Eddy Current Displacement Sensor with LTCC Technology Dissertation zur Erlangung des Doktorgrades der Fakultät für Angewandte Wissenschaften der Albert-Ludwigs Universität Freiburg im Breisgau vorgelegt von Yuqing Lai 2005
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Eddy Current Displacement Sensor with LTCC Technology
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ThesisDissertation zur Erlangung des Doktorgrades
der Fakultät für Angewandte Wissenschaften
der Albert-Ludwigs Universität Freiburg im Breisgau
vorgelegt von
Yuqing Lai
Referenten: Prof. Dr. J. Wilde, Prof. Dr. C. Ament
Datum der Promotion: 22. 03. 2005
To yongfeng
3 Aim of research and some basic principles and
concepts............................. 12
3.1 Aim of the work
..........................................................................................
12 3.2 The concept and principle of an eddy current
sensor................................. 12
3.2.1 The theory of eddy
currents....................................................................
13 3.2.2 Testing principle for turbine
blades........................................................
16
4 Design of the eddy current sensor
...................................................................
19
4.1 General principle and design factors
.......................................................... 19 4.2
Analytical calculation of parameters of a LTCC coil
................................ 20
4.2.1 Analytic model of the LTCC coil for analytic analysis
......................... 20 4.2.2 Inductance
calculations...........................................................................
21
4.2.2.1 Self-inductance
...............................................................................
22 4.2.2.2 The mutual inductance
...................................................................
23
4.2.3 The DC resistance of the
coil..................................................................
28 4.2.4 Capacitance calculation
..........................................................................
28 4.2.5 Quality factor, skin depth, self-resonant frequency
............................... 32
4.2.5.1 Quality factor (Q)
...........................................................................
32 4.2.5.2 Skin depth
.......................................................................................
33 4.2.5.3 Self-resonant frequency
(SRF).......................................................
34
4.3 Design and optimization of the eddy current
sensor.................................. 35 4.3.1 FEM
simulation.......................................................................................
35 4.3.2 Optimizing the sensor location - modal vibration
simulation ............... 36 4.3.3 Optimizing the sensor
sensitivity-EM evaluation..................................
39
4.3.3.1 2D
simulation..................................................................................
39 4.3.3.2 3D
simulation..................................................................................
46
4.3.4 Thermo-mechanical FE analysis
............................................................ 50 4.4
LTCC layout design for eddy current sensor
............................................. 54
4.4.1 Material selection of LTCC coil
............................................................. 54
4.4.2 Structural design optimization with fabrication
guideline..................... 55 4.4.3 Layout
design..........................................................................................
56
ii
5.1 LTCC fabrication of the eddy current sensor
coil.......................................58 5.2 Sensor
characterization
................................................................................59
5.2.1 Static impedance of sensors (L, C, R)
.....................................................59 5.2.2
Static position measurement system
.......................................................59
5.2.2.1 Proximity
testing..............................................................................60
5.2.2.2 System for impedance testing by frequency
sweep........................60
5.4 System for real-time measurements
............................................................63
5.4.1 Rotation control and generator
................................................................64
5.4.2 Electronic signal acquisition system
.......................................................65 5.4.3
Test
objects...............................................................................................67
6.1.2.1 Proximity
testing..............................................................................69
6.1.2.2 Horizontal passage
testing...............................................................70
6.2 Temperature influence on the sensor
impedance........................................80 6.2.1 Thermal
coefficient of resistance of the sensor coil
...............................80 6.2.2 Temperature influence on
the impedance of the sensor .........................81
6.2.2.1 Influence of temperature on the resistance of the sensor
...............81 6.2.2.2 Influence of temperature on the
inductance of the sensor..............84
6.3 Real-time
measurements..............................................................................87
6.3.1 Response of the sensor to rotation of the rotor
.......................................87 6.3.2 Influence of the
clearance between sensor surface and tip of blades .....88 6.3.3
Measurement for the changes of blades
geometry..................................91 6.3.4 Influence of
testing circuits
.....................................................................95
7 Conclusions and prospects
................................................................................99
1 Introduction
Eddy current non-contact measuring systems have been widely used
for more than 30 years for measurement of position, displacement,
vibration, proximity, alignment, and dimensioning, as well as parts
sorting applications [1-5]. In this work, the novel low temperature
co-fired ceramics (LTCC) technology was applied to a planar
displacement eddy current sensor in order to improve the
performance of the sensor for displacement measurements in high
temperature environments. The improved sensor can be used as a
blade tip sensing probe within a “health monitoring” system for
rotary instruments, such as aero-engines, gas turbine engines,
steam turbines or turbocharges.
To date, prediction of displacements in aerodynamic systems has
been difficult due to the lack of computational fluid dynamics
fidelity, structural modeling accuracy, instrumentation effects and
insufficient characterization of instrumentation installation
effects. Therefore, to improve the lifetime and performance of
conventional displacement sensors, such as eddy current sensor or
strain gages, and transforming them for engine health monitoring
applications has become very important [6]. Especially for a
turbo-machinery system, the working environment is very harsh and
the movements of blades are complicated (see Figure 1.1). Incipient
failure of rotor blades and disks can be anticipated by detecting a
damage signature early on, and detecting incipient failures in
advance can avoid or prevent further damages [7].
Figure 1.1 Illustration of turbine blades and an example of their
vibrations analyzed by finite elements method.
Recently, a measurement technique known as non-destructive blade
tip-timing method was developed [8-12] for health monitoring of
turbine blades. This method uses multiple sensing probes installed
in the engine casing to sense points in time
1 Introduction
2
when the blades are passing the probes. The changing vibration
characteristics are analyzed according to acquisition timing data.
Further more, the related blade's fatigue life and the health
condition of the turbine are evaluated. In such an on-line blade
monitoring system, non-contact displacement sensors play an
important role.
Several physical principles are possible for non-contact
measurements. Among these, eddy current, optical reflection and
capacitive sensors have good properties. But in harsh environments,
eddy current sensors are superior to other types of sensors and
have become the best choice because they are inherently immune to
nonmetallic materials, e.g. plastic, opaque fluid or transparent
fluid and dirt [13].
The sensor coil is the main component of an eddy current sensor. In
this work the manufacturing technique of the sensor coil was
changed in order to meet the requirement that such a sensor works
at high temperature. The novel LTCC technology was applied to
fabricate these eddy current sensors.
Low temperature co-fired ceramics (LTCC) are multilayer
glass-ceramic composites that can bear high temperatures up to the
melting point of the conductor metal. Its typical advantages are as
follows [14,15]:
• Temperature stability
• Green tape for single layers available in a variety of uniform
thicknesses
• Co-fireable and post-fireable Au and Pd/Ag conductors with
oxidation resistance
• Tape has low dielectric constant and dielectric loss
• Material has low TCE
• Small x-y fired shrinkage
Because of these advantages, an LTCC application for sensors and
actuators was developed recently rendering a technology suitable
for micro-system technology (MST) [16,17]. The objective of this
work is to apply LTCC technology to a planar eddy current sensor in
order to improve the feasibility and reliability of displacement
measurements in harsh and high temperature environments.
1 Introduction
3
For sensors with a new packaging, their sensitivities and
feasibilities must be controlled and evaluated. In this work, the
design of the sensor was first optimized . A set of calculating
methods were built using analytic analysis for electric parameters
of a planar film coil, such as unloaded impedance, skin depth and
self-resonant frequency. Various properties of eddy current sensors
were evaluated by finite elements method (FEM) analysis such as the
optimal mounting position, optimum structure and materials. The FEM
analysis involves three aspects: modal, electromagnetic and thermal
mechanical analysis. According to the results of analytic and FEM
analyses and combining them with the LTCC fabrication guidelines, a
comprehensive optimization flow chart was developed, and a
corresponding optimization layout was designed and implemented.
With the realized LTCC sensor examples, experimental
characterization was carried out. In addition, the influence of
temperature on the properties of the eddy current sensor was
evaluated. It was found that the change of the resistance of the
sensor with the change of the target displacement follows the same
trend at different temperatures up to 600 oC. Also the values of
inductance below 1 MHz bear little temperature dependence.
Therefore, it was justified that LTCC eddy current sensors are
feasible at high temperatures. Finally, a rotating system
consisting of a motor, a rotor with blades, a testing circuit, and
a data acquisition system was built. This equipment was used to
simulate the rotation displacement of blades. The testing signals
represent the rotating speed of the motor up to 3000 rpm, clearance
between sensor and blade tip, and changes of the blade geometry
correctly. Thus, the capability of the LTCC eddy current sensor to
measure displacements of rotary blades was proved. All stages of
the development of our work are illustrated in Figure 1.2.
In this thesis, chapter 2 describes the literature and addresses
the state of the art for the blade tip timing technique. Several
conventional displacement sensor and packaging technologies are
introduced. Chapter 3 elaborates on the aim of this project. The
basic principles of eddy current sensors and LTCC technology are
also presented. Chapter 4 is concerned with the design optimization
of the LTCC eddy current sensor. The analytic and numerical
calculations and empirical work have been done to design a novel
LTCC eddy current sensor for the measurement of rotor blade tips.
