Analysis of the structure of vibration signals from mechanical systems in the process of growth of a defect
- PDF / 1,080,618 Bytes
- 10 Pages / 595.276 x 793.701 pts Page_size
- 101 Downloads / 137 Views
ANALYSIS OF THE STRUCTURE OF VIBRATION SIGNALS FROM MECHANICAL SYSTEMS IN THE PROCESS OF GROWTH OF A DEFECT I. I. Mats’ko,1, 2 I. B. Kravets’,1 and I. M. Yavors’kyi1, 3
UDC 621.319:519.22
We construct a statistical model of vibration response of a thin body containing a crack and study the dynamics of changes in the cross-correlation links between the stationary components of the vibration signal. It is shown that the crack size affects neither the shape of correlation functions nor the width of their central maximum. Keywords: vibration signal, periodically correlated random process, cross-correlation functions.
Vibration signals emitted by large industrial machine complexes carry information about the actual state of the assemblies of these complexes. Hence, the statistical analysis of vibration processes in mechanical systems is a powerful diagnostic tool for the monitoring of their state by the methods of nondestructive testing. The defects of mechanical units manifest themselves by changes in the characteristics of vibration signals. Some types of defects lead to the appearance of harmonic components in the vibration signal and the other lead either to modulations or to the formation of shock pulses. Hence, for the detection of defects in the early stage of their development, it is necessary to analyze all possible probability characteristics of the vibration signals. As shown in [1, 2], the structure of correlation functions of the vibration signals depends on the crack length. In the process of crack growth, parallel with the zero-order component of the correlation structure, we observe the appearance of the first correlation component whose intensity increases in course of crack propagation. The attenuation factors of the components of correlation functions vary as functions of the relative crack length. In practice, it is very difficult to approximate the components of correlations function because they are expressed via the sums of autocorrelation and cross-correlation functions of the forming periodically correlated random processes (PCRP) of the stationary components [4]. Thus, in our subsequent investigations, it is reasonable to use the methods of processing capable of selection of the indicated components. The vibrations of a thin body containing a crack are described by the following system of second-order nonlinear differential equations [7, 8]:
⎧ X ′′ + 2β c X ′ + ω 2c X = f (t), ⎪ ⎨ ⎪⎩ X ′′ + 2β s X ′ + ω 2s X = f (t),
X ≤ 0,
(1)
X > 0,
where ω 2c = kc /m , ω 2s = k s /m , ω 2c and ω 2s are the eigenfrequencies of vibrations, kc and k s are the stiffnesses of the body at the times when the crack is closed and open, respectively, and m is the reduced mass of the body. The driving force is chosen in the form 1
Karpenko Physicomechanical Institute, Ukrainian National Academy of Sciences, Lviv, Ukraine. Corresponding author; e-mail: [email protected]. 3 Institute of Telecommunications, University of Technology and Life Sciences, Bydgoszcz, Poland. 2
Translated from Fizyko-Khimichna Mekha
Data Loading...
