Infante’s Structural Model: Preliminary Design Process and

Analysis

Nuno Maria Mota Paiva de Andradanuno.andrada@tecnico.ulisboa.pt

Instituto Superior Tecnico, Universidade de Lisboa, Portugal

June 2019

Abstract

Over the last couple of decades there has been a paradigm shift in the space sector. Large andexpensive satellites with long operation cycles are being replaced by constellations of smaller and cheaperones with shorter lifetime cycles, faster developed and manufacture times, and easily replaced in caseof failure. This paradigm shift is motivated by the standardization of the cubesat design and bydevelopments in the mobile, automotive and computer industries which result in smaller, lighter, cheaperand more powerful electronic components as well as in new manufacturing techniques and technologies.These factors have made it financially viable for private companies to invest in the space industry andservices. INFANTE is a pioneer Portuguese Research and Development (R&D) project that appears inthe context of the ”New Space” era. It is divided in two areas, Space and Ground. The Space segmentincludes a low cost smallsat platform for Earth observation (EO) applications. This work focuses on thesatellite’s structural subsystem development up to the preliminary design review (PDR). First, a cubesatstructure state of the art is presented and is used as market study to derive different solution concepts.Then, several trade-offs concerning major design points are discussed. Afterwards, a computationalmodel is derived to study the structure’s behaviour by performing static, modal, harmonic response andrandom vibrations analyses. The applied loads were provided by the launch vehicle entity (LVE). Afterdiscussing the analysis results, the conclusions are presented and future work proposals are made.Keywords: Smallsat, Structure, Design Development, Static Analysis, Dynamic analysis, Preliminarydesign review

1. IntroductionThe main objective of this paper is to document thedevelopment of INFANTE’s 16U structural subsys-tem up to preliminary design review. This work ex-plores the cubesat structure state of the art whichis used as benchmark to then address major de-sign aspects, considerations and trade-offs madeduring the preliminary design process. Following,a computer-aided design (CAD) model is devel-oped using SolidWorks 2016. To study the model’sbehaviour when subjected to the launcher loads,quasi-static and dynamic simulations are performedusing ANSYS 18.1 software.

INFANTE is a Portuguese R&D project that ap-pears in the context of the New Space era wheresmall satellites and massive constellations lead theway of space access. The project proposes the de-sign, production, launch and operation of a smallsatellite based on the cubesat standards which isintended to be a precursor of a constellation formaritime surveillance, Earth observation and com-munications between satellites and ground stations.

This is a pioneer project in Portugal given it’s

magnitude and the number of parties involved. Intotal 20 entities, from companies, to R&D centres,institutes and international organizations, form aconsortium, lead by Tekever, which will launch thefirst satellite completely designed, manufacturedand operated solely by the Portuguese industry.

The space industry has been evolving, mov-ing towards a democratization. According tonanosats.eu, a nanosat database that keeps recordsof missions, constellations, new technologies, launchproviders and many more detailed information, thenumber of launched nanosatellites has been steadilyincreasing from just two in 1998 to more than twohundred in 2017 and in 2018. Figure 1, shows thenumber of launched nanosatellites in the period be-tween 1998 and 2018 and the predictions made byNanosats Database and SpaceWorks, compiled byNanosats Database. Nanosats Database [1] predictsthat in the next six years more than three thou-sand nanosatellites will be launched, more than fivehundred of which will be launched in 2019 alone.It is possible to see that the tendency is for thenanosatellite launch numbers to keep increasing and

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it is predicted that in 2023 will be launched morethan 700 nanosatellites.

Figure 1: Nanosatellites launches between 1998 and2023 - Including nanosats.eu predictions (Adaptedfrom [1])

The increasing number of operating nanosatel-lites, have remarkable repercussions in both thecommercial and the scientific world. By havingaccess to Space, universities are able to test awide variety of payloads in orbit that otherwisewould not be possible for most of them, therefore,pushing the scientific boundaries further at eachlaunch. With the increasing number of companiesflying their nanosatellites for commercial applica-tions, like Planet, Spire, OneWeb and many others,the consumer will benefit from the market competi-tion where better and cheaper products are alreadyimproving areas like agriculture, fishery, weatherforecast, broadband internet or Internet of Things(IoT).