The layout for an optimal sensor structure is obtained for LTCC
fabrication. In Chapter 5, the set-up of the experimental system
and the related calculation method for data processing are
introduced. It comprises the instruments for the characterization
of the sensor and the measurement of temperature dependent
properties, and the system integration including motor, rotor with
eight blades, sensor and its supporting frame, as well as the
electronic measurement and data acquisition system etc. Chapter 6
displays the experimental results and corresponding discussion.
Finally, Chapter 7 summarizes the work and gives the conclusions
and the prospect for possible improvements as well as further
applications.
1 Introduction
Modal , electromagnetic, thermo-mechanical Analytic
calculation:
Resistance, inductance, capacitance, skin depth, self- resonant fr
e q uency
Design layout and LTCC fabrication Selection of LTC C materials and
structure Layout design by software CAM350 LTCC fabrication
Experiment and measurement Static behavior:
Sensor character i zation for impedance Temperature influence on
sensor behavior
Dynamic behavior: Test system (rotating system, circuit and data
acquisition system) Measurement for rotary speed, clearance,
changes of the blade geometry Signal processing and analysis
Figure 1.2 Flow chart of project work.
5
2 State of the art
This chapter provides a starting point for this research by a
literature survey. The relevant state of the art for application
and development is essential for defining the aim of our
work.
2.1 Importance of and developments in blades vibration
monitoring
A common failure mode for turbomachinery is high-cycle fatigue of
the turbine blades due to high dynamic stresses caused by blade
vibration in resonance within the operating range of the machinery
[18]. A large number of engine shut-downs can also be explained by
blade failures caused by resonance vibration or flutter. Therefore,
it is very important for the health diagnosis of turbomachinery to
monitor the blades’ vibrations and to obtain dynamic stress
information.
The conventional practice in vibration measurement for
turbomachinery has been using strain gauges mounted on the blade
surface. The testing signal is received on the stationary side
using a wireless telemeter system. With this method the responses
to all excited vibration modes of the instrumented blades can be
captured continuously. However, a conventional telemetry system
requires costly installation on the rotor side where it must
withstand centrifugal forces and high temperatures, and it can
provide only 5~6 testing data simultaneously because of the
limitation of the usable radio wave band [7,19,20].
Recently, a non-contact measurement technique for vibrations of
turbomachinery rotor blade tips using blade tip timing was
developed and has become an industry- standard procedure. In these
systems, the time points when the rotor blade tips are passing a
given point are recorded and extracted to obtain vibration
information by blade deflection signal processing. Many
organizations and companies, such as NASA Glenn Research Center,
Mitsubishi, Hood Technology, and SKF, carried out related
researches in this field [6,20-26]. In this system, the tip sensor
is the key component. The sensors are integrated with a non-contact
stress measurement system to measure blade resonance (high-cycle
fatigue), detect cracks in blades and disks (high- and low-cycle
fatigue), detect damage from foreign objects, investigate rotating
stall, and analyze blade flutter along with other rotational
anomalies. The equipment also has the potential to perform
real-time monitoring of an engine during flight. Figure 2.1.1
illustrates a complete tip timing system with optical
sensors.
2 State of the art
6
Figure 2.1.1 Overview of a non-contact stress measurement system
[6].
2.2 Conventional displacement sensors
Displacement sensors are generally grouped in four categories:
magnetic sensors, capacitive sensors, optical sensors, and strain
gages. Choosing the right sensor is vitally import, because the
environment in which the sensor is situated can affect the sensor
and its operation dramatically. The concepts of these are described
and a comparison is made in this section.
(a)Eddy current (b) Inductive (c) Hall effect (d) Capacitive (e)
Optical
Figure 2.2.1 Principles of displacement sensors [27].
Magnetic sensor: This includes magnetic field sensors, magnetic
switches and instruments measuring magnetic fields and/or magnetic
fluxes by evaluating a
2.2 Conventional displacement sensors
7
potential (Hall effect), current (wire coil / flux gate), or
resistance change because of the field strength and direction
[28].
• Eddy current sensor
If a nonmagnetic conductive target material is introduced into the
coil field, eddy currents are induced in the target's surface.
These currents generate a secondary magnetic field, inducing a
secondary voltage in the sensor coil. The result is a decrease in
the coil's inductive reactance. The coil-target interaction is
similar to the field interaction between the windings of a
transformer. Eddy current sensors work most efficiently at high
oscillation frequencies. This type of system is also known as
variable impedance because of the significance of the impedance
variations in defining its complex nature. Ferromagnetic target
materials can also effectively decrease the coil's inductive
reactance if there is sufficient eddy current flow to counteract
the increased field strength resulting from a higher permeability
of the target (µ>1). For high-precision measurements, however,
preferable applications should make use of nonmagnetic conductive
target materials for reasons discussed later [1]. Eddy current
sensors can be used whether access to the blade is available or not
(i.e., they can “see through the case”, and are unaffected by the
presence of oil and other contaminants [19]).
• Magnetic inductive sensor
The sensor comprises a coil, a coil core and a permanent magnet.
The coil core and the magnet are magnetically coupled. This
generates a permanent magnetic flow inside the coil. A
ferromagnetic substance that influences the field of the magnet can
cause changes in the magnetic flow. This change in flow induces a
voltage inside the coil. The magnitude of the induced voltage
depends on the magnitude and the speed of the change in flow
[29].
• Hall effect sensor
In a differential Hall sensor, two Hall generators are arranged
close to each other. The individual Hall generators operate along
the same principle as the magnetic field dependent semi-conductor
in single Hall sensors. Both Hall elements of the sensor are biased
with a permanent magnet [29].
Strain gage: An ideal strain gage would change resistance only due
to the deformations of the surface to which the sensor is attached.
It belongs to the contact sensors and must be mounted directly on
the surface of the tested object.
2 State of the art
8
Capacitive sensor: Capacitive proximity sensors are contactless
position sensors, which react to the presence of objects of nearly
any material within the supervised range. Capacitance works well
when clear access to the blade tip is available and the dielectric
properties of the medium in the gap between the sensor and the
blade are constant. These sensors tend to be unreliable at
medium-to-high temperatures, and cannot be used when oil
contamination is present. Special materials are needed for
operations at cryogenic temperatures [19][30].
Optical sensor: Taking the principle of the optical triangulation
for contactless position measurement as an example, a laser beam
emitted from the sensor produces a light spot on the surface of the
measured object that is projected by high-quality optics on a
position-sensitive detector. Optical devices require clear access
to the blade tip, and the medium in the gap must be transparent.
Optical sensors can be used at very high temperatures but not in
the presence of contaminants.
Contact sensor:
Strain gage Noncontact sensor: Eddy current sensor capacitive
sensor optical sensor
Figure 2.2.2 Mounting illustration of several displacement sensors
on a turbine wheel [6].
The mounting method for strain gauge and non-contact sensors is
shown in Figure 2.2.2. Non-contact position measurement devices
offer several advantages over contact-type sensors. They provide
higher dynamic response with higher measurement resolution, have
lower or no hysteresis, and can measure small, fragile parts. There
is no risk of damaging delicate structures by the probe, and they
can operate in highly dynamic processes and environments [31]. A
detailed comparison of the four kinds of sensors concerning their
advantages and disadvantages is provided in Table 2.1.
2.3 High temperature properties of sensors
9
Table 2.1 The comparison of the advantages and disadvantages of
several displacement sensors
Sensor type
Advantage/disadvantage
Eddy current Advantage: Simple structure, low cost, light weight,
durable, immune to gas stream properties (dirt, water vapor,
moisture etc.) Disadvantage: Measuring signal will change with
material properties of the blade.
Capacitive Advantage: Simple structure, low cost Disadvantage:
Durability and changing dielectric properties of the gas stream can
cause problems; needs high voltage power supply.
Optical Advantage: High precision, direct measurement of the
position Disadvantage: Cooling requirements and associated added
weight; installation complexity and susceptibility to optical
contamination; rather for ground based laboratory testing than
harsh environments.
Strain gage Advantage: Direct measurement of stress in-situ
Disadvantage: Attached to rotor and root of blades, therefore must
withstand centrifugal force and high temperature.
2.3 High temperature properties of sensors
Sometimes, displacement sensors must work at high temperatures,
especially for turbomachinery, whose environment normally involves
high temperatures because the turbine is rotating at high speed.
Therefore it is very important to improve the high temperature
properties of the sensor [32,33]. According to the literature,
there are two methods to improve the operating temperature of
sensors.
The first method is to change the material and packaging of the
sensor [34]. For example, inductive sensors cannot be used at high
temperatures because their magnetic components are limited to the
Curie temperature. Eddy current sensors can be suitable for high
temperature applications but must consist of ceramic material for
insulation. There are two types of eddy current sensor coil. One is
a sensor coil with a ferrite core, and the other type has a ceramic
core. The latter has better high
2 State of the art
10
temperature properties than the former. For the sensor with a
magnet core, the working temperature is below 300 oC because the
normal curie temperature of ferrite magnets is below 450 oC and the
maximum operating temperature is below 300 oC [35]. Whereas when
the sensor has a ceramic core, its working temperature can be up to
about 1000 oC. Therefore the ceramic core is applied for eddy
current sensor in high temperature environment of turbine system.
Use of heat-resistant materials such as ceramics for sensor
packaging is an effective method to improve its thermal properties
[8,10,31].
