Spacecraft Loads Analysis - PDF Free Download

Spacecraft Loads Analysis An Overview Adriano Calvi, PhD ESA / ESTEC, Noordwijk, The Netherlands This presentation is distributed to the students of the University of Liege Satellite Engineering Class November 21, 2011 This presentation is not for further distribution Spacecraft Loads Analysis - A. Calvi 1

Spacecraft Loads Analysis - Contents 1. Introduction and general aspects 2. Mechanical environment 3. Requirements for spacecraft structures 4. Mathematical models and structural analyses 5. Spacecraft mechanical testing 6. Mathematical models validation 7. Conclusions Spacecraft Loads Analysis - A. Calvi 2

Example of satellite structural design concept Spacecraft Loads Analysis - A. Calvi 3

What is Loads Analysis The task of loads analysis Loads analysis substantially means establishing appropriate loads for design and testing. The goal or purpose of loads analysis Nearly always to support design or to verify requirements for designed or built hardware. Spacecraft Loads Analysis - A. Calvi 4

Spacecraft loads analysis process disciplines Legal aspects Requirements, contracts Philosophical aspects General logic, verification approach, criteria Physics Structural dynamics, validation of mathematical models, criteria Mathematics Computational models, verification of models It is 3 years that I work in this company. Now, finally I have understood what I do, but still I have to understand why. Spacecraft Loads Analysis - A. Calvi 5

Organizations and Levels of Assembly an example Launcher Authority Spacecraft Authority Spacecraft Prime Contractor Payload Contractor Other Contactors Spacecraft + launcher Spacecraft Spacecraft Instruments/sub-systems Units/components/parts Spacecraft Loads Analysis - A. Calvi 6

Levels of Assembly RPM RFFE Spacecraft Loads Analysis - A. Calvi 7

Design Loads Cycles A load cycle is the process of: Generating and combining math models for a proposed design Assembling and developing forcing functions, load factors, etc. to simulate the critical loading environment Calculating design loads and displacements for all significant ground, launch and mission events Assessing the results to identify design modifications or risks Then, if necessary, modifying the design accordingly or choosing to accept the risk Spacecraft Loads Analysis - A. Calvi 8

Design loads cycle process Spacecraft Loads Analysis - A. Calvi 9

Loads and Factors ECSS E-ST-32-10 Satellites Test Logic Common Design Logic Expendable launch vehicles, pressurized hardware and manned system Test Logic Limit Loads - LL Increasing Load Level x KQ QL x KA AL x Coef. A Design Limit Loads DLL x Coef. B x Coef. C x KQ x KA DYL DUL AL QL Protoflight Prototype Spacecraft Loads Analysis - A. Calvi 10

2. Mechanical environment Spacecraft Loads Analysis - A. Calvi 11

Mechanical loads are caused by: Transportation Rocket Motor Ignition Overpressure Lift-off Loads Engine/Motor Generated Acoustic Loads Engine/Motor Generated Structure-borne Vibration Loads Engine/Motor Thrust Transients Pogo Instability, Solid Motor Pressure Oscillations Wind and Turbulence, Aerodynamic Sources Liquid Sloshing in Tanks Stage and Fairing Separation Loads Pyrotechnic Induced Loads Manoeuvring Loads Flight Operations, Onboard Equipment Operation Spacecraft Loads Analysis - A. Calvi 12

Accelerations some remarks The parameter most commonly used (in the industry) to define the motion of a mechanical system is the acceleration Good reasons: accelerations are directly related to forces/stresses and easy to specify and measure In practice accelerations are used as a measure of the severity of the mechanical environment Some hidden assumptions Criteria for equivalent structural damage (e.g. shock response spectra) Note: failures usually happen in the largest stress areas, regardless if they are the largest acceleration areas! Rigid or static determinate junction (e.g. quasi-static loads) Important consequences Need for considering the actual (e.g. test or flight ) boundary conditions (e.g. for the purpose of notching ) Need for a valid F.E. model (e.g. to be used for force and stress recovery) Spacecraft Loads Analysis - A. Calvi 13

