Download Magnetic Barkhausen Noise Measurements Using Tetrapole Probe Designs Paul McNairnay

Magnetic Barkhausen Noise Measurements Using Tetrapole
Probe Designs
by
Paul McNairnay
A thesis submitted to the
Department of Physics, Engineering Physics and Astronomy
in conformity with the requirements for
the degree of Master of Applied Science
Queen’s University
Kingston, Ontario, Canada
December 2014
Copyright © Paul McNairnay, 2014
Abstract
A magnetic Barkhausen noise (MBN) testing system was developed for Defence Research and
Development Canada (DRDC) to perform MBN measurements on the Royal Canadian Navy’s
Victoria class submarine hulls that can be correlated with material properties, including residual
stress. The DRDC system was based on the design of a MBN system developed by Steven White
at Queen’s University, which was capable of performing rapid angular dependent
measurements through the implementation of a flux controlled tetrapole probe. In tetrapole
probe designs, the magnetic excitation field is rotated in the surface plane of the sample under
the assumption of linear superposition of two orthogonal magnetic fields. During the course of
this work, however, the validity of flux superposition in ferromagnetic materials, for the
purpose of measuring MBN, was brought into question. Consequently, a study of MBN
anisotropy using tetrapole probes was performed. Results indicate that MBN anisotropy
measured under flux superposition does not simulate MBN anisotropy data obtained through
manual rotation of a single dipole excitation field. It is inferred that MBN anisotropy data
obtained with tetrapole probes is the result of the magnetic domain structure’s response to an
orthogonal magnetization condition and not necessarily to any bulk superposition magnetization in the sample. A qualitative model for the domain configuration under two orthogonal
magnetic fields is proposed to describe the results. An empirically derived fitting equation, that
describes tetrapole MBN anisotropy data, is presented. The equation describes results in terms
of two largely independent orthogonal fields, and includes interaction terms arising due to
competing orthogonally magnetized domain structures and interactions with the sample’s
magnetic easy axis. The equation is used to fit results obtained from a number of samples and
tetrapole orientations and in each case correctly identifies the samples’ magnetic easy axis.
i
Acknowledgements
First and foremost I would like to thank my supervisors Thomas Krause and Lynann Clapham
and express my gratitude for your guidance throughout this project. Thank you for all the
advice and assistance you provided me over these past years.
I would like to give my thanks to Arash Samimi for the countless helpful discussions we had
on both work and life. They made this project infinitely easier. Thank you also to Robbie
Edwards and Chris Mohr for all the time spent in the lab helping with the build.
These past few years have been immensely enjoyable thanks in large part to a wonderful
group of friends whose company I am incredibly grateful for.
Finally, I would like to thank my family. I cannot describe how much the support you have
given me my entire life means to me. Thank you for everything.
ii
Table of Contents
Abstract.......................................................................................................................................... i
Acknowledgements ...................................................................................................................... ii
Table of Contents ........................................................................................................................ iii
List of Tables ............................................................................................................................... vii
List of Figures ..............................................................................................................................viii
List of Symbols and Acronyms ....................................................................................................xii
Chapter 1
Introduction ............................................................................................................ 1
1.1
Residual Stress in Victoria Class Submarines.................................................................. 2
1.2
Magnetic Barkhausen Noise ........................................................................................... 3
1.2.1 MBN and Stress................................................................................................... 4
1.3
Stress Anisotropy Measurement and Steven White’s MBN System .............................. 6
1.4
Development of a MBN System for DRDC ...................................................................... 8
1.5
Organization of Thesis .................................................................................................... 9
Chapter 2
2.1
Theory and Background ........................................................................................ 10
Stress Measurement ..................................................................................................... 11
2.1.1 Stress and Strain ............................................................................................... 11
2.1.2 Stress Measurement Techniques ..................................................................... 13
iii
2.2
Maxwell’s Equations ..................................................................................................... 14
2.3
Magnetic Materials ....................................................................................................... 15
2.4
Domain Theory ............................................................................................................. 19
2.4.1 Magnetic Energy ............................................................................................... 20
2.4.2 Magnetization Process...................................................................................... 25
2.5
Magnetic Measurements.............................................................................................. 27
2.6
Magnetic Barkhausen Noise ......................................................................................... 28
2.6.1 MBN Parameters............................................................................................... 29
2.6.2 MBN Energy ...................................................................................................... 30
2.6.3 MBN Anisotropy................................................................................................ 32
2.6.4 MBN Energy under Orthogonal Fields .............................................................. 34
Chapter 3
3.1
DRDC MBN System and Experimental Setup ....................................................... 36
Hardware ...................................................................................................................... 38
3.1.1 Data Acquisition Boards (DAQs) ....................................................................... 38
3.1.2 Flux Control System .......................................................................................... 38
3.1.3 Power Supply .................................................................................................... 39
3.1.4 Preamplifier ...................................................................................................... 40
3.2
Software........................................................................................................................ 40
3.3
Probe............................................................................................................................. 41
3.3.1 Pickup Coil Design ............................................................................................. 47
3.3.2 Probe Summary ................................................................................................ 49
3.4
Experimental Setup and Samples ................................................................................. 50
3.4.1 Dipole Anisotropy Measurements .................................................................... 51
3.4.2 Tetrapole Anisotropy Measurements............................................................... 51
3.4.3 Samples ............................................................................................................. 52
iv
Chapter 4
4.1
System Performance & Study of Flux Superposition Validity ............................. 54
System Performance..................................................................................................... 55
4.1.1 System Error...................................................................................................... 55
4.1.2 BN Envelope ...................................................................................................... 60
4.1.3 BN Normalized Power Spectrum ...................................................................... 64
4.1.4 BN Energy Anisotropy ....................................................................................... 66
4.2
Detailed Study of Flux Superposition Validity in Tetrapole Probes ............................. 68
4.2.1 Dipole MBN Anisotropy Results Using the FDP Probe ..................................... 70
4.2.2 Tetrapole MBN Anisotropy Results: The effect of tetrapole orientation
using the FTP probe ..................................................................................... 72
4.2.3 Tetrapole MBN Anisotropy Results: High resolution
measurements
on mild steel using both the FTP and STP probes ............................................ 77
4.2.4 Comparison of Dipole and Tetrapole Results: Studies involving
independent orthogonal dipoles ...................................................................... 82
4.2.5 Field Amplitude Effects of Anisotropy .............................................................. 89
4.2.6 Voltage (Field) and Flux Control of the MBN Excitation Field: Effects on
anisotropy results ............................................................................................. 91
4.2.7 Empirical Fitting of Tetrapole Data ................................................................... 92
Chapter 5
Discussion .............................................................................................................. 99
5.1
Construction and Evaluation of DRDC MBN System .................................................. 100
5.2
Tetrapole MBN Anisotropy and Empirical Fitting Equation ....................................... 102
5.3
Origin of Tetrapole MBN Anisotropy .......................................................................... 103
5.3.1 Pickup Coil and Probe Coupling Effects .......................................................... 104
5.3.2 Domain Structure Effects ................................................................................ 105
5.4
DRDC System and Residual Stress Anisotropy ........................................................... 108
v
Chapter 6
Conclusion and Future Work .............................................................................. 109
6.1
Tetrapole MBN Anisotropy ......................................................................................... 110
6.2
System Performance................................................................................................... 111
6.3
Future Work and Recommendations ......................................................................... 111
6.3.1 MBN Anisotropy.............................................................................................. 112
6.3.2 MBN System Design ........................................................................................ 113
Bibliography.............................................................................................................................. 114
Appendix A
FCS of the Original Queen’s and DRDC Systems ............................................. 120
Appendix B
Calibration Procedure ...................................................................................... 122
Appendix C
Empirical Fitting on Polar Plots ........................................................................ 124
Appendix D
Empirical Fitting of Tetrapole Data on Laminate Samples ............................. 126
Appendix E
Skin Depth and Diffusion of Time Harmonic and Transient Fields into a
Semi-Infinite Slab ............................................................................................. 129
Appendix F
Derivation of Diffusion of Time Harmonic and Transient Fields into a
Semi-Infinite Slab ............................................................................................. 133
vi
List of Tables
2.1
Classification of magnetic materials in terms of magnetic susceptibility ..................... 17
3.1
FTP coil parameters ....................................................................................................... 43
3.2
FDP coil parameters ....................................................................................................... 44
3.3
STP coil parameters ....................................................................................................... 46
3.4
Summary of probes used in this work and their relevant coil parameters ................... 49
3.5
Sample material investigated in this work .................................................................... 53
4.1
Best fit parameters for the dipole MBN energy fitting equation (2.32) and the
MBN energy ratio for all samples. ................................................................................. 72
4.2
Fitting parameters for equation (4.3) for angular dependent MBN energy
measurements performed on mild steel with the FTP probe at various probe
orientation angles ......................................................................................................... 96
4.3
Fitting parameters for equation (4.3) for angular dependent MBN energy
measurements performed on mild steel with the STP probe at various probe
orientation angles ......................................................................................................... 96
4.4
Fitting parameters for equation (4.3) for angular dependent MBN energy
measurements performed on HY-80 with the FTP probe at various probe
orientation angles ......................................................................................................... 97
vii
List of Figures
1.1
A simplified magnetic Barkhausen noise setup and signal ............................................. 5
1.2
The original Queen’s system spring-loaded 4-pole (SL4P) tetrapole probe design ........ 7
2.1
The Cauchy stress tensor represented on a continuous solid in Cartesian
coordinates .................................................................................................................... 11
2.2
Hysteresis loops observed in ferromagnetic materials ................................................. 18
2.3
Ferromagnetic crystal showing domain walls that separate magnetic domains of
different magnetic orientation ...................................................................................... 19
2.4
Bethe curve describing the variation in exchange energy for increasing ratio of
interatomic distance to radius of the 3d electron shell. ............................................... 21
2.5
Minimization of the magnetostatic energy by reducing the demagnetizing field
through the creation of more magnetic domains ......................................................... 22
2.6
BCC crystal with magnetic easy axis in the [100] direction and hard axis in the
[111] direction ............................................................................................................... 23
2.7
Representation of magnetostriction and the Villari effect .......................................... 24
2.8
The magnetization process illustrated in five stages .................................................... 26
2.9
Typical non-linear increase of MBN energy with increasing excitation field
amplitude....................................................................................................................... 31
2.10
Typical MBN energy anisotropy measurement using manual dipole rotation in
increments of
.......................................................................................................... 33
viii
2.11
Tetrapole oriented at an angle
(
3.1
from a reference direction on the sample
), generating a superposition field
at an angle
. ............................... 35
Block diagram of system of the DRDC system, hardware and probe assembly
components. .................................................................................................................. 37
3.2
CAD model of FTP probe ............................................................................................... 43
3.3
CAD model of FDP probe ............................................................................................... 44
3.4
CAD model of STP probe ............................................................................................... 46
3.5
Large radius pickup coil assembly consisting of aluminum shield and pickup coil
with ferrite core ............................................................................................................. 49
3.6
Angular measurement guide (AMG) and tetrapole orientation (
) measurement
setup .............................................................................................................................. 50
4.1
System error
for various excitation frequencies
and flux densities for
the (a) DRDC system and (b) original Queen’s system. ................................................. 58
4.2
Measured excitation/feedback coil inductance
frequency
4.3
as a function of excitation
. ................................................................................................................ 59
BN envelopes measured by the (a) STP probe and (b) SL4P probe for various flux
densities
4.4
/
at an excitation frequency
on mild steel B sample. ........... 61
Typical BN envelope parameters for STP and SL4P probe as a function of flux
density. (a) MBN energy, (b) BN envelope peak voltage and (c) BN envelope peak
phase. ............................................................................................................................ 63
4.5
Typical BN envelope parameters for STP and SL4P probe as a function of excitation
frequency
. (a) MBN energy, (b) BN envelope peak voltage and (c) BN envelope
peak phase ..................................................................................................................... 63
ix
4.6
Differences in the normalized power spectrum measured by the SL4P and the STP
probes. ........................................................................................................................... 65
4.7
MBN Energy anisotropy as measured by the STP, SL4P and FDP probes under flux
control at
4.8
and
.................................................................... 67
MBN energy anisotropy measured with a dipole on (a) mild steel A at
, (b) HY-80 at
, (c) grain-oriented SiFe at
(d) non-oriented laminate at
4.9
4.10
)
on grain-oriented laminate
) and non-oriented laminate (
). ...................................... 76
MBN energy anisotropy measured using the FTP at various ‘high resolution’ probe
orientations
4.12
on mild steel A (
). ........................................................................................... 74
MBN energy anisotropy using FTP for various
(
4.11
. ................................................................ 71
MBN energy anisotropy using FTP for various
and HY-80 (
and
on mild steel A. .................................................................................... 79
MBN energy anisotropy measured using the STP at various probe orientations
on mild steel A. .............................................................................................................. 81
4.13
Experimental setup for measurements of MBN using independent orthogonal
dipoles ........................................................................................................................... 84
4.14
MBN energy resulting from a superposition field
independent fields
4.15
4.16
at various probe orientation angles ................................. 86
MBN energy resulting from a superposition field
independent fields
and two orthogonal
and two orthogonal
at various flux densities .................................................... 88
MBN energy anisotropy at peak flux densities of (a)
, (b)
and (c)
.
Measurements performed under flux control with STP on the mild steel B sample. .. 90
x
4.17
Tetrapole MBN energy anisotropy of under flux and voltage control with FTP on
mild steel B sample ........................................................................................................ 91
4.18
MBN energy anisotropy measurements using the FTP probe on mild steel A at
various probe orientation angles
4.19
MBN energy anisotropy measurements using the STP probe on mild steel A at
various probe orientation angles
4.20
. ............................................................................ 95
............................................................................. 95
MBN energy anisotropy measurements using the FTP probe on HY80 at various
probe orientation angles
.......................................................................................... 98
xi
List of Symbols and Acronyms
̅
Vector area (m2)
Feedback coil area (m2)
̅
Magnetic flux density (T)
Initial magnetic flux density at sample surface (T)
Magnetic flux density as a function of depth z and t (T)
Peak magnetic flux density at 1-3 pole-pair (T)
Peak magnetic flux density at 2-4 pole-pair (T)
Measured peak magnetic flux density in the feedback coils (T)
Target peak magnetic flux density in the feedback coils (T)
Electric field (V/m)
Total magnetic energy (J)
Exchange energy (J)
Magnetostatic energy (J)
Magnetocrystalline anisotropy energy (J)
Domain wall energy (J)
Magnetostrictive energy (J)
Zeeman energy (J)
xii
̅
Force (N)
Feedback voltage gain (unitless)
Circuit gain (unitless)
̅
Magnetic field (A/m)
Magnetic field generated under superposition (A/m)
̅
Demagnetizing field (A/m)
Magnetic field generated by the 1-3 pole-pair (A/m)
Magnetic field generated by the 2-4 pole-pair (A/m)
Current (A)
̅
Current density (A/m2)
̅
Bound current density (A/m2)
̅
Free current density (A/m2)
Excitation coil inductance (H)
Feedback coil inductance (H)
Pickup coil inductance (H)
̅
Magnetization field (A∙turns/m)
Saturation magnetization (A∙turns/m)
Magnetic Barkhausen noise energy (V2∙s)
MBN energy when running the 1-3 pole-pair (
) independently (V2∙s)
MBN energy when running the 2-4 pole-pair (
) independently (V2∙s)
MBN energy measured by the tetrapole probes (V2∙s)
xiii
MBN energy measured under ‘no superposition’, where the MBN energy from
each orthogonal pole-pair is measured separately (V2∙s)
Number of coil turns (turns)
Number of feedback coil turns (turns)
Power (W)
Resistance (Ω)
Period (s)
Voltage (V)
Target feedback voltage (V)
Feedback voltage (V)
Younge’s modulus (Pa)
Coefficient of Barkhausen events contributing to anisotropy (V 2∙s)
Coefficient of Barkhausen events contributing to isotropic background (V2∙s)
Skin depth (m)
Strain (unitless)
Permittivity of free space (8.8542 × 10-12 F/m)
Angle of excitation field in the sample reference frame (°)
Angle of the assumed superposition excitation field in the probe reference
frame (°)
Angle of the probe in the sample reference frame (°)
MBN energy ratio (unitless)
MBN energy ratio for tetrapole data (unitless)
xiv
Magnetostriction constant (unitless)
Permeability of free space (4π × 10-7 H/m)
Relative permeability (unitless)
Electric charge density (C/m3)
Stress tensor (Pa)
Conductivity (S/m)
Time constant (s)
Magnetic flux (Wb)
Easy axis direction (°)
Magnetic susceptibility (unitless)
Angular frequency (rad/s)
Coil diameter (m)
RMS error (VRMS)
Normalized RMS error (unitless)
Total system error (unitless)
Excitation frequency
̅
Dipole magnetization
Elementary charge (1.6022 × 10-19 C)
̅
Time (s)
Velocity (m/s)
Poisson’s ratio (unitless)
xv
ABS
Acrylonitrile Butadiene Styrene
AMG
Angular Measurement Guide
BCC
Body Centered Cubic
BN
Barkhausen Noise
CAD
Computer Aided Design
CANDU
CANadian Deuterium Uranium
DAQ
Data Acquisition
DRDC
Defence Research and Development Canada
FCS
Flux Control System
FDP
Feeder Dipole Probe
FEM
Finite Element Modeling
FTP
Feeder Tetrapole Probe
IACS
International Copper Annealed Standard
MBN
Magnetic Barkhausen Noise
MFL
Magnetic Flux Leakage
NDE
Non-Destructive Evaluation
NDT
Non-Destructive Testing
NI
National Instruments
NPSBN
Normalized Power Spectrum of Barkhausen Noise
PCB
Printed Circuit Board
RMS
Root Mean Squared
xvi
SL4P
Spring-Loaded 4 Pole (original Queen’s System Probe)
STP
Submarine Tetrapole Probe
UPS
Uninterruptible Power Supply
xvii
Chapter 1
Introduction
Engineered materials are designed to achieve specific performance requirements, which allow
for efficient and safe operation during their service lifetime. Depending on their application and
operating conditions, material properties of these components can change over time increasing
the likelihood of in-service failure. In applications where the cost of failure is high, a method for
the evaluation of fitness for service is required. Furthermore, when the replacement cost of a
component is significant, extending the service lifetime through such evaluations is desired.
Non-destructive testing and evaluation (NDT/NDE) are methods by which engineered
components are inspected to ensure material properties remain within their operational
envelope while leaving them otherwise intact. Such testing methodologies allow for efficient
risk assessment and lowers operational costs associated with the repair/replacement of
degraded components [1].
NDE technologies have been developed to measure numerous material conditions. One
parameter that is significant in almost all engineering considerations is the presence of material
stress. Exceeding design stress limits often leads to catastrophic failure and thus the stress state
of components is a crucial factor to monitor. Despite this, there are relatively few methods for
non-destructive stress measurement that can be performed in the field and are not time
1
CHAPTER 1.
INTRODUCTION
2
intensive [2]. One method that shows stress sensitivity and, which can be performed rapidly
and on-site, is the magnetic Barkhausen noise (MBN) technique. Furthermore, MBN is sensitive
to anisotropic surface stresses, as may be investigated through angular dependent
measurements [3], [4].
The goal of this thesis was to develop and evaluate a MBN testing system for the Defence
Research and Development Canada (DRDC). The system was to be capable of performing rapid
angular dependent MBN measurements, which can be correlated with residual stress, on the
Royal Canadian Navy’s Victoria class submarine hulls. This chapter presents the important
considerations regarding residual stress in Victoria class submarines and introduces the
magnetic Barkhausen noise method and its ability to measure residual stress. The importance
of measuring residual stress anisotropy is discussed and the design of a MBN system developed
by Steven White at Queen’s University [5], [6] is briefly reviewed. The development of the MBN
testing system for DRDC, based on the design of the original Queen’s system, is discussed.
1.1 Residual Stress in Victoria Class Submarines
Victoria class submarine hulls were originally manufactured from Q1N steel [7], a type of highstrength steel used for pressure vessel applications. HY-80 is a similar high-strength steel, which
has been used as a substitute in repairs and is known for its high strength-to-weight ratio,
exceptional toughness and it ability to resist fracture [8]. As with most structural steels, Victoria
class submarine hulls contain residual stress arising from a variety of sources. Initial fabrication
often locks in residual strain due to hot or cold rolling and cutting. Thermal strain occurs around
welds or flame cut sections due to shrinkage during cooling. Heating and cooling can also lead
to transformation strains with non-homogeneous volume changes. Misalignment of
prefabricated plates generates strains, as does surface treatment such as grinding. Hull damage
due to collisions and diving cycles may also be a source of residual stress. Inspection of the hull
requires the removal of acoustic tiles, which has been known to create a thin surface layer of
CHAPTER 1.
INTRODUCTION
3
compressive stress [7]. Finally in the case of dry-docked submarines, static loading strains are
present due to weight dispersion [7].
All these sources combine to produce complex strain fields that can impact the safe
operational limits of the submarine. Among the most significant factors is the level of tensile
stress at the inner and outer surface of the hull, which can facilitate crack growth [9]. The
aggressive operating environment can enhance the chances of buckling, fatigue and stress
corrosion cracking. Also, specific sections of the submarine, such as areas near the exhaust,
exhibit a decrease in toughness due to prolonged heat exposure and require regular
replacement [7]. For these reasons, the stress state of the hull must be monitored.
Neutron and X-ray diffraction techniques have previously been used to address the
measurement of residual stress, but the development of a MBN residual stress measurement
system would be beneficial for a number of reasons. Neutron diffraction requires a stable
neutron source (typically a nuclear reactor), which prevents on-site measurements and raises
measurement costs. X-ray diffraction can be performed on-site [7], however, it has a small
penetration depth and requires careful surface preparation, which itself can induce residual
stresses [7]. MBN technology allows for in situ stress measurements, has penetration depth
greater than X-ray diffraction, can perform rapid measurement with minimal surface
preparation and has several other benefits outlined in Section 1.2.
1.2 Magnetic Barkhausen Noise
Magnetic Barkhausen noise (MBN) is the term given to the abrupt changes in domain
configuration (see Section 2.4) that occur when a ferromagnetic material is magnetized. The
Barkhausen effect was first discovered by Heinrich Barkhausen in 1919 [10]. With the
application of an external magnetic field, the magnetic domain structure changes but these
changes are inhibited by irregularities in the crystal lattice, which represent potential barriers to
domain wall motion. With higher applied fields, these potential barriers, also known as ‘pinning
CHAPTER 1.
INTRODUCTION
4
sites’, are overcome and there is a discontinuous change in the local magnetization commonly
referred to as a Barkhausen event. These changes in magnetization can be measured in terms
of a voltage induced in a nearby coil, according to Faraday’s law of induction.
Typical MBN measurements are performed using a time harmonic excitation field to
magnetize the sample, and a pickup coil, which detects Barkhausen events in the form of a
voltage. Figure 1.1a shows a simplified MBN setup in which a dipole electromagnet generates
the excitation field. A pickup coil with an axis perpendicular to the surface, detects induced
Barkhausen events. The MBN signal is measured over one full excitation period and consists of
a series of discontinuous voltage jumps representing each Barkhausen event. An example of a
typical signal is shown in Figure 1.1b.
The MBN signal is multivariate and contains information about both the residual stress and
microstructure [11]. It has been shown to contain vastly more information than that which can
be obtained from hysteresis measurements [12]. This is both a benefit and drawback because,
while it is useful to observe a multitude of microstructural effects, it also becomes difficult to
isolate the influence of a single parameter. Furthermore, MBN is stochastic in nature, meaning
that the domain configuration is determined probabilistically. As a result, a specific domain
configuration can likely never be reproduced, only the average domain properties [13].
1.2.1 MBN and Stress
The relationship between stress and magnetism was first discovered by Joule in 1842 [14], who
found that ferromagnetic materials were slightly deformed in the presence of a magnetic field.
In 1865, Villari discovered the reverse effect, where an applied stress altered the magnetic
properties of a ferromagnet [15]. This second discovery by Villari has allowed for the nondestructive evaluation of stress in ferromagnetic materials through the examination of
magnetization processes [16]. More specifically, applied and residual stresses affect the
magnetic domain configuration [17]–[19] which in turn affects magnetic properties such as
CHAPTER 1.
INTRODUCTION
5
permeability, coercivity [20] or more complex magnetic phenomena such as magnetic
Barkhausen noise [3], [4], [21], [22].
(a)
200
300
Pickup Coil Voltage
Excitation Flux Density
Pickup Coil Voltage (mV)
150
200
100
100
50
0
0
-50
-100
-100
-200
Excitation Flux Density (mT)
(b)
-150
-200
0
90
180
270
-300
360
Phase (°)
Figure 1.1: A simplified magnetic Barkhausen noise setup and signal. (a) A dipole electromagnet
and surface mounted pickup coil. (b) A Barkhausen signal (solid line) generated from an
alternating magnetic field (dashed line) over one excitation cycle (360° of the signal phase).
CHAPTER 1.
INTRODUCTION
6
Because of this relationship, a significant amount of MBN research has focused on the
measurement of residual stress in terms of parameters that characterize the MBN signal [20],
[21], [23], [24] (discussed in detail in Section 2.6.1). Stress, even at low levels, has been shown
to generate large changes in the energy of the MBN signal [25]. As examples, investigations of
pipeline steels under uniaxial tensile stress demonstrated that tensile strains increase MBN
energy, while compressive strains decrease MBN energy [3]. It has also been shown that above
a critical stress level the MBN energy reaches saturation [4], [26] and below a critical strain level
(e.g. 1000 μstrain for HY-80) the MBN signal energy becomes less sensitive to changes in strain
[27]. In addition to the MBN energy, other MBN signal parameters have been used to evaluate
stress in poor magnetic materials [21] and around weldments in ship steel plates [25].
1.3 Stress Anisotropy Measurement and Steven White’s MBN System
The basic design of MBN measurement systems has not changed significantly over the years
[20], [26], [28], [29], and generally consists of an excitation electromagnet, to magnetize the
sample and a pickup sensor, to detect Barkhausen noise (BN) emissions. As mentioned
previously and shown in Figure 1.1a, the excitation field is generally produced using a dipole
electromagnet consisting of a magnetically soft u-core yoke. This represents a directional
measurement, and thus, to fully characterize the residual stress anisotropy, a series of
measurements in different directions, termed ‘angular dependent measurements’, are
required. This is typically done by manually rotating the dipole probes in 10° to 15° increments,
and at each angular position measuring the MBN response [20], [30], [31]. While such time
consuming measurements do not pose a significant problem in a laboratory setting, this manual
rotation method limits the industrial applicability of the technology. For this reason, systems
designed for rapid angular measurement have been developed, such as a ‘tetrapole’ probe
design [6], [32], [33].
CHAPTER 1.
INTRODUCTION
7
One such tetrapole design, developed by Steven White at Queen’s University [5], [6]
consisted of two orthogonal U-core dipoles, shown in Figure 1.2. Instead of manual rotation of
the probe, the applied field between the poles could be electronically rotated, by suitably
varying the magnetic field at the four poles. This design assumed a region at the center of the
four poles where there was a vector addition of the orthogonal flux densities. This was termed
the ‘flux superposition’ region. There are only a handful tetrapoles in existence and engineering
details are not available for most designs. The main question surrounding tetrapoles is the
validity of using flux superposition in ferromagnetic materials for the purpose of MBN
measurement. Finite element modeling was performed during the original development of the
tetrapole to evaluate flux superposition, but these models did not incorporate non-linear
effects, magnetic anisotropy or domain structure [5]. Ultimately, a comparison of angular MBN
measurements performed using a tetrapole and a manually rotated dipole is required. This
comparison formed part of the work in the current thesis (Section 4.2).
Figure 1.2: The original Queen’s system spring-loaded 4-pole (SL4P) tetrapole probe design [5].
CHAPTER 1.
INTRODUCTION
8
In addition to the novel tetrapole probe design, the Queen’s system designed by White [5]
implemented flux control at the four poles of the tetrapole probe. This was achieved by using
feedback coils at each pole tip, which measured the flux waveforms through the magnetic
circuits. The flux waveforms were then controlled using a four-channel analog feedback circuit
and a digital error correction algorithm. Control of the excitation waveform is common in MBN
system designs to improve measurement repeatability, but is typically applied to the excitation
voltage or current. By controlling the flux waveforms directly, the Queen’s system tetrapole
was less susceptible to the effects of probe-sample liftoff, when compared to traditional
voltage control [5], [6], [23].
1.4 Development of a MBN System for DRDC
The design of the MBN system developed by White [5], referred to from this point on as the
‘original Queen’s system’, offered two significant advantages over previous designs. Foremost
was the tetrapole probe design, which through an assumed flux superposition, enabled rapid
MBN anisotropy measurements to be conducted. Second, was the implementation of flux
control which reduced the effects of probe-sample liftoff and improved measurement
repeatability. For these reasons the original Queen’s system design was selected for the
development of a MBN system for DRDC submarine hull stress measurement application.
In the development of the DRDC system, the original Queen’s system was examined for
areas in which the design could be improved. With the goal of improving measurement
repeatability, the flux control system was modified to increase flux waveform accuracy. In
addition, the tetrapole probe was redesigned to reduce complexity and make it suitable for drydock conditions. The effects of design changes implemented in the DRDC system are examined
through a direct comparison with the original Queen’s system. The two systems are compared
in terms of flux waveform accuracy and measured MBN signals.
CHAPTER 1.
INTRODUCTION
9
During the course of this work, the validity of using flux superposition generated by a
tetrapole probe, to measure MBN, was brought into question. As a result, a detailed study was
performed that investigated flux superposition and the ability of tetrapole probes to accurately
reproduce anisotropic MBN measurements.
1.5 Organization of Thesis
This thesis is organized as follows:

