Bouncing and Pitching Oscillations of Magnetically Levitated Body due to the Guideway Roughness

Abstract

The bouncing and pitching oscillations of a levitated body, which is assumed to be moved in a vertical plane and suspended by the magnetic force of a guideway, are examined theoretically and experimentally. A pair of nonlinear differential equations with periodic variable coefticients and nonhomogeneous terms, which governs the oscillation of the levitated body due to the guideway roughness, is derived. Using the above equations, it is shown that the oscillation is parametrically excited by the nonlinear component of the magnetic force even if the levitated body is symmetrical about the horizontal axis passing through the center of gravity. Also, the steady-state response of the oscillation under the parametric excitation is studied in more detail. Furthermore, the experimental results are shown to be in good quantitative agreement with the theoretical ones.