eddy current displacement sensor with ltcc technology

ThesisDissertation zur Erlangung des Doktorgrades
der Fakultät für Angewandte Wissenschaften
der Albert-Ludwigs Universität Freiburg im Breisgau
vorgelegt von
Yuqing Lai
Referenten: Prof. Dr. J. Wilde, Prof. Dr. C. Ament
Datum der Promotion: 22. 03. 2005
To yongfeng
3 Aim of research and some basic principles and concepts............................. 12
3.1 Aim of the work .......................................................................................... 12 3.2 The concept and principle of an eddy current sensor................................. 12
3.2.1 The theory of eddy currents.................................................................... 13 3.2.2 Testing principle for turbine blades........................................................ 16
4 Design of the eddy current sensor ................................................................... 19
4.1 General principle and design factors .......................................................... 19 4.2 Analytical calculation of parameters of a LTCC coil ................................ 20
4.2.1 Analytic model of the LTCC coil for analytic analysis ......................... 20 4.2.2 Inductance calculations........................................................................... 21
4.2.2.1 Self-inductance ............................................................................... 22 4.2.2.2 The mutual inductance ................................................................... 23
4.2.3 The DC resistance of the coil.................................................................. 28 4.2.4 Capacitance calculation .......................................................................... 28 4.2.5 Quality factor, skin depth, self-resonant frequency ............................... 32
4.2.5.1 Quality factor (Q) ........................................................................... 32 4.2.5.2 Skin depth ....................................................................................... 33 4.2.5.3 Self-resonant frequency (SRF)....................................................... 34
4.3 Design and optimization of the eddy current sensor.................................. 35 4.3.1 FEM simulation....................................................................................... 35 4.3.2 Optimizing the sensor location - modal vibration simulation ............... 36 4.3.3 Optimizing the sensor sensitivity-EM evaluation.................................. 39
4.3.3.1 2D simulation.................................................................................. 39 4.3.3.2 3D simulation.................................................................................. 46
4.3.4 Thermo-mechanical FE analysis ............................................................ 50 4.4 LTCC layout design for eddy current sensor ............................................. 54
4.4.1 Material selection of LTCC coil ............................................................. 54 4.4.2 Structural design optimization with fabrication guideline..................... 55 4.4.3 Layout design.......................................................................................... 56
ii
5.1 LTCC fabrication of the eddy current sensor coil.......................................58 5.2 Sensor characterization ................................................................................59
5.2.1 Static impedance of sensors (L, C, R) .....................................................59 5.2.2 Static position measurement system .......................................................59
5.2.2.1 Proximity testing..............................................................................60 5.2.2.2 System for impedance testing by frequency sweep........................60
5.4 System for real-time measurements ............................................................63 5.4.1 Rotation control and generator ................................................................64 5.4.2 Electronic signal acquisition system .......................................................65 5.4.3 Test objects...............................................................................................67
6.1.2.1 Proximity testing..............................................................................69 6.1.2.2 Horizontal passage testing...............................................................70
6.2 Temperature influence on the sensor impedance........................................80 6.2.1 Thermal coefficient of resistance of the sensor coil ...............................80 6.2.2 Temperature influence on the impedance of the sensor .........................81
6.2.2.1 Influence of temperature on the resistance of the sensor ...............81 6.2.2.2 Influence of temperature on the inductance of the sensor..............84
6.3 Real-time measurements..............................................................................87 6.3.1 Response of the sensor to rotation of the rotor .......................................87 6.3.2 Influence of the clearance between sensor surface and tip of blades .....88 6.3.3 Measurement for the changes of blades geometry..................................91 6.3.4 Influence of testing circuits .....................................................................95
7 Conclusions and prospects ................................................................................99
1 Introduction
Eddy current non-contact measuring systems have been widely used for more than 30 years for measurement of position, displacement, vibration, proximity, alignment, and dimensioning, as well as parts sorting applications [1-5]. In this work, the novel low temperature co-fired ceramics (LTCC) technology was applied to a planar displacement eddy current sensor in order to improve the performance of the sensor for displacement measurements in high temperature environments. The improved sensor can be used as a blade tip sensing probe within a “health monitoring” system for rotary instruments, such as aero-engines, gas turbine engines, steam turbines or turbocharges.
To date, prediction of displacements in aerodynamic systems has been difficult due to the lack of computational fluid dynamics fidelity, structural modeling accuracy, instrumentation effects and insufficient characterization of instrumentation installation effects. Therefore, to improve the lifetime and performance of conventional displacement sensors, such as eddy current sensor or strain gages, and transforming them for engine health monitoring applications has become very important [6]. Especially for a turbo-machinery system, the working environment is very harsh and the movements of blades are complicated (see Figure 1.1). Incipient failure of rotor blades and disks can be anticipated by detecting a damage signature early on, and detecting incipient failures in advance can avoid or prevent further damages [7].
Figure 1.1 Illustration of turbine blades and an example of their vibrations analyzed by finite elements method.
Recently, a measurement technique known as non-destructive blade tip-timing method was developed [8-12] for health monitoring of turbine blades. This method uses multiple sensing probes installed in the engine casing to sense points in time
1 Introduction
2
when the blades are passing the probes. The changing vibration characteristics are analyzed according to acquisition timing data. Further more, the related blade's fatigue life and the health condition of the turbine are evaluated. In such an on-line blade monitoring system, non-contact displacement sensors play an important role.
Several physical principles are possible for non-contact measurements. Among these, eddy current, optical reflection and capacitive sensors have good properties. But in harsh environments, eddy current sensors are superior to other types of sensors and have become the best choice because they are inherently immune to nonmetallic materials, e.g. plastic, opaque fluid or transparent fluid and dirt [13].
The sensor coil is the main component of an eddy current sensor. In this work the manufacturing technique of the sensor coil was changed in order to meet the requirement that such a sensor works at high temperature. The novel LTCC technology was applied to fabricate these eddy current sensors.
Low temperature co-fired ceramics (LTCC) are multilayer glass-ceramic composites that can bear high temperatures up to the melting point of the conductor metal. Its typical advantages are as follows [14,15]:
• Temperature stability
• Green tape for single layers available in a variety of uniform thicknesses
• Co-fireable and post-fireable Au and Pd/Ag conductors with oxidation resistance
• Tape has low dielectric constant and dielectric loss
• Material has low TCE
• Small x-y fired shrinkage
Because of these advantages, an LTCC application for sensors and actuators was developed recently rendering a technology suitable for micro-system technology (MST) [16,17]. The objective of this work is to apply LTCC technology to a planar eddy current sensor in order to improve the feasibility and reliability of displacement measurements in harsh and high temperature environments.
1 Introduction
3
For sensors with a new packaging, their sensitivities and feasibilities must be controlled and evaluated. In this work, the design of the sensor was first optimized . A set of calculating methods were built using analytic analysis for electric parameters of a planar film coil, such as unloaded impedance, skin depth and self-resonant frequency. Various properties of eddy current sensors were evaluated by finite elements method (FEM) analysis such as the optimal mounting position, optimum structure and materials. The FEM analysis involves three aspects: modal, electromagnetic and thermal mechanical analysis. According to the results of analytic and FEM analyses and combining them with the LTCC fabrication guidelines, a comprehensive optimization flow chart was developed, and a corresponding optimization layout was designed and implemented. With the realized LTCC sensor examples, experimental characterization was carried out. In addition, the influence of temperature on the properties of the eddy current sensor was evaluated. It was found that the change of the resistance of the sensor with the change of the target displacement follows the same trend at different temperatures up to 600 oC. Also the values of inductance below 1 MHz bear little temperature dependence. Therefore, it was justified that LTCC eddy current sensors are feasible at high temperatures. Finally, a rotating system consisting of a motor, a rotor with blades, a testing circuit, and a data acquisition system was built. This equipment was used to simulate the rotation displacement of blades. The testing signals represent the rotating speed of the motor up to 3000 rpm, clearance between sensor and blade tip, and changes of the blade geometry correctly. Thus, the capability of the LTCC eddy current sensor to measure displacements of rotary blades was proved. All stages of the development of our work are illustrated in Figure 1.2.