Chapter 2 presents the necessary theory required for the development of the DRDC
MBN system and interpretation of measurements. It reviews the concepts of stress
and strain, electromagnetic theory, properties of magnetic materials, domain theory
and magnetic Barkhausen noise phenomena.

Chapter 3 describes the design and construction of the DRDC MBN system developed
as part of this thesis. It also describes the basic experimental procedure for MBN
measurements with the system as well as the samples investigated in this work.

Chapter 4 presents an investigation into the performance of the DRDC system through
a comparison with the original Queen’s system. Chapter 4 also contains a detailed
study of the ability of tetrapole probe designs to achieve flux superposition and
generate accurate angular dependent MBN results. Tetrapole results are compared to
those obtained with traditional dipoles and are fit with the empirical fitting equation in
Section 2.6.5.

Chapter 5 presents a discussion of the results from Chapter 4.

Chapter 6 presents the major conclusions of this work and offers suggestions for
future work in this field.
Chapter 2
Theory and Background
Presented here is the theoretical background for the subsequent chapters. This chapter begins
with a review of stress and strain and the techniques used to measure them. Maxwell’s
equations and the properties of magnetic fields in matter are also reviewed. The various types
of magnetic materials are introduced and their magnetic behavior is explained. A detailed
discussion of domain theory is presented in terms of domain structure, magnetic energies and
the process of magnetization. Methods of magnetic measurement are discussed and magnetic
Barkhausen noise is introduced. Barkhausen events are explained in terms of domain wall
motion and the basic method for their detection is outlined. The common analyses of MBN
signals are also presented. Finally, the dynamics of MBN generation under orthogonal fields is
discussed.
10
CHAPTER 2.
THEORY AND BACKGROUND
11
2.1 Stress Measurement
2.1.1 Stress and Strain
In material science, stress is defined as the force per unit area that neighboring particles within
a continuous body exert on each other. In crystalline materials these forces act in three
dimensions with a general stress state expressed in terms of the Cauchy stress tensor
[
]
[34]:
(2.1)
Since, in a Cartesian coordinate system any given point in space lies on three orthogonal planes,
there is one normal and two orthogonal (shear) stresses associated with that point. Therefore,
a second order stress tensor with nine elements is required to fully describe the stress state, as
illustrated in Figure 2.1. In the Cauchy stress tensor, normal stresses are represented by the
diagonal elements and shear stresses by the off-diagonal elements. While equation (2.1)
represents the most general case of a triaxial stress, the stress normal to a free surface is zero
Figure 2.1: The Cauchy stress tensor represented on a continuous solid in cartesian coordinates.
CHAPTER 2.
THEORY AND BACKGROUND
12
and can thus only be at most biaxial. In NDE stresses are generally measured at the sample
surface, therefore biaxial and uniaxial stresses are the focus of most studies [35].
There are two categories of stress, applied and residual. Applied stress is simply the
external force applied to a sample divided by its cross section. Every material has a maximum
stress that it can withstand before undergoing plastic deformation. This is known as the yield
stress. Below the yield stress, when external force is removed, the stress of the sample returns
largely to its original state [35]. Exceeding the yield stress permanently changes the shape of
the material. Upon release of the external stress, a non-uniform plastic deformation generates
an internal, residual stress field. Residual stress is often introduced during fabrication processes
such as welding, extrusion, bending or can be a result of physical damage such as grinding,
gouges and dents [35].
For the purposes of NDE, stress cannot be measured directly, but the induced deformation
of the crystal lattice can be. This deformation is known as strain
and is defined by the
fractional change in length due to an applied stress [35]:
(2.2)
where is the length under stress,
*
is the unstressed length and
+ correspond to
the nine elements of (2.1). Equation (2.2) holds for stresses well below the yield strength. The
stress-strain relationship for an isotropic material is described by Hooke’s law in its general
form [34]:
0
where
is Young’s modulus and
(
)1
(2.3)
is Poisson’s ratio. Both are material dependent properties,
describing the stiffness of the material and
describing the magnitude of the Poisson effect,
whereby an axially strained material develops a negative transverse strain. The case of an
CHAPTER 2.
THEORY AND BACKGROUND
13
anisotropic material is more complicated, with stress and strain being related by a fourth order
stiffness tensor
[34]:
(2.4)
Because polycrystalline materials are composed of grains with different crystallographic
orientations, a uniform macroscopic stress will also induce different local intragranular and
intergranular microstresses [35]. The distance over which these stresses self-equilibrate
provides the distinction between a macrostress (several grains) and microstress (≤ single grain)
[2]. As a result different measurement techniques vary in their sensitivity to macro- and
microstresses based largely on their sampling area.
2.1.2 Stress Measurement Techniques
The predominant non-destructive residual stress measurement techniques are based on
measuring the diffraction of a beam (X-Ray or Neutron) incident on the sample surface. Both
techniques have a relatively small sampling volume, on the order of 1 mm 3, and are thus
sensitive to both macro- and microstresses [2]. Neutron diffraction can achieve a penetration
depth of several centimeters in iron and steel and has an accuracy on the order of ±50 x 10-6
strain [2]. Neutron diffraction measurements cannot be performed on-site and are relatively
expensive. X-Ray diffraction achieves accuracy similar to neutron diffraction but only has a
penetration depth on the order of 10 μm [2], [34]. X-Ray diffraction systems can be made
portable for on-site measurements [7]. Another method of non-destructive residual stress
measurement is ultrasonics, which measures the change in wave velocity due to stress. The
ultrasonic method detects macroscopic stress over large volumes due to its large depth of
penetration but there are difficulties in separating the effects of microstructural
inhomogeneities and multiaxial stresses [2]. Finally, magnetic measurements are also capable
CHAPTER 2.
THEORY AND BACKGROUND
14
of measuring stress by observing changes in the magnetic properties of materials under applied
or residual stresses. The relationship between magnetism and stress is detailed in subsequent
sections, beginning with a review of Maxwell’s equation and magnetic materials.
2.2 Maxwell’s Equations
The relationship between the electric field
and magnetic flux density
is described by
Maxwell’s equations. In a vacuum, the set of four equations are Gauss’ law (2.5), Gauss’ law for
Magnetism (2.6), Faraday’s law (2.7) and Ampere’s law with Maxwell’s correction (2.8) [36]:
̅
(2.5)
̅
(2.6)
̅
̅
̅
where
̅
̅
is the permittivity of free space,
(2.7)
is the permeability of free space,
(2.8)
is the electric
charge density, ̅ is the current density and is time. The Lorentz Force law [36]:
̅
(̅
describes the force on a particle with charge
̅
̅ ),
(2.9)
and velocity ̅ due to an electric or magnetic
field. Equations (2.5) to (2.9) provide the foundation for classical electrodynamics. When
CHAPTER 2.
THEORY AND BACKGROUND
15
examining magnetic fields in matter the equations can be combined and simplified to provide
an expression for the magnetic flux density resulting from magnetization ̅ and the auxiliary
field ̅ [36]. In the case of slowly varying electric and magnetic fields ( 108 Hz [37]), equation
̅
(2.8) can be simplified assuming ̅
and rewritten as:
̅
̅
(2.10)
In magnetized matter, the current density ̅ is the sum of bound ̅ and free ̅ currents [36]:
̅
̅
̅
(2.11)
Bound currents are attributed to the magnetization field ̅ , and free currents to the auxiliary
field ̅ , according to equations (2.12) and (2.13):
̅
̅
(2.12)
̅
̅
(2.13)
Combining equations (2.10), (2.11), (2.12) and (2.13) gives an expression for the magnetic flux
in magnetized matter:
̅
(̅
̅)
(2.14)
2.3 Magnetic Materials
The magnetization vector ̅ expresses the magnetic dipole density (both permanent and
induced) and is material dependent. The relation between ̅ and ̅ is given by:
CHAPTER 2.
THEORY AND BACKGROUND
16
̅
where
̅
(2.15)
is known as the magnetic susceptibility and is related to the relative permeability by
[36]. Both are essentially proportionality constants, relating ̅ and ̅ such that
equation (2.14) can be rewritten as:
̅
and
)̅
(
̅
(2.16)
are used to classify materials into magnetic categories, the four predominant ones
being; diamagnetic, paramagnetic, ferromagnetic and ferrimagnetic, as summarized in Table
2.1 [38]. The categories are determined by the dominant magnetic response of the material to
an applied field.
Diamagnetism and paramagnetism are the result of an interaction of the external magnetic
field with magnetic moments inside the material. The orbital motion and spin of electrons
constitute tiny current loops, which generate magnetic moments proportional to the loop area
according to [36]:
̅
̅
(2.17)
where ̅ is the magnetic moment vector, is the current and ̅ is the vector area. The current
loop generated by spin is small compared to the orbital motion, but still experiences a torque in
the presence of an external magnetic field [18]. This has the effect of aligning the magnetic
dipoles parallel to the field, and is called paramagnetism. Because electrons in the same orbitals
CHAPTER 2.
THEORY AND BACKGROUND
17
Table 2.1: Classification of magnetic materials in terms of magnetic susceptibility [38]
Magnetic Classification
Magnetic Susceptibility
Example Materials
Diamagnetic
-10-6 to -10-5
Cu, Hg, Bi, B, Si, P, S, H2, N2
Paramagnetic
10-5 to 10-3
Cr, Mn, O2, NO
Ferromagnetic
10 to 106
Fe, Co, Ni
Ferrimagnetic
10 to 104
Fe3O4
have opposite spin, due to the Pauli exclusion principle, their magnetic dipoles cancel each
other out [18]. Thus a macroscopic paramagnetic effect is only observed in materials with an
odd number of electrons.
The effective current loop generated by the orbital motion of the electron is much larger
than that of the spin, and while there is a small paramagnetic effect, the torque on the current
loop is not enough to align the magnetic dipole parallel to the external field. The larger effect is
on the speed of the orbiting electron. The external magnetic field has the effect of increasing or
decreasing the electron speed, in both cases generating a dipole moment antiparallel to the
external field, a result of Lenz’s and Faraday’s law. This phenomenon is known as diamagnetism
and is present in all materials, but is a relatively weak effect.
Like paramagnetism, ferromagnetism arises from the magnetic dipole moments of
unpaired electrons. In ferromagnets, however, unpaired electrons located in inner shells are
prevented from forming pairs with electrons in neighboring atoms due to a shielding effect by
outer electrons (e.g. unpaired 3d electrons are shielded by 4s electrons in Fe) [19]. Neighboring
unpaired electrons do interact, however, through what is known as the exchange force
(described in detail Section 2.4.1), which has the effect of aligning magnetic moments parallel
to each other [18]. The end result is a configuration of separate regions of aligned magnetic
moments called domains, with a distribution which minimizes the total energy of the system. In
materials with multiple atomic species in a crystal lattice, each can have its own magnetic
CHAPTER 2.
THEORY AND BACKGROUND
18
moment. When these moments oppose each other in direction but are unequal in magnitude,
these materials are said to be ferrimagnetic.
Ferro- and ferrimagnets are non-linear materials unlike dia- and paramagnets. As such, in
equation (2.16)
is not a constant, but dependent on ̅ . As the external field is increased,
approaches one. If the field is then removed, the ferromagnet retains a residual magnetization.
This phenomenon in known as hysteresis and is shown in Figure 2.2. The mechanism for
hysteresis is explained in detail in Section 2.4.
Figure 2.2: Hysteresis loops observed in ferromagnetic materials. As the applied field is
increased, the initial magnetization follows the red curve from the origin. Magnetization
approaches saturation ( ) as the field is increased. When the applied field is reversed the
magnetization follows the blue curve (major loop). The green curve (minor loop) shows the
magnetization loop when the applied field is cycled but does not reach saturation.
CHAPTER 2.
THEORY AND BACKGROUND
19
2.4 Domain Theory
Magnetic dipoles in ferromagnetic materials align themselves in groups known as domains as a
result of the minimization of magnetic energies, discussed in Section 2.4.1. Within a domain the
magnetization is uniform and at saturation. The bulk magnetization is determined by the vector
sum of each domain’s magnetization. The boundaries between domains are known as domain
walls, across which the magnetic dipoles change their alignment [11]. An example of a
ferromagnetic crystal with 90 and 180 degree domains walls is shown in Figure 2.3.
Figure 2.3: Ferromagnetic crystal showing domain walls that separate magnetic domains of
different magnetic orientation. Insets highlight incremental rotation of magnetic spins across
90 degree (upper inset) and 180 degree (lower inset) domain walls.
CHAPTER 2.
THEORY AND BACKGROUND
20
2.4.1 Magnetic Energy
Domain structure arises from the minimization of various magnetic energies within a
ferromagnetic crystal. There are six energies that contribute to the domain configuration; the
exchange energy (
energy (
), the magnetostatic energy (
) [39], the domain wall energy (
Zeeman energy (
), the magnetocrystaline anisotropy
), the Magnetoelastic energy ( ) and the
) [40], [41]. The total magnetic energy associated with a ferromagnetic
crystal can be written as:
(2.18)
Each of these terms is discussed briefly below.
Exchange Energy
The exchange interaction is the quantum mechanical phenomenon that gives rise to
ferromagnetism. Neighboring unpaired electrons will undergo the interaction and by summing
over all pairs, the system will have an exchange energy given by [39]:
∑
where
(| ̅
̅ |) ̅ ( ̅ ) ̅ ( ̅ )
( )
(2.19)
is the exchange integral for two electrons with spin ̅ and ̅ located at ̅ and ̅ and
( ) is the angle between the spins. In the case of ferromagnetic materials, equation (2.19) is
minimized when
, (i.e. when the spins are aligned)[39]. Because equation (2.15) depends
on the distance between spins, | ̅
̅ |, the atomic separation also affects the exchange
energy. In the case of α Fe, as the distance between atoms decreases, the exchange force
increases up to a peak value after which it decreases again [19]. The variation in exchange
energy with atomic separation is described by the Bethe curve shown in Figure 2.4.
CHAPTER 2.
THEORY AND BACKGROUND
21
Figure 2.4: Bethe curve describing the variation in exchange energy for increasing ratio of
interatomic distance to radius of the 3d electron shell,
. The curve is representative of the
trend with example paramagnetic elements Cr, Mn and γ Fe and ferromagnetic elements α Fe,
Co, Ni and Gd, plotted at their approxamite locations.
Magnetostatic Energy
If the exchange energy was the only factor in determining domain structure, ferromagnetic
crystals would exhibit a single uniform domain. This configuration, however, would result in a
demagnetizing field ( ̅ ) extending outside the ferromagnetic crystal, representing energy
stored in a magnetic potential. This magnetostatic energy is given by [40]:
∫
where ∫
̅
(2.20)
is the integral over all space. The magnetostatic energy can be reduced by
introducing domains with opposing magnetic moments, minimizing the demagnetizing field.
Figure 2.5a shows a ferromagnetic crystal with a uniform magnetic domain with a large
demagnetizing field. Figures 2.5b to 2.5c show the reduction of the demagnetizing field through
the addition of new domains [19].
CHAPTER 2.
THEORY AND BACKGROUND
22
Figure 2.5: Minimization of the magnetostatic energy by reducing the demagnetizing field
through the creation of more magnetic domains. (a) object with uniform magnetization and
large demagnetizing field, (b) the introduction of a 180° domain wall between two magnetic
domains reduces the demagnetizing field, (c) combination of 180° and 90° domain walls
separating four domains creates a flux closed object
Magnetocrystalline Anisotropy Energy
In a ferromagnetic crystal lattice there are energetically preferred crystallographic directions
along which magnetic dipoles align themselves. The energy associated with magnetization
along an axis is known as the magnetocrystalline anisotropy energy and for cubic crystals is
given by [42]:
(
where
and
)
(
)
are the first and second order anisotropy constants and
(2.21)
,
and
are the
cosines between the magnetization and the crystallographic directions. Directions of low
energy are known as an ‘easy axis’ whereas those with higher energy are termed a ‘hard axis’.
In BCC crystals the [100] is the easy axis and the [111] the hard axis as shown in Figure 2.6.
CHAPTER 2.
THEORY AND BACKGROUND
23
Figure 2.6: BCC crystal with magnetic easy axis in the [100] direction and hard axis in the [111]
direction.
Domain Wall Energy
As discussed above, adjacent domains with opposing magnetizations lowers the magnetostatic
energy. Domain wall energy is the energy associated with the creation of the wall between
such domains. Across the width of the wall, magnetic dipoles gradually rotate from one domain
orientation to the other (see Figure 2.3). Because these dipoles are no longer aligned along a
crystallographic direction or parallel to each other there is an increase in magnetocrystalline
anisotropy energy and the exchange energy associated with the wall. Thus for the creation of a
domain wall, the decrease in the magnetostatic energy must be larger than the increase in all
other energies.
Magnetoelastic Energy
The interaction between magnetic dipoles not only affects domain structure but also affects the
crystal lattice itself. The interaction between the magnetic moments and the stress and strain
fields is known as magnetoelasticity and presents itself in two forms shown in Figure 2.7.
CHAPTER 2.
THEORY AND BACKGROUND
24
Figure 2.7: Representation of magnetostriction (left) and the Villari effect (right).
The first is termed ‘magnetostriction’, where the magnetization of domains induces a strain
on the crystal lattice. The generated strain measured at magnetic saturation is called the
magnetostriction constant, , and is often used to define the magnetostrictive behavior of
ferromagnetic materials. For example, in Fe, the saturation magnetostriction is measured in the
[100] direction (
). In this case the magnetostrictive energy is given by [43]:
∫(
where
is the uniaxial stress, is Poisson’s ratio,
the domain orientation and ∫
)
(2.22)
is the angle between the applied stress and
is the volume integral over the ferromagnetic crystal.
CHAPTER 2.
THEORY AND BACKGROUND
25
The second manifestation of magnetoelasticity is known as the Villari effect, and describes
how externally applied stresses will change the internal domain structure of a magnetic
material. In response to strain on the crystal lattice, the number of 180° domain walls along the
direction of strain increases [44] until the energy associated with the creation of a new wall is
greater than the reduction in the magnetoelastic energy.
Zeeman Energy
Zeeman energy, also known as the external field energy, represents the potential energy of an
object with magnetization ̅ in a magnetic field ̅ [18]:
∫ ̅ ̅
(2.23)
The Zeeman energy is minimized when the magnetization of a domain is aligned with the
applied field. This is achieved through the growth of favorably aligned domains and domain
vector rotation. This process of domain reconfiguration, to minimize the Zeeman energy, is
detailed in Section 2.4.2.
2.4.2 Magnetization Process
The magnetization process is stochastic in nature, whereby the final domain configurations are
the result of the minimization of magnetic energies in equation (2.18) to reach a local minimum
potential energy [11]. With the application of an external magnetic field, the domain structure
changes due to increases in
and
. To lower the energy, magnetic domains tend to align
themselves in the direction of the applied field according to (2.23). As shown in Figure 2.8,
there are three mechanisms that accomplish this: (2) domain wall motion to increase the size of
preferentially aligned domains at the expense of misaligned domains; (3) domain wall creation
CHAPTER 2.
THEORY AND BACKGROUND
26
Figure 2.8: The magnetization process illustrated in five stages, (1) the initial domain
configuration, (2) growth of domains with magnetization aligned with the applied field primarily
through the motion of 180 degree domain walls, (3) further growth of domains through the
motion of 90 degree domain walls, (4) final domain wall motion leaving a uniform domain and
(5) domain vector rotation.
and annihilation; and (5) domain vector rotation to reduce the angle between the
magnetization of the domains and the applied field.
While all three mechanisms occur to some extent throughout the magnetization process,
domain wall motion (stages 2 to 4 in Figure 2.8) is the predominant magnetization mechanism.
The motion of domain walls will reduce the volume of misaligned domains until the energy
associated with the domain wall is greater than the reduction in magnetostatic energy
(
). At this point the domain wall is annihilated, removing the misaligned domain. As
CHAPTER 2.
THEORY AND BACKGROUND
27
the magnitude of the applied field is increased further, the magnetic moments in the remaining
domains will begin to rotate in the direction of the applied field. The majority of domain
rotation occurs last because the energy associated with the rotation of magnetic dipoles off
their preferred crystallographic directions (
), is much larger than the energy associated with
the motion and annihilation of domain walls [18]. Furthermore, in the case of BCC crystals (e.g.
Fe), which have 90° and 180° domain walls, the energy associated with the motion of each of
these two types of domain wall is different. A 90° domain wall represents the interface
