Experimental Investigation and Bifurcation Set Equation Modeling of Chip-Splitting Catastrophe

Abstract This paper presents the methods of designing experiments for observation of the critical conditions of chip-splitting catastrophe (CSC) based on the dichotomy principle and the methodology of modelling CSC with a bifurcation set equation on the basis of catastrophe theory. 355 groups of experiments are carried out for observing critical conditions of CSC in the symmetrical straight double-edged cutting. It is found that the occurrence of CSC is of obvious regularity. Besides, the specific cutting force is reduced by a maximum of 64.68% after CSC. The bifurcation set equation is established, which can predict the critical conditions of CSC in the symmetrical cutting with a straight double-edged tool with any combinations of cutting edge angles and rake angles. With verification, the predicted values of the critical cutting thickness of CSC based on the established equation are in good agreement with experimental values and yield an average absolute prediction error of 5.34%, which is satisfactorily low. This study lays the groundwork for energy-saving optimization of tool structure and process parameters through reasonable utilization of CSC.