kabe aiaa keynote pdf figures 04102013.pptx

7/30/2019 Kabe AIAA Keynote PDF Figures 04102013.Pptx

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The Aerospace Corporation 2013

Launch Vehicle and Spacecraft Structural Dynamics

State of the Art and Challenges for the Future

Alvar M. Kabe

The Aerospace Corporation

10 April 2013


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Overview

Launch Vehicle and SpacecraftStructural Dynamics

The Load Cycle Process Structural Dynamic Models and

An indispensable test Loads Analyses and Why is not three sigma,

Why root-sum-square combinationscan under predict the truth, and

Why envelope functions are the wayto go

Why many spacecraft are notproperly qualified while subjected tounnecessary risk before launch

Future NeedsCourtesyofNASA

3


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3

They Made it Possible

DAlemberts Principle

(1717 1783)

Newtons Laws (1642 - 1726)

Hamiltons Principle

(1805 1865)

Lagranges Equations

(1763 1813)

d

dtmv

(t)( ) =

f(t)

m

jw

j(t

i)+ f

l(t

i)

l

j

j=1

n

wj (ti ) = 0

TV( )

t1

t2

dt+ WNonconservativet1

t2

dt= 0

d

dt

T w

j

Tw

j

+Vw

j

fdj = fNonconservative j


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4

Launch Vehicles and Spacecraft Structural Dynamics

During launch and ascent, a launch vehicle, its upperstage, and spacecraft experience severe structural loads

In addition, the launch system undergoes dramatic

configuration changes


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Design and Verification Process is Highly Complex

Numerous organizations involved Launch vehicle, engines, spacecraft, payloads, etc.

Numerous technical disciplines required Structures, dynamics, fluids, propulsion, controls, flight mechanics,

statistics, atmospheric sciences, etc.

Determination of dynamic loads and stresses involves complexmodels, analyses, and tests

Fully integrated launch vehicle/spacecraft system needs to beaddressed

Integrated system cannot be tested prior to flight Significant engineering judgment involved

Schedule and cost play a major role


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Loads Analysis Process

Structural loads are a function of dynamic properties of integratedlaunch/upper stage/spacecraft system

Design changes in one element can result in load changes in allelements

Modeling errors in one element can result in load prediction errors in allelements

Dynamic properties of each element will be a function of structuraldesign of each element

Therefore, design process has to be iterative

No single entity/organization has control over the loads analysisprocess

Hence, negative outcomes can be problematic


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The Load Cycle Process

Air Force Space Command, Space and Missile Systems Center Standard SMC-S-004,

Independent Structural Loads Analysis, 13 June 2008.


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The Load Cycle Process - Models


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Loads Analysis Model - Technical Disciplines

Structures

Structural Dynamics Guidance Analysis

Fluid Mechanics

Flight Software

...

ConfigurationDefinition

Finite Element

Model 1

Drawings

Static, ModeSurvey, other tests

Flight Data

Component 1

Dynamic Model

MassProperties

LTM Definition LTM Generation

Finite Element

Model 2

Drawings

Static, Mode

Survey, other tests

Flight Data

Component 2

Dynamic Model

MassProperties


Structural

Model n

Drawings

Static, ModeSurvey, other tests

Flight Data

Component n

Dynamic Model

MassProperties


LoadsAnalysis Model

and LTM

Autopilot

and Engine

Actuator

Definitions

Control System

Model

Aerodynamic

CoefficientsAerodynamic

Loading

PropellantDefinition

HydroelasticModel of

Fluids

SpacecraftModel

ConfigurationDefinition


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Component Mode Synthesis

Technique allows for significant reduction in size and subsequentcoupling of structural dynamic models

From millions of equations in a Finite Element model to a few thousand Modal truncation level depends on frequency content of excitation

Technique invented by Professor Walter Hurty at UCLA in 1965 Craig and Bampton (University of Texas) simplified computation of

constraint modes in 1968, hence Hurty/Craig-Bampton models

Benfield and Hruda (MMC) introduced Component ModeSubstitution in 1971

Couples Hurty/Craig-Bampton spacecraft models to launch vehiclemodels Provides for rigorous coupling of substructure damping properties

Most likely results in complex modes


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Component Mode Synthesis (cont.)

