Satellite Design CourseSpacecraft 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 pg 3 pg 8 pg 14 pg 25 pg 30 pg 33 pg 38 pg 51 pg 59 pg 68 pg 73 Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 2 Origin of Structural Requirements ‘This ride not recommended for children’ Launch Vehicle 3 Feb 16 2005 ENAE 691 R.Farley NASA/GSFC Source of Launch Vehicle Loads Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 4 Typical Loads Time-Line Profile Max Q H2 vehicle to geo-transfer orbit MECO SECO 1st stage 2nd stage 3rd stage Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 5 . 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. mass. Foot print for subsystems Deployment of flexible structures Natural frequency.g. atomic oxygen) Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 6 . vibration. and c. thermal.Design Requirements. stowed and deployed Alignment stability (launch shift. Function • • • • • • • • • • Launch Vehicle volume. MECO. transonic. resonant burn from solid rocket boosters) Transient vibrations (lift off.Design Requirements. Loads Testing Transportation Launch loads • • • • • • Steady state accelerations (axial thrust) Steady vibrations (low frequency. thermal.Farley NASA/GSFC 7 . de-spin. deployments. maneuvers Feb 16 2005 ENAE 691 R. 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 spin-up. SECO) Acoustic and random accelerations (lift off. At 35o inclination. one 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. the precession period is ~ 55 days R.From the spacecraft’s point of view… Fixed solar array Articulating solar array. sometimes 2 axis Articulating solar array.Farley NASA/GSFC Feb 16 2005 ENAE 691 8 . but reaction wheels must be large enough to absorb in the interim Feb 16 2005 ENAE 691 R.Farley NASA/GSFC LEO nadir pointing 9 .Spacecraft Configuration Examples EOS aqua ‘one oar in the water’ produces an aerodynamic torque that averages to zero per orbit. HST High inclination WIRE Articulated solar array Feb 16 2005 ENAE 691 Fixed solar array sun-sync orbit R.Configuration Types LEO stellar pointing Low inclination XTE.Farley NASA/GSFC 10 . Configuration Types GEO nadir pointing Intelsat V TDRSS A Feb 16 2005 ENAE 691 R.Farley NASA/GSFC Articulated s/a spin once per 24 hours 11 . ¼ rpm Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 12 .Configuration Types HEO IMAGE 2000 AXAF-1 CHANDRA required to stare uninterrupted 250m long wire booms. body-mounted solar array Lunar Prospector Body-mounted s/a Cassini to Saturn Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 13 .Configuration types misc Sun shield MAP at L2 Sky surveys in the ecliptic plane Cylindrical. Farley NASA/GSFC 14 . Honeycomb Panels.Structural Configuration Examples • Cylinders and Cones • Box structures • Triangle structures • Rings • • high buckling resistance hanging electronics and equipment sometimes needed transition structures and interfaces extending a ‘hard point’ (picking up point loads) • Trusses As much as possible. payload connections should be kinematic Skin Frame. Extrusions NOTE: ALWAYS PROVIDE A STIFF AND DIRECT LOAD PATH! AVOID BENDING! STRUCTURAL JOINTS ARE BEST IN SHEAR! Feb 16 2005 ENAE 691 R. Machined Panels. Farley NASA/GSFC 15 .Structural examples MAGELLAN box. truss Feb 16 2005 ENAE 691 R. ring. Structural examples HESSI ring. truss and deck Feb 16 2005 ENAE 691 OAO cylinder/stringer and decks R.Farley NASA/GSFC 16 . Farley NASA/GSFC 17 .Structural examples Hybrid ‘one of everything’ Feb 16 2005 ENAE 691 Archetypical cylinder and box R. bus Hard points created at intersections Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 18 .“Egg crate” torque box composite panel bus structure Structural examples EOS aqua. Structural examples COBE STS version 5000 kg ! COBE Delta II version 2171 kg ! Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 19 . Farley NASA/GSFC 20 .Structural examples TRIANA L1 orbit Boxes mounted to outer panels to radiate heat Feb 16 2005 ENAE 691 R. equatorial mount Kinematic Flexure mounts to remove enforced displacement loads Instrument module Launch Vehicle adapter Deck-mounted or wall-mounted boxes Bus module Propulsion module Feb 16 2005 ENAE 691 R. polar mount Solid kick motor. telescope type Interface isolation Reaction structure wheels Astronomy Mission Station-keeping hydrazine.Farley NASA/GSFC 21 .Anatomy of s/c Axial viewing. detector Bus Module (house keeping) Propulsion Module Modules allow separate organizations. 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 ENAE 691 R.Farley NASA/GSFC 22 .Modular Assembly Instrument Module –optics. procurements. building and testing schedules. 2.2.2.2 Hexapod arrangement 1 JPL perfect joint for GALEX primary mirror 1.1.1 1 3 2 Rod flexures arranged in 3.1 Breathes from point ‘3’ Feb 16 2005 ENAE 691 R.1. tangential flexures Breathes from center point Ball-in-cone.1 3 2 Note: vee points towards cone Bi-pod legs.Farley NASA/GSFC 23 . Ball on flat Breathes from point ‘3’ 2.1. Ball-in-vee.Attaching distortion-sensitive components 3.1. 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.Farley NASA/GSFC 24 . and attitude control sensors Feb 16 2005 ENAE 691 R. and communication antennas. Farley NASA/GSFC 25 . on-orbit configuration Overall dimensions and field of views (FOV) Antennas showing field of regard (FOR) Feb 16 2005 ENAE 691 R.3-view layout. stowed 26 . launch configuration Solar array panels array drive Star trackers Torquer bars Payload Adapter Fitting (PAF) Make note of protrusions into payload envelope Omni antennas Feb 16 2005 ENAE 691 R.Farley NASA/GSFC High gain antenna.3-view layout. Launch Vehicle Interfaces and Volumes Payload Fairings Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 27 . Farley NASA/GSFC 28 .Pegasus Interface Coupled loads analysis necessary Feb 16 2005 ENAE 691 R. Coupled Loads Analysis (CLA) are required to qualify the design. if the spacecraft meets minimum lateral frequency requirements. the space that the payload must stay in during launch to account for all payload deflections If frequency requirements are not met.Farley NASA/GSFC 29 . the space that the payload must fit inside of when integrated to the vehicle DYNAMIC ENVELOPE. or for protrusions outside the designated envelope. Feb 16 2005 ENAE 691 R. STATIC ENVELOPE. in cooperation with the LV engineers.Payload Envelope For many vehicles. then the static envelope accounts for fairing dynamic motions. Farley NASA/GSFC 30 . or “Marmon” clamp-band Shear Lip Clamp-band 6019 3-point adapter 6915 4-point adapter Feb 16 2005 ENAE 691 R.Launch Vehicle Payload Adapters “V-band” clamp. Structural Materials Material Aluminum 6061-T6 7075-T651 Magnesium AZ31B Titanium 6Al-4V Beryllium S 65 A S R 200E Ferrous INVAR 36 AM 350 304L annealed 4130 steel Heat resistant Non-magnetic Metallic Guide (μm/m K˚) ρ (kg/m3) 2800 2700 1700 4400 2000 8082 7700 7800 7833 E (GPa) 68 71 45 110 304 150 200 193 200 Fty (MPa) 276 503 220 825 207 345 620 1034 170 1123 E/ρ Fty/ρ α κ (W/m K˚) 24 26 26 25 151 18.6 24.5 26 25 25 98.5 103.5 76.3 129.2 12.5 1.3 21.5 167 130 79 7.0 12 12 31 R.66 11.7 16.5 125.Farley NASA/GSFC .6 23.5 170 14 40-60 16 48 A286 Inconel 600 Inconel 718 Feb 16 2005 7944 8414 8220 200 206 203 585 206 1034 ENAE 691 25 24 25 73.9 17.8 143 23.4 26 9 11.7 134.4 187.6 186.4 23. the ratio of stiffness to density specific strength.Farley NASA/GSFC 32 . but difficult to process Titanium has the lowest thermal conductivity. good for metallic isolators Feb 16 2005 ENAE 691 R. brittle) INVAR has the lowest coefficient of thermal expansion. the ratio of strength to density coefficient of thermal expansion CTE coefficient of thermal conductivity 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. kg/m3 Young’s modulus. toxic to machine. Pascals material allowable yield strength Note: Pa = Pascal = N/m2 specific stiffness.Materials Guide Definitions ρ E