Nonsmooth Gear-Contact Vibration Suppression Under Variable-Speed Operation Using Phase-Consistent Modelling and Bounded Line-of-Action Force Learning

Nonsmooth gear-contact vibration under variable-speed operation is strongly affected by mesh-phase evolution, backlash-induced contact switching, and unilateral tooth contact. This study investigates local line-of-action vibration suppression in a single-stage spur-gear pair performing a repetitive acceleration–braking–cruising task. The modelling contribution is a control-oriented hybrid-coordinate formulation that separates the prescribed mean-speed motion from local dynamic transmission error (DTE), reconstructs the time-varying mesh stiffness (TVMS) phase from the mean angle and local relative displacement, and retains a distinct mean-coordinate phase for transmission error (TE). The learning contribution is a bounded line-of-action force strategy that combines finite-time application, low-pass filtering, plateau DC removal, amplitude and rate constraints, and trial-level contact-response acceptance and rollback. Thus, an input-feasible candidate can still be rejected when its executed contact response violates the prescribed limits. Under the nominal same-initial-condition baseline, the trade-off iteration reduces DTE and mesh-force AC RMS by 11.52% and 24.85%, respectively. Contact loss decreases from 3.35% to 0.55%, and re-engagements decrease from 29 to 5. In 100 paired perturbation samples, 94 cases improve both RMS measures. The results support the proposed framework within the tested numerical task and perturbation range.