1. INTRODUCTION - Aalborg Universitet · 1. INTRODUCTION CubeSat is the name of a satellite concept...

1.1. IINTRODUCTIONNTRODUCTION

CubeSat is the name of a satellite concept that was started by Stanford University in USA. The aim of the concept is to design and launch extremely small satellites (picosatellites), thereby showing that it is possible to make small and low cost satellites. The limited dimensions and weight of the satellites also reduce power consumption and launch costs considerably. This is in accordance with the current philosophy for satellite design: “smaller, cheaper, faster, better”. The CubeSat picosatellites have dimensions of 100 x 100 x 100 mm (cubic shape) and must have a mass of no more than 1 kg. Other than this, and meeting requirements for deployment, there are no design restrictions

for the satellites. The CubeSat picosatellites are launched into Low Earth Orbit (LEO), which is an orbit with an altitude of 300 to 900 km above the surface of the Earth. There are no demands or restrictions regarding the payload of the satellites. The objective of the mission is completely up to the people designing the satellite. In early 2000 the deployment of picosatellites from the OPAL microsatellite, which was build by Stanford University, demonstrated the usefulness of such small satellites. This led to the CubeSat concept in which several universities and organizations from all over the world are now participating. For the universities participating, the objective is to build a student designed satellite and bring it into orbit around the Earth. The first CubeSats are scheduled to be launched on November 15, 2001. The launch will be made by a Dnepr rocket from Kazakhstan and will carry 18 CubeSats. California Polytechnic State University is responsible for the deployer system, which releases the satellites into their orbit. The launch will be carried out through a

number of stages to bring the satellite into orbit. The mission profile of the Dnepr rocket is shown on the figure below.

Figure 1.1: Mission profile of Dnepr rocket Aalborg University has decided to participate in this project and will design and build its own CubeSat. The project, called AAU CubeSat, has started September 2001 and is scheduled to finish in May 2002 where the flight model will be brought to the final tests. According to plan the AAU CubeSat will together with other CubeSats be launched from Kazakhstan in November 2002. As mentioned, the objective of the mission is to design and build a satellite and bring it into orbit. The satellite will carry a payload, but because of the dimensional limitations it is simply not possible to perform any advanced scientific experiments or carry measuring instruments, and therefore the purpose of the

payload is of secondary importance to the project. It has been decided that the AAU CubeSat will carry a CCD camera in order to take pictures of the Earth during orbit. The pictures will be taken within the visible spectrum, and will be taken of locations within Denmark. The pictures will be sent to the ground station and made publicly available on the Internet. It is desired that the satellite should remain functional for at least 1 year. Space engineering involves a multitude of disciplines, and thus AAU CubeSat is a collaboration between several institutes on Aalborg University; Institute of Electronic Systems, Institute of Mechanical

Engineering, Institute of Energy Technology and Department of Control Engineering. Each of these will contribute with different parts of the satellite system.

The part of the satellite that this report is concerned with is the structure and the mechanical systems. The structure must be designed to withstand the loads occurring during launch as well as the environment the satellite will be in, when it is in orbit. The loads on the structure will be vibrations, forces occurring from acceleration, acoustic loads and thermal stresses. As for the environment in space, factors such as radiation and corrosion (free oxygen) etc. will have to be taken into account. Since weight is of vital importance, the aim of the mechanical design of AAU CubeSat is to make the structure as low-weight as possible while still avoiding failure. Another challenge during the design of the satellite will be the collaboration with the other student groups involved in the AAU CubeSat. Other than the aspects mentioned above, the fastening of the payload, hardware and power and control systems on the structure must also be considered, as well as the distribution

of mass throughout the satellite. This project is for the 9. semester in mechanical engineering. It will be continued as the graduation project on 10. semester.

2.2. MMASTER ASTER IINTERFACESNTERFACES

Scope

An identification of the interfaces between the AAU CubeSat and the Poly Picosatellite Orbital Deployer (P-POD) involved in this chapter will be used in the implementation of the AAU CubeSat structural design. The purpose in particular with reference to this chapter is to establish the design and test requirements and

thereby insuring a proper AAU CubeSat design, in such a manner that the mission goals are upheld.

General

The structural design and test restrictions are based upon the P-POD developer teams restrictions. Each structure consists of two overall interfaces, the outer surface, which is called the master interface (MI) and the inner surface, which is referred to as the slave interface (SI). This chapter is only concerned with the MI. Furthermore the structure is divided into a primary and secondary structure, PS and SS respectively. Hence the following is valid:

• The master interface of the primary structure (MIPS)

• The slave interface of the primary structure (SIPS)

• The master interface of the secondary structure (MISS)

• The slave interface of the secondary structure (SISS) The PS shall serve the function of containing and protecting all internal components. The SS serves as a container for the antenna system.

2.12.1 MM ASTER ASTER SS TRUCTURE TRUCTURE IINTERFACE NTERFACE OO VERVIEWVERVIEW

Figure 2.1 shows a functional block diagram of the MIPS and MISS. The P-POD interfaces (to the right) are restricted by the requirements set up by the P-POD developer team, whereas the interfaces of the external subsystems (to the left) are partially determined by the AAU CubeSat design group.

Photovoltaic Solar CellsPSU

CCD Camera LinsePL

Electromagnetic CoilsACS

Solar CensorsACS

MISubsystems

Rail Contact Surfaces Kill Switch

Rail Contact Feet Ethernet Connector

Separation Springs Move Before Flight Pin

MIP-POD

MISSAntenna

MIPS

Figure 2.1: A functional block Diagram showing the MIPS between MI of the external subsystems, the P-POD and SS

2.22.2 GG ENERAL ENERAL GG UIDELINESUIDELINES

AAU CubeSat must not present any danger to neighboring CubeSats in the P-POD:

• AAU CubeSat must properly fit within the P-POD for launching and may not jam on ejection.

• No AAU CubeSat parts may detach during launch and ejection from the P-POD. In addition, AAU CubeSat may not create any separate space debris after deployment.

AAU CubeSat must be powered off during integration and launch to prevent any electrical or RF interference with the launch vehicle and primary payloads. AAU CubeSat must use designated space materials approved by NASA to prevent contamination of other

CubeSats in the P-POD or other payloads in the Multi-Payload Adapter (MPA) during integration, testing and launch. CalPoly and Stanford hold final approval of all CubeSat designs. Any deviations from the CubeSat design specification document (CDSD) must be discussed with CalPoly/Stanford launch personnel before the final CubeSat design is approved for launch. In addition to these basic guidelines the P-POD developer team introduces some standard requirements:

• To better stabilize the P-POD, the center of mass of the AAU CubeSat must be within 2 cm of the geometric center.

• The maximum allowable mass of AAU CubeSat is 1000 g.

• The use of 7075 or 6061 Aluminum is suggested for the main structure of the AAU CubeSat. If other materials are used, the CubeSat thermal expansion must be consistent with the P-POD deployer (7075 Aluminum) and approved by CalPoly/Stanford personnel.

[PPPG and CDSD]

2.32.3 MMASTER ASTER IINTERFACE OF THE NTERFACE OF THE PPRIMARY RIMARY SSTRUCTURE AND TRUCTURE AND SSUBSYSTEMSUBSYSTEMS

In this section the MI between the PS and the main parts of the other subsystems (see Figure 2.1, left) are evaluated.

2.3.1 Requirement

In addition to the previous guidelines and specifications presented in [Appendix A], the MI between the PS

and external parts must comply with the following requirement [CDSD]:

• On top of each side, excluding space for the rails and rail contact feet, an additional 6.5 mm space is available to accommodate solar panels, antennas or other components extending beyond the 100 mm limit.

2.3.2 Physical connections

Physical connection MI Attach to Type Interfaces with

Photovoltaic solar cells PS Adhesive bonding PSU Solar censors PS Adhesive bonding ACS Electromagnetic coils PS Adhesive bonding ACS CCD camera PS Adhesive bonding (and inserts) PL Table 2.1: The PS and external subsystems must have the MI as defined in this table

Table 2.1 defines the MI between the main parts of the other subsystems and the PS. The physical connection types inserts and adhesive bonding are described in section 2.4.2 Physical connections. Structural mechanical joints can be grouped into; inserted, bolted and riveted joints where fastening may be combined with adhesive bonding. The actual detail design of the structural mechanical joints is not made in this chapter. Photovoltaic Solar Cells The solar cells on the sides of AAU CubeSat supplies power to the rechargeable battery, which allows the

satellite to be operative for a given period of time. Solar Censors The solar censors allow the CubeSat to register it position relative to the suns position. The censors are essentially photovoltaic solar cells, which are used to detect the optimum position for retrieving solar energy. Electromagnetic coils The electromagnetic coils or magnetic torquers are basically wires, which generate a magnetic field when electrocuted. The generated electromagnetic field aligns with the earth’s magnetic field.

CCD Camera The CCD Camera is the payload of the satellite.

2.42.4 MMASTER ASTER IINTERFACES OF THE NTERFACES OF THE PPRIMARY RIMARY SSTRUCTURE ATRUCTURE A ND ND PP--PODPOD

In the forthcoming section a discussion of interface-types for the PS and P-POD (see Figure 2.1, mid) will be presented based upon the guidelines stated by CalPoly.

2.4.1 Requirements

In addition to the general guidelines and specifications presented in [Appendix A], the MIPS and P-POD must comply with the following requirements [PPPG and CDSD]:

• Internal P-POD rails and walls cannot be used to constrain deployable mechanisms.

• To avoid jamming, internal P-POD walls cannot contact any part of the CubeSat.