Fty E/ρ Fty / ρ α κ mass density. stringers. low CTE ENAE 691 Expensive. low thermal conductivity. oxidizes if not stainless steel. magnetic. brittle. low CTE. toxic to machine R. strength.Farley NASA/GSFC Mirrors. stiffness critical parts 33 . strength at high temperatures. difficult to machine Attach fittings for composites. threaded parts. brackets. high temperature parts Beryllium Feb 16 2005 Very high stiffness to weight. oxidation resistance and non-magnetic Fasteners. flexures Steel High stiffness. low cost and available Poor galling resistance. high CTE Truss structure. skins. good at high temperatures Expensive. Stainless galls easily Heavy. thermal isolators. bearings and gears Heat-resistant Steel High stiffness. difficult to machine Fasteners. low cost. good machining. weldable Heavy.Metallic Materials Usage Guide Advantages Disadvantages Applications Aluminum High strength to weight. face sheets Titanium High strength to weight. 2 Small telescopes w/ camera ~ 325 Scaling Laws: If a smaller instrument exists as a model.Farley NASA/GSFC . then if SF is the linear dimension scale factor… Area proportional to SF2 Mass proportional to Stress proportional to SF 34 SF3 Area inertia proportional to SF4 Frequency proportional to 1/ SF Mass inertia proportional to SF5 BEWARE THE SQUARE-CUBE LAW! STRESS WILL INCREASE WITH SF! Feb 16 2005 ENAE 691 R.Subsystem Mass Estimation Techniques Preliminary Design Estimates for Instrument Mass Approximate instrument mass densities. kg / m3 Spectrometers ~ Mass spectrometers ~ 250 800 Synthetic aperture radar ~ 32 Rain radars ~ Cameras ~ Small instruments ~ 150 500 1000 thickness / diameter ~ 0. cowling. equipment decks. struts. 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. RF switches Band reject filters Coaxial cable Thermal Radiators Louvers Heat pipes Blankets Heaters Heat straps Sun shield Cryogenic pumps Cryostats ENAE 691 Power Batteries Solar array panels Articulation mechanisms Articulation electronics Array diode box Shunt dissipaters Power Supply Elec.Farley NASA/GSFC Electrical C&DH box Wire harness Instrument electronics Instrument harness 35 . brackets.Typical List of Boxes. Battery a/c ducting Propulsion Propulsion tanks Pressurant tanks Thrusters Pressure sensors Filters Fill / drain valve Isolator valves Tubing R. hardware Payload Adapter Fitting Feb 16 2005 Communication S-band omni antenna S-band transponder X-band omni antenna X-band transmitter Parabolic dish reflector 2-axis gimbal Gimbal electronics Diplexers. Comm is Communication subsystem Feb 16 2005 ENAE 691 R.5 % 2% 2% 2% 13-20 % 30 % 7% 14 % 1% 3% 15 % 2-axis gimball 0% Mass fractions as percentage of total spacecraft observatory mass.Mass Estimation. mass fractions Mi/Mdry Some Typical Mass Fractions for Preliminary Design Payload LEO nadir (GPM) LEO stellar (COBE) GEO nadir (DSP 15) LEO (Pegasus class) nadir (FireSat) 37 % Structure 24 % Power 13 % Fixed arrays 12 % spins at 1 rpm 20 % spins at 6 rpm 17 % Articulat ing arrays Electrical harness 7% ACS 6% Thermal 4% C&DH 1% Comm 3% Propulsion. dry 5% 26 % w/fuel 0% 52 % 14 % 8% 8% 2% 3% 1% 37 % 22 % 7% 6% 0. 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.Farley NASA/GSFC 36 . 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 ENAE 691 R.Farley NASA/GSFC 37 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 Feb 16 2005 Total wet mass, observatory mass Mlaunch = Mwet + payload adapter fitting Launch mass ENAE 691 R.Farley NASA/GSFC 38 Mass Ratios, Generalized Formula Mi M dry = 1 unknown known mj Generalized Formula Sum of known masses / (1-sum of unknown masses as ratios) Mi known = M payload M power M PropDry Typical knowns + calculated mj = unknown + m structure m ACS m elec m CDH m therm Typical unknowns m comm Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 39 Mass Estimation example Low Earth Orbit Earth-Observing Mission Known or calculated masses: Mpayload = 750 kg Mpower = 200 kg MPropDry = 40 kg Will use these ratios: melec = 0.07 mCDH = 0.01 mtherm = 0.04 mcomm = 0.03 mACS = 0.06 mstruct = 0.20 Mi known = 750 200 40 = 990 mj = unknown M dry Feb 16 2005 + 0.20 0.06 0.07 0.03 0.01 0.04 = 0.41 = 990 ( 1 0.41 ) = 1678 kg ENAE 691 R.Farley NASA/GSFC 40 5 (MDry – Mpayload) watts. 