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.

The paper presents the result of the experimental research regarding the influence of the parameters of the laser cutting regime of the HARDOX 400 steel on the roughness of the processed surface. The study was carried on by means of experimental research, based on a plan developed according to the Taguchi method, a fractionated factorial one, applied for three input parameters: assistant gas pressure, laser power, and cutting speed, each having three levels. The statistical processing of the experimental data was performed by ANOM (analysis of means) and S/N indexes (signal to noise), according to Taguchi Method approach, validated by ANOVA (analysis of variation). Particularly, the paper analyses the combined influence of laser power and the pressure of the assistant gas on the roughness. The main conclusion is that among the two parameters, the most significant influence is that of the pressure of assistant gas.