Launch mechanical environment Steady state accelerations Low frequency vibrations Broad band vibrations Random vibrations Acoustic loads Shocks Loads (vibrations) are transmitted to the payload (e.g. satellite) through its mechanical interface Acoustic loads also directly excite payload surfaces Spacecraft Loads Analysis - A. Calvi 14

Steady-state and low-frequency transient accelerations Spacecraft Loads Analysis - A. Calvi 15

Acoustic Loads During the lift off and the early phases of the launch an extremely high level of acoustic noise surrounds the payload The principal sources of noise are: Engine functioning Aerodynamic turbulence Acoustic noise (as pressure waves) impinging on light weight panel-like structures produce high response Spacecraft Loads Analysis - A. Calvi 16

Broadband and high frequency vibrations Broad band random vibrations are produce by: Engines functioning Structural response to broad-band acoustic loads Aerodynamic turbulent boundary layer Spacecraft Loads Analysis - A. Calvi 17

Shocks Mainly caused by the actuation of pyrotechnic devices: Release mechanisms for stage and satellite separation Deployable mechanisms for solar arrays etc. Spacecraft Loads Analysis - A. Calvi 18

Shocks [g] [g] Time [t] Frequency [Hz] Spacecraft Loads Analysis - A. Calvi 19

Static and dynamic environment specification (typical ranges) Spacecraft Loads Analysis - A. Calvi 20

Static and dynamic environment specification (typical ranges) Spacecraft Loads Analysis - A. Calvi 21

Quasi-Static Loads (accelerations) Loads independent of time or which vary slowly, so that the dynamic response of the structure is not significant (ECSS-E-ST-32). Note: this is the definition of a quasi-static event! Combination of static and low frequency loads into an equivalent static load specified for design purposes as C.o.G. acceleration (e.g. NASA RP- 1403, NASA-HDBK-7004). Note: this definition is fully adequate for the design of the spacecraft primary structure. For the design of components the contribution of the high frequency loads, if relevant, is included as well! CONCLUSION: quasi static loading means under steady-state accelerations (unchanging applied force balanced by inertia loads). For design purposes (e.g. derivation of design limit loads, selection of the fasteners, etc.), the quasi-static loads are normally calculated by combining both static and dynamic load contributions. In this context the quasi static loads are equivalent to (or interpreted by the designer as) static loads, typically expressed as equivalent accelerations at the C.o.G. Spacecraft Loads Analysis - A. Calvi 22

3. Requirements for spacecraft structures Spacecraft Loads Analysis - A. Calvi 23

Typical Requirements for Spacecraft Structures Strength Structural life Structural response Stiffness Damping Mass Properties Dynamic Envelope Positional Stability Mechanical Interface Basic requirement: the structure shall support the payload and spacecraft subsystems with enough strength and stiffness to preclude any failure (rupture, collapse, or detrimental deformation) that may keep them from working successfully. Spacecraft Loads Analysis - A. Calvi 24

Requirements evolution Spacecraft Loads Analysis - A. Calvi 25

Some definitions Design: The process used to generate the set information describing the essential characteristics of a product (ECSS-P-001A) Design means developing requirements, identifying options, doing analyses and trade studies, and defining a product in enough detail so it can be built (T. P. Sarafin) Verification: Confirmation by examination and provision of objective evidence that specified requirements have been fulfilled (ISO 8402:1994) Verification means providing confidence through disciplined steps that a product will do what it is supposed to do (T. P. Sarafin) Note: we can prove that the spacecraft satisfies the measurable criteria we have defined, but we cannot prove a space mission will be successful Spacecraft Loads Analysis - A. Calvi 26