• To maintain spacing and to prevent CubeSats from sticking together, a contact foot must exist at the ends of each rail.

• To assure separation of AAU CubeSats after release, a separation spring will be installed at CalPoly in the mount locations shown in the [Appendix A]. AAU CubeSat developers are allowed to provide custom separation systems. CalPoly/Stanford personnel, before AAU CubeSat delivery, must

approve custom systems.



Rail contact surface Form part of PS Sliding surfaces P-POD Rail contact feet Form part of PS Separation discs P-POD or an other CubeSat Separation springs PS (Insert) P-POD or an other CubeSat Kill switch PS Adhesive bonding P-POD or an other CubeSat Ethernet connector PS Adhesive bonding (and insert) COM Move before flight pin hole PS Adhesive bonding (and insert) PSU Table 2.2: The PS and P-POD must have the MI as defined in this table

Table 2.2 defines the MI between the P-POD and PS. Adhesive bonding types in general aerospace use are epoxy, silicone, polyimide and bismaleimide, where the most widely used for metals and composites is epoxy if there is not called for temperature use over 170ºC [ESA PSS-03-212, p. 3.13]. Hence if nothing else

is specified the adhesive bonding is made by epoxy. An insert is a part of a detachable fixation device allowing joining, mounting or support of another subsystem. Inserts are a subgroup in mechanical joining. It is not determined in this chapter which type of insert to be. Moreover it is likely that inserts will only be used if the PS is made of other materials than metals.

Rail Contact surface

To assure proper sliding and release from the P-POD, CubeSats must have a minimum of 75% rail contact (7.5 cm per rail). CalPoly/Stanford personnel must approve any cuts in the rails prior to final design acceptance. Rail Contact Feet Eight 7 mm standoff (rail contact feet) on the top and bottom faces of the AAU CubeSat are required to provide separation between The CubeSats in the P-POD. The Area of the rail-ends must be at least 60 % of the original area in order to ensure contact between the CubeSats. Moreover they have to be filleted with a radius of 2 mm to avoid jamming, see [Appendix A]. Separation Springs There must be a mounting guidance hole for the separation springs. CalPoly mounts the springs.

Kill switch There must be interfaces provided in the PS for a power off switch/kill switch to be activated with pressure and to be flushed with the surface of the PS when the switch is compressed. Ethernet Connector There must be interfaces provided in the PS for a RJ-45 Ethernet connector as showed in [Appendix A] Move Before Flight Pin hole There must be interfaces provided in the PS for a remove before flight pin as showed in [Appendix A]

2.52.5 MMASTER ASTER IINTERFACE OF THE NTERFACE OF THE PPRIMARY AND RIMARY AND SSECONDARY ECONDARY SSTRUCTURETRUCTURE

In this section the MI between the PS and SS (see Figure 2.1, right) are evaluated.

2.5.1 Requirement

The requirements for the MIPS and MISS must comply with the restrictions described in 2.3.1 Requirement.



Antenna (SS) PS Mechanical joining COMP Table 2.3: The PS and SS must have the MI as defined in this table

Table 2.3 defines the MI between the PS and SS.

Antennas (SS)

The antenna system is called the secondary structure (SS) because it is seen as a module, which is mounted on the PS via a MI.

2.62.6 TT ESTINGESTING

In addition to previous requirements, the AAU CubeSat must undergo testing prior to launch. The tests are outlined below.

• Dimensional tolerances must be tested by the AAU CubeSat’s ability to slide freely in the Test Pod, which is provided by CalPoly/Stanford.

• AAU CubeSat must withstand a vibration and shock qualification test (125% of launch-loads) while

in the test-pod. AAU CubeSat developer institutions, in which case proper documentation will be required, can complete this test.

• AAU CubeSat must undergo a thermal-vacuum test that can be completed by the developer.

• At CalPoly, the CubeSats will undergo a vibration and shock acceptance test (100% launch-loads) inside the P-POD.

• An additional vibration and shock acceptance test (100% launch-loads) will be performed at One Stop Satellite Solutions (OSSS) with the P-POD mounted on the multi payload adapter (MPA).

3.3. MMATERIALS ATERIALS SSELECTION IN ELECTION IN CCUBEUBESSAT AT DDESIGNESIGN

Scope

An analysis of the overall material selection in the CubeSat design, which encloses and identifies, among the full range of materials, a subset of most likely materials to perform optimally for the given application or substructure. The material analysis is based upon a trade-off technique where each relevant material property

is evaluated and compared.

General

The geometry of the AAU CubeSat’s mechanical structure can be described as a combination of the following three categories:

A. Tension bars B. Beams, columns and shafts C. Plates and discs

These three groups of structural elements will be evaluated by a material index M, which consist of an objective and a constraint. The material performance is determined by the density ñ, Young’s modulus E, strength óf, facture toughness KIC, loss coefficient (damping) ç, thermal conductivity ë, temperature T, linear thermal expansion coefficient á and the relative cost Cp in relation to the price of mild steel. The objective is to optimize the material performance indices of low density with respect to the primary constrain-parameters, which are Young’s modulus, strength and the coefficient of thermal expansion (CTE). All other constraint-parameters are secondary targets in relation to the desirable material performance of the AAU CubeSat. This chapter is appended to a calculation routine in relation to the material analysis, which can be found on

the CDROM:\Chapter 3\Selection of Material.xls.

3.13.1 RR ESTRICTIONS OF ESTRICTIONS OF MM ATERIAL ATERIAL PP ROPERTIESROPERTIES

In this section some restrictions of the material selection will be set up in order to act in accordance with the constraints stated by CalPoly.

3.1.1 Macroscopic Material Failures of substructures

Macroscopic material failures of substructures are determined by the structures ability to support the design loads. The probability of material failure is determined by material properties, e.g. yield, fracture and instability. Structural Strength When a larger structural system deforms the other attached minor subsystems must deform consistently. With this geometric relation in mind, it is required that the ultimate elongation åu of the selected materials is

greater than the one for aluminum 7075-T6, which is used as structural material for the major structures in the P-POD and LV. This means that the aluminum structure most likely is the first to fail when influenced by quasi-static overload, if the stress levels are assumed the same for both structures and substructures. Structural Stiffness The launch and environment loads determine adequate structural stiffness where the material parameter Young’s modulus is the determining factor for the performance of this structural stiffness. Choosing materials with a ratio of Yong’s modulus E and the ultimate strength óu approximately that of aluminum accommodates the previous mentioned material restriction.

008.0E

u =σ

óu = 579 [MPa] The ultimate strength of aluminum 7075-T6 [Fuchs, p. 298] E = 70.103 [MPa] The Young’s modulus for aluminum The materials, which will be taken into account in this material analysis, are (see Figure 3.1 with the guideline óu/E = 0.008): Engineering Alloys

• Steel

• Ni alloys

• Ti alloys

• Al alloys

• Mg alloys Engineering Composites

• CFRP - Carbon Fiber Reinforced Polymer

• KFRP - Kevlar Fiber Reinforced Polymer

• GFRP - Glass Fiber Reinforced Polymer

(3.1)

Figure 3.1: Young’s modulus vs. strength [Ashby, p. 33] The dotted line around the engineering ceramics and porous ceramics in Figure 3.1 indicates that they are only valid for compressive strength. Moreover the strength in the chart for the engineering composites is only valid for tensile failure. Hence the engineering ceramics and porous ceramics are filtered out of the material selection, because they only have high compressive strength and highly sensitive to cracks (extremely brittle materials). I the forthcoming material analysis the engineering composites in the structural element group A and B will use unidirectional material properties and group C will be correlated with laminate material properties. The

material properties used for steel are taken as for high strength steel and Al alloys the material values are used for Al 7075-T6. The specific values of the material properties and calculations can be seen in the calculation sheet on the CDROM:\Chapter 3\Selection of Material.xls The used material properties for each material are typical values, which categorizes the materials widely. More precisely the used values have been taken form the figures in Appendix B.

3.23.2 OO BJECTIVE VSBJECTIVE VS . P. P RIMARY RIMARY CC ONSTRAINTONSTRAINT --PP ARAMETERSARAMETERS

The objective is to find the lightest material with respect to the primary constraint-parameters, which are the stiffness and the strength.

3.2.1 Density

The material indices for Young’s modulus/strength vs. density are sensitive to the geometric shape. Therefore it is assumed that the construction element groups A and B have free section areas. Consequently this means that the load, length and shape are specified. Element group C has the thickness as a free parameter where the load, length and width are locked parameters.

Figure 3.2: Young’s modulus vs. density [Ashby, p. 28] Figure 3.2 shows the chart guide selection of materials for low density and stiff structural elements. The guidelines E/ñ, E½/ñ and E�/ñ are for structural element-groups A, B and C, respectively. Materials offering the utmost stiffness-to-weight ratio are located towards the upper left corner in Figure 3.2.

Figure 3.3: Strength vs. density [Ashby, p. 30] Figure 3.3 illustrates the chart guide selection of materials for high strength and low density. The guidelines óf/ñ, óf

� /ñ and óf½/ñ represent group A, B and C, respectively. Materials offering the greatest strength-to-

weight ratio are also located towards the upper left corner.

Chart

Group

A [%]

B [%]

C [%]

Young’s modulus vs. density

CFRP KFRP GFRP

Ti alloys Ni alloys Al alloys Mg alloys

Steel

34.6 14.7 10.9 8.6 7.7 7.7 7.3 8.3

26.3 17.7 14.8 8.3 5.7 9.7 11.5 6.0

17.8 16.1 16.2 9.6 6.1 12.3 15.6 6.3

Strength vs. density

CFRP KFRP GFRP


Steel

25.9 18.4 24.7 7.8 4.7 8.7 4.4 5.4

23.7 19.2 23.0 7.8 4.5 9.7 7.0 5.0

21.8 16.1 18.9 9.3 5.3 12.2 10.6 5.8

Table 3.1: Valid materials for the structural elements of the AAU CubeSat design based upon the density-objective.

