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An Introduction to

Spacecraft Mechanical Loads Analysis

(from preliminary design to final verification)

Adriano Calvi, PhD ESA / ESTEC, Noordwijk, The Netherlands

PART B Liege 16 November 2016

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1. Introduction to the course 2. Spacecraft mechanical environment 3. Structural dynamic analysis for spacecraft 4. Mechanical loads specifications (& introduction to “notching”) 5. Spacecraft structure requirements for design and verification 6. Design Loads Cycles 7. Spacecraft-Launcher Coupled Loads Analysis 8. Spacecraft mechanical testing & verification by test 9. Reduction of overtesting in vibration testing (“notching”) 10. Verification and validation of Finite Element models 11. Final verification & Verification Loads Cycle 12. Conclusions

A. Calvi - Spacecraft Mechanical Loads Analysis - Liege November 2016

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8. Spacecraft mechanical testing & verification by test 8.1 General aspects 8.2 Static loads test 8.3 Sine vibration environment & test 8.4 Modal survey test & experimental modal analysis 8.5 Acoustic noise test & vibroacoustic environment 8.6 Random vibration test 8.7 Shock environment & shock tests


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Testing techniques – Introduction (1)

• Without testing, an analysis can give completely incorrect results • Without the analysis, the tests can represent only a very limited reality

• Two types of tests according to the objectives to be reached:

– Simulation tests for structure qualification or acceptance – Identification tests (a.k.a. analysis-validation tests) for structure

identification (the objective is to determine the dynamic characteristics of the tested structure in order to “update” the mathematical model)

• Note: identification and simulation tests are generally completely dissociated. In certain cases (e.g. spacecraft sine test) it is technically possible to perform them using the same test facility.


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Testing techniques – Introduction (2)

• Generation of mechanical environment – Small shakers (with flexible rod; electrodynamic) – Large shakers (generally used to impose motion at the base)

• Electrodynamic shaker • Hydraulic jack shaker

– Shock machines (pyrotechnic generators and impact machines) – Noise generators + reverberant acoustic chamber (homogeneous and

diffuse field)

• Measurements – Force sensors, calibrated strain gauges – Accelerometers (*), velocity or displacement sensors

(*) accelerometers are often used because they are small and light, and therefore do not affect the response of the structure. In addition, they are easy to mount on the structure, reducing the total measurement time.


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Classes of tests used to verify requirements (purposes)

• Development test – Demonstrate design concepts and acquire necessary information for

design • Qualification test

– Show a design is adequate by testing a single article • Acceptance test

– Show a product is adequate (test each flight article) • Analysis validation test

– Provide data which enable to confirm critical analyses or to change (“update/validate”) mathematical models and redo analyses


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Tests for verifying mechanical requirements (purposes)

• Static loads test – Verify strength for structures that would not be adequately tested in

random vibration or acoustic testing – Verify stiffness

– Note 1: a set of loads at a constant level are applied and maintained – Note 2: test load cases are developed that are as severe as the

combined effects of design limit loads (and, in case, increased by an appropriate factor)

– Note 3: the acquired data can (and should!) be used for improving the structure mathematical model


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Tests for verifying mechanical requirements (purposes) • Sinusoidal vibration test

– Verify strength for structures that would not be adequately tested in random vibration or acoustic testing

– Note 1: cyclic loads at varying frequencies are applied to excite the structure modes of vibration

– Note 2: sinusoidal vibration testing at low levels are performed to verify natural frequencies

– Note 3: the acquired data can be used for further processing (e.g. experimental modal analysis)

– Note 4: this may seem like an environmental test, but it is not. Responses are monitored and input forces are reduced as necessary (“notching”) to make sure the target responses or member loads are not exceeded.


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Tests for verifying mechanical requirements (purposes) • Acoustic test

– Verify strength and structural life by introducing random vibration through acoustic pressure (vibrating air molecules)

– Note: acoustic tests at spacecraft level are used to verify adequacy of electrical connections and validate the random vibration environments used to qualify components

• (Pyrotechnic) shock test – Verify resistance to high-frequency shock waves caused by separation

explosives (introduction of high-energy vibration up to 10,000 Hz) – Note: system-level tests are used to verify levels used for component

testing • Random vibration test

– Verify strength and structural life by introducing random vibration through the mechanical interface (typically up to 2000 Hz )


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Rockot Dynamic Specification

Marketed by: Eurockot

Actually flight qualified

Manufactured by: Khrunichev

Capability: 950 kg @ 500 km

Launch site: Plesetsk

Environment Level

Sine vibration Longitudinal= 1 g on [5-10] Hz 1.5 g at 20 Hz 1 g on [40-100] Hz

Lateral = 0.625 g on [5-100] Hz

Acoustic

31.5 Hz = 130.5 dB 63 Hz = 133.5 dB 125 Hz = 135.5 dB 250 Hz = 135.7 dB

500 Hz = 130.8 dB 1000 Hz = 126.4 dB 2000 Hz = 120.3 dB

Shock 100 Hz = 50 g 700 Hz = 800 g 1000 Hz ® 1500 Hz = 2000 g

4000 Hz ® 5000 Hz = 4000 g 10000 Hz = 2000 g


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Example: Arrangement for a Static Test


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Static load test – Example of protoflight logic


Similarity?

OK!

MoS > 0 ?

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Sentinel 3 – Static load test


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Sine vibration environment

• Swept sinusoidal testing is the most commonly used test to simulate a low-frequency launch environment because of its simplicity in specification and testing

• In the test, sinusoidal vibrations are applied sequentially at the base of the spacecraft along the three principal axes

• Sinusoidal testing results in higher loads at the spacecraft resonant frequencies and they are highly dependent on structural damping in comparison with transient environment

• The (primary) notching in sinusoidal testing eliminates overtesting of primary structure, but may result in under-testing of the other structures

• The most important problem related to transient testing is the dependence of the test specification on possible variations of launch vehicle and spacecraft dynamic characteristics


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Ariane 5 - Sine excitation at spacecraft base (sine-equivalent dynamics)


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Diagram of Electrodynamic Vibration Test System


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Sine vibration for different launchers (longitudinal)


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Sine vibration for different launchers (lateral)


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Test Set-up for Vibration Tests


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Herschel on Hydra


Dynamic amplification factors vs. number of excitation cycles

A. Calvi - Spacecraft Mechanical Loads Analysis - Liege November 2016 23

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The effects of the sine sweep rate on the structural response

• The acceleration enforced by the shaker is a swept frequency function • The sweep is amplitude modulated • Acceleration transient response can be significantly lower that the steady-state

frequency response

2 oct/min


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Effect of sweep rate on isolated peak for increasing and decreasing frequency sweeps

The sweep rate V has 3 effects:

• a variation (sign of V) of the frequency of the peak: Δf

• A decrease of the peak amplitude: ΔA

• An increase of the peak width (with loss of symmetry): Δζ


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Sine-burst load test

• The sine-burst test is used to apply a quasi-static load to a test item in order to strength qualify the item and its design for flight

• A secondary objective is to minimize potential fatigue damage to the test item

• For components and subsystems, the fixture used for vibration testing often can also be used for sine-burst strength testing. For this reason, strength qualification and random vibration qualification can often be performed during the same test session which saves time and money

• Since the test is intended to impart a quasi-static load to the test item, the test frequency “must be” (in principle) below the fundamental resonant frequency of the test item

• The sine-burst test is a cost effective alternative to either static loads or to centrifuge testing


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Typical Sine Burst Waveform


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“(Sine) quasi static load test” (sine burst)


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Modal survey test (identification test)

Purpose: provide data for dynamic mathematical model validation Note: the normal modes are the most appropriate dynamic characteristics for the identification of the structure

