# Modeling of Cutting Force in the Turning of AISI 4340 Using Gaussian Process Regression Algorithm
## 1 Introduction
It is very important to model and forecast cutting force in the turning mechanism, since it is directly connected to the consistency of the processed surface, self-excited vibrations, tool wear, etc. To estimate the strength needs for machinery tools, an understanding of cutting force is crucial. An awareness of cutting force is necessary for the appropriate selection of operative conditions and machine equipment because equipment and tools contribute to an effective machining operation. In addition, the monitoring of the cutting force is used for detecting breakage and tool wear. The cutting method is highly complex, and so it is difficult to precisely model the cutting force due to the many highly interconnected variables that influence those forces. Several investigations to model the cutting force in the turning process exist in the literature. [PERSON] et al. [8] established a model to examine the impact of cutting parameters on cutting force using a high-speed steel (HSS) instrument during the red brass turning process (C23000). Multiple regression as well as artificial neural network (ANN) techniques were used. The ANN model was considered to be more precise compared to the regression model. For turning mechanisms, a mechanistic cutting force model was introduced by [PERSON] and [PERSON] [9]. This model defines the cutting region distribution and measures  
Figure 1: Turning process geometry. the immediate efficient tool angles, cutting force, cutting parameters, force intensity, and their distribution. The findings suggest that the force and the force intensity distributions on the instrument edge provide important information for the estimation of the turning force/power and a possible additional estimation of tool wear existence. [PERSON] et al. [10] demonstrated how Gaussian white noise stochastic processes could be used to characterize the cutting force in material-eliminating mechanisms. This method contributes to stochastic differential equations that are mathematically dynamic problems. The findings showed that the variability of the calculated force signal typically stands at about 4-9% of the average value, which is greater than the noise emerging from the measuring device. [PERSON] et al. [11] applied the ANN and response surface methodology (RSM) approach for modeling output parameters in the dry hard turning process of AISI 420 (matrensitic stainless steel) processed at 59 HRC. The findings showed that cutting depth has a strong effect on the cutting force, the removal capability, and the material removal rate (MRR). The association between the essential parameters (nose radius, feed rate, and cutting speed) and their effect on the turning force components was investigated by [PERSON] et al. [12]. The distinction between the resultant values of the cutting force factors and the simulations revealed an improvement in the association of over 89%. The values obtained from the mathematical model were also based on the confirmed appropriateness in line with the corresponding finite element model values. As an operation of cutting parameters, [PERSON] and [PERSON] [13] established an analytical trend for cutting forces. The force model is expanded with an empirical method focused on the Waldorf principle in ideal cutting conditions, taking into account the progression of flank wear. The findings demonstrated the efficiency of analytical models established for the estimation of cutting force. [PERSON] et al. [14] suggested a prediction model for the cutting force for hard turning operations. In this work, the ANOVA research showed how each machining parameter contributes to the estimation and analysis of the cutting force. The established fuzzy model was considered to be satisfactory and better than the regression model for estimation purposes. The association between the cutting force coefficients and the cutting power was analyzed by [PERSON] [15]. A linear relationship between the MRR and spindle strength was developed in the cutting power model.