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Mathematical Problems in Engineering
Volume 2016, Article ID 4368680, 16 pages
Research Article

Nonlinear Modeling and Dynamic Simulation Using Bifurcation and Stability Analyses of Regenerative Chatter of Ball-End Milling Process

School of Mechanical Engineering, College of Engineering, Chung-Ang University, 84 HeukSeok-Ro, DongJak-Gu, Seoul 156-756, Republic of Korea

Received 10 November 2015; Revised 15 January 2016; Accepted 18 January 2016

Academic Editor: Gen Qi Xu

Copyright © 2016 Jeehyun Jung 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.


A dynamic model for a ball-end milling process that includes the consideration of cutting force nonlinearities and regenerative chatter effects is presented. The nonlinear cutting force is approximated using a Fourier series and then expanded into a Taylor series up to the third order. A series of nonlinear analyses was performed to investigate the nonlinear dynamic behavior of a ball-end milling system, and the differences between the nonlinear analysis approach and its linear counterpart were examined. A bifurcation analysis of points near the critical equilibrium points was performed using the method of multiple scales (MMS) and the method of harmonic balance (MHB) to analyse the local chatter behaviors of the system. The bifurcation analysis was conducted at two subcritical Hopf bifurcation points. It was also found that a ball-end milling system with nonlinear cutting forces near its critical equilibrium points is conditionally stable. The analysis and simulation results were compared with experimental data reported in the literature, and the physical significance of the results is discussed.