In this thesis, chapter 2 describes the literature and addresses the state of the art for the blade tip timing technique. Several conventional displacement sensor and packaging technologies are introduced. Chapter 3 elaborates on the aim of this project. The basic principles of eddy current sensors and LTCC technology are also presented. Chapter 4 is concerned with the design optimization of the LTCC eddy current sensor. The analytic and numerical calculations and empirical work have been done to design a novel LTCC eddy current sensor for the measurement of rotor blade tips. The layout for an optimal sensor structure is obtained for LTCC fabrication. In Chapter 5, the set-up of the experimental system and the related calculation method for data processing are introduced. It comprises the instruments for the characterization of the sensor and the measurement of temperature dependent properties, and the system integration including motor, rotor with eight blades, sensor and its supporting frame, as well as the electronic measurement and data acquisition system etc. Chapter 6 displays the experimental results and corresponding discussion. Finally, Chapter 7 summarizes the work and gives the conclusions and the prospect for possible improvements as well as further applications.
1 Introduction
Modal , electromagnetic, thermo-mechanical Analytic calculation:
Resistance, inductance, capacitance, skin depth, self- resonant fr e q uency
Design layout and LTCC fabrication Selection of LTC C materials and structure Layout design by software CAM350 LTCC fabrication
Experiment and measurement Static behavior:
Sensor character i zation for impedance Temperature influence on sensor behavior
Dynamic behavior: Test system (rotating system, circuit and data acquisition system) Measurement for rotary speed, clearance, changes of the blade geometry Signal processing and analysis
Figure 1.2 Flow chart of project work.
5
2 State of the art
This chapter provides a starting point for this research by a literature survey. The relevant state of the art for application and development is essential for defining the aim of our work.
2.1 Importance of and developments in blades vibration monitoring
A common failure mode for turbomachinery is high-cycle fatigue of the turbine blades due to high dynamic stresses caused by blade vibration in resonance within the operating range of the machinery [18]. A large number of engine shut-downs can also be explained by blade failures caused by resonance vibration or flutter. Therefore, it is very important for the health diagnosis of turbomachinery to monitor the blades’ vibrations and to obtain dynamic stress information.
The conventional practice in vibration measurement for turbomachinery has been using strain gauges mounted on the blade surface. The testing signal is received on the stationary side using a wireless telemeter system. With this method the responses to all excited vibration modes of the instrumented blades can be captured continuously. However, a conventional telemetry system requires costly installation on the rotor side where it must withstand centrifugal forces and high temperatures, and it can provide only 5~6 testing data simultaneously because of the limitation of the usable radio wave band [7,19,20].
Recently, a non-contact measurement technique for vibrations of turbomachinery rotor blade tips using blade tip timing was developed and has become an industry- standard procedure. In these systems, the time points when the rotor blade tips are passing a given point are recorded and extracted to obtain vibration information by blade deflection signal processing. Many organizations and companies, such as NASA Glenn Research Center, Mitsubishi, Hood Technology, and SKF, carried out related researches in this field [6,20-26]. In this system, the tip sensor is the key component. The sensors are integrated with a non-contact stress measurement system to measure blade resonance (high-cycle fatigue), detect cracks in blades and disks (high- and low-cycle fatigue), detect damage from foreign objects, investigate rotating stall, and analyze blade flutter along with other rotational anomalies. The equipment also has the potential to perform real-time monitoring of an engine during flight. Figure 2.1.1 illustrates a complete tip timing system with optical sensors.
2 State of the art
6
Figure 2.1.1 Overview of a non-contact stress measurement system [6].
2.2 Conventional displacement sensors
Displacement sensors are generally grouped in four categories: magnetic sensors, capacitive sensors, optical sensors, and strain gages. Choosing the right sensor is vitally import, because the environment in which the sensor is situated can affect the sensor and its operation dramatically. The concepts of these are described and a comparison is made in this section.
(a)Eddy current (b) Inductive (c) Hall effect (d) Capacitive (e) Optical
Figure 2.2.1 Principles of displacement sensors [27].
Magnetic sensor: This includes magnetic field sensors, magnetic switches and instruments measuring magnetic fields and/or magnetic fluxes by evaluating a
2.2 Conventional displacement sensors
7
potential (Hall effect), current (wire coil / flux gate), or resistance change because of the field strength and direction [28].
• Eddy current sensor
If a nonmagnetic conductive target material is introduced into the coil field, eddy currents are induced in the target's surface. These currents generate a secondary magnetic field, inducing a secondary voltage in the sensor coil. The result is a decrease in the coil's inductive reactance. The coil-target interaction is similar to the field interaction between the windings of a transformer. Eddy current sensors work most efficiently at high oscillation frequencies. This type of system is also known as variable impedance because of the significance of the impedance variations in defining its complex nature. Ferromagnetic target materials can also effectively decrease the coil's inductive reactance if there is sufficient eddy current flow to counteract the increased field strength resulting from a higher permeability of the target (µ>1). For high-precision measurements, however, preferable applications should make use of nonmagnetic conductive target materials for reasons discussed later [1]. Eddy current sensors can be used whether access to the blade is available or not (i.e., they can “see through the case”, and are unaffected by the presence of oil and other contaminants [19]).
• Magnetic inductive sensor
The sensor comprises a coil, a coil core and a permanent magnet. The coil core and the magnet are magnetically coupled. This generates a permanent magnetic flow inside the coil. A ferromagnetic substance that influences the field of the magnet can cause changes in the magnetic flow. This change in flow induces a voltage inside the coil. The magnitude of the induced voltage depends on the magnitude and the speed of the change in flow [29].
• Hall effect sensor
In a differential Hall sensor, two Hall generators are arranged close to each other. The individual Hall generators operate along the same principle as the magnetic field dependent semi-conductor in single Hall sensors. Both Hall elements of the sensor are biased with a permanent magnet [29].
Strain gage: An ideal strain gage would change resistance only due to the deformations of the surface to which the sensor is attached. It belongs to the contact sensors and must be mounted directly on the surface of the tested object.
2 State of the art
8
Capacitive sensor: Capacitive proximity sensors are contactless position sensors, which react to the presence of objects of nearly any material within the supervised range. Capacitance works well when clear access to the blade tip is available and the dielectric properties of the medium in the gap between the sensor and the blade are constant. These sensors tend to be unreliable at medium-to-high temperatures, and cannot be used when oil contamination is present. Special materials are needed for operations at cryogenic temperatures [19][30].
Optical sensor: Taking the principle of the optical triangulation for contactless position measurement as an example, a laser beam emitted from the sensor produces a light spot on the surface of the measured object that is projected by high-quality optics on a position-sensitive detector. Optical devices require clear access to the blade tip, and the medium in the gap must be transparent. Optical sensors can be used at very high temperatures but not in the presence of contaminants.
Contact sensor:
Strain gage Noncontact sensor: Eddy current sensor capacitive sensor optical sensor
Figure 2.2.2 Mounting illustration of several displacement sensors on a turbine wheel [6].
The mounting method for strain gauge and non-contact sensors is shown in Figure 2.2.2. Non-contact position measurement devices offer several advantages over contact-type sensors. They provide higher dynamic response with higher measurement resolution, have lower or no hysteresis, and can measure small, fragile parts. There is no risk of damaging delicate structures by the probe, and they can operate in highly dynamic processes and environments [31]. A detailed comparison of the four kinds of sensors concerning their advantages and disadvantages is provided in Table 2.1.
2.3 High temperature properties of sensors
9
Table 2.1 The comparison of the advantages and disadvantages of several displacement sensors
Sensor type
Advantage/disadvantage
Eddy current Advantage: Simple structure, low cost, light weight, durable, immune to gas stream properties (dirt, water vapor, moisture etc.) Disadvantage: Measuring signal will change with material properties of the blade.
Capacitive Advantage: Simple structure, low cost Disadvantage: Durability and changing dielectric properties of the gas stream can cause problems; needs high voltage power supply.
Optical Advantage: High precision, direct measurement of the position Disadvantage: Cooling requirements and associated added weight; installation complexity and susceptibility to optical contamination; rather for ground based laboratory testing than harsh environments.
Strain gage Advantage: Direct measurement of stress in-situ Disadvantage: Attached to rotor and root of blades, therefore must withstand centrifugal force and high temperature.
2.3 High temperature properties of sensors
Sometimes, displacement sensors must work at high temperatures, especially for turbomachinery, whose environment normally involves high temperatures because the turbine is rotating at high speed. Therefore it is very important to improve the high temperature properties of the sensor [32,33]. According to the literature, there are two methods to improve the operating temperature of sensors.
The first method is to change the material and packaging of the sensor [34]. For example, inductive sensors cannot be used at high temperatures because their magnetic components are limited to the Curie temperature. Eddy current sensors can be suitable for high temperature applications but must consist of ceramic material for insulation. There are two types of eddy current sensor coil. One is a sensor coil with a ferrite core, and the other type has a ceramic core. The latter has better high
2 State of the art
10
temperature properties than the former. For the sensor with a magnet core, the working temperature is below 300 oC because the normal curie temperature of ferrite magnets is below 450 oC and the maximum operating temperature is below 300 oC [35]. Whereas when the sensor has a ceramic core, its working temperature can be up to about 1000 oC. Therefore the ceramic core is applied for eddy current sensor in high temperature environment of turbine system. Use of heat-resistant materials such as ceramics for sensor packaging is an effective method to improve its thermal properties [8,10,31].
