 describes the weakest points of thelatter.


Design Von Mises stress [MPa] Eigenfrequency [Hz]1UCubeSat 0.285 198Stretched 3UCubeSat 0.387 106Circular 3UCubeSat 0.192 98Layer 3UCubeSat 0.173 365Cubic Microsatellite 2.7 48Octagonal Microsatellite 1.4 59

Table 6.19: Highest von Mises stress and lowest eigenfrequency of the satellite designs

Design Weakest points1UCubeSat PCBsCircular 3UCubeSat PCBs

Cubic microsatellitePCBsPanelsFrame: crossbars

Octagonal microsatellitePCBsFrame: sidebarsFrame: inertial Wheel attachement

Table 6.20: Weakest parts in frame design

Chapter 7

Summary

7.1 CDF interface design

A structure CDF interface was developed. it is based on the standard CDF MS Excel interface,including the Inputs, Outputs and Calculations Worksheets. In the latter, the parameters goingout to the CDF database are defined. They are:

• The mass of the satellite

• The mass of the structure parts

• The volume of the satellite

• The Surface of the satellite

• The center of gravity of the satellite

• The inertia matrix of the satellite

Additional to those three worksheets, several more worksheets are defined:

• CATIA: Responsible for the parameter exchange with CATIA

• Materials: Lists all the used materials and their properties

• Budget: Lists the mass, volume, surface, center of gravity and matrix of inertia of all parts.It sums up the mass, volume and surface of the structure parts as well as of all parts.

• Structure: Lists the mechanical properties of the satellite

• Frame, Panel, Spacer, Payload, PCB, MB, Battery and Wheel: Lists all the dimensions of thepart. Some of the dimensions are free to chose by the user, but most are related to otherdimensions

• Launch vehicles: Lists the most probable launch vehicles to be used and some of their mostimportant properties.

The parameter exchange, done in the CATIA worksheet,synchronizes the parameters withthe CATIA model: first, the dimensions are updated, then, the new physical properties aredownloaded to the interface.

79


7.2 Structure design

All the structure designs were done with CATIA. The designed parts consist in the structureparts: the frame, the panels and the spacers; and the mechanical representation of the subsys-tems: the PCBs, the motherboard, the payload, the battery and the inertial wheels. Smallerparts, such as screws, were not designed.

The frame is considered being a monoblock. This is actually the case for the SwissCubeanyway, and it can be imagined using monoblock frames for the 1UCubeSat and 3UCubeSatdesigns. For the larger microsatellites, this will not be possible. The construction of their framesmust be reviewed, welding or screwing together several parts is the most probable solution. Thebattery and payload parts, which are quite complex constructions in themselves, are designedbeing a single part.

Six different satellites have been designed: one 1UCubeSat, three 3UCubeSats, one cubicmicrosatellite and one octagonal microsatellite. Out of the three 3UCubeSats, only one is rec-ommended for use, the circular design. The other two have too serious drawbacks. Table 7.1summarizes the six satellite designs.

Name Description Advantages(+) andDisadvantage(-)

1UCubeSat100× 100× 100

[mm3

]+ Light frame

SwissCube design + Efficient use of volumePCBs placed on 2 sides of the payload - Small

Stretched 3UCubeSat100× 100× 300

[mm3

]+ Simple design

Directly derived from 1UCubeSat - Inefficient use of volumePCBs placed on 2 sides of the payload - Only 4 PCBs

Circular 3UCubeSat100× 100× 300

[mm3

]+ Efficient use of volume

Improvement of stretched 3UCubeSat + Up to 6 PCBsPCBs placed on 4 sides of the payload - Difficult to assemble

Layer 3UCubeSat 100× 100× 300[mm3

]+ Stiff structure

PCBs used to strengthen structure - Small PCB surfacePCBs have a hole in the middle


400× 400× 400[mm3

]+ Large volume

Derived from 1UCubeSat + Easy to assembleSeveral sidebars and crossbars - Inefficient use of volumePCBs placed on one side - Rather big deformations3 Inertial wheels


400×�400[mm3

]+ Stiff structure

octagonal base shape + Large volumePCBs placed on six sides + Efficient use of volume3 Inertial wheels - Complicated to assemble

Table 7.1: Overview of satellite designs


7.3 FEM analysis

Four types of FEM analysis were done:

• Static load: The deformation and stresses are calculated under the influence of 10g, whichis the worst case scenario acceleration. The test has been done for the frame alone and thesatellite.

