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Response Sensitivity Analysis of the Dynamic Milling Process Based on the Numerical Integration Method

Response Sensitivity Analysis of the Dynamic Milling Process Based on the Numerical Integration 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:《Chinese Journal of Mechanical Engineering》 (中国机械工程学报(英文版))

年 卷 期:2012年第25卷第5期

页      面:940-946页

核心收录:

学科分类:07[理学] 08[工学] 070102[理学-计算数学] 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 National Key Basic Research Program (973 Program, Grant No. 2011CB706804) National Natural Science Foundation of China (Grant No. 50805093) Science & Technology Commission of Shanghai Municipality, China (Grant No. 09QH1401500) 

主  题:milling stability sensitivity of the stability boundary numerical integration method 

摘      要:As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.

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