0.14. if omnidirectional in one plane.5 watts/kg 41 . AF = 3.Mass Estimation. watts area factor. if articulated arrays AF = 1. spherical coverage AF = 4 standard cell efficiency.Farley NASA/GSFC Dry bus mass.18 gallium. then estimate with: Poa ~ PREQpayload + 0.145 silicon. 0. mass in kg Power for payload instruments and associated electronics ~ 1 watt/kg * Mpayload Feb 16 2005 ENAE 691 R.25 multi-junction ηcell If the required orbital average power is not settled. Power Subsystem Givens: ALT Poa AF circular orbit altitude. kg. ~ 0. 0. km required orbital average power. estimate good for 300<ALT<1000 km Sun syncronous 1 EtoD 0. Power Subsystem EtoD EtoD = 3. m2 Physical panel area. 10 .576 50) 0. ALT 4 6.069.9 0. 10 .2. m2 Total solar array panel area considering energy balance going thru eclipse and geometric area factors. ( ALT = 0. Area Psa Required solar array projected area normal to sun. ALT Maximum eclipse-todaylight time ratio.Mass Estimation.54 Area Psa = P OA .2 0.3 7 2 1. 997.768. m2 Feb 16 2005 ENAE 691 R. η cell Area SA = AreaFactor.Farley NASA/GSFC 42 . 0 x ASA for aluminum panels for composite panels kg kg Since multi junction cells usually go on composite substrates.85 x ASA Mass of solar array panels.Mass Estimation.5 x ASA Msubstrates ~ 2.4 x ASA for multi-junction cells for silicon cells kg kg 93% packing efficiency Mass of honeycomb substrates: Msubstrates ~ 2. wires. Power Subsystem Mass of cells.Farley NASA/GSFC 43 .8 x ASA Melec ~ 3. terminal boards: Melec ~ 3. insulation. and silicon cells went on aluminum substrates. electrical and structure: MPANELS = Melec + Msubstrates kg kg Feb 16 2005 ENAE 691 R. it all comes out in the wash: MPANELS ~ 5. kg Mpower = Mpanels + MSAD + MSAdeploy + Mbattery + MPSE Total power subsystem mass estimate.Mass Estimation. ‘High noon’ power input can be enormous sometimes. Power Subsystem Mbattery = 0. depending on orbit inclination and drag reduction techniques) Battery mass. kg Ni-Cads Power systems electronics.06 Poa MPSE = 0. kg Solar array retention and deployment mechanisms. kg Feb 16 2005 ENAE 691 R. kg Solar array drives and electronics.27 Mpanels Tracking array (this can vary greatly due to the peak power input and charging profile allowed.04 Poa MSAD = 0.33 Mpanels MSAdeploy = 0.Farley NASA/GSFC 44 . 25 standard cell efficiency Mdry = 1000 kg Mpayload = 350 kg (35% of dry mass) Ppayload = 350 watts (1 watt/kg * 350kg) estimate Pbus = 325 watts (0. givens ALT = 700 km circular orbit altitude.5 watts/kg * (1000-350)) estimate Poa = Ppayload + Pbus = 350 + 325 = 675 watts estimated orbital average power Feb 16 2005 ENAE 691 R.Power System Mass Example.Farley NASA/GSFC 45 . sun synchronous AF = 1 area factor ηcell = 0. calculations EtoD = 0.33 .768 .6 0.203 AF .1 Total panel area m2 M panels M battery M PSE M SAD = = = = M SAdeploy = 0.P oa .5 0.10 .27 .06 .9 0.M panels = 6.ALT 7 2 1.P oa = 40.η cell 5.85 .6 M power Feb 16 2005 = M panels M SAD M SAdeploy M battery M PSE = 106.54 = 4.069 .8 kg 46 ENAE 691 R.Farley NASA/GSFC .576 4 6.10 .Power System Mass Example.238 Sun synchronous Area SA = 1 EtoD 0.04 .ALT = 0.M panels = 8.Area SA = 24. 997 .P oa = 27 0. seconds (227 for hydrazine. 