Stable dynamics of micro-machined inductive contactless suspensions

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 behavior 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 the Lagrange-Maxwell formalism. The linear model allows us to investigate the general stability properties of 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 designing MIS. Additionally, we demonstrate the successful application of this technique to study the dynamics and stability of symmetric and axially symmetric MIS designs, both based on 3D micro-coil technology.