Table 3.1 lists the percentage of the relative material indices M for each material group. The material indices M are relative to the accumulated values of M. Hence each material chart has an accumulated value of 100 %

where each material have a percentage according to its index M. This is done so that the values for the treated material charts can be compared to each other. This comparison cannot be done if e.g. Al-alloys is set to index 100, because a big difference in material properties will give a high amount of points, which single handed can be determining the material assessment, see subchapter 3.4.

3.33.3 PP RIMARY VSRIMARY VS . S. S ECONDARY ECONDARY CC ONSTRAINTONSTRAINT --PP ARAMETERSARAMETERS

Next step is to look at the primary constraint-parameters vs. the secondary constraint-parameters, which is starting with the strength, Young’s modulus and finally the CTE.

3.3.1 Strength

The chart in Figure 3.4 shows the strength dependency of the operating temperature. When the tangent to a contour plot for a certain material group is horizontal then the strength is temperature independent. A conservative set of the CubeSat’s operating temperature is -90�C to 90�C [ESA PSS-03-212, p. 2-16]. In this case a guideline at 90�C is set in the chart. It is seen that the strength is temperature independent for all the materials in the given temperature range. Therefore none of the material groups are excluded or penalized in the material analysis.

Figure 3.4: Strength vs. temperature [Ashby, p. 49]

3.3.2 Young’s Modulus

The chart in Figure 3.5 shows the fracture toughness as a function of the Young’s modulus. The guideline (KIC)2/E is the same as GIC when the structure is in plane stress. GIC is called the critical energy release-rate

and is a description of crack propagation. Moreover it is independent of the load system and it is a geometrically determined constant. The energy release-rate GIC is only valid for materials that have linear elastic behavior until fracture. Therefore high values of KIC can only be used as ranking quantity as it is done in this material analysis. When designing against fracture e.g. at the crack tip a process zone is formed. In ductile materials it is a plastic zone, and a zone of delamination, debonding and fiber pullout in composite materials. Therefore the guideline assists in design against fracture when the material is subjected to cyclic loading. The best suitable materials are located at the top and to the left.

Figure 3.5: Fracture toughness vs. Young’s modulus [Ashby, p. 36] The guideline Eç in Figure 3.6 is a measurement of intrinsic damping (internal friction) and hysteresis. These material properties are important when structures vibrate. The chart ranks the materials after low and high damping, where it is wishful for the CubeSat to be a vibration mitigating system, e.g. high damping. The value increases as the guideline is displaced upward and to the right.

Figure 3.6: Loss coefficient vs. Young’s modulus [Ashby, p. 40]

Table 3.2 ranks the materials. Ti alloys are the best choice when designing against fracture propagation and KFRP are the best materials to use if one wants an energy dissipating system. The values displayed are a percentage of the total accumulated properties of all the materials, see page15.

Chart

Group

A/B [%]

C [%]

Fracture toughness vs. Young’s modulus

CFRP KFRP GFRP


Steel

2.8 13.5 20.3 22.8 16.9 5.9 1.7 16.1

3.7 13.5 13.3 25.0 18.5 6.5 1.9 17.6

Loss coefficient vs. Young’s modulus

CFRP KFRP GFRP


Steel

26.4 39.7 14.6 1.7 7.0 1.5 6.3 2.9

13.5 25.2 14.7 4.0 16.8 3.5 15.1 7.1

Table 3.2: A ranking of the materials based upon the best fatigue and damping properties for the AAU CubeSat design.

3.3.3 Thermal expansion

Figure 3.7 displays the material chart for the CTE as a function of the Young’s modulus. When the guideline áE is decreased to the bottom and left the induced thermal stresses also decreases. Hence this chart is a design of minimizing the thermal stresses generated per K.

Figure 3.7: CTE vs. Young’s modulus [Ashby, p. 45] The chart in Figure 3.8 shows the guidelines for the ratio ë/á, which is a design application against thermal deformation. To the bottom and right of the chart the materials with the smallest thermal strain mismatch are shown. Small thermal strain mismatch is desirable for the CubeSat’s structures.

Figure 3.8: CTE vs. thermal conductivity [Ashby, p. 44] Table 3.3 ranks the materials when designing for minimal induced thermal stresses and small thermal strain mismatch.

Chart

Group

A/B [%]

C [%]

CTE vs. Young’s modulus

CFRP KFRP GFRP


Steel

15.7 7.7 7.2 9.9 20.2 9.6 6.6 23.1

4.2 2.6 3.8 12.7 26.0 12.4 8.5 29.7

CTE vs. thermal conductivity

CFRP KFRP GFRP


Steel

0.4 0.2 0.3 6.0 5.9 39.7 33.9 13.5

0.4 0.2 0.3 6.0 5.9 39.7 33.9 13.5

Table 3.3: Ranking of materials when designing against thermal stresses and thermal strain mismatch.

3.3.4 Relative Cost

The next step is to determine the best cost-efficient material. Figure 3.9 and Figure 3.10 displays the relative cost in relation to the Young’s modulus and strength, respectively. The guidelines for minimum cost design with respect to the Young’s modulus is E/Cp, E½/Cp and E�/Cp which represents group A, B and C, respectively. The relative cost is associated with the raw material cost and relative to the price of mild steel.

Figure 3.9: Young’s modulus vs. relative cost [Ashby, p. 50] The most cost-efficient materials with respect to the strength are given by the guidelines óf/Cp, óf

�/Cp and óf

½/Cp, which is in relation to the A, B and C element group, respectively.

Figure 3.10: Strength vs. relative cost [Ashby, p. 51] By examining the charts in Figure 3.9 and Figure 3.10, where the best suitable materials are located upwards and to the left, the following ranking of the materials are made (see Table 3.4).

Chart

Group

A [%]

B [%]

C [%]

Young’s modulus vs. relative cost

CFRP KFRP GFRP


Steel

7.1 3.4 13.5 4.9 8.6 21.0 10.1 31.5

5.2 4.0 17.6 4.5 6.1 25.4 15.2 22.0

3.0 2.8 15.3 4.7 5.8 28.8 18.7 20.8

Strength vs. relative cost

CFRP KFRP GFRP


Steel

5.3 4.3 30.6 4.4 5.2 23.6 6.1 20.4

4.8 4.4 27.8 4.4 4.9 25.8 9.5 18.5

3.9 3.0 19.0 4.9 5.4 30.5 13.4 20.0

Table 3.4: Valid materials for the structural mechanics of the AAU CubeSat design based upon the cost-parameter

3.43.4 MM ATERIAL ATERIAL AA SSESSE SSMENTSSMENT

To select a feasible design material for each of the material groups, a trade-off map is established. Each material is listed with associated objectives, primary and secondary constraint-parameters. The density-objective is assigned a weight of 3 points, the cost-parameter is assigned a weight of a quarter of a point and the constraint-parameters are assigned a weight of 1 point. The weight of each material parameter is purely a subjective evaluation, but it describes what we think is important when choosing a material group. Since mass is of essential importance when designing the AAU CubeSat we have chosen to correlate the density-parameter with 3 points. We see the cost-parameter as a little gain factor especially when only one satellite is to be built. Moreover the structural budget is very small compared to the other subsystems. Hence we select to correlate the cost-parameter with a quarter of a point.

The other material parameters are of equal importance therefore the weight is set to 1 point.

3.4.1 Trade-off map

The following subchapter establishes the trade-off maps for each structural group A, B and C.

Element Group A

Table 3.5 shows the trade-off map for the density-objective and cost constrain-parameter of element group A.

Chart

Material Weight CFRP KFRP GFRP

Ti alloys

Ni alloys

Al alloys

Mg alloys Steel

Young’s modulus vs. Density 3 103.8 44.1 32.8 25.9 23.2 23.2 22.0 25.0

Strength vs. Density

3 77.8 55.1 74.1 23.4 14.2 26.1 13.3 16.1

Young’s modulus vs. relative cost ¼ 1.3 1.1 7.6 1.1 1.3 5.9 1.5 5.1

Strength vs. relative cost ¼ 1.8 0.9 3.4 1.2 2.1 5.2 2.5 7.9

Total - 184.7 101.1 117.9 51.7 40.8 60.4 39.3 54.1 Table 3.5: Trade-off map for the element group A and in collision with the objectives The values in Table 3.1 and Table 3.4 are modified with the designated weight factor, which results in the total values of each material as displayed in Table 3.6.

Element Group B

The trade-off map below summarizes the percentage score with assigned weight factors of Table 3.1 and Table 3.4 in relation to element group B.

Chart


Ti alloys

Ni alloys

Al alloys

Mg alloys

Steel

Young’s modulus vs. Density 3 79.0 53.1 44.4 24.8 17.2 29.1 34.4 18.1

Strength vs. Density 3 71.2 57.7 68.9 23.5 13.6 29.1 21.1 15.0

Young’s modulus vs. relative cost

¼ 1.2 1.1 6.9 1.1 1.2 6.4 2.4 4.6


Total - 152.6 112.8 124.6 50.5 33.6 71.0 61.6 43.2 Table 3.6: Trade-off map for the element group B with association of the objectives Table 3.6 lists the trade-off map for element group B. The engineering composites are the most favorable to use when only the objective vs. the primary constrain-parameters are considered.

