Robust stability and surface error assessment in interrupted turning under spindle speed variation

Abstract Predicting stability in turning becomes especially difficult when the process combines interrupted cutting with spindle-speed variation (SSV). The resulting time-dependent delays and discontinuous dynamics call for advanced numerical tools beyond conventional chatter analysis. This paper develops a numerical framework for analysing interrupted turning with SSV using a matrix-free Floquet approach for stability and an affine mapping for periodic solution evaluation. These tools provide the basis for quantifying vibration amplitudes and linking them to surface waviness. The study reveals that process stability is extremely sensitive to the phase shift between the SSV modulation and the workpiece geometry. Even small variations of this uncontrolled phase can shift the process from stable to unstable behaviour, highlighting the necessity of robust stability evaluation. To address this, an efficient robustness framework is introduced based on the Multi-Dimensional Bisection Method (MDBM), enabling accurate and computationally feasible mapping of stability boundaries with respect to phase uncertainty. The proposed approach offers a practical route for selecting chatter-free and robust cutting conditions in advanced turning.