Surface roughness modeling using response surface methodology and a variant of multiquadric radial basis function

There are several methods for modeling surface roughness in computerized numerical control (CNC) milling process. This work proposes for the first time the use of response surface methodology (RSM) and a variant of the multiquadric radial basis function (MRBF) for the modeling of surface roughness ( R a ) of graphite generated by means of the CNC milling process. In this variant, a norm with coefficients (weights) denoting the weighting of the effects of machining parameters is used. The machining parameters that have been most reported in literature were considered, which are cutting speed ( S ), feed rate ( F ), and cutting depth ( D ). Three mathematical models were developed to adjust the values of surface roughness: one model was obtained using RSM and two others were generated with the variant of MRBF. Values were assigned to effects of the weighted norm reducing it to the Euclidean norm, named Euclidean norm model (ENM). For the weighted norm model (WNM), values of effects of the machining parameters calculated by means of a factorial design were considered. Finally, in each model, the mean absolute percentage error (MAPE) was calculated: the lowest value and highest value of MAPE were obtained with response surface methodology model (RSMM) and ENM, respectively. However, lowest surface roughness was estimated and generated experimentally in graphite specimens with the machining parameter values obtained by means of WNM.