Modeling of the catastrophe of chip flow angle in the turning with double-edged tool with arbitrary rake angle based on catastrophe theory

It has been found experimentally that when planing or turning with double-edged tool with 0° rake angle, the chip flow angle will suddenly change with the continuous change of cutting parameters. This phenomenon, named the catastrophe of chip flow angle, is caused by the nonlinearities in non-free cutting process, but further study has not been conducted. To explore the mechanism of the catastrophe of chip flow angle, in this paper, a mathematical model (cusp catastrophe model) of the catastrophe of chip flow angle in the turning with straight double-edged tool with arbitrary rake angle is established based on catastrophe theory. Applying this model, the main characteristics of the catastrophe of chip flow angle are analyzed, and a set of critical conditions of the catastrophe of chip flow angle is predicted. To verify the predicted critical conditions of this model, a group of experiments on 6061 aluminum alloy with double-edged tool with given rake angle is designed. In this experiment, the continuous change of width of cut is achieved by turning the specially designed tapered end face of 6061 aluminum alloy, and the critical conditions of the catastrophe of chip flow angle are captured by analyzing the chip flow videos and the dynamic cutting forces. The agreement between the critical conditions predicted by the model and the experimental results is satisfactory.