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