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