Structures and Thermal
Control
Dr Andrew Ketsdever
MAE 5595
Lesson 12
Outline
• Structures and Mechanisms
– Introduction
– Structural Loads
• Static
• Dynamic
–
–
–
–
Mechanics of Materials
Material Selection
Launch
Structural Design
• Thermal Control
– Introduction
– Thermal Loads
– Design
• Passive
• Active
Structures and Mechanisms
Structures and Mechanisms
Introduction
• Structures
– Mechanically supports all other subsystems
• Provides load path and distribution
– Attaches spacecraft to the launch vehicle
• Isolation and vibration damping
– Provides for separation from the launch vehicle
– Provides shielding for components
• MMOD, Radiation, AO
– Satisfy all strength and stiffness requirements
– Primary structure
• Carries spacecraft’s major loads
– Secondary structure
• Support of wires, propellant feed lines, etc.
• Brackets
Structures and Mechanisms
Introduction
• Mechanisms
– Two applications
• High cycle
– Antenna gimbals
– Solar array drives
– Reaction wheels
• Low cycle
– Gravity gradient boom
– Solar array or antenna deployment
– Contamination cover removal
Structural Loads
• Static (constant with time)
– External
• Weight of supported components during integration
– Internal
• Pressurized tanks
• Mechanical preloads
• Thermoelastic loads
• Dynamic (time varying)
– External
•
•
•
•
•
Transport to launch site
Launch vehicle
Acoustic loads
Wind gusts
Attitude control actuators
– Internal
• Thermal cycling
• Mechanism operation
Mechanics of Materials
• The 3 over-riding design criteria for space vehicle
structures are:
– Strength: ability to support a static load
– Stiffness (Rigidity): measure of flexibility (need to
avoid L/V natural frequencies)
– Stability (Buckling): resistance to collapse under
compression
• For simplicity, we will consider only spacecraft
that resemble beams
Strength
A

..
.
B C
A
0.002
.. .
B
C
A: Proportional Limit
B: Yield Point
(0.2% residual strain)
C: Ultimate Failure

Stress:
Strain:
Load P
 

Area
A
L

L
Poisson’s Ratio:  
Young’s Modulus:
E
 lateral
 axial


Stiffness
• Natural frequency is the frequency at which an unforced,
vibrating system will vibrate
1
fn 
2
where
k
m
k  stiffness(springconstant)
m  mass
• When vibrating freely, a single degree of freedom system will
always vibrate at the same frequency, regardless of
amplitude
Stiffness
• Without energy dissapation, harmonic motion will go on forever. Of
course, things do quit vibrating eventually.
• A damping force is one that resists vibration and dissipates energy,
normally through heat (friction).
• A viscous damping force is proportional to velocity; we typically
assume viscous damping to simplify analysis. Assuming a spring is
linear-elastic,
mx(t )  cx (t )  kx(t )  F (t )
where
m  mass
k  stiffness
c  dampingfactor
F (t )  externallyappliedforceas a functionof time
x(t ), x (t ), x(t )  position,velocity,acceleration
Stability
• Theoretically, a linear-elastic column will buckle at a critical, or Euler
Buckling Load, Pcr, given by
Pcr 
 2 EI
L2
(SMAD,11- 49)
where
L  effective length 2L (for beam)
• This equation applies only if the axial stress at buckling (Pcr/A) does
not exceed the materials proportional limit. Otherwise, replace E with
Et, the tangent modulus which is the slope of the stress/strain curve
at the operating stress level (the buckling stress in this case).
Cyclic Failure
• Fatigue failure is caused by repeated, cyclical
loading of a component at a load well below
ultimate or yield

Fatigue
limit
n-cycles
It is difficult
(or impossible)
to accurately
predict the
actual fatigue
limit for a
given part. The
only sure way
is to test to
failure.
Mechanics of Materials
• Flexibility
– Measure of how much a structure deflects under a
load
• Stiffness (Rigidity)
– Inverse of flexibility
– Below Elastic Limit
• Material returns to initial length after stress removed
• Material becomes plastic above the elastic limit
• Material yields and has residual strain
• Materials
– Ductile
• Yields substantially without failing
– Brittle
• Yields without much deformation
Mechanics of Materials
Cantilever Beam in tension
P
tension
Load P


