Accurate Analytical Determination of Electromagnetic Bearing Coefficients
Electromagnetic contactless bearings have unique advantages over conventional bearings including no wear, reduced pollution and maintenance, and active control prospects. Their existing mathematical models are however very simplistic, and not very accurate leading to inferior (and, sometimes, catastrophic) performance under demanding conditions. This paper seeks to derive a better model from a basic consideration of the fundamental physics of the problem. It also intends to provide a family of curves suitable for use by an engineering designer. First, the fundamental electromagnetic equations are presented for a typical radial magnetic bearing configuration. The bearing is divided into four subdomains and the resulting partial differential equations and the boundary conditions are formulated over the different subdomains. The rotor is placed into a circular orbit, which leads to a moving boundary problem. The equations are then solved in closed form using an approximate asymptotic technique. The resulting magnetic fields and forces are computed, and the results are presented in a form suitable for use by a bearing designer. The results are also in a form that is decoupled from the active control strategy which greatly enhances their applicability.
KeywordsMagnetic bearings Rotor dynamics Electromagnetics Analytical solutions
This work was partially supported by a grant from Office of Naval Research under Grant No. N00014-07-10866. The author would like to gratefully acknowledge Dr. Mark Spector who is the project manager; in addition, much appreciation is due to the assistance of Matthew Frank (NAVSSES – Philadelphia).
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