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衛星結構設計
祝飛鴻5/25/2006
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What are the main functions of structure subsystem?
Provide support all other subsystems and attach the spacecraft to launch vehicle.
What factors need to be considered for structure design? Size Weight Field-of-view Interference Alignment Loads
ARGO Satellite- The first Taiwan designed satellite
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Size: Fit into the fairing of candidate launch vehicle. Provide adequate space for component mounting.
123 cm
135 cm
132 cm
30 cm
Falcon-1Envelope
13mm clearance
11mm clearance
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Weight: Not to exceed lift-off weight of the selected launch vehicle.
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Field-of-view (FOV): Define by other subsystems, e.g. attitude control
sensors, payload instruments, antenna subsystem, etc.
X Band Antenna FOV
110 °65 °65 °110 °
MSI FOV= 6 °
Star Camera FOV= 6.7° on short axis
9.2° on long axis
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Interference: With the launch vehicle fairing. Between components for physical contact
and assembly. Falcon-1Envelope
SectionY=1219
Solar Panel19mm clearance
X-Band Ant15.5mm clearance
GPS Ant.8.6mm clearance
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Alignment: Define by other subsystems, e.g. attitude control sensors,
payload instrument, etc. Ground alignment. On-orbit thermal & hydroscopic distortion.
Requirement
Star Camera
Orientation
± 0.5 (TBR)
Thruster Orientation ±1.5 (TBR)
X-antenna Orientation ±5 (TBR)
S-antenna Orientation ±5 (TBR)
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Loads: Environmental loads for structure design. Not-to-exceed loads for components and payloads.
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What are major tasks to be performed for structure design?:
Configuration design
Environmental loads
Structure design and analysis
Design verification
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To accommodate all the components in a limited space while
satisfying its functional requirements, every spacecraft will
end up with a unique configuration.
Configuration Design
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Configuration Design - ARGO
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To successfully deliver the spacecraft into the orbit, the launcher has to go through several stages of state changes from lift-off to separation. Each stage is called a “flight event” and those events critical to the spacecraft design is called “critical flight events”.
Environmental Loads
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Environmental Loads Each flight event will introduce loads into the spacecraft.
Major types of loads include: Transient dynamic loads caused by the changes of
acceleration state of the launcher, i.e. F = ma. F will
be generated if a or m is introduced. Random vibration loads caused by the launcher engine
and aero-induced vibration transmitted through the
spacecraft mechanical interface. Acoustic loads generated from noise in the fairing of the
launcher, e.g. at lift-off and during transonic flight. Shock loads induced from the separation device.
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Environmental Loads
The above mentioned launcher induced loads are typically
defined in the launch vehicle user’s manual. However,
these loads are specified at the spacecraft interface except
for acoustic environment. The loads to be used for the
spacecraft structure design has to be derived.
For picosat design, if P-POD is used, please refer to “The P-
POD Payload Planner’s Guide” Revision C – June 5, 2000
for definition of launch loads.
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Dynamic Coupling
Among all the launch loads, the derivation of transient
dynamic loads is most involved and typically is the
dominate load for spacecraft primary structure design.
To understand the derivation of transient dynamic loads,
the concept of “dynamic coupling” needs to be explained.
Based on the basic vibration theory, the natural frequency
of a mass spring system can be expressed as:
1 f = ------ K/M 2
Where
f = natural frequency (Hz: cycle/second)
M = mass of the system
K = spring constant of the system
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Dynamic Coupling Based on the above equation, a spring-mass system with K1 = 654,000 lb/in and weight W1= 4,000 lbs will have f1 = 40Hz (verify it!). Assume a second system has f2 = 75Hz. (if this system has 30 lbs weight, what should be the value of K2?) The forced response of these two systems subjected to 1g sinusoidal force base excitation with 3% damping ratio will have 16.7g response at their natural frequency, i.e. For system 1: 16.7g at 40Hz For system 2: 16.7g at 75Hz
(Please refer to any vibration text book for derivation of results)
W
K
1g
a
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Dynamic Coupling
Suppose we stack these two system together, the response
of the system can be derived as:
39.8Hz 75.4Hz a1 16.6g 0.4g
a2 23.1g 6.4g
where 39.8Hz and 75.4Hz are the natural
frequencies of the combined system. (Please refer to advanced vibration text book
for derivation of results)
W2
W1
K2
K1
1g
a1
a2
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Dynamic Coupling
Now, let’s change the second system to have natural
frequency of 40Hz, then the responses will be:
38.3Hz 41.8Hz a1 9.9g 9.2g
a2 99.2g 83.4g
where 38.3Hz and 41.8Hz are the natural
frequencies of the combined system.
W2
W1
K2
K1
1g
a1
a2
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Dynamic Coupling
It can be seen that by changing the natural frequency
of the second system to be identical to the first
system, the maximum response of the second
system will increase from 23.2g to 99.2g.
