Theoretical modeling and experimental verification of chip flow angle catastrophe in double-edged cutting considering non-linear effects

Abstract

It is found that when linear double-edged cutting tool is employed and the control variables are continuously changed into certain critical values, the chip flow angle (CFA) will change abruptly, and the cutting force and cutting power will drop sharply when the catastrophe occurs. This provides a possibility to keep the cutting process in a low energy consumption state by controlling the catastrophe of CFA. The root cause of the catastrophe is the strong non-linearity of the system. To this end, a modified method for establishing a mathematical model of the CFA catastrophe in double-edged cutting based on the catastrophe theory is proposed in this paper. In this method, the non-linear empirical formulas of cutting process parameters fitted by the finite element analysis (FEA) results of orthogonal cutting are used to reflect the non-linear effects of material deformation mode in the primary shear zone and the tool-chip friction status in the friction zone on the cutting process. Moreover, the sudden change of the shear area is utilized to tell the non-linearity of cutting process caused by geometric factors, when control variables of the cutting process change continuously. As a consequence, the accuracy of predicted results derived from the established model are improved. With the derived cutting power function as potential function, a mathematical model (cusp model) of the CFA catastrophe consisting of potential function, manifold and bifurcation set is established by the aforementioned approach. And a set of critical cutting width of the CFA catastrophe and the CFA before and after the catastrophe are obtained under the condition that the end face of 6061-T6 aluminum alloy workpiece is turned transversely by different straight double-edged turning tools. In order to validate the model and the prediction results, a series of cutting experiments are completed to indirectly measure the critical cutting width and the CFA before and after the catastrophe. The end face of 6061-T6 workpiece is turned transversely by straight double-edged turning tools with different tool geometry. Comparing the experimental results with the predicted results, it is found that the two have good consistency.