• Modal analysis: The first ten eigenfrequencies were calculated for the frame and the satel-lite.

• Harmonic dynamic response: The dynamic response of the satellite to white noise is calcu-lated.

• Transient dynamic response: The dynamic response of the satellite to a shock is calculated.

The assembly used for obtaining the mechanical properties of the satellite were altered fordoing the FEM calculations. Instead of using 3D tetrahedral meshes on all parts, 2D shellmeshes and 1D beam meshes were used whenever possible. These meshes speed up the calcu-lation because the number of nodes is much smaller. It also increases the accuracy of the resultsas 3D meshes tend to produce faulty results if the tetrahedrons are very irregular.

Shell meshes were used for the PCBs, the motherboard and the panels. Additional, dis-tributed masses were added to the PCBs and the panels in order to simulate the electroniccomponents and the solar cells. Beam meshes were used for the spacers.

The results of the FEM analyses were done on different mesh sizes in order to guaranteetheir independce. The results for the 1UCubeSat reproduce the results found for SwissCube.All satellite designs are compatible with existing launch vehicles.

Tables 7.2 summarizes the results of the FEM analyses and table 7.3 discusses the weakestpoints of the four satellite design which are recommended for use.

Design Von Mises stress [MPa] Eigenfrequency [Hz]1UCubeSat 0.285 198Stretched 3UCubeSat 0.387 106Circular 3UCubeSat 0.192 98Layer 3UCubeSat 0.173 365Cubic Microsatellite 2.7 48Octagonal Microsatellite 1.4 59

Table 7.2: Highest von Mises stress and lowest eigenfrequency of the satellite designs

Design Weakest points1UCubeSat PCBsCircular 3UCubeSat PCBs

Cubic microsatellitePCBsPanelsFrame: crossbars

Octagonal microsatellitePCBsFrame: sidebarsFrame: inertial Wheel attachement

Table 7.3: Weakest parts in frame design

Chapter 8

Conclusions

This master thesis project was performed at the Spacer Center EPFL during the 2009 springsemester. A structure subsystem for nano and microsatellites was established and six satelliteswere designed: one 1UCubeSat, three 3UCubeSats, one cubic and one octagonal microsatellite.It consists in a CDF interface and two CATIA assembly. The CDF interface is the connectionpart between the CATIA assemblies and the CDF database. It enables the change of dimensionsof the parts and synchronizes them with the CATIA assemblies.

The first CATIA assembly is a 3D representation of the satellite and is used to calculate themechanical properties of the satellite: its mass, volume, surface, center of gravity and matrix ofinertia. The second CATIA assembly is used for FEM analysis. The 3D parts for the panels, PCBsand motherboard were replaced by 2D shells and the 3D parts for the spacers were replaced by1D beams.

Four type of FEM analyses were performed: static loads, modal analysis, harmonic and tran-sient dynamic responses. The FEM results were verified by varying mesh sizes and comparingthe 1UCubeSat’s results with SwissCube. For the 1UCubeSat design, the SwissCube resultswere reproduced. The results of the other satellite design give a first order overview of theirreaction to static loads and their eigenfrequencies. All values are well within the requirementsand the weakest points were spotted.

For future work, the following points are recommended, in no particular order:

• Design a detailed assembly of the Payload

• Determine the optimal edge bar and side bar width for the microsatellite designs

• Strengthen the weakest points of the microsatellite designs

• Make a trade-off between weight and stiffness for the PCB thickness

• Define the construction method for the microsatellite designs

• Set up assembly plans

July 31, 2009Andreas Fuglistaler

82

Appendix A

User Manual

This user manual gives an overview of all the possibilities on using the CDF interface togetherwith CATIA models. The first section explains how to use an existing satellite design. Thesecond section explains how to create a new satellite design.

A.1 Using an existing design

All the examples are done using the 1UCubeSat, SwissCube design, but they can as well bedone using the other satellite designs.

A.1.1 Interface description

A complete satellite design consists of three parts:

• CDF database MS Excel file (interface)

• Mechanical CATIA assembly model

• FEM CATIA assembly model

When starting the MS Excel file, make sure that the macros are activated (cf figure A.1), in orderto use the interface.

