Transcript של PowerPoint - Iby and Aladar Fleischman Faculty of Engineering

TEL AVIV UNIVERSITY
The Iby and Aladar Fleischman Faculty of Engineering
The Zandman-Slaner School of Graduate Studies
Measuring Ultrasonic Lamb Waves Using Fiber
Bragg Grating Sensors
By
Eyal Arad (Dery)
Under the supervision of
Prof. Moshe Tur
1
This study…
Deals with the detection of propagating
ultrasonic waves in plates, used for damage
detection.
The detection is performed using a fiber
optic sensor (specifically, a Fiber Bragg
Grating sensor) bonded to or embedded in
the plate.
2
Contents
• General Introduction:
– Structural Health Monitoring and Non-Destructive Testing
– Lamb Waves in NDT
– Fiber Bragg Grating Sensors
• The goals of this work
• Analysis and results
–
–
–
–
Analytical solutions
Numerical solutions and comparison
Tangentially bonded FBG
Setup and Experimental Results
• Effects and implications
– Angular Dependence
– Rosette Calculations
• Summary of Findings
• Future Work
3
General Introduction
Structural Health Monitoring (SHM) and NonDestructive Testing (NDT)
• SHM- the process of damage identification (detection, location,
classification and severity of damage) and prognosis
• SHM Goal- increase reliability, improve safety, enable light weight
design and reduce maintenance costs
• NDT- an active approach of SHM
• Several NDT techniques exist, among them is Ultrasonic Testing
• Many Ultrasonic Testing techniques for plates utilizes Lamb Waves in
a Pulse- Echo method (damage= another source)
• Usually, both transducer and sensor are
piezoelectric elements
4
Lamb Waves Implementations in NDT
• Lamb waves are Ultrasonic (mechanic) waves propagating in a thin
plate (thickness<<wavelength)
• Important characteristics for NDT:
– Low attenuation over long distances
– Velocity depends on the frequency (could be dispersive)
– Creates strain changes that can be detected
5
Lamb Waves Implementations in NDT
• Some examples for
suggested implementations
in the aerospace field:
– Qing (Smart Materials and Structures, v.14 2005)
– Kojima (Hitachi Cable Review, v. 23, 2004)
6
Lamb Waves Propagation
• In infinite material 3 independent modes of displacement exist
• In thin plates the x and y displacements are coupled (boundary
conditions) and move together
• Two types of modes exist:
– Symmetric waves
(around x)
7
– Antisymmetric waves
Lamb Waves Propagation
• Plane wave (infinite plate)
– Symmetric waves (displacement)
u x  i B cosy  C cos y e i x t 
u y   B sin y  C sin y e i x t 
tan b
4 2

tanb
2 2


2
Where ξ is the wave number ω/vph, and α,β are proportional to the
material’s constants
– Antisymmetric waves
u x  iA sin y  D sin y e i x t 
u y  A cosy  D cos y e i x t 

8
tan b
2 2

tanb
4 2

2
α,β
Lamb Waves Propagation
• Cylindrical Lamb wave
YZ
rX
– In the area close to the transducer
– Symmetric case


 it
 2   '2 cosh ' b

e
ur  AH1 r  2
cosh

'
z

cosh

'
z
 '   '2 
2 2 cosh  ' b

 it
' 
2 2 sinh  ' b

e
u z   AH0 r  2
sinh

'
z

sinh

'
z
 '   '2 
 2   '2 sinh  ' b

• H0 and H1 are Hankel Function of zero and first kind.
– For the antisymmetric solution it is only necessary to
interchange sinh and cosh
9
Lamb Waves Propagation
• Dispersion relations (Vph(f)):
• Lamb wave modes
• The selected working mode is A0
10
tan b
4 2

tanb
2 2


tan b

tanb
2

2
2
4 2

2
Fiber Bragg Grating (FBG) Sensors
• Permanent, periodic perturbation of the refractive index
• λB=2neffΛ
• Reflection curve
• Measuring Ultrasound according to:
11
16
12
R08
ΔR
R
R  R0  B 