between two different induced strain fields ( ). Therefore the motion or annihilation of the wall
would represent an increase in
. The strain field across a 180° domain wall, however, is
identical and therefore does not cause an increase in
. Thus, during the initial magnetization,
180° domain wall motion is the dominant change in the domain structure.
The force
on a domain wall is a function of the parallel component of the mean field
in
the vicinity of the domain wall, and can be written as [28]:
(2.24)
where
is the domain saturation magnetization and
is the angle between
and the length
of the domain wall. As a result of equation (2.24), in materials that have an anisotropic
distribution of domain walls (i.e. a large population of domain walls which are aligned)
magnetization of the material will have an angular dependence. This dependence is
characterized by a majority of domains aligned in a particular direction, which is generally
known as the magnetic easy axis direction .
2.5 Magnetic Measurements
As described in Section 2.4, a material’s domain configuration is the result of the minimization
of magnetic energies and is therefore influenced by microstructure, magnetic history, external
CHAPTER 2.
THEORY AND BACKGROUND
28
magnetic fields as well as applied and residual stresses [1], [11], [17], [42]. For these reasons,
observing the effect of applied magnetic fields on ferromagnetic objects can provide
information on material properties [11], [17], [42]. Numerous magnetic inspection methods
have arisen to measure material properties such as grain size and residual stress, as well as
material damage like cracks and corrosion [1]. Because magnetization is directional and
because many of these properties are anisotropic in nature, angular dependent measurements
are required to fully characterize many material properties [11], [17], [42].
One of the earliest magnetic inspection methods is the measurement of hysteresis [1],
[45]. The flux density ̅ within a ferromagnetic material not only depends on the applied field ̅
but on its magnetic history. Cyclical magnetization traces out what is known as a hysteresis
curve (see Figure 2.2), which has been described with macroscopic parameters such as
coercivity, remnant flux density and saturation flux density [20]. The significant limitation of
hysteresis measurements has been the strong dependence on sample geometry, flux waveform
and frequency [12], making repeatable measurements difficult. Another common magnetic
inspection method, used extensively in the pipeline industry, is magnetic flux leakage (MFL) [1].
MFL techniques are based on passing magnetic flux through a sample and measuring the flux
that ‘leaks’ out of the sample due to inhomogeneities such as cracks, corrosion and to a small
extent stress [1]. The topic of the current thesis, magnetic Barkhausen noise (MBN) results from
the abrupt motion of domain walls that occurs during magnetization, and has also been shown
to be sensitive to residual stress [16].
2.6 Magnetic Barkhausen Noise
The motion of domain walls in response to an applied magnetic field is not a continuous
process. As domain walls move through the crystal lattice they encounter crystal imperfections,
impurities, dislocations, grain boundaries and other quantities that represent potential barriers
CHAPTER 2.
THEORY AND BACKGROUND
29
[13]. These are known as ‘pinning sites’, which obstruct the motion of domain walls. As the
external field is increased, domain walls ‘jump’ over these pinning sites, resulting in an abrupt
change in the local magnetization [13]. These are known as Barkhausen events and manifest in
two forms: (1) the change in the strain field due to magnetostriction, which generates acoustic
noise; and (2) the discrete magnetization changes induce corresponding voltage pulses in an
appropriately placed coil. The latter is the more commonly measured quantity and is termed
magnetic Barkhausen noise. MBN is attributed primarily to the motion of 180° domain walls, as
compared with 90° domain walls. This is because 180° wall motion requires magnetic dipoles to
rotate through twice the angle of that associated with 90° domain wall motion. Because the
volume change is nominally larger for 180° domains, it is the dominant contribution to the MBN
signal [13]. However, because 90° domain wall motion requires changes to the local strain
fields, their motion is the dominant source of magneto acoustic noise [46], [47].
2.6.1 MBN Parameters
The MBN voltage signal (see Figure 1.1b) lends itself to a wide variety of analyses and can be
characterized by a number of parameters. The repeatability and correlation of these
parameters with various microstructural properties varies significantly and as such, a large
amount of research in the area of MBN is focused on identifying these correlations and
developing repeatable measurement techniques [23]. The most common analysis of MBN
utilizes the RMS voltage of the signal or the integral of the squared voltage signal known as the
Magnetic Barkhausen Noise energy,
. It is one of the most repeatable parameters
[31], [48] but because of its non-linear relationship with magnetizing current [31], [32] the
applied field must be carefully controlled. Other commonly used parameters include the peak
height of the signal, the peak position and the peak width [24]. Peak height has been shown to
increase, and peak location to decrease, for increasing stress and both have been used to
characterize stress fields around weldments in naval steels [25]. MBN has also been used to
CHAPTER 2.
THEORY AND BACKGROUND
30
determine several macroscopic properties such as coercivity [13], [42] and magnetic
permeability [25]. Some less common MBN parameters that have been investigated as well, are
the MBN power spectra [24] and Barkhausen counts/events [21], [26] both of which have been
correlated with residual stress. The MBN power spectra represents the frequency distribution
in the MBN signal. BN count is the number of data points above a voltage threshold and BN
events is the number of voltage peaks above that threshold [21].
The MBN signal is typically filtered using a bandpass filter in the range of 1 kHz to 100 kHz
to remove high frequency background noise, low frequency power line harmonics, pickup coil
resonance peaks and aliasing frequencies [13], [23], [26]. In addition to intentional filtering, the
BN noise spectrum is affected by attenuation due to the skin effect in the sample [2], [13]. The
effect of pickup coil lift off is very significant [5], [23] and pickup coils are typically pressed on
the sample using a spring to achieve consistent liftoff or a fixed liftoff is introduced [23], [48].
Lastly, the detected MBN is significantly dependent on the geometry [12], [23] and frequency
response [5] of the pickup coil. This dependence is one of the main limitations in achieving
repeatability of MBN across different platforms.
2.6.2 MBN Energy
The multivariate nature of MBN lends itself to a wide variety of analyses to characterize a
signal. Because MBN signals are typically measured as a voltage across a pickup coil, a simple
and appropriate parameter used to quantify a MBN response is the energy in the voltage signal:
∫
where
is the energy,
(2.25)
is the power and the integral is over the excitation period, . Equation
(2.25) can be rewritten in MBN terms as:
CHAPTER 2.
THEORY AND BACKGROUND
31
∫
where
is the MBN voltage,
(2.26)
is a constant representative of the pickup coil resistance and the
integral is over one excitation period. MBN energy tends to be a consistent and reproducible
parameter for Barkhausen noise analysis [31], [48] but it has a non-linear dependence on
excitation field amplitude typically of the form shown in Figure 2.9 [31]. This non- linear
dependence can be split in to regions of ‘low’, ‘medium’ and ‘high’ field amplitude. The low
field region represents the excitation field amplitudes that are only high enough to move a
small number of weakly pinned domain walls. The medium field region is characterized by a
large increase in MBN energy with field amplitude, as a larger number of domain walls can now
overcome their respective pinning sites. As the excitation field amplitude increases further into
the high region, there remain fewer and fewer domain walls that can still be un-pinned and the
MBN energy approaches a maximum value. The positions of these regions are not exact and
serve primarily to assist in the discussion of the non-linear variation of MBN energy with the
excitation field amplitude.
Figure 2.9: Typical non-linear increase of MBN energy with increasing excitation field amplitude
[31].
CHAPTER 2.
THEORY AND BACKGROUND
32
2.6.3 MBN Anisotropy
Polycrystalline ferromagnetic materials are comprised of very small crystals, or grains, each of
which has a particular crystallographic orientation. If the population of grains exhibits a
preferred orientation, known as texture, the material may also exhibit bulk magnetic
anisotropy. In addition, bulk magnetic anisotropy may also result from anisotropic
microstructural effects as well as residual stress. As a result,
is dependent on the
direction of the magnetizing field, relative to that of the bulk magnetic anisotropy. During
magnetization, each Barkhausen event and the associated increased magnetic moment
represents a change in energy
according to [49]:
(
where
is a coefficient of the Barkhausen event,
mean field in the vicinity of the event,
)
(2.27)
is the sum of the applied field and the
is the angle of the applied field and
is the angle of
the magnetic easy axis, where both angles are relative to a given reference direction. The total
MBN energy is the sum of all the energy changes
associated with
∑
(
Barkhausen events:
)
(2.28)
Equation (2.28) can be re-written in terms of energies contributing to the net easy axis
(anisotropic contributions) and the isotropic background:
∑
(
)
∑
(
)
(2.29)
Equation (2.29) can then be simplified through the introduction of constants representing the
anisotropic , and isotropic , Barkhausen events, given by:
CHAPTER 2.
THEORY AND BACKGROUND
33
∑
(2.30)
∑
(
)
(2.31)
Using equations (2.29), (2.30) and (2.31), the angular dependence of MBN energy can be
written as [49]:
( )
(
)
(2.32)
Figure 2.10 shows typical MBN energy anisotropy data. Such measurements are typically
performed by physically rotating a dipole probe, through 180° on the sample, taking
measurements at 10-15° intervals. The red line through the data is the line of best fit obtained
using equation (2.32).
105
90
75
120
4
60
135
3
45
30
MBN Energy (mV2s)
150
2
1
0
1
2
3
4
165
15
180
0
195
345
330
210
225
315
240
300
255
270
285
Figure 2.10: Typical MBN energy anisotropy data plot using manual dipole rotation in
increments of
. The measurements are performed under flux control at
. The line of
best fit is obtained using equation (2.32).
CHAPTER 2.
THEORY AND BACKGROUND
The parameters of equation (2.32), namely , ,
34
and
can all be obtained from this fitting
line. The relative anisotropy of a sample can also be described by the MBN energy ratio,
[50]:
(2.33)
which is the ratio of the maximum MBN energy to the isotropic background, where a ratio of 1
represents the case of a sample that is purely isotropic.
2.6.4 MBN Energy under Orthogonal Fields
Traditionally, angular dependent MBN measurements were performed using the manual
rotation of a MBN dipole probe [20], [31], [49]. However, the tetrapole designed and developed
in the original Queen’s system was intended to eliminate the need for this manual rotation. In
the tetrapole probe design, orthogonal magnetic fields generate a superposition field in the
center of the tetrapole. Through suitable manipulation of the magnitude of the orthogonal
fields, it is assumed that a uniform superposition field can be electronically rotated though
360°, thus generating an angular MBN plot such as that seen in figure 2.10 [5], [32], [33]. This is
explained in more detail below.
The tetrapole principle operates under the assumption that the two orthogonal fields are
added vectorially in the sample. The direction of the resulting superposition field is determined
by varying the magnitude of the orthogonal fields according to [5], [48]:
̅
where ̅
(
)
represents the superposition field,
(
)
(2.34)
and
are the magnitudes of the
orthogonal flux densities (through pole-pairs 1 and 3, and 2 and 4, respectively),
magnetic permeability and
is the
is the angle of the superposition field. Equation (2.34) requires
that: (1) the magnetic flux is controlled through the orthogonal magnetic circuits; (2) the
CHAPTER 2.
THEORY AND BACKGROUND
magnetic permeability
35
is isotropic, constant (
) and is not itself a function of
; and (3)
the effects of anisotropic domain structure and magnetic hysteresis in the circuit can be
neglected. It is assumed that with the implementation of flux control and in the case of small
anisotropic permeability variations, requirements (1) and (2) hold to a first approximation. In
addition to the above requirements, because of the geometry of a tetrapole, equation (2.34)
will only be valid in a small area at the center of the probe. In the surrounding region, the
magnetic flux will be non-uniform in both magnitude and direction.
Figure (2.11) shows a tetrapole probe oriented at an angle
the sample (
with
from a reference direction on
), generating a hypothetical superposition field according to equation (2.34),
at an angle
to the angle
. The relationship between ,
and
can be
described by the following equation:
(2.35)
Figure 2.11: A tetrapole (having poles 1,2,3 and 4) oriented at an angle
from a reference
direction on the sample (
), generating a superposition field
at an angle
from
the angle .
Chapter 3
DRDC MBN System and Experimental Setup
The MBN system that was rebuilt and modified for DRDC in this work is based on the original
Queen’s system designed by Ph.D. student Steven White [5], [6]. As part of the current M.Sc.
work, changes were made for the purposes of improving overall system performance and
adapting the design to be suitable for use by a technician, on submarines in dry-dock. This
chapter provides a basic description of the design modifications as well as the construction of
the DRDC system. Emphasis is placed on design changes, their justification and their
implementation. The chapter concludes with a brief explanation of the MBN measurement
procedure and the samples investigated in this work.
A block diagram of the final, completed, DRDC system developed as part of this thesis, is
shown in Figure 3.1. The system consists of a hybrid analog/digital controller implemented in
LabVIEW 2011 capable of generating up to four controlled excitation waveforms at the poles of
a tetrapole electromagnet, while measuring induced Barkhausen noise with a pickup coil. The
system was implemented in three main parts shown in Figure 3.1: (1) the PC with LabVIEW
2011 software; (2) the flux control hardware (PCI 6259, PCI 6133, SR560 Preamp, FCS, SEG100R
UPS, Power Supply); and (3) the probe assembly (Excitation, feedback and pickup coils).
36
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
37
Figure 3.1: Block diagram of the DRDC system with software, hardware and probe assembly
components. Arrows denote direction of power or signal.
The integrated nature of the original Queen’s system design, particularly the FCS and the
LabVIEW 2011 software required that modifications to the system be limited. To provide DRDC
with a MBN system with established performance capabilities, design changes were either
incremental or self-contained. For this reason changes to the control circuitry and software
were limited but numerous changes were made regarding the probe design. In both the original
Queen’s system and DRDC system, the probe is removable and thus measurements can be
performed with different hardware-probe configurations (discussed in Section 4.1).
In each section that follows, the significant design elements of the original Queen’s system
are briefly explained in order to explain and highlight the modifications needed for the new
DRDC system. Section 3.1 describes the hardware components, Section 3.2 describes the
software and Section 3.3 describes the probe assembly. A number of different probes were
examined in this work, which are summarized in Section 3.3.
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
38
3.1 Hardware
Hardware refers to the system components that generate and control the excitation waveforms
applied to the probe excitation coils and measure the MBN signal induced in the probe pickup
coil. Specifically this refers to the data acquisition boards (DAQs), flux control system (FCS),
power supplies and preamplifier.
3.1.1 Data Acquisition Boards (DAQs)
The DRDC system is controlled in National Instruments® (NI) LabVIEW® 2011 which is
implemented through the use of two National Instruments® data acquisition boards. The NI PCI6259 is responsible for generating and sampling the excitation and feedback voltage waveforms
in all four channels of the tetrapole (through the FCS). The NI PCI-6133 samples the MBN
voltage signal in the pickup coil (through the preamplifier). The original Queen’s system
implemented a NI PCI-6229, which is structurally identical to the NI PCI-6259 used in the DRDC
system, but has a maximum sampling rate of only 250 kHz compared to 1 MHz for the PCI-6259.
The PCI-6259 was selected for the DRDC system because the 1 MHz sampling rate would meet
the Nyquist criterion for measuring Barkhausen noise (which has significant frequency
components up to 300 kHz) and could allow the entire system to be run with only one DAQ. The
required modifications to the LabVIEW 2011 software, however, proved to be significant, and
because such changes would only result in a minor reduction in system complexity, the DRDC
system was implemented with two DAQs.
3.1.2 Flux Control System
The flux control system (FCS) provides analog control of excitation waveforms in parallel over
four channels through the use of a negative feedback amplifier circuit. The circuit design in the
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
39
new DRDC system is identical to that used in the original Queen’s system [6] but is
implemented with a modified printed circuit board layout to address noise and heat issues
affecting system performance [5]. See Appendix A for a comparison of the FCS circuits of the
original Queen’s and DRDC systems.
Each channel employs a LM388T high power audio amplifier, H11F1M optocouplers for
digital switching between a voltage follower and flux feedback circuit configuration and BUF634
buffer amplifiers for accurate sampling of shunt and feedback voltages. The FCS is connected to
the PCI-6259 DAQ through two 68-pin D-Sub connections and to the probe through an 18-pin
Maxi-Con-X connection.
The circuit layout of the FCS used in the DRDC system was created in National Instruments®
Ultiboard® and manufactured by SpeedyPCB® in Ottawa, Ontario. Compared to the original
Queen’s system, the layout of the circuit was modified in the following ways:

The length of non-inverting input traces were minimized and the inverting and noninverting traces were physically separated, to reduce capacitive effects/noise [51].

The size of ground traces were increased to reduce the impedance of ground
connections with the intention of decreasing conducted noise [51].

Larger op-amp heat sinks were attached to prevent previously observed thermal
overload at high currents [5]. Heat sink power dissipation requirements were
calculated for continuous operation at 40°C under natural convection conditions [52]
to ensure functionality in dry-dock conditions for submarine hull measurements.

The circuit layout and labeling was modified for simplified debugging by an
operator/technician.
3.1.3 Power Supply
During the testing of the original Queen’s system, a significant reduction of noise in the system
was observed when using a pure sinusoid uninterruptable power supply. With the aim of
reducing system noise, the DRDC system was implemented with a SEG100R STABILINE
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
40
uninterruptible power supply and Power-One HCC24-2.4-AG linear power supply with ±0.05%
output regulation [53] compared to ±1% output regulation of the Anatek 25-2D power supply
used in the original Queen’s system [54].
3.1.4 Preamplifier
The low voltage signal induced in the pickup coil by Barkhausen events requires amplification
before it can be sampled by the PCI-6133 DAQ. The original Queen’s system used an Ithaco
1201 preamplifier with a 400 kHz bandwidth, 60 dB gain and 7
√
DRDC system implemented a Stanford Research® SR 560 that
meets or exceeds these
requirements and has a notably superior noise floor at 4
√
noise floor [5]. The
[55].
3.2 Software
The FCS is controlled in LabVIEW® 2011 using software developed for the original Queen’s
system. The feedback mode of the FCS (voltage or flux) is controlled in the software by digital
outputs on the PCI-6259 to the H11F1 optocouplers. Under flux control, the software also
includes an optional digital error correction algorithm that can correct the excitation
waveforms once the analog feedback circuit has achieved a specified waveform accuracy
(relative to a reference waveform). Changes to the software were limited to adding alternative
excitation waveforms (e.g. square wave) and adjusting constants for the purposes of calibrating
probes (see Appendix B).
For a measurement in either voltage of flux control mode, the system begins by sampling
the ambient background noise in the pickup and excitation coils over a number of cycles so it
can be subtracted off during measurement. The PCI-6259 then outputs a reference excitation
waveform to the FCS. The FCS amplifies the reference waveform, which is then controlled
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
41
though a voltage or flux feedback circuit. The software monitors the waveforms and other
important system parameters throughout the measurement. Once all four waveforms are
below the target waveform error threshold (discussed in Section 4.1.1), the PCI-6133 samples
the MBN pickup voltage over a specified number of cycles. The raw MBN and waveform data is
then stored in text files.
3.3 Probe
The probe refers to the U-core magnetic yokes, excitation coils, feedback coils, pickup coil and
the housing in which they are contained. Four different probes are examined in this work, one
which was part of the original Queen’s system, and three of which were constructed by the
author for this thesis work. The four probes are referred to in this work by the following names:

Spring-Loaded 4 Pole (SL4P) – Tetrapole probe designed and built for the original
Queen’s system.

