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衛星結構設計

祝飛鴻10/13/2005

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Design Considerations

Environmental Loads

Configuration Design

Structure Analysis

Design Verification

Contest Problem #1

Homework Problems

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Structure exists everyplace in our life; building, bridge, car,

airplane, etc. What making the spacecraft structure differs

from those structures?

Everybody knows the spacecraft is delivered to space by a

launcher. Therefore, the spacecraft structure has to comply

with the constraints induced by the selected launcher. In

addition, the structure will be useless unless it can serve the

intended function. What are the constraints from the

launcher and what are the intended functions of spacecraft

structure?

Design Considerations

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External loads or so called environmental loads will be

induced to the spacecraft during the lift-off and flight of

the launcher. Determination of these loads for the structure

design is not a straightforward process. As a matter of fact,

the loads depend on the design, i.e. changing the design may

affect the loads. We will explain this process in more detail

later.

Besides environmental loads, the launcher will also introduce

weight and size limitation to the spacecraft design.

Design Constraints

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We all know it is expensive to reach space. With today’s

technology, the cost is around $10,000 USD per pound

although the price

varies considerably.

Every launcher has

weight limitation for

a specific orbit height.

More costly larger

launcher has to be

used if the weigh

limitation is exceeded.

Weight Constraints

Falcon-1

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Besides the launcher limitation, weight saving from the

structure can be used to enhance the spacecraft performance

by adding more fuel or adopt more powerful components.

Therefore, minimizing the structure weight is always a

challenge on spacecraft design.

Weight Constraints

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To launch a spacecraft into space,

the launcher has to provide a

streamline cover, i.e. fairing, in order

to protect the spacecraft from the air

heating effects. As a consequence, the

spacecraft has to fit into the limitation

of fairing size.

123 cm

135 cm

132 cm

30 cm

Falcon-1Envelope

Size Constraints

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Just like other structures, the basic function of spacecraft

structure is to provide mechanical support to other

subsystems and components. However, the spacecraft

structure is more complicated in the sense that it has to

satisfy the stringent alignment and field of view

requirements as well as long term stability under space

environment for critical sensors and payload instruments.

We will discuss the mechanical layout issue in more detail

later.

Functional Constraints

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Design Considerations

Launcher constraints:

Environmental loads

Size

Weight

Others, e.g. CG Offset, mechanical interface, etc.

Functional constraints:

Field of view

Alignment

Stability

Others, e.g. jitter, etc.

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Environmental Loads

There are two types of loads for spacecraft structure

design: loads induced from the launcher and the loads

induced from the on-orbit environment.

The major on-orbit environmental load, unless for

special mission, mainly due to the temperature

variation during mission operation of the spacecraft.

For picosat design, except for composite material, effects

of the on-orbit environmental loads can be ignored if

material with same thermal expansion coefficient is used.

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Flight Events

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”.

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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.

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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Coupled Loads Analysis

The natural frequencies of a spacecraft can be predicted by

mathematical model, e.g. finite element model. This model

will be delivered to the launcher supplier for coupling with

the launch vehicle model. Dynamic analysis can be performed

using this combined model and critical responses of the

spacecraft can be derived for the spacecraft structure design.

Spacecraft Model

Launch VehicleModel

CombinedModel

DynamicAnalysis

Forcing Functionsof

Critical Flight Events

SpacecraftResponses

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Quasi-Static Design Loads

As one can see from the above process that a structure

model is needed to determine the loads. However, the

model can not be constructed without a design and the

design can not be started without loads. How can we

get out of this loop?

Fortunately, the quasi-static loads defined in launcher

user’s manual can be used as a good starting point. These

loads were derived by assuming the spacecraft is designed

with frequencies higher than a specified minimum

frequency to avoid dynamic coupling with the launcher.

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Spacecraft Preliminary Design

Transient Dynamic Loads

Quasi-staticLoads

Spacecraft Model

PreliminaryCLA

Spacecraft Detailed Design

Spacecraft Model

FinalCLA

Design Verification

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Environmental Loads

Transient Dynamic Loads

Quasi-static loads

Quasi-static loads

Sine vibration loads

Random Vibration Loads

Acoustic Loads

Shock Loads

Others, deployment loads, thermal shock, etc.

