ausat final report
TRANSCRIPT
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H STATIC LOADING ANALYSIS
Figure 96: Compressive Force in Panel Divided by Critical Compressive Force
Acceleration, a
Density,
Cross section area, A
Length of components, L
The sensitivity in the calculated shear stress, , to a valriable, y, is given by Eq. 139:
y
a2 L1+
A2 A1 L2+
A3 A1
L3
y(139)
y = a, , A1, A2, L1, L2
Subscripts refer to different sections of the structure
This sensitivity analysis is a general analysis for all of the stress calculations to gain an
understanding of the effects of changes in the governing variables. General values for
each of the variables will therefore be used, these are listed in Table 34:
Sensitivity to Acceleratin Let y = acceleration, a, Eq. 139 becomes Eq. 140:
a
a2 L1+
A2 A1
L2+ A3 A1
L3
a=
2L1 +
A2 A1
L2 + A3 A1
L3 (140)
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H STATIC LOADING ANALYSIS
Table 34: Sensitivity Analysis ValuesVariable Value
Acceleration, a [m/ s2] 100Density, [kg/ m3] 2730
Cross Section Area of Stressed Section, A1 [m2] 5105
Cross Section Area of Section Effecting Stress A2, A3 [m2] 510
5
Length of Stressed Section, L1 [m] 0.1Length of Section Effecting Stress, L2, L3 [m] 0.1
Eq. 140 shows that if the value of acceleration increases by 10%, the shear stress in
the section increases by approximately4095 N / m2. This increase is 8 104% of the yield
stress.
Sensitivity to Density Let y = density, , Eq. 139 becomes Eq. 141:
a2 L1+
A2 A1
L2+ A3 A1
L3
= a
2L1 +
A2 A1
L2 + A3 A1
L3 (141)
Eq. 141shows that if the density of the material increases by 10%, the shear stress in
the section increases by approximately 8190 N / m2. This increase is 1.6 103% of the yield
stress.
Sensitivity to Cross Section Area of Stresses Section Let y = area of stressed section,
A1, Eq. 139 becomes Eq. 142:
A1
a2 L1+
A2 A1
L2+ A3 A1
L3
A1= a
2 A2 A21
L2 + A3 A21
L3 (142)
Eq. 142 shows that if the cross section area of the stressed section descreases by 10%,
the shear stress in the section increases by approximately 2730 N / m2. This increase is
5.4104% of the yield stress.
Sensitivity to Cross Section Area of a Section Effecting the Stressed Section Let y =
area of section effecting stress, A2, Eq. 139 becomes Eq. 143:
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H STATIC LOADING ANALYSIS
A2
a2 L1+
A2 A1
L2+ A3 A1
L3
A2= a
2L2
A1(143)
Eq. 143 shows that if the cross section area of a section effecting the stressed
section increases by 10%, the shear stress in the section increases by approximately
1.83104N / m2.
Sensitivity to Length of Stresses Section Let y = length of stressed section, L1, Eq. 139
becomes Eq. 144:
L1
a2 L1+
A2 A1
L2+ A3 A1
L3
L1= a
2 (144)
Eq. 144 shows that if the length of the stressed section increases by 10%, the shearstress in the section increases by approximately 1365 N / m2. This increase is 2.710
4% of
the yield stress.
Sensitivity to Length of Section Effecvting Stressed Section Let y = length of stress
section, L2, Eq. 139 becomes Eq. 145:
L1
a2 L1+
A2 A
1L2+
A3 A
1L3
L2 = a
2 A
2 A1 (145)
Eq. 145 shows that if the length of a section effecting the stressed section increases by
10%, the shear stress in the section increases by approximately 1365 N / m2.
Discussion The sensitivity analysis shows that a ten percent change in a governing
variable will have a maximum effect of increasing the the shear stress by 1.6 103% of
the yield stress. This sensitivity analysis justies the simplications made to the model.
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I RANDOM VIBRATION FEA ANALYSIS REPORT
I Random Vibration FEA Analysis Report
A random vibration analysis of the structure was conducted in ANSYS, the report for this
analysis is as follows:
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As part of the final year project Design, build and launch of a small satellite based on CubeSat
designs random vibration analysis was performed for launch vehicle integration qualification. The
project is being undertaken by five undergraduate students and is called AUSAT. The following
analysis was a preliminary validation to determine whether the satellite structure could withstand
loading due to launch vehicle vibrations. This directly related to the CubeSat standards which statethat to prove flightworthiness random vibration testing must be completed at a level higher than the
published launch vehicle envelope outlined in the Mission Test Plan (MTP).
The finite element analysis (FEA) package, ANSYS Workbench, was used to simulate random
vibrations present during the launch of the satellite. The model of the satellite was constructed in Pro
Engineer Wildfire in sufficient detail to be unambiguously constructed by an external workshop at BAE
Systems. The model was then defeatured to improve mesh quality without significantly altering the
design. Firstly a static structural pre-loading was applied to the internal rails to simulate the loads of
internal electronics. A modal analysis was conducted then conducted in order to determine the natural
frequencies of the satellite. Following the modal analysis, stochastic vibration loads were applied to
the structure to determine the maximum stresses and deformation of vital components.
Flight worthiness of the satellite will be granted if the maximum Von-Mises stresses of the structure
are below the yield stress and also the maximum deflection of the solar panel printed circuit boards
(PCBs) are within specified limits. Success in these two criteria will mean that the structure will not fail
and the solar cells will not break during launch. Although FEA alone is not sufficient to evaluate
launch qualification it provides a preliminary check of any major problems before a prototype is
constructed. Experimental results obtained later in the year will validate launch qualification and FEA
analysis.
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In this analysis it was essential to model the entire satellite despite the satellite having an axis of
symmetry. This was due to the asymmetric mode shapes in the modal response. Therefore, modelling
half the satellite and applying symmetric boundary conditions would not accurately model the modal
response of the structure. The model was adapted from a computer aided design (CAD) model, Fig. 1,
which was constructed in Pro Engineer for the final year project, AUSAT. The model was adapted bydefeaturing the model to improve the quality of the mesh. The CubeSat model was simplified in a
number of areas for the ANSYS analysis in order to make the system solvable. The screws and screw
holes were removed to improve the mesh on the side panels. This simplification has also been used to
appropriately perform a random vibration analysis of a similar pico-satellite structure (Pierlot, 2009). As
electronic components have not been finalised in the final year project a detailed model of the boards
were omitted. However, the approximate mass of the boards were know allowing a load to be applied
to the internal rails to simulate the boards. The pre-loading applied represented a static loading of the
mass of the board at 10g. Also all roundings on rails and cross brackets were removed to increase
mesh quality and reduce the number of small angled elements.
Figure 1: Pro Engineer Wildfire detailed CAD model
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A static structural pre-loading, representing internal electronic boards, and two types of analysis were
required to determine the launch qualification of the satellite. A modal analysis was conducted in order
to find the natural frequencies of the satellite structure. The launch vehicle standards require any
resonance frequencies below 2000 Hz to be analysed by a random vibration test. The random
vibration analysis that was conducted used a power spectral density (PSD) specified by testing
requirements for the Dnepr launch vehicle, Appendix C.
The mesh was defined in the static pre-loading and verified in the modal analysis before determining
the natural frequencies. As the geometry was imported from a 3D CAD model the automatic element
type where chosen as 3D tetrahedral. Firstly an automatic mesh was applied to the model, Fig. 2.
This mesh size obtained accurate results in the verification model and would be sufficient to model
areas of uniform geometry where detailed solution are not required such as the side panels.
Figure 2: Initial automatic tetrahedral mesh applied to entire structure
The frame structure and cross brackets were not crucial areas of analysis, which was seen in
preliminary random vibration analysis, and therefore the mesh size of these components were left
coarse. The meshes of these components were mapped reducing irregular shaped elements and
improving the quality of the mesh, seen in Fig. 3.
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Figure 3: Manual meshing of the frame and cross brackets to reduce irregular shaped elements.
The PCBs, which supported the solar cells, were refined to a 5 mm element size, Fig. 4. This was
done after preliminary modal and vibration analysis which indicated that the mode shapes and
vibrations affected the top and bottom panel more so than the structural panels, frame and cross
brackets. Also this was necessary to determine accurate deflections of the PCBs to evaluate whether
the solar cells would be damaged, deflection under 1mm.
Figure 4: Refinement of mesh of PCB to 5 mm.
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Determination of the damping coefficient was important to model the satellite appropriately. A similar
CubeSat project, OUFTI, analysed random vibrations for launch qualification. The quality factor
(amplification factor) of the OUFTI CubeSat structure was estimated at Q = 10 (Galli, 2008). Using the
following relationship (Roberts, 2009),
the damping coefficient of the satellite could be found by reaaranging to the following,
The frame, structural panels and cross brackets of the satellite are made from aluminium 6061-T6.
This material was chosen for the primary structure as it is lightweight and recommended by CDS
(Munakata, 2008). The PCBs were modelled as RF-4 which is a common material used in electronicboards (Orly, 2009). The spacers between PCBs and structural panels were modelled as
Polytetrafluoroethylene (PTFE) to reduce wear and provide appropriate support to the PCBs. The
internal rails, used to support electronics, were modelled as structural steel as these were vital in
distributing the load of electronics and important to have higher strength than aluminium 6061-T6. The
materials properties used in the analysis can be seen in Table 3.