307 bi-prop) deltaV required for maneuvers during the mission. m/s total spacecraft observatory mass. kg Isp is the amount of “kick” that the fuel has to offer per kg dMfuel/dt = Thrust / (g*Isp) kg per second Feb 16 2005 ENAE 691 R.Mass Estimation.Farley NASA/GSFC 47 . Propulsion Subsystem Givens: Isp ΔV Mdry fuel specific thrust. dry of fuel. e 1 Or expressed as a ratio: M fuel M dry = e ΔV Isp.Farley NASA/GSFC 48 .Mass Estimation.g 1 Feb 16 2005 ENAE 691 R. Propulsion Subsystem If the fuel is to be saved for a de-orbit maneuver: ΔV Isp.g M fuel = M dry . kg M PropDry 0.Farley NASA/GSFC 49 . Feb 16 2005 ENAE 691 R.. dry. Propulsion Subsystem Approximate ΔV to de-orbit to a 50km perigee: From 400km circular ~ 100 m/s From 500km circular ~ 130 m/s From 600km circular ~ 160 m/s From 700km circular ~ 185 m/s If the thrusters are too small for one large ΔV de-orbit maneuver..25.Mass Estimation. lines. This means iterating with a better dry mass estimate for a better fuel calculation. the dry mass estimate now includes the mass of the dry prop system components. M fuel Propulsion system mass. then 2-3 times the calculated fuel maybe required (TRMM experience) Add 10% for ‘ullage’ M fuel M fuelDRAG M fuelMANV Total fuel mass. Total spacecraft observatory mass with fuel. kg M wet M dry M fuel Remember. kg tank. thrusters. etc. 7 kg M PropDry = 0.807 m/s2 Mdry = 1000 kg Mfuel = M dry . fuel lines. e ΔV Isp.7 kg Fuel tank.25 . etc… MS/C wet = Mfuel + Mdry = 1087 kg 50 Feb 16 2005 ENAE 691 R.g 1 = 1000 .Fuel Estimate Example Orbit is a 700km circular. e 185 227 . so Isp = 227 seconds g = 9. so ΔV to de-orbit ~185 m/s Fuel is hydrazine. thrusters. M fuel = 21. valves.Farley NASA/GSFC .807 1 = 86.9. Vibration Primmer • A vibrating structure can be thought of as the superposition of many ‘mode’ shapes • Each mode has a particular natural resonant frequency and distortion shape • If the resonant frequencies are sufficiently separated. then the structural response can be estimated by treating each mode as a single-degree-of-freedom (sdof) system 3 usual flavors of vibration: Harmonic Feb 16 2005 Random ENAE 691 R.Farley NASA/GSFC Impulsive 51 . Harmonic (sinusoidal) Vibration.Farley NASA/GSFC 0. sdof Transfer function Hz Natural frequency of vibration for a single degree of freedom system Recall: 2 π f = ω ‘Circular frequency’. radians / s Feb 16 2005 ENAE 691 R.05 typical 52 . Farley NASA/GSFC 53 .Harmonic Vibration. Hz fn is the natural resonant frequency Typical structural values for Q: 10 to 20 For small amplitude (jitter). sdof con’t Gain function Harmonic output acceleration = Harmonic input acceleration x T f is the applied input sinusoidal frequency. or cryo temperatures: Q >100 Resonant Load Acceleration = input acceleration x Q Feb 16 2005 ENAE 691 R. Farley NASA/GSFC 54 .Natural Frequency Estimation evenly distributed mass and stiffness E is the Young’s Modulus of Elasticity of the structural material Feb 16 2005 ENAE 691 R. Farley NASA/GSFC 55 .Natural Frequency Estimation discrete and distributed mass and stiffness E is the Young’s Modulus of Elasticity of the structural material Feb 16 2005 ENAE 691 R. not the overall spacecraft structure So Input spectrum ‘So’ described in power spectral density g2 per Hz Miles’ equation gives a statistical equivalent peak g load for a single degree of freedom system. Q is the resonant amplification. Mechanically conducted random and Acoustically conducted random Feb 16 2005 ENAE 691 R.Farley NASA/GSFC fn is the natural frequency of the system. and So is the input acceleration power spectral density. For 99. multiply by 3. g2/Hz 56 .Base-Driven Random Vibration • Random loads affect mostly smaller. high frequency components. 68% of the time (1σ).73% confidence (3σ). Farley NASA/GSFC payload mass vs. there are • Thermal loads Limit loads do not have stress factors of safety incorporated yet Feb 16 2005 ENAE 691 R.g. c.Developing Limit Loads for Structural Design • Quasi-Static loads – Linear and rotational accelerations + dynamic Dynamic Loads included in Quasi-Static: – Harmonic vibration (sinusoidal) – Random vibration (mostly of acoustic origin) – Vibro-acoustic for light panels Don’t forget. height limitations for the launch vehicle’s payload adapter fitting 57 . less than 1.4 +/.0.0 5.6 +/.5 +/.0 6.2 2.3.5 +/.1.2.7 for 2000kg +/.Farley NASA/GSFC 58 .2.7 27Hz min 10Hz min 15Hz