Theoretical Framework for Target-Oriented Parameter Selection in Laser Cutting

Surface roughness is a critical quality attribute in laser cutting, directly influencing edge integrity, dimensional accuracy, and post-processing requirements. While most studies address surface roughness through forward modeling and optimization, practical manufacturing tasks often require solving inverse parameter selection problems, where process parameters must be chosen to satisfy prescribed surface quality requirements. In this study, surface roughness control in laser cutting is formulated within an inverse target-tracking framework based on response surface methodology (RSM). A quadratic response surface model is established using a Box–Behnken experimental design, with cutting speed, laser power, and assist-gas pressure as input factors. The fitted response surface provides an explicit forward mapping within a bounded operating window and serves as a local surrogate for methodological demonstration of target-oriented parameter estimation. Based on this surrogate model, a model-predicted feasible roughness range within the investigated design space is identified as Ra = 1.952–4.212 μm. For prescribed roughness targets within this interval, an inverse least-squares target-tracking formulation is employed to compute model-based parameter estimates. The inverse results are presented as continuous set-point maps and tabulated operating conditions, accompanied by a target-versus-predicted consistency check performed at the model level. Owing to the statistically significant lack-of-fit of the forward response surface, the inverse results presented in this study should be interpreted as theoretical, model-based estimates intended to illustrate the proposed framework rather than as experimentally validated process set-points. The proposed approach highlights both the potential and the limitations of inverse target-tracking strategies based on response surface models and underscores the need for statistically adequate models and independent experimental validation for industrial application.