Analysis of a coupled magneto-quasistatic--mechanical model of an eddy current brake

Abstract

We study a coupled magneto-quasistatic model for an eddy current brake. The model leads to a nonlinear infinite-dimensional differential-algebraic system in which the nonlinearity is structural rather than caused by nonlinear material laws. It is generated by the closed electromechanical feedback loop: the angular momentum determines the velocity of the conducting disk, the velocity and the magnetic field generate motional eddy currents, and these currents induce a Lorentz torque acting back on the rotor. We introduce a finite-dissipation solution concept and prove global existence and uniqueness of weak solutions for initial data given by the magnetic field and the angular momentum, and for inputs given by the supplied coil current and the externally applied torque.