Non contact eddy current dampers for control systems

Abstract

A time-varying magnetic field induces eddy current in a conductive structure. For a vibrating system, the conductor is moving in the magnetic field, generating eddy currents that will decay the vibration of the dynamic system. This process causes the system to function as a damper. In this paper an eddy current damper is designed for controlling the vibrating system. The concept and theoretical model of the eddy current damper is developed to predict the amount of damping induced on the structure. As the eddy current damper is a non-contacting system, it can be easily applied to any conductive vibrating system. The designed eddy current damper is applied to a vibrating beam. Modal testing is conducted in order to estimate the damping factors of a beam. The accuracy of theoretical model of eddy current damper is evaluated using the experimental data. Nomenclature A Magnetic potential M Mass matrix A s Cross-section area , o Permeability of the free space B Magnetic flux density Ø(x) Mode shapes b Radius of the circular magnet Q External force C Damping matrix Area density C b Damping of beam s Electrical resistivity C e Eddy current damping coefficient r(t) Temporal coordinate D Non-conservative force r c Equivalent radius of the conductor 4 Thickness of the conductor and Dirac delta function S Continuous surface E' Electric field 7 Conductivity E Modulus of elasticity T Kinetic energy F Damping force t Time F Concentrated forces U Potential energy F T Transformer eddy current damping force u Displacement F M Motional eddy current damping force V Volume f Distributed forces V s Voltage I Moment of inertia v Velocity of the conductor I(t) Electric current v b Velocity of the beam in the z direction J Eddy current density : Frequency K Stiffness matrix X L Inductive reactance = Continuous line = s Length of the conductor 1. Introduction: