Summary
High-efficiency and high-accuracy manufacturing relies on theoretical foundation of cutting vibration and its control, which plays a key role in intelligent manufacturing. Based on a new model considering both of regenerative and frictional cutting forces, we improved the prediction accuracy of cutting instability. Moreover, nonlinearity and non-smoothness in regenerative cutting incurs subcritical Hopf bifurcation to introduce large-amplitude chatter into linearly stable region, yielding cutting multi-stability called unsafe cutting (UC) in unsafe zones (UZs). Due to the time delay induced by regenerative effect in chip formation, the cutting multi-stability cannot be analyzed by conventional basin of attraction since delayed terms involve infinite-many dimension. To address this issue, infinite-many dimensional time-delayed states are approximated by a Fourier series aligned on a straight line, and the coefficients of the basis functions and the cutting process are used to construct the statistical basin of attraction. Inside the statistical basin of attraction, there exists a safe basin with no chatter. This findings are instrumental in designing a new state-dependent intermittent control to guide the cutting dynamics towards the safe basins. It is also seen that the state-dependent intermittent control is efficient in improving the cutting safety and shrinking the unsafe zones, even when the targeted basin for the control is larger than the real safe basin.
