<p>Ultrafast femtosecond lasers, with their unique “cold ablation” characteristics, exhibit broad application prospects in the machining of complex hard surfaces of high-end aerospace equipment (e.g., face gears). However, existing femtosecond ablation prediction models are mostly based on the assumption of normal plane irradiation, severely ignoring the drastic variations in the dynamic angle of incidence (<InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\theta\)</EquationSource></InlineEquation>) caused by complex three-dimensional geometric topologies. Addressing this theoretical gap, this paper innovatively proposes a 3D nonlinear ablation prediction model coupling the dynamic evolution of local incident angles and the multi-pulse incubation effect. First, the spatial incident angles at the micro-nodes of the face gear tooth surface are extracted via a discrete meshing method. Subsequently, by integrating the dynamic polarization reflectivity of the 18Cr2Ni4WA alloy with the spatial projection distortion of the Gaussian beam, closed-form analytical solutions for the elliptical spot area, the effective material removal area, and the central pit depth—incorporating the effective penetration depth—are derived. Simultaneous five-axis laser machining experiments and computer vision-based morphological feature extraction (eccentricity quantification) confirm that: within the range of small to medium incident angles (<InlineEquation ID="IEq2"><EquationSource Format="TEX">\(\theta < 60^\circ\)</EquationSource></InlineEquation>), the experimentally measured morphological evolution is highly consistent with the theoretical model (<InlineEquation ID="IEq3"><EquationSource Format="TEX">\(R^2 > 0.93\)</EquationSource></InlineEquation>). However, approaching the extreme large angle (<InlineEquation ID="IEq4"><EquationSource Format="TEX">\(\theta \ge 73^\circ\)</EquationSource></InlineEquation>), the ablation spot severely degrades into an asymmetrical “spindle” shape, and the machining depth experiences an anomalous nonlinear plunge. Combined with ultrafast dynamic analysis, it is revealed that this extreme morphological distortion is primarily attributed to the asymmetrical plasma inverse Bremsstrahlung shielding induced by the large angle, as well as the hindered recast layer expulsion dynamics under high-frequency thermal accumulation. This study profoundly reveals the microscopic evolution laws of laser-material spatiotemporal coupling on complex continuous surfaces, providing a solid theoretical foundation for adaptive trajectory and energy compensation strategies in future multi-axis femtosecond laser precision modifications.</p>

Coupling mechanism of dynamic incidence angle and multipulse accumulation in femtosecond laser ablation of complex spatial surfaces

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2026年5月19日

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Rong Wang,
Yang Hu,
Xingzu Ming,
Qiqing Yue,
Wan Li

摘要

Ultrafast femtosecond lasers, with their unique “cold ablation” characteristics, exhibit broad application prospects in the machining of complex hard surfaces of high-end aerospace equipment (e.g., face gears). However, existing femtosecond ablation prediction models are mostly based on the assumption of normal plane irradiation, severely ignoring the drastic variations in the dynamic angle of incidence (\(\theta\)) caused by complex three-dimensional geometric topologies. Addressing this theoretical gap, this paper innovatively proposes a 3D nonlinear ablation prediction model coupling the dynamic evolution of local incident angles and the multi-pulse incubation effect. First, the spatial incident angles at the micro-nodes of the face gear tooth surface are extracted via a discrete meshing method. Subsequently, by integrating the dynamic polarization reflectivity of the 18Cr2Ni4WA alloy with the spatial projection distortion of the Gaussian beam, closed-form analytical solutions for the elliptical spot area, the effective material removal area, and the central pit depth—incorporating the effective penetration depth—are derived. Simultaneous five-axis laser machining experiments and computer vision-based morphological feature extraction (eccentricity quantification) confirm that: within the range of small to medium incident angles (\(\theta < 60^\circ\)), the experimentally measured morphological evolution is highly consistent with the theoretical model (\(R^2 > 0.93\)). However, approaching the extreme large angle (\(\theta \ge 73^\circ\)), the ablation spot severely degrades into an asymmetrical “spindle” shape, and the machining depth experiences an anomalous nonlinear plunge. Combined with ultrafast dynamic analysis, it is revealed that this extreme morphological distortion is primarily attributed to the asymmetrical plasma inverse Bremsstrahlung shielding induced by the large angle, as well as the hindered recast layer expulsion dynamics under high-frequency thermal accumulation. This study profoundly reveals the microscopic evolution laws of laser-material spatiotemporal coupling on complex continuous surfaces, providing a solid theoretical foundation for adaptive trajectory and energy compensation strategies in future multi-axis femtosecond laser precision modifications.