Post on 21-Apr-2015
Fundamentals of Vibration and Modal AnalysisMeasurement functions Excitation techniques Testing practiceMeasurement functions – Excitation techniques – Testing practice
Sales New Hires Training 2008Swen Vandenberk
Lecture objectives
Know how measurements are
By completing this lecture, you will:
x(t)
f(t)
x(t)
f(t)
performed for Experimental Modal Analysis
Understand what an FRF and aground
m
ck
ground
m
ck
Understand what an FRF and a coherence is
Have a feeling for the practicalities of structural testing
Be able to talk about excitation techniquestec ques
2 copyright LMS International - 2008
Modal Analysis – Understanding the Dynamic Properties of Structures
Seat Vibration
Wheel & TireSteering Wheel
Shake
Engine
Noise at Driver’s &
RoadRearview mirror
vibrationTurbomachinery
Passenger’s Ears
Gearbox and TransmissionRotor
Cockpit vibration & noise
Cabin comfort
Environmental
System TransferSystem Transfer ReceiverReceiverX =
Accessories
Structural Integritysources
SourceSource
3 copyright LMS International - 2008
TransferTransfer
Systematic approach to noise & vibration testing The “source – transmitter - receiver” approach
Receiver!
Response:• noise• vibrations == =
XX X
TransmitterSystem characteristics:• structural• acoustic
Source
XX X
Operating loads:
acoustic
criticaldynamics
criticalloads
worst casescenario
p g• structural• acoustic
4 copyright LMS International - 2008
dynamicsloads scenario
Structural Dynamics ModellingSDOF (Single degree of freedom) system
System TransferSystem Transfer ReceiverReceiverX =SourceSource
100 Frequency Response Function
e
xf H
( ) 1( ) x ω
2
10-1
Log-
Mag
nitu
de damping controlled region
stiffness controlled region
mass controlled region
2( ) 1( )( )
xHf m cj kω
ω = =ω − ω + ω+
0 2 4 6 8 10 12 14 16 18 2010
-2
Frequency Hz
-50
0mx(t)
f(t)
-200
-150
-100Phas
e
ground
ck
The simplest dynamic system
5 copyright LMS International - 2008
0 2 4 6 8 10 12 14 16 18 20200
Frequency Hz
Structural Dynamics ModellingMDOF system
und
k1
f1(t)
undkn+1k2
f2(t) fn(t)
More complex dynamic system
HHFF XX
InputInput SystemSystem OutputOutput
grou m1
c1
k1m2 mn gr
ou2
c2 cn+1x1(t) x2(t) xn(t)
HHFF XX
Eigenfrequency = Peak in FRF
abstract
0.10
As many peaks as masses
g q yDamping ratio = Width of FRF peak / decay in IRFMode shape = ± Deformation at eigenfrequency
Modal parameters =
( )pqH jω
10.0e-6
Log
( g/N
)
180 00
0.91
lN)
eigenfrequency
( )pqH j∠ ω-180.00
180.00
Phas
e°
0.00 6.00 s-1.07
Rea
l( g
/N
6 copyright LMS International - 2008
0.00 80.00 Hz
Freq. domain: Frequency Response Function (FRF) Time Domain: Impulse Response Function (IRF)
Mode Shapes
Mode 1
2Mode 21
7 copyright LMS International - 2008
Analytical Modal Analysis: only for simple cases
OK for
Distributed parameters Lumped parametersww
xx
024
4
=ω− wEIm
dxwd
But what about real-lifestructures?
We have to look for other approaches• Virtual prototype: Finite Element Modal Analysis• Physical prototype: Experimental Modal Analysis
See CAE technology lecture
See here!
