Study of eccentric round-rotor synchronous machines through conformal mapping. Part II: Unbalanced magnetic pull

The study of electric machines subject to rotor eccentricity is usually performed using a winding and permeance function approach. In a companion paper, an alternative method is investigated based on conformal mapping. The geometry of a an eccentric round-rotor machine has been mapped into a uniform air-gap topology by means of Moebius conformal map. In this paper, the approach is used to derive explicit formulas to compute the unbalanced magnetic pull of the eccentric machine. It shown how, unlike conventional winding-function theory, the proposed method yields closed-form formulas which do not involve series expansions nor require numerical integrations and are thus particularly fit for implementation into fast simulation programs. Such expressions are assessed by comparison with Finite Element Analysis (FEA).