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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 A Liege 16 November 2016

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Spacecraft Mechanical Loads Analysis

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 and Verification Loads Cycle 12. Conclusions

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

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1. Introduction


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Objectives of the Course

• To introduce the participants to the process of spacecraft mechanical loads analysis (loads analysis substantially means establishing appropriate loads for design and testing)

• To provide an overview about structural dynamics & loads and its importance in the development of the spacecraft structures (design, analysis & test)

• To point out the “logic and criteria” of the loads analysis process

• To explain some “advanced” topics (e.g. “notching”, effective masses, FE model validation) with minimum mathematics

What, Why, Who, Where, When + How


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Loads Analysis: task and purpose

• 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.

• (Linear) Structural Dynamics is the “backbone” of spacecraft

mechanical loads analysis (a more general term is “mechanical vibrations & shocks”)

• A number of ancillary disciplines are involved: computational mechanics, signal analysis, mechanics of materials…


Spacecraft loads analysis vs. structural dynamics

A. Calvi - Spacecraft Mechanical Loads Analysis - Liege November 2016 6

m Static loads (e.g. pressure) m Dimensional stability - Thermo-elastic distortion - Moisture release - Gravity release

m Quasi-static loads m Sine vibration m Random vibration m Vibro-acoustics m Shock

m Fatigue and Fracture Control

m Micro-vibrations m Micro-gravity

m LV/SC Coupled Loads Analysis

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Structural dynamics: a definition Structural dynamics is the study of structures subjected to a mechanical environment which depends on time and leading to a

movement

• Excitation transmission types (mechanical & acoustic) • Type of time functions (sinusoidal, transient, random) • Type of frequencies involved (low frequency, broadband) • Domain of analysis (time domain, frequency domain) • Structure representation with a mathematical model (continuous or

discrete)


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The Role of Structural Dynamics in Spacecraft Loads Analysis • Mechanical environment definition (structural response and loads identification

by analysis) – Launcher/Spacecraft coupled loads analysis – Random vibration and vibroacoustic analyses – Test predictions (e.g. sine vibration test by frequency response analysis) – Micro-vibrations (jitter) analysis – Input to structural life analysis (e.g. generation of the fatigue spectra) – …

• Structural identification (by analysis and test) – Modal analysis – Modal survey test and experimental modal analysis – Mathematical model updating and validation

• Test results evaluation (e.g. environment & test requirements verification)

– Qualification and Acceptance tests (sine, random, acoustic noise, shock)


Calculating accurate responses is important not only to assess the structure ability to survive but also to provide design and test environments and requirements for units and subsystems

Scope of the Mechanical Loads Analysis Handbook • The ECSS-E-HB-32-26 recommends engineering practices for

European programs and projects. • It makes available a set of well proved methods and procedures for

– the prediction and assessment of structural design loads and for – the evaluation of the test loads.

• The target users of the handbook are engineers involved in design, analysis and verification of spacecraft and payloads in relation to general structural load analysis issues.

• Goal: to harmonize methodologies, procedures and practices currently applied for the conduct of spacecraft and payloads loads analysis.

• Note: ECSS-E-HB-32-26 is the outcome of the consensus reached by the Working Group members


ECSS-E-HB-32-26A Handbook - Table of Contents


1. Scope 2. References 3. Terms, definitions and abbreviated terms 4. Overview of the loads analysis process 5. Background on structural dynamics 6. Launcher / spacecraft coupled load analysis 7. Static loads 8. Sine vibration 9. Random vibration and vibro-acoustics 10. Shock 11. Dimensional stability 12. Fatigue and fracture control 13. Micro-gravity & micro-vibrations 14. Soft stowed packaging 15. Nonlinear structures 16. Finite element models

About 500 pages

www.ecss.nl

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Spacecraft loads analysis process… “layers” of disciplines

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.

• “Management” contractual/programmatic/managerial aspects, e.g. contractual agreements, project schedule, risk management, available budget…

• “Philosophy” Spacecraft verification approach, heritage, good

engineering practice, criteria…

• “Physics” Structural dynamics (of real structures),

validation of mathematical models, criteria…

• “Mathematics” Theory of vibrations, computational models,

verification of mathematical models…


Criteria… can be… (a personal view)

• A criterion is a standard by which you judge or evaluate something (thefreedictionary.com)

• “Well established”, e.g. based on experimental evidence, e.g. Von Mises yield criterion

• “Reasonable” based on good engineering practice, e.g. design and test factors

• “Mantra” i.e. “a sacred verbal formula” e.g. "Test as You Fly - Fly as You Test" approach

• “Rather questionable under certain circumstances”, e.g. sine-equivalent input, environment severity based on accelerations

• “Theoretically wrong”, e.g. SRS ratio used as transfer functions


A number of structural requirements are design and verification criteria!

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Accelerations… some preliminary remarks • The parameter most commonly used (in 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… but… see the note in next bullet! • In practice accelerations are used as a measure of the severity of the

mechanical environment (note: effects of frequencies and mode shapes are important and should be considered. Forces and stresses are often more relevant!)

