2007 4th International Conference on Electrical and Electronics Engineering (ICEEE 2007)

IJu J

Finite Element Analysis and Design of a CubeSatClass Picosatellite StructureC. Quiroz-Garfias, G. Silva-Navarro and H. Rodriguez-CortesCentro de Investigacion y de Estudios Avanzados del I.P.N.Departamento de Ingenieria Electrica - Area Mecatronica

Av. Instituto Politecnico Nacional No.2580, C.P. 07360, Mexico D.F., Mexico.cquiroz @cinvestav.mx, gsilva@cinvestav.mx, hrodriguez@ cinvestav.mx

Abstract-This paper focuses on the mechanical design of alow-cost picosatellite structure which complies with the CubeSatprogram design specifications. Being the quasi-static loads biggerthan any other expected load, we consider failures due to columnbending as a design criteria. The overall design is validated usingfinite element methods. The satellite structure is treated as acombination of beams and thin plate elements. The mechanicaldesign process leads to three different prototypes which complywith the dimensional and structural requirements of the CubeSatprogram. The natural frequencies of the prototypes are computednumerically through finite element based methods.Keywords- Beam, CubeSat, finite element method, plate,

picosatellite, structure.

I. INTRODUCTION

During the last two decades there has been a gradualtendency to reconfigurate Earth-orbiting architectures from thesingle large satellite architecture to constellations of a numberof small satellites. Constellations of small satellites promisebetter mission flexibility and success by distributing the tasksand by reducing the possibility of a catastrophic failure. If onesmall satellite of the constellation fails, others can continueoperating until a replacement is launched.A fast growing small satellite industry has enabled increas-

ingly capable and cost-effective space missions by embracingreduced requirements and integrating commercial technology.This growing small satellite interest has also spread throughoutthe academic research and has resulted in nanosatellites (< 10kg) and picosatellites (< 1 kg) with an emphasis on decreasingthe size through application of advanced technologies whiletrading off capability. In this framework, the California Poly-technic State University (Cal Poly) at San Luis Obispo togetherwith the Space Systems Development Laboratory (SSDL) atStanford University developed the CubeSat program whoseaim is to provide a standard low-cost platform to design aclass of picosatellites, called CubeSats [1].The main contributions of this program are the development

of a standard deployment mechanism -the Poly PicosatelliteOrbital Deployer (P-Pod)- and creation of launch opportu-nities, by profiting the relative low cost of being treated assecondary payload, for developers previously unable to accessspace. The standardization leads to reduction in developmenttime and cost as well as imposes restraints in size and mass.

Although many institutions have developed satellites of thisclass (see, e.g. [2]), there is a few literature devoted to the

1-4244-1166-1/07/$25.00 ©2007 IEEE.

mechanical design (see, e.g., [3]) and modeling of CubeSat'smechanical structure. Almost all the publications are missionoriented or describe each subsystem in a general sense.Moreover, a CubeSat kit has been developed by Pumpkin,Inc. [4], which is the best option for those who do not wantto be involved in the design of the structure and the powersupply subsystems. However, this is not suitable for low-budget developers.

This paper presents the mechanical design and finite elementanalysis of a CubeSat class picosatellite structure using amixed approach between classical and finite element designmethods. The paper is organized as follows. In Section II theCubeSat design specifications are presented. In Section III theload types, design considerations and design methodology aredescribed. In Section IV is presented the stress analysis ofthe main structural elements as well as the determination ofthe natural frequencies. Finally, in Section V some concludingremarks are given.

II. CUBESAT SPECIFICATION

The design and testing requirements which have to besatisfied for every satellite that pretends to be launched bythe P-Pod are stated in [5]. Those of interest for this papercan be subdivided in two categories: dimensional and massrequirements and structural requirements. The first one statesthat each CubeSat must have a cube shape with a nominallenght of 100 mm per side and also a maximum weight of 1kg. The second one specifies some design criteria which haveto be met in order to avoid launch failures like jam, cold-welding, reduce wear and provide electrical isolation betweenCubeSats and the P-Pod. Aluminum alloys 7075 or 6061-T6are suggested for the main structure although it is possible touse other materials with similar thermal expansion coefficient.

In addition, in [6], [7] the guidelines for vibration quali-fication tests are presented. Each satellite must be submittedto sine sweep tests in the overall range of frequencies up to2 kHz, as well as random vibration tests with some specificpower spectral density profiles. The power spectral densityprofiles depend on the launch vehicle. A more detailed study ofthe posible environment inside the P-Pod and Test PicosatelliteOrbital Deployer (Test-Pod) is presented in [8].