The CDF interface consists in several worksheets (cf figure A.2). Each one has a specifictask. The first three worksheets, Inputs, Outputs and Calculation are used for exchanging datawith the CDF database. No changes should be done for the first one, and it is recommendednot to change the third one either as long as possible.

The CATIA worksheet (cf figure A.3)is the core of the interface. The four Buttons Clear all,make Output List, make Input List and Synchronize launch internal VBA macros. Their use will beexplained in the next sections.

The two yellow lines in define the files for the mechanical CATIA assembly and the FEMCATIA assembly. Make sure these file names are correct. Otherwise, you run the risk of over-writing files you do not want to be overwritten.

The Output Variables list and the Input Variables list define the parameters to be uploaded anddownloaded. Do not change those list manually, they are created directly by the VBA macros.

The Budget worksheet (cf figure A.4) is for informational use only. These values are directlyread from the mechanical CATIA model. They list the mass, volume, surface, center of gravityand matrix of inertia for all parts. The mass, volume and surface are then summed up for thestructure parts (Frame, Panels and spacers) and for all satellite parts.

83


Figure A.1: Macro activation window

Figure A.2: CDF user interface worksheet names

The Structure worksheet (cf figure A.5) is again only for informational use. It presents themass, volume, surface, center of gravity and inertia matrix for the whole satellite. Those valuesare calculated by CATIA.

It is a good indication that something is going wrong if the mass on this sheet is not equal tothe total mass of the Budget sheet. If this is the case, you probably should start looking for theerror.

In the remaining worksheets (Frame, Panel, Spacer, Payload, PCB, MB and Battery) the pa-rameters of the parts with the indicated name are defined. These are the actual user inputworksheets, how to handle them is described in the following sections.

A.1.2 Changing parameters

In the user input worksheets (cf figure A.6), there are two types of values, which are differ incolor. The white ones are user input values, which can, to a certain extend, be freely chosen. Theyellow ones are values which depend on other parameters. It is recommended not to changethe yellow parameters unless you are sure what you are doing.

In order to change a parameter, one must:

• Change the value in the worksheet

• Synchronize


Figure A.3: CDF interface CATIA worksheet

Figure A.4: CDF interface Budget worksheet

• Verify the CATIA models for errors

The first step is very easy: just chose the value you want to change and enter the value.Please note that you can also change the unit, as the unit is part of the information sent to theCATIA model, but it is highly recommended to use the same dimensioning unit for all parts, asotherwise the relations between the parts become very complicated.

To synchronize, simply push the button Synchronize in the CATIA worksheet (cf figure A.3).If you want to see the whole procedure, you can first push the Clear all button, which will clearboth the output variables and the input variables. Then, pushing Make Output List, the OutputVariables list is created. Last, when pushing the Make Input List button, the Input Variables listis created. Please note that the Value in this list remains empty as this list is filled during thesynchronization.

The last point, verifying the model, is very important. All the parameters are defined us-ing dependencies so that by changing one dimension, all the parts which depend directly orindirectly on this dimension are changed as well. This nevertheless does not exclude errors.For example, if you define a payload length longer than the y dimension, you will get negativevalues in the Payload worksheet and CATIA will complain.

Even though all the parameters are linked to each other, the choice of the parameters stillneeds to be done rationally and in the spirit of the satellite design, otherwise the CATIA modelswill not be correct.


Figure A.5: CDF interface Structure worksheet

A.1.3 Changing parts

The most common part to change is the payload. All the satellite designs are made with acamera as payload, but of course, other payloads are possible as well.

In order to change a part, the following steps need to be done for both the mechanical CATIAmodel and the FEM CATIA model:

• Exchange the part

• Set the new constraints (if necessary)

• define the new parameters (if necessary)

• Link parameters to the new part

For the first step, you need to right click on the part to exchange, choose Components andthen Replace Component . . . . After, a window opens and you can select the new part.

The exchange of parts is much more easier if the new part is of similar form and constructedthe same way. If this is the case, CATIA proposes to reuse the constraints of the old part forthe new part and there is therefore no need for resetting the constraints. If the new part is quitedifferent, you need to manually delete the old constraints and replace them with new ones.