Pr,opt ( )  Pin,opt R( )
neutral
with
strain
Reflection
B  0.79B
ΔλB
4
Pout,opt
0
1549.0
1549.2
1549.4
λB
1549.6
Wavelength ,nm
1549.8
1550.0
FBG’s advantages for NDT:
–
–
–
–
–
–
12
Directional Sensitivity
Small Size
Fast Response – up to several MHz
Ability to Embed inside Composites
EMI, RFI Immunity
Ability to Multiplex (several sensors on the
same fiber)
Summary of Introduction
SHM & NDT concept and goal
Lamb waves and their importance to NDT
FBG principle and advantages in NDT
13
Purpose of This Study
• To build an analytical model for a pulse
of propagating Lamb wave, in order to
validate a Finite Element (numerical)
model, for applying on complex cases
which cannot be solved analytically.
• Extending published plane wave
analysis, to analyze the effect of close
range sensing on the angular dependence
of FBGs and on angle-to-source
calculations.
PZT
FBG
Incident wave
ε1
y,εyy
εA
ε2
θ
• To analyze the behavior of the detected
ultrasonic signal at close range to the
transducer, where the wave is cylindrical.
wavefront
FBG
x,εxx
14
arbitrary direction
Analysis and Results
Lamb Wave Solutions for a Pulse Input
– x=0
u x x  0, y  b, t   signal
u~ x  0, y  b,    F (signal)  iA sin b  D sin b
x
1
0.8
0.6
0.4
Amplitude
• Input: single period sine function pulse
• Plane wave A0:
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
2.3
 A
F ( signal)
i sin b  G sin b 
2.4
2.5
time
2.6
2.7
2.8
4-
x 10
5
 u~y ( x  0, y  b)  A cosy  G cosy 
Using inverse Fourier transform
to convert to the time domain
Displacement
4
3
2
1
0
-1
1.5
2
2.5
3
t
15
3.5
4
-4
x 10
A0 plane wave displacements ux (blue) and uy (green) vs. time at
x=0 and y=b
watch
Lamb Wave Solutions for a Pulse Input
6000
5000
• For all x (Plane wave A0)
Vph[m/s]
4000
– Dispersion relation- A0 is dispersive
2000
u~x ( x, y  b,  )  u~x ( x  0, y  b,  )eix
u~ ( x, y  b,  )  u~ ( x  0, y  b,  )eix
y
3000
1000
0.5
y
1
1.5
2
2.5
f[Hz]
3
3.5
4
4.5
x 10
5
Dispersion relation for A0 (blue) and S0 (black)
1
5
0.6
4
0.4
3
Displacement
Displacement
0.8
0.2
0
-0.2
2
1
0
-0.4
-1
-0.6
-2
-0.8
-1
2
2.5
3
3.5
4
4.5
5
5.5
6
-4
t
x 10
ux displacements of A0 at distances of 0 (blue), 10(green), 20 (red) and 30cm (cyan)
16
3
4
5
t
6
x 10
-4
uy displacements of A0 at distances of 0 (blue), 10(green), 20 (red) and 30cm (cyan)
watch
Lamb Wave Solutions for a Pulse Input
1
• Cylindrical Lamb wave
r
A
0
0.6
0.4
Displacement
ur (r  r0 , z  b, t )  input_ signal
u~ (r  r , z  b,  )  F input_ signal  F (signal)
0.8
F ( signal)



 2   '2 sinh ' b
 sinh ' b 
H1 r0  2
sinh  ' b 
2 
2
 '  ' 
2
sinh  ' b

0.2
0
-0.2
-0.4
-0.6
-0.8
-1
2.5
3
3.5
4
t
4.5
x 10
-4
ur displacements of A0 at r= PZT edge (blue), 5 (green), 10 (red) and 20cm (cyan)

