OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 2 4 An adequate description of deformations in the high-frequency region requires more complex models in which the interacting subsystems are systems with distributed parameters and physical interactions unrelated to the mechanics of the cutting process are additionally taken into account, for example, molecular-adhesion ones. The adequacy of the mathematical description of cutting dynamics also depends on the machining modes. It has been established that with increasing cutting speed there is an expansion of the frequency range in which the mathematical toolkit allows adequate evaluation of the deformations of the tool tip relative to the workpiece. This is indicated by the coherence function ( ) 2 , ( ) U S S X X K ω . It is enough to compare the graphs in fig. 5 a, c and d. In the region of frequencies close to the resonances of the tool subsystem, the coherence function approaches unity. As wear increases, the frequency range in which mathematical modeling is adequate, also decreases. At frequencies equal or divisible to the rotational frequency of the workpiece Ω, a sharp decrease in the coherence function was observed. The general trend of the uncertainty of the mathematical model is as follows: as the attenuation introduced by the dynamical system increases, the uncertainty of modeling the dynamical system as system (2) increases. This is also indicated by the estimation of the modeling error ( ) , ( ) S S i X X ℘ ω in the frequency domain (fig. 5, e). e Fig. 5. Examples of coherence function variation and estimation of proximity of amplitude-frequency characteristics of the model and the real process a b c d
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