Hurty/Craig-Bampton model of a spacecraft

Benfield/Hruda coupled launch vehicle/spacecraft model

Non-Interface

Interface

xSC(t){ }

N

xSC(t){ }

I

=

SC NC

SC N

0 I

qSC(t){ }

xSC(t){ }

I

MSC =

I

SC

MSC

qI

MSC Iq

MSC II

DSC =

2n SC

0

0 0 II

KSC =

n2

SC

0

0 KSC

II

M** =I

SC

MSC

qI CE LV

I

LVI

T

CE T

MSCIq

I LV

D**

=

2n SC

0

0 2n LV

K**

=

n

2

SC

0

0 n2

LV


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Loads Analysis Model Validation and Verification

Accurate loads analysis models can only be achieved with testverification

Substructure models with over 1,000,000 degrees of freedom typical5-10 million degrees of freedom not unusual

Detail required to model complex hardware makes process costly Significant engineering judgment involved

To date, not a single analytical model of a complex structure has hadacceptable agreement with its mode survey test data prior to

adjustment Significant changes in loads from analytical to test-verified model

Static and other tests, which are performed to qualify structure toanalytically predicted loads, also used to adjust structural analysis models


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Mode Survey Tests, an Absolute Requirement

Performed to measure mode shapes, natural frequencies and damping Rigorous success criteria includes:

All modes within frequency range of interest measured Empirical modes, , satisfy orthogonality requirements of , where

Tests typically performed with: Hundreds of accelerometers Multi-shaker, broadband, uncorrelated random excitation

Measured acceleration and force time histories converted to frequencyresponse functions and modal parameters are extracted

Parameters used to adjust analytical finite element models with goals of

mT M

m = I T I

m

0.1

mT M

a = M

Mij 0.95 i= j

Mij 0.10 i j

n

measured n

analytical

n

measured 0.03


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Mode Survey Data and Model Correlation

Program

Number+of+

Measured+

Modes

Did+Model+

Need+

Adjustment

Program

Number+of+

Measured+

Modes

Did+Model+

Need+

Adjustment

Program

Number+of+

Measured+

Modes

Did+Model+

Need+

Adjustment

Program'1 9 yes Program'15 18 yes Program'32 23 yes

Program'2 20 yes Program'16'(11) 24''3 yes Program'33 12 yes


Program'4 45 yes Program'18 35 yes Program'35 6 no

Program'5A 35 yes ''''Subsystem'1 18 yes Program'36 13 yes

Program'5B 30 yes ''''Subsystem'2 9 yes Program'37 17 yes

''''Subsystem'1 9 yes Program'19 26 yes Program'38 25 yes

''''Subsystem'2 4 yes ''''Subsystem'1 Program'39 28 yes

''''Subsystem'3 4 yes '''''Conf.'1 5 yes Program'40 14 yes

Program'6 39 yes '''''Conf.'2 6 yes Program'41 8 yes

Program'7 16 yes '''''Conf.'3 6 yes Program'42 42 yes



Program'10 23 yes Program'22' 30 yes Program'45 14 yes

Program'11 13 yes Program'23' 6 yes Program'46 42 yes


Program'12 11 yes ''Subsystem'1 8 yes Program'48 17 yes


Program'14 Program'26 23 yes Program'50 15 yes

''''Conf.'1 28 yes Program'27A 21 yes Program'51 18 yes''''Conf.'2 42 yes Program'27B 20 yes Program'52 55 yes

''''Conf.'3 39 yes Program'27C 6 yes Program'53 17 yes






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The Load Cycle Process Loads Analyses


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Launch Vehicles and Spacecraft Loads

Critical load producing events include:

LiftoffAtmospheric flight (Transonic, Max-q)

Engine ignitions and shutdowns

Jettison events


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Courtesy of NASA

Courtesy of ULA

Courtesy of SpaceX

Courtesy of NASA

Courtesy of ULA

Liftoff


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Liftoff Nonlinear transient phenomenon

Vehicle/launch stand interaction Produces critical loads for launch vehicleand spacecraft structure

Forcing function Thrust transients and differentials Ignition overpressure pulse

Ground winds

Gravity Launch stand interaction Dispersions

Modeling considerations Up to several thousand modes to 60 Hz Finite Element Models of substructurestransformed into component mode

models, hydroelastic models of fluids

Residual flexibility Coupled system damping

CourtesyofUS

AirForce

Launch Stand!Interaction

!

