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
Dekan: Prof. Dr. J.G. Korvink
Referenten: Prof. Dr. J. Wilde, Prof. Dr. C. Ament
Datum der Promotion: 22. 03. 2005
To yongfeng
CONTENTS
1 Introduction ...... 1
2 State of the art...... 5 2.1 Importance of and developments in blades vibration monitoring ...... 5 2.2 Conventional displacement sensors...... 6 2.3 High temperature properties of sensors...... 9 2.4 Introduction of the planar coil technology ...... 10 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 3.3 Introduction to LTCC technology ...... 17 3.3.1 Concept of LTCC technology...... 17 3.3.2 Materials and process of LTCC...... 17 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
i
5 Experimental system and methods ...... 58 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 5.3 Measurement of the temperature properties...... 61 5.3.1 Experimental system...... 61 5.3.2 Method for calculation of temperature coefficient of resistance for sensor coil ...... 63 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 Results and discussion...... 68 6.1 Characterization of the sensor ...... 68 6.1.1 Static unloaded impedance of sensors (L, C, R) ...... 68 6.1.2 Static position measurement...... 69 6.1.2.1 Proximity testing...... 69 6.1.2.2 Horizontal passage testing...... 70 6.1.3 Frequency sweep of sensor...... 71 6.1.4 Material properties of target ...... 73 6.1.5 Response to target lateral displacement at different frequencies ...... 75 6.1.6 Influence of surface area of target...... 78 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 7.1 Summary and conclusions ...... 99 7.2 Outlook...... 100 Zusammenfassung ...... 103
Bibliography...... 105
Abbreviations and symbols ...... 109
ii 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 1 Introduction 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
• Compatible with low-temperature brazing conductors
• 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.
2 1 Introduction
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. 3 1 Introduction
Simulation and design FEM simulation (Ansys): Modal, electromagnetic, thermo-mechanical Analytic calculation: Resistance, inductance, capacitance, skin depth, self- resonant fre q uency
Design layout and LTCC fabrication Selection of LTCC materials and structure Layout design by software CAM350 LTCC fabrication
Experiment and measurement Static behavior: Sensor characteri 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.
4 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.
5 2 State of the art
Besides optical sensors, alternative sensor technologies for blade vibration measurement presently are capacitive sensors, and eddy current sensors [6],[7].
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
6 2.2 Conventional displacement sensors 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.
7 2 State of the art
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.
8 2.3 High temperature properties of sensors
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 9 2 State of the art 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.
10 2.4 Introduction of the planar coil technology
Table 2.2 Comparison of four processing technologies for planar coils
Technology Introduction/ advantages or disadvantages
HTCC 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.
Disadvantages: Low conductive material (W, Mo), complex process, no printed resistor and high capital cost.
Thick film 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%.
Disadvantages: multiple printing steps and multiple firings for multilayers, thickness control of dielectric and limited layer count
LTCC 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.
Advantages: low processing temperature, low resistive metal (Au,Ag), printed resistor, TCE match Si, unlimited number of layers, good thermal properties etc.
PCB 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.
Disadvantages: low operating temperature, larger size of circuit and low thermal conductivity.
11 3 Aim of research and some basic 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
12 3.2 The concept and principle of an eddy current sensor 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 dΦ origins based on Faraday's law of electromagnetic induction: ε = − B , where ε is dt 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
13 3 Aim of research and some basic principles and concepts 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.
I1 M I2
R1 R2
U ~ L1 L2
(a) (b)
Figure 3.2.2 Equivalent circuit model of an eddy current sensor with air core as a transformer (a)with a coupling coefficient that depends on standoff . (b) The simplified model of an inductor and resistor that both depend on standoff x.
According to Kirchhoff ’s Law, the circuit model of a transformer (Figure 3.2.2 (a)) can be expressed in Equation (3.1).
⎧ loop1 : ⎪R1 I1 + jωL1 I1 − jωM I 2 = U ⎨ (3.1) loop2 : ⎪ ⎩− jωM I1 + R2 I 2 + jωL2 I 2 = 0
It is evident that:
U I1 = 2 2 2 2 (3.2) ω M R2 ω M L2 R1 + + jω(L1 − ) 2 2 2 2 2 2 R2 + ω L2 R2 + ω L2
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:
14 3.2 The concept and principle of an eddy current sensor
2 2 2 2 ω M R2 ω M L2 Z = R + jω L = R1 + + jω(L1 − ) (3.3) 2 2 2 2 2 2 R2 + ω L2 R2 + ω L2
2 2 ω M R2 R = R1 + 2 2 2 R2 + ω L2 (3.4)
2 2 ω M L2 L = L1 − 2 2 2 R2 + ω L2 (3.5)
2 2 ω M L2 ω(L1 − ) L 2 2 2 ω R2 + ω L2 Q = = 2 2 (3.6) R ω M R2 R1 + 2 2 2 R2 + ω L2 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
15 3 Aim of research and some basic principles and concepts 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.
V V
t 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.
16 3.3 Introduction to LTCC technology
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
17 3 Aim of research and some basic principles and concepts 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].
18 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 19 4 Design of the eddy current sensor
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
20 4.2 Analytical calculation of parameters of a LTCC coil 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
21 4 Design of the eddy current sensor 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.
2l w + t nH Lself = 2l(ln +0.5+ ) (4.1) w + t 3l cm 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.
22 4.2 Analytical calculation of parameters of a LTCC coil
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,
N Ltotal-self = ∑ Lself (i) *2*K (4.2) i=1 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.
23 4 Design of the eddy current sensor
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. x z
Conductor 1 l2 Conductor 2 ll Dz D x y
Dy
Figure 4.2.4 3D geometric model of two strips for Hoer’s formula.
The formula referred to this model is as follows [55]:
⎡⎡ 2 2 2 0.008 ⎡⎛ y 2 z 2 y 4 z 4 ⎞ ⎛ x + x + y + z ⎞ L = ⎢⎢⎢⎜ − − ⎟ ⋅ x ⋅ ln⎜ ⎟ h 2 2 ⎢ ⎜ ⎟ ⎜ 2 2 ⎟ w t ⎢⎢⎝ 4 4 4 ⎠ y + z ⎣⎢⎣⎣ ⎝ ⎠ ⎛ z 2 x 2 x 4 z 4 ⎞ ⎛ y + x 2 + y 2 + z 2 ⎞ + ⎜ − − ⎟ ⋅ y ⋅ ln⎜ ⎟ ⎜ ⎟ ⎜ 2 2 ⎟ ⎝ 4 4 4 ⎠ ⎝ z + x ⎠ ⎛ x 2 y 2 x 4 y 4 ⎞ ⎛ z + x 2 + y 2 + z 2 ⎞ + ⎜ − − ⎟ ⋅ z ⋅ ln⎜ ⎟ ⎜ ⎟ ⎜ 2 2 ⎟ ⎝ 4 4 4 ⎠ ⎝ x + y ⎠ 1 + (x 4 + y 4 + z 4 − 3x 2 y 2 − 3y 2 z 2 − 3z 2 x 2 ) x 2 + y 2 + z 2 60 xyz 3 ⎛ xy ⎞ xy 3 z ⎛ xz ⎞ − tan −1 ⎜ ⎟ − tan −1 ⎜ ⎟ ⎜ 2 2 2 ⎟ ⎜ 2 2 2 ⎟ 6 ⎝ z x + y + z ⎠ 6 ⎝ y x + y + z ⎠
t l w ⎤ ⎤ x 3 yz ⎛ yz ⎞⎤ ⎥ − tan −1 ⎜ ⎟⎥ (x)⎥ ( y) (z) ⎜ ⎟ ⎥ ⎥ 6 x x 2 + y 2 + z 2 ⎥ ⎥ (4.3) ⎝ ⎠⎦ 0 ⎦⎥ 0 ⎦ 0 24 4.2 Analytical calculation of parameters of a LTCC coil
2 2 2 r s1 ⎡⎡⎡ q1 1 i+ j +k +1 where ⎢ f (x, y, z)]q (x)] ( y)] (z) ≡ (−1) ⋅ f (qi , rj , sk ) . ⎢⎢ 2 r2 s ∑∑∑ ⎣⎣⎣ 2 ijk===1 1 1
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, th th where Mi,j means the mutual inductance between i turn and j turn.
The number of positive mutual inductances is 2N(N-1), and the number of negative 2 mutual inductance is 2N . 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
25 4 Design of the eddy current sensor 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.
26 4.2 Analytical calculation of parameters of a LTCC coil
Figure 4.2.7 General position of two conductors (filament) for Grover’s formula.
Grover’s formula reads [55]:
−1 α −1 β −1 γ −1 δ Lg = 0.001[α sinh ( ) − β sinh ( ) − γ sinh ( ) + δ sinh ( ) d d d d (4.4) − α 2 + d 2 + β 2 + d 2 + γ 2 + d 2 − δ 2 + d 2 ] where
sinh-1(x)=ln(x+ x 2 +1 ), 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) Greenhouse: 15.37 Hoer: 232 247.37 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.
27 4 Design of the eddy current sensor
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:
l l R = ρ = ρ (4.5) A wt 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
28 4.2 Analytical calculation of parameters of a LTCC coil
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.