• 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. See relevant slides)

• Some other aspects to keep in mind… – Need for considering the “actual” (e.g. “test” or “launch”) boundary conditions i.e.

mechanical impedance of the “mounting structure” (e.g. for the purpose of “notching”)

– Need for a “valid” F.E. model (e.g. to be used for force and stress recovery) A. Calvi - Spacecraft Mechanical Loads Analysis - Liege November 2016

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Example of satellite structural design concept



Euclid – Overall Configuration

Euclid mechanical architecture


Euclid SVM Structure


v Key Features – Structure: v It consists of a central Cone connected to 6 lateral panels (hosting units and

equipment) by means of eight shear panels v It shall:

ÿ Provide support, to Payload Module, Sunshield & Solar Array Subsystem, Hydrazine and Cold Gas Tanks, Equipment and Units installed on SVM

ÿ Transfer properly launch loads ÿ Provide handling and lifting points to allow transportation of fully equipped S/C ÿ Assure high thermo-structural dimensional stability ÿ Concur to meet stiffness and strength requirements in accordance to S/C

specification (1st mode above 15 Hz lateral & 35 Hz Longitudinal) ÿ Not exceed mass target of 204 kg

SVM equipment accommodation - Internal view


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“Organizations”, “Levels of Assembly” and Procurement…

• Launcher Authority

• Spacecraft Authority (“customer”)

• Spacecraft Prime Contractor

• Payload and sub-systems Contractors

• Other Contactors

• Spacecraft + launcher

• Spacecraft

• Spacecraft

• Payload module, instruments, sub-systems…

• Units/components/parts


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Spacecraft Levels of Assembly

RFFE

RPM

RFFE

RPM


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2. Spacecraft mechanical environments


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Mechanical loads are caused by:

• Transportation • Rocket Motor Ignition Overpressure • Lift-off Loads • Engine Generated Acoustic Loads • Engine Generated Structure-borne Vibration Loads • Engine 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


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Launch mechanical environment and categorization

• 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


Note: most of the vibration in rocket (and jet) powered flight vehicles is random in nature rather than periodic.

http://upload.wikimedia.org/wikipedia/it/8/87/Ariane_5_Launch_2.jpg

Spacecraft loaded by pressure loads and enforced acceleration


It is normally assumed that during the launch the “support structure” of the spacecraft (i.e. launch vehicle adapter + etc.) behaves as a “low pass system” with respect to the “broad band vibrations”. There are exceptions, e.g. Soyuz launcher.

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A5 Typical Longitudinal Static Acceleration


“Steady-state” accelerations

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

“Soyuz steady-state” accelerations

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“Steady-state”, low-frequency transients, broad-band random and shock loads


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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


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Broadband and high frequency vibrations

Broad band random vibrations are produce by: • Structural response to broad-band acoustic loads • Aerodynamic turbulent boundary layer • Engines functioning


In spacecraft loads analysis “random vibrations” and “acoustic loads” are (usually) the two sides of the same coin!

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Shocks

Mainly caused by the actuation of pyrotechnic devices: • Release mechanisms for stage and satellite separation • Deployable mechanisms for solar arrays, antennae etc.


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Shocks

Time [t]

[g]


Shock: local transient mechanical loading of short duration, high frequency and high amplitude, with substantial initial rise time (ECSS-E-HB-32-25A)

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3. Elements of structural dynamic analyses for spacecraft

3.1 Basic concepts in vibration data analysis 3.2 Dynamic analysis types for spacecraft loads analysis

Real eigenvalue analysis (“modal analysis”) Linear frequency response analysis Linear transient response analysis Random vibration analysis (and Power Spectral Density) Vibro-acoustic analysis (and Sound Pressure Levels) “Shock” response spectrum and its applications

3.3 Modal Effective Mass 3.4 Craig-Bampton Method


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Basic concepts in vibration data analysis


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Classifications of vibration environments


In spacecraft loads analysis it is usually assumed that the vibration is either deterministic or stationary random.

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Classification of vibration data. Definitions. • A stationary vibration is one whose basic properties do not vary with time • A non-stationary vibration is one whose basic properties vary with time,

but slowly relative to the lowest frequency of the vibration • A deterministic vibration is one whose value at any time can be

predicted from its value at any other time • A random vibration is one whose instantaneous magnitude is not

specified at any given time. The instantaneous magnitudes of a random vibration are specified only by probability functions giving the probable fraction of the total time that the magnitude (or some sequence of magnitudes) lies within a specified range

Note: virtually all stationary random vibrations can be represented by an

ergodic random process meaning the properties of the random process {x(t)} can be described by time averages over a signal sample record x(t)


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Random process


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Quantitative description of stationary vibrations

• Mean value:

• Mean-square value:

• Variance:


In spacecraft loads analysis it is usually assumed that the mean of the random vibration is zero.

Misunderstanding are always possible…

For example, the frequency domain representation of a function (or signal) is usually called the spectrum, however the mathematical definition and physical meanings of the “spectra” used in spacecraft mechanical loads analysis can be quite different, e.g.:

• Fourier spectrum • Frequency response function • Sine vibration spectrum • Power spectral density • Sound Pressure Level • Shock response spectrum • Equivalent sine spectrum • …


- There are too many graphs and diagrams and not enough people that are able to interpret them.

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Finite Fourier Transforms • The finite Fourier transform of a sample record x(t) is defined as:

Note: The finite Fourier transform is generally a complex number that is defined for both positive and negative frequencies, that is, X(f,T); −∞ < f < ∞. However, X(−f,T) = X*(f,T), where the asterisk denotes the complex conjugate, meaning that values at mathematically negative frequencies are redundant and provide no information beyond that provided by the values at positive frequencies. Since engineers typically think of frequency as a positive value, it is common to present finite Fourier transforms as 2X(f,T); 0 < f < ∞.


More about spectra… small signals are not hidden

The same signal is composed of a large sine wave and significant other sine wave components. When these components are separated in the frequency domain, the small components are easy to see because they are not masked by larger ones.


More about spectra… examples

A signal which is periodic and exists for all time has a discrete frequency spectrum. The transient signal has a continuous spectrum. The frequency spectrum of an impulse is flat, i.e., there is energy at all frequencies. It would, therefore, require infinite energy to generate a true impulse.


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Dynamic analysis types for spacecraft loads analysis

• 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.

• Vibro-acoustics (FEM/BEM, SEA) & Random vibration analysis (FEM) – Vibro-acoustic test prediction & random vibration environment definition – Loads analysis for base-driven random vibration (e.g. for instruments)

• “Shock” response spectrum (and its applications) – Specification of equivalent environments (e.g. equivalent sine input) – Shock environment specifications, etc.


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Real eigenvalue analysis (“modal analysis”)


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Real eigenvalue analysis

mNote: mode shape normalization Scaling is arbitrary

Convention: “Mass”, “Max” or “Point”


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Mode shapes

mCantilever beam mSimply supported beam


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Satellite Normal Modes Analysis

Mode 1: 16.2 Hz Mode 2: 18.3 Hz

INTEGRAL Satellite (FEM size 120000 DOF’s)


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Reasons to compute normal modes (real eigenvalue analysis)

• To verify stiffness requirements • To assess the dynamic interaction between a component and its

supporting structure (in particular the modes with large modal effective masses are important)

• To guide experiments (e.g. modal survey test) • To validate computational models (e.g. test/analysis correlation) • As pre-requisite for subsequent dynamic analyses (mode superposition

method: see note) • To evaluate design changes • Mathematical model quality check (model verification) • Numerical methods: Lanczos,…


Note: just as a real waveform can be represented as a sum of much simpler sine waves, any vibration can be represented as a sum of much simpler vibration modes.

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Frequency response analysis


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Frequency Response Analysis • Used to compute structural response to steady-state harmonic

excitation (note: “ideal case” with important practical applications”!) • 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 approaches: direct and modal • Damped forced vibration equation of motion with harmonic

excitation:

Complex equation of motion: the actual steady-state motion will be given by either the real part of x or its imaginary part, depending on whether the excitation is of cos ωt or sin ωt type.


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Harmonic forced response with damping


Q = 1/(2ζ) amplification at

resonance

Note: Q (Quality Factor) is a measure of the sharpness of resonance

Note: in the figure it can be assumed either unitary input spectrum at the base or output/input spectrum ratio be reported.

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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


Definition of Frequency Response Functions

R = Response Parameter; F = Harmonic Force


Frequency Response Analysis of Multi-DOFs


Example of “Receptance” for a 2-DOFs system

Frequency Response Functions


i

j

Properties of FRF and Experimental FRF

• The quantity H(ω) is known as the frequency response function of the system. It relates the Fourier transform of the system input to the Fourier transform of the system response.

• The FRF is a property of a linear system, not dependent on the input. • From an experimental point of view the frequency response function is

actually estimated via the discrete Fourier transform.


Analysis methodologies w.r.t. frequency range


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Transient response analysis


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Transient Response Analysis • Purpose is to compute the behaviour of a structure subjected to time-

varying 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 approaches: direct (e.g. Newmark) and modal (e.g. Lanczos + Duhamel’s integral or Newmark)

• Dynamic equation of motion:


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Modal Transient Response Analysis


Mode superposition

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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


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Random vibration analysis (& Power Spectral Density)


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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 (“was”) often performed with simplified techniques (e.g. based on “Miles’ equation” + effective modal mass models)


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Stationary random vibrations By definition, random vibrations cannot be described by an explicit

mathematical function and, hence, must be described in statistical terms. This can be done:

a) in the amplitude domain by probability functions

b) in the time domain by correlation functions (a few practical applications to vibration problems)

c) in the frequency domain by spectral density functions Note: the power spectrum describes the frequency content of the

vibration and, hence, is generally the most important and widely used function for engineering applications


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Random noise with normal amplitude distribution


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Probability Density Functions • The probability density function of a stationary random vibration x(t) may

be defined as:

where T(x,Δx) is the time that x(t) is within the magnitude interval Δx centered at x during the sample record duration T. The integral of the probability density function between any two magnitudes x1 and x2 defines the probability at any future instant that the value of x(t) will fall between x1 and x2, that is:

Note: it is common to omit the computation of probability density functions from the analysis of random vibration data, and to simply assume the p.d.f. is Gaussian


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Power Spectral Density Functions. (Equivalent definitions).

(also called the power spectrum, autospectral density function, or autospectrum)

a) Fourier transform of the autocorrelation function

b) :

c) :


Note: Power spectral density is the limiting mean-square value (e.g., of acceleration, velocity, displacement, stress, or other random variable) per unit bandwidth, i.e., the limit of the mean-square value in a given rectangular bandwidth divided by the bandwidth, as the bandwidth approaches zero. Also called autospectral density. The term power is used because the dynamical power in a vibrating system is proportional to the square of the vibration amplitude.

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Power Spectral Density (conceptual model)


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Time-histories and autospectra for wide-bandwidth (A) and narrow-bandwidth (B) random vibrations


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PSD functions. Properties 1) Given two or more statistically independent vibrations, the PSD for the

sum of the vibrations is equal to the sum of the PSDs for the individual vibrations, that is

2) The area under the PSD between any two frequencies, fa and fb, equals the mean-square value of the vibration in the frequency range from fa to fb, that is,

3) Given an excitation x(t) to a structural system with a frequency response function H(f), the PSD of the response y(t) is given by:


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Miles’ Equation


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Random vibration analysis by FEM (test prediction)


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Vibro-acoustics Analysis (& Sound Pressure Level)


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Sound Pressure Level (conceptual model)


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Example – A5 SPL under the fairing


Note 1: the decibel is a tenth of a bel, the logarithm (base 10) of a power ratio (it is accepted that power is proportional to the “square of the rms” of acceleration, velocity, pressure, etc.) Note 2: it must be emphasized that dB in acoustics is not an unit of acoustic pressure but simply a power ratio with respect to a reference pressure which must be stated or clearly implicit

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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



Conceptual generation of a random vibration specification

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Shock response spectrum and its applications


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“Shock” Response Analysis vs. Shock Response Spectrum (and its applications)