This phenomenon is called “dynamic
coupling”. The more closer natural
frequencies of the two systems, the
higher response the system will get.
W2
W1
K2
K1
1g
a1
a2
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Dynamic Coupling
Now you can think the first system as a launcher and the
second system as a spacecraft. To minimize
response of the spacecraft, the spacecraft
should be designed to avoid dynamic
coupling with the launcher, i.e. designed
above the launch vehicle minimum
frequency requirement. Obviously the launcher and spacecraft are
more complicated than the two degrees
of freedom system. Coupled loads analysis
(CLA) is required to obtain the responses.
W2
W1
K2
K1
1g
a1
a2
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Structure Design & Analysis
Once the mechanical layout is completed, the structural
design and analysis can be started. Major items include:
Mass property analysis
Structure member and load path
Material selection
Dynamic and Stress analysis
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Mass Property Analysis One of the important factors associated with the mechanical
layout is the mass property analysis, i.e. weight and moment
of inertia (MOI) of the spacecraft. Mass property of a spacecraft can be
calculated based on the mass property
of each individual elements e.g.
components, structure, hardness, etc. The main purpose of mass property
analysis is to assure the design satisfies
the weight and CG offset constraints
from the selected launcher.
W1
W2 X
Y
D2
D1
Total Weight ?
MOI about Z axis ?
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0 200 400 600 800 1000 1200 1400
Spacecraft Weight (lb)
2.5
2.0
1.5
1.0
0.5
0.0
Lateral CG centerline offset (in)
Falcon-1 Launcher
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Structure Member and Load Path
The spacecraft is supported by the launcher interface
therefore all the loads acting on the spacecraft has to
properly transmitted through the internal structure
elements to the interface. This load path needs to be
checked before spending extensive time on structural
analysis.
No matter how complex the structure is, it is always
made of basic elements, i.e. bar, beam, plate, shell, etc.
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PlateBeam
Components => Supporting Plate => Beam => Supporting Points
Structure Member and Load Path
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Material Selection
From purely structure design point of view, it is always
desirable to use material with high stiffness, high
strength, and low density, i.e. high strength/stiffness to
weight ratio. However, other factors may affect the
material selection, e.g. thermal conductivity, CTE
(coefficient of thermal expansion), cost, manufacture,
lead time, stability, etc.
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Material Selection
Material Density
(Kg/m )
Young’sModule E (Gpa)
YieldStrength S (Mpa)
E/ S/ CTE(m/m K)
Aluminum
7075 T6
2700 71 503 26 186.3 23.4
Magnesium
AZ31B
1700 45 220 26 129.4 26
Titanium
Ti-6Al-4V
4400 110 825 25 187.5 9
Beryllium
S 65 A
2000 304 207 152 103.5 11.5
Fiber Composite - Kevlar - Graphite
1380 1640
76 220
1240 760
55 134
898.5 463.4
-4 -11.7
3
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Dynamic & Stress Analysis Finite element analysis is the most popular and accurate method to determine the natural frequencies and internal member stresses of a spacecraft. This analysis requires construction of a finite element model.
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Dynamic & Stress Analysis
Once the environmental loads, configuration and mass
distribution have been determined, analysis can be
performed to determine sizing of the structure members.
Major analysis required for spacecraft structure design
include dynamic (stiffness) and stress (strength) analysis.
Major goal of the dynamic analysis is to determine
natural frequencies of the spacecraft in order to avoid
dynamic coupling between the structure elements and
with the launch vehicle.
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Dynamic & Stress Analysis Purpose of the stress analysis is to determine the Margin of Safety (M. S.) of structure elements: Allowable Stress or Loads M. S. = - 1 0 Max. Stress or Loads x Factor of Safety
Allowable stresses or loads depends on the material used and can be obtained from handbooks, calculations, or test data.
Maximum stress or loads can be derived from the structure analysis.
Factor of Safety is a factor to cover uncertainty of the analysis. Typically 1.25 is used for yield stress and 1.4 for ultimate stress.
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Construction finite element model of a spacecraft is not
an easy task. Local models, e.g. panel and beam models,
can be used to determine a first approximation sizing of
the structure members.
Dynamic & Stress Analysis
close form solution(Simply supported platewith uniform loading)
Finite element solution(Simply supported platewith concentrated mass)
close form solution(beam with concentrated force)
reaction force
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Design Verification
Mechanical Layout – Assembly and integration
Mass Property – Mass property measurement
Quasi-static Loads – Static load test
Transient Dynamic Loads – Sine vibration test
Random Vibration Loads – Random vibration test
Acoustic Loads – Acoustic test
Shock Loads – Shock test
On-orbit loads – Thermal vacuum test
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Future Challenge
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Homework Problem
Derive a complete structure development process charts.
Input Input
Step 1
Output
Step 2
Output
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References
Spacecraft Systems Engineering, 2nd edition, Chapter 9,
Edited by Peter Fortescue and John Stark,
Wiley Publishers, 1995.