Safety estimation for a new model of regenerative and frictional cutting dynamics

Abstract In our previous study on regenerative and frictional cutting dynamics, a new model considering both time-delayed effect Stribeck as sources of instability has been proposed [7], which improved the prediction linear stability in zone low velocity. Based model, this investigation explores complex nonlinear dynamics. More specifically, criticality Hopf bifurcation boundaries is studied by perturbation analysis showing co-existence stationary chatter linearly stable region, i.e., unsafe zones (UZs). Then analytical estimation compared with numerical simulation revealing possibility underestimation due to large-amplitude entering expands UZs. Beside local analysis, global diagrams are constructed simulation, yielding various responses including multiple stability, loss tool-workpiece contact stick-slip vibration. Finally, safety UZs based basin estimation, where initial conditions approximated Fourier series occurrence estimated via Monte Carlo simulation. It found that from statistical point view, hardly influences