• Response Spectrum Analysis is an approximate (“historical”) method of computing the peak response of a transient excitation applied to a structure or component (it is not used to assess the ability of the spacecraft structure to survive a “shock”)

• 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

• The use of the spectrum for dynamic response evaluation has nowadays a limited use in loads analysis of spacecraft (e.g. limited to preliminary design and analysis) since the accuracy of the method may be questionable

• The concept of Shock Response Spectrum has two important applications in spacecraft loads analysis

– Mechanical shock specification – Sine vibration test specification (definition of equivalent sine input)

• Note: the term “shock” can be misleading (not necessarily a “shock” is involved. It would be better to use the term “response spectrum”)


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Generation of a response spectrum (1)


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Generation of the Shock Response Spectrum


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Response spectrum considerations

• 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 (and duration) information since only the magnitude of peak response is computed

• The shock spectrum is a transformation of the time history which is not reversible (contrary to Fourier transform)

• 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


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SRS for environments specification

• 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)

• The absolute acceleration spectrum is used, which provides information about the maximum internal forces and stresses

• 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)

• Two important applications in spacecraft loads analysis: – Mechanical shock specification

– Sine vibration test specification (equivalence: transient → sine environment)

• Note: 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!)



Conceptual generation of a shock specification

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Shock Response Spectrum

(A) is the shock spectrum of a terminal peak sawtooth (B) of 500 G peak amplitude and 0.4 millisecond duration


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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.

• The equivalent sine input (ESI) is defined as:


QSRSESI =

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SRS/ESI of the following transient acceleration:

QSRSESI =

ESI

ESI


87

/[ sm

][s

2 .41

[Hz

]/[ sm 2 .46

2DOF ]/[ sm

][s

01.0=zHz23frequencynatural @

[Hz

Hz23frequencynatural @1 .97 01.0=z

]/[ sm

Transient response Transient response

Frequency response at ESI level Frequency response at ESI level

SDOF


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Modal effective mass


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Definitions • Primary (or fundamental) Mode Mode associated with a large effective mass Note: no cut-off criterion can be given. Primary modes are identified in

relative terms by examination of the table of modal effective masses. • Secondary mode Mode that is not primary i.e. with small effective mass • Global mode Mode which corresponds to a global movement Note: a global mode can be a secondary mode e.g. when opposed motion

is present • Local mode Mode which corresponds to a local movement Note: a local mode can be a primary mode e.g. tank mode


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Modal effective mass (1) - Definition

• 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 (in

practice this is the only case of interest in spacecraft loads analysis) • 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”!

Dynamic amplification factor

Modal reaction forces

Base (junction) excitation


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Modal effective mass (2) - Calculation

• 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)

Gen. mass

Resultant of modal interface forces

i-th mode Rigid body modes

Modal participation factors Effective mass

Eigenvector max value


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Modal effective mass (3) - Properties

• The effective mass characterises the mode and it is independent from the eigenvector normalisation

• 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 (primary or secondary) 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)


Physical interpretation of effective and residual mass concepts


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Example of Effective Mass table (MPLM test and FE model)


Force measurement techniques and effective masses


Method Advantages Drawbacks

Load Cells (FMD) - Accuracy - Added mass and flexibility of test fixture at interface

- Limited availability

Strain Gages - Simple setup - Difficulties with calibration and sensitivity

Coil Current (electrodynamic shaker)

- No test fixture required - Single force measurement along excitation direction

- Influence of mobile mass of shaker

- Limited accuracy

Mass Operator - Requires only acceleration measurements

- Finite element model required

- Accuracy depends on quality of FE model

4. Mechanical Loads Specifications for design and testing (and introduction to “notching”)

• Quasi-static Loads • Statically determinate and indeterminate structures • Boundary Conditions • Fundamentals of specification development • Test Specifications in ESA / ECSS Projects • Mechanical Impedance (and introduction to “notching”)


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Quasi-Static Loads (an initial note…)

• 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.


98

Quasi-Static Loads (ECSS-E-HB-32-26 definitions) • Quasi static loads Combination of static and dynamic loads into an equivalent static load

specified for design purposes Note 1: QSLs are equivalent to (or interpreted by the designer as) static

loads, typically expressed as equivalent accelerations at the C.o.G. Note 2: in some contexts quasi static loads are understood as: “loads

associated to a quasi static event” (especially in LV/SC CLA terminology) • Quasi static acceleration (Depending on the context:)

– quasi-static load expressed as equivalent acceleration at the CoG (general) – quasi-static component of the acceleration (specific, e.g. in LV/SC CLA

terminology) – acceleration associated to a quasi-static event (specific)

• Quasi static event Event generated by external forces which change slowly with time so that

the dynamic response of the structure is not significant



Spacecraft equivalent accelerations at CoG

An approximate evaluation is performed by:

Statically determinate and indeterminate structures

• Statically determinate structure (“Isostatic”) – Number of kinematic constraints strictly sufficient to avoid the motion of

the system. – Reactions and internal forces can be determined solely from free-body

diagrams and equations of equilibrium. – Results are independent of the material from which the structure has

been made. • Statically indeterminate structure (“Hyperstatic”)

– Number of kinematic constraints higher than the strictly sufficient to avoid the motion of the system.

– Reactions and internal forces cannot be found by statics alone (more unknown forces than independent equations of equilibrium).

– Results are dependent on the material from which the structure has been made.