Another method is to change the mounting position of the sensor and make it insulated from the thermal sources. Usually a non-contact sensor is mounted in the engine casing by drilling a hole through the case. But recent literature [21,36] describes the development of a novel sensor that can make the same detailed measurements while mounted on the outside of the engine case. There are no holes, and no interruption in the gas path. They can also diagnose problems and help predict the service life of the rotor. Because the engine case without hole insulates the thermal sources, the sensor avoids the high temperature problem.
2.4 Introduction of the planar coil technology
In this section, several planar coil technologies are introduced briefly and compared to the novel LTCC technology. These are high temperature cofired ceramic (HTCC), thick film and printed circuit board (PCB) technologies. Details are listed in Table 2.2.
2.4 Introduction of the planar coil technology
11
Table 2.2 Comparison of four processing technologies for planar coils
Technology Introduction/ advantages or disadvantages
High temperature cofired ceramic technology uses alumina green tape layers that require firing at high temperatures above 1500 °C to become a uniform and reliable dielectric insulator.
HTCC
Disadvantages: Low conductive material (W, Mo), complex process, no printed resistor and high capital cost.
A precision thick film ink pattern is screened onto a ceramic substrate and cured at elevated temperatures. Then a laser is used to trim the resistance values to a high degree of precision, up to 0.1%.
Thick film
Disadvantages: multiple printing steps and multiple firings for multilayers, thickness control of dielectric and limited layer count
LTCC combines the benefits of HTCC and thick film technologies. It is made from multilayer glass-ceramic dielectric tape by conductor screen-printing on the green ceramic tape with sintering temperature below 900°C that is common to thick film materials.
LTCC
Advantages: low processing temperature, low resistive metal (Au,Ag), printed resistor, TCE match Si, unlimited number of layers, good thermal properties etc.
Printed circuit board. The normal laminate is constructed from glass fabric impregnated with epoxy resin (known as "pre-preg") and copper foil. The copper foil is partly etched away, and the remaining copper forms a network of electrical connections between the components mounted on it.
PCB
Disadvantages: low operating temperature, larger size of circuit and low thermal conductivity.
12
principles and concepts
3.1 Aim of the work
The aim of this research is to develop a novel eddy current sensor with sufficient sensitivity to match the requirements of displacement measurement under given working environments and testing objects. In our work, the working environment is harsh and is full of non-metallic impurities such as oil drops, steam, dirt, etc. In addition, high temperatures above the Curier temperature of ferrite magnets are another limit to a sensor. The testing objects are rotating turbine blades of high- conductivity and non-magnetic metals such as Ti alloys, or stainless steel. Because of these requirements, it was our research aim to develop an eddy current sensor with LTCC technology [37-39].
Among several possible sensors for blade tip timing systems, only magnetic sensors are suitable for harsh environments because they are inherently immune to nonmetallic materials. But for magnetic inductive sensors and Hall sensors, their testing objects must include ferrite magnet or permanent magnet. In addition, because inductive sensors and Hall sensors must contain permanent magnetic materials according to their working principle, it is impossible that they work at high temperatures. Therefore, eddy current becomes the only option for our research. Then, the novel packaging technology of LTCC is applied to the sensor fabrication because it provides better heat-resistant properties and other advantages such as a better TCE match between the conductor and the substrate, etc. The design of the LTCC sensor has been optimised to obtain a better sensitivity for the measurement of the blade's rotating displacement. The purpose of the experimental testing is to justify the feasibility of the sensor for working at high temperatures, and to evaluate the capability of the sensor for the measurement of the rotating displacement at laboratory level. Of course, the final aim of our work is to apply this LTCC sensor as a tip probe for practical rig testing in turbomachinery or other fields.
3.2 The concept and principle of an eddy current sensor
The eddy current sensor belongs to the group of inductive sensors [40]. In the past it has been used mainly in the proximity probes application. Recently it was developed also as a diagnostic and prognostic tool for turbomachinery in terms of a blade tip
13
sensing system [8]. This chapter addresses the concept of the eddy current induction and the operating principle of a blade tip sensing system.
3.2.1 The theory of eddy currents
In 1831, Faraday and Henry discovered that a moving magnetic field induces a voltage in an electrical conductor proportional to the rate of change of the exciting current for magnetic field. In 1879, Hughes recorded changes in the properties of a coil when placed in contact with metals of different conductivity and permeability. However, it was not until the Second World War that these effects were put to practical use for testing materials. Much work was done in the 1950's and 60's, particularly in the aircraft and nuclear industries. Eddy current testing is now a widely used and well-understood technique for crack inspection or position sensing [41-43].
Eddy current sensors applied for position or displacement measurement have their
origins based on Faraday's law of electromagnetic induction: dt
Φd B−=ε , where ε is
induced emf (electromotive force), and dΦB/dt is the rate of change of the magnetic flux. The physical model of measurements (see Figure 3.2.1) consists of the target object and the main component of the sensor that is an induction coil. When an alternating voltage or current is applied to the stranded coil, it generates an oscillating magnetic field, which induces eddy currents on the surface of the conductive target, according to the principle of eddy current induction [8]. Eddy currents circulate in a direction opposite to that of the coil, reducing the magnetic fluxes in the coil and thereby its inductance. Eddy currents also dissipate energy, and therefore lead to an increase in the resistance of the coil [44].
(a) (b)
Figure 3.2.1 Physical principle of an eddy current sensor: (a) target with large surface [45] (b) target with narrow surface.
Consider a coil of wire wound in a helical shape with an air core. Low resistive nonferrous material is typically used in inductive sensor coils to avoid magnetic
3 Aim of research and some basic principles and concepts
14
hysteresis effects and nonlinearity errors caused by ferrous materials. This kind of wire coil is considered as an inductor. The coil and the target constitute the primary coil and the shorted secondary coil of a weakly coupled air-core transformer [44]. Figure 3.2.2 (a) shows this kind of electronic circuit model converted from the physical model.
L1
(a) (b)

=++−
=−+
= (3.2)
Therefore, the circuit model of a transformer can be converted to the model of an inductor and a resistor shown in Figure 3.2.2 (b). The equivalent impedance Z, resistance R, inductance L and quality factor Q of the sensor model become:
15
)( 2
== (3.6)
where R1 and L1 are the resistance and self-inductance of the sensor coil depending on the material and structure of the coil; R2 and L2 are the equivalent resistance and self-inductance of the target depending on the eddy current path, resistivity ρ and permeability μ of the target; ω is the exciting angular frequency of the power source, proportional to frequency f; and M is the mutual inductance between the sensor coil and the target depending on the relative position x between sensor and target.
With the change of relative position x between the sensor coil and target, Z, L, R and Q change with mutual inductance M. Following the equation above, Z, L, R and Q can be derived using x, ρ, μ and the exciting frequency ω. Whereby
Z, L, R or Q = ƒ (x, ρ, μ, ω) (3.7)
When sensor coil, target and exciting frequency are given, a one-variable function is obtained for displacement measurement. That is:
Z, L, R or Q = ƒ (x) (3.8)
When the surface of the target is infinitely large as in Figure 3.2.1(a), x is the standoff between sensor and target in vertical direction. Whereas, when the surface of the target is narrow as shown in Figure 3.2.1(b) and the standoff between sensor and coil is given, x is the horizontal displacement of the target referring to the
16
position of the coil. Therefore, the testing principles of the eddy current sensor for proximity and horizontal displacement of the target can be formulated in the following.
3.2.2 Testing principle for turbine blades
According to the measuring principle, the eddy current sensors are suitable to be applied to monitoring movements of turbine blades. In a rotating system, the sensor is mounted directly above the tip of the blades with its surface normal to the direction passing through the rotating centre as illustrated in Figure 3.2.3 (a). When a conductive blade comes below the eddy current sensor, the impedance or other related parameters of the sensor coil change. Through a suitable circuit, a positive or negative voltage peak corresponding to the arrival of a blade can be measured. All blade movements can be inferred by the measurements of their elapsed time. Comparing the arrival time and the amplitude of these voltage peaks, the movement of blades can be derived.
t
(a) (b) (c)
Figure 3.2.3 Testing principle for movement of turbine blades: (a) illustration of mounting for sensor (b) arrival time of every blade (c) clearance between sensor and tip of blade.