min 10Hz min 30Hz min 10Hz min 18Hz min Beware 32Hz MECO-POGO 10Hz min 35Hz min 15Hz min Note: the static and dynamic loads do not occur at the same time (usually) Feb 16 2005 ENAE 691 R.Launch Loads and Fundamental Frequency Launch Vehicle Delta IV steady state dynamic Atlas II steady state dynamic H-II steady state dynamic Ariane V steady state dynamic Delta II steady state dynamic Axial Load Factor Naxial.7 +/.0 +/.2.1.0 Lateral Load Factor Nlateral.8 +/.2 +/.25 +/.1.0 4. g’s 6.0.0.0 +/.8 +/.0.0.0 5.0 +/. g’s +/.5. Pegasus Loads For Pegasus.Farley NASA/GSFC 59 . quasi-static loads are equivalent to low frequency dynamic loads Feb 16 2005 ENAE 691 R. 1. boil down to 3 load case combinations to analyze: Drop transient z ~ 6.5g axial.5g lateral R.7g lateral First lateral bending frequency > 20 Hz Aerodynamic pull-up 4.Farley NASA/GSFC Feb 16 2005 ENAE 691 60 .5g lateral Stage burnout 10.7g axial 3.Pegasus Loads con’t To simplify. Lcg Reaction loads The structural analyst will determine which load case produces the greatest combined axial-bending stress in the structure (I. then the low frequency sinusoidal environment is enveloped in the limit loads. however. A.g. and should be analyzed separately. height) Feb 16 2005 ENAE 691 R.Loads for primary structure.Farley NASA/GSFC 61 . example If the structure meets minimum frequency requirements from the launch vehicle. mass and c. Secondary structures with low natural frequencies may couple in. 5m Case a) load combination: Axial load = Mwet*Naxial*g = 2000*6.5*9.5 = 14710.807 = 9807 N Moment = Lateral load * Lcg = 9807*1.Farley NASA/GSFC 62 . cont 2 major load case combinations: a) 0.5g lateral + 6.807 = 39228 N Moment = Lateral load * Lcg = 39228*1.5g axial Given: Mwet = 2000 kg g = 9.5*9.0*9.5 = 58842 N-m Feb 16 2005 ENAE 691 R.5*9.5 N-m Case b) load combination: Axial load = Mwet*Naxial*g = 2000*3.807 = 68649 N Lateral load = Mwet*Nlateral*g = 2000*2.807m/s2 Lcg = 1.5g axial b) 2.807 = 127491 N Lateral load = Mwet*Nlateral*g = 2000*0.0g lateral + 3.Loads example. Mass-Acceleration Curve JPL acceleration curve for component sizing 100 Mass Acceleration Curve Applicable Launch Vehicles: STS Acceleration g's Titan gload i 10 Atlas Delta Ariane H2 1 1 10 i Mass kg mass 100 3 1 10 Proton Scout This curve envelopes limit loads for small components under 500 kg Apply acceleration load separately in critical direction Add static 2.Farley NASA/GSFC Simplified design curve for components on ‘appendage-like’ structures under 80 Hz fundamental 63 frequency .Component Loads.5 g in launch vehicle thrust direction Feb 16 2005 ENAE 691 R. 4 (stability very dependent on boundary conditions….so watch out!) Feb 16 2005 ENAE 691 R.5 Pegasus) Verification by Analysis 2.4 / 1.25 / 1.0 / 1.Farley NASA/GSFC 64 .Sizing the Primary Structure rigidity.25 (1.0 (2.6 2.25 Pegasus) Factors of safety for buckling (stability) elements ~ FS buckling = 1.10 1. metallic structures Factors of safety FS yield FS ultimate Verification by Test 1. strength and stability Factors of safety NASA / INDUSTRY.6 / 2. the primary structure is some form of cylinder Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 65 . in many cases.Primary Structure Simplified Model E is the Young’s Modulus of Elasticity of the structural material For example. usually aluminum e. Tapering thickness will drop frequency 5% to 12%.: 7075-T6 E = 71 x 109 N/m2 or t = I / (π R3) or t = A / (2π R) A = 2π R t Determine the driving requirement resulting in the thickest wall t. BENDING STIFFNESS Select material for E.g. When given frequency requirements from the launch vehicle users guide for 1st major axial frequency and 1st major lateral frequency. Recalculate A and I with the chosen t.Farley NASA/GSFC . but greatly reduce structural mass 66 Calculate for a 10% – 15% frequency margin Feb 16 2005 ENAE 691 R. flateral: Material modulus E times AXIAL STIFFNESS cross sectional area A Material modulus E