29 4 Design of the eddy current sensor
According to the basic Equation (4.6) [28] for capacitance, calculation of two parallel planar conductors (see Figure 4.2.9) yields:
ε ε A ε ε lw C = 0 r = 0 r e (4.6) d d 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 ), -12 ε0 = dielectric constant of free space (8.8542 · 10 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
30 4.2 Analytical calculation of parameters of a LTCC coil 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
V 1 R = = . When we add a reference resistor with the value of 1pΩ and apply I ωC ω
I V V16 the voltage of 1 volt to V , = = . Because R16< ω R + R16 R16 V V16 12 ≈ = VC and C=V16·10 (pF). The result is computed by the circuit simulation R R16 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. R32 R33 605.5mV 173.92m 173.92m R1 R2 R3 173.87m 173.87m 173.87m R11 R14 R22 R23 R24 174m 174m 174m 174m 174m R7 R8 R9 R10 R13 R15 R17 R18 R19 R20 R21 18.27m 18.27m 18.27m 18.27m 18.27m 18.27m 18.27m 18.27m 18.27m 18.27m 18.27m R12 R25 R26 R27 R28 174m 174m 174m 174m 174m 729.4mVR4 R5 337.3mVR6 173.87m 173.87m 173.87m R29 464.5mV R30 R31 270.6mV 173.87m 173.87m 173.87m 171.2mV 1.000V R34662.7mV R35 394.5mV 828.8mV 535.5mV 173.92m R36 173.92mR37 173.92m 173.92m R38 R39 173.92m 173.92m V1 R16 0V 15.13pV 1Vdc 1p 0 Figure 4.2.10 Simplified electronic circuit model for the stray capacitance of the whole coil with N=12 layers. 31 4 Design of the eddy current sensor 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. R L sensor C Figure 4.2.11 The equivalent circuit model of the sensor. 4.2.5 Quality factor, skin depth, self-resonant frequency 4.2.5.1 Quality factor (Q) The quality factor of an inductor coil is the ratio of its ability to store energy to the total sum of all energy losses within the component. ωL(x) Q = Q(x) = (4.7) R(x) 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. 32 4.2 Analytical calculation of parameters of a LTCC coil 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]. 2 δ = (4.8) σωμ where δ : skin depth (meters), ω : radian frequency (radians/second), -6 μ : magnetic permeability (H/m), e,g. non-magnetic metal, μ=μ0·μr=1.26·10 H/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 Metal Conductivity Resistivity Skin depth (µm) (106 S/m) (10-8Ωm) 10 kHz 100 kHz 1 MHz 10 MHz 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. 33 4 Design of the eddy current sensor 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] 1 SRF = (4.9) 2π L(Ccable + Ciwc) 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. 34 4.3 Design and optimization of the eddy current sensor 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 35 4 Design of the eddy current sensor 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. ConceptConcept of the ofsimulation work 100 80 Ω 60 40 Resistance / Modal Simulation 20 0 -80-60-40-200 20406080 Horizontal distance / mm Physical level----ElectroMagnetic Simulation(Ansys) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 -4 x 10 Test: Fuction Investigation Figure 4.3.1 Optimization concept by FEM analysis. 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 36 4.3 Design and optimization of the eddy current sensor 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. 37 4 Design of the eddy current sensor sub=1 sub=14 f = 4.846 f = 331.8 sub=3 sub=2 f = 35.006 f = 34.778 sub=6 sub=6 f = 101.85 f = 110.12 sub=10 sub=5 f = 238.13 f = 79.858 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). 38 4.3 Design and optimization of the eddy current sensor 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 −8 part material ρ (10 Ωm) μr coil Ag 1.60 1 target Cu 1.73 1 Geometry coil ro (mm) ri (mm) Height h (mm) fill factor turns 5 0.2 1 1/20 200 target l/2 (mm) thickness (mm) gap (mm) 2.5 5 1 Electrical conditions f=1 MHz voltage=5 V Results R − R L − L R0(Ω) L0(μH) Rs(Ω) Ls(μH) s 0 (%) s 0 (%) Q0 R0 L0 43.56 127.43 48.76 112.82 11.9 11.5 18.38 39 4 Design of the eddy current sensor 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: V V Rs= cosθ , Ls= sinθ Re(I ) 2 + Im(I)2 Re(I ) 2 + Im(I)2 At the same time, the sensitivity of the sensor in the case of target existence was define as: 40 4.3 Design and optimization of the eddy current sensor Rs − R0 × 100% is for resistance, Ls − L0 × 100% is for inductance R0 L0 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=2 MHz f=0.5 MHz U=10 v U=1 v f=1 MHz,Voltage U=5 v f=1 M 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 R − R 11.9 17.6 8.19 11.9 11.9 s 0 (%) R0 L − L 11.5 11.7 11.19 11.5 11.5 s 0 (%) L0 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. 41 4 Design of the eddy current sensor Table 4.5 The influence of the change of materials of target on the sensor sensitivity Results Refer. condition Al-ρ=2.6·10-8 Ωm Ti-ρ=40·10-8 Ωm Cu-ρ=1.73·10-8 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 R − R 11.9 14.3 45.7 s 0 (%) R0 L − L 11.5 11.3 8.93 s 0 (%) L0 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. 30 28 Resistance 26 senstivity inductance 24 senstivity 22 20 18 16 14 12 Sensitivity / % 10 8 6 4 2 0 2 4 6 8 10 12 14 16 18 W idth of target / m m 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 42 4.3 Design and optimization of the eddy current sensor 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 Fill1/10 Fill1/40 Turns300 Turns100 turns=200 Fill=3/40 Fill=1/40 fill=1/20 thin layer thick layer narrow film 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 R − R 11.9 23.8 6.0 17.9 6.0 s 0 (%) R0 L − L 11.5 11.5 11.5 11.5 11.5 s 0 (%) L0 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=1.5 mm H=.5 mm H=0.5 mm h=1 mm,fill=1/20, Turns=300 Turns=100 Fill=1/10 turns=200 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 R − R 11.9 14.2 7.5 15.2 s 0 (%) R0 L − L 11.5 9.9 13.4 13.4 s 0 (%) L0 Q0 18.38 25.55 9.97 19.9 43 4 Design of the eddy current sensor 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 ri=1 mm ro =6 mm ro =4, ro =6 mm ro=5 mm, narrow Wide film small coil ri =1.2 ri=0.2 mm film 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 R − R 11.9 11.80 12.6 10.14 12.24 s 0 (%) R0 L − L 11.5 11.3 10.2 12.12 9.93 s 0 (%) L0 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. 44 4.3 Design and optimization of the eddy current sensor Table 4.9 The influence of the coil materials on the sensor sensitivity Coil/ρ R (Ω) L (μH) R (Ω) L (μH) Q0 0 0 s s Rs − R0 (%) Ls − L0 (%) -8 10 Ωm R0 L0 Ag 43.56 127.43 48.76 112.82 11.9 11.5 18.4 1.6 Au 59.90 127.43 65.09 112.82 11.5 11.5 13.37 2.2 Pt 288.61 127.43 293.80 112.82 1.8 11.5 2.77 10.6 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. 800 700 Ω L Resistance ω 600 Inductance 80 60 Resistance / / Resistance Inductance Inductance 40 20 0 0,5 1,0 1,5 2,0 2,5 3,0 Clearance between sensor and target / mm 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, almost the changes of all the influence factors such as increasing turns, fill 45 4 Design of the eddy current sensor factors, the size of conductor film and layer can improved it even if the structure of coil does not change. 4.3.3.2 3D simulation For the 2D simulation, there are some limitations for application. For example, when the structures of the coil and the target do not possess axis symmetry and a displacement measurement in horizontal direction is evaluated, a 3D EM analysis must be used although the calculation effort increases very much [58]. Like the 2D model, the 3D FEM model is also composed of coil, turbine blade, near field air and far-field infinite air, but it has no symmetric constrains and loads because neither of the coil nor blade possesses axial symmetry. According to the conclusions from modal analysis, the sensor is mounted over the sharp end of the blade. For simulating the movement of shark shape blade, the blade is rotated 45o and is put onto static individual horizontal positions in order to simulate the passage movement. Firstly, a rectangle or racetrack shape for the coil is brought out according to the long and narrow structure of the target. A solid sphere and a hollow sphere describe the near field air and the infinite field air. For the loads application, the definition of current flow must use a local coordinate system. Because the real constant of the current direction only can be defined as one value, the local coordinate system must be rotated and moved so that the current flow in related parts possesses the same direction value. The whole model is given in Figure 4.3.7. All the parameters and conditions are listed in Table 4.3. Figure 4.3.7 Model of EM simulation for the measurement system of eddy current sensor in 3D EM analysis composed of the target in shark shape, coil in racetrack structure, and air in sphere model. 46 4.3 Design and optimization of the eddy current sensor Table 4.10 The parameters for the 3D EM simulation Material −8 part material ρ ( 10 Ωm) μr coil Ag 1.6 1 target Ti 40 1 Geometry coil lo(mm) li(mm) wo lo height fill factor turns h(mm) 6 3 4 1 1 0.8 150 target w(mm) L(mm) thickness(mm) gap(mm) 2.5 30 50 times skin depth δ 0.7 Conditions f=5 MHz Voltage=20 v Through the 3D harmonic electromagnetic analysis, electromagnetic properties are obtained, such as: • Eddy currents on the turbine blade. Figure 4.3.8 shows the current density distribution in the blade when the blade lies at different positions. • Electromagnetic field distribution • Loaded impedance and inductance of the sensor coil. Figure 4.3.9 shows the curve of inductance and resistance in the range of –30 to 30 mm in horizontal direction. (a) (b) Figure 4.3.8 The eddy current distribution with movement of positions (a) just over; (b) away 2 mm. 140 100 130 80 120 Ω H 60 μ 110 40 100 Resistance /Resistance inductance / 20 90 80 0 -40 -20 0 20 40 -40 -30 -20 -10 0 10 20 30 40 Horizontal distance / mm Horizontal distance / mm Figure 4.3.9 The relationship between horizontal displacements and the resistance/inductance of the system. 47 4 Design of the eddy current sensor These results offer us some useful information. First, the eddy current in the blade distributes not only on the surface of blade, but also distribute in the lateral part of the blade. In FEM model, we do not build the whole structure of the target. For the thickness of target, we assume that the electromagnetic field does not act in the part of target that is far away 50 times of standard skin depth at high frequency. Therefore the thickness of the target is set to 50 times of standard skin depth shown in Table 4.10. It is observed that the depth of the eddy current on the surface or in the lateral side of blade is always not over the safety thickness of target according to Figure 4.3.8, although the vertical depth of lateral eddy current is deeper than that of surface eddy current. Hence, the assumption for the thickness of target is identified right. With this conclusion, the whole thickness of blade does not need to be considered. Hence the number of elements decreases and the calculation task reduces. Second, according to the key curves in Figure 4.3.9 that reflect the test principle of the eddy current, the resistance of the coil increases obviously with the passage of blade in horizontal direction, but the inductance decreases with the same movement of blade. The change rate is smaller than that of the resistance. This result has a close relationship with the target material. When the resistivity of the target is over 20·10-8 Ωm like for Ti, the change rate of the resistance is larger than that of the inductance. Therefore, the influence of the resistance must be taken into account when we calculate the test signal because the change tendencies of resistance and inductance are opposite. Whereas, when the resistivity of the target is below 10·10-8 Ωm like in the cases of Cu and Al, we can predict that the change rate of the resistance decreases and that of the inductance increases according to the conclusion of the 2D EM analysis. Therefore, the inductance or impedance can be used as testing signal at high frequencies because the absolute value of resistance is far smaller than that of the inductance and the change rate is smaller too. With the same method, another three FEM model are built. The only difference of them is the top view shape. The shapes are round, square and rectangle (racetrack). The sensitivity for the target in the situations with target and without target is compared. For the purpose of saving calculation time, the rectangle shape replacing the shark shape is used as the target, and ¼ symmetric is applied. The results are shown in the Table 4.11. 