1.1. Cubesat Structures State of the ArtCubesats are small satellites specially used by uni-versities, schools and private companies for re-search, experiment and business purposes. A cube-sat is composed by one or more 10cm x 10cm x11.35cm units (U) and each unit weights up to1.33Kg [4]. The most common cubesats are 1U,2U and 3U, but there are larger configurations. Itis fairly common for these kind of satellites to useoff-the-shelf (COTS) electronic and structural com-ponents. This allows for a rapid and cheap devel-opment of subsystems. These satellites expandedthe ride-share market. It is not financially viableto purchase a primary flight slot. The solutionadopted is to buy a secondary flight slot on an al-ready scheduled flight. However, the cubesat owneris subjected to the conditions agreed by the LVEand the primary satellite owner such as the launchtime window, the deployment orbit or the safety re-quirements imposed by both entities. To minimizethe risk of damaging the primary satellite, cubesatsmay be launched inside pods, such as the Poly Pi-

cosatellite Orbital Deployer (P-POD) [3] standard-ized deployment system developed by Cal Poly.

Traditionally, satellite structures are designedconsidering the requirements of a specific mission,therefore, a given structure cannot fit in satellitesfor different missions. The cubesat standards havechanged this to a certain extent. By following thestandards and its requirements, the costs and de-velopment time of the preliminary design are cut.Then, it is possible to adopt different solutions tosolve specific problems.

There are many companies selling 1U, 2U and3U cubesat structures. Those are the most com-mon, however, the cubesat market is expanding,naturally the need for different formats arises, so to-day, the cubesat development is heading for biggercubesats. Many of the specialized cubesat compa-nies have developed 6U structures. There are also8U, 12U and 16U structures being both commer-cialized and developed, however, these formats areless common and are usually customized accordingto the client’s needs.

1.2. Metal Sheet Folding

Pumpkin Inc. is a pioneer in the cubesat market.They have been commercializing cubesat productssince 2000. Pumpkin’s 1U, 2U and 3U structureshave a main chassis, a base plate and a cover platewhich adopt a riveted aluminium sheet folding ap-proach. Using this solution, the loads are carriedby the skin, the internal available volume is maxi-mized and the strength to weight ratio is great. Onthe other hand, the required design tolerances maybe difficult to respect because of the bending pro-cess. Regarding the riveting, although it ensures agreat fastening capability, it may limit the assemblyprocess.

1.3. Modular Frame Designs

ISIS SPACE developed a family of highly adaptablemodular structures ranging from 1U to 16U con-figurations based on the Cubesat Standards. Thestructures are machined from an aluminium alloy,feature several mounting configurations to satisfythe needs of different customers, comply with thePC/104 form factor. While the frame carries mostof the loads, the detachable panels carry the shearstress and allow access to the spacecraft avionicsfacilitating also the assembly and integration pro-cesses. The larger platforms may be customizedaccording to the customer’s requests.

1.4. Card Slot Design

Complex Systems and Small Satellites (C3S) is aHungarian company created in 2012 to developedhardware and software solutions in the cubesat mar-ket. C3S developed a 3U and a 6U structures whosephilosophy is a card slot system. This approach

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makes it easier to access individual cards during theassembly, integration and testing procedures, thanthe classic PC/104 solution. According to C3S andthe European Space Agency (ESA) the 3U struc-ture will fly in late 2019 , being part of RadCube, acubesat mission to demonstrate miniaturized tech-nologies that measure in-situ the space radiationand magnetic field environment in low-earth orbit(LEO) for space weather monitoring purposes aspart of ESA’s Cubesat Technology Development ac-tivities.

1.5. Additive Manufacturing - 3D Printed Struc-tures

Additive manufacturing technology frees the de-signer from the constraints of the traditional manu-facturing methods, allowing for CAD models to bebuilt by adding materials layer by layer. This pro-cess helps to speed up product development. Al-though it has been proposed for years for primarystructures, only recently it has actually been imple-mented in a few projects.