294 IEEE Catalog Number: 07EX1762CISBN: 1-4244-1166-1Library of Congress: 2007923398

Authorized licensed use limited to: CINVESTAV IPN. Downloaded on October 30, 2008 at 13:11 from IEEE Xplore. Restrictions apply.

2007 4th International Conference on Electrical and Electronics Engineering (ICEEE 2007)

2Iu J

III. DESIGN ASPECTS

A. Load Types

Three types of mechanical loads are identified throughthe whole launching process: static, quasistatic and dynamic(though the first and the second are commonly grouped). Theseare result of different accelerations on the launch vehicleall along. As stated before, each launch vehicle user guidespecifies its particular vibration and acceleration levels (see,e.g. [9]-[12]).

B. Design Considerations

The following considerations were used in the design:. Maximum static acceleration of 10 g.. Each CubeSat will have the maximum specified mass of

1 kg.Now, we present some design guidelines. Each CubeSat

must have a mass of 1 kg and according to the literature 30%of this is allocated for the structure. The main goal of thedesign is to obtain a sufficiently stiff structure which supportsits own weight, the components inside and the weight of twoCubeSats. Whereas it has to be as light as possible and easyto manufacture and assemble at a low cost.

C. Methodology

First, the extreme loading conditions of a CubeSat wereidentified. Fig. l.a and l.b describe the maximum and mini-mum loading conditions inside the P-Pod, respectively. Be-cause the position of each CubeSat into the P-Pod is notknown, the worst case was considered. According to the pre-viously stated considerations the worst static case is describedby a load of 294.3 N applied to the lower CubeSat on thevertical arrangement. Note that in the horizontal arrangementeach CubeSat is loaded with 98.1 N.We proceed now to the material selection. There is a variety

of materials and compounds that might meet the requirementsof the thermal expansion coefficient, however, the cheaper andsort of commercial is the aluminum 6061-T6 -commercialavailability was the main reason of choosing it-. Table I showssome of the principal properties of this aluminum alloy.

....................

Figure 1: CubeSat loading conditions. a) vertical arrangement. b)horizontal arrangement.

1-4244-1166-1/07/$25.00 ©2007 IEEE.

Table I: Properties of the aluminum alloy 6061-T6aMaterial property Magnitude

Modulus of elasticity 68.9 GPaTensile Yield Strength 276 MPa

Poisson's ratio 0.33Density 2700 kg/m3

Coefficient of thermal expansionb 23.6 x 10 -6 c-1a Source www.matweb.comb Typical, average over 20-100 °C range.

After material selection, a first design was obtained andanalyzed. In order to determine the maximum stress due tostatic loads in each part of the structure, individual analytic andfinite element based analysis were performed. Fig. 2 shows theassembled and exploding isometric views of the first design.

In the vertical arrangement the elements from 1 to 4 arein a state of compression, whereas the others are not directlyloaded -that is why those do not directly contribute to thestrength-. Opposite to this, in the horizontal arrangement theelements from 5 to 7 and 9 provide the strength.

According to classical mechanics, elements from 1 to 4 arecolumns and the others are connected thin plates. Both of themwould fail by buckling instead of compression -because oftheir dimensions and loading conditions-. The critical load isdefined as the axial compression load in which the combina-tion of stresses due to compression and bending would result inthe element failure. Perhaps the most important considerationin failure by buckling is to determine the boundary conditions,i.e., the support conditions. The elements were consideredsimply supported which is the worst case because the lateralconstraints were neglected.

Finite element simulations were performed in order to verifythe analytic results. The type and size of the elements and theconstraints selected must describe as much as possible thephysical behavior in order to get valid results. Therefore, itis important to be aware of the capabilities of each elementneeded as well as try to reduce the complexity of the problem.Hence, one-dimensional beam and two-dimensional plate finiteelements were used with the same constraints stated before.

Since the picosatellite shape is quite restrained by thespecification, only slightly changes could be made to ourfirst model. Two lighter models were similarly obtained andanalyzed. The second model differs from the first one in the

4r

Figure 2: Assembled and exploding isometric views of the firstdesign.

295 IEEE Catalog Number: 07EX1762CISBN: 1-4244-1166-1Library of Congress: 2007923398

Authorized licensed use limited to: CINVESTAV IPN. Downloaded on October 30, 2008 at 13:11 from IEEE Xplore. Restrictions apply.