• Usually performed on structural models (SM or STM) in flight representative configurations

• Modal parameters (natural frequencies, mode shapes, damping, effective masses…) can be determined in two ways:

– by a method with appropriation of modes, sometimes called phase resonance, which consists of successively isolating each mode by an appropriate excitation and measuring its parameters directly

– by a method without appropriation of modes, sometimes called phase separation, which consists of exciting a group of modes whose parameters are then determined by processing the measurements


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Different ways to get modal data from tests

• Hammer test

• Vibration test data analysis

• Dedicated FRF measurement & modal analysis

• Full scale modal survey with mode tuning In

crea

sing

eff

ort

Dat

a co

nsis

tenc

y


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Modal Survey Test vs. Modal Data extracted from the Sine Vibration Test

• Modal Survey:

– requires more effort (financial and time) – provides results with higher quality

• Modal Data from Sine Vibration:

– easy access / no additional test necessary – less quality due to negative effects from vibration

• fixtures / facility tables not indefinitely stiff • higher sweep rate (brings along effects like beating or control instabilities)


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Main phases of a modal test

Test structure


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8.5 Acoustic noise test & vibro-acoustic environment


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Acoustic test (objectives)

• Demonstrate the ability of a specimen to withstand the acoustic environment during launch

• Validation of analytical models

• System level tests verify equipment qualification loads

• Acceptance test for S/C flight models


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Diagram of Typical High Intensity Acoustic Reverberation Room


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Ariane 5 – Acoustic noise spectrum under the fairing


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Acoustic spectra for different launchers


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Random Vibration Test (vs. Acoustic Test) Purpose: verify strength and structural life by introducing random

vibration through the mechanical interface

• Random Vibration – base driven excitation – better suited for Subsystem / Equipment tests – limited for large shaker systems

• Acoustic

– air pressure excitation – better suited for S/C and large Subsystems with low mass / area

density


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Random vibration test with slide table


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Shock test. Objectives and remarks

• Demonstrate the ability of a specimen to withstand the shock loads during launch and operation

• Verify equipment qualification loads during system level tests

• System level shock tests are generally performed with the actual shock generating equipment (e.g. clamp band release)

• or by using of a sophisticated pyro-shock generating system (SHOGUN for ARIANE 5 payloads)


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Shock response spectra for different launchers (spacecraft separation)

Note: for a consistent comparison, data should refer to the same adapter.


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Shock machine (metal-metal pendulum impact machine)


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9. Reduction of overtesting in vibration testing (“notching”)

1. Introduction to overtesting 2. Definitions and objectives 3. Basic principles for notching justification 4. Approaches to alleviate the overtesting problem 5. Criteria for notching justification 6. Recommendations


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GOCE on ESTEC Large Slip Table Herschel on ESTEC Large Slip Table


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Overtesting: an introduction (vibration absorber effect)


Y. Soucy, A. Côté , Canadian Aeronautics and Space Journal, March 2002

Load = Test Item Source = Mounting Structure

Reaction force during the “test” is 12.3 (469/38) times higher than at the coupled system level!

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The overtesting problem (causes) • Difference in boundary conditions (i.e. mechanical impedance of the

“mounting structure”) between test and flight configurations – during a vibration test, the structure is excited with a specified input

acceleration that is the envelope of the flight interface acceleration, despite the amplitude at certain frequencies drops in the flight configuration (there is a feedback from the launcher [“mounting structure”] to the spacecraft [“test item”] in the main modes of the spacecraft)

• The excitation during the flight is not a steady-state sine function and neither a sine sweep but a transient excitation with some cycles in a few significant resonance frequencies

• The objective of notching of the specified input levels is to take into account the real dynamic response for the different flight events. In practice the (primary) notching simulates the antiresonances in the coupled configuration


Mechanical impedance is a measure of how much a structure resists motion when subjected to a harmonic force

Sentinel 3 sine test predicted notching compared to sine-equivalent levels coming from LV/SC CLA – Axial direction


51 A. Calvi - Spacecraft Mechanical Loads Analysis - Liege November 2016

52 A. Calvi - Spacecraft Mechanical Loads Analysis - Liege November 2016

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Notching

ESI (equivalent sine)


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Random vibration test: examples of notching


Notching: definition and objectives • Notching is the reduction of acceleration input levels around

resonant frequencies, to avoid over testing

• “Notching” can be distinguished in “primary notching” and “secondary notching”

• Primary notching is performed to limit the shaker-test specimen interface forces to the target values, normally qualification or acceptance loads. This is basically the same as to limit the equivalent accelerations to the centre of gravity of the test item

• Secondary notching is performed to limit local accelerations with the purpose of protecting equipment, instruments or sub-systems


Justification of primary notching • In sine testing is mainly justified by the fact that:

– the real environment in flight is of transient nature and is simulated on shaker by a sine sweep based on an

– envelope interface levels. – This envelope doesn’t account for the possible reactions of the “test

item” which can produce level reductions in some frequency bands.

• These potential level reductions (with respect to a rigid test item) are due to a high test item dynamic mass at the interface which reduces the effect of the exciting forces according to the Newton’s law. This high dynamic mass is generated by eigenmodes with high effective masses with respect to the interface.


“Phenomenology” of secondary notching

• The secondary notching is related to level reduction on critical areas inside the “test item”.

• In this case, the frequency response function involved is the “test item” dynamic transmissibility between the considered area and the test item interface with the mounting structure, and the unique criterion for mode selection should be based on the modal effective transmissibilities.

• Similar concepts apply to random (primary & secondary) notching


A few equations:


Dynamic amplification

Modal reaction forces

Base (junction) excitation

Dynamic transmissibilities

Response at the observation DOF

Base (junction) excitation

Effective transmissibilities of the modes Dynamic amplification

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10. Verification and validation of Finite Element models

• Definitions & Terminology • Model Verification and Quality Checks • Model Validation • Model Updating Using Design Sensitivity and Optimisation


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Verification and Validation Definitions (ASME Standards Committee: “V & V in Computational Solid Mechanics”)

• Verification (of codes, calculations): Process of determining that a model implementation accurately represents the developer’s conceptual description of the model and the solution to the model

– Math issue: “Solving the equations right”

• Validation: Process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model

– Physics issue: “Solving the right equations”

Note 1: “objective of the validation is to maximise confidence in the predictive capability of the model”

Note 2: “the purpose of the validation is to develop evidence that the model reflects the real world as accurately as necessary to support critical decision making”


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Model verification and quality checks


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Model checks (ECSS-E-ST-32-03C)

a) Model geometry checks for unreduced models b) Elements topology checks for unreduced models c) Rigid body motion checks for reduced and unreduced models d) Static analysis checks for reduced and unreduced models e) Stress free thermo-elastic deformation check for unreduced

models f) Modal analysis checks for reduced and unreduced models g) Reduced model versus non reduced model consistency checks


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Rigid body motion and modal analysis checks

• (Rigid body motion) mass matrix check

• (Rigid body motion) strain energy check

• Residual forces check

• Modal analysis check N “zero Hz” frequencies


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Model Validation. General aspects.


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Validation of Finite Element Models (with emphasis on Structural Dynamics)

“Everyone believes the test data except for the

experimentalist, and no one believes the finite element model except for the analyst”

“All models are wrong, but some are still useful”


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Terminology: Correlation, Updating and Validation • Correlation:

– the process of quantifying the degree of similarity and dissimilarity between two models (e.g. FE analysis vs. test)

• Error Localization: – the process of determining which areas of the model need to be modified

• Updating: – mathematical model improvement using data obtained from an associated

experimental model (it can be “consistent” or “inconsistent”)

• Valid model : – model which predicts the required dynamic behaviour of the subject

structure with an acceptable degree of accuracy, or “correctness”

Personal note: the above, general definition of “valid model” is rather unsatisfactory in the real-life process of validation of spacecraft finite element models. A more realistic target (output) would be to estimate relevant “Model Uncertainty Factors”.


