Stable dynamics of micro-machined inductive contactless suspensions

Abstract

In this article, we present a qualitative approach to study the dynamics and stability of micro-machined inductive contactless suspensions (MIS). In the framework of this approach, the induced eddy current into a levitated micro-object is considered as a collection of m-eddy current circuits. Assuming small displacements and the quasi- static behaviour of the levitated micro-object, a generalized model of MIS is obtained and represented as a set of six linear differential equations corresponding to six degrees of freedom in a rigid body by using Lagrange-Maxwell formalism. The linear model allows us to investigate the general stability properties of the MIS as a dynamic system, and these properties are synthesized in three major theorems. In particular, we prove that the stable levitation in the MIS without damping is impossible. Based on the approach presented herewith, we give general guidelines for MIS designing. In addition to we demonstrate the successful application of this technique to study the dynamics and stability of the symmetric and axially symmetric MIS designs both based on 3D micro-coil technology.Comment: 39 pages, 11 figure

Efficient calculation of the mutual inductance of arbitrarily oriented circular filaments via a generalisation of the Kalantarov-Zeitlin method

“…of this axis lying on the surface x By around the vertical z axis, respectively, as it is shown in Figure 2 The same angular position can be determined through the α and β angle, which corresponds to the angular rotation around the x axis and then around the y axis, respectively, as it is shown in Figure 2(b). This additional second manner is more convenient in a case of study dynamics and stability issues, for instance, applying to axially symmetric inductive levitation systems [23,25]…”

“…The efficiency and flexibility of the Kalantarov-Zeitlin method allow us to extend immediately the application of the obtained result to a case of the calculation of the mutual inductance between a primary circular filament and its projection on a tilted plane. For instance, this particular case appears in micro-machined inductive suspensions and has a direct practical application in studying their stability [25] and pull-in dynamics [27,28]. The new analytical formulae were verified by comparison with series of reference examples covering all cases given by Grover [4], Kalantarov and Zeitlin [8], and using direct numerical calculations performed by the Babič Matlab function [2] and the FastHenry software [9].…”

Levitating Micro-Actuators: A Review

“…Inductive levitation micro-actuators: (a) two coils design, I is the electric alternate current (AC) [47]; (b) spiral coil design [52]; (c) two racetrack-shaped solenoidal 3D wire-bonded micro-coils [17].…”

“…In the framework of this prototype, Wallrabe's group demonstrated stable levitation of a disc having a diameter of 3.2 mm and a thickness of 25 µm, as well as a large increase in actuation range along the vertical axis up to 125 µm by means of changing the AC current in the coils within the range 80 mA to 100 mA. This design was further intensively studied and characterized in terms of stability, dynamics, and electrical performance [17,[54][55][56][57]. In particular, recently Badilita's group at the Karlsruhe Institute of Technology presented a new ILMA design based on 3D micro-coil technology, where the coil structure consists of two racetrack-shaped solenoidal 3D wire-bonded micro-coils, to be used as Maglev rails as shown in Figure 4c [17].…”

“…This design was further intensively studied and characterized in terms of stability, dynamics, and electrical performance [17,[54][55][56][57]. In particular, recently Badilita's group at the Karlsruhe Institute of Technology presented a new ILMA design based on 3D micro-coil technology, where the coil structure consists of two racetrack-shaped solenoidal 3D wire-bonded micro-coils, to be used as Maglev rails as shown in Figure 4c [17]. The design allowed an additional translational degree of freedom to the levitated micro-object, and was proposed to be applied as a micro-transporter.…”