Another method is to change the mounting position of the sensor and
make it insulated from the thermal sources. Usually a non-contact
sensor is mounted in the engine casing by drilling a hole through
the case. But recent literature [21,36] describes the development
of a novel sensor that can make the same detailed measurements
while mounted on the outside of the engine case. There are no
holes, and no interruption in the gas path. They can also diagnose
problems and help predict the service life of the rotor. Because
the engine case without hole insulates the thermal sources, the
sensor avoids the high temperature problem.
2.4 Introduction of the planar coil technology
In this section, several planar coil technologies are introduced
briefly and compared to the novel LTCC technology. These are high
temperature cofired ceramic (HTCC), thick film and printed circuit
board (PCB) technologies. Details are listed in Table 2.2.
2.4 Introduction of the planar coil technology
11
Table 2.2 Comparison of four processing technologies for planar
coils
Technology Introduction/ advantages or disadvantages
High temperature cofired ceramic technology uses alumina green tape
layers that require firing at high temperatures above 1500 °C to
become a uniform and reliable dielectric insulator.
HTCC
Disadvantages: Low conductive material (W, Mo), complex process, no
printed resistor and high capital cost.
A precision thick film ink pattern is screened onto a ceramic
substrate and cured at elevated temperatures. Then a laser is used
to trim the resistance values to a high degree of precision, up to
0.1%.
Thick film
Disadvantages: multiple printing steps and multiple firings for
multilayers, thickness control of dielectric and limited layer
count
LTCC combines the benefits of HTCC and thick film technologies. It
is made from multilayer glass-ceramic dielectric tape by conductor
screen-printing on the green ceramic tape with sintering
temperature below 900°C that is common to thick film
materials.
LTCC
Advantages: low processing temperature, low resistive metal
(Au,Ag), printed resistor, TCE match Si, unlimited number of
layers, good thermal properties etc.
Printed circuit board. The normal laminate is constructed from
glass fabric impregnated with epoxy resin (known as "pre-preg") and
copper foil. The copper foil is partly etched away, and the
remaining copper forms a network of electrical connections between
the components mounted on it.
PCB
Disadvantages: low operating temperature, larger size of circuit
and low thermal conductivity.
12
principles and concepts
3.1 Aim of the work
The aim of this research is to develop a novel eddy current sensor
with sufficient sensitivity to match the requirements of
displacement measurement under given working environments and
testing objects. In our work, the working environment is harsh and
is full of non-metallic impurities such as oil drops, steam, dirt,
etc. In addition, high temperatures above the Curier temperature of
ferrite magnets are another limit to a sensor. The testing objects
are rotating turbine blades of high- conductivity and non-magnetic
metals such as Ti alloys, or stainless steel. Because of these
requirements, it was our research aim to develop an eddy current
sensor with LTCC technology [37-39].
Among several possible sensors for blade tip timing systems, only
magnetic sensors are suitable for harsh environments because they
are inherently immune to nonmetallic materials. But for magnetic
inductive sensors and Hall sensors, their testing objects must
include ferrite magnet or permanent magnet. In addition, because
inductive sensors and Hall sensors must contain permanent magnetic
materials according to their working principle, it is impossible
that they work at high temperatures. Therefore, eddy current
becomes the only option for our research. Then, the novel packaging
technology of LTCC is applied to the sensor fabrication because it
provides better heat-resistant properties and other advantages such
as a better TCE match between the conductor and the substrate, etc.
The design of the LTCC sensor has been optimised to obtain a better
sensitivity for the measurement of the blade's rotating
displacement. The purpose of the experimental testing is to justify
the feasibility of the sensor for working at high temperatures, and
to evaluate the capability of the sensor for the measurement of the
rotating displacement at laboratory level. Of course, the final aim
of our work is to apply this LTCC sensor as a tip probe for
practical rig testing in turbomachinery or other fields.
3.2 The concept and principle of an eddy current sensor
The eddy current sensor belongs to the group of inductive sensors
[40]. In the past it has been used mainly in the proximity probes
application. Recently it was developed also as a diagnostic and
prognostic tool for turbomachinery in terms of a blade tip
3.2 The concept and principle of an eddy current sensor
13
sensing system [8]. This chapter addresses the concept of the eddy
current induction and the operating principle of a blade tip
sensing system.
3.2.1 The theory of eddy currents
In 1831, Faraday and Henry discovered that a moving magnetic field
induces a voltage in an electrical conductor proportional to the
rate of change of the exciting current for magnetic field. In 1879,
Hughes recorded changes in the properties of a coil when placed in
contact with metals of different conductivity and permeability.
However, it was not until the Second World War that these effects
were put to practical use for testing materials. Much work was done
in the 1950's and 60's, particularly in the aircraft and nuclear
industries. Eddy current testing is now a widely used and
well-understood technique for crack inspection or position sensing
[41-43].
Eddy current sensors applied for position or displacement
measurement have their
origins based on Faraday's law of electromagnetic induction:
dt
Φd B−=ε , where ε is
induced emf (electromotive force), and dΦB/dt is the rate of change
of the magnetic flux. The physical model of measurements (see
Figure 3.2.1) consists of the target object and the main component
of the sensor that is an induction coil. When an alternating
voltage or current is applied to the stranded coil, it generates an
oscillating magnetic field, which induces eddy currents on the
surface of the conductive target, according to the principle of
eddy current induction [8]. Eddy currents circulate in a direction
opposite to that of the coil, reducing the magnetic fluxes in the
coil and thereby its inductance. Eddy currents also dissipate
energy, and therefore lead to an increase in the resistance of the
coil [44].
(a) (b)
Figure 3.2.1 Physical principle of an eddy current sensor: (a)
target with large surface [45] (b) target with narrow
surface.
Consider a coil of wire wound in a helical shape with an air core.
Low resistive nonferrous material is typically used in inductive
sensor coils to avoid magnetic
3 Aim of research and some basic principles and concepts
14
hysteresis effects and nonlinearity errors caused by ferrous
materials. This kind of wire coil is considered as an inductor. The
coil and the target constitute the primary coil and the shorted
secondary coil of a weakly coupled air-core transformer [44].
Figure 3.2.2 (a) shows this kind of electronic circuit model
converted from the physical model.
L1
(a) (b)
=++−
=−+
= (3.2)
Therefore, the circuit model of a transformer can be converted to
the model of an inductor and a resistor shown in Figure 3.2.2 (b).
The equivalent impedance Z, resistance R, inductance L and quality
factor Q of the sensor model become:
3.2 The concept and principle of an eddy current sensor
15
)( 2
== (3.6)
where R1 and L1 are the resistance and self-inductance of the
sensor coil depending on the material and structure of the coil; R2
and L2 are the equivalent resistance and self-inductance of the
target depending on the eddy current path, resistivity ρ and
permeability μ of the target; ω is the exciting angular frequency
of the power source, proportional to frequency f; and M is the
mutual inductance between the sensor coil and the target depending
on the relative position x between sensor and target.
With the change of relative position x between the sensor coil and
target, Z, L, R and Q change with mutual inductance M. Following
the equation above, Z, L, R and Q can be derived using x, ρ, μ and
the exciting frequency ω. Whereby
Z, L, R or Q = ƒ (x, ρ, μ, ω) (3.7)
When sensor coil, target and exciting frequency are given, a
one-variable function is obtained for displacement measurement.
That is:
Z, L, R or Q = ƒ (x) (3.8)
When the surface of the target is infinitely large as in Figure
3.2.1(a), x is the standoff between sensor and target in vertical
direction. Whereas, when the surface of the target is narrow as
shown in Figure 3.2.1(b) and the standoff between sensor and coil
is given, x is the horizontal displacement of the target referring
to the
3 Aim of research and some basic principles and concepts
16
position of the coil. Therefore, the testing principles of the eddy
current sensor for proximity and horizontal displacement of the
target can be formulated in the following.
3.2.2 Testing principle for turbine blades
According to the measuring principle, the eddy current sensors are
suitable to be applied to monitoring movements of turbine blades.
In a rotating system, the sensor is mounted directly above the tip
of the blades with its surface normal to the direction passing
through the rotating centre as illustrated in Figure 3.2.3 (a).
When a conductive blade comes below the eddy current sensor, the
impedance or other related parameters of the sensor coil change.
Through a suitable circuit, a positive or negative voltage peak
corresponding to the arrival of a blade can be measured. All blade
movements can be inferred by the measurements of their elapsed
time. Comparing the arrival time and the amplitude of these voltage
peaks, the movement of blades can be derived.
t
(a) (b) (c)
Figure 3.2.3 Testing principle for movement of turbine blades: (a)
illustration of mounting for sensor (b) arrival time of every blade
(c) clearance between sensor and tip of blade.
For example, Figure 3.2.3 (b) shows the arrival time difference Δt
between two voltage peaks. This kind of signal indicates the
interval time between two blades and offers information on rotating
speed, and on anomalous horizontal displacements including
vibration signals. Figure 3.2.3 (c) illustrates different
amplitudes of blades. This kind of signal can reflect the change of
clearance between sensor coil and the tip of blade and can offer
the information on the creep through long-term trend of turbine
blade length, FOD (Foreign Object Damage) of the blade, and shifts
in resonance etc. By analysing both types of the output signal from
the eddy current sensor, one can diagnose the incipient failure.