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Some remarks on the validation of “critical analyses”

• Loads analysis is probably the single most influential task in designing a space structure. It is doubly important because it is the basis for static test loads as well as the basis for identifying the target responses and “notching criteria” in sine tests

• A single mistake in the loads analysis can mean that we design and test the structure to the wrong loads

• We must be very confident in our loads analysis, which means we must check the sensitivity of our assumptions and validate the loads analysis that will be the basis of strength analysis and static testing

• It should be noted: – Vibro-acoustic, random and “shock-attenuation” analyses are usually

“less critical” in the sense that we normally use “environmental tests” to verify mechanical requirements

– In principle all mathematical models used for verification by analysis must be validated


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Targets of the correlation (features of interest for quantitative comparison)

Characteristics that most affect the structure response to applied forces

• Natural frequencies • Mode shapes • Modal effective masses • Modal damping • … • Total mass, mass distribution • Centre of Gravity, inertia • Static stiffness • Interface forces • …


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Correlation of mode shapes

• Spacehab FEM coupled to the test rig model & Silhouette


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GOCE modal analysis and survey test


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Cross-Orthogonality Check (COC) and Modal Assurance Criterion (MAC)

• The cross-orthogonality between the analysis and test mode shapes with respect to the mass matrix is given by:

• The MAC between a measured mode and an analytical mode is defined as:

aTm FF MC =

( )as

Tasmr

Tmr

asTmr

rsMACffff

ff2

=

Note: COC and MAC do not give a “useful” measure of the error!


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Columbus: Cross-Orthogonality Check up to 35 Hz (target modes) TEST

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

FEM Err.% [Hz] 13.78 15.80 17.20 23.81 24.23 24.65 25.36 25.59 26.59 27.19 27.53 28.87 30.19 30.55 32.73 33.15 33.86 34.57 35.21 36.16

1 -2.94 13.37 1.00

2 -0.95 15.65 1.00

3 -1.73 16.90 0.99

4 -3.26 23.03 0.93 0.35

5 -1.16 23.95 0.34 0.93

6 -2.00 24.16 0.95

7 -1.98 24.86 0.95 0.27

8 -0.12 25.56 0.86

9 -0.95 26.34 0.22 0.90

10 -2.65 26.47 0.95

11 -0.40 27.42 0.26 0.96

12 -3.65 27.82 0.82 0.27

13 -6.00 28.38 0.46 0.89

15 1.19 30.91 0.26 0.95

17 1.63 33.26 0.94 0.21 0.32

18 - 33.71 0.64 0.34 0.62

19 -4.72 34.45 0.95

20 1.21 34.99 0.57 0.81


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MPLM Modal Correlation A. Calvi - Spacecraft Mechanical Loads Analysis - Liege November 2016

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MPLM Modal Effective Masses (Final Correlation)


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Soho SVM – Cross-Orthogonality Check F.E.M.

1 2 3 4 8 9 10 15 21 26 29 30 31TEST Err. % Freq. Hz 34.83 37.24 44.07 45.19 51.51 52.68 55.46 62.18 70.92 77.99 81.53 82.25 84.42

1 2.87 35.86 0.87 0.462 0.00 37.24 0.47 0.873 4.17 45.99 0.874 4.78 47.46 0.77 0.245 -3.39 49.82 -0.33 0.766 0.96 53.19 0.75 0.227 2.10 56.65 0.79 0.218 58.67 -0.28 -0.35 -0.229 60.24 -0.30 -0.22 0.46 0.4610 3.30 64.30 0.6111 66.40 0.21 0.3212 67.50 0.45 -0.4313 68.73 -0.3814 69.6815 71.6916 72.71 0.37 -0.3317 3.30 73.34 0.21 0.8518 74.7819 75.6320 78.77 -0.2421 82.1222 7.72 84.51 0.7623 5.54 86.31 0.87 -0.2324 7.21 88.64 0.6425 5.45 89.29 -0.33 0.6326 94.4427 97.1528 99.56


