Mathematical model for electric and mechanical faults in an ac machine ⋆ Francisco-Javier Villalobos-Pi˜ na * Nancy Visairo ** Ricardo Alvarez-Salas *** * Universidad Aut´ onoma de San Luis Potosi, Av. Manuel Nava 8 Zona Universitaria, 78290 San Luis Potosi, Mexico Tel: +52 444 8173381; e-mail: fvillalobospia@yahoo.com ** e-mail: nvisairoc@uaslp.mx *** e-mail: ralvarez@uaslp.mx Abstract: This paper presents a new ac three-phase complete dynamical model undergoes four simultaneous faults for an ac machine. The faults considered are rotor, stator, static eccentricity and bearing faults. The electrical faults are modeled including the parameter variation of resistance and inductance, the mechanical bearing fault modifies the friction element and the eccentricity fault is modeled as a function of mutual inductance. Mapping the stator currents to d-q reference frame and using the Park’s instantaneous space phasor and frequency analysis it is possible to isolate the simultaneous faults. Simulation and experimental results validate the proposed model. 1. INTRODUCTION The electric machines represent the principal source of movement in the industrial sector. Motors are critical components for electrical utilities and process industries. The three phase induction motor is widely recognized as the workhorse in industry. This class of motor occupies a top position, almost exclusive, in the conversion of elec- trical energy into mechanical energy, being responsible for about 90% of the electrical energy consumed by electrical motors. It represents almost 60% of all the used electric motors (Nandi [2005]), the main reason is the practically null maintenance. In recent years, direct current machines have gradually been replaced by induction motors in many industrial applications. The success of the induction motor is due to its low cost, robustness, and high performance which may be achieved thanks to the development of new control laws and semiconductors devices. However, most control algorithms become ineffective and even danger- ous when faults occur. The faults in the stator circuit of three-phase induction machines represent a significant percentage of motor failures. Included in this category are the faults in the stator windings, such as interturn short circuits, and in the magnetic circuit. In the first case, the internal asymmetry will cause the circulation of extremely high currents in the portion of the winding affected by the fault, thus contributing to the degradation of other portions of the winding. The lead time between the initial start of the fault and the complete failure of the machine depends on several factors, namely the initial number of shorted turns, winding configuration, rated power, rated voltage, and environmental conditions, among others (S` ergio M. A. Cruz [2005]). Unfortunately, an induction motor can fail due to other fault mechanisms. For example, rotor cage faults, such as broken bars or end- rings, can occur due to a combination of various stresses ⋆ This work was supported by SEP-84616 and UASLP-CA-78. that act on the rotor (S. M. A. Cruz [2000]). Another fault is the airgap eccentricity, which can occur due to great variety of causes leading to several adverse effects to the machines, if its level increases beyond a certain limit. One of the most obvious examples is a rub between the rotor and stator, which can result in serious damage to the stator core and windings (A. J. Marques Cardoso [1993]).Besides the bearing fault is one of the most common kind of fault. Machine vibration analysis is one of the monitoring tech- niques most widely used. Vibration monitoring is very effective in detecting bearing faults, but it requires ad- ditional sensors to be fitted to the machines. While some large motors may already come with vibration transducers, it is not economically or physically feasible to provide the same devices for smaller machines. This means that small to medium size motors, must be checked periodically by portable equipment that moves from machine to machine (Jos` e L. H. Silva [2005]). With the aim of designing a fault diagnosis scheme con- sidering four kind of faults, in this work we present a mathematical model which describes the behavior of the machine undergoes faults. The proposed model is bases on the three-phase induction motor dynamic model which takes into account stator, rotor, static eccentricity and bearing faults by means of parameters variation. This paper is divided as follows, section 2 presents the ma- chine dynamic model that includes the four simultaneous faults and the description of the effect produced for each one. Section 3 describes the model validation and behavior of each kind of fault showing simulation and experimental results. Section 4 shows the fault diagnosis based on the instantaneous space (ISP) and frequency analysis. Some conclusions and future work are presented in section 5. Proceedings of the 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes Barcelona, Spain, June 30 - July 3, 2009 978-3-902661-46-3/09/$20.00 © 2009 IFAC 167 10.3182/20090630-4-ES-2003.0134