Element Group C

The following trade-off map display the percentage score of element group C and is based upon Table 3.1 and Table 3.4. Moreover it is modified with the weight factors.

Chart


Ti alloys

Ni alloys

Al alloys

Mg alloys Steel

Young’s modulus vs. density 3 53.4 48.4 48.7 28.7 18.3 36.8 46.8 19.0

Strength vs. density

3 65.3 48.2 56.8 28.0 16.0 36.7 31.7 17.3

Young’s modulus vs. relative cost ¼ 1.0 0.7 4.7 1.2 1.4 7.6 3.4 5.0


Total - 120.4 98.0 114.1 59.1 37.1 88.3 86.5 46.5 Table 3.7: Trade-off map for the element group C when only the objectives are considered

Element Group A/B

Table 3.8 Shows a trade-off map valid for the element groups A and B. The charts used are the primary vs. the secondary constraint-parameters. The highest material-score is the Al-alloys.

Chart


Ti alloys

Ni alloys

Al alloys

Mg alloys

Steel

Facture toughness vs. Young’s modulus 1 2.8 13.5 20.3 22.8 16.9 5.9 1.7 16.1

Loss coefficient vs. Young’s modulus 1 26.4 39.7 14.6 1.7 7.0 1.5 6.3 2.9

CTE vs. Young’s modulus

1 -15.7 -7.7 -7.2 -9.9 -20.2 -9.6 -6.6 -23.1

CTE vs. thermal conductivity 1 0.4 0.2 0.3 6.0 5.9 39.7 33.9 13.5

Total - 14.0 45.7 28.0 20.6 9.6 37.5 35.2 9.4 Table 3.8: Trade-off map valid for all element groups The value for the material chart CTE vs. Young’s modulus is set to a negative value, because in this case it is not desirable to have a high value but a low value, see Table 3.3.

Element Group C

Table 3.9 establishes the trade-off map for element group C based upon the primary vs. the secondary constraint-parameters.

Chart


Ti alloys

Ni alloys

Al alloys

Mg alloys Steel

Facture toughness vs. Young’s modulus 1 3.7 13.5 13.3 25.0 18.5 6.5 1.9 17.6

Loss coefficient vs. Young’s modulus

1 13.5 25.2 14.7 4.0 16.8 3.5 15.1 7.1

CTE vs. Young’s modulus 1 -4.2 -2.6 -3.8 -12.7 -26.0 -12.4 -8.5 -29.7

CTE vs. thermal conductivity 1 0.4 0.2 0.3 6.0 5.9 39.7 33.9 13.5

Total - 13.3 36.4 24.5 22.3 15.3 37.3 42.3 8.5 Table 3.9: Trade-off map valid for all element groups

Overall Material Performance of Element Group A, B and C

Table 3.10 - Table 3.12 sums up the previous trade-off maps for each element group so that all objectives and constraints are considered in the material selection.

Table

Material CFRP KFRP GFRP

Ti alloys

Ni alloys

Al alloys

Mg alloys

Steel

Element group A 184.7 101.1 117.9 51.7 40.8 60.4 39.3 54.1 Element group A/B 14.0 45.7 28.0 20.6 9.6 37.5 35.2 9.4

Total 198.7 146.8 145.9 72.3 50.4 97.9 74.5 63.5 Table 3.10: A trade-off map for element group A based upon the objectives, primary and secondary constraint-parameters

Table 3.10 shows that with 198.7 points CFRP is the highest scoring material in element group A. This is primarily due to the lightweight and high stiffness of the CFRP.

Table


Ti alloys

Ni alloys

Al alloys

Mg alloys

Steel

Element group B 152.6 112.8 124.6 50.5 33.6 71.0 61.6 43.2 Element group A/B 14.0 45.7 28.0 20.6 9.6 37.5 35.2 9.4

Total 166.6 158.5 152.6 71.1 43.2 108.4 96.8 52.7 Table 3.11: An overall trade-off map for the element group B

When designing with element group B the overall trade-off map in Table 3.11 arguments that GFRP is the best material to use as before in Table 3.10.

Table


Ti alloys

Ni alloys

Al alloys

Mg alloys

Steel

Element group C 120.4 98.0 114.1 59.1 37.1 88.3 86.5 46.5 Element group C 13.3 36.4 24.5 22.3 15.3 37.3 42.3 8.5

Total 133.7 134.4 138.6 81.4 52.3 125.6 128.9 55.0 Table 3.12: An overall trade-off map for the element group C

Table 3.12 shows that composite engineering materials are the best materials to select if one want to design with element group C. The composite materials are close followed by the Mg- and Al-alloys.

3.53.5 SS UMMARYUMMARY

The final and overall ranking order of the investigated materials is as showed in Table 3.13 below.

Element group A Element group B Element group C Material Points Material Points Material Points

CFRP GFRP KFRP

Ti alloys Steel

Al alloys Ni alloys

Mg alloys

198.7 146.8 145.9 97.9 74.5 72.3 63.5 50.4

CFRP KFRP GFRP

Al alloys Mg alloys Ti alloys

Steel Ni alloys

166.6 158.5 152.6 108.4 96.8 71.1 52.7 43.2

GFRP KFRP CFRP

Mg alloys Al alloys Ti alloys

Steel Ni alloys

138.6 134.4 133.7 128.9 125.6 81.4 55.0 52.3

Total 850 850 850 Table 3.13: A ranking order of the materials with points The structure of the CubeSat will mainly be constructed of beam-columns and plates, e.g. element group B and C. Furthermore the structure of the AAU CubeSat will either be homogeneous (one material) or a hybrid of two materials. A hybrid of three or more materials is not evaluated due to further complexity in relation to fabrication and joining. Therefore the conclusion in relation to this material analysis (see Table 3.13) will be that the structure must be constructed of the engineering composite KFRP or CFRP and/or the engineering metals Mg or Al alloys. These four materials have the best overall performance within the composite and metal materials and in relation to both element group B and C, which is within the range of the design of the AAU CubeSat.

Al-alloys are selected over Mg alloys because they score the highest points when both element group B and

C are taken into account. Moreover due to the fact that the CubeSat main load carrying structure must be constructed in Al alloys in order to comply with P-POD regulations, without any intervention and approval by CalPoly, it is concluded that the structure must be made of Al alloys and not Mg alloys. Furthermore it is determined that the structure also must be made of CFRP if a hybrid is selected. This is chosen since CFRP is the highest scoring composite material when both element group B and C is considered.

4.4. LLOADS AND OADS AND CCYCLIC YCLIC SSTRESSINGTRESSING

Scope

The purpose of this chapter is to assess launch and mission environment-induced loads. The considered load types are quasi-static and dynamic loads, thermal effects such as temperature flux, temperature and humidity profile, gas-dynamic loads and environmental pressure changes. Other considerations are high-intensity

vibrations, which are associated with random vibrations, shock loads and vibro-acoustics. Low intensity vibrations are harmonic oscillations. These environmental loads are associated with various segments of the flight profile. When all types of load cases are considered they will be segmented into worst-case scenarios. Therefore this chapter will determine which finite element analyses (FEA) that are necessary to verify the AAU CubeSat structural design. Moreover it will determine the single load requirements and load combinations that are needed to obtain a reliable design result.

General

The maximum load levels define the requirements for the AAU CubeSat design. These loads act simultaneous but the occurrence of maximum values acting at the same time is improbable. Therefore a root-mean-square (RMS) and a root-sum-square (RSS) approach for combined loads are sufficient for a flight event [NASA-STD-7001, p.10]. The environmental factors for the CubeSat during handling on Earth, under launch and in space are summarized in Table 4.1.

Environment Earth Launch Space

Temperature Vibrations Temperature Moisture Quasi static loads Thermal flux

Dynamic loads Vacuum/outgassing Shock loads Radiation Acoustic loads Atomic oxygen

Table 4.1: Environmental factors taken into account when designing the CubeSat

4.24.2 LL OADSOADS

In the following each type of load case is considered and investigated in preparation for a set up of single design loads and worst-case scenario for a load combination.

4.2.1 Quasi-Static and Dynamic Loads

Table 4.2 lists the maximum quasi-static and dynamic loads on the AAU CubeSat. The measured values have reference to the center of gravity. The first term contains the static components of the g-loads and the second term the dynamic g-loads.

Spacecraft and LV joint Load Source Axial g-load

[g] Lateral g-load

[g] Launch: Movement inside the launch canister After exit from the launch canister

2.4 ± 0.2 0.0 ± 0.5

0.2 ± 0.3 0.8 ± 0.3

First stage flight: Maximum dynamic head Maximum axial g-load

3.1 ± 0.3 7.0 ± 0.5

0.35 ± 0.3 0.1 ± 0.4

Second stage flight: Maximum axial g-load

7.7 ± 0.50

0.1

Third stage flight 0.3 … 0.5 Table 4.2: Maximum quasi-static and dynamic g-loads [Wood, p.1] The axial and lateral static g-loads act simultaneously while the dynamic g-loads act within the range of 2 to 20 Hz. Table 4.2 shows that the second stage flight is the worst-case scenario. This means that the structures must be able to withstand a dynamic maximum loading during launch of 8.2g and 1.1g in longitudinal and in the two lateral directions, respectively.

4.2.2 Harmonic Vibrations

The structures are subjected to harmonic oscillations during launch that are given in Table 4.3 and Table 4.4. The vibrations are characterized by the frequency range, amplitude and duration of exposure.

