The effect of different materials on the
propagation of guided waves in multi-wire cables
R. Mijarez 1
1Gerencia
de Control e Instrumentación,
Instituto de Investigaciones Eléctricas, CP 62490 Cuernavaca, Morelos, México.
G. Trane 1 , A. Baltazar 2
2 Centro
de Investigación y Estudios Avanzados del IPN, Unidad, Saltillo,
Saltillo, Coahuila, Mexico
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Outline
Introduction
Objective
Work in progress
Conclusions
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Introduction
Multi-wire metal strands are commonly used in civil
structures as tensioning components of concrete structures
and in cable systems of cable-stayed and suspension bridges
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Aging and corrosion issues
Environmental degradation such as
random overloads and corrosion
can lead to failure
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Overhead Transmission Lines (OHTL)
Many of the overhead power supply faults occurs due
to failure in transmission lines
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Overhead Transmission Lines
Periodic inspections are carried out using X-ray
equipment, or visually with the help of helicopters.
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Overhead Transmission Lines
X-ray inspections has exhibited good results; however,
they require the deployment of personnel or a robot to
operate the system.
Airborne inspections are specially a dangerous task due
to sun glare, cloud cover, close proximity to power
lines and the rapidly changing visual circumstances.
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Objective: SHM via guided waves
Continuous and autonomous monitoring of OHTL could
reduce risk to human pilots & expedite the inspection process
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Work in progress
Guided wave propagation in rods
Signal processing (wavelet transform)
Experiment setup at 500 kHz using an ACSR cable
Modes identification & Signal processing
Energy-transference analysis
3-D FEM analysis
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Guided waves in rods
• Tubes and rods excel as wave-guides, propagation is complex due
to their curved geometries
• Travelling of the waves can be both around the cylinder and along
it, e.g. there can be spiral waves
• Dispersive, i.e. phase velocities dependent on the frequency and
thickness or diameter, and possess modal behaviour
• The number of modes increase with frequency
u
u
ur
uz
Flexural
F(M,n) non-axisymmetric
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ur
uz
Longitudinal
L(0,n) axisymmetric
Torsional
T(0,n) axisymmetric
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Dispersion Curves
12.0
L(0,1)
10.0
4.0
L(0,4)
L(0,2)
L(0,3)
F(1,5)
8.0
F(1,2)
F(1,3)
F(1,4)
Vgr (m/ms)
L(0,2)
6.0
F(1,3)
L(0,1)
F(1,2)
2.0
L(0,4)
F(1,1)
L(0,3)
F(1,4)
4.0
F(1,5)
2.0
0.0
F(1,1)
0.0
1.0
2.0
Frequency-Thickness (MHz-mm)
3.0
4.0
1.0
2.0
3.0
4.0
Frequency-Thickness (MHz-mm)
Waves propagation are related to the frequency of the wave and
diameter of the rod
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Signal processing
Spectral analysis
Amplitude
Amplitude (V)
Chip signal 1-150 Hz
Time (seg)
Frequency (Hz)
Non stationary signals possess its average power increasing
continuously or one of its components steadily increase in frequency
Guided wave signals are non stationary; hence, the FFT does not
provide enough information for its analysis
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Wavelet transform
The wavelet transform addresses the general problem of timefrequency analysis, and provides the means to analyse non-stationary
signals. In this work the Gabor wavelet was used.
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Experiment set up, using an ACSR cable
ACSR (Aluminum Conductor Steel Reinforced)
PC
WT
analysis
3.5 mm
diameter
Function
generator
7 steel wires
26 aluminium wires
Amplifier
Wave propagation
2.7 mm
diameter
Cross section view
Oscilloscope
Transducer
emitter
0.9m ACSR cable
Transducer
receiver
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Guided wave modes identification (DisperseTM)
An analytical solution that can describe the wave propagation in
multi-wire cables does not exist.