If the new part does not use the same parameters or additional parameters, you need todefine them. First, in the MS Excel file, remove the unused parameters and add the new param-eters. Secondly, you need to define the new parameters in the CATIA assembly environment.This is done by clicking on the formula button (cf A.7), there, you need to create the new pa-rameters by pushing the button new Parameter of type, make sure the type in on Length(cf figureA.8). The name of the parameter must be

worksheetName parameterName

Once all the new parameters are defined in the CATIA assembly environment, you can linkthe parameters of the new part with those parameters. This is done by opening the formulabutton, then clicking on the new part, which filters the parameters of this part. If you renamedthe parameters of the new part (if you did not, it is probably a good idea to do it now), set theFilter Type on Renamed parameters.

In order to link these parameters with the parameters you created, you need to set formulas.This is done by selecting the parameter you would like to link and pushing the Add formula


Figure A.6: CDF interface Frame worksheet

Figure A.7: CATIA formula button

button, this opens a new window shown in figure A.9. In the entry box, enter the name of theparameter you would like to link, then push the button OK.

If you have finished linking all the parameters, you successfully exchanged a part in theassembly and can continue to work with the CDF interface as before.


Figure A.8: CATIA Formula window

Figure A.9: CATIA “add formula” window


A.2 Creating a new satellite design

There are two ways of creating a new satellite design, a simple way and a not so simple way.The first one uses an already created satellite design, copies everything it needs, removes allthe rest and links the missing parameters. The second one means starting everything from thebeginning. This method is not recommended, it wastes unnecessarily a lot of time, therefore,only the first method will be discussed here.

In order to create a new satellite design, the following steps need to be done:

• copy an existing satellite design

• “outsmart” CATIA

• Delete all constraints

• Remove the unused parts

• Add all the new parts

• Link the new parts

In the first step, it is worth thinking a second or two before deciding which satellite designyou want to copy. If it is going to be a 1UCubeSat, it is probably a good idea to copy theSwissCube design. If it going to be a microsatellite, you better take a microsatellite design.Once you have chosen the satellite design, just copy the whole directory to a new place.

The second step is very important. Even though you copied everything to a new place, thenew assemblies are still using the old parts. In order to avoid this, there is an easy way to changethis: You can “outsmart” CATIA by renaming the old satellite design directory name. Simplyad a “ 1” or something else to the directory name. Then, start the new assembly, which will notfind the parts in the old directory anymore, and therefore starts looking for them in the mostprobable place, which is the same directory as the assembly. Using this technique, the new partsare directly linked to the new assembly. It is important to safe the assembly after having donethis, otherwise, next time you open it, it will once again use the parts of the new old design.Do not forget to rename the directory name of the old design once you finished outsmartingCATIA.

The next step is not totally necessary but rather recommended, it is much easier to redefineall the constraints again instead of finding out which constraints are still working and whichare not.

Once you’ve done the precedent steps, you can start redesigning your satellite. You want tokeep as many parts as possible, even if you are going to change them slightly, as you then canuse their parameters. Make sure to parametrize the new parts correctly in the CDF interface andto create the corresponding parameters in the CATIA assembly. You will probably also have tochange the relations between the parameters, as they are different for each satellite.

The final step is to link the parameters of the parts with the parameters defined in the as-sembly.

Appendix B

Technical details

B.1 1UCubeSat, SwissCube design

B.1.1 Frame

Name DefinitiondimX User inputdimY User inputdimZ User inputrailX User inputrailY User inputfeetPlus User inputfeetMinus User inputbarWidth User inputbarHeigth User inputpayloadRad Payload radpayloadWidth barWidthpayloadHeigth barHeigthpayloadSquare 2 · payloadRad + barWidthattBarLength railX-barWidth + attLengthattWidth barWidthattDist Battery height + 2 · Battery attWidthattLength 2 · Spacer outerRad

Table B.1: 1UCubeSat, SwissCube design, Frame Parameters

90


Figure B.1: 1UCubeSat, SwissCube design, frame drafting

B.1.2 Panel


Name Definitionthickness User inputheight Frame dimZXwidth Frame dimXYwidth Frame dimYrad Payload radZDimX Frame dimXZDimY Frame dimYZHoleX Frame railZHoleY Frame railY