Table 3: Material properties used in analysis of CubeSat
Material
Properties
Youngs
Modulus (GPa)
Density
(kg/m3
)
Poissons
Ratio
Tensile yield
Strength (MPa)
Coefficient of thermal
expansion (10-5
x C-1
) Aluminium 6061-T6 68.9 2700 0.33 276 2.4
RF-4 18.6 1820 0.136 276 1.2
PTFE 1 2200 0.46 20 13
Structural steel 200 7850 0.3 250 1.2
The boundary conditions change for each direction analysed as per the testing requirements for the
Dnepr Launch Vehicle. The testing requirements state that a CubeSat is to be oriented on a shaker in
the x, y and z directions and a vibration analysis performed for each of the three axes. For the x and y
directions the fixed support is located on the surfaces of the rails perpendicular to the axis direction.
For the z direction the fixed support is placed on the bottom of the four rails. In random vibration
analysis all supports that are not fixed are automatically assigned as free boundaries, which would be
the case in determining random vibrations in each axis individually.
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First a static structural preloading was applied to the internal rails of the satellite to represent the
weight of electronics, Fig 5. The magnitude of this load was determined by multiplying the mass of the
internal electronics, 500 grams, by a constant acceleration of 10g which is present in the launch of the
Dnepr launch vehicles. The load was applied at the central locations of the rail as exact location of
electronic boards have not been finalised. This would over estimate the stresses in the rails as the
bending moment would be maximised in this instance.
Figure 5: Representation of the loads of electronic boards on internal rails
A number of satellite launch providers offer CubeSat launches, as a secondary payload, to Low Earth
Orbit (LEO) however as a launch has not yet been finalised for this analysis the Dnepr launch vehiclewill be selected to provide random vibration statistics. The Dnepr launch vehicle is a Russian rocket
that has successfully launched seven CubeSats and had one failure during launch, destroying 14
CubeSats. The Dnepr launch vehicle currently has the most severe vibration response and it is likely
if the CubeSat structure can withstand a Dnepr launch it will be qualified for all launch vehicles
(CubeSat, 2009). The spectral density for each frequency range for both the high level and low level
qualification profile for a typical Dnepr Launch are shown in Table 4 and Table 5 respectively. The
high level qualification profile must be applied to the CubeSat for 35 seconds and the low level
qualification profile for 831 seconds to simulate a typical launch. These loads will be applied through
the fixed support boundary conditions, simulating the physical connection of the CubeSat and
experimental shaker.
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A verification model was first constructed to determine an appropriate mesh size for the CubeSat finite
element model (FEM). Once a converged solution was determine for the verification model by
comparing analytical solutions to FEA the CubeSat FEM was analysed. First a static structural pre-
loading was applied to simulate the electronic boards and then modal response of the satellite
structure was determined and all natural frequencies below 2000 Hz were tabulated. Once the modalanalysis was complete a random vibration analysis was performed for each of the CubeSat primary
axis. Von Mises stress and deformation in each of the CubeSat axis was investigated to determine
whether the qualification parameters, Table 2, were satisfied.
In order to validate the fidelity of random vibration analysis of the CubeSat model two verification
models were constructed. The two verification models were of a cantilever beam and a flat plate
clamped at one edge. These simplified models were chosen as the CubeSat structure is a
combination of both beam and plate components. Additionally, analytical solutions have been welldocumented to provide a reliable validation method. Hand calculations, Appendix A, were performed
for each of the models to determine the natural frequency using analytical methods. A modal analysis
was then performed using ANSYS Workbench on both models. The geometries of the models were
constructed in the design modeller section and aluminium alloy properties were assigned in the
material library. A detailed material model was not developed in the verification stage as the
aluminium alloy in the general material library was sufficient to validate convergence. The mesh sizes
of both models were varied to determine when the solution had converged. Varying the mesh size also
allowed for the number of nodes and elements to be recorded which would affect the size of the mesh
that could be used in the CubeSat FEM. The following sections detail the verification procedure.
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The first model constructed was a simple cantilever beam, Fig. 6. This beam represents the four rails
of the CubeSat that are constrained within the Poly-Picosatellite Orbital Deployer (P-POD). Hand
calculations were undertaken to determine the fundamental natural frequency of the beam using
theory highlighted in Inham. These analytical solutions were compared to a modal analysis performed
in ANSYS Workbench. Fig. 6 shows the model with a fixed support at the left face to simulate the
cantilever.
Figure 6: Cantilever beam model used in verification, left face is fixed.
A modal analysis was selected in ANSYS Workbench to determine the fundamental natural frequency
using FEA methods. The design modeller was used to first construct a square of width 8.5 mm and
then extruded to form a bar of 100 mm length. Although beam elements would accurately model the
bending modes of a cantilever beam, solid elements was used as it was necessary to model torsional
and lateral modes in the satellite structure. Also, simplifying the CubeSat FEM as beams and plates
removes additional stiffness at thickened joints and therefore would not accurately model the naturalfrequencies of the satellite structure.
To test for convergence and determine an appropriate mesh size for the CubeSat FEM the mesh size
for the beam was set at 15 mm to form a coarse mesh and then decreased to 8 mm to form a fine
mesh, Fig. 7 left and right respectively.
Figure 7: Left: Cantilever with 15 mm mesh size. Right: Cantilever with an 8 mm mesh size.
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The material properties used in both the FEA and hand calculations for the cantilever beam
verification model were generic aluminium alloy, Table 6. This was sufficient as the verification model
was analysing solution convergence of an implicit material not the dependence of material properties
on the solution.
Table 6: Material properties of aluminium alloy used inverification modelProperty Value
Youngs Modulus 71.0 GPa
Density 2770 kg/m
Poissons Ratio 0.33
A fixed support was applied to one of the end surfaces to form the cantilever, Fig. 6.
The result of the analytical method is compared to the FEA model of the cantilever beam for a variety
of meshes, Table 7. The percent error from the analytical fundamental frequency was found for mesh
sizes of 15, 10, 9 and 8 mm. It can be seen that there is a significant difference in frequencies
between 8 and 9 mm. This is because the element size is larger than the beam width until 8 mm. It
should be aimed to at least have the element size less than the minimum dimension of the beam.
Table 7: Comparison of Analytical and FEA Solutions for Beam Verification Model.
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The second verification model consisted of a flat plate that was clamped at one edge, Fig. 8. The
reason this model was chosen is similar to the cantilever beam, it resembles the panels found on the
satellite and analytical solution have been well documented.
Figure 8: Verification model of a flat plate clamped along left edge.
Similar to the cantilever beam the flat plate was modelled in design modeller by first making a square
plate with length of 100 mm and then extruding by 1.8 mm to form a flat plate. A thickness of 1.8 mm
was chosen in the verification model as this matches the panel thickness used in the CubeSat design.
To test for convergence and determine an appropriate mesh size for the CubeSat FEM the mesh sizefor the beam was set at 15 mm to form a coarse mesh and then decreased to 2.5 mm to form a fine
mesh, Fig. 9 left and right respectively.
Figure 9: Left: Flat plate with 15 mm element size. Right: Flat Plate with a 2.5 mm element size.
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Similar to the beam verification model aluminium alloy was chosen from the general materials material
library in engineering data. The specifications for this material are listed in Table 6.
A fixed support was applied to one of the edge surfaces to form the clamped plate, Fig. 8.
The result of the analytical method is compared to the FEA model of the flat plate for a variety of
meshes, Table 8. The percent error from the analytical fundamental frequency is not applicable as the
analytical solution only estimates an upper bound for the fundamental frequency. The analysis was
performed at a mesh size of 1 mm as well but this exceeded the node limit of the ANSYS licence.
Table 8: Results of Flat Plate Verification Model
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The verification models indicated that there were no appreciable differences in natural frequencies by
decreasing the mesh size below 8 mm and 5 mm for panel and beam respectively. The only major
effect of decreasing mesh size below this size is to increase the node count. Also identified was the
significant decrease in errors by limiting the element size to less than the minimum dimension of
meshed component. Therefore, to comply with these results and avoid maximum node limits the frame
and cross brackets were meshed using 8.5 mm tetrahedral elements. As the deflection of the solar cell
PCBs was required to determine whether the solar cells would be damaged the mesh was refined for
these components to 5 mm. The element sizes used in satellite FEM are summarised in Table 9.
Table 9: Mesh Sizes for CubeSat FEM
Component Mesh Size (mm)
Frame 8.5 mm
Cross Brackets 8.5 mm
Top & Bottom Panel 10 mm
Side Panels 10 mm
Solar cell PCB 5 mm
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Modal and random vibration analysis was performed on the simplified CubeSat FEM constructed
using the appropriate mesh size obtained in the verification model, boundary conditions, damping and
material properties obtained in review of literature highlighted in previous sections. First the modal
response of the satellite was obtained and all natural frequencies below 2000 Hz were tabulated. Von
Mises stress and displacement in each axis were then evaluated using the PSD stated in the CDS for
Dnepr launch vehicles. The stress distribution and maximum deflection of each axis random vibration
analysis were then tabulated to evaluate whether the objectives of the analysis were satisfied.
