OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 Fig. 8. Example of AE spectrum changes depending on wear a b The spectra represent the AE signal measured after the conversion of forces into acoustic waves. Let the vibration sequence X(t) be defined within the frequency window Δω0∈(ω0,1, ω0,2). Then, the following information features of the AE signal are considered: 0,2 0,2 0,2 0,1 0,1 0,1 1 4 Ï ( ) ( , ) ( , 0) ( , 0) , w S w d S d S d − ω ω ω ω ω ω = ω ω − ω ω ω ω ∫ ∫ ∫ (10) where S(ω, w) is the AE signal spectrum of a worn tool; S(ω, 0) is the AE signal spectrum at the initial stage of wear. 0, 0,2 0,2 0,1 0, 0,1 1 5 Ï ( ) ( , ) ( , 0) ( , 0) , ñ ñ w S w d S d S d − ω ω ω ω ω ω = ω ω − ω ω ω ω ∫ ∫ ∫ (11) where ω0,c is the average frequency of the spectrum within the window Δω0∈(ω0,1, ω0,2). Since calculating the frequency within Δω0∈(ω0,1, ω0,2) can be challenging, it is convenient to select a frequency ω0,c = 0.5(ω0,1 + ω0,2) and ensure, for w = 0, the condition ω ω ω ω ω ω = ω ω ∫ ∫ 0, 0,2 0,1 0, ( , ) ( , 0) ñ ñ S w d S d holds. Finally, to estimate the irregularity of the pulse sequence amplitude, the amplitude modulation signal of the selected high-frequency signal X(t) can be considered. The modulation level of x(t), determined after detecting the signal X(t) and estimating its dispersion using moving average algorithms ( ) ( ) t T t x d Ò −∆ σ = ξ ξ ∫ , is highly informative. Then, { } 1 6 Ï ( ) ( ) { } w w t − = σ − σ σ . (12) Depending on the hardware implementation and the vibration sequences available for measurement, all the above-mentioned information features Π = {Π1, Π2, … Π6} T∈ ℜ Π 6 can be used.
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