Overview

This book presents inductive and hybrid levitation micro-systems and their applications in micro-sensors and –actuators. It proposes and discusses analytical and quasi-finite element techniques for modeling levitation micro-systems based on the Lagrangian formalism. In particular, micro-bearings, -actuators, -accelerators and –accelerometers based on inductive levitation are comprehensively described with accompanying experimental measurements.

Full Product Details

Author:   Kirill Poletkin
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   1st ed. 2021
Weight:   0.454kg
ISBN:  

9783030589073

ISBN 10:   3030589072
Pages:   174
Publication Date:   19 November 2020
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

1 Introduction to levitation micro-systems 7 1.1 Levitation micro-systems. Classification . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Electric levitation micro-systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Magnetic levitation micro-systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Diamagnetic levitation micro-systems . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5 Superconducting levitation micro-systems . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 Inductive levitation micro-systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.7 Hybrid levitation micro-systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.8 Future Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Micro-fabrication techniques 17 2.1 Planar coil technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 3D micro-coil technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Analytical modelling 21 3.1 Analytical mechanics of micro-electro-mechanical-systems . . . . . . . . . . . . . . 22 3.2 Statement of the problem for modelling . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Stability of inductive levitation systems . . . . . . . . . . . . . . . . . . . . . . . . 31 3.4 Modelling of IL-micro-systems based on symmetric designs . . . . . . . . . . . . . 34 4 Quasi-finite element modelling 39 4.1 Statement of problem for modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.2 Procedure for the analysis of IL-micro-systems . . . . . . . . . . . . . . . . . . . . 43 4.3 Calculation of the mutual inductance of circular filaments . . . . . . . . . . . . . . 44 4.3.1 The Kalantarov-Zeitlin method . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.3.2 Derivation of Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5 Inductive levitation micro-systems 53 5.1 Micro-bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.1.1 Design and fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.1.2 Measurement of stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.1.3 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.4 Coil impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.1.5 Levitation height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.1.6 Lateral Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.1.7 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.2 Micro-bearings with lowest energy consumption . . . . . . . . . . . . . . . . . . . . 71 5.2.1 Experimental results and further discussion . . . . . . . . . . . . . . . . . . 72 6 Hybrid levitation micro-systems 77 6.1 Micro-actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.1.1 Design and micro-machined fabrication . . . . . . . . . . . . . . . . . . . . 77 6.1.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.1.3 Eddy current simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.1.4 Analytical model of static linear pull-in actuation . . . . . . . . . . . . . . . 86 6.1.5 Quasi-FEM of static linear pull-in actuation . . . . . . . . . . . . . . . . . . 87 6.1.6 Preliminary analysis of developed models . . . . . . . . . . . . . . . . . . . 89 6.1.7 Comparison with experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.1.8 A light disc of a 2.4mm diameter . . . . . . . . . . . . . . . . . . . . . . . . 93 6.1.9 Angular pull-in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.2 Micro-accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.2.1 Operating principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.2.2 Micro-fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.2.3 Linear motion due to the gravity . . . . . . . . . . . . . . . . . . . . . . . . 105 6.2.4 Modelling of stable levitation . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.3 Micro-accelerometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.3.1 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.3.2 Operating principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.3.3 Preliminary experimental results . . . . . . . . . . . . . . . . . . . . . . . . 114 6.3.4 Analytical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.3.5 The accelerometer equation of motion . . . . . . . . . . . . . . . . . . . . . 117 6.3.6 Static pull-in instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.3.7 Dynamic pull-in instability . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7 Mechanical thermal noise in levitated micro-gyroscopes 123 7.1 Model of an ideal levitated two-axis rate gyroscope . . . . . . . . . . . . . . . . . . 124 7.2 Mechanical thermal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 7.3 Johnson noise. Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.4 Analysis of resolution of reported gyroscopes . . . . . . . . . . . . . . . . . . . . . 129 7.5 Scale factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 7.6 Mechanical thermal noise in vibratory and levitated gyroscopes . . . . . . . . . . . 133 A Mathematical notation 135 B Mutual inductance between two filaments 143 B.1 MATLAB functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 B.2 Determination of angular position of the secondary circular filament . . . . . . . . 145 B.3 Presentation of developed formulas via the pair of angles α and β . . . . . . . . . . 146 C Mutual inductance between two filaments 149 C.1 Derivation of a levitated gyroscope model . . . . . . . . . . . . . . . . . . . . . . . 149 C.2 Integral of equation (7.15) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

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Kirill Poletkin obtained his Ph.D. degree at Moscow Aviation Institute (Moscow State Aviation Technological University), Russia in 2007. Since 2016, he is a scientist at Karlsruhe Institute of Technology as a scientist. In 2020, he is also appointed as an assistant professor at Innopolis University. His research interest includes micro- and nano-scales electromechanical devices and processes of the energy transfer within these scales. 

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