So, it becomes possible to take some improvements in time to avoid
larger loss and enhance the reliability of the whole system.
3.3 Introduction to LTCC technology
17
3.3 Introduction to LTCC technology
3.3.1 Concept of LTCC technology
The Low Temperature Cofired Ceramic (LTCC) technology can be
defined as a way to produce multilayer circuits with the help of
single tapes, which are to be used to apply conductive, dielectric
and resistive pastes on. These single sheets have to be laminated
together and fired in one step. Because of the low firing
temperature of about 850°C it is possible to use the low resistive
materials silver or gold with melting points of 960 oC and 1100 oC
instead of molybdenum and tungsten used in conjunction with the
HTCC [46]. The LTCC technology is especially well suited for RF
applications, and for products where a high integration level
and/or a high reliability are needed.
LTCC technology is a very novel technology beginning from the 80’s.
The first publication on LTCC can be found by INSPEC in 1984 [47].
Because low temperature cofired ceramic tape technology displays
excellent properties for packaging, interconnection and passive
component integration, it has been widely used in the last twenty
years for high reliability applications in military, avionics and
automotive areas, as well as in MCM's (Multi Chip Modules) for
telecommunications and computer applications. Recently, its
application has been expanded to the sensor and actuator area,
rendering a technology suitable for micro- system technology (MST)
at the meso-scale level from fifty microns to several millimetres
because its material system is compatible with hybrid
microelectronics, suitable for thermal, mechanical and electrical
properties, and easy to fabricate and inexpensive to process
[14,16]. LTCC technology can match all the requirements of
micro-systems such as: small size, low costs, short response time,
corrosion resistant materials, low power consumption, and high
temperature operation.
During fabrication every single layer can be inspected and in the
case of inaccuracy or damage it can be replaced before firing. This
prevents the need of manufacturing a whole new circuit. The
advantages of the LTCC are: cost efficiency for high volumes, high
packaging density, reliability, integrated and embedded passives
component (capacitors, inductors and resistors) in the LTCC, good
dielectric thickness control, high print resolution of conductors
and low K dielectric material.
3.3.2 Materials and process of LTCC
LTCC are glass-ceramic composites in the form of tapes. They are
also called green ceramic tapes because they are manipulated in the
green stage before firing and sintering. Tapes are easily machined
while still in the green stage before firing. They are soft,
pliable, and easily abraded, so it is possible to use mechanical
CNC, punching machines or laser methods. Once the material is fired
and fully sintered, it
3 Aim of research and some basic principles and concepts
18
becomes hard and highly rigid. The composite material includes a
ceramic filler, usually alumina, Al2O3, a glass frit binder to
lower processing temperature and an organic vehicle for binding and
viscosity control. This renders a material compatible with thick
film technology. Tapes are commercially produced in flat sheets of
various thicknesses in the range of 100 to 400 µm.
LTCC technology is based on the extension and improvement of
standard ceramic processing, multilayer technology and unique
design rules. One approach taken by such companies as DuPont,
Ferro, and Heraeus is to supply green tape as the raw material used
to make LTCC modules and the necessary design rules to those who
design and manufacture their own modules. Others, like Murata, have
chosen to develop materials, design rules, and manufacturing
processes in-house, and then produce functional solutions such as
LC filters, RF front ends, and complete radio modules.
The LTCC processing is very similar to that of HTCC without the
complex firing conditions, flattening fires and plating steps. The
process flow is shown in Figure 3.3.1. In the process flow, LTCC's
parallel processing capability facilitates rapid turnaround times
with reduced costs for packages and large layer counts.
Figure 3.3.1 Fabrication process flow of LTCC [48].
19
4 Design of the eddy current sensor
The purpose of optimization the design of a displacement sensor is
to select the optimal structure, suitable materials and operating
conditions so that the sensor has enough sensitivity and precision
with a size as small as possible to match the practical
application. Analytical methods can calculate the parameters of the
coil for a given structure for the unloaded case (without measuring
target). But, which structure with the proper L, R, and C
parameters can obtain better sensitivity depends on the interaction
of the coil and the target. This kind of interaction is
complicated. Therefore, the finite elements method (FEM) will be
used for simulation and design optimization because of its powerful
calculation ability.
4.1 General principle and design factors
During the process of sensor design, different factors that
influence the properties of the sensor such as the structure,
mounting position and material of the sensor measurement system are
analyzed and compared. The optimization objective is that the
optimal parameters of the whole sensor system should achieve the
best sensitivity under a given environment with stability and
feasibility. These factors, which affect the properties of the
sensor significantly, and some guidelines of design are sorted in
three types as follows [49,50].
The factors of the first type are determined by the coil itself and
are as follows: • Mounting position of the sensor relative to the
target • Geometric parameters of the coil such as thickness, turns,
etc. • Inductance and resistance of the sensor coil. The
requirement for a standard
design is that the unloaded quality factor Q is over 15 [13].
The factors of the second type come from the target itself, they
are: • The geometric factors such as area, flatness, and thickness
of the target • The material properties of the target, especially
conductivity and magnetic
permeability of the target. For example, high-conductivity,
nonmagnetic metals such as aluminum or copper are the best targets
because of the greater conductivity of the material, and the
greater flow of the eddy currents on the surface [13]. Therefore,
our optimization only takes into account good conductive metals as
target material with a constant relative permeability close to
1.
• Skin depth of eddy current: If the lateral dimensions of the
target are less than twice of the sensor diameter, the eddy current
distribution is difficult to predict
4 Design of the eddy current sensor
20
analytically [13]. Though these situations are difficult to model,
50 times of standard skin can be assumed reasonably as effective
thickness of the target for FEM analysis. The simulation results in
section 4.3.3.2 identify the correctness of this assumption.
Besides the sensor coil and target, environment factors must be
taken into account: • Operating frequency and resonant frequency.
The basic point is that the sensor
must operate below its resonant frequency as an inductor at all. •
Temperature of the target and the coil • Thermo-mechanical
properties for the reliability • Standoff between sensor coil and
target
In addition, the testing circuit and the signal acquisition system
must also be taken into account. Inductance, resistance, impedance
amplitude or phase, and some related parameters of the sensor are
all possible testing properties. The optimal parameter must be
selected from these as unique testing signal so that the
sensitivity of the sensor for the displacement measurement is best.
The testing circuit must convert it into a voltage or a current
signal for the process. The signal acquisition system must record
the clear signal and filter out the noise. In summary, all the
factors must be calculated and optimised so that the best
sensitivity of sensor can be obtained.
4.2 Analytical calculation of parameters of a LTCC coil
4.2.1 Analytic model of the LTCC coil for analytic analysis
As chapter 1 introduces, the design of a LTCC planar sensor was
selected as one of the main research objectives of this thesis. The
central component of our eddy current sensor is a planar LTCC coil.
In this chapter, the structural details of the planar coil will be
determined and its main parameters will be analyzed by an analytic
method.
According to its working principle, eddy current sensors belong to
the group of inductive sensors. The requirements of the coil are
high inductance, low capacitance and low resistance. The structure
of the coil must be designed in a way to match these
requirements.
Most of the conventional geometries for planar coils of single
layer (see Figure 4.2.1 (a) (b)) are meander-types or spiral-types
[51,52]. A meander-type inductor is simple to fabricate but it
suffers from low overall inductance because of the negative turn-
to-turn mutual inductance. A spiral type coil has a relatively high
inductance but its size is large compared to other coil types with
the same number of turns. Due to the
4.2 Analytical calculation of parameters of a LTCC coil
21
requirement of high inductance, the spiral type was selected for
the pattern of single layers. Because the number of the turns of a
single layer is limited for a given area, a structure of multiple
layers with the same solenoid direction and via fill connection
(see Figure 4.2.1 (c)) was finally selected. This geometric
structure of the LTCC coil matches the requirements for high
inductance and small size. However, the serious drawback of a
multi-layer structure is that this structure introduces a high
stray capacitance and furthermore induces a resonant status of the
coil at its self-resonant frequency. Therefore, parameters of the
coil must be calculated so that the operation properties of the
coil can be evaluated.
(a) (b) (c) Figure 4.2.1 (a) Simplified schematic of a meander-type
inductor; (b) a spiral-type inductor; (c) a solenoid multiplayer
coil.
Analytic calculations can provide electric parameters of a LTCC
sensor coil. These include inductance, self-capacitance,
resistance, self-resonant frequency (SRF), skin depth and so on.
These parameters are essential for the design of a LTCC coil. The
model structure used for the analytic calculation is illustrated in
Figure 4.2.1 (c). In this model, the conductor is composed of many
spiral-like thin rectangular films in three dimensions and its
material is the metal compatible with LTCC fabrication. Therefore,
some special formulas for inductance calculation of strips are used
which are different from those for normal solenoid coils. The
limitation of an analytic calculation is that it can evaluate only
the static parameters of the sensor coil itself. As for the
properties of sensor coils which are concerned with frequency and
temperature dependence, we will utilize the finite elements method
(FEM) using the software ANSYS because of the complexity of the
sensor structure and the difficulty of solving the equations of an
analytic calculation. For all the calculations of parameters the
influences of via fill were neglected because its geometric size is
very small compared to the thin strip in a planar coil.