Students at Tomsk Polytechnic University (TPU)developed a 3U cubesat, weighting 5kg to test newspace materials technology. The entire casing ofthe satellite is 3D printed. The small satellite waslaunched to the International Space Station (ISS)in March 2016, where it performed a series of teststo assess its behaviour. On August 2017, the 3Dprinted spacecraft was deployed manually from theISS. This was the first project to demonstrate thatit is possible to use additive manufacturing on pri-mary small satellite structures.

2. Numerical Analysis

To study the structure’s behaviour when subjectedto the launcher loads both static and dynamic anal-ysis will be performed. This chapter comprehendsthe theoretical background behind said analyses.

2.1. Quasi-Static Numerical Analysis

Quasi-static analyses differ from dynamic analysesbecause the dynamic behaviour of the response isnegligible due to the small variation that exists withtime. The quasi-static loads are equivalent to staticloads, typically expressed by equivalent accelera-tions in the centre of gravity (CoG).

This analysis aims to calculate the stresses,strains and displacements in the satellite when sub-jected to the accelerations presented in Table 4.

Considering linear materials and considering thetheory of linear tension [5], the relation between thestress and the strain is given by:

σ

= [D]εel

(1)

whereσ

is the stress vector, [D] is the elasticity

matrix defined by the material properties,εel

is

the elastic strain vector. Strains can be calculatedby inverting equation (1):

ε

= [D]−1σ

(2)

where [D]−1 must be positive definite.Displacements are calculated based on the in-

finitesimal strain tensor definition:

ε =1

2[∇u + (∇u)T] (3)

where ε is the infinitesimal strain tensor, u rep-resents the displacements and ∇ is the differentialoperator.

2.2. Modal Numerical AnalysisThe objective of the modal analysis carried outwithin this work is to determine the natural fre-quencies of the system. The natural frequency of asystem is the frequency of a harmonic motion thatcharacterizes its natural mode. In a modal analy-sis the system is considered linear, so, the stiffnessand mass effects are constant, plus, the forces, dis-placements, pressures and temperatures applied areindependent of time.

According to [6] the equation of motion with nodamping and with no external applied forces is:[

M]u

+[K]u

= 0 (4)

where[M]

is the mass matrix and[K]

is the sys-

tem’s stiffness matrix.u

=

Φicos(ωit).

Φ

is the eigenvector that represents the mode shape ofthe ith natural frequency, ωi is the natural angularfrequency

[rad/s

]and t is time. Thus, equation (4)

takes the form:(− ω2

i

[M]

+[K])

Φi

= 0 (5)

Equation (5) has two solutions that satisfy it.One is trivial and has no interest for the anal-ysis, the other is obtained if the determinant of([K]− ω2

[M])

is equal to zero:∣∣[K]− ω2[M]∣∣ = 0 (6)

Solving the previous eigenvalue problem we ob-tain the angular natural frequencies for each mode.The natural frequencies, fi, are obtained from theirdirect relation with the natural angular frequencies:

fi =ωi

2π(7)

2.3. Harmonic Numerical AnalysisThe harmonic numerical analysis evaluates the re-sponse of a system when excited by a harmonic vi-bration. In this type of analysis the system hasconstant stiffness, damping and mass effects. All

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displacements vary harmonically at the same fre-quency, although they may have different phases.

To calculate the system’s response when sub-jected to a harmonic load the mode superpositionmethod was used. It takes advantage of the naturalfrequencies and mode shapes previously calculatedin the modal analysis to decrease the computationaltime. In this method, the motion equation is con-verted into a modal form:

yj + 2ωjξj yj + ω2j yj = fj (8)

where yj is the modal coordinate , ωj is the nat-ural angular frequency of mode j, ξj is the fractionof critical damping for mode j and fj is the forcein modal coordinates.

For steady harmonic vibrations, fj has the form:

fj = fjceiΩt (9)

where fjc is the complex force amplitude and Ωis the imposed angular frequency.

For equation (8) to be true at all times, yj musthave a similar form as fj :

yj = yjceiΩt (10)

where yjc is the complex amplitude of the modalcoordinate for mode j.