Influence of the number of constraints on structural design and loads analysis

Statically determinate structure

• Less sensitive to thermal loads (no thermal stress for isotropic materials: structure is free to expand/shrink). Preferred when thermo-elastic decoupling is requested

• Easier alignment, integration and reduced distortion → Preferred structures for optical applications

• Preferred boundary conditions when structural “decoupling” is needed

• Reactions (interface loads and their distributions) depend only on the resultant of applied forces

• Can become “mechanisms” in presence of a failure

Statically indeterminate structure

• “Redundant”, e.g. provide redundant loads path • Enhanced stability (e.g. w.r.t. failures or

“buckling” phenomena) • Enhanced stiffness (e.g. higher nat. frequency) • Interface loads will develop as the support

structure deforms (e.g. reactions can exists without applied forces)

• More sensitive to thermal loads • Note 1: a system can be statically determinate

externally and statically indeterminate internally • Note 2: modern matrix structural analysis

methods can easily deal with statically indeterminate structures


Boundary conditions: hard-mounted structure

• Hard-mounted means mounted on a rigid interface i.e. grounding to a rigid support (note: not necessarily “clamped”!)

• It is a “convenient” (even if not always “realistic”) boundary condition, especially within an Industrial context, for specifying requirements (e.g. minimum natural frequency, quasi-static loads, etc.)

• Major consequences of hard-mounted assumption are: – Support structure cannot deform and cannot develop additional interface

loads (by definition!). It also means that, in dynamic analyses, the mechanical impedance of the adjacent structure is not taken into account.

– Interface motion is defined by 6 DOFs of the “rigid support” (3 translations and 3 rotations)


Note: in dynamic analyses, the “adjacent structure” (support structure) is often the shaker.

Boundary conditions: flight events and analysis

• In flight the Launcher + Spacecraft system is unconstrained (free structure or “free-free”)

• In general dynamic equilibrium is established at any time “t” between applied external forces and inertia forces (e.g. LV/SC CLA)

• Special case: quasi-static loading: applied and inertia forces do not vary with time (body under steady-state acceleration)

• Structural analysts can simulate unconstrained structures in a static analysis by using the “inertia relief” technique

• In practice the system is assumed to be in a state of static equilibrium (acceleration is computed to counterbalance the applied loads)

• Inertia relief technique is used (e.g. Space Shuttle quasi-static coupled loads analysis combining inertial and thermal loads) but not common. Preferred approach is:

– To perform structural dynamic analysis, especially for “coupled” systems, transient phenomena, etc.

– To perform constrained “quasi-static analysis” normally in hard-mounted conditions


Hard-mounted quasi-static analysis

• Hard-mounted quasi-static analysis is the most common approach for structural design and verification, especially for (preliminary) sizing of primary structures and interfaces

• The basic principle is to calculate a set of equivalent accelerations at the C.o.G. of the (“un-deformed”) structure such that it can represent, ideally “reproduce”, the maximum interface forces occurring during system lifetime (i.e. a “worst, global, static loading condition”)

• The maximum interface forces are identified among all loading events (normally, dynamic events)

• Nevertheless an “exact equivalence” between equivalent accelerations at C.o.G. and interface forces can only be established in terms of resultant of forces (6 forces/moments vs 6 translational/rotational accelerations)

• Conclusion: hard-mounted quasi static analysis can rigorously reproduce only the interface forces of isostatic structures (note: it is a general property of isostatic structures that the reaction forces depends only on the resultant of applied forces, regardless the assumption of rigid interface)


Hard-mounted quasi-static analysis

Limitations • “Hardmounted”: the interface is

assumed rigid, by definition, thus the analysis cannot take into account the support deformations.

• “Non-isostatic structures”: since the interface is assumed rigid, the reaction forces can be “incorrect” for statically redundant structures.

• Not (usually) a “worst condition” for structure internal sizing. In fact a quasi static load case is selected by applying the maximum resultant interface force criterion.

Possible recovery actions • General: perform “coupled analysis” (static /

dynamic analyses, in practice by modelling adjacent / support structures)

• Assess that QS loads combination rules (e.g. for lateral loads) are sufficiently conservative

• Increase load factors for taking into account the coupling with the adjacent structure i.e. the deformation of the interface

• Include the “warpage” (e.g. by imposing displacements at the I/F) in the standard static analysis procedure which includes load factors only

• Perform relevant dynamic analyses (e.g. sine, random vibration) and recover internal response


Boundary conditions: testing and analysis

• In most of mechanical testing (both static and dynamic) the test item is constrained (e.g. to the ground, to the shaker).

• Exceptions: in some cases such as modal testing (even if generally not recommended) and acoustic noise tests, the test item can be in “free-free” conditions. In practice these are realized by means of elastic suspensions.

• For structural analysis simulating constrained test conditions, the system is normally assumed to be hard-mounted.

• However test adapters/text fixtures are often modelled (rarely the shaker) • For test set-up and results evaluation, a number of procedures can partially

take into account the elastic behaviour of the interface (e.g. piloting strategies for dynamic tests, etc.).

• However the major issue in sine and random vibration testing is the infinite mechanical impedance of the shaker combined with the standard practice of specifying the input accelerations as the frequency envelope of the flight interface acceleration. This is the major cause of overtesting in vibration tests.


Summarizing… a note on quasi static loading

• Quasi static loading conditions are (or modelled as): – “Inertial relief” (free-free static equilibrium: unchanging applied force balanced by inertia

loads + e.g. thermal loading) – “Hard-mounted” (constrained rigid interface; load factors applied at the C.o.G.)

– It should be noted that, regardless the assumption of rigid interface, isostatic structures under quasi static loading reproduce the exact interface forces w.r.t. the dynamic load case which has defined the equivalent accelerations at C.o.G.

• Common aspects to isostatic structures and rigid interface – Structure is not loaded by support static displacement (for rigid I/F) or deformation (for

isostatic structure). In fact in both cases a rigid body motion occurs. – A forced vibration at the base/support is fully defined by 6 DOFs, 3 translations and 3

rotations, i.e. the 6 rigid body modes (nevertheless it is an ideal condition for tests on the shaker)

– It should be noted that either the assumption of isostatic structure or the assumption of rigid interface is needed for defining the modal effective masses (as commonly used by space industry)


Fundamentals of Specification Development (in dynamic environments testing)

• Specifications are established at the beginning of a project for the product design and are used during the tests to show that the product meets the requirements concerning its resistance to the environment [Lalanne].