4.2.2 Inductance calculations
Firstly, the inductance of the sensor coil is calculated. The
inductance is a peculiar property of a coil which only relates to
its structure. This parameter is the most
4 Design of the eddy current sensor
22
important parameter of a sensor coil because it determines the
inductive ability of an inductor coil [53].
The total inductance of a coil is the sum of the self-inductance
being generated from every conductive metal strip separately and
mutual inductance due to interaction of two strips in different
turns or layers.
4.2.2.1 Self-inductance
In this section, the self-inductance of a planar coil made of
non-magnetic conductor is calculated. The basis of the calculation
is Greehouse’s formula [54] (see Equation (4.1)) which calculates
the self-inductance of a thin strip as shown in Figure 4.2.2.
Lself = 2l(ln tw
nH (4.1)
where Lself is the self-inductance in nH; l is the length of the
conductor in cm; w is the width of the conductor in cm; and t is
the thickness of the conductor in cm.
Figure 4.2.2 Illustration of geometric parameters of a single
conductor strip.
Because the thickness t and width w is the same for every strip of
the coil, we only need to input different lengths of strip from lo
to li in x direction and from wo to wi in y direction with the
number of turns N to the Greehouse’s formula (Equation (4.1)) for
different strips. Here, N describes the number of turns of the coil
in one layer. By summing up these separate values, about half
self-inductance of coil in one single layer (see. Figure 4.2.3) was
obtained. In fact we needn’t input different lengths of the strip
individually because there is a regulation between them. This
regulation is:
ln=li+(n-1)•P,
where n=1, 2, …, N, and means nth turn; P is twice of the sum of
pitch pt between two strip and the width of the strip.
4.2 Analytical calculation of parameters of a LTCC coil
23
Figure 4.2.3 Top view of the LTCC coil which is designed and
fabricated (see section 4.4.3).
We assume that the coil has mirror symmetry and the patterns are
the same in each layer. Therefore, to multiply the sum of above by
the number for symmetry and the number of layers K, the total
self-inductance of one whole coil is obtained from the equation
shown as follows,
Ltotal-self =∑ =
N
1 )( *2*K (4.2)
where i is the number of the turn; N describes N pieces of strips
in long side and wide side of the coil respectively.
Using the design shown in Figure 4.2.3 as an example, the numerical
parameters can be found in Table 4.15, which are K=12, N=16,
w=pt=131.7 μm, t=10 μm, lo=15.8 mm, wo=8.76 mm. Using all the
values and the equation above, the final total self- inductance of
the whole coil Ltotal-self is 15.370 μH.
4.2.2.2 The mutual inductance
The basic theory of the calculation of mutual inductances is the
formula for calculating the mutual inductance between two single
strips in the same layer or between different layers. Two formulae
are used and compared. One is Hoer’s formula, and another is
Grover’s formula. The main difference between them is whether it
takes the thickness of the strip into account or not. We will
introduce them individually.
4 Design of the eddy current sensor
24
Method 1—Hoer’s formula (for 3D geometric structure)
The geometric model of Hoer’s formula is shown in Figure 4.2.4. 3D
geometric dimensions including the thickness of strip t are all
taken into account. Dx, Dy, Dz describe the relative position of
two strips. When two strips are parallel in the same layer, Dx is
zero. When two strips are parallel but not in the same layer and
turn, Dz=(l1-12)/2. When two strips are in the same turn but in
different layers, Dy=0 and Dz=0. These three cases cover all
situations for mutual inductance calculation of a planar
coil.
ll
Conductor 1
Dz Dx
Figure 4.2.4 3D geometric model of two strips for Hoer’s
formula.
The formula referred to this model is as follows [55]:
)()()(tan 6
tan 6
tan 6
)333( 60
25
where ] ] ] ∑∑∑ = = =
q q srqfzyxzyxf .
We will then use this formula to calculate the mutual inductance in
the three situations referred to before. In the first step, we
calculate the mutual inductance between two strips in one layer
which means Dx=0. The mutual inductance exists in signed positive
and negative values. When current flows in two strips are the same,
the value of the mutual inductance is positive, whereas, when the
current flows are opposite, the value is negative.
Figure 4.2.5 Illustration of a spiral coil with mark for direction
of current flow.
When it was assumed that the calculating sequence is from out side
to inside, positive mutual inductance reads M+= M1,5+M3,7+M2,6+M4,8
in y-z plane, and the negative mutual inductance reads
M-=-M1,7-M1,3-M5,7-M5,3-M5,7-M2,4-M2,8-M6,4-M6,8,
where Mi,j means the mutual inductance between ith turn and jth
turn.
The number of positive mutual inductances is 2N(N-1), and the
number of negative mutual inductance is 2N2. Summing up M+ and M-
and multiplying the result by the number of layers K, the mutual
inductance of the whole coil due to the interaction of strips on
the same layer was obtained.
With the same method, we can calculate the mutual inductance due to
the interaction of the strips on different layers illustrated in
Figure 4.2.6. When we exclude the interaction of two strips having
the same number of turn such as the interaction between the 1st
turn in the top layer and the 1st turns in the 2nd layer, the
calculation sequence and the numbers of positive and negative
mutual inductances for the strips on two layers are the same as
that for the calculation of one layer case but with Dx ≠0. In the x
direction being the normal direction of the layers, all mutual
inductances for different assemblies of two layers must be
calculated. For example, the 1st layer can be connected to 2nd
layer, 3rd layer, until the Kth layer, and the (K-1)th layer only
can be connected to Kth layer. The number of calculations of two
layers is K(K-1)/2. The
4 Design of the eddy current sensor
26
total number of calculations for two strips is N(N-1)K(K-1) for
positive mutual inductance and N2 K(K-1) for negative values.
Figure 4.2.6 Illustration of coils in different layers.
Finally, we calculate the case of two strips in the same turn but
in different layers. In respect of this situation, the mutual
inductance between two strips is always positive, and the number of
individual values is 2NK(K-1).
Summing up all the values for the three situations, the total
mutual inductance of the whole coil is obtained. Because the basic
formula is complicated and the calculation number is large, a
program under the software Mathematica is used for computer
calculation.
Using the same model (see Figure 4.2.3) as that in the last section
and one new parameter Ph=96,36 μm, which is the pitch between two
layers, we obtained the total mutual inductance of this coil which
Mtotal is 232 μH.
Method 2—Grover’s formula (for filament structure)
For Grover’s formula, the geometric model is shown in Figure 4.2.7.
The thickness and the width of the strip were neglected so that the
strip is regarded as a filament. For the two strips in one layer,
it is d=0. When two strips are parallel but not in the same layer
and turn, d is the absolute distance between two centers of the
strips. When two strips are in the same turn but in different
layers, d is the perpendicular distance of the two layers.
Especially, δ is always negative with the value of
−(l1+l2)/2.
4.2 Analytical calculation of parameters of a LTCC coil
27
Figure 4.2.7 General position of two conductors (filament) for
Grover’s formula.
Grover’s formula reads [55]:
]
where
sinh-1(x)=ln(x+ 12 +x ), α=l+m+δ, β=l+δ, γ=m+δ.
Νote that in the case when the two conductors are overlapped then δ
is negative.
With the same calculation procedure as for Hoer’s formula, the
total mutual inductance of the same coil is obtained: Mtotal= 194
μΗ. Of course, the parameters w and t are dispensable.
Finally, the self-inductance and mutual inductance are summed up
for the total inductance of the coil. The value of the inductance
is as follow:
Table 4.1 The inductances calculated by three formulas
Lself (μH) Mtotal (μH) Ltotal (μH)
Hoer: 232 247.37 Greenhouse: 15.37
Grover: 194 209.37
Comparing the two formulae for calculation of the mutual
inductance, the Hoer’s formula achieves a better precision but is
more complicated and needs more computation time.
4 Design of the eddy current sensor
28
4.2.3 The DC resistance of the coil
An ideal inductor coil would have no resistance and no capacitance.
For a planar coil, the resistance is relatively large, because the
cross sections for current flow are very narrow. The resistance of
the coil is a very important factor affecting the quality factor Q
of the coil. It also can lead to energy dissipation of
electromagnetic field. The basic equation for the resistance
calculation of a conductor is as follows:
ρρ wt l
A lR == (4.5)
where l = total length of the coil windings; ρ = resistivity of the
coil material; w = width of trace of a coil ; t = thickness of
traces in a coil .
According to the coil model used in Figure 4.2.3, the length of the
strip on one layer is Lsingle = (lo+li+wo+wi)N=0.523 m. Therefore,
the total length of the strip in the whole coil (l) is equal to
lsingle·K, which is 6.27 m. The conductor material of this LTCC
coil is silver, and ρ =1.6·10-8 Ωm. Then the resistance of a single
layer is Rsingle=6.4 Ω, and the resistance of the total LTCC coil
is R=76.6 Ω.
Compared to the value offered by the manufacturer of this LTCC coil
that is 6.5Ω per single layer and 83 Ω in total, the analytical
value is close to this reference values. The difference in the
total resistance mainly comes from the contribution of via fills
because the analytical value of the resistance in a single layer is
better matched with the measured one than that of the total
coil.
4.2.4 Capacitance calculation
Normally, capacitance is defined as the ability to hold charge by a
pair of conductors separated by empty space or by a non-conductor.