Differentiating equation (10), substituting equa-tions (9) and (10) into equation (8), and solving foryjc:

yjc =fjc(

ω2j − Ω2

)+ i(2ωjΩξj

) (11)

The contribution for each mode is:Cj

=φjyjc (12)

whereCj

is the contribution of mode j and φj

is the mode shape of mode j.Finally, the displacement are obtained fromu

=∑n

i=1

φiyi as:

uc

=

n∑j=1

Cj

(13)

whereuc

is the displacements vector.

2.4. Random Numerical AnalysisRandom vibrations are non-deterministic. Theseare vibrations containing frequencies whose instan-taneous magnitude cannot be explicitly defined. Arandom vibration analysis takes into account theexcitation of all frequencies in a given spectrum,with the initial phase and magnitude of each fre-quency being random [6] .

This spectrum is presented as power spectral den-sity (PSD) which is statistically originated from a

large set of data collected from various measure-ments taken during the repetition of the event ofinterest. The shape of the graph represents the av-erage acceleration of the signal at any frequency.The area under the curve is the mean accelerationof the signal squared and its square root is calledthe root-mean-squared (RMS) of the signal.

Figure 2: Input PSD profile[Hz]vs[g2

Hz

]It is also necessary to define the probability den-

sity function (PDF). It allows to predict the rangeof accelerations that will be output. The area underthe curve has probability 1. The area under PDFcurve and between two

[G]

values is the signal’sprobability of being in that range of accelerations.

The horizontal axis of PDF has[Gpeak

]units,

which is normalized by dividing the[G]

values bythe signal’s RMS value. The signals usually havea bell shape form where 68.27% of the curve is be-tween ±σ and 99.73% is between ±3σ.

Figure 3: PDF Example

Most controllers consider that the control signalis a Gaussian distribution in which most of the in-tangible accelerations fall within the range of ±3σ.This removes the peak accelerations that representthe most danger to the system being analysed. De-spite its limitations, the Gaussian model is the mostwidely used and will also be used in this work.

3. Design Concept GenerationA classical subsystem design approach was takenas presented in [8]. First, a list of requirementsand constraints was done, then the preliminary de-sign approach and overall configuration was chosen,the third step was to estimate the mass budget, af-terwards a preliminary design was developed andfinally, a baseline spacecraft configuration was cre-ated.

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3.1. Requirements

The requirements derive from the mission andproject constraints, as such, INFANTE’s require-ments are based on the cubesat ones [4], but areadapted and supplemented according to missionconstraints. Following are the general structure re-quirements for INFANTE:

• R-D-001 The INFANTE satellite shall be de-signed according to 16U configuration.

• R-D-002 The total mass of the INFANTE satel-lite at launch, including the separation adap-tor, shall be less than 25kg.

• R-D-003 No single point of failure shall lead tocatastrophic or critical events.

• R-D-004 The structure, including all fastenersand launch separation mechanism shall be lessthan 3kg.

• R-D-005 The structure shall be a rectangularprism with the following dimensions 454 x 267x 234 [mm].

• R-D-006 The system’s first natural frequencyshall be above 120Hz.

• R-D-007 The structure shall be compatiblewith the loads defined by the LVE.

• R-D-008 The structure shall be compatiblewith modules following the PC/104 standards.

• R-D-009 The spacecraft C.o.G shall be locatedwithin 4.5cm from its geometric centre (G.C)in the X and Y directions, and within 7 cmfrom its G.C in the Z direction.

In addition to these requirements there are sev-eral others for each subsystem that will not be pre-sented because they are not relevant to this paper.

3.2. Design Approach, Materials and FasteningMethods

The main goals during development are to createa robust and lightweight structure that guaranteesthe physical integrity of all subsystems. One of themain drivers to INFANTE is modularity [7].

The spacecraft has 16 modules, each module hasdimensions similar to a 1U cubesat, compatiblewith printed circuit boards (PCB) featuring thePC/104 connector. A drilling pattern was then cre-ated having in mind the maximization of volumebetween modules to facilitate harnessing.

Figure 4 and Figure 5 show the drilling pattern onthe bottom plates and lateral plates, respectively.

