Milling stability analysis using the spectral method

作     者：DING Ye ZHU LiMin ZHANG XiaoJian DING Han 

作者机构：State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University Shanghai 200240 China State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan 430074 China 

出 版 物：《Science China(Technological Sciences)》 (中国科学（技术科学英文版）)

年 卷 期：2011年第54卷第12期

页      面：3130-3136页

核心收录：

学科分类：080503[工学-材料加工工程] 07[理学] 08[工学] 070104[理学-应用数学] 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] 0701[理学-数学] 080201[工学-机械制造及其自动化] 

基　　金：supported by the National Key Basic Research Program (Grant No. 2011CB706804) the Science & Technology Commission of Shanghai Municipality (Grant Nos. 09QH1401500 and 10JC1408000) 

主　　题：milling stability delayed differential equation integral equation spectral method Floquet theory 

摘      要：This paper focuses on the development of an efficient semi-analytical solution of chatter stability in milling based on the spectral method for integral equations. The time-periodic dynamics of the milling process taking the regenerative effect into account is formulated as a delayed differential equation with time-periodic coefficients, and then reformulated as a form of integral equation. On the basis of one tooth period being divided into a series of subintervals, the barycentric Lagrange interpolation polynomials are employed to approximate the state term and the delay term in the integral equation, respectively, while the Gaussian quadrature method is utilized to approximate the integral tenn. Thereafter, the Floquet transition matrix within the tooth period is constructed to predict the chatter stability according to Floquet theory. Experimental-validated one-degree-of-freedom and two-degree-of-freedom milling examples are used to verify the proposed algorithm, and compared with existing algorithms, it has the advantages of high rate of convergence and high computational efficiency.