2007 4th International Conference on Electrical and Electronics Engineering (ICEEE 2007)

2I00

cross sectional area of the columns at the four parallel edges,whereas the third does not have any column but only platesassembled with uniform thickness and small supports at thecorners in contact.

Finally, joints had to be designed in order to guarantee thatthe elements will remain joined. Also it allows to make theimportant modelling assumption that surfaces in contact in thebeginning will remain in contact all along.

IV. ANALYTICAL AND SIMULATION RESULTS

All the methods which will be mentioned in this paper canbe found, for instance, in [13]. The finite element modellingcriteria can be found in [14]. The first individual analysis ofstress is presented and then stresses and natural frequenciesare determined for the overall structure.

A. Columns

Although some geometrical characteristics like chamfersand fillets must be met by the columns according to thestructural specification, simplifications were taken into accountin the analysis and simulations but not in the prototypes.The columns of the first prototype were considered to havea squared cross section of 8.5 cm per side. On the other hand,the columns of the second design were considered to have aconstant pentagonal cross section. Both columns have a totaland effective length of 113.5 cm. It is important to note that inthe latter the loading point differs from the geometrical center.

Classic Euler and J. B. Johnson methods were used for theanalysis of the squared cross section columns -because thereis not a specific boundary between short and large columns-,as well as generalized Euler and classic Euler methods for theanalysis of the pentagonal cross section columns. The analyticand simulation results of both columns are shown in Tables IIand III, respectively, in which a load equal to 73.575 N wasapplied because the total load is supported by four columns.As it could be noted, the simulation results match those

obtained by means of the classic Euler method. Moreover, theapplied load is below the critical load in the worst case ofboth kinds of columns. Table IV shows the safety factors ofboth columns considering the lowest critical load in each one.

Table II: Critical loads of the squared cross section columnsAnalytic Results (kN) Simulation (kN)

Euler J. B. Johnson22.967 15.612 22.962

Table III: Critical loads of the pentagonal cross sectioncolumns

Analytic Results (kN) Simulation (kN)Euler (p :p)a Euler (p = p')

2.086 5.770 5.754alp p1= 1.574 mm

Table IV: Safety factors of columns.Column Safety Factor

B. Plates

Although the real plates have bends and are slightly differentin each design, those were simplified as if it were squaredplates of 100 mm per side with thickness equal to 1.25 mm.Also simply supported boundary conditions were consideredin each of the 100 mm edges. Moreover, the whole load issupported by the columns in the vertical arrangement and fourplates provide the strength in the horizontal direction. Becauseof this, each plate is uniaxialy loaded with a quarter of the totalload, i.e., 24.525 N.The analytic and finite element simulation of the critical

loads are shown in Table V. As it can be seen, the applied loadis well below the critical load. A safety factor of 202.577 isobtained. It might seem to be overdesigned, however, it mustresist also the mass of the components inside.

Table V: Critical loads of platesAnalytic Results (kN) Simulation (kN)

4.968 4.829

C. Joints

Screw joints were considered. These are normally subject toseveral kinds of stresses. Here it has been considered that onlyfour elements support the total load -either columns or platesdepending on the arrangement- and also the loads are appliedin a perpendicular direction to their cross section. Hence, itcould be considered that the only state of stress needed toensure that the elements will remain in contact is the axialtensile stress in the screws, i.e., shear stress on screws andstresses on plates can be neglected by a proper selection ofscrews.

The maximum axial tensile stress is calculated in order totighten the screws at a tension known as pre-load. This ensures

that, if the joint failed, then it would be due to a failureon the screw but not in the plates. Taking into account theguidelines suggested by [15], [16], standard steel M3 screws

were selected such that a maximum tensile load of 563.455 Nis obtained when a safety factor of 4 is considered.

D. Stresses and natural frequencies in the structure

Due to the complex analysis of the assembled structure withall its mechanical components, the finite element method was

used to verify and validate the static and dynamic specifi-cations. Beam and plate finite elements with six degrees offreedom in each node are suitable for this purpose, becausethose allow three-dimensional deformations. Simply supportedboundary conditions as well as an axial compression loadof 73.575 N were applied at the lower and higher points ofthe columns respectively. Moreover, displacements in its cross

section plane and axial rotation were constrained to be zero.

The distribution of the Von Mises stresses is shown inFig. 3.a, which result in a safety factor of 53.28. It isremarkable that under this loading condition a critical loadof 29041 N would result in a buckling analysis, although thiswould be wrong because leads to stresses over the yield stress.