Feeder Tetrapole Probe (FTP) – The initial tetrapole probe constructed for the DRDC
system designed to emulate the SL4P as closely as possible.

Feeder Dipole Probe (FDP) – Dipole probe constructed for the DRDC system. This was
similar to the FTP with one U-core magnetic yoke removed.

Submarine Tetrapole Probe (STP) – Final tetrapole probe constructed for the DRDC
system with a modified design optimized for use in dry-dock conditions on submarine
hulls.
Unlike the FCS and software discussed in earlier sections, the probe design could be modified
more significantly, while still maintaining compatibility with the rest of the system. In theory
the FCS and software are able to control the excitation waveforms through any four
independent excitation/feedback coil pairs. Therefore, the coil geometry and number of turns
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
42
can be modified with only correspondingly minor adjustments in the software. The three
probes constructed as part of this thesis work share several common design elements including
orthogonal Supermendur dipole cores with 500 turn excitation and 50 turn feedback coils at
each pole end. Each probe was also equipped with a centrally mounted pickup coil, which was
significantly modified from the SL4P design which is discussed in Section 3.3.1. CAD models of
the probe components were designed in Solidworks® 2010 and constructed of acrylonitrile
butadiene styrene (ABS) using a Stratasys® Dimension 1200es 3D printer. The accuracy of the
models was limited by the horizontal resolution of the Dimension 1200es to 0.5 mm. The design
of the three probes and their parameters are presented below.
Feeder Tetrapole Probe (FTP)
The Feeder Tetrapole Probe (FTP), shown in Figure 3.2, was built to emulate the original
Queen’s system probe (SL4P) design as closely as possible . The FTP used a spring-loaded U-core
to achieve even contact of the poles to the sample. Mounted at the center of the FTP was a 700
turn 5.5 mm diameter pickup coil. Coil parameters of the FTP are shown in Table 3.1.
Feeder Dipole Probe (FDP)
The Feeder Dipole Probe (FDP) uses the same housing as the FTP but contains only a single long
U-core dipole and is shown in Figure 3.3. As a result there are only two excitation/feedback coil
pairs whose parameters are summarized in Table 3.2. The pickup coil in the FDP was 5 mm in
diameter and had 400 turns. The symmetric nature of the pin header connection allows the coil
pairs to be run using FCS feedback circuits 1 and 3 or 2 and 4. For consistency, all
measurements using the FDP in this work were performed using feedback circuits 2 and 4. The
FDP’s primary purpose was to serve as a dipole reference for anisotropy measurements
performed by the tetrapole probes. The FTP, STP, SL4P and FDP anisotropy results are
compared in detail in Chapter 4.
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
43
Figure 3.2: CAD model of FTP probe.
Table 3.1: FTP Coil Parameters. is coil resistance and
Precision® 878B LCR meter at 1 kHz.
is coil inductance measured on a BK
Parameter
Excitation 1
Excitation 2
Excitation 3
Excitation 4
Feedback 1
Feedback 2
Feedback 3
Feedback 4
Pickup Coil
(Ω)
28.2
28.9
28.2
28.9
2.70
2.79
2.69
2.69
29.4
(mH)
29.2
32.8
33.7
35.2
0.27
0.35
0.33
0.35
4.41
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
44
Figure 3.3: CAD model of FDP probe.
Table 3.2: FDP Parameters. is coil resistance and
Precision® 878B LCR meter at 1 kHz.
is coil inductance measured on a BK
Parameter
Excitation 2
Excitation 4
Feedback 2
Feedback 4
Pickup Coil
(Ω)
30.4
32.8
2.88
2.82
23.6
(mH)
31.2
30.5
0.33
0.32
2.11
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
45
Submarine Tetrapole Probe (STP)
The Submarine Tetrapole Probe (STP) was developed from the FTP design to improve its
functionality in the field. It is shown in Figure 3.4. The main challenge with the earlier FTP
housing design was the poor cable connectivity. The pin headers for the excitation/feedback
coils and the pickup coils were located on opposite ends of the probe causing problems with
cable management. Furthermore the pin header connectors were held in place by friction
allowing cables to easily slip out. Using a pin header for the pickup coil also required a custom
cable for connection. Other problems with the FTP design related to the probe housing. For
example, the dipole poles extended well past the probe housing (see Figure 3.2) exposing the
coils to potential damage. The FTP housing was also very small (to accommodate CANDU feeder
pipe spacing, the focus of Steven Whites’ Ph.D. work [5]) leading to difficulties in manufacturing
To address these issues, the size of the probe housing was increased to accommodate
handheld use more comfortably. The pickup cable was redirected through an internal, shielded
channel to connect at the rear of the housing. The pickup cable was terminated with a BNC
jack, allowing any standard BNC cable to connect the probe to the preamplifier. The
excitation/feedback cables were terminated with two shielded CAT5 (RJ45 Ethernet) jacks. The
BNC and CAT5 connections locked cables in place, maintaining good connections during
measurements. Each CAT5 jack was connected to the two excitation/feedback coil pairs on
each dipole, which allowed for switching between feedback circuits.
Because the STP probe is designed for use on surfaces with very little curvature, the springloaded design was replaced in favor of fixing the dipoles in position using epoxy. Although this
limited the sample geometries the probe could accommodate, it allowed for consistent
coupling to flat samples.
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
46
Figure 3.4: CAD model of STP probe.
Table 3.3: STP Coil Parameters. is coil resistance and
Precision® 878B LCR meter at 1 kHz.
is coil inductance measured on a BK
Parameter
Excitation 1
Excitation 2
Excitation 3
Excitation 4
Feedback 1
Feedback 2
Feedback 3
Feedback 4
Pickup Coil
(Ω)
28.7
28.7
28.8
28.6
3.16
3.08
3.14
3.11
15.6
(mH)
35.3
38.3
37.5
37.8
0.35
0.31
0.34
0.32
1.34
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
47
3.3.1 Pickup Coil Design
The original pickup coil used in the SL4P was designed primarily to achieve a small sensing
radius of <2.5 mm, which finite element modeling (FEM) suggested was the region over which
flux superposition (discussed in Section 2.6.4) was most accurate [5]. To achieve such a sensing
radius, the pickup coil employed a ferrite core (0.5 mm radius) inside a 100 turn pancake coil
(1.5 mm outer radius), inside a ferrite sheath, inside a copper shield. There were two significant
challenges with this design: (1) sensitivity to liftoff; and (2) a complex design which made
construction difficult.
Because of the low number of turns as well as limited sensing radius, the pickup coil was
significantly affected by liftoff [5]. Therefore, despite the spring loaded design, liftoff due to
layers of paint, rust or other debris on the sample surface could reduce the MBN signal. The
second issue was that the intricate design required delicate and time consuming
manufacturing. Upon consultation with Steven White, the designer of the original Queen’s
system, the SL4P pickup coil was revealed to be the only working coil among dozens of
prototypes [56]. Based on these design and construction issues it was determined that a
simplified pickup coil design was required.
The first step in redesigning the pickup coil was to enlarge the pickup shield. Increasing the
radius of the pickup shield allowed for a larger area to connect leads to the pickup coil. As a
result, the lead solder joints could be made more robust, reducing the likelihood of a
poor/open connection. The increased space could then be used to thoroughly insulate leads
from each other as well as the shield. The inner radius of the shield was increased to 2.5 mm,
which would leave a 1.5 mm space to solder and insulate leads. The shield was made from
aluminum, which, due to its higher conductivity when compared to brass (50% International
Copper Annealed Standard (IACS) for Al compared to 27% IACS for brass [57]), would provide
superior shielding. This is reflected in the skin depth equation (E.2), where the attenuation of
electromagnetic waves increases with conductivity. The pickup coils used in FTP, FDP and STP
probes were implemented without a ferrite sheath as used in the original design [5] to further
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
48
reduce complexity. The effects on the performance of the new pickup coil design are examined
in Chapter 4.
The redesigned pickup shield is shown in Figure 3.5. The increased size of the pickup shield
not only simplified construction but also accommodated a larger radius pickup coil. It was
inferred that a pancake pickup coil with a larger radius and a larger number of turns would be
more sensitive to BN emissions according to Faraday’s law of induction:
(3.1)
where
is the number of turns in the coil and
is the magnetic flux passing through the coil
turns. Furthermore, because the effect of liftoff scales with coil diameter, increasing the size of
the coil would make the pickup assembly less sensitive to liftoff variations. Both of these effects
were expected to improve the signal-to-noise ratio of the measured BN events. The larger
sensing radius, however, would also increase the sensitivity of the pickup coil to the effects of
non-uniform field superposition, which FEM modeling indicated was significant for coils with
sensing radii above 2.5 mm [5]. The impact of modifying the pickup assembly on BN results,
including a comparison to the original pickup coil design, is presented in Chapter 4.
3.3.2 Probe Summary
The four probes examined in this work are summarized in Table 3.4. Three (FTP, FDP and STP)
were constructed by the author as described above and a fourth (SL4P) was the probe in the
original Queen’s system [5], [6].
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
49
Figure 3.5: Large radius pickup coil assembly consisting of aluminum shield and pancake pickup
coil with ferrite core (left) and cross-section view with dimensions (right).
Table 3.4: Summary of probes used in this work and their relevant pickup coil parameters.
is
the number of coil turns, is the outer coil diameter, is the coil resistance, is the coil
inductance and is the coil time constant. SL4P parameters retrieved from [5].
Probe Name
Feeder Tetrapole
Probe
Feeder Dipole
Probe
Submarine Tetrapole
Probe
Spring Loaded
4 Pole
Probe
Acronym (turns)
(mm)
(Ω)
(mH)
(ms)
FTP
700
5.5
29.4
4.41
0.15
FDP
400
5.0
23.6
2.11
0.09
STP
300
4.0
15.6
1.34
0.08
SL4P
100
3.0
4.7
0.12
0.03
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
50
3.4 Experimental Setup and Samples
The measurements presented in this work were performed using a custom built angular
measurement guide (AMG) to maintain alignment of the pickup coil over the target sensing
area for a given probe orientation angle
, shown in Figure 3.6. The AMG is comprised of two
pieces, a circular alignment ring, which is mounted on the sample using a double-sided
adhesive, and a circular probe housing guide in which the probe is inserted. The housing guide
is free to rotate within the alignment ring allowing for rotation of the probe to any angle with
an estimated uncertainty of
. Once aligned in the AMG the probes were pressed on the
sample using a plastic gator-clamp.
Measurements were performed with a sinusoidal excitation waveform, at a specified
excitation frequency
. Unless otherwise noted, all measurements in this work were
performed at
. During testing of the system,
was determined to be the
lowest frequency at which the system was consistently stable, with a low system error (see
Figure 3.6: Angular measurement guide (AMG) (left) and probe orientation (
setup (right)
) measurement
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
51
Section 4.1.1). Under flux control, the peak flux density through the feedback coil
(i.e. flux
waveform amplitude) is specified. Under voltage control, the peak voltage through the
excitation coil
(i.e. voltage waveform amplitude) is specified.
Because waveform error increases significantly at low field amplitudes (discussed in
Section 4.1.1) measurements under flux control were performed at a minimum of
. However, even at
, the possibility that thin samples could be driven to
saturation needed to be addressed. To provide an alternative path for excess flux, thin samples
were mounted on steel backing plates. Because MBN signals are detected at shallow depth
[18], [30] (for the excitation frequencies used in this work) the influence of MBN signals
originating from the backing plate was considered negligible.
3.4.1 Dipole Anisotropy Measurements
Dipole anisotropy measurements were performed using manual rotation of the probe in the
AMG. Measurements were made in increments of
from
to
, relative to an
arbitrary reference angle on the sample. The symmetric nature of the sinusoidal excitation field
makes measurements from
to
to
unnecessary as they are identical to those from
. To account for variation in probe-sample coupling between measurements, an
average of 5 measurements at each probe orientation was obtained, removing and mounting
the probe for each measurement. Multiple measurements at each location also provided an
estimation of measurement error.
3.4.2 Tetrapole Anisotropy Measurements
In tetrapole anisotropy measurements it is possible to vary a number of parameters as shown
in Figure 2.11. In this work, tetrapole measurements were performed by orienting the probe at
an angle
, relative to a reference direction on the sample (
). The field was then
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
electronically rotated in increments of
appropriate superposition field angles
or
from
52
to
or
, by selecting
, as described in Section 2.6.4.
3.4.3 Samples
The purpose of angular dependent MBN measurements is to characterize the magnetic
anisotropy of a material. Therefore, any investigation into the ability of tetrapole probes to
perform angular dependent MBN measurements must examine materials with a wide range of
magnetic anisotropy. In this work, five sample materials were selected for investigation, whose
properties are summarized in Table 3.5. The sample with the highest magnetic anisotropy was
the grain-oriented laminate (3% Si-Fe), which is engineered to be highly magnetically
anisotropic to improve efficiency in magnetic devices such as transformers. The second most
magnetically anisotropic steel was the mild steel A sample which exhibited a large magnetic
easy axis in its rolling direction, which is a common result of fabrication processes. The third
sample, HY-80 steel, also exhibited magnetic anisotropy in its rolling direction as did the fourth
sample, mild steel B. The fifth sample, which displayed the least amount of magnetic anisotropy
was a non-oriented laminate. Non-oriented laminates are engineered to be as magnetically
isotropic as possible [58].
The majority of measurements were performed on the mild steel samples (A and B). This
was done for a number of reasons. The dimensions of the mild steel samples were significantly
larger than the other samples, limiting the potential influence of sample geometry. The samples
were also significantly thicker than other samples as shown in Table 3.5 and had a higher
magnetic permeability reducing the likelihood of saturating the magnetic circuit. The validity of
flux superposition is dependent on a vector addition of flux through the sample and thus
removing the influence of geometry and magnetic saturation on the flux path was important.
CHAPTER 3.
DRDC MBN SYSTEM AND EXPERIMENTAL SETUP
53
Table 3.5: Sample materials investigated in this work, in order of decreasing magnetic
anisotropy (as determined by dipole MBN anisotropy measurements shown in Section 4.2.1).
Aside from sample thickness and associated saturation effects, it was assumed the differences
in sample dimensions would not affect MBN anisotropy measurements.
Sample Material
Grain-Oriented Laminate
Mild Steel A
HY-80
Mild Steel B
Non-Oriented Laminate
Length
(mm)
100
1600
178
193
275
Width
(mm)
30
100
34
102
30
Thickness
(mm)
0.17
4.0
1.0
5.0
0.35
Chapter 4
System Performance & Study of Flux
Superposition Validity
Following the construction of the new DRDC system, it was tested and compared to the original
Queen’s system. The results of these tests are covered in Section 4.1. During the testing of the
DRDC system, however, questions arose as to the validity of the principle of flux superposition
as it pertains to the measurement of MBN, which was the basis of the original Queen’s system
as well as the new DRDC one. This prompted a detailed study of the validity of using flux
superposition in tetrapole probes to perform angular dependent MBN measurements. This
study is presented in Section 4.2. Note that since this represented a ‘sideline study’, it is
somewhat self-contained, in that the discussion of experimental parameters, as well as
associated theory, is contained within Section 4.2 rather than being included in earlier Chapters
2 or 3.
54
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
55
4.1 System Performance
To measure the performance of the new DRDC system a series of comparative measurements
were performed against the original Queen’s system. Of interest were the performance of the
new hardware/flux control circuitry and the effects of the new probe and pickup coil design.
Differences between the systems were measured in terms of waveform error in Section 4.1.1,
BN envelope in Section 4.1.2 and 4.1.3 and BN energy anisotropy in Section 4.1.4.
As noted in Chapter 3, the DRDC system and the original Queen’s system can be run using
any of the probes summarized in Table 3.4. To isolate the differences in hardware performance
between the DRDC system, the original Queen’s system, and the various probe designs,
measurements were performed using a number of hardware-probe configurations. For
example, to remove the effects that different probes may have on hardware performance,
measurements were performed with the DRDC and original Queen’s system, both running the
STP probe.
The results presented in this section highlight an important limitation of MBN, namely the
repeatability of measurements across different MBN platforms. As discussed in Chapter 2, MBN
measurements are highly dependent on the measurement system, requiring accurate
calibration to obtain meaningful results. Section 4.1 not only demonstrates differences
between the systems but also similarities, providing insights into how different MBN platforms
can be compared or calibrated.
4.1.1 System Error
In this section, the hardware performance of the DRDC and original Queen’s system is
compared in terms of system error. For the tetrapole probes, the analog feedback and digital
correction algorithms are designed to achieve waveform accuracy over four excitation
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
56
channels. The extent to which this is achieved is reflected in the rms error
of each
waveform and is calculated as [6]:
√ ∑.
where
is the length of the waveform vector,
/
(4.1)
is the target voltage at phase
and
is
the measured feedback voltage at phase . The total rms error can be normalized with respect
to the total flux rate and expressed as a percentage according to:
(4.2)
√
where
is the normalized rms error,
feedback turns,
the
is the excitation frequency,
is the area of the feedback coil and
is the number of
is the peak flux density. Averaging
of all coils gives the total normalized rms system error,
. This section
provides a series of measurements to identify the ability of both systems to minimize
under varying measurement parameters.
System error is dependent on the target voltage/flux and the excitation frequency
. This
is because the gain of the feedback circuits and coil inductances are frequency dependent
properties. Furthermore because of eddy current effects in the coils and potential magnetic
saturation of the circuit, feedback gain is also dependent on flux density [5], [6]. To establish
the convergence of the system, measurements were made at various flux densities and
frequencies
while recording
. The final
of the system was calculated by
averaging the final 50 cycles after running the measurement for a minimum of 200 cycles.
To isolate for the performance of the hardware (FCS, power supply, etc.) and remove the
potential effects of differences in probe construction (between the DRDC system’s STP and
original Queen’s system’s SL4P probe), measurements with the two systems were performed
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
57
both using the STP. All measurements were performed at a superposition field angle (defined in
Section 2.6.4) of
on the mild steel B sample. The original Queen’s system and DRDC
system were calibrated at
and
prior to all measurements.
Calibration of the probe refers to the adjustment (in the LabVIEW software) of the feedback
circuit gain
and the feedback coil gain
minimize the
of each circuit during the feedback loop to
of the waveforms. The calibration procedure is described in detail in
Appendix B.
Figure 4.1 shows the
of the DRDC and original Queen’s system both using the STP
probe at various flux densities as a function of excitation frequency
. Both systems show the
same general pattern of a minimum error in the frequency range between 30 and 65 Hz. At
frequencies below 30 Hz the error increases rapidly in both systems with maximum
of
2.5 % and 3.1 % at 10 Hz for the DRDC and original Queen’s systems, respectively. In addition,
the DRDC system is able to operate at 5 Hz with a maximum
of 5.8 %. During testing,
the original Queen’s system was unable to establish waveforms at 5 Hz and thus there is no
data at that frequency in Figure 4.1b. The larger errors at low frequencies are likely a result of
decreased signal-to-noise ratio in the feedback coil [5], [6]. This conclusion is based on equation
(3.1), which describes how as frequency decreases so does
, resulting in a lower induced
voltage in the feedback coil. Therefore, at lower frequencies, the signal-to-noise ratio increases,
reducing the effectiveness of the analog and digital feedback system to correct the waveform.
The increased error at low frequency may also be the result of the frequency response of the
excitation and feedback coils. The measured inductance of the coils (particularly the feedback
coil) varies significantly at frequencies below 20 Hz as seen in Figure 4.2. At low frequencies,
small changes in the feedback waveform frequency result in large changes in feedback coil
inductance. This could result in instabilities in the analog and digital control system causing the
increase in
.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
58
(a) DRDC System
Total rms error errtotal (%)
10
100 mT
200 mT
300 mT
400 mT
1
0
10
20
30
40
50
60
70
80
90
100
Excitation Frequency fex(Hz)
(b) Original Queen's System
Total rms error errtotal (%)
10
100 mT
200 mT
300 mT
400 mT
1
0
10
20
30
40
50
60
70
80
90
100
Excitation Frequency fex(Hz)
Figure 4.1: System error
for various excitation frequencies
and flux densities for the
(a) DRDC system and (b) original Queen’s system. Lines are to guide the eye.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
59
1.2
Excitation Inductance LEx (H)
0.22
1.0
0.8
0.20
0.6
0.18
0.4
0.16
0.2
0.0
0.14
-0.2
0.12
-0.4
-0.6
0.10
Feedback Inductance LF (mH)
Excitation
Feedback
-0.8
0
10
20
30
40
50
60
Frequency fex (Hz)
Figure 4.2: Measured excitation/feedback coil inductance
/ as a function of excitation
frequency
. Measurements performed with HP 4192 LF Impedance Analyzer.
At higher frequencies the error increases again and appears to peak at 90 Hz for both
systems and then decreases again. The trend is not explored above 100 Hz because MBN
measurements at higher frequencies result in eddy currents and overlapping BN events [23]. In
both systems, there is a small peak at 60 Hz, which could be explained by noise entering the
system at power line frequencies. This does not, however, explain a similar peak at 70 Hz
observed in both systems.
Both the DRDC and original Queen’s systems show decreasing error with increasing flux
density, particularly at low excitation frequencies. For identical excitation frequencies, higher
maximum flux densities require that
increase as well. According to equation (3.1), this
results in a larger induced voltage in the feedback coil. This is another indication that the signalto-noise ratio in the feedback voltage waveform is a significant factor in the total system error.
The importance of improving
lies in the ability to perform controlled low frequency
MBN measurements. Figure 4.1 demonstrates the improvement of the DRDC system design
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
60
over the Queen’s system in terms of a reduction in system error particularly at low frequencies
and low flux densities. This reduced error can be attributed to a reduction in overall system
noise through the implementation of a UPS, low noise power supplies and modified flux control
circuit layout. It should be noted, however, that measurements on the two systems were
performed in different locations, each with its particular ambient electromagnetic noise
signature. The effect of ambient noise can therefore not be ruled out as a contributor to the
differences observed in Figure 4.1.
4.1.2 BN Envelope
As described in Section 3.3.1, the pickup coil was significantly modified from the original design.
With a larger sensing radius (
) and greater number turns (see Table 3.4) it was expected
that the new pickup coil would produce a larger amplitude BN voltage signal according to
equation (3.1), however, the effects on BN envelope parameters (peak height, peak phase, etc.)
was unknown. This section presents a comparison of the BN envelopes as measured by the STP
and the SL4P, whose pickup coil parameters are summarized in Table 3.4. Measurements with
the two probes were all performed using the original Queen’s system hardware to remove any
possible effect that hardware differences between the DRDC system and original Queen’s
system could have on the BN envelope. All measurements were performed under flux control
on the mild steel B sample with a superposition field angle of
sample magnetic easy axis
in the direction of the
.
Figure 4.3 shows the BN envelopes detected by each probe at flux densities from
to
and an excitation frequency of
. The amplitude of the
envelopes detected by the STP probe is larger at all flux densities, as is expected, because the
pickup coil has a greater number of turns and a greater sensing area (see Table 3.4), which
according to Faraday’s law results in a higher induced voltage. The larger coil area also results in
a higher number of total BN events being detected.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
61
(a) STP Probe
100
550 mT
BNenv (mV)
80
450 mT
350 mT
60
40
250 mT
20
150 mT
0
0
50
100
150
200
250
300
350
Phase (°)
(b) SL4P Probe
100
BNenv (mV)
80
550 mT
60
450 mT
350 mT
40
250 mT
20
150 mT
0
0
50
100
150
200
250
300
350
Phase (°)
Figure 4.3: BN envelopes measured by the (a) STP probe and (b) SL4P probe for various flux
densities
at an excitation frequency
on mild steel B.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
62
For both probes the envelope peak increases with flux density and the peak position
decreases. For both probes the position of the trailing edge of the envelope does not appear to
change between
and
. From Figure 4.3 it appears the STP and SL4P detect the
same BN envelopes at different amplitudes/flux densities.
Figures 4.4 and 4.5 examine the BN envelopes detected by the STP and SL4P in terms of
MBN energy, peak voltage (height) and peak phase (position), all as functions of flux density
and excitation frequency, respectively. MBN energy is calculated using equation (2.26). The
peaks of the BN envelopes are located using a Gaussian fit of the peaks. The results are plotted
on double y-axis graphs with different scales for the STP and SL4P data. Of most interest in
these figures is the comparison of trends between the probes, not the absolute values. By
modifying the scales such that the first and last data points are approximately at the same
location, the behavior of the two probes can be compared more easily.
Figure 4.4 shows the envelope parameters as a function of flux density from
to
. In Figure 4.4a the STP and SL4P both show a non-linear increase in MBN energy with
flux density. Figure 4.4b shows a similar non-linear increase in peak voltage for both probes. In
this case the peak voltage appears to be approaching a maximum value. In Figure 4.4c, aside
from an apparent outlier peak phase with the SL4P at
, both probes follow a similar
trend, of decreasing phase with flux. Figures 4.4a to 4.4c demonstrate that although the
absolute values of the results for the STP and SL4P probes are different, they both exhibit
similar trends with variation in excitation flux density.
Figure 4.5 shows the BN envelope parameters for low excitation frequencies from
to
. Figure 4.5a appears to show a linear relationship for both the STP and
SL4P for MBN energy in the given frequency range. Figure 4.5b shows an increase of peak
voltage for both probes which, like Figure 4.4b, appears to approach a maximum value. In
Figure 4.5c, the SL4P shows a linear decrease in peak phase, whereas the STP demonstrates an
exponential decrease in peak phase with increasing frequency.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
80
30
20
20
10
0
75
(b)
60
45
50
30
15
SL4P Probe
MBNe (mV2s)
BN Envelope
Peak Voltage (mV)
STP Probe
40
STP
SL4P
40
0
100
63
MBNe (mV2s)
(a)
60
BN Envelope
Peak Voltage (mV)
CHAPTER 4.
0
0
90
90
80
80
70
BN Envelope
Peak Phase (°)
BN Envelope
Peak Phase (°)
(c)
70
100
200
300
400
500
600
Flux Density (mT)
60
40
BN Envelope
Peak Voltage (mV)
STP Probe
20
120
100
80
60
100
BN Envelope
Peak Phase (°)
(b)
(c)
100
95
95
90
90
85
SL4P Probe
80
BN Envelope
70
60
50
40
30
20
10
0
90
80
70
60
50
40
30
STP
SL4P
Peak Voltage (mV)
(a)
BN Envelope
Peak Phase (°)
MBNe (mV2s)
100
MBNe (mV2s)
Figure 4.4: Typical BN envelope parameters for STP and SL4P probe as a function of flux density.
(a) MBN energy, (b) BN envelope peak voltage and (c) BN envelope peak phase. Lines are to
guide the eye.
85
20
25
30
35
40
45
50
55
Frequency (Hz)
Figure 4.5: Typical BN envelope parameters for STP and SL4P probe as a function of excitation
frequency
. (a) MBN energy, (b) BN envelope peak voltage and (c) BN envelope peak phase.
Lines are to guide the eye.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
64
The similar trends of the BN envelope parameters in Figures 4.4 and 4.5 are significant
because they suggest that a scaling factor could be developed to perform direct comparisons of
MBN data between different probes. Direct comparisons of data from different probes has
often been difficult with MBN measurements [23]. Furthermore, the results also indicate that
the new pickup coil design did not significantly affect basic BN envelope parameters.
4.1.3 BN Normalized Power Spectrum
The BN signal contains significant frequency components between 3 kHz and 400 kHz. The
normalized power spectrum of the BN signal represents the power of each frequency
component. Figure 4.6 shows a comparison of the normalized power spectrum detected by the
STP and SL4P probes. In each figure the area of the normalized power spectrum is normalized
to provide a comparison of the shape of the power spectrums.
Figure 4.6a shows a direct comparison of the normalized power spectrum obtained with
the SL4P and the STP. Both measurements were performed at a superposition field angle
on the mild steel B sample at
and a flux density of
. The difference
between the SL4P and STP results is primarily attributed to the intrinsically different frequency
responses of the two pickup coils. Due to different inductance and resistance values, the time
constants of the coils will be different (see Table 3.4) resulting in different normalized power
spectrums. This is one of the primary reasons that absolute comparisons between Barkhausen
noise measurement systems are limited.
Figures 4.6b and 4.6c compare the normalized power spectrums of each probe at
superposition field angles of
and
. Figure 4.6b shows how, aside from a slight
increase at low frequencies, the normalized power spectrum remains relatively unchanged for
the SL4P probe when the field is rotated to
. In comparison, the STP shows much
larger differences between the normalized power spectrums at
and
. At
the peak is diminished and appears to contain more high frequency components
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
65
0.035
Normalized Power
(unitless)
0.030
SL4P
(a) 0°
0.025
0.020
STP
0.015
0.010
0.005
0.000
0.035
Normalized Power
(unitless)
(b) SL4P
0.030
0°
0.025
45°
0.020
0.015
0.010
0.005
0.035
Normalized Power
(unitless)
0.030
0.000
(c) STP
0°
0.025
0.020
45°
0.015
0.010
0.005
0.000
0
100k
200k
300k
400k
500k
Frequency (Hz)
Figure 4.6: Differences in the normalized power spectrum measured by the SL4P and the STP
probes. (a) direct comparison of normalized power spectrum of SL4P and STP measured at
. (b) comparison of normalized power spectrum measured by SL4P at
and
and (c) comparison of normalized power spectrum measured by STP at
and
. All measurements were on mild steel B under flux control with a peak flux
density of
and an excitation frequency of
.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
66
in the signal, compared to the SL4P case, Figure 4.6b. The changes in the normalized power
spectrum demonstrated by the STP are most likely a result of its larger sensing radius, which
would make it more sensitive to non-uniform field effects. This suggests that at non-zero
values, the superposition field may be significantly non-linear and non-uniform. It also suggests
that the anisotropy measurements of each probe may be influenced by the sensing radius of
the pickup up coils, which is explored in Section 4.1.4.
4.1.4 BN Energy Anisotropy
This section presents a series of comparative MBN anisotropy measurements between the SL4P
and STP tetrapole probes under the assumption of flux superposition (see Section 2.6.4). The
purpose of these measurements was to examine the effect of STP’s redesigned pickup coil
(detailed in Section 3.3.1) on angular dependent MBN measurements. All measurements were
performed on the mild steel B sample under flux control at a flux density of
excitation frequency of
and
.
Figure 4.7a shows the measured anisotropy of the STP and SL4P with the probe oriented in
the
direction. The magnitudes of the STP MBN energies are larger, as expected, due to
the higher number of coil turns and larger radius pickup coil. Both probes exhibit a four-lobe
pattern with a large peak in the easy axis direction (
), and a smaller peak perpendicular
to the easy axis. The ratio of the large peak to the small peak is 2.0 for the SL4P and the STP
indicating the four-lobe pattern is equally as pronounced in both probes.
Figure 4.7b shows the measured anisotropy of the STP and SL4P with the probe oriented in
the
direction. Once again the magnitudes of the STP MBN energies are larger and
both probes show the four-lobe pattern with a large peak in the easy axis direction and a
smaller peak perpendicular to the easy axis. At an orientation of
the ratio of the large
peak to the small peak is 3.3 for the SL4P and 2.4 for the STP. Due to the symmetry of the
tetrapole probe, it would be expected that the results at
and
be identical.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
67
The difference in peak ratios, however, suggests that there is an ‘imbalance’ between the flux
density through the dipole pairs 1-3 and 2-4 (see Section 2.6.4), despite the use of flux control.
This imbalance could be the result of a number of factors but is most likely due differences in
the coupling of the poles to the sample.
(a) 0
SL4P
STP
90
35
120
(b) 90
35
60
20
30
150
15
10
5
180
0
5
10
15
330
210
20
MBN Energy (mV2s)
20
30
150
15
10
5
0
180
0
5
10
15
330
210
20
25
25
30
30
240
35
300
240
35
(c) 45
SL4P
STP
90
35
120
(d) FDP
70
60
30
40
5
180
0
5
10
15
330
210
MBN Energy (mV2s)
MBN Energy (mV2s)
150
10
30
150
30
20
10
0
180
0
10
20
30
40
330
210
50
25
60
30
35
60
50
30
15
20
90
120
60
25
0
300
270
270
20
60
25
25
MBN Energy (mV2s)
120
30
30
0
SL4P
STP
90
240
300
270
70
240
300
270
Figure 4.7: MBN Energy anisotropy as measured by the STP, SL4P and FDP probes under flux
control at
and
on Mild Steel B. (a)-(c) tetrapole measurements
performed using the STP and SL4P under flux superposition for probe orientation angles
of
(a)
(b)
and (c)
. Lines are to guide the eye. (d) dipole anisotropy measurements
performed using the FDP under manual rotation. Line represents fit of equation (2.32) with fit
parameters of
,
,
and an
correlation
factor of 0.98.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
68
Figure 4.7c illustrates the imbalance of the two probes more clearly with both probes
oriented at
and
. Unlike in Figures 4.7a and 4.7b, the lobe peaks are now located at
. The symmetry of the anisotropy measured by the STP, as well as the small
change in peak ratios from Figures 4.7a and 4.7b, indicates the STP probe is significantly better
balanced than the SL4P.
The most interesting result observed in Figures 4.7a-c is not the difference in anisotropy
between the SL4P and STP probe, but rather the four-lobe pattern that both probes exhibit.
Figure 4.7d shows the MBN energy anisotropy data as measured by the FDP (dipole probe)
using traditional manual rotation. As is clear from Figure 4.7, the MBN anisotropy measured by
the tetrapole probes (SL4P and STP) under the assumed principle of flux superposition is very
different from that measured by the dipole. Unlike the four-lobe pattern of the tetrapoles, the
FDP measurements demonstrate a two-lobe pattern, which is fit using MBN energy anisotropy
fitting equation (2.32) in Figure 4.7d. The difference between dipole and tetrapole
measurements throws into question the validity of the flux superposition principle for tetrapole
probes, and was a severe concern. As such, a significant effort was subsequently focused on
examining the validity of flux superposition for MBN anisotropy measurements.
4.2 Detailed Study of Flux Superposition in Tetrapole Probes
As mentioned earlier, the comparative study between the Queen’s and DRDC systems threw
into question the validity of flux superposition using tetrapole probes. This section presents a
detailed study of the nature of flux superposition in these probes. Because Section 4.2 is fairly
lengthy, it is worthwhile providing an overview of this section to the reader, as follows.
MBN anisotropy has traditionally been measured by manual rotation of the MBN excitation
field using a dipole [20], [31], [49]. Results are well documented in the literature and physical
models have been developed based on domain theory to describe MBN energy anisotropy. For
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
69
this reason, any investigation of MBN anisotropy measurements obtained using a tetrapole
probe requires a set of dipole results for comparison. These dipole results are presented in
Section 4.2.1.
As discussed in Section 2.6.4, the measurement of magnetic anisotropy utilizing flux
superposition has several assumptions associated with it, as highlighted by equation (2.34).
These assumptions have been thrown into question based on the experimental data seen in
Figure 4.7. Understanding the magnetic anisotropy measured by tetrapole probes however,
may provide insight into the magnetization process and MBN generation mechanisms when
orthogonal magnetic fields are applied. This could allow for alternative analysis methods to
characterize materials using tetrapole data. A series of MBN measurements were performed
with the tetrapole (FTP and STP) to examine the ability of the tetrapole probe to reproduce the
dipole results shown in Figure 4.8 and investigate reasons for differences.
Sections 4.2.2 and 4.2.3 examine the effect of probe angle on MBN anisotropy across
multiple steel sample grades. Following the studies on different types of steel, the following
studies were done, focusing on the mild steel A sample:

Section 4.2.4 examines the tetrapole MBN anisotropy as the result of MBN generated
by two independent, but orthogonal, dipoles on mild steel.

Section 4.2.5 examines the effect of field amplitude on MBN anisotropy in mild steel.

Section 4.2.6 examines the effect of voltage and flux control on MBN anisotropy in
mild steel.

Section 4.2.7 examines the ability of an empirical fitting equation to describe tetrapole
results and identify the magnetic easy axis.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
70
4.2.1 Dipole MBN Anisotropy Results Using the FDP Probe
FDP anisotropy results for the mild steel A, HY-80, grain-oriented laminate and non-oriented
laminate samples are presented in Figure 4.8. FDP anisotropy results for the mild steel B sample
are shown in Figure 4.7d. For each sample, data was fit using the dipole MBN energy equation
(2.32). Best fit parameters of equation (2.32) , ,
and equation (2.33)
are summarized for
all samples in Table 4.1 (note that the table heading summarizes the meaning and significance
of each of these parameters).
Figure 4.8, and the
(MBN energy ratio) values in Table 4.1, indicate that the mild steel A
and the grain-oriented laminate are the most anisotropic of the samples studied. A high level of
anisotropy is expected in grain-oriented laminates (Figure 4.8c) as these types of steels are
designed to have ‘cube on edge’ Goss texture [18]. This texture aligns the magnetically easy
[100] crystallographic direction perpendicular to the magnetically harder [110] direction in the
surface plane of the sample. This creates a well-defined macroscopic easy axis of magnetization
in the rolling direction, which is useful in reducing core loss in transformers.
The anisotropy evident in the mild steel A sample (Figure 4.8a) indicates an easy axis in the
direction, which corresponds to the rolling direction in this case. In general, mild steels
are hot rolled. Hot rolling can produce mild to relatively strong anisotropy depending on the
crystallographic texture and residual stress that is introduced. This anisotropy typically
manifests itself in the form of a magnetic easy axis in the rolling direction [28], [59].
Figure 4.8b and Table 4.1 indicate that the HY-80 has a lower magnetic anisotropy than the
mild steel A or grain-oriented laminate samples. This is confirmed by the MBN energy ratio
2.3 for the HY-80 sample compared to 5.4 and 5.6 for the mild steel A and grain-oriented
laminate respectively.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
(a) Mild Steel A
(b) HY-80
105
90
75
120
4
105
60
135
45
15
180
0
195
345
2
45
30
150
165
15
1
0
180
0
1
2
3
330
210
195
345
330
210
4
3
225
315
225
315
5
4
240
300
255
270
240
285
105
90
270
285
(d) Non-Oriented Laminate
75
120
2
300
255
(c) Grain-Oriented Laminate
135
105
0.75
60
0.45
30
1
90
75
120
0.60
45
150
MBN Energy (mV2s)
MBN Energy (mV2s)
165
3
MBN Energy (mV2s)
MBN Energy (mV2s)
2
60
135
30
150
1
75
4
2
0
90
120
5
3
1
71
60
135
45
30
150
0.30
165
15
165
15
0.15
0
180
0
0.00
180
0
0.15
195
345
330
210
2
195
345
0.30
1
225
315
240
300
255
270
285
0.45
0.60
0.75
330
210
225
315
240
300
255
270
285
Figure 4.8: MBN energy anisotropy measured with the FDP (dipole) on (a) mild steel A at
, (b) HY-80 at
, (c) grain-oriented SiFe at
and (d) nonoriented laminate at
. Lines of best fit using equation (2.32) are shown and
summarized in Table 4.1. Note that the radial units are not the same for each material.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
72
Table 4.1: Best fit parameters for the dipole MBN energy fitting equation (2.32)
(
)
and the MBN energy ratio (equation (2.33))
(
)
for all samples.
represents Barkhausen events that contribute to the anisotropy, represents Barkhausen
events that contribute to the isotropic background, represents the direction of the magnetic
easy axis and is a measure of the relative anisotropy of the material.
Sample
(
)
(
)
()
Grain-Oriented
Laminate
1.71 ± 0.07
0.37 ± 0.4
2±1
5.6 ± 0.3
0.97
Mild Steel A
2.9 ± 0.1
0.66 ± 0.09
0±1
5.4 ± 0.3
0.95
HY-80
2.88 ± 0.09
2.16 ± 0.05
0 ± 0.9
2.3 ± 0.1
0.98
Mild Steel B
35.6 ± 0.9
30.7 ± 0.6
4.9 ± 0.8
2.2 ± 0.1
0.98
Non-Oriented
Laminate
0.26 ± 0.02
0.46 ± 0.01
129 ± 2
1.6 ± 0.1
0.90
Finally, the non-oriented laminate shown in Figure 4.8d demonstrates the least amount of
magnetic anisotropy among the samples with a
of only 1.6. It is also the only sample that has
a magnetic easy axis that does not lie in the rolling direction. As the name suggests, nonoriented laminates are manufactured to achieve magnetic isotropy and are commonly used in
electric motors or other machines where a rotational magnetic field is present. Their lack of
preferred magnetic anisotropy reduces core loss and improves machine efficiency for
engineering applications in which the magnetization direction is always changing [58].
4.2.2 Tetrapole MBN Anisotropy Results: The effect of tetrapole orientation
using the FTP probe
If the assumption of linear flux superposition is correct, the physical orientation of the tetrapole
probe should not affect MBN anisotropy measurements. The results in this section serve to
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
examine the effect of tetrapole probe orientation
73
on MBN anisotropy. The measurements
presented were performed as described in Section 3.4.2 with the DRDC system using the FTP
probe, for probe orientation angles of
and
on the mild steel A, HY-80,
grain-oriented and non-oriented samples.
Figure 4.9 shows the effect of tetrapole orientation on MBN energy anisotropy for the mild
steel A and HY-80 samples. For both types of steels, it is observed that the tetrapole orientation
has a significant effect on the measured MBN anisotropy. As previously observed in Figure
4.7, the most obvious difference between the tetrapole result of Figure 4.9 and the dipole
result of Figure 4.8 is that the tetrapole results display a ‘four-lobe’ pattern.
Examining Figure 4.9, for mild steel A with the tetrapole orientation at
anisotropy result indicates a magnetic easy axis in the
, the MBN
direction. While this is consistent
with the dipole result of Figure 4.8, a smaller set of lobes exist at
tetrapole result of Figure 4.9. This suggests another easy axis along the
and
for the
direction,
which does not agree with the dipole results. This four-lobe pattern is also observed on the HY80 sample in Figure 4.9, with
but the lobes are much sharper and there are very
pronounced minima at roughly
and
. The lobes in both the mild steel A and HY-80
results are suspiciously located in the direction of the tetrapole probe poles, while the minima
lie in the directions between them.
When
is increased to
, Figure 4.9 shows that the lobe angular positions once again
correspond to the direction of the probe poles. Furthermore, these
easy axis at
results suggest an
, which is inconsistent with the dipole results. Interestingly the four-lobe
pattern produced when
does not appear symmetrical like the one produced when
; rather they appear slightly stretched along the
direction, which the dipole
results indicated was the easy axis direction for both the mild steel A and HY-80 samples. This
suggests that the tetrapole results, while distorted, are still affected by the sample’s magnetic
anisotropy.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
Mild Steel A
0°
HY-80
0°
90
12
120
180
0
2
4
MBN Energy (mV2s)
MBN Energy (mV2s)
2
300
0
180
0
3
6
330
210
45°
120
45°
90
18
60
120
12
30
150
4
2
180
0
2
4
MBN Energy (mV2s)
8
9
30
150
6
3
0
180
0
3
6
9
330
210
330
210
12
8
15
10
240
12
300
240
18
90°
90°
90
24
120
120
12
4
180
0
4
8
MBN Energy (mV2s)
30
150
8
9
30
150
6
3
0
180
0
3
6
9
330
210
330
210
12
16
15
20
240
24
300
240
18
135°
135°
90
12
120
2
180
0
2
4
330
210
MBN Energy (mV2s)
MBN Energy (mV2s)
60
12
30
150
4
9
30
150
6
3
0
180
0
3
6
9
330
210
12
8
15
10
12
120
15
8
6
90
18
60
10
0
300
270
270
6
60
15
16
MBN Energy (mV2s)
90
18
60
20
12
300
270
270
0
60
15
10
12
300
270
90
12
240
18
270
MBN Energy (mV2s)
3
15
240
12
6
30
150
6
12
10
0
9
9
330
210
8
6
60
12
30
150
4
6
120
15
8
0
90
18
60
10
6
74
240
300
270
18
240
300
270
Figure 4.9: MBN energy anisotropy using FTP for various
on mild steel A (
) and
HY-80 (
). Dotted red lines indicate fit of dipole data for comparison. Solid lines are
to guide the eye. Radial scale is doubled for mild steel A result at
.
CHAPTER 4.
At
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
in Figure 4.9 the MBN energy lobe in the
when compared to the
scale at
direction is much larger
case, particularly for mild steel A (note that the MBN energy
is twice that of the other
lobe at
75
). For both the mild steel A and the HY-80, the
is also significantly suppressed to the point where the overall result appears
qualitatively similar to that of the dipole.
The final two polar plots in Figure 4.9 with the tetrapole aligned at
qualitatively similar to those at
appear
with slight differences in the peak amplitudes in the
probe pole directions.
Figure 4.10 shows the tetrapole orientation effects on MBN energy anisotropy for the
grain-oriented laminate and the non-oriented laminate, again for the same four
angles that
were considered in Figure 4.9. The effect of tetrapole orientation is very different in these
samples compared to the mild steel A and HY-80 of Figure 4.9, since the four-lobe pattern is not
apparent in the results for either sample, at any tetrapole angle. For the grain-oriented
laminate sample, measurements with the tetrapole orientation at
and
produce a result very similar to that obtained with the dipole, as seen in Figure 4.8.
Interestingly these two cases correspond to the probe poles being aligned with the magnetic
easy axis of the sample (as determined by the dipole). In Figure 4.9, the mild steel A and HY-80
results also were most similar to the dipole results for tetrapole orientations
and
, but not to the extent of the grain-oriented laminate. The grain-oriented laminate
result in Figure 4.10 at
and
does not reproduce the dipole result.
The non-oriented laminate results in Figure 4.10 are the most peculiar of the tetrapole
results. Results from other samples would suggest that the tetrapole result should be most
similar to the dipole result when the probe poles are aligned with the easy axis. Because the
magnetic easy axis is at
the case for
and
for the non-oriented laminate sample, this should be
. However, at
resemble the dipole result in Figure 4.8d, and at
the tetrapole result does not
there is only partial similarity with
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
Grain-Oriented Laminate
0°
Non-Oriented Laminate
0°
90
14
120
76
90
6
60
12
120
60
5
10
4
30
150
6
4
2
0
180
0
2
4
6
8
MBN Energy (mV2s)
MBN Energy (mV2s)
8
12
240
14
45°
120
0
4
6
MBN Energy (mV2s)
MBN Energy (mV2s)
180
2
300
180
0
0
1
2
330
210
90°
120
300
270
90°
90
14
240
6
270
90
6
60
12
120
60
5
10
4
30
150
6
4
2
180
0
2
4
6
MBN Energy (mV2s)
MBN Energy (mV2s)
1
5
240
14
30
150
3
2
1
0
180
0
1
2
3
330
210
330
210
4
10
12
5
240
14
300
135°
120
300
270
135°
90
14
240
6
270
90
6
60
12
120
60
5
10
4
30
150
6
4
2
180
0
2
4
6
330
210
MBN Energy (mV2s)
MBN Energy (mV2s)
30
2
4
12
3
30
150
2
1
0
180
1
2
3
330
210
4
10
5
12
14
60
150
3
3
330
210
10
8
90
120
4
30
150
2
0
300
5
4
8
240
6
6
8
330
210
45°
60
10
0
2
270
12
8
0
1
6
90
14
8
180
0
5
300
270
0
1
4
10
8
2
3
330
210
30
150
3
240
300
270
6
240
300
270
Figure 4.10: MBN energy anisotropy using FTP for various
on grain-oriented laminate
(
) and non-oriented laminate (
). Dotted red lines indicate fit of dipole
data scaled by a factor of 2 and 3 respectively, for comparison. Lines are to guide the eye.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
the tetrapole indicating a magnetic easy axis at around
77
. The non-oriented laminate
results in Figure 4.10 also do not exhibit the four-lobe pattern that was observed in the mild
steel A and HY-80 results in Figure 4.9.
4.2.3 Tetrapole MBN Anisotropy Results: High resolution
measurements on
mild steel using both the FTP and STP probes
To gain a more detailed understanding of the tetrapole results observed in Figures 4.9 and 4.10,
a set of higher resolution measurements (
in
increments rather than
)
was
performed on the mild steel A sample. The mild steel A was selected for these measurements
because its physical dimensions are the largest (see Table 3.5) of the samples, which was
expected to minimize any geometry effects. Furthermore the mild steel A sample had a wellestablished magnetic easy axis, allowing for an investigation of the effects of magnetic
anisotropy.
In this part of the study, measurements were made using both the FTP and also the STP
probe. The STP probe measurements were added to this study with the aim of providing an
insight into how probe design and construction affect MBN results. The data collected in this
part of the study was used to develop an empirical fitting equation. It was hoped that this
fitting equation might be able to extract useful MBN anisotropy information from the four-lobe
patterns (see Section 2.6.5 and 4.2.7).
Figure 4.11 shows the results obtained using the FTP probe, with
seen in Figure 4.11 these smaller changes in
in
increments. As
indicate that the four-lobe MBN energy pattern
undergoes a steady, progressive rotation as
increases. Furthermore, the 4 lobes (MBN
energy peaks) are consistently located within roughly 5° of the pole-pair directions for each
value of
. When
the largest lobe pair is located at
pole-pair position. The minor peak appears at
, this corresponds to the 1-3
, corresponding to the 2-4 pole-pair
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
position. As the probe is rotated (
78
increases) the lobe associated with the 1-3 pole-pair
decreases in magnitude, and the 2-4 pole peak increases in magnitude.
At
the lobes are roughly equivalent in magnitude. For probe orientation angles
greater than
the lobes associated with the 2-4 pole-pair increase up to
,
where they dominate the pattern and the 1-3 lobe peaks are barely visible. In fact, at
the pattern appears to resemble an elongated dipole result (see Figure 4.8a).
The final plot in Figure 4.11 is a direct comparison of the
and
results.
Theoretically, given the symmetry of the tetrapole and the use of flux control, these two results
are expected to be identical.
It is helpful at this stage to quantify the comparative magnitude of the lobes associated
with the 1-3 pole-pair, with that of the 2-4 pole-pair. Therefore a quantity termed the
‘tetrapole peak ratio’
is defined as:
(4.1)
which is the peak MBN energy magnitude in the 2-4 pole-pair direction over the sum of the
magnitudes in the two pole-pair directions. If all lobes have the same magnitude,
the results shown in Figure 4.11, for
,
and for
,
. For
.
Figure 4.12 presents the results for a similar set of measurements as were made for Figure
4.11, except in this case the STP is used. The STP measurements were made for comparison
purposes – to determine if the results seen in Figure 4.11 are probe-specific, or are generically
associated with the fundamental tetrapole superposition principle as described by equation
(2.34). The results shown in Figure 4.12 indicate that the STP probe results are very similar to
those for the FTP probe in Figure 4.11. Specifically, the common trends are as follows:

Both sets of probe results exhibit a four-lobe pattern that rotates with the probe,
which suggests that the lobe positions are a result of probe geometry.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
0
15
90
10
120
8
6
30
150
4
2
0
180
0
2
4
6
120
330
210
30
150
4
2
0
180
0
2
4
6
8
330
210
8
240
10
300
240
10
270
30
120
45
6
30
150
2
180
0
2
4
MBN Energy (mV2s)
MBN Energy (mV2s)
120
330
210
30
150
4
2
0
180
0
2
4
6
8
330
210
8
240
10
300
240
10
270
60
120
75
6
30
150
2
180
0
2
4
MBN Energy (mV2s)
MBN Energy (mV2s)
120
330
210
30
150
4
2
0
180
0
2
4
6
8
330
210
8
240
10
300
240
10
270
90
120
0 and 90
10
60
8
180
0
2
4
330
210
8
10
MBN Energy (mV2s)
MBN Energy (mV2s)
6
30
150
2
6
90
120
60
8
4
0
300
270
90
10
6
60
8
4
6
90
10
60
8
0
300
270
90
10
6
60
8
4
6
90
10
60
8
0
300
270
90
10
6
60
8
MBN Energy (mV2s)
MBN Energy (mV2s)
6
90
10
60
79
30
150
4
2
0
180
0
2
4
6
330
210
8
240
300
270
10
240
300
270
Figure 4.11: MBN energy anisotropy measured using the FTP at various ‘high resolution’ probe
orientations
on mild steel A. Solid lines are to guide the eye. Dotted lines indicated fit of
dipole data using equation (2.32) for comparison, except the final plot for
and
.
CHAPTER 4.

SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
Both probes exhibit a stretching of the four-lobe pattern in the
80
direction, which
corresponds to the magnetic easy axis of the sample.
This latter observation is an indication that the tetrapole measurements are sensitive to the
magnetic anisotropy of the sample. This is a promising result, because it suggests that magnetic
easy axis information may still be extracted from the tetrapole data, even though the results do
not match those obtained with a dipole.
There are also minor differences in the FTP (Figure 4.11) and STP (Figure 4.12) results,
namely:

Unlike the FTP, in the STP results the peak amplitudes appear to be closest in
magnitude at

At
.
the largest peak is once again in the
direction, however, unlike
results shown in Figure 4.11, the four-lobe pattern is not significantly elongated.

In the final plot of Figure 4.12 the difference between the
and
case
is shown to be much less significant than that for the FTP probe (Figure 4.11).
Quantitatively, for
,
and for
,
, which is in much
better agreement than the results obtained with the FTP probe. The differences
between the FTP and STP probes with respect to this is discussed in greater detail
below.
As mentioned above, the magnitude of the 4 lobes for the STP probe is more similar than it
is for the FTP probe. It is useful to examine the MBN energy measured in the
for FTP probe orientations of
measured in the
. At
and
(Figure 4.11). At
direction
the MBN energy
direction (thus under excitation from the 1-3 pole-pair only) was
the MBN energy measured in the
excitation from the 2-4 pole pair only) was
.
direction (now under
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
0
15
90
30
120
25
180
0
5
10
MBN Energy (mV2s)
MBN Energy (mV2s)
5
15
15
30
150
10
5
0
180
0
5
10
15
330
210
20
330
210
20
25
25
240
30
300
240
30
270
30
45
25
25
20
20
30
150
10
5
0
180
0
5
10
15
15
20
120
30
150
5
0
180
0
5
10
330
210
20
25
25
240
30
300
240
30
270
60
120
75
10
5
180
0
5
10
15
30
150
10
5
0
180
0
5
10
15
330
210
20
330
210
20
25
25
240
30
300
240
30
270
90
120
0 and 90
30
60
25
180
0
5
10
330
210
20
MBN Energy (mV2s)
MBN Energy (mV2s)
5
15
30
150
10
5
0
180
0
5
10
15
330
210
20
25
30
60
20
30
150
10
15
90
120
25
20
0
300
270
90
30
15
60
20
30
150
MBN Energy (mV2s)
MBN Energy (mV2s)
120
25
20
15
90
30
60
25
0
300
270
90
30
15
60
10
15
330
210
90
30
60
MBN Energy (mV2s)
MBN Energy (mV2s)
120
300
270
90
30
15
60
20
30
150
10
0
120
25
20
15
90
30
60
81
25
240
300
270
30
240
300
270
Figure 4.12: MBN energy anisotropy measured using the STP at various probe orientations
on mild steel A. Solid lines are to guide the eye. Dotted lines indicated fit of dipole data using
equation (2.32) for comparison, except the final plot for
and
.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
82
The comparison of these MBN energies from these two difference pole-pairs indicates that
the flux density through the 1-3 pole-pair in the FTP was less than that through the 2-4 polepair. This suggested that an air gap (large enough that the flux control system could not
compensate) was present in the 1-3 pole-pair magnetic circuit. Upon inspection of the FTP
probe, a small air gap was observed on pole 1 or 3 (depending on the pressure applied to the
probe). Despite efforts to adjust the probe housing and spring loaded design, a more effective
coupling of the 1-3 pole-pair to the sample could not be achieved with this probe. A similar air
gap on the STP probe was not observed, which can explain the similar results for probe
orientations of
and
in Figure 4.11.
The cause of the air gap in the FTP probe is most likely a result of a combination of factors
affecting the orientation of the 1-3 pole-pair. As described in Section 3.3, in the FTP the 1-3
dipole couples to the sample using a spring loaded design. If the force of the springs is not
balanced or the core cannot slide smoothly in the housing, one end of the dipole may couple to
the sample, while the other has a gap. Comparatively, the STP probe pole-pairs are epoxied
together to form a ridged tetrapole. From the results in Figures 4.11 and 4.12, it appears that
this allows for more balanced coupling of the pole-pairs on a flat surface.
4.2.4 Comparison of Dipole and Tetrapole Results: Studies involving
independent orthogonal dipoles
The tetrapole results of Figures 4.11 and 4.12, in comparison with the dipole results of Figure
4.8a indicated that the orthogonal fields were not superimposing as originally expected.
Indeed, the two-lobe results from the dipole probe (FDP) are markedly different from the fourlobe results obtained with both tetrapole probes (FTP and STP). This section of the thesis
attempts to experimentally determine why this is the case. It is helpful to define some terms:
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY

83
– The theoretical MBN result assuming ‘ideal superposition’ (IS). Recall that the
original premise of the tetrapole flux superposition assumed that, at the central
location between the pole-pairs, the magnetic field created by the two orthogonal
pole-pairs would vectorially add to provide a ‘sum’ field of the required magnitude and
direction.

– The experimentally measured MBN result from the tetrapole (T) probes (i.e.
as shown in Figures 4.11, 4.12, etc.)

– This is an experimentally measured result where there is ‘no superposition’
(NS), where the MBN value from each orthogonal pole-pair is measured separately.
This is achieved by activating one pole-pair (of the FTP or STP) and measuring the MBN
result, and then activating the other pole-pair and measuring the result. This is
followed by adding the two MBN values together. The details of the experiments to
obtain
are outlined below.
Both the FTP and STP probes were used to obtain the
data. As described above, each
pole-pair (either 1-3 or 2-4) was activated independently. The field amplitude used for each
pole-pair corresponded to that required to produce the target superposition field at a particular
angle. This is illustrated in Figure 4.13.
at a superposition angle
represents the target superposition field amplitude
. MBN measurements were performed first with the
(with the other pole-pair switched off) and then the
field. For any particular
field
the
result was obtained by summing the independent MBN results for each pole-pair:
(4.2)
where
The
and
are the MBN results from the
value was subsequently compared to
and
fields, respectively.
, obtained using the tetrapole
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
84
Figure 4.13: Experimental setup for measurements of MBN using independent orthogonal
dipoles.
and
correspond to field amplitudes used to measure the MBN of two
independent orthogonal dipoles.
is the superposition field amplitude used to measure
MBN at an angle
, which is achieved under the assumption of linear superposition of the
flux.
superposition field. This procedure was performed for various probe orientation angles
flux densities. Results are discussed below, comparing the
function of the probe orientation angle
and
and
, first as a
and then as a function of the excitation field
amplitude.
4.2.4.1 Effects of Probe Orientation Angle
Figure 4.14 shows the comparison of the experimental
orientation angles of
and
results for probe
using the FTP. This figure indicates that
both exhibit similar trends at all three probe orientation angles
and
. This result is highly
significant, since it suggests that the assumption of flux superposition in the tetrapole probe is
not valid. It further suggests that the four-lobed pattern observed in the tetrapole MBN energy
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
85
data may, primarily, be the result of the orthogonal fields acting essentially independently to
produce their own MBN result.
Although Figure 4.14 indicates similar trends between the two sets of data, a careful
examination of the results does show some differences between the
and
results. Figures 4.14a and 4.14c represent the case of one of the probe pole-pairs aligned with
the magnetic easy axis at
field angle
and
results decrease as the
is rotated away from the easy axis, the drop in the
result is larger for both
and
. Although both the
in the initial part of the graph. The difference is evident from
for
and from
to
for
to
. These differences indicate that the
behavior of the pole-pairs is not entirely independent (as it is in the
case) but that there
is some interaction between the fields that results in a reduction of MBN energy.
It is speculated that, during magnetization, the two pole-pairs are ‘competing’ to
magnetize domains with their respective fields and this interaction or competition between the
domains magnetized by the independent orthogonal fields reduces the overall MBN energy.
Consider Figure 4.14a, where the 1-3 pole-pair is aligned in the easy axis direction and the 2-4
pole-pair is perpendicular to it. As the superposition field angle is rotated away from the easy
axis at
, according to equation (2.34), the field of the 2-4 pole-pair increases as shown in
Figure 4.13. Because this field is perpendicular to the 1-3 pole-pair it has the effect of reducing
the growth of domains that are being induced by the 1-3 pole-pair. This reduction in domain
growth, results in the observed decrease in MBN energy. As the superposed field angle is
rotated further, the relative amplitude of the 2-4 pole-pair field increases and so does the
competition, resulting in even less
equal again at
difference between the
to
. In Figures 4.14a and 4.14c,
and remain relatively so up to
and
from
to
and
are
. Thus the larger
is attributed to the easy axis at
, which magnifies the competition between the pole-pairs.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
0
20
40
60
80
86
100
MBNenergy (mV2s)
40
MBNNS
30
MBNT
20
10
(a) T = 0°
MBNenergy (mV2s)
0
25
20
15
10
(b) T = 45°
5
MBNenergy (mV2s)
30
25
20
15
10
(c) T = 90°
5
0
20
40
60
80
100
Field Angle  (°)
Figure 4.14: MBN energy resulting from a superposition field
and two orthogonal
independent fields
at probe orientation angles (a)
, (b)
and (c)
all at a flux density of
. Measurements were performed using the FTP.
Lines are to guide the eye.
Figure 4.14b compares the
and
trend in angular dependence of
differences, particularly at
for the case of
and
and
. While the general
appear similar, there are significant
. Unlike Figures 4.14a and 4.14c, in Figure 4.14b
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
is higher than
for field angles near the easy axis at
87
. Continuing from the
idea introduced in the previous paragraph, the competition between the pole-pairs should be
highest at a superposition field angle
amplitude), which, for
of the easy axis (
(i.e. when the orthogonal fields are of equal
corresponds to
)
and
is larger than
. Interestingly, in the direction
. This suggests the easy axis reduces
competition between the orthogonal fields and results in an increase in MBN activity. At
, with the target superposition field perpendicular to the easy axis, the reverse effect is
observed, suggesting increased competition reduces
relative to
.
There are three concepts that emerge from the analysis of Figure 4.14:

The
and
angular dependence shows that the four-lobe pattern is most
likely a result of the fact that the two pole-pairs do not appear to be creating the
expected superposition field, but rather are acting more independently.

The orthogonal fields exhibit competition between pole-pairs, which results in a
reduction in the measured MBN energy.