Design requirements and verification Spacecraft Loads Analysis - A. Calvi 27

Examples of (Mechanical) Requirements (1) The satellite shall be compatible with 2 launchers (potential candidates: VEGA, Soyuz in CSG, Rockot, Dnepr)... The satellite and all its units shall withstand applied loads due to the mechanical environments to which they are exposed during the service-life Design Loads shall be derived by multiplication of the Limit Loads by a design factor equal to 1.25 (i.e. DL= 1.25 x LL) The structure shall withstand the worst design loads without failing or exhibiting permanent deformations. Buckling is not allowed. The natural frequencies of the structure shall be within adequate bandwidths to prevent dynamic coupling with major excitation frequencies The spacecraft structure shall provide the mounting interface to the launch vehicle and comply with the launcher interface requirements. Spacecraft Loads Analysis - A. Calvi 28

Examples of (Mechanical) Requirements (2) All the Finite Element Models (FEM) prepared to support the mechanical verification activities at subsystem and satellite level shall be delivered in NASTRAN format The FEM of the spacecraft in its launch configuration shall be detailed enough to ensure an appropriate derivation and verification of the design loads and of the modal response of the various structural elements of the satellite up to 140 Hz A reduced FEM of the entire spacecraft correlated with the detailed FEM shall be delivered for the Launcher Coupled Loads Analysis (CLA) The satellite FEMs shall be correlated against the results of modal survey tests carried out at complete spacecraft level, and at component level for units above 50 kg The structural model of the satellite shall pass successfully qualification sine vibration Test. The flight satellite shall pass successfully acceptance sine vibration test. Spacecraft Loads Analysis - A. Calvi 29

Spacecraft stiffness requirements for different launchers Launch vehicle manuals specify minimum values for the payload natural (fundamental) frequency of vibration in order to avoid dynamic coupling between low frequency dynamics of the launch vehicle and payload modes Spacecraft Loads Analysis - A. Calvi 30

4. Mathematical models and structural analyses 4.1 Dynamic analysis types - Overview 4.2 Effective mass concept 4.3 Launcher/Spacecraft coupled loads analysis Spacecraft Loads Analysis - A. Calvi 31

Dynamic analysis types Real eigenvalue analysis (undamped free vibrations) Modal parameter identification, etc. Linear frequency response analysis (steady-state response of linear structures to loads that vary as a function of frequency) Sine test prediction, transfer functions calculation, LV/SC CLA etc. Linear transient response analysis (response of linear structures to loads that vary as a function of time). LV/SC CLA, base drive analysis, jitter analysis, etc. Shock response spectrum analysis Specification of equivalent environments (e.g. equivalent sine input), Shock test specifications, etc. Vibro-acoustics (FEM/BEM, SEA) & Random vibration analysis Vibro-acoustic test prediction & random vibration environment definition Loads analysis for base-driven random vibration Spacecraft Loads Analysis - A. Calvi 32

Reasons to compute normal modes (real eigenvalue analysis) To verify stiffness requirements To assess the dynamic interaction between a component and its supporting structure To guide experiments (e.g. modal survey test) To validate computational models (e.g. test/analysis correlation) As pre-requisite for subsequent dynamic analyses To evaluate design changes Mathematical model quality check (model verification) Numerical methods: Lanczos, Spacecraft Loads Analysis - A. Calvi 33

Real eigenvalue analysis Note: mode shape normalization Scaling is arbitrary Convention: Mass, Max or Point Spacecraft Loads Analysis - A. Calvi 34

Mode shapes Cantilever beam Simply supported beam Spacecraft Loads Analysis - A. Calvi 35

Satellite Normal Modes Analysis Mode 1: 16.2 Hz Mode 2: 18.3 Hz INTEGRAL Satellite (FEM size 120000 DOF s) Spacecraft Loads Analysis - A. Calvi 36

Frequency Response Analysis Used to compute structural response to steady-state harmonic excitation The excitation is explicitly defined in the frequency domain Forces can be in the form of applied forces and/or enforced motions Two different numerical methods: direct and modal Damped forced vibration equation of motion with harmonic excitation: Spacecraft Loads Analysis - A. Calvi 37

Frequency response considerations If the maximum excitation frequency is much less than the lowest resonant frequency of the system, a static analysis is probably sufficient Undamped or very lightly damped structures exhibit large dynamic responses for excitation frequencies near natural frequencies (resonant frequencies) Use a fine enough frequency step size (Δf) to adequately predict peak response. Smaller frequency spacing should be used in regions near resonant frequencies, and larger frequency step sizes should be used in regions away from resonant frequencies Spacecraft Loads Analysis - A. Calvi 38

