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.
Author(s): Kirill Poletkin
Series: Microsystems and Nanosystems
Publisher: Springer
Year: 2020
Language: English
Pages: 174
City: Cham
Acknowledgements
Contents
1 Introduction to Levitation Micro-Systems
1.1 Levitation Micro-Systems. Classification
1.2 Electric Levitation Micro-Systems
1.3 Magnetic Levitation Micro-Systems
1.4 Diamagnetic Levitation Micro-Systems
1.5 Superconducting Levitation Micro-Systems
1.6 Inductive Levitation Micro-Systems
1.7 Hybrid Levitation Micro-Systems
1.8 Future Trends
References
2 Micro-Coil Fabrication Techniques
2.1 Planar Coil Technology
2.2 3D Micro-Coil Technology
References
3 Analytical Modelling
3.1 Analytical Mechanics of Micro-Electro-Mechanical Systems
3.2 Statement of the Problem for Modelling
3.3 Stability of Inductive Levitation Systems
3.4 Modelling of IL-Micro-Systems Based on Symmetric Designs
References
4 Quasi-finite Element Modelling
4.1 Statement of Problem
4.2 Procedure for the Analysis of IL-Micro-Systems
4.3 Calculation of the Mutual Inductance of Circular Filaments
4.3.1 The Kalantarov-Zeitlin Method
4.3.2 Derivation of Formulas
References
5 Inductive Levitation Micro-Systems
5.1 Micro-Bearings
5.1.1 Design and Fabrication
5.1.2 Measurement of Stiffness
5.1.3 Modelling
5.1.4 Coil Impedance
5.1.5 Levitation Height
5.1.6 Lateral Stability
5.1.7 Temperature
5.2 Micro-Bearings with Lowest Energy Consumption
5.2.1 Experimental Results and Further Discussion
References
6 Hybrid Levitation Micro-Systems
6.1 Micro-Actuators
6.1.1 Design and Micromachined Fabrication
6.1.2 Experimental Results
6.1.3 Eddy Current Simulation
6.1.4 Analytical Model of Static Linear Pull-In Actuation
6.1.5 Quasi-FEM of Static Linear Pull-In Actuation
6.1.6 Preliminary Analysis of Developed Models
6.1.7 Comparison with Experiment
6.1.8 Angular Pull-In
6.2 Micro-Accelerators
6.2.1 Operating Principle
6.2.2 Micro-Fabrication
6.2.3 Linear Motion Due to the Gravity
6.2.4 Modelling of Stable Levitation
6.3 Micro-Accelerometers
6.3.1 Fabrication
6.3.2 Operating Principle
6.3.3 Preliminary Experimental Results
6.3.4 Analytical Model
6.3.5 The Accelerometer Equation of Motion
6.3.6 Static Pull-In Instability
6.3.7 Dynamic Pull-In Instability
References
7 Mechanical Thermal Noise in Levitation Micro-Gyroscopes
7.1 Model of an Ideal Levitated Two-Axis Rate Gyroscope
7.2 Mechanical Thermal Noise
7.3 Noise Floor. Angular Random Walk
7.4 Johnson Noise. Resolution
7.5 Analysis of Resolution of Reported Gyroscopes
7.6 Scale Factor
7.7 Mechanical Thermal Noise in Vibratory and Levitated Gyroscopes
References
Appendix Mathematical Notation
Appendix Mutual Inductance Between Two Filaments
B.1 MATLAB Functions
B.2 Determination of Angular Position of the Secondary Circular Filament
B.3 Presentation of Developed Formulas via the Pair of Angles α and β
Appendix Levitation Gyroscopes
C.1 Derivation of a Levitating Gyroscope Model
C.2 Integral of Eq.(7.29摥映數爠eflinkeq:Johnsonnosieentirefrequencyrange7.297)
Index