48 4.3 Design and optimization of the eddy current sensor Table 4.11 The comparison of sensitivity for the target with different coil shape Q Coil shape Ls(μH) Rs(Ω) L0(μH) R0(Ω) R − R L − L s s 0 s 0 (%) R0 L0 Racetrack 53.1 50.63 60.5 5.04 9.05 12.23 32.9 Round 21.66 19.46 24.39 2.48 6.85 11.19 34.9 Square 25.85 22.61 29.20 2.93 6.72 11.47 35.9 According to the Table 4.11 above, we find that the sensitivity of the resistance and the inductance for the coil with rectangle shape is better than that of the round and the square shape. Therefore, the rectangle shape of the sensor coil is optimal for the displacement measurement of the blade. Then, for the rectangle shape, its width, area, and fill rate can be evaluated according to the conclusion. For example, in the direction of the long side of the coil, we consider that the longer the long side of rectangle is, the better the sensitivity is, because rectangle shape is better than the square shape. Of course, the side cannot be too long because it must be over the part of blade with the largest vibration. Then, for the wide side of rectangle shape, the sensitivity is better with more narrow side according to the results of 2D analysis (see section 4.3.3.1). But, we must emphasize that this side cannot be too narrow because when the blade is too wide and passes under the sensor, the change of impedance is too small when the effective surface area of the blade is twice of the size of the coil. Therefore, it is reasonable that the size of the coil is bigger than the size of the target because the requirement for change of impedance is not only a big change of absolute value between two situations of with and without target, but also the curve of impedance exists a sharp peak when the blade pass the centre of the sensor. In summary, 3D EM analysis can offer a clear display of the distribution of eddy current density in the whole blade. The impedance change detail for the horizontal movement of the blade was obtained. This signal can be used to evaluate sensitivity of the sensor in testing the movement of blade. The sharper the curve and the bigger the change rate is, the better the sensitivity is. The 3D structure of the coil is investigated and rectangle shape is found to be the optimal shape and its related optimal size was discussed. This kind of optimal sensor can be transferred to the 49 4 Design of the eddy current sensor LTCC structure that is composed of a spiral shape thin strip. Its thermal reliability is evaluated with different materials for the sensor coil. 4.3.4 Thermo-mechanical FE analysis For the LTCC process, the stress and strain around one via hole are bigger than in other parts. Therefore, we focused on this part and built a detailed model (see. Figure 4.3.10), that we use to evaluate different conductor materials in order to achieve better thermo-mechanical properties. The FEM model reflects a bilayer structure. The material of the substrate is the green tape, and that of thin film is the comparison object in this section. Figure 4.3.10. The element model of the detail parts around the connecting via. For the thermo-mechanical analysis, the temperature dependent properties of LTCC material system are the key input. Here we consider that the properties of substrate do not relate with the temperature. Main changes come from the conductor of the coil. E-modulus (Young’s modulus), temperature coefficient of expansion (TCE) and the stress-strain curve are all functions of the temperature. Their original material data are from the material handbook [59] as shown in Table 4.12. Table 4.12 The material properties of conductor platinum and silver [59] Pt (Platinum) Temperature 0.2% offset Ultimate Tensile Young’s Modulus E TCE o 5 -6 o ( C) Yield Stress σ0.2 Stress (UTS) σu (10 MPa) 10 / C (MPa) (MPa) 20 49.03 137.29 1.697 9.0 250 39.23 107.87 1.640 9.3 500 29.42 76.49 1.559 9.4 750 19.61 43.15 1.383 9.5 50 4.3 Design and optimization of the eddy current sensor Ag (Silver) 20 29.42 147.10 8.04 18.89 250 24.52 117.68 7.25 20.69 500 19.61 78.45 6.02 23.75 750 16.67 44.13 4.85 26.25 The meaning of σ0.2 can be explained by the stress-stain curve shown in Figure 4.3.11. The yield point corresponds to the point where the material begins to have unrecoverable deformation. When some materials have no distinct yield point like in Figure 4.3.11 (b), a 0.2% offset is used to obtain an approximate yield point in order to replace the well-defined yield region (see Figure 4.3.11 (a)). The 0.2% offset point is determined by drawing a line parallel to the linear region of the curve starting from point 0.002 on the strain axis. The intersection of this line and the stress-strain curve defines the 0.2% yield point. In addition, the curve shown in Figure 4.3.11 (a) is not suitable for FE simulation. (a) (b) Figure 4.3.11 The illustration of strain-stress curve for yield point: (a) a well-defined yield region which not suitable for FE simulation (b) definition of the 0.2% yield point. When stress σ is below σp1 and strain ε is below εp1, the stress is linearly related to the strain, i.e., the curve is a linear straight line through zero point, and its slope is the value of Young’s Modulus E. The end point of this region is the proportional limit, i.e., the point where the stress-strain curve begins to become nonlinear. When the stress σ is between σp1 and σy and the strain ε is between εp1 and εy, the curve is nonlinear. The total 0.2% offset yield strain (ε0.2) is (σ0.2/E)+0.002, and the stress- strain relationship close to the 0.2% offset yield point satisfies the empirical function σ = k ε . Assuming one point near the 0.2% offset yield point with a difference of strain of 0.01%, its stress can be calculated: σ 1 = k ε 0.2 − 0.0001 . Meanwhile, it isσ 0.2 = k ε 0.2 . Therefore, 51 4 Design of the eddy current sensor σ 0.2 σ 1 = ε 0.2 − 0.0001 ε 0.2 As a first order approximation, a simplified curve of the complete stress-stain relationship is obtained and shown in Figure 4.3.12. σy P1 εy Figure 4.3.12 The simplified stress-strain curve for whole range. The curve is linear in every region. The regions A1 and A2 are called elastic region, and A3 is called plastic region. Then, the slope t1 of region A2 can be described: t1= (σ0.2−σ1)/0.0001. For the proportional limit point pl, it is the intersection of A1 and A2. ⎧ σ pl = E ⋅ε pl for region A1 ⎨ ⎩σ 0.2 −σ pl = t1 ⋅ (ε 0.2 − ε pl ) for region A2 Solve these equations: 4 σ 0.2 - 10 ⋅ (σ 0.2 -σ 1 )ε 0.2 ε pl = 4 E −10 ⋅ (σ 0.2 -σ 1 ) According to the related equation and assuming the strain corresponding to the ultimate stress being 15%, all the values for three points can be obtained. The stress- strain curves at four different temperatures for materials of platinum and silver shown in Figure 4.3.13 are analysed by ANSYS, respectively. 52 4.3 Design and optimization of the eddy current sensor 160 o 20oC 20 C 140 o 250oC 140 250 C o o 120 500 C 120 500 C 750oC 750oC 100 100 80 80 60 60 40 40 Stress / MPa Stress / MPa 20 20 0 0 -20 -20 -0,02 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 -0,020,000,020,040,060,080,100,120,140,16 Strain Strain (a) (b) Figure 4.3.13 Stress-strain curve as input of material properties for FEM analysis (a) conductor is Platinum (b) conductor is silver. A temperature cycle condition as load is applied to a thermo-mechanical analysis [60]. The system is first heated up from room temperature (20 ˚C) to 600 ˚C rapidly, then held at 600 °C for some time and finally cooled down to –20 ˚C quickly. Stresses and strains are induced due to the thermal expansion in combination with the plasticity of the materials. Figure 4.3.14 Equivalent stress distribution comparison between Ag and Pt as conductive metal after a temperature cycle (a) Platinum σm= 182 MPa (b) Silver σm = 239 Mpa. Figure 4.3.14 shows that the maximum stress values of silver are somewhat higher than those of platinum. So, in prototype fabrication, platinum should be the better material than silver to be selected as the conductive material with respect to the thermo-mechanical reliability. Whereas in respect of the cost, the price of Pt is about 60 times of the price of silver. In addition, the resistivity of Pt is about 6.6 times of Si. The coil using Pt will have too high resistance. Therefore, the cost and the properties of the conductor must be considered comprehensively according to different application fields. 53 4 Design of the eddy current sensor 4.4 LTCC layout design for eddy current sensor The Institute of Circuit Technology and Electronics, TU Ilmenau is the implementer for our design of the LTCC sensor coil. For the LTCC process, first we must know the guideline that is process standard or capability. According to all the guidelines for LTCC fabrication, the modification of the sensor design was done and the final layout was obtained for fabrication. 4.4.1 Material selection of LTCC coil Dupont 951 green tape material system was used for fabrication of our sensor. Its material properties are shown in Table 4.13. The Dupont 951-AT tape is chosen as the material of substrate for our sensor coil, because the thickness of sensor should be as thin as possible. According to 2D EM simulation, a thinner sensor coil can result in a better sensitivity and a thinner substrate can implement more layers in a given thickness of whole sensor coil. Table 4.13 Material properties of Dupont 951 green tape [61] Unfired Properties Typical Fired Properties System Capability Electrical Via Diameter Resolution 100 µm Dielectric Constant 7.8 (10 MHz) Line/space Resolution 100 µm/100 Dissipation Factor 0.15% µm (10 MHz) Maximum Layer Count >80 layers Insulation >1012 Ω Resistance (100 V DC) Thickness Breakdown >1000 V Voltage (V/25 µm) 951-AT 114 µm ±7% Physical 951-A2 165 µm ±7% Thermal Expansion 5.8 ppm/°C (25-300 °C) 951-AX 254 µm ±7% Density 3.1 g/cm3 Shrinkage Camber Conforms to setter (x,y) 12.27%±0.3% Refire at 850 °C Stable (z) 15% ±0.5% Surface 0.22 µm Smoothness Tensile Strength 1.7 MPa Thermal 3.0 W/mK Conductivity Young's Modulus 152 GPa Flexural Strength 320 MPa 54 4.4 LTCC layout design for eddy current sensor The material of coil conductor is silver ink 6145. It is the successor of silver ink 6142. The printed thickness is higher (fired about 14 microns, 6142 less than 5 microns), but the printability is better, which means that the sensor coil can get a lower resistance. The material of the solder is Pd/Ag because it is suitable for corresponding silver ink. 4.4.2 Structural design optimization with fabrication guideline For the Dupont 951 green tape material system, the fabrication capability complies the limit for the size of line and via as shown in Table 4.14. Table 4.14 System Capability of Dupont 951 green tape material system [61] System Capability Via Diameter Resolution 100 µm Line/space Resolution 100 µm/100 µm Maximum Layer Count >80 layers These guidelines for LTCC fabrication were used as the limit condition and attend the optimization design flow shown in Figure 4.4.1. This design flow concerns with all the conclusions of simulation, analytic calculating method and limit of LTCC guidelines. The final design size and geometric parameter of optimisation are listed in Table 4.15. Table 4.15 Geometric parameter for LTCC fabrication Unfired Fired Border (mm) 50×50 43.7×43.7 Outer Size (mm) long 18, wide 10 long 15.7, wide 8.7 Lines Width/space(μm ) 150 131 Layers 12 12 Turns 16 16 Via (μm) 286 250 Padstack (μm) 400 350 Drill (mm) 1.15 1.0 Solder (mm) 2.29 2.0 55 4 Design of the eddy current sensor Figure 4.4.1 A complete optimization design flow for LTCC eddy current sensor. 4.4.3 Layout design The layout design software CAM350 demo was used. It reads fabrication rules into the PCB design domain (compatible with LTCC) and presents them in a way that is understood by the designer. It can offer a complete flow, from design through fabrication, which streamlines the transition of engineering data into successful physical fabrication. The format of CAM350 is *.pcb or *.cam. Layout files in Gerber format are used for practical fabrication. These Gerber files must include all 56 4.4 LTCC layout design for eddy current sensor the information concerning the pattern of every layer, solder mask, drill and scribe. The design graph for odd and even layer is shown in Figure 4.4.2. A sensor with square shape is also designed for fabrication so that the sensor with rectangle shape has a comparing object. (a) (b) Figure 4.4.2 CAM350 design graph (a) top layer with board line, drill and scribe lines (b) the second layer with solder pad. 57 5 Experimental system and methods 5.1 LTCC fabrication of the eddy current sensor coil The Institute of Circuit Technology and Electronics, TU Ilmenau implemented our design of the LTCC sensor coil finally. Along the scriber line, one board was diced into 4 sensors respectively by rotating blade. One of them was cut and polished so that to observe the lines in the cross-section (see Figure 5.1.1) of every layer by microscope. The top view of sensor examples was displayed in Figure 5.1.2. These sensors became experimental measurement objects. 100μm Figure 5.1.1 Cross section of LTCC coil under microscope. Figure 5.1.2 Top view of LTCC eddy current sensors. 58 5.2 Sensor characterization 5.2 Sensor characterization The principle of the eddy current sensor is the impedance change of the coil with the relative displacement between the sensor and the conductive object. Therefore, its main characters involve impedance influenced by factors of exciting frequency, temperature of environments, displacement of the sensor in vertical and horizontal directions relative to the object, surface area and material properties of measurement target. Through the characterization of the relation between the impedance of the sensor and the influencing factors, the sensitivity, stability and feasibility of sensors under harsh environments can be evaluated. 5.2.1 Static impedance of sensors (L, C, R) We assume the electronic model of sensor is composed of an inductor (L), a resistor (R) and a capacitor (C). As shown in Figure 4.2.11, L is in serial with R and in parallel with C. At low frequencies the sensor is analogous to L in serial with R, because C can be regarded as an open circuit. At high frequencies, the sensor is effectively resembled of C in parallel with R because L reacts as a resistor with large resistance. R L sensor C Figure 5.2.1 The equivalent electronic model of the sensor. Resistance and inductance of the sensor at low frequency without object were measured by HP/Agilent LCR meter 4263B. The data can be compared with analytic calculations. Normally, the values of analytic calculations are a little smaller than the real value because the analytic calculation neglects the details of the corner parts of every layer and filled parts in through-holes. As for the capacitance value, we measured an approximated value at the maximum frequency of impedance analyser Solartron1260, which is 20 MHz. The equivalent circuit of the sensor coil is a capacitor in parallel with a resistor of large resistance. 5.2.2 Static position measurement system In fact, the influences of eddy current on the impedance of the sensor coil are very different between the vertical proximity direction and the horizontal passage direction. We will test them separately. 