OBRABOTKAMETALLOV technology Vol. 25 No. 1 2023 Modeling results and discussion of the second hypothesis For an adequate comparison of the experimental results in the previous section and the convenience of representing the system character, the simulation was carried out similarly to the previous version in the Matlab/Simulink 2014 package, where the system (29) was directly modeled in Simulink; and the Mikhailov vector (34) was calculated by a cycle in Matlab itself, where at every step of the cycle the determinant D(jω) for a specific frequency value ω was calculated and the resulting value was plotted along the complex plane, then everything was repeated. The simulation results for the case of processing with a cutting speed 900 rev/min are shown below. Let’s consider the dynamics of a nonlinear cutting system at a cutting speed 900 rev/min and h = 0.24 mm, a graph of the coordinates of the deformation motion of the tool tip and the corresponding phase trajectories are shown in Figure 10. Fig. 10. For the case of wear h = 0.24: a – deformations along the x coordinate; b – deformations along the y coordinate; c – deformations along the z coordinate; d – phase trajectory along the x coordinate; e – phase trajectory along the y coordinate; f – phase trajectory along the z coordinate x, mm (10-3) y, mm z, mm t, s a) b) c) t, s t, s dx/dt, mm/sec d) e) f) z, mm*10-3 y, mm*10-3 dy/dt, mm/sec dz/dt, mm/sec x, mm *10-3 The dynamics of the cutting process reflected in Figure 10 shows a steady cutting process, which is associated with minimizing the vibration activity of the tool. The stability margin can be estimated from the starting point of the Mikhailov vector hodograph on the complex plane, which is shown in Figure 11. As it can be seen from Figure 11, the stability margin depends on the distance of the hodograph curve beginning from the origin of the complex plane coordinates. The second part of the hodograph is not a b c d e f
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