OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 2 2024 ( ) ( ) ( ) ( ) 1 2 2 ( ) ( ) , , , , 0 0 ( ) ( ) ( ) , 1, 2; 1, 2,3, è è è è S S S S S S S S i i X X X X X X X X S S d S d i s ∞ ∞ - ω ω σ = ω - ω ω × ω ω = = ∫ ∫ (8) where ω∞ is the frequency that is an order of magnitude higher than the upper natural frequency of the oscillating contour of the tool subsystem. When analyzing adequacy, it is necessary to consider also the evaluation of the influence of additional interactions not included in themathematical description of themodel (2). For example, adhesive interactions, formation of dissipative structures (e.g., growth), and additional disturbances (e.g., kinematic disturbances from the machine itself). Moreover, these perturbations can be applied not directly to the forces, but to other elements of the system, in the case of kinematic perturbations – these are variations in feed rate. For this purpose, the coherence function between the observed strain displacements ( ) 1 ( ) è X t and the calculated 1( ) X t is considered. Then ( ) 2 , 1 ( ) , 1, 2,3, 1 ( ) u S S X X S K s ω = = + δ ω (9) where , 2 ( ) ( ) ( ) ( ) S S u S S W j θ ω δ ω = ω ; , ( ) S Sθ ω is spectrum of additional unmeasured noise; 2 ( ) ( ) u S W jω is square of the modulus of transformation of “white” noise into deformations ( )( ) è S X t . Equation (9) shows that the coherence function tends to unity in two cases: there are no additional interaction forces unaccounted for in the model or the unaccounted for interactions with respect to the accounted perturbations are small. Estimates (7)–(9) also allow us to perform a terminal correction of the parameters of model (2). Let’s consider an example of analyzing the adequacy of the model for small oscillations during longitudinal turning on a 1K62 machine tool (fig. 2). The 20X steel shaft D = 20 mm was machined with a tool equipped with non-transferable T15K6 tetrahedral plates. Generalized mass was equal to 0.015 kg∙s2/mm. The parameters are given in Table 1 and Table 2, determined according to the methodology described in [22, 23, 61]. Rotational speed of the workpiece was equal to 25 Hz. The corresponding cutting speed was equal to 1.5 m/s. Cutting depth and feed rate were equal: (0) p t = 2 mm; (0) p S = 0.1 mm. a b Fig 2. General views of the equipment (a) and measurement interface (b) used for experiments Ta b l e 1 Dynamic link options ρ, kg/mm2 σ, (mm/s)-1 T(0), s μ χ 1 χ2 χ3 Ω, s -1 200–1.000 0.0011 0.0002 0.5 0.4 0.51 0.76 5–50
RkJQdWJsaXNoZXIy MTk0ODM1