59 5 Experimental system and methods 5.2.2.1 Proximity testing (a) Target with big surface (b) Target with small surface Figure 5.2.2 Proximity measurement system for different target surfaces. As shown in Figure 5.2.2, a linear stage in 3 directions, a supporting frame for the sensor, a sensor, a copper target plate with a width of 30mm and a thickness of 1mm and an impedance analyser constitute the testing system. The exciting frequency was fixed to a constant value of 1 MHz. The proximity distance was changed from 0.1 mm (near sensor surface) to 4.5 mm (far away from sensor surface). 5.2.2.2 System for impedance testing by frequency sweep The frequency of the exciting source affects the sensor behavior greatly as seen in the last section. In this section, we study the influence of frequency on the behavior of the sensor by testing the sensor with a wide frequency range of the exciting source. HP IB High frequency test modul Computer Labview Control sola rtron Zwic k Data ac quisition R, L, Ph a se , Z, measuring Movement and adjust temperature Figure 5.2.3 Measurement system of frequency sweep. 60 5.3 Measurement of the temperature properties As shown in Figure 5.2.3, the frequency sweep function of Solartron 1260 played an important role in this system. Through a HP interface board, all the measured data can be recorded online by a computer. A tensile machine (type: Zwick BW91250) was used to move the target, a thin copper plate, to pass by the sensor. First, the frequency sweep measurement of the impedance properties of sensor without target was carried out. Four parameters were measured. They are the inductance (L), the resistance (R), the amplitude (A), and the phase angle (φ). The impedance can be expressed as a complex number by these parameters: Z=R+jωL=Aejφ. Of course, the resistance and the inductance are not commonly regarded values, but are real and imaginary parts of a complex number. jφ The impedance can be described as a complex Z=|Z|e =Re+jΙm=1/Y, 1 R − jωL R L Y = + jωC = + jωC = + jω[C − ] R + jωL R2 + (ωL)2 R2 + (ωL)2 R2 + (ωL)2 L At resonant frequency, Im=0, that is, C − = 0 . It deduces R 2 + (ωL) 2 1 R 2 ω resonant = − (5.1) LC L2 5.3 Measurement of the temperature properties The main purpose of applying LTCC technology to eddy current sensors is to improve the thermal properties of the planar sensor. The feasibility to work at high temperature up to 600oC must be evaluated by experiments. 5.3.1 Experimental system As for electronic measurement systems, a current source and a voltage meter were used for the measurement of resistance at DC condition. A constant DC source was applied on the sensor and, the voltage between the two ends of the sensor was measured. The four-wire measurement method, more commonly known as Kelvin measurement, was utilized because the resistance of the cables in the oven will change largely with the increase of the temperature. The test lead or test interface wiring was automatically nulled out due to the use of the four-wire technique. The 61 5 Experimental system and methods circuit of electronic connection is demonstrated in Figure 5.3.1. Besides the DC resistance measurements, the same instruments shown in Figure 5.2.3 are used for the frequency sweep impedances measurements. The Solartron 1260 and its computer data acquisition system were also used with a similar four-wire connection method. L0 R0 sensor C0 R-cable R-cable A Meter AMP IAc or IDc V Meter VOLT Figure 5.3.1 Schematic of four-wire measurement method. Two ovens were used in this experiment to offer different temperature environments. One chamber furnace is from company Carbolite and can be heated from room temperature up to 600oC. Another one is from company Binder with a maximum temperature of 300oC. Thermistor Figure 5.3.2 Testing system of Impedance measurements at different temperature in oven. 62 5.4 System for real-time measurements The support frame of the sensor is made of machinable ceramic, Duratec 750. This kind of material can bear temperatures up to 1000oC. The insulation material of cable is glass-fiber. When working at 300oC, the pad on the surface of the sensor was connected with cable by normal solder electrically. When the sensor worked at 600oC furnace, a direct mechanical contact implements the electrical combination. Especially, a K-type thermistor located close to the eddy current sensor was used to measure the real temperature value. The photograph of the whole system is shown in Figure 5.3.2. 5.3.2 Method for calculation of temperature coefficient of resistance for sensor coil Temperature coefficient of resistance α is defined as the amount of change of the resistance of a material for a given change in temperature. A positive value of α indicates that R increases with the increase of temperature; a negative value of α indicates that R decreases with the increase of temperature; and zero α indicates that R is constant over a given temperature range. An approach to model the temperature dependency leads one to expect a fractional change in resistance being proportional to the temperature change: ΔR = αΔT (5.2) Rs where ΔR = change in resistance (Ω), o Rs = standard resistance at reference temperature 20 C (Ω), α = temperature coefficient of resistance (K-1), ΔT = change in temperature (K). The temperature coefficient of resistance α can be described as dR 1 α = ⋅ (5.3) dT Rs 5.4 System for real-time measurements The dynamical testing system is composed of three main parts, a rotating system, an electronic signal measurement and acquisition system and the testing objects. Figure 5.4.1 demonstrates the construction diagram and Figure 5.4.2 shows a photograph of the testing system. The detail of every subsystem will be introduced in the following sections. 63 5 Experimental system and methods Adjustable clearance Testing Circuit Oscilloscope GPIB Interface Multifunction, Tektronix HP-IB ISA LTCC self-designed TDS2014 Sensor DC power supply Labview for data acquisition Computer AC Motor Speed controller Siemens 1LA7 Siemens Software Metal rotor Micromaster 410 STARTER Figure 5.4.1 General structural diagram of whole testing system. Figure 5.4.2 Photograph of the testing system. 5.4.1 Rotation control and generator Motor, frequency inverter and the configuration software of manufacturer Siemens form a rotating system. A standard asynchronous low voltage motor 1LA7073 was selected. The specifications of the motor are listed in Table 5.1. This kind of AC motor can rotate at different speeds proportional to the frequency of the power supply offered by inverter Micromaster 410. The configuration of parameters of inverter can be implemented by operating panel manually or through serial port RS485 by computer. “Starter” or “Drivermonitor” is suitable software for controlling setup. The connection diagram about working principle is shown in Figure 5.4.3. Because the relationship between the rotating speed and the output frequency is 64 5.4 System for real-time measurements linear, for the quick configuration it just needs to change the minimum frequency and maximum frequency that is set to constant 50 Hz. Therefore the real rotating speed is fmin·3000/fmax (rpm). Table 5.1 Specification of the motor 3000 rpm, 2-pole, 50 Hz Rated Size Order Efficiency Starting Starting Stalling Torque Moment Weight output No. Operating data Torque Current Torque class Of (Kg) (KW) at rated output (Nm) (A) (Nm) (KL) inertia Rated Rated Rated J speed Current Torque (Kg m2) (rpm) (A) (Nm) 0.55 71M 1LA7 2800 1.36 1.9 2.5 4.3 2.6 16 0.00041 6 073 – 2AA RS 485 Starter/ drivermonitor Power 230V/50Hz Micromaster 410 Figure 5.4.3 Diagram of rotating generator system. 5.4.2 Electronic signal acquisition system The testing circuit plays a very important role in this system. This circuit has two separate functions: Current source for voltage measurement directly, voltage source for response of resonant status changes. The principle is illustrated in Figure 5.4.4. As for the current function, a current source with constant amplitude and frequency is an exciting source. The output signal V-output is the multiplication of the exciting current and the impedance of the sensor. The amplitude of the output voltage includes the information on change of blade in approximate direction and the time interval of two peaks of the signal reflects the movement of blade when it passes the sensor. 65 5 Experimental system and methods I1 V1 V-output C R1 R0 2 C0 sensor C1 L1 sensor L0 1 R1 2k 2 + 3 V-output 1 - (a) current function (b) voltage function Figure 5.4.4 The schematic picture of signal testing. As for the voltage function (see Figure 5.4.4 (b)), a voltage source with constant amplitude and frequency is the exciting source. The constant frequency here must be adjusted to keep the sensor and the capacitor C of the circuit in resonant status. The output signal V-output is the product of the current passing through the sensor and the reference resistance R1. Compared to the voltage function, the current function can obtain the testing signal including clear information on the clearance between the sensor and the blade tip, but the voltage function cannot get this kind of information. However, the voltage function is more sensible for the initial resonant position of the blade and the peak of the signal reflecting the arrival of the blade is sharper. The main component of the generator in the circuit is the Maxim038. This system was manufactured by the electronics service center of the IMTEK. The oscilloscope Tektronik TDS2014 with 1260 byte memory and Agilent 54622D with 2M bytes memory was chosen as waveform display and only the latter was used as date acquisition device because of its large memory. According to the Nyquist Theorem, the highest frequency that can be accurately represented is less than one- half of the sampling rate. Based on the analysis in the last chapter, we select about 1 MHz as exciting frequency. Therefore the sampling rate must be 2 MHz at least. If the rotating speed of the motor is 1200 rpm, which corresponds to 20 Hz, and we want to record 2 periods of the motor rotations that is 100 milliseconds, the requirement for memory is to multiply the sampling rate by the record time that equals to 100k bytes at least. This is the reason why we select the Agilent 54622D as data acquisition device. A programme written with Labview reads the data into 66 5.4 System for real-time measurements computer through GPIB card and cable. These data can further be analyzed by mathematical software such as Matlab. 5.4.3 Test objects The movement of blades in the rotating rotor were our testing targets. Two rotors were fabricated with the same geometrical structure (see Figure 5.4.5 (a)), but in different materials. One of them is made of copper and another of Aluminum. The diameter of the rotors is 100 mm and the thickness is 30 mm. The length of the blades is 25 mm and their width is 5 mm. There are 8 pieces of blades on one rotor. 25 50 100 100 5 (a) (b) Figure 5.4.5 Testing objects (a: The geometric size of rotor; b: picture for mount of sensor and rotor). The sensor was mounted in a ceramic support. This kind of ceramic Duratec 750 material can be mechanically fabricated and can bear high temperatures up to 1000 oC. It possesses good thermal and electric insulation properties, and therefore does not influence the electromagnetic field and testing signal. The related vertical position and the clearance between the tip of the blades and the surface of the sensor can be adjusted by a linear stage. 67 6 Results and discussion 6.1 Characterization of the sensor 6.1.1 Static unloaded impedance of sensors (L, C, R) Firstly, the basic resistance, inductance and capacitance of the sensor without target were obtained. The measurement results are shown in Table 6.1 and correspond to the electronic model of the sensor shown in Figure 5.2.1. Table 6.1 Unloaded impedance (L, C, R) of sensor coil HP/Agilent LCR meter Frequency (Hz) L (μH) R (Ω) 50 295-365(not stable) 81.56 100 256 81.53 200 261 81.51 500 262 81.52 1k 264 81.51 10k 264 81.51 100k 263 82.20 Solartron 1260 Frequency (Hz) C(pF) R (Ω) 20M(with target) 15.5 2.3k 20M(without target) 16.0 2.5k L(uH) R (Ω) 100(with target) 242 81.9 100(without target) 239 82.0 Analytic value DC L=232 μH, R=76.6 Ω, C=15.7 pF At low frequencies, the influence of the target on the inductance of the sensor coil is very limited. Similarly, at high frequencies, the influence of the target on the capacitance of the sensor coil is also very small. These parameters can be compared with related parameters of analytic calculation. Both the values calculated by analytic analysis and those measured by experiment are approximate. The correctness of analytic calculations was verified by the experiments. 68 6.1 Characterization of the sensor 6.1.2 Static position measurement In fact, the influences of eddy current on the impedance of the sensor coil are very different between vertical proximity direction and horizontal passage direction. We tested them separately in this section. 6.1.2.1 Proximity testing Figure 6.1.1 and Figure 6.1.2 show the values of L and R with different proximity. The target surface widths are 30 mm and 1 mm, respectively. The exciting frequency of the sensor is 1 MHz and the testing conditions corresponding these two curves are shown in Figure 5.2.2 (a) and (b) respectively. 350 inductance resistance 300 H Ω μ 250 200 Resistance R / Resistance Inductance L / 150 012345 vertical distance / mm Figure 6.1.1 The relationship between resistance, inductance and proximity distance for copper target with 30mm surface width. 400 380 360 inductance1/2 H Ω μ 340 inductance1/4 resistance1/2 170 resistance1/4 160 Resistance R/ Inductance L / 150 140 012345 vertical distance/mm Figure 6.1.2 The relationship between resistance, inductance and proximity distance for copper target with 1mm surface width (The thin plate lies over the center and up ¼ of sensor coil). The experimental results shown in Figure 6.1.1 and Figure 6.1.2 are in line with our FE simulation results (see Figure 4.3.6). For the proximity measurement, when the target surface area is bigger than that of the sensor, the change of inductance is obvious, while the influence of the resistance can be neglected. On the contrary, if the target surface area is smaller than that of the sensor, the narrow surface cuts the 69 6 Results and discussion eddy current. Then the change of inductance is small and the change of the resistance becomes comparable to that of inductance and must be taken into account for practical design of the measurement circuit. 