Advanced Modal Analysis Techniques. Advanced Modal Seminar Brasil, Februari 2017

Transcription

1 Advanced Modal Analysis Techniques Advanced Modal Seminar Brasil, Februari 2017 Unrestricted Siemens AG 2016 Realize innovation.

2 Agenda Operational Modal Analysis Rigid Body Properties Modification Prediction Page 2

3 Operational Modal Analysis

4 How would you excite these structures? Page 4

5 Operational Modal Analysis In-operation testing Some applications permit the acquisition of Input - output (FRF) data during normal operation Require special setups for forced excitation Rotating wing-tip vanes Electromagnetic bearings Low-frequency exciters Drop-weights Unbalance shakers Pyrotechnics Control Surface Input Servo-drive inputs (robots) Testing complexity Data quality (undesired ambient sources) Some applications permit simulating inoperation conditions in I/O (FRF) tests (car suspension ) The normal EMA processes can be followed Page 5 NASA EMPA KUL

6 In-operation EMA example: Business jet, wing-vane in-flight excitation In-flight excitation, 2 wing-tip vanes 9 responses 2 min sine sweep Higher order harmonics Very noisy data e Phase g/n Log 1.00e FRF w ing:vvd:+z/f200:fed:+z FRF back:vde:+y/f200:fed:+z Phase Hz Amplitude / g/n Log Page Hz Coherence w ing:vvd:+z/multiple Coherence back:vde:+y/multiple Hz

7 Operational Modal Analysis What? Identification of modal parameters from response data only Eigenfrequencies Damping Mode shapes No scaling! Using measurements (accelerations) in operational conditions Why? Real operating conditions laboratory conditions Non-linearities Environmental effects Aero-elastic interaction Temperature Boundary conditions Inability to measure the inputs Too difficult, timeconsuming, expensive Permanent monitoring Page 7

8 Operational Modal Analysis Positioning Laboratory measurements FRFs impact random stepped sine Normal mode testing Operational measurements - time histories, spectra - selection of reference stations - multiple runs Modal analysis (FRFs) CMIF LSCE, PolyMax,... Peak picking - power spectra - principal comp. (oper. deflection shapes) Operational modal analysis (freq, damping, mode shapes) F E M / B E M Page 8

9 Operational Modal Analysis Operational modal analysis = identifying H Based on Y Without knowing U Input System Output White noise U White noise + harmonic H Y Additional input poles identified No problem if: poles input system poles Low damping, related to rpm Page 9

10 Operational Modal Analysis Background Typically, output-only data Fed by correlations between outputs and outputs serving as references direct in time domain inverse DFT of auto-and crosspower spectra Unknown input is assumed to be stationary white-noise (theoretical assumption) in practice: colored noise, impulse excitation, swept sine,.. = OK The frequency band of excitation has to include the modes Mode shapes cannot be mass-normalized Colored noise: Additional input poles identified: harmonics = low damping, related to rpm poles input system poles Sum of Cross powers Page 10

11 Traditional (IO) modal parameter estimation Modal model 0.10 Frequency domain Time domain g/n ( Log ) e Phase Hz Inverse Fourier transform g/n ) ( Real s 6.00 FRF H n * n Ai Ai it ( ) h( t) A e A i1 j i j * i i1 i * i e * t i IRF T A Q v l T i i i i i i * 2 i, i ii j 1 i i Page 11

12 PolyMAX Pre-processing for Operational Modal Analysis Spectrum estimation: leakage-free and Hanning window-free 1. High-speed estimation of timedomain correlations Data reduction 2. Exponential window Reduces the effect of leakage Reduces the influence of noise Compatible with the modal model ( Hanning window is not compatible and leads to biased damping) 3. Fourier transform of windowed correlations g Real s 2.50e-9 g 2 Real -2.50e s g db Phase Time-domain correlations Fourier transform AutoPow er ref:2b06:+z AutoPow er ref:2b06:+z Time ref:2b06:+z AutoCorrelation ref:2b06:+z AutoCorrelation ref:2b06:+z Page Hz 50.00

13 Pre-processing for Operational Modal Analysis: classical and non-classical spectrum estimate Operational data yk Classical spectrum ( Periodogram ) s) Y DFT[window y S S ( ( s) k ( s) ( s) ( s) H yy Y Y P 1 ( s) yy ( ) S yy ( ) P s1 ] Half spectrum ( Correlogram ) R S S i yy yy 1 N 1 k0 N y ki y T k ( ) DFT[window { R L,..., R0,..., RL}] ( ) DFT[window { R0 / 2,..., RL}] 10.0e-9 Periodogram with Hanning window 1.00e-9 Correlogram with exponential window ( ) Log (m/s 2 ) 2 Log autopow er_spectr roof:1:+z / roof:1:+z crosspow er_spect roof:1:+x / roof:1:+z AutoPow er roof:1:+z CrossPow er roof:1:+x/roof:1:+z 1.00e Phase Page Hz e Phase Hz 8.00