For example, Figure 3.2.3 (b) shows the arrival time difference Δt between two voltage peaks. This kind of signal indicates the interval time between two blades and offers information on rotating speed, and on anomalous horizontal displacements including vibration signals. Figure 3.2.3 (c) illustrates different amplitudes of blades. This kind of signal can reflect the change of clearance between sensor coil and the tip of blade and can offer the information on the creep through long-term trend of turbine blade length, FOD (Foreign Object Damage) of the blade, and shifts in resonance etc. By analysing both types of the output signal from the eddy current sensor, one can diagnose the incipient failure. So, it becomes possible to take some improvements in time to avoid larger loss and enhance the reliability of the whole system.
3.3 Introduction to LTCC technology
17
3.3 Introduction to LTCC technology
3.3.1 Concept of LTCC technology
The Low Temperature Cofired Ceramic (LTCC) technology can be defined as a way to produce multilayer circuits with the help of single tapes, which are to be used to apply conductive, dielectric and resistive pastes on. These single sheets have to be laminated together and fired in one step. Because of the low firing temperature of about 850°C it is possible to use the low resistive materials silver or gold with melting points of 960 oC and 1100 oC instead of molybdenum and tungsten used in conjunction with the HTCC [46]. The LTCC technology is especially well suited for RF applications, and for products where a high integration level and/or a high reliability are needed.
LTCC technology is a very novel technology beginning from the 80’s. The first publication on LTCC can be found by INSPEC in 1984 [47]. Because low temperature cofired ceramic tape technology displays excellent properties for packaging, interconnection and passive component integration, it has been widely used in the last twenty years for high reliability applications in military, avionics and automotive areas, as well as in MCM's (Multi Chip Modules) for telecommunications and computer applications. Recently, its application has been expanded to the sensor and actuator area, rendering a technology suitable for micro- system technology (MST) at the meso-scale level from fifty microns to several millimetres because its material system is compatible with hybrid microelectronics, suitable for thermal, mechanical and electrical properties, and easy to fabricate and inexpensive to process [14,16]. LTCC technology can match all the requirements of micro-systems such as: small size, low costs, short response time, corrosion resistant materials, low power consumption, and high temperature operation.
During fabrication every single layer can be inspected and in the case of inaccuracy or damage it can be replaced before firing. This prevents the need of manufacturing a whole new circuit. The advantages of the LTCC are: cost efficiency for high volumes, high packaging density, reliability, integrated and embedded passives component (capacitors, inductors and resistors) in the LTCC, good dielectric thickness control, high print resolution of conductors and low K dielectric material.
3.3.2 Materials and process of LTCC
LTCC are glass-ceramic composites in the form of tapes. They are also called green ceramic tapes because they are manipulated in the green stage before firing and sintering. Tapes are easily machined while still in the green stage before firing. They are soft, pliable, and easily abraded, so it is possible to use mechanical CNC, punching machines or laser methods. Once the material is fired and fully sintered, it
18
becomes hard and highly rigid. The composite material includes a ceramic filler, usually alumina, Al2O3, a glass frit binder to lower processing temperature and an organic vehicle for binding and viscosity control. This renders a material compatible with thick film technology. Tapes are commercially produced in flat sheets of various thicknesses in the range of 100 to 400 µm.
LTCC technology is based on the extension and improvement of standard ceramic processing, multilayer technology and unique design rules. One approach taken by such companies as DuPont, Ferro, and Heraeus is to supply green tape as the raw material used to make LTCC modules and the necessary design rules to those who design and manufacture their own modules. Others, like Murata, have chosen to develop materials, design rules, and manufacturing processes in-house, and then produce functional solutions such as LC filters, RF front ends, and complete radio modules.
The LTCC processing is very similar to that of HTCC without the complex firing conditions, flattening fires and plating steps. The process flow is shown in Figure 3.3.1. In the process flow, LTCC's parallel processing capability facilitates rapid turnaround times with reduced costs for packages and large layer counts.
Figure 3.3.1 Fabrication process flow of LTCC [48].
19
4 Design of the eddy current sensor
The purpose of optimization the design of a displacement sensor is to select the optimal structure, suitable materials and operating conditions so that the sensor has enough sensitivity and precision with a size as small as possible to match the practical application. Analytical methods can calculate the parameters of the coil for a given structure for the unloaded case (without measuring target). But, which structure with the proper L, R, and C parameters can obtain better sensitivity depends on the interaction of the coil and the target. This kind of interaction is complicated. Therefore, the finite elements method (FEM) will be used for simulation and design optimization because of its powerful calculation ability.
4.1 General principle and design factors
During the process of sensor design, different factors that influence the properties of the sensor such as the structure, mounting position and material of the sensor measurement system are analyzed and compared. The optimization objective is that the optimal parameters of the whole sensor system should achieve the best sensitivity under a given environment with stability and feasibility. These factors, which affect the properties of the sensor significantly, and some guidelines of design are sorted in three types as follows [49,50].
The factors of the first type are determined by the coil itself and are as follows: • Mounting position of the sensor relative to the target • Geometric parameters of the coil such as thickness, turns, etc. • Inductance and resistance of the sensor coil. The requirement for a standard
design is that the unloaded quality factor Q is over 15 [13].
The factors of the second type come from the target itself, they are: • The geometric factors such as area, flatness, and thickness of the target • The material properties of the target, especially conductivity and magnetic
permeability of the target. For example, high-conductivity, nonmagnetic metals such as aluminum or copper are the best targets because of the greater conductivity of the material, and the greater flow of the eddy currents on the surface [13]. Therefore, our optimization only takes into account good conductive metals as target material with a constant relative permeability close to 1.
• Skin depth of eddy current: If the lateral dimensions of the target are less than twice of the sensor diameter, the eddy current distribution is difficult to predict
20
analytically [13]. Though these situations are difficult to model, 50 times of standard skin can be assumed reasonably as effective thickness of the target for FEM analysis. The simulation results in section 4.3.3.2 identify the correctness of this assumption.
Besides the sensor coil and target, environment factors must be taken into account: • Operating frequency and resonant frequency. The basic point is that the sensor
must operate below its resonant frequency as an inductor at all. • Temperature of the target and the coil • Thermo-mechanical properties for the reliability • Standoff between sensor coil and target
In addition, the testing circuit and the signal acquisition system must also be taken into account. Inductance, resistance, impedance amplitude or phase, and some related parameters of the sensor are all possible testing properties. The optimal parameter must be selected from these as unique testing signal so that the sensitivity of the sensor for the displacement measurement is best. The testing circuit must convert it into a voltage or a current signal for the process. The signal acquisition system must record the clear signal and filter out the noise. In summary, all the factors must be calculated and optimised so that the best sensitivity of sensor can be obtained.
4.2 Analytical calculation of parameters of a LTCC coil
4.2.1 Analytic model of the LTCC coil for analytic analysis
As chapter 1 introduces, the design of a LTCC planar sensor was selected as one of the main research objectives of this thesis. The central component of our eddy current sensor is a planar LTCC coil. In this chapter, the structural details of the planar coil will be determined and its main parameters will be analyzed by an analytic method.
According to its working principle, eddy current sensors belong to the group of inductive sensors. The requirements of the coil are high inductance, low capacitance and low resistance. The structure of the coil must be designed in a way to match these requirements.
Most of the conventional geometries for planar coils of single layer (see Figure 4.2.1 (a) (b)) are meander-types or spiral-types [51,52]. A meander-type inductor is simple to fabricate but it suffers from low overall inductance because of the negative turn- to-turn mutual inductance. A spiral type coil has a relatively high inductance but its size is large compared to other coil types with the same number of turns. Due to the
21
requirement of high inductance, the spiral type was selected for the pattern of single layers. Because the number of the turns of a single layer is limited for a given area, a structure of multiple layers with the same solenoid direction and via fill connection (see Figure 4.2.1 (c)) was finally selected. This geometric structure of the LTCC coil matches the requirements for high inductance and small size. However, the serious drawback of a multi-layer structure is that this structure introduces a high stray capacitance and furthermore induces a resonant status of the coil at its self-resonant frequency. Therefore, parameters of the coil must be calculated so that the operation properties of the coil can be evaluated.
(a) (b) (c) Figure 4.2.1 (a) Simplified schematic of a meander-type inductor; (b) a spiral-type inductor; (c) a solenoid multiplayer coil.