• The SDOF linear model is normally used to characterize the relative severity of numerous vibrations. In practice it is assumed that:

– if the greatest stresses and damage due to fatigue generated in the a SDOF system by different excitations are equal, then these excitations are of the same severity in the SDOF model and, by extension in a real structure undergoing such excitations.

• Two criteria (and two types of spectra) are used: – SRS (Shock response Spectrum) – FDS (Fatigue Damage Spectrum)


Fundamentals of Specification Development (2)

A specification should satisfy the following criteria:

• To test should be at least as severe as the real environment

• The test should be representative of real conditions but not excessively severe compared to the real environment

• Conclusion: a good test should produces failures that would be observed in a real environment and should not cause failures that would not arise during operation.


Fundamentals of Specification Development (3)

In principle specifications can be:

• Established by Standards (large coverage of real levels, risk of oversizing and overtesting the equipment)

• Based on real environment data (“tailoring a product to its environment”) – Simulation of the actual environment (“ideal”; not practicable for several

reasons: e.g. exact environment simply not available before having flown the system, duration of the test time, reproducibility in laboratory, representativeness of recordings, especially for equipment with several attachment points)

– Simulation of the damaging effects of the environment (it is attempted to reproduce the effects of the environment rather than the environment itself. The principal disadvantage is the problem of establishing acceptable criteria for equivalent damage)


Mechanical Specifications in ESA / ECSS Projects (1)

• In ESA / ECSS Projects both basic approaches, i.e. by “Standards” and by “Tailoring”, are applied for establishing specifications

• Currently the most common approach is “hybrid”, e.g. : – Test duration and sine sweep rates (ECSS or other standards) – Test levels are tailored (mechanical analysis, envelopes + notching

implementation, exploitation of databases)

• For spacecraft, the following steps are typically applied (from design to test verification):

– Performing mechanical analyses which basically consist of environment and test requirements “flow-down” from launcher User’s Manual

– Enveloping of spectra and establishing of loads combination rules – Tailoring of levels by mechanical impedance considerations (notching)


Mechanical Specifications in ESA / ECSS Projects (2)

Note: In principle, by applying the criteria of equivalent damage, a single mechanical test could be envisaged to cover all different vibration environments. However the normal approach in ESA projects is to establish specifications by environments, in line with launcher mechanical environments and good engineering practice:

• Quasi static loads • Sine vibration environment • Random vibration/acoustic noise environments • Shock environment

However, often we would like to show that some tests are not strictly needed → severity criteria have to be recalled/established


Spacecraft design limit load factors for Soyuz (QSL)


Mechanical analyses at spacecraft level for defining loads specifications of payloads, sub-systems and units

• Mainly a “flow-down” of environment and test requirements from Launcher User’s Manual

• “System” frequency response analysis

• “System” vibro-acoustic analysis

• “System” shock (attenuation) analysis


Design requirements and verification


Design Verification

System Requirements

Mission Requirements

Subsystem Requirements

Unit Requirements

Unit Test

Subsystem Test

System Test

Define what to build Integrate and verify what has been built

Advantages of testing at lower levels of assembly

• It is prudent to test before accepting delivery from a supplier

• A more thorough workmanship screen can generally be performed at lower levels of assembly

• Post-test inspections are easier and more thorough than at higher levels of assembly

• Most importantly, there is more time to diagnose and fix problems found in tests at lower levels of assembly



Frequency response analysis & Sine loads Specification

Euclid Spacecraft F.E.M.

(Surfaces loaded by acoustic diffuse field in red) A. Calvi - Spacecraft Mechanical Loads Analysis - Liege November 2016 118

Vibro-acoustic analysis & Random Vibration Specifications

“Check-points” (1) to verify adequacy of the loads specifications i.e. design/test vs. “flight” (i.e. launch mechanical environment)

• Quasi-static Loads (2)

• Sine loads (2)

• Random vibration loads

• Shock loads

• Spacecraft/Launcher CLA

• Spacecraft/Launcher CLA

• S/C acoustic noise test

• Shock (“system’) test


Note (1): in fact the “flow down” approach can be severely conservative Note (2): no “system” test can be performed → validation of the (critical) analysis

Flight sine vibrations levels at the spacecraft/adapter interface (longitudinal axis)


Soyuz/Euclid Coupled Loads Analysis

Mechanical Impedance

• The mechanical impedance of a point on a structure is the complex ratio of the harmonic force applied at a point to the resulting harmonic velocity at that point (“direct or driving point impedance”):

• Mechanical impedance is a convenient measure of the resistance of a structure to vibration, the impedance being high for a structure that is inherently difficult to excite, and low for a structure that is readily excited. For typical lightly damped structures the impedance varies sharply as a function of frequency over a range of about two orders of magnitude. Minimum or zero values of impedance correspond to resonant frequencies, whereas maximum or infinite values of direct impedance correspond to the antiresonant frequencies associated with the driving point under consideration.


Mechanical Impedance Considerations (1)

All currently used vibration test specifications establish the test levels by specifying the vibration level as a function of frequency

• If the vibration data used to write a test specification is based upon actual measurements or accurate predictions at structural locations of interest with all components mounted as in service, no problems arise.

• If the mechanical impedance of the supporting structure is not large compared to the mounted components, then the vibration response characteristics of the unloaded structure will be quite different from the vibration in actual service with all components installed.

• In the such cases, when a vibration test specification is written on a basis of the vibratory motion of the unloaded supporting structure, the end result is a tendency to produce an overly severe vibration test .

• The same effect occurs when a vibration test specification is established by enveloping peaks in a measured response power spectrum.


