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 . . . . . . . . . . . . . . . . . . . . . . . . .
About the Author: 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.