8 copyright LMS International - 2008
• Physical prototype: Experimental Modal Analysis
Engineering for improved Noise & Vibration performance Experimental Modal Analysis
Excitation techniquesDSPDSPFrequency Response Functions (FRFs)Curve-fitting / (modal) parameter estimationest at oValidation
Modal Parameters:Modal Parameters:FrequencyFrequencyDampingDampingp gp gMode shapesMode shapes
9 copyright LMS International - 2008
Experimental Modal Analysis:Aircraft Test Setup Example
Responses
Ground Vibration Test
InputsInputs
F4
F3 Ground Vibration Test
(GVT) System
⎥⎥⎥⎤
⎢⎢⎢⎡
24232221
14131211
HHHHHHHHHHHH
pons
espo
nses
F2
F1 ⎥⎥
⎦⎢⎢
⎣ 44434241
34333231
HHHHHHHH
Res
pR
esp
Force Inputs
0 . 1 0
N)
1 row or column suffices to determine modal parametersReciprocity
0 . 0 0
Log
( (m/s
2 )/N
1 8 0 . 0 0
Phas
e
°
qppq HH =
10 copyright LMS International - 2008
0 . 0 0 8 0 . 0 0H z- 1 8 0 . 0 0
Experimental Modal Analysis
Required knowledge for a successful modal test
Test Setup Purpose of the test • Knowledge of expected modes of the
system• Expected results • Transducers and excitation devices
Make measurements • Knowledge of digital signal processing, parameters such as leakage, windows,parameters such as leakage, windows, time and frequency relationships, FFT, excitation techniques
Identify Parameters • Knowledge of modal theory • Knowledge of modal parameter estimation
techniquestechniquesVerify/document results • Knowledge of modal theory
• Synthesis. MAC
11 copyright LMS International - 2008
Experimental Modal Analysis vs.Finite Element Modal Analysis
Experimental Numerical
( )H ω , ,{ },i i i iQω ξ φ , ,M C K , ,{ },i i i iQω ξ φ
Requires prototypeVery fast (1-5 days)Very accurate for frequency
Requires FE modelMany days/weeksFast alternative evaluationVery accurate for frequency
More reliable for dampingLimited number of points
Fast alternative evaluationA lot of model uncertainties
(joints / damping / …)High number of points
12 copyright LMS International - 2008
Experimental Modal Analysis
5. Use modal parametersTroubleshooting
1. Measure FRFsTroubleshooting
• Check frequencies• Qualitative descriptions of
mode shapesSimulation and predictionDesign optimisationDiagnostics and health monitoringFinite Element model
2. Estimate poles
Finite Element model verification/improvementHybrid system model building
3. Estimate shapes
4. Validate
13 copyright LMS International - 2008
Experimental Modal Analysis Applications
Car body, fully equipped car, car interior cavitycavity, …Aircraft fuselage, full aircraft, interior cavity, …Components: engine block, suspension systems, brakes, antennasProcessing plants: piping systems, equipment mountingMechanical equipment: turbine blades, q p ,compressors, pumpsAudio & household: CD-drive, washing machine, loudspeakersInfrastructure: bridge off shore platformsInfrastructure: bridge, off-shore platforms
14 copyright LMS International - 2008
Digital Signal Processing for Structural TestingToC
Basic DSPFourier transform
See DSP lecture
Fourier transformQuantisationAliasingLeakageea age
Frequency Response Function(FRF) estimatorsCoherence functions
InputInput SystemSystem OutputOutput
HHFF XX
15 copyright LMS International - 2008
Frequency Response Function (FRF) Measurements –SISO
Frequency Response FunctionInputInput SystemSystem OutputOutput
( ) ( ) ( )X H Fω = ω ω
How to estimateIdeal world
HHFF XX( ) ( ) ( )X H Fω = ω ω
Real life: averaging required
“Naïve” averaging approaches
FXH =
∑ ==
N
i iXNH
1
1Random excitation: averaging of linear• Mechanical noise
• Non-linear behaviour• Electrical noise in the instrumentation
∑ =
=N
i iFN
H
1
1
∑N X1
averaging of linear spectra go to 0
∑ ==
N
ii
i
FX
NH
1
1May be 0 (very small) at some spectral lines
Use statistical noise modelling instead
16 copyright LMS International - 2008
Use statistical noise modelling instead
FRF measurements
Time signals Linear spectra Power andcross spectra
FRF andcoherence
DFT averaging calc.