' 
2 2 cosh ' b

cosh

'
z

cosh  ' z 
2
2 
2
2
 '  ' 
   ' cosh  ' b

2
2



  '
 sinh  ' b 
H1 r0  2
sinh  ' b 
2 
2
 '  ' 
2

 H 0 r 
u~z (r , z,  ) 
17
4
3
Displacement


 2   '2 sinh ' b


F ( signal) H1 r  sinh  ' z 
sinh

'
z
2
2

sinh

'
b


u~r r , z,   
2
2


  '
H1 r0  sinh  ' b 
sinh  ' b 
2
2


2
1
0
-1
2
2.5
3
3.5
t
4
4.5
5
x 10
-4
uz displacements of A0 at r= PZT edge (blue), 5 (green), 10 (red) and 20cm (cyan)
Numerical solutions and comparison
• Finite Element Method (FEM)
Analytical model
A computer simulation which divides the
plate into small elements and solves the
energy relations between them.
11
AnalyticalUr
Uzatatr r0(5mm)
(5mm)
analytical
0
Analytical Uz at 11 cm
analytical Ur at 11cm
Analytical
at 31 cm
FEM
Ur at rUz(5mm)
FEM U at 0r (5mm)
z
0
FEM
FEMUr
U at
at11cm
11 cm
z
FEM U at 31 cm
0.8
0.8
0.6
0.6
0.4
Displacement
Displacement
Numerical model
z
0.2
0.4
0
0.2
-0.2
y
x
z
-0.40
-0.6
-0.2
-0.8
-0.4
-1
2.4 2.5 2.6
3 2.8
3.53
t
time
4
3.2
3.44.5
3.6
-4
10-4
xx10
– The analytical solutions Were crucial in
choosing the parameters for the FE
Models in order to receive the correct
model
– The FEM enables solving even more
complex cases (e.g. plate with a damage) z
Courtesy of Iddo Kressel of IAI ltd.
18
r
Tangentially bonded FBG
• What is the analytical influence of cylindrical
waves in Lamb wave detection by a FBG?
• The FBG signal is angular dependent (as
opposed to PZT sensor)
• FBG parallel to the Plane wavefront- No
Signal in the tangential FBG
• Cylindrical wave- Signal (strain) Exists
u r
r
u
  r
r
wavefront
wavefront
PZT
FBG
FBG
r 
0.8
anlytical strain (normalized)
• The tangential strain is:
1
– Different in its shape than the radial strain
– It can not be neglected at close distance
– Decays faster
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
19
2.2
2.4
2.6
2.8
time
3
3.2
x 10
radial (blue) and tangential (green) strains at 21mm
-4
setup
Purpose- to measure an ultrasonic
Lamb wave via FBG sensor
and validate analytical and
numerical models
Basic measurement setup:
Laser
source
y

Function
Generator
+Amplifier
x
θ
20
Detector
r

• Function Generator produces an input
signal.
• The PZT transforms the electrical
signal to an ultrasonic wave that
propagates through the plate.
• The sound vibrations affect the FBG
which is bonded to the plate.
• The FBG transforms the mechanical
vibrations to an optical Bragg
reflection shift.
• This shift is identified by the optical
interrogation system.
Signal
Processing
x
PZT Exciter
FBG sensor
Experimental Results
Tangential strain
Radial strain
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
strain
tangential strain (normalized)
1
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
2.6
2.7
2.8
2.9
time
3
3.1
3.2
3.3
x 10
-0.8
-4
2.4
2.6
2.8
3
3.2
3.4
time
measured (red) and analytic (blue) strains for tangential FBG at 7cm
3.6
3.8
-4
x 10
εr strains of measured (red) vs. analytic (blue) at 7cm, with analytic S0 included
• These figures reinforce two claims:
– The tangential strain, though smaller and decaying faster than the
radial strain, exists
– Experimental and analytical results match
21
Angular Dependence
y
Goal: to show the different angular dependence
of FBGs for plane and cylindrical waves
wavefront
• Plane wave:
 FBG   max cos2    xx cos2 
• Cylindrical wave:
β
PZT
r
x
FBG
For θ=0 (PZT-FBG angle) the principal strains are in the x,y
directions:
u
u
u
 xx   r  r
 FBG   xx cos 2    yy sin 2   r cos 2   r sin 2 
r
r
r
1.2
u
 yy     r
1
r
( FBG   max cos2  )

x
PZT Exciter
normalized strain amplitude
FBG sensor
0.8
0.6
0.4
0.2
0
-0.2
22
0
15
30
45
60
75
90 105 120 135 150 165 180
angle
Analytical angular dependence for plane wave assumption (cos2(β), green
line) and cylindrical assumption (blue line) at 21mm from the source
Angular Dependence
Cylindrical wave (cont.):
When ignoring the tangential effect, the error could be
large. For example, at β=75 degrees:
y
1
strain (normalized)
0.8
0.6
0.4
r
0.2
x
0
PZT Exciter
FBG sensor
-0.2
-0.4
-0.6
2.5
2.6
2.7
2.8
2.9
time
3
3.1
3.2
x 10
-4
75 degrees comparison of general analytic strain (blue) measured
signal (green) and analytic without tangential strain (red)
Conclusion: The tangential strain affects the angular dependence
and cannot be ignored at small distances from the source.
23