Area A
x
Cantilever Beam in bending
P
c Neutral axis
x
Moment
Mc
b 
I
where
Tension
Neutral axis
Compression
 b  bendingstress( N / m 2 )
b
3
Neutral axis
M=Px
bh
I

h
12
M  moment ( Nm)
c  distancefrom neutralaxis (m)
I  area moment of inertia(NOT mass moment
of inertia)
Mechanics of Materials
Satellite
P2
P1 Mc
c  
A
I
Neutral axis
P1
x
Tension
LV interface
Compression
Mechanics of Materials
 x

Shear Strain:  
G
y
E
G
2(1   )
G = shear modulus

Structural Design
• Design Stress x Factor Safety < Allowable Stress
• Allowable Stress depends on
– Type of stress
– Material used
Option
Design Factors of Safety
Critical for
Not Critical for
Personnel Safety
Personnel Safety
Yield
Ultimate
Yield
Ultimate
1) Ultimate test of a dedicated
qualification article
1.1
1.4
1.0
1.25
2) Proof test of all flight structures
1.1
1.4
1.1
1.25
3) Proof test of one flight unit of a
fleet
1.25
1.4
1.25
1.4
4) No structural test
1.6
2.25
1.6
2.0
SSAM, Table 12.5
(Source:
SMAD, Table 11.54
DOD-HDBK-343, MIL-HDBK-340 and MSFC-HDBK-505A offer similar options.)
Material Selection
Performance Characteristics
 Stiffness (Young’s modulus and
Poisson’s ratio)
 Rupture and yield strength (allowable
stresses)
 Ductility (elongation)
 Fatigue resistance and fracture
toughness
Cost, Schedule, and Risk
 Availability
 Cost of raw material
 Cost of developing processes and tooling
 Cost of processing (recurring)
 Mass density
 Ease of controlling processes
 Corrosion resistance
 Variability in key properties
 Creep resistance
 Versatility of attachment options
 Wear or galling resistance
 Outgassing
 Thermal conductivity, absorptivity, and
emissivity
 Coefficient of thermal expansion
Material Selection
Material
Advantages
Disadvantages
Aluminum
 High strength vs. weight
 Ductile; tolerant of concentrated stresses
 Easy to machine
 Low density; efficient in compression
 Relatively low strength vs. volume
 Low hardness
 High coefficient of thermal expansion
Steel
 High strength
 Wide range of strength, hardness, and ductility
obtained by treatment
 Not efficient for stability (high density)
 Most are hard to machine
 Magnetic
Heat-resistant
alloy
 High strength vs. volume
 Strength retained at high temperatures
 Ductile
 Not efficient for stability (high density)
 Not as hard as some steels
Magnesium
 Low density – very efficient for stability
 Susceptible to corrosions
 Low strength vs. volume
Titanium
 High strength vs. weight
 Low coefficient of thermal expansion
 Hard to machine
 Poor fracture toughness if solution treated and aged
Beryllium
 High stiffness vs. density
 Low ductility and fracture toughness
 Low short transverse properties
 Toxic
Composite
 Can be tailored for high stiffness, high strength, and  Costly for low production volume; requires
extremely low coefficient of thermal expansion
development program
 Low density
 Strength depends on workmanship; usually requires
individual proof testing
 Good in tension (e.g., pressurized tanks)
 Laminated composites are not as strong in
compression
 Brittle; can be hard to attach
Material Selection
6061-T62 Al plate
.25-2”
A286 Bar steel <2.499”
Ti-6AI-4V Bar 2”
(annealed)
Density (gm/cm3)
2.71
7.95
4.43
Young’s Modulus, E (103
MPa)
69.0
201
110
Poisson’s ratio, n
0.33
0.31
0.31
Allowable Tensile Ultimate
stress, Ftu (MPa)
290
896
923
Allowable compressive
yield stress, Fcy (MPa)
240
590
903
Allowable Shear Stress, Fsu
(MPa)
190
590
570
Thermal conductivity
(W/mK)
150
12
7.3
Coefficient of thermal
expansion, a, (10-6 m/m/ºC)
22.9
23.0
8.5
Corrosion resistance
Good
Excellent
Excellent
Weld-ability
Good
Good
Fair
Very Good
Good
Fair
Property
Machinability
Adapted from Sarafin, Spacecraft Structures and Mechanisms, 1998.
Launch Profile
1.
2.
3.
4.
5.
6.
7.
8.
Launch
S-IC Inboard Engine Cut Off
S-IC Outboard Engine Cut Off
S-II Ignition
S-II O/F Mixture Change (lower F)
S-II Shut Down
S-IVB Ignition (one J2 engine)
S-IVB Shut Down
Launch
• Axial and Lateral Loads
– Acceleration due to thrust
• Typically increases with time
due to launch vehicle mass
reduction
• Can be several to tens of g’s
– Vibration
• Random vibe
• Shock (burst)
– Liftoff
– Staging
– Acoustic
• Sound pressure waves
LV Interface: Shock Ring
• Needed a design to provide axial and
lateral isolation to satellite payloads
• Variation of axial shock ring
– Increases the path the shock has to
travel while providing parallel
damping
• All metallic load path
• Aluminum construction for light
payloads
– Titanium for larger payloads
• Easily manufactured and assembled
• Integrates in a stacked configuration
• Viscoelastic constrained layer damping
on outer and/or inner circumference
Flexible Body Dynamics
• Finite Element Method
– Used to predict structural
modes, natural
frequencies, and
responses to applied loads
– Models of the structure with
discrete degrees of
freedom
– Break a complex structure
into simple structures that
are easy to analyze
– Matrix math
Payload
M1
k1
Oxidizer
M2
k2
Fuel
M3
F(t)
Launch Vehicle Loads
Power Spectral Density (PSD)
Mean
Square
Accel. (g2)
Cumulative
Mean-square
acceleration
PSD
Power
Spectral
Density
(g2/Hz)
Frequency (Hz)
At a given frequency, the PSD is the slope of the function of cumulative mean square acceleration.
The area under the acceleration PSD curve is equal to the overall mean square acceleration. Thus, the
the overall root-mean-square value equals the square root of the area under the PSD curve.
Launch Vehicle Loads
Using a PSD curve
• Given a PSD for a LV, for example, we’d like to know the
acceleration experienced by our spacecraft
• Miles’ Equation tells us this
xrms
f nWx ( f n )