Modal analysis of the CubeSat structure indicated that there were 40 modes, Fig 10 & Table 10, under
2000 Hz that would be of particular interest in random vibration analysis. There were three distinct
frequencies ranges corresponding to modes 1 to 5, 6 to 20 and 21 to 40 which if prolonged excitation
was presented would lead to large increases of stress and deflections. It would be possible to shift thehigher frequency range, modes 21 to 40, above 2000 Hz through the addition of mass to the structure.
This would be advantageous as the launch vehicle and deployer structure would then damp out the
random vibrations above 2000 Hz reducing the likelihood of excitation of CubeSat natural frequencies.
However, as several components of the satellite have not been finalised it was important to model the
empty structure as a worst case scenario.
Figure 10: The modal frequencies of all modes below 2000 Hz of the CubeSat structure
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Table 10: Modal response of the CubeSat structure
Mode Frequency Mode Frequency Mode Frequency Mode Frequency
1 657.14 11 1107.8 21 1674.3 31 1902.9
2 657.4 12 1116.2 22 1733.2 32 1907.1
3 658.45 13 1162.1 23 1820.9 33 1920.9
4 768.58 14 1162.8 24 1850.5 34 1922.6
5 774.77 15 1163.4 25 1888.4 35 1935.5
6 1080 16 1208.4 26 1891.4 36 1942.9
7 1084.6 17 1209.9 27 1896.7 37 1944.6
8 1084.8 18 1212.4 28 1899 38 1979.5
9 1086.3 19 1319.5 29 1899.3 39 1980.5
10 1091.1 20 1322.2 30 1901 40 1981.9
To model random vibrations in the x-axis fixed boundary conditions, simulating connection between
test pod and structure, were applied to the side of the rails of the CubeSat. The results of the x-axis
random vibration analysis are summarised in Table 11. The Von Mises stress distribution, shown in
Fig 11, was maximum in the solar cell PCB at the connection between the PCB and the spacers.
Illustrations of the maximum deflection which occurred at the centre of the solar cell PCB and can be
seen in Fig 12.
Figure 11: Von Mises stress for x-axis random vibration analysis.
Figure 12: X-axis displacement for x-axis random vibration analysis.
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Similarly y-axis vibrations were modelled with fixed boundary conditions applied to the face of the
frames of the CubeSat. The results of the y-axis random vibration analysis are summarised in Table
11. The Von Mises stress distribution, shown in Fig 13, was maximum in the solar cell PCB at the
connection between the PCB and the spacers. Illustrations of maximum deflection which occurred at
the centre of the solar cell PCB can be seen in Fig 13 and 14 respectively.
Figure 13: Von Mises stress for y-axis random vibration analysis.
Figure 14: Y-axis displacement for y-axis random vibration analysis.
Finally z-axis vibrations were modelled with fixed boundary conditions applied to the bottom face ofthe CubeSat rails. The results of the z-axis random vibration analysis are summarised in Table 11.
The Von Mises stress distribution, shown in Fig 14, was maximum in the solar cell PCB at the
connection between the PCB and the spacers. Illustrations of the maximum deflection which occurred
at the centre of the top solar cell PCB can be seen in Fig 15.
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Figure 15: Von Mises stress for z-axis random vibration analysis.
Figure 16: Z-axis displacement for z-axis random vibration analysis.
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The random vibration analysis indicated that the maximum deflection occurred in the direction of
excitation, as expected. The location of the maximum deflection occurred in the centre of the solar
cell PCB for each loading condition. All deflections were below the specification of maximum
deflection of the solar cell of 1mm, shown in Table 11. The maximum deflection throughout the
analysis was the X axis excitation, with a deflection of 0.02027mm, which corresponds to a factor of
safety of 49. This ensures the solar cells will survive the launch environment and will be operational on
orbit.
As indicated by previous literature, failure of the structure is unlikely during launch. This has been
verified by the stress distribution obtained during the random vibration analysis, results shown in Table
11. The maximum stress was shown to occur in the Y axis excitation, between the solar cell PCB and
the spacer. The value of stress recorded was 1.41MPa, this results in a factor of safety 14 for the RF-
4 PCB material. The stresses in the satellite structure were considered negligible, resulting in a
successful result for random vibration analysis.
Table 11: Results of Random Vibration Analysis of the CubeSat
Direction of Vibration X Deflection
(mm)
Y Deflection
(mm)
Z Deflection
(mm)
Stress
(MPa)
X 0.02027 0.00060 0.00109 1.10
Y 0.00064 0.01980 0.00076 1.41
Z 0.00073 0.00074 0.01692 1.36
During the modelling of the satellite some simplifications that were made would change modal
response. These simplifications include the removal of screw holes and screws, simplifying curves to
rectangular sections and neglecting internal components of the satellite. These simplifications would
change the mass distribution and total mass, resulting in lower natural frequencies. Further analysis is
required upon finalisation of satellite components. Additionally cut outs for wiring on the solar cell
PCB and structural panels were neglected. This would reduce the structural rigidity of the side panels
therefore decreasing the natural frequency. However these simplifications were necessary improve
the mesh quality and satisfy the node limit of 32000 nodes. The mesh body sizing feature in ANSYS
was used after verification modelling to optimise the number of nodes with the quality of the mesh.The resultant number of nodes utilised was 31343.
Shielding of the satellite from nose cone and deployer would maintain the temperature of the satellite
at ambient conditions. Thermal analysis will therefore not be required in this analysis of the launch of
the satellite.
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The random vibration analysis using ANSYS posed some potential problems both in the software itself
and also in the system being analysed. Firstly, the ANSYS licence at The University of Adelaide only
allows for a maximum of 32000 nodes, which restricts the refinement of the mesh and therefore the
potential accuracy of the results. The CubeSat CAD model itself also posed a problem in our analysis
due to its complexity. As a result the model had to be simplified in order to for an appropriate mesh tobe generated.
The results of random vibration analysis at Dnepr launch vehicle levels indicated that the maximum
deflections of the solar cell PCBs were well below the specified limit of 1 mm. Additionally, the stress
within all structural components was significantly below the yield strength of aluminium 6061-T6.
These results would indicate that both the structure and solar cells would not be damaged in the
launch environment allowing successful operation of the satellite once in orbit. To further validate the
results of FEA and satisfy launch qualification regulations random vibration testing will also be
performed on the fully constructed structure, including solar cells and internal electronics.
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J MAGNETORQUER TEST THEORY
J Magnetorquer Test Theory
The torque created by a magnetorquer has to be calculated so that the attitude of the
satellite can be controlled. A test suggested in the thesis Development of an Active
Magnetic Attitude Determination and Control System for Picosatellites on highly inclined
circular Low Earth Orbits by Jens Gieelmann from RMIT will be implemented.
Test Setup
Apparatus:
Helmholtz Coil Pair
Light Triggered Timer
Retort stand
Coil
Schematic - Figure 97:
Figure 97: Schematic of Experiment Setup
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J MAGNETORQUER TEST THEORY
The coil is set up so that it is between the Helmholtz Coil Pair in the uniform magnetic
eld. The plane of the coil is to be perpendicular to the magnetic eld where to torque is
a minimum. The retort stand will be set up to hold up the coil by a wire supplying the
current to the coil. The wire supporting the coil will allow the coil to oscillate to small
angles and the period of oscillation will be calculated using the Light Triggered Timer.
Theory
To measure the torque as a function of theta created by the coil it is necessary to sum the
forces acting on this system. The two main forces acting on the system are the force due
to the current in the coil and the magnetic eld strength and the force due to the torsional
stiffness of wire suspending the coil. The angle of the magnetorquer is measured from
perpendicular to the magnetic eld, Figure 98.
Figure 98: Schematic of the torqu acting on the system
Calculating the torque due to the current in the coil and the magnetic eld strength:
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J MAGNETORQUER TEST THEORY
Substituting Eqs. 149 and 150 into Eq. 151 gives Eq. 152:
= k MBsin () (152)
The torque acting on the system can be written in terms of the mass moment of inertia
and the angular acceleration of the system Eq. 153:
= J = J d2dt2
= J (153)
Where J is the mass moment of inertia of the magnetorquer coil (kgm2)
Solving Eq. 153: Eq. 154 can be created by substituting Eq. 152 into Eq. 153:
J = k MBsin () (154)In this experiment will be kept small, less than 15, and thus the small angle
approximation, Eq. 155:
sin () (155)Using Eq. 155, Eq. 154 becomes Eq. 156:
+ k + MB
J = 0 (156)
Eq. 156 is in the form of a standard differential equation and can be solved letting = Ae t
and solving the characteristic equation.
The characteristic equation of Eq. 156 is given in Eq. 157:
2 + k + MB
J = 0 (157)
Solving Eq. 157 gives Eqs. 158 and 159:
= k + MB J = i k + MB J = i (158)
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J MAGNETORQUER TEST THEORY
= c1cos ( t) + c2sin ( t) (159)
Eq. 159 has the initial conditions listed in Eqs. 160 and 161:
(t = 0) = 0 Initial Angular Displacement (160)
(t = 0) = 0 Initial Angular Velocity (161)From the initial conditions, Eq. 159 becomes Eq. 162:
= 0cos k + MB J t = 0cos 2 T t (162) Where T is the period of oscillation of the system (s), as measured by the light
triggered timer
Calculation of J:
J, the mass moment of inertia of the magnetorquer coil can be calculated by Eq. 163:
J = mcL2
6 (163)
Where mcis the mass (kg) of the magnetorquer coil.
