Suppression efficiency of self-excited vibrations in machining evaluated by changes in their energy

The aim was to develop an approach for evaluation and suppression of undesirable self-excited vibrations during the machining process. The suppression efficiency of self-excited vibrations was evaluated by the amount of their internal energy created by the radial cutting force. This force was assumed to be proportional to the difference in the area of the cut metal layer at the tool exit from the workpiece and penetration in each vibration. The research object was a low-rigidity shaft with a diameter of 48 mm, cantilevered with an outreach of 150 mm. Changes in the energy of self-excited vibrations were evaluated using a software package in the SciLab language. The shaft was machined with a cutting tool at a spindle speed of 208 rpm with a feed of 0.122 mm/rev and a cutting depth of 0.8 mm. The modulation frequency of the cutting speed per workpiece revolution was assumed to be 0.5. The difference in the area of the cut metal layer at the tool exit from the workpiece and penetration was calculated sequentially when varying the depth of cutting speed modulation in the range from 0 to 30% with an interval of 1%. The results obtained were used to draw a plot of changes in the relative difference of the cut layer areas (proportional to the internal energy of self-excited vibrations), similar to a cosine curve with a decreasing magnitude. An increase in the depth of cutting speed modulation was established to sharply reduce the internal energy of self-excited vibrations, periodically pulsing around zero values. The local minima of the plot corresponded to the condition of suppression of self-excited vibrations. The fourth local minimum corresponding to the depth of cutting speed modulation equal to 13.5% was selected as a parameter for practical use. At this depth, cutting speed modulation ensured a more than 10-fold decrease in the vibration range and a 12-fold decrease in the vibration amplitude, in comparison with similar parameters at the constant cutting speed. The results obtained confirm the efficiency of the proposed method for evaluating changes in the energy of self-excited vibrations during the machining process. 

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