Harmonic forced response with damping Spacecraft Loads Analysis - A. Calvi 39

Transient Response Analysis Purpose is to compute the behaviour of a structure subjected to timevarying excitation The transient excitation is explicitly defined in the time domain Forces can be in the form of applied forces and/or enforced motions The important results obtained from a transient analysis are typically displacements, velocities, and accelerations of grid points, and forces and stresses in elements Two different numerical methods: direct (e.g. Newmark) and modal (e.g. Lanczos + Duhamel s integral or Newmark) Dynamic equation of motion: Spacecraft Loads Analysis - A. Calvi 40

Modal Transient Response Analysis Spacecraft Loads Analysis - A. Calvi 41

Transient response considerations The integration time step must be small enough to represent accurately the variation in the loading The integration time step must also be small enough to represent the maximum frequency of interest ( cut-off frequency ) The cost of integration is directly proportional to the number of time steps Very sharp spikes in a loading function induce a high-frequency transient response. If the high-frequency transient response is of primary importance in an analysis, a very small integration time step must be used The loading function must accurately describe the spatial and temporal distribution of the dynamic load Spacecraft Loads Analysis - A. Calvi 42

Shock response spectrum (and analysis) Response spectrum analysis is an approximate method of computing the peak response of a transient excitation applied to a structure or component There are two parts to response spectrum analysis: (1) generation of the spectrum and (2) use of the spectrum for dynamic response such as stress analysis Note 1: the part (2) of the response spectrum analysis has a limited use in structural dynamics of spacecraft (e.g. preliminary design) since the accuracy of the method may be questionable Note 2: the term shock can be misleading (not always a physical shock, i.e. an environment of a short duration, is involved. It would be better to use response spectrum ) Spacecraft Loads Analysis - A. Calvi 43

Generation of a response spectrum (1) Spacecraft Loads Analysis - A. Calvi 44

Generation of a response spectrum (2) the peak response for one oscillator does not necessarily occur at the same time as the peak response for another oscillator there is no phase information since only the magnitude of peak response is computed It is assumed in this process that each oscillator mass is very small relative to the base structural mass so that the oscillator does not influence the dynamic behaviour of the base structure Spacecraft Loads Analysis - A. Calvi 45

Shock Response Spectrum. Some remarks The 1-DOF system is used as reference structure (since the simplest) for the characterization of environments (i.e. quantification of the severity equivalent environments can be specified) In practice, the criterion used for the severity is the maximum response which occurs on the structure (note: another criterion relates to the concept of fatigue damage ) A risk in comparing two excitations of different nature is in the influence of damping on the results (e.g. maxima are proportional to Q for sine excitation and variable for transient excitation!) The absolute acceleration spectrum is used, which provides information about the maximum internal forces and stresses The shock spectrum is a transformation of the time history which is not reversible (contrary to Fourier transform) Spacecraft Loads Analysis - A. Calvi 46

Shock Response Spectrum (A) is the shock spectrum of a terminal peak sawtooth (B) of 500 G peak amplitude and 0.4 millisecond duration Spacecraft Loads Analysis - A. Calvi 47

Random vibration (analysis) Random vibration is vibration that can be described only in a statistical sense The instantaneous magnitude is not known at any given time; rather, the magnitude is expressed in terms of its statistical properties (such as mean value, standard deviation, and probability of exceeding a certain value) Examples of random vibration include earthquake ground motion, wind pressure fluctuations on aircraft, and acoustic excitation due to rocket and jet engine noise These random excitations are usually described in terms of a power spectral density (PSD) function Note: in structural dynamics of spacecraft, the random vibration analysis is often performed with simplified techniques (e.g. based on Miles equation + effective modal mass models) Spacecraft Loads Analysis - A. Calvi 48

Random noise with normal amplitude distribution Spacecraft Loads Analysis - A. Calvi 49