Calculation of K : To calculate the torsional stiffness of the wire, k , the power to the
coils is to be switched off (making M=0), the coil set to oscillate about = 0 (small ) and
T k is to be measured by the light triggered timer. The torsional stiffness of the wire can
then be calculated by Eq. 162, this is shown in Eq. 164:
k = J 4
2
T 2K (164)
Calculation of M:
M = J 4 2
T 2B k B
(165)
The torque of the coil:
cl
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J MAGNETORQUER TEST THEORY
Now that M is known the equation for the torque of the coil can be found by Eq. 166:
c = MB (166)
In the case of the satellite, B is the magnet eld strength of the earth at a given time. B
would have to be known for the control of the satellite.
Error in Measurement
The total error in the calculation of the torque, c, as calculated by Eq. 167:
c c
2= 4
2
M J
T 2B
2 Mc Mc
2+ 2 LL
2+ BB
2 + 2 T T 2
+ k B
2 Mc Mc
2+ 2 L
L
2+ 2
T k
2+ B
B
2+ B
B2
+
2(167)
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K TESTS RESULTS
K Tests Results
The test results that are included in this appendix are for the following tests:
Magnetorquer Tests - K1
Thermal Vacuum Tests - K2
Vibration Tests - K2
K.1 Magnetorquer Tests
The magnetorquer tests were completed for the three magnetorquers. The results of the
tests for each magnetorquer are shown in the following tables.
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K.1 Magnetorquer Tests K TESTS RESULTS
Magnetorquer 1:
Table 35: Physical properties of magnetorquer 1Magnetorquer physical properties
Mass 1 0.0171 kg
Length 1 0.07566 mHeight 1 0.07339 maverage length 0.074525 m
Moment of Inertia, J1 1.58288E-05 kg.m2wire mass 0.002 kg
wire distance 0.04 mTot. Mom of Inertia 1.90288E-05 kg.m2
Mag eld strength, Beta 0.00178 T
Table 36: Measured and calculated values for magnetorquer 11 Helmholtz Coil Pair: B = 17.8 gauss, V = 8.2volts, I = .75Amps
Magnetorquer volatge and currentV 0volts 7.1volts 13.2volts 18.4volts 26volts 32.2voltsI 0A 0.05A 0.1A 0.15A 0.2A 0.23A
Five measurements of ten periods of oscillation [s]1 5.811 5.639 5.487 5.374 5.28 5.222 5.816 5.638 5.478 5.368 5.291 5.233 5.815 5.639 5.479 5.379 5.294 5.2334 5.81 5.639 5.487 5.376 5.287 5.2275 5.812 5.639 5.484 5.376 5.287 5.23
k [N.m] 2.223 E-3Avg. T [s] 0.58128 0.56388 0.5483 0.53746 0.52878 0.5228
M 0 0.078275 0.15477 0.21197 0.26033 0.29506 .[N.m.deg] 0 -1.3932 -2.7550 -3.7732 -4.6340 -5.2521
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K.1 Magnetorquer Tests K TESTS RESULTS
Magnetorquer 2:
Table 37: Physical properties of magnetorquer 2Magnetorquer physical properties
Mass 2 0.0168 kg
Length 2 0.07509 mHeight 2 0.0728 maverage length 0.073945 m
Moment of Inertia, J2 1.531E-05 kg.m2wire mass 0.002 kg
wire distance 0.04 mtot. Mom of Inertia 1.851E-05 kg.m2Mag eld strength 0.00154 T
Table 38: Measured and calculated values for magnetorquer 22 Helmholtz Coil Pair: B = 15.4 gauss, V = 8.2volts, I = .75Amps
Magnetorquer volatge and currentV 0volts 7.8volts 13volts 19.6volts 27.5volts 32.2voltsI 0A 0.05A 0.1A 0.15A 0.2A 0.22A
Five measurements of ten periods of oscillation [s]1 5.835 5.679 5.569 5.466 5.369 5.3762 5.839 5.674 5.564 5.469 5.382 5.3723 5.84 5.674 5.565 5.472 5.38 5.3794 5.841 5.673 5.561 5.464 5.388 5.3795 5.837 5.674 5.565 5.459 5.385 5.391
k [N.m] 0.002143773Avg. T [s] 0.58384 0.56748 0.55648 0.5466 0.53808 0.53794
M 0 0.08142 0.14024 0.19614 0.24683 0.24769 .[N.m.deg] 0 -1.2538 -2.1598 -3.0206 -3.8013 -3.8144
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K.2 Thermal Vacuum Tests K TESTS RESULTS
K.2 Thermal Vacuum Tests
The results for the thermal vacuum tests are shown in the following tables:
Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
0 21 21.38 21.33 21.09 21.29 21.19 0.21 207.5 0.22 214.3 0.21
1 21.82 22.01 21.32 21.09 21.27 21.19 0.22 207.4 0.22 214.1 0.21
2 22.63 22.93 21.27 21.09 21.24 21.19 0.2278 206.9 0.2160 213.8 0.2140
3 23.45 23.66 21.36 21.19 21.35 21.29 0.2351 207.8 0.2170 214.9 0.2150
4 24.27 24.50 21.25 21.09 20.31 21.29 0.2435 206.7 0.2160 204.5 0.2150
5 25.08 25.36 21.24 21.09 21.27 21.09 0.2521 206.6 0.2160 214.1 0.2130
6 25.90 26.15 21.22 21.19 21.28 21.09 0.2600 206.4 0.2170 214.2 0.2130
7 26.72 26.64 21.34 21.39 21.52 21.29 0.2649 207.6 0.2190 216.6 0.2150
8 27.53 28.77 21.48 21.49 21.63 21.29 0.2862 209.0 0.2200 217.7 0.2150
9 28.35 28.43 21.19 21.29 21.45 21.09 0.2828 206.1 0.2180 215.9 0.2130
10 29.17 29.26 21.25 22.99 22.86 21.89 0.2911 206.7 0.2350 230.0 0.2210
11 29.98 29.99 21.58 21.79 21.76 21.39 0.2984 210.0 0.2230 219.0 0.2160
12 30.80 31.44 21.48 21.79 21.86 21.29 0.3129 209.0 0.2230 220.0 0.2150
13 31.62 31.76 21.56 22.19 22.09 21.69 0.3161 209.8 0.2270 222.3 0.2190
14 32.43 33.00 24.18 23.39 22.44 22.19 0.3285 236.0 0.2390 225.8 0.2240
15 33.25 33.40 21.58 22.19 22.86 21.39 0.3325 210.0 0.2270 230.0 0.2160
16 34.07 34.02 21.45 22.19 22.24 21.29 0.3387 208.7 0.2270 223.8 0.2150
17 34.88 35.45 21.66 22.39 22.46 21.59 0.3530 210.8 0.2290 226.0 0.2180
18 35.70 35.82 21.56 22.49 22.54 21.39 0.3567 209.8 0.2300 226.8 0.2160
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K.2 Thermal Vacuum Tests K TESTS RESULTS
Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
19 36.52 36.83 21.66 22.69 22.74 21.49 0.3668 210.8 0.2320 228.8 0.2170
20 37.33 36.91 21.81 22.99 23.00 21.59 0.3676 212.3 0.2350 231.4 0.2180
21 38.15 38.40 22.16 23.29 23.33 21.89 0.3825 215.8 0.2380 234.7 0.2210
22 38.97 39.02 22.37 23.59 23.86 22.19 0.3887 217.9 0.2410 240.0 0.2240
23 39.78 40.03 22.46 23.59 23.78 22.39 0.3988 218.8 0.2410 239.2 0.2260
24 40.60 41.00 22.31 24.09 23.84 21.99 0.4085 217.3 0.2460 239.8 0.2220
25 41.42 41.34 22.41 24.09 24.25 22.19 0.4119 218.3 0.2460 243.9 0.2240
26 42.23 42.38 22.59 24.49 24.39 22.69 0.4223 220.1 0.2500 245.3 0.2290
27 43.05 42.98 22.78 24.59 24.51 22.49 0.4283 222.0 0.2510 246.5 0.2270
28 43.87 44.07 22.86 24.79 24.75 22.59 0.4392 222.8 0.2530 248.9 0.2280
29 44.68 44.85 23.07 25.09 25.03 22.79 0.4470 224.9 0.2560 251.7 0.2300