Frequency sub-bands [Hz]

Amplitude [g]

Duration [s]

Frequency sub-bands [Hz]

Amplitude [g]

Duration [s]

5 … 10 0.5 10 2 … 5 0.2 … 0.5 100 10 … 15 0.6 30 5 … 10 0.5 100 15 … 20 0.5 60 10 … 15 0.5 … 1.0 100

Table 4.3: Longitudinal amplitudes of harmonics oscillations at spacecraft attachment points

Table 4.4: Lateral amplitudes of harmonics oscillations at spacecraft attachment points [Wood, p.2]

It is seen that the highest magnitude of the g-forces are in the frequency range of 10-15 Hz for the longitudinal direction and the two lateral directions with a maximum vibro-acceleration of 0.6g and 1.0g,

respectively.

4.2.3 Random Vibrations

The spectral density measures the intensity of the random vibrations acting on the AAU CubeSat at the attachment points. The spectral density is a superposing of sinusoidal oscillations in all-possible frequency-modes measured in the frequency sub-bands as showed in Table 4.5.

Frequency sub-band [Hz]

Spectral density [g2/Hz]

20…40 0.007 40…80 0.007 80…160 0.007…0.022 160…320 0.022…0.035 320…640 0.035 640…1280 0.035…0.017 1280…2000 0.017…0.005 Duration [s] 90

Table 4.5: Spectral densities of vibro- accelerations at spacecraft attachment points [Wood, p.3]

Figure 4.1: Spectral Density Distribution

The value of the spectral densities in Table 4.5, which are plotted in Figure 4.1, are random vibrations acting on the AAU CubeSat. The values of amplitude and spectral densities are given in the extreme octave points. The change of these values within the limits of each octave is linear in the logarithm frequency scale [Wood, p.2]. Hence a trapezoidal numeric integration must be efficient enough to find the root mean square of the random vibro-accelerations, which is called gRMS. The root mean square of the random vibro-acceleration gRMS is given by the trapezoidal rule of integration:

{ } [ ]g47.6)f(G)f(G2

fg

2/17

1i1ii

i,rangeRMS =

+⋅= ∑

=+

frange,1 = 20 [Hz] The frequency sub-band range for i=1, other values see [Table 4.5] G(f1) = 0.007 [g2/Hz] The spectral density for i=1, other values see [Table 4.5] The mean frequency is determined by (4.2) when the duration of exposure for each frequency sub-band is assumed the same:

]Hz[25.441t)ff(21

t1

f8

1i1iimean =∆⋅+⋅⋅= ∑

=+

f1 = 20 [Hz] The frequency sub-band lower limit for i=1, other values see [Table 4.5] f1+1 = 40 [Hz] The frequency sub-band upper limit for i=1, other values see [Table 4.5] Ät = 11.25 [s] Assumed value [See text] t = 90 [s] Total duration time [Table 4.5]

(4.1)

(4.2)

The structure must be able to withstand a dynamic loading throughout the launch sequence as showed in Figure 4.1, corresponding to a gRMS of 6.5g and a mean frequency fmean of 441 Hz, which must be applied in

all tree axes simultaneously. The highest random vibration is present in the frequency sub-band of 1280-2000 [Hz] with a maximum spectral density of 0.017 [g2/Hz]. This gives a span of the vibration load of 6.69 [g] or amplitude of 3.35 [g].

4.2.4 Acoustic Vibrations

The acoustic loads are given in Table 4.6 and plotted in Figure 4.2. The acoustic loads are formed when the

first stage propulsion unit is ignited. After this no acoustic loads from the propulsion unit influences the LV’s payload due to fact that the sound of speed is exceeded. But due to effects of pressure pulsations at the frame surface in the boundary layer in front of the LV’s payload additional acoustic loads are introduced.

Octave Frequency Band

Mean Geometric frequency

[Hz]

Sound Pressure level [dB]

31.5 125 63.0 132 125 135 250 134 500 132 1000 129 2000 126 4000 121 8000 115

Overall level [dB] 140 Test duration [s] 35

Table 4.2: Acoustic loads [Wood, p.4] Figure 4.2: Acoustic loads The duration of exposure is 35 [s]. The sound wave contributes with a sound pressure as follows [Wood, p.3]:

[ ]Pa2000p10ppp

log20L 020

L

0

=⋅=⇔

⋅=

p0 = 2.10-5 [Pa] Bench mark value of the sound pressure (0 dB) [ESA PSS-03-212, p.4.6] L = 140 [dB] Integral level sound pressure (overall level)

(4.3)

The RMS of the acoustic loads is determined to 105 [Pa] by using the same method as for the RMS of random vibro-acceleration.

The behavior of the sound waves are based solely on the assumption that, in a homogeneous medium, sounds propagation from a single point source is purely spherical. Figure 4.3 illustrates the sound propagation at ignition of first stage propulsion unit, because the sound wave front has to travel a large distance of ca. 30 [m], from the propulsion unit to the payload bay, compared to the AAU CubeSat satellite’s size it is assumed that the acoustic load effects all the surfaces of the AAU CubeSat in the longitudinal direction. This is also assumed for the acoustic loads generated from the pressure pulsation in the boundary layer.

4.2.5 Shock Loads

The activation of the separation pyro-devices is a source of the vibro-pulse loads at the spacecraft attachment joints [Wood, p.3].

Frequency [Hz]

Shock spectrum value [g]

30…50 5…10 50…100 10…25 100…200 25…100 200…500 100…350 500…1000 350…1000 1000…2000 1000 2000…5000 1000

Table 4.3: Shock spectrum [Wood, p.3] Figure 4.4: Shock spectrum/vibro-pulse loads

The shock spectrum values and correlated frequency wide-bands are listed in Table 4.3 and displayed in Figure 4.4. The duration of exposure for one shock process is 100 [ms]. The vibro-pulse loads are accurate within the value of 10. The structure must be able to withstand the vibro-pulse loads as showed in Figure 4.4. An RMS value of the shock loads is determined to 619g with a mean frequency of 904 [Hz], which acts in three arbitrary perpendicular directions.

Figure 4.3: Sound propagation

4.2.6 Gas-dynamic loads

The gas-dynamic pressure loads on the surface of the P-POD due to separation from the payload platform and third stage motor plume are given in Table 4.4 and displayed in Figure 4.5.

Distance [m]

Pressure [kg/cm2]

1.4 0.4·10-5 2.6 0.1·10-4 4.0 0.9·10-4 6.0 0.2·10-3 8.0 0.1·10-3 16 0.8·10-4 40 0.2·10-4 50 0.13·10-4

Table 4.4: Gas-dynamic loads [Wood, p.4] Figure 4.5: Spectrum of gas-dynamic loads The pressure values are gas stagnation pressure on the P-POD surfaces and the distance is defined as the distance between the lower edge of the P-POD and the payload platform. The pressure calculation error is ±50% [Wood, p.5]. The gas-dynamic loads has little or no effects on the AAU CubeSat due to the P-POD’s shielding of the AAU CubeSat. Hence these gas-dynamic loads will not be considered further in this analysis of the required design loads for the AAU CubeSat-system.

4.2.7 Environmental Pressure under the LV Fairing

The environmental pressure ratio inside of the LV front fairing is given by Table 4.5 and illustrated in Figure 4.6.

Mach number

Pressure ratio

0 0 0.7 -2.4 ± 0.06 1.19 -0.18 ± 0.04 1.81 -0.06 ± 0.03 2.29 -0.04 ± 0.03 3.30 -0.01 ± 0.03

Table 4.5: Environmental pressure ratio [Wood, p.5] Figure 4.6: Environmental pressure ratio vs. the Mach number The environmental pressure has influence on the AAU CubeSat only if it carries pressure vessels since this is not the case the environmental pressure under the LV fairing is not to be considered further in this analysis of the required design loads.

4.2.8 Conditions of Thermal Induced Stresses

Launch environment Thermal flux due to third stage motor plume to the surface of spacecraft that has separated from the LV and is moving along the axis of the LV shall not exceed 4800 [W/m2]. Integral thermal flux due to motor plume during spacecraft separation shall not exceed 5 ± 1.25 [W/m2]. Thermal flux calculation error is ± 25% [Woods, p.5]. Thermal flux acting on the spacecraft from the gas-dynamic shield will not exceed 1000 [W/m2] after the fairing drop [Woods, p.4]. The Launch environmental thermal induced stresses are only necessary to evaluate if the CTE and the CTC of the AAU CubeSat and P-POD are different, because it will introduce thermal mismatch. Due to the fact

that no P-POD FE-model is available, this phenomenon cannot be taken into account and therefore it must be evaluated during test. Mission environment The solar flux is between 1367 - 5 [W/m2] where an albedo of 30 - 5% of the solar flux reflected from earth is expected. The Earth contributes with an additional infrared value of 237 – 21 [W/m2] and the background space temperature is -270ºC [Terma, FH]. The AAU CubeSat operating temperature in LEO is expected to be within the range of:

• -40ºC to 65ºC [PPPG, p. 16]

• -40ºC to 70ºC [SSC00-V-5, p. 16]

• -40ºC to 80ºC [PPPG, p. 5]

• -90ºC to 90ºC [ESA PSS-03-212, p. 2-16] The AAU CubeSat’s exact operating temperature will be determined when the thermal analysis is completed.

4.34.3 CC YCLIC YCLIC SS TRESSINGTRESSING

Cyclic stressing caused by the previously described various forms of loads will be evaluated. It is intended that the AAU CubeSat must sustain cyclic stressing during test, launch and one year of mission operatives. The cyclic loads occur at a wide range of frequencies and a combination of different loads, which forms a

complex stress distribution in the AAU CubeSat structure. Therefore it is necessary to map the cyclic stressing loads in an ordered manner, which is done in the following subchapter. The failure criteria used for fatigue life expectancy is Palmgren-Miner’s cumulative damage ratio for aluminum and the method used in ESA PSS-03-203, p. 12.11 for engineering composites.