1-4244-1166-1/07/$25.00 ©2007 IEEE.296 IEEE Catalog Number: 07EX1762C

ISBN: 1-4244-1166-1Library of Congress: 2007923398

Squared cross section 212.201Pentagonal cross section 28.360

Authorized licensed use limited to: CINVESTAV IPN. Downloaded on October 30, 2008 at 13:11 from IEEE Xplore. Restrictions apply.

2007 4th International Conference on Electrical and Electronics Engineering (ICEEE 2007)

IJu J

4

(1) V)

Figure 3: a) Von Mises stress b) 1st mode of vibration 0 200 400 600 800 1000 1200 1400 1600 1800 2000Frequency [Hz]

Figure 5: Spectrum of acceleration measured in a sine-sweep test.

The natural frequencies in the 0 to 2,000 Hz bandwidthare shown in Table VI, whereas the first mode of vibrationis depicted in Fig. 3.b. The symmetry of the structure causesthat some natural frequencies are almost equal.

Table VI: Natural frequencies of the structure in the 0 to 2 kHzrange

Mode Natural Frequency (Hz) II Mode Natural Frequency (Hz)1 764.06 7 1635.702 840.97 8 1635.703 973.02 9 1866.204 973.02 10 1866.205 999.63 11 1912.006 1104.40 12 1961.30

A Testbed was designed in order to validate the previouslyobtained results (see Fig. 4). Fig. 5 shows the spectrum ofthe acceleration measured in the top face of the structure, inwhich the real natural frequencies are identified by means ofexperimental modal analysis.

V. CONCLUSIONS

The mechanical desing of three low-cost picosatellite struc-tures, which comply with the CubeSat program specificationwas developed usig a mixed approach between classical andfinite element methods. Two of the resulting designs haveless mass than the budgeted (see Table VII). An analyticfinite element analyisis of a simplified structure is currentlybeing performed and dynamic tests will be done in order toexperimentally validate the designed prototypes.

Table VII: Total mass of the prototypes.Design Mass (kg)1 0.3172 0.2703 0.236

Figure 6: Prototypes.

REFERENCES

[1] Cubesat project webpage. [Online]. Available: http://cubesat.atl.calpoly.edu

[2] Cassat project. [Online]. Available: http://cassat.acfr.usyd.edu.au[3] A. Bettridge, "Cassat structural subsystem," Final Year Thesis, Univer-

sity of Sydney, 2004.[4] Cubesat kit webpage. [Online]. Available: http://

www.cubesatkit.com/index.html[5] A. Toorian, CubeSat Design Specification (CDS), 9th ed., CubeSat

Program, 2005. [Online]. Available: http://cubesat.atl.calpoly.edu/media/Documents/Developers/CDS%20R9.pdf

[6] J. Brown, Test Pod User's Guide, 6th ed., CubeSat Pro-gram, 2006. [Online]. Available: http://cubesat.atl.calpoly.edu/media/Documents/Developers/compliance_dnepr_l-v.pdf

[7] A. Toorian, DNEPR Safety Compliance Requirements, 1st ed.,CubeSat Program, 2004. [Online]. Available: http://cubesat.atl.calpoly.edu/media/test-pod_user_guide.pdf

[8] V. Bashbush, "Characterization of the internal and external environmentsof the cubesat p-pod and test pod," Master's thesis, California Polytech-nic State University, San Luis Obispo, 2004.

[9] DNEPR Space Launch System, 2nd ed., International Space CompanyKosmotras, 2001.

[10] Rockot user's guide, 4th ed., EUROCKOT Launch Services Providers,2004.

[11] Pegasus user's guide, 5th ed., Orbital Sciences Corporation, 2000.[12] Taurus user's guide, 4th ed., Orbital Sciences Corporation, 2006.[13] R. L. Mott, Diseno de elementos de maquinas, 2nd ed., 1995.[14] S. S. Rao, The Finite Element Method in Engineering, 4th ed., 2005.[15] R. L. Norton, Diseno de maquinas, 1st ed.[16] A. Pytel and F. L. Singer, Resistencia de materiales, 4th ed., 1994.

Figure 4: Testbed

1-4244-1166-1/07/$25.00 ©2007 IEEE.297 IEEE Catalog Number: 07EX1762C

ISBN: 1-4244-1166-1Library of Congress: 2007923398

Authorized licensed use limited to: CINVESTAV IPN. Downloaded on October 30, 2008 at 13:11 from IEEE Xplore. Restrictions apply.