Non-linear modal analysis: industrial context, current capabilities, challenges for the future Journée Modes non-lineaires, Université de Liège, 9 novembre 2010 Bart Peeters, Simone Manzato, Gianpiero Rocca
Abstract When applying system identification to mechanical engineering structures such as cars and airplanes, nonparametric estimates of requency Response unctions (Rs) are typically used as primary data. One or more shakers excite the structure and the response is measured at multiple locations along the structure. The measured Rs are then used to identify a linear model of the structure in terms of so-called modal parameters. This process is called modal analysis. By using Rs and estimating the modal parameters, it is assumed that the structure is linear. However, in many cases, structures are not perfectly linear. In industrial practice, the degree of nonlinearity is assessed by (visually) comparing Rs measured with different excitation amplitudes. Also coherence functions are inspected, but these quality indicators combine effects of leakage, noise and nonlinearity. This presentation will discuss the industrial context for non-linear modal analysis, the current capabilities for non-linear vibration testing, and challenges for the future like identification techniques and relation to the mechanical product development process. 2 copyright LMS International - 2010
Outline Industrial context Linear modal analysis Cases Current capabilities Non-linear vibration testing Assessment of non-linearities Challenges for the future Identification techniques Positioning in the mechanical product development process 3 copyright LMS International - 2010
Introduction Modal Analysis: cornerstone of structural dynamics Experimental Modal Analysis has been developing for 40 years Still a cornerstone of structural dynamics analysis and optimization What are the key strengths Experimental analysis characterizes the real structure Relatively fast and accurate Results are compatible with engineering approach What are the key limitations Requires the real structure Requires quite some expertise Requires extensive (and expensive) equipment Only valid for the tested structure A future? Definitely, but depends on the ability to keep addressing the real (and changing) challenges of its (old & new) users Current research Parameter identification methods Confidence bounds Combined use of artificial excitation and unknown ambient field excitation Monitoring / automatic data analysis Non-linear / active systems 4 copyright LMS International - 2010
Non-linearity in structural dynamics Sources of nonlinearity Composite materials Connections Damping and acoustical layers Mounts Shock absorbers ree play friction 5 copyright LMS International - 2010
Car tire-suspension system Z X Y Mode EMA req [Hz] EMA Damp [%] OMA req [Hz] OMA Damp [%] Vertical 3.978 1.33% 2.341 6.56% Z Pitch Roll 4.742 6.830 3.59% 2.25% 3.293 5.255 6.07% 2.58% X X Z Y Y Non-linear behavior of tire-suspension system: EMA frequencies higher than OMA frequencies riction phenomena are present inside the dampers and bushing elements (and into the tire) Hammer force not sufficient to overcome friction (stiffening effect in EMA) 6 copyright LMS International - 2010
Ground Vibration Testing of A400M aircraft Non-linearity assessment Significant sources of nonlinearity in aerospace structures Riveted metallic construction Nacelle latches Hydraulic actuators of control surfaces Elastomeric engine mounts Underwing carriage Excitation J. Rodríguez Ahlquist, J. Martinez Carreño, H. Climent, R. de Diego and J. de Alba, Assessment of Nonlinear Structural Response in A400M GVT, IMAC 28, 2010 7 copyright LMS International - 2010
Environmental testing Real & virtual shaker testing Example: ESA-ESTEC quad shaker Components Seismic block, magnesium table, drive bars, guiding system, bearings Shakers Controller Satellite ESA ESTEC quad shaker system during assembly Quad shaker acceptance testing 8 copyright LMS International - 2010
Virtual Shaker Testing software VL Motion: Mechanical part, lexible body Imagine.Lab AMESim: Electrical part Coil Velocity orce Control Voltage MATLAB / Simulink Controller 10 1 Control harmonic spectra Table Acceleration Control Voltage amplitude [g] 10 0 10-1 10-2 experimental virtual test run frequency [Hz] 10-3 10 0 10 1 10 2 9 copyright LMS International - 2010