Figure 4: Drilling PatternBottom Plate [mm]

Figure 5: Drilling PatternLateral Plate [mm]

The chosen design approach was to have aprimary structure composed by seven aluminiumsheets; two for the ±X faces (Top and Bottomplates), two for the ±Y faces (lateral plates), twofor the ±Z faces (prism bases) and another one tomake an internal panel that concedes strength androbustness to the structure, while also facilitatingthe interface of some modules.

The aluminium sheets are machined, in Tekever’sPonte de Sor facility, so that the final panels arecomposed by the longitudinal stringers togetherwith transverse skin (skin-stringer structures). Thelateral panels carry bending moments, shear forcesand torsional loads which induce axial stress in thestringers and skin together with shear stress in theskin. Several holes are cut off the structures tosave weight. The holes are filleted in the cornersto avoid fracture due to stress concentration. Oneof the main features of these panels is that the railsare integral part of the ±X panels. This way we re-duce the amount of bolts in the structure, therefore,decreasing the design complexity, saving mass, fa-cilitating the assembly process and simplifying theintegration process given that we only have to un-bolt one panel to have access to any module.

Figure 6 shows the seven panels (prior to machin-ing):

Figure 6: Panels Prior to Machining

Materials are selected based on several differentcharacteristics, such as strength, stiffness, density,thermal, conductivity, thermal expansion, corrosionresistance, ductility, fracture toughness, ease of fab-rication, versatility of attachment options, availabil-ity and cost [8]. For cubesats and small satellites,aluminium is a widely used material, however, ma-terials such as steel or titanium are also used insome cases.

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For INFANTE, it is important to have a materialwith a high strength-to-weight ratio, that is read-ily available and it’s low cost. For those reasons,the material chosen for INFANTE’s structure wasan aluminium alloy. Even though steel is also a lowcost material, its strength-to-weight is usually lowerthan aluminium because of it’s higher density. Forthe same mass, aluminium shell or plate would bethicker and thus able to carry greater compressiveloads before it buckles. Also, steel has magneticproperties which can easily interfere with instru-ments such as magnetorquers [2]. As for titanium, although it’s strength-to weight ratio is similar toaluminium, it is much harder to machine.

7075-T6 is the aluminium alloy chosen for theINFANTE structure because it is flight proven andit has a high yield tensile strength which means thathigher loads may be applied to the structure beforethe material enters in plastic state.

To attach structural elements, adhesive bonds,welds and mechanical fasteners are the most com-mon methods. Mechanical fastener methods havea much higher impact on the mass budget thanthe other ones and allow for stress concentrationsaround the fasteners that can cause failure at lowerload levels. However, by well dimensioning thestructure and respecting the norms regarding thesekind of fasteners, it is possible to get around this is-sue. The fact that it is possible to disassemble twobolted parts, makes it the best fit for INFANTE.

The primary and secondary structures will bebolted together using space graded bolts. Thesebolts are not procured or chosen yet, nor are thenuts, but Tekever has been in contact with fas-tener provider Johann Maier GmbH &Co.KG tofind the best fit for INFANTE’s needs. Tables 1and 2 present, respectively, a selection of potentialbolts and nuts to be used (available in stainless steeland titanium):

Bolt Size

ISO 4762 M2/M3/M4ISO 14583 M2.5/M3/M4

Table 1: Potential bolts to be used in INFANTE

Nuts Size

ISO 7092 M2.5/M3/M4DIN 934 M4

Table 2: Potential nuts to be used in INFANTE

3.3. ConfigurationThe internal arrangement has to use the availablespace in the most efficient way possible, it has totake in consideration the performance constraints

of each subsystem and also take in considerationthe electric, magnetic, mechanical and thermal in-terfaces. It needs to take in consideration the as-sembly and integration processes. Thus, finding theideal internal arrangement in a spacecraft is a verydemanding task. As it is heavily dependent on everysubsystem, it is not possible to define the internalarrangement at this point in the development pro-cess. However, it is possible to establish a baselinearrangement based on solid assumptions.

To respect R-D-009 the weight has to be evenlydistributed. The tactic used is to put heavy com-ponents near the G.C. This tactic also has a posi-tive impact in inertia, decreasing it, which helps theADCS to control the spacecraft’s attitude.

Figure 7 shows the INFANTE’s structure prelim-inary design.

