Robust active control of milling chatter under actuator constraints: A spindle speed mapped framework with experimental validation

Milling productivity is still heavily constrained by the onset of chatter. While active control can enlarge chatter free operating windows, practical deployment is limited by actuator force saturation, which degrades performance and may destabilise the controller. This study proposes and validates a saturation aware, spindle speed mapped optimisation of direct velocity feedback (DVF) control that explicitly constrains actuator demand at each spindle speed. A self-adaptive differential evolution algorithm selects the DVF gain per spindle speed by targeting higher stability boundary without actuator saturation and rejecting candidates that exceed available maximum actuation force, thereby aligning controller tuning with realistic hardware limits. The approach is evaluated on a flexible workpiece driven by a proof mass actuator during machining of Al-7075-T6 with a 16 mm diameter, 4 flutes, 45°helical tool at half immersion and 0.05 mm/tooth feed. Stability lobe diagram predictions and cutting tests span between 500 and 3000 rpm, with the resulting controller gains map applied across the range. Results show that saturation aware, spindle speed specific tuning increases the stable axial depth of cut by up to 13 times. Compared with a conventional single gain strategy optimised over a spindle speed range but limited by the most demanding conditions, the proposed method achieves significantly larger productivity improvements. By coupling actuator saturation awareness with spindle speed resolved DVF optimisation, this work provides a practical and generalisable framework for robust active damping of milling chatter on flexible systems, enabling aggressive yet safe expansion of chatter free cutting conditions with experimentally verified benefits.