f(t) F(ω) GFF(ω)
Inpu
t
FF
XF
GGH =1
GXF(ω)
H(ω)
ross
XFG 2
hX(ω) G (ω)
XF( )
coh(ω)
Cr
FFXX
XF
GGcoh =
x(t)
X(ω) GXX(ω)
Out
put
17 copyright LMS International - 2008
O
FRF estimators – graphical interpretation
X H1 X H2 X Hv
At single frequency ω: N measurements available
X 1 X 2 v
F F F
H1 estimateLeast squares
Output noise
H2 estimateLeast squares
Input noise
Hv estimateTotal least squares
Input noiseOutput noise
XF
N
N
i ii
GG
FF
FXNH ==∑
∑=
*
1*
1 1
1
FX
XX
N
N
i ii
GG
XF
XXNH ==∑
∑=
*
1*
2 1
1
18 copyright LMS International - 2008
FFi ii
GFFN ∑=1
FXi ii
GXFN ∑=1
Coherence
Cross spectrum inequalityNon coherent noise
8
6
7
(ms-2/N)
0 800100 200 300 400 500 600 700
01.2
1
Hz
linear amplitude
FRF8
6
7
(ms-2/N)
0 800100 200 300 400 500 600 700
01.2
1
Hz
linear amplitude
FRFNon-coherent noise
FFXXFX GGG ≤2
2
3
4
5
ar amplitude
0 800100 200 300 400 500 600 700
01.2
1
Hz
linear amplitude
2
3
4
5
ar amplitude
0 800100 200 300 400 500 600 700
01.2
1
Hz
linear amplitude
Coherence
FX
GGG 2
2 =γ0 800100 200 300 400 500 600 7000
1
Hz
linea1.2
0 800100 200 300 400 500 600 7000
1
Hz
linea1.2
Smaller than 1 when
FFXXGG
10 2 ≤γ≤
0 800100 200 300 400 500 600 700
08
12
34
56
7
Hz
linear amplitude (ms-2/N)
1amplitude
0 800100 200 300 400 500 600 700
08
12
34
56
7
Hz
linear amplitude (ms-2/N)
1amplitude
Smaller than 1 when …Noise in the measurementsNonlinearitiesLeakage
0 800100 200 300 400 500 600 700
08
12
34
56
7
Hz
linear amplitude (ms-2/N)
0
linear a
Coherence
0 800100 200 300 400 500 600 700
08
12
34
56
7
Hz
linear amplitude (ms-2/N)
0
linear a
Coherence
19 copyright LMS International - 2008
g
0 800100 200 300 400 500 600 700
08
12
34
56
7
Hz
linear amplitude (ms-2/N)
0 800100 200 300 400 500 600 7000
Hz
0 800100 200 300 400 500 600 700
08
12
34
56
7
Hz
linear amplitude (ms-2/N)
0 800100 200 300 400 500 600 7000
Hz
FRF + CoherenceTypical Examples
Lo g
100
1
10
24
2040
1.05 10.0
g/N
0.001
0.01
0.1
1
0 0000.0004
0.002
0.004
0.020.04
0.20.4
Leakage
Hz
0 2047.5
1000
200 400 600 800 1200
1400
1600
1800
1e-05
0.0001
3e-05
0.00024
1
0.9
Ampl
itude
/ dB
( (m
/s2)
/N)
Ampl
itude
/
0 3
0.4
0.5
0.6
0.7
0.8
Hz
0 2047.5
1000
200 400 600 800 1200
1400
1600
1800
0
0.1
0.2
0.3
0.00 45.00 Hz
0.00 -70.08.38
F coherence DRV:1:+XB FRF DRV:1:+X / FOR:1:+XB FRF DRV:1:+X / FOR:2:+X
20 copyright LMS International - 2008
Coherence and FRF Variance
FRF Variance
Large coherence
2
222 1.
)1(2 γγ−
−=σ
NH
H
a ge co e e cecorresponds to a goodFRF estimationWhen the coherence is low take more averageslow, take more averages
90% confidence bounds on the estimated FRF magnitude and phase
21 copyright LMS International - 2008
p
Aircraft In-flight Testing “Noisy” FRFs
In-flight excitation, 2 wing-tip vanes, 2 min sine sweep9 accelerometersNoisy data (additional unmeasurable turbulence excitation)Noisy data (additional unmeasurable turbulence excitation)
1.00 1.00
Coherences FRFs
Log
(m/s
2)/N
)
Ampl
itude
/
0.00
( (180.00
0 00
F Coherence w ing:vvd:+Z/MultipleF Coherence back:vde:+Y/Multiple
-180 00
180.00
Phas
e°
22 copyright LMS International - 2008
Hz
0.00
Hz
180.00
Vehicle FRFs
Body-in-white Fully-trimmed vehicle
Lowly-damped structure, sharp peaks
Highly-damped structure, rounded peaks
0.10
)/N)
98.1e-3
)/N)
100e-6
Log
( (m
/s2 )
180 00
98.1e-6
Log
( (m
/s2
FRF moto:9:+Z/karo:25:+Z
180 00
0.00 80.00 Hz-180.00
180.00
Phas
e°
3.50 30.00 Hz-180.00
180.00
Phas
e°
FRF moto:9:+Z/karo:25:+Z
23 copyright LMS International - 2008
Demo_car Porsche
Radarsat Satellite
5 shaker excitation
1.00
Log
( (m
/s2)
/N)
100e-9180.00
10.00 64.00 Hz
-180.00
Phas
e°
Low contribution of “red” input to response
24 copyright LMS International - 2008
Low contribution of red input to response
Structural testing equipment
ExcitationShakers or hammerShakers or hammerForce cell
ResponseAccelerometerscce e o ete sLDV (laser)
25 copyright LMS International - 2008
Boundary Conditions
Fixed boundary conditionsDifficult to realise
• Flexibility of fixtures
Free-free suspensionIn practice: almost free-free
• Soft spring elastic cord• Flexibility of fixtures• Added damping• Environmental noise
• Soft spring, elastic cord• Soft cushion
Check if your Check if your suspension is soft suspension is soft
enough !enough !