Figure 7: INFANTE’s structure preliminary design

3.4. Total MassTable 3 presents the mass of each subsystem fea-tured in the computational model.

Subsystem Total Mass [g]

Primary Structure 3698Secondary Structure 1344Propulsion 3000Battery Packs 1936OBC 200OBDH 200Gammalink 600SAR radio 200PCDU 700PDRU 1200ADCS Core Unit 1000Reaction Wheels 360Multispectral Camera 2000Solar Panels 394Communications Antennas 170Payload Computer 85Experiments Unit 1000

System Total Mass [g] 18,087.0

Table 3: System Mass

The system’s total mass is 18.087kg and it willdefinitely increase. There are subsystems that atthis point surpass the maximum required mass.

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However it is expected that their mass will decreasewith future iterations of their development.

4. Computational Modelling Analysis andResults Discussion

All simulations were performed using ANSYS 18.1Workbench software.

4.1. Computational Model

To decrease the computational time two major sim-plifications were made: all the fillets and chamferswere suppressed; the subsystems were modelled asmass points. These have the same mass and are lo-cated at the centres of mass of the respective subsys-tems and are attached to the rods by one dimension(1D) elements. Mass points do not take the geome-try in consideration and do not allow to define theconnections as the preliminary subsystems’ CADmodels would, which influence the results. Becauseof its limitations mass points should not be consid-ered as representations of the subsystems after thePDR phase. Nevertheless, these assumptions havethe advantages of decreasing the number of meshelements in the order of millions and allow to studythe structure’s behaviour before the preliminary de-signs of every subsystem are ready.

4.2. Boundary Conditions

The computational model used has the same bound-ary conditions for all simulations. The boundaryconditions depend on the design of the satellite in-terface with the launcher. In INFANTE’s case, theexisting interface that hosts the satellite during thelaunch is a picosatellite orbital deployer (POD).

The POD will have an approximately prismaticshape. It will have a cage-like structure, which isnot completely closed. The POD is connected tothe satellite and to an adapter which is connectedto the launcher.

The boundary conditions are: 6 fixed point total,four in the -Z face (in red) and two in the -X face.There are four edges (in blue) that are free in the Zdirection but cannot move in neither X and Y direc-tion nor rotate. Figure 8 represents the boundaryconditions in the computational model.

Figure 8: Computational model boundary condi-tions

4.3. Applied LoadsThe load profiles to performed the analysis are pro-vided by the launcher entity and are presented inTables 4, 5 and 6.

Quasi-static loads Loads [g]

Main Structure 10.05

Table 4: Quasi-static qualification load profile

Freq. [Hz] Qual.

Structure 5-8 1.15g8-100 3g

Sweep Rate 2 Oct/min

Table 5: Harmonic qualification load profile

Freq. [Hz] PSD [g2/Hz]

Each axis 20 0.002110 0.002250 0.0341000 0.0342000 0.009

g RMS 6.7Duration 2 min/axis

Table 6: Random vibration qualification load pro-file

4.4. Mesh GenerationANSYS offers a wide variety of elements that fit dif-ferent needs. Considering the computational modeland the simulations planed, the elements chosen areshown in Table 7. The mechanical properties of alu-minium 7075-T6 were assigned to all mesh elements.

The computational model mesh was constitutedby elements 1D, 2D and 3D:

• 1D elements were used to represent the rodsof the PCB stacks, screws and the connectionsbetween different parts.• 2D elements were used to represent parts ide-

alized as surfaces.• 3D elements were used to represent parts ide-

alized as solids.

Part Element Type

Stack’s rods Beam188Screws Beam188Structural Panels Shell181Sec. Structure (Solid) Solid185Sec. Structure (Surface) Shell181

Table 7: Mesh element types per part

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4.5. Static Analysis Results

During the static analysis the spacecraft was posi-tioned horizontally, a 10.05g acceleration was ap-plied on the spacecraft’s C.o.G in each axis at atime. Figures 9, 10 and 11 show the maximum dis-placement, maximum Von-Mises stress and maxi-mum Von-Mises strain. Note that the figures pre-sented only concern the analysis performed with theloads applied in the zz direction. The maximumvalues were registered when the loads were appliedin said direction, therefore, these simulations areconsidered critical. Table 8 shows the maximumdeformation, stress and strain values for the simu-lations in each direction.

