Spacecraft Structures Space System Design, MAE 342, Princeton University Robert Stengel Copyright 2016 by Robert Stengel. All rights reserved. For educational use only. http://www.princeton.edu/~stengel/MAE342.html • Discrete (lumped-mass) structures • Distributed structures • Buckling • Fracture and fatigue • Structural dynamics • Finite-element analysis 1 • 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 Spacecraft Mounting for Launch 2
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Spacecraft Structures!Space System Design, MAE 342, Princeton University!
Robert Stengel
Copyright 2016 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/MAE342.html
•! 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
Spacecraft Mounting for Launch
2
Communications Satellite and Delta II Launcher
3
Satellite Systems •!Structure–!Skin, frames, ribs, stringers, bulkheads–!Propellant tanks–!Heat/solar/ micrometeoroid shields, insulation–!Articulation/ deployment mechanisms–!Gravity-gradient tether–!Re-entry system (e.g., sample return)
•! Power and Propulsion–!Solar cells–! Kick motor/ payload assist module (PAM)–!Attitude-control/orbit-adjustment/station-keeping thrusters–!Batteries, fuel cells–!Pressurizing bottles–!De-orbit/
graveyard systems
•!Electronics–!Payload–!Control computers–!Control sensors and actuators–!Control flywheels–!Radio transmitters and receivers–!Radar transponders–!Antennas
4
Typical Satellite Mass Breakdown
Satellite without on-orbit propulsionKick motor/ PAM can add significant massTotal mass: from a few kg to > 30,000 kg
Landsat-3
5
Pisacane, 2005
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
6
Pisacane, 2005
•! 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
Solar TErrestrial RElations Observatory
STEREO Spacecraft Primary Structure
Configuration
7Pisacane, 2005
•! 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
Upper-Atmosphere Research Satellite (UARS) Primary and
Secondary Structure
8
Expanded Views of Spacecraft Structures
9
Structural Material Properties•! Stress, !: Force per unit area•! Strain, ": Elongation per unit length
! = E "•! 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
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
Pressure stiffening effectNo internal pressure
! c
E= 9 t
R"#$
%&'1.6
+ 0.16 tL
"#$
%&'1.3
With internal pressure
! c = Ko + Kp( )E tRwhere
Ko = 9tR
"#$
%&'0.6
+ 0.16 RL
"#$
%&'1.3 t
R"#$
%&'0.3
Kp = 0.191pE
"#$
%&'
Rt
"#$
%&'2
16Sechler, Space
Technology, 1959
Quasi-Static Loads
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Fortescue, 2003
Oscillatory Components
!!!x = fx m = "kd!!x " ks!x + forcing function( ) m
!!!x + kd
m!!x + ks
m!x = forcing function
m
!˙ ̇ x + 2"#n!˙ x + #n2!x = #n
2!u! n = natural frequency, rad/s
" = damping ratio#x = displacement, m
#u = disturbance or control
Newton s second law leads to a 2nd-order dynamic system for
each discrete mass
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Examples of Oscillatory Discrete Components
19
Springs and Dampers
fx = !ks"x = !ks x ! xo( ) ; k = springconstant
fx = !kd"!x = !kd"v = !kd v ! vo( ) ; k = dampingconstant
Force due to linear spring
Force due to linear damper
20
Response to Initial Condition
•! Lightly damped system has a decaying, oscillatory transient response
•! Forcing by step or impulse produces a similar transient response
! n = 6.28 rad/sec" = 0.05
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Oscillations
!x = Asin "t( )
!!x = A" cos "t( )= A" sin "t +# 2( )
!!!x = "A# 2 sin #t( )= A# 2 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 %–! Acceleration amplitude is proportional to %2
22
Response to Oscillatory Input
Compute Laplace transform to find transfer function
L !x(t)[ ] = !x(s) = !x(t)e" st dt0
#
$ ,
s =% + j& , ( j = i = "1)
L !!x(t)[ ] = s!x(s)L !!!x(t)[ ] = s2!x(s)
Neglecting initial conditions
23
Transfer Function
or L !!!x + 2"# n!!x +# n
2!x( ) = L # n2!u( )
s2 + 2!"ns+ "n2( )#x(s) = "n
2#u(s)
Transfer function from input to displacement
!x(s)!u(s)
= "n2
s2 + 2#"ns+ "n2( )
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Transfer Functions of Displacement, Velocity, and Acceleration
!x(s)!u(s)
= "n2
s2 + 2#"ns + "n2( )
!˙ x (s)!u(s)
= "n2s
s2 + 2#"ns + "n2( )
!˙ ̇ x (s)!u(s)
= "n2s2
s2 + 2#"ns + "n2( )
•! Input to velocity: multiply by s
•! Input to acceleration: multiply by s2
•! Transfer function from input to displacement
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From Transfer Function to Frequency Response
Displacement frequency response (s = j#)
!x( j")!u( j")
= "n2
j"( )2 + 2#"n j"( ) + "n2
!x(s)!u(s)
= "n2
s2 + 2#"ns+ "n2( )
Displacement transfer function
Real and imaginary components
26
Frequency Response!!n: natural frequency of the system
!!: frequency of a sinusoidal input to the system
!x( j" )!u( j" )
= " n2
j"( )2 + 2#" n j"( ) +" n2
= " n2
" n2 $" 2( ) + 2#" n j"( ) %
" n2
c "( ) + jd "( )
= " n2
c "( ) + jd "( )&
'(
)
*+c "( )$ jd "( )c "( )$ jd "( )
&
'(
)
*+ =
" n2 c "( )$ jd "( )&' )*c2 "( ) + d 2 "( )
% a(" )+ jb(" ) % A(" )e j, (" )
Frequency response is a complex functionReal and imaginary components, or
Amplitude and phase angle27
Frequency Response of the 2nd-Order System
•! Convenient to plot response on logarithmic scale
ln A(!)e j" (! )[ ] = lnA(!) + j"(!)
28
•! 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
Acceleration Response of the 2nd-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
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Spacecraft Stiffness* Requirements for Primary Structure