Regularization of mathematical model for chip flow angle catastrophe

作     者：Shao-Nan Zhang Dong-Dong Cheng Liang-Shan Xiong Shao-Nan Zhang;Dong-Dong Cheng;Liang-Shan Xiong

作者机构：School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhan 430074People’s Republic of China 

出 版 物：《Advances in Manufacturing》 (先进制造进展（英文版）)

年 卷 期：2021年第9卷第4期

页      面：568-579页

核心收录：

学科分类：080503[工学-材料加工工程] 0817[工学-化学工程与技术] 08[工学] 0807[工学-动力工程及工程热物理] 0805[工学-材料科学与工程（可授工学、理学学位）] 0802[工学-机械工程] 0811[工学-控制科学与工程] 0801[工学-力学（可授工学、理学学位）] 080201[工学-机械制造及其自动化] 

基　　金：the National Natural Science Foundation of China(Grant No.51675203) 

主　　题：Chip flow angle(CFA)catastrophe Mathematical model Regularization Potential function Catastrophe theory Cusp catastrophe model 

摘      要：The chip flow angle(CFA)catastrophe in double-edged cutting results in a significant reduction in the cutting force,which can benefit the ***,established potential functions(i.e.,cutting power calculation functions)of mathematical models for the CFA catastrophe are presented in the form of transcendental functions with two control parameters and one state parameter,which are extremely complex.A method is proposed herein to realize the regularization of the potential functions and establish mathematical models in a standard form and with complete content for the CFA *** this method,the potential function of the CFA catastrophe is expanded into a k-order Taylor polynomial at each midpoint of N end-to-end equally partitioned intervals of the state parameter using the Taylor function provided in *** potential function after piecewise Taylor expansion is transformed into the same form as the potential function of the standard cusp catastrophe model by truncating the first five terms of the Taylor polynomial and eliminating the third-order term of the state parameter with elementary ***,the regularization of potential function is ***,the regularization of equilibrium surface and bifurcation set can be realized based on the conclusions of the catastrophe *** errors of the potential function,equilibrium surface,and bifurcation set are defined to evaluate the effectiveness of this regularization *** problem of calculating regularization errors is regarded as an optimization ***‘‘simulannealbnd’’function provided in MATLAB is used to solve the *** the proposed method,the regularization of a mathematical model for the CFA catastrophe established by the predecessor is completed;a mathematical model(i.e.,standard cusp catastrophe model)in a standard form and with complete content for the CFA catastrophe is established;and the corresponding regularization errors