Figure 9: Structure’s deformation during QSL onzz direction

Figure 10: Structure’s Von-Mises stress during QSLon zz direction

Figure 11: Structure’s Von-Mises strain during QSLon zz direction

Axis xx yy zz

Max Def. [mm] 0.420 4.58 4.68Max Stress [MPa] 272.82 248.14 368.69Max Strain 0.0041 0.0035 0.0052

Table 8: QSL maximum diplacements, stresses andstrains

During launch the body structure has a maxi-mum displacement of 4.68 mm when the load isapplied in the zz direction.

Figures 10 and 11 show that the stress and strainare quite uniform throughout the structure andthat the maximum values occur in the stack frameswhere the rods are fixed. The maximum stress andstrain values are 368.69 MPa and 0.0052, recep-tively. The tensile yield strength and the elonga-tion at break of aluminium 7075-T6 are 503 MPaand 11% which are above the maximum values reg-istered by the analysis, giving a safety factor ofSf = 503

368.57 = 1.36.

4.6. Modal Analysis ResultsNo loads were applied during the execution of thisanalysis. Figure 12 shows the displacement on thefirst vibration mode:

Figure 12: Structure’s deformation during modalanalysis

The first vibration mode occurs at a natural fre-quency of 32.221 Hz, making the propulsion stackenter in resonance. Given that the first natural fre-quency shall be above 120Hz, it is clear that actionsneed to be taken so that the first natural mode is incompliance with the requirements. The two mainreasons that contribute for such low values are:

• Early stage of development At this stage,there are several open points regarding the de-sign of the structure, thus, it is natural thatresults may not be ideal.• Over simplifications of the model Ideally

the computational model would be the sameas the design model and would include all thesystems details. However, due to the dimen-sions of the spacecraft, the still roughly de-veloped design of the subsystems, a limitedtime frame and limited computational capacityavailable, simplifications to the computationalmodel needed to be made so that the develop-ment could progress. These simplifications, asmentioned in section 4.4, have a great impacton the results, specially the substitution of thesubsystems design by mass points which con-tributes to a decrease in the system’s stiffness.

However, these results offer good indication onhow to move forward. The natural frequencies must

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increase, otherwise requirement R-D-006 will notbe respected. Equation (4) tells us that to influ-ence the natural frequencies of a system there aretwo driving factors. The system’s mas and stiffness.From the theory of dynamics we get equation (14),that tell us that natural frequencies of a system in-crease if the mass decreases for the same stiffnessor if the stiffness increases for the same mass. Ide-ally we could increase the stiffness and decrease themass. Fortunately, at this point both are possible.To increase the system’s stiffness we can change thematerials or the boundary conditions. It is unlikelythat the structure’s material will change in the fu-ture, because aluminium 7075-T6 is the best fit forINFANTE. As the spacecraft is in a early is stageof development there is flexibility to make signif-icant changes to the structure’s overall design, tothe interface design and to the subsystems designs.The mass will decrease at each design iteration andstructure optimization.

fnat =1

2π

√k

m(14)

4.7. Harmonic Analysis Results

The harmonic vibrations analyses were performedto determine the stress and displacements of thestructure when subjected to the harmonic exci-tations described in Table 5. The analysis wereperformed considering the excitations applied ineach one of the three orthogonal directions inde-pendently.

Figures 13 and 14 show the deformation and theequivalent stress in the structure when the excita-tions are applied on the yy (critical analysis).Table9 shows the maximum displacements and stress val-ues.

Figure 13: Structure’s deformation during har-monic analysis on yy direction

Figure 14: Structure’s stress during harmonic anal-ysis on yy direction

Axis xx yy zz

Max Def. [mm] 0.168 0.694 0.362Max Stress [MPa] 92.8 280.5 81.5

Table 9: Harmonic maximum displacements andstresses

The displacements and the stresses in each sim-ulation are relatively small. The maximum val-ues recorded occur in the secondary structure.As showed in Table 9 the maximum stress is280.5

[MPa

]which means that the structure is at

all times in the linear state, therefore, it neverenters in a plastic or rupture state. The lowestsafety factor for these analysis is in the yy direc-tion, Sf = 503

280.5 = 1.79.

