Multiple-delay modulation for suppressing micro-milling chatter

Existing chatter suppression methods using piezoelectric actuators face significant limitations in micro-milling, as they often require either complex multi-actuator setups, additional sensors for tool condition monitoring, or alterations to the spindle itself. To address these limitations, this study introduces an active chatter suppression method using a single piezoelectric actuator, which simplifies integration and enhances compatibility with space-constrained micro-milling conditions. By generating controlled feed-direction displacements that match the feed per tooth, the actuator disrupts the single-delay structure of micro-milling, introducing multiple time delays to expand the stable cutting zone. A critical challenge lies in the fact that the coupling between the rotating cutter and the workpiece, vibrating under actuator excitation, leads to uncertain initial contact positions and variable delay interactions. To ensure controllable suppression under these conditions, a sinusoidal modulation trajectory has been specifically designed. By precisely controlling the duration ratio and amplitudes of the positive/negative half-waves in each modulation cycle, the system ensures robust multiple-delay modulation, independent of the initial contact state. This ensures stable synchronization between the vibration trajectory of the workpiece and cutter tooth engagements. An open-loop system is proposed to achieve the preset workpiece vibration trajectory. The micro-milling dynamics is thereby formulated as a modulated multiple-delay chatter problem, with its stability subsequently analyzed through stability lobe diagrams (SLDs). To enhance computational efficiency, an optimization algorithm integrating a Bayesian approach with directional-factor pruning is presented for solving the SLDs. Several micro-milling tests demonstrate the effectiveness of the method.