This study supports the research in the field of laser cutting of steel sheets HARDOX400 (H400), a less well-known and analysed material. An H400 sheet with a thickness of 10 mm was used; a cutting plan was prepared according to Taguchi's method; the input parameters (laser power, assistant gas pressure and cutting speed) were varied according to a specific rule, producing nine pieces. The initial factorial experiment was replicated four times under the same conditions as the initial one. The values for the cutting width between the piece and the plate, the hardness, and the roughness of the 45 resulting pieces were measured. The results were interpreted for each measured parameter, and by using design of experiments (DOE) from the Statistics 7.0 software, we obtained the description of roughness (R a ) in terms of power and speed using Response Surface Method (RSM) for prediction and correlation formula.
Highlights• Indication of the mathematical expression of the roughness R a from algebraic and differential points of view. • Description of the cutting parameters of the CO 2 laser installation for cutting a Hardox400 plate according to a cutting plan, consisting of 45 pieces. • The use of the response surface and the three dimensional (3D) graph to determine the roughness R a depending on the input parameters, laser power, and cutting speed. • Establishing the formula for correlating the roughness R a according to the laser power and the cutting speed within the linear and quadric model, respectively the statistical calculation within the linear and quadratic interaction.