6.1.2.2 Horizontal passage testing The measurement system was the same as shown in Figure 5.2.2 (b), but movement direction was changed to 90o of the horizontal passage direction. The gap between the coil and the conductive object was kept constant at 1 mm. Figure 6.1.3 and Figure 6.1.4 present the variations of the inductance and the resistance of a rectangular coil at three frequencies. At 2 MHz, the resistance values are fitted with a Gaussian curve because the measured resistance values are rather noisy. 1000 900 800 H μ 700 L500k L1Mhz 600 L2Mhz Inductance / 500 400 300 0 5 10 15 20 25 Horizontal distance /mm Figure 6.1.3 The variation of the inductance of a rectangle coil at 500 kHz, 1 MHz and 2 MHz in the distance range of 26 mm. 200 R500k R1MHz R2MHz 180 (Gauss fit) Ω 160 140 Resistance / 120 100 0 5 10 15 20 25 30 Horizontal distance / mm Figure 6.1.4 The variation of the resistance of a rectangle coil at 500 kHz, 1 MHz and 2 MHz (fitted curve) in the distance range of 26 mm. 70 6.1 Characterization of the sensor Observing Figure 6.1.3, we find an interesting phenomenon. The experimentally obtained tendency of inductance change does not exactly resemble the simulated results. In the middle part of the curve there exists an inverse peak. This can be explained by the influence of the capacitance in the equivalent model of the sensor. When a thin target passes the sensor and is placed exactly over the centre of the sensor, two surfaces of metal proximate and the effect of capacitor is greatest. When this kind of behaviour become comparable and even over the properties of inductor, the change tendency will inverse. For the wide target, the curve tendency is same as the results of simulation shown in Figure 4.3.9. As an example, the inductance change of the sensor when a copper plate with 5 mm thickness passing through was shown in Figure 6.1.5. As for the resistance, a similar conclusion can be drawn as before. When the change of resistance is comparable to that of the inductance, the resistance or the quality factor are proportional to the inductance and the inverse of resistance can be regarded as testing signal. In addition, the amplitude of the impedance cannot be regarded as the testing signal because the change tendencies of the resistance and the inductance are negative. In fact, the change tendency is not always the same because it is related to frequency and surface area of target. We will discuss this according to the frequency-sweep curve in next section. 350 5mm 340 330 320 H μ 310 300 290 Inductance / 280 270 260 0 5 10 15 20 25 30 35 Horizontal distance / mm Figure 6.1.5 Inductance change when a 5 mm thickness target passes the sensor with 1 MHz exciting frequency and 1.5 mm clearance to blade tip. 6.1.3 Frequency sweep of sensor First, the frequency sweep measurement of the impedance properties of a sensor without target was carried out. Four parameters were measured. These are the 71 6 Results and discussion inductance (L), the resistance (R), the amplitude (A), and the phase angle (φ). The impedance can be expressed as a complex number by these parameters: Z=R+jωL=Aejφ The resistance and the inductance are real and imaginary parts of a complex number. 80 L 60 R 40 Ω H 20 μ 0 -20 inductance / x50 / inductance -40 Resistance / x1500 -60 -80 0 1M2M3M4M5M Frequency / Hz Figure 6.1.6 Change of inductace and resistance of sensor with frequency. 100 phase |Z| 80 60 40 Ω 20 o 0 -20 Phase / -40 -60 Impedence / x1500 -80 -100 0 1M2M3M4M5M Frequency / Hz Figure 6.1.7 Change of impedance amplitude and phase angle of sensor with frequency. The frequency sweep curve can be explained by the equivalent electronic model of the sensor. Because the sensor coil contains an inductor and a resistor, all the values 72 6.1 Characterization of the sensor will produce significant changes of the resonant frequency. The resonant frequency can be evaluated by Equation (4.9). Using the testing values in Table 6.1, R = 81.5, L=256H, and C=16pF and the equation (4.9), one finds ω=15.62, f=ω/2π =2.486 MHz. This frequency is very similar to the experimental value of 2.16 MHz. Both are not exactly the same because many factors such as capacitance and inductance of cables and parasite capacitance were not taken into account for calculation. Therefore, the experimental value is always smaller than the calculated one. Looking at the curves in Figure 6.1.6 and Figure 6.1.7, one finds that below the resonant frequency, the behaviour of the sensor is similar to an inductor. The value of inductance increases with the frequency and reaches its maximum value at the resonant frequency. Correspondingly, the phase angle increases and tends to +90o at which angle the component is a pure inductor. At resonant frequency, the angle and value change suddenly. The inductance changes from positive maximum value to negative value, and the angle change from approximate +90o to -90o. The sensor begins to act as a capacitor. Therefore, the working frequency of an eddy current sensor must be smaller than the resonant frequency according to its inductive principle. As for the separate resistance and the absolute value of impedance, both increase from initial values to reach the maximum value at resonant frequency and then decrease abruptly. Because the working frequency must be smaller than the resonant frequency, the impedance properties above the resonant frequency are not considered in our case. 6.1.4 Material properties of target One copper plate and one aluminum plate with the same thickness of 5 mm are chosen as targets. The clearance between the tip of plate and the surface of the sensor is 1 mm. The main difference between the two materials is resistivity (ρ). The -8 -8 resistivities of copper (ρCu) and aluminum (ρAl ) are 1.73·10 Ωm and 2.6·10 Ωm, respectively. The inductance and resistance of the sensor with targets of these two materials and a reference curves without a target as a function of frequencies are shown in Figure 6.1.8 and Figure 6.1.9. According to the two figures, one finds that the influence of the target material on the measured sensor inductance and resistance are weak, although there is a big difference in the resistivity between the two target materials. ρAl is about 1.5 times larger than ρCu, but in the whole measured frequency range the difference of resistance is smaller than 6% and the difference of inductance is smaller than 0.5%. Combining with the results in Table 4.2, we know that the inductance of the sensor is 73 6 Results and discussion hardly influenced by the target’s resistivity. When the target’s resistivity changes because of variation in environments such as a temperature change or a material property changes, the inductance of the sensor keeps essentially unchanged. However, the influence of the resistivity of the target on the resistance of the sensor is higher than on the inductance, but this change is not proportional to the change of the resistivity. When resitivity changes 1.5 and 15 times at 1 MHz, the resistance change 3% and 34%. The change rate of resistance of the sensor is about 2% of the change rate of the target resistivity. 400 Cu 1m 380 without Target Al 500 360 340 0 320 Inductance / H Inductance -500 300 280 -1m Inductance / H Inductance 260 0 1M2M3M4M5M Frequency / Hz 240 220 200 200.0k 400.0k 600.0k 800.0k 1.0M 1.2M 1.4M 1.6M Frequency / Hz Figure 6.1.8 Inductance of the sensor as a function of frequency without target, with Cu target and with Al target. 40,0k Cu 560 35,0k without Target Al 30,0k 480 25,0k Ω 20,0k 400 Ω Resistance / Resistance 15,0k 320 10,0k 5,0k Resistance / Resistance 240 0,0 0 1M2M3M4M5M Frequency / Hz 160 80 0,0 200,0k 400,0k 600,0k 800,0k 1,0M 1,2M 1,4M 1,6M Frequency / Hz Figure 6.1.9 Resistance of the sensor as a function of frequency without target, with Cu target and with Al target. 74 6.1 Characterization of the sensor 6.1.5 Response to target lateral displacement at different frequencies In this section, the same thin copper plate is put at five different positions as shown in Figure 6.1.10. Then, the frequency sweep measurements are carried out individually. target Far . . . Up 1/4 mid coil Down 1/4 . . . D ow n Figure 6.1.10 Illustration for testing position of target plate in testing system shown in Figure 5.2.2 (b). 440 Lfar 420 L-up1/4 Lmid 5,0m L-down1/4 Lfar 400 4,0m L14 Ldown Lmid 3,0m 380 L41 H 2,0m Ldown μ 1,0m 360 0,0 340 -1,0m Inductance / H / Inductance Inductance / -2,0m 320 -3,0m -4,0m 300 0,00 1,00M 2,00M 3,00M 4,00M 5,00M Frequency / Hz 280 500,0k 600,0k 700,0k 800,0k 900,0k 1,0M 1,1M 1,2M Frequency / Hz (a) (b) 1k Lfar 950 L-up1/4 380 900 Lmid 850 L-down1/4 375 Ldown 800 370 H μ 750 365 700 Inductance 650 360 600 355 Inductance / / Inductance 550 -3 -2 -1 0 1 2 500 Horizontal distance 450 400 1,2M 1,3M 1,4M 1,5M 1,6M 1,7M 1,8M 1,9M Frequency / Hz (c) (d) Figure 6.1.11 Inductance of sensor with target at different positions. (a) whole frequency range; (b) enlarged curve with frequency interval of 500 kHz to 1.2 MHz; (c) enlarged curve with frequency interval of 1.2 MHz to 1.9 MHz; (d) illustration for change tendency when target passes by the sensor at 1 MHz. 75 6 Results and discussion The measurement results shown in Figure 6.1.11 tell us that the change tendency of the inductance is always the same when the working frequency is smaller than the resonant frequency. However, as for the resistance (see Figure 6.1.12), the change tendency is different within different frequency ranges. Here, we define a frequency called critical frequency. Below this critical frequency, the resistance change tendency follows the simulation results and the principle of eddy current. The resistance increases with the approach of a target. Above this frequency, the resistance changes in such a way that is similar to the change tendency of inductance. According to Figure 6.1.12, the critical frequency of this LTCC sensor is about 1.5 MHz. This phenomenon is also reflected in the amplitude of impedance, because its value is the square root of the sum of the squares of resistance and inductance. Below the critical frequency, the resistance must be taken into account because the change tendencies of resistance and inductance are opposite and it cancels the contribution of the inductance to the amplitude. 180 Rfar 170 R-up1/4 f =1 MHz Rmid 160 R-down1/4 147 Rdown 150 146 Ω 140 145 130 144 Resistance 143 120 resistance / 142 110 141 100 -3 -2 -1 0 1 2 Horizontal distance 90 500,0k 600,0k 700,0k 800,0k 900,0k 1,0M 1,1M 1,2M Frequency / Hz (a) Rfar 800 R-up1/4 f =1.5 MHz Rmid 700 R-down1/4 340 Rdown 600 Ω 500 400 resistance / / resistance Resistance 300 200 320 -3 -2 -1 0 1 2 1,2M 1,3M 1,4M 1,5M 1,6M 1,7M 1,8M Horizontal distance Frequency / Hz (b) 76 6.1 Characterization of the sensor 120000 Rfar Rfar 120000 R14 R14 100000 Rmid Rmid R41 100000 R41 Rdown Rdown 80000 80000 Ω Ω 60000 60000 40000 resistance / resistance resistance / / resistance 40000 20000 20000 0 0,0 1,0M 2,0M 3,0M 4,0M 5,0M 1,8M 1,9M 2,0M 2,1M 2,2M 2,3M 2,4M 2,5M Frequency / Hz Frequency / Hz (c) (d) Figure 6.1.12 Influence of target position on the frequency dependent sensor resistance. (a) resistance at 500 kHz-1.2 MHz and its change tendency within this frequency range illustrated at 1 MHz; (b) Resistance at 1.2 MHz-1.8 MHz and its change tendency between 1.2 MHz and resonant frequency illustrated at 1.5 MHz; (c) Resistance at 1.8 MHz-2.5 MHz; (d)whole frequency range. Zfar Z1/4 3,0 Zmid Z-1/4 Zdown 2,5 Ω (a) 2,0 Impedance / k 1,5 1,0 500,0k 600,0k 700,0k 800,0k 900,0k 1,0M 1,1M 1,2M frequency / Hz 12 Zfar Z1/4 Zmid 10 Z-1/4 Zdown Ω 8 (b) 6 Impedance k / 4 1,2M 1,3M 1,4M 1,5M 1,6M 1,7M 1,8M 1,9M frequency / Hz Figure 6.1.13 Amplitude of impedance of the sensor coil at frequencies from 500 kHz to 1.5 MHz. 77 6 Results and discussion As shown in Figure 6.1.13, the changing rate of amplitude below the critical frequency at different positions is smaller than that of inductance. The changing rate of amplitude over the critical frequency at different positions is similar to that of inductance because the change tendency of resistance is the same as that of inductance. However, because the frequency is very high meaning that ωL is much larger than the value of resistance, the positive influence of the resistance on the amplitude of impedance is not obvious. This conclusion is very important for the design of the testing circuit. When the working frequency is over the critical frequency, the amplitude of impedance or inductance of the sensor can be chosen as testing signal. When the working frequency is below the critical frequency, however, inductance, resistance or quality factor are optional testing signals. 