Table B.2: 1UCubeSat, SwissCube design, Panel Parameters

Figure B.2: Drafting of a 1UCubeSat sidepanel


Figure B.3: Drafting of a 1UCubeSat toppanel


B.1.3 Spacer

Name DefinitionouterRad User inputinnerRad User inputlength1 User inputlength2 1

2 (Frame dimY − Frame attDist)− 2 · Frame barWidth−2 · PCB thickness− length1− length3

length3 User inputlength4 User inputlength5 1

2 ( 12 (Frame dimY − Frame attDist)− 2 · Frame barWidth

−2 · PCB thickness− length4− length7)

length6 length5length7 User input

Table B.3: 1UCubeSat, SwissCube design, Spacer parameters

Figure B.4: Drafting of a Spacer

B.1.4 Payload


Name Definitionrad User inputlength User inputconLength Frarme dimX− FrarmerailX − 1

2Frarme attLength−Frarme attWith− 1

2Battery width− length

conWidth Battery heightsquare Frame payloadSquare

Table B.4: 1UCubeSat, SwissCube design, Payload parameters

Figure B.5: Drafting of the Payload

B.1.5 PCB

Name Definitionthickness User inputheight1 Frame dimZheight2 height1−MB thicknesswidth Xdist + 2 · Frame attLengthXdist Frame dimX− 2 · Frame railX− Frame attLengthZdist Frame dimZ− 2 · Frame barHeigth− FrameattLength

rad Spacer innerRad

Table B.5: 1UCubeSat, SwissCube design, PCB parameters


Figure B.6: Drafting of a PCB

B.1.6 Motherboard

Name Definitionthickness User inputdimX Frame dimXdimY Frame dimYrailX Frame railXrailY Frame railY

Table B.6: 1UCubeSat, SwissCube design, Motherboard (MB) parameters


Figure B.7: Drafting of a PCB

B.1.7 Battery

Name Definitionwidth User inputheight User inputlength User inputattLength dist + 2 · Frame barWidthattWidth User inputdist Frame dimY − 2 · Frame barHeigth− Frame attLengthrad Spacer innerRad

Table B.7: 1UCubeSat, SwissCube design, Battery parameters


Figure B.8: Drafting of the battery

B.2 3UCubeSat, stretched SwissCube design

B.2.1 Frame


Name DefinitiondimX User inputdimY User inputdimZ User inputrailX User inputrailY User inputfeetPlus User inputfeetMinus User inputbarWidth User inputbarHeigth User inputpayloadRad Payload radpayloadWidth barHeigthpayloadHeigth barHeigthpayloadSquare 2 · payloadRad + barWidthattBarLength railX-barWidth + attLengthattWidth barWidthattDist Battery height + 2 · Battery attWidthattLength 2 · Spacer outerRadattRad Spacer innerRadMBlength barWidth + 1

2MB thickness

Table B.8: 3UCubeSat, stretched SwissCube design, Frame Parameters


Figure B.9: 3UCubeSat, stretched SwissCube design, frame drafting


B.2.2 Panel

Name Definitionthickness User inputheight Frame dimZXwidth Frame dimXYwidth Frame dimYrad Payloadrad

ZDimX Frame dimXZDimY Frame dimYZHoleX Frame railXZHoleY Frame railY

Table B.9: 3UCubeSat, stretched SwissCube design, Panel Parameters

B.2.3 Spacer

Name DefinitionouterRad User inputinnerRad User inputlength1 1

2 ( 12Frame dimY − 1

2Frame attDist− Frame attWidth−Frame barWidth− PCB thickness)

length2 length1length3 length1length4 length1

Table B.10: 3UCubeSat, stretched SwissCube design, Spacer parameters

B.2.4 Payload

Name Definitionrad User inputlength User inputconLength Frarme dimZ− Frame barHeigth− Frame payloadWidth

−Frame attLength− Battery width− length


Table B.11: 3UCubeSat, stretched SwissCube design, Payload parameters

B.2.5 PCB


Name Definitionthickness User inputheight1 1

2Frame dimZ− Frame barHeigthheight2 height1−MB thicknesswidth Xdist + 2 · Frame attLengthXdist Frame dimX− 2 · Frame railX− Frame attLengthZdist Frame dimZ− 2 · Frame barHeigth− Frame attLengthrad Spacer innerRadZpos 1