Ignition!Overpressure!

Gravity!

Ground!Winds!


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Liftoff Ignition Overpressure Pulse

Computational Fluid Dynamics (CFD) simulation (3.5 sec real time) 30.7 million cells; 120,000 cpu hours or 5000 cpu days

Aerospace Corporation Fluid Mechanics Dept.


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Atmospheric Flight Loads

CourtesyofNASA


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Atmospheric Flight

Static-aeroelastic Due to relative wind and non-zero angle ofattack, which varies slowly relative to the

fundamental mode frequency of the system

Turbulence/Gust Non-persistent wind features cause

changes in local angle of attack

Buffet Interaction between separated flow

turbulence, attached boundary layerturbulence, and shock wave oscillations

Autopilot-induced Maneuvering/steering Autopilot noise Mechanical noise (engine gimbal friction)

Other analyses include lack of wind persistenceand dispersions

Aerodynamic!Loading!

Relativ

e!Win

d!

Gust!Turbulence!

Maneuvering!Forces!

Thrust!

Buffet!


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Atmospheric Flight Loads

Computed for various times of flight Ten to twenty Mach numbers (times of flight) Transonic and maximum dynamic pressure (Max-q) times of flight tend to

be most critical

Transonic (maximum buffet) will yield design loads for significantportions of spacecraft

Maximum dynamic pressure will yield critical launch vehicle loadsand some significant spacecraft primary structure loads

Can occur during flight through jet stream and associated highturbulence (gust) loading

Loads analyses incorporate structural dynamic models, aeroelasticeffects, control system, atmosphere, and thrust effects


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Buffet Loads

Buffet event relatively long induration compared to othertransient events

Treated as steady state,ergodic random process

Objective of analysis is tocomputeprobability densityfunctions of response quantities,such as loads, from whichstatistical enclosure values can

be determined Mean, standard deviation Monte Carlo

!!y(t)

!!y(t)

!!y(t)

, !

, !

, !

, ! , !

Flight 1

Flight 2

Flight n


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Buffet Loads Analysis Approaches

Time domain - developed in 1984, first used for buffet analysis in 1988 Frequency domain - first large system implementation in 1988

Broussinos, P., and Kabe, A. M., Multi-Mode Random Response Analysis Procedure,Aerospace Technical Report SSD-TR-90-53, 1990.

I[ ] q(t){ }+ 2n q(t){ }+ n2 q(t){ } = [ ]

T

F(t){ }

Wind Tunnel TestF(t){ }

L2{ } = diag

1

2LTM Hx

*() T

Gf()

Hx ()

T

LTM T

d0

n

L

{ } = L2{ }meanL + kL{ }

Convert to PSDs

andCross PSDs

Retain TimeDomain

DefinitionL(t){ } = LTMT[ ] [ ] q(t){ }+ LTMV[ ] F(t){ }

L

2{ } =1

TL

2(t){ }dt0

T

mean square

values

root mean square (RMS)or

standard deviation

CourtesyofNASA

mean squarevalues


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Why a Mean Response in a Zero-Mean Process?

Of concern are the peak loads; therefore, we are interested in the statisticaldescription of peaks which have a mean

Envelope function of a stationary, narrow-band Gaussian process describedby Rayleigh probability density function

For broadband, multi-mode peak responses, Rayleigh assumption guaranteesreasonable conservatism

maxx

Rayleigh

Normal

Envelope

Max-Peak

!x(t)

!

2"

fx(x) =

1

2!"e

#x2

2"2

$

%&

'

()

f!x ( !x) = !x

!2e

" !x2

2!2

#

$%

&

'(

x(t)


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Turbulence/Gust Loads

Relatively small-scale, short-duration wind features

Loads analyses performed with fully integrated structural dynamic /aeroelastic / control system simulations - two types of excitation:

Synthetic profiles (e.g., 1-cos individual cases) Turbulence profiles extracted from measured winds (Monte Carlo)

Kabe, A. M., Spiekermann, C. E., Kim, M. C., and Lee, S. S., A Refined and Less Conservative

Day-of-Launch Atmospheric Flight Loads Analysis Approach, Journal of Spacecraft and Rockets,

Vol. 37, No. 4, pp. 453-458 (2000).