4.3.1 Cyclic Stressing During Launch

The cyclic g-loading data is listed in Table 4.6. The duration of the quasi-static and dynamic load source is taken for an Ariane 4 rocket or estimated since no launch profile is available for the Dnepr rocket. Metal alloys have an efficient span of stress (Eff. span in Table 4.6) referring to a load where the crack opens. This means that Irwin’s rule is valid. Therefore the Eff. span must be used when designing against fatigue in metal alloys. When designing against fatigue in composite materials one must use the total span of stress (Span in Table 4.6), because when the crack opens the rule of Irwin is valid, and when the crack is closed buckling of the delaminated fiber in the matrix can occur.

Axial g-loads Load Source Mean

[g] Amplitude

[g] Span [g]

Eff. span [g]

Frequency [Hz]

Duration [s] Cycles

Quasi-Static Loads Launch: Movement inside the launch canister After exit from the launch canister

2.4 0.0

0.2 0.5

0.4 1.0

0.4 0.5

20 20

10‡ 10‡

200 200


3.1 7.0

0.3 0.5

0.6 1.0

0.6 1.0

20 20

100† 110†

2000 2200

Second stage flight: Maximum axial g-load

7.7

0.5

1.0

1.0

20

130†

2600

Harmonic Vibrations - - -

0.5 0.6 0.5

1.0 1.2 1.0

0.5 0.6 0.5

10 15 20

10 30 60

100 450 1200

Random Vibrations - - - - - - -

0.26 0.37 0.94 1.67 2.37 3.35 2.92

0.53 0.75 1.88 3.35 4.73 6.69 5.83

0.26 0.37 0.94 1.67 2.37 3.35 2.92

40 80 160 320 640 1280 2000

90/7* 90/7* 90/7* 90/7* 90/7* 90/7* 90/7*

514 1029 2057 4114 8229 16457 25714

Acoustic Loads - - - - - - - - -

[Pa] 178 398 562 501 398 282 200 112 56

[Pa] 336 796 1125 1002 796 564 399 224 113

[Pa] 178 398 562 501 398 282 200 112 56

31.5 63.0 125 250 500 1000 2000 4000 8000

35/9* 35/9* 35/9* 35/9* 35/9* 35/9* 35/9* 35/9* 35/9*

123 245 486 972 1944 3889 7778 15556 31111

Shock Loads - - - - - - -

10 25 100 350 1000 1000 1000

10 25 100 350 1000 1000 1000

10 25 100 350 1000 1000 1000

50 100 200 500 1000 2000 5000

1/70* 1/70* 1/70* 1/70* 1/70* 1/70* 1/70*

1 1 3 7 14 29 71

‡ Estimated values † Ariane 4 quasi-static acceleration profile during launch * Assumed value Table 4.6: Axial quasi-static and dynamic g-loads that introduces cyclic stressing in the structure The mean values of the harmonic vibration, random vibration, acoustic and shock loads are set to zero.

Furthermore one should note that the shock loads are not considered wave loads as all the other load types, but as an impulse. Therefore the span and amplitude is set to the same values.

Moreover the duration in each frequency sub-band of the random vibration, acoustic and shock loads are assumed to be of equal size and the highest value in each frequency sub-band and load sub-band is used.

This gives a conservative estimation of the various cycles and spans. The lateral quasi-static and dynamic cyclic g-loading data is listed in Table 4.7.

Lateral g-loads Load Source Mean

[g] Amplitude

[g] Span [g]

Eff. span [g]

Frequency [Hz]

Duration [s]

Cycles

Quasi-Static Loads Launch: Movement inside the launch canister After exit from the launch canister

0.2 0.8

0.3 0.3

0.6 0.6

0.4 0.6

20 20

10‡ 10‡

200 200


0.35 0.1

0.3 0.4

0.6 0.8

0.25 0.7

20 20

100† 110†

2000 2200

Harmonic Vibrations - - -

0.5 0.6 0.5

1.0 1.2 1.0

0.5 0.6 0.5

10 15 20

10 30 60

100 450 1200

Random Vibrations - - - - - - -

0.26 0.37 0.94 1.67 2.37 3.35 2.92

0.53 0.75 1.88 3.35 4.73 6.69 5.83

0.26 0.37 0.94 1.67 2.37 3.35 2.92

40 80 160 320 640 1280 2000

90/7* 90/7* 90/7* 90/7* 90/7* 90/7* 90/7*

514 1029 2057 4114 8229 16457 25714

Shock Loads - - - - - - -

10 25 100 350 1000 1000 1000

20 50 200 700 2000 2000 2000

10 25 100 350 1000 1000 1000

50 100 200 500 1000 2000 5000

1/70* 1/70* 1/70* 1/70* 1/70* 1/70* 1/70*

1 1 3 7 14 29 71

‡ Estimated values † Ariane 4 quasi-static acceleration profile during launch * Assumed value Table 4.7: Lateral quasi-static and dynamic g-loads that introduces cyclic stressing in the structure One should note that the acoustic loads are not used in the fatigue estimation of the lateral loads due to the assumption on page 32.

4.3.2 Cyclic Stressing During Mission

In LEO the time for one orbit is approximately 90 min, which imply 16 thermal cycles per day [ESA PSS-03-212, side 2-16]. The AAU CubeSat must have a lifetime expectancy of one year; this means that it must endure a total of 5840 thermal cycles.

4.44.4 SS TRUCTURAL TRUCTURAL DD EGRADATIONEGRADATION

Moisture and temperature during manufacture and storage can degrade the mechanical performance e.g. strength and modulus of composite materials. This is called hygrothermal effects. In addition to property alterations it influences the geometric stability due to swelling and once in space the composite starts an outgassing process. The hygrothermal effect needs to be considered when designing the composite materials. This is done based upon the temperature humidity profile set up in this subchapter.

Conditions During Fabrication, Testing and Storage

The delivery of the flight-ready AAU CubeSat engineering model is done 4 months before the launch campaign in Kazakhstan.

• The AAU CubeSat is fabricated and stored at the AAU where the ambient air temperature is maintained within 20-25ºC and a relative humidity of 60% - 65%. The handling time is estimated to 70 days.

• Delivery to OSSS, shipment to CalPoly, Integration in P-POD, functional tests. The AAU CubeSat is stored within a temperature interval of 18-28ºC with a humidity of 40-80%. The test period is

estimated to 30 days.

• Shipment to OSSS, integration into carrier, environmental and functional tests. The temperature is within 18-28ºC with a humidity of 40-80%. The test period is estimate to 60 days.

Conditions During Launch Preparation

The launch campaign typically takes 20 days [Terma, FH]. Moreover the Kosmotras uses a 90-day launch window for CubeSat launches. The launch campaign is divided as showed below; the timeframes of each

operation is an estimation done on our part.

• During operations at the clean room of the spacecraft processing facility, the air temperature is maintained within 18-28ºC, with a relative humidity of up to 40-80%. The handling time is estimated to 90 days, as the launch window.

• During operations at the space head processing facility, the air temperature is maintained at 5-30ºC, with a relative humidity of max. 70%. The process time is estimated to 10 days.

• Transporting the space head to the launch silo, the temperature is maintained within the range of 10-

25ºC with a relative humidity of max. 70%. The process time is estimated to 12 hours.

• Loading of the space head unto the LV, the temperature is maintained within 5-30ºC with a humidity of max. 70%. The process time is estimated to 5 days.

• Storage until LV launch, the temperature is within 10-30ºC with a humidity of max. 70%. Process time is estimated to 5 days. [Wood, p. 4]

Temperature and Humidity Profile

The text above is summarized in Table 4.8, which gives a profile over the temperature, relative humidity and time.

Temperature [K]

Relative humidity [%]

Time [Days]

298 65 70 301 80 30 301 80 60 301 80 90 303 70 10 298 70 0.5 303 70 5 303 70 5

Table 4.8: Temperature and humidity profile

4.54.5 AA TOMIC OXYGENTOMIC OXYGEN

4.64.6 RR ADIATIONADIATION

4.74.7 SS AFETY AFETY FF ACTORSACTORS

Safety factors can be categorized into two types of factors, namely: 1. Design factors that are multiplying factors to be applied to the design loads for an analytical

assessment 2. Test factors that are test verification of structural adequacy in strength and stability.

The test factor is set by the CalPoly due to the test criteria, which states that the AAU CubeSat must undergo a vibration and shock test corresponding to 125% of the launch-loads. The used safety factors in the

analytical assessment are listed in Table 4.9.

Application Safety Factor Comments Yield 1.25 For metal alloys

Ultimate 1.4 For metal alloys Ultimate 1.5 For composite materials, uniform material Ultimate 1.5 (2.0)‡ For composite materials, discontinuities Ultimate 1.2 (1.4)† For fasteners and preloaded joints Lifetime 4.0 For fatigue analysis

‡ Joints that maintain pressure and/or hazardous material in a safety-critical applications † For safety-critical applications. Factor applied to concentrated stresses. Table 4.9: Safety factors used for analytical assessment

The used safety factors are in correlation to ESA PSS-03-212, p.1.12 and NASA-STD-5001, p.7.

4.84.8 SS TRUCTURAL TRUCTURAL AA NALYSESNALYSES

It is now possible to set up the required analyses for the verification of the AAU CubeSat’s structural design based upon the treated load cases and structural degradation. Important note: All loads have to be multiplied with a factor of 1.25 due to the test criterion described in 2.6 Testing, except the acoustic loads.

