Abstract
In this chapter, the quasi-finite element approach for modelling of electromagnetic levitation micro-systems is developed [1]. The developed approach allows calculating accurately and efficiently a distribution of induced eddy current within a levitated micro-object by means of using finite elements. The combination of finite element manner to calculate induced eddy current and the set of six differential equations describing the behaviour of the mechanical part of electromagnetic levitation system is the resulting essence of the proposed quasi-finite element approach to simulate IL-micro-systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
K. Poletkin, Static pull-in behavior of hybrid levitation micro-actuators: simulation, modelling and experimental study. IEEE/ASME Trans. Mechatron. 1-1, (2020)
Y.G. Martynenko, Analytical Dynamics of Electromechanical Systems (Izd. Mosk. Ehnerg. Inst, Moscow, 1985)
B.G. Levich, Theoretical Physics: An Advanced Text (North-Holland, Amsterdam, 1971)
K. Poletkin, Z. Lu, U. Wallrabe, J. Korvink, V. Badilita, Stable dynamics of micro-machined inductive contactless suspensions. Int. J. Mech. Sci. 131–132, 753–766 (2017). https://doi.org/10.1016/j.ijmecsci.2017.08.016
K. Poletkin, A.I. Chernomorsky, C. Shearwood, U. Wallrabe, An analytical model of micromachined electromagnetic inductive contactless suspension, in the ASME 2013 International Mechanical Engineering Congress & Exposition (ASME, San Diego, California, USA 2013), pp. V010T11A072–V010T11A072. https://doi.org/10.1115/IMECE2013-66010
S. Babic, F. Sirois, C. Akyel, C. Girardi, Mutual inductance calculation between circular filaments arbitrarily positioned in space: alternative to Grovers formula. IEEE Trans. Magn. 46, 3591–3600 (2010)
K.V. Poletkin, J.G. Korvink, Efficient calculation of the mutual inductance of arbitrarily oriented circular filaments via a generalisation of the Kalantarov-Zeitlin method. J. Magn. Magn. Mater. 483, 10–20 (2019). https://doi.org/10.1016/j.jmmm.2019.03.078
F. Grover, Inductance Calculations: Working Formulas and Tables (Dover publications, Chicago, 2004)
K. Poletkin, A. Chernomorsky, C. Shearwood, U. Wallrabe, A qualitative analysis of designs of micromachined electromagnetic inductive contactless suspension. Int. J. Mech. Sci. 82, 110–121 (2014). https://doi.org/10.1016/j.ijmecsci.2014.03.013
P.L. Kalantarov, L.A. Zeitlin, Raschet induktivnostey (Calculation of Inductors) (Energoatomizdat, Leningrad 1986), p. 488 (in Russian)
J.C. Maxwell, A Treatise on Electricity and Magnetism, vol. 2, 3 edn. (Dover Publications Inc., 1954)
E. Rosa, F. Grover, Formulas and Tables for the Calculation of Mutual and Self-Inductance (US Dept. of Commerce and Labor, Bureau of Standards, Chicago, 1912)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Poletkin, K. (2021). Quasi-finite Element Modelling. In: Levitation Micro-Systems. Microsystems and Nanosystems. Springer, Cham. https://doi.org/10.1007/978-3-030-58908-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-58908-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-58907-3
Online ISBN: 978-3-030-58908-0
eBook Packages: EngineeringEngineering (R0)