For an ideal straight conductor, there is no capacitance. But for a
coil or an inductor, it has normally some stray capacitance because
of its spiral, meander, or solenoid structure and the interaction
between the coil and its surroundings such as its core or
substrate. The capacitance interacts with the inductance of the
coil and induces a resonance status at self- resonant frequency.
Hence, the working behavior of the coil will be changed.
The stray capacitance of a coil is a result of three mechanisms
[51,52,56,57].
• When a single layer inductor works, a lead wire is required to
connect the inside end of the coil on the top layer to the outside,
which introduces an
4.2 Analytical calculation of parameters of a LTCC coil
29
unnecessary capacitance between the conductors and the lead wire.
This is the first kind of capacitance source.
• Then the second type of stray capacitance is the capacitance
between conductor layers and its resistive substrate or ground
plane.
• The third kind of capacitance is between two conductor strips of
the coil itself on the same layer or on different layers.
According to the LTCC coil model used before, the conductor is a
thin metal strip and the structure is a spiral coil of multiple
layers without a ground metal plane. The LTCC substrate is a
material of low dielectric constant and permittivity and good
insulation properties. Because of the special structure and
material properties, the separate lead wire does not exist because
it is only a part of the conductor on the bottom layer, and the
influence of substrate or ground is also not existent. So, the
first two kinds of capacitance for coils which are induced by the
interaction of conductor-to-lead wire and layer-to-substrate or
ground are neglected and the third type of stay capacitance is
focused on
In fact the capacitance between two turns on the same layer also
can be neglected. The reason can be explained by a physical model
for the capacitance of this LTCC coil shown in Figure 4.2.8.
Figure 4.2.8 Equivalent physical model for calculation of the stray
capacitance between conductor strips shown in the cross-sectional
direction of a coil.
4 Design of the eddy current sensor
30
According to the basic Equation (4.6) [28] for capacitance,
calculation of two parallel planar conductors (see Figure 4.2.9)
yields:
d
lw
d
A C err εεεε 00 == (4.6)
where εr = relative dielectric constant, namely relative
permittivity (a dimensionless number; 4.2 for FR-4 PC board, 7.8
for LTCC at 10 MHz ), ε0 = dielectric constant of free space
(8.8542 · 10-12 F/m), d = distance between the center of two planar
conductor surface (meters), A= effective interacting area (m2), l=
length of strip; we= effective width of strip.
The capacitance is direct proportional to the effective area of two
conductors and inverse proportional to their distance. With this
equation, the capacitance of two turns on the same layer such as
Turn1 and Turn2 in Figure 4.2.8 is much less than that of two turns
on different layers such as Turn1 and Turn4 because the interacting
width t=10 μm of Turn1 and Turn2 is about 7% of that w=150 μm of
Turn1 and Turn4, and the distance pt=150 μm between Turn1 and Turn2
is about 1.5 times of that ph=100 μm between Turn1 and Turn4.
Therefore, the capacitance between two conductors on the same layer
can be neglected by setting Ct =0 for simplification of its
physical model. Further more, the resistance R connecting two turns
on the same layer is small, and R=0 is assumed for simplification
of the physical model.
Figure 4.2.9 Geometric model of a pair of parallel planar
conductors.
With these assumptions, the physical model can be converted to a
PSPICE electronic circuit model shown in Figure 4.2.10. In the DC
electronic circuit with passive components consisting of pure
capacitors or resistors, the serial and parallel relation for two
resistors is the inverse of that for two capacitors. The symbol of
capacitance between two different layers can be described as
resistor, but the inverse of the resistance value is the final
value of capacitance, that is C~1/R in the unit F. The
4.2 Analytical calculation of parameters of a LTCC coil
31
capacitance of grade 1 is defined as the capacitance between two
layers which are adjacent to each other such as layer 1 and layer
2. For example, R7 is sum of capacitances of two turns between the
adjacent layers such as Cturn1,turn4, Cturn2,turn5, Cturn1,turn5
and is sorted to capacitances of grade 1. The capacitance of grade
2 is defined as the capacitance between two layers which has an
interval of 1 layer such as layer 1 and layer 3. For example, R11
of grade 2 shown in Figure 4.2.10 is the sum of capacitances of two
turns between layer 1 and layer 3 such as Cturn1,turn8,
Cturn2,turn7. The rest may be deduced by analogy. We just calculate
until capacitances of grade 4 because the distance between two
layers is far enough to further neglect values of capacitance. For
a circuit only with capacitors as passive components, it is
ωω
R
CI
V ==
1 . When we add a reference resistor with the value of 1pΩ and
apply
the voltage of 1 volt to V , 16
16
VC R
V
R
V =≈
16
16 and C=V16·1012 (pF). The result is computed by the circuit
simulation
software PSPICE. V16 is equal to 15.13 pV and the capacitance of
the whole coil Ctotal
is 15.13 pF according its converting relation with V16.
R13
18.27m
R18
18.27m
R24
174m
R26
174m
464.5mV
171.2mV
R28
174m
R39
173.92m
337.3mV
R12
174m
R7
18.27m
R23
18.27m
605.5mV
R3
173.87m
0V
729.4mV
V1
1Vdc
0
R5
173.87m
R17
18.27m
R8
18.27m
R31
173.87m
R33
173.92m
535.5mV
15.13pV
R37
173.92m
R9
18.27m
R2
173.87m
R25
174m
R21
18.27m
828.8mV
R15
18.27m
270.6mV
R34
173.92m
R27
174m
R30
173.87m
R35
173.92m
394.5mV
R16
1p
R14
174m
R29
173.87m
R22
174m
R4
173.87m
R10
18.27m
1.000V
R20
18.27m
R1
173.87m
R32
173.92m
R38
173.92m
R11
174m
662.7mV
R6
173.87m
R36
173.92m
Figure 4.2.10 Simplified electronic circuit model for the stray
capacitance of the whole coil with N=12 layers.
4 Design of the eddy current sensor
32
So far, the three parameters concerning DC impedance of the coil,
which are inductance, capacitance and resistance, were obtained.
According to these basic parameters, a whole electronic model of
the sensor shown in Figure 4.2.11 can be built. Some other
parameters concerning the operating properties of coils at high
frequency can be further obtained as follows.
sensor
L
C
R
4.2.5 Quality factor, skin depth, self-resonant frequency
4.2.5.1 Quality factor (Q)
)(
xLxQQ ω == (4.7)
where Q is the quality factor (no units), ω is the operating
frequency of the coil in radians per second, L is the inductance of
the coil (in H), R is the total resistance associated with energy
losses (in Ohms).
Q depends on the standoff x between the sensor and the target,
because both L and R are functions of the displacement. The higher
the value of Q is, the stronger the effect of inductance is and the
weaker the effect of resistance is. A high Q leads to high accuracy
and stability.
For example, in the coil with geometric sizes shown in Table 4.15,
its inductance is 247 μΗ and the resistance is 83 Ω. We find that
the unloaded quality factor Q is 19.9 at 1 MHz according to the
equation above. This Q matches the requirements [28] that the
unloaded Q must be over 15 for a typical design of the eddy current
sensor. It means that the design of this coil is qualified for the
requirement of electronic parameter Q.
4.2 Analytical calculation of parameters of a LTCC coil
33
4.2.5.2 Skin depth
Skin depth is defined as the characteristic penetration distance
which a plane wave travels through a conducting medium. For the
eddy current measurement system, the depth that eddy currents
penetrate into the target is affected by the frequency of the
excitation current and the electrical conductivity and magnetic
permeability of the specimen. The depth of penetration decreases
with increasing frequency and increasing conductivity and magnetic
permeability. The depth at which the eddy current density has
decreased to 1/e or about 37% of the surface density, is called the
standard depth of penetration δ (see Equation (4.8)) [13,41].
δ = σωμ
2 (4.8)
where δ : skin depth (meters), ω : radian frequency
(radians/second), μ : magnetic permeability (H/m), e,g.
non-magnetic metal, μ=μ0·μr=1.26·10-6H/m, σ : conductivity
(Siemens/meter),e.g. copper’s is 5.78·107S/m. Table 4.2 Skin depth
δ for various metals and frequencies
Skin depth (µm) Metal Conductivity (106 S/m)
Resistivity (10-8Ωm)
Copper 58 1.73 660 210 66 21
Aluminum 38 2.6 820 260 82 26
Titanium Alloy 0.59 16.9 6600 2100 660 210 The skin depths for
several nonmagnetic metals at various frequencies are listed in
Table 4.2. For example, the skin depth of copper at 10 kHz is
roughly 0.66 mm. Although the whole eddy currents in target
penetrate deeper than one standard depth of penetration, they
decrease rapidly with the depth of the target (see Figure 4.2.12).
Therefore, the effective part of target for the measurement by the
eddy current sensor is only the tip of the target. When we build a
simulation model with an exciting frequency of over 10 kHz for a
copper target, 50 times of skin depth tip should be enough. That is
about 30 mm.
4 Design of the eddy current sensor
34
Figure 4.2.12 Illustration of skin depth for inductive eddy current
[41].