Rosette Calculations
• Rosettes are used for damage location in NDT
• Prior work uses only plane wave rosettes
 Our work intends to:
 Enable accurate location of damages in a close range
 Present different calculation for each wave (planar/
cylindrical)
What is a rosette?
24
Rosette Calculations
• For a Plane wave:
– Only 2 FBGs are required!
– Signals are in-phase.
– Max. values can be used
 FBG   max cos2 
1
0.8
0.6
normaized strain
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
3.5
4
4.5
time
25
5
5.5
x 10
Signals of 2 FBGs oriented at different angles in the plane wave case
-4
Rosette Calculations
• For a cylindrical wave:
– 3 FBGs are required!
– Signals are not
necessarily in phase and
differ from each other!!!
– Signal values should be
taken at a specific time!
A0°
B45°
C90°
C
0.8
0.6
normalized strain
y
1
B
0.4
0.2
0
-0.2
FB
G
B
FBG C
-0.4
26
C
-0.6
B
2.4
A
FBG A
A
x
2.6
2.8
3
time
3.2
3.4
x 10
-4
Measured strains for angles: 0 (blue), 45 (green) and 90 (red) degrees
Rosette Calculations
y
• Cylindrical wave (cont.)
Angle to the source:
– Analytically (θ is 0).
tan(2 ) 
angle
strain 0 deg.
strain 45 deg.
strain 90 deg.
80
60
r
PZT Exciter
FBG sensor
40
20
y
A0°
B45°
C90°
0
C
-20
B
-40
-60
2.6
2.65
2.7
2.75
2.8 2.85
time
2.9
2.95
FB
G
B
-80
27

x
FBG C
approximated angle (analytical)
2 45   90   0
 0   90
3
x 10
-4
Estimated angle to the source (bold blue line), using
analytical strain solutions (also added for time reference)
C
B
A
FBG A
A
x
Rosette Calculations
• Cylindrical wave (cont.)
Angle to the source:
– Angle from measured signal was not as expected!!!
– Applying a 1mm shift to one of the FBGs in the
analytical calculation shows a similar effect ☺
approximated angle
30
20
10
0
-10
-20
-30
-40
2 45   90   0
 0   90
40
approximated angle (shifted analytic)
angle
strain 0 deg.
strain 45 deg.
strain 90 deg.
40
tan(2 ) 
angle
strain 0 deg.
strain 45 deg.
strain 90 deg.
30
20
10
0
-10
-20
-30
-40
2.6
2.65
2.7
time
2.75
2.8
2.65
x 10
-4
Estimated angle to the source (bold blue line), using
measured strain signals (also added for time
reference)
28
2.7
2.75
time
2.8
x 10
-4
The effect of 8*10-7 [sec] time shift (~1 mm) of one of the
analytical strain solutions on the angle estimation capability
Rosette Calculations
• Conclusions and Implications
Golden Rule: For long distance use
plane wave rosette, For short
distance- cylindrical wave rosette
29
tan(2 ) 
2 45   90   0
 0   90
angle
strain 0 deg.
strain 45 deg.
strain 90 deg.
40
30
approximated angle
– Realistically, the estimated angle will
never be constant
– Improved analysis method for
cylindrical rosettes:
• Perform analysis for each time step
• Choose the angle for which the
denominator is maximal
– In plane wave rosettes this problem
does not exist since it is possible to
assume signals are in phase
20
10
0
-10
-20
-30
-40
2.6
2.65
2.7
time
2.75
2.8
x 10
-4
Estimated angle to the source (bold blue line), using
measured strain signals (also added for time
reference)
Summary of Findings
Exact analytical solutions for a pulse of plane and
cylindrical Lamb waves was calculated.
Parameters for a Finite Element Model were
determined.
The angular dependence of FBGs at close range
to the transducer, where the wave is cylindrical,
was analyzed and measured.
Three FBG rosette calculations were performed
and the effect of the tangential strain on the angle
finding was analyzed.
The effect of co-location error was demonstrated.
30
Future Work
Applying FBGs to NDT system for damage detection
Real time monitoring
High accuracy at all distances
Anisotropy
Composite plates, which are common in the industry, are
usually anisotropic
Ability to embed optical fibers
Phase and group velocities are angle dependent
S0 Slowness Curve
90
120
60
0.15
Slowness Surface, z/x10
3
0.20
0.10
30
150
0.05
0.00 180
0
0.05
0.10
330
210
0.15
31
0.20
240
300
270
Acknowledgements
• Prof. Moshe Tur
• Lab colleagues, and especially:
– Yakov Botsev
– Dr. Nahum Gorbatov
• Iddo Kressel
• Shoham
32