Analytical Model of Eccentric Induction Machines Using the Conformal Winding Tensor Approach

Induction machines (IMs) are a critical component of many industrial processes, and their failure can cause large economic losses. Condition-based maintenance systems (CBMs) that are capable of detecting their failures at an incipient stage can reduce these risks by continuously monitoring the IMs’ condition. The development and reliable operations of CBMs systems require rapid modeling of the faulty IM. Due to the fault-induced IM asymmetries, these models are much more complex than those used for a healthy IM. In particular, a mixed eccentricity fault (static and dynamic), which can degenerate into rubbing and destruction of the rotor, produces a non-uniform IM air gap that is different for each rotor position, which makes its very difficult to calculate the IM’s inductance matrix. In this work, a new analytical model of an eccentric IM is presented. It is based on the winding tensor approach, which allows a clear separation between the air gap and winding-related faults. Contrary to previous approaches, where complex expressions have been developed for obtaining mutual inductances between conductors and windings of an eccentric IM, a conformal transformation is proposed in this work, which allows using the simple inductance expressions of a healthy IM. This novel conformal winding tensor approach (CWFA) is theoretically explained and validated with the diagnosis of two commercial IMs with a mixed eccentricity fault.