Parallel-motion-type eddy current damper model of rectangular magnet and conductor

Abstract

Eddy currents in a conductor moving in a non-uniform magnetic field in a static coordinate system are expressed as the superposition of the term by the partial derivative of the magnetic vector potential with respect to time and by the gradient of scalar potential in a stationary-conductor coordinate system. In this study, we proposed the general equation of “gradient of scalar potential is zero” condition (GSPZ condition) throughout the conductor. Additionally, under satisfying the GSPZ condition, we propose the method of obtaining the magnetic damping force from both the magnetic flux densities and the eddy currents calculated using the Biot-Savart law and Fleming's left-hand rule for the parallel-motion-type eddy current damper (GSPZ-A method). The precision of the GSPZ-A method is similar to that of the three-dimensional finite element method (3D-FEM); however, the effect of the secondary magnetic field was not considered. In this study, the GSPZ condition for the parallel-motion-type eddy current damper of a rectangular magnet and conductor of arbitrary dimensions was established. Furthermore, the GSPZ condition was applied to two types of eddy current dampers—one composed of the single square magnet and the other of the combined square magnet with oppositely aligned magnetic poles. The magnetic damping forces calculated using the GSPZ-A method were compared with those obtained from the 3D-FEM and experiments. As a result, the errors from the GSPZ-A method to 3D-FEM for the single and combined magnets were 10 and 0.4 %, respectively.

Keywords

• eddy current damper
• magnetic damper
• three dimensional finite element method (3d-fem)
• gradient of scalar potential
• magnetic vector potential