Spacecraft Structures and Mechanisms

spacecraft structures and mechanisms from concept to launch, spacecraft structures and mechanisms, spacecraft structures and mechanisms pdf
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Published Date:23-07-2017
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Spacecraft Structures Space System Design, MAE 342, Princeton University Robert Stengel • Discrete (lumped-mass) structures • Distributed structures • Buckling • Fracture and fatigue • Structural dynamics • Finite-element analysis 1 Copyright 2016 by Robert Stengel. All rights reserved. For educational use only. http://www.princeton.edu/stengel/MAE342.html Spacecraft Mounting for Launch • Spacecraft protected from atmospheric heating and loads by fairing • Fairing jettisoned when atmospheric effects become negligible • Spacecraft attached to rocket by adapter, which transfers loads between the two • Spacecraft (usually) separated from rocket at completion of thrusting • Clamps and springs for attachment and separation 2Communications Satellite and Delta II Launcher 3 Satellite Systems • Power and • Structure• Electronics Propulsion –Skin, frames, ribs, –Payload stringers, bulkheads –Solar cells –Control computers –Propellant tanks – Kick motor/ –Control sensors payload assist –Heat/solar/ and actuators module (PAM) micrometeoroid –Control flywheels shields, insulation –Attitude-control/ –Radio transmitters orbit-adjustment/ –Articulation/ and receivers station-keeping deployment –Radar thrusters mechanisms transponders –Batteries, fuel cells –Gravity-gradient –Antennas tether –Pressurizing bottles –Re-entry system (e.g., –De-orbit/ sample return)  graveyard systems 4Landsat-3 Typical Satellite Mass Breakdown Satellite without on-orbit propulsion Pisacane, 2005  Kick motor/ PAM can add significant mass 5 Total mass: from a few kg to 30,000 kg Fairing Constraints for Various Launch Vehicles • Static envelope • Dynamic envelope accounts for launch vibrations, with sufficient margin for error • Various appendages stowed for launch • Large variation in spacecraft inertial properties when appendages are deployed Pisacane, 2005 6STEREO Spacecraft Primary Structure Configuration Solar TErrestrial RElations Observatory • Spacecraft structure typically consists of – Beams – Flat and cylindrical panels – Cylinders and boxes • Primary structure is the  rigid skeleton of the spacecraft • Secondary structure may bridge the primary structure to hold components Pisacane, 2005 7 Upper-Atmosphere Research Satellite (UARS) Primary and Secondary Structure • Primary Structure provides – Support for 10 scientific instruments – Maintains instrument alignment boresights – Interfaces to launch vehicle (SSV) • Secondary Structure supports – 6 equipment benches – 1 optical bench – Instrument mounting links – Solar array truss – Several instruments have kinematic mounts 8Expanded Views of Spacecraft Structures 9 Structural Material Properties • Stress, : Force per unit area =E" • Strain, ": Elongation per unit length • Proportionality factor, E: Modulus of elasticity, or Young s modulus • Strain deformation is reversible below the elastic limit • Elastic limit = yield strength • Proportional limit ill-defined for many materials • Ultimate stress: Material breaks Poisson s ratio, : " lateral = " axial typically 0.1to 0.35 Thickening under compression Thinning under tension Nice explanation at http://silver.neep.wisc.edu/lakes/ PoissonIntro.html 10Uniform Stress Conditions Average axial stress, = P A = Load CrossSectional Area P : Load, N Average axial strain, " 2 A : Cross-sectional area, m L : Length, m ="L L Effective spring constant, k s L =P A=E" =E L AE P=L=kL s L Pisacane, 2005 11 Stresses in Pressurized, Thin-Walled Cylindrical Tanks R: radius • For the cylinder = pR/T hoop T : wall thickness = pR/2T axial p: pressure " negligible radial : stress • For the spherical end cap = = pR/2T hoop axial " negligible radial Hoop stress is limiting factor 