# Modeling of Cutting Force in the Turning of AISI 4340 Using Gaussian Process Regression Algorithm
## 1 Introduction  
Turning is one of the most commonly employed manufacturing methods. With the growing number of applications for precision machining and machining of challenging materials, the modeling process is extremely necessary for evaluating the cutting force and the processing parameters to be optimized [1]. During the turning process, the surface finish is highly affected by parameters such as feed rate, cutting depth, cutting speed, and the radius of the tool nose [2]. For any machining operation, the selection of optimal cutting parameters is an important factor in increasing the quality and efficiency of the machined products, minimizing the costs of machining, and increasing production volume. The optimization of cutting parameters is also required to reduce cutting force during machining, since a high cutting force leads to several adverse effects, such as decreased tool life, high energy usage, increased surface roughness, bad finishing surfaces, etc. The cutting force plays a vital role in the metal cutting phase in the turning method, as it influences tool-workpiece deflection, vibration of machine tools, and finally the quality of the pieces. An accurate prediction of the cutting force during turning thus becomes an essential factor for process optimization and process characterization, and above all for improving machining efficiency [3]. However, defining the components of the cutting force is important for reducing energy usage in the process of metal cutting. Minimization of the cutting force directly controls the power consumption in the metal cutting industry, resulting in a greener, more ecological manufacturing operation by optimizing cutting parameters including cutting depth, feed rate, as well as cutting speed. The feed rate was identified as the primary cutting force parameter, whereas cutting speed is the prime parameter in reducing power consumption [4]. In addition, to acquire dimensional precision and machining device stability, the cutting force is necessary. In the area of interaction between the tools and the material, a cutting force occurs in all classic metal cutting processes, and it can be disintegrated by three orthogonal components [5]. In addition, it is exceedingly difficult to create an effective model because of the multiple interrelated parameters such as feedrate, cutting depth, cutting speed, nose radius, as well as cutting-edge angles, all of which affect the cutting force [6]. The cutting method is carried out while the tool is displaced, extracting a thin portion of the surface, which decreases the workpiece's diameter. The schematic in Figure 1 illustrates the normal turning mechanism forces; the parallel position of the cutting tool and speed of the spindle are shown as well. Force equilibrium is identified as the connection between forces. The resultant cutting force is shown by Altintas [7], and it is produced from the feed force (\(F_{f}\)), the tangential cutting force (\(F_{t}\)), and the radial force (\(F_{r}\)) [7; 8]. \[F_{c}=\sqrt{F_{f}+F_{t}+F_{r}} \tag{1}\]  
\(F_{f}\) (feed force) is viewed in the direction of the thickness of the uncut chip and is influenced mainly by the feed rate. However, the feed force increases as the feed rate increases. \(F_{t}\) (tangential force) acts on the cutting speed (\(V\)) direction. \(F_{r}\) (feed force) is a radial force that moves the tool away from the workpiece, and it acts along the radial direction of the workpiece. According to the principle of equilibrium, the tool receives the same force in the same amplitude but in the opposite direction. The predicted cutting force \(F_{c}\) can then be defined as:  
\[F_{c}=kv^{c_{1}}f^{c_{2}}d^{c_{3}} \tag{2}\]  
where \(k,c_{1},c_{2}\), and \(c_{3}\) are model parameters. In the last few decades, there has been diverse modeling processes focused on artificial neural networks and fuzzy sets; most researchers use these tools to forecast various machining processing parameters including tool wear, cutting force, and machined-piece surface roughness.