2Frame attLength

Table B.12: 3UCubeSat, stretched SwissCube design, PCB parameters

B.2.6 Motherboard

Name Definitionthickness User inputdimX Frame dimXdimY Frame dimYrailX Frame railXrailY Frame railYattBarlength Frame attBarLength + Frame barWidthattDist Frame attDistsquare Frame payloadSquare

Table B.13: 3UCubeSat, stretched SwissCube design, Motherboard (MB) parameters

B.2.7 Battery

Name Definitionwidth User inputheight User inputlength User inputattLength dist + 2 · Frame attLengthattWidth User inputdist Frame dimX− 2 · Frame railX− Frame attLengthrad Spacer innerRad

Table B.14: 3UCubeSat, stretched SwissCube design, Battery parameters

B.3 3UCubeSat, circular SwissCube design

B.3.1 Frame


Name DefinitiondimX User inputdimY User inputdimZ User inputrailX User inputrailY User inputfeetPlus User inputfeetMinus User inputbarWidth User inputbarHeigth User inputpayloadRad Payload radpayloadWidth barHeigthpayloadHeigth barHeigthpayloadSquare 2(·payloadRad) + barWidthattBarLength railX-barWidth + attLengthattWidth barWidthattDist Battery height + 2 · Battery attWidthattLength 2 · Spacer outerRadattRad Spacer innerRadMBlength barWidth + 1

2MB thickness

Table B.15: 3UCubeSat, circular SwissCube design, Frame Parameters


Figure B.10: 3UCubeSat, circular SwissCube design, frame drafting


B.3.2 Panel



Table B.16: 3UCubeSat, circular SwissCube design, Panel Parameters

B.3.3 Spacer




length2 length1length3 length1length4 length1length5 1

2 (Frame attBarLength− PCB thickness)length6 length5length7 length5length8 length5

Table B.17: 3UCubeSat, circular SwissCube design, Spacer parameters

B.3.4 Payload




Table B.18: 3UCubeSat, circular SwissCube design, Payload parameters

B.3.5 PCB


Name Definitionthickness User inputheight1 1

2Frame dimZ− Frame barHeigthheight2 height1−MB thicknesswidth Xdist + 2 · Frame attLengthXdist Frame dimX− 2 · Frame railX− Frame attLengthYdist Frame attDist− Frame attLengthZdist Frame dimZ− 2 · Frame barHeigth− Frame attLengthrad Spacer innerRadZpos 1

2Frame attLength

Table B.19: 3UCubeSat, circular SwissCube design, PCB parameters

B.3.6 Motherboard

Name Definitionthickness User inputdimX Frame dimXdimY Frame dimYrailX Frame railXrailY Frame railYattBarlength Frame attBarLength + Frame barWidthattDist Frame attDistattWidth Frame attWidthsquare Frame payloadSquare

Table B.20: 3UCubeSat, circular SwissCube design, Motherboard (MB) parameters

B.3.7 Battery


Table B.21: 3UCubeSat, circular SwissCube design, Battery parameters

B.4 3UCubeSat, layer PCB design

B.4.1 Frame


Name DefinitiondimX User inputdimY User inputdimZ User inputrailX User inputrailY User inputfeetPlus User inputfeetMinus User inputbarWidth User inputbarHeigth User inputpayloadRad Payload radpayloadWidth barWidthpayloadHeigth barHeigthpayloadSquare 2 · payloadRad + barWidthattBarLength railX-barWidth + attLengthattWidth barWidthattDist Battery height + 2 · Battery attWidthattLength 2 · Spacer outerRadattRad Spacer innerRad

Table B.22: 3UCubeSat, layer PCB design, Frame Parameters

B.4.2 Panel



Table B.23: 3UCubeSat, layer PCB design, Panel Parameters


Figure B.11: 3UCubeSat, layer PCB design, frame drafting


B.4.3 Spacer




length2 length1

Table B.24: 3UCubeSat, layer PCB design, Spacer parameters

B.4.4 Payload




Table B.25: 3UCubeSat, layer PCB design, Payload parameters

B.4.5 PCB

Name Definitionthickness User inputdimx Frame dimXdimy Frame dimYrailx Frame railXraily Frame railYrad Payload radycut Frame railY + MB thicknessattLength Frame attLengthbackcutx Frame attLength + Frame railXbackcuty 1