The approach taken employed individual dispersion curves of rods of
aluminum and steel 3.5mm and 2.7mm of diameter, respectively
L(0,1) &
F(1,1) can
be
Excited at
500 kHz
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Guided wave modes identification (DisperseTM)
0.0
1.0
-0.5
Simulation of L(0,1) and F(1,1) propagation in an aluminium rod and
a 0.5steel rod of 0.9m, independently, were performed using 5 sine cycles
at 500 kHz in relation to the experiment setup
-1.0
0.0
0.0
Sum
1.0
0.5
L(0,1)
1.0
F(1,1)
1.5
Aluminium rod 1.75 radius
0.5
-0.5
0.0
-0.5
-1.0
-1.0
0.0
1.00.0
0.5
L(0,1)
F(1,1)
0.5
1.0
1.5
1.0
1.5
Steel rod 1.35 radius
Time (ms)
Sum
0.5
L(0,1) and
F(1,1) modes
are clearly
separated
0.0
-0.5
0.0
0.5
1.0
1.5
Time (ms)
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Acquired guided wave modes in time domain
Multiplewire cables
make the
interaction of
the guided
wave modes
complicated
to
distinguish.
Identified mode
L(0,1) steel
L(0,1) aluminium
F(1,1) steel
F(1,1) aluminium
TOA
(s)
0.00018
0.00021
0.00028
0.000295
Length
(m)
0.9
0.9
0.9
0.9
Calculated
Vgr (m/s)
5000
4285.71
3214.28
3050.84
Disperse
Vgr (m/s)
4957.84
4397.28
3313.5
3223.61
L(0,1) was
predominantly;
however, some
energy was
identified as
F(1,1).
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Guided wave modes time-frequency domain
Frequency-time signals with fundamental group velocity
dispersion curves, for steel and aluminium rods, were
superimposed.
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Radial and axial displacements for the L(0,1)
Longitudinal ultrasound transducers ,with ideal uniform pressure
distribution, are employed in the experiment; hence, L(0,1) mode in
aluminium and steel rods are expected to be excited, which is
composed by its axial (uz) and radial (ur) displacements .
Aluminium rod 3.5mm diameter
at 503 kHz
Steel rod 2.7mm diameter
at 504 kHz
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Energy transfer analysis
An energy-transfer analysis, based on radial displacements, has been
used to model wave propagation in two rods that are in contact.
Longitudinal modes are
expected to be excited
Longitudinal & flexural are
expected to be excited
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FEM simulation
Transient analysis of guided waves propagation in real multi-wire
cables using finite elements 3-D models is computationally very
demanding
The approach considered consists of a simplified 3-D model. The
model consists only of two straight rods of 70mm lengths made of
aluminum and steel, which possess the diameters of the ACSR cable
under test, and a friction contact line between them was specified .
Energy transfer, due to contact in between rods, caused by radial
displacements is considered to have a significant role in guided waves
propagation.
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FEM simulation (two aluminium rods)
Nodal forces of 10 N were applied at the base of the rods. The contact
between rods is specified as bonded, which the nodes on the two edges
are matched and are in perfect contact during the analysis..
Axisymmetric longitudinal
guided wave propagation and
mode shapes, very likely L(0,1),
can be observed, which agrees
the model.
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FEM simulation (two aluminium rods)
Separated 500 µm
Separated 50 nm
Separated 200 nm
Without separation
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FEM simulation (aluminium & steel rods)
Nodal forces of 10 N were applied at the base of the rods and the
contact between rods and the coefficient of friction was set as previous
model.
Guided wave propagation and
mode shapes is non
axisymmetric, and could
correspond not only to the
longitudinal mode L(0,1), but
also to the flexural mode F(1,1).
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FEM simulations (an aluminium rod & steel rod)
Separated 500 µm
Separated 50 nm
Separated 200 nm
Without separation
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Conclusions
This study analyses how guided wave energy is propagated in a
multiple wire ACSR cable. Experimentally, L(0,1) and F(1,1) modes
were identified using dispersion curves and the wavelet transform.
 An energy-transfer model, using a two rod system, was developed
to approximate the coupling mechanism between adjoining rods
through friction.
 Energy transference due to inter-wire coupling caused by radial
displacements is considered to have an important role in the excitation
not only of longitudinal modes, but also of flexural modes.
 3-D FEM simulation results that visualize de mechanism of flexural
and longitudinal modes generation are adequately related to experimental
measurements. The energy-transfer model approach serves as basis for
future studies of multiple-wire ACSR cables with damage
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Conclusions
Thanks
?
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Further work
PC
WT
analysis
Oscilloscope
Function
generator
Amplifier
Wave propagation
0-9mm cut
0.9m ACSR cable
Transducer
emitter
Transducer
receiver
Maximum amplitude (V)
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4
3
2
L(0,1) steel measured data
Exponential tendency
L(0,1) aluminium measured data
Exponential tendency
1
0
2
4
6
8
10
Cut depth (mm)
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Further work
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