4.8.1 Material Properties

The prediction of the ultimate strength and Young’s modulus of the applied composite materials must be corrected according to the humidity and temperature profile in subchapter 4.4 Structural Degradation. The method used is described in ESA PSS-03-203, chapter 13. The safety factors will be introduced in the material properties by reducing these, because all analyses are linear and no coupling between the moments and elongations, the forces and curvatures and vice visa in the applied composite materials are present. Therefore superposing of results and reducing material criteria by safety factors are allowed.

4.8.2 Response Analysis

The response analysis is concerned with high and low frequency analysis. The load types involved are the harmonic and random vibrations, acoustic and shock loads.

Low Frequency Analysis, Harmonic Vibrations

• The response analysis must be performed with a sinusoidal excitation in the longitudinal direction

where the frequency must be in the range of 10-15 [Hz] and amplitude of 0.3g. In addition the structure must be able to withstand a sinusoidal excitation in the two lateral directions with a frequency range of 10-15 [Hz] and amplitude of 0.5g. The longitudinal and lateral loads acts simultaneously and at the attachments points. For further information see Table 4.3 and Table 4.4.

High Frequency Analysis, Random Vibrations, Acoustic and shock loads

• The structure must be able to withstand a sinusoidal excitation of amplitude 3.4g and within the frequency range of 1280-2000 [Hz] in three arbitrary perpendicular directions. The load must be applied at attachments points. For further information see Table 4.5. The acoustic and shock loads are high frequent loads, which will not be taken into account in the response analysis.

4.8.3 Stress Analysis

The design loads for the static stress analysis is the shock load and the quasi-static and dynamic loads. The stress analysis will be accompanied by hand calculations wherever it is possible and feasible.

• The structure must be able to withstand a static and dynamic load of 8.2g and 1.1g in longitudinal

and the two lateral directions, respectively. The longitudinal and lateral loads acts simultaneously and at the center of gravity. For further information see Table 4.2.

• The structure must be able to withstand a sound pressure of 2000 [Pa]; the load is applied to all surfaces in longitudinal direction. For further information see equation (4.3).

4.8.4 Buckling Analysis

The buckling analysis is related to the response of the major primary structure elements when subjected to compression loads.

• The load cases used must be the same as for the stress analysis.

4.8.5 Modal Analysis

The modal analysis is used to determine the natural frequencies of the structures. The analysis must be

performed in frequency sub-band of 1-100 [Hz]. The traditional modal analysis can be used to determine natural frequencies over 100 [Hz], but it must usually be verified by a Statistical Energy Analysis (SEA).

A design criterion not mentioned in this chapter is the lowest feasible natural frequencies. No data concerning this subject with relation to the Dnepr rocket (SS 18) is available; therefore the requirements

concerning the resonant frequencies are taken for the Ariane 4 rocket. It is stated in ESA PSS-03-212, p.1-17 that the primary structure shall exhibit resonant frequencies under hard-mount conditions of a lateral load of 15 [Hz] and a longitudinal load of 35 [Hz]. Secondary structures, equipment and appendages shall exhibit resonant frequencies at higher values.

4.8.6 Thermal Analysis

A thermal analysis must be performed due to the surrounded environmental effects under mission operatives.

For further information see subchapter 4.2.8.

4.8.7 Combined Load Analysis

A design load is the combined load analysis, which must be executed in order to verify the AAU CubeSat design. The applied loads are listed in Table 4.10. The used values are based on an RMS calculation.

Load source Longitudinal direction

[g] Lateral directions

[g] Comments

Quasi-static load 8.2 1.1 Applied at AAU CubeSat center of gravity Harmonic vibration 0.3·sin(2ð·15·t) 0.25·sin(2ð·15·t) Applied at attachment points Random vibration 3.2·sin(2ð·441·t) 3.2·sin(2ð·441·t) Applied at attachment points Shock load 309.5·sin(2ð·904·t) 309.5·sin(2ð·904·t) Applied at attachment points

Acoustic load [Pa] 105

- Applied at all surfaces

Table 4.10: Combined load cases

4.8.8 Fatigue Analysis

The structure must withstand 3 tests, one test with 125% of the launch-loads and two tests with 100% of the launch-loads. In addition to this it must also withstand the actual launch. The fatigue analysis requires an area of interest on the structure. The area should be located at the highest stress concentration. One needs to conduct several stress analysis:

• Stress analyses where the structure is subjected to a load of 1g at the center of gravity and in each of

the three directions. The stress level in the designated area is recorded for each of the analyses.

• Stress analyses where the structure is subjected to a load of 1g at one of the attachment points and in each of the three directions. The stress level in the designated area is recorded for each of the analyses.

• Stress analyses where the structure is subjected to a load of 1 [Pa] at each surface an only in the

longitudinal direction. The stress level in the designated area is recorded. The stress level in the designated area is scaled according Table 4.11, which is dependent of the type of material that is under investigation. The stress levels and correspondent cycles are used in fatigue calculations. Moreover the fatigue analysis must include the stress levels produced by the thermal cycling.

Longitudinal g-loads Lateral g-loads Load Source Location

Type Span [g]

Eff. span [g] Cycles

Span [g]

Eff. span [g] Cycles

Quasi-Static Loads Center of gravity 2 x 100% test and launch 1 x 125% test

0.4 1.0 0.6 1.0 0.5 1.25 0.75 1.25

0.4 0.5 0.6 1.0 0.5 0.63 0.75 1.25

600 600 6000 28800 200 200 2000 4800

0.6 0.6 0.6 0.8 0.75 0.75 0.75 1.0

0.4 0.6 0.25 0.7 0.5 0.75 0.31 0.88

600 600 6000 13200 200 200 2000 2200

Harmonic Vibrations Attachment point 2 x 100% test and launch 1 x 125% test

1.0 1.2 1.25 1.5

0.5 0.6 0.63 0.75

3900 1350 1300 450

1.0 1.2 1.25 1.5

0.5 0.6 0.63 0.75

3900 1350 1300 450

Random Vibrations Attachment point 2 x 100% test and launch 1 x 125% test

0.53 0.75 1.88 3.35 4.73 6.69 5.83 0.66 0.94 2.35 4.12 5.91 8.36 7.29

0.26 0.37 0.94 1.67 2.37 3.35 2.92 0.33 0.47 1.17 2.09 2.96 4.18 3.64

1542 3087 6171 12342 24687 49371 77142 514 1029 2057 4114 8229 16457 25714

0.53 0.75 1.88 3.35 4.73 6.69 5.83 0.66 0.94 2.35 4.12 5.91 8.36 7.29

0.26 0.37 0.94 1.67 2.37 3.35 2.92 0.33 0.47 1.17 2.09 2.96 4.18 3.64

514 1029 2057 4114 8229 16457 25714 514 1029 2057 4114 8229 16457 25714

Acoustic Loads All surfaces Launch

[Pa] 336 796 1125 1002 796 564 399 224 113

[Pa] 178 398 562 501 398 282 200 112 56

123 245 486 972 1944 3889 7778 15556 31111

- - -

Shock Loads Attachment point 2 x 100% test and launch 1 x 125% test

10 25 100 350 1000 12.5 31.3 125

437.5 1250

10 25 100 350 1000 12.5 31.3 125

437.5 1250

3 3 9 21 342 1 1 3 7

114

10 25 100 350 1000 12.5 31.3 125

437.5 1250

10 25 100 350 1000 12.5 31.3 125

437.5 1250

3 3 9 21 342 1 1 3 7

114 Table 4.11: Data for fatigue analysis

5.5. PPRELIMINARY RELIMINARY DDESIGNESIGN

Scope

The purpose of the chapter is to determine the geometric form of the load carrying structure. This is done by evaluating four types of structures and setting up a simple FE model of these.

General

The typical design evaluation criterion of the structural subsystem is the natural/fundamental/lowest frequency, which is determined by the LV. Moreover mass is a critical design parameter. Therefore the different structural systems are evaluated on the mass and natural frequency.

5.15.1 DD ESIGN ESIGN CC ONSIDERATIONSONSIDERATIONS

Trusses and frames

The trusses and frames are the load carrying components in the structure with removable panels or panels that are mounted last in the assembly order. This gives easy access to internal components, and thereby the interior of the satellite is accessible for the installing and wiring of components. The panels work as shear-panels meaning that they transfer shear loads to the frame. Machining a full structure or part of it rather than assembling individual members are often easier and more economical when constructing a satellite due to the fact that only one is to be made.

Solid Skin

The solid skin or facings structure, which can be reinforced with skin-stringers, carries the loads in a plate state. This is not quite possible since the other subsystems are to be attached to the skins, and therefore it must carry shear forces, which will produce local bending phenomena. Therefore it is difficult to mount components without overloading the skins. It can be difficult to assemble the satellite if a facing is used, therefore it may be required that it has removable panels in order to access the other subsystems. Often blind fasteners must be used due to the accessibility of the shell structure.

The facings are often simple and least expensive structures to manufacture.

Evaluation

The frame configuration seems to fit the structural requirements for the satellite best, due to the fact that it has to be easy to access when installing subsystems and wiring. It also reduces the complexity of the strain state of the structure when loaded, and thereby raises the probability of success. Hence it is chosen to work with a structural system of frames and trusses.