14 Why half spectra? 10e-9 (m/s 2 ) 2 Real Time roof:1:+x Unw indow ed Time roof:1:+x Lower order models S ( ) S ( ) S ( ) S yy yy ( j) yy n i1 v yy i gi j i H * v * gi * j i i -10e-9-90 db (m/s 2 ) Phase s Unrestricted Siemens AG Hz 2013 All rights reserved Page 14 AutoPow er roof:1:+x Unw indow ed AutoPow er roof:1:+x Exponential window Reduces the effect of leakage Reduces the influence of the higher time lags having a larger variance Compatible with the modal model ( Hanning window with biased damping)

15 Operational Modal Analysis The Vasco da Gama Bridge Vertical acc. Transversal acc g Real g 2 Real 0.00 s Time data Correlations s g 2 Log Hz 2.50 Spectra Page 15

16 Operational Modal Analysis The Vasco da Gama Bridge Page 16

17 Operational Modal Analysis The Vasco da Gama Bridge Page 17

18 Operational Modal Analysis Measured Cross Spectra vs. Modal Model 10X-15Z 10Z-112Z g 2 Log Phase g 2 Log Phase Hz Hz 1.05 Page 18

19 Operational Modal Analysis Øresund Bridge Measurements of cable vibrations allow to monitor cable forces (vibrating string theory) f S n n 1 2L H m Page 19

20 Other Operational Modal Analysis Applications In-flight testing Flutter High-speed train Road test of a car Page 20

21 Operational Modal Analysis in Ship-Building Background: Performing EMA(Experimental Modal Analysis) on large ships is very difficult Most customers only perform ODS (Operational Deflection Shapes) using vibration data Using the same vibration data, customer can determine the modal properties of the ship with OMA (Operational Modal Analysis) Data Measurement Operational Modal Analysis 前後 左右 上下方向 Tokai University - Boseimaru Correlation 次数成分の周波数比較 with Anchoring Test Test.Lab & SCADAS-Mobile 周波数 (Hz) アンカリングテストランアップテスト 次数 ( 次 ) 1 st Bending Mode Page 21

22 OMA on Tokai University ship Page 22

23 First and second bending Page 23

24 Torsion and third bending mode Page 24

25 Scania: Enhanced exploitation of oilpan vibration data by Operational Modal Analysis 2168 FlyWheel (T1) rpm Hz Small_Block:12:+Z (CH3) 12 db Design of a silent oilpan Single measurement for Sound level evaluation Operational Deflection Shapes creating the sound Operational Modal Analysis Benefits Reduced testing time Consistent data FlyWheel g 2 (T1) Real rpm db Hz s Small_Block:12:+Z (CH3) 12 FlyWheel (T1) rpm Hz 650 Unrestricted Small_Block:12:+Z Siemens (CH3) AG 2013 All rights reserved. Page 25 db -38 OMA vs. impact modes (mass and temp diff)

26 Operational Modal Analysis (OMA) More than Operational Deflection Shapes (ODS) ODS Animate: Auto & Cross Spectra, FRFs, Orders Peak picking Deformation at a chosen frequency line No damping information Combination of modes and forced responses Combination of closely spaced modes Phenomena OMA Curve-fit: Auto & Cross Spectra Modal model Frequency Damping Mode shape (No modal scaling) Use of system identification methods Structural characteristics Separation of closely spaced modes Root causes Vibration problem root cause discriminator Page 26

27 Conclusions Operational Modal Analysis is a mature technology High-quality data acquisition Advanced parameter estimation algorithms Commercial software implementations Industrial applications Only care on the assumption made Evolutions since more than 20 years Technology Usability Applicability: no isolated results but part of engineering workflow Civil engineering Aerospace engineering Automotive engineering Page 27

28 Rigid Body Properties

29 Why are inertia properties needed? Verification of CoG & MoI values Input for simulation models Kinematic and dynamic prediction (multibody dynamics calculation) Coupling of an FE model with smaller rigid components Accurate Modal based modification or Substructuring requires flexible modes + rigid body modes Complete modal model A complete modal model contains 3 components: Rigid body modes Flexible modes Residual terms? Page 29

