Computation of magnetic flux density and iron losses by Fourier-Bessel and Fourier-Laurent series in an electromagnetic vibration damper

A special machine, an electromagnetic vibration damper, is designed to create an attractive rotating force, in synchronism with the rotor. It consists of a laminated slotted stator and a massive, smooth, passive rotor. The aim of the authors is the computation of magnetic-flux density and iron losses by means of Fourier-Bessel and Fourier-Laurent series. The proposed analytical method assumes the stator currents to be surface located on the smooth airgap-stator boundary, and the machine is divided into three areas of constant permeability. Maxwell equations, with vector potential, lead to different solutions, including Fourier-Bessel or Fourier-Laurent series for space unknowns (radius and angle), where time appears as another Fourier series. Magnetic-flux density and iron losses come, respectively, from spatial and time derivatives. Iron losses, due to slot field pulsation losses, are added by means of a classical analytical formula