Mechanical Impedance Considerations (2)

There are five possible approaches to the mechanical impedance problem [NASA CR-234, May 1965]

• To simply ignore the problem and accept the possibility of severe overtesting as an added safety factor in the design of the spacecraft components

• To analytically consider the effects of impedance on the motion response for the loaded and unloaded supporting structure, and to include some correction of these effects when establishing the vibration test levels to be specified

• To measure the actual impedance of the supporting structure for each component to be tested, and then simulate this impedance in the vibration testing machine (not practical within an industrial context!)

• To test the components along with the basic structure to which they are attached in service. This in effect means increasing the assembly level for the test

• To obtain measurements of the vibration response in actual service with all components installed. Mechanical impedance considerations will be accounted for in the motion response measurements (usually not feasible!)


124

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!

125

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

126

Static and dynamic environment specification (typical ranges)


127

Static and dynamic environment specification (typical ranges)


http://www.aerospace-technology.com/projects/artemis/

Equivalence criteria for loads and environments - 1 The loads are usually specified in terms of:

• Equivalent accelerations at the CoG, for the quasi-static loads

• Sine spectra of the acceleration, for the low frequency transients

and harmonic loads

• Power spectral densities (usually of the acceleration), for the broad band random vibrations

• Shock response spectra for the shock loads


Equivalence criteria for loads and environments - 2

• A very first “equivalence criterion” is implicit in the way the loads are defined

• For example two random vibration environments are equivalent if, assuming they have equal durations, they are represented by the same acceleration PSD, regardless the differences in the time histories.

• On the other hand, it is a common mistake to use the rms value of the input acceleration as a measure of its severity.

• Establishing an equivalence between different environments, or identifying which is the most severe, typically involves the evaluation and comparison of the (expected) structural responses.


Equivalence criteria for loads and environments - 3 The following criteria are applied in industrial applications

• Two mechanical environments are considered equivalent if they have the same SRS (for random vibrations the same RRS). In this case the equivalence is established on the base of the SDOF response. This criterion is often applied to structure with base excitation

• Another criterion is based on the evaluation and comparison of the structural response to the mechanical environments. The comparison is often performed in terms of accelerations and interface forces. In this case the equivalence is established on the base of the response of the actual structure


Equivalence criteria for loads and environments - 4

• Equivalence between a low frequency transient and the “sine equivalent dynamics”

• Equivalence between the base-driven random vibration environment with the vibro-acoustic environment

• Equivalence between the random vibration environment and the shock environment

• Comparison of the random vibration environment with the quasi-static loads


For more details: ECSS Spacecraft Mechanical Loads Analysis Handbook

132

5. Spacecraft Structure Requirements for Design and Verification (some aspects, with emphasis on mechanical loads analysis)


133

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


134

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.


135

ECSS - Standard


136

Requirements evolution


Prototype vs. Proto-flight

• Prototype Hardware: hardware of a new design. Includes Qualification Models that are identical to Flight Hardware. It is usually subject to a design qualification test program and tested beyond expected life limits. It is not a flight article.

• Protoflight hardware: flight hardware of a new design that is to be used operationally in space. It is subject to a “Qualification”/Acceptance test program. The test article is the flight article.

• Protoflight Approach (i.e. there is no qualification item): – cost savings, but more risk, in fact… – no formal demonstration of remaining life for the flight items, moreover… – structural oversizing w.r.t. the prototype approach (higher design loads)

• Proto-flight tests: are formal environmental tests performed on flight hardware to demonstrate both design adequacy and workmanship of the assembled item (source JPL)

• For ECSS, the proto-flight test levels and durations are (general approach): – test levels: as qualification levels – test durations: as acceptance durations


Common Design LogicSatellitesTest Logic

Limit Loads - LL

Design Limit LoadsDLL

x Coef. A

DYL

x Coef. B

DUL

x Coef. C

x KQ x KA

QLAL

Incr

easi

ng L

oad

Leve

l

Loads and Factors ECSS E-ST-32-10

“Flight Limit Loads” • KQ = Qualification Factor • KP = Project Factor • KM = Model Factor

• DLL = Design Limit Load • DYL = Design Yield Load • DUL = Design Ultimate Load

DLL = “functional” requirements DYL = “no yield” requirements

DUL = “no rupture” requirements A. Calvi - Spacecraft Mechanical Loads Analysis - Liege November 2016 138

139

Loads and Factors ECSS E-ST-32-10

“Protoflight” “Prototype” A. Calvi - Spacecraft Mechanical Loads Analysis - Liege November 2016

“Flight Limit Loads”

Example: protoflight vs prototype


141

Loads and levels of assembly System

Limit Loadsat system level

(KQ(1)), KP, KM,

Design Limit Loads

=

Limit Loadsfor subsystem or component

Subsystem or componentKP, KM,

Design Limit Loads

KLD , FOS(KMP(2))

DYL, DUL

KQ(1): for satellite KMP(2): for launch vehicles

Factors of Safety and levels of assembly

ECSS E-ST-32-10


Spacecraft verification logic (Soyuz launcher)


Spacecraft test factors, rate and duration (Soyuz launcher)


144

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). Note: this req. not anymore consistent with current ECSS-E-ST-32-10!.

• 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.


145

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.


146

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


147

Test and analysis types used for verify mechanical loads


148

6. Design Loads Cycles (with emphasis on structural loading and preliminary design)


149

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


150

Design loads cycle process


151

Load Factors for Preliminary Design (Ariane 5)


152

Quasi-Static Flight Limit loads for Dnepr and Soyuz


153

Quasi-static loads for different launchers


154

Typical Mass Acceleration Curve for preliminary design of payload hardware or equipment items


Note 1: MAC loads replaced by CLA results as spacecraft design matures. Note 2: MAC loads do not apply to components with fundamental coupled component/spacecraft frequency > 80 Hz.