30 45.50 45.71 23.26 25.39 25.28 22.99 0.4556 226.8 0.2590 254.2 0.2320
31 46.32 46.50 23.51 25.79 25.76 23.49 0.4635 229.3 0.2630 259.0 0.2370
32 47.13 47.50 23.71 26.19 25.90 23.29 0.4735 231.3 0.2670 260.4 0.2350
33 47.95 48.37 24.58 27.19 26.31 23.69 0.4822 240.0 0.2770 264.5 0.2390
34 48.77 48.95 24.18 27.19 26.60 24.29 0.4880 236.0 0.2770 267.4 0.2450
35 49.58 49.76 24.48 27.29 26.96 24.19 0.4961 239.0 0.2780 271.0 0.2440
36 50.40 51.13 26.58 28.49 28.42 25.29 0.5098 260.0 0.2900 285.6 0.2550
37 51.22 50.39 25.05 28.09 27.64 24.69 0.5024 244.7 0.2860 277.8 0.2490
38 52.03 52.68 25.20 28.29 27.86 24.79 0.5253 246.2 0.2880 280.0 0.2500
39 52.85 53.10 25.49 28.69 28.26 25.09 0.5295 249.1 0.2920 284.0 0.2530
40 53.67 53.74 25.77 29.09 28.56 25.39 0.5359 251.9 0.2960 287.0 0.2560
41 54.48 54.70 26.08 29.49 29.01 25.69 0.5455 255.0 0.3000 291.5 0.2590
42 55.30 55.48 26.44 29.89 29.46 26.09 0.5533 258.6 0.3040 296.0 0.2630
43 56.12 56.31 26.76 30.29 29.86 26.29 0.5616 261.8 0.3080 300.0 0.2650
44 56.93 57.15 27.07 30.69 30.29 26.69 0.5700 264.9 0.3120 304.3 0.2690
45 57.75 57.95 27.43 31.19 30.73 26.99 0.5780 268.5 0.3170 308.7 0.2720
46 58.57 58.56 27.78 31.69 31.18 27.29 0.5841 272.0 0.3220 313.2 0.2750
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K.2 Thermal Vacuum Tests K TESTS RESULTS
Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
47 59.38 59.42 28.18 32.19 31.69 27.69 0.5927 276.0 0.3270 318.3 0.2790
48 60.20 60.45 28.53 32.59 32.11 28.09 0.6030 279.5 0.3310 322.5 0.2830
49 61.02 61.48 28.98 33.19 32.64 28.49 0.6133 284.0 0.3370 327.8 0.2870
50 61.83 61.90 29.34 33.59 33.10 28.89 0.6175 287.6 0.3410 332.4 0.2910
51 62.65 62.56 29.75 34.09 33.59 29.29 0.6241 291.7 0.3460 337.3 0.2950
52 63.47 63.53 30.17 34.69 34.09 29.69 0.6338 295.9 0.3520 342.3 0.2990
53 64.28 63.68 30.62 35.19 34.63 30.09 0.6353 300.4 0.3570 347.7 0.3030
54 65.10 63.90 31.04 35.69 35.13 30.49 0.6375 304.6 0.3620 352.7 0.3070
55 65.92 66.01 31.50 36.29 35.68 30.99 0.6586 309.2 0.3680 358.2 0.3120
56 66.73 66.88 31.96 36.79 36.26 31.39 0.6673 313.8 0.3730 364.0 0.3160
57 67.55 67.73 32.43 37.29 36.46 31.89 0.6758 318.5 0.3780 366.0 0.3210
58 68.37 68.71 32.92 37.79 37.43 32.39 0.6856 323.4 0.3830 375.7 0.3260
59 69.18 69.21 33.43 38.39 38.02 32.89 0.6906 328.5 0.3890 381.6 0.3310
60 70.00 69.94 33.91 38.99 38.61 33.29 0.6979 333.3 0.3950 387.5 0.3350
61 70.00 70.48 34.56 39.69 39.30 33.99 0.7033 339.8 0.4020 394.4 0.3420
62 70.00 70.19 35.24 40.19 39.86 34.39 0.7004 346.6 0.4070 400.0 0.3460
63 70.00 70.28 35.50 40.69 40.46 34.89 0.7013 349.2 0.4120 406.0 0.3510
64 70.00 70.48 36.13 41.39 41.06 35.59 0.7033 355.5 0.4190 412.0 0.3580
65 70.00 70.39 36.62 41.89 41.66 35.99 0.7024 360.4 0.4240 418.0 0.3620
66 70.00 70.29 37.15 42.39 42.16 36.49 0.7014 365.7 0.4290 423.0 0.3670
67 70.00 70.37 37.73 42.99 42.76 37.09 0.7022 371.5 0.4350 429.0 0.3730
68 70.00 70.27 38.25 43.39 43.26 37.59 0.7012 376.7 0.4390 434.0 0.3780
69 70.00 70.23 38.80 43.99 43.76 38.19 0.7008 382.2 0.4450 439.0 0.3840
70 70.00 70.31 39.34 44.49 44.26 38.69 0.7016 387.6 0.4500 444.0 0.3890
71 70.00 70.31 39.88 44.99 44.76 39.19 0.7016 393.0 0.4550 449.0 0.3940
72 70.00 70.35 43.88 48.99 48.56 45.49 0.7020 433.0 0.4950 487.0 0.4570
73 70.00 70.75 41.28 46.49 46.36 40.89 0.7060 407.0 0.4700 465.0 0.4110
74 70.00 70.35 41.38 46.49 46.36 40.99 0.7020 408.0 0.4700 465.0 0.4120
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K.2 Thermal Vacuum Tests K TESTS RESULTS
Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
75 70.00 70.17 41.78 46.79 46.66 41.29 0.7002 412.0 0.4730 468.0 0.4150
76 70.00 70.37 42.38 47.39 47.26 41.99 0.7022 0.418 0.4790 0.474 0.4220
77 70.00 70.39 42.88 47.69 47.56 42.39 0.7024 0.423 0.4820 0.477 0.4260
78 70.00 70.30 43.18 47.99 47.96 42.79 0.7015 0.426 0.4850 0.481 0.4300
79 70.00 70.19 43.58 48.39 48.26 43.19 0.7004 0.430 0.4890 0.484 0.4340
80 70.00 70.19 44.08 48.69 48.66 43.69 0.7004 0.435 0.4920 0.488 0.4390
81 70.00 70.23 44.48 49.19 49.16 44.39 0.7008 0.439 0.4970 0.493 0.4460
82 70.00 70.46 45.08 49.69 49.66 44.79 0.7031 0.445 0.5020 0.498 0.4500
83 70.00 70.32 45.28 49.79 49.86 44.99 0.7017 0.447 0.5030 0.500 0.4520
84 70.00 70.95 54.68 50.09 50.16 45.39 0.7080 0.541 0.5060 0.503 0.4560
85 70.00 70.24 46.08 50.39 50.46 45.79 0.7009 0.455 0.5090 0.506 0.4600
86 70.00 70.23 46.38 50.79 50.86 46.19 0.7008 0.458 0.5130 0.510 0.4640
87 70.00 70.18 46.78 51.09 51.16 46.59 0.7003 0.462 0.5160 0.513 0.4680
88 70.00 70.16 47.08 51.39 51.46 46.89 0.7001 0.465 0.5190 0.516 0.4710
89 70.00 70.18 47.48 51.69 51.76 47.29 0.7003 0.469 0.5220 0.519 0.4750
90 70.00 70.22 47.98 46.69 52.06 47.59 0.7007 0.474 0.4720 0.522 0.4780
91 70.00 70.00 48.08 52.19 52.36 47.89 0.6985 0.475 0.5270 0.525 0.4810
92 70.00 70.14 48.38 52.49 52.66 48.29 0.6999 0.478 0.5300 0.528 0.4850
93 70.00 70.18 48.68 52.69 52.96 48.59 0.7003 0.481 0.5320 0.531 0.4880
94 70.00 69.96 48.98 52.99 53.16 48.89 0.6981 0.484 0.5350 0.533 0.4910
95 70.00 69.22 49.18 53.09 53.46 49.19 0.6907 0.486 0.5360 0.536 0.4940
96 70.00 69.50 49.58 53.39 53.66 49.39 0.6935 0.490 0.5390 0.538 0.4960
97 70.00 70.36 49.78 53.59 53.96 49.69 0.7021 0.492 0.5410 0.541 0.4990
98 70.00 68.65 49.98 53.79 54.16 49.99 0.6850 0.494 0.5430 0.543 0.5020
99 70.00 70.93 50.28 54.09 54.46 50.29 0.7078 0.497 0.5460 0.546 0.5050
100 70.00 70.65 50.58 54.29 54.76 50.79 0.7050 0.500 0.5480 0.549 0.5100
101 70.00 70.34 51.08 54.69 55.16 51.09 0.7019 0.505 0.5520 0.553 0.5130
102 70.00 69.83 50.98 54.59 55.06 50.99 0.6968 0.504 0.5510 0.552 0.5120
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K.2 Thermal Vacuum Tests K TESTS RESULTS
Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
103 70.00 70.54 51.18 54.79 55.16 51.19 0.7039 0.506 0.5530 0.553 0.5140
104 70.00 70.31 51.48 54.99 55.46 51.49 0.7016 0.509 0.5550 0.556 0.5170
105 70.00 70.12 51.68 55.19 55.66 51.69 0.6997 0.511 0.5570 0.558 0.5190
106 70.00 70.29 52.28 55.69 56.26 52.29 0.7014 0.517 0.5620 0.564 0.5250
107 70.00 70.25 52.08 55.49 55.96 52.09 0.7010 0.515 0.5600 0.561 0.5230