Power Spectral Density (conceptual model) Spacecraft Loads Analysis - A. Calvi 50

Sound Pressure Level (conceptual model) Spacecraft Loads Analysis - A. Calvi 51

Vibro acoustic analysis at spacecraft level Detailed analysis using Finite Elements (FE), Boundary Elements (BEM) and Statistical Energy Analysis (SEA) Random levels on units and instruments can be compared to specifications or qualification levels Spacecraft Loads Analysis - A. Calvi 52

4. Mathematical models and structural analyses 4.1 Dynamic analysis types - Overview 4.2 Effective mass concept 4.3 Launcher/Spacecraft coupled loads analysis Spacecraft Loads Analysis - A. Calvi 53

Modal effective mass (1) It may be defined as the mass terms in a modal expansion of the drive point apparent mass of a kinematically supported system Note: driving-point FRF: the DOF response is the same as the excitation This concept applies to structure with base excitation Important particular case: rigid or statically determinate junction It provides an estimate of the participation of a vibration mode, in terms of the load it will cause in the structure, when excited Note: avoid using: it is the mass which participates to the mode! Modal reaction forces Dynamic amplification factor Base (junction) excitation Spacecraft Loads Analysis - A. Calvi 54

Modal effective mass (2) Effective mass Modal participation factors Resultant of modal interface forces Gen. mass i-th mode Rigid body modes Eigenvector max value The effective mass matrix can be calculated either by the modal participation factors or by using the modal interface forces Normally only the values on the leading diagonal of the modal effective mass matrix are considered and expressed in percentage of the structure rigid body properties (total mass and second moments of inertia) The effective mass characterises the mode and it is independent from the eigenvector normalisation Spacecraft Loads Analysis - A. Calvi 55

Modal effective mass (3) For the complete set of modes the summation of the modal effective mass is equal to the rigid body mass Contributions of each individual mode to the total effective mass can be used as a criterion to classify the modes (global or local) and an indicator of the importance of that mode, i.e. an indication of the magnitude of participation in the loads analysis It can be used to construct a list of important modes for the test/analysis correlation and it is a significant correlation parameter It can be used to create simplified mathematical models (equivalent models with respect to the junction) Spacecraft Loads Analysis - A. Calvi 56

Example of Effective Mass table (MPLM test and FE model) Spacecraft Loads Analysis - A. Calvi 57

4. Mathematical models and structural analyses 4.1 Dynamic analysis types - Overview 4.2 Effective mass concept 4.3 Launcher/Spacecraft coupled loads analysis Spacecraft Loads Analysis - A. Calvi 58

A5 Typical Sequence of events Spacecraft Loads Analysis - A. Calvi 59

A5 Typical Longitudinal Static Acceleration Spacecraft Loads Analysis - A. Calvi 60

Sources of Structural Loadings (Launch) g 8 7 6 5 4 3 2 1 acceleration [m/s 2 ] 80 70 60 50 40 30 20 10 0-10 -20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t [s] 0 0 50 100 150 200 250 300 t, s Axial-Acceleration Profile for the Rockot Launch Vehicle Spacecraft Loads Analysis - A. Calvi 61

80 70 60 50 acceleration [m/s 2 ] 40 30 20 10 0-10 -20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t [s] Axial Acceleration at Launcher/Satellite Interface (Engines Cut-off) Spacecraft Loads Analysis - A. Calvi 62

Load Factors for Preliminary Design (Ariane 5) Spacecraft Loads Analysis - A. Calvi 63

Quasi-Static Flight Limit loads for Dnepr and Soyuz Spacecraft Loads Analysis - A. Calvi 64

Launcher / Satellite C.L.A. A5 / Satellite Recovered System Mode shapes CLA: simulation of the structural response to low frequency mechanical environment Main Objective: to calculate the loads on the satellite caused by the launch transients (liftoff, transonic, aerodynamic gust, separation of SRBs ) Loads (in this context): set of internal forces, displacements and accelerations that characterise structural response to the applied forces Effects included in the forcing functions : thrust built-up, engine shut-down/burnout, gravity, aerodynamic loads (gust), separation of boosters, etc. Mode 18: 2.93 Hz Mode 53: 16.9 Hz Spacecraft Loads Analysis - A. Calvi 65