155

Load Combination Criteria for Components (International Space Station Program)


Random vibration loads (for preliminary design)

• From Standards, e.g. ECSS-E-10-03A, “Space Engineering, Testing”, 2002

• Exploitation of databases (e.g. “VibroSpec”)

• “System Level” vibro-acoustic analysis (if mathematical models are available)


157

7. Spacecraft / Launcher Coupled Loads Analysis

• The role of the C.L.A. within the loads cycle • CLA Output • Low frequency vibrations & quasi-static loads • SC/LV interface accelerations and sine-equivalent spectrum



The role of the C.L.A. within the loads cycle

In principle CLA can be performed anytime in the development process of a new spacecraft. CLA may be considered as:

• A single (and normally mandatory) indicator of compliance

(between the overall environment specified by the launcher at the interface with the spacecraft and the strength of the spacecraft structure)

• Example: Ariane 5, Vega, etc.

• An integrated tool in the design process of a spacecraft structure

• Example: Space Shuttle

159

Launcher / Satellite C.L.A.

Mode 18: 2.93 Hz Mode 53: 16.9 Hz

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 (lift-off, 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.


A typical Delta II mission profile and the associated accelerations


Source: The Aerospace Corporation: www.aero.org


From low frequency vibrations to quasi-static loads and sine spectrum


From steady state accelerations and low frequency vibrations to quasi-static loads and sine spectrum

163

Ariane-5 Dynamic Mathematical Model PAYLOAD

UPPER COMPOSITE

EAP+ EAP-

EPC

– 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



VEGA Launcher and adapter F.E. models

165

Sizing flight events (CLA with VEGA Launcher)

1. Lift-off (P80 Ignition and Blastwave)

2. Mach1/QMAX Gust

3. P80 Pressure Oscillations

4. Z23 Ignition

5. Z23 Pressure Oscillations

6. Z9 Ignition


166

Launcher/Spacecraft CLA Output


167

CLA Output • LV-SC interface accelerations

– Equivalent sine spectrum

• LV-SC interface forces – Equivalent accelerations at CoG

• Internal responses

– Accelerations, – Displacements – Forces – Stresses – …


168

CLA Output S/C Quasi Static Loads


169

Equivalent Sine Input for Spacecraft

CLA (Coupled Load Analysis)

0 10 20 30 40 50 60 70 800

50

100

150

200

250

SR

S [m

/s2 ]

frequency [Hz]

SRS Q

SRSESI =

ESI

1 2 + =

Q

SRS ESI

SRS

Difference is negligible for small damping ratios


170

CLA Output S/C Sine envelopes


171

Payload / STS CLA

Lift-off Force Resultant in X [lbf]

Lift-off Main Fitting

I/F Force X Dir. [N]

Lift-off Main Fitting

I/F Force Z Dir. [N]

Lift-off Keel Fitting

I/F Force Y Dir. [N]


An Introduction to��Spacecraft Mechanical Loads Analysis�� (from preliminary design to final verification) �Spacecraft Mechanical Loads Analysis1. IntroductionObjectives of the CourseLoads Analysis: task and purposeSpacecraft loads analysis vs. structural dynamics Structural dynamics: a definitionThe Role of Structural Dynamics in Spacecraft Loads AnalysisScope of the Mechanical Loads Analysis HandbookECSS-E-HB-32-26A Handbook - Table of ContentsSpacecraft loads analysis process… “layers” of disciplinesCriteria… can be… (a personal view)Accelerations… some preliminary remarksExample of satellite structural design conceptEuclid – Overall ConfigurationEuclid mechanical architectureEuclid SVM Structure SVM equipment accommodation - Internal view“Organizations”, “Levels of Assembly” and Procurement…Spacecraft Levels of Assembly2. Spacecraft mechanical environmentsMechanical loads are caused by:Launch mechanical environment and categorization Spacecraft loaded by pressure loads� and enforced accelerationA5 Typical Longitudinal Static AccelerationSlide Number 26“Steady-state”, low-frequency transients,� broad-band random and shock loadsAcoustic LoadsBroadband and high frequency vibrationsShocksShocks3. Elements of structural dynamic analyses for spacecraftBasic concepts in vibration data analysisClassifications of vibration environmentsClassification of vibration data. Definitions.Random processQuantitative description of stationary vibrationsMisunderstanding are always possible…Finite Fourier TransformsMore about spectra… small signals are not hiddenMore about spectra… examplesDynamic analysis types for spacecraft loads analysisReal eigenvalue analysis (“modal analysis”)Real eigenvalue analysisMode shapesSlide Number 46Reasons to compute normal modes (real eigenvalue analysis)Frequency response analysisFrequency Response AnalysisHarmonic forced response with dampingFrequency response considerationsDefinition of Frequency Response Functions Frequency Response Analysis of Multi-DOFsFrequency Response FunctionsProperties of FRF and Experimental FRFAnalysis methodologies w.r.t. frequency rangeTransient response analysisTransient Response AnalysisModal Transient Response AnalysisTransient response considerationsRandom vibration analysis (& Power Spectral Density)Random vibration (analysis)Stationary random vibrationsRandom noise with normal amplitude distributionProbability Density FunctionsPower Spectral Density Functions. (Equivalent definitions).Power Spectral Density (conceptual model)Time-histories and autospectra for wide-bandwidth (A) and narrow-bandwidth (B) random vibrationsPSD functions. PropertiesMiles’ EquationRandom vibration analysis by FEM (test prediction)Vibro-acoustics Analysis (& Sound Pressure Level)Sound Pressure Level (conceptual model)Example – A5 SPL under the fairingVibro acoustic analysis at spacecraft levelSlide Number 76Shock respo

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