Rigid bod modeRigid bod mode freq enc < 10 % of firstfreq enc < 10 % of first fle ible modefle ible mode
26 copyright LMS International - 2008
Rigid body modeRigid body mode frequency < 10 % of firstfrequency < 10 % of first flexible modeflexible mode
Boundary ConditionsPractical Examples
Fixed-free± Free-free (soft tires)
27 copyright LMS International - 2008
ATA Engineering, IMAC 05
GVT of Embraer 170Influence of Tire Pressure
Tires not soft enough
28 copyright LMS International - 2008
Embraer, IMAC 05
Boundary ConditionsPractical Examples
Pneumatic suspension
Courtesy Airbus France
Elastic cords Operational boundary conditionsElastic cords Operational boundary conditions
29 copyright LMS International - 2008
FRF measurements Impact Testing
AdvantagesLimited equipmentEasy and fast
TimeTime FrequencyFrequency
put
puty
Low costExcellent for troubleshooting
Disadvantages
Inp
Inp
nse
nse
DisadvantagesPoor Signal to Noise ratioPoor for non-linear structuresDouble impactsADC underload / overload
Res
pon
Res
pon
ADC underload / overload
Typically: fixed response accelerations -roving impact location
FRFFRF
roving impact location
30 copyright LMS International - 2008
Impact testingAbout Hammer Tips
Force spectrumSoft tipCoherence
FRF
Soft tip
Hard tip
Right tip
31 copyright LMS International - 2008
FRF measurements Shaker Testing
Fast & reliable
Best ratio quality/time tt
TimeTime FrequencyFrequency
Better energy distribution over structure
Excellent for trouble shooting &
modification simulation
Inpu
tIn
put
ee
Typically fixed excitation point, multiple
response points - measured in batches
Only way to characterize non-linearities
Res
pons
eR
espo
nse
FRFFRF
32 copyright LMS International - 2008
Shaker testingRequired instrumentation
An excitation device is attached to the structure using a rod (“stinger”)rod ( stinger )
Characteristics of the stinger to ensure that the only input is along the shaker excitation axis
• High axial stiffness• Low transverse and bending stiffness
Multiple shakers can be used Energy distribution over structure
• All responses are above the background noise• All responses are above the background noise• Exciting different parts of a real structure (e.g.
wing and tail plane of an aircraft)Exciting a 3D-structure in different directions (X,Y,Z)Multiple-reference measurements
• Mode multiplicity• Less risk to miss modes (“controllability”)
33 copyright LMS International - 2008
Shaker Excitation signals
Random
Burst Random
Stepped SineNormal mode excitation
ChirpSwept Sine
34 copyright LMS International - 2008
p
Random excitationAveraging
3 averages3.50
plitu
de/
2.70 litu
de/
10 averages0.00
Amp
0.00 1100.00 Hz
-180.00
180.00
Phas
e°
0.00
Ampl/
0.00 1100.00 Hz
-180.00 180.00
Phas°
2.20
e
20 averages
0.00 Am
plitu
de/
-180.00 180.00
hase°
2.10
40 averages
0.00 1100.00 Hz
Ph
0.00
Ampl
itude
/
180 00se35 copyright LMS International - 2008
0.00 1100.00 Hz
-180.00 180.00
Phas°
Random excitationWith Hanning window
Comparison of random with and without a Hanning window after 40 averages
CoherenceFRF2.80 1.00 1.00 1.00
FRF random with Hanning
FRF random without Hanning
Ampl
itude
/
Ampl
itude
Ampl
itude
/
Ampl
itude
FRF random with Hanning
0.00 1100.00 Hz
0.00 0.00
0.00 1100.00 Hz
0.00 0.00
FRF random with Hanning
FRF random without Hanning
The smearing of energy to neighboring spectral lines in the FRF’s is far less when a Hanning window is applied, which result in a far better approximation of the studied system and a vast improvement of the coherence
36 copyright LMS International - 2008
Shaker testing(MIMO) burst excitation
Advantages: applicable for lightly and heavily damped systemssyste sLeakage? Only if the responses do not die out within the observation period (“block”)Disadvantage wrt random: less energy in structure, less good Signal to Noise ratioSignal to Noise ratio
37 copyright LMS International - 2008
Shaker testingComparison random and burst random
Random with Hanning
B t R dBurst Random
FRF comparison
Conclusion:
Avoid Random on lightly
38 copyright LMS International - 2008
damped structures !
