This paper estimates cutting safety by using basin stability and introduces state-dependent intermittent controls to improve it. Due to inherent nonlinearity and non-smoothness in tool–workpiece interactive forces, metal cutting processes often exhibit subcritical instability when they lose linear stability, inducing coexistence of large-amplitude vibration, also called regenerative chatter, with stable stationary cutting. This phenomenon makes a considerable part of linearly stable region unsafe, where pure parameter selection is insufficient to maintain the cutting stability. To use the unsafe zones for higher material removal rate without incurring chatter, the possibility of chatter occurrence should be estimated as an index of cutting safety. This is achieved by basin stability estimation with delayed initial cutting states approximated by Fourier series and the coefficients generated based on Monte Carlo principle. It is found that the cutting safety in the “boundary layer” adjacent to linear stability boundaries is very severe, and a larger waviness height in workpiece surface can make the situation even severer. To improve the safety by decreasing the possibility of chatter occurrence, state-dependent intermittent control with various perturbation strategies, i.e. linear and nonlinear velocity feedbacks and spindle speed variation, is proposed. With respect to the increase in control threshold or perturbation strength, the chatter orbits are gradually destroyed so that the majority of the UZs becomes globally stabilized.
Yan, Y., Xu, J., & Wiercigroch, M. (2019). Estimation and improvement of cutting safety. Nonlinear Dynamics, 98(4), 2975–2988. https://doi.org/10.1007/s11071-019-04980-0