Analysis of the influence of defocused laser beam on uneven material surface processing based on mathematical model and simulation approach

Laser-processing technology has advanced precision surface material processing, but challenges remain in maintaining the laser beam waist position on uneven surfaces. Surface irregularities cause defocus and non-perpendicular alignment leading to distortions in beam spot size and shape, which reduce processing quality. This study develops a mathematical model and simulation framework to analyze beam waist positioning errors during surface processing. Using MATLAB Partial Differential Equation (PDE) and finite element method, the simulation evaluates how variables like laser incidence angle and focal distance affect beam spot characteristics. Results reveal that defocus and misalignment enlarge and distort the laser beam spot, with higher incidence angles causing elliptical deformation. The simulation is critical in advancing the understanding of laser-material interactions under suboptimal conditions such as defocus and misalignment. It provides critical insights into the geometrical of laser beam, enabling the development of precise error detection methods for beam spot irregularities. Furthermore, these findings lay the groundwork for designing adaptive mechanisms that enhance the precision and reliability of laser-based surface material processing, addressing challenges posed by uneven workpiece surfaces. This approach aims to optimize laser processing quality and expand its applicability in high-precision manufacturing.