Dynamic Limits of Spur Gear Tip Relief Under Center-Distance Variation: Coexisting Impacts and Dynamical Integrity

Quasi-static tip relief design alone cannot determine the range of relief amounts that satisfies dynamic contact requirements and ensures recovery from finite perturbations. This study determines this range and its controlling mechanisms for spur gears assembled at different center distances. A single-degree-of-freedom model uses a pairwise piecewise-linear mesh force table accounting for extended tooth contact and gear-body coupling. Periodic-solution continuation, boundary tracking and a local integrity measure assess persistent contact, premature mesh-in and recovery. Premature mesh-in near primary or superharmonic resonance sets a dynamic lower bound that differs from the quasi-static limit. In the baseline case, an impacting isola erodes the basin of attraction of the normal periodic solution while it remains stable and in persistent contact. Recovery therefore fails before contact loss, setting the upper bound. For the speed range considered and a dimensionless perturbation radius of 0.10, the admissible range is 7.7–15.7 µm. Increasing the center distance changes the mechanisms and speeds controlling the bounds and narrows the range until it vanishes at a center-distance increase of about 1.56 mm.