Quasi-static Stability of Microscale Contactless Inductive Suspension with Electrostatic Stiffness Control Loop

The present paper is devoted to analytical investigation of the nonlinear dynamics of a conductive rigid ring in a contactless electromagnetic suspension. Using Lagrange-Maxwell formalism of nonlinear electro-mechanics and asymptotic methods of perturbation theory, the equilibrium positions of an inertial body in an alternating current magnetic field are found, taking into account the action of an electrostatic control system for the effective stiffness of the suspension. Suspension stability is investigated in mechanical and electromagnetic parameters space. Approximate analytical expressions for small oscillations of the ring near the stable equilibrium are obtained.