Modeling and experimental validation of dynamic defocusing effects in femtosecond laser ablation of complex gear surfaces

Femtosecond (fs) laser ablation has emerged as a disruptive technology for the ultra-precision finishing of aerospace face gears. However, its application to complex 3D curved topologies is fundamentally bottlenecked by spatially varying nonlinear laser-material interactions. In this study, we propose a comprehensive 3D nonlinear mathematical model for the fs laser ablation of 18Cr2Ni4WA alloy steel to reveal the mechanism of spatial light field distortion. By discretizing the involute face gear topology, the model explicitly couples the localized incidence angle with dynamic defocusing, elliptical beam stretching, and incidence-dependent Fresnel reflection. Theoretical analyses demonstrate that geometrical variations severely distort the energy-coupling efficiency, with the dynamic defocusing distance being directly proportional to the tangent of the incidence angle (tanθ), drastically attenuating the absorbed volumetric energy density in highly inclined regions. Comparison with CNC gear-center measurements yielded descriptive model-measurement differences with a whole-grid MAE of 0.131μm, an RMSE of 0.137μm, and a maximum absolute difference of 0.255μm (6.53% relative difference). These differences were below the expanded measurement uncertainty and therefore are not interpreted as metrological proof of submicrometer resolution. The spatial error pattern is consistent with, but does not directly prove, enhanced plasma-plume shielding within geometrically confined concave valleys. This study provides a model-based foundation for adaptive multi-axis parameter compensation in advanced aerospace manufacturing.