4.2.5.3 Self-resonant frequency (SRF)
As shown before, any inductor exhibits stray a capacitance between
windings. This capacitance in conjunction with the inductance forms
a "self resonant frequency" for the loop or inductor. The frequency
where the inductance peaks is called the self- resonant frequency
(SRF). It is defined as [13]
)(2π
SRF +
= (4.9)
where Ciwc is the inter-winding capacitance or stray capacitance of
the coil, and Ccable is capacitance per unit length from the cable
length and the manufacturer's specification.
For example, in the coil (see Figure 4.2.3) that is the example for
LRC calculations, having an inductance of 247.37 μΗ and a
capacitance of 15.13 pF, we find that the SRF is 2.60 MHz. The
exciting frequency must be below this frequency for an inductive
eddy current sensor.
4.3 Design and optimization of the eddy current sensor
35
In summary, the basic structure of a spiral pattern with solenoid
structure for the LTCC plane sensor coil was determined. For this
kind of coil, a set of analytic formulas was defined. Using these
methods, very important static unloaded frequency dependent
parameters L, R, C and Q, δ, SRF can be calculated and the matching
for the related requirement of a suitable eddy current sensor can
also be evaluated. However, the analytic method can only evaluate
the feasibility of a sensor coil alone when the geometric sizes of
the coil are given. With respect to the interaction between the
sensor and the target, and the optimal geometric sizes for
sufficient sensitivity of the sensor, computer simulation must be
carried out.
4.3 Design and optimization of the eddy current sensor
4.3.1 FEM simulation
In the field of engineering design, when complex problems are
encountered, of which the mathematical formulation is tedious and
its solution is impossible by analytical methods, numerical
techniques must be used. FEM is a very powerful tool for getting
the numerical solution of a wide range of engineering problems. The
basic concept is that a body or structure is divided into smaller
elements of finite dimensions called “Finite Elements”. The
original body or structure is then considered as an assembly of
these elements connected at a finite number of joints called as
“Nodes” or “Nodal Points”. The properties of the elements are
formulated and combined so that to obtain the properties of the
entire body.
The software package ANSYS/Multiphysics is a popular FEM solution
tool. It can provide advanced coupled physics technology, combining
structural, thermal, acoustic and electromagnetic simulation
capabilities in a single software product and its applications
involves many respects from rotating machines (motors and
alternators), sensors and actuators, power generators and
transformer systems, and Micro Electro Mechanical Systems (MEMS).
Therefore, ANSYS was chosen as the main tool for the FEM analysis
of the eddy current sensor. Three functions of ANSYS, modal,
harmonic electromagnetic and thermal-mechanical analysis, are
utilized in our work.
For the optimization of the eddy current sensors, a comprehensive
analysis method based on FEM concerning multiple aspects such as
vibration of blades, interaction between the sensor coil and the
target and the thermo-mechanical reliability was developed. Figure
4.3.1 shows the whole process of optimization of the sensor. First,
the modal analysis for the vibration mode of a blade was done. In
order to find the optimal mounting position, a model of the whole
system including target and sensor was built and their interaction
was investigated by electromagnetic (EM) calculation to find an
optimal structure and exciting conditions. This structure was
converted to a
4 Design of the eddy current sensor
36
LTCC model and its thermo-mechanical reliability was evaluated.
Meanwhile, the impedance change of a sensor with different
displacement of the target was analysed. The results can be used by
some mathematic softwares such as Matlab, Mathmatica to evaluate
the sensitivity. On the contrary, when reliability and sensitivity
of the sensor is not sufficient, EM simulation must be repeated in
order to offer better results for other types of analysis.
Therefore, all steps in the whole process of optimization are
interlinked and must be taken into account together. The analysis
details will be addressed in the next section.
-80 -60 -40 -20 0 20 40 60 80 0
20
40
60
80
100
Re
8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8
x 10 -4
4.3.2 Optimizing the sensor location - modal vibration
simulation
In this section, the object of modal simulation analysis is the
vibration of the target blades. From the optimization point of
view, the mounting position of sensor must be decided first.
Because we want to monitor the movement including the vibration of
the blades, the sensor should be mounted at the position where it
can detect the largest vibration amplitudes of the blades. The
vibration of a blade is very complex, but it can be composed of
many basic vibrational modes at different frequencies. Therefore
the mode shapes are analyzed by modal analysis for different
resonance frequencies in order to find a proper position where the
amplitude is large for many
Concept of the simulation
37
modes of vibration. This location is considered as the optimal
mounting position for the sensor.
For the FEM model, two kinds of shapes of the tip surface, the
shark shape and rectangle shape, are analyzed (see Figure 4.3.2).
The 3D model reflects the actual turbine blade product and its
material is Titanium. The width of the blade is 30 mm, the
thickness is 2.5 mm, and the length is 100 mm. One end of the blade
is constrained without movement and the other end is free. From the
analysis results, the first 15 modes are extracted from a frequency
of 4.83 Hz to 338 Hz with the subspace method.
Figure 4.3.2 FEM model of blade with two different end
shapes.
Figure 4.3.3 shows the results of mode shape. The colour labels
describe the scale of deformation and the text offers the
information on various natural frequencies corresponding to the
number of the sub-step. According to these results, for most modes
of vibration of the blade, the largest deformation occurs in the
point that lies at the end of the blade tip. Therefore it can be
concluded that the reasonable mounting position of a sensor should
be just over the sharp end of the turbine blade as shown with a red
arrow in Figure 4.3.3. For the shark shape, there is only one
optimal mounting position for the sensor, and for a rectangular
shape there are two optimal positions because of the mirror
symmetry of the blade. This conclusion is very important for the
situation that the width of the blade is far longer than the size
of the sensor coil. The whole rotor integrating individual
vibration mode of blades shown in Figure 1.1 also can be obtained
using its cyclic symmetry.
4 Design of the eddy current sensor
38
Figure 4.3.3 Vibration modes of the blade at different natural
frequencies in Hz, (note: figures with blue border show the blades
with tip of rectangle shape, the rest show the blades with tip of
shark shape).
sub=1 f = 4.846
sub=14 f = 331.8
sub=10 f = 238.13
sub=5 f = 79.858
sub=3 f = 35.006
sub=2 f = 34.778
sub=6 f = 101.85
sub=6 f = 110.12
39
4.3.3 Optimizing the sensor sensitivity-EM evaluation
The harmonic electromagnetic analysis was done to calculate the
electromagnetic field that interacts between sensor coil and target
blade. Through harmonic electromagnetic analysis (EMAG in ANSYS),
some useful electromagnetic properties of turbine blade and coil
are obtained, such as the eddy currents on the turbine blade, the
electromagnetic field distribution, the impedance and the
inductance. Hence, the results can identify the working principle
of the eddy current sensor and evaluate its sensitivity. 2D and 3D
analyses are used individually for their different application
field.
4.3.3.1 2D simulation
The 2D electromagnetic analysis is applied in the case of axial
symmetry. For the eddy current measurement system, two situation
with target and without target can be investigated for the
horizontal displacement evaluation. The relation between the
sensitivity of the sensor and some influence factors for 2D
simulation can be investigated. In addition, the relation between
the impedance of the sensor and the clearance between the sensor
and the target is obtained.
First, we build a reference structure according to some simple
evaluations (see Table 4.3). Then, the influence factors are
changed and the resulting sensitivity is compared with that of the
reference model so that one can get the optimal parameters for the
influence factors. Finally, a detailed relationship between
impedance and the clearance is obtained.
Table 4.3 Simulation parameters and their results
Material part material ρ (10−8 Ωm) μr coil Ag 1.60 1
target Cu 1.73 1 Geometry
ro (mm) ri (mm) Height h (mm) fill factor turns coil 5 0.2 1 1/20
200 l/2 (mm) thickness (mm) gap (mm) target
2.5 5 1 Electrical conditions
f=1 MHz voltage=5 V Results R0(Ω) L0(μH) Rs(Ω) Ls(μH)
0
0
R
40
The FEM model is composed of an exciting coil forced by voltage,
turbine blade, near field air and far-field infinite air (see
Figure 4.3.4(b)). Element type is plane53 with voltage-fed or
current–fed, and element INFIN111 is used for define infinite
far-field air shown in out-layer of the FEM model. The results in
the form of 2D flux (see Figure 4.3.4(a)(c)) present clearly the
influence of the target to the electromagnetic field. All
parameters and results are listed in Table 4.3.
(a) (b) (c) Figure 4.3.4 (a) results of 2D flux when there is a
target; (b) 2D EM model; (c) ) results of 2D flux without target
when target material was set as air.
For the calculation of the impedance of the sensor coil, ANSYS can
offer an inductance Ls and an unloaded resistance R0 calculated by
its geometric structure. Also, ANSYS can provide the real part
Re(I) and imaginary part Im(I) of the current through the coil.
Hence, we can obtain the inductance and the resistance of the whole
system through electric circuit equation because the voltage
applied to the coil is fixed. The related calculation principles
are as follows:
Current I=Re(I)+jIm(I), Impedance Z=Rs+jωLs
Because of Z=V/I=V/ [Re(I) +jIm(I)], θ= tg-1[(Im(I)/Re(I))], the
loaded impedance values of sensor coil can be obtained as:
Rs= 22 Im(I))(R +Ie
V sinθ
At the same time, the sensitivity of the sensor in the case of
target existence was define as:
4.3 Design and optimization of the eddy current sensor
41
0
0
R
0
L
LLs − × 100% is for inductance
where the subscript note 0 means unloaded, and s mean loaded.
