<p>The qualification of turning processes is established using quality and productivity indicators. Traditional qualification approaches focus mainly on process factors, especially in the case of orthogonal machining. This study aims to model through experiments the correlations between the Tool-Material-Process (TPM) to optimize the finishing machining of conical surfaces in CNC turning of Toolox 44 steel. Thus, the Taguchi experimental design methodology (L36), combined with stepwise ANOVA regression, is adopted to model surface roughness.The machining parameters considered are related to the workpiece (taper angle), the cutting tool (inclination angle and tool nose radius) and the cutting regime (cutting speed, feed rate, depth of cut). The results indicated that surface roughness (Ra) is strongly influenced by the feed rate (<i>f</i>), the tool nose radius (<i>r</i>), and, additionally, the workpiece taper angle (<i>θ</i>). Thus, the aim is to extract the optimal conditions to improve the finished surface quality and process productivity. The desirability function (DF) was used to minimize both arithmetic mean roughness (Ra) and cutting time (Tc). Indeed, two different machining conditions can give the same order of magnitude of arithmetic roughness, so that machining time must be involved as an additional criterion for process selection and parameterization. Optimization results for a targeted desirability function per unit revealed regression/experiment model errors of no more than 11.73% for (Ra). The optimal parameters for minimizing (Ra) and (Tc) were as follows: (<i>θ</i> = 0°, Vc = 160 m/min, <i>f</i> = 0.16 mm/rev, and <i>r</i> = 0.957 mm). This study proved that the results of the work on orthogonal turning should be considered with prudence in the case of real industrial processes, especially for finite conical surfaces such as that of industrial molds.</p>