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Satellite Design Course Spacecraft Configuration Structural Design Preliminary Design Methods

Feb 16 2005

ENAE 691

R.Farley NASA/GSFC

Contents • • • • • • • • • • •

Origin of structural requirements Spacecraft configuration examples Structural configuration examples General arrangement drawings Launch vehicle interfaces and volumes Structural materials Subsystem mass estimation techniques Vibration primmer Developing limit loads for structural design Sizing the primary structure Structural subsystem mass

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pg 3 pg 8 pg 14 pg 25 pg 30 pg 33 pg 38 pg 51 pg 59 pg 68 pg 73

2

Origin of Structural Requirements ‘This ride not recommended for children’

Launch Vehicle

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Source of Launch Vehicle Loads

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Typical Loads Time-Line Profile Max Q

H2 vehicle to geo-transfer orbit

MECO SECO

1st stage

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2nd stage

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3rd stage

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Design Requirements, Function • • • • • • • • • •

Launch Vehicle volume, mass, and c.g. Foot print for subsystems Deployment of flexible structures Natural frequency, stowed and deployed Alignment stability (launch shift, thermal, vibration, material shrinkage) Field Of View (FOV) RF and magnetic compatibility Jitter disturbance response Thermal steady state and transient distortions Materials for space environment (out gassing, atomic oxygen)

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Design Requirements, Loads Testing Transportation Launch loads • • • • • •

Steady state accelerations (axial thrust) Steady vibrations (low frequency, resonant burn from solid rocket boosters) Transient vibrations (lift off, transonic, MECO, SECO) Acoustic and random accelerations (lift off, max Q leading to max lateral loads) Shock (payload separation from upper stage adapter) Depressurization (influence on enclosed volumes including blankets inside of instruments)

Orbit Loads

Feb 16 2005

spin-up, de-spin, thermal, deployments, maneuvers

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From the spacecraft’s point of view… Fixed solar array

Articulating solar array, one axis

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Articulating solar array, sometimes 2 axis

The sun in the orbit plane changes due to the seasonal change in the sun’s declination (the tilt in the Earth’s axis) and orbit plane precession due to the Earth’s equatorial bulge. At 35o inclination, the precession period is ~ 55 days R.Farley NASA/GSFC

8

Spacecraft Configuration Examples

EOS aqua

‘one oar in the water’ produces an aerodynamic torque that averages to zero per orbit, but reaction wheels must be large enough to absorb in the interim Feb 16 2005

LEO nadir pointing

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Configuration Types LEO stellar pointing High inclination WIRE

Low inclination XTE, HST

Articulated solar array Feb 16 2005

Fixed solar array sun-sync orbit ENAE 691

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Configuration Types GEO nadir pointing Intelsat V

Articulated s/a spin once per 24 hours

TDRSS A Feb 16 2005

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Configuration Types HEO

IMAGE 2000

AXAF-1 CHANDRA required to stare uninterrupted

250m long wire booms, ¼ rpm Feb 16 2005

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Configuration types misc

Sun shield

MAP at L2 Sky surveys in the ecliptic plane

Cylindrical, body-mounted solar array

Lunar Prospector Body-mounted s/a

Cassini to Saturn Feb 16 2005

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Structural Configuration Examples • Cylinders and Cones • Box structures

hanging electronics and equipment

• Triangle structures • Rings

sometimes needed

transition structures and interfaces

• Trusses • •

high buckling resistance

extending a ‘hard point’ (picking up point loads)

As much as possible, payload connections should be kinematic Skin Frame, Honeycomb Panels, Machined Panels, Extrusions

NOTE: ALWAYS PROVIDE A STIFF AND DIRECT LOAD PATH! AVOID BENDING! STRUCTURAL JOINTS ARE BEST IN SHEAR!

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Structural examples

MAGELLAN box, ring, truss

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Structural examples

HESSI ring, truss and deck Feb 16 2005

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OAO cylinder/stringer and decks R.Farley NASA/GSFC

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Structural examples

Archetypical cylinder and box

Hybrid ‘one of everything’ Feb 16 2005

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“Egg crate” torque box composite panel bus structure

Structural examples EOS aqua, bus

Hard points created at intersections Feb 16 2005

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Structural examples COBE STS version

COBE

5000 kg !