= +

Turbulence/Gust!

Aerodynamic!Loading! Turbulence!

Gust!

Control!Forces!

Thrust!

Relati

ve!Win

d!


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Lack of Wind Persistence in Gust Loads Analysis

Spiekermann, C. E., Sako, B. H., and Kabe, A. M., Identifying Slowly Varying and Turbulent

Wind Features for Day-of-Launch Flight Loads Analyses, Journal of Spacecraft and Rockets,

Vol. 37, No. 4, pp. 426-433 (2000).

AverageWavelength(ft.)

Turbulent Region

Slowly Varying Region

0 50 100 150

Lack-of-Wind-Persistence Time T (min.)

8000

6000

4000

2000

0

460 T

Rapidly and slowly varying wind components can be separated The boundary is a function of how far into the future (in minutes) one

wishes to predict

40 80 1200

Wind Magnitude (ft/sec)

40 80 1200


40 80 1200


10

20

30

40

50

Altitude(Kft)

10

20

30

40

50

Altitude(Kft)

10

20

30

40

50

Altitude(Kft)

60 Min 45 Min 30 Min


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Lack of Wind Persistence and Day of Launch Placards

60 min. before launch



Kabe, A. M., Spiekermann, C. E., Kim, M. C., and Lee, S. S., A Refined and Less Conservative

Day-of-Launch Atmospheric Flight Loads Analysis Approach, Journal of Spacecraft and Rockets,

Vol. 37, No. 4, pp. 453-458 (2000).

=! +!

=! +!

=! +!

Increasingturbu

lentcomponents

Increasingpersistentcomponents


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Statistical Distributions of Atmospheric Flight Loads

Turbulence/gust loads Gamma, Gumbel

pBN

(x,y)

!

BN(x,y)

1.0

1

3!

x x

yy

Buffet loads Rayleigh

Lack of wind persistence,other dispersions Bivariate Gaussian

pGB

(x;!,")!

GB(x;",#)

!= "1

#= 0.5

!=1

"= 0.5

!=1, "= 0.75

!=1, "=1

!= 1, "= 1

!=

"1

#= 0.5

!=1, "= 0.75

!=1, "= 0.5

x x


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Monte Carlo Combination of Atmospheric Flight Loads

Sako, B. H., Kabe, A. M., Lee, S. S., Statistical Combination of Time-Varying Loads,

AIAA Journal, Vol. 47, No. 10, October 2009.

!8 sec

Turbulence/Gust

Thrust Oscillation

Buffet

Totalij(t) = G

ij(t)+TO

ij(t)+ B

ij(t)

Gij(t)

TO

ij(t)

B

ij(t)

t t

t

t

i = Load Parameter (1-950)

j = Monte Carlo Run (1-3000)


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Monte Carlo Results Compared to Combination Equations

Sako, B. H., Kabe, A. M., Lee, S. S., Statistical Combination of Time-Varying Loads,

AIAA Journal, Vol. 47, No. 10, October 2009.

RSS G, TO,B( ) = G99/90( )2

+ TO99/90( )2

+ B99/90( )22

CLT G,TO,B( ) = G

Mean+TO

Mean+ B

Mean+ G

99/90G

Mean( )

2

+ TO99/90

TOMean

( )2

+ B99/90

BMean

( )22

ENV G,TO,B( ) = 2G +

2

TO+

2B+ G

99/90

2

G( )2

+ TO99/90

2

TO( )2

+ B99/90

2B( )

22

Underprediction

(Load Combination Equation / Monte Carlo) Ratio Histograms

Percen

tof950

Loads

Ratio

Central LimitEnvelope FunctionRoot Sum Square


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So Why Does an RSS Combination Under Predict ?

