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

In our previous study on regenerative and frictional cutting dynamics, a new model considering both time-delayed regenerative effect and Stribeck effect as sources of cutting instability has been proposed [7], which has improved the prediction of linear stability in the zone of low cutting velocity. Based on the new model, this investigation explores complex nonlinear cutting dynamics. More specifically, the criticality of Hopf bifurcation on the cutting stability boundaries is studied by perturbation analysis showing the co-existence of cutting stationary and chatter in the linearly stable region, i.e., the unsafe zones (UZs). Then this analytical estimation is compared with numerical simulation revealing a possibility of underestimation due to the large-amplitude frictional chatter entering the stable region, which expands the UZs. Beside this local perturbation analysis, global bifurcation diagrams are constructed by numerical simulation, yielding various complex responses 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 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.