6.1.6 Influence of surface area of target As mentioned before, the surface area is an important influence factor to the impedance of the sensor. We use three copper plates with thicknesses of 1, 4 and 5 mm as target objects. The clearances between the tip of the plates and the surface of the sensor are 1 mm. As shown in Figure 6.1.14, the bigger the target surface area is, the more the influence on the inductance of sensor is, which means that the sensitivity of the sensor is better. As for resistance properties (see Figure 6.1.15), different target surface areas induce different critical frequencies of changing tendency. The critical frequencies are inversely proportional to the surface area of the target. The critical frequency for the target with big area is smaller than the target with small area. In terms of the impedance amplitude of the sensor (see Figure 6.1.16), the conclusion in section 6.1.5 is identified again. At low frequencies the change of impedance amplitude is very small because the changes of the inductance and the resistance cancel each other. When the surface is bigger, the change increases more quickly. Therefore, when we select testing signal and an optional exciting frequency, the surface area of the target must be taken into account. For bigger target, working frequency needs not to be very high. We can choose the frequency at half of resonant frequency as working frequency. This ensures that the sensor works in inductive principle because the frequency is far away from the frequency for its capacitive properties. At the same time, this frequency is normally above the critical frequency for change tendency so that the contributions of inductance and resistance to the impedance do not cancel each other. It must be born in mind that the critical frequency for change tendency of resistance is much higher when the target is very thin. Impedance amplitude cannot be regarded as the testing signal below this critical frequency. Only resistance, inductance, or quality factor can be used as the testing signal. When the working frequency is over the critical frequency and close to the resonant frequency, both inductance and impedance amplitude can be used as testing 78 6.1 Characterization of the sensor signal, but the capacitor properties will influence both signals when target is located close the center of the sensor. The center peak of the signal will produce an opposite change that complicates the signal processing. Thickness 1,5x10-3 320 1mm 4mm -3 5mm 1,0x10 300 far -4 5,0x10 H 280 μ 0,0 260 Inductance -5,0x10-4 Inductance / / Inductance 240 -3 -1,0x10 220 -1,5x10-3 0 1x106 2x106 3x106 4x106 5x106 200 Frequency / Hz 200,0k 400,0k 600,0k 800,0k 1,0M Frequency / Hz Figure 6.1.14 Inductance as a function of sweep frequency for targets with different thickness. 160 Thickness 35k 150 1mm 30k 4mm 140 5mm 25k far 130 Ω 20k Ω 120 15k 110 Resistance / / Resistance 10k Resistance / 100 5k 90 0 80 -5k 0 1M2M3M4M5M Frequency / Hz 200.0k 400.0k 600.0k 800.0k Frequency / Hz Figure 6.1.15 Resistance as a function of sweep frequency for targets with different thickness. 1,4k Thickness 35k 1mm 4mm 30k 1,2k 5mm Ω far 25k 1,0k Ω 20k 800,0 15k 600,0 10k Impedance Amplitude / 400,0 5k Impedance Amplitude / 0 200,0 0 1M2M3M4M5M Frequency / Hz 200,0k 400,0k 600,0k 800,0k Frequency / Hz Figure 6.1.16 Impedance amplitude as a function of sweep frequency for target with different thickness. 79 6 Results and discussion 6.2 Temperature influence on the sensor impedance In this section, thermal coefficient of resistance of the sensor coil and other temperature influences on properties of the sensor are obtained. Further more, the feasibility of the sensor working at high temperature up to 600 oC is evaluated. 6.2.1 Thermal coefficient of resistance of the sensor coil Based on the measured temperature dependent resistance values at different frequencies, we are able to calculate values of frequency dependent coefficient α according to Equation (5.3). 140 120 Ω 100 80 Resistance / Resistance 60 40 0 100 200 300 400 500 600 Temperature / oC Figure 6.2.1 DC resistance of square sensor at different temperature. Figure 6.2.1 shows a linear temperature (T) dependent DC Resistance (R) following a Ω relationship of R= 39.514Ω + 0.168 T. The slope equals to dR/dT and resistance at Κ 20 oC equals to 42.88 Ω. Deducing from Equation (5.2), the DC temperature coefficient of resistance is: dR 1 α = ⋅ = 0.00391(Κ −1 ) dT Rs Using the same principle, temperature coefficient of resistance at 50 Hz follows the Ω relation R=74.72394Ω+0.3104 T, which is shown in Figure 6.2.2. Hence, it is α (at Κ 50 Hz) = 0.00384 K-1. 80 6.2 Temperature influence on the sensor impedance 260 Rectangle sensor 240 220 200 Ω 180 160 140 120 Resistance(50Hz) / / Resistance(50Hz) 100 80 60 0 100 200 300 400 500 600 Temperature / oC Figure 6.2.2 Resistance of the rectangular sensor at different temperatures at 50 Hz. The conductor of sensor coil is made of silver. Silver’s temperature coefficient of resistance at DC is 0.0038 K-1. Comparing this standard value with our measured value, we reach the conclusion that the change of DC or low frequency resistance of the sensor coil are mainly due to the temperature dependent resistance change of the conductor material (silver), but has no relationship with its structure. 6.2.2 Temperature influence on the impedance of the sensor In this section, the sensors are tested in two ovens in succession. The first oven can reach a maximum temperature of 300 oC. Thus, the soldering with lead alloy that is able to sustain temperature over 350 oC was used for the interconnection between sensor and lead. In this condition, we expect that the temperature disturbance to this kind of interconnection is relatively smaller than that to the mechanical contacting connection used for the sensor worked in the other oven with maximum temperature of 600 oC. The sweeping frequency measurements of impedance were carried out to evaluate whether the eddy current sensor of LTCC can work properly at high temperature or not. Therefore, the properties of impedance of sensor at a high temperature up to 600 oC were tested and compared with those obtained at room temperature in order to elucidate whether the designed LTCC eddy current sensor can also be applied at high temperatures or not. We have carried out this comparison by considering two aspects. One is the absolute value of resistance and inductance of the sensor, and the other one is the change rate and tendency of them. According to this experiment, the testing principle of the eddy current sensor and the optimal working frequency and testing signal for high temperatures are further identified. 6.2.2.1 Influence of temperature on the resistance of the sensor First, we evaluate the temperature influence on the resistance of the sensor at different frequencies when it was put in a heating oven with maximum temperature 81 6 Results and discussion of 300 oC. The working frequency range up to 1.5 MHz is focused on. The results are shown in Figure 6.2.3. According to this figure we have learned that the resistance of the sensor increases not only with frequency but also with temperature. The change of resistance due to temperature increases with the frequency increase. It is evident from Figure 6.2.4 that at low frequencies the temperature dependent resistance change is linear. At 1 MHz, there is only a small derivation from the linearity, and above this frequency, the linearity becomes worse quickly. 600 Only sensor 10000 23oC 50oC 5000 500 100oC 150oC 0 200oC 400 250oC Ω -5000 o Ω 300 C -10000 300 Resistance / -15000 -20000 / Resistance 200 -25000 0 1M2M3M4M5M 100 Frequency / Hz 0 0,0 500,0k 1,0M 1,5M Frequency / Hz Figure 6.2.3 The resistance of the rectangular sensor without target at different frequencies and its detail figure until 1.5 MHz at 7 different temperatures from 23 to 300oC. 1100 10Hz 1000 1kHz 900 100kHz 464kHzMHz 800 1MHz 1.5MHz 700 600 Ω 500 300 250 Resistance / / Resistance 200 150 100 50 0 0 100 200 300 Temperature / oC Figure 6.2.4 The relation between resistance of the sensor without target and temperature at different frequencies. In succession, a blade with a thickness of 0.5 mm in an aluminium rotor was put in the oven, too. The clearance between the tip of the blade and the sensor was about 82 6.2 Temperature influence on the sensor impedance 1.5 mm. Both the resistance of sensor with target from room temperature to 150 oC and the reference resistance of sensor without target (in Figure 6.2.3) were shown in Figure 6.2.5. From this figure, it can be concluded that the resistance of the sensor with the target is also increased with temperature increasing, but the values are not the same as those without a target. The converting frequency for change tendency still exists. Below this frequency, the resistance values with target are always bigger than those without a target, but above this frequency, the change tendency is changed and the resistance of sensor is smaller than those without target. With the increase of the temperature, the converting frequency decreases. 400 Only sensor 23oC 300 o 50 C 100oC Ω 150oC 200oC o 250 C 200 300oC near blade Resistance / 23oC 50oC 100oC 100 o 150 C 0,0 500,0k 1,0M 1,5M Frequency / Hz Figure 6.2.5 The resistance of a sensor with an aluminium target blade from room temperature to 150 oC and the resistance of a sensor without target from room temperature to 300 oC. Tested as reference value in the Binder oven with maximum temperature 300 oC. As for the testing results from the oven with higher maximum temperature (shown in Figure 6.2.6), the same phenomena can be found. The resistance increases with the increase of temperature regardless if there is a target or not. But the relationship between the resistance of the sensor with target and the one without target is not so clear. We consider that this is due to the interconnection between sensor and wire being the mechanical contact. In the oven with high temperature, the movement of wire due to active fan of airflow in the oven influences the contact resistance and causes the instability of measuring value of the resistance of the sensor. However, according to the results, it is evident that the sensor can work properly at high temperatures because the obtained resistance values are within the error limit during in situ high temperature measurements and are exactly the same when retested at room temperature after a high temperature experiment. The appearance and the initial impedance of the sensor are the same as those before suffered high 83 6 Results and discussion temperature. What we must be very careful is the packaging of sensor and testing environments when considering the resistance of the sensor at high temperature. 900 Only sensor 200oC 800 300oC 400oC 700 500oC near blade 600 o 200 C Ω 300oC 500 400oC 500oC 400 Resistance / 300 200 100 500,0k 1,0M 1,5M Frequency / Hz Figure 6.2.6 The resistance of a sensor with an aluminium target blade from 200 to 500 oC and the resistance of a sensor without target in same temperature range. Both were tested in the oven with maximum temperature 600 oC. 6.2.2.2 Influence of temperature on the inductance of the sensor The inductances at different temperatures were measured at the same time as the measuring of the resistance of the sensor. The measurement conditions were the same as described in the last section. Figure 6.2.7 showed that the inductance of sensor suffers from far smaller influences from temperature than the resistance does although it also increases with the increase of temperature. Below 500 kHz, the changes of the inductance are less than 0.3%. As for the whole working frequency range, the change rate of inductance increases with the increase of frequency, but the change rate of inductance is far smaller than that of the resistance. Like in the last section, the inductances of sensor in two ovens individually were measured when one aluminium blade was near the sensor. According to the results (Figure 6.2.8 and Figure 6.2.9), it is clear that the inductances of the sensor at different temperatures decrease when a metal blade approaches the sensor. This change of inductance is very similar to that at room temperature. Observing the data tested in the oven with lower maximum temperature (Figure 6.2.8), the inductance of sensor with target changes scarcely with temperature increasing when exciting frequency was below 1 MHz. Even in the oven with higher temperatures (Figure 6.2.9), the change of inductance with temperature increasing is still very small. The inductance of the sensor with the target below 1 MHz decreases with temperature 84 6.2 Temperature influence on the sensor impedance increasing. When frequency increases, the inductance increases with the temperature increase gradually. 2,5k Only sensor 23oC 50oC 2,0k 100oC 150oC 1,5k 200oC o H 250 C μ 1,0k 300oC 500,0 Inductance / 0,0 -500,0 -1,0k 0 1M2M3M4M5M Frequency / Hz Figure 6.2.7 The inductance of the sensor itself at different frequency and at 7 different temperatures from 23 to 300oC Only sensor 23oC 50oC 600 100oC 150oC 200oC 250oC H μ 300oC near blade o 24 C 400 50oC 100oC o Inductance / Inductance 150 C 200 500,0k 1,0M 1,5M Frequency / Hz Figure 6.2.8 The inductance of a sensor with an aluminium target blade from room temperature to 150 oC and the inductance of a sensor without target from room temperature to 300 oC. Tested as reference value in Binder oven with maximum temperature of 300 oC below 1.5 MHz. 85 6 Results and discussion 700 sensor-200oC sensor-300oC 600 sensor-350oC sensor-400oC sensor-500oC 500 o H with rotor-200 C μ with rotor-300oC with rotor-400oC 400 with rotor-500oC Inductance / 300 200 500,0k 1,0M 1,5M 2,0M Frequency / Hz Figure 6.2.9 The inductance of a sensor with an aluminium target blade from 200 to 500 oC and the inductance of sensor without target in same temperature range. Both were tested in the oven with maximum temperature 600 oC. In summary, the influence of the environment temperature on the resistance of the sensor is much more pronounced than that on the inductance of the sensor. As for the resistance, the change tendency for the target keeps the same as that at room temperature although the absolute value of resistance increases obviously with temperature increasing. The converting frequency for change tendency still exists but the value increases with temperature increasing. The influence of packaging and environment such as airflow must be taken into account for measurement of the resistance. As for the inductance of the sensor with and without target, both of its absolute value and its change tendency didn’t change so much with temperature change. Especially when the exciting frequency is below 1 MHz, the change is very small. Therefore, we can conclude that the LTCC eddy current sensor can work properly at high temperature at least up to 600 oC because the measuring mechanism of the eddy current sensor can be implemented properly. The inductance of the sensor is a better testing signal than the resistance of the sensor for measurement at high temperature environment. 