Time-varying chatter evaluation and proactive control in arc-end gear form grinding

Titanium alloy and nickel-based superalloy arc-end gears are critical connecting components in aero-engine rotor systems. Their load-bearing capacity and operational reliability depend strongly on tooth profile accuracy and surface integrity achieved in form grinding. However, the difficult-to-machine nature of these materials accelerates wheel wear and thermal accumulation, leading to non-stationary excitations that can induce time-varying regenerative chatter. A closed-loop stability-management framework is proposed that integrates online sensing, Thermo-Force-Wear (TFW) rolling model updating, probabilistic stability prediction, and adaptive parameter adjustment. A Three-Degree-of-Freedom (3-DOF) time-varying regenerative dynamic model is established, and Operational Modal Analysis/Stochastic Subspace Identification (OMA/SSI) is used to track working-condition modal parameters online. On this basis, modal frequency, damping ratio, and vibration response are incorporated as dynamic-side inputs for rolling Frequency Response Function (FRF) reconstruction and stability-boundary updating. A probabilistic time-varying Stability Lobe Diagram (SLD) and a composite Stability Index (SI) are then constructed for graded decision-making and parameter adjustment. Grinding experiments on TC11 and FGH95 specimens show that, compared with a static SLD, the proposed TFW-coupled probabilistic stability-evaluation method improves stability-state classification accuracy from 68.7% to 88.0%. Closed-loop trials reduce the dominant-band vibration amplitude by 82%–89% while maintaining tooth-flank roughness within the target range, demonstrating the effectiveness and engineering applicability of the proposed stability-management strategy.