Virtual sine control testing of a satellite Influence of sweep rata Sweep rate: better control performance at lower sweep rates. At lower sweep rates, more control updates are possible. The order in decreasing control quality is: 1 Oct/min > 2 Oct/min > 1 Hz/s > 2 Hz/s Number of periods: less periods yield slightly better control, but noisier amplitude estimates. If less periods are used to estimate the sine amplitudes, indeed more control updates are possible. Compression factor: a low factor gives better control, whereas a higher factor yields more stable control in the sense that the spectrum is smoother and that less beating occurs. Amplitude [g] Amplitude [g] 10 0.3 lin-1hzs-cf4-1p 10 0.1 10-0.1 10-0.3 reference control 10 1 10 2 f [Hz] log-1omin-cf4-1p 10 0.3 10 0.1 10-0.1 10-0.3 reference control 10 1 10 2 f [Hz] Amplitude [g] Amplitude [g] 10 0.3 lin-2hzs-cf4-1p 10 0.1 10-0.1 10-0.3 reference control 10 1 10 2 f [Hz] log-2omin-cf4-1p 10 0.3 10 0.1 10-0.1 10-0.3 reference control 10 1 10 2 f [Hz] 10 copyright LMS International - 2010
Overview over typical structural non-linearities in spacecraft structures Physical source of non-linearity Effect on dynamic responses Characterisation criteria Consequences on qualification process Weak non-linearity (sliding at interface) Variation of damping factor Small or no effect on eigenfrequencies Transmissibility variations Potential need for intermediate run(s) Estimation of qualification levels possible Small gap or material nonlinearity Eigenfrequency shift Large variations of amplitude Eigenfrequency variations Intermediate run is required Close monitoring of qualification levels is required Large gap or nonlinear stiffness Large perturbations of dynamic test runs High frequency content ( shocks ) Differences between global & fundamental levels Difficult control of excitation input Successful qualification is jeopardised European Space Agency Directorate of Technical and Quality Management, Statement of work: Advancement of Mechanical Verification Methods for Non-linear Spacecraft Structures, 20 June 2007 11 copyright LMS International - 2010
Example of the effect of local non-linearities 10.00 10.00 k2 g Real 1.00 g Real 1.00-1.00-1.00 k1 d 100.00-10.00 Time Slip_Table_zdd.2(m_s2) TimeHistories_D_0_1 Time Slip_Table_zdd.2(m_s2) TimeHistories_D_0_5 Time Slip_Table_zdd.2(m_s2) TimeHistories_D_0_9 10.00 s 50.00 AutoPow er Slip_Table_zdd.2(m_s2) W 187 [0-99.194 s] -10.00 Time Slip_Table_zdd.2(m_s2) TimeHistories_D_0_1 Time Slip_Table_zdd.2(m_s2) TimeHistories_D_0_5 Time Slip_Table_zdd.2(m_s2) TimeHistories_D_0_9 36.73 s 36.80 10.00 Context: ESA-ESTEC study Advancement of Mechanical Verification Methods for Nonlinear Spacecraft Structures (Contract 21539/08/NL/Se). Time s db g 12 copyright LMS International - 2010 10.00 0.00 Hz 640.00 Slip Table zdd.2(m s2) (CH5) -90.00
Base-driven tests Non-linear components in modern satellite designs Base-driven test objectives Identify the effects of non-linear behavior Identify at what level the non-linear effects occur Verify that the qualification level is in accordance with required level No evidence of structural or mechanical failure by visual inspection and by low level comparison 3.00 1.00 Harmonic Spectrum 231X:+X Harmonic Spectrum 231X:+X Harmonic Spectrum 231X:+X Harmonic Spectrum 231X:+X 12.00 g Amplitude Amplitude Amplitude g 1.00 1.00 33:224Z:+Z Log Amplitude g 1.00 Amplitude Spectrum Reference Spectrum UpAbort Spectrum UpAlarm Spectrum Low Alarm Spectrum Low Abort Spectrum AvgCtrl 0.10 5.00 Hz 100.00 0.00 0.00 23.97 s 35.62 0.00 13 copyright LMS International - 2010 0.00 8.25 44.50 5.00 Hz 60.50 0.00
Base-driven tests M. Link, M. Böswald, S. Laborde, M. Weiland, and A. Calvi, An approach to non-linear Experimental Modal Analysis, IMAC 2010 14 copyright LMS International - 2010
Overview excitation methods (burst) Random Swept Sine Stepped Sine Normal Modes AP() [N²] AP() [N²] AP() [N²] tap() [N²] f ω [Hz] ω [Hz] ω [Hz] ω resonance ω [Hz] 15 copyright LMS International - 2010
Non-linearity assessment Current capabilities / Linearity assumption Rs and modal parameters Assessment of linearity Linear model Optimal experimental design Error margins Nonlinear model Current industrial practice Different excitation amplitudes Comparing Rs Comparing modal parameters Coherence, BUT combines: Measurement noise Leakage Nonlinearity Unknown inputs 0.50 (m/s2)/n Log 1.00 Amplitude 161e-6 0.00 Hz 400.00 0.02 16 copyright LMS International - 2010
Improved R estimation Pure random Pure Random Random Amplitude Random Phase Windowing Needed Windows ALWAYS distort data!!! If possible it s better not to use windows 17 copyright LMS International - 2010
Improved R estimation Burst random Burst Random Random Amplitude: no control over frequency-domain amplitudes for each realization Random Phase NO Windowing Needed Leakage for lightly damped structure Transient Response influence Lower Signal to Noise Ratio 18 copyright LMS International - 2010