Frequency (Hz)

PSD

Re

sponses

Greater Likelihood ofPeaks Adding onto PeaksSynthesized Time Histories from Average PSDs

Time (Sec)

Gust

Gust and TO Average PSDs for a Load Parameter

TOFrequencySeparation


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Ignition and Shutdown Loads

CourtesyofUS

AirForce


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Ignition and Shutdown Dynamic Responses

Variability in ignition and shut-down transients will producevariability in dynamic responses

Expectedpeak positive andpeak negative responses that will occurduring future mission are of most interest

Thrust transients from past flights are samples from large family ofpossible profiles

Therefore, no guarantee that worst transients for a given responseparameter included in current dataset

If measured thrust transients are random samples of possibleexcitation, then an estimate of theprobability density function ofeach response quantity can be generated

Estimates of probability of non-exceedance (enclosure level) can then beobtained

Accuracy depends on number of samples, hence confidence limits mustbe computed


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Significant variability in thrust transients from engine to engine, andflight to flight

Frequency content is different for translation (sum: ) than rotation(difference: )

Engine Ignition and Shutdown Thrust Transients

f

E1

y

f

y

E2

E1 E2( )

E1+ E2( )

Response Spectra for Two Engines on Same Vehicle

E1+ E2

E1 E2


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Small Sample Enclosure and Confidence Levels

(Tolerance Bounds)

p(x)

x

p(x)

x

One thousand

99% enclosure

values

Ten-sampleSimulations

Twenty-sampleSimulations

90% confidence

One thousand

99% enclosure

values

First ten of

one thousand

simulations

First ten of

one thousand

simulations

90% confidence

Since the number of available thrust transients is usually small, wemust account for the small sample size


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Enclosure and Confidence Levels

Closed form solutions exist fornormaland Rayleigh distributions Numerical simulations can be used for other distributions

Example - eight samples, 99% enclosure with 90% confidence (99/90):1 10 100 1 10 100

1

10

1

10

Sample Size n Sample Size n

50%

90%Enclosure

90%

95%

99%

50%

90%

95% 99%

99%Enclosure

Kabe, A. M., Sako, B. H., Structural Dynamics, to be published.

NormalNormal

y99/90

= y + 3.783


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So, When Does 3 Not Equal Three Sigma ?

NormalOne-sided

Upper Tolerance Bound

NormalTwo-sided

Tolerance Interval

Rayleigh

Tolerance Bound

33330.5

Small Sample Size Tolerance Bound Factors for a Sample Size of 11(for 90 and 50 percent confidence levels)

Normal Rayleigh

0.9987 0.9973 0.9889

0.9987 / 90 k= 4.4032

0.9987 / 50 k= 3.1112

0.9973/ 90 k= 4.4772

0.9973/ 50 k= 3.3208

0.9889 / 90 k= 3.7555

0.9889 / 50 k= 3.0465

k


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The Load Cycle Process Structural Qualification


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Structural Qualification and Acceptance

Adequacy of structure defined via design qualification and hardwareacceptance Designs qualifiedto account for part-to-part variability due to assembly

procedures, build-to-build tolerances, and uncertainties in redundant load

paths

Flight hardware acceptedto screen out poor workmanship or preclude ahazardous condition such as a leak in a pressure vessel

Verification requires consideration of all potential failure modes andall potential load conditions

Potential failure modes include: detrimental deformation, material yield,ultimate failure, structural collapse, buckling, fatigue, delamination

Load conditions include: quasi-static and dynamic launch loads, acousticenvironment, pressure, temperature, gravity, handling loads

AIAA S-110-2005, Space Systems Structures, Structural Components, and Structural AssembliesStandard, July 2005.


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Spacecraft Static Strength and Base Shake Tests

Static Strength Testing Flight/flight-like structure (system and component level) subjected toenvelope of: operational loads (including pressure and thermal), load

cycle computed statistical loads, and design requirements

Strains, deflections, and applied loads measured Known margin included (e.g., limit to ultimate, temperature effects)

Base Shake Testing Flight/flight-like structure (less propellants) subjected to unidirectional,

swept sinusoidal base excitation

Sine environment derived from computed launch vehicle/spacecraftinterface responses and/or measured flight responses

Base and system response accelerations measured and used to limittest article responses


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Issues with Base Shake Tests

Spacecraft modes of vibration on a shake table will be different thanwhen coupled to a launch vehicle

Merged launch vehicle/spacecraft modes form coupled system modes Shake tables do not replicate interface impedance of a launch vehicle

Spacecraft dynamic properties on a shake table are not equivalent tothose on seismic mass, which are used in mode survey tests