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GOCE - MAC and Effective Mass


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Aeolus STM: comparison of transfer functions

Sine test response, FEM predicted response and post-test (updated FEM) response


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Lack of Matching between F.E. Model and Test • Modelling uncertainties and errors (model is not completely physically

representative) – Approximation of boundary conditions – Inadequate modelling of joints and couplings – Lack or inappropriate damping representation – The linear assumption of the model versus test non-linearities – Mistakes (input errors, oversights, etc.)

• Scatter in manufacturing

– Uncertainties in physical properties (geometry, tolerances, material properties)

• Uncertainties and errors in testing – Measured data or parameters contain levels of errors – Uncertainties in the test set-up, input loads, boundary conditions etc. – Mistakes (oversights, cabling errors, etc.)


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Test-Analysis Correlation Criteria The degree of similarity or dissimilarity establishing that the correlation between measured and predicted values is acceptable

ECSS-E-ST-32-11 Proposed Test / Analysis Correlation Criteria


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11. Final Verification and Verification Loads Cycle


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Final Verification

Consist of:

• Making sure all requirements are satisfied (“compliance”)

• Validating the methods and assumptions used to satisfy

requirements

• Assessing risks


Main inconsistencies of the loads verification process - 1 • Uni-axial vibration and shock test facilities while the dynamic

environments for space vehicle hardware are typically multiple-axis. In practice, tests are performed axis by axis.

• Tests are performed environment by environment, even if they occur simultaneously. For this reason loads superposition/combination techniques are applied and the verification of the structural integrity by analysis is normally required to prove the qualification of the spaceflight hardware.

• Low frequency transient often simulated at the subsystem and system assembly level using a swept-sine vibration test, mainly because of its simplicity in specification and testing.


Main inconsistencies of the loads verification process - 2

• “Infinite” mechanical impedance of the shaker and the standard practice of specifying the input acceleration as envelope of the flight interface acceleration (despite the amplitude drop in the flight configuration). This is the major cause of over testing in aerospace vibration tests.

• Vibro-acoustic environment often simulated at the subsystem and units assembly level using a random vibration test.

• Test levels largely based on computational analyses. For this reason it is important to validate critical load analyses.


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Final Verification (crucial aspects)

• To perform a Verification Loads Cycle for structures designed and tested to predicted loads

• To make sure the random-vibration environments used to qualify units/components were high enough (based on data collected during the spacecraft acoustic test)

• To make sure the shock environments used to qualify units/components were high enough (based on data collected during the spacecraft shock test)


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Verification Loads Cycle

• The Verification Loads Cycle for structures designed and tested to predicted loads consists mainly of:

– Finite element models correlation with the results of modal and static testing

– Loads prediction with the current forcing functions – Compliance with analysis criteria (e.g. MOS>0)

• Note: in the verification loads cycle instead of identifying required design changes (as in the design loads cycles) the adequacy of the structure that has already been built and tested is assessed


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Criteria for Assessing Verification Loads (strength)

• Analysis: margins of safety must me greater than or equal to zero • Test: Structures qualified by static or sinusoidal testing

– Test loads or stresses “as predicted” (test-verified math model and test conditions) are compared with the total predicted loads during the mission (including flying transients, acoustics, random vibration, pressure, thermal effects and preloads)

• Test: Structures qualified by acoustic or random vibration testing – Test environments are compared with random-vibration environments

derived from system-level acoustic testing • Test: Structures qualified by acoustic or random vibration testing

– Test environments are compared with shock environments derived from system-level shock testing


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Random vibration test: data-processing bandwidth

• The figures show how the data-processing bandwidth can affect a calculated power spectral density. Whether a PSD satisfies criteria for level and tolerance depends on the frequency bandwidth used to process the measured acceleration time history.