4
where
..
xrms  t he RMS responseacceleraton
i (g' s)
f n  st ruct ure's nat uralfrequency(Hz)
Wx ( f n )  input acceleraton
i P SD at f n
  dampingcoefficient
Structural Design
Secondary structures:
Primary structures:
• body structure
• launch vehicle adapter
•
•
•
•
•
appendage booms
support trusses
platforms
solar panels
antenna dishes
Tertiary structures:
SSAM: Fig. 1.1
• brackets
• electronics boxes
Structural components are categorized by the different types of
requirements, environments, and methods of verification that drive their
design
– Primary structures are usually designed to survive steady-state
accelerations and transient loading during launch and for stiffness
– Designs of secondary and tertiary structures tend to be driven by
stiffness, positional stability, and fatigue life
Structural Requirements
•
•
Manufacture & Assembly (handling fixtures)
Transport & Handling (cranes, dollies, transport to
launch site)
Testing (vibration, acoustic)
Pre-launch (stacking and preflight checks)
Launch
•
•
•
–
–
–
–
•
Mission Operations (thrusters, attitude maneuvers)
–
•
Steady state acceleration
(typical max acceleration 6 g’s axial, 3 g’s lateral)
Vibration and acoustic noise
Shock from staging and separation
Very benign compared to launch and testing
Reentry
Structures
Example: Thin-Walled Pressure Vessels
• Thin walled vessel defined as having an inner radius to wall
thickness of 10 or greater.
L
H
rinner
 10
t wall
Structures
Example: Cylindrical Pressure Vessels
dA H  t w dy
pressure directed
radially outward
x
vessel section of length dy
with inner radius ri and
wall thickness tw
y
hoop stress circumferentially
in walls, H
longitudinal stress
axially in walls, L
dAL   ro  ri    ri  t w   ri 
2