UPPER COMPOSITE Ariane-5 Dynamic Mathematical Model PAYLOAD Dynamic effects up to about 100 Hz 3D FE models of EPC, EAP, UC Dynamic Reduction using Craig-Bampton formulation Incompressible or compressible fluids models for liquid propellants Structure/fluid interaction Nearly incompressible SRB solid propellant modeling Pressure and stress effects on launcher stiffness SRB propellant and DIAS structural damping Non-linear launch table effects EAP- EAP+ Spacecraft Loads Analysis - A. Calvi 66 EPC

Sizing flight events (CLA with VEGA Launcher) 6. Z9 Ignition 5. Z23 Pressure Oscillations 4. Z23 Ignition 3. P80 Pressure Oscillations 2. Mach1/QMAX Gust 1. Lift-off (P80 Ignition and Blastwave) Spacecraft Loads Analysis - A. Calvi 67

CLA Output LV-SC interface accelerations Equivalent sine spectrum LV-SC interface forces Equivalent accelerations at CoG Internal responses Accelerations, Displacements Forces Stresses Spacecraft Loads Analysis - A. Calvi 68

Payload / STS CLA Lift-off Main Fitting I/F Force X Dir. [N] Lift-off Main Fitting I/F Force Z Dir. [N] Lift-off Force Resultant in X [lbf] Lift-off Keel Fitting I/F Force Y Dir. [N] Spacecraft Loads Analysis - A. Calvi 69

Shock Response Spectrum and Equivalent Sine Input A shock response spectrum is a plot of maximum response (e.g. displacement, stress, acceleration) of single degree-of-freedom (SDOF) systems to a given input versus some system parameter, generally the undamped natural frequency. Spacecraft Loads Analysis - A. Calvi 70

SRS/ESI of the following transient acceleration: ESI SRS Q ESI ESI Spacecraft Loads Analysis - A. Calvi 71

ESI for Spacecraft CLA (Coupled Load Analysis) Difference is negligible for small damping ratios 250 SRS SRS [m/s 2 ] 200 150 100 SRS ESI ESI SRS Q SRS Q 2 1 50 ESI 0 0 10 20 30 40 50 60 70 80 frequency [Hz] Spacecraft Loads Analysis - A. Calvi 72

[ m / s ] SDOF 0.01 natural frequency 23Hz [ m/ s 2.41 2DOF Transient response Transient response [s] [s] [ m/ s ] 0. natural frequency 23 Hz 1.97 01 [ m/ s ] 2.46 Frequency response at ESI level Frequency response at ESI level Spacecraft Loads Analysis - A. Calvi 73 [Hz [Hz

5. Spacecraft testing 5.1 Introduction and general aspects 5.1 Mechanical tests Modal survey test Sinusoidal vibration test Acoustic noise test Shock test Random vibration test 5.2 Over-testing and under-testing Spacecraft Loads Analysis - A. Calvi 74

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 Spacecraft Loads Analysis - A. Calvi 75

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 Spacecraft Loads Analysis - A. Calvi 76

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 Spacecraft Loads Analysis - A. Calvi 77

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) 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 ) Spacecraft Loads Analysis - A. Calvi 78

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. Spacecraft Loads Analysis - A. Calvi 79

Marketed by: Eurockot Actually flight qualified Environment Manufactured by: Khrunichev Capability: 950 kg @ 500 km Level Launch site: Plesetsk Sine vibration Acoustic Shock Longitudinal= 1 g on [5-10] Hz 1.5 g at 20 Hz 1 g on [40-100] Hz 31.5 Hz = 130.5 db 63 Hz = 133.5 db 125 Hz = 135.5 db 250 Hz = 135.7 db 100 Hz = 50 g 700 Hz = 800 g 1000 Hz 1500 Hz = 2000 g Lateral = 0.625 g on [5-100] Hz 500 Hz = 130.8 db 1000 Hz = 126.4 db 2000 Hz = 120.3 db 4000 Hz 5000 Hz = 4000 g 10000 Hz = 2000 g Rockot Dynamic Specification Spacecraft Loads Analysis - A. Calvi 80