Analytic calculations can provide electric parameters of a LTCC sensor coil. These include inductance, self-capacitance, resistance, self-resonant frequency (SRF), skin depth and so on. These parameters are essential for the design of a LTCC coil. The model structure used for the analytic calculation is illustrated in Figure 4.2.1 (c). In this model, the conductor is composed of many spiral-like thin rectangular films in three dimensions and its material is the metal compatible with LTCC fabrication. Therefore, some special formulas for inductance calculation of strips are used which are different from those for normal solenoid coils. The limitation of an analytic calculation is that it can evaluate only the static parameters of the sensor coil itself. As for the properties of sensor coils which are concerned with frequency and temperature dependence, we will utilize the finite elements method (FEM) using the software ANSYS because of the complexity of the sensor structure and the difficulty of solving the equations of an analytic calculation. For all the calculations of parameters the influences of via fill were neglected because its geometric size is very small compared to the thin strip in a planar coil.
4.2.2 Inductance calculations
Firstly, the inductance of the sensor coil is calculated. The inductance is a peculiar property of a coil which only relates to its structure. This parameter is the most
22
important parameter of a sensor coil because it determines the inductive ability of an inductor coil [53].
The total inductance of a coil is the sum of the self-inductance being generated from every conductive metal strip separately and mutual inductance due to interaction of two strips in different turns or layers.
4.2.2.1 Self-inductance
In this section, the self-inductance of a planar coil made of non-magnetic conductor is calculated. The basis of the calculation is Greehouse’s formula [54] (see Equation (4.1)) which calculates the self-inductance of a thin strip as shown in Figure 4.2.2.
Lself = 2l(ln tw
nH (4.1)
where Lself is the self-inductance in nH; l is the length of the conductor in cm; w is the width of the conductor in cm; and t is the thickness of the conductor in cm.
Figure 4.2.2 Illustration of geometric parameters of a single conductor strip.
Because the thickness t and width w is the same for every strip of the coil, we only need to input different lengths of strip from lo to li in x direction and from wo to wi in y direction with the number of turns N to the Greehouse’s formula (Equation (4.1)) for different strips. Here, N describes the number of turns of the coil in one layer. By summing up these separate values, about half self-inductance of coil in one single layer (see. Figure 4.2.3) was obtained. In fact we needn’t input different lengths of the strip individually because there is a regulation between them. This regulation is:
ln=li+(n-1)•P,
where n=1, 2, …, N, and means nth turn; P is twice of the sum of pitch pt between two strip and the width of the strip.
23
Figure 4.2.3 Top view of the LTCC coil which is designed and fabricated (see section 4.4.3).
We assume that the coil has mirror symmetry and the patterns are the same in each layer. Therefore, to multiply the sum of above by the number for symmetry and the number of layers K, the total self-inductance of one whole coil is obtained from the equation shown as follows,
Ltotal-self =∑ =
N
1 )( *2*K (4.2)
where i is the number of the turn; N describes N pieces of strips in long side and wide side of the coil respectively.
Using the design shown in Figure 4.2.3 as an example, the numerical parameters can be found in Table 4.15, which are K=12, N=16, w=pt=131.7 μm, t=10 μm, lo=15.8 mm, wo=8.76 mm. Using all the values and the equation above, the final total self- inductance of the whole coil Ltotal-self is 15.370 μH.
4.2.2.2 The mutual inductance
The basic theory of the calculation of mutual inductances is the formula for calculating the mutual inductance between two single strips in the same layer or between different layers. Two formulae are used and compared. One is Hoer’s formula, and another is Grover’s formula. The main difference between them is whether it takes the thickness of the strip into account or not. We will introduce them individually.
24
Method 1—Hoer’s formula (for 3D geometric structure)
The geometric model of Hoer’s formula is shown in Figure 4.2.4. 3D geometric dimensions including the thickness of strip t are all taken into account. Dx, Dy, Dz describe the relative position of two strips. When two strips are parallel in the same layer, Dx is zero. When two strips are parallel but not in the same layer and turn, Dz=(l1-12)/2. When two strips are in the same turn but in different layers, Dy=0 and Dz=0. These three cases cover all situations for mutual inductance calculation of a planar coil.
ll
Conductor 1
Dz Dx
Figure 4.2.4 3D geometric model of two strips for Hoer’s formula.
The formula referred to this model is as follows [55]:
)()()(tan 6
tan 6
tan 6
)333( 60
25
where ] ] ] ∑∑∑ = = =
q q srqfzyxzyxf .
We will then use this formula to calculate the mutual inductance in the three situations referred to before. In the first step, we calculate the mutual inductance between two strips in one layer which means Dx=0. The mutual inductance exists in signed positive and negative values. When current flows in two strips are the same, the value of the mutual inductance is positive, whereas, when the current flows are opposite, the value is negative.
Figure 4.2.5 Illustration of a spiral coil with mark for direction of current flow.
When it was assumed that the calculating sequence is from out side to inside, positive mutual inductance reads M+= M1,5+M3,7+M2,6+M4,8 in y-z plane, and the negative mutual inductance reads M-=-M1,7-M1,3-M5,7-M5,3-M5,7-M2,4-M2,8-M6,4-M6,8,
where Mi,j means the mutual inductance between ith turn and jth turn.
The number of positive mutual inductances is 2N(N-1), and the number of negative mutual inductance is 2N2. Summing up M+ and M- and multiplying the result by the number of layers K, the mutual inductance of the whole coil due to the interaction of strips on the same layer was obtained.
With the same method, we can calculate the mutual inductance due to the interaction of the strips on different layers illustrated in Figure 4.2.6. When we exclude the interaction of two strips having the same number of turn such as the interaction between the 1st turn in the top layer and the 1st turns in the 2nd layer, the calculation sequence and the numbers of positive and negative mutual inductances for the strips on two layers are the same as that for the calculation of one layer case but with Dx ≠0. In the x direction being the normal direction of the layers, all mutual inductances for different assemblies of two layers must be calculated. For example, the 1st layer can be connected to 2nd layer, 3rd layer, until the Kth layer, and the (K-1)th layer only can be connected to Kth layer. The number of calculations of two layers is K(K-1)/2. The
26
total number of calculations for two strips is N(N-1)K(K-1) for positive mutual inductance and N2 K(K-1) for negative values.
Figure 4.2.6 Illustration of coils in different layers.
Finally, we calculate the case of two strips in the same turn but in different layers. In respect of this situation, the mutual inductance between two strips is always positive, and the number of individual values is 2NK(K-1).
Summing up all the values for the three situations, the total mutual inductance of the whole coil is obtained. Because the basic formula is complicated and the calculation number is large, a program under the software Mathematica is used for computer calculation.
Using the same model (see Figure 4.2.3) as that in the last section and one new parameter Ph=96,36 μm, which is the pitch between two layers, we obtained the total mutual inductance of this coil which Mtotal is 232 μH.
Method 2—Grover’s formula (for filament structure)
For Grover’s formula, the geometric model is shown in Figure 4.2.7. The thickness and the width of the strip were neglected so that the strip is regarded as a filament. For the two strips in one layer, it is d=0. When two strips are parallel but not in the same layer and turn, d is the absolute distance between two centers of the strips. When two strips are in the same turn but in different layers, d is the perpendicular distance of the two layers. Especially, δ is always negative with the value of −(l1+l2)/2.
27
Figure 4.2.7 General position of two conductors (filament) for Grover’s formula.
Grover’s formula reads [55]:
]
where
sinh-1(x)=ln(x+ 12 +x ), α=l+m+δ, β=l+δ, γ=m+δ.
Νote that in the case when the two conductors are overlapped then δ is negative.
With the same calculation procedure as for Hoer’s formula, the total mutual inductance of the same coil is obtained: Mtotal= 194 μΗ. Of course, the parameters w and t are dispensable.
Finally, the self-inductance and mutual inductance are summed up for the total inductance of the coil. The value of the inductance is as follow:
Table 4.1 The inductances calculated by three formulas
Lself (μH) Mtotal (μH) Ltotal (μH)
Hoer: 232 247.37 Greenhouse: 15.37
Grover: 194 209.37
Comparing the two formulae for calculation of the mutual inductance, the Hoer’s formula achieves a better precision but is more complicated and needs more computation time.
28
4.2.3 The DC resistance of the coil
An ideal inductor coil would have no resistance and no capacitance. For a planar coil, the resistance is relatively large, because the cross sections for current flow are very narrow. The resistance of the coil is a very important factor affecting the quality factor Q of the coil. It also can lead to energy dissipation of electromagnetic field. The basic equation for the resistance calculation of a conductor is as follows:
ρρ wt l
A lR == (4.5)
where l = total length of the coil windings; ρ = resistivity of the coil material; w = width of trace of a coil ; t = thickness of traces in a coil .
