OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 4 which determines the inertia of the cutting process, has a noticeable influence on the frequency response. As T(0) increases, the damping of oscillations increases with frequency. Consequently, the sensitivity of frequency properties to parameter variations depends on cutting speed and plastic deformation volume. Therefore, in the high-frequency region at ω∈[(T(0))-1, ∞), the influence of the change in the dynamic coupling on the transformation of forces into deformations is cancel out. Experimental studies of VAE signals measured with Brüel & Kjær vibration accelerometers confirm the peculiarities of the wear effect on the frequency properties of the signal, and allowed to reveal its additional features in the high-frequency region. The intensity of accelerations versus displacements in a quadratic dependence increases with increasing frequency, allowing the investigation of VAEs in the high-frequency region. The auto spectra are considered as Fourier images from the autocorrelation function. Therefore, the effect increases to an even greater extent. While in the calculated spectra in fig. 4 the vibrational displacements after the resonance frequencies are practically null, the measurement of vibrational accelerations in the high-frequency region reveals bursts, which we interpret as a response to the force emission formed by cutting (highlighted by the dotted line). Let us consider the modeling of the emission. Force emission and wear. Let us represent the power emission as a random pulse sequence [59]. It depends on two processes: periodic convergence of the auxiliary flank with the workpiece during the formation of articular and (or) elemental chips are formed (fig. 6) and on the increase in the contact area of the tool auxiliary flank and the workpiece as the tool wear develops, in which force interactions are formed. Each elementary interaction at the auxiliary flank contact site (Fig. 6), which is of molecularmechanical nature, can be characterized by two stages. At the first stage, energy accumulation is observed (time interval τi (1)), at the second, its release (time interval τ i (2)). The properties of an impulse can be revealed if it is represented in a triangular form. Then it will be characterised by three parameters: the distance between pulses Ti (0), its duration τ i and height Hi (0). When modelling the sequence, we can introduce hypotheses: parameters Ti (0), τ i and Hi (0) are statistically independent; its variations obey the law of normal distribution; its distribution parameters are known and they are equal. To clarify the basic properties of the signal, let us assume that its orientation in space remains unchanged and is directed by the cutting force and its modulus is equal to f(t). For such a process, its spectral representation is known [49] 2 2 2 2 2 ( ) ( ) ( ) ( ) 2 ( ) Re , 1, 2,3 , 1 ( ) n S a K a H i f f T π ϕ ω ω = s + ω + ω = ∆ - ϕ ω , (10) where n is a number of pulses on the segment T ∆ ; σ is a standard deviation of amplitudes (0) i H ; а is an expected value of (0) i H ; ( ) p τ is an interval distribution function (0) i T ; 0 ( ) ( ) j e p d ∞ ωτ ϕ ω = τ τ ∫ is a characteristic function of intervals. Equation (10) includes K(ω) and H(ω), which depend on the spectrum of the standard unit pulse 2 (0) (0) (0) (0) 2 0 ( ) ( ) ( , ) ( ) ( ) K T S T p T d T ∞ ω = ω ∫ , where (0) ( , ) S T ω is a standard pulse spectral density; (0) ( ) p T is a probability distribution function of pulse duration; (0) T is an expected value of distances; 0 ( ) ( ) ( , ) ( ) ( ) H S p d ∞ ω = τ ω τ τ τ ∫ . Symbol “^” means that the mathematical expectation is considered. The functions K(ω) and H(ω) “paint” the spectra without changing the structure of the spectral representation. The expected values and dispersions of pulses are of main importance. The spectrum (10) is transformed by the dynamic system into the VAE signal, which is measurable after amplification.
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