A qualitative analysis of designs of micromachined electromagnetic inductive contactless suspension

Journal of Magnetism and Magnetic Materials

Korvink

2019

In this article, we present a new analytical formulation for calculation of the mutual inductance between two circular filaments arbitrarily oriented with respect to each other, as an alternative to Grover [1] and Babič [2] expressions reported in 1944 and 2010, respectively. The formula is derived via a generalisation of the Kalantarov-Zeitlin method, which showed that the calculation of mutual inductance between a circular primary filament and any other secondary filament having an arbitrary shape and any desired position with respect to the primary filament is reduced to a line integral. In particular, the obtained formula provides a solution for the singularity issue arising in the Grover and Babič formulas for the case when the planes of the primary and secondary circular filaments are mutually perpendicular. 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. Newly developed formulas have been successfully validated through a number of examples available in the literature, and by a direct comparison with the results of calculation performed by the FastHenry software.

Section: Preliminary Discussionmentioning

confidence: 99%

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

Journal of Magnetism and Magnetic Materials

Korvink

2019

“…Moreover, upon ensuring a condition described further below, Equation (3) can be approximated well by the logarithmic function [34]:…”

Section: The Accelerometer Equation Of Motionmentioning

confidence: 99%

“…In this work, pull-in phenomena based on the combination of an inductive suspension and electrostatic actuation are analytically and numerically studied in more detail. The qualitative technique developed in [34] to model micro-machined inductive contactless suspensions, where the eddy current within the levitated micro-object is approximated by a magnetic dipole, is used. We note that this method has been recently further generalized in [35,36], where the eddy current is more accurately approximated by a system of dipoles.…”

Section: Introductionmentioning

confidence: 99%

Modeling a Pull-In Instability in Micro-Machined Hybrid Contactless Suspension

Korvink

2018

Actuators

Self Cite

A micro-machined hybrid contactless suspension, in which a conductive proof mass is inductively levitated within an electrostatic field, is studied. This hybrid suspension has the unique capability to control the stiffness, in particular along the vertical direction, over a wide range, which is limited by a pull-in instability. A prototype of the suspension was micro-fabricated, and the decrease of the vertical component of the stiffness by a factor of 25% was successfully demonstrated. In order to study the pull-in phenomenon of this suspension, an analytical model was developed. Assuming quasi-static behavior of the levitated proof mass, the static and dynamic pull-in of the suspension was comprehensively studied, also yielding a definition for the pull-in parameters of the hybrid suspension.

“…Additionally, the levitation coil induces the eddy current in the PM, the maximum value of which is distributed within a ring with the same radius as the levitation coil, as shown in [12]. Assuming that the levitation height of the proof mass is small and the fact that the function of mutual inductance between the disk-shaped proof mass and the ring-shaped coils can be simplified and expressed in terms of simple functions, the qualitative approach developed in [20] can be applied to the present study. Hence, the mutual induction can be represented in quadratic form as follows:…”

Section: Theoretical Calculation Of the Input Current And Frequencymentioning

confidence: 99%

Performance Characterization of Micromachined Inductive Suspensions Based on 3D Wire-Bonded Microcoils

Wallrabe

et al. 2014

Micromachines

Self Cite

We present a comprehensive experimental investigation of a micromachined inductive suspension (MIS) based on 3D wire-bonded microcoils. A theoretical model has been developed to predict the levitation height of the disc-shaped proof mass (PM), which has good agreement with the experimental results. The 3D MIS consists of two coaxial wire-bonded coils, the inner coil being used for levitation, while the outer coil for the stabilization of the PM. The levitation behavior is mapped with respect to the input parameters of the excitation currents applied to the levitation and stabilization coil, respectively: amplitude and frequency. At the same time, the levitation is investigated with respect to various thickness values (12.5 to 50 µm) and two materials (Al and Cu) of the proof mass. An important characteristic of an MIS, which determines its suitability for various applications, such as, e.g., micro-motors, is the dynamics in the lateral direction. We experimentally study the lateral stabilization force acting on the PM as a function of the linear displacement. The analysis of this dependency allows us to define a transition between stable and unstable levitation behavior. From an energetic point of view, this transition corresponds to the local maximum of the MIS potential energy. 2D simulations of the potential energy help us predict the location of this maximum, which is proven to be in good agreement with the experiment. Additionally, we map the temperature distribution for Micromachines 2014, 5 1470 the coils, as well as for the PM levitated at 120 µm, which confirms the significant reduction of the heat dissipation in the MIS based on 3D microcoils compared to the planar topology.