33Complex(1) - Tutorial paper July 98 DIRECTIONAL SPECTRUM...

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Tutorial paper, July 98 DIRECTIONAL SPECTRUM ANALYSIS AND ITS APPLICATIONS TO ROTATING MACHINE DIAGNOSIS Chong-Won Lee, and Yun-Sik Han Center for Noise and Vibration Control(NOVIC), Department of Mechanical Engineering KAIST, Science Town, Taejon, 305-701, KOREA Tel : 82-42-869-3016, Fax : 82-42-869-8220, E_mail : [email protected] A new vibration signal processing technique is presented to diagnose defective elements of rotating machine via directional spectral analysis, adopting the complex notation. The convention for representing the complex-valued signal is written in polar form using Euler's formula, and the shape and directivity index is established to quantify the shape and directivity information. The directional power spectrum of complex-valued stationary signal preserves the important directivity and shape information of whirling orbits, whereas the phase of the directional cross-spectrum indicates its inclination angle. In order to characterize the instantaneous planar motion in a rotating machine from its transient complex-valued signal, the directional auto- and cross- Wigner distribution (dWDs) and directional harmonic wavelet maps (dHWMs) are developed, and their properties are examined. Finally, the developed directional signal processing techniques are successfully applied for the vibration signals taken from actual rotating and reciprocating machines: a diagnosis of the misalignment and an identification of the instantaneous backward whirling orbit in the laboratory test rig, and characterization of the planar motions of a point of interest on the engine block during transient operations. 1. INTRODUCTION The operational vibration monitoring in rotating machinery gives useful information about machinery malfunctions. Although the orbits taken from a rotor well represent the planar motions, they are usually complicated in shape, containing many frequency components, so that it is not straight forward to relate them with any potential malfunctions. Spectral analysis is probably the most popular signal processing technique for diagnosing the rotor systems because the frequency components and the corresponding amplitudes and phases vary in accordance with various fault mechanisms. Conventional spectral analysis techniques enable the display of the corresponding frequency contents in a systematic way, but they treat the rotor vibrations as real quantities so that their frequency spectra lose such an important orbital information as directivity, i.e. forward (the same direction as the rotor rotation) or backward (the direction opposite to the rotor rotation)[1, 2]. On the other hand, the directional power spectra (dPS) of complex-valued signals, which preserve the important directivity and shape information of planar motion, has proven to be a powerful diagnostic tool for rotating and reciprocating machinery [2-9]. The key idea is that, in general, a planar whirling can be decomposed into forward and backward harmonic components and that the harmonic components, backward or forward
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