12Weight Comparison of Thin-Walled Spherical and Cylindrical Tanks Sechler, Space Technology, 1959 Pressure vessels have same volume and maximum shell stresses due to internal pressure; hydraulic head is neglected R = cylindrical radius c R = spherical radius s Hydraulic head = Liquid pressure per unit of weight x load factor 13 Staged Spherical vs. Cylindrical Tanks Sechler, Space Technology, 1959 Pressure vessels have same volume and same maximum shell stresses due to internal pressure with and without hydraulic head (with full tanks) Numerical example for load factor of 2.5 Cylindrical tanks lighter than comparable spherical tanks 14Critical Axial Stress in Thin-Walled Cylinders 1.6 1.3 t t "%"% c = 9 +0.16 no internalpressure '' && E R L • Compressive axial stress can lead to buckling failure • Critical stress, " , can be c increased by – Increasing E – Increasing wall thickness, t • solid material • honeycomb Sechler, Space – Adding rings to decrease Technology, 1959 effective length – Adding longitudinal stringers – Fixing axial boundary conditions – Pressurizing the cylinder 15 SM-65/Mercury Atlas • Launch vehicle originally designed with balloon propellant tanks to save weight – Monocoque design (no internal bracing or stiffening) – Stainless steel skin 0.1- to 0.4-in thick – Vehicle would collapse without internal pressurization – Filled with nitrogen at 5 psi when not fuelled to avoid collapse With internal pressure Pressure stiffening effect Et No internal pressure = K +K ( ) c o p R 1.6 1.3 where t t "%"% c 0.6 1.3 0.3 = 9 +0.16 t R t "%"%"% '' K = 9 +0.16 ''' o && E R L &&& R L R 2 p R "%"% K = 0.191 Sechler, Space p'' && E t Technology, 1959 16Quasi-Static Loads Fortescue, 2003 17 Oscillatory Components Newton s second law leads to nd a 2 -order dynamic system for each discrete mass x = f m ="kx"kx+forcing function m ( ) x d s k k forcing function d s x+x+x= m m m = natural frequency, rad/s n " = damping ratio 2 2 ˙ x ˙ +2"x ˙ +x =u n n n x= displacement, m u= disturbance or control 18 Examples of Oscillatory Discrete Components 19 Springs and Dampers Force due to linear spring f =k"x =k x x ; k = springconstant ( ) x s s o Force due to linear damper f =k"x =k"v =k vv ; k = dampingconstant ( ) x d d d o 20Response to Initial Condition • Lightly damped system has a decaying, oscillatory transient response • Forcing by step or impulse produces a similar transient response = 6.28 rad/sec n " = 0.05 21 Oscillations x = Asin"t ( ) x = A" cos"t ( ) = A"sin"t + 2 ( ) 2 x="A sint ( ) 2 = A sin(t +) • Phase angle of velocity (wrt displacement) is /2 rad (or 90°) • Phase angle of acceleration is rad (or 180°) • As oscillatory input frequency, % varies – Velocity amplitude is proportional to % 2 – Acceleration amplitude is proportional to % 22Response to Oscillatory Input Compute Laplace transform to find transfer function "st Lx(t) =x(s)=x(t)e dt, 0 s =% + j&, (j = i ="1) Neglecting initial conditions Lx(t) = sx(s) 2 Lx(t) = sx(s) 23 Transfer Function 2 2 Lx+2"x+x = Lu ( ) ( ) n n n or 2 2 2 s + 2" s +"x(s) ="u(s) ( ) n n n Transfer function from input to displacement 2 x(s)" n = 2 2 u(s) s + 2" s +" ( ) n n 24 Transfer Functions of Displacement, Velocity, and Acceleration 2 • Transfer function x(s)" n from input to = 2 2 displacement u(s) s + 2" s +" ( ) n n 2 • Input to ˙ x (s)" s n velocity: = 2 multiply by s 2 u(s) s + 2" s +" ( ) n n 2 2 • Input to ˙ ˙ x (s)" s n acceleration: = 2 2 2 multiply by s u(s) s + 2" s +" ( ) n n 25 From Transfer Function to Frequency Response Displacement transfer function 2 x(s)" n = 2 2 u(s) s + 2" s +" ( ) n n Displacement frequency response (s = j) 2 x(j")" n = 2 2 u(j") j" + 2" j" +" ( ) ( ) n n Real and imaginary components 26 Frequency Response : natural frequency of the system n : frequency of a sinusoidal input to the system 2 x(j")" n = 2 2 u(j") j" +2" j" +" ( ) ( ) n n 2 2 "" n n =% 2 2 c" + jd" "" +2" (j") ( ) ( ) ( ) n n 2 2 &)&)"&c(") jd(")) " c(") jd(") n' n = = (+(+ 2 2 