5. Spacecraft testing 5.1 Introduction and general aspects 5.2 Mechanical tests Modal survey test Sinusoidal vibration test Acoustic noise test Shock test Random vibration test 5.3 Over-testing and under-testing Spacecraft Loads Analysis - A. Calvi 81

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 Spacecraft Loads Analysis - A. Calvi 82

Different ways to get modal data from tests Increasing effort Data consistency Hammer test Vibration test data analysis Dedicated FRF measurement & modal analysis Full scale modal survey with mode tuning Spacecraft Loads Analysis - A. Calvi 83

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) Spacecraft Loads Analysis - A. Calvi 84

Ariane 5 - Sine excitation at spacecraft base (sine-equivalent( dynamics) Spacecraft Loads Analysis - A. Calvi 85

Test Set-up for Satellite Vibration Tests Spacecraft Loads Analysis - A. Calvi 86

Herschel on Hydra Spacecraft Loads Analysis - A. Calvi 87

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 Spacecraft Loads Analysis - A. Calvi 88

Ariane 5 Acoustic noise spectrum under the fairing Spacecraft Loads Analysis - A. Calvi 89

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 pyroshock generating system (SHOGUN for ARIANE 5 payloads) Spacecraft Loads Analysis - A. Calvi 90

Shock machine (metal-metal pendulum impact machine) Spacecraft Loads Analysis - A. Calvi 91

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 Spacecraft Loads Analysis - A. Calvi 92

Random vibration test with slide table Spacecraft Loads Analysis - A. Calvi 93

Overtesting: an introduction (vibration absorber effect) Spacecraft Loads Analysis - A. Calvi 95

Introduction to overtesting and notching The qualification of the satellite to low frequency transient is normally achieved by a base-shake test The input spectrum specifies the acceleration input that should excite the satellite, for each axis This input is definitively different from the mission loads, which are transient Notching: Reduction of acceleration input spectrum in narrow frequency bands, usually where test item has resonances (NASA-HDBK-7004) Spacecraft Loads Analysis - A. Calvi 96

GOCE on ESTEC Large Slip Table Herschel on ESTEC Large Slip Table Spacecraft Loads Analysis - A. Calvi 97

The overtesting problem (causes) Difference in boundary conditions 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 to the spacecraft 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 notching simulates the antiresonances in the coupled configuration Spacecraft Loads Analysis - A. Calvi 98

Notching ESI (equivalent sine) Spacecraft Loads Analysis - A. Calvi 99

Spacecraft Loads Analysis - A. Calvi 100

Spacecraft Loads Analysis - A. Calvi 101

Random vibration test: notching of test specification Illustration of notching of random vibration test specification, at the frequencies of strong test item resonances Spacecraft Loads Analysis - A. Calvi 102

6. Mathematical models validation Spacecraft Loads Analysis - A. Calvi 103

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 Spacecraft Loads Analysis - A. Calvi 104

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: objective of the validation is to maximise confidence in the predictive capability of the model Spacecraft Loads Analysis - A. Calvi 105

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 Spacecraft Loads Analysis - A. Calvi 106

Some remarks on the validation of critical analyses Loads analysis is probably the single most influential task in designing a space structure Loads analysis 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 Note: Vibro-acoustic, random and shock analyses are usually not critical in the sense that we normally use environmental tests to verify mechanical requirements Spacecraft Loads Analysis - A. Calvi 107

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 Spacecraft Loads Analysis - A. Calvi 108

Correlation of mode shapes Spacehab FEM coupled to the test rig model & Silhouette Spacecraft Loads Analysis - A. Calvi 109