Delta II version

2171 kg !

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Structural examples TRIANA L1 orbit

Boxes mounted to outer panels to radiate heat Feb 16 2005

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Anatomy of s/c Axial viewing, telescope type Interface isolation Reaction structure wheels

Astronomy Mission Station-keeping hydrazine, polar mount

Kinematic Flexure mounts to remove enforced displacement loads

Solid kick motor, equatorial mount

Instrument module Launch Vehicle adapter

Deck-mounted or wall-mounted boxes

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Propulsion module

Bus module

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Modular Assembly Instrument Module –optics, detector Bus Module (house keeping) Propulsion Module Modules allow separate organizations, procurements, building and testing schedules. It all comes together at observatory integration and test (I&T) AXAF

Interface control between modules is very important: structural, electrical, thermal Feb 16 2005

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Attaching distortion-sensitive components 2

3,2,1

Note: vee points towards cone

Bi-pod legs, tangential flexures Breathes from center point

2,2,2

Ball-in-cone, Ball-in-vee, Ball on flat

3

Breathes from point ‘3’ Hexapod arrangement

1

JPL perfect joint for GALEX primary mirror

1,1,1,1,1,1 1 3 2 Rod flexures arranged in 3,2,1 Breathes from point ‘3’ Feb 16 2005

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General Arrangement Drawings • Stowed configuration in Launch Vehicle • Transition orbit configuration • Final on-station deployed configuration • Include Field of View (FOV) for instruments and thermal radiators, and communication antennas, and attitude control sensors

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3-view layout, on-orbit configuration Overall dimensions and field of views (FOV) Antennas showing field of regard (FOR)

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3-view layout, launch configuration Solar array panels

Star trackers

array drive

Payload Adapter Fitting (PAF)

Torquer bars

Make note of protrusions into payload envelope

Omni antennas Feb 16 2005

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High gain antenna, stowed 26

Launch Vehicle Interfaces and Volumes Payload Fairings

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Pegasus Interface

Coupled loads analysis necessary Feb 16 2005

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Payload Envelope For many vehicles, if the spacecraft meets minimum lateral frequency requirements, then the static envelope accounts for fairing dynamic motions. STATIC ENVELOPE; the space that the payload must fit inside of when integrated to the vehicle

DYNAMIC ENVELOPE; the space that the payload must stay in during launch to account for all payload deflections

If frequency requirements are not met, or for protrusions outside the designated envelope, Coupled Loads Analysis (CLA) are required to qualify the design, in cooperation with the LV engineers.

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Launch Vehicle Payload Adapters “V-band” clamp, or “Marmon” clamp-band Shear Lip

Clamp-band

6019 3-point adapter

Feb 16 2005

6915 4-point adapter

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Structural Materials ρ (kg/m3)

E (GPa)

Fty (MPa)

E/ρ

Aluminum 6061-T6 7075-T651

2800 2700

68 71

276 503

24 26

Magnesium AZ31B

1700

45

220

Titanium 6Al-4V

4400

110

Beryllium S 65 A S R 200E

2000 -

Ferrous INVAR 36 AM 350 304L annealed 4130 steel

Material

Metallic Guide α

κ

(μm/m K˚)

(W/m K˚)

98.6 186.3

23.6 23.4

167 130

26

129.4

26

79

825

25

187.5

9

7.5

304 -

207 345

151 -

103.5 -

11.5 -

170

8082 7700 7800 7833

150 200 193 200

620 1034 170 1123

18.5 26 25 25

76.7 134.3 21.8 143

1.66 11.9 17.2 12.5

14 40-60 16 48

7944 8414 8220

200 206 203

585 206 1034

25 24 25

73.6 24.5 125.7

16.4 23.0

12 12

Fty/ρ

Heat resistant Non-magnetic

A286 Inconel 600 Inconel 718 Feb 16 2005

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Materials Guide Definitions ρ

mass density, kg/m3

E

Young’s modulus, Pascals

Fty

material allowable yield strength

E/ρ

specific stiffness, the ratio of stiffness to density

Fty / ρ

specific strength, the ratio of strength to density

α

coefficient of thermal expansion CTE

κ

coefficient of thermal conductivity

Note: Pa = Pascal = N/m2

Material Usage Conclusions: USE ALUMINUM WHEN YOU CAN!!! Aluminum 7075 and Titanium 6Al-4V have the greatest strength to mass ratio Beryllium has the greatest stiffness to mass ratio and high damping 4130 Steel has the greatest yield strength

(expensive, toxic to machine, brittle)

INVAR has the lowest coefficient of thermal expansion, but difficult to process Titanium has the lowest thermal conductivity, good for metallic isolators Feb 16 2005

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Metallic Materials Usage Guide Advantages

Disadvantages

Aluminum

High strength to weight, good machining, low cost and available

Titanium

High strength to weight, low CTE, low thermal conductivity, good at high temperatures

Steel

Heat-resistant Steel

Beryllium Feb 16 2005

High stiffness, strength, low cost, weldable

High stiffness, strength at high temperatures, oxidation resistance and non-magnetic

Very high stiffness to weight, low CTE ENAE 691

Poor galling resistance, high CTE

Expensive, difficult to machine

Heavy, magnetic, oxidizes if not stainless steel. Stainless galls easily Heavy, difficult to machine

Expensive, brittle, toxic to machine R.Farley NASA/GSFC

Applications

Truss structure, skins, stringers, brackets, face sheets

Attach fittings for composites, thermal isolators, flexures

Fasteners, threaded parts, bearings and gears

Fasteners, high temperature parts

Mirrors, stiffness critical parts 33

Subsystem Mass Estimation Techniques Preliminary Design Estimates for Instrument Mass Approximate instrument mass densities, kg / m3 Spectrometers ~

250

Mass spectrometers ~

800

Synthetic aperture radar ~ 32 Rain radars ~

150

thickness / diameter ~ 0.2

Cameras ~

500

Small telescopes w/ camera ~ 325

Small instruments ~

1000

Scaling Laws: If a smaller instrument exists as a model, then if SF is the linear dimension scale factor… Area proportional to

SF2

Mass proportional to

SF3

Area inertia proportional to SF4

Mass inertia proportional to SF5

Frequency proportional to 1/ SF

Stress proportional to SF

BEWARE THE SQUARE-CUBE LAW! STRESS WILL INCREASE WITH SF! Feb 16 2005

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Typical List of Boxes, Bus Components ACS Reaction wheels Torquer bars Nutation damper Star trackers Inertial reference unit Earth scanner Digital sun sensor Coarse sun sensor Magnetometer ACE electrical box Mechanical Primary structure Deployment mechanisms Fittings, brackets, struts, equipment decks, cowling, hardware Payload Adapter Fitting Feb 16 2005

Communication

Power

S-band omni antenna S-band transponder X-band omni antenna X-band transmitter Parabolic dish reflector 2-axis gimbal Gimbal electronics Diplexers, RF switches Band reject filters Coaxial cable

Batteries Solar array panels Articulation mechanisms Articulation electronics Array diode box Shunt dissipaters Power Supply Elec. Battery a/c ducting

Thermal

Propulsion

Radiators Louvers Heat pipes Blankets Heaters Heat straps Sun shield Cryogenic pumps Cryostats

Propulsion tanks Pressurant tanks Thrusters Pressure sensors Filters Fill / drain valve Isolator valves Tubing

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Electrical C&DH box Wire harness Instrument electronics Instrument harness 35

Mass Estimation, mass fractions Mi/Mdry Some Typical Mass Fractions for Preliminary Design Payload

Structure

Power

Electrical harness

ACS

Thermal

C&DH

Comm

Propulsion, dry

LEO nadir (GPM)

37 %

24 %

13 % Fixed arrays

7%

6%

4%

1%

3%

5% 26 % w/fuel

LEO stellar (COBE)

52 %

14 %

12 % spins at 1 rpm

8%

8%

2%

3%

1%

0%

GEO nadir (DSP 15)

37 %

22 %

20 % spins at 6 rpm

7%

6%

0.5 %

2%

2%

2%

LEO (Pegasus class) nadir (FireSat)

13-20 %

30 %

17 % Articulat ing arrays

7%

14 %

1%

3%

15 % 2-axis gimball

0%

Mass fractions as percentage of total spacecraft observatory mass, less fuel COBE with 52% payload fraction is unusually high and not representative ACS is Attitude Control System, C&DH is Command and Data Handling, Comm is Communication subsystem Feb 16 2005