According to the coil model used in Figure 4.2.3, the length of the strip on one layer is Lsingle = (lo+li+wo+wi)N=0.523 m. Therefore, the total length of the strip in the whole coil (l) is equal to lsingle·K, which is 6.27 m. The conductor material of this LTCC coil is silver, and ρ =1.6·10-8 Ωm. Then the resistance of a single layer is Rsingle=6.4 Ω, and the resistance of the total LTCC coil is R=76.6 Ω.
Compared to the value offered by the manufacturer of this LTCC coil that is 6.5Ω per single layer and 83 Ω in total, the analytical value is close to this reference values. The difference in the total resistance mainly comes from the contribution of via fills because the analytical value of the resistance in a single layer is better matched with the measured one than that of the total coil.
4.2.4 Capacitance calculation
Normally, capacitance is defined as the ability to hold charge by a pair of conductors separated by empty space or by a non-conductor. For an ideal straight conductor, there is no capacitance. But for a coil or an inductor, it has normally some stray capacitance because of its spiral, meander, or solenoid structure and the interaction between the coil and its surroundings such as its core or substrate. The capacitance interacts with the inductance of the coil and induces a resonance status at self- resonant frequency. Hence, the working behavior of the coil will be changed.
The stray capacitance of a coil is a result of three mechanisms [51,52,56,57].
• When a single layer inductor works, a lead wire is required to connect the inside end of the coil on the top layer to the outside, which introduces an
29
unnecessary capacitance between the conductors and the lead wire. This is the first kind of capacitance source.
• Then the second type of stray capacitance is the capacitance between conductor layers and its resistive substrate or ground plane.
• The third kind of capacitance is between two conductor strips of the coil itself on the same layer or on different layers.
According to the LTCC coil model used before, the conductor is a thin metal strip and the structure is a spiral coil of multiple layers without a ground metal plane. The LTCC substrate is a material of low dielectric constant and permittivity and good insulation properties. Because of the special structure and material properties, the separate lead wire does not exist because it is only a part of the conductor on the bottom layer, and the influence of substrate or ground is also not existent. So, the first two kinds of capacitance for coils which are induced by the interaction of conductor-to-lead wire and layer-to-substrate or ground are neglected and the third type of stay capacitance is focused on
In fact the capacitance between two turns on the same layer also can be neglected. The reason can be explained by a physical model for the capacitance of this LTCC coil shown in Figure 4.2.8.
Figure 4.2.8 Equivalent physical model for calculation of the stray capacitance between conductor strips shown in the cross-sectional direction of a coil.
30
According to the basic Equation (4.6) [28] for capacitance, calculation of two parallel planar conductors (see Figure 4.2.9) yields:
d
lw
d
A C err εεεε 00 == (4.6)
where εr = relative dielectric constant, namely relative permittivity (a dimensionless number; 4.2 for FR-4 PC board, 7.8 for LTCC at 10 MHz ), ε0 = dielectric constant of free space (8.8542 · 10-12 F/m), d = distance between the center of two planar conductor surface (meters), A= effective interacting area (m2), l= length of strip; we= effective width of strip.
The capacitance is direct proportional to the effective area of two conductors and inverse proportional to their distance. With this equation, the capacitance of two turns on the same layer such as Turn1 and Turn2 in Figure 4.2.8 is much less than that of two turns on different layers such as Turn1 and Turn4 because the interacting width t=10 μm of Turn1 and Turn2 is about 7% of that w=150 μm of Turn1 and Turn4, and the distance pt=150 μm between Turn1 and Turn2 is about 1.5 times of that ph=100 μm between Turn1 and Turn4. Therefore, the capacitance between two conductors on the same layer can be neglected by setting Ct =0 for simplification of its physical model. Further more, the resistance R connecting two turns on the same layer is small, and R=0 is assumed for simplification of the physical model.
Figure 4.2.9 Geometric model of a pair of parallel planar conductors.
With these assumptions, the physical model can be converted to a PSPICE electronic circuit model shown in Figure 4.2.10. In the DC electronic circuit with passive components consisting of pure capacitors or resistors, the serial and parallel relation for two resistors is the inverse of that for two capacitors. The symbol of capacitance between two different layers can be described as resistor, but the inverse of the resistance value is the final value of capacitance, that is C~1/R in the unit F. The
31
capacitance of grade 1 is defined as the capacitance between two layers which are adjacent to each other such as layer 1 and layer 2. For example, R7 is sum of capacitances of two turns between the adjacent layers such as Cturn1,turn4, Cturn2,turn5, Cturn1,turn5 and is sorted to capacitances of grade 1. The capacitance of grade 2 is defined as the capacitance between two layers which has an interval of 1 layer such as layer 1 and layer 3. For example, R11 of grade 2 shown in Figure 4.2.10 is the sum of capacitances of two turns between layer 1 and layer 3 such as Cturn1,turn8, Cturn2,turn7. The rest may be deduced by analogy. We just calculate until capacitances of grade 4 because the distance between two layers is far enough to further neglect values of capacitance. For a circuit only with capacitors as passive components, it is
ωω
R
CI
V ==
1 . When we add a reference resistor with the value of 1pΩ and apply
the voltage of 1 volt to V , 16
16
VC R
V
R
V =≈
16
16 and C=V16·1012 (pF). The result is computed by the circuit simulation
software PSPICE. V16 is equal to 15.13 pV and the capacitance of the whole coil Ctotal
is 15.13 pF according its converting relation with V16.
R13
18.27m
R18
18.27m
R24
174m
R26
174m
464.5mV
171.2mV
R28
174m
R39
173.92m
337.3mV
R12
174m
R7
18.27m
R23
18.27m
605.5mV
R3
173.87m
0V
729.4mV
V1
1Vdc
0
R5
173.87m
R17
18.27m
R8
18.27m
R31
173.87m
R33
173.92m
535.5mV
15.13pV
R37
173.92m
R9
18.27m
R2
173.87m
R25
174m
R21
18.27m
828.8mV
R15
18.27m
270.6mV
R34
173.92m
R27
174m
R30
173.87m
R35
173.92m
394.5mV
R16
1p
R14
174m
R29
173.87m
R22
174m
R4
173.87m
R10
18.27m
1.000V
R20
18.27m
R1
173.87m
R32
173.92m
R38
173.92m
R11
174m
662.7mV
R6
173.87m
R36
173.92m
Figure 4.2.10 Simplified electronic circuit model for the stray capacitance of the whole coil with N=12 layers.
32
So far, the three parameters concerning DC impedance of the coil, which are inductance, capacitance and resistance, were obtained. According to these basic parameters, a whole electronic model of the sensor shown in Figure 4.2.11 can be built. Some other parameters concerning the operating properties of coils at high frequency can be further obtained as follows.
sensor
L
C
R
4.2.5 Quality factor, skin depth, self-resonant frequency
4.2.5.1 Quality factor (Q)
)(
xLxQQ ω == (4.7)
where Q is the quality factor (no units), ω is the operating frequency of the coil in radians per second, L is the inductance of the coil (in H), R is the total resistance associated with energy losses (in Ohms).
Q depends on the standoff x between the sensor and the target, because both L and R are functions of the displacement. The higher the value of Q is, the stronger the effect of inductance is and the weaker the effect of resistance is. A high Q leads to high accuracy and stability.
For example, in the coil with geometric sizes shown in Table 4.15, its inductance is 247 μΗ and the resistance is 83 Ω. We find that the unloaded quality factor Q is 19.9 at 1 MHz according to the equation above. This Q matches the requirements [28] that the unloaded Q must be over 15 for a typical design of the eddy current sensor. It means that the design of this coil is qualified for the requirement of electronic parameter Q.
33
4.2.5.2 Skin depth
Skin depth is defined as the characteristic penetration distance which a plane wave travels through a conducting medium. For the eddy current measurement system, the depth that eddy currents penetrate into the target is affected by the frequency of the excitation current and the electrical conductivity and magnetic permeability of the specimen. The depth of penetration decreases with increasing frequency and increasing conductivity and magnetic permeability. The depth at which the eddy current density has decreased to 1/e or about 37% of the surface density, is called the standard depth of penetration δ (see Equation (4.8)) [13,41].
