OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 2 4 Ta b l e 2 Parameters of the matrices of velocity coefficients and elasticity of the tool subsystem h1,1, kg∙s/mm h2,2, kg∙s/mm h3,3, kg∙s/mm h1,2=h2,1, kg∙s/mm h1,3=h3,1, kg∙s/mm h2,3=h3,2, kg∙s/mm 1.3 1.1 0.8 0.6 0.5 0.4 c1,1, kg/mm c2,2, kg/mm c3,3, kg/mm c1,2=c2,1, kg/mm c1,3=c3,1, kg/mm c2,3=c3,2, kg/mm 2.000 900 350 200 150 80 Two sets of time sequences were considered: those calculated using the model parameters and those actually measured. General views of the experimental stand for research and the instrument equipped with sensors for vibration measurement are shown in fig. 2. The “white” noise model of power disturbances in the frequency range up to 30.0 kHz was used to determine the calculated time sequences. Examples of time realizations of “white” noise, computed and measured time sequences X1 in the direction are shown in fig. 3. In fig. 4 shows examples of spectra normalized to dispersion determined from the calculated (2) , ( ) S S X X S ω (а) and measured ( ) ( ) , ( ) U U S S X X S ω (b) sequences. The analytically calculated spectra are also shown in red color on the graphs (1) , ( ) S S X X S ω , and also in fig. 4, c shows a fragment of force perturbation in the form of sinusoidal change of additional forces with slowly changing frequency. In addition, an example of strain amplitude variations in the direction of 1 X , i.e., the amplitude-frequency response of the model, is given (fig. 4, c). It should be noted that these characteristics remain unchanged at small amplitudes of force excitation. In the example under consideration, variations in the amplitude of the force disturbance up to 10 kHz do not change it. When the amplitude increases, the nonlinear properties of the model are noticeable. It is manifested in changes in the resonance frequency, in the redistribution of frequencies and amplitudes of the main oscillators, in the broadening of its spectral line, and so on. a b с d e Fig. 3. Examples of trajectories: a – power “white” noise; b, c – calculated deformations in two time scales; d, e – measured deformations in two time scales
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