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Configuration Design

Typically the spacecraft structure starts with configuration

design. This includes mechanical layout and determination

of load path.

To serve its function, the structure must accommodate all

the components within the launch vehicle fairing size

constraint. Major consideration factors include component

size, orientation and field-of-view requirements, e.g. sun

sensor must able to view the sun, antenna must able to

communicate with the earth, etc.

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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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Configuration Design - YAMSAT

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+Y Panel•Battery•Magnetic Coil

-X Panel•Magnetometer•Magnetic Coil•CW Antenna x 1

-Z Panel•TT&C•Antenna x 1

+X Panel•Payload_Micro-Spectrometer•CW Antenna x 1

-Y Panel•OBMU

+Z Panel•DRU•Antenna x 1

XY

Z

Configuration Design - YAMSAT

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Configuration Design

Hardware List

Hardware Size

StructureConfiguration

OrientationRequirements

FOVRequirements

Mechanical Layout

StructureAnalysis

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Structure 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

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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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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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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Dynamic & Stress Analysis

Besides primary structure members, detailed analysis

and design are needed for other parts of the spacecraft

structure, e.g. joints between panels and beams, support

bracket for components, etc.

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Yamsat Design - Load Cases & FEM

Load cases from P-POD requirements:

15g acting in any directions FEM:No. of GRID : 1017

No. of BAR elements: 240

No. of Quad elements : 1040

Material:7075-T6

Total Weight : 0.991Kg

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Yamsat Design – Stress Contour

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M.S. YieldM.S.YieldVon Mises

M.S.Ultimate

M.S.Ultimate VonMises

Min M.S 17 20 22 24

Lateral mode : 221 Hz >> 25Hz (requirement)

Longitudinal mode : 1156Hz >> 40Hz (requirement)

Yamsat Design – M. S. & Frequency

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Bolts used for Yamsat:ultimate stress allowable =700Mpayield stress allowable = 560Mpanominal tightening torque = 0.21 Nm

S.F.

1.25MS

yieldMS

ultimateMS

slipping

MSgapping

withmoment

Min MS 0.195 0.494 3.424 13.821

Location INTERFACE INTERFACE INTERFACE INTERFACE

LoadCase

Bolt Stress Bolt Installation

Static

Yamsat Design – Bolts Analysis

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StructureConfiguration

Dynamic & Stress Analysis

MechanicalLayout

Load PathCheck

Quasi-StaticLoads

MaterialSelection

ApproximationSizing

Finite ElementModel

PreliminaryAnalysis/Design

PreliminaryCLA

DetailedAnalysis/Design

FinalCLA

DesignVerification

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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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Description:

Design an aluminum cube box of 10cm side and an

internal holding mechanism for a raw egg. The weight

of the box shall not exceed 500g and shall not be wrapped

around by any material. This box will also be used as the

thermal box for contest problem no. 3. The team shall

generate documents and procedures for the design and

test. These documents and procedures will be scored.

Contest Problem No. 1

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Process: 1. Measure the box weight including the internal holding mechanism. Lighter box will get higher score. 2. Remove internal holding mechanism and install material for contest problem no. 3. 3. Conduct contest no. 3 4. Remove the material and install the holding mechanism with the raw egg. 5. Drop the box from a height to the ground covered with a carpet without damaging the box or cracking the egg. The height will be between 50 to 100cm or defined by the team. Higher distance from the ground will get higher score.

Contest Problem No. 1

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Homework ProblemsAn aluminum cube box of 10cm side contains 5 componentswith the following size (W x L x H) and weight:

1. 47 x 81 x 25 mm 133 gram

2. 23 x 23 x 19 mm 30 gram

3. 70 x 70 x 16 mm 80 gram

4. 85 x 65 x 20 mm 110 gram

5. 94 x 94 x 14 mm 20 gram

6. 17 x 43 x 10mm 35 gram

HW #1: Layout the components which will produce

the smallest MOI about the Z axis.

HW #2: Calculate the CG offset

HW #3: Assuming the box is supported at the bottom of

the four corners. Describe load path of the design.

HW #4: Estimate required panel thickness and column area under 15g

loading condition

10cm10cm

10cm

XY

Z

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References

Spacecraft Systems Engineering, 2nd edition, Chapter 9,

Edited by Peter Fortescue and John Stark,

Wiley Publishers, 1995.