OBRABOTKAMETALLOV technology Vol. 25 No. 1 2023 The Mikhailov vector hodograph, shown in Figure 3, confirms the conclusion about the stability of the cutting control system, which is made by analyzing the coordinates of the deformation motions of the tool tip earlier. A feature of the Mikhailov vector hodograph is a constant increase in the amplitude of the hodograph with the increase in the frequency of modeling, therefore, the description of the hodograph has to be done in two figures, in the first one we see the movement of the hodograph through the first five quadrants, and in the second the hodograph covers the point zero through three more quadrants. The stability limit for the case of processing at a speed of 1,600 rpm, occurs at a wear value of 0.473 mm, the results of modeling the Mikhailov vector hodograph for this variant of modeling the cutting control system are shown in Figure 4. Fig. 3. The hodograph of the Mikhailov vector, a stable system: a – the beginning of the Mikhailov vector; b – the end of the Mikhailov vector а b Fig. 4. The hodograph of the Mikhailov vector, the system on the boundary of stability: a – the beginning of the Mikhailov vector; b – the end of the Mikhailov vector Re Jm Точка касания Re Jm а b
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