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Mathematical Problems in Engineering
Volume 2017, Article ID 7898369, 15 pages
Research Article

Milling Stability Prediction with Multiple Delays via the Extended Adams-Moulton-Based Method

State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Correspondence should be addressed to Jianfeng Tao; nc.ude.utjs@oatfj

Received 16 February 2017; Revised 27 March 2017; Accepted 29 March 2017; Published 7 May 2017

Academic Editor: Oleg V. Gendelman

Copyright © 2017 Jianfeng Tao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The occurrence of machining chatter may undermine the workpiece surface quality, accelerate the tool wear, and even result in serious damage to the machine tools. Consequently, it is of great importance to predict and eliminate the presence of such unstable and detrimental vibration. In this paper, we present an extended Adams-Moulton-based method for the stability prediction of milling processes with multiple delays. Taking the nonuniform pitch cutters or the tool runout into account, the regenerative chatter for milling operations can be formulated as delay differential equations with multiple delays. The dynamics model for milling regenerative chatter is rewritten in the state-space form. Dividing the spindle rotation period equally into small time intervals, the delay terms are approximated by Lagrange interpolation polynomials, and the Adams-Moulton method is adopted to construct the Floquet transition matrix. On this basis, the milling stability can be derived from the spectral radius of the transition matrix based on Floquet theory. The calculation efficiency and accuracy of the proposed algorithm are verified through making comparisons with the semidiscretization method (SDM) and the enhanced multistage homotopy perturbation method (EMHPM). The results show that the proposed method has both high computational efficiency and accuracy.