δ = σωμ
2 (4.8)
where δ : skin depth (meters), ω : radian frequency (radians/second), μ : magnetic permeability (H/m), e,g. non-magnetic metal, μ=μ0·μr=1.26·10-6H/m, σ : conductivity (Siemens/meter),e.g. copper’s is 5.78·107S/m. Table 4.2 Skin depth δ for various metals and frequencies
Skin depth (µm) Metal Conductivity (106 S/m)
Resistivity (10-8Ωm)
Copper 58 1.73 660 210 66 21
Aluminum 38 2.6 820 260 82 26
Titanium Alloy 0.59 16.9 6600 2100 660 210 The skin depths for several nonmagnetic metals at various frequencies are listed in Table 4.2. For example, the skin depth of copper at 10 kHz is roughly 0.66 mm. Although the whole eddy currents in target penetrate deeper than one standard depth of penetration, they decrease rapidly with the depth of the target (see Figure 4.2.12). Therefore, the effective part of target for the measurement by the eddy current sensor is only the tip of the target. When we build a simulation model with an exciting frequency of over 10 kHz for a copper target, 50 times of skin depth tip should be enough. That is about 30 mm.
34
Figure 4.2.12 Illustration of skin depth for inductive eddy current [41].
4.2.5.3 Self-resonant frequency (SRF)
As shown before, any inductor exhibits stray a capacitance between windings. This capacitance in conjunction with the inductance forms a "self resonant frequency" for the loop or inductor. The frequency where the inductance peaks is called the self- resonant frequency (SRF). It is defined as [13]
)(2π
SRF +
= (4.9)
where Ciwc is the inter-winding capacitance or stray capacitance of the coil, and Ccable is capacitance per unit length from the cable length and the manufacturer's specification.
For example, in the coil (see Figure 4.2.3) that is the example for LRC calculations, having an inductance of 247.37 μΗ and a capacitance of 15.13 pF, we find that the SRF is 2.60 MHz. The exciting frequency must be below this frequency for an inductive eddy current sensor.
4.3 Design and optimization of the eddy current sensor
35
In summary, the basic structure of a spiral pattern with solenoid structure for the LTCC plane sensor coil was determined. For this kind of coil, a set of analytic formulas was defined. Using these methods, very important static unloaded frequency dependent parameters L, R, C and Q, δ, SRF can be calculated and the matching for the related requirement of a suitable eddy current sensor can also be evaluated. However, the analytic method can only evaluate the feasibility of a sensor coil alone when the geometric sizes of the coil are given. With respect to the interaction between the sensor and the target, and the optimal geometric sizes for sufficient sensitivity of the sensor, computer simulation must be carried out.
4.3.1 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
36
LTCC model and its thermo-mechanical reliability was evaluated. Meanwhile, the impedance change of a sensor with different displacement of the target was analysed. The results can be used by some mathematic softwares such as Matlab, Mathmatica to evaluate the sensitivity. On the contrary, when reliability and sensitivity of the sensor is not sufficient, EM simulation must be repeated in order to offer better results for other types of analysis. Therefore, all steps in the whole process of optimization are interlinked and must be taken into account together. The analysis details will be addressed in the next section.
-80 -60 -40 -20 0 20 40 60 80 0
20
40
60
80
100
Re
8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8
x 10 -4
4.3.2 Optimizing the sensor location - modal vibration simulation
In this section, the object of modal simulation analysis is the vibration of the target blades. From the optimization point of view, the mounting position of sensor must be decided first. Because we want to monitor the movement including the vibration of the blades, the sensor should be mounted at the position where it can detect the largest vibration amplitudes of the blades. The vibration of a blade is very complex, but it can be composed of many basic vibrational modes at different frequencies. Therefore the mode shapes are analyzed by modal analysis for different resonance frequencies in order to find a proper position where the amplitude is large for many
Concept of the simulation
37
modes of vibration. This location is considered as the optimal mounting position for the sensor.
For the FEM model, two kinds of shapes of the tip surface, the shark shape and rectangle shape, are analyzed (see Figure 4.3.2). The 3D model reflects the actual turbine blade product and its material is Titanium. The width of the blade is 30 mm, the thickness is 2.5 mm, and the length is 100 mm. One end of the blade is constrained without movement and the other end is free. From the analysis results, the first 15 modes are extracted from a frequency of 4.83 Hz to 338 Hz with the subspace method.
Figure 4.3.2 FEM model of blade with two different end shapes.
Figure 4.3.3 shows the results of mode shape. The colour labels describe the scale of deformation and the text offers the information on various natural frequencies corresponding to the number of the sub-step. According to these results, for most modes of vibration of the blade, the largest deformation occurs in the point that lies at the end of the blade tip. Therefore it can be concluded that the reasonable mounting position of a sensor should be just over the sharp end of the turbine blade as shown with a red arrow in Figure 4.3.3. For the shark shape, there is only one optimal mounting position for the sensor, and for a rectangular shape there are two optimal positions because of the mirror symmetry of the blade. This conclusion is very important for the situation that the width of the blade is far longer than the size of the sensor coil. The whole rotor integrating individual vibration mode of blades shown in Figure 1.1 also can be obtained using its cyclic symmetry.
38
Figure 4.3.3 Vibration modes of the blade at different natural frequencies in Hz, (note: figures with blue border show the blades with tip of rectangle shape, the rest show the blades with tip of shark shape).
sub=1 f = 4.846
sub=14 f = 331.8
sub=10 f = 238.13
sub=5 f = 79.858
sub=3 f = 35.006
sub=2 f = 34.778
sub=6 f = 101.85
sub=6 f = 110.12
39
4.3.3 Optimizing the sensor sensitivity-EM evaluation
The harmonic electromagnetic analysis was done to calculate the electromagnetic field that interacts between sensor coil and target blade. Through harmonic electromagnetic analysis (EMAG in ANSYS), some useful electromagnetic properties of turbine blade and coil are obtained, such as the eddy currents on the turbine blade, the electromagnetic field distribution, the impedance and the inductance. Hence, the results can identify the working principle of the eddy current sensor and evaluate its sensitivity. 2D and 3D analyses are used individually for their different application field.
4.3.3.1 2D simulation
The 2D electromagnetic analysis is applied in the case of axial symmetry. For the eddy current measurement system, two situation with target and without target can be investigated for the horizontal displacement evaluation. The relation between the sensitivity of the sensor and some influence factors for 2D simulation can be investigated. In addition, the relation between the impedance of the sensor and the clearance between the sensor and the target is obtained.
First, we build a reference structure according to some simple evaluations (see Table 4.3). Then, the influence factors are changed and the resulting sensitivity is compared with that of the reference model so that one can get the optimal parameters for the influence factors. Finally, a detailed relationship between impedance and the clearance is obtained.
Table 4.3 Simulation parameters and their results
Material part material ρ (10−8 Ωm) μr coil Ag 1.60 1
target Cu 1.73 1 Geometry
ro (mm) ri (mm) Height h (mm) fill factor turns coil 5 0.2 1 1/20 200 l/2 (mm) thickness (mm) gap (mm) target
2.5 5 1 Electrical conditions
f=1 MHz voltage=5 V Results R0(Ω) L0(μH) Rs(Ω) Ls(μH)
0
0
R
40
The FEM model is composed of an exciting coil forced by voltage, turbine blade, near field air and far-field infinite air (see Figure 4.3.4(b)). Element type is plane53 with voltage-fed or current–fed, and element INFIN111 is used for define infinite far-field air shown in out-layer of the FEM model. The results in the form of 2D flux (see Figure 4.3.4(a)(c)) present clearly the influence of the target to the electromagnetic field. All parameters and results are listed in Table 4.3.
(a) (b) (c) Figure 4.3.4 (a) results of 2D flux when there is a target; (b) 2D EM model; (c) ) results of 2D flux without target when target material was set as air.
For the calculation of the impedance of the sensor coil, ANSYS can offer an inductance Ls and an unloaded resistance R0 calculated by its geometric structure. Also, ANSYS can provide the real part Re(I) and imaginary part Im(I) of the current through the coil. Hence, we can obtain the inductance and the resistance of the whole system through electric circuit equation because the voltage applied to the coil is fixed. The related calculation principles are as follows:
Current I=Re(I)+jIm(I), Impedance Z=Rs+jωLs
Because of Z=V/I=V/ [Re(I) +jIm(I)], θ= tg-1[(Im(I)/Re(I))], the loaded impedance values of sensor coil can be obtained as:
Rs= 22 Im(I))(R +Ie
V sinθ
At the same time, the sensitivity of the sensor in the case of target existence was define as:
41
0
0
R
0
L
LLs − × 100% is for inductance
where the subscript note 0 means unloaded, and s mean loaded.