108 70.00 70.25 52.28 55.69 56.16 52.29 0.7010 0.517 0.5620 0.563 0.5250
109 70.00 70.08 52.48 55.79 56.36 52.49 0.6993 0.519 0.5630 0.565 0.5270
110 70.00 70.18 52.58 55.99 56.46 52.69 0.7003 0.520 0.5650 0.566 0.5290
111 70.00 70.17 52.78 55.99 56.56 52.89 0.7002 0.522 0.5650 0.567 0.5310
112 70.00 70.35 53.08 56.29 56.86 53.19 0.7020 0.525 0.5680 0.570 0.5340
113 70.00 70.27 53.08 56.29 56.86 53.19 0.7012 0.525 0.5680 0.570 0.5340
114 70.00 70.21 53.18 56.39 56.96 53.39 0.7006 0.526 0.5690 0.571 0.5360
115 70.00 70.14 53.28 56.39 57.06 53.49 0.6999 0.527 0.5690 0.572 0.5370
116 70.00 70.38 53.48 56.69 57.26 53.69 0.7023 0.529 0.5720 0.574 0.5390
117 70.00 70.15 53.58 56.69 57.26 53.79 0.7000 0.530 0.5720 0.574 0.5400
118 70.00 70.27 53.88 56.99 57.56 54.09 0.7012 0.533 0.5750 0.577 0.5430
119 70.00 70.42 53.88 56.79 57.46 53.99 0.7027 0.533 0.5730 0.576 0.5420
120 70.00 70.38 53.88 56.99 57.56 54.09 0.7023 0.533 0.5750 0.577 0.5430
121 69.18 69.68 54.08 57.09 57.76 54.29 0.6953 0.535 0.5760 0.579 0.5450
122 68.37 68.49 54.18 57.29 57.86 54.49 0.6834 0.536 0.5780 0.580 0.5470
123 67.55 67.67 54.08 57.09 57.76 54.39 0.6752 0.535 0.5760 0.579 0.5460
124 66.73 67.25 54.28 57.29 57.86 54.59 0.6710 0.537 0.5780 0.580 0.5480
125 65.92 66.07 54.48 57.49 58.16 54.79 0.6592 0.539 0.5800 0.583 0.5500
126 65.10 64.75 52.58 57.29 57.96 54.79 0.6460 0.520 0.5780 0.581 0.5500
127 64.28 64.25 54.58 57.39 58.06 54.89 0.6410 0.540 0.5790 0.582 0.5510
128 63.47 63.91 54.48 57.29 57.86 54.79 0.6376 0.539 0.5780 0.580 0.5500
129 62.65 63.05 54.48 57.29 57.96 54.99 0.6290 0.539 0.5780 0.581 0.5520
130 61.83 61.93 54.78 57.29 57.96 54.99 0.6178 0.542 0.5780 0.581 0.5520
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K.2 Thermal Vacuum Tests K TESTS RESULTS
Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
159 38.15 41.09 49.68 49.39 50.46 50.49 0.4094 0.491 0.4990 0.506 0.5070
160 37.33 40.70 49.38 49.09 50.16 50.19 0.4055 0.488 0.4960 0.503 0.5040
161 36.52 40.33 48.98 48.69 49.76 49.79 0.4018 0.484 0.4920 0.499 0.5000
162 35.70 39.98 48.68 48.29 49.46 49.49 0.3983 0.481 0.4880 0.496 0.4970
163 34.88 39.64 48.38 47.89 49.06 48.79 0.3949 0.478 0.4840 0.492 0.4900
164 34.07 39.33 48.08 47.59 48.76 48.89 0.3918 0.475 0.4810 0.489 0.4910
165 33.25 38.91 47.58 47.19 48.26 48.49 0.3876 0.470 0.4770 0.484 0.4870
166 32.43 38.67 47.38 46.89 47.96 48.19 0.3852 0.468 0.4740 0.481 0.4840
167 31.62 38.37 47.08 46.49 47.66 47.89 0.3822 0.465 0.4700 0.478 0.4810
168 30.80 38.05 46.68 46.19 47.26 47.49 0.3790 0.461 0.4670 0.474 0.4770
169 29.98 37.70 46.38 45.79 46.86 47.19 0.3755 0.458 0.4630 0.470 0.4740
170 29.17 37.32 46.08 45.49 46.56 44.89 0.3717 0.455 0.4600 0.467 0.4510
171 28.35 36.94 45.68 45.09 46.16 46.59 0.3679 0.451 0.4560 0.463 0.4680
172 27.53 36.53 45.38 44.69 45.86 46.19 0.3638 0.448 0.4520 0.460 0.4640
173 26.72 36.18 45.08 44.39 45.56 45.89 0.3603 0.445 0.4490 0.457 0.4610
174 25.90 35.82 44.68 44.09 45.16 45.59 0.3567 0.441 0.4460 0.453 0.4580
175 25.08 35.48 44.38 43.79 44.86 45.19 0.3533 0.438 0.4430 0.450 0.4540
176 24.27 35.15 44.08 43.39 44.46 44.89 0.3500 0.435 0.4390 0.446 0.4510
177 23.45 34.84 43.68 43.09 44.16 44.49 0.3469 0.431 0.4360 0.443 0.4470
178 22.63 34.55 43.38 42.69 43.86 44.19 0.3440 0.428 0.4320 0.440 0.4440
179 21.82 34.24 43.08 42.39 43.46 43.89 0.3409 0.425 0.4290 0.436 0.4410
180 21.00 33.99 42.78 42.09 43.16 43.59 0.3384 0.422 0.4260 0.433 0.4380
181 21.00 33.73 42.38 41.69 42.86 43.29 0.3358 0.418 0.4220 0.430 0.4350
182 21.00 33.48 42.08 41.39 42.46 42.89 0.3333 0.415 0.4190 0.426 0.4310
183 21.00 33.24 41.78 41.09 42.16 42.59 0.3309 0.412 0.4160 0.423 0.4280
184 21.00 32.96 41.38 40.69 41.76 42.19 0.3281 0.408 0.4120 0.419 0.4240
185 21.00 32.59 40.88 40.19 41.26 41.69 0.3244 0.403 0.4070 0.414 0.4190
186 21.00 32.54 40.78 40.09 41.16 41.59 0.3239 0.402 0.4060 0.413 0.4180
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K.2 Thermal Vacuum Tests K TESTS RESULTS
Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
187 21.00 32.35 40.58 39.89 40.86 41.39 0.3220 0.400 0.4040 0.410 0.4160
188 21.00 32.14 40.18 39.49 40.56 40.99 0.3199 0.396 0.4000 0.407 0.4120
189 21.00 31.90 39.88 39.19 40.26 40.69 0.3175 0.393 0.3970 0.404 0.4090
190 21.00 31.75 39.58 38.89 39.96 40.39 0.3160 0.390 0.3940 0.401 0.4060
191 21.00 31.56 39.38 38.59 39.66 40.09 0.3141 0.388 0.3910 0.398 0.4030
192 21.00 31.37 39.08 38.39 39.36 39.79 0.3122 0.385 0.3890 0.395 0.4000
193 21.00 31.19 38.78 38.09 39.06 39.49 0.3104 0.382 0.3860 0.392 0.3970
194 21.00 31.01 38.48 37.79 38.76 39.19 0.3086 0.379 0.3830 0.389 0.3940
195 21.00 30.83 38.18 37.49 38.46 38.89 0.3068 0.376 0.3800 0.386 0.3910
196 21.00 30.65 37.88 37.19 38.26 38.59 0.3050 0.373 0.3770 0.384 0.3880
197 21.00 30.46 37.58 36.99 37.86 38.29 0.3031 0.370 0.3750 0.380 0.3850
198 21.00 30.29 37.38 36.69 37.66 38.09 0.3014 0.368 0.3720 0.378 0.3830
199 21.00 30.12 37.08 36.39 37.36 37.79 0.2997 0.365 0.3690 0.375 0.3800
200 21.00 29.96 36.78 36.19 37.06 37.49 0.2981 0.362 0.3670 0.372 0.3770
201 21.00 29.73 36.58 35.79 36.66 37.09 0.2958 0.360 0.3630 0.368 0.3730
202 21.00 29.65 36.38 35.69 36.56 36.99 0.2950 0.358 0.3620 0.367 0.3720
203 21.00 29.49 36.19 35.39 36.26 36.69 0.2934 0.3561 0.3590 0.364 0.3690
204 21.00 29.34 35.94 35.19 36.06 36.49 0.2919 0.3536 0.3570 0.362 0.3670
205 21.00 29.20 35.69 34.89 35.86 36.19 0.2905 0.3511 0.3540 0.360 0.3640
206 21.00 29.05 35.43 34.69 35.54 35.89 0.2890 0.3485 0.3520 0.357 0.3610
207 21.00 28.91 35.19 34.49 35.28 35.59 0.2876 346.1 0.3500 354.2 0.3580
208 21.00 28.76 34.94 34.19 35.04 35.39 0.2861 343.6 0.3470 351.8 0.3560
209 21.00 28.64 34.72 33.99 34.82 35.19 0.2849 341.4 0.3450 349.6 0.3540
210 21.00 28.50 34.48 33.79 34.59 34.99 0.2835 339.0 0.3430 347.3 0.3520
211 21.00 28.37 34.25 33.49 34.36 34.69 0.2822 336.7 0.3400 345.0 0.3490
212 21.00 28.25 34.03 33.29 34.11 34.49 0.2810 334.5 0.3380 342.5 0.3470
213 21.00 28.12 33.79 33.09 33.88 34.19 0.2797 332.1 0.3360 340.2 0.3440
