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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

Airborne inspections are specially a dangerous task due to sun glare, cloud cover, close proximity to power lines and the rapidly changing visual circumstances.

X-ray inspections has exhibited good results; however, they require the deployment of personnel or a robot to operate the system.

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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

ur

uz

u

Flexural

ur

uz

Longitudinal

u

Torsional

F(M,n) non-axisymmetric L(0,n) axisymmetric T(0,n) axisymmetric

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Dispersion Curves

1.0 2.0 3.0 4.00.0

2.0

4.0

6.0

8.0

10.0

12.0

Frequency-Thickness (MHz-mm)

Vph (

m/m

s)

F(1,1)

L(0,1)

F(1,2)

F(1,3)

L(0,2) F(1,4)

L(0,3)

F(1,5)

L(0,4)

1.0 2.0 3.0 4.0

0.0

2.0

4.0

Frequency-Thickness (MHz-mm)

Vgr

(m

/ms)

F(1,1)

L(0,1)

F(1,2)

F(1,3)

L(0,2)

F(1,4)

L(0,3)

F(1,5)

L(0,4)

Waves propagation are related to the frequency of the wave and diameter of the rod

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Signal processing

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

Chip signal 1-150 Hz Spectral analysis

Am

pli

tud

e (V

)

Am

pli

tud

e

Time (seg) Frequency (Hz)

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Wavelet transform

The wavelet transform addresses the general problem of time-frequency 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

3.5 mm diameter

2.7 mm diameter

Cross section view

ACSR (Aluminum Conductor Steel Reinforced)

7 steel wires26 aluminium wires

PCWTanalysis

Functiongenerator

Amplifier

Oscilloscope

0.9m ACSR cable

Wave propagation

Transduceremitter

Transducerreceiver

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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

beExcited at500 kHz

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Guided wave modes identification (DisperseTM)

Simulation of L(0,1) and F(1,1) propagation in an aluminium rod and a steel rod of 0.9m, independently, were performed using 5 sine cycles at 500 kHz in relation to the experiment setup

0.0 0.5 1.0 1.5

-1.0

-0.5

0.0

0.5

1.0

Time (ms)

Sum

0.0 0.5 1.0 1.5

-1.0

-0.5

0.0

0.5

1.0

Com

ponents Aluminium rod 1.75 radius

0.0 0.5 1.0 1.5

-0.5

0.0

0.5

1.0

Time (ms)

Sum

0.0 0.5 1.0 1.5

-1.0

-0.5

0.0

0.5

1.0

Com

ponents

Steel rod 1.35 radius

L(0,1) F(1,1)

L(0,1) F(1,1)

L(0,1) and F(1,1) modes

are clearly separated

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Acquired guided wave modes in time domain

Identified mode TOA (s)

Length (m)

Calculated Vgr (m/s)

Disperse Vgr (m/s)

L(0,1) steel 0.00018 0.9 5000 4957.84 L(0,1) aluminium 0.00021 0.9 4285.71 4397.28 F(1,1) steel 0.00028 0.9 3214.28 3313.5 F(1,1) aluminium 0.000295 0.9 3050.84 3223.61

Multiple-wire cables make the

interaction of the guided

wave modes complicated

to distinguish.

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 200 nm

Separated 50 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 200 nm

Separated 50 nm Without separation

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ConclusionsThis 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

PCWTanalysis

Functiongenerator

Amplifier

Oscilloscope

0.9m ACSR cable

Wave propagation

Transduceremitter

Transducerreceiver

0-9mm cut

0 2 4 6 8 10

C ut depth (m m )

1

2

3

4

5

Ma

xim

um a

mpl

itud

e (V

)

L(0,1) steel m easured dataExponential tendencyL(0,1) alum inium m easured dataExponential tendency

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Further work