Shaker testing(MIMO) Sine Shaker Signals
Stepped sine Normal modes
Sinusoidal excitationCovering entire frequency rangeBuild FRF line by lineAll h k t i l f
Excite the structure at resonance frequency with “tuned” input force combination (several shakers) such that only one mode in resonance
pp
All shaker energy at single frequencyHigh qualityBest signal to characterize non-linear properties
resonanceOldest methodVery accurateFeel the mode directlyB t ti iBut ... time consuming
Traditionally preferred method by aircraft manufacturers
39 copyright LMS International - 2008
Shaker testingOverview Excitation Methods
Random Swept Sine Stepped Sine Normal Modes
t
AP
(F) [
N²]
AP
(F) [
N²]
AP
(F) [
N²]
AP
(F) [
N²]
t
ω [Hz] ω [Hz] ω [Hz] ω [Hz]ωresonance
f
40 copyright LMS International - 2008
Shaker testingOverview Processes
Random Swept Sine Stepped Sine Normal Modes
t
AP
(F) [
N²]
AP
(F) [
N²]
AP
(F) [
N²]
AP
(F) [
N²]
t
ω [Hz] ω [Hz] ω [Hz] ω [Hz]ωresonance
f
Phase Seperation or Frequency Response Function (FRF) based methods
Phase Resonance /Mode Appropriation
Measure Modal Parameter Experimental Modal Measure / IdentifyMeasure FRF
Modal Parameter Estimator
Experimental Modal Model [ ω, ξ, ψ ]
Measure / Identify Mode [ ω, ξ, ψ ]
-19.83
2)/N
)
41 copyright LMS International - 2008
-89.83
dB( (
m/s
2
FRF DRV :1:+X / FOR:1:+FRF DRV :2:+X / FOR:2:+
Data Verification
Excitation power spectraDriving point FRFsReciprocityReciprocityLinearityCoherences
Input 1 at right wing
Input 2 at the rear part of fuselage
100e+6
F AutoPow er FOR:1:+XF AutoPow er FOR:2:+X
Log
N2
10 0e 3
42 copyright LMS International - 2008
0.00 400.00 Hz
10.0e-3
Driving Point FRFs
Selection and verification of excitation locationsAll modes present in driving point FRF ? Bad quality driving Bad quality driving All modes present in driving point FRF ?Alternating resonances and anti-resonancesPhases between 0-180°
q y gq y gpoint FRF = Bad point FRF = Bad
quality modal model !quality modal model !
0.07
Log
( g/N
)
33.6e-6
FRF DRV:1:+X/FOR:1:+XFRF DRV:2:+X/FOR:2:+X
180.00
Phas
e°
43 copyright LMS International - 2008
0.00 100.00 Hz-180.00
Reciprocal FRFs
Alignment stinger – force cell – accelerometer
1.00
FRF DRV:1:+X / FOR:2:+XFRF DRV:2:+X / FOR:1:+X
Log
( (m
/s2)
/N)
100e-6
0.00 100.00 Hz
-180.00
180.00
Phas
e°
44 copyright LMS International - 2008
Linearity of FRFs
3 different excitation levels FHXFHXα=α
=
1.00 0.10
Log
N2
Log
( g/N
)
F AutoPow er FOR:1:+XF AutoPow er FOR:1:+XF AutoPow er FOR:1:+X 10.0e-6
FRF DRV:1:+X/FOR:1:+XFRF DRV:1:+X/FOR:1:+X (1)FRF DRV:1:+X/FOR:1:+X (2)
180 00
0.00 100.00 Hz
1.00e-6
0.00 100.00 Hz
-180.00
180.00
Phas
e°
45 copyright LMS International - 2008
Coherences
Coherence differs from 1 in case of:Non Linearity 1 00Non-LinearityLeakageUnmeasured sourcesOther noise
1.00
Ot e o se
Rea
l/
F Coherence DRV:1:+XF Coherence DRV:2:+XF Coherence ENG:1:+YF Coherence FUSL:5:+X
0.00 100.00 Hz
0.00
46 copyright LMS International - 2008
Course summary
Structural ExcitationBoundary conditions
testing in source –transfer –
Excitation techniques
transfer receiver model
DSP for Structural T ti FRF d
Introduction to Experimental
M d l Testing: FRFs and coherences
Modal Analysis
47 copyright LMS International - 2008
Thank you
Sales New Hires Training 2008Swen Vandenberk