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

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