214 21.00 27.99 33.58 32.89 33.68 33.99 0.2784 330.0 0.3340 338.2 0.3420
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K.2 Thermal Vacuum Tests K TESTS RESULTS
Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
215 21.00 27.87 33.36 32.69 33.46 33.79 0.2772 327.8 0.3320 336.0 0.3400
216 21.00 27.76 33.15 32.49 33.25 33.59 0.2761 325.7 0.3300 333.9 0.3380
217 21.00 27.64 32.93 32.29 33.03 33.39 0.2749 323.5 0.3280 331.7 0.3360
218 21.00 27.53 32.73 32.09 32.83 33.09 0.2738 321.5 0.3260 329.7 0.3330
219 21.00 27.42 32.52 31.89 32.62 32.89 0.2727 319.4 0.3240 327.6 0.3310
220 21.00 27.31 32.32 31.69 32.42 32.69 0.2716 317.4 0.3220 325.6 0.3290
221 21.00 27.21 32.13 31.49 32.23 32.49 0.2706 315.5 0.3200 323.7 0.3270
222 21.00 27.10 31.93 31.29 32.04 32.29 0.2695 313.5 0.3180 321.8 0.3250
223 21.00 27.00 31.74 31.09 31.84 32.09 0.2685 311.6 0.3160 319.8 0.3230
224 21.00 26.89 31.55 30.99 31.64 31.89 0.2674 309.7 0.3150 317.8 0.3210
225 21.00 26.80 31.37 30.79 31.46 31.69 0.2665 307.9 0.3130 316.0 0.3190
226 21.00 26.70 31.18 30.59 31.28 31.49 0.2655 306.0 0.3110 314.2 0.3170
227 21.00 26.59 30.99 30.39 31.08 31.39 0.2644 304.1 0.3090 312.2 0.3160
228 21.00 26.50 30.83 30.29 30.92 31.19 0.2635 302.5 0.3080 310.6 0.3140
229 21.00 26.41 30.65 30.09 30.75 30.99 0.2626 300.7 0.3060 308.9 0.3120
230 21.00 26.31 30.46 29.89 30.56 30.79 0.2616 298.8 0.3040 307.0 0.3100
231 21.00 26.23 30.30 29.79 30.41 30.59 0.2608 297.2 0.3030 305.5 0.3080
232 21.00 26.13 30.14 29.59 30.23 30.39 0.2598 295.6 0.3010 303.7 0.3060
233 21.00 26.05 29.98 29.39 30.07 30.29 0.2590 294.0 0.2990 302.1 0.3050
234 21.00 25.96 29.82 29.29 29.91 30.09 0.2581 292.4 0.2980 300.5 0.3030
235 21.00 25.88 29.66 29.09 29.75 29.89 0.2573 290.8 0.2960 298.9 0.3010
236 21.00 25.79 29.50 28.99 29.59 29.79 0.2564 289.2 0.2950 297.3 0.3000
237 21.00 25.69 29.30 28.79 29.39 29.59 0.2554 287.2 0.2930 295.3 0.2980
238 21.00 25.62 29.17 28.69 29.26 29.39 0.2547 285.9 0.2920 294.0 0.2960
239 21.00 25.56 29.05 28.59 29.14 29.29 0.2541 284.7 0.2910 292.8 0.2950
240 21.00 25.49 28.90 28.39 28.98 29.19 0.2534 283.2 0.2890 291.2 0.2940
241 21.82 25.42 28.76 28.29 28.83 28.99 0.2527 281.8 0.2880 289.7 0.2920
242 22.63 25.36 28.62 28.09 28.70 28.89 0.2521 280.4 0.2860 288.4 0.2910
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K.2 Thermal Vacuum Tests K TESTS RESULTS
Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
243 23.45 25.29 28.48 27.99 28.56 28.69 0.2514 279.0 0.2850 287.0 0.2890
244 24.27 25.23 28.35 27.89 28.43 28.59 0.2508 277.7 0.2840 285.7 0.2880
245 25.08 25.34 28.22 27.79 28.29 28.49 0.2519 276.4 0.2830 284.3 0.2870
246 25.90 26.12 28.08 27.59 28.16 28.29 0.2597 275.0 0.2810 283.0 0.2850
247 26.72 27.16 27.89 27.49 28.03 28.19 0.2701 273.1 0.2800 281.7 0.2840
248 27.53 27.48 27.83 27.49 27.94 28.09 0.2733 272.5 0.2800 280.8 0.2830
249 28.35 28.33 27.71 27.39 27.85 27.89 0.2818 271.3 0.2790 279.9 0.2810
250 29.17 28.90 27.60 27.29 27.78 27.79 0.2875 270.2 0.2780 279.2 0.2800
251 29.98 29.81 27.49 27.29 27.73 27.69 0.2966 269.1 0.2780 278.7 0.2790
252 30.80 30.94 27.39 27.29 27.69 27.59 0.3079 268.1 0.2780 278.3 0.2780
253 31.62 31.78 27.30 27.29 27.68 27.49 0.3163 267.2 0.2780 278.2 0.2770
254 32.43 32.57 27.22 27.29 27.69 27.39 0.3242 266.4 0.2780 278.3 0.2760
255 33.25 33.40 27.15 27.29 27.71 27.29 0.3325 265.7 0.2780 278.5 0.2750
256 34.07 34.29 27.09 27.39 27.76 27.29 0.3414 265.1 0.2790 279.0 0.2750
257 34.88 35.13 27.05 27.49 27.82 27.19 0.3498 264.7 0.2800 279.6 0.2740
258 35.70 35.82 27.02 27.49 27.89 27.19 0.3567 264.4 0.2800 280.3 0.2740
259 36.52 36.77 27.00 27.59 28.00 27.09 0.3662 264.2 0.2810 281.4 0.2730
260 37.33 37.53 27.00 27.79 28.10 27.09 0.3738 264.2 0.2830 282.4 0.2730
261 38.15 38.32 27.02 27.89 28.21 27.09 0.3817 264.4 0.2840 283.5 0.2730
262 38.97 38.90 27.04 27.99 28.34 27.09 0.3875 264.6 0.2850 284.8 0.2730
263 39.78 39.43 27.08 28.09 28.47 27.09 0.3928 265.0 0.2860 286.1 0.2730
264 40.60 40.77 27.14 28.29 28.61 27.19 0.4062 265.6 0.2880 287.5 0.2740
265 41.42 41.56 27.21 28.49 28.76 27.19 0.4141 266.3 0.2900 289.0 0.2740
266 42.23 42.26 27.30 28.69 28.94 27.29 0.4211 267.2 0.2920 290.8 0.2750
267 43.05 43.39 27.40 28.79 29.13 27.39 0.4324 268.2 0.2930 292.7 0.2760
268 43.87 44.08 27.52 28.99 29.33 27.49 0.4393 269.4 0.2950 294.7 0.2770
269 44.68 44.64 27.64 29.19 29.52 27.59 0.4449 270.6 0.2970 296.6 0.2780
270 45.50 45.29 27.77 29.39 29.71 27.69 0.4514 271.9 0.2990 298.5 0.2790
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Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
271 46.32 46.50 27.92 29.69 29.91 27.79 0.4635 273.4 0.3020 300.5 0.2800
272 47.13 47.28 28.08 29.89 30.17 27.99 0.4713 275.0 0.3040 303.1 0.2820
273 47.95 47.95 28.25 30.19 30.38 28.09 0.4780 276.7 0.3070 305.2 0.2830
274 48.77 48.90 28.44 30.39 30.62 28.19 0.4875 278.6 0.3090 307.6 0.2840
275 49.58 49.49 28.63 30.69 30.90 28.39 0.4934 280.5 0.3120 310.4 0.2860
276 50.40 50.38 28.85 30.99 31.20 28.59 0.5023 282.7 0.3150 313.4 0.2880
277 51.22 51.42 29.06 31.29 31.46 28.79 0.5127 284.8 0.3180 316.0 0.2900
278 52.03 52.10 29.27 31.59 31.75 29.19 0.5195 286.9 0.3210 318.9 0.2940
279 52.85 53.03 29.51 31.89 32.05 29.19 0.5288 289.3 0.3240 321.9 0.2940
280 53.67 53.94 29.76 32.29 32.39 29.49 0.5379 291.8 0.3280 325.3 0.2970
281 54.48 54.69 30.02 32.69 32.77 29.79 0.5454 294.4 0.3320 329.1 0.3000
282 55.30 55.35 30.30 33.09 33.13 29.99 0.5520 297.2 0.3360 332.7 0.3020
283 56.12 56.08 30.60 33.49 33.54 30.29 0.5593 300.2 0.3400 336.8 0.3050
284 56.93 56.95 30.89 33.89 33.89 30.59 0.5680 303.1 0.3440 340.3 0.3080
285 57.75 57.90 31.18 34.19 34.25 30.79 0.5775 306.0 0.3470 343.9 0.3100
286 58.57 58.65 31.20 34.59 34.63 31.09 0.5850 306.2 0.3510 347.7 0.3130
287 59.38 58.25 32.01 35.19 35.21 31.49 0.5810 314.3 0.3570 353.5 0.3170
288 60.20 57.95 32.23 35.39 35.46 31.79 0.5780 316.5 0.3590 356.0 0.3200
289 61.02 59.87 32.51 35.79 35.77 32.09 0.5972 319.3 0.3630 359.1 0.3230
290 61.83 62.27 32.87 36.29 36.23 32.39 0.6212 322.9 0.3680 363.7 0.3260