c" + jd" c" jd" c" +d" ( ) ( ) ( ) ( ) ( ) ( ) '' j,(" ) % a(")+ jb(")% A(")e Frequency response is a complex function Real and imaginary components, or Amplitude and phase angle 27 Frequency Response of the nd 2 -Order System • Convenient to plot response on logarithmic scale j"() ln A()e = lnA() + j"() • Bode plot – 20 log(Amplitude Ratio) dB vs. log % – Phase angle (deg) vs. log • Natural frequency characterized by – Peak (resonance) in amplitude response – Sharp drop in phase angle • Acceleration frequency response has the same peak 28Acceleration Response of the nd 2 -Order System • Important points: – Low-frequency acceleration response is attenuated – Sinusoidal inputs at natural frequency resonate, I.e., they are amplified – Component natural frequencies should be high enough to minimize likelihood of resonant response 29 Spacecraft Stiffness Requirements for Primary Structure Natural frequency 30Typical Spacecraft Layout • Atlas IIAS launch vehicle • Spacecraft structure meets primary stiffness requirements • What are axial stiffness requirements for Units A and B? – Support deck natural frequency = 50 Hz Octave Rule: Component natural frequency & 2 x natural frequency of Pisacane, 2005 supporting structure Unit A: 2 x 15 Hz = 30 Hz, supported by primary structure Unit B: 2 x 50 Hz = 100 Hz, supported by secondary structure 31 Factors and Margins of Safety Factor of Safety Typical values: 1.25 to 1.4 Load(stress)that causesyield or failure Expectedservice load Margin of Safety  the amount of margin that exists above the material allowables for the applied loading condition (with the factor of safety included) Skullney, Ch. 8, Pisacane, 2005 Allowableload(yieldstress) "1 Expectedlimit load(stress)Designfactor of safety 32Worst-Case Axial Stress on a Simple Beam Pisacane, 2005 Maximum stress Axial stress due to bending M h/2 ( ) = My I = I Worst-case axial stress due to bending and axial force " % M h/2 P ( ) = ± ± ' wc & A I max 33 Stress on Spacecraft Adapter • Spacecraft weight = 500 lb • Atlas IIAS launch vehicle • Factor of safety = 1.25 • Maximum stress on spacecraft adapter? Pisacane, 2005 Atlas IIAS Limit Loads (g) 34Example, con t. Worst-case stress 2 A= 2rt = 7.1in " % P Mc = ± ± ' wc 3 4 I =r t = 286 in A& I max Worst-case axial load at BECO (5±0.5 g) 500"5.5 500"0.5"42"9 & = +"1.25= 897.1psi wc %( 7.1 286 ' Worst-case lateral load at BECO (2.5 ± 1 g) or Maximum Flight Winds (2.7 ± 0.8 g) 500"3.5 500"2"42"9 & = +"1.25=1960psi wc %( 7.1 286 ' 35 Force and Moments on a Slender Cantilever (Fixed-Free) Beam • Idealization of – Launch vehicle tied-down to a launch pad – Structural member of a payload • For a point force – Force and moment must be opposed at the base – Shear distribution is constant – Bending moment increases as moment arm increases – Torsional moment and moment arm are fixed 36Structural Stiffness • Geometric stiffening property of a structure is portrayed by the area moment of inertia • For bending about a y axis (producing distortion along an x axis) z max 2 I = x(z)z dz x z min • Area moment of inertia for simple cross- sectional shapes 3 • Solid rectangle of height, h, and I = wh /12 y width, w: 4 I =r /4 • Solid circle of radius, r: y 4 4 • Circular cylindrical tube with inner I = r" r /4 ( ) y o i radius, r : and outer radius, r : i o 37 Bending Stiffness • Neutral axis neither shrinks nor stretches in bending • For small deflections, the bending radius of curvature of the neutral axis is EI r = M • Deflection at a point characterized by displacement and angle: 38Bending Deflection Second derivative of z and first derivative of "" are inversely proportional to the bending radius: 2 M d z d y = = 2 dx dx EI y 39 Maximum Deflection and Bending Moment of Beams (see Fundamentals of Space Systems for additional cases) Fixed-Free Beam Fixed-Fixed Beam Pinned-Pinned Beam Y = maximum deflection max M = maximum bending moment max 40 Pisacane, 2005

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