1 MHz is optimal exciting frequency, namely, the working frequency of sensor. At this frequency, the impedance amplitude can also be chosen as testing signal because the change tendency of the resistance and the inductance are the same and moreover the inductance of sensor plays a major role. 86 6.3 Real-time measurements 6.3 Real-time measurements 6.3.1 Response of the sensor to rotation of the rotor The purpose of this experiment is to check whether the sensor can test rotating speed of rotor or not. The experimental conditions are that the material of the rotor was copper, the testing circuit was set in current function, and the clearance between the tips of the rotor and the surface of the sensor was 1 mm. Firstly, ideal values of frequency fideal of the rotating speed are calculated by Equation (6.1) -1 fideal= foutput·nmax·Nblades / fmax (min ) = 8·foutput (Hz) (6.1) where foutput: controlling frequency of converter (Hz) ; Nblades: number of rotor blades (8 pieces); nmax: rated maximum rotating speed (3000 rpm); fmax: maximum controlling frequency for nmax (50 Hz). (a) (b) Figure 6.3.1 The examples of waveform measured by the sensor. (a) when controlling frequency of converter is 50 Hz; (b) when controlling frequency of converter is 20 Hz. 87 6 Results and discussion The controlling frequencies of the converter were changed in 5 steps between 10 and 50 Hz. The corresponding waveforms (see Figure 6.3.1) display the testing signal of the sensor with different number of peaks (Npeak) within the same recording time (Trecord). Every negative peak corresponds to one blade. According to these waveforms, we can calculate the frequency of the testing signal by Equation (6.2). ftest =Npeak / Trecord (6.2) Comparing two frequencies of the ideal value and the testing value, the ability of sensors to test the rotating speed up to 3000 rpm can be evaluated. Table 6.2 shows all the values of the rotating rotor and the testing results. One finds that the testing signal can reflect the rotating speed of rotor exactly (see column 2 and column 6 in this table). Therefore, the function of sensor to test rotating speed of rotors was identified. Table 6.2 Initial values of rotor and testing results using the sensor Ideal values Testing results Motor Blades Acquisition Number of Period Frequency speed speed time (ms) Peaks between (Hz) (rpm) (Hz) two peaks (ms) 600 80 25 2 12.5 80 1200 160 25 4 6.25 160 1800 240 25 6 4.167 240 2400 240 25 8 3.125 240 3000 400 25 10 2.5 400 6.3.2 Influence of the clearance between sensor surface and tip of blades In this section, the clearance between sensor surface and tip of blades was changed from 1 to 5 mm with steps of 0.5 mm. The amplitude of peaks is the object we focus on. As shown in Figure 6.3.2, the amplitude of the negative peak changes abruptly with the clearance. 88 6.3 Real-time measurements Apeak Amodul (a) (b) Figure 6.3.2 The waveforms of test signals at different clearance. (a) when the clearance is 1.5 mm; (b) when the clearance is 3.5 mm. The sensitivity S of the sensor can be defined as: S=100%×|(Amodul-Apeak)|/ Amodul (6.3) where the illustration of parameter can be found in Figure 6.3.2 (a): Amodul is the amplitude of the modulation signal; Apeak is the amplitude of the testing signal of the sensor for the target position. 89 6 Results and discussion The testing results and sensitivities of the sensor are listed in Table 6.3. Table 6.3 Testing results of a sensor with different clearance Clearance Amplitude of Amplitude of Sensitivity of (mm) modulation signal testing signal sensor pk-pk(v) pk-pk(v) (%) 1.0 6.91 3.05 55.861 1.5 6.91 3.83 44.573 2.0 6.91 4.57 33.864 2.5 6.91 4.96 28.220 3.0 6.91 5.82 15.774 3.5 6.91 5.98 13.459 4.0 6.91 6.33 8.394 4.5 6.91 6.48 6.223 5.0 6.91 6.64 3.907 According to the results, the relation between the sensitivity of the sensor and the clearance is shown in Figure 6.3.3. From this figure, some conclusions can be made. The sensitivity decreases with the clearance. When the clearance is shorter than 2 mm, the change of sensitivity with the clearance is almost linear. Then with the clearance increasing, the decrease of sensitivity slows down continuously and finally the value of sensitivity tends to 0. Therefore, if we want to get higher and linear sensitivity, the clearance should be set shorter than 2 mm. 0,7 0,6 0,5 0,4 0,3 sensitivity 0,2 0,1 0,0 012345 distance / mm Figure 6.3.3 Clearance dependency of the sensitivity of the sensor. 90 6.3 Real-time measurements 6.3.3 Measurement for the changes of blades geometry First, a 0.3 mm copper strip was covered on the surface of one blade of the copper rotor. This modification for the blade can be considered to increase the length of the blade. In other words, the tip of this blade moved close to the sensor surface, therefore the clearance between blade and sensor is shortened. According to the results in last section, the amplitude of signal peaks for this modified blade should be lower than the others and the peak will appear one time in the signal every 8 peaks. The testing waveform (see Figure 6.3.4) shows this modification for one blade. The amplitude of the one peak in the signal was changed, but the frequency is the same. Figure 6.3.4 The test waveform of a sensor for the copper rotor with one longer blade. Then, more changes were made in the blades of that aluminum rotor in order to evaluate the sensor performance. Some parts of blades were taken away to make blades shorter and thinner. At the same time an aluminum film with a thickness of 0.3 mm also was covered to one blade and this blade was considered as a reference blade, because its amplitude of the peak in the measurement signal should be the lowest like Figure 6.3.4. The modification details of all the blades illustrate in Figure 6.3.5, and all the blades will pass the sensor along the sequence from left to right. The corresponding testing signal of the sensor is shown in Figure 6.3.6. Not only the amplitude of the peak is changed, but also the arrival times of the peaks for the thinner blades are changed. The lowest peak marked with a red circle corresponds to the reference blade. In this waveform, 1,249,996 data points in 50 milliseconds with 4·10-8 second increment of x-axis were contained. These data will be the input to an extra mathematical software such as MATLAB for analysis. What we are interested in are the amplitude and the arrival time of every peak in the waveform. Then, we can check whether the signal reflects every modification correctly, and thereby the working ability of sensor can be evaluated. 91 6 Results and discussion 1 2 3 4 5 6 7 8 short long right thin short left thin 0.3mm 0.3mm 0.5mm 0.1mm 0.1mm Figure 6.3.5 Details of the blade modifications of the aluminum rotor. Figure 6.3.6 Test waveform of a sensor corresponding to the modification of the blades in Al rotor. The peak marked by a cycle defines the signal for the longest blade. The group of Systems Theory at IMTEK helps us to process the acquisition data of the sensor. First, the acquisition data shown in Figure 6.3.7 are read in a programme and the exact modulating frequency is obtain by FFT (Fast Fourier Transform). The peak of the spectral power density appears at frequency 828.1 kHz. Then, demodulation of waveform is done because the information what we are interested is the peaks of signal. The complex Fourier coefficient of first grade for every 500 samples with modulating basic frequency are calculated and their average amplitudes are obtained. The demodulation signal shown in Figure 6.3.8 is obtained by reploting the average amplitudes. This demodulation method can release the noise which different from the modulation frequency. Least square error fit is used to get the coordinates of the 8 peaks. Figure 6.3.9 displays the figure with 8 peaks after the smooth fit. The corresponding coordinates of 8 peaks are shown in Table 6.4. According to these values, the peak “intensity” is defined as the reverse to the voltage and is shown in Figure 6.3.10. Comparing these values to the real length modification of blades shown in Figure 6.3.5, the right sequence of blades in the 92 6.3 Real-time measurements order of numbers 7-8-1-2-3-4-5-6 corresponding to Fig. 6.3.5 is obtained. When the length of a blade is longer than others, the clearance between the sensor and the blade is shorter, therefore the electromagnetic interaction between them is stronger and inductance of the sensor decreases more quickly. The corresponding peak “intensity” is reverse to the original peak, therefore it is proportional to the length of blade. The stronger the peak “intensity” is, the longer the balde’s length is. In addition, when a blade becomes narrow, that is, the surface of the blade becomes small, the inductance of the sensor decreases very little. This kind of situation is like that the length of blade becomes a little short but the influence is not so big. Based on this comparison, we found that the testing signal reflects the modification of blade geometry. The capability of the sensor to measure the clearance is identified. Figure 6.3.7 The measured data of the sensor for changes of clearance between blade and sensor. Table 6.4 The coordinate of 8 peaks of signal shown in Figure 6.3.9 No. of 1 2 3 4 5 6 7 8 peak T(s) 0.0041 0.0104 0.0167 0.0230 0.0292 0.0354 0.0417 0.0480 U(v) 1.5301 1.5407 1.5024 1.8569 1.3168 1.6154 1.4685 1.5392 93 6 Results and discussion Figure 6.3.8 Demodulated signal displaying the information of 8 peaks. Figure 6.3.9 The 8 peaks after square smooth fit. 94 6.3 Real-time measurements Figure 6.3.10 Peak “intensity” of the signal compared to the length changes of blades above. 6.3.4 Influence of testing circuits The testing signals have very close relation with the testing circuit. It can be applied in two modes: in current function of the circuit, the impedance amplitude is chosen as testing parameter, but in voltage function of the circuit, the inductance is the main testing parameter. In this section the voltage function of circuit was adopted and compared to the signal of current function. Using voltage function, adjusting of exciting frequency is very important. Exciting frequency must make the circuit composed of sensor and capacitor in resonant status. Because the inductance of sensor is different when the blade is near the sensor or far away from the sensor, different initial position of blade for the resonant status will result in a different exciting frequencies and testing signal. 95 6 Results and discussion Figure 6.3.11 Voltage waveform for the rotor with one longer blade. The resonant status exists in a position where normal blade is near sensor surface. Figure 6.3.12 Voltage waveform for the rotor with one shorter blade. The resonant status exists in a position where normal blade is near sensor surface. First, we place a normal blade without modification approximate to the sensor as near as possible. In this position the exciting frequency was adjusted to make the amplitude of modulation signal to be maximum. Then, two rotors with one longer blade and one shorter blade respectively are measured with rotating speed of 1200 rpm. The testing signals of the sensor for the rotor rotation are shown in Figure 6.3.11 and Figure 6.3.12. The former is for the rotor with one longer blade, and the latter is for the rotor with one shorter blade. The signals look very different with signal tested by current function, because the position with minimum inductance was set as the initial position with maximum voltage amplitude of testing signal. 96 6.3 Real-time measurements Comparing the signals corresponding to the longer blade and the shorter blade in both figures marked by the red circles, we find that not only the amplitude of peaks but also the shape of them occurs to change. The reason for these changes can be found in Figure 6.3.13. As for the long blade, the resonant inductance of the normal blade is in point P1, but there are two points P2 and P3 with this inductance value for longer blade. Therefore, in position of points P2 and P4 two peaks occur with the same amplitude of the normal blades. Inversely, the inductance in position P4 is different from that in P1, therefore in position P4 the amplitude is lower than the maximum peak. With the same principle, if the inductance of P4 was chosen as resonant inductance of normal blades, all the inductances of shorter blades are different from the resonant inductance, and in position P1 the inductance is most near the inductance in P4. Therefore, there is only one peak in position P1 for shorter blade but the amplitude of the peak is lower than one of normal blades. Shorter blade Inductance Inductance P2 P1 P3 P4 Longer blade Horizontal distance Figure 6.3.13 Illustration of the inductance and position of peaks in testing signal. Next, the resonant position was changed. In positions where the normal blade without modification is far away from the sensor, the sensor circuit is set to be resonant status by adjusting the exciting frequency. The corresponding signal for the rotor with a longer blade is shown in Figure 6.3.14. The shape of signal here is very similar to that using current function of the circuit because both functions choose the position with maximum inductance as the position where the amplitude of testing signal is highest, whereas the difference between two testing functions must be made clear. The testing signal of the sensor with current function of circuit is corresponding to the real value of inductance of sensor, while the testing signal with voltage function of circuit is corresponding to not real value of inductance of sensor but the value relative to resonant inductance. 