Sequentially, the various influence factors on the sensitivity are
changed and compared to the results of the reference system. First,
the exciting source was investigated. Table 4.4 shows the
difference of results by this kind of comparison. Table 4.4 The
comparison between various exciting sources for the coils with
reference structure
Results Reference conditions f=1 MHz,Voltage U=5 v
f=2 MHz f=0.5 MHz U=10 v f=1 M
U=1 v f=1 M
R0(Ω) 43.56 43.56 43.56 43.56 43.56
L0(μH) 127.43 127.43 127.43 127.43 127.43
Rs(Ω) 48.76 51.24 47.13 48.76 48.76
Ls(μH) 112.82 112.57 113.17 112.82 112.82
0
0
R
0
0
L
LLs − (%) 11.5 11.7 11.19 11.5 11.5
According to these comparisons, some conclusions about the exciting
source are obtained. The sensitivity of the resistance and the
inductance both increase with exciting frequency increasing. Higher
exciting frequency can obtain better sensitivity. Whereas, they
have no relation with the amplitude of exciting source, therefore,
we can choose any voltage value according to the data acquisition
requirement.
In the next step, the structure and material of the target become
the comparing objects. The results are shown in Table 4.5.
Comparing the change of sensitivity because of different target
material, some conclusions about the influence of resistivity of
the material can be obtained. The loaded resistance and inductance
of the sensor coil increase with the target material resistivity,
but their changes are not proportional to the change of
resistivity. For example, when resistivity is 1.5 times and 23
times to the reference value, the resistance changes 2% and 30%
respectively, and the inductance changes only 0.17% and 3%. The
resistivity influence on the resistance of eddy current sensor
coils is much larger than the influence on the inductance, but all
the change is far smaller than the change of resistivity
itself.
4 Design of the eddy current sensor
42
Table 4.5 The influence of the change of materials of target on the
sensor sensitivity
Results Refer. condition Cu-ρ=1.73·10-8 Ωm
Al-ρ=2.6·10-8 Ωm Ti-ρ=40·10-8 Ωm
R0(Ω) 43.56 43.56 43.56 L0(μH) 127.43 127.43 127.43 Rs(Ω) 48.76
49.82 63.46 Ls(μH) 112.82 113.01 116.05
0
0
R
LLs − (%) 11.5 11.3 8.93
In this part, the geometry of the target is also considered. The
thickness of a target does not influence the impedance of the
sensor when it meets the requirement that the thickness of the
target must be over 50 times of the skin depth as discussed in
section 4.1. This point can be identified by the results on the 2D
flux. The width of the target will influence sensitivity seriously.
The relation between the width of the target and the sensitivity of
the sensor coil is shown in Figure 4.3.5. When the size of target
is smaller than twice of the size of the sensor coil, the
sensitivity of inductance decreases with the decrease of the width
of the target quickly. For the sensitivity of the resistance, the
influence of the width of the target is less than that of the
inductance, but when the width is smaller than 1.6 times of the
size of the sensor, the sensitivity change of the resistance of the
sensor is also very large. Therefore, for the displacement
measurement of a narrow blade, evaluation of its sensitivity before
the fabrication is very important.
2 4 6 8 10 12 14 16 18 0 2 4 6 8
10 12 14 16 18 20 22 24 26 28 30
Se ns
iti vi
%
W id th o f ta rg e t / m m
R e s is ta n ce se n s tiv ity
in d u c ta n ce se n s tiv ity
Figure 4.3.5 The relation between width of target and sensitivity
of sensor coil.
Next, the parameters concerning the sensor coil are investigated.
These parameters include coil fill factor, turns, the width and
thickness of conductor film, and the width and thickness of the
whole coil. In fact, these structural parameters interact with each
other. For example, when the thickness of the coil is constant, the
change of the coil fill factor leads to a change of the width and
thickness of the conductor
4.3 Design and optimization of the eddy current sensor
43
film. Table 4.6, Table 4.7 and Table 4.8 show the influences of
coil geometry on the sensitivity of the sensor. Table 4.6 The
influence on impedance and sensitivity of sensor because of the
size changes of conductor film and layer numbers when outer size of
coil is constant
Results Reference turns=200 fill=1/20
Fill1/10
Fill1/40
narrow film
thick layer wide film
R0(Ω) 43.56 21.78 87.12 65.34 21.78 L0(μH) 127.43 127.43 127.43
286.72 31.86 Rs(Ω) 48.76 26.97 92.31 77.03 23.08 Ls(μH) 112.82
112.82 112.82 253.85 28.20
0
0
R
0
0
L
LLs − (%) 11.5 11.5 11.5 11.5 11.5
Q0 18.38 36.76 9.19 27.57 3.39
According to Table 4.6, we know that the size of the conductor film
such as its thickness and width cannot influence the inductance
sensitivity of the sensor, but changes the resistance sensitivity
of the sensor much. When the number of turns of the coil increases,
resistance and inductance both increase, but the sensitivity of
inductance does not change. Therefore, the conclusion can be drawn
that the changes in a coil such as size of the conductor film or
the number of layers can not affect the sensitivity of inductance
although the absolute values of the inductance and the resistance
are changed much when the outer size of the whole coil is given.
Table 4.7 The influence on impedance and sensitivity of sensor when
height of coil changes
Results Refer. conditions h=1 mm,fill=1/20,
turns=200
H=0.5 mm Fill=1/10 thin layers
R0(Ω) 43.56 65.34 21.78 43.56 L0(μH) 127.43 265.7 34.56 138.24
Rs(Ω) 48.76 74.64 23.43 50.17 Ls(μH) 112.82 239.39 29.94
119.74
0
0
R
0
0
L
4 Design of the eddy current sensor
44
According to Table 4.7, the height of the sensor coil can influence
the sensitivity of inductance. The thinner the coil is, the better
the inductance sensitivity of the sensor will be. The height of the
coil is the only factor that can influence the sensitivity of the
inductance although other parameters can change the value of the
inductance. When the height is given, the influence of other
parameters such as layers, turns, fill factor etc. appears to be
the same as shown in Table 4.6. Here, the quality factor is
considered because the height cannot decrease infinitely by
decreasing of the number of turns of the coil. The quality factors
should meet its requirement of greater than 15 as discussed before.
Therefore, to make the layer as thin as possible, it is a better
method to decrease the height of the coil.
Table 4.8 The influence on impedance and sensitivity of sensor when
surface area of coil changes
Results Refer. conditions ro=5 mm, ri=0.2 mm
ri=1 mm narrow
ro =4, small coil
ro =6 mm ri =1.2
R0(Ω) 43.56 60.32 42.99 44.45 60.32 L0(μH) 127.43 177.46 154.89
100.11 218.62 Rs(Ω) 48.76 67.44 48.36 48.96 67.71 Ls(μH) 112.82
157.39 139.09 87.98 196.91
0
0
R
0
0
L
LLs − (%) 11.5 11.3 10.2 12.12 9.93
Q0 18.38 18.48 22.63 14.15 22.77
According to Table 4.8, a big coil cannot bring good sensitivity of
inductance. This conclusion is the same as that comes from Figure
4.3.5. The sensor coil with the size similar to that of the target
has better sensitivity of inductance than the one having bigger
size than that of target. In addition, smaller inner radius of
sensor can bring a better sensitivity of the inductance and
resistance. Therefore, the sensor coil should be as small as
possible and be filled as full as possible in area of whole sensor
for the good sensitivity of inductance.
In respect of the coil material, the change of resistivity can
change the resistance of a coil but cannot change the unloaded
inductance of the coil. According to the principle of
electromagnetic induction, it does not change the exciting field,
and the inductive field also does not change for the same target.
Hence, the loaded inductance of the sensor does not change, but the
resistance and its sensitivity change. Table 4.9 identifies this
analysis.
4.3 Design and optimization of the eddy current sensor
45
Table 4.9 The influence of the coil materials on the sensor
sensitivity
Coil/ρ 10-8Ωm
Au 2.2
Pt 10.6
288.61 127.43 293.80 112.82 1.8 11.5 2.77
Finally, the clearance between sensor and target is evaluated.
Figure 4.3.6 shows the resistance and inductance of a sensor coil
dependent of the clearance between sensor coil and target. Except
the parameter of clearance, all other parameters and conditions are
the same as those of the reference model shown in Table 4.3. These
curves can demonstrate the measurement principle of eddy current
sensor for proximity of target. When the proximity changes, the
inductance and resistance of coil both change. The change
tendencies of inductance and resistance are opposite and the change
rate of the inductance is larger than that of the resistance.
0,5 1,0 1,5 2,0 2,5 3,0 0
20
40
60
80
600
700
800
Resistance Inductance
Figure 4.3.6 Resistance and inductance of sensor coil dependent of
proximity between sensor coil and target.
In summary, 2D EM simulation identifies the measurement principle
of the eddy current sensor for proximity of the target and some
important properties such as the influence on the sensitivity from
the width of target, and the influence from the materials of coil
and target. With respect to the improvement of the inductance
sensitivity, only structures of whole coil such as thinner, smaller
and full coil and increasing frequency can be implemented. For the
sensitivity of the resistance of the coil