Time-Frequency Analysis for Rotor-Rubbing Diagnosis

Abstract

The developments of new manufacturing processes have impacted modern machinery. Nowadays, mechanical parts are produced with tighter tolerances that allow very high precise assemblies. On the other hand, new materials and design techniques have developed lighter elements. Thus, modern machinery operates at very high speeds and accelerations, which, in many cases, shows nonlinear dynamic behaviors. Intelligent manufacturing systems require on line monitoring equipment coordinated by the control systems. Traditionally, monitoring systems are based on the Fast Fourier Transform (FFT), which, due to its basis is unable to identify transient responses, and nonlinear behaviors. On the other hand, the FFT requires a considerable processing time that limits its application to early fault detections. The development of new sensors, signal processing techniques and faster microprocessors are key elements for modern monitoring systems. These systems require a better understanding of the machine response and the nature of the output signals. The evolution of the phase space, or phase diagram, represents how the dynamic system evolves in time. Nonlinearities and transient responses can be determined from the smoothness of the tangent vector of the phase diagram accordingly to Liouville’s theorem. Therefore, the phase diagram is a useful technique for predicting transient and nonlinear behavior in mechanical systems. Even more, the phase diagram can be implemented electronically for on line monitoring, and it can identify faults in real time. Mathematical modeling refers to the use of mathematical language to simulate the behavior of a system. Its role is to provide a better understanding and characterization of the system. In the theory of mechanical vibrations, mathematical models are helpful for the analysis of dynamic behavior of the structure being modeled (Kerschen et al. 2006). Even with advanced computers, experimental testing and system identification help designers to evaluate numerical predictions with experimental data. The term “system identification” is sometimes used in a broader context and may also refer to the extraction of information about the structural behavior directly from experimental data. In this case, it is referred as any systematic way of deriving models from experimental data. This is the main objective of any machinery monitoring systems (Masri 1994). For linear systems, modal analysis is the most popular approach for system identification. It can describe the behavior of a system for any input. Examples of this are: Ibrahim time domain method, eigensystem realization algorithm, stochastic subspace identification method, polyreference least-square complex frequency domain method among others.