2

  2ri t w  t w2  2ri t w 
F
x
 0  2 H dAH   p Awall (effective) 
 2 H t w dy  p2ri dy
 H 
pri
pr

tw
t
F
y
 0   L dAL   p Aend cap 
 
  L 2ri t w   p ri 2
 L 
pri pr

2t w 2t
Structures
Example: Spherical Pressure Vessels
vessel section with inner
radius ri and wall thickness tw
x
y
pressure directed
radially outward
hoop stress spherically in
walls, S
dAS   ro  ri   2ri t w 
2
F
y
 0   S dAS   p Across section 
 
  S 2ri t w   p ri 2
 S 
pri
pr

2t w 2t
Structure Subsystem
• How do you know the structure will meet
the requirements?
– Inspection
• Is it built the way it was designed?
• Are the right materials used?
– Analysis
• Finite element modeling
– Test and Evaluation
• Did the structure perform as designed?
Thermal Control Subsystem
Introduction
• Thermal Control Subsystem
– Maintain all spacecraft and payload
components within their required temperature
limits over the entire mission
• Operational Limits
• Survival Limits
• Gradient Limits
– Can be accomplished by active or passive
means
Operating
Temperature
Ranges
Spacecraft Thermal Environment
Spacecraft Thermal Environment
Spacecraft Thermal Environment
Solar Flux
qs = Gs = 1418 W/m2 @ winter solstice
= 1326 W/m2 @ summer solstice
Emitted
Qw
Albedo
qr = a = 30%  5%
Earth IR (Earthshine)
qI = 237  21 W/m2
(at Earth’s Surface)
Earth
Heat Transfer Methods
• Conduction (Fourier’s Law)
– Heat flow in a medium,
generally solid
q   kA
dT
dx
where
q  power  energy/t ime (W )
k  t hermalconduct ivit y (W /mK)
A  area (m2 )
T  t emperat ure (K)
x  dist ance(m)
• Convection
– Heat flow using stirring
medium, liquid or gas
– May use gravity to stir
passively
q  hAT
q  power (W)
h  convectioncoefficient (W/mK)
A  surface area (m2 )
T  tempdifference(Tsurface  Tflow )
Heat Transfer Methods
• Radiation (Stefan-Boltzman Law)
– Electromagnetic (EM) energy through free space (mostly in the
IR spectrum)
Q = σεAT4
where
σ = S – B constant = 5.67 x 10-8 (W/m2K4)
ε = emmissivity (typically in IR spectrum)
• Heat Flux
Q
4
q    T
A
Design Options
• Passive thermal control
– Coatings: paints, mirrors
– Insulation: multi-layer insulation (MLI) blankets
• Alternating layers of aluminized Mylar and thin net
• Often use Kapton for innermost / outermost layers
(stronger)
– Radiators: radiate waste heat to deep space
• Locate radiators on S/C side not exposed or only
partially exposed to Sun or Earth
– Phase Change Devices: paraffin absorbs heat as it
melts (latent heat of fusion)
• For use next to equipment with high, short bursts of
power
– Thermal Isolators: isolate propellant lines, etc
– Placement of components
Design Options
• Active thermal control
– Heaters and Thermostats
– Louvers: modulate a radiator
– Heat Pipes
• Liquid near hot component evaporates
• Moves to cold end of pipe and condenses
• Wicking device or capillary action brings liquid
back to hot end (active or passive)
• Hard to test in 1g
– Cold Plate: cooling fluid passes through plate
– Cryogenic systems: refrigerator (thermodynamic
cycle) or vented gas
– Attitude Maneuvers
TCS—Intro
Thermal-Optical Properties
 = % energy emitted with
respect to a perfect black
body. Usually averaged
over IR range,IR
• a = absorptivity, % of