2 (Frame dimY − Frame attDist)− FramerailX

Table B.26: 3UCubeSat, layer PCB design, PCB parameters

B.4.6 Motherboard


Name Definitionthickness User inputdimX Frame dimX− 2Frame railXdimZ Frame dimZ− 2Frame barHeigthXdist Frame dimX− 2Frame railX− Frame attLengthZdist Frame dimZ− 2Frame barHeigth− Frame attLengthrad Spacer innerRad

Table B.27: 3UCubeSat, layer PCB design, Motherboard (MB) parameters

B.4.7 Battery


Table B.28: 3UCubeSat, layer PCB design, Battery parameters

B.5 Microsatellite, cubic design

B.5.1 Frame

Name DefinitiondimX User inputdimY User inputdimZ User inputmainWidth User inputminorWidth User inputfeetPlus User inputfeetMinus User inputpayloadRad Payload radattLength 2 · Spacer outerRadattRad Spacer innerRadinertiaRad Wheel conRad12 (inertiaDist dimY − 2payloadRad− 4minorWidth− 2mainWidth)

Table B.29: Microsatellite, cubic design, Frame Parameters


Figure B.12: Microsatellite, cubic design, frame drafting

B.5.2 Panel


ZDimX Frame dimXZDimY Frame dimYZHoleX Frame mainWidthZHoleY Frame mainWidth

Table B.30: Microsatellite, cubic design, Panel Parameters

B.5.3 Spacer



4 ( 12 (Frame dimY − Frame payloadRad)− 2Frame minorWidth

−Frame mainWidth− PCB thickness)

length2 length1length3 length1length4 length1

Table B.31: Microsatellite, cubic design, Spacer parameters

B.5.4 Payload

Name Definitionrad User inputlength User inputconLength Frarme mainWidthconHeight Frame minorWidthconWidth Frame dimX− Frame mainWidth− Frame inertiaDist

−Frame minorWidth− length− Batterywidth

square Battery square

Table B.32: Microsatellite, cubic design, Payload parameters

B.5.5 PCB


Name Definitionthickness User inputheight Frame dimZ− Frame mainWidth− ( 1

2Frame dimZ−Frame payloadRad− 2Frame minorWidth

width 12 (Frame dimZ− 2Frame mainWidth− FrameminorWidth)

Xdist width− Frame attLengthZdist Frame dimZ− Frame mainWidth− ( 1

2Frame dimZFrame payloadRad− Frame minorWidth)− Frame attLength

rad Spacer innerRadholeDist 1

2Frame attLength + Frame minorWidthmiddleDist Spacer innerRadmiddleDist 1

2Frame dimZ− Frame mainWidth

Table B.33: Microsatellite, cubic design, PCB parameters

B.5.6 Motherboard

Name Definitionthickness User inputdimX Frame dimXdimY Frame dimY − 1

2 (Frame dimY − 2Frame payloadRad)−2Frame minorWidth)− Frame minorWidth

cutWidth Frame minorWidthcutHeight 1

2Frame dimY − Frame payloadRad−mainWidthrail Frame mainWidthsemiY 1

2Frame dimY − Frame mainWidth

Table B.34: Microsatellite, cubic design, Motherboard (MB) parameters

B.5.7 Battery

Name Definitionwidth User inputsquare User input

Table B.35: Microsatellite, cubic design, Battery parameters

B.5.8 Wheel


Name DefinitionmainRad User inputconRad User inputbaseRad User inputconLength Frame minorWidthlength Frame inertiaDist + Frame minorWidththickness User inputholeOuter User inputholeInner User input

Table B.36: Microsatellite, cubic design, wheel parameters

Figure B.13: Drafting of an inertial wheel

B.6 Microsatellite, octagonal design, Frame Parameters

B.6.1 Frame


Name Definitionheight User inputrad Payload radwidth User inputcercleWidth User inputcrossWidth User inputinertiaWidth 1

2widthinertiaHeight User inputPCBSpace User inputbigRail User inputsmallRail User inputattDist Spacer outerRadattRad Spacer innerRadwheelRad User inputbatteryDist Battery distbatteryRad Battery radxDist User input

Table B.37: Microsatellite, octagonal design, Frame Parameters


Figure B.14: Microsatellite, octagonal design, frame drafting


B.6.2 Panel

Name Definitionthickness User inputheight Frame heigthwidth 2(Frame rad + Frame cercleWidth + Frame inertiaHeight