The magnetic anisotropy (i.e. the easy axis population) affects the extent of such
competition.
4.2.4.2 Effects of Field Amplitude
Figure 4.15 shows the measured
for flux densities of
and
,
and
and
at a single probe orientation angle
using the STP. At
(Figure 4.15a)
exhibit similar trends, as observed previously in Figure 4.14a and 4.14c.
However, at the higher values of
large difference between the
(Figure 4.15b) and
and
result.
(Figure 4.15c), there is a
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
0
20
40
60
80
88
100
MBNenergy (mV2s)
15
MBNNS
MBNT
10
5
(a) 150mT
MBNenergy (mV2s)
0
60
50
40
30
(b) 350 mT
MBNenergy (mV2s)
100
20
90
80
70
60
(c) 550 mT
50
0
20
40
60
80
100
Field Angle  (°)
Figure 4.15: MBN energy resulting from a superposition field
and two orthogonal
independent fields
at flux densities
of (a)
, (b)
and (c)
all at
a probe orientation angle
. Measurements were performed using the STP. Lines are to
guide the eye.
The interesting result in Figure 4.15 is that as flux increases, the magnitude of the
result is less than the
result, for superposition fields between
and
. This is
significant as it demonstrates the effect of the previously introduced concept of competition
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
89
and shows the extent of the independent behavior of the pole-pairs in generating MBN. It is
speculated that as flux is increased, the competition between the orthogonal fields reduces the
number of domain walls that each field is able to move, resulting in an overall decrease in MBN
energy for the tetrapole case (
). For the purely independent case of
, there is no
interaction between the fields and each is able to move a larger number of domain walls. As
flux is increased, MBN energy increases non-linearly (as seen in Figure 2.9) resulting in the
peaks at
, observed in both Figure 4.15b and 4.15c.
The result in Figure 4.15 also indicates that the effect of competition is most significant at
higher flux densities. Although the
result appears very similar to the
result at
(suggesting predominantly independent behavior), as flux increases, competition
dominates the
result.
4.2.5 Field Amplitude Effects on Anisotropy
The
results in Figure 4.15 indicated differences in MBN anisotropy at various flux
densities. These results however, did not highlight the flux density effect on the four-lobe
tetrapole pattern. This is considered in this section, using the STP probe.
Figure 4.16 shows the angular dependent MBN energy measured by the STP at flux
densities
of
,
and
. In Figure 4.16a, at flux density of
typical four-lobe pattern is observed with an elongation in the easy axis direction at
Applying equation (4.1) a tetrapole peak ratio
. In Figure 4.16c, at
.
is observed. In Figure 4.16b at a flux of
the four-lobe pattern becomes less pronounced, although the
slightly to
, the
value decreases only
the four-lobe pattern is barely visible and
, representing a modest decrease in the tetrapole peak ratio from the results at
and
.
The smoothing of the four-lobe pattern from
to
can be attributed to: (1)
the non-linear relationship between MBN energy and flux density (shown in Figure 2.9); and (2)
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
90
the independent behavior of the orthogonal fields. As seen in Figure 2.9, at lower flux densities
MBN energy increases exponentially with flux, but at higher flux densities the rate of MBN
energy increase is lower. The superposition field
orthogonal fields
and
at a non-zero
consists of two
of lower magnitude as described by equation (2.34) (see
Figure 4.13). Therefore, as flux density is increased, the relative increase in MBN energy
generated by these independently behaving orthogonal fields will be larger than that of a single
field at
. This results in the observed smoothing of the pattern.
(a) 150 mT
2.4
(b) 350 mT
90
120
70
60
50
40
30
150
MBN Energy (mV2s)
MBN Energy (mV2s)
1.6
0.8
0.4
0.0
180
0
0.4
0.8
1.2
330
210
30
150
30
20
10
0
180
0
10
20
30
330
210
40
1.6
50
2.0
2.4
60
60
2.0
1.2
90
120
60
240
300
240
70
270
300
270
(c) 550 mT
120
90
120
60
100
MBN Energy (mV2s)
80
60
30
150
40
20
0
180
0
20
40
60
330
210
80
100
120
240
300
270
Figure 4.16: MBN energy anisotropy at peak flux densities of (a) 150, (b) 350 and (c) 550 mT.
Measurements performed under flux control with STP on the mild steel B sample. Lines are to
guide the eye. Note that the scales for each plot are different.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
91
4.2.6 Voltage (Field) and Flux Control of the MBN Excitation Field: Effects on
MBN anisotropy results
Flux control for the MBN excitation field has been shown to improve MBN measurement
repeatability compared to voltage (field) control [5]. This was the basis for using flux control in
the DRDC system. The flux density through a sample is dependent on the relative permeability
of the material, which can be both non-linear and anisotropic in ferromagnetic materials. Given
our revised understanding of tetrapole MBN behavior, this study examined tetrapole MBN
measurements, comparing flux and voltage control for the MBN excitation field.
Figure 4.17 compares MBN anisotropy measurements performed under flux and voltage
control at probe orientation angles
and
. It is apparent that both flux and voltage
control produce the four-lobe pattern. This confirms that the flux control, which compensates
for changes in permeability, is not the cause of the four-lobe pattern.
00 Deg
30
45 Deg
90
120
21
60
15
12
30
150
10
5
180
0
5
10
15
330
210
20
30
150
9
6
3
0
180
0
3
6
9
12
330
210
15
25
30
MBN Energy (mV2s)
MBN Energy (mV2s)
20
0
60
18
25
15
90
120
18
240
300
270
21
240
300
270
Figure 4.17: MBN energy anisotropy under flux control ( 200 mT) and voltage control ( 1 V) at
probe orientation angles
of and
. Measurements performed with FTP probe on the
mild steel B sample. Lines are to guide the eye.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
92
4.2.7 Empirical Fitting of Tetrapole Data
As described in Section 2.6.3, the angular dependence of MBN energy measured with a dipole
probe can be fit with equation (2.32). This fitting equation was developed under the
assumption of a single, uniform excitation field [49] and has been shown to correctly identify
and quantify the magnetic easy axis in ferromagnetic materials for data collected using dipoles
[31], [60], [61]. The tetrapole results presented in Section 4.2.2 and 4.2.3, however,
demonstrated a significantly different MBN anisotropy from that obtained with a dipole. These
results indicate that the traditional fitting equation (2.32) used for dipole measurements is not
appropriate for tetrapole MBN anisotropy data and a new fitting equation is required. Section
4.2.7.1 describes the development of a new empirical fitting equation and Section 4.2.7.2
presents the fitting of tetrapole MBN anisotropy data with the new empirical equation.
4.2.7.1 Development of Empirical Fitting Equation for Tetrapole MBN Anisotropy Data
The empirical fitting equation presented here was developed with the primary purpose of
identifying the sample magnetic easy axis in a similar manner to equation (2.32). To achieve
this, the independent behavior of the orthogonal fields and the concept of competition were
incorporated into the fitting equation. Alternative fitting equations have been developed
previously to describe the magnetic anisotropy of dual easy axis systems [49] and Si-Fe
laminates [62], by taking into account significant magnetic domain interactions due to sample
composition. The fitting equation developed in this work incorporates separate terms for each
orthogonal pole-pair, an orthogonal dipole-dipole interaction term and a term which accounts
for an asymmetric imbalance in the system. Combining these terms yielded the following
fitting function:
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
(
)
(
where
( (
)
(4.3)
))
is the angle of the field in the sample reference frame and where the best fit
parameters are;
and
)
(
93
the probe orientation angle,
the direction of the easy axis and
,
,
are coefficients. This equation was developed by attempting to describe the observed
patterns mathematically and by incorporating interaction terms present in other alternative
fitting equations [49], [62]. All the fitting parameters in equation 2.34 contain a
term in their
angular dependence, which is the direction of the sample’s magnetic easy axis.
In the tetrapole fitting equation (4.3) the
and
terms are intended to describe the
independent behavior of the orthogonal fields for a tetrapole probe oriented at
terms
and
. The two
describe MBN energy lobes in the direction of each pole-pair separately,
accounting for the different flux densities of each pole-pair for different
(2.34). In contrast to equation (2.32) the
and
according to
are multiplied by fourth-order cosine and
sine terms, which have been used previously to account for higher-order dipole interactions
[49], [62]. The
in the tetrapole fitting equation is an asymmetric term intended to describe
an imbalance in the system, possibly due to probe coupling imbalances.
is multiplied by a
first-order cosine term, which has been introduced in previous dipole fitting equations as well
[28], [62], [63]. The final term,
, is an interaction term, which accounts for the competition
between pole-pairs resulting in a decrease in MBN energy. Such interaction terms have been
used in previous fitting equations to describe the reduction in MBN energy due to eddy current
interactions [62]. The
term is multiplied by a double angle sine function, which describes the
maximum competition at
.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
94
4.2.7.2 Fitting of Tetrapole MBN Anisotropy Data Using Empirical Equation
Figures 4.18 and 4.19 show the angular dependent MBN energy data from Section 4.2.2 for
orientation angles
of
,
,
and
, as measured by the FTP (Figure 4.18) and STP
(Figure 4.19) probes. The fit of equation (4.3) to the data is superimposed (in red). Tables 4.3
and 4.4 show the fitting parameters obtained using equation (4.3) for various
interest are the ‘predicted’ fitting parameters
and
. Of most
, which predict the probe orientation
and sample’s magnetic easy axis, respectively. As seen in Tables 4.2 and 4.3 the fitting of both
the FTP and STP results correctly predicts
within
for all probe orientation angles.
More importantly the fitting equation also appears to correctly predict the direction of the
sample’s magnetic easy axis . For the FTP probe, the fitting parameters in Table 4.2 correctly
identify the magnetic easy axis (at
the error in
is
) to within
for all
except at
where
. This variation can be explained by the tetrapole imbalance identified in
the FTP (Section 4.2.3). In comparison, the fitting results using the STP (which exhibited
significantly less imbalance compared to the FTP), correctly identify
values of
to within
at all
.
In both the results from the FTP and STP, a similar pattern is observed in the values of
and
, which describe the magnitude of lobes of the four-lobe pattern in the direction of the
pole-pairs. For both probes, as
increases,
decreases and
increases, which is consistent
with the observations made in Section 4.2.3. It is expected, due to the symmetry of the probe,
that at
,
. For the FTP (Table 4.2) at
. In the STP fitting results (Table 4.3) at
,
is almost twice as large as
the difference between
and
is much
smaller. This is a reflection of the STP exhibiting better balance between the coupling of the
probe poles to the sample, when compared to the FTP probe.
In Table 4.2 (FTP) the
term, which is associated with an asymmetric imbalance in the
system, shows a large variation as the probe is rotated from
the variation in the
term from
to
. In Table 4.3 (STP)
to 90 is not as significant. This is another indication
of the larger coupling imbalance present in the FTP probe when compared to the STP. In both
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
95
MBNenergy (mV2s)
5.5
5.0
T = 0°
4.5
T = 15°
T = 30°
4.0
T = 45°
3.5
3.0
2.5
2.0
1.5
1.0
-20
0
20
40
60
80
100 120 140 160 180 200
Field Angle  (°)
Figure 4.18: MBN energy anisotropy measurements using the FTP probe on mild steel A at
various probe orientation angles . The empirical fitting equation (4.3) is shown in red for each
set of data. Table 4.2 includes the fitting parameters for each data set. Plots of the data and
fitting equations on polar graphs can be found in Appendix C.
30
T = 0°
25
T = 15°
MBNenergy (mV2s)
T = 30°
T = 45°
20
15
10
5
-20
0
20
40
60
80
100 120 140 160 180 200
Field Angle  (°)
Figure 4.19: MBN energy anisotropy measurements using the STP probe on mild steel A at
various probe orientation angles . The empirical fitting equation (4.3) is shown in red for each
set of data. Table 4.3 includes the fitting parameters for each data set. Plots of the data and
fitting equations on polar graphs can be found in Appendix C.
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
96
Table 4.2: FTP probe: Fitting parameters for equation (4.3) for angular dependent MBN energy
measurements performed on mild steel A at various probe orientation angles .
Probe Angle
(mV2s) (mV2s) (mV2s) (mV2s) (mV2s)
(°)
(°)
(°)
0
0.03
4.18
2.36
0.0009
0.29
1.8
-1.3
0.98
15
-0.36
3.61
2.51
0.0005
0.41
14.0
1.3
0.99
30
-0.66
2.87
3.05
0.0007
0.60
30.7
-0.5
0.99
45
-0.57
2.22
4.24
0.0014
0.49
40.6
5.6
0.99
60
-0.55
2.16
6.24
0.0090
0.10
62.0
-0.1
0.99
75
-0.32
2.37
8.24
0.0132
-0.39
76.9
0.1
0.98
90
-0.07
2.75
9.18
0.0119
-0.78
90.7
0.3
0.98
Table 4.3: STP probe: Fitting parameters for equation (4.3) for angular dependent MBN energy
measurements performed on mild steel A at various probe orientation angles .
Probe Angle
(mV2s) (mV2s) (mV2s) (mV2s) (mV2s)
(°)
(°)
(°)
0
-0.17
23.9
3.7
0.074
3.87
0.2
-0.1
0.99
15
-0.63
23.8
5.8
0.014
3.06
13.9
-0.2
0.99
30
-0.73
19.9
8.6
0.056
3.03
27.8
-0.1
0.99
45
-1.53
14.5
12.2
0.002
1.78
45.3
0.2
0.99
60
-1.20
11.8
16.8
0.025
1.42
61.2
0.0
0.99
75
-0.61
10.0
20.9
0.044
1.80
76.0
0.1
0.99
90
0.43
5.7
20.7
0.050
2.29
89.5
0.0
0.99
Tables 4.2 and 4.3
,
or
is several orders of magnitude smaller than the other fitting parameters
suggesting that the asymmetric imbalance is a small effect.
Similar to
,
(which was intended to describe the competition between the orthogonal
fields) has a minimum at
since at
for the STP probe (Table 4.3). This is a reasonable result,
, due to the symmetry of the probe with respect to the easy axis at
,
competition between the pole-pairs would be at a maximum (assuming a perfectly balanced
probe). The minimum
coupling imbalance.
for the FTP (Table 4.2) is shifted to
again indicating probe
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
97
Figures 4.18 and 4.19 and Tables 4.2 and 4.3 show the ability of the tetrapole fitting
equation to describe data from two different probes. This demonstrates the versatility of the
fitting equation for probes with different coupling balances. Both sets of measurements were,
however, performed on mild steel A. To establish whether equation (4.3) is able to describe
measurements on other types of steel, the data from Figure 4.9 on HY-80 was fit as well.
Figure 4.20 shows the empirical fit of tetrapole MBN anisotropy data on HY80. Table 4.4
summarizes the HY80 steel fitting parameters for probe angles
,
and
. As with
the measurements on mild steel, the fitting equation is able to identify the magnetic easy axis
to within
for all probe angles. In Table 4.4,
consistent with mild steel. However,
is at a minimum at
is maximum at
which is
, which is the opposite of what
was observed in mild steel, possibly due to a change in coupling imbalance between
measurements. The quality of the fits in terms of
is still high for HY-80 suggesting that the
tetrapole fitting equation is versatile across multiple steels.
From the fitting results in Figures 4.18 and 4.19 and Tables 4.3, 4.4 and 4.5 it can be seen
that the tetrapole fitting equation (4.3) is capable of identifying the magnetic easy axis to within
in all but two measurements in this study. Although derived empirically, this suggests that,
the fitting equation is capable of accurately describing angular dependent MBN energy data
obtained with tetrapole probes. Empirical fitting results of the grain-oriented and non-oriented
laminates samples are shown in Appendix D.
Table 4.4: Fitting parameters for equation (4.3) for angular dependent MBN energy
measurements performed on HY-80 with the FTP probe at various probe orientation angles.
Probe Angle
(mV2s) (mV2s) (mV2s) (mV2s) (mV2s)
(°)
(°)
(°)
0
0.67
29.4
23.3
0.034
-9.7
0.1
0.1
0.97
45
-2.11
32.4
14.2
0.053
-7.3
43.4
0.0
0.99
90
-0.12
15.3
38.4
0.002
-9.5
94.0
-4.0
0.99
CHAPTER 4.
SYSTEM PERFORMANCE & STUDY OF FLUX SUPERPOSITION VALIDITY
98
MBNenergy (mV2s)
30
25
T = 0°
20
T = 90°
T = 45°
15
10
5
0
-20
0
20
40
60
80
100 120 140 160 180 200
Field Angle  (°)
Figure 4.20: MBN energy anisotropy measurements using the FTP probe on HY80 at various
probe orientation angles . The empirical fitting equation (4.3) is shown in red for each set of
data. Table 4.4 includes the fitting parameters for each data set.
Chapter 5
Discussion
This M.Sc. work began with the purpose of developing a MBN testing system for DRDC, capable
of measuring residual stress anisotropy in submarine hulls. The DRDC system was based on an
existing MBN system developed by Steven White at Queen’s University [5], [6]. The
construction and evaluation of the DRDC system performance is discussed in Section 5.1.
The original Queen’s system used a tetrapole probe design to perform rapid MBN
anisotropy measurements. The tetrapole principle assumed that two orthogonal fields would
add vectorially in the sample to create a superposition field. This superposition field would then
act to generate MBN in the same manner as traditional dipole probe designs. During the course
of this work, it became apparent that the MBN anisotropy measured using tetrapole probes did
not, in fact, reproduce the MBN results obtained through manual rotation of a dipole. As a
consequence a large focus of this thesis was devoted to a detailed study of MBN anisotropy
measurements performed with tetrapole probes. These results are discussed in Section 5.2. The
tetrapole MBN anisotropy results were characterized by a four-lobe pattern, which was
affected by a number of factors, including magnetic anisotropy. The possible origins of this
pattern are discussed in Section 5.3.
99
CHAPTER 5. DISCUSSION
100
Although the original goal of this thesis was to provide DRDC with a MBN measurement
system capable of measuring residual stress anisotropy, from the results presented here, the
ability of the DRDC system to perform such measurements has come into question. Section 5.4
discusses what further work may be required for the DRDC system to achieve its original design
goals.
5.1 Construction and Evaluation of DRDC MBN System
As described in Chapter 3 the system constructed for DRDC was based on the original Queen’s
system design. The original Queen’s system offered two key design elements; the tetrapole
probe and flux control of the excitation waveforms. During the development of the DRDC
system modifications to the original Queen’s system design were made for the purpose of
improving performance and simplifying the design where possible. The effects of these design
changes were measured through a comparison with the original Queen’s system (see Section
4.1). The comparison was made in terms of total system error and the measured BN envelopes.
In Section 4.1.1 the total system error
of the DRDC system was shown to be lower
than that of the original Queen’s system at all flux densities (
frequencies (
at
to
with an
to
) and excitation
). Furthermore, the DRDC system was capable of operating
, a frequency at which the Queen’s system was unable to
establish excitation flux waveforms.
These measurements were performed with the same probe (STP) on the same sample and
thus any differences between the systems must be attributable to the Flux Control Systems and
associated power supplies. The increase in
at low excitation frequencies, where the
excitation voltages are lower, suggested that the signal-to-noise ratio was the primary factor
affecting waveform accuracy. This indicates that the DRDC system design represents a
reduction in system noise, however, because the effects of the low noise power supply, UPS
CHAPTER 5. DISCUSSION
101
and modified FCS and printed circuit board layout cannot be isolated the individual impact of
each of these modifications is unclear.
The importance of the reduction of system error lies in the ability to operate the system at
lower frequencies. Low frequency MBN measurements have advantages, including the ability to
discern individual Barkhausen events and a reduction in the impact of eddy currents [23], [64].
At higher frequencies, overlapping BN events limit analysis of parameters such as BN counts
and BN events [23].
In addition to system error, the impact of the pickup coil redesign was examined through a
comparison of the BN envelopes measured by the STP and SL4P probes. The major modification
to the pickup coil was the increase in the coil turn number and radius, and the removal of the
ferrite sheath. These changes had the effect of increasing the coil sensing radius. Increasing the
number of turns in the pickup coil also had the effect of increasing the sensitivity of the coil to
Barkhausen events according to Faraday’s law of induction (3.1). These design modifications did
not appear to have significant qualitative effects on the BN envelope or BN envelope
parameters. Although, absolute values for peak height, peak phase and MBN energy were
different, results appeared scalable. This scaling is due to Faraday’ law (3.1) and in the case of
MBN energy is also scaled by equation (2.26), which indicates that
. Because
of the intrinsically different inductances however, the frequency response of the SL4P and STP
probes in terms of the normalized power spectrum was very different. Furthermore, the STP
probe, with its larger sensing radius, appeared to be more affected by non-uniform field effects
than the SL4P. Both probes demonstrated the four-lobe pattern in MBN energy anisotropy
measurements, suggesting that the cause of the four-lobe pattern was not a result of coil
sensing radius.
The comparison of the SL4P and STP pickup coil designs indicates that increasing coil
radius, and therefore sensing radius, does not significantly alter the measured MBN signal.
Larger coils with more turns result in an amplification of the observed BN envelope and more
importantly do not cause or alter the angular dependent MBN measurements. This is a
CHAPTER 5. DISCUSSION
102
significant result because it suggests that a calibration for BN envelope parameters could be
developed so that data from different probes or entire MBN systems could be directly
compared.
Based on the comparisons of total system error and the measured BN envelopes, it can be
concluded that the DRDC system successfully met or exceeded the performance of the original
Queen’s system it was modeled after.
5.2 Tetrapole MBN Anisotropy and Empirical Fitting Equation
During the course of this work, the ability of the tetrapole probe design to perform MBN
anisotropy measurements, under assumed flux superposition, was brought into question.
Section 4.2 presented a detailed study into tetrapole MBN anisotropy measurements. The
results on mild steel (Section 4.2.3) identified a number of trends among tetrapole MBN
anisotropy data.
In all measurements, tetrapole MBN anisotropy exhibited a four-lobe pattern with lobes
extended in the direction of the probe poles. Under physical rotation of the probe, the lobes
maintained alignment with the probe poles. This suggested that the geometry of the probe was
a significant factor in the measured MBN anisotropy. It also suggested partially independent
behavior of the pole-pairs. This concept of independent behavior was then supported by a
comparison of tetrapole MBN anisotropy measured using a superposition field and two
independent orthogonal fields (see Section 4.2.4). These results also indicated a form of
competition between the orthogonal fields that led to a reduction in MBN energy at particular
angles (see Figures 4.14 and 4.15). Another trend to emerge from the results was the
elongation of the four-lobe pattern in the direction of the magnetic easy axis. This implied that
tetrapole MBN anisotropy was affected by the sample’s magnetic anisotropy and presented the
CHAPTER 5. DISCUSSION
103
possibility that magnetic properties could be extracted from tetrapole MBN anisotropy data.
This was explored through the development of an empirical fitting equation.
The empirical fitting equation (4.3), developed in Section 2.6.5, was shown to describe the
data obtained on mild steel and HY80 very well. It was able to accurately predict the magnetic
easy axis
for the majority of probe orientation angles
The error in the predicted
was maximum at
using both the FTP and STP probes.
and only significant (>5°) for the FTP
probe. Other fitting parameters appear to correlate with probe and sample properties.
and
describe the majority of the four-lobe pattern variation and their relative values at
provide a measure of probe coupling imbalance.
was negative in all fits, which is
consistent with the proposition that it represent a competition term, which is maximized at
. Finally,
which describes an asymmetric imbalance in the system was a relatively
small value in all fits, but showed larger variation for the more imbalanced FTP probe. Equation
(4.3) was compiled from previous fitting equations [28], [49], [62], attempting to incorporate
the additional complexity of the orthogonal magnetization condition and tetrapole
configuration. During the development of the equation it was observed that removal of any one
of the parameters resulted in an inaccurate prediction of the magnetic easy axis
, therefore,
necessitating the incorporation of all the fitting terms.
The empirical fitting equation is a promising sign that valuable material information can be
gained from tetrapole data. Currently however, the ability to extract material condition such as
the presence of residual stress is unclear. The work required to identify residual stress from
tetrapole MBN anisotropy data is discussed in Section 5.4.
5.3 Origin of Tetrapole MBN Anisotropy
This section examines the factors responsible for producing the four-lobe pattern observed in
tetrapole MBN anisotropy results. More specifically, the cause of the largely independent
CHAPTER 5. DISCUSSION
104
generation of MBN by the pole-pairs and apparent minimal superposition of orthogonal fields is
explored. In developing a model for MBN generation under orthogonal fields the effects of
pickup coil alignment, pickup coil sensing radius, probe-sample liftoff/coupling, domain
structure and magnetic anisotropy are considered.
5.3.1 Pickup Coil and Probe Coupling Effects
Misalignment of the pickup coil refers to the deviation of the center of the pickup coil from the
intersection of the pole-pair axes. Accurate positioning of the pickup coil is dependent on the
careful construction of all probe components. All probes built during this work showed a
deviation from center of no more than
0.5 mm. With increasing distance from the center of
the superposition field the accuracy of the magnetic flux density
field angle
and the superposition
decreases. A misaligned coil would therefore demonstrate a systematic error
with respect to an aligned coil. FEM modeling performed during the design of the original
system indicated that the mean error in the superposition field was relatively independent of
field angle
up to a radius of 4 mm [5]. Consequently, a misaligned coil would still observe
the angular variation in MBN that an aligned coil would and therefore could not be the cause of
the four-lobe pattern.
The pickup coil sensing radius refers to the region in which the coil is most sensitive to
MBN events. The pickup coil of the original Queen’s system probe (SL4P) had a 1.5 mm coil
radius and a sensing radius of 2.5 mm. The pickup coil of the STP, in comparison, had a 2 mm
coil radius and an estimated sensing radius of at least 5 mm. Both the SL4P and the STP probes,
however, exhibited similar four-lobe patterns (Section 4.1.4) suggesting that the sensing radius
of the pickup coil was not a significant factor in producing the four lobe pattern.
Pole-sample liftoff represents an increase in the reluctance of the magnetic circuit.
Although the flux control system has been shown to compensate for liftoff to a degree [48],
