Induction machine model with space harmonics for the diagnosis of rotor eccentricity, based on the convolution theorem

Abstract

Condition based maintenance (CBM) systems of induction machines (IMs) require fast and accurate models that can reproduce the fault related harmonics generated by different kinds of faults. Such models are needed to develop new diagnostic algorithms for detecting the faults at an early stage, to analyse the physical interactions between simultaneous faults of different types, or to train expert systems that can supervise and identify these faults in an autonomous way. To achieve these goals, these models must take into account the space harmonics of the air gap magnetomotive force (MMF) generated by the machine windings under fault conditions, due to the complex interactions between spatial and time harmonics in a faulty machine. One of the most common faults in induction machines is the rotor eccentricity, which can cause significant radial forces and, in extreme cases, produce destructive rotor-stator rub. However, the development of a fast, analytical model of the eccentric IM is a challenging task, due to the non-uniformity of the air gap. In this paper, a new method is proposed to obtain such a fast model. This method, which is theoretically justified, first enables a fast calculation of the self and mutual inductances of the stator and rotor phases for every rotor position, taking into account the non-uniform air-gap length and the actual position of all the stator and rotor conductors. Once these inductances are calculated, they are used in a coupled circuits analytical model of the IM, which in this way is able to calculate the time evolution of the electrical and mechanical quantities that characterize the machine functioning, under any type of eccentricity. Specifically, the model is able to reproduce accurately the characteristic eccentricity fault related harmonics in the spectrum of the stator current.The proposed approach is validated through two different methods. First, using a finite elements (FEM) model, in order to validate the correctness of the proposed method for calculating self and mutual inductances, taking into account the non-uniform air-gap. Finally, through an experimental test-bed using a commercial induction motor with a forced mixed eccentricity fault, in order to validate that the full model correctly reproduces the phase currents in such a way that their spectra accurately show the harmonics related with the eccentricity fault, which are the basis of many MCSA diagnostic approaches.