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Mass Estimation, Refinements The largest contributors to mass are (neglecting the instrument payload)

Structural subsystem (primary, secondary) Propulsion fuel mass, if required Power subsystem Define ratio mi = Mi / Mdry Mdry = mass of spacecraft less fuel Remember to target a mass margin of ~20% when compared to the throw weight of the launch vehicle and payload adapter capability. There must be room for growth, because evolving from the cartoon to the hardware, it always grows! The following slides will show the ‘cheat-sheet’ for making preliminary estimates on some of these subsystems Feb 16 2005

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Mass Estimation with Mass Ratios Mdry = Mpayload + Mpower + MPropDry + Mstruct + Melec + MCDH + MACS + Mcomm + Mtherm Dry mass = sum of subsystem masses without fuel 1st GUESS

mpayload ~ 0.4(large sat) ~0.2(small sat) for a first guess ratio Mdry = Mpayload / mpayload 2nd GUESS Mdry = Mpayload + Mdry(mpower+ mPropDry + mstruct + melec + mCDH + mACS + mcomm + mtherm)

3rd GUESS, more refined Mdry = Mpayload + Mpower+ MPropDry + Mdry (mstruct + melec + mCDH + mACS + mcomm + mtherm)

Mwet = Mdry + Mfuel

Total wet mass, observatory mass Mlaunch = Mwet + payload adapter fitting Launch mass Feb 16 2005

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Mass Ratios, Generalized Formula Mi M dry

Generalized Formula

known

= 1

Sum of known masses / (1-sum of unknown masses as ratios)

mj unknown

Mi

=

M payload

M power

m structure

m elec

M PropDry

Typical knowns + calculated

known

mj = unknown

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+

m ACS

m comm

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m CDH m therm

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Typical unknowns

39

Mass Estimation example Low Earth Orbit Earth-Observing Mission

Will use these ratios:

Known or calculated masses:

melec = 0.07

Mpayload = 750 kg

mCDH = 0.01

Mpower = 200 kg

mtherm = 0.04

MPropDry = 40 kg

mcomm = 0.03 mACS = 0.06

Mi

mstruct = 0.20

=

750

200

40

0.20

0.07

0.01

=

990

known mj =

M dry Feb 16 2005

0.06

0.03

990 ( 1 0.41 )

=

+

unknown

=

=

0.41

0.04

1678 kg ENAE 691

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Mass Estimation, Power Subsystem Givens: ALT

circular orbit altitude, km

Poa

required orbital average power, watts

AF

area factor, if articulated arrays AF = 1, if omnidirectional in one plane, AF = 3.14, spherical coverage AF = 4

ηcell

standard cell efficiency, 0.145 silicon, 0.18 gallium, 0.25 multi-junction

If the required orbital average power is not settled, then estimate with: Poa ~ PREQpayload + 0.5 (MDry – Mpayload) watts, mass in kg Power for payload instruments and associated electronics ~ 1 watt/kg * Mpayload Feb 16 2005

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Dry bus mass, kg, ~ 0.5 watts/kg 41

Mass Estimation, Power Subsystem EtoD

= 3.2. ( ALT

EtoD

= 0.576

50)

0.2

0.3

4 6.069. 10 . ALT

7 2 1.768. 10 . ALT

Maximum eclipse-todaylight time ratio, estimate good for 300 20 Hz

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Aerodynamic pull-up 4.7g axial 3.5g lateral R.Farley NASA/GSFC

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Loads for primary structure, example If the structure meets minimum frequency requirements from the launch vehicle, then the low frequency sinusoidal environment is enveloped in the limit loads. Secondary structures with low natural frequencies may couple in, however, and should be analyzed separately.