5.25.2 MM ODEL ODEL 11

Model 1 is based upon the concept of having a structure of trusses and frames see Figure 5.1. The rails act as

beam columns and the 45º members as tension/compression bars, due to the fact that the arrangement of the structure forms triangles. The 45º members can only withstand loads applied to its joints and in the axial direction. This is an approximation since the members are not pinned at the ends.

Figure 5.1: Model 1 for the load carrying structure The dimensions of the rails are consistent with CubeSat regulations and no alterations have been made e.g.

the magnitude of the lengths are 8.5 x 8.5 x 113.5 [mm], which are measured in local coordinate system x (red), y (green) and z-direction (blue), respectively. The straight upper and lower members have dimensions corresponding to 83 x 6.5 x 6.5 [mm]. The 45º members have a diameter of 6.5 [mm] and a length of 130.0 [mm].

Analysis of Model 1

Material Properties The material properties are set to be consistent with aluminum 7075 - T6. The elasticity modulus Ex is set to

71⋅109 [Pa] and Poisson’s ratio υxy is set to 0.3, which describes the transverse contraction. The mass density is set 2800 [kg/m3] [Ashby and Jones 2, p.10]. Element Type The stiffness matrix of the discreet continuum is calculated using 29 Gaussian or Quadrature points. Using the 29-point rule makes the calculation of the element stiffness less sensitive to the distortion level of

tetrahedral element.

The structure is meshed with solid elements, which are 3-D parabolic tetrahedral elements with 4 corner nodes and 6 mid-side nodes and 6 edges that can be straight or parabolic. Each node has 3 degrees of freedom (DOF) describing translational motions in the X, Y, and Z directions. The element does not have any rotational DOF.

Finite Element Modal Analysis The Finite Element (FE) model is shown on Figure 5.3 where the mesh consists of 68,302 elements. The

green arrows symbolize the prescribed displacements, which are defined by the surfaces that interface with the P-POD. The surfaces are supported in such a manner that the movements in the normal direction of the surfaces are prevented for all points (nodes). However, they are allowed to move (slide) in their plane, e.g. the boundary conditions are set as sliding surfaces.

Figure 5.3: Mesh density of model 1 Figure 5.4: Shape mode 1 of model 1

Figure 5.2: 3-D parabolic tetrahedral element

Figure 5.4 displays the first mode shapes of the model where the corresponding natural frequency is

calculated to be 2359.3 [Hz]. The mass of the structure is 211,0 [g].


Model 2 is shown in Figure 5.5 and this model is based upon a pure frame structure. This means that all parts acts as beam columns or beams. The model has been trimmed compared to the previous model, because the mass seemed unnecessarily high. The 45º trusses have been removed and the connection beams between the rails have a cross section area of 5 x 5 [mm].

Figure 5.5: Model 2 for the load carrying structure The rails have been trimmed in order to save mass. The removed material does not conflict with CubeSat regulations, since 75% of the contact area between the P-POD and CubeSat is still present. But this model has to be approved by CalPoly, because it has cuts in the rails. Moreover, support has to be attached to the rails in order to accommodate for the shear panels.

Analysis of Model 2

The same material, element type and structural support, as in the previous model, are used in this model. 50,009 elements constitute the FE model.

Figure 5.6: Mesh density of model 2 Figure 5.7: Shape mode 1 of model 2 Figure 5.6 displays the element density and Figure 5.7 shows the first shape mode of the model. The lowest natural frequency is estimated to be 3270.2 [Hz]. The mass of the structure is 121.8 [g].


Model 3 shown in Figure 5.8 has the same dimensions as model 2, but the material of the beam columns is now CFRP.

Figure 5.8: Model 3 for the load carrying structure

Analysis of Model 3

Material Properties The rails are in this model also made of aluminum 7075-T6, which is the same material as in the two previous models. The material properties of the beams are taken as unidirectional (UD) properties for T300 carbon fibers and the matrix material is set as M10 epoxy. Test results of a fiber-volume content of 60% gives a longitudinal

elasticity modulus E?? of 137.54⋅109 [Pa], a shear modulus G?? of 5.258⋅109 [Pa] and a Poisson’s ratio υ??⊥ of 0.274. The density is set to 1500 [kg/m3] [ESA PSS-03-203, p. 4-6].

Finite Element Modal Analysis Cosmos/DesignStar is not the most suitable FE program to use for orthotropic materials, even though it supports orthotropic materials. The material coordinate system is defined in each element by the base nodes. Since it is not possible to control this feature in the program it is not recommended to use it for composite materials, because one has any control over the orientation of the material properties and thereby the result. But since the structure consists of beams and columns, which can be approximated as one-dimensional members and with awareness of the described complication above, the composite is considered as an isotropic material with the above material characteristic. This is primarily done in order to get an idea of what one could expect in association to the natural frequency of the system.

Figure 5.9: Mesh density of model 3 Figure 5.10: Mode shape 1 of model 3 Figure 5.9 displays the element density of model 3. Figure 5.10 shows the first shape mode of the model. The lowest natural frequency is estimated to be 4657.9 [Hz]. The mass of the structure is 99.0 [g].


Odessy Model

In this chapter the method of designing the structural frame by optimization is described. An introduction to the system will be given, followed by a short description of the theory behind it. The optimization model used for the CubeSat is presented as well as the assumptions made. The criteria for the model are described, and the results obtained from the optimization are discussed at the end.

When designing it is often the case that a great number of possible solutions will come up. Since many factors are involved, it will be a cumbersome task to fully analyze all possible solutions. Furthermore there is no guarantee that any of the proposed solutions is the optimum design. We often know what we wish to achieve, but the problem is to determine the best way of accomplish this. This is where optimum design systems come into the picture.

5.5.1 The Optimum Design System

The Optimum Design System (Odessy) is a system for optimizing designs. It was started in 1991 by the Computer-Aided Design Group at the Institute of Mechanical Engineering at Aalborg University, and is under continuous development. In its current form, Odessy is a tool that can be used for modeling, analyzing and optimizing the design of mechanical structures. Odessy’s capabilities of doing analysis are similar to other systems such as ANSYS and Cosmos/M. What distinguishes Odessy from these systems is the ability to do synthesis, thus enabling it to optimize an existing structure. It is a parametric system, and since it works with sensitivity analysis, it can approach an optimum design without having to analyze all combinations. The analysis requires the load cases and boundary conditions to be defined. There are two main forms of optimization; form and topology optimization. Form optimization requires that you specify restrictions on how the design variables can change, e.g. assigning intervals to point coordinates

or wall thickness. The solution will be found within the given intervals of the variables. Form optimization is mostly used for determining accurate, optimum geometries. Topology optimization is better for suggesting initial designs as it rearranges material until an optimum design has been found. It is useful for determining whether a frame and a shell structure are desirable. Topology optimization is used to determine the overall design of the CubeSat.

5.5.2 The Optimization Model

The geometry of the Odessy model of the CubeSat is defined by a number of points, curves and surfaces in the plane. The surfaces are then extruded to create the volumes of the 3D model. The profile used to extrude the model is shown in Figure 5.11. The model is seen from above such that the four corners in the picture are the end faces of the rails. Four walls are connecting the rails. It is seen that another surface is defined within the corner squares that designate the rails. These are auxiliary surfaces corresponding to the areas of the rails that are in contact with the P-POD deployer. Their purpose is

to make it possible to define boundary conditions and loads due to the deployer.

Figure 5.11: Profile from which the rest of the model is extruded The load cases for the model are as described in chapter 4. These loads are volume forces, but as yet it is not possible to take volume loads into account when performing a topology optimization with Odessy. Instead the loads are applied as surface pressures across the areas where the satellite is in contact with the deployer.

Three different load cases are defined for the model, where none of these occur at the same time. The boundary conditions are defined in a way that corresponds to the CubeSat’s contact with the deployer. Thus the sliding surfaces are prohibited to move in directions normal to the face, and it is assumed that the friction between the rails and the deployer is negligible. The extruded model with meshing is shown in Figure 5.12. The cube is hollow, so no material will be moved to the inner of the satellite where the components will be. The picture shows the model after meshing. The blue elements are designated a material that is allowed to be redistributed. The red elements designate areas that must not be changed during the optimization. This is done in order to prevent the optimizer to redistribute mass from where the loads on the rails are applied. The material for the entire model is Aluminum 7075-T6.

Figure 5.12: Odessy model with generated mesh When a mesh size and element type is defined, the optimization can be started. The mesh size used in the final model is 3.5 mm, and the elements are 3D-Kirchhoff shell elements. A picture of the final result is

shown in Figure 5.13.

Figure 5.13: Final result of the Odessy optimization When elements with low density are deselected, it is seen that the Odessy optimization suggests a frame with bars connecting the rails. It should be noted that the picture above is the result of an interpretation. The

selection of elements by density is done by the user, and the final structure can appear different depending on the chosen density. However, in this case it is seen that model has converged well (almost all elements are

close to having element density 1.0), so the selection of elements by density does not influence the output significantly. A CAD model of the suggested design is made (see Figure 5.14). It is sought to draw a model as close to the result of the Odessy optimization as possible.

Figure 5.14: Picture of the frame used for the further analysis The bars connecting the rails are placed towards the center plane of the CubeSat. The bars are rounded off with large fillets where meeting the rails to accommodate the distributed forces along the sides of the rails. An amount of material has been cut from the rails in order to reduce the mass without interfering with their function, but little attention has been paid to make the curves smooth. The final CAD model is analyzed in Cosmos/DesignStar in order to compare it to the other proposals. The mass of this model is 116 g, and the lowest eigenfrequency is 3627 Hz.

1. INTRODUCTION - Aalborg Universitet · 1. INTRODUCTION CubeSat is the name of a satellite concept...

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