4.8. Random Vibration Analysis Results

The random vibrations analyses were performed todetermine the acceleration and the stress on thestructure when subjected to random excitations asdescribed in Table 6 and represented in Figure 2.

Figure 15 shows the body directional accelerationresults when the random excitations are applied inthe yy direction.

Figure 15: Directional Acceleration. Random vi-brations in yy direction

Figure 16 show the body equivalent stress whenthe random vibrations are applied in the zz direc-tion.

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Figure 16: Stress under random vibrations in zzdirection

Table 10 show the maximum acceleration andstress values for each analysis.

Axis xx yy zz

Acceleration [G] 20.303 20.666 2.928Max Stress [MPa] 14.3 7.85 151.98

Table 10: Random vibrations maximum accelera-tions and stresses

There’s only a 0.27% probability of accelerationsto exceed 20.666

[G], when excitations are applied

in the yy direction. This probability is a conse-quence of using the Gaussian model and 3σ. Thereis a 99.73% probability of the maximum equivalentstress not exceed 151.98

[MPa

]when the loads are

applied in the zz direction. These values are all be-low the material’s yield stress. The safety factor isSf = 503

151.98 = 3.3, therefore we can conclude thatno structural harm will be done to the structurebecause of random vibrations.

5. Conclusions and Future WorkThis work provides Tekever with a preliminary de-sign of a smallsat structure while capturing its de-velopment process. It is relevant for the company tobridge the knowledge gap to more established com-petitors. The work developed adds experience andexpertise on small spacecraft design and provides afirm baseline that allows the company to speed upthe structure design process for future smallsats.This work accomplished all the initially proposedgoals as INFANTE has now a preliminary designfor its structural subsystem which is ready to beiterated and improved as the project progresses.

5.1. Future WorkThis work is the first step of INFANTE’s structuralsubsystem development. As the project progressesthe design will be iteratively refined. The next sug-gested next steps are as follows:

• It is necessary to increase the structure’s natu-ral frequencies. The first step is to increase therepresentativeness of the computational modelby including the other subsystems’ computa-tional models on the existent one. Then amodal analysis should be run to check if the

natural frequencies increased to satisfying lev-els. Depending if they did or not different ap-proaches are taken.• Assuming that the natural frequencies are not

yet high enough a design solution should be im-plemented. Said design solution can be focusedon two variables, stiffness or mass. The inter-face between the structure and the subsystemscould be redesigned to increase the structure’soverall stiffness.• We can then run a topology analysis where the

aim is to decrease the mass of the subsystemwithout compromising structural performance.• If as consequence of increasing the model rep-

resentativeness the natural frequencies are sat-isfying, we can remove material to decreasethe structure’s mass thus optimizing the inter-nal volume available, production and launchingcosts.• Afterwards the static, harmonic and random

vibrations analyses should be performed againto make sure that the structure survives undersuch loads.

After these steps, the structure model will needto be produced and go through experimental testingto validate the simulations results.

AcknowledgementsI would like to thank Professor Filipa Moleiro, Eng.Francisco Vilhena da Cunha, Eng. Vitor Cristina,Rui Santos, Eng. Marie Campana and Eng. CarlosDias.

References[1] Nanosats Database. https://www.nanosats.eu/

(Accessed on 2 March 2019).

[2] Technical report, European Cooperation forSpace Standardization. ECSS-E-HB-20-07A– Electromagnetic Compatibility Handbook,2012.

[3] California Polytechnic State University. Poly Pi-cosatellite Orbital Deployer user Guide Mk. IIIRev E, March 2014.

[4] California Polytechnic State University. Cube-Sat Design Specification Revision 13, April2015.

[5] A. M. Barros. Behaviour Law PDF, InstitutoSuperior Tecnico, 2016.

[6] S. Rao. Mechanical Vibrations. Prentice Hall,5th edition, 2011.

[7] Tekever. Infante system design and justification.October 2018.

[8] J. Wertz. Space Mission Analysis and Design.Kluwer Academic Publishers, 3th edition, 1999.

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