Compliance: specific approaches for random vibration

• Peaks clipping – commonly used rule is that all narrowband spectral peaks should be

clipped by 3 dB

• Data-processing bandwidth – to compute the spectra with a resolution bandwidth that is

proportional to frequency, e.g., a 1/6 octave bandwidth

• Random Response Spectrum (Vibration Response Spectrum) – SRS approach applied to random vibration

Note: the criteria applied to show compliance are similar to the ones used to generate the random vibration specifications


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12. Conclusions


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1. Introduction to the course 2. Spacecraft mechanical environment 3. Structural dynamic analysis for spacecraft 4. Mechanical loads specifications (& introduction to “notching”) 5. Spacecraft structure requirements for design and verification 6. Design Loads Cycles 7. Spacecraft-Launcher Coupled Loads Analysis 8. Spacecraft mechanical testing & verification by test 9. Reduction of overtesting in vibration testing (“notching”) 10. Verification and validation of Finite Element models 11. Final verification & Verification Loads Cycle 12. Conclusions


From NASA-HDBK-7008…

Spacecraft designers often complain that they must design to pass a test, rather than to survive the flight environment. This problem is exacerbated by the fact that the test levels are typically more severe and of longer duration than the flight environment, both intentionally (test margin) and unintentionally (test artifacts). The overtesting resulting from artifacts (frequency enveloping, shaker impedance, fixture resonances, tolerances, overshoot, etc.) are often justified by the environmental engineer as being conservative. However, from the designer's point of view, overtesting is unconservative. Therefore, it is good practice to periodically compare the test simulations with actual flight data to ensure that the "conservatisms" that invariably creep into test specifications do not become excessive.


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Bibliography • Sarafin T.P. Spacecraft Structures and Mechanisms, Kluwer, 1995 • Craig R.R., Structural Dynamics – An introduction to computer methods, J. Wiley

and Sons, 1981 • Clough R.W., Penzien J., Dynamics of Structures, McGraw-Hill, 1993 • Ewins D.J., Modal Testing – Theory, practice and applications, Research Studies

Press, Second Edition, 2000 • Wijker J., Mechanical Vibrations in Spacecraft Design, Springer, 2004 • Girard A., Roy N., Structural Dynamics in Industry, J. Wiley and Sons, 2008 • Steinberg D.S., Vibration Analysis for Electronic Equipment, J. Wiley and Sons,

2000 • Friswell M.I., Mottershead J.E., Finite Element Model Updating in Structural

Dynamics, Kluwer 1995 • Ariane 5 User’s Manual, Arianespace, http://www.arianespace.com/


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Bibliography - ECSS Documents • ECSS-E-HB-32-26 Spacecraft Mechanical Loads Analysis • ECSS-E-ST-32 Space Project Engineering - Structural • ECSS-E-ST-32-03 Structural finite element models • ECSS-E-ST-32-10 Structural factors of safety for spaceflight

hardware • ECSS-E-ST-32-02 Structural design and verification of

pressurized hardware • ECSS-E-ST-32-11 Modal survey assessment • ECSS-E-ST-32-01 Fracture control

• ECSS-E-ST-10-02 Space Engineering - Verification • ECSS-E-ST-10-03 Space Engineering - Testing


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THE END! Acknowledgements: TAS France for the data concerning the project SENTINEL-3 ALENIA SPAZIO and TAS Italy for the data concerning the projects EUCLID,

GOCE, COLUMBUS, MPLM and SOHO EADS ASTRIUM, UK, for the data concerning the project AEOLUS and

EarthCARE ESA/ESTEC, Structures Section, NL, for the data concerning ARIANE 5 FE

model and LV/SC CLA