Improved R estimation Pseudo Random Pseudo Random Block1 Block1 Block1 Block2 Block2 Block2 Block3 Block3 Block3 Realization 1 Realization 2 Realization 3 Controlled Amplitude Random Phase Intrinsically Periodic NO Leakage, NO Windows Very light transient effects if one or more delay blocks are used It should give the best R estimate 19 copyright LMS International - 2010
Multisines & Nonlinearity Special measurement sequence of pseudo random signals lat multisine Random phases u( t) N S = k = 1 A k cos(2πkf t + φ 0 k M sequences ) σ 1 σ R R realisations Delay block(s) σ Noise+ NL σ 2 Noise = 1 R 2 R i= 1 σ 2 i J. Schoukens, J. Swevers, R. Pintelon, H. Van der Auweraer, Excitation design for R measurements in the presence of nonlinear distortions, ISMA 2002. 20 copyright LMS International - 2010
-16 Demo 21 copyright LMS International - 2010
Classical non-linearity assessment -10.00-35.00 R ALDP:-Z/ALDP:+Z Low orce R ALDP:-Z/ALDP:+Z Medium orce R ALDP:-Z/ALDP:+Z High orce N db g/n db AutoPower ALDP:+Z AutoPower ALDP:+Z AutoPower ALDP:+Z -60.00 180.00 Phase -40.00 0.00 Hz 100.00-180.00 15.00 Hz 23.00 22 copyright LMS International - 2010
Classical non-linearity assessment 0.04 g/n Amplitude PseudoRandom Stepped Sine 5 N Stepped Sine 10 N Stepped Sine 15 N s s s v s s s v v v s s v v s s s v s s v o o v s s v s s v s v o o o s s s v vv v v s v o 6.51 Linear 7.51 Hz 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1.00e-3 180.00 Phase -180.00 6.50 Hz 7.50 23 copyright LMS International - 2010
Quality of R measurements: Random, burst random, multisine -20.00 R ALDP:-Z/ALDP:+Z Multisine R R ALDP:-Z/ALDP:+Z std Random R ALDP:-Z/ALDP:+Z std Burst Random R ALDP:-Z/ALDP:+Z std Multisine -20.00 1.00 g/n db g/n db Amplitude / R ALDP:-Z/ALDP:+Z Multisine R Coherence ALDP:-Z/ALDP:+Z Random Coherence ALDP:-Z/ALDP:+Z Burst Random Coherence ALDP:-Z/ALDP:+Z Multisine -120.00 1.00 Hz 20.00 24 copyright LMS International - 2010 Standard deviation σ avg -90.00 2 1 1 = N 1.00 Hz 20.00 γ 2 γ 2 H 2 Coherence 0.00
Non-linearity assessment using multisines -20.00 R ALDP:-Z/ALDP:+Z R R ALDP:-Z/ALDP:+Z Noise R ALDP:-Z/ALDP:+Z Noise + Non-Lin -20.00 R S:Radome:+X/ALDP:+Z R R S:Radome:+X/ALDP:+Z Noise R S:Radome:+X/ALDP:+Z Noise + Non-Lin -20.00 R RHT:TA:+Z/ALDP:+Z R R RHT:TA:+Z/ALDP:+Z Noise R RHT:TA:+Z/ALDP:+Z Noise + Non-Lin g/n db g/n db g/n db -120.00 0.00 Hz 20.00-120.00 1.00 Hz 20.00-120.00 1.00 Hz 20.00-20.00 g/n db R ALDP:-Z/ALDP:+Z R R ALDP:-Z/ALDP:+Z Noise R ALDP:-Z/ALDP:+Z Noise + Non-Lin Aircraft nose: R mainly affected by noise Horizontal tail plane: non-linear std: +15 db Driving point Zoom ull band -120.00 0.00 Hz 100.00 25 copyright LMS International - 2010
Aircraft development process Vehicle Level Analysis Vehicle Level Verification/Certification Design / Loads Cycles Physical Performance Certification Assembly Verification/Certification Component Verification/Certification Virtual Performance Certification Assembly Analysis Concept Validation arget Cascading Component Analysis easibility Concept Definition Development GVT In-flight 26 copyright LMS International - 2010 In Service Market Study Concept Selected Authority To Offer Program Launch Agreement With Primary Partners Component Design Major Assemblies Major Body Sections irst light Certification Entry Into Service Pressure on test time is extreme end-of-project stress
Test EM correlation requency correlations within 5% EM updating: 1. Configuration 2. Rigid body modes 3. lexible modes 27 copyright LMS International - 2010
Next: aero-elastic simulation and in-flight flutter testing Traditional EM, GVT-updated EM, or direct GVT M x( t) + Cx ( t) + Kx( t) ( x) = a 0 Aerodynamic panel method Due to presence of aero-dynamic term, modes of structural system are changing with airspeed and altitude lutter analysis = assessing evolution of modes (zero-crossing of damping value) E Model Test Model (GVT) Aerodyn. Panel Model Physical prototype 28 copyright LMS International - 2010
Conclusions & outlook Modal analysis is 40 years young Still, it is the subject of significant and relevant research efforts Sensing Testing Analysis & model estimation Use of modal model data Modal analysis has evolved from research tool to mature technology Modal analysis has become part of the standard product development process The demands are these of professionals, not (only) researchers Research efforts have considered this and look into user added value to be relevant 29 copyright LMS International - 2010
Thank you Journée Modes non-lineaires, Université de Liège, 9 novembre 2010 Bart Peeters, Simone Manzato, Gianpiero Rocca