97 6 Results and discussion Figure 6.3.14 Voltage waveform for the rotor with one longer blade. The resonant status exists in a position where normal blade is far away the sensor surface. To summarise this chapter, all the testing signals whether using current function or voltage function can correspond to the displacement and to the change of structure of blades in rotors rightly, hence the feasibility to monitor the movements of blades in rotors was identified by practical on-line measurements. 98 7 Conclusions and prospects 7.1 Summary and conclusions It is indispensable to improve the lifetime and performance of conventional displacement sensors and to transform these sensors to match the requirements of engine health monitoring such as a blade tip sensing systems in turbo-machinery. In this work, first literature and information were collected and compared. An eddy current displacement sensor using the novel LTCC technology was found to match the related measurement conditions such as harsh and high temperature environments, non-magnetic metal blades, etc. Then, according to the structure of the LTCC sensor coil, a set of analytic calculating methods based on fundamental equations of the inductance and the capacitance between two simple thin strips was built. The inductance, resistance, capacitance, quality factor, self-resonant frequency of a complete sensor coil and standard skin depth of eddy current in target blade were considered. Subsequently, the FEM method was used for further calculations. It was found via modal analysis that the position over the sharp end of a blade tip is the optimal mounting position for a sensor. Electromagnetic analysis showed that the sensitivity of the sensor inductance has one principal influence factor, which is the outer size of the sensor coil. Effects on the resistance of the sensor and on the quality factor concerning changes of layers, turns and fill factor were also investigated. In addition, the 3D eddy current distribution and the relations between the impedance of the sensor and the blade displacement in horizontal and vertical directions were obtained. Finally, a complete optimization work flow was proposed based on the methods and conclusions of analytic and FEM analysis as well as LTCC fabrication guideline. The layout was designed for the sensor variation with the optimal parameters, and it was realized by LTCC fabrication. Eight sensors were obtained for further experimental testing. With respect to experimental work, the characteristics of the sensors were measured by LCR meter and impedance analyzer. These testing results were used to check the results of the FEM simulation and analytic calculation. Temperature dependent experiments were carried out to identify the feasibility of the LTCC sensor at high temperature using the eddy current operating mechanism. Finally, a complete displacement sensor system composed of a motor, a rotor with blades, a testing circuit, a data acquisition system, a computer control and signal processing system were built to simulate a blade tip measurement system. The recording rate was up to 24000 blades per minute. The clearance between sensor and blade tip, and the blade 99 7 Conclusions and prospects change of geometry were measured and proven to reflect the corresponding information correctly. All the results identified that the comprehensive optimization method combined with analytic analysis and FEM simulation is an effective design approach to LTCC planar sensor. FEM simulation comprises modal, electromagnetic and thermal- mechanical analysis. In addition, our LTCC eddy current sensor shows good properties for high temperature environments up to 500 oC and high-speed measurements up to 3000 rpm (24000 bpm). Its feasibility to work for turbomachinery in harsh and high temperature environments was verified under laboratory conditions. 7.2 Outlook With respect to further work on the testing system there still exist some aspects to be improved and developed. First, the size of the sensor can be further reduced and its properties can be improved by means of the stronger LTCC fabrication capability from foundries. For the testing object, the rotor can be improved so that it can provide more complicated displacements of the blades. The measurement capability of the sensor for various movements can be further identified. The improvement also can be conducted for the testing environment. The testing system including rotating blades and the sensor can be put into an oven to identify the feasibility of the sensor at high temperature via dynamic displacement measurements. Second, with respect to the testing circuit, a PLL function can be included. This function will be able to keep the resonant status of the sensor circuit by changing the exciting frequency of the voltage source. The signal from the frequency changes of the PLL circuit indicates the inductance changes of the sensor. The signal from the voltage of the sensor gives the information on the resistance of the sensor. Third, with respect to the signal processing, online data processing can be implemented. A smart control system is able to solve possible problems according to online signal analysis. This will make the system intelligent and it can become a real health diagnosing monitor. In addition, LTCC packaging can also be applied to other similar sensors which exhibit a coil as a main component. This kind of sensor is also used for high temperature environments, for example, a microwave with a single layer of coil. In fact, our heat-resistant sensor applies not only to tip timing measurements of 100 7.2 Outlook turbomachinery, but also to the entire field of measuring displacement, proximity etc. at high temperatures. 101 Zusammenfassung Zur Überwachung der Rotorschaufeln in Turbomaschinen sind berührungsfrei arbeitende Sensoren notwendig. Obwohl die von herkömmlichen Abstandssensoren bekannten Prinzipien grundsätzlich genutzt werden können, ist es notwendig, diese Sensoren insbesondere den Anforderungen des Hochtemperaturbetriebs anzupassen und die Robustheit und Lebensdauer signifikant zu verbessern. Ziel dieser Arbeit war der Entwurf und die Realisierung eines Sensorkonzepts, um statische und dynamische Geometrieabweichungen von Turbinenschaufeln im Betrieb auch bei nichtmagnetischen Werkstoffen zu detektieren. In der vorliegenden Arbeit wurde zunächst eine Literaturrecherche zu geeigneten Sensorprinzipien und Aufbauformen durchgeführt und ausgewertet. Basierend hierauf wurde das Prinzip des Wirbelstrom-Abstandssensors ausgewählt. Um Einsatzrandbedingungen wie aggressive Atmosphäre und Hochtemperaturumgebung sowie nichtmagnetische Schaufelblätter aus Metall zu erfüllen, wurde die Umsetzung mit Hilfe der Low Temperature Cofired Ceramics Technologie (LTCC) weiter untersucht. Sequenziell wurde zunächst die Finite-Elemente-Methode benutzt, um verschiedene Berechnungen und Optimierungen bei der Auslegung durchzuführen. In der Modalanalyse wurde ermittelt, dass radial über dem spitzen Ende der Schaufel die optimale Position zum Anbringen des Sensors liegt. Aus elektromagnetischen Analysen konnte der Rückschluss gezogen werden, dass die Empfindlichkeit der Sensorinduktivität einen dominanten Einfluss auf die äußere Größe der Sensorspule hat. Entsprechend den Strukturen der LTCC Sensorspulen wurde eine Serie analytischer Berechnungen, basierend auf den Grundgleichungen für Induktivität L und Kapazität C zwischen zwei einfachen dünnen Streifen aufgestellt. Induktivität L, Widerstand R, Kapazität C, Qualitätsfaktor Q und Resonanzfrequenz einer Sensorspule sowie die Skintiefe des Stroms in der Zielschaufel wurden betrachtet. Die Einflüsse durch Änderung von Schichten, Umdrehungsraten und Füllfaktoren auf den Widerstand des Sensors und den Qualitätsfaktor wurden ebenfalls untersucht. Zusätzlich wurden die dreidimensionale Wirbelstromverteilung und die Relationen zwischen Widerstand des Sensors und Blattversetzung in horizontaler und vertikaler Richtung erhalten. Letztlich wurde auf Grundlage dieser Methoden, bestehend aus analytischer Berechnung, FEM-Analyse und LTCC-Herstellungsrichtlinien ein kompletter Entwurfs- und Optimierungsprozess vorgeschlagen. Eine Variante des Sensors wurde gemäß den optimalen Parametern entworfen und durch Herstellung eines LTCC realisiert. Hierdurch wurden die Sensoren für die weiteren Experimente erhalten. 103 In Bezug auf die experimentellen Arbeit wurden die Eigenschaften des Sensors durch ein LCR-Meter und ein Widerstandsmessgerät bestimmt. Diese Testergebnisse wurden auch dazu benutzt, die Ergebnisse der FEM-Simulationen und der Berechnungen qualitativ und quantitativ zu überprüfen. Dabei ergab sich, dass die wesentlichen Effekte und Abhängigkeiten richtig prognostiziert wurden. Temperaturexperimente wurden durchgeführt, um festzustellen, ob der LTCC Sensor auch bei hohen Temperaturen und Hochfrequenzwirbelstrom funktioniert. Dies konnte bis zu Temperaturen von 500 °C bestätigt werden. Schließlich wurde ein komplettes dynamisches Abstandsmesssystem bestehend aus Motor, Rotor mit Schaufeln, Prüfstromkreis, Datenerfassung, Computersteuerung und Signalprozessor aufgebaut, um den Einsatz in einer Turbine nachzubilden. Dabei wurden Parameter wie die Frequenz der Rotorblätter, bis zu 24000 Blätter min-1, der Abstand zwischen Sensor und Spitze des Rotorblattes und die Blattgeometrie systematisch untersucht, um das Testsystem zu charakterisieren. Alle Ergebnisse zeigen, dass die umfassende Optimierungsmethode bestehend aus FEM-Simulation inklusive Modalanalyse, elektromagnetischer und thermomechanischer Analyse ein effektiver Weg zum Entwickeln von planaren LTCC Sensoren ist. Zusätzlich zeigt der hier entwickelte LTCC Wirbelstromsensor gute Eigenschaften bei hohen Temperaturen bis 600°C und hohen Drehzahlen bis 3000 upm (24000 Blätter min-1). 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[61] "951 Green Tape Material Systems", Website of company DuPont, www.dupont.com. 108 Abbreviations and symbols C Capacitance [pF] E Young’s modulus [MPa] I Current [A] L Inductance [mH] L0 Unloaded inductance of the sensor coil [mH] Ls Loaded inductance of coil [mH] Lself Self-inductance between two strips [mH] M Mutual inductance between two strips [mH] Q Quality factor Q0 Unloaded quality factor of coil R Resistance [Ω] R0 Unloaded resistance of coil [Ω] Rs Loaded resistance of coil [Ω] V Voltage [v] Y Admittance [Siemens] Z Impedance [Ω] f Frequency [Hz] t Turns x Displacement [mm] δ Skin depth [m] ε Dielectric constant [F/m] ε Strain ε0 Dielectric constant of free space [F/m] εr Relative dielectric constant μ Permeability [H/m] μ0 Permeability of free space [H/m] μr Relative permeability ρ Resistivity [Ωm] σ Conductivity [S/m] σ Stress [MPa] σ0.2 0.2% offset yield stress [MPa] σu Ultimate tensile stress [MPa] ω Radian frequency [radians/s] Geometry: h Height of coil [mm] l Length of blade tip [mm] li Inner length of racetrack coil [mm] 109 lo Outer length of racetrack coil [mm] ri Inner radius of coil(2D FEM) [mm] ro Outer radius of coil(2D FEM) [mm] wi Inner width of racetrack coil [mm] wo Outer width of racetrack coil [mm] Abbreviations: EM, Emag Electromagnetic field FEM Finite elements method HTCC High temperature cofired ceramic LTCC Low temperature cofired ceramic SRF Self-resonant frequency of coil TCE Temperature coefficient of expansion [K-1] 110 Acknowledgement I would like to thank all persons who have helped me on this work. My special thanks are due to Prof. Dr. Jürgen Wilde for providing me the opportunity to work in IMTEK and on this interesting topic, being my first supervisor, showing me the research method and giving me many helps whenever I need. Prof. Dr. Christoph Ament for not only being my second supervisor, but also for his kind helps in signal analysis and correcting the English of my dissertation with much patience and time. Mrs. Christine Jägle for her kind helps in many aspects including both my private and the academic matters. All my colleagues in the group of AVT, Mrs. Elena Zukowski, Mr. Erik Deier, Mr. Sebastian Fischer, Mr. Daniel Arnold and Mr. David Pustan, for the friendly working atmosphere and all kinds of helps for my work and life. Mr. Vassil Jankov for helps in circuit design and fabrication, and paying some time to adjust the electronic system for the experiments. Mr. Peter Wissmann and Mr. Benjamin Rutschinski for helps in mechanical fabrications of the testing system and other mechanical parts. Dr. Zhenyu Liu for discussions on the simulation method and friendship between his family and me. Group members of Electrical Instrumentation for their supports on the key electronic instruments used in this work. Dr. Druee for the LTCC fabrication of the sensors and the helpful discussions on the layout design of LTCC. Finally, I express my thanks to my family and especially to my husband, Yongfeng Men. His encouragements and supports are always my most important motivation in my life and work even if when he lived in another city for two years. Curriculum Vitae YuQing Lai Born: 18.Sept 1973; Sex: Female ; Status: Married (September 1991 ---- July 1995) Physics department, SouthEast University, Nanjing China Major: Applied Physics; Subsidiary subject: Wireless Engineering Bachelor’s degree was awarded in June 1995 (July 1995 ---- September 1997) Microelectronics lab, Institute of electronic engineering, Academy of engineering physics of China (CAEP), Mianyang, China Worked as an assistant engineer (September 1997 ----March 2000) Institute of high energy electronics, University of electronic science and technology of China (UESTC) , Chengdu China Major: Microwave Electronics Master’s Degree was awarded in April 2000 (April 2000 ---- October 2000) Sprachenkolleg, Freiburg Germany German learning (December 2000 ---- March 2001) Laboratory for assembly and packaging, Institute of Microsystem Technology (IMTEK), University of Freiburg, Freiburg i. Brsg. Germany Worked as an assistant (March 2001 ----present) Laboratory for assembly and packaging, Institute of Microsystem Technology (IMTEK), University of Freiburg, Freiburg i. Brsg. Germany Supervisor: Prof. Dr. J.Wilde Dissertation: Eddy current displacement sensor with LTCC technology