because the flux is controlled at the pole end and not on the sample, an air gap results in flux
CHAPTER 5. DISCUSSION
105
leakage out of the magnetic circuit. Therefore, larger liftoffs reduce the magnetic flux through
the sample. This effect is most significant when the coupling of the pole-pairs are unequal,
resulting in a larger flux density through one pole-pair than the other. This causes the
differences in the magnitude of the lobes in the four-lobe pattern, when the probe orientation
is changed by 90°. These liftoff effects, however, cannot explain the origin of the four-lobe
pattern. The STP probe demonstrated the most equal coupling between pole-pairs as seen in
Figure 4.12, but still exhibited a clear four-lobe pattern.
5.3.2 Domain Structure Effects
The pickup coil and probe coupling effects described in Section 5.3.1 cannot account for the
four-lobe pattern observed in the experimental data. This suggests that the cause of the
pattern must be the ferromagnetic nature of the materials examined. At this point it is
important to remember that MBN is the result of abrupt domain wall motion, which occurs as
the domain structure reorganizes itself, in response to an applied magnetic field. Consequently,
MBN is primarily sensitive to the domain structure, and not necessarily to the bulk
magnetization of the sample. Considering this, the non-superposition effects observed under
the orthogonal magnetization conditions of the tetrapole, can be attributed to the domain
structure’s response to the application of two orthogonal magnetic fields, and not necessarily
to any bulk superposition magnetization in the sample. The MBN anisotropy measured by the
tetrapole probes can therefore be explained in terms of the complex domain structure that
results from the application of two orthogonal fields. Such a structure, and a possible
mechanism for producing it, is described below.
When performing anisotropy measurements with a dipole, domain growth occurs in
response to a single field, which in the region between the poles is approximately uniform [5].
As a result, domains will all experience growth in the same direction. During magnetization
under orthogonal fields the situation is different. In the region between the four poles, the field
CHAPTER 5. DISCUSSION
106
will be non-uniform and domains in different locations will experience different internal ̅
fields. The motion of domain walls (and therefore domain growth) is a result of the ‘mean field’
in the vicinity of the wall [62], [65] and thus would be most significantly influenced by the
magnetization of neighboring domains. This interaction between neighboring domains or
‘coupling’ is quantified by the mean field coupling coefficient
[66]. Because of this coupling,
magnetization of a single domain can initiate a magnetic avalanche in the material [66]. For a
non-uniform excitation field this suggests that the order in which domains are magnetized will
influence the final domain configuration. The first domains to be magnetized will be those that
experience the highest flux density. Intuitively and through finite element modelling, the
location with the highest flux density is near the poles. At that distance from the center of the
probe, however, the field is mostly parallel with the pole-pair axis and not in the assumed
superposition field direction
[5]. Therefore, domains in this region will grow to align their
magnetization in the direction of the pole-pair axis. Neighboring domains will follow and the
magnetization will propagate toward the center of the probe. The resulting domain
configuration would have two populations of domains magnetized in the pole-pair directions.
Since these two populations are orthogonal to each other, they would not influence each
other’s magnetization significantly. It is speculated that at the center of the sample, a small
number of domains will be affected by the magnetization of both pole-pairs and magnetize in
the superposition direction. As observed in the results, this is restricted to a smaller region
because of the early domain growth near the poles forcing the majority of domains to align in
the direction of one of the pole-pair axes. The final domain configuration would therefore be
significantly different than that induced by a single uniform field and yield a very different MBN
results.
Should the domain configuration under orthogonal fields be similar to that described
above it could explain the tetrapole MBN anisotropy results, more specifically, the four-lobe
pattern. As described by equation (2.27), MBN energy associated with a Barkhausen event is
proportional to the magnitude of the local ̅ field. In the domain configuration described above
CHAPTER 5. DISCUSSION
107
domains in the pole-pair axis directions are magnetized by only one of the two orthogonal and
lower magnitude fields, as described by equation (2.34). This magnetization process essentially
represents a competition between the orthogonal fields to magnetize the domains. The
competition results in a minimal number of domains magnetized in the superposition field
direction,
, since domains are magnetized by either one pole-pair or the other. In terms of
the MBN energy observed by a pickup coil, this would result in maximum energies for
the pole-pair directions and a minimum at superposition angles of
in
, where the
competition is the strongest (for a perfectly balanced probe), which is what is observed in the
results.
Applying this theory to Figure 4.7c, the minimum MBN energy of a given tetrapole should
occur at an angle that represents the maximum competition between the pole-pairs. For the
relatively balanced STP this would be
pole-pair coupling) it would be
. As can be seen in Figure 4.7c the STP shows a clear
minimum for a superposition angle of
energy at
° and
and for the SL4P (which has slightly better 1-3
,
whereas the SL4P shows almost equal
suggesting a minimum in that region, attributed to the slight
coupling imbalance.
The last major pattern observed among the tetrapole data was consistent elongation of the
four-lobe pattern in the direction of the magnetic easy axis. In dipole anisotropy measurements
the stretching of the two-lobe pattern indicates the magnetic easy axis direction and this would
appear to be the case for tetrapole measurements as well. This is a result of the sample having
a large population of 180° domain walls parallel to the magnetic easy axis. When a magnetic
field is applied in the easy axis direction a higher number of domain walls move resulting in a
larger MBN energy. Although the final domain configuration would appear significantly more
complex under orthogonal fields, the 180° domain wall population along the easy axis still
‘amplifies’ the MBN response in a similar fashion to dipole results.
CHAPTER 5. DISCUSSION
108
5.4 DRDC System and Residual Stress Anisotropy
Based on the results presented in this work, the ability of the DRDC system to perform residual
stress anisotropy measurements remains in question. The tetrapole MBN anisotropy results
were affected by the sample’s magnetic anisotropy, which suggests that correlations between
tetrapole MBN anisotropy and residual stress could be developed. Already in this work, the
empirical fitting equation was able to correctly identify the sample’s magnetic easy axis based
on the elongation of the four-lobe pattern observed in tetrapole results. A study on the effects
of stress on the four-lobe pattern would provide valuable insight into the possibility of
extracting residual stress information from tetrapole MBN anisotropy data. The effect of stress
on the empirical fitting equation may also identify fitting parameters that correlate with stress.
Should further studies of tetrapole MBN anisotropy not be pursued, the DRDC system can still
be operated in a dipole probe configuration using traditional manual rotation of the probe.
Furthermore, such measurements could be aided by the ability of the tetrapole to rapidly
identify the magnetic easy axis.
Chapter 6
Conclusions and Future Work
Non-destructive testing and evaluation methods allow for the efficient monitoring of critical
material properties, enabling the safe and cost effective operation of engineered components.
Magnetic Barkhausen noise (MBN) is a ferromagnetic inspection technique that has
demonstrated the ability to identify a number of material properties, including stress. The
tensor nature of stress requires angular dependent MBN characterization, which has typically
been performed through manual rotation of dipole electromagnets. The time consuming nature
of such measurements has led to alternative MBN system designs, such as tetrapole probes.
Tetrapole probes, under the assumption of linear flux superposition, electronically rotate the
excitation field. The validity of flux superposition in ferromagnetic materials for the purpose of
generating MBN, however, has not yet been established in the literature.
Based on the design of a tetrapole MBN system developed by Steven White at Queen’s
University [5], [6], a MBN system was built for Defence Research and Development Canada
(DRDC) for the purpose of performing angular dependent MBN measurements on the Royal
Canadian Navy’s Victoria class submarine hulls. Modifications to the original Queen’s system
design were implemented to improve performance and were evaluated through a comparison
with the original Queen’s system. During the course of this thesis the validity of flux
superposition for the purpose of measuring MBN anisotropy was brought into question.
109
CHAPTER 6. CONCLUSIONS AND FUTURE WORK
110
Because this was a fundamental design element of the new DRDC system, a detailed study of
the ability of tetrapole probes to perform angular dependent MBN measurements was
performed.
6.1 Tetrapole MBN Anisotropy
MBN anisotropy measurements performed with a tetrapole under an assumed flux
superposition were not comparable to measurements performed with manual rotation of a
dipole. Dipole MBN energy anisotropy results were distinguished by a two-lobe pattern, with
lobes extended in the direction of the magnetic easy axis. Tetrapole results, however, exhibited
a four-lobe pattern with lobes in the direction of pole-pairs. This four-lobe pattern appeared to
be affected by a number of factors including probe orientation, probe-sample coupling and
magnetic anisotropy.
Measurements of MBN energy in terms of two orthogonal and independent pole-pairs
suggested that the four-lobe pattern was a result of largely independent behavior of the
orthogonal magnetic fields. It was speculated that the tetrapole MBN anisotropy was the result
of the domain structure’s response to two orthogonal magnetic fields, and not to any bulk
superposition field. A qualitative model was proposed to explain the observed largely
independent behavior as well as ‘competition’ in generated Barkhausen events. It was
suggested that domains near the pole-pairs are the first to magnetize due to the relatively
higher flux density, and do so in the direction of a pole-pair axis. Because the motion of domain
walls, and therefore domain growth, is heavily influenced by the local mean field, the
magnetized domain near the pole-pairs result in an avalanche of magnetization in the direction
of the pole-pair axis. This propagates to the center of the probe, where the orthogonally
magnetized domain structures converge, greatly reducing the number of domains magnetized
in the target superposition direction.
CHAPTER 6. CONCLUSIONS AND FUTURE WORK
111
An empirical fitting equation was developed to describe the four-lobe pattern and was able
to correctly identify the magnetic easy axis, on both mild steel and HY-80 with the FTP and STP
probes. The empirical model indicated that, although tetrapole MBN anisotropy results differ
from those obtained with a manually rotated dipole, useful material properties may still be
extracted from the data.
6.2 System Performance
Modifications to the original Queen’s system design included the addition of low noise power
supplies, revised flux control circuit layout and a simplified probe design. The DRDC system
demonstrated an average reduction in system error of 0.5% over the original Queen’s system
that was primarily attributed to better signal-to-noise ratios. The larger pickup coil radius and
number of turns increased the signal-to-noise ratio in the pickup coil signal, while still
generating qualitatively similar BN envelopes. The increased pickup sensing area did not have a
significant effect on measured MBN energy anisotropy. Comparison with the original Queen’s
system indicated that a scaling factor could be applied to directly compare MBN data from
different probes or systems.
6.3 Future Work and Recommendations
During the course of this work, several areas for further study and development were
identified. This section discusses further analysis of tetrapole MBN anisotropy as well as
alternative methods for angular MBN measurement. Potential improvements to the DRDC
system design are also discussed.
CHAPTER 6. CONCLUSIONS AND FUTURE WORK
112
6.3.1 MBN Anisotropy
As seen in this work, the angular dependence of MBN using the tetrapole probe is significantly
more complex than that obtained with a dipole. The qualitative model presented here, which
describes the predominantly independent magnetization of domains in the pole-pair directions,
could be tested by direct observation of domains. One such technique is the magneto-optical
Kerr effect [18], which is used to observe domain wall motion. By examining the magnetization
process of domains under orthogonal magnetic fields, the MBN anisotropy observed with
tetrapole probes could be better understood and potentially lead to the development of a
theoretical model that describes the orthogonal magnetization condition. The empirical model
presented here may also assist in the development of a theoretical model, by suggesting the
possible elements within it.
While it is obvious that the development of a model to describe the tetrapole data should
be pursued, more basic system designs, which can perform angular dependent MBN should
also be explored. A MBN system, which can measure magnetic anisotropy similar to a manually
rotated dipole has the benefit of a wide knowledge base with which to compare or analyze
data. For this reason, a MBN system consisting of a dipole with a computer controlled stepper
motor to rotate the field incrementally may be the most reasonable design to implement.
Alternatively, a continuous rotational MBN system, which has been developed [61] could be
explored. It is not clear, however, whether the mechanism of continuous rotational
magnetization generates MBN signals that are comparable to conventional dipole
measurements.
CHAPTER 6. CONCLUSIONS AND FUTURE WORK
113
6.3.2 MBN System Design
The reductions in system noise allowed the DRDC system to operate with less system error at
lower frequencies. Identifying the modifications (UPS, redesign PCB layout, etc.) that were most
effective in reducing noise was difficult because the effects of each element could not be
separated. A series of tests running the system in different configurations (e.g without the UPS,
without the new PCB, etc.) could help identify the most important source of noise in the
system.
Further modifications to the design could include adding a layer of conductive material to
the probe casing to shield the excitation and feedback coils from ambient electromagnetic
noise. Also, as previously noted, it was suspected that the strongly varying inductance of the
feedback coils at low frequency (Figure 4.2) contributed to the increasing error in the system.
Exploring the effects of coil shape and number of turns on the inductance of the feedback coil
may produce a coil with a more stable frequency response at low frequencies.
As outlined in Appendix E.1, MBN at low frequencies generates Barkhausen events at
greater depths within the sample due to the skin effect. As shown in Appendix E.2 transient
excitation waveforms may allow for the detection of Barkhausen events even deeper within the
sample. To investigate this, square wave excitation voltage could be implemented and the MBN
signals obtained could be compared to those from time harmonic waveforms.
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Appendix A
FCS of the Original Queen’s and DRDC Systems
This appendix contains pictures of the original Queen’s and DRDC systems FCS circuit boards.
Figure A.1: Flux control system (FCS) circuit board of the original Queen’s system.
120
APPENDIX A
Figure A.2: Flux control system (FCS) circuit board front (top) and back (bottom) of the DRDC
system. The circuit board implemented the changes described in Section 3.1.2.
121
Appendix B
Calibration Procedure
Calibration of the probe refers to the adjustment of the feedback circuit gain
feedback coil gain
of each circuit during the feedback loop to minimize the
and the
of the
waveforms. These gains can be electronically adjusted in the LabVIEW 2011 software during the
operation of the system.
During calibration, the target threshold error is set at 0%, resulting in the continuous
operation of the system. This allows the operator to observe the
and
of the
system and the effects of adjusting the gain values in the LabVIEW 2011 software. The
superposition field angle
is set to 45° so that the flux density is equal in all channels. Once
the system is running, the feedback circuit gain
observed. Once the value of
of channel 1 is adjusted and the effect on
which results in a minimum
on that channel is
found, the process is repeated for the other channels. This procedure is then repeated with the
feedback coil gain
values of
of each channel as well. Often after the optimum
are obtained, the
can be adjusted further to lower the error. For this reason, the minimization of the
total system error involves an iterative adjustment between
considered calibrated once any change in
or
122
increases
then
.
. The system is
APPENDIX B
123
Because system error is dependent on a number of factors (e.g. probe-sample coupling,
sample magnetic permeability, excitation frequency, flux density etc.) this calibration procedure
should be performed before any new measurement.
Appendix C
Empirical Fitting on Polar Plots
This appendix contains the empirical fitting equation results for the FTP and STP probes plotted
on polar graphs.
0
15
90
120
60
4
4
30
2
1
180
30
150
MBN Energy (mV2s)
MBN Energy (mV2s)
150
0
1
2
2
1
0
180
0
1
2
330
210
330
210
3
3
4
240
4
300
240
270
30
120
45
60
MBN Energy (mV2s)
MBN Energy (mV2s)
3
30
150
180
0
1
330
210
60
30
150
2
1
0
180
0
1
2
3
3
4
120
4
1
2
90
5
3
0
300
270
90
4
2
60
3
3
0
90
120
330
210
4
240
300
5
270
240
300
270
Figure C.1: MBN energy anisotropy measurements on mild steel A (Figure 4.11) with fitting
equation (4.2) using FTP probe at various probe orientation angles
plotted on a polar graph.
124
APPENDIX C
125
0
15
90
30
120
25
180
0
5
10
MBN Energy (mV2s)
MBN Energy (mV2s)
5
15
15
30
150
10
5
0
180
0
5
10
15
330
210
20
330
210
20
25
25
240
30
300
240
30
270
30
45
60
10
5
180
0
5
10
330
210
15
20
240
300
270
MBN Energy (mV2s)
MBN Energy (mV2s)
10
30
150
90
120
15
20
0
300
270
90
120
15
60
20
30
150
10
0
120
25
20
15
90
30
60
60
30
150
5
0
180
0
5
10
15
330
210
240
300
270
Figure C.2: MBN energy anisotropy measurements on mild steel A (Figure 4.12) with fitting
equation (4.2) using STP probe at various probe orientation angles
plotted on a polar graph.
Appendix D
Empirical Fitting of Tetrapole Data on Laminate
Samples
14
12
MBNenergy (mV2s)
10
T = 0°
T = 45°
8
T = 90°
6
T = 135°
4
2
-20
0
20
40
60
80
100 120 140 160 180 200
Field Angle  (°)
Figure D.1: MBN energy anisotropy measurements using the FTP probe on grain-oriented
laminate sample at various probe orientation angles . The empirical fitting equation (4.3) is
shown in red for each set of data. Table D.1 includes the fitting parameters for each data set.
126
APPENDIX D
127
MBNenergy (mV2s)
6
T = 0°
4
T = 45°
T = 90°
T = 135°
2
-20
0
20
40
60
80
100 120 140 160 180 200
Field Angle  (°)
Figure D.2: MBN energy anisotropy measurements using the FTP probe on non-oriented
laminate sample at various probe orientation angles . The empirical fitting equation (4.3) is
shown in red for each set of data. Table D.2 includes the fitting parameters for each data set.
Table D.1: FTP probe: Fitting parameters for equation (4.3) for angular dependent MBN energy
measurements performed on grain-oriented laminate at various probe orientation angles .
Probe Angle
(mV2s) (mV2s) (mV2s) (mV2s) (mV2s)
(°)
(°)
(°)
0
-4.22
0.08
1.93
0.0031
6.38
51.0
0.7
0.99
45
-0.51
3.10
0.00
0.0005
4.70
42.1
-4.6
0.97
90
-5.36
3.18
1.83
0.1088
5.81
42.9
0.0
0.99
135
0.64
0.60
0.81
-0.0105
4.81
41.4
0.0
0.85
APPENDIX D
128
Table D.2: FTP probe: Fitting parameters for equation (4.3) for angular dependent MBN energy
measurements performed on non-oriented laminate at various probe orientation angles .
Probe Angle
(mV2s) (mV2s) (mV2s) (mV2s) (mV2s)
(°)
(°)
(°)
0
0.78
0.68
1.87
0.0038
3.46
0.2
-0.2
0.96
45
-1.78
1.15
1.52
-0.0010
3.08
51.4
1.4
0.99
90
-0.69
1.94
0.00
0.0018
2.64
4.4
-0.7
0.99
135
-1.08
0.46
1.58
0.0089
2.31
30.9
0.0
0.98
Appendix E
Skin Depth and Diffusion of Time Harmonic and
Transient Fields into a Semi-Infinite Slab
E.1 Skin Depth
The amplitude of an electromagnetic wave incident upon a conductor will decrease
exponentially as a function of depth due to ohmic losses within the medium. This is known as
the skin effect and is given by (in the case of an incident magnetic field ̅ ( )) [36]:
̅( )
where
is the initial amplitude,
(E.1)
is the depth into the conductor and
is the skin depth,
which represents the distance equal to a decrease in amplitude by a factor of
. The skin
depth can be written as [36]:
√
where
and
is the permeability of free space,
(E.2)
is the relative permeability,
is the angular frequency of the incident field. In linear materials,
because
and
is considered constant
are constant. In ferromagnetic materials, however,
129
is the conductivity
is non-linear and
APPENDIX E
130
dependent upon the hysteresis curve. As the applied field ̅ is increased, ̅ approaches
saturation as seen in Figure 2.2 and
̅ ̅ . This has the effect of
decreases according to
increasing the skin depth according to E.2.
In relation to this work, MBN signals generated within ferromagnetic samples are also
attenuated as they propagate toward the surface. This is the limiting factor in the depth of
MBN signals that can be detected by a surface mounted pickup coil. By examining the effect of
varying skin depth, alternative excitation waveforms can be found, which increase skin depth,
allowing MBN signals deeper in the sample to be observed.
E.2 Time Harmonic vs. Transient Excitation Fields
MBN excitation waveforms are typically time harmonic, with frequencies between 1 and 60 Hz
[23]. In this section, the diffusion of such waveforms into conducting materials is compared to
an alternative, transient excitation signal. To accomplish this, analytical models for both signals
are derived by solving the diffusion equation under boundary conditions determined by a
simplified geometry of a traditional MBN setup. In both models, the excitation field is parallel to
a semi-infinite slab of conductivity
and relative permeability , as shown in Figure E.1. For the
given geometry, the time harmonic solution is:
(
)
(
)
.
/
(E.3)
)+
(E.4)
and the transient solution is:
*
( √
APPENDIX E
131
Figure E.1: Analytical model geometry for parallel magnetic field diffusing into a semi-infinite
slab.
where for both solutions,
is the field amplitude, is the depth into the sample and is time.
Detailed derivations of (E.3) and (E.4) can be found in Appendix F. Figures E.2a and E.2b show
the field amplitudes as a function of depth for various times for time harmonic fields and
transient fields, respectively. Figures E.2a and E.2b are scaled with a magnetic field amplitude
of 1.
In the time harmonic solution, as the field propagates through the sample, the flux density
at the surface decreases. In the case of the transient solution, however, a high flux is
maintained near the surface as the field diffuses into the sample. If the initial field amplitude
is near saturation, the regions inside the sample with high flux represent areas of higher skin
depth according to equation (E.2) and Figure 2.2. For the transient case, this would suggest that
the attenuation of Barkhausen events deeper in the sample is reduced because of the large flux
density near the surface, unlike the time harmonic case. From Figure E.2 it appears that a
transient excitation field may be able to increase MBN measurement depth over the common
time harmonic fields.
APPENDIX E
132
0.5 s
2.0 s
3.5 s
a) Time Harmonic
1.0
0.8
Flux, B (T)
0.6
0.4
0.2
0.0
0.0
-0.2
0.1
0.2
0.3
Depth, z (mm)
-0.4
0.5 s
2.0 s
3.5 s
b) Transient
1.0
0.8
Flux, B (T)
0.6
0.4
0.2
0.0
0.0
-0.2
0.1
0.2
0.3
Depth, z (mm)
-0.4
Figure E.2: (a) Time harmonic and (b) transient solutions to diffusion of a magnetic field into a
semi-infinite slab
Appendix F
Derivation of Diffusion of Time Harmonic and
Transient Fields into a Semi-Infinite Slab
F.1 Time Harmonic Solution
To find an expression for the magnetic field in the slab as a function of space and time, the diffusion
equation in one dimension (F.1) must be solved under specific boundary conditions (F.2), (F.3) and
initial condition (F.4). Where
(
) is the magnetic field inside the conductor and
( )
( ) is
the applied magnetic field.
(
)
(
(
)
( )
(
(
)
)
(F.1)
(F.2)
(F.3)
)
(F.4)
We begin by assuming a separable solution of the form:
(
Where B(z) and T(t) are of the form:
)
( ) ( )
(F.5)
APPENDIX G
134
( )
(F.6)
( )
(F.7)
We will only be concerned with the real components of (F.6) and (F.7) but using exponential form
simplifies the math. In (F.6) and (F.7) ω is the angular frequency and k is given by:
(
)√
(F.8)
Substituting (F.7) and (F.7) into (F.5) and using the equation for skin depth, (E.2), we find:
(
(
Where
and
)
(
)
(F.9)
)
(
)
(F.10)
are constants. To determine them we look at the real part of (F.10) and use the
boundary conditions. (F.3) indicates that C must equal 0 since the field is finite as
. We are left
with:
(
)
(
)
(F.11)
Where the cosine term comes from taking the real part of the imaginary exponential. Using the
boundary condition (F.2),
.
(
)
(
)
(F.12)
Equation (F.12) is the solution to the steady state diffusion of the sinusoidal magnetic field into the
sample. This result is not surprising since we expect with a time-harmonic applied field that the field
inside the conductor is also time harmonic with the same frequency. The exponential decay according to
the skin depth is also expected.
F.2 Transient Solution
To find the transient solution, that is, for an abruptly applied and constant field, we use a completely
different procedure. As before we must still solve the diffusion equation (F.1), and we use the same
APPENDIX G
135
boundary condition (F.3) and initial conditions (F.4), but have a new boundary condition (15) where
( ) is now a step function.
(
)
(
(
(F.1)
)
(
(
)
(F.13)
)
(F.3)
)
(F.4)
For the transient case we will use an integral transform method which involves taking the Laplace
transform to both sides of equation (F.1) with respect to t:
(
∫
)
(
)
(
∫
)
(
)
(F.14)
Looking at the LHS of (F.14), the double derivative comes out of the integral, and the integral is then
equal to 1, leaving us on the LHS with:
̅̅̅(
Where ̅̅̅(
) is the Laplace transform of
(
,
(
(
)
(
From the initial condition (F.4)
(
)
(F.15)
). On the RHS, using integration by parts we find:
(
∫
)
)
))
(
∫
∫
(F.16)
)
(
)
(
)
(
)
(F.17)
(F.18)
and we are left with:
̅̅̅(
)
̅̅̅(
(
∫
)
̅̅̅(
(F.19)
)
(F.20)
)
Equation (F.20) is a simple differential equation that has a solution of the form:
̅̅̅(
)
(√
)
( √
)
(F.21)
APPENDIX G
Where
and
the value of
136
are constants. From the boundary condition (F.3), we require that
we use the boundary condition (F.13),
(
)
. To determine
, and find that under the Laplace
transform the boundary condition becomes:
̅̅̅(
)
̅̅̅(
∫
(
)
(
)
∫
(
)
̅̅̅(
Thus,
(F.22)
)
(F.23)
(F.24)
)
, and the solution of the Laplace transform is:
̅̅̅(
)
( √
(F.25)
)
To find the final solution we take the inverse Laplace transform, which can be found calculated using
complex contour integration or can be found in tables, and gives:
(
Where
)
*
( √
( )is the error function which has the properties
(F.26)
)+
( )
and
( )
. By inspection
we see that it satisfies both boundary conditions. It should be noted however, that the solution has a
singularity at
and thus cannot model the diffusion of the magnetic field from