Lcg

Reaction loads

The structural analyst will determine which load case produces the greatest combined axial-bending stress in the structure (I, A, mass and c.g. height) Feb 16 2005

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Loads example, cont 2 major load case combinations:

Given: Mwet = 2000 kg

a) 0.5g lateral + 6.5g axial

g = 9.807m/s2

b) 2.0g lateral + 3.5g axial

Lcg = 1.5m

Case a) load combination: Axial load

= Mwet*Naxial*g = 2000*6.5*9.807 = 127491 N

Lateral load = Mwet*Nlateral*g = 2000*0.5*9.807 = 9807 N Moment = Lateral load * Lcg = 9807*1.5 = 14710.5 N-m Case b) load combination: Axial load

= Mwet*Naxial*g = 2000*3.5*9.807 = 68649 N

Lateral load = Mwet*Nlateral*g = 2000*2.0*9.807 = 39228 N Moment = Lateral load * Lcg = 39228*1.5 = 58842 N-m

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Component Loads, Mass-Acceleration Curve JPL acceleration curve for component sizing Mass Acceleration Curve

100

Applicable Launch Vehicles:

Acceleration g's

STS Titan gload

i

Atlas

10

Delta Ariane H2 Proton

1 1

10

100

mass

i Mass kg

3 1 10

Scout

This curve envelopes limit loads for small components under 500 kg Apply acceleration load separately in critical direction Add static 2.5 g in launch vehicle thrust direction

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Simplified design curve for components on ‘appendage-like’ structures under 80 Hz fundamental 63 frequency

Sizing the Primary Structure rigidity, strength and stability

Factors of safety NASA / INDUSTRY, metallic structures Factors of safety

Verification by Test

Verification by Analysis

FS yield

1.25 / 1.10

2.0 / 1.6

FS ultimate

1.4 / 1.25 (1.5 Pegasus)

2.6 / 2.0 (2.25 Pegasus)

Factors of safety for buckling (stability) elements ~ FS buckling = 1.4 (stability very dependent on boundary conditions….so watch out!)

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Primary Structure Simplified Model E is the Young’s Modulus of Elasticity of the structural material

For example, in many cases, the primary structure is some form of cylinder

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Sizing for Rigidity (frequency) Working the equations backwards…. When given frequency requirements from the launch vehicle users guide for 1st major axial frequency and 1st major lateral frequency, faxial, flateral: Material modulus E times AXIAL STIFFNESS cross sectional area A Material modulus E times bending inertia I

BENDING STIFFNESS

For a thin-walled cylinder:

Select material for E, usually aluminum

I = π R3 t ,

or t = I / (π R3)

e.g.: 7075-T6

A = 2π R t

or t = A / (2π R)

Determine the driving requirement resulting in the thickest wall t. Recalculate A and I with the chosen t.

Calculate for a 10% – 15% frequency margin Feb 16 2005

E = 71 x 109 N/m2

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Tapering thickness will drop frequency 5% to 12%, but greatly reduce structural mass 66

R.Farley NASA/GSFC

Sizing for Strength Design Loads using limit loads and factors of safety Plateraldes = (M + Mtip) g NlimitL

Lateral Design Load, N

Paxialdes = (M + Mtip) g NlimitA

Axial Design Load, N

Momentdes = Plateraldes * Lcg

Moment Design Load, N-m

Recalling from mechanics of materials: axial stress = P/A, bending stress = Moment*R/I

(in a cylinder, the max shear and max compressive stress occur in different areas and so for preliminary design shear is not considered)

Max stress σmax = Paxialdes / A + (Plateraldes Lcg R) / I Margin of safety MS = {σallowable / (FS x σmax)} – 1

0 < MS acceptable

For 7075-T6 aluminum, the yield allowable , σallowable = 503 x 106 N/m2 With less stress the higher up, the more tapered the structure can be, saving mass Feb 16 2005

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Sizing for Structural Stability Determine the critical buckling stress for the cylinder In the general case of a cone:

Compare critical stress to the maximum stress as calculated in the previous slide. Update the max stress if a new thickness is required.

