Experimental Data Based Model Establishment Of The Bifurcation Set Of Chip-splitting Catastrophe In The Symmetrical And Asymmetrical Straight Double-edged Cutting

The chip-splitting catastrophe(CSC)generated by cutting with a straight double-edged tool will lead to a significantly reduced cutting force.This has enormous potential in energysaving machining and in the design of energy efficient cutting tools.Therefore,on the foundation of this catastrophe theory and its suggested swallowtail catastrophe and butterfly catastrophe,a proposal was made to establish the bifurcation set equation of CSC in the symmetrical straight double-edged cutting.In this method,the mapping relationship between the actual control variables of CSC and the theoretical control variables of the standard catastrophes was set as a set of linear functions with undetermined coefficients.To solve these coefficients,the cutting experiment designed by dichotomy to obtain critical conditions of CSC was conducted,and the corresponding experimental data for the critical conditions of CSC with a straight double-edged tool symmetric transverse feeding AISI 1045 steel disc workpieces were acquired.Using the experimental data of CSC and modern optimization technique,the coefficients of mapping functions were computed,and established the bifurcation set equation based on the swallowtail catastrophe and butterfly catastrophe,which can predict the critical conditions of CSC in the symmetrical cutting using a straight double-edged tool with any combinations of tool edge angles and rake angles.With verification,the predicted results of the critical cutting thickness of CSC based on the established model captured an acceptable tendency with experimental results and yielded an average absolute prediction error both being smaller than 11.2%,which was satisfactorily low.Besides,a maximum of 64.68% reduced the specific cutting force after CSC.A group of cutting experiments were designed and completed with a straight doubleedged tool asymmetrical transverse feeding AISI 1045 steel disc workpieces and the chip morphology and dynamic cutting force were observed.It not only obtained fourteen groups of experimental data for the critical conditions of CSC in the same cutting manner,but also found the law of CSC in asymmetrical cutting that the smaller the unequal division coefficient is,the greater the average reduction of the specific cutting force is.This study preliminarily laid the groundwork for energy-saving optimization of tool structure and processing parameters through reasonable utilization of CSC,while solving various process problems caused by excessive cutting force and realized energy conservation cutting.