OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 3 2024 The expressions 0, ( ) ( ) / ( ), 1, 2,3 i i F X X W p p p i = ∆ ∆ = make sense of the dynamic compliance in the i-direction. The structural diagram (fig. 3) can be put in accordance with (8). It shows that the DCS can be represented as an object (tool subsystem), which is covered by negative feedback (dynamic link formed by cutting). In the internal regulator, two main channels can be distinguished, which have common gain coefficients in the open state: 0 1 (0) ,1 (0) Σ = ρ F X P k W S and 0 2 (0) ,2 (0) Σ = ρ F X P k W t . The effect of dynamic coupling on the frequency response depends on it. It is not difficult to see that ,2 ,1 Σ Σ k k , since (0) (0) P P t S . Let us focus on the conversion of force emission f(t) into deformation displacements of the tool. To clarify other disturbances, it is sufficient to convert it to forces by adding an appropriate dynamic link. In the structural diagram (Fig. 3), the dashed line shows the conversion of the disturbance ΔS(t) to forces. Transfer function 1, 2,3 = ( ), i f,X W p i , which defines the transformation of the force emission into tool deformations is calculated using the following equation: [ ] { } 0 0 1 0 2 , , ( ) (0) (0) , , 0 ( ) ( ) , 1, 2,3 1 ( ) ( ) 1 exp( ) 1 i i F X f X v F X F X P P W p W p i S W p t W p Tp T p = = ρ + + - - + . (9) Two main channels can be distinguished in the internal controller. The main one is the loop with open loop transfer function [ ] { } 0 2 (0) ( ) , 0 ( ) 1 exp( ) 1 v F X P t W p Tp T p ρ - - + . It follows from (9) that due to dynamic coupling, the frequency properties of the force-to-strain transformation change. The changes depend on the modes and on the parameters ρ(ν) and T(0). Consider the cases. 1) If ρ(ν) = 0, then = i 0 i f,X F ,X W (p) W (p) , and { } ( ) 0 i F ,X Mod W p has three resonances ω0,i, i = 1, 2, 3 and two antiresonances. The effect of approximation of DSM frequency characteristics to the characteristics of the tool subsystem is also observed at small values of SP (0) and t P (0). Therefore, the changes in the frequency characteristics of the tool subsystem can be used to judge about the changes in the parameters of the dynamic coupling formed by cutting. At small oscillations, the main value is the parameter ρ(ν). Fig. 3. Block diagram of a linearized dynamic system perturbed by forces f (p) and variations in the area of the cut layer ΔS(p)
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