GOCE modal analysis and survey test Spacecraft Loads Analysis - A. Calvi 110

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: T m C M The MAC between a measured mode and an analytical mode is defined as: T 2 mr as MAC rs T T mr mr as as Note: COC and MAC do not give a useful measure of the error! a Spacecraft Loads Analysis - A. Calvi 111

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 Spacecraft Loads Analysis - A. Calvi 112

Soho SVM Cross-Orthogonality Check F.E.M. 1 2 3 4 8 9 10 15 21 26 29 30 31 TEST 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 0.46 2 0.00 37.24 0.47 0.87 3 4.17 45.99 0.87 4 4.78 47.46 0.77 0.24 5-3.39 49.82-0.33 0.76 6 0.96 53.19 0.75 0.22 7 2.10 56.65 0.79 0.21 8 58.67-0.28-0.35-0.22 9 60.24-0.30-0.22 0.46 0.46 10 3.30 64.30 0.61 11 66.40 0.21 0.32 12 67.50 0.45-0.43 13 68.73-0.38 14 69.68 15 71.69 16 72.71 0.37-0.33 17 3.30 73.34 0.21 0.85 18 74.78 19 75.63 20 78.77-0.24 21 82.12 22 7.72 84.51 0.76 23 5.54 86.31 0.87-0.23 24 7.21 88.64 0.64 25 5.45 89.29-0.33 0.63 26 94.44 27 97.15 28 99.56 Spacecraft Loads Analysis - A. Calvi 113

GOCE - MAC and Effective Mass Spacecraft Loads Analysis - A. Calvi 114

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.) Spacecraft Loads Analysis - A. Calvi 115

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 Spacecraft Loads Analysis - A. Calvi 116

7. Conclusions Spacecraft Loads Analysis - A. Calvi 117

Final Verification Consist of: Making sure all requirements are satisfied ( compliance ) Validating the methods and assumptions used to satisfy requirements Assessing risks Spacecraft Loads Analysis - A. Calvi 119

Criteria for Assessing Verification Loads (strength) Analysis: margins of safety must me greater that 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 Spacecraft Loads Analysis - A. Calvi 120

Final Verification (crucial points) To perform a Verification Loads Cycle for structures designed and tested to predicted loads 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) To make sure the random-vibration environments used to qualify components were high enough (based on data collected during the spacecraft acoustic test) Note: in the verification loads cycle instead of identifying required design changes (design loads cycle) the adequacy of the structure that has already been built and tested is assessed Spacecraft Loads Analysis - A. Calvi 121

Technical inconsistencies Uni-axial vibration and shock test facilities Low frequency transient often simulated at the subsystem and system assembly level using a swept-sine vibration test Infinite mechanical impedance of the shaker (and the standard practice of controlling the input acceleration to the frequency envelope of the flight data) Vibro-acoustic environment often simulated at the subsystem and units assembly level using a random vibration test Test levels largely based on computational analyses (we must validate critical load analyses!) Spacecraft Loads Analysis - A. Calvi 122

NEW TRENDS Protoflight vs prototype Testing (force limited vibration testing) Computational mechanics Vibro-acoustic analysis Random vibration analysis Complexity of the Industrial organization Spacecraft Loads Analysis - A. Calvi 123

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/ Spacecraft Loads Analysis - A. Calvi 124

Bibliography - ECSS Documents ECSS-E-HB-32-26 ECSS-E-ST-32 ECSS-E-ST-32-03 ECSS-E-ST-32-10 ECSS-E-ST-32-02 ECSS-E-ST-32-11 ECSS-E-ST-32-01 Spacecraft Loads Analysis (to be published) Space Project Engineering - Structural Structural finite element models Structural factors of safety for spaceflight hardware Structural design and verification of pressurized hardware Modal survey assessment Fracture control ECSS-E-10-02 ECSS-E-10-03 Space Engineering - Verification Space Engineering - Testing Spacecraft Loads Analysis - A. Calvi 125

THE END! Acknowledgements: TAS France for the data concerning the project SENTINEL-3 ALENIA SPAZIO, Italy, for the data concerning the projects 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 Spacecraft Loads Analysis - A. Calvi 126