291 62.65 62.79 33.22 36.69 36.68 32.79 0.6264 326.4 0.3720 368.2 0.3300
292 63.47 61.55 33.61 37.19 37.18 33.19 0.6140 330.3 0.3770 373.2 0.3340
293 64.28 62.83 33.99 37.59 37.63 33.49 0.6268 334.1 0.3810 377.7 0.3370
294 65.10 64.36 34.30 38.09 38.11 33.89 0.6421 337.2 0.3860 382.5 0.3410
295 65.92 66.14 34.79 38.59 38.64 34.29 0.6599 342.1 0.3910 387.8 0.3450
296 66.73 66.06 35.23 39.19 39.18 34.69 0.6591 346.5 0.3970 393.2 0.3490
297 67.55 67.69 35.65 39.69 39.70 35.19 0.6754 350.7 0.4020 398.4 0.3540
298 68.37 68.53 36.11 40.29 40.36 35.59 0.6838 355.3 0.4080 0.405 0.3580
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Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
299 69.18 68.65 36.58 40.89 40.96 36.09 0.6850 360.0 0.4140 0.411 0.3630
300 70.00 69.59 37.07 41.49 41.56 36.59 0.6944 364.9 0.4200 0.417 0.3680
301 70.00 70.23 37.55 42.09 42.06 36.99 0.7008 369.7 0.4260 0.422 0.3720
302 70.00 70.01 38.07 42.69 42.66 37.49 0.6986 0.3749 0.4320 0.428 0.3770
303 70.00 70.24 38.58 43.19 43.26 37.99 0.7009 0.380 0.4370 0.434 0.3820
304 70.00 70.28 39.08 43.79 43.86 38.49 0.7013 0.385 0.4430 0.440 0.3870
305 70.00 70.25 39.58 44.29 44.36 38.99 0.7010 0.390 0.4480 0.445 0.3920
306 70.00 70.29 40.18 44.89 44.96 39.49 0.7014 0.396 0.4540 0.451 0.3970
307 70.00 70.24 40.58 45.49 45.56 40.09 0.7009 0.400 0.4600 0.457 0.4030
308 70.00 70.29 41.08 45.89 45.96 40.59 0.7014 0.405 0.4640 0.461 0.4080
309 70.00 70.20 41.58 46.49 46.56 41.09 0.7005 0.410 0.4700 0.467 0.4130
310 70.00 70.21 42.08 46.99 47.06 41.69 0.7006 0.415 0.4750 0.472 0.4190
311 70.00 70.31 42.68 47.39 47.46 42.19 0.7016 0.421 0.4790 0.476 0.4240
312 70.00 70.24 43.08 47.89 47.96 42.69 0.7009 0.425 0.4840 0.481 0.4290
313 70.00 70.14 43.68 48.39 48.46 43.19 0.6999 0.431 0.4890 0.486 0.4340
314 70.00 70.37 44.08 48.69 48.86 43.69 0.7022 0.435 0.4920 0.490 0.4390
315 70.00 70.18 44.58 49.19 49.26 44.19 0.7003 0.440 0.4970 0.494 0.4440
316 70.00 70.20 45.08 49.59 49.66 44.59 0.7005 0.445 0.5010 0.498 0.4480
317 70.00 70.18 45.48 49.99 50.06 45.09 0.7003 0.449 0.5050 0.502 0.4530
318 70.00 70.13 45.98 50.29 50.46 45.59 0.6998 0.454 0.5080 0.506 0.4580
319 70.00 70.15 46.38 50.69 50.86 45.99 0.7000 0.458 0.5120 0.510 0.4620
320 70.00 70.16 46.78 51.09 51.26 46.49 0.7001 0.462 0.5160 0.514 0.4670
331 70.00 70.14 50.58 54.29 54.66 50.39 0.6999 0.500 0.5480 0.548 0.5060
332 70.00 70.16 50.88 54.49 54.96 50.69 0.7001 0.503 0.5500 0.551 0.5090
333 70.00 70.17 51.08 54.69 55.16 50.99 0.7002 0.505 0.5520 0.553 0.5120
334 70.00 70.16 51.38 54.99 55.36 51.29 0.7001 0.508 0.5550 0.555 0.5150
335 70.00 70.21 51.58 55.19 55.66 51.59 0.7006 0.510 0.5570 0.558 0.5180
336 70.00 70.20 51.88 55.39 55.86 51.79 0.7005 0.513 0.5590 0.560 0.5200
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Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
337 70.00 70.20 52.08 55.49 56.06 52.09 0.7005 0.515 0.5600 0.562 0.5230
338 70.00 70.13 52.28 55.69 54.96 52.29 0.6998 0.517 0.5620 0.551 0.5250
339 70.00 70.04 52.48 55.89 56.46 52.59 0.6989 0.519 0.5640 0.566 0.5280
340 70.00 70.20 52.68 56.09 56.66 52.79 0.7005 0.521 0.5660 0.568 0.5300
341 70.00 70.19 52.98 56.29 56.86 52.99 0.7004 0.524 0.5680 0.570 0.5320
342 70.00 70.13 53.08 56.39 56.96 53.19 0.6998 0.525 0.5690 0.571 0.5340
343 70.00 70.15 53.28 56.59 56.96 53.39 0.7000 0.527 0.5710 0.571 0.5360
344 70.00 70.18 53.48 56.69 56.56 53.59 0.7003 0.529 0.5720 0.567 0.5380
345 70.00 70.16 53.68 56.89 56.96 53.79 0.7001 0.531 0.5740 0.571 0.5400
346 70.00 70.14 53.78 56.99 57.66 53.99 0.6999 0.532 0.5750 0.578 0.5420
347 70.00 70.16 53.98 57.19 57.86 54.09 0.7001 0.534 0.5770 0.580 0.5430
348 70.00 70.24 54.08 57.29 57.96 54.29 0.7009 0.535 0.5780 0.581 0.5450
349 70.00 70.20 54.28 57.39 58.06 54.49 0.7005 0.537 0.5790 0.582 0.5470
350 70.00 70.21 54.48 57.49 58.26 54.59 0.7006 0.539 0.5800 0.584 0.5480
351 70.00 70.21 54.58 57.69 58.36 54.79 0.7006 0.540 0.5820 0.585 0.5500
352 70.00 70.24 54.68 57.79 58.46 54.89 0.7009 0.541 0.5830 0.586 0.5510
353 70.00 70.18 54.88 57.89 58.66 55.09 0.7003 0.543 0.5840 0.588 0.5530
354 70.00 70.16 54.98 57.99 58.76 54.19 0.7001 0.544 0.5850 0.589 0.5440
355 70.00 70.34 55.08 58.09 58.86 55.29 0.7019 0.545 0.5860 0.590 0.5550
356 70.00 70.05 55.28 58.49 58.96 55.49 0.6990 0.547 0.5900 0.591 0.5570
357 70.00 70.03 55.28 58.29 59.06 55.59 0.6988 0.547 0.5880 0.592 0.5580
358 70.00 70.19 55.38 58.39 59.16 55.69 0.7004 0.548 0.5890 0.593 0.5590
359 70.00 70.29 55.48 58.49 59.26 55.79 0.7014 0.549 0.5900 0.594 0.5600
360 70.00 69.92 55.58 58.49 59.36 55.89 0.6977 0.550 0.5900 0.595 0.5610
361 69.18 69.27 55.68 58.59 59.46 55.99 0.6912 0.551 0.5910 0.596 0.5620
362 68.37 68.50 55.78 58.69 59.46 56.09 0.6835 0.552 0.5920 0.596 0.5630
363 67.55 67.62 55.88 58.69 59.56 56.19 0.6747 0.553 0.5920 0.597 0.5640
364 66.73 66.91 55.98 58.79 59.66 56.29 0.6676 0.554 0.5930 0.598 0.5650
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Time T Aim T Amb T 1 T 2 T 3 T 4 Readings from Multimeters
min deg C deg C deg C deg C deg C deg C Amb T1 T2 T3 T4
365 65.92 66.12 55.98 58.79 59.66 56.39 0.6597 0.554 0.5930 0.598 0.5660
366 65.10 65.23 56.08 58.79 59.66 56.39 0.6508 0.555 0.5930 0.598 0.5660
367 64.28 64.46 56.08 58.69 59.56 56.49 0.6431 0.555 0.5920 0.597 0.5670
368 63.47 63.79 56.18 58.69 59.56 56.59 0.6364 0.556 0.5920 0.597 0.5680
369 62.65 62.85 56.18 58.59 59.46 56.59 0.6270 0.556 0.5910 0.596 0.5680
370 61.83 62.08 56.18 58.49 59.46 56.59 0.6193 0.556 0.5900 0.596 0.5680
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K.3 Random Vibration Test Results
The following images are of the vibration prole that was applied to the satellite for the
high and low spectrums. The green line is the planned vibration spectrum and the red
line is the vibration spectrum that was actually applied to the test pod. The red line is
within the error bounds specied by the test plan.
Figure 99: High level spectrum
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Figure 100: Low level spectrum
The following gures are resonance plots for the h