Vibration-assisted stabilization of turning processes with state-dependent delay

We develop vibration-assisted stabilization strategies of turning processes using feed rate and spindle controls, where the feed rate is proportional to the delayed bending position of the cutting tool in the feed direction and the spindle speed is either a constant or proportional to the delayed bending position orthogonal to the feed direction. We show that turning processes which contain intrinsic state-dependent delays can be stabilized by the proposed stabilization strategies and develop analytical descriptions of the stability regions in the parameter space for the system with different stabilization strategies. In contrast to the smoothness of the stability lobes for the vibration-assisted stabilization strategy with constant spindle speed, the stability lobes for the system with the spindle speed proportional to the delayed bending position can be non-smooth at finitely many points, for which we provide algorithms for determining their locations. Numerical simulations of the stability regions are also given to illustrate the general results.