Correlation of Cutting Area with Cutting Force During Self-Excited Vibration : Vibration, Control Engineering, Engineering for Industry

An algorithm for the accurate evaluation of a cutting area considering the tool tip radius and the multiple regenerative effect was proposed. This made it possible to follow the time historical behaviour of the cutting area during self-excited vibration. The cutting area which was accurately evaluated showed good agreement with the cutting force. The ratio of the cutting area to that for stationary cutting reaches about 3 at the maximum. The ratio was sbout 4 for cases where the tool tip radius and the multiple regenerative effect were neglected. These evaluations were kept constant even though the amplitude of the vibration was varied. The behaviour of the number of multiple regenarations during the vibration was also obtained. It is related to the amplitude. it was shown that the number was 4 or 4 while the amplitude was kept constant. however, it reached 12 when the vibration was disturbed by varying the rotational speed. The correlation of the cutting area with the cutting force was evaluated by adopting a factor to minimize the square root of the sum of the squares of the difference for both quantities.