Data from two systems shows 20% difference in fundamental modefrequencies when measured on shake table vs. fixed to a seismic mass

Properties on shake table are those of the satellite/shake table system Assumption inherent in loads analysis models (Hurty/Craig-Bampton

model) is that modal coordinates (mode shapes) are relative to a fixed/cantilevered interface

Rigid body motion and interface stiffness are accounted for by constraintmodes

Kabe, A. M., Perl, E., Limitations of Base Shake Analysis and Testing of Flight Configured Spacecraft,

12th European Conference on Space Structures, Materials & Environmental Testing, ESA/ESTEC, March 2012.


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Issues with Base Shake Tests (cont.)

Only translational motions are applied at base, one axis at a time Launch vehicle/spacecraft system, however, vibrates simultaneously in all

degrees of freedom during flight

Some spacecraft modes will be difficult, if not impossible, to excitethrough base excitation

For example, to excite fundamental torsional mode requires offset betweenspacecraft center of gravity and shear center that leads to modal gains thatdo not cancel

Coupled launch vehicle/spacecraft vibration is broadband, notsingle frequency sinusoidal, as in base shake tests

Vibration of spacecraft undergoing sinusoidal base shake will be significantlydifferent than in flight

Flight response involves significant, simultaneous vibration in many modesKabe, A. M., Perl, E., Limitations of Base Shake Analysis and Testing of Flight Configured Spacecraft,



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Because of stroke limitations, shake tables are not capable ofinducing steady-state acceleration experienced in flight

Loads must be achieved dynamically, which causes over testing some partsto achieve proper minimum loads elsewhere

Thus, spacecraft must be designed to survive test, in addition to flight

Results in weight penalty and additional cost to spacecraft program

Most internal loads experienced during base shake testing cannot bemeasured and must be established with analytical model

Experience indicates that within the frequency range of base shake testing(up to several hundred Hz), these models are highly uncertain, even when

adjusted to mode survey test data




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Spacecraft test article will most likely not be in flight configuration Might not include actual spacecraft launch vehicle adapter Typically, propellants not included in tanks because of safety and

contamination concerns

This leads to a test article with different dynamic properties relativeto a flight-configured spacecraft Makes it very difficult, if not impossible, to induce proper load levels in

many (most) parts of a spacecraft

Invariably requires supplemental static strength tests




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For operational launch vehicles, base excitation environments derivedfrom flight data

Measured with limited number of accelerometers near launch vehicle/spacecraft interface

Local responses, including warping of interface area, lead toartificially high environments when rigid interface assumption used Can result in an over test of spacecraft

Assumption that measurements are an input at base of spacecraft istechnically not correct

Measurements are those of the response of a coupled system Spacecraft participates in producing the responses




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Impossibility of Inducing Flight-Like Loads in a Base

Shake Test

Coupled launch vehicle/spacecraft responses (e.g. accelerations,loads) to broad band excitation computed

Computed interface accelerations used to establish base excitationper widely used approach

Coupled system responses compared to base excitation results

Tuttle, R. E., Lollock, J. A., Assessment of Base Drive Analysis and Test for Complex Systems,

Spacecraft and Launch Vehicle Dynamic Environments Workshop, The Aerospace Corp., 2012.


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Future Needs


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49

Future Needs

Increased rigor in statistical analysis, with Monte Carlo analysesoffering a way forward Specify enclosure/confidence levels, not number of standard deviations

Increase complex spacecraft mode survey test limits to 75-100 Hz Currently 50-60 Hz

Improved techniques for adjusting analytical models to better matchmode survey test data

Despite progress, its still trial and error

Reduce/eliminate use of base shake tests of large, flight configuredspacecraft Static and subsystem tests offer proven way forward


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In Closing, a Few Photographs


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51

Launch Vehicles

Gemini-Titan II 1965

Cou

rtesyofNASA

First Space Shuttle 1981

Cou

rtesyofNASA


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52

Launch Vehicles

Titan IV

C

ourtesyofULA

Delta IV

Courtesy

ofUS

AirForce


53/55

53

Launch Vehicles

CourtesyofSpaceX

Falcon 9

C

ourtesyofULA

Atlas V


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Earths City Lights

Courtesy of NASA


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