A mathematical model for ultrafast laser processing of the slight curvature surface

The precise control of the amount of material removal in the ultrafast laser ablation process is hindered by a number of factors, rendering it unable to meet the demand for accurate processing of complex surfaces. It is essential to employ an effective simulation method to predict the outcomes of ablation processing, thereby facilitating subsequent optimisation of parameters and precision process research. In this paper, a pulse-by-pulse mathematical model is presented for simulating the ultrafast laser ablation process for general materials. The mathematical model of the focused Gaussian beam considers the influences of key parameters, including the propagation direction of the beam, the position of the focal point, and the laser fluence, among others. The evolution process of etching materials was analysed, and the material ablation rate under different beam states was calculated. The actual processing was then simulated pulse by pulse using the grid division method. The model is straightforward and accessible, with parameters determined through a limited number of calibration experiments. The simulation accuracy for points, lines, and planes is approximately 0.9, with a mean simulation time of 1.3 s for a single pulse. The ablation model is well-suited for simulating complex curved surfaces, offering a valuable tool for precise ultra-fast laser machining.