Sequentially, the various influence factors on the sensitivity are changed and compared to the results of the reference system. First, the exciting source was investigated. Table 4.4 shows the difference of results by this kind of comparison. Table 4.4 The comparison between various exciting sources for the coils with reference structure
Results Reference conditions f=1 MHz,Voltage U=5 v
f=2 MHz f=0.5 MHz U=10 v f=1 M
U=1 v f=1 M
R0(Ω) 43.56 43.56 43.56 43.56 43.56
L0(μH) 127.43 127.43 127.43 127.43 127.43
Rs(Ω) 48.76 51.24 47.13 48.76 48.76
Ls(μH) 112.82 112.57 113.17 112.82 112.82
0
0
R
0
0
L
LLs − (%) 11.5 11.7 11.19 11.5 11.5
According to these comparisons, some conclusions about the exciting source are obtained. The sensitivity of the resistance and the inductance both increase with exciting frequency increasing. Higher exciting frequency can obtain better sensitivity. Whereas, they have no relation with the amplitude of exciting source, therefore, we can choose any voltage value according to the data acquisition requirement.
In the next step, the structure and material of the target become the comparing objects. The results are shown in Table 4.5. Comparing the change of sensitivity because of different target material, some conclusions about the influence of resistivity of the material can be obtained. The loaded resistance and inductance of the sensor coil increase with the target material resistivity, but their changes are not proportional to the change of resistivity. For example, when resistivity is 1.5 times and 23 times to the reference value, the resistance changes 2% and 30% respectively, and the inductance changes only 0.17% and 3%. The resistivity influence on the resistance of eddy current sensor coils is much larger than the influence on the inductance, but all the change is far smaller than the change of resistivity itself.
42
Table 4.5 The influence of the change of materials of target on the sensor sensitivity
Results Refer. condition Cu-ρ=1.73·10-8 Ωm
Al-ρ=2.6·10-8 Ωm Ti-ρ=40·10-8 Ωm
R0(Ω) 43.56 43.56 43.56 L0(μH) 127.43 127.43 127.43 Rs(Ω) 48.76 49.82 63.46 Ls(μH) 112.82 113.01 116.05
0
0
R
LLs − (%) 11.5 11.3 8.93
In this part, the geometry of the target is also considered. The thickness of a target does not influence the impedance of the sensor when it meets the requirement that the thickness of the target must be over 50 times of the skin depth as discussed in section 4.1. This point can be identified by the results on the 2D flux. The width of the target will influence sensitivity seriously. The relation between the width of the target and the sensitivity of the sensor coil is shown in Figure 4.3.5. When the size of target is smaller than twice of the size of the sensor coil, the sensitivity of inductance decreases with the decrease of the width of the target quickly. For the sensitivity of the resistance, the influence of the width of the target is less than that of the inductance, but when the width is smaller than 1.6 times of the size of the sensor, the sensitivity change of the resistance of the sensor is also very large. Therefore, for the displacement measurement of a narrow blade, evaluation of its sensitivity before the fabrication is very important.
2 4 6 8 10 12 14 16 18 0 2 4 6 8
10 12 14 16 18 20 22 24 26 28 30
Se ns
iti vi
%
W id th o f ta rg e t / m m
R e s is ta n ce se n s tiv ity
in d u c ta n ce se n s tiv ity
Figure 4.3.5 The relation between width of target and sensitivity of sensor coil.
Next, the parameters concerning the sensor coil are investigated. These parameters include coil fill factor, turns, the width and thickness of conductor film, and the width and thickness of the whole coil. In fact, these structural parameters interact with each other. For example, when the thickness of the coil is constant, the change of the coil fill factor leads to a change of the width and thickness of the conductor
43
film. Table 4.6, Table 4.7 and Table 4.8 show the influences of coil geometry on the sensitivity of the sensor. Table 4.6 The influence on impedance and sensitivity of sensor because of the size changes of conductor film and layer numbers when outer size of coil is constant
Results Reference turns=200 fill=1/20
Fill1/10
Fill1/40
narrow film
thick layer wide film
R0(Ω) 43.56 21.78 87.12 65.34 21.78 L0(μH) 127.43 127.43 127.43 286.72 31.86 Rs(Ω) 48.76 26.97 92.31 77.03 23.08 Ls(μH) 112.82 112.82 112.82 253.85 28.20
0
0
R
0
0
L
LLs − (%) 11.5 11.5 11.5 11.5 11.5
Q0 18.38 36.76 9.19 27.57 3.39
According to Table 4.6, we know that the size of the conductor film such as its thickness and width cannot influence the inductance sensitivity of the sensor, but changes the resistance sensitivity of the sensor much. When the number of turns of the coil increases, resistance and inductance both increase, but the sensitivity of inductance does not change. Therefore, the conclusion can be drawn that the changes in a coil such as size of the conductor film or the number of layers can not affect the sensitivity of inductance although the absolute values of the inductance and the resistance are changed much when the outer size of the whole coil is given. Table 4.7 The influence on impedance and sensitivity of sensor when height of coil changes
Results Refer. conditions h=1 mm,fill=1/20,
turns=200
H=0.5 mm Fill=1/10 thin layers
R0(Ω) 43.56 65.34 21.78 43.56 L0(μH) 127.43 265.7 34.56 138.24 Rs(Ω) 48.76 74.64 23.43 50.17 Ls(μH) 112.82 239.39 29.94 119.74
0
0
R
0
0
L
44
According to Table 4.7, the height of the sensor coil can influence the sensitivity of inductance. The thinner the coil is, the better the inductance sensitivity of the sensor will be. The height of the coil is the only factor that can influence the sensitivity of the inductance although other parameters can change the value of the inductance. When the height is given, the influence of other parameters such as layers, turns, fill factor etc. appears to be the same as shown in Table 4.6. Here, the quality factor is considered because the height cannot decrease infinitely by decreasing of the number of turns of the coil. The quality factors should meet its requirement of greater than 15 as discussed before. Therefore, to make the layer as thin as possible, it is a better method to decrease the height of the coil.
Table 4.8 The influence on impedance and sensitivity of sensor when surface area of coil changes
Results Refer. conditions ro=5 mm, ri=0.2 mm
ri=1 mm narrow
ro =4, small coil
ro =6 mm ri =1.2
R0(Ω) 43.56 60.32 42.99 44.45 60.32 L0(μH) 127.43 177.46 154.89 100.11 218.62 Rs(Ω) 48.76 67.44 48.36 48.96 67.71 Ls(μH) 112.82 157.39 139.09 87.98 196.91
0
0
R
0
0
L
LLs − (%) 11.5 11.3 10.2 12.12 9.93
Q0 18.38 18.48 22.63 14.15 22.77
According to Table 4.8, a big coil cannot bring good sensitivity of inductance. This conclusion is the same as that comes from Figure 4.3.5. The sensor coil with the size similar to that of the target has better sensitivity of inductance than the one having bigger size than that of target. In addition, smaller inner radius of sensor can bring a better sensitivity of the inductance and resistance. Therefore, the sensor coil should be as small as possible and be filled as full as possible in area of whole sensor for the good sensitivity of inductance.
In respect of the coil material, the change of resistivity can change the resistance of a coil but cannot change the unloaded inductance of the coil. According to the principle of electromagnetic induction, it does not change the exciting field, and the inductive field also does not change for the same target. Hence, the loaded inductance of the sensor does not change, but the resistance and its sensitivity change. Table 4.9 identifies this analysis.
45
Table 4.9 The influence of the coil materials on the sensor sensitivity
Coil/ρ 10-8Ωm
Au 2.2
Pt 10.6
288.61 127.43 293.80 112.82 1.8 11.5 2.77
Finally, the clearance between sensor and target is evaluated. Figure 4.3.6 shows the resistance and inductance of a sensor coil dependent of the clearance between sensor coil and target. Except the parameter of clearance, all other parameters and conditions are the same as those of the reference model shown in Table 4.3. These curves can demonstrate the measurement principle of eddy current sensor for proximity of target. When the proximity changes, the inductance and resistance of coil both change. The change tendencies of inductance and resistance are opposite and the change rate of the inductance is larger than that of the resistance.
0,5 1,0 1,5 2,0 2,5 3,0 0
20
40
60
80
600
700
800
Resistance Inductance
Figure 4.3.6 Resistance and inductance of sensor coil dependent of proximity between sensor coil and target.
In summary, 2D EM simulation identifies the measurement principle of the eddy current sensor for proximity of the target and some important properties such as the influence on the sensitivity from the width of target, and the influence from the materials of coil and target. With respect to the improvement of the inductance sensitivity, only structures of whole coil such as thinner, smaller and full coil and increasing frequency can be implemented. For the sensitivity of the resistance of the coil

eddy current displacement sensor with ltcc technology

Documents