times bending inertia I For a thin-walled cylinder: I = π R3 t . faxial.Sizing for Rigidity (frequency) Working the equations backwards…. N Moment Design Load. the max shear and max compressive stress occur in different areas and so for preliminary design shear is not considered) axial stress = P/A. N Axial Design Load. saving mass Feb 16 2005 ENAE 691 R. σallowable = 503 x 106 N/m2 With less stress the higher up.Sizing for Strength Design Loads using limit loads and factors of safety Plateraldes = (M + Mtip) g NlimitL Paxialdes = (M + Mtip) g NlimitA Momentdes = Plateraldes * Lcg Lateral Design Load. the more tapered the structure can be. bending stress = Moment*R/I 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 . N-m Recalling from mechanics of materials: (in a cylinder.Farley NASA/GSFC 67 . I. moment arm will be different Feb 16 2005 ENAE 691 R. Allowable Critical Buckling Stress 0 < MS acceptable Sheet and stringer construction will save ~ 25% mass 68 Margin of safety MS = {σCR /(FSbuckling x σmax)} – 1 Check top and bottom of cone: σmax. Update the max stress if a new thickness is required.Farley NASA/GSFC .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. An efficient structure.5) x MCYL This number can vary significantly Feb 16 2005 ENAE 691 R. So.a good trade Secondary structure (brackets. strength. optimization calls for ‘tapering’ of the structure. and stability. then the typical structure (primary + secondary): MSTRUCTURE ~ (2.Structural Subsystem Mass For all 3 cases of stiffness.5. interfaces…. The frequency may drop between 5% to 12% with tapering But the primary structural mass savings may be 25% to 35% . truss points. A typical structure. assume 1.) may equal or exceed the primary structure. if the mass calculated for the un-optimized constant-wall thickness cylinder (primary structure) is MCYL.Farley NASA/GSFC 69 . assume secondary structure = 1.0 x primary structure.0 to 3. Farley NASA/GSFC 70 .Backup Charts. Extras Feb 16 2005 ENAE 691 R. Farley NASA/GSFC Launch Vehicle I/F Hydrazine tank equatorial mount on a skirt with a parallel load path ! The primary structure barely 71 knows it’s there.Anatomy of s/c Heat of boxes radiating outward Transverse viewing. . Earth observing type Cylinder-in-box ‘Egg-crate’ extension Instruments FOV Drag make-up Propulsion module Feb 16 2005 ENAE 691 R. Farley NASA/GSFC XTE in Delta II 10’ fairing 72 .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 R. Drawing of deployment phase Pantograph deployment mechanism EOS aqua Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 73 . diamond tipped) Cons Costly provided by Jeff Stewart Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 74 .Composite Materials Pros Lightweight (Strength to Weight ratio) Ability to tailor CTE High Strength Good conductivity in plane Thermal property variation possible (K1100) Low distortion due to zero CTE possible Ability to coat with substances (SiO) Electrical bonding a problem Some types of joints are more difficult to produce/design Fiber print through (whiskers) Upper temperature limit (Gel temperature) Moisture absorption / desorption / distortion Tooling more exotic. expensive/specialized tooling (higher rpms. Farley NASA/GSFC 75 .0. 0.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.ie.00113D) microns per meter of length.00113D Graphite-Epoxy Shrinkage in Vacuum 0 0 1000 2000 D Days 3000 4000 5000 Feb 16 2005 ENAE 691 R. 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): Shrinkage ~ 27 (1 – e . Microns per Meter Shrinkage( D ) 20 Shrinkage ( D) 40 27 .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. where D is the number of days in orbit. epoxy) NOTE! A single pin hole in the aluminum foil will allow water de-sorption and shrinkage. 1 e . cos π EtoD π 1 Solar array orbital average projected drag area for a tracking solar array that feathers during eclipse ENAE 691 R. orbital average. Propulsion Subsystem Givens: Isp ΔV TM YSM AP ALT Mdry fuel specific thrust. km total spacecraft observatory mass. m2 circular orbit flight altitude.Farley NASA/GSFC Feb 16 2005 76 . 