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

Figure 8

Phase-plane representations of an unstable limit cycle solution: the solid line represents the time histories obtained using the direct integrations (with varying time step), and the dashed line represents the hypothetical periodic time histories obtained using the MHB estimated at the unstable limit cycle point. The arrow shows a brief behavioural time trace of the unstable limit cycle solution.