## 1 Introduction
However, the effect of the interaction between cutting parameters has no definite tendency based on the machining conditions used in the tests. [PERSON] et al. [23] conducted an investigation on the interactive effects of cutting parameters and tool vibration on surface roughness. Their results indicated that feed rate was the dominant factor affecting surface roughness, and vibrations in the radial and main cutting force directions had a low effect on surface roughness. Further, to obtain a desirable surface finish, optimum cutting parameters with less machining vibration were obtained using a predictive regression model. [PERSON] et al. [24] and [PERSON] et al. [25] showed that the interaction of cutting speed and feed rate had a greater influence on surface roughness compared to other interactions. As mentioned previously, tool vibration and chatter affect the surface quality of the machined product and the machining performance directly. Therefore, monitoring and controlling machining vibration has been considered an effective approach to enhance the surface precision and dimension accuracy of a machined product [26; 27; 28]. [PERSON] et al. [2] employed mathematical models to predict the surface finish, tool vibration, and tool wear with different combinations of cutting parameters. With these models, the optimum feed rate, cutting depth, and cutting speed were obtained to reduce tool vibrations and enhance surface finish. [PERSON] and [PERSON] [20] proposed a multiobjective optimization algorithm to minimize vibration amplitude and surface roughness. The objective functions and the second-order response surface models for surface roughness and vibration amplitude were created by performing regression analysis on experimentally collected data. Surface roughness modeling has been comprehensively investigated using artificial neural network (ANN) analysis incorporated with optimization algorithms [11; 25; 27; 29; 30]. For example, [PERSON] et al. [11] employed artificial neural networks and multiple regression approaches to model the surface roughness of AISI 1040 steel in turning. Three training algorithms--back-propagation training, scaled conjugate gradient (SCG), and Levenberg-Marquardt (LM)--were used in ANN modeling; the SCG algorithm was proven to achieve the best prediction accuracy. [PERSON] et al. [29] proposed statistical regression and ANN models to predict the surface roughness on aluminum 6061 after end milling based on three cutting parameters (spindle speed, feed rate, and cutting depth) and machining vibration. The experimental results show that the ANN surface recognition model has a higher accuracy rate compared with the regression model. In addition, a two hidden-layer ANN model shows a slightly higher accuracy (99.27%) than that of the one hidden-layer model (95.87%); however, it has low efficiency in the training model. A similar study was reported by [PERSON] [31], who developed a feedforward neural network integrated with a genetic algorithm to optimize machining conditions for obtaining the best surface finish of a plastic injection mold. The model was finally validated with prediction errors of 5.34% in comparison with the measurement of the machined surface roughness. [PERSON] et al. [32] explored the influence of the cutting parameters and interactions between them on surface roughness; further, they established a surface roughness model based on ANN analysis, in which the SCG training algorithm with nine neurons demonstrates the best fitness and prediction accuracy in ANN modeling. [PERSON] et al. [33] presented an ANN model to predict surface roughness in end milling. In ANN modeling, the number of layers and neurons in the hidden layers are factors that determine the prediction accuracy. Based on the prediction model, the best combination of cutting conditions for achieving the best surface roughness value can be obtained at a high speed with a low feed rate and radial rake angle.