Surface roughness modeling using response surface methodology and a variant of multiquadric radial basis function
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ORIGINAL ARTICLE
Surface roughness modeling using response surface methodology and a variant of multiquadric radial basis function 1 1 · Cuauhtemoc-H ´ ´ ´ ´ ´ ˜ ´ 2· Orqu´ıdea Sanchez-L opez · Ignacio Hernandez-Castillo ector Castaneda-Rold an 3 2 ´ Agustin Santiago-Alvarado · Angel-Sinue Cruz-Felix
Received: 27 June 2020 / Accepted: 1 September 2020 / Published online: 21 September 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract 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 (Ra) 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. Keywords Surface roughness modeling · Weighted norm · Multiquadric radial basis function · Response surface methodology · CNC milling
1 Introduction Currently, there are various manufacturing processes for material removal, which have been classified as conventional such as milling, drilling, or turning, and nontraditional such as electrical discharge machining (EDM), water jet, plasma, or electrochemical [1]. The surface of a part generated by means of these processes has properties and a behavior different from the rest of its geometry. It has Orqu´ıdea S´anchez-L´opez
[email protected] 1
Instituto de Ingenier´ıa Industrial y Automotriz, Universidad Tecnol´ogica de la Mixteca, Huajuapan de Le´on, Oaxaca, M´exico
2
Instituto de F´ısica y Matem´aticas, Universidad Tecnol´ogica de la Mixteca, Huajuapan de Le´on, Oaxaca, M´exico
3
Divisi´on de Estudios de Posgrado, Universidad Tecnol´ogica de la Mixteca, Huajuapan de Le´on, Oaxaca, M´exico
a certain finish that is known as surface roughness, which is an important quality characteristic, since it influences both the performance of the manufactured parts and the production costs [2].
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