+Frame PCBSpace) ∗ tan(22◦)

octRad Frame rad + Frame cercleWidth + Frame PCBSpace + Frame width

Table B.38: Microsatellite, octagonal design, Panel Parameters

B.6.3 Spacer


2 (Frame PCBSpace− PCB thickness)length2 length1

Table B.39: Microsatellite, octagonal design, Spacer parameters

B.6.4 Payload



conWidth Battery heightsquare Battery square

Table B.40: Microsatellite, octagonal design, Payload parameters

B.6.5 PCB


Name Definitionthickness User inputheight1 Frame heightheight2 height1−MB thicknesswidth Frame xDist + 2Frame attDistXdist Frame XdistZdist Frame height− Frame width− Frame inertiaHeight

− 12 (Frame inertiaWidth + Frame width

rad Spacer innerRadattDist Frame attDist

Table B.41: Microsatellite, octagonal design, PCB parameters

B.6.6 Motherboard

Name Definitionthickness User inputrad Battery radoctRad Frame rad + Frame cercleWidth + Frame PCBSpace

Table B.42: Microsatellite, octagonal design, Motherboard (MB) parameters

B.6.7 Battery

Name Definitionwidth User inputsquare User inputdist User inputrad Spacer innerRadbigRad dist + Frame width

Table B.43: Microsatellite, octagonal design, Battery parameters

B.6.8 Wheel


Name DefinitionmainSmallRad User inputmainBigRad User inputconRad User inputbaseRad User inputconLength Frame widthsmallLength Frame PCBSpacebigLength Frame inertiaHeightthickness User inputholeOuter User inputholeInner User input

Table B.44: Microsatellite, octogonal design, Wheel parameters

Appendix C

Dynamic response

C.1 Harmonic

Figure C.1: Response of 3UCubeSat, stretched SwissCube design to white noise; pink: top panel;green: x side panel; dark blue: y side panel; yellow, light blue and pink: x, y and z responses ofthe frame; black: PCB

Figure C.2: Response of 3UCubeSat, circular SwissCube design to white noise; pink: top panel; green:x side panel; dark blue: y side panel; yellow, light blue and pink: x, y and z responses of theframe; black: PCB

120


Figure C.3: Response of 3UCubeSat, layer PCB design to white noise; pink: top panel; green: x sidepanel; dark blue: y side panel; yellow, light blue and pink: x, y and z responses of the frame;black: PCB; dark green: motherboard

Figure C.4: Response of Microsatellite, cubic design to white noise; pink: top panel; green: x sidepanel; dark blue: y side panel; yellow, light blue and pink: x, y and z responses of the frame;black: PCB; dark green: inertial wheel

Figure C.5: Response of Microsatellite, octagonal design to white noise; pink: top panel; green: sidepanel; dark blue, yellow, light blue, x, y and z responses of rail pink: PCB; black: inertial wheel


C.2 Transient

Figure C.6: Response of 3UCubeSat, stretched SwissCube design to a shock; pink: top panel; green:x side panel; dark blue: y side panel; yellow, light blue and pink: x, y and z responses of theframe; black: PCB

Figure C.7: Response of 3UCubeSat, circular SwissCube design to a shock; pink: top panel; green:x side panel; dark blue: y side panel; yellow, light blue and pink: x, y and z responses of theframe; black: PCB


Figure C.8: Response of 3UCubeSat, layer PCB design to a shock; pink: top panel; green: x sidepanel; dark blue: y side panel; yellow, light blue and pink: x, y and z responses of the frame;black: PCB; dark green: motherboard

Figure C.9: Response of Microsatellite, cubic design to a shock; pink: top panel; green: x side panel;dark blue: y side panel; yellow, light blue and pink: x, y and z responses of the frame; black:PCB; dark green: inertial wheel

Figure C.10: Response of Microsatellite, octagonal design to a shock; pink: top panel; green: sidepanel; dark blue, yellow, light blue, x-, y- and z responses of rail pink: PCB; black: inertialwheel

Documents

Final report Conception of nano-satellites in a …fueglist/pdfs/AndreasFueglistaler_MSc.pdf · 3. Contents I Record of ... [R4]Werner Koehldorfer, Finite-Elemente-Methoden mit CATIA