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.

Autorentext
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.

Inhalt

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</p&gt...