30 How to determine inertia properties? Based on measured Frequency response functions Typical modal test with hammer or shaker excitation At least 6 excitation locations (SDOF) 8 12 response locations (3 DOF) Pendulum test No extra equipment is needed Limited measurement effort Highly accurate alternative to conventional pendulum test Page 30 Time consuming Requires multiple suspensions - difficult for complex structures

31 Rigid body modes To synthesize rigid body modes based on FRF measurements Input: Geometry (nodes and coordinates) FRF data Output: Inertial properties: Center of gravity Mass Moments of inertia Directions of the principle axes of inertia 3 translational rigid body modes 3 rotational rigid body modes Page 31

32 Rigid Body Properties Calculation How does it work - Theory Approximate structure as Single DOF system Resonance frequency of this SDOF system is the first actual RBM of the structure Line above resonance is called the mass line Page 32

33 Rigid Body Properties Calculation How does it work Test setup Test Setup: Weigh the test item to obtain mass [kg] Suspend Test item (once) in free-free conditions Create geometry wire-frame model in global or local coordinates Measure FRF matrix preferably with hammer Page 33

34 Rigid Body Properties Calculation How does it work - Mass line methods Extract mass line: Unchanged FRFs Rigid body modes and first deformation modes are sufficiently spaced Measured FRFs are used Corrected FRFs Rigid body modes and first deformation modes are not sufficiently spaced Estimate first set of flexible modes from measured FRFs Correct measured FRFs by subtraction of contribution of flexible modes Lower Residual No accurate FRFs are measured in the frequency range directly above rigid body modes Lower residuals represent the influence of the modes below the deformation modes, and are therefore representative of the rigid body modes. Page 34

35 Rigid Body Properties Calculation How does it work - Calculation and results Calculate Rigid Body Properties: Least square solution over all measured DOF Least squares over selected frequency band of mass-line Validation through animation of rigid body motion Results: Coordinates of center of gravity Moments and products of inertia about CoG and any user defined reference point Principal moments of inertia and their direction Synthesis of 6 scaled rigid body modes with user defined frequency and damping for use in simulation models Page 35

36 Modification Prediction

37 Modification Prediction Why? The major advantages of Structural Modification Prediction within prototype optimization procedures are: Prediction of the effect of a structural modification without physically changing the structure. Evaluation of alternative design variation without repeated testing The LMS Test.Lab Modification Prediction workbook helps you to: Efficiently dissipate vibration energy using a tuned absorber Add masses or change local stiffness to move resonant frequencies Evaluation of the impact of a selected modification on the structure in a global sense Page 37

38 Modification Prediction Modification Prediction Theoretical background (1) Modal models for structures with flexible coupling and viscous damping 1. Laplace domain 2 p M pc K X p F p 2. Extended system equation pa B Y F ' A 3. Eigenvalue problem 0 M M C B M 0 0 K 4. Premultiply extended system equation with 5. Orthogonality condition t \ t A a and B,, Y A B 0 i i t px X, 0 F ' F i i i \ \ \ \ b b a \ \ \ \ i \ 6. Transformation to modal space Y q Page 38

39 Modification Prediction Modification Prediction Theoretical background (2) Modification of structure Structure modification Modified system equation M, C, K A, B A A B B p Y F ' Applying modal transformation New Eigenvalue problem in modal space to be solved q r m Modified system poles and modified eigenvectors in modal coordinates Back substitution to physical coordinates gives new modal vectors ψ ψ q m r m Page 39

40 Modification Prediction Automotive example Tuned absorbers in cars: (sometimes up to 30) tuned absorbers/vehicle gr / absorber (exceptionally up to 1.5 kg) Page 40

41 Modification Prediction Automotive example Mass modification on attachment bracket Bi-directional tuned absorber on an engine anti-roll mount Page 41

42 Modification Prediction Aero examples Aircraft cabin noise reduction Engine vibration reduction Page 42

43 Modification Prediction Aero example Helicopter design Page 43

44 Modification Prediction Civil construction Wobbling Bridge Will Stay Shut BBC News Modifications 58 Tuned Absorbers 4 Vertical dampers 17 Chevron dampers 16 Pier dampers Cost Construction: 18m Modifications: 5m!! Bridge closed for 2 years Page 44

45 Modification Prediction Other industries Everyone else interested in the vibration related product performance Page 45

46 Thank you! Advanced Modal Seminar Brasil, Februari 2017 Restricted Siemens AG 2016 Realize innovation.