Machine Diagnosis Based on Amplitude-Phase Characteristics, Determined from the Experimental Amplitude Spectrum and the Calculated Phase Spectrum

EasyChair Preprint no. 3275, version 4

Abstract

In the process of diagnosing machines, due to their universality and efficiency, vibroacoustic methods become more important. The basic signals of these methods are: time courses, amplitude and phase spectra. Time courses and amplitude spectra are often processed and used in current maintenance (diagnostic) practice. Currently, little attention is given to phase spectra, due to the difficulties encountered in their measurement. However, as is known from the principles of automation, the phase spectrum by Bode formulas can be calculated based on the amplitude spectrum. We have the relationship [1] : φ(ω)=2ω/π ∫_0^∞▒〖ln⁡A(λ)/(λ^2-ω^2 ) dλ〗 which can be calculated assuming that A(λ) will be described by a "sharpened" Gaussian curve in the form [2]: A(λ)=1/(σ^3 √2π) e^(〖-(λ-ω)〗^2/(2σ^4 )). Therefore, having the measured amplitude spectrum A(λ) and the calculated phase spectrum φ(ω), one can determine the amplitude - phase characteristics of the machine imported into the automation system. The amplitude - phase characteristics of the "closed" system determined in this way can be converted to the amplitude-phase characteristics of the "open" system, which allows determining the phase and module reserves of the tested machine. In this situation (always difficult to determine) in the diagnosis process, the diagnostic thresholds result directly from the principles of automation: phase supply ∆φ>45° and module supply ∆L>6÷10 dB.

[1] Osowski J., “Zarys rachunku operatorowego”, WNT, Warszawa 1982. [2] Beauchamp K., “Przetwarzanie sygnałów metodami analogowymi i cyfrowymi”, WNT, Warszawa 1978.

Keyphrases: amplitude spectrum, Amplitude-phase characteristics, diagnostics, phase spectrum

@Booklet{EasyChair:3275,
  author = {Paweł Lindstedt and Tomasz Sudakowski and Edward Rokicki},
  title = {Machine Diagnosis Based on Amplitude-Phase Characteristics, Determined from the Experimental Amplitude Spectrum and the Calculated Phase Spectrum},
  howpublished = {EasyChair Preprint no. 3275},

  year = {EasyChair, 2020}}