incident radiation absorbed
Usually averaged over the
solar range,aSOL
• r = reflectivity, % reflected.
•  = transmissivity, %
transmitted.
•
Q
Qr
Qa
Q
r a   1
r = reflectivity
a = absorptivity
 = transmissivity
TCS—Intro
Thermal Analysis
• Gray body
– Assume a  over entire spectrum of interest. Most
real objects can be treated as gray bodies if we
restrict the wavelength under consideration, e.g. solar
spectrum (0.3 – 3.0 mm) or IR (3.0 – 30.0 mm).
– Thus, aSOL  SOL , aIR  IR
• S/C absorb most energy in the solar spectrum
and emit in the IR. So when we compare
materials, we’re interested in the ratio,
– aSOL /IR
Emissivity / Absorptivity vs Wavelength
Solar Band
IR Band
1
a or 
0
wavelength, 
Radiation Properties of Materials
Thermal Nodes and Networks
• Thermal Networks
– S/C thermal network is analogous to an electrical
network. Instead of electrical nodes with electrical
capacitance connected by electrical
resistors/conductors, we have thermal nodes with
thermal capacitance connected by thermal
resistors/conductors.
– Thus, we can use basic laws such as Ohm’s Law,
Kirchhoff’s Law to solve thermal networks.
• Thermal Nodes
– To conduct thermal analysis of a complex system we
break it into a set of finite subvolumes called nodes.
Types of Thermal Nodes
• Diffusion Nodes
– Most commonly used in a thermal network. They have finite
thermal mass. Represents normal material/components whose
temperature can change due to heat flow in/out of the node.
– Temperature of the node depends on nodal heat capacitance, net
heat flow into/out of the node, time.
– Example: Battery Box
• Arithmatic Nodes
– Zero thermal mass, don’t exist physically. Useful in constructing
thermal models. Can change temperature instantly. Can be used
for bolts, low mass insulators, coatings.
– Example: Thermal coating
• Boundary Nodes
– Infinite thermal mass, represent a source or sink. Temperature
can’t change no matter how much heat is added. T= constant.
– Example: Deep space.
• Number of nodes
– The more nodes you have in a network model, the potentially more
accurate (within the bounds of diminishing returns). But the more
nodes, the more computationally intensive the analysis.
TCS—Design
Network Example
Deep Space
N4
G3
Cond.
N5
G4 rad
N3
G2 conduction
Physical Model
N2
G1 radiation
Sun
N1
TCS—Design
View Factors
• A view factor, F, is the fraction of energy leaving one
surface that strikes another surface.
• The sun is far enough away that it can be considered to
be a point source of energy. We can use the cosine law
to determine the fraction of energy hitting a surface.
• For LEO orbits, Earth is close enough that this
assumption doesn’t apply to Earth-source energy.
Instead, we must use view plane geometry to determine
the fraction of energy striking a surface. Luckily, we don’t
have to integrate over both surfaces. There are
analytical solutions for simple shapes (planes, spheres).
TCS Preliminary Design Process
TCS Preliminary Design Process
TCS—Design
SMAD Thermal Analysis
• Balance heat in and heat out
Qemitted
Qabsorbed
→ Also must consider heat generated
internally, or heat energy converted to
other forms
QS  QR  QI  QW  QE  QC




