Inductances of an Eccentric Induction Machine via Conformal Mapping and the Convolution Theorem

Abstract

The development of new methods for the fault diagnosis of induction machines (IMs) require fast models of the machine under fault conditions that are able to reproduce the harmonics generated by different kinds of faults. These models must take into account the space harmonics of the air gap magnetomotive force (MMF) generated by the machine windings, due to the complex interactions between spatial and time harmonics in a faulty machine. A common fault in induction machines is the rotor eccentricity, which can cause significant radial forces, and destructive rotor-stator rub. On the one hand, FEM models can simulate the eccentric machine, but, due to the asymmetry of the air gap length, they require high computational resources. On the other hand, analytical models of the eccentric machine are very fast, but the computation of the inductances needed in analytical models is very complex, due to the non-uniformity of the air gap. In this paper, a new method is proposed to obtain the inductances of an eccentric induction machine. It is based on the combination of a conformal mapping, which transforms the eccentric machine into a non-eccentric one, followed by a convolution that is able to extract from this conformal mapping model the inductances of the eccentric machine. The proposed method is theoretically justified, and is validated using a FEM model.