## 1 Introduction  
High-speed, high-precision machining with a high material removal rate has been an important goal in the manufacturing industry because of the high-efficiency and high-quality requirements. Further, machined parts with a high surface finish are in high demand under considerations of assemblage precision, fatigue strength, and tribological properties of the mechanical product. To achieve high productivity and high precision, machining is implemented with a higher level of cutting parameters. However, surface quality and dimensional accuracy are affected by several factors such as machiningconditions, tool geometry and vibrations, cutting parameters, and machining dynamics [1]. In particular, surface finish deteriorates because of the machining vibration caused by inappropriate machining conditions and process parameters [2; 3; 4; 5; 6; 7]. [PERSON] et al. [2] suggested that cutting speed is a major factor affecting tool vibration, which thereby affects surface finish. [PERSON] et al. [3] showed the effect of chatter amplitude on surface roughness under various cutting conditions with different tool holders via machining experiments. [PERSON] et al. [5] demonstrated that the surface topography of the machined part is influenced by cutting tool vibrations. Further, [PERSON] et al. [6] demonstrated that workpiece topography is affected by the vibration caused by a poor runout of the cutter. They found that an increased cutting force with an increasing cutting depth and feed rate leads to higher vibration, and it accordingly increases surface roughness. [PERSON] [7] reported that surface roughness was affected by the vibration amplitude of the machine tool and the axial cutting depth. The vibration levels are closely related to the cutting parameters and they increase with an increase in the cutting speed and feed rate [8; 9; 10]. To ensure machining performance with better surface quality, the selection of optimum process parameters is crucial in metal machining. To achieve this goal, a majority of studies has employed experimental and modeling approaches to determine strategies to obtain the best final surface quality and dimensional accuracy [11; 12; 13; 14; 15]. The effect of cutting parameters on surface roughness can be effectively examined via the statistical data analysis of data collected from machining experiments under specifically designed process parameters. Subsequently, the optimization of the machining process with a better surface quality and less vibration can be obtained based on prediction models established by various approaches such as analytical modeling, statistical regression based on response surface methodology, and artificial intelligence-based models [16]. Response surface methodology is a statistical technique used to establish relationships between continuous dependent variables with independent variables in terms of mathematical models using multiple regression analysis. Prediction models derived from experimental data can help clarify the influences and contributions of cutting parameters on surface roughness or tool vibration; these models can further be applied to optimize cutting parameters [2; 4; 17; 18; 19; 20; 21]. [PERSON] et al. [17] identified that all three cutting parameters (spindle speed, cutting depth, and feed rate) and their interactions have significant effects on surface roughness. Further, the surface response model shows significant dependence on the combination of the tool and workpiece material. [PERSON] et al. [14] proposed an optimization process for machining conditions to ensure a desirable surface roughness based on surface response methodology. With an optimized solution, the material removal rate can be improved significantly without sacrificing surface roughness. [PERSON] et al. [22] and [PERSON] et al. [18], respectively, reported that feed rate has a significant effect on the surface roughness of machined alumina material compared with spindle speed and cutting depth.