0 to 11 years projected area in the velocity direction. years years since last solar maximum.Mass Estimation. m/s mission time in orbit. seconds (227 for hydrazine. dry of fuel. kg 1 Area SAoa Area SA . 307 bi-prop) deltaV required for maneuvers during the mission. V circular . m/s Assumed Drag coefficient 2 Density atm.986 .Mass Estimation. g 6 Fuel mass for drag make-up. Newtons M fuelDRAG Feb 16 2005 Drag. this is the approximate fuel mass for drag over the mission life 77 Note: g = 9. C D .2 1.536 .Farley NASA/GSFC If the mission requires altitude control. influenced by the 11 year solar maximum cycle (sin() argument in radians) Corrected atmospheric density. Propulsion Subsystem Densitymax = 4. T M .0136 ALT) DF = 1 – 0. 10 ( 6371 11 Approximate maximum atmospheric density at the altitude ALT (km). 2 ALT) Circular orbit velocity. 10 Isp . kg ENAE 691 R.807 m/s2 . kg / m3 good for 300 < ALT < 700 km Density factor.18 x 10-9 x e(-0.9 sin [π x YSM / 11] Densityatm = DF x Densitymax 3. 31. A P Drag force. kg / m3 V circular CD Drag 2. g) 1 R.Mass Estimation.g) 1 Maneuvering fuel mass.Farley NASA/GSFC 78 .g) 1 Maneuvering fuel mass. kg end of mission case (de-orbit) Or expressed as a ratio: Feb 16 2005 M fuelMANV M dry ENAE 691 = e ΔV ( Isp . e ΔV ( Isp . e ΔV ( Isp . 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 . kg beginning of mission case If the fuel is to be saved for a de-orbit maneuver: M fuelMANV M dry . equations for impact torque Io Rotational mass inertia about point “o”. N-m dθ/dt can just be the velocity at time of impact if not critically damped 79 Feb 16 2005 ENAE 691 R. kg-m2 Dynamic system is critically damped Hinge point “o” Maximum Impact torque at lock-in.Farley NASA/GSFC .Deployable Boom. Static Beam Deflections For Quick Hand Calculations.Farley NASA/GSFC 80 . these are the most common and useful Feb 16 2005 ENAE 691 R. 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 Q = I x alpha Fc = m x r x Ω2 v = Aω cos(ωt) a = -Aω2 sin(ωt) Feb 16 2005 ENAE 691 R.Farley NASA/GSFC 81 . Solar arrays and other low area-density exposed components will react to vibro-acoustic loads.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. The primary structure will have a different limit load than attached components. luckily.Farley NASA/GSFC 82 . Feb 16 2005 ENAE 691 R. Loads for a component.015 g2 per Hz Feb 16 2005 ENAE 691 R. Ω= 10.Farley NASA/GSFC 83 .5 rad/s (100 rpm) Random input So = 0.10% Tstatic at 150 Hz (resonant burn. example Mpayload = 500 kg Mkickmotor = 50 kg Tstatic = 30000 N Tdynamic = +/.5m R = 1m The axial frequency is sufficiently close to the driven dynamic frequency that we can consider the axial mode to be in resonance. “chuffing”) dry mass m = 1 kg Antenna boom component fnaxial = 145 Hz with Q = 15 fnlateral = 50 Hz with Q = 15 L = 0. rad/s ω = 2 π fnLateral Plateral Equivalent additional lateral load = AtoL x Paxial Feb 16 2005 ENAE 691 R. con’t Axial-to-lateral coupling Ω Length L Radius R L Paxial Deflection y: y = R (Ω / ω)2 [ 1 – (Ω / ω)2 ] Axial-to-lateral coupling AtoL = y / L R y Deflection y Lateral circular bending frequency.Farley NASA/GSFC 84 .Spinning upper stage example. 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. g’s.5π fnaxial Q So] Axial Limit Load Factor. Newtons. Newtons Plateral = g x m x Nlateral Moment at boom base Moment = L x Plateral + y x Paxial g’s g’s g’s g’s Feb 16 2005 ENAE 691 R. Paxial = g x m x NaxialL Static lateral acceleration GstaticL = (R+y) Ω2 / g Random lateral acceleration GrmdL = AtoL x 3 sqr[0.Loads for a component.5π fnlateral Q So] Dynamic lateral acceleration GdynL ~ 0 Lateral Limit Load Factor. g’s. Naxial = GstaticA + GdynA + GrmdA Axial Limit Load.Farley NASA/GSFC 85 . Nlateral = GstaticL + GdynL + GrmdL Lateral Limit Load.