Allowable Critical Buckling Stress

Margin of safety MS = {σCR /(FSbuckling x σmax)} – 1 Check top and bottom of cone: σmax, I, moment arm will be different Feb 16 2005

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0 < MS acceptable Sheet and stringer construction will save ~ 25% mass

68

Structural Subsystem Mass For all 3 cases of stiffness, strength, and stability, optimization calls for ‘tapering’ of the structure. The frequency may drop between 5% to 12% with tapering But the primary structural mass savings may be 25% to 35% - a good trade

Secondary structure (brackets, truss points, interfaces….) may equal or exceed the primary structure. An efficient structure, assume secondary structure = 1.0 x primary structure. A typical structure, assume 1.5. So, if the mass calculated for the un-optimized constant-wall thickness cylinder (primary structure) is MCYL, then the typical structure (primary + secondary): MSTRUCTURE ~ (2.0 to 3.5) x MCYL This number can vary significantly

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Backup Charts, Extras

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Anatomy of s/c Transverse viewing, Earth observing type

Heat of boxes radiating outward

‘Egg-crate’ extension

Cylinder-in-box

Instruments

FOV

Launch Vehicle I/F

Drag make-up Propulsion module Feb 16 2005

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Hydrazine tank equatorial mount on a skirt with a parallel load path ! The primary structure barely 71 knows it’s there.

Spacecraft Drawing in Launch Vehicle Launch Vehicle electrical interface

Fairing access port for the batteries Feb 16 2005

Pre-launch electrical access “red-tag” item ENAE 691

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XTE in Delta II 10’ fairing 72

Drawing of deployment phase

Pantograph deployment mechanism

EOS aqua Feb 16 2005

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Composite Materials Cons

Pros

Costly Lightweight (Strength to Weight ratio) Tooling more exotic, expensive/specialized tooling (higher rpms, diamond tipped)

Ability to tailor CTE High Strength

Electrical bonding a problem

Good conductivity in plane

Some types of joints are more difficult to produce/design

Thermal property variation possible (K1100)

Fiber print through (whiskers)

Low distortion due to zero CTE possible

Upper temperature limit (Gel temperature)

Ability to coat with substances (SiO)

Moisture absorption / desorption / distortion

provided by Jeff Stewart Feb 16 2005

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Composite Material Properties Graphite Fiber Reinforced Plastic (GFRP) density ~ 1800 kg/m3 If aluminum foil layers are added to create a quasi-isotropic zero coefficient of thermal expansion (CTE < 0.1 x10-6 per Co) then density ~ 2225 kg/m3 Aluminum foil layers are used to reduce mechanical shrinkage due to desorption / outgassing of water from the fibers and matrix (adhesive,ie. epoxy) NOTE! A single pin hole in the aluminum foil will allow water de-sorption and shrinkage. This strategy is not one to trust… Cynate esters are less hydroscopic than epoxies Shrinkage of a graphite-epoxy optical metering structure due to de-sorption may be described as an asymptotic exponential (HST data):

27 . 1

e

. 0.00113D

Graphite-Epoxy Shrinkage in Vacuum

40 Microns per Meter

Shrinkage ~ 27 (1 – e - 0.00113D) microns per meter of length, where D is the number of days in orbit.

Shrinkage( D)

Shrinkage( D ) 20

0 0

1000

2000

3000

4000

D Days

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5000

Mass Estimation, Propulsion Subsystem Givens: Isp

fuel specific thrust, seconds (227 for hydrazine, 307 bi-prop)

ΔV

deltaV required for maneuvers during the mission, m/s

TM

mission time in orbit, years

YSM

years since last solar maximum, 0 to 11 years

AP

projected area in the velocity direction, orbital average, m2

ALT

circular orbit flight altitude, km

Mdry

total spacecraft observatory mass, dry of fuel, kg 1

Area SAoa

Feb 16 2005

Area SA .

cos

π EtoD π

1

Solar array orbital average projected drag area for a tracking solar array that feathers during eclipse ENAE 691

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Mass Estimation, Propulsion Subsystem Approximate maximum atmospheric density at the altitude ALT (km), kg / m3

Densitymax = 4.18 x 10-9 x e(-0.0136 ALT)

good for 300 < ALT < 700 km

DF = 1 – 0.9 sin [π x YSM / 11] Densityatm = DF x Densitymax 3.986 . 10

V circular CD Drag

( 6371

2

Corrected atmospheric density, kg / m3

11

Circular orbit velocity, m/s

ALT)

Assumed Drag coefficient

2.2 1.