 

absorbed
internally
generated
emitted
converted
TCS—Design
Spacecraft Thermal Equilibrium Calculations
Qabsorbed
Qemitted
Model spacecraft as a spherical satellite with planar solar arrays. Find
equations for equilibrium temperature of the solar arrays and the
spacecraft body.
TCS—Design
Solar Array Thermal Equilibrium Calculations
QemittedSA 
Qabsorbed SA
Qabsorbed( SA)  Qemitted( SA)  Qpower generated( SA)  0
- Absorbed energy
Qabsorbed ( SA)  QS ( SA)  QR( SA)  QI ( SA)
QS ( SA)  a t GS At
Direct
Solar
Earth IR
FP  sin 2 r
sin r 
Albedo
QI ( SA)   b GI Ab
QR( SA)  a b GR Ab
GI  q I FP
GR  aGS FP K a
K a  0.664 0.521r  0.203r 2
R
rad
R  H
TCS—Design
Solar Array Thermal Equilibrium Calculations
Qabsorbed SA
QemittedSA 
- Emitted energy
Qemitted( SA)   b AbTeq4 ( SA)   t At Teq4 ( SA)
- Generated energy (taken out of array)
Qpower generated( SA)  GS At
TCS—Design
Solar Array Thermal Equilibrium Calculations
Qabsorbed SA
QemittedSA 
- Maximum temperature – all sources
Tmax(SA)
a t G S   b G I  a b G R  G S  


  b   t 


1/ 4
a t GS   b q I FP  a b aGS K a FP  GS 


  b   t 


- Minimum temperature – only Earth IR
  b GI 
Tmin(SA)  

  b   t  
1/ 4
  q F 
 b I P 
  b   t  
1/ 4
1
4
TCS—Design
S/C Body Thermal Equilibrium Calculations
QabsorbedS / C 
Qabsorbed( S / C )  Qdissipated( S / C )  Qemitted( S / C )  0
QemittedS / C 
- Maximum temperature
Tmax(S / C )
aG A  GI A  aGR A  QW 
 S C

A


1/ 4
aG A  q I FS A  aaGS K a FS A  QW 
 S C

A


- Minimum temperature
Tmin(S / C )
 G A  QW 
 I

 A 
1/ 4
 q F A  QW 
 I S

A


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where:
FS 
1  cos r 
2
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TCS—Design
Thermal Equilibrium Example
Perform the preliminary thermal analysis for a spacecraft with
the characteristics given in the table. Calculate worst case hot
and cold temperatures. Identify any assumptions you make.
Cylindrical Spacecraft Shape
Orbit Altitude
Electrical Energy Dissipation, Qw
1 m radius
3 m height
800 km
200 watts
TCS—Design
Thermal Equilibrium Example
•Find the radius of an equivalent sphere with same surface area as the
2
cylinder:
Acylinder  2rcyl
 2rcyl h  8 m2
2
Asphere  4rsphere
,
rsphere  2 m 2
2
 AC  rsphere
 2 m2
•Find r, Ka, and F:

R 
6378km 
  sin 1 
  62.69 deg  1.0942rad
 6378 800 km 
 R  H 
r  sin 1 
K a  0.664  0.521r  0.203r 2  0.9910
F
1  cos r
 0.2706
2
TCS—Design
Thermal Equilibrium Example
•Use the following table of parameters:
Parameter
Hot
Value
Cold
Value
Source
Gs
1418
1326
SMAD
qI
258
216
237  21 W/m2
QW
200
200
Given
a
0.3
0.3

0.8
0.8
Typical values for preliminary
thermal analysis
a
0.35
0.25
SMAD
TCS—Design
Thermal Equilibrium Example
•Worst Case Hot will occur at local noon with the spacecraft directly
overhead
Tmax(S / C )
Tmax(S / C )



 A G a  AaaGS K a F  AqI F  QW 
 C S

A








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
 2 m 2 1418W/m2 0.3  8 m 2 0.30.35 1418W/m2 0.9910.2706  8 m 2 258 W/m2 0.80.2706  200 W 


8 m 2 5.67 108 W/m2 0.8





 Tmax(S / C )  260.87 K  12.18 C
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TCS—Design
Thermal Equilibrium Example
•Worst Case Cold will occur at local midnight.
Tmin(S / C )
 Aq F  QW 
 I

A


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


 8 m 2 216 W/m2 0.80.2706  200 W 


8 m 2 5.67 108 W/m2 / K 4 0.8 



 Tmin(S / C )  186.36 K  86.79 C

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