Abstract
This paper presents a result of study of the pull-in phenomenon in the hybrid micro-machined contactless suspension (µ-HCS), combining inductive suspension and electrostatic actuation, reported at PowerMEMS 2015 [1]. Assuming the quasi-static behavior of a levitated proof mass, a non-linear analytical model describing the pull-in actuation along the vertical direction is developed. The developed model allows us to predict the static pull-in parameters of the suspension and to show a dependence of these parameters on suspension design. It is shown that the pull-in displacement can be larger by almost a factor of two than one occurring in a spring-mass system with constant stiffness (classic pull-in). The model is verified by using numerical estimations as well as experimental data and agrees well with measurements and calculations.
Highlights
Micro-machined contactless suspensions (μ-CS), employing the phenomena of electromagnetic levitation, eliminate mechanical attachments between stationary and moving parts in MicroElectro-Mechanical Systems (MEMS) and as a result provide the solution of fundamental issue in MEMS related to the domination of friction over inertial forces in the micro-world
Where m is the mass of levitated proof mass (PM), g is the gravity acceleration, I is the amplitude of a harmonic current i of coils, L is the self inductance of the PM, M is the mutual inductance between the PM and coils, U is the applied voltage to the electrodes both of each which has the same area of Ae, A = ε0Ae, ε0 is the permeability of free space, F is the force acting on the PM along the y-axis
Worth noting that in all known prototypes of μ-HCS published in the literature the parameter ξ is less than 0.25. This fact provides the applicability of the reduced model for further analytical study of μ-HCS
Summary
Micro-machined contactless suspensions (μ-CS), employing the phenomena of electromagnetic levitation, eliminate mechanical attachments between stationary and moving parts in MicroElectro-Mechanical Systems (MEMS) and as a result provide the solution of fundamental issue in MEMS related to the domination of friction over inertial forces in the micro-world. The pull-in phenomenon in μ-HCS shown in Fig. 1 is analytically and numerically studied. In order to model micro-machined inductive CSs, the qualitative technique developed in [14], where the induced eddy current within a levitated micro-object is approximated by a magnetic dipole, is used.
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