Density factor, influenced by the 11 year solar maximum cycle (sin() argument in radians)

2 Density atm. V circular . C D . A P

Drag force, Newtons

Drag. T M . 31.536 . 10

6

M fuelDRAG Feb 16 2005

Isp . g

Note: g = 9.807 m/s2

Fuel mass for drag make-up, kg ENAE 691

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If the mission requires altitude control, this is the approximate fuel mass for drag over the mission life 77

Mass Estimation, Propulsion Subsystem Fuel mass for maneuvering If maneuvers are conducted at the beginning of the mission (attaining proper orbit): M fuelMANV

M dry

M fuelDRAG . e

ΔV ( Isp .g)

1

Maneuvering fuel mass, kg beginning of mission case

If the fuel is to be saved for a de-orbit maneuver:

M fuelMANV

M dry . e

Or expressed as a ratio: Feb 16 2005

ΔV ( Isp .g)

1

M fuelMANV M dry ENAE 691

Maneuvering fuel mass, kg end of mission case (de-orbit)

=

e

ΔV ( Isp .g)

R.Farley NASA/GSFC

1

78

Deployable Boom, equations for impact torque

Io

Rotational mass inertia about point “o”, kg-m2

Dynamic system is critically damped Hinge point “o” Maximum Impact torque at lock-in, N-m dθ/dt can just be the velocity at time of impact if not critically damped

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Static Beam Deflections For Quick Hand Calculations, these are the most common and useful

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Rigid-body accelerations • Linear force

F = m x a = m x g x Nfactor

– N is the load factor in g’s – Low frequency sinusoidal below first natural frequency will produce ‘near-static’ acceleration a = A x (2 π f)2 where f is the driving frequency and A x = A sin(ωt) is the amplitude of sinusoidal motion

• Rotational torque • Centrifugal force

Feb 16 2005

Q = I x alpha Fc = m x r x Ω2

ENAE 691

R.Farley NASA/GSFC

v = Aω cos(ωt) a = -Aω2 sin(ωt)

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Combining the loads to form ‘quasi-static’ levels Limit Load = Static + dynamic + resonant + random (low frequency)

Note: The maximum values for each usually occur at different times in the launch environment, luckily. The primary structure will have a different limit load than attached components. Solar arrays and other low area-density exposed components will react to vibro-acoustic loads. Feb 16 2005

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R.Farley NASA/GSFC

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Loads for a component, example Mpayload = 500 kg Mkickmotor = 50 kg

dry mass

Tstatic = 30000 N Tdynamic = +/- 10% Tstatic at 150 Hz (resonant burn, “chuffing”)

m = 1 kg

Antenna boom component

fnaxial = 145 Hz with Q = 15 fnlateral = 50 Hz with Q = 15 L = 0.5m

The axial frequency is sufficiently close to the driven dynamic frequency that we can consider the axial mode to be in resonance.

Feb 16 2005

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R = 1m

Ω= 10.5 rad/s (100 rpm) Random input So = 0.015 g2 per Hz

R.Farley NASA/GSFC

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Spinning upper stage example, con’t Axial-to-lateral coupling Ω

Length L Radius R

L

R

Deflection y y

Paxial Deflection y: y = R (Ω / ω)2

Plateral

Lateral circular bending frequency, rad/s ω = 2 π fnLateral

[ 1 – (Ω / ω)2 ] Axial-to-lateral coupling AtoL = y / L Equivalent additional lateral load = AtoL x Paxial Feb 16 2005

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R.Farley NASA/GSFC

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Loads for a component, con’t Static axial acceleration GstaticA = Tstatic / g (Mpayload + Mkickmotor) g’s Dynamic axial acceleration GdynA = Tdynamic x Q / g (Mpayload + Mkickmotor) g’s g’s Random axial acceleration GrmdA = 3 sqr[0.5π fnaxial Q So] Axial Limit Load Factor, g’s, Naxial = GstaticA + GdynA + GrmdA Axial Limit Load, Newtons, Paxial = g x m x NaxialL

g’s

Static lateral acceleration GstaticL = (R+y) Ω2 / g Random lateral acceleration GrmdL = AtoL x 3 sqr[0.5π fnlateral Q So] Dynamic lateral acceleration GdynL ~ 0

g’s g’s

Lateral Limit Load Factor, g’s, Nlateral = GstaticL + GdynL + GrmdL Lateral Limit Load, Newtons Plateral = g x m x Nlateral Moment at boom base Moment = L x Plateral + y x Paxial

g’s

Feb 16 2005

ENAE 691

R.Farley NASA/GSFC

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