Experimental Establishment Of The Bifurcation Set Equation Of The Chip-splitting Catastrophe In Cylindrical Turning Based On The Butterfly Castrophe

Researches found that the chip-splitting catastrophe(CSC)generated in cylindrical turning with double-edged tool when cutting control parameters change continuously,will lead to a significant reduction in cutting force and cutting power,which has a great potential for production and application.To find out the occurrence law of CSC has important theoretical and practical significance.For this reason,a method using modern optimization technology to establish the bifurcation set equation of CSC based on the butterfly catastrophe model in catastrophe theory and the experimental data of the critical condition of CSC is proposed.Firstly,the control space where the butterfly model's bifurcation set is located according to whether the theoretical control point passes through the bifurcation set surface along a specific control path and the feature of the mutation is divided,secondly,a set of simple linear mapping functions from 4 actual control parameters to 4 theoretical control parameters is established,Then,based on the experimental data and the established objective function,modern optimization methods are used to solve the mapping function coefficients to establish the bifurcation set equation of the CSC butterfly model.To obtain the experimental data,two rounds of 246 sets of experiment with different tool rake angles,tool nose angles and feed and continuous change of the depth of cut were completed.A total of 152 groups experimental data were obtained.By analyzing the measured dynamic cutting force signal,it is found that the sudden change of chip bifurcation will cause the main cutting force to be reduced by up to 23.0%.Applying the proposed method,the linear mapping function coefficients are solved,the corresponding bifurcation set equations of the chip bifurcation mutation butterfly model are established,using the obtained experimental data and modern optimization techniques.Using the established bifurcation set equation and the experimental observation results of the CSC,applying the relevant conclusions of the catastrophe theory,the internal mechanism of the mutation occurrence is analyzed,the law of the CSC is revealed,and a set of prediction values for the critical condition of CSC in given cutting conditions are obtained.The verification experiment found that there is a good agreement between the predicted value and the experimental observation value.This shows that the proposed method and the established bifurcation set equation are effective.The above research results provide a new way for the reasonable selection of cutting parameters to cause the chip bifurcation mutation in the cutting process,and then to solve the related process problems caused by the excessive cutting force during the cutting process,and to achieve energy saving and consumption reduction.